id	sid	tid	token	lemma	pos
ejpam-3877	1	1	european	european	PROPN
ejpam-3877	1	2	journal	journal	PROPN
ejpam-3877	1	3	of	of	ADP
ejpam-3877	1	4	pure	pure	ADJ
ejpam-3877	1	5	and	and	CCONJ
ejpam-3877	1	6	applied	apply	VERB
ejpam-3877	1	7	mathematics	mathematic	NOUN
ejpam-3877	1	8	vol	vol	NOUN
ejpam-3877	1	9	.	.	PUNCT
ejpam-3877	2	1	14	14	NUM
ejpam-3877	2	2	,	,	PUNCT
ejpam-3877	2	3	no	no	INTJ
ejpam-3877	2	4	.	.	NOUN
ejpam-3877	2	5	1	1	NUM
ejpam-3877	2	6	,	,	PUNCT
ejpam-3877	2	7	2021	2021	NUM
ejpam-3877	2	8	,	,	PUNCT
ejpam-3877	2	9	204	204	NUM
ejpam-3877	2	10	-	-	SYM
ejpam-3877	2	11	233	233	NUM
ejpam-3877	2	12	issn	issn	PROPN
ejpam-3877	2	13	1307	1307	NUM
ejpam-3877	2	14	-	-	SYM
ejpam-3877	2	15	5543	5543	NUM
ejpam-3877	2	16	–	–	PUNCT
ejpam-3877	2	17	ejpam.com	ejpam.com	X
ejpam-3877	2	18	published	publish	VERB
ejpam-3877	2	19	by	by	ADP
ejpam-3877	2	20	new	new	PROPN
ejpam-3877	2	21	york	york	PROPN
ejpam-3877	2	22	business	business	PROPN
ejpam-3877	2	23	global	global	PROPN
ejpam-3877	2	24	radon	radon	PROPN
ejpam-3877	2	25	measure	measure	NOUN
ejpam-3877	2	26	-	-	PUNCT
ejpam-3877	2	27	valued	value	VERB
ejpam-3877	2	28	solutions	solution	NOUN
ejpam-3877	2	29	for	for	ADP
ejpam-3877	2	30	nonlinear	nonlinear	ADJ
ejpam-3877	2	31	strongly	strongly	ADV
ejpam-3877	2	32	degenerate	degenerate	ADJ
ejpam-3877	2	33	parabolic	parabolic	ADJ
ejpam-3877	2	34	equations	equation	NOUN
ejpam-3877	2	35	with	with	ADP
ejpam-3877	2	36	measure	measure	NOUN
ejpam-3877	2	37	data	data	PROPN
ejpam-3877	2	38	quincy	quincy	PROPN
ejpam-3877	2	39	stévène	stévène	PROPN
ejpam-3877	2	40	nkombo1,∗	nkombo1,∗	NOUN
ejpam-3877	2	41	,	,	PUNCT
ejpam-3877	2	42	fengquan	fengquan	ADJ
ejpam-3877	2	43	li1	li1	NOUN
ejpam-3877	2	44	1	1	NUM
ejpam-3877	2	45	school	school	NOUN
ejpam-3877	2	46	of	of	ADP
ejpam-3877	2	47	mathematical	mathematical	ADJ
ejpam-3877	2	48	sciences	sciences	PROPN
ejpam-3877	2	49	,	,	PUNCT
ejpam-3877	2	50	dalian	dalian	PROPN
ejpam-3877	2	51	university	university	PROPN
ejpam-3877	2	52	of	of	ADP
ejpam-3877	2	53	technology	technology	PROPN
ejpam-3877	2	54	,	,	PUNCT
ejpam-3877	2	55	dalian	dalian	PROPN
ejpam-3877	2	56	,	,	PUNCT
ejpam-3877	2	57	liaoning	liaoning	PROPN
ejpam-3877	2	58	,	,	PUNCT
ejpam-3877	2	59	china	china	PROPN
ejpam-3877	2	60	abstract	abstract	NOUN
ejpam-3877	2	61	.	.	PUNCT
ejpam-3877	3	1	in	in	ADP
ejpam-3877	3	2	this	this	DET
ejpam-3877	3	3	paper	paper	NOUN
ejpam-3877	3	4	,	,	PUNCT
ejpam-3877	3	5	we	we	PRON
ejpam-3877	3	6	prove	prove	VERB
ejpam-3877	3	7	the	the	DET
ejpam-3877	3	8	existence	existence	NOUN
ejpam-3877	3	9	of	of	ADP
ejpam-3877	3	10	radon	radon	PROPN
ejpam-3877	3	11	measure	measure	NOUN
ejpam-3877	3	12	-	-	PUNCT
ejpam-3877	3	13	valued	value	VERB
ejpam-3877	3	14	solutions	solution	NOUN
ejpam-3877	3	15	for	for	ADP
ejpam-3877	3	16	nonlinear	nonlinear	ADJ
ejpam-3877	3	17	strongly	strongly	ADV
ejpam-3877	3	18	degenerate	degenerate	ADJ
ejpam-3877	3	19	parabolic	parabolic	ADJ
ejpam-3877	3	20	equations	equation	NOUN
ejpam-3877	3	21	with	with	ADP
ejpam-3877	3	22	nonnegative	nonnegative	ADJ
ejpam-3877	3	23	bounded	bounded	ADJ
ejpam-3877	3	24	radon	radon	PROPN
ejpam-3877	3	25	measure	measure	NOUN
ejpam-3877	3	26	as	as	ADP
ejpam-3877	3	27	initial	initial	ADJ
ejpam-3877	3	28	data	datum	NOUN
ejpam-3877	3	29	.	.	PUNCT
ejpam-3877	4	1	moreover	moreover	ADV
ejpam-3877	4	2	,	,	PUNCT
ejpam-3877	4	3	we	we	PRON
ejpam-3877	4	4	show	show	VERB
ejpam-3877	4	5	the	the	DET
ejpam-3877	4	6	uniqueness	uniqueness	NOUN
ejpam-3877	4	7	of	of	ADP
ejpam-3877	4	8	the	the	DET
ejpam-3877	4	9	radon	radon	PROPN
ejpam-3877	4	10	measure	measure	NOUN
ejpam-3877	4	11	-	-	PUNCT
ejpam-3877	4	12	valued	value	VERB
ejpam-3877	4	13	solutions	solution	NOUN
ejpam-3877	4	14	when	when	SCONJ
ejpam-3877	4	15	the	the	DET
ejpam-3877	4	16	radon	radon	PROPN
ejpam-3877	4	17	measure	measure	NOUN
ejpam-3877	4	18	as	as	ADP
ejpam-3877	4	19	a	a	DET
ejpam-3877	4	20	forcing	force	VERB
ejpam-3877	4	21	term	term	NOUN
ejpam-3877	4	22	is	be	AUX
ejpam-3877	4	23	diffuse	diffuse	NOUN
ejpam-3877	4	24	with	with	ADP
ejpam-3877	4	25	respect	respect	NOUN
ejpam-3877	4	26	to	to	ADP
ejpam-3877	4	27	the	the	DET
ejpam-3877	4	28	parabolic	parabolic	ADJ
ejpam-3877	4	29	capacity	capacity	NOUN
ejpam-3877	4	30	and	and	CCONJ
ejpam-3877	4	31	the	the	DET
ejpam-3877	4	32	radon	radon	ADJ
ejpam-3877	4	33	measure	measure	NOUN
ejpam-3877	4	34	as	as	ADP
ejpam-3877	4	35	a	a	DET
ejpam-3877	4	36	initial	initial	ADJ
ejpam-3877	4	37	value	value	NOUN
ejpam-3877	4	38	is	be	AUX
ejpam-3877	4	39	diffuse	diffuse	NOUN
ejpam-3877	4	40	with	with	ADP
ejpam-3877	4	41	respect	respect	NOUN
ejpam-3877	4	42	to	to	ADP
ejpam-3877	4	43	the	the	DET
ejpam-3877	4	44	newtonian	newtonian	ADJ
ejpam-3877	4	45	capacity	capacity	NOUN
ejpam-3877	4	46	.	.	PUNCT
ejpam-3877	5	1	we	we	PRON
ejpam-3877	5	2	also	also	ADV
ejpam-3877	5	3	deduce	deduce	VERB
ejpam-3877	5	4	that	that	SCONJ
ejpam-3877	5	5	the	the	DET
ejpam-3877	5	6	concentrated	concentrated	ADJ
ejpam-3877	5	7	part	part	NOUN
ejpam-3877	5	8	of	of	ADP
ejpam-3877	5	9	the	the	DET
ejpam-3877	5	10	radon	radon	PROPN
ejpam-3877	5	11	measure	measure	NOUN
ejpam-3877	5	12	-	-	PUNCT
ejpam-3877	5	13	valued	value	VERB
ejpam-3877	5	14	solution	solution	NOUN
ejpam-3877	5	15	with	with	ADP
ejpam-3877	5	16	respect	respect	NOUN
ejpam-3877	5	17	to	to	ADP
ejpam-3877	5	18	the	the	DET
ejpam-3877	5	19	newtonian	newtonian	ADJ
ejpam-3877	5	20	capacity	capacity	NOUN
ejpam-3877	5	21	depends	depend	VERB
ejpam-3877	5	22	on	on	ADP
ejpam-3877	5	23	time	time	NOUN
ejpam-3877	5	24	.	.	PUNCT
ejpam-3877	6	1	2020	2020	NUM
ejpam-3877	6	2	mathematics	mathematic	NOUN
ejpam-3877	6	3	subject	subject	NOUN
ejpam-3877	6	4	classifications	classification	NOUN
ejpam-3877	6	5	:	:	PUNCT
ejpam-3877	6	6	35k20	35k20	NUM
ejpam-3877	6	7	,	,	PUNCT
ejpam-3877	6	8	35k65	35k65	NUM
ejpam-3877	6	9	,	,	PUNCT
ejpam-3877	6	10	35k59	35k59	NUM
ejpam-3877	6	11	,	,	PUNCT
ejpam-3877	6	12	35r06	35r06	NUM
ejpam-3877	6	13	,	,	PUNCT
ejpam-3877	6	14	28a33	28a33	NUM
ejpam-3877	6	15	key	key	ADJ
ejpam-3877	6	16	words	word	NOUN
ejpam-3877	6	17	and	and	CCONJ
ejpam-3877	6	18	phrases	phrase	NOUN
ejpam-3877	6	19	:	:	PUNCT
ejpam-3877	6	20	radon	radon	PROPN
ejpam-3877	6	21	measure	measure	NOUN
ejpam-3877	6	22	-	-	PUNCT
ejpam-3877	6	23	valued	value	VERB
ejpam-3877	6	24	solutions	solution	NOUN
ejpam-3877	6	25	,	,	PUNCT
ejpam-3877	6	26	nonlinear	nonlinear	ADJ
ejpam-3877	6	27	degenerate	degenerate	ADJ
ejpam-3877	6	28	parabolic	parabolic	NOUN
ejpam-3877	6	29	equations	equation	NOUN
ejpam-3877	6	30	,	,	PUNCT
ejpam-3877	6	31	capacity	capacity	NOUN
ejpam-3877	6	32	1	1	NUM
ejpam-3877	6	33	.	.	PUNCT
ejpam-3877	7	1	introduction	introduction	NOUN
ejpam-3877	7	2	in	in	ADP
ejpam-3877	7	3	this	this	DET
ejpam-3877	7	4	work	work	NOUN
ejpam-3877	7	5	we	we	PRON
ejpam-3877	7	6	address	address	VERB
ejpam-3877	7	7	the	the	DET
ejpam-3877	7	8	nonhomogeneous	nonhomogeneous	ADJ
ejpam-3877	7	9	nonlinear	nonlinear	NOUN
ejpam-3877	7	10	strongly	strongly	ADV
ejpam-3877	7	11	degenerate	degenerate	ADJ
ejpam-3877	7	12	parabolic	parabolic	ADJ
ejpam-3877	7	13	equations	equation	NOUN
ejpam-3877	7	14	having	have	VERB
ejpam-3877	7	15	the	the	DET
ejpam-3877	7	16	nonnegative	nonnegative	ADJ
ejpam-3877	7	17	bounded	bounded	ADJ
ejpam-3877	7	18	radon	radon	PROPN
ejpam-3877	7	19	measure	measure	NOUN
ejpam-3877	7	20	on	on	ADP
ejpam-3877	7	21	the	the	DET
ejpam-3877	7	22	right	right	ADJ
ejpam-3877	7	23	-	-	PUNCT
ejpam-3877	7	24	hand	hand	NOUN
ejpam-3877	7	25	side	side	NOUN
ejpam-3877	7	26	with	with	ADP
ejpam-3877	7	27	the	the	DET
ejpam-3877	7	28	nonnegative	nonnegative	ADJ
ejpam-3877	7	29	bounded	bounded	ADJ
ejpam-3877	7	30	radon	radon	PROPN
ejpam-3877	7	31	measure	measure	NOUN
ejpam-3877	7	32	as	as	ADP
ejpam-3877	7	33	initial	initial	ADJ
ejpam-3877	7	34	data	datum	NOUN
ejpam-3877	7	35	.	.	PUNCT
ejpam-3877	8	1	this	this	DET
ejpam-3877	8	2	problem	problem	NOUN
ejpam-3877	8	3	is	be	AUX
ejpam-3877	8	4	described	describe	VERB
ejpam-3877	8	5	as	as	SCONJ
ejpam-3877	8	6	follows	follow	VERB
ejpam-3877	8	7			PRON
ejpam-3877	8	8	ut	ut	PUNCT
ejpam-3877	8	9	−∆ψ(u	−∆ψ(u	PROPN
ejpam-3877	8	10	)	)	PUNCT
ejpam-3877	8	11	=	=	SYM
ejpam-3877	8	12	µ	µ	X
ejpam-3877	8	13	in	in	ADP
ejpam-3877	8	14	q	q	NOUN
ejpam-3877	8	15	:	:	PUNCT
ejpam-3877	9	1	=	=	SYM
ejpam-3877	9	2	ω×	ω×	X
ejpam-3877	9	3	(	(	PUNCT
ejpam-3877	9	4	0	0	NUM
ejpam-3877	9	5	,	,	PUNCT
ejpam-3877	9	6	t	t	NOUN
ejpam-3877	9	7	)	)	PUNCT
ejpam-3877	9	8	,	,	PUNCT
ejpam-3877	9	9	u	u	NOUN
ejpam-3877	9	10	=	=	NOUN
ejpam-3877	9	11	0	0	NUM
ejpam-3877	9	12	on	on	ADP
ejpam-3877	9	13	∂ω×	∂ω×	PROPN
ejpam-3877	9	14	(	(	PUNCT
ejpam-3877	9	15	0	0	NUM
ejpam-3877	9	16	,	,	PUNCT
ejpam-3877	9	17	t	t	NOUN
ejpam-3877	9	18	)	)	PUNCT
ejpam-3877	9	19	,	,	PUNCT
ejpam-3877	9	20	u(x	u(x	NOUN
ejpam-3877	9	21	,	,	PUNCT
ejpam-3877	9	22	0	0	NUM
ejpam-3877	9	23	)	)	PUNCT
ejpam-3877	9	24	=	=	PRON
ejpam-3877	10	1	u0	u0	ADJ
ejpam-3877	10	2	in	in	ADP
ejpam-3877	10	3	ω	ω	PROPN
ejpam-3877	10	4	,	,	PUNCT
ejpam-3877	10	5	(	(	PUNCT
ejpam-3877	10	6	p	p	NOUN
ejpam-3877	10	7	)	)	PUNCT
ejpam-3877	10	8	where	where	SCONJ
ejpam-3877	10	9	t	t	PROPN
ejpam-3877	10	10	>	>	X
ejpam-3877	10	11	0	0	PROPN
ejpam-3877	10	12	,	,	PUNCT
ejpam-3877	10	13	ω	ω	PROPN
ejpam-3877	10	14	⊂	⊂	PROPN
ejpam-3877	10	15	rn	rn	PROPN
ejpam-3877	10	16	(	(	PUNCT
ejpam-3877	10	17	n	n	CCONJ
ejpam-3877	10	18	≥	≥	NOUN
ejpam-3877	10	19	2	2	NUM
ejpam-3877	10	20	)	)	PUNCT
ejpam-3877	10	21	is	be	AUX
ejpam-3877	10	22	an	an	DET
ejpam-3877	10	23	open	open	ADJ
ejpam-3877	10	24	bounded	bounded	ADJ
ejpam-3877	10	25	domain	domain	NOUN
ejpam-3877	10	26	with	with	ADP
ejpam-3877	10	27	smooth	smooth	ADJ
ejpam-3877	10	28	boundary	boundary	ADJ
ejpam-3877	10	29	∂ω	∂ω	PROPN
ejpam-3877	10	30	,	,	PUNCT
ejpam-3877	10	31	the	the	DET
ejpam-3877	10	32	initial	initial	ADJ
ejpam-3877	10	33	value	value	NOUN
ejpam-3877	10	34	data	datum	NOUN
ejpam-3877	10	35	u0	u0	NOUN
ejpam-3877	10	36	is	be	AUX
ejpam-3877	10	37	a	a	DET
ejpam-3877	10	38	nonnegative	nonnegative	ADJ
ejpam-3877	10	39	bounded	bounded	ADJ
ejpam-3877	10	40	radon	radon	PROPN
ejpam-3877	10	41	measure	measure	NOUN
ejpam-3877	10	42	on	on	ADP
ejpam-3877	10	43	ω	ω	PROPN
ejpam-3877	10	44	and	and	CCONJ
ejpam-3877	10	45	µ	µ	NOUN
ejpam-3877	10	46	is	be	AUX
ejpam-3877	10	47	a	a	DET
ejpam-3877	10	48	nonnegative	nonnegative	ADJ
ejpam-3877	10	49	bounded	bounded	ADJ
ejpam-3877	10	50	radon	radon	PROPN
ejpam-3877	10	51	measure	measure	NOUN
ejpam-3877	10	52	on	on	ADP
ejpam-3877	10	53	q.	q.	PROPN
ejpam-3877	10	54	the	the	DET
ejpam-3877	10	55	nonlinear	nonlinear	ADJ
ejpam-3877	10	56	strongly	strongly	ADV
ejpam-3877	10	57	degenerate	degenerate	ADJ
ejpam-3877	10	58	parabolic	parabolic	ADJ
ejpam-3877	10	59	equations	equation	NOUN
ejpam-3877	10	60	(	(	PUNCT
ejpam-3877	10	61	p	p	NOUN
ejpam-3877	10	62	)	)	PUNCT
ejpam-3877	10	63	is	be	AUX
ejpam-3877	10	64	the	the	DET
ejpam-3877	10	65	special	special	ADJ
ejpam-3877	10	66	case	case	NOUN
ejpam-3877	10	67	derived	derive	VERB
ejpam-3877	10	68	∗corresponding	∗corresponde	VERB
ejpam-3877	10	69	author	author	NOUN
ejpam-3877	10	70	.	.	PUNCT
ejpam-3877	11	1	doi	doi	NOUN
ejpam-3877	11	2	:	:	PUNCT
ejpam-3877	11	3	https://doi.org/10.29020/nybg.ejpam.v14i1.3877	https://doi.org/10.29020/nybg.ejpam.v14i1.3877	VERB
ejpam-3877	11	4	email	email	NOUN
ejpam-3877	11	5	addresses	address	NOUN
ejpam-3877	11	6	:	:	PUNCT
ejpam-3877	11	7	quincysnk@yahoo.fr	quincysnk@yahoo.fr	PROPN
ejpam-3877	11	8	(	(	PUNCT
ejpam-3877	11	9	q.	q.	PROPN
ejpam-3877	11	10	s.	s.	PROPN
ejpam-3877	11	11	nkombo	nkombo	PROPN
ejpam-3877	11	12	)	)	PUNCT
ejpam-3877	11	13	,	,	PUNCT
ejpam-3877	11	14	fqli@dlut.edu.cn	fqli@dlut.edu.cn	NOUN
ejpam-3877	11	15	(	(	PUNCT
ejpam-3877	11	16	f.	f.	PROPN
ejpam-3877	11	17	li	li	PROPN
ejpam-3877	11	18	)	)	PUNCT
ejpam-3877	11	19	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3877	12	1	204	204	NUM
ejpam-3877	12	2	c	c	X
ejpam-3877	12	3	©	©	PROPN
ejpam-3877	12	4	2021	2021	NUM
ejpam-3877	12	5	ejpam	ejpam	VERB
ejpam-3877	12	6	all	all	DET
ejpam-3877	12	7	rights	right	NOUN
ejpam-3877	12	8	reserved	reserve	VERB
ejpam-3877	12	9	.	.	PUNCT
ejpam-3877	13	1	quincy	quincy	PROPN
ejpam-3877	13	2	s.	s.	PROPN
ejpam-3877	13	3	nkombo	nkombo	PROPN
ejpam-3877	13	4	,	,	PUNCT
ejpam-3877	13	5	fengquan	fengquan	PROPN
ejpam-3877	13	6	li	li	PROPN
ejpam-3877	13	7	/	/	SYM
ejpam-3877	13	8	eur	eur	PROPN
ejpam-3877	13	9	.	.	PUNCT
ejpam-3877	14	1	j.	j.	PROPN
ejpam-3877	14	2	pure	pure	PROPN
ejpam-3877	14	3	appl	appl	PROPN
ejpam-3877	14	4	.	.	PROPN
ejpam-3877	14	5	math	math	PROPN
ejpam-3877	14	6	,	,	PUNCT
ejpam-3877	14	7	14	14	NUM
ejpam-3877	14	8	(	(	PUNCT
ejpam-3877	14	9	1	1	NUM
ejpam-3877	14	10	)	)	PUNCT
ejpam-3877	14	11	(	(	PUNCT
ejpam-3877	14	12	2021	2021	NUM
ejpam-3877	14	13	)	)	PUNCT
ejpam-3877	14	14	,	,	PUNCT
ejpam-3877	14	15	204	204	NUM
ejpam-3877	14	16	-	-	SYM
ejpam-3877	14	17	233	233	NUM
ejpam-3877	14	18	205	205	NUM
ejpam-3877	14	19	from	from	ADP
ejpam-3877	14	20	the	the	DET
ejpam-3877	14	21	study	study	NOUN
ejpam-3877	14	22	of	of	ADP
ejpam-3877	14	23	quasilinear	quasilinear	PROPN
ejpam-3877	14	24	parabolic	parabolic	PROPN
ejpam-3877	14	25	equations	equation	NOUN
ejpam-3877	14	26	with	with	ADP
ejpam-3877	14	27	degenerate	degenerate	ADJ
ejpam-3877	14	28	coercivity	coercivity	NOUN
ejpam-3877	14	29	involving	involve	VERB
ejpam-3877	14	30	a	a	DET
ejpam-3877	14	31	quadratic	quadratic	ADJ
ejpam-3877	14	32	gradient	gradient	ADJ
ejpam-3877	14	33	term	term	NOUN
ejpam-3877	14	34	(	(	PUNCT
ejpam-3877	14	35	see	see	VERB
ejpam-3877	14	36	[	[	X
ejpam-3877	14	37	4	4	NUM
ejpam-3877	14	38	,	,	PUNCT
ejpam-3877	14	39	7	7	NUM
ejpam-3877	14	40	]	]	NUM
ejpam-3877	14	41	)	)	PUNCT
ejpam-3877	14	42	.	.	PUNCT
ejpam-3877	15	1	the	the	DET
ejpam-3877	15	2	general	general	ADJ
ejpam-3877	15	3	model	model	NOUN
ejpam-3877	15	4	of	of	ADP
ejpam-3877	15	5	the	the	DET
ejpam-3877	15	6	problem	problem	NOUN
ejpam-3877	15	7	(	(	PUNCT
ejpam-3877	15	8	p	p	NOUN
ejpam-3877	15	9	)	)	PUNCT
ejpam-3877	15	10	is	be	AUX
ejpam-3877	15	11	given	give	VERB
ejpam-3877	15	12	by	by	NOUN
ejpam-3877	15	13	ut	ut	PROPN
ejpam-3877	15	14	−	−	PROPN
ejpam-3877	15	15	div	div	X
ejpam-3877	15	16	(	(	PUNCT
ejpam-3877	15	17	α(u)∇u	α(u)∇u	PROPN
ejpam-3877	15	18	)	)	PUNCT
ejpam-3877	15	19	=	=	PUNCT
ejpam-3877	15	20	β(u	β(u	PROPN
ejpam-3877	15	21	)	)	PUNCT
ejpam-3877	15	22	|	|	ADV
ejpam-3877	15	23	∇u	∇u	VERB
ejpam-3877	15	24	|2	|2	NUM
ejpam-3877	15	25	+	+	NOUN
ejpam-3877	15	26	f(x	f(x	PROPN
ejpam-3877	15	27	,	,	PUNCT
ejpam-3877	15	28	t	t	PROPN
ejpam-3877	15	29	)	)	PUNCT
ejpam-3877	15	30	in	in	ADP
ejpam-3877	15	31	q	q	NOUN
ejpam-3877	15	32	:	:	PUNCT
ejpam-3877	15	33	=	=	SYM
ejpam-3877	15	34	ω×	ω×	X
ejpam-3877	15	35	(	(	PUNCT
ejpam-3877	15	36	0	0	NUM
ejpam-3877	15	37	,	,	PUNCT
ejpam-3877	15	38	t	t	NOUN
ejpam-3877	15	39	)	)	PUNCT
ejpam-3877	15	40	,	,	PUNCT
ejpam-3877	15	41	u	u	NOUN
ejpam-3877	15	42	=	=	NOUN
ejpam-3877	15	43	0	0	NUM
ejpam-3877	15	44	on	on	ADP
ejpam-3877	15	45	∂ω×	∂ω×	PROPN
ejpam-3877	15	46	(	(	PUNCT
ejpam-3877	15	47	0	0	NUM
ejpam-3877	15	48	,	,	PUNCT
ejpam-3877	15	49	t	t	NOUN
ejpam-3877	15	50	)	)	PUNCT
ejpam-3877	15	51	,	,	PUNCT
ejpam-3877	15	52	u(x	u(x	NOUN
ejpam-3877	15	53	,	,	PUNCT
ejpam-3877	15	54	0	0	NUM
ejpam-3877	15	55	)	)	PUNCT
ejpam-3877	15	56	=	=	PRON
ejpam-3877	15	57	u0	u0	ADJ
ejpam-3877	15	58	in	in	ADP
ejpam-3877	15	59	ω	ω	PROPN
ejpam-3877	15	60	,	,	PUNCT
ejpam-3877	15	61	(	(	PUNCT
ejpam-3877	15	62	s	s	X
ejpam-3877	15	63	)	)	PUNCT
ejpam-3877	15	64	where	where	SCONJ
ejpam-3877	15	65	α	α	NOUN
ejpam-3877	15	66	and	and	CCONJ
ejpam-3877	15	67	β	β	X
ejpam-3877	15	68	are	be	AUX
ejpam-3877	15	69	real	real	ADJ
ejpam-3877	15	70	continuous	continuous	ADJ
ejpam-3877	15	71	functions	function	NOUN
ejpam-3877	15	72	,	,	PUNCT
ejpam-3877	15	73	moreover	moreover	ADV
ejpam-3877	15	74	α	α	PRON
ejpam-3877	15	75	is	be	AUX
ejpam-3877	15	76	positive	positive	ADJ
ejpam-3877	15	77	bounded	bounded	ADJ
ejpam-3877	15	78	and	and	CCONJ
ejpam-3877	15	79	may	may	AUX
ejpam-3877	15	80	vanish	vanish	VERB
ejpam-3877	15	81	at	at	ADP
ejpam-3877	15	82	±∞	±∞	PROPN
ejpam-3877	15	83	,	,	PUNCT
ejpam-3877	15	84	u0	u0	PROPN
ejpam-3877	15	85	∈	∈	PROPN
ejpam-3877	15	86	l∞(ω	l∞(ω	NOUN
ejpam-3877	15	87	)	)	PUNCT
ejpam-3877	15	88	and	and	CCONJ
ejpam-3877	15	89	f	f	PROPN
ejpam-3877	15	90	∈	∈	PROPN
ejpam-3877	15	91	lm(ω)(m	lm(ω)(m	VERB
ejpam-3877	15	92	>	>	X
ejpam-3877	16	1	1	1	NUM
ejpam-3877	17	1	+	+	CCONJ
ejpam-3877	17	2	n	n	DET
ejpam-3877	17	3	2	2	NUM
ejpam-3877	17	4	)	)	PUNCT
ejpam-3877	17	5	(	(	PUNCT
ejpam-3877	17	6	see	see	VERB
ejpam-3877	17	7	[	[	X
ejpam-3877	17	8	4	4	NUM
ejpam-3877	17	9	]	]	NUM
ejpam-3877	17	10	)	)	PUNCT
ejpam-3877	17	11	.	.	PUNCT
ejpam-3877	18	1	for	for	ADP
ejpam-3877	18	2	the	the	DET
ejpam-3877	18	3	problem	problem	NOUN
ejpam-3877	18	4	(	(	PUNCT
ejpam-3877	18	5	s	s	NOUN
ejpam-3877	18	6	)	)	PUNCT
ejpam-3877	18	7	,	,	PUNCT
ejpam-3877	18	8	the	the	DET
ejpam-3877	18	9	typical	typical	ADJ
ejpam-3877	18	10	example	example	NOUN
ejpam-3877	18	11	of	of	ADP
ejpam-3877	18	12	functions	function	NOUN
ejpam-3877	18	13	α	α	PROPN
ejpam-3877	18	14	and	and	CCONJ
ejpam-3877	18	15	β	β	X
ejpam-3877	18	16	are	be	AUX
ejpam-3877	18	17	expressed	express	VERB
ejpam-3877	18	18	as	as	SCONJ
ejpam-3877	18	19	follows	follow	VERB
ejpam-3877	18	20	α(s	α(s	PROPN
ejpam-3877	18	21	)	)	PUNCT
ejpam-3877	19	1	=	=	PUNCT
ejpam-3877	19	2	1√	1√	NUM
ejpam-3877	19	3	1	1	NUM
ejpam-3877	19	4	+	+	CCONJ
ejpam-3877	19	5	s2	s2	PROPN
ejpam-3877	19	6	and	and	CCONJ
ejpam-3877	19	7	β(s	β(	NOUN
ejpam-3877	19	8	)	)	PUNCT
ejpam-3877	20	1	=	=	SYM
ejpam-3877	20	2	1√	1√	NUM
ejpam-3877	20	3	(	(	PUNCT
ejpam-3877	20	4	1	1	NUM
ejpam-3877	20	5	+	+	CCONJ
ejpam-3877	20	6	s2)3	s2)3	X
ejpam-3877	20	7	.	.	PUNCT
ejpam-3877	21	1	in	in	ADP
ejpam-3877	21	2	[	[	X
ejpam-3877	21	3	7	7	NUM
ejpam-3877	21	4	]	]	PUNCT
ejpam-3877	21	5	,	,	PUNCT
ejpam-3877	21	6	the	the	DET
ejpam-3877	21	7	authors	author	NOUN
ejpam-3877	21	8	studied	study	VERB
ejpam-3877	21	9	the	the	DET
ejpam-3877	21	10	problem	problem	NOUN
ejpam-3877	21	11	(	(	PUNCT
ejpam-3877	21	12	s	s	X
ejpam-3877	21	13	)	)	PUNCT
ejpam-3877	21	14	with	with	ADP
ejpam-3877	21	15	more	more	ADJ
ejpam-3877	21	16	general	general	ADJ
ejpam-3877	21	17	assumptions	assumption	NOUN
ejpam-3877	21	18	in	in	ADP
ejpam-3877	21	19	which	which	PRON
ejpam-3877	21	20	(	(	PUNCT
ejpam-3877	21	21	s	s	X
ejpam-3877	21	22	)	)	PUNCT
ejpam-3877	21	23	is	be	AUX
ejpam-3877	21	24	a	a	DET
ejpam-3877	21	25	nonlinear	nonlinear	ADJ
ejpam-3877	21	26	degenerate	degenerate	ADJ
ejpam-3877	21	27	parabolic	parabolic	NOUN
ejpam-3877	21	28	equation	equation	NOUN
ejpam-3877	21	29	.	.	PUNCT
ejpam-3877	22	1	meanwhile	meanwhile	ADV
ejpam-3877	22	2	,	,	PUNCT
ejpam-3877	22	3	in	in	ADP
ejpam-3877	22	4	[	[	PUNCT
ejpam-3877	22	5	32	32	NUM
ejpam-3877	22	6	]	]	SYM
ejpam-3877	22	7	bogelein	bogelein	PROPN
ejpam-3877	22	8	,	,	PUNCT
ejpam-3877	22	9	duzaarr	duzaarr	NOUN
ejpam-3877	22	10	and	and	CCONJ
ejpam-3877	22	11	gianazza	gianazza	NOUN
ejpam-3877	22	12	dealt	deal	VERB
ejpam-3877	22	13	with	with	ADP
ejpam-3877	22	14	nonhomogenous	nonhomogenous	ADJ
ejpam-3877	22	15	porous	porous	ADJ
ejpam-3877	22	16	medium	medium	ADJ
ejpam-3877	22	17	type	type	NOUN
ejpam-3877	22	18	equations	equation	NOUN
ejpam-3877	22	19	related	relate	VERB
ejpam-3877	22	20	to	to	ADP
ejpam-3877	22	21	cauchydirichlet	cauchydirichlet	NOUN
ejpam-3877	22	22	problem	problem	NOUN
ejpam-3877	22	23	in	in	ADP
ejpam-3877	22	24	a	a	DET
ejpam-3877	22	25	space	space	NOUN
ejpam-3877	22	26	-	-	PUNCT
ejpam-3877	22	27	time	time	NOUN
ejpam-3877	22	28	cylinder	cylinder	NOUN
ejpam-3877	22	29	q	q	NOUN
ejpam-3877	22	30	:	:	PUNCT
ejpam-3877	22	31	=	=	SYM
ejpam-3877	22	32	ω	ω	NUM
ejpam-3877	22	33	×	×	NOUN
ejpam-3877	22	34	(	(	PUNCT
ejpam-3877	22	35	0	0	NUM
ejpam-3877	22	36	,	,	PUNCT
ejpam-3877	22	37	t	t	NOUN
ejpam-3877	22	38	)	)	PUNCT
ejpam-3877	22	39	(	(	PUNCT
ejpam-3877	22	40	see	see	VERB
ejpam-3877	22	41	also	also	ADV
ejpam-3877	22	42	[	[	X
ejpam-3877	22	43	13	13	NUM
ejpam-3877	22	44	]	]	NUM
ejpam-3877	22	45	)	)	PUNCT
ejpam-3877	22	46	.	.	PUNCT
ejpam-3877	23	1	likewise	likewise	ADV
ejpam-3877	23	2	,	,	PUNCT
ejpam-3877	23	3	fiorenza	fiorenza	NOUN
ejpam-3877	23	4	,	,	PUNCT
ejpam-3877	23	5	mercaldo	mercaldo	NOUN
ejpam-3877	23	6	and	and	CCONJ
ejpam-3877	23	7	rakotoson	rakotoson	NOUN
ejpam-3877	23	8	[	[	X
ejpam-3877	23	9	1	1	NUM
ejpam-3877	23	10	]	]	PUNCT
ejpam-3877	23	11	studied	study	VERB
ejpam-3877	23	12	some	some	DET
ejpam-3877	23	13	regularity	regularity	NOUN
ejpam-3877	23	14	and	and	CCONJ
ejpam-3877	23	15	uniqueness	uniqueness	NOUN
ejpam-3877	23	16	results	result	NOUN
ejpam-3877	23	17	of	of	ADP
ejpam-3877	23	18	the	the	DET
ejpam-3877	23	19	evolution	evolution	NOUN
ejpam-3877	23	20	n	n	CCONJ
ejpam-3877	23	21	-	-	PUNCT
ejpam-3877	23	22	laplacian	laplacian	ADJ
ejpam-3877	23	23	equation	equation	NOUN
ejpam-3877	23	24	with	with	ADP
ejpam-3877	23	25	right	right	ADJ
ejpam-3877	23	26	hand	hand	NOUN
ejpam-3877	23	27	term	term	NOUN
ejpam-3877	23	28	µ	µ	PRON
ejpam-3877	23	29	∈	∈	PROPN
ejpam-3877	23	30	l1((0	l1((0	NOUN
ejpam-3877	23	31	,	,	PUNCT
ejpam-3877	23	32	t	t	PROPN
ejpam-3877	23	33	)	)	PUNCT
ejpam-3877	23	34	,	,	PUNCT
ejpam-3877	23	35	m(ω	m(ω	PROPN
ejpam-3877	23	36	)	)	PUNCT
ejpam-3877	23	37	)	)	PUNCT
ejpam-3877	23	38	.	.	PUNCT
ejpam-3877	24	1	furthermore	furthermore	ADV
ejpam-3877	24	2	porzio	porzio	NOUN
ejpam-3877	24	3	,	,	PUNCT
ejpam-3877	24	4	smarrazzo	smarrazzo	NOUN
ejpam-3877	24	5	and	and	CCONJ
ejpam-3877	24	6	tesei	tesei	VERB
ejpam-3877	24	7	[	[	X
ejpam-3877	24	8	23	23	NUM
ejpam-3877	24	9	]	]	PUNCT
ejpam-3877	24	10	introduced	introduce	VERB
ejpam-3877	24	11	the	the	DET
ejpam-3877	24	12	definition	definition	NOUN
ejpam-3877	24	13	of	of	ADP
ejpam-3877	24	14	radon	radon	PROPN
ejpam-3877	24	15	measure	measure	NOUN
ejpam-3877	24	16	-	-	PUNCT
ejpam-3877	24	17	valued	value	VERB
ejpam-3877	24	18	solutions	solution	NOUN
ejpam-3877	24	19	to	to	PART
ejpam-3877	24	20	quasilinear	quasilinear	VERB
ejpam-3877	24	21	parabolic	parabolic	ADJ
ejpam-3877	24	22	equations	equation	NOUN
ejpam-3877	24	23	with	with	ADP
ejpam-3877	24	24	initial	initial	ADJ
ejpam-3877	24	25	value	value	NOUN
ejpam-3877	24	26	as	as	ADP
ejpam-3877	24	27	measure	measure	NOUN
ejpam-3877	24	28	data	datum	NOUN
ejpam-3877	24	29	.	.	PUNCT
ejpam-3877	25	1	more	more	ADV
ejpam-3877	25	2	precisely	precisely	ADV
ejpam-3877	25	3	,	,	PUNCT
ejpam-3877	25	4	in	in	ADP
ejpam-3877	25	5	[	[	X
ejpam-3877	25	6	23	23	NUM
ejpam-3877	25	7	]	]	PUNCT
ejpam-3877	25	8	authors	author	NOUN
ejpam-3877	25	9	proved	prove	VERB
ejpam-3877	25	10	the	the	DET
ejpam-3877	25	11	existence	existence	NOUN
ejpam-3877	25	12	,	,	PUNCT
ejpam-3877	25	13	uniqueness	uniqueness	NOUN
ejpam-3877	25	14	and	and	CCONJ
ejpam-3877	25	15	qualitative	qualitative	ADJ
ejpam-3877	25	16	properties	property	NOUN
ejpam-3877	25	17	of	of	ADP
ejpam-3877	25	18	radon	radon	ADJ
ejpam-3877	25	19	measure	measure	NOUN
ejpam-3877	25	20	-	-	PUNCT
ejpam-3877	25	21	valued	value	VERB
ejpam-3877	25	22	solutions	solution	NOUN
ejpam-3877	25	23	to	to	ADP
ejpam-3877	25	24	the	the	DET
ejpam-3877	25	25	following	following	NOUN
ejpam-3877	25	26	problem	problem	PUNCT
ejpam-3877	25	27	ut	ut	PROPN
ejpam-3877	25	28	=	=	PROPN
ejpam-3877	25	29	∆ϕ(u	∆ϕ(u	PROPN
ejpam-3877	25	30	)	)	PUNCT
ejpam-3877	25	31	in	in	ADP
ejpam-3877	25	32	q	q	NOUN
ejpam-3877	25	33	,	,	PUNCT
ejpam-3877	25	34	u	u	NOUN
ejpam-3877	25	35	=	=	NOUN
ejpam-3877	25	36	0	0	NUM
ejpam-3877	25	37	on	on	ADP
ejpam-3877	25	38	∂ω×	∂ω×	PROPN
ejpam-3877	25	39	(	(	PUNCT
ejpam-3877	25	40	0	0	NUM
ejpam-3877	25	41	,	,	PUNCT
ejpam-3877	25	42	t	t	NOUN
ejpam-3877	25	43	)	)	PUNCT
ejpam-3877	25	44	,	,	PUNCT
ejpam-3877	25	45	u(x	u(x	NOUN
ejpam-3877	25	46	,	,	PUNCT
ejpam-3877	25	47	0	0	NUM
ejpam-3877	25	48	)	)	PUNCT
ejpam-3877	25	49	=	=	PRON
ejpam-3877	25	50	u0	u0	ADJ
ejpam-3877	25	51	in	in	ADP
ejpam-3877	25	52	ω	ω	PROPN
ejpam-3877	25	53	,	,	PUNCT
ejpam-3877	25	54	(	(	PUNCT
ejpam-3877	25	55	f	f	PROPN
ejpam-3877	25	56	)	)	PUNCT
ejpam-3877	25	57	where	where	SCONJ
ejpam-3877	25	58	u0	u0	PROPN
ejpam-3877	25	59	∈m+(ω	∈m+(ω	PROPN
ejpam-3877	25	60	)	)	PUNCT
ejpam-3877	25	61	is	be	AUX
ejpam-3877	25	62	a	a	DET
ejpam-3877	25	63	bounded	bounded	ADJ
ejpam-3877	25	64	radon	radon	NOUN
ejpam-3877	25	65	measure	measure	NOUN
ejpam-3877	25	66	and	and	CCONJ
ejpam-3877	25	67	ϕ(s	ϕ(s	PRON
ejpam-3877	25	68	)	)	PUNCT
ejpam-3877	25	69	=	=	SYM
ejpam-3877	26	1	γ	γ	X
ejpam-3877	26	2	[	[	PUNCT
ejpam-3877	26	3	1−	1−	NUM
ejpam-3877	26	4	1	1	NUM
ejpam-3877	26	5	(	(	PUNCT
ejpam-3877	26	6	1	1	NUM
ejpam-3877	26	7	+	+	NOUN
ejpam-3877	26	8	s)σ	s)σ	NOUN
ejpam-3877	26	9	]	]	PUNCT
ejpam-3877	26	10	(	(	PUNCT
ejpam-3877	26	11	a.1	a.1	NOUN
ejpam-3877	26	12	)	)	PUNCT
ejpam-3877	26	13	with	with	ADP
ejpam-3877	26	14	γ	γ	PROPN
ejpam-3877	26	15	∈	∈	PROPN
ejpam-3877	26	16	(	(	PUNCT
ejpam-3877	26	17	0,+∞	0,+∞	NUM
ejpam-3877	26	18	)	)	PUNCT
ejpam-3877	26	19	,	,	PUNCT
ejpam-3877	26	20	σ	σ	X
ejpam-3877	26	21	>	>	X
ejpam-3877	26	22	0	0	X
ejpam-3877	26	23	.	.	PUNCT
ejpam-3877	27	1	since	since	SCONJ
ejpam-3877	27	2	ϕ	ϕ	NOUN
ejpam-3877	27	3	increases	increase	VERB
ejpam-3877	27	4	monotonically	monotonically	ADV
ejpam-3877	27	5	to	to	ADP
ejpam-3877	27	6	limiting	limit	VERB
ejpam-3877	27	7	value	value	NOUN
ejpam-3877	27	8	γ	γ	NOUN
ejpam-3877	27	9	as	as	ADP
ejpam-3877	27	10	s→	s→	PROPN
ejpam-3877	27	11	+	+	NOUN
ejpam-3877	27	12	∞.	∞.	PROPN
ejpam-3877	27	13	therefore	therefore	ADV
ejpam-3877	27	14	,	,	PUNCT
ejpam-3877	27	15	ϕ′(s	ϕ′(s	PROPN
ejpam-3877	27	16	)	)	PUNCT
ejpam-3877	27	17	→	→	SYM
ejpam-3877	27	18	0	0	NUM
ejpam-3877	27	19	,	,	PUNCT
ejpam-3877	27	20	thus	thus	ADV
ejpam-3877	27	21	the	the	DET
ejpam-3877	27	22	problem	problem	NOUN
ejpam-3877	27	23	(	(	PUNCT
ejpam-3877	27	24	f	f	X
ejpam-3877	27	25	)	)	PUNCT
ejpam-3877	27	26	is	be	AUX
ejpam-3877	27	27	strongly	strongly	ADV
ejpam-3877	27	28	degenerate	degenerate	ADJ
ejpam-3877	27	29	parabolic	parabolic	ADJ
ejpam-3877	27	30	equation	equation	NOUN
ejpam-3877	27	31	at	at	ADP
ejpam-3877	27	32	infinity	infinity	NOUN
ejpam-3877	27	33	.	.	PUNCT
ejpam-3877	28	1	another	another	DET
ejpam-3877	28	2	interesting	interesting	ADJ
ejpam-3877	28	3	problems	problem	NOUN
ejpam-3877	28	4	similar	similar	ADJ
ejpam-3877	28	5	to	to	ADP
ejpam-3877	28	6	the	the	DET
ejpam-3877	28	7	problem	problem	NOUN
ejpam-3877	28	8	(	(	PUNCT
ejpam-3877	28	9	p	p	NOUN
ejpam-3877	28	10	)	)	PUNCT
ejpam-3877	28	11	has	have	AUX
ejpam-3877	28	12	been	be	AUX
ejpam-3877	28	13	investigated	investigate	VERB
ejpam-3877	28	14	in	in	ADP
ejpam-3877	28	15	[	[	X
ejpam-3877	28	16	18	18	NUM
ejpam-3877	28	17	,	,	PUNCT
ejpam-3877	28	18	22	22	NUM
ejpam-3877	28	19	,	,	PUNCT
ejpam-3877	28	20	24	24	NUM
ejpam-3877	28	21	,	,	PUNCT
ejpam-3877	28	22	28	28	NUM
ejpam-3877	28	23	,	,	PUNCT
ejpam-3877	28	24	30	30	NUM
ejpam-3877	28	25	,	,	PUNCT
ejpam-3877	28	26	31	31	NUM
ejpam-3877	28	27	]	]	PUNCT
ejpam-3877	28	28	in	in	ADP
ejpam-3877	28	29	which	which	PRON
ejpam-3877	28	30	authors	author	NOUN
ejpam-3877	28	31	showed	show	VERB
ejpam-3877	28	32	the	the	DET
ejpam-3877	28	33	existence	existence	NOUN
ejpam-3877	28	34	and	and	CCONJ
ejpam-3877	28	35	uniqueness	uniqueness	NOUN
ejpam-3877	28	36	of	of	ADP
ejpam-3877	28	37	radon	radon	ADJ
ejpam-3877	28	38	measure	measure	NOUN
ejpam-3877	28	39	valued	value	VERB
ejpam-3877	28	40	solutions	solution	NOUN
ejpam-3877	28	41	to	to	ADP
ejpam-3877	28	42	nonlinear	nonlinear	ADJ
ejpam-3877	28	43	parabolic	parabolic	ADJ
ejpam-3877	28	44	equations	equation	NOUN
ejpam-3877	28	45	.	.	PUNCT
ejpam-3877	29	1	to	to	PART
ejpam-3877	29	2	obtain	obtain	VERB
ejpam-3877	29	3	the	the	DET
ejpam-3877	29	4	problem	problem	NOUN
ejpam-3877	29	5	(	(	PUNCT
ejpam-3877	29	6	p	p	NOUN
ejpam-3877	29	7	)	)	PUNCT
ejpam-3877	29	8	,	,	PUNCT
ejpam-3877	29	9	we	we	PRON
ejpam-3877	29	10	replace	replace	VERB
ejpam-3877	29	11	the	the	DET
ejpam-3877	29	12	function	function	NOUN
ejpam-3877	29	13	ϕ	ϕ	NOUN
ejpam-3877	29	14	by	by	ADP
ejpam-3877	29	15	ψ	ψ	PRON
ejpam-3877	29	16	which	which	PRON
ejpam-3877	29	17	is	be	AUX
ejpam-3877	29	18	defined	define	VERB
ejpam-3877	29	19	by	by	ADP
ejpam-3877	29	20	ψ(s	ψ(s	PROPN
ejpam-3877	29	21	)	)	PUNCT
ejpam-3877	30	1	=	=	PUNCT
ejpam-3877	31	1	∫	∫	PROPN
ejpam-3877	31	2	s	s	PART
ejpam-3877	31	3	0	0	NUM
ejpam-3877	31	4	e−|z|	e−|z|	PROPN
ejpam-3877	31	5	m	m	VERB
ejpam-3877	31	6	dz	dz	X
ejpam-3877	31	7	(	(	PUNCT
ejpam-3877	31	8	0	0	NUM
ejpam-3877	31	9	<	<	X
ejpam-3877	31	10	m	m	VERB
ejpam-3877	31	11	≤	≤	NOUN
ejpam-3877	31	12	1	1	NUM
ejpam-3877	31	13	)	)	PUNCT
ejpam-3877	31	14	(	(	PUNCT
ejpam-3877	31	15	1.1	1.1	NUM
ejpam-3877	31	16	)	)	PUNCT
ejpam-3877	31	17	quincy	quincy	PROPN
ejpam-3877	31	18	s.	s.	PROPN
ejpam-3877	31	19	nkombo	nkombo	PROPN
ejpam-3877	31	20	,	,	PUNCT
ejpam-3877	31	21	fengquan	fengquan	PROPN
ejpam-3877	31	22	li	li	PROPN
ejpam-3877	31	23	/	/	SYM
ejpam-3877	31	24	eur	eur	PROPN
ejpam-3877	31	25	.	.	PUNCT
ejpam-3877	32	1	j.	j.	PROPN
ejpam-3877	32	2	pure	pure	PROPN
ejpam-3877	32	3	appl	appl	PROPN
ejpam-3877	32	4	.	.	PROPN
ejpam-3877	32	5	math	math	PROPN
ejpam-3877	32	6	,	,	PUNCT
ejpam-3877	32	7	14	14	NUM
ejpam-3877	32	8	(	(	PUNCT
ejpam-3877	32	9	1	1	NUM
ejpam-3877	32	10	)	)	PUNCT
ejpam-3877	32	11	(	(	PUNCT
ejpam-3877	32	12	2021	2021	NUM
ejpam-3877	32	13	)	)	PUNCT
ejpam-3877	32	14	,	,	PUNCT
ejpam-3877	32	15	204	204	NUM
ejpam-3877	32	16	-	-	SYM
ejpam-3877	32	17	233	233	NUM
ejpam-3877	32	18	206	206	NUM
ejpam-3877	32	19	the	the	DET
ejpam-3877	32	20	function	function	NOUN
ejpam-3877	32	21	ψ	ψ	NOUN
ejpam-3877	32	22	increases	increase	NOUN
ejpam-3877	32	23	monotonically	monotonically	ADV
ejpam-3877	32	24	to	to	ADP
ejpam-3877	32	25	limiting	limit	VERB
ejpam-3877	32	26	value	value	NOUN
ejpam-3877	32	27	γ	γ	NOUN
ejpam-3877	32	28	as	as	ADP
ejpam-3877	32	29	s	s	PROPN
ejpam-3877	32	30	→	→	SYM
ejpam-3877	32	31	+	+	PROPN
ejpam-3877	32	32	∞.	∞.	PROPN
ejpam-3877	32	33	therefore	therefore	ADV
ejpam-3877	32	34	,	,	PUNCT
ejpam-3877	32	35	the	the	DET
ejpam-3877	32	36	problem	problem	NOUN
ejpam-3877	32	37	(	(	PUNCT
ejpam-3877	32	38	p	p	NOUN
ejpam-3877	32	39	)	)	PUNCT
ejpam-3877	32	40	is	be	AUX
ejpam-3877	32	41	nonlinear	nonlinear	ADJ
ejpam-3877	32	42	strongly	strongly	ADV
ejpam-3877	32	43	degenerate	degenerate	ADJ
ejpam-3877	32	44	parabolic	parabolic	ADJ
ejpam-3877	32	45	equation	equation	NOUN
ejpam-3877	32	46	at	at	ADP
ejpam-3877	32	47	infinity	infinity	NOUN
ejpam-3877	32	48	and	and	CCONJ
ejpam-3877	32	49	the	the	DET
ejpam-3877	32	50	function	function	NOUN
ejpam-3877	32	51	ψ	ψ	NOUN
ejpam-3877	32	52	is	be	AUX
ejpam-3877	32	53	given	give	VERB
ejpam-3877	32	54	by	by	ADP
ejpam-3877	32	55	oleinik	oleinik	ADJ
ejpam-3877	32	56	-	-	PUNCT
ejpam-3877	32	57	kruzhkov	kruzhkov	NOUN
ejpam-3877	32	58	in	in	ADP
ejpam-3877	32	59	[	[	X
ejpam-3877	32	60	26	26	NUM
ejpam-3877	32	61	]	]	PUNCT
ejpam-3877	32	62	.	.	PUNCT
ejpam-3877	33	1	the	the	DET
ejpam-3877	33	2	choice	choice	NOUN
ejpam-3877	33	3	of	of	ADP
ejpam-3877	33	4	the	the	DET
ejpam-3877	33	5	special	special	ADJ
ejpam-3877	33	6	function	function	NOUN
ejpam-3877	33	7	ψ	ψ	X
ejpam-3877	33	8	in	in	ADP
ejpam-3877	33	9	(	(	PUNCT
ejpam-3877	33	10	1.1	1.1	NUM
ejpam-3877	33	11	)	)	PUNCT
ejpam-3877	33	12	is	be	AUX
ejpam-3877	33	13	motivated	motivate	VERB
ejpam-3877	33	14	by	by	ADP
ejpam-3877	33	15	the	the	DET
ejpam-3877	33	16	connection	connection	NOUN
ejpam-3877	33	17	with	with	ADP
ejpam-3877	33	18	the	the	DET
ejpam-3877	33	19	function	function	NOUN
ejpam-3877	33	20	ϕ	ϕ	NOUN
ejpam-3877	33	21	in	in	ADP
ejpam-3877	33	22	(	(	PUNCT
ejpam-3877	33	23	a.1	a.1	NOUN
ejpam-3877	33	24	)	)	PUNCT
ejpam-3877	33	25	,	,	PUNCT
ejpam-3877	33	26	such	such	ADJ
ejpam-3877	33	27	as	as	ADP
ejpam-3877	33	28	ψ′	ψ′	PROPN
ejpam-3877	33	29	≤	≤	NOUN
ejpam-3877	33	30	ϕ′	ϕ′	PUNCT
ejpam-3877	33	31	in	in	ADP
ejpam-3877	33	32	r+	r+	NOUN
ejpam-3877	33	33	.	.	PUNCT
ejpam-3877	34	1	this	this	DET
ejpam-3877	34	2	comparison	comparison	NOUN
ejpam-3877	34	3	leads	lead	VERB
ejpam-3877	34	4	to	to	ADP
ejpam-3877	34	5	the	the	DET
ejpam-3877	34	6	connection	connection	NOUN
ejpam-3877	34	7	of	of	ADP
ejpam-3877	34	8	the	the	DET
ejpam-3877	34	9	problem	problem	NOUN
ejpam-3877	34	10	(	(	PUNCT
ejpam-3877	34	11	p	p	NOUN
ejpam-3877	34	12	)	)	PUNCT
ejpam-3877	34	13	with	with	ADP
ejpam-3877	34	14	the	the	DET
ejpam-3877	34	15	previous	previous	ADJ
ejpam-3877	34	16	study	study	NOUN
ejpam-3877	34	17	problem	problem	NOUN
ejpam-3877	34	18	(	(	PUNCT
ejpam-3877	34	19	f	f	NOUN
ejpam-3877	34	20	)	)	PUNCT
ejpam-3877	34	21	.	.	PUNCT
ejpam-3877	35	1	in	in	ADP
ejpam-3877	35	2	order	order	NOUN
ejpam-3877	35	3	to	to	PART
ejpam-3877	35	4	construct	construct	VERB
ejpam-3877	35	5	the	the	DET
ejpam-3877	35	6	problem	problem	NOUN
ejpam-3877	35	7	(	(	PUNCT
ejpam-3877	35	8	p	p	NOUN
ejpam-3877	35	9	)	)	PUNCT
ejpam-3877	35	10	,	,	PUNCT
ejpam-3877	35	11	we	we	PRON
ejpam-3877	35	12	add	add	VERB
ejpam-3877	35	13	a	a	DET
ejpam-3877	35	14	radon	radon	ADJ
ejpam-3877	35	15	measure	measure	NOUN
ejpam-3877	35	16	as	as	ADP
ejpam-3877	35	17	a	a	DET
ejpam-3877	35	18	forcing	force	VERB
ejpam-3877	35	19	term	term	NOUN
ejpam-3877	35	20	µ	µ	NOUN
ejpam-3877	35	21	∈m+(q	∈m+(q	NOUN
ejpam-3877	35	22	)	)	PUNCT
ejpam-3877	35	23	(	(	PUNCT
ejpam-3877	35	24	a	a	DET
ejpam-3877	35	25	nonnegative	nonnegative	ADJ
ejpam-3877	35	26	bounded	bounded	ADJ
ejpam-3877	35	27	radon	radon	PROPN
ejpam-3877	35	28	measure	measure	NOUN
ejpam-3877	35	29	with	with	ADP
ejpam-3877	35	30	respect	respect	NOUN
ejpam-3877	35	31	to	to	ADP
ejpam-3877	35	32	the	the	DET
ejpam-3877	35	33	parabolic	parabolic	ADJ
ejpam-3877	35	34	capacity	capacity	NOUN
ejpam-3877	35	35	)	)	PUNCT
ejpam-3877	35	36	to	to	ADP
ejpam-3877	35	37	the	the	DET
ejpam-3877	35	38	problem	problem	NOUN
ejpam-3877	35	39	(	(	PUNCT
ejpam-3877	35	40	f	f	PROPN
ejpam-3877	35	41	)	)	PUNCT
ejpam-3877	35	42	.	.	PUNCT
ejpam-3877	36	1	the	the	DET
ejpam-3877	36	2	first	first	ADJ
ejpam-3877	36	3	difficulty	difficulty	NOUN
ejpam-3877	36	4	when	when	SCONJ
ejpam-3877	36	5	studying	study	VERB
ejpam-3877	36	6	the	the	DET
ejpam-3877	36	7	problem	problem	NOUN
ejpam-3877	36	8	(	(	PUNCT
ejpam-3877	36	9	p	p	NOUN
ejpam-3877	36	10	)	)	PUNCT
ejpam-3877	36	11	is	be	AUX
ejpam-3877	36	12	due	due	ADJ
ejpam-3877	36	13	to	to	ADP
ejpam-3877	36	14	the	the	DET
ejpam-3877	36	15	presence	presence	NOUN
ejpam-3877	36	16	of	of	ADP
ejpam-3877	36	17	a	a	DET
ejpam-3877	36	18	forcing	force	VERB
ejpam-3877	36	19	term	term	NOUN
ejpam-3877	36	20	µ	µ	NOUN
ejpam-3877	36	21	and	and	CCONJ
ejpam-3877	36	22	the	the	DET
ejpam-3877	36	23	second	second	ADJ
ejpam-3877	36	24	difficulty	difficulty	NOUN
ejpam-3877	36	25	is	be	AUX
ejpam-3877	36	26	a	a	DET
ejpam-3877	36	27	lack	lack	NOUN
ejpam-3877	36	28	of	of	ADP
ejpam-3877	36	29	coercivity	coercivity	NOUN
ejpam-3877	36	30	of	of	ADP
ejpam-3877	36	31	the	the	DET
ejpam-3877	36	32	differential	differential	ADJ
ejpam-3877	36	33	operator	operator	NOUN
ejpam-3877	36	34	u→	u→	NOUN
ejpam-3877	36	35	div(ψ′(u)∇u	div(ψ′(u)∇u	NOUN
ejpam-3877	36	36	)	)	PUNCT
ejpam-3877	36	37	.	.	PUNCT
ejpam-3877	37	1	in	in	ADP
ejpam-3877	37	2	the	the	DET
ejpam-3877	37	3	study	study	NOUN
ejpam-3877	37	4	of	of	ADP
ejpam-3877	37	5	degenerate	degenerate	ADJ
ejpam-3877	37	6	parabolic	parabolic	NOUN
ejpam-3877	37	7	equations	equation	NOUN
ejpam-3877	37	8	,	,	PUNCT
ejpam-3877	37	9	a	a	DET
ejpam-3877	37	10	physical	physical	ADJ
ejpam-3877	37	11	model	model	NOUN
ejpam-3877	37	12	may	may	AUX
ejpam-3877	37	13	be	be	AUX
ejpam-3877	37	14	imagined	imagine	VERB
ejpam-3877	37	15	in	in	ADP
ejpam-3877	37	16	which	which	PRON
ejpam-3877	37	17	the	the	DET
ejpam-3877	37	18	degenerate	degenerate	ADJ
ejpam-3877	37	19	parabolic	parabolic	ADJ
ejpam-3877	37	20	equations	equation	NOUN
ejpam-3877	37	21	described	describe	VERB
ejpam-3877	37	22	arise	arise	NOUN
ejpam-3877	37	23	in	in	ADP
ejpam-3877	37	24	nonlinear	nonlinear	ADJ
ejpam-3877	37	25	fluid	fluid	ADJ
ejpam-3877	37	26	mechanics	mechanic	NOUN
ejpam-3877	37	27	,	,	PUNCT
ejpam-3877	37	28	heat	heat	NOUN
ejpam-3877	37	29	transfer	transfer	NOUN
ejpam-3877	37	30	or	or	CCONJ
ejpam-3877	37	31	diffusion	diffusion	NOUN
ejpam-3877	37	32	.	.	PUNCT
ejpam-3877	38	1	moreover	moreover	ADV
ejpam-3877	38	2	the	the	DET
ejpam-3877	38	3	radon	radon	NOUN
ejpam-3877	38	4	measures	measure	NOUN
ejpam-3877	38	5	involved	involve	VERB
ejpam-3877	38	6	as	as	SCONJ
ejpam-3877	38	7	data	datum	NOUN
ejpam-3877	38	8	describe	describe	VERB
ejpam-3877	38	9	the	the	DET
ejpam-3877	38	10	distribution	distribution	NOUN
ejpam-3877	38	11	of	of	ADP
ejpam-3877	38	12	mass	mass	NOUN
ejpam-3877	38	13	in	in	ADP
ejpam-3877	38	14	the	the	DET
ejpam-3877	38	15	length	length	NOUN
ejpam-3877	38	16	area	area	NOUN
ejpam-3877	38	17	,	,	PUNCT
ejpam-3877	38	18	and	and	CCONJ
ejpam-3877	38	19	volume	volume	NOUN
ejpam-3877	38	20	.	.	PUNCT
ejpam-3877	39	1	the	the	DET
ejpam-3877	39	2	last	last	ADJ
ejpam-3877	39	3	decades	decade	NOUN
ejpam-3877	39	4	some	some	DET
ejpam-3877	39	5	authors	author	NOUN
ejpam-3877	39	6	studied	study	VERB
ejpam-3877	39	7	the	the	DET
ejpam-3877	39	8	parabolic	parabolic	ADJ
ejpam-3877	39	9	and	and	CCONJ
ejpam-3877	39	10	elliptic	elliptic	ADJ
ejpam-3877	39	11	equations	equation	NOUN
ejpam-3877	39	12	involving	involve	VERB
ejpam-3877	39	13	measure	measure	NOUN
ejpam-3877	39	14	data	datum	NOUN
ejpam-3877	39	15	,	,	PUNCT
ejpam-3877	39	16	but	but	CCONJ
ejpam-3877	39	17	the	the	DET
ejpam-3877	39	18	solutions	solution	NOUN
ejpam-3877	39	19	of	of	ADP
ejpam-3877	39	20	these	these	DET
ejpam-3877	39	21	equations	equation	NOUN
ejpam-3877	39	22	are	be	AUX
ejpam-3877	39	23	not	not	PART
ejpam-3877	39	24	measures	measure	NOUN
ejpam-3877	39	25	(	(	PUNCT
ejpam-3877	39	26	see	see	VERB
ejpam-3877	39	27	[	[	X
ejpam-3877	39	28	2	2	NUM
ejpam-3877	39	29	,	,	PUNCT
ejpam-3877	39	30	17	17	NUM
ejpam-3877	39	31	,	,	PUNCT
ejpam-3877	39	32	25	25	NUM
ejpam-3877	39	33	]	]	PUNCT
ejpam-3877	39	34	)	)	PUNCT
ejpam-3877	39	35	.	.	PUNCT
ejpam-3877	40	1	due	due	ADP
ejpam-3877	40	2	to	to	ADP
ejpam-3877	40	3	this	this	DET
ejpam-3877	40	4	reason	reason	NOUN
ejpam-3877	40	5	,	,	PUNCT
ejpam-3877	40	6	the	the	DET
ejpam-3877	40	7	main	main	ADJ
ejpam-3877	40	8	purpose	purpose	NOUN
ejpam-3877	40	9	of	of	ADP
ejpam-3877	40	10	this	this	DET
ejpam-3877	40	11	paper	paper	NOUN
ejpam-3877	40	12	is	be	AUX
ejpam-3877	40	13	to	to	PART
ejpam-3877	40	14	study	study	VERB
ejpam-3877	40	15	the	the	DET
ejpam-3877	40	16	degenerate	degenerate	ADJ
ejpam-3877	40	17	parabolic	parabolic	ADJ
ejpam-3877	40	18	equations	equation	NOUN
ejpam-3877	40	19	with	with	ADP
ejpam-3877	40	20	measure	measure	NOUN
ejpam-3877	40	21	data	datum	NOUN
ejpam-3877	40	22	which	which	PRON
ejpam-3877	40	23	the	the	DET
ejpam-3877	40	24	solutions	solution	NOUN
ejpam-3877	40	25	of	of	ADP
ejpam-3877	40	26	such	such	ADJ
ejpam-3877	40	27	equations	equation	NOUN
ejpam-3877	40	28	are	be	AUX
ejpam-3877	40	29	measures	measure	NOUN
ejpam-3877	40	30	as	as	ADV
ejpam-3877	40	31	well	well	ADV
ejpam-3877	40	32	.	.	PUNCT
ejpam-3877	41	1	this	this	DET
ejpam-3877	41	2	result	result	NOUN
ejpam-3877	41	3	is	be	AUX
ejpam-3877	41	4	possible	possible	ADJ
ejpam-3877	41	5	because	because	SCONJ
ejpam-3877	41	6	of	of	ADP
ejpam-3877	41	7	the	the	DET
ejpam-3877	41	8	definition	definition	NOUN
ejpam-3877	41	9	of	of	ADP
ejpam-3877	41	10	weak	weak	ADJ
ejpam-3877	41	11	radon	radon	ADJ
ejpam-3877	41	12	measure	measure	NOUN
ejpam-3877	41	13	-	-	PUNCT
ejpam-3877	41	14	valued	value	VERB
ejpam-3877	41	15	solutions	solution	NOUN
ejpam-3877	41	16	introduced	introduce	VERB
ejpam-3877	41	17	in	in	ADP
ejpam-3877	41	18	[	[	X
ejpam-3877	41	19	23	23	NUM
ejpam-3877	41	20	]	]	PUNCT
ejpam-3877	41	21	,	,	PUNCT
ejpam-3877	41	22	hence	hence	ADV
ejpam-3877	41	23	the	the	DET
ejpam-3877	41	24	main	main	ADJ
ejpam-3877	41	25	motivation	motivation	NOUN
ejpam-3877	41	26	to	to	PART
ejpam-3877	41	27	study	study	VERB
ejpam-3877	41	28	of	of	ADP
ejpam-3877	41	29	the	the	DET
ejpam-3877	41	30	problem	problem	NOUN
ejpam-3877	41	31	(	(	PUNCT
ejpam-3877	41	32	p	p	NOUN
ejpam-3877	41	33	)	)	PUNCT
ejpam-3877	41	34	.	.	PUNCT
ejpam-3877	42	1	the	the	DET
ejpam-3877	42	2	unique	unique	ADJ
ejpam-3877	42	3	point	point	NOUN
ejpam-3877	42	4	of	of	ADP
ejpam-3877	42	5	the	the	DET
ejpam-3877	42	6	novelty	novelty	NOUN
ejpam-3877	42	7	of	of	ADP
ejpam-3877	42	8	this	this	DET
ejpam-3877	42	9	paper	paper	NOUN
ejpam-3877	42	10	is	be	AUX
ejpam-3877	42	11	the	the	DET
ejpam-3877	42	12	study	study	NOUN
ejpam-3877	42	13	of	of	ADP
ejpam-3877	42	14	the	the	DET
ejpam-3877	42	15	uniqueness	uniqueness	NOUN
ejpam-3877	42	16	of	of	ADP
ejpam-3877	42	17	the	the	DET
ejpam-3877	42	18	radon	radon	PROPN
ejpam-3877	42	19	measure	measure	NOUN
ejpam-3877	42	20	-	-	PUNCT
ejpam-3877	42	21	valued	value	VERB
ejpam-3877	42	22	solutions	solution	NOUN
ejpam-3877	42	23	when	when	SCONJ
ejpam-3877	42	24	the	the	DET
ejpam-3877	42	25	radon	radon	PROPN
ejpam-3877	42	26	measure	measure	NOUN
ejpam-3877	42	27	as	as	ADP
ejpam-3877	42	28	a	a	DET
ejpam-3877	42	29	forcing	force	VERB
ejpam-3877	42	30	term	term	NOUN
ejpam-3877	42	31	is	be	AUX
ejpam-3877	42	32	diffuse	diffuse	NOUN
ejpam-3877	42	33	with	with	ADP
ejpam-3877	42	34	respect	respect	NOUN
ejpam-3877	42	35	to	to	ADP
ejpam-3877	42	36	the	the	DET
ejpam-3877	42	37	parabolic	parabolic	ADJ
ejpam-3877	42	38	capacity	capacity	NOUN
ejpam-3877	42	39	and	and	CCONJ
ejpam-3877	42	40	the	the	DET
ejpam-3877	42	41	radon	radon	ADJ
ejpam-3877	42	42	measure	measure	NOUN
ejpam-3877	42	43	as	as	SCONJ
ejpam-3877	42	44	initial	initial	ADJ
ejpam-3877	42	45	data	data	NOUN
ejpam-3877	42	46	is	be	AUX
ejpam-3877	42	47	diffuse	diffuse	NOUN
ejpam-3877	42	48	with	with	ADP
ejpam-3877	42	49	respect	respect	NOUN
ejpam-3877	42	50	to	to	ADP
ejpam-3877	42	51	the	the	DET
ejpam-3877	42	52	newtonian	newtonian	ADJ
ejpam-3877	42	53	capacity	capacity	NOUN
ejpam-3877	42	54	.	.	PUNCT
ejpam-3877	43	1	to	to	ADP
ejpam-3877	43	2	the	the	DET
ejpam-3877	43	3	best	good	ADJ
ejpam-3877	43	4	of	of	ADP
ejpam-3877	43	5	our	our	PRON
ejpam-3877	43	6	knowledge	knowledge	NOUN
ejpam-3877	43	7	there	there	PRON
ejpam-3877	43	8	is	be	VERB
ejpam-3877	43	9	no	no	DET
ejpam-3877	43	10	existing	exist	VERB
ejpam-3877	43	11	results	result	NOUN
ejpam-3877	43	12	of	of	ADP
ejpam-3877	43	13	the	the	DET
ejpam-3877	43	14	problem	problem	NOUN
ejpam-3877	43	15	(	(	PUNCT
ejpam-3877	43	16	p	p	NOUN
ejpam-3877	43	17	)	)	PUNCT
ejpam-3877	43	18	are	be	AUX
ejpam-3877	43	19	known	know	VERB
ejpam-3877	43	20	in	in	ADP
ejpam-3877	43	21	the	the	DET
ejpam-3877	43	22	literature	literature	NOUN
ejpam-3877	43	23	.	.	PUNCT
ejpam-3877	44	1	hence	hence	ADV
ejpam-3877	44	2	,	,	PUNCT
ejpam-3877	44	3	this	this	DET
ejpam-3877	44	4	interesting	interesting	ADJ
ejpam-3877	44	5	case	case	NOUN
ejpam-3877	44	6	will	will	AUX
ejpam-3877	44	7	be	be	AUX
ejpam-3877	44	8	discussed	discuss	VERB
ejpam-3877	44	9	in	in	ADP
ejpam-3877	44	10	this	this	DET
ejpam-3877	44	11	paper	paper	NOUN
ejpam-3877	44	12	.	.	PUNCT
ejpam-3877	45	1	the	the	DET
ejpam-3877	45	2	plan	plan	NOUN
ejpam-3877	45	3	of	of	ADP
ejpam-3877	45	4	this	this	DET
ejpam-3877	45	5	paper	paper	NOUN
ejpam-3877	45	6	is	be	AUX
ejpam-3877	45	7	organized	organize	VERB
ejpam-3877	45	8	as	as	SCONJ
ejpam-3877	45	9	follows	follow	VERB
ejpam-3877	45	10	.	.	PUNCT
ejpam-3877	46	1	in	in	ADP
ejpam-3877	46	2	the	the	DET
ejpam-3877	46	3	next	next	ADJ
ejpam-3877	46	4	section	section	NOUN
ejpam-3877	46	5	,	,	PUNCT
ejpam-3877	46	6	we	we	PRON
ejpam-3877	46	7	recall	recall	VERB
ejpam-3877	46	8	some	some	DET
ejpam-3877	46	9	preliminaries	preliminary	NOUN
ejpam-3877	46	10	about	about	ADP
ejpam-3877	46	11	capacity	capacity	NOUN
ejpam-3877	46	12	and	and	CCONJ
ejpam-3877	46	13	radon	radon	NOUN
ejpam-3877	46	14	measures	measure	NOUN
ejpam-3877	46	15	.	.	PUNCT
ejpam-3877	47	1	then	then	ADV
ejpam-3877	47	2	in	in	ADP
ejpam-3877	47	3	section	section	NOUN
ejpam-3877	47	4	3	3	NUM
ejpam-3877	47	5	,	,	PUNCT
ejpam-3877	47	6	we	we	PRON
ejpam-3877	47	7	state	state	VERB
ejpam-3877	47	8	the	the	DET
ejpam-3877	47	9	main	main	ADJ
ejpam-3877	47	10	results	result	NOUN
ejpam-3877	47	11	,	,	PUNCT
ejpam-3877	47	12	while	while	SCONJ
ejpam-3877	47	13	in	in	ADP
ejpam-3877	47	14	section	section	NOUN
ejpam-3877	47	15	4	4	NUM
ejpam-3877	47	16	-	-	SYM
ejpam-3877	47	17	6	6	NUM
ejpam-3877	47	18	,	,	PUNCT
ejpam-3877	47	19	we	we	PRON
ejpam-3877	47	20	prove	prove	VERB
ejpam-3877	47	21	the	the	DET
ejpam-3877	47	22	main	main	ADJ
ejpam-3877	47	23	results	result	NOUN
ejpam-3877	47	24	.	.	PUNCT
ejpam-3877	48	1	2	2	X
ejpam-3877	48	2	.	.	X
ejpam-3877	48	3	preliminaries	preliminary	NOUN
ejpam-3877	48	4	2.1	2.1	NUM
ejpam-3877	48	5	about	about	ADP
ejpam-3877	48	6	capacity	capacity	NOUN
ejpam-3877	48	7	and	and	CCONJ
ejpam-3877	48	8	measures	measure	NOUN
ejpam-3877	48	9	for	for	ADP
ejpam-3877	48	10	any	any	DET
ejpam-3877	48	11	borel	borel	NOUN
ejpam-3877	48	12	set	set	NOUN
ejpam-3877	48	13	e	e	PROPN
ejpam-3877	48	14	⊂	⊂	PROPN
ejpam-3877	48	15	ω	ω	PROPN
ejpam-3877	48	16	,	,	PUNCT
ejpam-3877	48	17	the	the	DET
ejpam-3877	48	18	c2	c2	PROPN
ejpam-3877	48	19	-	-	PUNCT
ejpam-3877	48	20	capacity	capacity	NOUN
ejpam-3877	48	21	of	of	ADP
ejpam-3877	48	22	e	e	PROPN
ejpam-3877	48	23	in	in	ADP
ejpam-3877	48	24	ω	ω	PROPN
ejpam-3877	48	25	is	be	AUX
ejpam-3877	48	26	defined	define	VERB
ejpam-3877	48	27	as	as	ADP
ejpam-3877	48	28	c2(e	c2(e	NOUN
ejpam-3877	48	29	)	)	PUNCT
ejpam-3877	48	30	=	=	SYM
ejpam-3877	48	31	inf	inf	NOUN
ejpam-3877	48	32	{	{	PUNCT
ejpam-3877	48	33	∫	∫	PROPN
ejpam-3877	48	34	ω	ω	PROPN
ejpam-3877	48	35	|	|	PROPN
ejpam-3877	48	36	∇u	∇u	PROPN
ejpam-3877	48	37	|2dx	|2dx	PROPN
ejpam-3877	48	38	/	/	SYM
ejpam-3877	48	39	u	u	NOUN
ejpam-3877	48	40	∈	∈	NOUN
ejpam-3877	48	41	zeω	zeω	NOUN
ejpam-3877	48	42	}	}	PUNCT
ejpam-3877	48	43	where	where	SCONJ
ejpam-3877	48	44	zeω	zeω	NOUN
ejpam-3877	48	45	denotes	denote	VERB
ejpam-3877	48	46	the	the	DET
ejpam-3877	48	47	set	set	NOUN
ejpam-3877	48	48	of	of	ADP
ejpam-3877	48	49	u	u	PROPN
ejpam-3877	48	50	belongs	belong	VERB
ejpam-3877	48	51	to	to	PART
ejpam-3877	48	52	h1	h1	VERB
ejpam-3877	48	53	0	0	NUM
ejpam-3877	48	54	(	(	PUNCT
ejpam-3877	48	55	ω	ω	NOUN
ejpam-3877	48	56	)	)	PUNCT
ejpam-3877	48	57	such	such	ADJ
ejpam-3877	48	58	that	that	SCONJ
ejpam-3877	48	59	0	0	NUM
ejpam-3877	48	60	≤	≤	NUM
ejpam-3877	48	61	u	u	NOUN
ejpam-3877	48	62	≤	≤	ADV
ejpam-3877	48	63	1	1	NUM
ejpam-3877	48	64	almost	almost	ADV
ejpam-3877	48	65	everywhere	everywhere	ADV
ejpam-3877	48	66	in	in	ADP
ejpam-3877	48	67	ω	ω	NUM
ejpam-3877	48	68	,	,	PUNCT
ejpam-3877	48	69	and	and	CCONJ
ejpam-3877	48	70	u	u	NOUN
ejpam-3877	48	71	=	=	NOUN
ejpam-3877	48	72	1	1	NUM
ejpam-3877	48	73	almost	almost	ADV
ejpam-3877	48	74	everywhere	everywhere	ADV
ejpam-3877	48	75	in	in	ADP
ejpam-3877	48	76	a	a	DET
ejpam-3877	48	77	neighborhood	neighborhood	NOUN
ejpam-3877	48	78	e	e	NOUN
ejpam-3877	48	79	(	(	PUNCT
ejpam-3877	48	80	see	see	VERB
ejpam-3877	48	81	[	[	X
ejpam-3877	48	82	23	23	NUM
ejpam-3877	48	83	]	]	PUNCT
ejpam-3877	48	84	)	)	PUNCT
ejpam-3877	48	85	.	.	PUNCT
ejpam-3877	49	1	let	let	VERB
ejpam-3877	49	2	w	w	NOUN
ejpam-3877	49	3	=	=	PRON
ejpam-3877	49	4	{	{	PUNCT
ejpam-3877	49	5	u	u	NOUN
ejpam-3877	49	6	∈	∈	PROPN
ejpam-3877	49	7	l2((0	l2((0	PROPN
ejpam-3877	49	8	,	,	PUNCT
ejpam-3877	49	9	t	t	PROPN
ejpam-3877	49	10	)	)	PUNCT
ejpam-3877	49	11	,	,	PUNCT
ejpam-3877	49	12	h1	h1	PROPN
ejpam-3877	49	13	0	0	NUM
ejpam-3877	49	14	(	(	PUNCT
ejpam-3877	49	15	ω	ω	NOUN
ejpam-3877	49	16	)	)	PUNCT
ejpam-3877	49	17	)	)	PUNCT
ejpam-3877	49	18	and	and	CCONJ
ejpam-3877	49	19	ut	ut	PROPN
ejpam-3877	49	20	∈	∈	PROPN
ejpam-3877	49	21	l2((0	l2((0	PROPN
ejpam-3877	49	22	,	,	PUNCT
ejpam-3877	49	23	t	t	PROPN
ejpam-3877	49	24	)	)	PUNCT
ejpam-3877	49	25	,	,	PUNCT
ejpam-3877	49	26	h−1(ω	h−1(ω	PROPN
ejpam-3877	49	27	)	)	PUNCT
ejpam-3877	49	28	)	)	PUNCT
ejpam-3877	49	29	}	}	PUNCT
ejpam-3877	49	30	endowed	endow	VERB
ejpam-3877	49	31	with	with	ADP
ejpam-3877	49	32	its	its	PRON
ejpam-3877	49	33	natural	natural	ADJ
ejpam-3877	49	34	norm	norm	NOUN
ejpam-3877	49	35	‖	‖	PROPN
ejpam-3877	49	36	u	u	PROPN
ejpam-3877	49	37	‖w=‖	‖w=‖	PUNCT
ejpam-3877	49	38	u	u	X
ejpam-3877	49	39	‖l2((0,t	‖l2((0,t	NOUN
ejpam-3877	49	40	)	)	PUNCT
ejpam-3877	49	41	,	,	PUNCT
ejpam-3877	49	42	h1	h1	PROPN
ejpam-3877	49	43	0	0	NUM
ejpam-3877	49	44	(	(	PUNCT
ejpam-3877	49	45	ω	ω	NOUN
ejpam-3877	49	46	)	)	PUNCT
ejpam-3877	49	47	)	)	PUNCT
ejpam-3877	50	1	+	+	CCONJ
ejpam-3877	50	2	‖	‖	PROPN
ejpam-3877	50	3	ut	ut	PROPN
ejpam-3877	50	4	‖l2((0,t	‖l2((0,t	PROPN
ejpam-3877	50	5	)	)	PUNCT
ejpam-3877	50	6	,	,	PUNCT
ejpam-3877	50	7	h−1(ω	h−1(ω	PROPN
ejpam-3877	50	8	)	)	PUNCT
ejpam-3877	50	9	)	)	PUNCT
ejpam-3877	50	10	a	a	DET
ejpam-3877	50	11	banach	banach	NOUN
ejpam-3877	50	12	space	space	NOUN
ejpam-3877	50	13	.	.	PUNCT
ejpam-3877	51	1	for	for	ADP
ejpam-3877	51	2	any	any	DET
ejpam-3877	51	3	open	open	ADJ
ejpam-3877	51	4	set	set	NOUN
ejpam-3877	51	5	u	u	PROPN
ejpam-3877	51	6	⊂	⊂	PROPN
ejpam-3877	51	7	q	q	INTJ
ejpam-3877	51	8	,	,	PUNCT
ejpam-3877	51	9	we	we	PRON
ejpam-3877	51	10	define	define	VERB
ejpam-3877	51	11	the	the	DET
ejpam-3877	51	12	parabolic	parabolic	ADJ
ejpam-3877	51	13	capacity	capacity	NOUN
ejpam-3877	51	14	as	as	ADP
ejpam-3877	51	15	cap(u	cap(u	PROPN
ejpam-3877	51	16	)	)	PUNCT
ejpam-3877	51	17	=	=	SYM
ejpam-3877	51	18	inf	inf	NOUN
ejpam-3877	51	19	{	{	PUNCT
ejpam-3877	51	20	‖	‖	PROPN
ejpam-3877	51	21	u	u	PROPN
ejpam-3877	51	22	‖w	‖w	NOUN
ejpam-3877	51	23	/u	/u	PUNCT
ejpam-3877	51	24	∈	∈	PROPN
ejpam-3877	51	25	vuq	vuq	NOUN
ejpam-3877	51	26	}	}	PUNCT
ejpam-3877	51	27	quincy	quincy	PROPN
ejpam-3877	51	28	s.	s.	PROPN
ejpam-3877	51	29	nkombo	nkombo	PROPN
ejpam-3877	51	30	,	,	PUNCT
ejpam-3877	51	31	fengquan	fengquan	PROPN
ejpam-3877	51	32	li	li	PROPN
ejpam-3877	51	33	/	/	SYM
ejpam-3877	51	34	eur	eur	PROPN
ejpam-3877	51	35	.	.	PUNCT
ejpam-3877	52	1	j.	j.	PROPN
ejpam-3877	52	2	pure	pure	PROPN
ejpam-3877	52	3	appl	appl	PROPN
ejpam-3877	52	4	.	.	PROPN
ejpam-3877	52	5	math	math	PROPN
ejpam-3877	52	6	,	,	PUNCT
ejpam-3877	52	7	14	14	NUM
ejpam-3877	52	8	(	(	PUNCT
ejpam-3877	52	9	1	1	NUM
ejpam-3877	52	10	)	)	PUNCT
ejpam-3877	52	11	(	(	PUNCT
ejpam-3877	52	12	2021	2021	NUM
ejpam-3877	52	13	)	)	PUNCT
ejpam-3877	52	14	,	,	PUNCT
ejpam-3877	52	15	204	204	NUM
ejpam-3877	52	16	-	-	SYM
ejpam-3877	52	17	233	233	NUM
ejpam-3877	52	18	207	207	NUM
ejpam-3877	52	19	where	where	SCONJ
ejpam-3877	52	20	vuq	vuq	PROPN
ejpam-3877	52	21	denotes	denote	VERB
ejpam-3877	52	22	the	the	DET
ejpam-3877	52	23	set	set	NOUN
ejpam-3877	52	24	of	of	ADP
ejpam-3877	52	25	u	u	PROPN
ejpam-3877	52	26	belongs	belong	VERB
ejpam-3877	52	27	to	to	ADP
ejpam-3877	52	28	w	w	ADP
ejpam-3877	52	29	such	such	ADJ
ejpam-3877	52	30	that	that	DET
ejpam-3877	52	31	0	0	NUM
ejpam-3877	52	32	≤	≤	NUM
ejpam-3877	52	33	u	u	NOUN
ejpam-3877	52	34	≤	≤	ADV
ejpam-3877	52	35	1	1	NUM
ejpam-3877	52	36	almost	almost	ADV
ejpam-3877	52	37	everywhere	everywhere	ADV
ejpam-3877	52	38	in	in	ADP
ejpam-3877	52	39	q	q	NOUN
ejpam-3877	52	40	,	,	PUNCT
ejpam-3877	52	41	and	and	CCONJ
ejpam-3877	52	42	u	u	X
ejpam-3877	52	43	=	=	NOUN
ejpam-3877	52	44	1	1	NUM
ejpam-3877	52	45	almost	almost	ADV
ejpam-3877	52	46	everywhere	everywhere	ADV
ejpam-3877	52	47	in	in	ADP
ejpam-3877	52	48	a	a	DET
ejpam-3877	52	49	neighborhood	neighborhood	NOUN
ejpam-3877	52	50	u	u	NOUN
ejpam-3877	52	51	(	(	PUNCT
ejpam-3877	52	52	see	see	VERB
ejpam-3877	52	53	[	[	X
ejpam-3877	52	54	16	16	NUM
ejpam-3877	52	55	]	]	PUNCT
ejpam-3877	52	56	)	)	PUNCT
ejpam-3877	52	57	.	.	PUNCT
ejpam-3877	53	1	let	let	VERB
ejpam-3877	53	2	m(ω	m(ω	NOUN
ejpam-3877	53	3	)	)	PUNCT
ejpam-3877	53	4	be	be	AUX
ejpam-3877	53	5	the	the	DET
ejpam-3877	53	6	space	space	NOUN
ejpam-3877	53	7	of	of	ADP
ejpam-3877	53	8	bounded	bounded	ADJ
ejpam-3877	53	9	radon	radon	NOUN
ejpam-3877	53	10	measures	measure	NOUN
ejpam-3877	53	11	on	on	ADP
ejpam-3877	53	12	ω	ω	NUM
ejpam-3877	53	13	,	,	PUNCT
ejpam-3877	53	14	and	and	CCONJ
ejpam-3877	53	15	m+(ω	m+(ω	NOUN
ejpam-3877	53	16	)	)	PUNCT
ejpam-3877	54	1	⊂	⊂	PROPN
ejpam-3877	54	2	m(ω	m(ω	PROPN
ejpam-3877	54	3	)	)	PUNCT
ejpam-3877	54	4	the	the	DET
ejpam-3877	54	5	cone	cone	NOUN
ejpam-3877	54	6	of	of	ADP
ejpam-3877	54	7	nonnegative	nonnegative	ADJ
ejpam-3877	54	8	bounded	bounded	ADJ
ejpam-3877	54	9	radon	radon	NOUN
ejpam-3877	54	10	measures	measure	NOUN
ejpam-3877	54	11	on	on	ADP
ejpam-3877	54	12	ω	ω	NUM
ejpam-3877	54	13	.	.	PUNCT
ejpam-3877	55	1	for	for	ADP
ejpam-3877	55	2	any	any	DET
ejpam-3877	55	3	µ	µ	PRON
ejpam-3877	55	4	∈	∈	PROPN
ejpam-3877	55	5	m(ω	m(ω	PROPN
ejpam-3877	55	6	)	)	PUNCT
ejpam-3877	55	7	a	a	DET
ejpam-3877	55	8	bounded	bound	VERB
ejpam-3877	55	9	radon	radon	NOUN
ejpam-3877	55	10	measure	measure	NOUN
ejpam-3877	55	11	on	on	ADP
ejpam-3877	55	12	ω	ω	PROPN
ejpam-3877	55	13	,	,	PUNCT
ejpam-3877	55	14	we	we	PRON
ejpam-3877	55	15	set	set	VERB
ejpam-3877	55	16	‖	‖	PROPN
ejpam-3877	55	17	µ	µ	X
ejpam-3877	55	18	‖m(ω):=|	‖m(ω):=|	X
ejpam-3877	55	19	µ	µ	X
ejpam-3877	55	20	|	|	NOUN
ejpam-3877	55	21	(	(	PUNCT
ejpam-3877	55	22	ω	ω	NOUN
ejpam-3877	55	23	)	)	PUNCT
ejpam-3877	55	24	where	where	SCONJ
ejpam-3877	55	25	|	|	ADV
ejpam-3877	55	26	µ	µ	NOUN
ejpam-3877	55	27	|	|	ADV
ejpam-3877	55	28	stands	stand	VERB
ejpam-3877	55	29	for	for	ADP
ejpam-3877	55	30	the	the	DET
ejpam-3877	55	31	total	total	ADJ
ejpam-3877	55	32	variation	variation	NOUN
ejpam-3877	55	33	of	of	ADP
ejpam-3877	55	34	µ.	µ.	NOUN
ejpam-3877	55	35	the	the	DET
ejpam-3877	55	36	duality	duality	NOUN
ejpam-3877	55	37	map	map	NOUN
ejpam-3877	55	38	〈	〈	PROPN
ejpam-3877	55	39	·	·	SYM
ejpam-3877	55	40	,	,	PUNCT
ejpam-3877	55	41	·	·	PUNCT
ejpam-3877	55	42	〉	〉	PROPN
ejpam-3877	55	43	ω	ω	PROPN
ejpam-3877	55	44	between	between	ADP
ejpam-3877	55	45	the	the	DET
ejpam-3877	55	46	space	space	NOUN
ejpam-3877	55	47	m(ω	m(ω	PROPN
ejpam-3877	55	48	)	)	PUNCT
ejpam-3877	55	49	and	and	CCONJ
ejpam-3877	55	50	cc(ω	cc(ω	NUM
ejpam-3877	55	51	)	)	PUNCT
ejpam-3877	55	52	is	be	AUX
ejpam-3877	55	53	defined	define	VERB
ejpam-3877	55	54	by	by	ADP
ejpam-3877	55	55	〈	〈	PROPN
ejpam-3877	55	56	µ	µ	NOUN
ejpam-3877	55	57	,	,	PUNCT
ejpam-3877	55	58	ϕ〉ω	ϕ〉ω	PROPN
ejpam-3877	55	59	=	=	SYM
ejpam-3877	55	60	∫	∫	PROPN
ejpam-3877	55	61	ω	ω	NUM
ejpam-3877	55	62	ϕdµ.	ϕdµ.	NOUN
ejpam-3877	55	63	for	for	ADP
ejpam-3877	55	64	any	any	DET
ejpam-3877	55	65	µ	µ	PROPN
ejpam-3877	55	66	∈	∈	PROPN
ejpam-3877	55	67	m(ω	m(ω	PROPN
ejpam-3877	55	68	)	)	PUNCT
ejpam-3877	55	69	and	and	CCONJ
ejpam-3877	55	70	any	any	DET
ejpam-3877	55	71	borel	borel	NOUN
ejpam-3877	55	72	set	set	VERB
ejpam-3877	55	73	b	b	PROPN
ejpam-3877	55	74	⊆	⊆	NUM
ejpam-3877	55	75	ω	ω	NUM
ejpam-3877	55	76	,	,	PUNCT
ejpam-3877	55	77	the	the	DET
ejpam-3877	55	78	restriction	restriction	NOUN
ejpam-3877	55	79	µxb	µxb	NOUN
ejpam-3877	55	80	of	of	ADP
ejpam-3877	55	81	µ	µ	NUM
ejpam-3877	55	82	to	to	PART
ejpam-3877	55	83	b	b	PROPN
ejpam-3877	55	84	is	be	AUX
ejpam-3877	55	85	defined	define	VERB
ejpam-3877	55	86	by	by	ADP
ejpam-3877	55	87	setting	set	VERB
ejpam-3877	55	88	(	(	PUNCT
ejpam-3877	55	89	µxb)(a	µxb)(a	ADV
ejpam-3877	55	90	)	)	PUNCT
ejpam-3877	55	91	:	:	PUNCT
ejpam-3877	56	1	=	=	PRON
ejpam-3877	56	2	µ(b	µ(b	PROPN
ejpam-3877	56	3	∩a	∩a	PROPN
ejpam-3877	56	4	)	)	PUNCT
ejpam-3877	56	5	for	for	ADP
ejpam-3877	56	6	every	every	DET
ejpam-3877	56	7	borel	borel	NOUN
ejpam-3877	56	8	set	set	VERB
ejpam-3877	56	9	a	a	DET
ejpam-3877	56	10	⊆	⊆	NUM
ejpam-3877	56	11	ω	ω	NOUN
ejpam-3877	56	12	.	.	PUNCT
ejpam-3877	57	1	it	it	PRON
ejpam-3877	57	2	is	be	AUX
ejpam-3877	57	3	worth	worth	ADJ
ejpam-3877	57	4	observing	observe	VERB
ejpam-3877	57	5	that	that	SCONJ
ejpam-3877	57	6	(	(	PUNCT
ejpam-3877	57	7	µxb)(∅	µxb)(∅	NUM
ejpam-3877	57	8	)	)	PUNCT
ejpam-3877	57	9	=	=	SYM
ejpam-3877	58	1	0	0	X
ejpam-3877	58	2	.	.	PUNCT
ejpam-3877	59	1	m+	m+	NUM
ejpam-3877	59	2	s	s	PART
ejpam-3877	59	3	(	(	PUNCT
ejpam-3877	59	4	ω	ω	NOUN
ejpam-3877	59	5	)	)	PUNCT
ejpam-3877	59	6	denotes	denote	VERB
ejpam-3877	59	7	the	the	DET
ejpam-3877	59	8	set	set	NOUN
ejpam-3877	59	9	of	of	ADP
ejpam-3877	59	10	nonnegative	nonnegative	ADJ
ejpam-3877	59	11	measures	measure	NOUN
ejpam-3877	59	12	singular	singular	ADJ
ejpam-3877	59	13	with	with	ADP
ejpam-3877	59	14	respect	respect	NOUN
ejpam-3877	59	15	to	to	ADP
ejpam-3877	59	16	the	the	DET
ejpam-3877	59	17	lebesgue	lebesgue	NOUN
ejpam-3877	59	18	measure	measure	NOUN
ejpam-3877	59	19	,	,	PUNCT
ejpam-3877	59	20	namely	namely	ADV
ejpam-3877	59	21	m+	m+	NUM
ejpam-3877	59	22	s	s	PART
ejpam-3877	59	23	(	(	PUNCT
ejpam-3877	59	24	ω	ω	NOUN
ejpam-3877	59	25	)	)	PUNCT
ejpam-3877	59	26	:	:	PUNCT
ejpam-3877	60	1	=	=	X
ejpam-3877	60	2	{	{	PUNCT
ejpam-3877	60	3	µ	µ	X
ejpam-3877	60	4	∈m+(ω)/∃	∈m+(ω)/∃	VERB
ejpam-3877	60	5	a	a	DET
ejpam-3877	60	6	borel	borel	NOUN
ejpam-3877	60	7	set	set	NOUN
ejpam-3877	60	8	e	e	PROPN
ejpam-3877	60	9	⊆	⊆	NUM
ejpam-3877	60	10	ω	ω	NUM
ejpam-3877	60	11	;	;	PUNCT
ejpam-3877	60	12	|	|	ADV
ejpam-3877	60	13	e	e	NOUN
ejpam-3877	60	14	|=	|=	X
ejpam-3877	60	15	0	0	NUM
ejpam-3877	60	16	,	,	PUNCT
ejpam-3877	60	17	µ	µ	X
ejpam-3877	60	18	=	=	SYM
ejpam-3877	60	19	µxb	µxb	X
ejpam-3877	60	20	}	}	PUNCT
ejpam-3877	60	21	we	we	PRON
ejpam-3877	60	22	will	will	AUX
ejpam-3877	60	23	consider	consider	VERB
ejpam-3877	60	24	|	|	ADV
ejpam-3877	60	25	·	·	PUNCT
ejpam-3877	61	1	|	|	ADV
ejpam-3877	61	2	the	the	DET
ejpam-3877	61	3	lebesgue	lebesgue	ADJ
ejpam-3877	61	4	measure	measure	NOUN
ejpam-3877	61	5	on	on	ADP
ejpam-3877	61	6	rn	rn	PROPN
ejpam-3877	61	7	.	.	PUNCT
ejpam-3877	62	1	similarly	similarly	ADV
ejpam-3877	62	2	,	,	PUNCT
ejpam-3877	62	3	m+	m+	NOUN
ejpam-3877	62	4	ac(ω	ac(ω	ADV
ejpam-3877	62	5	)	)	PUNCT
ejpam-3877	62	6	the	the	DET
ejpam-3877	62	7	set	set	NOUN
ejpam-3877	62	8	of	of	ADP
ejpam-3877	62	9	nonnegative	nonnegative	ADJ
ejpam-3877	62	10	measures	measure	NOUN
ejpam-3877	62	11	absolutely	absolutely	ADV
ejpam-3877	62	12	continuous	continuous	ADJ
ejpam-3877	62	13	with	with	ADP
ejpam-3877	62	14	respect	respect	NOUN
ejpam-3877	62	15	to	to	ADP
ejpam-3877	62	16	the	the	DET
ejpam-3877	62	17	lebesgue	lebesgue	NOUN
ejpam-3877	62	18	measure	measure	NOUN
ejpam-3877	62	19	,	,	PUNCT
ejpam-3877	62	20	namely	namely	ADV
ejpam-3877	62	21	m+	m+	NOUN
ejpam-3877	62	22	ac(ω	ac(ω	ADV
ejpam-3877	62	23	)	)	PUNCT
ejpam-3877	62	24	:	:	PUNCT
ejpam-3877	63	1	=	=	X
ejpam-3877	63	2	{	{	PUNCT
ejpam-3877	63	3	µ	µ	X
ejpam-3877	63	4	∈m+(ω)/µ(e	∈m+(ω)/µ(e	NUM
ejpam-3877	63	5	)	)	PUNCT
ejpam-3877	64	1	=	=	SYM
ejpam-3877	64	2	0	0	NUM
ejpam-3877	64	3	,	,	PUNCT
ejpam-3877	64	4	for	for	ADP
ejpam-3877	64	5	every	every	DET
ejpam-3877	64	6	borel	borel	NOUN
ejpam-3877	64	7	sete	sete	NOUN
ejpam-3877	64	8	⊆	⊆	NUM
ejpam-3877	64	9	ω	ω	NOUN
ejpam-3877	64	10	;	;	PUNCT
ejpam-3877	64	11	|	|	ADV
ejpam-3877	64	12	e	e	NOUN
ejpam-3877	64	13	|=	|=	X
ejpam-3877	64	14	0	0	NUM
ejpam-3877	64	15	}	}	PUNCT
ejpam-3877	64	16	.	.	PUNCT
ejpam-3877	65	1	recall	recall	VERB
ejpam-3877	65	2	that	that	DET
ejpam-3877	65	3	m+	m+	PRON
ejpam-3877	65	4	s	s	PART
ejpam-3877	65	5	(	(	PUNCT
ejpam-3877	65	6	ω	ω	NOUN
ejpam-3877	65	7	)	)	PUNCT
ejpam-3877	65	8	∩	∩	NOUN
ejpam-3877	65	9	m+	m+	NUM
ejpam-3877	65	10	ac(ω	ac(ω	ADV
ejpam-3877	65	11	)	)	PUNCT
ejpam-3877	65	12	=	=	PUNCT
ejpam-3877	65	13	{	{	PUNCT
ejpam-3877	65	14	0	0	NUM
ejpam-3877	65	15	}	}	PUNCT
ejpam-3877	65	16	.	.	PUNCT
ejpam-3877	66	1	moreover	moreover	ADV
ejpam-3877	66	2	,	,	PUNCT
ejpam-3877	66	3	by	by	ADP
ejpam-3877	66	4	the	the	DET
ejpam-3877	66	5	lebesgue	lebesgue	NOUN
ejpam-3877	66	6	decomposition	decomposition	NOUN
ejpam-3877	66	7	and	and	CCONJ
ejpam-3877	66	8	radon	radon	PROPN
ejpam-3877	66	9	-	-	PUNCT
ejpam-3877	66	10	nikodym	nikodym	PROPN
ejpam-3877	66	11	theorem	theorem	NOUN
ejpam-3877	66	12	(	(	PUNCT
ejpam-3877	66	13	see	see	VERB
ejpam-3877	66	14	[	[	X
ejpam-3877	66	15	9	9	NUM
ejpam-3877	66	16	]	]	NUM
ejpam-3877	66	17	)	)	PUNCT
ejpam-3877	66	18	,	,	PUNCT
ejpam-3877	66	19	for	for	ADP
ejpam-3877	66	20	any	any	DET
ejpam-3877	66	21	µ	µ	NOUN
ejpam-3877	66	22	∈m+(ω	∈m+(ω	NOUN
ejpam-3877	66	23	):	):	PUNCT
ejpam-3877	66	24	(	(	PUNCT
ejpam-3877	66	25	i	i	NOUN
ejpam-3877	66	26	)	)	PUNCT
ejpam-3877	66	27	there	there	PRON
ejpam-3877	66	28	exists	exist	VERB
ejpam-3877	66	29	a	a	DET
ejpam-3877	66	30	unique	unique	ADJ
ejpam-3877	66	31	couple	couple	NOUN
ejpam-3877	66	32	µac	µac	DET
ejpam-3877	66	33	∈m+	∈m+	PROPN
ejpam-3877	66	34	ac(ω	ac(ω	ADV
ejpam-3877	66	35	)	)	PUNCT
ejpam-3877	66	36	,	,	PUNCT
ejpam-3877	66	37	µs	µs	X
ejpam-3877	66	38	∈m+	∈m+	PROPN
ejpam-3877	66	39	s	s	PART
ejpam-3877	66	40	(	(	PUNCT
ejpam-3877	66	41	ω	ω	NOUN
ejpam-3877	66	42	)	)	PUNCT
ejpam-3877	66	43	such	such	ADJ
ejpam-3877	66	44	that	that	SCONJ
ejpam-3877	66	45	µ	µ	NOUN
ejpam-3877	66	46	=	=	SYM
ejpam-3877	66	47	µac	µac	PROPN
ejpam-3877	66	48	+	+	PROPN
ejpam-3877	66	49	µs	µs	X
ejpam-3877	66	50	(	(	PUNCT
ejpam-3877	66	51	2.1	2.1	NUM
ejpam-3877	66	52	)	)	PUNCT
ejpam-3877	66	53	(	(	PUNCT
ejpam-3877	66	54	ii	ii	NOUN
ejpam-3877	66	55	)	)	PUNCT
ejpam-3877	66	56	there	there	PRON
ejpam-3877	66	57	exist	exist	VERB
ejpam-3877	66	58	a	a	DET
ejpam-3877	66	59	unique	unique	ADJ
ejpam-3877	66	60	nonnegative	nonnegative	ADJ
ejpam-3877	66	61	function	function	NOUN
ejpam-3877	66	62	ur	ur	INTJ
ejpam-3877	66	63	∈	∈	PROPN
ejpam-3877	66	64	l1(ω	l1(ω	PROPN
ejpam-3877	66	65	)	)	PUNCT
ejpam-3877	66	66	called	call	VERB
ejpam-3877	66	67	the	the	DET
ejpam-3877	66	68	density	density	NOUN
ejpam-3877	66	69	of	of	ADP
ejpam-3877	66	70	the	the	DET
ejpam-3877	66	71	measure	measure	NOUN
ejpam-3877	66	72	µac	µac	INTJ
ejpam-3877	66	73	such	such	ADJ
ejpam-3877	66	74	that	that	DET
ejpam-3877	66	75	µac(e	µac(e	PROPN
ejpam-3877	66	76	)	)	PUNCT
ejpam-3877	66	77	=	=	SYM
ejpam-3877	66	78	∫	∫	PROPN
ejpam-3877	66	79	e	e	NOUN
ejpam-3877	66	80	urdx	urdx	NOUN
ejpam-3877	66	81	,	,	PUNCT
ejpam-3877	66	82	for	for	SCONJ
ejpam-3877	66	83	every	every	DET
ejpam-3877	66	84	borel	borel	NOUN
ejpam-3877	66	85	set	set	VERB
ejpam-3877	66	86	e	e	PROPN
ejpam-3877	66	87	⊆	⊆	NUM
ejpam-3877	66	88	ω	ω	NUM
ejpam-3877	66	89	.	.	PUNCT
ejpam-3877	67	1	(	(	PUNCT
ejpam-3877	67	2	2.2	2.2	NUM
ejpam-3877	67	3	)	)	PUNCT
ejpam-3877	67	4	letm+	letm+	NOUN
ejpam-3877	67	5	c,2(ω	c,2(ω	ADV
ejpam-3877	67	6	)	)	PUNCT
ejpam-3877	68	1	be	be	VERB
ejpam-3877	68	2	the	the	DET
ejpam-3877	68	3	set	set	NOUN
ejpam-3877	68	4	of	of	ADP
ejpam-3877	68	5	nonnegative	nonnegative	ADJ
ejpam-3877	68	6	measures	measure	NOUN
ejpam-3877	68	7	on	on	ADP
ejpam-3877	68	8	ω	ω	NUM
ejpam-3877	68	9	which	which	PRON
ejpam-3877	68	10	are	be	AUX
ejpam-3877	68	11	concentrated	concentrate	VERB
ejpam-3877	68	12	with	with	ADP
ejpam-3877	68	13	respect	respect	NOUN
ejpam-3877	68	14	to	to	ADP
ejpam-3877	68	15	the	the	DET
ejpam-3877	68	16	newtonian	newtonian	ADJ
ejpam-3877	68	17	capacity	capacity	NOUN
ejpam-3877	68	18	m+	m+	NUM
ejpam-3877	68	19	c,2(ω	c,2(ω	ADV
ejpam-3877	68	20	)	)	PUNCT
ejpam-3877	69	1	:	:	PUNCT
ejpam-3877	69	2	=	=	X
ejpam-3877	69	3	{	{	PUNCT
ejpam-3877	69	4	µ	µ	X
ejpam-3877	69	5	∈m+(ω)/∃	∈m+(ω)/∃	VERB
ejpam-3877	69	6	a	a	DET
ejpam-3877	69	7	borel	borel	NOUN
ejpam-3877	69	8	set	set	NOUN
ejpam-3877	69	9	e	e	PROPN
ejpam-3877	69	10	⊆	⊆	NUM
ejpam-3877	69	11	ω	ω	NUM
ejpam-3877	69	12	;	;	PUNCT
ejpam-3877	69	13	µ	µ	X
ejpam-3877	69	14	=	=	SYM
ejpam-3877	69	15	µxe	µxe	NOUN
ejpam-3877	69	16	and	and	CCONJ
ejpam-3877	69	17	c2(e	c2(e	NOUN
ejpam-3877	69	18	)	)	PUNCT
ejpam-3877	69	19	=	=	SYM
ejpam-3877	69	20	0	0	NUM
ejpam-3877	69	21	}	}	PUNCT
ejpam-3877	69	22	.	.	PUNCT
ejpam-3877	70	1	quincy	quincy	PROPN
ejpam-3877	70	2	s.	s.	PROPN
ejpam-3877	70	3	nkombo	nkombo	PROPN
ejpam-3877	70	4	,	,	PUNCT
ejpam-3877	70	5	fengquan	fengquan	PROPN
ejpam-3877	70	6	li	li	PROPN
ejpam-3877	70	7	/	/	SYM
ejpam-3877	70	8	eur	eur	PROPN
ejpam-3877	70	9	.	.	PUNCT
ejpam-3877	71	1	j.	j.	PROPN
ejpam-3877	71	2	pure	pure	PROPN
ejpam-3877	71	3	appl	appl	PROPN
ejpam-3877	71	4	.	.	PROPN
ejpam-3877	71	5	math	math	PROPN
ejpam-3877	71	6	,	,	PUNCT
ejpam-3877	71	7	14	14	NUM
ejpam-3877	71	8	(	(	PUNCT
ejpam-3877	71	9	1	1	NUM
ejpam-3877	71	10	)	)	PUNCT
ejpam-3877	71	11	(	(	PUNCT
ejpam-3877	71	12	2021	2021	NUM
ejpam-3877	71	13	)	)	PUNCT
ejpam-3877	71	14	,	,	PUNCT
ejpam-3877	71	15	204	204	NUM
ejpam-3877	71	16	-	-	SYM
ejpam-3877	71	17	233	233	NUM
ejpam-3877	71	18	208	208	NUM
ejpam-3877	71	19	notice	notice	NOUN
ejpam-3877	71	20	thatm+	thatm+	X
ejpam-3877	71	21	c,2(ω	c,2(ω	NOUN
ejpam-3877	71	22	)	)	PUNCT
ejpam-3877	71	23	can	can	AUX
ejpam-3877	71	24	be	be	AUX
ejpam-3877	71	25	also	also	ADV
ejpam-3877	71	26	defined	define	VERB
ejpam-3877	71	27	as	as	ADP
ejpam-3877	71	28	the	the	DET
ejpam-3877	71	29	set	set	NOUN
ejpam-3877	71	30	of	of	ADP
ejpam-3877	71	31	all	all	DET
ejpam-3877	71	32	measures	measure	NOUN
ejpam-3877	71	33	µ	µ	X
ejpam-3877	71	34	inm+(ω	inm+(ω	NOUN
ejpam-3877	71	35	)	)	PUNCT
ejpam-3877	71	36	which	which	PRON
ejpam-3877	71	37	are	be	AUX
ejpam-3877	71	38	singular	singular	ADJ
ejpam-3877	71	39	with	with	ADP
ejpam-3877	71	40	respect	respect	NOUN
ejpam-3877	71	41	to	to	ADP
ejpam-3877	71	42	the	the	DET
ejpam-3877	71	43	newtonian	newtonian	ADJ
ejpam-3877	71	44	capacity	capacity	NOUN
ejpam-3877	71	45	,	,	PUNCT
ejpam-3877	71	46	i.e.	i.e.	X
ejpam-3877	71	47	m+	m+	NUM
ejpam-3877	71	48	c,2(ω	c,2(ω	ADJ
ejpam-3877	71	49	)	)	PUNCT
ejpam-3877	71	50	:	:	PUNCT
ejpam-3877	72	1	=	=	X
ejpam-3877	72	2	{	{	PUNCT
ejpam-3877	72	3	µ	µ	X
ejpam-3877	72	4	∈m+	∈m+	PROPN
ejpam-3877	72	5	s	s	PART
ejpam-3877	72	6	(	(	PUNCT
ejpam-3877	72	7	ω)/∃	ω)/∃	INTJ
ejpam-3877	72	8	a	a	DET
ejpam-3877	72	9	borel	borel	NOUN
ejpam-3877	72	10	set	set	NOUN
ejpam-3877	72	11	e	e	PROPN
ejpam-3877	72	12	⊆	⊆	NUM
ejpam-3877	72	13	ω	ω	NUM
ejpam-3877	72	14	;	;	PUNCT
ejpam-3877	72	15	c2(e	c2(e	NOUN
ejpam-3877	72	16	)	)	PUNCT
ejpam-3877	72	17	=	=	SYM
ejpam-3877	72	18	0	0	NUM
ejpam-3877	72	19	}	}	PUNCT
ejpam-3877	72	20	.	.	PUNCT
ejpam-3877	73	1	it	it	PRON
ejpam-3877	73	2	is	be	AUX
ejpam-3877	73	3	clear	clear	ADJ
ejpam-3877	73	4	to	to	PART
ejpam-3877	73	5	observe	observe	VERB
ejpam-3877	73	6	that	that	DET
ejpam-3877	73	7	m+	m+	NOUN
ejpam-3877	73	8	c,2(ω	c,2(ω	ADJ
ejpam-3877	73	9	)	)	PUNCT
ejpam-3877	73	10	⊆m+	⊆m+	PROPN
ejpam-3877	73	11	s	s	X
ejpam-3877	73	12	(	(	PUNCT
ejpam-3877	73	13	ω	ω	NOUN
ejpam-3877	73	14	)	)	PUNCT
ejpam-3877	73	15	(	(	PUNCT
ejpam-3877	73	16	see	see	VERB
ejpam-3877	73	17	[	[	X
ejpam-3877	73	18	12	12	NUM
ejpam-3877	73	19	]	]	NUM
ejpam-3877	73	20	)	)	PUNCT
ejpam-3877	73	21	.	.	PUNCT
ejpam-3877	74	1	m+	m+	NUM
ejpam-3877	74	2	d,2(ω	d,2(ω	ADV
ejpam-3877	74	3	)	)	PUNCT
ejpam-3877	74	4	denotes	denote	VERB
ejpam-3877	74	5	the	the	DET
ejpam-3877	74	6	set	set	NOUN
ejpam-3877	74	7	of	of	ADP
ejpam-3877	74	8	nonnegative	nonnegative	ADJ
ejpam-3877	74	9	measures	measure	NOUN
ejpam-3877	74	10	on	on	ADP
ejpam-3877	74	11	ω	ω	NUM
ejpam-3877	74	12	which	which	PRON
ejpam-3877	74	13	are	be	AUX
ejpam-3877	74	14	diffuse	diffuse	NOUN
ejpam-3877	74	15	with	with	ADP
ejpam-3877	74	16	respect	respect	NOUN
ejpam-3877	74	17	to	to	ADP
ejpam-3877	74	18	the	the	DET
ejpam-3877	74	19	newtonian	newtonian	ADJ
ejpam-3877	74	20	capacity	capacity	NOUN
ejpam-3877	74	21	m+	m+	NUM
ejpam-3877	74	22	d,2(ω	d,2(ω	ADV
ejpam-3877	74	23	)	)	PUNCT
ejpam-3877	74	24	:	:	PUNCT
ejpam-3877	75	1	=	=	X
ejpam-3877	75	2	{	{	PUNCT
ejpam-3877	75	3	µ	µ	X
ejpam-3877	75	4	∈m+(ω)/µ(e	∈m+(ω)/µ(e	NUM
ejpam-3877	75	5	)	)	PUNCT
ejpam-3877	76	1	=	=	SYM
ejpam-3877	76	2	0	0	NUM
ejpam-3877	76	3	,	,	PUNCT
ejpam-3877	76	4	for	for	ADP
ejpam-3877	76	5	every	every	DET
ejpam-3877	76	6	borel	borel	NOUN
ejpam-3877	76	7	sete	sete	NOUN
ejpam-3877	76	8	⊆	⊆	NUM
ejpam-3877	76	9	ω	ω	NOUN
ejpam-3877	76	10	;	;	PUNCT
ejpam-3877	76	11	c2(e	c2(e	NOUN
ejpam-3877	76	12	)	)	PUNCT
ejpam-3877	76	13	=	=	SYM
ejpam-3877	76	14	0	0	NUM
ejpam-3877	76	15	}	}	PUNCT
ejpam-3877	76	16	.	.	PUNCT
ejpam-3877	77	1	due	due	ADP
ejpam-3877	77	2	to	to	ADP
ejpam-3877	77	3	c2(e	c2(e	NOUN
ejpam-3877	77	4	)	)	PUNCT
ejpam-3877	77	5	=	=	SYM
ejpam-3877	77	6	0	0	NUM
ejpam-3877	77	7	implies	imply	VERB
ejpam-3877	77	8	that	that	SCONJ
ejpam-3877	77	9	|	|	ADV
ejpam-3877	77	10	e	e	VERB
ejpam-3877	77	11	|=	|=	X
ejpam-3877	77	12	0	0	NUM
ejpam-3877	77	13	(	(	PUNCT
ejpam-3877	77	14	see	see	VERB
ejpam-3877	77	15	[	[	X
ejpam-3877	77	16	9	9	NUM
ejpam-3877	77	17	]	]	NUM
ejpam-3877	77	18	)	)	PUNCT
ejpam-3877	77	19	,	,	PUNCT
ejpam-3877	77	20	we	we	PRON
ejpam-3877	77	21	observe	observe	VERB
ejpam-3877	77	22	that	that	DET
ejpam-3877	77	23	m+	m+	NOUN
ejpam-3877	77	24	ac(ω	ac(ω	ADV
ejpam-3877	77	25	)	)	PUNCT
ejpam-3877	78	1	⊆m+	⊆m+	PROPN
ejpam-3877	78	2	d	d	NOUN
ejpam-3877	78	3	(	(	PUNCT
ejpam-3877	78	4	ω	ω	NOUN
ejpam-3877	78	5	)	)	PUNCT
ejpam-3877	78	6	.	.	PUNCT
ejpam-3877	79	1	it	it	PRON
ejpam-3877	79	2	is	be	AUX
ejpam-3877	79	3	known	know	VERB
ejpam-3877	79	4	that	that	SCONJ
ejpam-3877	79	5	a	a	DET
ejpam-3877	79	6	measure	measure	NOUN
ejpam-3877	79	7	µd,2	µd,2	PROPN
ejpam-3877	79	8	∈	∈	PROPN
ejpam-3877	79	9	m+	m+	NUM
ejpam-3877	79	10	d,2(ω	d,2(ω	ADV
ejpam-3877	79	11	)	)	PUNCT
ejpam-3877	79	12	if	if	SCONJ
ejpam-3877	79	13	there	there	PRON
ejpam-3877	79	14	exist	exist	VERB
ejpam-3877	79	15	f0	f0	PROPN
ejpam-3877	79	16	∈	∈	PROPN
ejpam-3877	79	17	l1(ω	l1(ω	PROPN
ejpam-3877	79	18	)	)	PUNCT
ejpam-3877	79	19	and	and	CCONJ
ejpam-3877	79	20	g0	g0	PROPN
ejpam-3877	79	21	∈	∈	PROPN
ejpam-3877	79	22	[	[	PUNCT
ejpam-3877	79	23	l2(ω	l2(ω	NOUN
ejpam-3877	79	24	)	)	PUNCT
ejpam-3877	79	25	]	]	PUNCT
ejpam-3877	79	26	n	n	X
ejpam-3877	79	27	such	such	ADJ
ejpam-3877	79	28	that	that	SCONJ
ejpam-3877	79	29	µd,2	µd,2	PROPN
ejpam-3877	79	30	=	=	SYM
ejpam-3877	79	31	f0	f0	PROPN
ejpam-3877	79	32	−	−	PROPN
ejpam-3877	79	33	divg0	divg0	NOUN
ejpam-3877	79	34	in	in	ADP
ejpam-3877	79	35	d′(ω	d′(ω	NOUN
ejpam-3877	79	36	)	)	PUNCT
ejpam-3877	79	37	.	.	PUNCT
ejpam-3877	80	1	(	(	PUNCT
ejpam-3877	80	2	2.3	2.3	NUM
ejpam-3877	80	3	)	)	PUNCT
ejpam-3877	80	4	for	for	ADP
ejpam-3877	80	5	any	any	DET
ejpam-3877	80	6	µ	µ	PRON
ejpam-3877	80	7	∈	∈	NOUN
ejpam-3877	80	8	m+(ω	m+(ω	NOUN
ejpam-3877	80	9	)	)	PUNCT
ejpam-3877	80	10	,	,	PUNCT
ejpam-3877	80	11	if	if	SCONJ
ejpam-3877	80	12	there	there	PRON
ejpam-3877	80	13	exists	exist	VERB
ejpam-3877	80	14	a	a	DET
ejpam-3877	80	15	unique	unique	ADJ
ejpam-3877	80	16	couple	couple	NOUN
ejpam-3877	80	17	µd,2	µd,2	PROPN
ejpam-3877	80	18	∈	∈	PROPN
ejpam-3877	80	19	m+	m+	NUM
ejpam-3877	80	20	d,2(ω	d,2(ω	ADV
ejpam-3877	80	21	)	)	PUNCT
ejpam-3877	80	22	,	,	PUNCT
ejpam-3877	80	23	µc,2	µc,2	PROPN
ejpam-3877	80	24	∈	∈	PROPN
ejpam-3877	80	25	m+	m+	NUM
ejpam-3877	80	26	c,2(ω	c,2(ω	NOUN
ejpam-3877	80	27	)	)	PUNCT
ejpam-3877	80	28	such	such	ADJ
ejpam-3877	80	29	that	that	SCONJ
ejpam-3877	80	30	µ	µ	NOUN
ejpam-3877	80	31	=	=	PUNCT
ejpam-3877	80	32	µd,2	µd,2	NOUN
ejpam-3877	80	33	+	+	ADJ
ejpam-3877	80	34	µc,2	µc,2	ADJ
ejpam-3877	80	35	.	.	PUNCT
ejpam-3877	81	1	(	(	PUNCT
ejpam-3877	81	2	2.4	2.4	NUM
ejpam-3877	81	3	)	)	PUNCT
ejpam-3877	81	4	notice	notice	VERB
ejpam-3877	81	5	that	that	SCONJ
ejpam-3877	81	6	µc,2	µc,2	PROPN
ejpam-3877	81	7	=	=	SYM
ejpam-3877	82	1	[	[	X
ejpam-3877	82	2	µ]c,2	µ]c,2	PROPN
ejpam-3877	82	3	and	and	CCONJ
ejpam-3877	82	4	µd,2	µd,2	NOUN
ejpam-3877	82	5	=	=	PUNCT
ejpam-3877	83	1	[	[	X
ejpam-3877	83	2	µ]d,2	µ]d,2	NOUN
ejpam-3877	83	3	.	.	PUNCT
ejpam-3877	83	4	for	for	ADP
ejpam-3877	83	5	the	the	DET
ejpam-3877	83	6	above	above	ADJ
ejpam-3877	83	7	assertions	assertion	NOUN
ejpam-3877	83	8	we	we	PRON
ejpam-3877	83	9	can	can	AUX
ejpam-3877	83	10	also	also	ADV
ejpam-3877	83	11	refer	refer	VERB
ejpam-3877	83	12	to	to	ADP
ejpam-3877	83	13	(	(	PUNCT
ejpam-3877	83	14	[	[	X
ejpam-3877	83	15	18	18	NUM
ejpam-3877	83	16	,	,	PUNCT
ejpam-3877	83	17	23	23	NUM
ejpam-3877	83	18	,	,	PUNCT
ejpam-3877	83	19	30	30	NUM
ejpam-3877	83	20	]	]	PUNCT
ejpam-3877	83	21	and	and	CCONJ
ejpam-3877	83	22	references	reference	NOUN
ejpam-3877	83	23	therein	therein	ADV
ejpam-3877	83	24	)	)	PUNCT
ejpam-3877	83	25	.	.	PUNCT
ejpam-3877	84	1	let	let	VERB
ejpam-3877	84	2	m(q	m(q	X
ejpam-3877	84	3	)	)	PUNCT
ejpam-3877	84	4	be	be	AUX
ejpam-3877	84	5	the	the	DET
ejpam-3877	84	6	space	space	NOUN
ejpam-3877	84	7	of	of	ADP
ejpam-3877	84	8	bounded	bounded	ADJ
ejpam-3877	84	9	radon	radon	NOUN
ejpam-3877	84	10	measures	measure	NOUN
ejpam-3877	84	11	on	on	ADP
ejpam-3877	84	12	q	q	NOUN
ejpam-3877	84	13	,	,	PUNCT
ejpam-3877	84	14	and	and	CCONJ
ejpam-3877	84	15	m+(q	m+(q	NUM
ejpam-3877	84	16	)	)	PUNCT
ejpam-3877	84	17	⊂m(q	⊂m(q	NOUN
ejpam-3877	84	18	)	)	PUNCT
ejpam-3877	84	19	the	the	DET
ejpam-3877	84	20	cone	cone	NOUN
ejpam-3877	84	21	of	of	ADP
ejpam-3877	84	22	nonnegative	nonnegative	ADJ
ejpam-3877	84	23	bounded	bounded	ADJ
ejpam-3877	84	24	radon	radon	NOUN
ejpam-3877	84	25	measures	measure	NOUN
ejpam-3877	84	26	on	on	ADP
ejpam-3877	84	27	q.	q.	NOUN
ejpam-3877	84	28	for	for	ADP
ejpam-3877	84	29	any	any	DET
ejpam-3877	84	30	µ	µ	NOUN
ejpam-3877	84	31	∈m(q	∈m(q	NOUN
ejpam-3877	84	32	)	)	PUNCT
ejpam-3877	84	33	,	,	PUNCT
ejpam-3877	84	34	we	we	PRON
ejpam-3877	84	35	set	set	VERB
ejpam-3877	84	36	‖	‖	PROPN
ejpam-3877	84	37	µ	µ	PROPN
ejpam-3877	84	38	‖m(q):=|	‖m(q):=|	NUM
ejpam-3877	84	39	µ	µ	NOUN
ejpam-3877	84	40	|	|	NOUN
ejpam-3877	84	41	(	(	PUNCT
ejpam-3877	84	42	q	q	NOUN
ejpam-3877	84	43	)	)	PUNCT
ejpam-3877	84	44	where	where	SCONJ
ejpam-3877	84	45	|	|	ADV
ejpam-3877	84	46	µ	µ	NOUN
ejpam-3877	84	47	|	|	NOUN
ejpam-3877	84	48	denotes	denote	VERB
ejpam-3877	84	49	the	the	DET
ejpam-3877	84	50	total	total	ADJ
ejpam-3877	84	51	variation	variation	NOUN
ejpam-3877	84	52	of	of	ADP
ejpam-3877	84	53	µ.	µ.	NOUN
ejpam-3877	84	54	for	for	ADP
ejpam-3877	84	55	any	any	DET
ejpam-3877	84	56	diffuse	diffuse	NOUN
ejpam-3877	84	57	measure	measure	NOUN
ejpam-3877	84	58	µ0	µ0	NOUN
ejpam-3877	84	59	∈	∈	PROPN
ejpam-3877	84	60	m+	m+	NUM
ejpam-3877	84	61	d,2(q	d,2(q	NOUN
ejpam-3877	84	62	)	)	PUNCT
ejpam-3877	84	63	,	,	PUNCT
ejpam-3877	84	64	there	there	PRON
ejpam-3877	84	65	exist	exist	VERB
ejpam-3877	84	66	f	f	PROPN
ejpam-3877	84	67	∈	∈	PROPN
ejpam-3877	84	68	l1(q	l1(q	CCONJ
ejpam-3877	84	69	)	)	PUNCT
ejpam-3877	84	70	,	,	PUNCT
ejpam-3877	84	71	g	g	PROPN
ejpam-3877	84	72	∈	∈	PROPN
ejpam-3877	84	73	l2((0	l2((0	PROPN
ejpam-3877	84	74	,	,	PUNCT
ejpam-3877	84	75	t	t	PROPN
ejpam-3877	84	76	)	)	PUNCT
ejpam-3877	84	77	,	,	PUNCT
ejpam-3877	84	78	h1	h1	PROPN
ejpam-3877	84	79	0	0	NUM
ejpam-3877	84	80	(	(	PUNCT
ejpam-3877	84	81	ω	ω	NOUN
ejpam-3877	84	82	)	)	PUNCT
ejpam-3877	84	83	)	)	PUNCT
ejpam-3877	84	84	and	and	CCONJ
ejpam-3877	84	85	g	g	PROPN
ejpam-3877	84	86	∈	∈	PROPN
ejpam-3877	84	87	[	[	PUNCT
ejpam-3877	84	88	l2(q	l2(q	PROPN
ejpam-3877	84	89	)	)	PUNCT
ejpam-3877	84	90	]	]	PUNCT
ejpam-3877	85	1	n	n	X
ejpam-3877	85	2	µ0	µ0	NOUN
ejpam-3877	85	3	=	=	SYM
ejpam-3877	85	4	f	f	X
ejpam-3877	85	5	−	−	NOUN
ejpam-3877	85	6	divg+	divg+	VERB
ejpam-3877	85	7	gt	gt	PROPN
ejpam-3877	85	8	in	in	ADP
ejpam-3877	85	9	d′(q	d′(q	NOUN
ejpam-3877	85	10	)	)	PUNCT
ejpam-3877	85	11	(	(	PUNCT
ejpam-3877	85	12	2.5	2.5	NUM
ejpam-3877	85	13	)	)	PUNCT
ejpam-3877	85	14	(	(	PUNCT
ejpam-3877	85	15	see	see	VERB
ejpam-3877	85	16	[	[	X
ejpam-3877	85	17	10	10	NUM
ejpam-3877	85	18	,	,	PUNCT
ejpam-3877	85	19	11	11	NUM
ejpam-3877	85	20	,	,	PUNCT
ejpam-3877	85	21	16	16	NUM
ejpam-3877	85	22	]	]	PUNCT
ejpam-3877	85	23	)	)	PUNCT
ejpam-3877	85	24	.	.	PUNCT
ejpam-3877	86	1	the	the	DET
ejpam-3877	86	2	rest	rest	NOUN
ejpam-3877	86	3	of	of	ADP
ejpam-3877	86	4	statements	statement	NOUN
ejpam-3877	86	5	of	of	ADP
ejpam-3877	86	6	m(q	m(q	NOUN
ejpam-3877	86	7	)	)	PUNCT
ejpam-3877	86	8	can	can	AUX
ejpam-3877	86	9	be	be	AUX
ejpam-3877	86	10	deduce	deduce	ADJ
ejpam-3877	86	11	from	from	ADP
ejpam-3877	86	12	the	the	DET
ejpam-3877	86	13	properties	property	NOUN
ejpam-3877	86	14	of	of	ADP
ejpam-3877	86	15	m(ω	m(ω	NOUN
ejpam-3877	86	16	)	)	PUNCT
ejpam-3877	86	17	.	.	PUNCT
ejpam-3877	87	1	let	let	VERB
ejpam-3877	87	2	e	e	PRON
ejpam-3877	87	3	be	be	AUX
ejpam-3877	87	4	a	a	DET
ejpam-3877	87	5	borel	borel	NOUN
ejpam-3877	87	6	subset	subset	NOUN
ejpam-3877	87	7	of	of	ADP
ejpam-3877	87	8	ω	ω	PROPN
ejpam-3877	87	9	,	,	PUNCT
ejpam-3877	87	10	for	for	ADP
ejpam-3877	87	11	t0	t0	PROPN
ejpam-3877	87	12	∈	∈	PROPN
ejpam-3877	87	13	(	(	PUNCT
ejpam-3877	87	14	0	0	NUM
ejpam-3877	87	15	,	,	PUNCT
ejpam-3877	87	16	t	t	NOUN
ejpam-3877	87	17	)	)	PUNCT
ejpam-3877	87	18	fixed	fix	VERB
ejpam-3877	87	19	,	,	PUNCT
ejpam-3877	87	20	one	one	NUM
ejpam-3877	87	21	has	have	VERB
ejpam-3877	87	22	cap(e	cap(e	PROPN
ejpam-3877	87	23	×	×	NOUN
ejpam-3877	87	24	{	{	PUNCT
ejpam-3877	87	25	t0	t0	NOUN
ejpam-3877	87	26	}	}	PUNCT
ejpam-3877	87	27	)	)	PUNCT
ejpam-3877	88	1	=	=	SYM
ejpam-3877	88	2	0	0	PUNCT
ejpam-3877	89	1	if	if	SCONJ
ejpam-3877	89	2	and	and	CCONJ
ejpam-3877	89	3	only	only	ADV
ejpam-3877	89	4	if	if	SCONJ
ejpam-3877	89	5	|	|	ADV
ejpam-3877	89	6	e	e	VERB
ejpam-3877	89	7	|=	|=	X
ejpam-3877	89	8	0	0	PUNCT
ejpam-3877	89	9	and	and	CCONJ
ejpam-3877	89	10	for	for	ADP
ejpam-3877	89	11	any	any	DET
ejpam-3877	89	12	0	0	NUM
ejpam-3877	89	13	≤	≤	NUM
ejpam-3877	89	14	t0	t0	PROPN
ejpam-3877	89	15	<	<	X
ejpam-3877	89	16	t1	t1	PROPN
ejpam-3877	89	17	≤	≤	PROPN
ejpam-3877	89	18	t	t	NOUN
ejpam-3877	89	19	,	,	PUNCT
ejpam-3877	89	20	there	there	PRON
ejpam-3877	89	21	holds	hold	VERB
ejpam-3877	89	22	cap(e	cap(e	PROPN
ejpam-3877	89	23	×	×	PROPN
ejpam-3877	89	24	(	(	PUNCT
ejpam-3877	89	25	t0	t0	PROPN
ejpam-3877	89	26	,	,	PUNCT
ejpam-3877	89	27	t1	t1	NOUN
ejpam-3877	89	28	)	)	PUNCT
ejpam-3877	89	29	)	)	PUNCT
ejpam-3877	90	1	=	=	SYM
ejpam-3877	90	2	0	0	PUNCT
ejpam-3877	91	1	if	if	SCONJ
ejpam-3877	91	2	and	and	CCONJ
ejpam-3877	91	3	only	only	ADV
ejpam-3877	91	4	if	if	SCONJ
ejpam-3877	91	5	c2(e	c2(e	NOUN
ejpam-3877	91	6	)	)	PUNCT
ejpam-3877	91	7	=	=	SYM
ejpam-3877	91	8	0	0	PUNCT
ejpam-3877	92	1	(	(	PUNCT
ejpam-3877	92	2	see	see	VERB
ejpam-3877	92	3	[	[	X
ejpam-3877	92	4	16	16	NUM
ejpam-3877	92	5	]	]	SYM
ejpam-3877	92	6	)	)	PUNCT
ejpam-3877	92	7	.	.	PUNCT
ejpam-3877	93	1	the	the	DET
ejpam-3877	93	2	relationship	relationship	NOUN
ejpam-3877	93	3	between	between	ADP
ejpam-3877	93	4	parabolic	parabolic	ADJ
ejpam-3877	93	5	capacity	capacity	NOUN
ejpam-3877	93	6	and	and	CCONJ
ejpam-3877	93	7	newtonian	newtonian	ADJ
ejpam-3877	93	8	capacity	capacity	NOUN
ejpam-3877	93	9	is	be	AUX
ejpam-3877	93	10	given	give	VERB
ejpam-3877	93	11	in	in	ADP
ejpam-3877	93	12	[	[	X
ejpam-3877	93	13	27	27	NUM
ejpam-3877	93	14	]	]	PUNCT
ejpam-3877	93	15	such	such	ADJ
ejpam-3877	93	16	that	that	PRON
ejpam-3877	93	17	:	:	PUNCT
ejpam-3877	93	18	(	(	PUNCT
ejpam-3877	93	19	i	i	NOUN
ejpam-3877	93	20	)	)	PUNCT
ejpam-3877	93	21	there	there	PRON
ejpam-3877	93	22	exist	exist	VERB
ejpam-3877	93	23	positive	positive	ADJ
ejpam-3877	93	24	constants	constant	NOUN
ejpam-3877	93	25	0	0	NUM
ejpam-3877	93	26	<	<	X
ejpam-3877	93	27	k1	k1	X
ejpam-3877	93	28	<	<	X
ejpam-3877	93	29	k2	k2	PROPN
ejpam-3877	93	30	such	such	ADJ
ejpam-3877	93	31	that	that	SCONJ
ejpam-3877	93	32	k1c2(e	k1c2(e	NOUN
ejpam-3877	93	33	)	)	PUNCT
ejpam-3877	93	34	≤	≤	PUNCT
ejpam-3877	93	35	cap(e	cap(e	PROPN
ejpam-3877	93	36	×	×	NOUN
ejpam-3877	93	37	{	{	PUNCT
ejpam-3877	93	38	t0	t0	NOUN
ejpam-3877	93	39	}	}	PUNCT
ejpam-3877	93	40	)	)	PUNCT
ejpam-3877	93	41	≤	≤	NUM
ejpam-3877	93	42	k2c2(e	k2c2(e	NOUN
ejpam-3877	93	43	)	)	PUNCT
ejpam-3877	93	44	.	.	PUNCT
ejpam-3877	94	1	(	(	PUNCT
ejpam-3877	94	2	ii	ii	NOUN
ejpam-3877	94	3	)	)	PUNCT
ejpam-3877	94	4	for	for	ADP
ejpam-3877	94	5	any	any	PRON
ejpam-3877	94	6	0	0	PUNCT
ejpam-3877	94	7	<	<	X
ejpam-3877	94	8	t0	t0	PROPN
ejpam-3877	94	9	<	<	X
ejpam-3877	94	10	t1	t1	PROPN
ejpam-3877	94	11	,	,	PUNCT
ejpam-3877	94	12	there	there	PRON
ejpam-3877	94	13	exist	exist	VERB
ejpam-3877	94	14	positive	positive	ADJ
ejpam-3877	94	15	constants	constant	NOUN
ejpam-3877	94	16	0	0	NUM
ejpam-3877	94	17	<	<	X
ejpam-3877	94	18	l1	l1	PROPN
ejpam-3877	94	19	<	<	X
ejpam-3877	94	20	l2	l2	NOUN
ejpam-3877	94	21	such	such	ADJ
ejpam-3877	94	22	that	that	DET
ejpam-3877	94	23	l1c2(e	l1c2(e	NOUN
ejpam-3877	94	24	)	)	PUNCT
ejpam-3877	94	25	≤	≤	PUNCT
ejpam-3877	94	26	cap(e	cap(e	PROPN
ejpam-3877	94	27	×	×	NOUN
ejpam-3877	94	28	(	(	PUNCT
ejpam-3877	94	29	t0	t0	PROPN
ejpam-3877	94	30	,	,	PUNCT
ejpam-3877	94	31	t1	t1	NOUN
ejpam-3877	94	32	)	)	PUNCT
ejpam-3877	94	33	)	)	PUNCT
ejpam-3877	94	34	≤	≤	NUM
ejpam-3877	94	35	l2c2(e	l2c2(e	NOUN
ejpam-3877	94	36	)	)	PUNCT
ejpam-3877	94	37	.	.	PUNCT
ejpam-3877	95	1	quincy	quincy	PROPN
ejpam-3877	95	2	s.	s.	PROPN
ejpam-3877	95	3	nkombo	nkombo	PROPN
ejpam-3877	95	4	,	,	PUNCT
ejpam-3877	95	5	fengquan	fengquan	PROPN
ejpam-3877	95	6	li	li	PROPN
ejpam-3877	95	7	/	/	SYM
ejpam-3877	95	8	eur	eur	PROPN
ejpam-3877	95	9	.	.	PUNCT
ejpam-3877	96	1	j.	j.	PROPN
ejpam-3877	96	2	pure	pure	PROPN
ejpam-3877	96	3	appl	appl	PROPN
ejpam-3877	96	4	.	.	PROPN
ejpam-3877	96	5	math	math	PROPN
ejpam-3877	96	6	,	,	PUNCT
ejpam-3877	96	7	14	14	NUM
ejpam-3877	96	8	(	(	PUNCT
ejpam-3877	96	9	1	1	NUM
ejpam-3877	96	10	)	)	PUNCT
ejpam-3877	96	11	(	(	PUNCT
ejpam-3877	96	12	2021	2021	NUM
ejpam-3877	96	13	)	)	PUNCT
ejpam-3877	96	14	,	,	PUNCT
ejpam-3877	96	15	204	204	NUM
ejpam-3877	96	16	-	-	SYM
ejpam-3877	96	17	233	233	NUM
ejpam-3877	96	18	209	209	NUM
ejpam-3877	96	19	let	let	VERB
ejpam-3877	96	20	u	u	PRON
ejpam-3877	96	21	⊂	⊂	PROPN
ejpam-3877	96	22	q	q	X
ejpam-3877	96	23	an	an	DET
ejpam-3877	96	24	open	open	ADJ
ejpam-3877	96	25	set	set	NOUN
ejpam-3877	96	26	and	and	CCONJ
ejpam-3877	96	27	k	k	PROPN
ejpam-3877	96	28	⊂	⊂	PROPN
ejpam-3877	96	29	q	q	X
ejpam-3877	96	30	a	a	DET
ejpam-3877	96	31	compact	compact	ADJ
ejpam-3877	96	32	set	set	NOUN
ejpam-3877	96	33	with	with	ADP
ejpam-3877	96	34	cap(k	cap(k	PROPN
ejpam-3877	96	35	)	)	PUNCT
ejpam-3877	96	36	=	=	SYM
ejpam-3877	96	37	0	0	NUM
ejpam-3877	96	38	,	,	PUNCT
ejpam-3877	96	39	then	then	ADV
ejpam-3877	96	40	there	there	PRON
ejpam-3877	96	41	exists	exist	VERB
ejpam-3877	96	42	ϕn	ϕn	ADP
ejpam-3877	96	43	∈	∈	PROPN
ejpam-3877	96	44	c∞c	c∞c	ADJ
ejpam-3877	96	45	(	(	PUNCT
ejpam-3877	96	46	u	u	NOUN
ejpam-3877	96	47	)	)	PUNCT
ejpam-3877	96	48	such	such	ADJ
ejpam-3877	96	49	that	that	SCONJ
ejpam-3877	96	50	(	(	PUNCT
ejpam-3877	96	51	iii	iii	NOUN
ejpam-3877	96	52	)	)	PUNCT
ejpam-3877	96	53	0	0	NUM
ejpam-3877	96	54	≤	≤	NOUN
ejpam-3877	96	55	ϕn	ϕn	VERB
ejpam-3877	96	56	≤	≤	NUM
ejpam-3877	96	57	1	1	NUM
ejpam-3877	96	58	a.e	a.e	NOUN
ejpam-3877	96	59	in	in	ADP
ejpam-3877	96	60	q	q	NOUN
ejpam-3877	96	61	,	,	PUNCT
ejpam-3877	96	62	(	(	PUNCT
ejpam-3877	96	63	iv	iv	X
ejpam-3877	96	64	)	)	PUNCT
ejpam-3877	96	65	ϕn	ϕn	NOUN
ejpam-3877	97	1	=	=	NOUN
ejpam-3877	97	2	1	1	NUM
ejpam-3877	97	3	a.e	a.e	PROPN
ejpam-3877	97	4	in	in	ADP
ejpam-3877	97	5	k	k	PROPN
ejpam-3877	97	6	,	,	PUNCT
ejpam-3877	97	7	(	(	PUNCT
ejpam-3877	97	8	v	v	NOUN
ejpam-3877	97	9	)	)	PUNCT
ejpam-3877	97	10	ϕn	ϕn	NOUN
ejpam-3877	97	11	→	→	SYM
ejpam-3877	97	12	0	0	NUM
ejpam-3877	97	13	in	in	ADP
ejpam-3877	97	14	w	w	PROPN
ejpam-3877	97	15	,	,	PUNCT
ejpam-3877	97	16	(	(	PUNCT
ejpam-3877	97	17	vi	vi	NOUN
ejpam-3877	97	18	)	)	PUNCT
ejpam-3877	97	19	ϕn	ϕn	ADP
ejpam-3877	97	20	converges	converge	VERB
ejpam-3877	97	21	to	to	ADP
ejpam-3877	97	22	zero	zero	NUM
ejpam-3877	97	23	cap	cap	NOUN
ejpam-3877	97	24	-	-	PUNCT
ejpam-3877	97	25	quasi	quasi	NOUN
ejpam-3877	97	26	continuous	continuous	ADJ
ejpam-3877	97	27	(	(	PUNCT
ejpam-3877	97	28	see	see	VERB
ejpam-3877	97	29	[	[	X
ejpam-3877	97	30	27	27	NUM
ejpam-3877	97	31	,	,	PUNCT
ejpam-3877	97	32	proposition	proposition	NOUN
ejpam-3877	97	33	2.2	2.2	NUM
ejpam-3877	97	34	]	]	PUNCT
ejpam-3877	97	35	)	)	PUNCT
ejpam-3877	97	36	.	.	PUNCT
ejpam-3877	98	1	on	on	ADP
ejpam-3877	98	2	the	the	DET
ejpam-3877	98	3	other	other	ADJ
ejpam-3877	98	4	hand	hand	NOUN
ejpam-3877	98	5	,	,	PUNCT
ejpam-3877	98	6	assume	assume	VERB
ejpam-3877	98	7	that	that	SCONJ
ejpam-3877	98	8	v	v	X
ejpam-3877	98	9	⊂	⊂	PROPN
ejpam-3877	98	10	ω	ω	NOUN
ejpam-3877	98	11	an	an	DET
ejpam-3877	98	12	open	open	ADJ
ejpam-3877	98	13	set	set	NOUN
ejpam-3877	98	14	and	and	CCONJ
ejpam-3877	98	15	k	k	PROPN
ejpam-3877	98	16	⊂	⊂	PROPN
ejpam-3877	98	17	ω	ω	NOUN
ejpam-3877	98	18	a	a	DET
ejpam-3877	98	19	compact	compact	ADJ
ejpam-3877	98	20	set	set	NOUN
ejpam-3877	98	21	with	with	ADP
ejpam-3877	98	22	cap(k	cap(k	PROPN
ejpam-3877	98	23	)	)	PUNCT
ejpam-3877	98	24	=	=	SYM
ejpam-3877	98	25	0	0	NUM
ejpam-3877	98	26	,	,	PUNCT
ejpam-3877	98	27	then	then	ADV
ejpam-3877	98	28	there	there	PRON
ejpam-3877	98	29	exists	exist	VERB
ejpam-3877	98	30	φn	φn	ADP
ejpam-3877	98	31	∈	∈	PROPN
ejpam-3877	98	32	c∞c	c∞c	ADJ
ejpam-3877	98	33	(	(	PUNCT
ejpam-3877	98	34	v	v	NOUN
ejpam-3877	98	35	)	)	PUNCT
ejpam-3877	98	36	such	such	ADJ
ejpam-3877	98	37	that	that	SCONJ
ejpam-3877	98	38	(	(	PUNCT
ejpam-3877	98	39	vii	vii	PROPN
ejpam-3877	98	40	)	)	PUNCT
ejpam-3877	98	41	0	0	NUM
ejpam-3877	99	1	≤	≤	NUM
ejpam-3877	99	2	φn	φn	ADP
ejpam-3877	99	3	≤	≤	NUM
ejpam-3877	99	4	1	1	NUM
ejpam-3877	99	5	a.e	a.e	PROPN
ejpam-3877	99	6	in	in	ADP
ejpam-3877	99	7	ω	ω	NUM
ejpam-3877	99	8	,	,	PUNCT
ejpam-3877	99	9	(	(	PUNCT
ejpam-3877	99	10	viii	viii	NOUN
ejpam-3877	99	11	)	)	PUNCT
ejpam-3877	99	12	φn	φn	NOUN
ejpam-3877	100	1	=	=	SYM
ejpam-3877	100	2	1	1	NUM
ejpam-3877	100	3	a.e	a.e	PROPN
ejpam-3877	100	4	in	in	ADP
ejpam-3877	100	5	k	k	PROPN
ejpam-3877	100	6	,	,	PUNCT
ejpam-3877	100	7	(	(	PUNCT
ejpam-3877	100	8	ivx	ivx	NOUN
ejpam-3877	100	9	)	)	PUNCT
ejpam-3877	100	10	φn	φn	PROPN
ejpam-3877	100	11	→	→	SYM
ejpam-3877	100	12	0	0	NUM
ejpam-3877	100	13	in	in	ADP
ejpam-3877	100	14	h1	h1	PROPN
ejpam-3877	100	15	0	0	NUM
ejpam-3877	100	16	(	(	PUNCT
ejpam-3877	100	17	ω	ω	NOUN
ejpam-3877	100	18	)	)	PUNCT
ejpam-3877	100	19	,	,	PUNCT
ejpam-3877	100	20	(	(	PUNCT
ejpam-3877	100	21	x	x	X
ejpam-3877	100	22	)	)	PUNCT
ejpam-3877	100	23	ϕn	ϕn	ADP
ejpam-3877	100	24	converges	converge	NOUN
ejpam-3877	100	25	to	to	ADP
ejpam-3877	100	26	zero	zero	NUM
ejpam-3877	100	27	cap	cap	NOUN
ejpam-3877	100	28	-	-	PUNCT
ejpam-3877	100	29	quasi	quasi	NOUN
ejpam-3877	100	30	continuous	continuous	ADJ
ejpam-3877	100	31	(	(	PUNCT
ejpam-3877	100	32	see	see	VERB
ejpam-3877	100	33	[	[	X
ejpam-3877	100	34	15	15	NUM
ejpam-3877	100	35	,	,	PUNCT
ejpam-3877	100	36	lemma	lemma	PROPN
ejpam-3877	100	37	4.e.1	4.e.1	NUM
ejpam-3877	100	38	]	]	PUNCT
ejpam-3877	100	39	.	.	PUNCT
ejpam-3877	101	1	by	by	ADP
ejpam-3877	101	2	l∞	l∞	NOUN
ejpam-3877	101	3	(	(	PUNCT
ejpam-3877	101	4	(	(	PUNCT
ejpam-3877	101	5	0	0	NUM
ejpam-3877	101	6	,	,	PUNCT
ejpam-3877	101	7	t	t	NOUN
ejpam-3877	101	8	)	)	PUNCT
ejpam-3877	101	9	,	,	PUNCT
ejpam-3877	101	10	m+(ω	m+(ω	NOUN
ejpam-3877	101	11	)	)	PUNCT
ejpam-3877	101	12	)	)	PUNCT
ejpam-3877	101	13	,	,	PUNCT
ejpam-3877	101	14	the	the	DET
ejpam-3877	101	15	set	set	NOUN
ejpam-3877	101	16	of	of	ADP
ejpam-3877	101	17	nonnegative	nonnegative	ADJ
ejpam-3877	101	18	radon	radon	NOUN
ejpam-3877	101	19	measures	measure	NOUN
ejpam-3877	101	20	u	u	PROPN
ejpam-3877	101	21	∈m+(q	∈m+(q	PROPN
ejpam-3877	101	22	)	)	PUNCT
ejpam-3877	101	23	which	which	PRON
ejpam-3877	101	24	satisfy	satisfy	VERB
ejpam-3877	101	25	the	the	DET
ejpam-3877	101	26	following	follow	VERB
ejpam-3877	101	27	property	property	NOUN
ejpam-3877	101	28	:	:	PUNCT
ejpam-3877	101	29	for	for	ADP
ejpam-3877	101	30	almost	almost	ADV
ejpam-3877	101	31	every	every	PRON
ejpam-3877	101	32	t	t	NOUN
ejpam-3877	101	33	∈	∈	PROPN
ejpam-3877	101	34	(	(	PUNCT
ejpam-3877	101	35	0	0	NUM
ejpam-3877	101	36	,	,	PUNCT
ejpam-3877	101	37	t	t	PROPN
ejpam-3877	101	38	)	)	PUNCT
ejpam-3877	101	39	,	,	PUNCT
ejpam-3877	101	40	there	there	PRON
ejpam-3877	101	41	exists	exist	VERB
ejpam-3877	101	42	a	a	DET
ejpam-3877	101	43	measure	measure	NOUN
ejpam-3877	101	44	u	u	NOUN
ejpam-3877	101	45	(	(	PUNCT
ejpam-3877	101	46	·	·	PUNCT
ejpam-3877	101	47	,	,	PUNCT
ejpam-3877	101	48	t	t	PROPN
ejpam-3877	101	49	)	)	PUNCT
ejpam-3877	101	50	∈m+(ω	∈m+(ω	NOUN
ejpam-3877	101	51	)	)	PUNCT
ejpam-3877	101	52	such	such	ADJ
ejpam-3877	101	53	that	that	SCONJ
ejpam-3877	101	54	(	(	PUNCT
ejpam-3877	101	55	a	a	NOUN
ejpam-3877	101	56	)	)	PUNCT
ejpam-3877	101	57	for	for	ADP
ejpam-3877	101	58	every	every	DET
ejpam-3877	101	59	ξ	ξ	PROPN
ejpam-3877	101	60	∈	∈	PROPN
ejpam-3877	101	61	c(q	c(q	PROPN
ejpam-3877	101	62	)	)	PUNCT
ejpam-3877	101	63	,	,	PUNCT
ejpam-3877	101	64	the	the	DET
ejpam-3877	101	65	map	map	NOUN
ejpam-3877	101	66	t	t	PROPN
ejpam-3877	101	67	7→	7→	NUM
ejpam-3877	101	68	〈	〈	PROPN
ejpam-3877	101	69	u	u	NOUN
ejpam-3877	101	70	(	(	PUNCT
ejpam-3877	101	71	·	·	PROPN
ejpam-3877	101	72	,	,	PUNCT
ejpam-3877	101	73	t	t	PROPN
ejpam-3877	101	74	)	)	PUNCT
ejpam-3877	101	75	,	,	PUNCT
ejpam-3877	101	76	ξ	ξ	X
ejpam-3877	101	77	(	(	PUNCT
ejpam-3877	101	78	·	·	PUNCT
ejpam-3877	101	79	,	,	PUNCT
ejpam-3877	101	80	t)〉ω	t)〉ω	PROPN
ejpam-3877	101	81	is	be	AUX
ejpam-3877	101	82	lebesgue	lebesgue	NOUN
ejpam-3877	101	83	measurable	measurable	ADJ
ejpam-3877	101	84	and	and	CCONJ
ejpam-3877	101	85	there	there	PRON
ejpam-3877	101	86	holds	hold	VERB
ejpam-3877	101	87	〈	〈	PROPN
ejpam-3877	101	88	u	u	NOUN
ejpam-3877	101	89	,	,	PUNCT
ejpam-3877	101	90	ξ〉q	ξ〉q	PROPN
ejpam-3877	101	91	=	=	SYM
ejpam-3877	101	92	∫	∫	PROPN
ejpam-3877	101	93	t	t	NOUN
ejpam-3877	101	94	0	0	PUNCT
ejpam-3877	102	1	〈	〈	PROPN
ejpam-3877	102	2	u	u	PROPN
ejpam-3877	102	3	(	(	PUNCT
ejpam-3877	102	4	·	·	PROPN
ejpam-3877	102	5	,	,	PUNCT
ejpam-3877	102	6	t	t	PROPN
ejpam-3877	102	7	)	)	PUNCT
ejpam-3877	102	8	,	,	PUNCT
ejpam-3877	102	9	ξ	ξ	X
ejpam-3877	102	10	(	(	PUNCT
ejpam-3877	102	11	·	·	PUNCT
ejpam-3877	102	12	,	,	PUNCT
ejpam-3877	102	13	t)〉ωdt	t)〉ωdt	NUM
ejpam-3877	102	14	(	(	PUNCT
ejpam-3877	102	15	2.6	2.6	NUM
ejpam-3877	102	16	)	)	PUNCT
ejpam-3877	102	17	(	(	PUNCT
ejpam-3877	102	18	b	b	NOUN
ejpam-3877	102	19	)	)	PUNCT
ejpam-3877	102	20	for	for	ADP
ejpam-3877	102	21	every	every	DET
ejpam-3877	102	22	borel	borel	NOUN
ejpam-3877	102	23	set	set	VERB
ejpam-3877	102	24	e	e	PROPN
ejpam-3877	102	25	⊆	⊆	NUM
ejpam-3877	102	26	ω	ω	NUM
ejpam-3877	102	27	,	,	PUNCT
ejpam-3877	102	28	the	the	DET
ejpam-3877	102	29	map	map	NOUN
ejpam-3877	102	30	t	t	PROPN
ejpam-3877	102	31	7→	7→	NUM
ejpam-3877	102	32	u	u	NOUN
ejpam-3877	102	33	(	(	PUNCT
ejpam-3877	102	34	·	·	PUNCT
ejpam-3877	102	35	,	,	PUNCT
ejpam-3877	102	36	t)(et	t)(et	NUM
ejpam-3877	102	37	)	)	PUNCT
ejpam-3877	102	38	is	be	AUX
ejpam-3877	102	39	lebesgue	lebesgue	NOUN
ejpam-3877	102	40	measurable	measurable	ADJ
ejpam-3877	102	41	and	and	CCONJ
ejpam-3877	102	42	there	there	PRON
ejpam-3877	102	43	holds	hold	VERB
ejpam-3877	102	44	u(e	u(e	NOUN
ejpam-3877	102	45	)	)	PUNCT
ejpam-3877	102	46	=	=	SYM
ejpam-3877	102	47	∫	∫	PROPN
ejpam-3877	102	48	t	t	PROPN
ejpam-3877	102	49	0	0	NUM
ejpam-3877	102	50	u	u	NOUN
ejpam-3877	102	51	(	(	PUNCT
ejpam-3877	102	52	·	·	PUNCT
ejpam-3877	102	53	,	,	PUNCT
ejpam-3877	102	54	t)(et)dt	t)(et)dt	PROPN
ejpam-3877	102	55	where	where	SCONJ
ejpam-3877	102	56	et	et	NOUN
ejpam-3877	102	57	=	=	PUNCT
ejpam-3877	102	58	{	{	PUNCT
ejpam-3877	102	59	x	x	PUNCT
ejpam-3877	102	60	∈	∈	NOUN
ejpam-3877	102	61	ω/(x	ω/(x	NOUN
ejpam-3877	102	62	,	,	PUNCT
ejpam-3877	102	63	t	t	PROPN
ejpam-3877	102	64	)	)	PUNCT
ejpam-3877	102	65	∈	∈	PROPN
ejpam-3877	102	66	e	e	X
ejpam-3877	102	67	}	}	PUNCT
ejpam-3877	102	68	(	(	PUNCT
ejpam-3877	102	69	c	c	X
ejpam-3877	102	70	)	)	PUNCT
ejpam-3877	102	71	there	there	PRON
ejpam-3877	102	72	exists	exist	VERB
ejpam-3877	102	73	a	a	DET
ejpam-3877	102	74	constant	constant	ADJ
ejpam-3877	102	75	c	c	NOUN
ejpam-3877	102	76	>	>	X
ejpam-3877	102	77	0	0	NUM
ejpam-3877	102	78	such	such	ADJ
ejpam-3877	102	79	that	that	SCONJ
ejpam-3877	102	80	ess	ess	NOUN
ejpam-3877	102	81	sup	sup	NOUN
ejpam-3877	102	82	t∈(0,t	t∈(0,t	NOUN
ejpam-3877	102	83	)	)	PUNCT
ejpam-3877	102	84	‖	‖	PROPN
ejpam-3877	102	85	u	u	PROPN
ejpam-3877	102	86	(	(	PUNCT
ejpam-3877	102	87	·	·	PROPN
ejpam-3877	102	88	,	,	PUNCT
ejpam-3877	102	89	t	t	NOUN
ejpam-3877	102	90	)	)	PUNCT
ejpam-3877	102	91	‖m(ω)≤	‖m(ω)≤	NOUN
ejpam-3877	102	92	c.	c.	NOUN
ejpam-3877	102	93	in	in	ADP
ejpam-3877	102	94	the	the	DET
ejpam-3877	102	95	following	following	NOUN
ejpam-3877	102	96	,	,	PUNCT
ejpam-3877	102	97	we	we	PRON
ejpam-3877	102	98	will	will	AUX
ejpam-3877	102	99	use	use	VERB
ejpam-3877	102	100	the	the	DET
ejpam-3877	102	101	notation	notation	NOUN
ejpam-3877	102	102	‖	‖	PROPN
ejpam-3877	102	103	u	u	PROPN
ejpam-3877	102	104	‖l∞((0,t	‖l∞((0,t	PROPN
ejpam-3877	102	105	)	)	PUNCT
ejpam-3877	102	106	,	,	PUNCT
ejpam-3877	102	107	m(ω))=	m(ω))=	PUNCT
ejpam-3877	102	108	ess	ess	NOUN
ejpam-3877	102	109	sup	sup	NOUN
ejpam-3877	102	110	t∈(0,t	t∈(0,t	PROPN
ejpam-3877	102	111	)	)	PUNCT
ejpam-3877	103	1	‖	‖	PROPN
ejpam-3877	103	2	u	u	PROPN
ejpam-3877	103	3	(	(	PUNCT
ejpam-3877	103	4	·	·	PROPN
ejpam-3877	103	5	,	,	PUNCT
ejpam-3877	103	6	t	t	PROPN
ejpam-3877	103	7	)	)	PUNCT
ejpam-3877	103	8	‖m(ω	‖m(ω	NOUN
ejpam-3877	103	9	)	)	PUNCT
ejpam-3877	103	10	.	.	PUNCT
ejpam-3877	104	1	if	if	SCONJ
ejpam-3877	104	2	u	u	PROPN
ejpam-3877	104	3	∈	∈	PROPN
ejpam-3877	104	4	l∞((0	l∞((0	PROPN
ejpam-3877	104	5	,	,	PUNCT
ejpam-3877	104	6	t	t	PROPN
ejpam-3877	104	7	)	)	PUNCT
ejpam-3877	104	8	,	,	PUNCT
ejpam-3877	104	9	m(ω	m(ω	PROPN
ejpam-3877	104	10	)	)	PUNCT
ejpam-3877	104	11	)	)	PUNCT
ejpam-3877	104	12	,	,	PUNCT
ejpam-3877	104	13	it	it	PRON
ejpam-3877	104	14	is	be	AUX
ejpam-3877	104	15	easily	easily	ADV
ejpam-3877	104	16	seen	see	VERB
ejpam-3877	104	17	that	that	SCONJ
ejpam-3877	104	18	uac	uac	NOUN
ejpam-3877	104	19	,	,	PUNCT
ejpam-3877	104	20	us	us	PROPN
ejpam-3877	104	21	∈	∈	PROPN
ejpam-3877	104	22	l∞((0	l∞((0	PROPN
ejpam-3877	104	23	,	,	PUNCT
ejpam-3877	104	24	t	t	PROPN
ejpam-3877	104	25	)	)	PUNCT
ejpam-3877	104	26	,	,	PUNCT
ejpam-3877	104	27	m(ω	m(ω	PROPN
ejpam-3877	104	28	)	)	PUNCT
ejpam-3877	104	29	)	)	PUNCT
ejpam-3877	104	30	as	as	ADV
ejpam-3877	104	31	well	well	ADV
ejpam-3877	104	32	and	and	CCONJ
ejpam-3877	104	33	that	that	SCONJ
ejpam-3877	104	34	ur	ur	PROPN
ejpam-3877	104	35	∈	∈	PROPN
ejpam-3877	104	36	l∞((0	l∞((0	PROPN
ejpam-3877	104	37	,	,	PUNCT
ejpam-3877	104	38	t	t	PROPN
ejpam-3877	104	39	)	)	PUNCT
ejpam-3877	104	40	,	,	PUNCT
ejpam-3877	104	41	l1(ω	l1(ω	PROPN
ejpam-3877	104	42	)	)	PUNCT
ejpam-3877	104	43	)	)	PUNCT
ejpam-3877	104	44	.	.	PUNCT
ejpam-3877	105	1	moreover	moreover	ADV
ejpam-3877	105	2	,	,	PUNCT
ejpam-3877	105	3	the	the	DET
ejpam-3877	105	4	inequality	inequality	NOUN
ejpam-3877	105	5	(	(	PUNCT
ejpam-3877	105	6	2.6	2.6	NUM
ejpam-3877	105	7	)	)	PUNCT
ejpam-3877	105	8	implies	imply	VERB
ejpam-3877	105	9	that	that	SCONJ
ejpam-3877	105	10	for	for	ADP
ejpam-3877	105	11	every	every	PRON
ejpam-3877	105	12	ξ	ξ	PROPN
ejpam-3877	105	13	∈	∈	PROPN
ejpam-3877	105	14	c(q	c(q	PROPN
ejpam-3877	105	15	)	)	PUNCT
ejpam-3877	105	16	〈	〈	NOUN
ejpam-3877	105	17	uac	uac	NOUN
ejpam-3877	105	18	,	,	PUNCT
ejpam-3877	105	19	ξ〉q	ξ〉q	PROPN
ejpam-3877	105	20	=	=	SYM
ejpam-3877	105	21	∫	∫	PROPN
ejpam-3877	105	22	q	q	PROPN
ejpam-3877	105	23	urξdxdt	urξdxdt	PROPN
ejpam-3877	105	24	and	and	CCONJ
ejpam-3877	105	25	〈	〈	PROPN
ejpam-3877	105	26	us	we	PRON
ejpam-3877	105	27	,	,	PUNCT
ejpam-3877	105	28	ξ〉q	ξ〉q	PROPN
ejpam-3877	105	29	=	=	SYM
ejpam-3877	105	30	∫	∫	PROPN
ejpam-3877	105	31	t	t	NOUN
ejpam-3877	105	32	0	0	PUNCT
ejpam-3877	106	1	〈	〈	PROPN
ejpam-3877	106	2	us	we	PRON
ejpam-3877	106	3	(	(	PUNCT
ejpam-3877	106	4	·	·	PROPN
ejpam-3877	106	5	,	,	PUNCT
ejpam-3877	106	6	t	t	PROPN
ejpam-3877	106	7	)	)	PUNCT
ejpam-3877	106	8	,	,	PUNCT
ejpam-3877	106	9	ξ	ξ	X
ejpam-3877	106	10	(	(	PUNCT
ejpam-3877	106	11	·	·	PUNCT
ejpam-3877	106	12	,	,	PUNCT
ejpam-3877	106	13	t)〉ωdt	t)〉ωdt	NUM
ejpam-3877	106	14	quincy	quincy	PROPN
ejpam-3877	106	15	s.	s.	PROPN
ejpam-3877	106	16	nkombo	nkombo	PROPN
ejpam-3877	106	17	,	,	PUNCT
ejpam-3877	106	18	fengquan	fengquan	PROPN
ejpam-3877	106	19	li	li	PROPN
ejpam-3877	106	20	/	/	SYM
ejpam-3877	106	21	eur	eur	PROPN
ejpam-3877	106	22	.	.	PUNCT
ejpam-3877	107	1	j.	j.	PROPN
ejpam-3877	107	2	pure	pure	PROPN
ejpam-3877	107	3	appl	appl	PROPN
ejpam-3877	107	4	.	.	PROPN
ejpam-3877	107	5	math	math	PROPN
ejpam-3877	107	6	,	,	PUNCT
ejpam-3877	107	7	14	14	NUM
ejpam-3877	107	8	(	(	PUNCT
ejpam-3877	107	9	1	1	NUM
ejpam-3877	107	10	)	)	PUNCT
ejpam-3877	107	11	(	(	PUNCT
ejpam-3877	107	12	2021	2021	NUM
ejpam-3877	107	13	)	)	PUNCT
ejpam-3877	107	14	,	,	PUNCT
ejpam-3877	107	15	204	204	NUM
ejpam-3877	107	16	-	-	SYM
ejpam-3877	107	17	233	233	NUM
ejpam-3877	107	18	210	210	NUM
ejpam-3877	107	19	notice	notice	NOUN
ejpam-3877	107	20	that	that	SCONJ
ejpam-3877	107	21	uac	uac	NOUN
ejpam-3877	107	22	(	(	PUNCT
ejpam-3877	107	23	·	·	PUNCT
ejpam-3877	107	24	,	,	PUNCT
ejpam-3877	107	25	t	t	PROPN
ejpam-3877	107	26	)	)	PUNCT
ejpam-3877	107	27	=	=	PUNCT
ejpam-3877	108	1	[	[	X
ejpam-3877	108	2	u	u	X
ejpam-3877	108	3	(	(	PUNCT
ejpam-3877	108	4	·	·	PUNCT
ejpam-3877	108	5	,	,	PUNCT
ejpam-3877	108	6	t)]ac	t)]ac	NUM
ejpam-3877	108	7	,	,	PUNCT
ejpam-3877	108	8	ur	ur	INTJ
ejpam-3877	108	9	(	(	PUNCT
ejpam-3877	108	10	·	·	PROPN
ejpam-3877	108	11	,	,	PUNCT
ejpam-3877	108	12	t	t	PROPN
ejpam-3877	108	13	)	)	PUNCT
ejpam-3877	108	14	=	=	PUNCT
ejpam-3877	109	1	[	[	X
ejpam-3877	109	2	u	u	X
ejpam-3877	109	3	(	(	PUNCT
ejpam-3877	109	4	·	·	PUNCT
ejpam-3877	109	5	,	,	PUNCT
ejpam-3877	109	6	t)]r	t)]r	NOUN
ejpam-3877	109	7	and	and	CCONJ
ejpam-3877	109	8	us	we	PRON
ejpam-3877	109	9	(	(	PUNCT
ejpam-3877	109	10	·	·	PROPN
ejpam-3877	109	11	,	,	PUNCT
ejpam-3877	109	12	t	t	PROPN
ejpam-3877	109	13	)	)	PUNCT
ejpam-3877	109	14	=	=	PUNCT
ejpam-3877	110	1	[	[	X
ejpam-3877	110	2	u	u	X
ejpam-3877	110	3	(	(	PUNCT
ejpam-3877	110	4	·	·	PUNCT
ejpam-3877	110	5	,	,	PUNCT
ejpam-3877	110	6	t)]s	t)]s	INTJ
ejpam-3877	110	7	(	(	PUNCT
ejpam-3877	110	8	see	see	VERB
ejpam-3877	110	9	[	[	X
ejpam-3877	110	10	18	18	NUM
ejpam-3877	110	11	,	,	PUNCT
ejpam-3877	110	12	23	23	NUM
ejpam-3877	110	13	,	,	PUNCT
ejpam-3877	110	14	30	30	NUM
ejpam-3877	110	15	]	]	PUNCT
ejpam-3877	110	16	)	)	PUNCT
ejpam-3877	110	17	.	.	PUNCT
ejpam-3877	111	1	assume	assume	VERB
ejpam-3877	111	2	that	that	SCONJ
ejpam-3877	111	3	the	the	DET
ejpam-3877	111	4	function	function	NOUN
ejpam-3877	111	5	ψ	ψ	X
ejpam-3877	111	6	satisfies	satisfy	VERB
ejpam-3877	111	7	the	the	DET
ejpam-3877	111	8	following	follow	VERB
ejpam-3877	111	9	conditions	condition	NOUN
ejpam-3877	111	10	:	:	PUNCT
ejpam-3877	111	11	(	(	PUNCT
ejpam-3877	111	12	i	i	NOUN
ejpam-3877	111	13	)	)	PUNCT
ejpam-3877	112	1			PROPN
ejpam-3877	112	2	(	(	PUNCT
ejpam-3877	112	3	i	i	NOUN
ejpam-3877	112	4	)	)	PUNCT
ejpam-3877	112	5	ψ	ψ	ADP
ejpam-3877	112	6	∈	∈	PROPN
ejpam-3877	112	7	l∞(r+	l∞(r+	PROPN
ejpam-3877	112	8	)	)	PUNCT
ejpam-3877	112	9	∩	∩	NOUN
ejpam-3877	112	10	c2(r+	c2(r+	NOUN
ejpam-3877	112	11	)	)	PUNCT
ejpam-3877	112	12	,	,	PUNCT
ejpam-3877	112	13	ψ(0	ψ(0	NOUN
ejpam-3877	112	14	)	)	PUNCT
ejpam-3877	112	15	=	=	SYM
ejpam-3877	112	16	0	0	NUM
ejpam-3877	112	17	,	,	PUNCT
ejpam-3877	112	18	ψ′	ψ′	PUNCT
ejpam-3877	112	19	>	>	X
ejpam-3877	112	20	0	0	PUNCT
ejpam-3877	113	1	in	in	ADP
ejpam-3877	113	2	r+	r+	X
ejpam-3877	113	3	,	,	PUNCT
ejpam-3877	113	4	(	(	PUNCT
ejpam-3877	113	5	ii	ii	NOUN
ejpam-3877	113	6	)	)	PUNCT
ejpam-3877	113	7	ψ(j	ψ(j	NOUN
ejpam-3877	113	8	)	)	PUNCT
ejpam-3877	113	9	∈	∈	PROPN
ejpam-3877	113	10	l∞(r∗+	l∞(r∗+	PROPN
ejpam-3877	113	11	)	)	PUNCT
ejpam-3877	113	12	,	,	PUNCT
ejpam-3877	113	13	for	for	ADP
ejpam-3877	113	14	any	any	DET
ejpam-3877	113	15	j	j	PROPN
ejpam-3877	113	16	=	=	SYM
ejpam-3877	113	17	1	1	NUM
ejpam-3877	113	18	,	,	PUNCT
ejpam-3877	113	19	2	2	NUM
ejpam-3877	113	20	,	,	PUNCT
ejpam-3877	113	21	.	.	PUNCT
ejpam-3877	113	22	.	.	PUNCT
ejpam-3877	113	23	.	.	PUNCT
ejpam-3877	114	1	,	,	PUNCT
ejpam-3877	114	2	n	n	CCONJ
ejpam-3877	114	3	if	if	SCONJ
ejpam-3877	114	4	0	0	NUM
ejpam-3877	114	5	<	<	X
ejpam-3877	114	6	m	m	VERB
ejpam-3877	114	7	≤	≤	ADJ
ejpam-3877	114	8	1	1	NUM
ejpam-3877	114	9	,	,	PUNCT
ejpam-3877	114	10	(	(	PUNCT
ejpam-3877	114	11	iii	iii	NOUN
ejpam-3877	114	12	)	)	PUNCT
ejpam-3877	114	13	ψ(s)→	ψ(s)→	NOUN
ejpam-3877	114	14	γ	γ	NOUN
ejpam-3877	114	15	as	as	ADP
ejpam-3877	114	16	s→	s→	PROPN
ejpam-3877	114	17	+	+	NOUN
ejpam-3877	114	18	∞	∞	PROPN
ejpam-3877	114	19	,	,	PUNCT
ejpam-3877	114	20	where	where	SCONJ
ejpam-3877	114	21	r+	r+	PUNCT
ejpam-3877	114	22	≡	≡	PROPN
ejpam-3877	115	1	[	[	X
ejpam-3877	115	2	0,+∞	0,+∞	NUM
ejpam-3877	115	3	)	)	PUNCT
ejpam-3877	115	4	and	and	CCONJ
ejpam-3877	115	5	γ	γ	PROPN
ejpam-3877	115	6	∈	∈	PROPN
ejpam-3877	115	7	r∗+	r∗+	PROPN
ejpam-3877	115	8	≡	≡	PROPN
ejpam-3877	115	9	(	(	PUNCT
ejpam-3877	115	10	0,+∞	0,+∞	NUM
ejpam-3877	115	11	)	)	PUNCT
ejpam-3877	115	12	.	.	PUNCT
ejpam-3877	116	1	by	by	ADP
ejpam-3877	116	2	ψ′	ψ′	ADP
ejpam-3877	116	3	and	and	CCONJ
ejpam-3877	116	4	ψ(j	ψ(j	NUM
ejpam-3877	116	5	)	)	PUNCT
ejpam-3877	116	6	we	we	PRON
ejpam-3877	116	7	denote	denote	VERB
ejpam-3877	116	8	the	the	DET
ejpam-3877	116	9	first	first	ADJ
ejpam-3877	116	10	and	and	CCONJ
ejpam-3877	116	11	j	j	PROPN
ejpam-3877	116	12	th	th	X
ejpam-3877	116	13	derivative	derivative	NOUN
ejpam-3877	116	14	of	of	ADP
ejpam-3877	116	15	the	the	DET
ejpam-3877	116	16	function	function	NOUN
ejpam-3877	116	17	ψ	ψ	NOUN
ejpam-3877	116	18	.	.	PUNCT
ejpam-3877	117	1	the	the	DET
ejpam-3877	117	2	assumption	assumption	NOUN
ejpam-3877	117	3	(	(	PUNCT
ejpam-3877	117	4	i)-(iii	i)-(iii	NOUN
ejpam-3877	117	5	)	)	PUNCT
ejpam-3877	117	6	stems	stem	VERB
ejpam-3877	117	7	from	from	ADP
ejpam-3877	117	8	(	(	PUNCT
ejpam-3877	117	9	i)-(i	i)-(i	PROPN
ejpam-3877	117	10	)	)	PUNCT
ejpam-3877	117	11	,	,	PUNCT
ejpam-3877	117	12	hence	hence	ADV
ejpam-3877	117	13	we	we	PRON
ejpam-3877	117	14	extend	extend	VERB
ejpam-3877	117	15	the	the	DET
ejpam-3877	117	16	function	function	NOUN
ejpam-3877	117	17	ψ	ψ	NOUN
ejpam-3877	117	18	in	in	ADP
ejpam-3877	117	19	[	[	X
ejpam-3877	117	20	0,+∞	0,+∞	NUM
ejpam-3877	117	21	]	]	X
ejpam-3877	117	22	defining	define	VERB
ejpam-3877	117	23	ψ(+∞	ψ(+∞	PROPN
ejpam-3877	117	24	)	)	PUNCT
ejpam-3877	117	25	=	=	SYM
ejpam-3877	118	1	γ	γ	X
ejpam-3877	118	2	.	.	PROPN
ejpam-3877	118	3	to	to	PART
ejpam-3877	118	4	prove	prove	VERB
ejpam-3877	118	5	the	the	DET
ejpam-3877	118	6	well	well	NOUN
ejpam-3877	118	7	-	-	PUNCT
ejpam-3877	118	8	posedness	posedness	NOUN
ejpam-3877	118	9	of	of	ADP
ejpam-3877	118	10	(	(	PUNCT
ejpam-3877	118	11	p	p	NOUN
ejpam-3877	118	12	)	)	PUNCT
ejpam-3877	118	13	(	(	PUNCT
ejpam-3877	118	14	if	if	SCONJ
ejpam-3877	118	15	n	n	PRON
ejpam-3877	118	16	≥	≥	NOUN
ejpam-3877	118	17	2	2	NUM
ejpam-3877	118	18	)	)	PUNCT
ejpam-3877	118	19	we	we	PRON
ejpam-3877	118	20	will	will	AUX
ejpam-3877	118	21	need	need	VERB
ejpam-3877	118	22	further	further	ADJ
ejpam-3877	118	23	assumption	assumption	NOUN
ejpam-3877	118	24	(	(	PUNCT
ejpam-3877	118	25	j	j	NOUN
ejpam-3877	118	26	)	)	PUNCT
ejpam-3877	118	27			VERB
ejpam-3877	118	28	there	there	ADV
ejpam-3877	118	29	exist	exist	VERB
ejpam-3877	118	30	γ	γ	X
ejpam-3877	118	31	>	>	X
ejpam-3877	118	32	0	0	NUM
ejpam-3877	118	33	,	,	PUNCT
ejpam-3877	118	34	s	s	VERB
ejpam-3877	118	35	<	<	X
ejpam-3877	118	36	s	s	X
ejpam-3877	118	37	and	and	CCONJ
ejpam-3877	118	38	l1	l1	PROPN
ejpam-3877	118	39	,	,	PUNCT
ejpam-3877	118	40	l2	l2	NOUN
ejpam-3877	118	41	>	>	X
ejpam-3877	118	42	0	0	NUM
ejpam-3877	118	43	,	,	PUNCT
ejpam-3877	118	44	l1	l1	PROPN
ejpam-3877	118	45	<	<	X
ejpam-3877	118	46	l2	l2	NOUN
ejpam-3877	118	47	such	such	ADJ
ejpam-3877	118	48	that	that	SCONJ
ejpam-3877	118	49	(	(	PUNCT
ejpam-3877	118	50	i	i	NOUN
ejpam-3877	118	51	)	)	PUNCT
ejpam-3877	118	52	ψ′(s	ψ′(s	PROPN
ejpam-3877	118	53	)	)	PUNCT
ejpam-3877	118	54	≥	≥	NOUN
ejpam-3877	118	55	l1e−|s|	l1e−|s|	NOUN
ejpam-3877	118	56	m	m	VERB
ejpam-3877	118	57	,	,	PUNCT
ejpam-3877	118	58	(	(	PUNCT
ejpam-3877	118	59	ii	ii	NOUN
ejpam-3877	118	60	)	)	PUNCT
ejpam-3877	118	61	ψ′(s	ψ′(s	PROPN
ejpam-3877	118	62	)	)	PUNCT
ejpam-3877	118	63	≤	≤	PUNCT
ejpam-3877	119	1	l2e−|s|	l2e−|s|	PROPN
ejpam-3877	119	2	m	m	VERB
ejpam-3877	119	3	,	,	PUNCT
ejpam-3877	119	4	for	for	ADP
ejpam-3877	119	5	any	any	PRON
ejpam-3877	119	6	s	s	X
ejpam-3877	119	7	<	<	X
ejpam-3877	119	8	s	s	X
ejpam-3877	119	9	<	<	X
ejpam-3877	119	10	s.	s.	PROPN
ejpam-3877	119	11	where	where	SCONJ
ejpam-3877	119	12	l1	l1	PROPN
ejpam-3877	119	13	,	,	PUNCT
ejpam-3877	119	14	l2	l2	NOUN
ejpam-3877	119	15	can	can	AUX
ejpam-3877	119	16	be	be	AUX
ejpam-3877	119	17	expressed	express	VERB
ejpam-3877	119	18	as	as	SCONJ
ejpam-3877	119	19	follows	follow	VERB
ejpam-3877	119	20	l1	l1	PROPN
ejpam-3877	119	21	=	=	SYM
ejpam-3877	119	22	min	min	PROPN
ejpam-3877	119	23	s∈[s	s∈[s	PROPN
ejpam-3877	119	24	,	,	PUNCT
ejpam-3877	119	25	s	s	X
ejpam-3877	119	26	]	]	X
ejpam-3877	119	27	ψ′(s)e|s|	ψ′(s)e|s|	PRON
ejpam-3877	119	28	m	m	VERB
ejpam-3877	119	29	and	and	CCONJ
ejpam-3877	119	30	l2	l2	NOUN
ejpam-3877	119	31	=	=	SYM
ejpam-3877	119	32	max	max	PROPN
ejpam-3877	119	33	s∈[s	s∈[s	PROPN
ejpam-3877	119	34	,	,	PUNCT
ejpam-3877	119	35	s	s	X
ejpam-3877	119	36	]	]	X
ejpam-3877	119	37	ψ′(s)e|s|	ψ′(s)e|s|	X
ejpam-3877	119	38	m	m	VERB
ejpam-3877	119	39	(	(	PUNCT
ejpam-3877	119	40	0	0	NUM
ejpam-3877	119	41	<	<	X
ejpam-3877	119	42	m	m	VERB
ejpam-3877	119	43	≤	≤	ADJ
ejpam-3877	119	44	1	1	NUM
ejpam-3877	119	45	)	)	PUNCT
ejpam-3877	119	46	.	.	PUNCT
ejpam-3877	120	1	3	3	X
ejpam-3877	120	2	.	.	X
ejpam-3877	120	3	statement	statement	NOUN
ejpam-3877	120	4	of	of	ADP
ejpam-3877	120	5	main	main	ADJ
ejpam-3877	120	6	results	result	NOUN
ejpam-3877	120	7	definition	definition	NOUN
ejpam-3877	120	8	3.1	3.1	NUM
ejpam-3877	120	9	.	.	PUNCT
ejpam-3877	121	1	for	for	ADP
ejpam-3877	121	2	any	any	DET
ejpam-3877	121	3	u0	u0	ADJ
ejpam-3877	121	4	∈	∈	PROPN
ejpam-3877	121	5	m+(ω	m+(ω	NOUN
ejpam-3877	121	6	)	)	PUNCT
ejpam-3877	121	7	and	and	CCONJ
ejpam-3877	121	8	µ	µ	PRON
ejpam-3877	121	9	∈	∈	NOUN
ejpam-3877	121	10	m+(q	m+(q	NUM
ejpam-3877	121	11	)	)	PUNCT
ejpam-3877	121	12	,	,	PUNCT
ejpam-3877	121	13	a	a	DET
ejpam-3877	121	14	measure	measure	NOUN
ejpam-3877	121	15	u	u	NOUN
ejpam-3877	121	16	is	be	AUX
ejpam-3877	121	17	called	call	VERB
ejpam-3877	121	18	a	a	DET
ejpam-3877	121	19	weak	weak	ADJ
ejpam-3877	121	20	solution	solution	NOUN
ejpam-3877	121	21	of	of	ADP
ejpam-3877	121	22	the	the	DET
ejpam-3877	121	23	problem	problem	NOUN
ejpam-3877	121	24	(	(	PUNCT
ejpam-3877	121	25	p	p	NOUN
ejpam-3877	121	26	)	)	PUNCT
ejpam-3877	121	27	,	,	PUNCT
ejpam-3877	121	28	if	if	SCONJ
ejpam-3877	121	29	u	u	PROPN
ejpam-3877	121	30	∈m+(q	∈m+(q	VERB
ejpam-3877	121	31	)	)	PUNCT
ejpam-3877	121	32	such	such	ADJ
ejpam-3877	121	33	that	that	SCONJ
ejpam-3877	121	34	(	(	PUNCT
ejpam-3877	121	35	i	i	NOUN
ejpam-3877	121	36	)	)	PUNCT
ejpam-3877	121	37	u	u	PROPN
ejpam-3877	121	38	∈	∈	PROPN
ejpam-3877	121	39	l∞((0	l∞((0	PROPN
ejpam-3877	121	40	,	,	PUNCT
ejpam-3877	121	41	t	t	PROPN
ejpam-3877	121	42	)	)	PUNCT
ejpam-3877	121	43	,	,	PUNCT
ejpam-3877	121	44	m+(ω	m+(ω	NOUN
ejpam-3877	121	45	)	)	PUNCT
ejpam-3877	121	46	)	)	PUNCT
ejpam-3877	121	47	(	(	PUNCT
ejpam-3877	121	48	ii	ii	NOUN
ejpam-3877	121	49	)	)	PUNCT
ejpam-3877	121	50	ψ(ur	ψ(ur	ADJ
ejpam-3877	121	51	)	)	PUNCT
ejpam-3877	121	52	∈	∈	PROPN
ejpam-3877	121	53	l1((0	l1((0	NOUN
ejpam-3877	121	54	,	,	PUNCT
ejpam-3877	121	55	t	t	PROPN
ejpam-3877	121	56	)	)	PUNCT
ejpam-3877	121	57	,	,	PUNCT
ejpam-3877	121	58	w	w	PROPN
ejpam-3877	121	59	1,1	1,1	NUM
ejpam-3877	121	60	0	0	NUM
ejpam-3877	121	61	(	(	PUNCT
ejpam-3877	121	62	ω	ω	NOUN
ejpam-3877	121	63	)	)	PUNCT
ejpam-3877	121	64	)	)	PUNCT
ejpam-3877	121	65	(	(	PUNCT
ejpam-3877	121	66	iii	iii	NOUN
ejpam-3877	121	67	)	)	PUNCT
ejpam-3877	121	68	for	for	ADP
ejpam-3877	121	69	every	every	DET
ejpam-3877	121	70	ξ	ξ	PROPN
ejpam-3877	121	71	∈	∈	PROPN
ejpam-3877	121	72	c1([0	c1([0	PROPN
ejpam-3877	121	73	,	,	PUNCT
ejpam-3877	121	74	t	t	X
ejpam-3877	121	75	]	]	PUNCT
ejpam-3877	121	76	,	,	PUNCT
ejpam-3877	121	77	c1	c1	PROPN
ejpam-3877	121	78	0	0	NUM
ejpam-3877	121	79	(	(	PUNCT
ejpam-3877	121	80	ω	ω	NOUN
ejpam-3877	121	81	)	)	PUNCT
ejpam-3877	121	82	)	)	PUNCT
ejpam-3877	121	83	,	,	PUNCT
ejpam-3877	121	84	ξ	ξ	X
ejpam-3877	121	85	(	(	PUNCT
ejpam-3877	121	86	·	·	PUNCT
ejpam-3877	121	87	,	,	PUNCT
ejpam-3877	121	88	t	t	NOUN
ejpam-3877	121	89	)	)	PUNCT
ejpam-3877	121	90	=	=	SYM
ejpam-3877	121	91	0	0	NUM
ejpam-3877	121	92	in	in	ADP
ejpam-3877	121	93	ω	ω	NUM
ejpam-3877	121	94	,	,	PUNCT
ejpam-3877	121	95	u	u	NOUN
ejpam-3877	121	96	satisfies	satisfy	VERB
ejpam-3877	121	97	the	the	DET
ejpam-3877	121	98	identity∫	identity∫	NOUN
ejpam-3877	121	99	t	t	NOUN
ejpam-3877	121	100	0	0	PUNCT
ejpam-3877	122	1	〈	〈	PROPN
ejpam-3877	122	2	u	u	PROPN
ejpam-3877	122	3	(	(	PUNCT
ejpam-3877	122	4	·	·	PROPN
ejpam-3877	122	5	,	,	PUNCT
ejpam-3877	122	6	t	t	PROPN
ejpam-3877	122	7	)	)	PUNCT
ejpam-3877	122	8	,	,	PUNCT
ejpam-3877	122	9	ξt	ξt	X
ejpam-3877	122	10	(	(	PUNCT
ejpam-3877	122	11	·	·	PUNCT
ejpam-3877	122	12	,	,	PUNCT
ejpam-3877	122	13	t)〉ωdt	t)〉ωdt	NUM
ejpam-3877	122	14	=	=	SYM
ejpam-3877	122	15	∫	∫	PROPN
ejpam-3877	122	16	q	q	PROPN
ejpam-3877	123	1	∇ψ(ur)∇ξdxdt−	∇ψ(ur)∇ξdxdt−	PROPN
ejpam-3877	123	2	∫	∫	PROPN
ejpam-3877	123	3	q	q	PROPN
ejpam-3877	123	4	ξdµ−	ξdµ−	PROPN
ejpam-3877	123	5	〈	〈	PROPN
ejpam-3877	123	6	u0	u0	PROPN
ejpam-3877	123	7	,	,	PUNCT
ejpam-3877	123	8	ξ	ξ	PROPN
ejpam-3877	123	9	(	(	PUNCT
ejpam-3877	123	10	·	·	PUNCT
ejpam-3877	123	11	,	,	PUNCT
ejpam-3877	123	12	0)〉ω	0)〉ω	PROPN
ejpam-3877	123	13	(	(	PUNCT
ejpam-3877	123	14	3.1	3.1	NUM
ejpam-3877	123	15	)	)	PUNCT
ejpam-3877	123	16	where	where	SCONJ
ejpam-3877	123	17	ur	ur	PRON
ejpam-3877	123	18	is	be	AUX
ejpam-3877	123	19	the	the	DET
ejpam-3877	123	20	density	density	NOUN
ejpam-3877	123	21	of	of	ADP
ejpam-3877	123	22	the	the	DET
ejpam-3877	123	23	absolutely	absolutely	ADV
ejpam-3877	123	24	continuous	continuous	ADJ
ejpam-3877	123	25	part	part	NOUN
ejpam-3877	123	26	of	of	ADP
ejpam-3877	123	27	the	the	DET
ejpam-3877	123	28	radon	radon	NOUN
ejpam-3877	123	29	-	-	PUNCT
ejpam-3877	123	30	measure	measure	NOUN
ejpam-3877	123	31	with	with	ADP
ejpam-3877	123	32	respect	respect	NOUN
ejpam-3877	123	33	to	to	ADP
ejpam-3877	123	34	the	the	DET
ejpam-3877	123	35	lebesgue	lebesgue	ADJ
ejpam-3877	123	36	measure	measure	NOUN
ejpam-3877	123	37	such	such	ADJ
ejpam-3877	123	38	that	that	SCONJ
ejpam-3877	123	39	0	0	NUM
ejpam-3877	123	40	≤	≤	NUM
ejpam-3877	123	41	ur	ur	INTJ
ejpam-3877	123	42	∈	∈	PROPN
ejpam-3877	123	43	l∞((0	l∞((0	PROPN
ejpam-3877	123	44	,	,	PUNCT
ejpam-3877	123	45	t	t	PROPN
ejpam-3877	123	46	)	)	PUNCT
ejpam-3877	123	47	,	,	PUNCT
ejpam-3877	123	48	l1(ω	l1(ω	PROPN
ejpam-3877	123	49	)	)	PUNCT
ejpam-3877	123	50	)	)	PUNCT
ejpam-3877	123	51	.	.	PUNCT
ejpam-3877	124	1	remark	remark	VERB
ejpam-3877	124	2	3.1	3.1	NUM
ejpam-3877	124	3	in	in	ADP
ejpam-3877	124	4	(	(	PUNCT
ejpam-3877	124	5	3.1	3.1	NUM
ejpam-3877	124	6	)	)	PUNCT
ejpam-3877	124	7	,	,	PUNCT
ejpam-3877	124	8	we	we	PRON
ejpam-3877	124	9	can	can	AUX
ejpam-3877	124	10	choose	choose	VERB
ejpam-3877	124	11	test	test	NOUN
ejpam-3877	124	12	functions	function	NOUN
ejpam-3877	124	13	ξ	ξ	PROPN
ejpam-3877	124	14	in	in	ADP
ejpam-3877	124	15	c1(q	c1(q	NOUN
ejpam-3877	124	16	)	)	PUNCT
ejpam-3877	124	17	which	which	PRON
ejpam-3877	124	18	vanish	vanish	VERB
ejpam-3877	124	19	on	on	ADP
ejpam-3877	124	20	∂ω×	∂ω×	PROPN
ejpam-3877	125	1	[	[	X
ejpam-3877	125	2	0	0	NUM
ejpam-3877	125	3	,	,	PUNCT
ejpam-3877	125	4	t	t	NOUN
ejpam-3877	125	5	]	]	PUNCT
ejpam-3877	125	6	and	and	CCONJ
ejpam-3877	125	7	t	t	PROPN
ejpam-3877	125	8	=	=	SYM
ejpam-3877	125	9	t	t	PROPN
ejpam-3877	125	10	.	.	PUNCT
ejpam-3877	126	1	the	the	DET
ejpam-3877	126	2	following	follow	VERB
ejpam-3877	126	3	theorem	theorem	NOUN
ejpam-3877	126	4	gives	give	VERB
ejpam-3877	126	5	necessary	necessary	ADJ
ejpam-3877	126	6	conditions	condition	NOUN
ejpam-3877	126	7	on	on	ADP
ejpam-3877	126	8	the	the	DET
ejpam-3877	126	9	measures	measure	NOUN
ejpam-3877	126	10	µ	µ	X
ejpam-3877	126	11	and	and	CCONJ
ejpam-3877	126	12	u0	u0	ADJ
ejpam-3877	126	13	for	for	ADP
ejpam-3877	126	14	the	the	DET
ejpam-3877	126	15	existence	existence	NOUN
ejpam-3877	126	16	of	of	ADP
ejpam-3877	126	17	weak	weak	ADJ
ejpam-3877	126	18	solutions	solution	NOUN
ejpam-3877	126	19	to	to	ADP
ejpam-3877	126	20	the	the	DET
ejpam-3877	126	21	problem	problem	NOUN
ejpam-3877	126	22	(	(	PUNCT
ejpam-3877	126	23	p	p	NOUN
ejpam-3877	126	24	)	)	PUNCT
ejpam-3877	126	25	with	with	ADP
ejpam-3877	126	26	respect	respect	NOUN
ejpam-3877	126	27	to	to	ADP
ejpam-3877	126	28	the	the	DET
ejpam-3877	126	29	parabolic	parabolic	ADJ
ejpam-3877	126	30	capacity	capacity	NOUN
ejpam-3877	126	31	and	and	CCONJ
ejpam-3877	126	32	newtonian	newtonian	ADJ
ejpam-3877	126	33	capacity	capacity	NOUN
ejpam-3877	126	34	respectively	respectively	ADV
ejpam-3877	126	35	.	.	PUNCT
ejpam-3877	127	1	theorem	theorem	VERB
ejpam-3877	127	2	3.1	3.1	NUM
ejpam-3877	127	3	.	.	PUNCT
ejpam-3877	128	1	assume	assume	VERB
ejpam-3877	128	2	that	that	SCONJ
ejpam-3877	128	3	(	(	PUNCT
ejpam-3877	128	4	i	i	NOUN
ejpam-3877	128	5	)	)	PUNCT
ejpam-3877	128	6	,	,	PUNCT
ejpam-3877	128	7	(	(	PUNCT
ejpam-3877	128	8	j	j	NOUN
ejpam-3877	128	9	)	)	PUNCT
ejpam-3877	128	10	,	,	PUNCT
ejpam-3877	128	11	µ	µ	X
ejpam-3877	128	12	∈	∈	NOUN
ejpam-3877	128	13	m+(q	m+(q	NUM
ejpam-3877	128	14	)	)	PUNCT
ejpam-3877	128	15	and	and	CCONJ
ejpam-3877	128	16	u0	u0	PROPN
ejpam-3877	128	17	∈	∈	PROPN
ejpam-3877	128	18	m+(ω	m+(ω	NOUN
ejpam-3877	128	19	)	)	PUNCT
ejpam-3877	128	20	hold	hold	VERB
ejpam-3877	128	21	.	.	PUNCT
ejpam-3877	129	1	if	if	SCONJ
ejpam-3877	129	2	u	u	NOUN
ejpam-3877	129	3	is	be	AUX
ejpam-3877	129	4	a	a	DET
ejpam-3877	129	5	weak	weak	ADJ
ejpam-3877	129	6	solution	solution	NOUN
ejpam-3877	129	7	to	to	ADP
ejpam-3877	129	8	the	the	DET
ejpam-3877	129	9	problem	problem	NOUN
ejpam-3877	129	10	(	(	PUNCT
ejpam-3877	129	11	p	p	NOUN
ejpam-3877	129	12	)	)	PUNCT
ejpam-3877	129	13	.	.	PUNCT
ejpam-3877	130	1	then	then	ADV
ejpam-3877	130	2	µ	µ	X
ejpam-3877	130	3	and	and	CCONJ
ejpam-3877	130	4	u0	u0	PROPN
ejpam-3877	130	5	⊗	⊗	PROPN
ejpam-3877	130	6	δ{t=0	δ{t=0	PROPN
ejpam-3877	130	7	}	}	PUNCT
ejpam-3877	130	8	are	be	AUX
ejpam-3877	130	9	absolutely	absolutely	ADV
ejpam-3877	130	10	continuous	continuous	ADJ
ejpam-3877	130	11	measures	measure	NOUN
ejpam-3877	130	12	with	with	ADP
ejpam-3877	130	13	respect	respect	NOUN
ejpam-3877	130	14	to	to	ADP
ejpam-3877	130	15	the	the	DET
ejpam-3877	130	16	parabolic	parabolic	ADJ
ejpam-3877	130	17	capacity	capacity	NOUN
ejpam-3877	130	18	.	.	PUNCT
ejpam-3877	131	1	quincy	quincy	PROPN
ejpam-3877	131	2	s.	s.	PROPN
ejpam-3877	131	3	nkombo	nkombo	PROPN
ejpam-3877	131	4	,	,	PUNCT
ejpam-3877	131	5	fengquan	fengquan	PROPN
ejpam-3877	131	6	li	li	PROPN
ejpam-3877	131	7	/	/	SYM
ejpam-3877	131	8	eur	eur	PROPN
ejpam-3877	131	9	.	.	PUNCT
ejpam-3877	132	1	j.	j.	PROPN
ejpam-3877	132	2	pure	pure	PROPN
ejpam-3877	132	3	appl	appl	PROPN
ejpam-3877	132	4	.	.	PROPN
ejpam-3877	132	5	math	math	PROPN
ejpam-3877	132	6	,	,	PUNCT
ejpam-3877	132	7	14	14	NUM
ejpam-3877	132	8	(	(	PUNCT
ejpam-3877	132	9	1	1	NUM
ejpam-3877	132	10	)	)	PUNCT
ejpam-3877	132	11	(	(	PUNCT
ejpam-3877	132	12	2021	2021	NUM
ejpam-3877	132	13	)	)	PUNCT
ejpam-3877	132	14	,	,	PUNCT
ejpam-3877	132	15	204	204	NUM
ejpam-3877	132	16	-	-	SYM
ejpam-3877	132	17	233	233	NUM
ejpam-3877	132	18	211	211	NUM
ejpam-3877	132	19	since	since	SCONJ
ejpam-3877	132	20	newtonian	newtonian	ADJ
ejpam-3877	132	21	capacity	capacity	NOUN
ejpam-3877	132	22	and	and	CCONJ
ejpam-3877	132	23	parabolic	parabolic	ADJ
ejpam-3877	132	24	capacity	capacity	NOUN
ejpam-3877	132	25	are	be	AUX
ejpam-3877	132	26	equivalent	equivalent	ADJ
ejpam-3877	132	27	,	,	PUNCT
ejpam-3877	132	28	then	then	ADV
ejpam-3877	132	29	µ	µ	NUM
ejpam-3877	132	30	and	and	CCONJ
ejpam-3877	132	31	u0	u0	PROPN
ejpam-3877	132	32	⊗	⊗	PROPN
ejpam-3877	132	33	δ{t=0	δ{t=0	PROPN
ejpam-3877	132	34	}	}	PUNCT
ejpam-3877	132	35	are	be	AUX
ejpam-3877	132	36	absolutely	absolutely	ADV
ejpam-3877	132	37	continuous	continuous	ADJ
ejpam-3877	132	38	measures	measure	NOUN
ejpam-3877	132	39	with	with	ADP
ejpam-3877	132	40	respect	respect	NOUN
ejpam-3877	132	41	to	to	ADP
ejpam-3877	132	42	the	the	DET
ejpam-3877	132	43	c2	c2	PROPN
ejpam-3877	132	44	-	-	PUNCT
ejpam-3877	132	45	capacity	capacity	NOUN
ejpam-3877	132	46	as	as	ADV
ejpam-3877	132	47	well	well	ADV
ejpam-3877	132	48	.	.	PUNCT
ejpam-3877	133	1	theorem	theorem	ADJ
ejpam-3877	133	2	3.2	3.2	NUM
ejpam-3877	133	3	.	.	PUNCT
ejpam-3877	134	1	assume	assume	VERB
ejpam-3877	134	2	that	that	SCONJ
ejpam-3877	134	3	the	the	DET
ejpam-3877	134	4	hypothesis	hypothesis	NOUN
ejpam-3877	134	5	(	(	PUNCT
ejpam-3877	134	6	i	i	NOUN
ejpam-3877	134	7	)	)	PUNCT
ejpam-3877	134	8	holds	hold	VERB
ejpam-3877	134	9	.	.	PUNCT
ejpam-3877	135	1	let	let	VERB
ejpam-3877	135	2	u	u	PRON
ejpam-3877	135	3	be	be	AUX
ejpam-3877	135	4	a	a	DET
ejpam-3877	135	5	weak	weak	ADJ
ejpam-3877	135	6	solution	solution	NOUN
ejpam-3877	135	7	to	to	ADP
ejpam-3877	135	8	the	the	DET
ejpam-3877	135	9	problem	problem	NOUN
ejpam-3877	135	10	(	(	PUNCT
ejpam-3877	135	11	p	p	NOUN
ejpam-3877	135	12	)	)	PUNCT
ejpam-3877	135	13	.	.	PUNCT
ejpam-3877	136	1	then	then	ADV
ejpam-3877	136	2	there	there	PRON
ejpam-3877	136	3	exist	exist	VERB
ejpam-3877	136	4	a	a	DET
ejpam-3877	136	5	set	set	NOUN
ejpam-3877	136	6	f	f	PROPN
ejpam-3877	136	7	⊂	⊂	PROPN
ejpam-3877	136	8	(	(	PUNCT
ejpam-3877	136	9	0	0	NUM
ejpam-3877	136	10	,	,	PUNCT
ejpam-3877	136	11	t	t	NOUN
ejpam-3877	136	12	)	)	PUNCT
ejpam-3877	136	13	with	with	ADP
ejpam-3877	136	14	zero	zero	NUM
ejpam-3877	136	15	lebesgue	lebesgue	NOUN
ejpam-3877	136	16	measure	measure	NOUN
ejpam-3877	136	17	and	and	CCONJ
ejpam-3877	136	18	νt	νt	PROPN
ejpam-3877	136	19	∈m+(ω	∈m+(ω	NOUN
ejpam-3877	136	20	)	)	PUNCT
ejpam-3877	136	21	such	such	ADJ
ejpam-3877	136	22	that	that	SCONJ
ejpam-3877	136	23	[	[	X
ejpam-3877	136	24	u	u	X
ejpam-3877	136	25	(	(	PUNCT
ejpam-3877	136	26	·	·	PUNCT
ejpam-3877	136	27	,	,	PUNCT
ejpam-3877	136	28	t)−	t)−	PROPN
ejpam-3877	136	29	u0]c,2	u0]c,2	ADJ
ejpam-3877	136	30	=	=	SYM
ejpam-3877	136	31	[	[	PUNCT
ejpam-3877	136	32	νt	νt	X
ejpam-3877	136	33	]	]	PUNCT
ejpam-3877	136	34	c,2	c,2	VERB
ejpam-3877	136	35	(	(	PUNCT
ejpam-3877	136	36	3.2	3.2	NUM
ejpam-3877	136	37	)	)	PUNCT
ejpam-3877	136	38	for	for	ADP
ejpam-3877	136	39	every	every	DET
ejpam-3877	136	40	t	t	NOUN
ejpam-3877	136	41	∈	∈	PROPN
ejpam-3877	136	42	(	(	PUNCT
ejpam-3877	136	43	0	0	NUM
ejpam-3877	136	44	,	,	PUNCT
ejpam-3877	136	45	t	t	NOUN
ejpam-3877	136	46	)	)	PUNCT
ejpam-3877	136	47	\	\	PROPN
ejpam-3877	137	1	f	f	PROPN
ejpam-3877	137	2	.	.	PUNCT
ejpam-3877	138	1	remark	remark	PROPN
ejpam-3877	138	2	3.2	3.2	NUM
ejpam-3877	138	3	.	.	PUNCT
ejpam-3877	139	1	theorem	theorem	ADJ
ejpam-3877	139	2	3.2	3.2	NUM
ejpam-3877	139	3	improves	improves	AUX
ejpam-3877	139	4	theorem	theorem	VERB
ejpam-3877	139	5	2.4	2.4	NUM
ejpam-3877	139	6	in	in	ADP
ejpam-3877	139	7	[	[	X
ejpam-3877	139	8	23	23	NUM
ejpam-3877	139	9	]	]	PUNCT
ejpam-3877	139	10	.	.	PUNCT
ejpam-3877	140	1	to	to	PART
ejpam-3877	140	2	prove	prove	VERB
ejpam-3877	140	3	the	the	DET
ejpam-3877	140	4	existence	existence	NOUN
ejpam-3877	140	5	of	of	ADP
ejpam-3877	140	6	solutions	solution	NOUN
ejpam-3877	140	7	to	to	ADP
ejpam-3877	140	8	the	the	DET
ejpam-3877	140	9	problem	problem	NOUN
ejpam-3877	140	10	(	(	PUNCT
ejpam-3877	140	11	p	p	NOUN
ejpam-3877	140	12	)	)	PUNCT
ejpam-3877	140	13	,	,	PUNCT
ejpam-3877	140	14	we	we	PRON
ejpam-3877	140	15	will	will	AUX
ejpam-3877	140	16	consider	consider	VERB
ejpam-3877	140	17	the	the	DET
ejpam-3877	140	18	approximating	approximate	VERB
ejpam-3877	140	19	problems	problem	NOUN
ejpam-3877	140	20			PRON
ejpam-3877	140	21	unt	unt	NOUN
ejpam-3877	140	22	=	=	SYM
ejpam-3877	140	23	∆ψn(un	∆ψn(un	PROPN
ejpam-3877	140	24	)	)	PUNCT
ejpam-3877	140	25	+	+	CCONJ
ejpam-3877	140	26	µn	µn	NOUN
ejpam-3877	140	27	in	in	ADP
ejpam-3877	140	28	q	q	NOUN
ejpam-3877	140	29	:	:	PUNCT
ejpam-3877	140	30	=	=	SYM
ejpam-3877	140	31	ω×	ω×	X
ejpam-3877	140	32	(	(	PUNCT
ejpam-3877	140	33	0	0	NUM
ejpam-3877	140	34	,	,	PUNCT
ejpam-3877	140	35	t	t	PROPN
ejpam-3877	140	36	)	)	PUNCT
ejpam-3877	140	37	,	,	PUNCT
ejpam-3877	140	38	un	un	PROPN
ejpam-3877	140	39	=	=	NOUN
ejpam-3877	140	40	0	0	NUM
ejpam-3877	140	41	on	on	ADP
ejpam-3877	140	42	∂ω×	∂ω×	PROPN
ejpam-3877	140	43	(	(	PUNCT
ejpam-3877	140	44	0	0	NUM
ejpam-3877	140	45	,	,	PUNCT
ejpam-3877	140	46	t	t	NOUN
ejpam-3877	140	47	)	)	PUNCT
ejpam-3877	140	48	,	,	PUNCT
ejpam-3877	140	49	u(x	u(x	NOUN
ejpam-3877	140	50	,	,	PUNCT
ejpam-3877	140	51	0	0	NUM
ejpam-3877	140	52	)	)	PUNCT
ejpam-3877	140	53	=	=	SYM
ejpam-3877	140	54	u0n	u0n	PROPN
ejpam-3877	140	55	in	in	ADP
ejpam-3877	140	56	ω	ω	PROPN
ejpam-3877	140	57	,	,	PUNCT
ejpam-3877	140	58	(	(	PUNCT
ejpam-3877	140	59	pn	pn	NOUN
ejpam-3877	140	60	)	)	PUNCT
ejpam-3877	140	61	where	where	SCONJ
ejpam-3877	140	62	{	{	PUNCT
ejpam-3877	140	63	u0n	u0n	NOUN
ejpam-3877	140	64	}	}	PUNCT
ejpam-3877	140	65	⊆	⊆	NUM
ejpam-3877	140	66	c∞0	c∞0	PROPN
ejpam-3877	140	67	(	(	PUNCT
ejpam-3877	140	68	ω	ω	NOUN
ejpam-3877	140	69	)	)	PUNCT
ejpam-3877	140	70	and	and	CCONJ
ejpam-3877	140	71	{	{	PUNCT
ejpam-3877	140	72	µn	µn	PROPN
ejpam-3877	140	73	}	}	PUNCT
ejpam-3877	140	74	⊆	⊆	NUM
ejpam-3877	140	75	c∞c	c∞c	ADJ
ejpam-3877	140	76	(	(	PUNCT
ejpam-3877	140	77	q	q	NOUN
ejpam-3877	140	78	)	)	PUNCT
ejpam-3877	140	79	satisfy	satisfy	PUNCT
ejpam-3877	140	80	u0n	u0n	PROPN
ejpam-3877	140	81	∗	∗	NOUN
ejpam-3877	140	82	⇀	⇀	NOUN
ejpam-3877	140	83	u0	u0	ADJ
ejpam-3877	140	84	in	in	ADP
ejpam-3877	140	85	m+(ω	m+(ω	PROPN
ejpam-3877	140	86	)	)	PUNCT
ejpam-3877	140	87	,	,	PUNCT
ejpam-3877	140	88	u0n	u0n	PROPN
ejpam-3877	140	89	→	→	SYM
ejpam-3877	140	90	u0r	u0r	PROPN
ejpam-3877	140	91	a.e	a.e	PROPN
ejpam-3877	140	92	in	in	ADP
ejpam-3877	140	93	ω	ω	NUM
ejpam-3877	140	94	,	,	PUNCT
ejpam-3877	140	95	‖	‖	PROPN
ejpam-3877	140	96	u0n	u0n	PROPN
ejpam-3877	140	97	‖l1(ω)≤‖	‖l1(ω)≤‖	PROPN
ejpam-3877	140	98	u0	u0	NOUN
ejpam-3877	140	99	‖m+(ω	‖m+(ω	PROPN
ejpam-3877	140	100	)	)	PUNCT
ejpam-3877	140	101	.	.	PUNCT
ejpam-3877	141	1	(	(	PUNCT
ejpam-3877	141	2	3.3	3.3	NUM
ejpam-3877	141	3	)	)	PUNCT
ejpam-3877	141	4	and	and	CCONJ
ejpam-3877	141	5	{	{	PUNCT
ejpam-3877	141	6	µn	µn	NOUN
ejpam-3877	141	7	∗	∗	X
ejpam-3877	141	8	⇀	⇀	X
ejpam-3877	141	9	µ	µ	NOUN
ejpam-3877	141	10	in	in	ADP
ejpam-3877	141	11	m+(q	m+(q	NUM
ejpam-3877	141	12	)	)	PUNCT
ejpam-3877	141	13	,	,	PUNCT
ejpam-3877	141	14	‖	‖	PROPN
ejpam-3877	141	15	µn	µn	PROPN
ejpam-3877	141	16	‖l1(q)≤‖	‖l1(q)≤‖	PROPN
ejpam-3877	141	17	µ	µ	X
ejpam-3877	141	18	‖m+(q	‖m+(q	NOUN
ejpam-3877	141	19	)	)	PUNCT
ejpam-3877	141	20	.	.	PUNCT
ejpam-3877	142	1	(	(	PUNCT
ejpam-3877	142	2	3.4	3.4	NUM
ejpam-3877	142	3	)	)	PUNCT
ejpam-3877	142	4	the	the	DET
ejpam-3877	142	5	approximating	approximate	VERB
ejpam-3877	142	6	function	function	NOUN
ejpam-3877	142	7	ψn	ψn	VERB
ejpam-3877	142	8	is	be	AUX
ejpam-3877	142	9	such	such	ADJ
ejpam-3877	142	10	that	that	PRON
ejpam-3877	142	11	ψn(u	ψn(u	X
ejpam-3877	142	12	)	)	PUNCT
ejpam-3877	142	13	=	=	SYM
ejpam-3877	142	14	ψ(u	ψ(u	PROPN
ejpam-3877	142	15	)	)	PUNCT
ejpam-3877	142	16	+	+	CCONJ
ejpam-3877	142	17	1	1	NUM
ejpam-3877	142	18	n	n	NOUN
ejpam-3877	142	19	(	(	PUNCT
ejpam-3877	142	20	3.5	3.5	NUM
ejpam-3877	142	21	)	)	PUNCT
ejpam-3877	142	22	for	for	ADP
ejpam-3877	142	23	every	every	DET
ejpam-3877	142	24	n	n	PRON
ejpam-3877	142	25	∈	∈	NOUN
ejpam-3877	142	26	n.	n.	NOUN
ejpam-3877	142	27	by	by	ADP
ejpam-3877	142	28	[	[	X
ejpam-3877	142	29	3	3	NUM
ejpam-3877	142	30	,	,	PUNCT
ejpam-3877	142	31	20	20	NUM
ejpam-3877	142	32	]	]	PUNCT
ejpam-3877	142	33	,	,	PUNCT
ejpam-3877	142	34	the	the	DET
ejpam-3877	142	35	approximating	approximate	VERB
ejpam-3877	142	36	problem	problem	NOUN
ejpam-3877	142	37	(	(	PUNCT
ejpam-3877	142	38	pn	pn	NOUN
ejpam-3877	142	39	)	)	PUNCT
ejpam-3877	142	40	has	have	VERB
ejpam-3877	142	41	a	a	DET
ejpam-3877	142	42	solution	solution	NOUN
ejpam-3877	142	43	un	un	PROPN
ejpam-3877	142	44	in	in	ADP
ejpam-3877	142	45	c((0	c((0	PROPN
ejpam-3877	142	46	,	,	PUNCT
ejpam-3877	142	47	t	t	NOUN
ejpam-3877	142	48	)	)	PUNCT
ejpam-3877	142	49	,	,	PUNCT
ejpam-3877	142	50	l1(ω))∩l∞(q	l1(ω))∩l∞(q	PROPN
ejpam-3877	142	51	)	)	PUNCT
ejpam-3877	142	52	.	.	PUNCT
ejpam-3877	143	1	theorem	theorem	VERB
ejpam-3877	143	2	3.3	3.3	NUM
ejpam-3877	143	3	.	.	PUNCT
ejpam-3877	144	1	assume	assume	VERB
ejpam-3877	144	2	that	that	SCONJ
ejpam-3877	144	3	(	(	PUNCT
ejpam-3877	144	4	i	i	NOUN
ejpam-3877	144	5	)	)	PUNCT
ejpam-3877	144	6	,	,	PUNCT
ejpam-3877	144	7	µ	µ	X
ejpam-3877	144	8	∈	∈	NOUN
ejpam-3877	144	9	m+(q	m+(q	NUM
ejpam-3877	144	10	)	)	PUNCT
ejpam-3877	144	11	and	and	CCONJ
ejpam-3877	144	12	u0	u0	PROPN
ejpam-3877	144	13	∈	∈	PROPN
ejpam-3877	144	14	m+(ω	m+(ω	NOUN
ejpam-3877	144	15	)	)	PUNCT
ejpam-3877	144	16	hold	hold	NOUN
ejpam-3877	144	17	.	.	PUNCT
ejpam-3877	145	1	then	then	ADV
ejpam-3877	145	2	there	there	PRON
ejpam-3877	145	3	exists	exist	VERB
ejpam-3877	145	4	a	a	DET
ejpam-3877	145	5	weak	weak	ADJ
ejpam-3877	145	6	solution	solution	NOUN
ejpam-3877	145	7	u	u	NOUN
ejpam-3877	145	8	to	to	ADP
ejpam-3877	145	9	the	the	DET
ejpam-3877	145	10	problem	problem	NOUN
ejpam-3877	145	11	(	(	PUNCT
ejpam-3877	145	12	p	p	NOUN
ejpam-3877	145	13	)	)	PUNCT
ejpam-3877	145	14	obtained	obtain	VERB
ejpam-3877	145	15	as	as	ADP
ejpam-3877	145	16	a	a	DET
ejpam-3877	145	17	limiting	limiting	NOUN
ejpam-3877	145	18	point	point	NOUN
ejpam-3877	145	19	of	of	ADP
ejpam-3877	145	20	the	the	DET
ejpam-3877	145	21	sequence	sequence	NOUN
ejpam-3877	145	22	{	{	PUNCT
ejpam-3877	145	23	un	un	PROPN
ejpam-3877	145	24	}	}	PUNCT
ejpam-3877	145	25	of	of	ADP
ejpam-3877	145	26	solutions	solution	NOUN
ejpam-3877	145	27	to	to	ADP
ejpam-3877	145	28	the	the	DET
ejpam-3877	145	29	problem	problem	NOUN
ejpam-3877	145	30	(	(	PUNCT
ejpam-3877	145	31	pn	pn	NOUN
ejpam-3877	145	32	)	)	PUNCT
ejpam-3877	145	33	such	such	ADJ
ejpam-3877	145	34	that	that	PRON
ejpam-3877	145	35	for	for	ADP
ejpam-3877	145	36	every	every	DET
ejpam-3877	145	37	t	t	NOUN
ejpam-3877	145	38	∈	∈	PROPN
ejpam-3877	145	39	(	(	PUNCT
ejpam-3877	145	40	0	0	NUM
ejpam-3877	145	41	,	,	PUNCT
ejpam-3877	145	42	t	t	PROPN
ejpam-3877	145	43	)	)	PUNCT
ejpam-3877	145	44	\h∗	\h∗	VERB
ejpam-3877	145	45	,	,	PUNCT
ejpam-3877	145	46	there	there	PRON
ejpam-3877	145	47	holds	hold	VERB
ejpam-3877	145	48	‖	‖	PROPN
ejpam-3877	145	49	u	u	PROPN
ejpam-3877	145	50	(	(	PUNCT
ejpam-3877	145	51	·	·	PROPN
ejpam-3877	145	52	,	,	PUNCT
ejpam-3877	145	53	t	t	PROPN
ejpam-3877	145	54	)	)	PUNCT
ejpam-3877	145	55	‖m+(ω)≤	‖m+(ω)≤	X
ejpam-3877	146	1	c	c	PROPN
ejpam-3877	146	2	(	(	PUNCT
ejpam-3877	146	3	‖	‖	PROPN
ejpam-3877	146	4	µ	µ	X
ejpam-3877	146	5	‖m+(q	‖m+(q	NOUN
ejpam-3877	146	6	)	)	PUNCT
ejpam-3877	146	7	+	+	CCONJ
ejpam-3877	146	8	‖	‖	ADJ
ejpam-3877	146	9	u0	u0	ADJ
ejpam-3877	146	10	‖m+(ω	‖m+(ω	PROPN
ejpam-3877	146	11	)	)	PUNCT
ejpam-3877	146	12	)	)	PUNCT
ejpam-3877	146	13	.	.	PUNCT
ejpam-3877	147	1	(	(	PUNCT
ejpam-3877	147	2	3.6	3.6	NUM
ejpam-3877	147	3	)	)	PUNCT
ejpam-3877	147	4	moreover	moreover	ADV
ejpam-3877	147	5	,	,	PUNCT
ejpam-3877	147	6	there	there	PRON
ejpam-3877	147	7	exists	exist	VERB
ejpam-3877	147	8	a	a	DET
ejpam-3877	147	9	radon	radon	ADJ
ejpam-3877	147	10	measure	measure	NOUN
ejpam-3877	147	11	νt	νt	PROPN
ejpam-3877	147	12	∈m+(ω	∈m+(ω	NOUN
ejpam-3877	147	13	)	)	PUNCT
ejpam-3877	147	14	such	such	ADJ
ejpam-3877	147	15	that	that	SCONJ
ejpam-3877	147	16	[	[	X
ejpam-3877	147	17	us	we	PRON
ejpam-3877	147	18	(	(	PUNCT
ejpam-3877	147	19	·	·	PUNCT
ejpam-3877	147	20	,	,	PUNCT
ejpam-3877	147	21	t)]±	t)]±	NOUN
ejpam-3877	147	22	≤	≤	NOUN
ejpam-3877	147	23	[	[	X
ejpam-3877	147	24	u0s	u0s	X
ejpam-3877	147	25	]	]	PUNCT
ejpam-3877	147	26	±	±	NOUN
ejpam-3877	148	1	+	+	CCONJ
ejpam-3877	148	2	[	[	X
ejpam-3877	148	3	νts	νts	NOUN
ejpam-3877	148	4	]	]	X
ejpam-3877	148	5	±	±	NUM
ejpam-3877	148	6	in	in	ADP
ejpam-3877	148	7	m+(ω	m+(ω	NOUN
ejpam-3877	148	8	)	)	PUNCT
ejpam-3877	148	9	(	(	PUNCT
ejpam-3877	148	10	3.7	3.7	NUM
ejpam-3877	148	11	)	)	PUNCT
ejpam-3877	148	12	where	where	SCONJ
ejpam-3877	148	13	c	c	NOUN
ejpam-3877	148	14	is	be	AUX
ejpam-3877	148	15	positive	positive	ADJ
ejpam-3877	148	16	constant	constant	ADJ
ejpam-3877	148	17	and	and	CCONJ
ejpam-3877	148	18	h∗	h∗	PROPN
ejpam-3877	148	19	a	a	DET
ejpam-3877	148	20	zero	zero	NUM
ejpam-3877	148	21	lebesgue	lebesgue	NOUN
ejpam-3877	148	22	measure	measure	NOUN
ejpam-3877	148	23	set	set	VERB
ejpam-3877	148	24	.	.	PUNCT
ejpam-3877	149	1	to	to	PART
ejpam-3877	149	2	get	get	VERB
ejpam-3877	149	3	the	the	DET
ejpam-3877	149	4	uniqueness	uniqueness	NOUN
ejpam-3877	149	5	of	of	ADP
ejpam-3877	149	6	the	the	DET
ejpam-3877	149	7	solution	solution	NOUN
ejpam-3877	149	8	to	to	ADP
ejpam-3877	149	9	the	the	DET
ejpam-3877	149	10	problem	problem	NOUN
ejpam-3877	149	11	(	(	PUNCT
ejpam-3877	149	12	p	p	NOUN
ejpam-3877	149	13	)	)	PUNCT
ejpam-3877	149	14	,	,	PUNCT
ejpam-3877	149	15	we	we	PRON
ejpam-3877	149	16	define	define	VERB
ejpam-3877	149	17	the	the	DET
ejpam-3877	149	18	notion	notion	NOUN
ejpam-3877	149	19	of	of	ADP
ejpam-3877	149	20	very	very	ADJ
ejpam-3877	149	21	quincy	quincy	PROPN
ejpam-3877	149	22	s.	s.	PROPN
ejpam-3877	149	23	nkombo	nkombo	PROPN
ejpam-3877	149	24	,	,	PUNCT
ejpam-3877	149	25	fengquan	fengquan	PROPN
ejpam-3877	149	26	li	li	PROPN
ejpam-3877	149	27	/	/	SYM
ejpam-3877	149	28	eur	eur	PROPN
ejpam-3877	149	29	.	.	PUNCT
ejpam-3877	150	1	j.	j.	PROPN
ejpam-3877	150	2	pure	pure	PROPN
ejpam-3877	150	3	appl	appl	PROPN
ejpam-3877	150	4	.	.	PROPN
ejpam-3877	150	5	math	math	PROPN
ejpam-3877	150	6	,	,	PUNCT
ejpam-3877	150	7	14	14	NUM
ejpam-3877	150	8	(	(	PUNCT
ejpam-3877	150	9	1	1	NUM
ejpam-3877	150	10	)	)	PUNCT
ejpam-3877	150	11	(	(	PUNCT
ejpam-3877	150	12	2021	2021	NUM
ejpam-3877	150	13	)	)	PUNCT
ejpam-3877	150	14	,	,	PUNCT
ejpam-3877	150	15	204	204	NUM
ejpam-3877	150	16	-	-	SYM
ejpam-3877	150	17	233	233	NUM
ejpam-3877	150	18	212	212	NUM
ejpam-3877	150	19	weak	weak	ADJ
ejpam-3877	150	20	solutions	solution	NOUN
ejpam-3877	150	21	as	as	SCONJ
ejpam-3877	150	22	follows	follow	VERB
ejpam-3877	150	23	.	.	PUNCT
ejpam-3877	151	1	definition	definition	NOUN
ejpam-3877	151	2	3.2	3.2	NUM
ejpam-3877	151	3	.	.	PUNCT
ejpam-3877	152	1	for	for	ADP
ejpam-3877	152	2	any	any	DET
ejpam-3877	152	3	µ	µ	PROPN
ejpam-3877	152	4	∈	∈	NOUN
ejpam-3877	152	5	m+	m+	NUM
ejpam-3877	152	6	d,2(q	d,2(q	NOUN
ejpam-3877	152	7	)	)	PUNCT
ejpam-3877	152	8	and	and	CCONJ
ejpam-3877	152	9	u0	u0	PROPN
ejpam-3877	152	10	∈	∈	PROPN
ejpam-3877	152	11	m+	m+	NUM
ejpam-3877	152	12	d,2(ω	d,2(ω	PROPN
ejpam-3877	152	13	)	)	PUNCT
ejpam-3877	152	14	,	,	PUNCT
ejpam-3877	152	15	a	a	DET
ejpam-3877	152	16	measure	measure	NOUN
ejpam-3877	152	17	u	u	NOUN
ejpam-3877	152	18	is	be	AUX
ejpam-3877	152	19	called	call	VERB
ejpam-3877	152	20	a	a	DET
ejpam-3877	152	21	very	very	ADV
ejpam-3877	152	22	weak	weak	ADJ
ejpam-3877	152	23	solution	solution	NOUN
ejpam-3877	152	24	to	to	ADP
ejpam-3877	152	25	the	the	DET
ejpam-3877	152	26	problem	problem	NOUN
ejpam-3877	152	27	(	(	PUNCT
ejpam-3877	152	28	p	p	NOUN
ejpam-3877	152	29	)	)	PUNCT
ejpam-3877	152	30	if	if	SCONJ
ejpam-3877	152	31	u	u	PROPN
ejpam-3877	152	32	∈	∈	PROPN
ejpam-3877	152	33	l∞((0	l∞((0	PROPN
ejpam-3877	152	34	,	,	PUNCT
ejpam-3877	152	35	t	t	PROPN
ejpam-3877	152	36	)	)	PUNCT
ejpam-3877	152	37	,	,	PUNCT
ejpam-3877	152	38	m+(ω	m+(ω	NOUN
ejpam-3877	152	39	)	)	PUNCT
ejpam-3877	152	40	)	)	PUNCT
ejpam-3877	153	1	such	such	ADJ
ejpam-3877	153	2	that∫	that∫	NOUN
ejpam-3877	153	3	t	t	NOUN
ejpam-3877	153	4	0	0	PUNCT
ejpam-3877	154	1	〈	〈	PROPN
ejpam-3877	154	2	u	u	PROPN
ejpam-3877	154	3	(	(	PUNCT
ejpam-3877	154	4	·	·	PROPN
ejpam-3877	154	5	,	,	PUNCT
ejpam-3877	154	6	t	t	PROPN
ejpam-3877	154	7	)	)	PUNCT
ejpam-3877	154	8	,	,	PUNCT
ejpam-3877	154	9	ξt	ξt	X
ejpam-3877	154	10	(	(	PUNCT
ejpam-3877	154	11	·	·	PUNCT
ejpam-3877	154	12	,	,	PUNCT
ejpam-3877	154	13	t)〉ωdt	t)〉ωdt	NUM
ejpam-3877	154	14	=	=	PUNCT
ejpam-3877	154	15	−	−	PROPN
ejpam-3877	154	16	∫	∫	PROPN
ejpam-3877	154	17	q	q	PROPN
ejpam-3877	154	18	ψ(ur)∆ξdxdt−	ψ(ur)∆ξdxdt−	NUM
ejpam-3877	154	19	∫	∫	PROPN
ejpam-3877	154	20	q	q	PROPN
ejpam-3877	154	21	ξdµ−	ξdµ−	PROPN
ejpam-3877	154	22	〈	〈	PROPN
ejpam-3877	154	23	u0	u0	PROPN
ejpam-3877	154	24	,	,	PUNCT
ejpam-3877	154	25	ξ(0)〉ω	ξ(0)〉ω	NOUN
ejpam-3877	154	26	(	(	PUNCT
ejpam-3877	154	27	3.8	3.8	NUM
ejpam-3877	154	28	)	)	PUNCT
ejpam-3877	154	29	for	for	ADP
ejpam-3877	154	30	every	every	DET
ejpam-3877	154	31	ξ	ξ	PROPN
ejpam-3877	154	32	∈	∈	PROPN
ejpam-3877	154	33	c2,1(q	c2,1(q	PROPN
ejpam-3877	154	34	)	)	PUNCT
ejpam-3877	154	35	,	,	PUNCT
ejpam-3877	154	36	which	which	PRON
ejpam-3877	154	37	vanishes	vanish	VERB
ejpam-3877	154	38	on	on	ADP
ejpam-3877	154	39	∂ω×	∂ω×	PROPN
ejpam-3877	155	1	[	[	X
ejpam-3877	155	2	0	0	NUM
ejpam-3877	155	3	,	,	PUNCT
ejpam-3877	155	4	t	t	X
ejpam-3877	155	5	]	]	PUNCT
ejpam-3877	155	6	,	,	PUNCT
ejpam-3877	155	7	for	for	ADP
ejpam-3877	155	8	t	t	PROPN
ejpam-3877	155	9	=	=	SYM
ejpam-3877	155	10	t	t	PROPN
ejpam-3877	155	11	.	.	PUNCT
ejpam-3877	156	1	the	the	DET
ejpam-3877	156	2	notion	notion	NOUN
ejpam-3877	156	3	of	of	ADP
ejpam-3877	156	4	very	very	ADV
ejpam-3877	156	5	weak	weak	ADJ
ejpam-3877	156	6	solutions	solution	NOUN
ejpam-3877	156	7	adapted	adapt	VERB
ejpam-3877	156	8	to	to	ADP
ejpam-3877	156	9	our	our	PRON
ejpam-3877	156	10	study	study	NOUN
ejpam-3877	156	11	can	can	AUX
ejpam-3877	156	12	be	be	AUX
ejpam-3877	156	13	found	find	VERB
ejpam-3877	156	14	in	in	ADP
ejpam-3877	156	15	[	[	X
ejpam-3877	156	16	18	18	NUM
ejpam-3877	156	17	,	,	PUNCT
ejpam-3877	156	18	33	33	NUM
ejpam-3877	156	19	]	]	PUNCT
ejpam-3877	156	20	.	.	PUNCT
ejpam-3877	157	1	definition	definition	NOUN
ejpam-3877	157	2	3.3	3.3	NUM
ejpam-3877	157	3	.	.	PUNCT
ejpam-3877	158	1	let	let	VERB
ejpam-3877	158	2	u0	u0	PROPN
ejpam-3877	158	3	∈m+	∈m+	PROPN
ejpam-3877	158	4	d,2(ω	d,2(ω	PROPN
ejpam-3877	158	5	)	)	PUNCT
ejpam-3877	158	6	and	and	CCONJ
ejpam-3877	158	7	µ	µ	DET
ejpam-3877	158	8	∈m+	∈m+	PROPN
ejpam-3877	158	9	d,2(q	d,2(q	NOUN
ejpam-3877	158	10	)	)	PUNCT
ejpam-3877	158	11	such	such	ADJ
ejpam-3877	158	12	that	that	DET
ejpam-3877	158	13	u0	u0	ADJ
ejpam-3877	158	14	=	=	PROPN
ejpam-3877	158	15	f0	f0	PROPN
ejpam-3877	158	16	−	−	PROPN
ejpam-3877	158	17	divg0	divg0	NOUN
ejpam-3877	158	18	,	,	PUNCT
ejpam-3877	158	19	f0	f0	PROPN
ejpam-3877	158	20	∈	∈	PROPN
ejpam-3877	158	21	l1(ω	l1(ω	PROPN
ejpam-3877	158	22	)	)	PUNCT
ejpam-3877	158	23	and	and	CCONJ
ejpam-3877	158	24	g0	g0	PROPN
ejpam-3877	158	25	∈	∈	PROPN
ejpam-3877	158	26	[	[	PUNCT
ejpam-3877	158	27	l2(ω	l2(ω	NOUN
ejpam-3877	158	28	)	)	PUNCT
ejpam-3877	158	29	]	]	X
ejpam-3877	159	1	n	n	X
ejpam-3877	159	2	.	.	PUNCT
ejpam-3877	160	1	µ	µ	X
ejpam-3877	160	2	=	=	SYM
ejpam-3877	160	3	f	f	X
ejpam-3877	160	4	−	−	NOUN
ejpam-3877	160	5	divg+	divg+	VERB
ejpam-3877	161	1	gt	gt	PROPN
ejpam-3877	161	2	,	,	PUNCT
ejpam-3877	161	3	f	f	PROPN
ejpam-3877	161	4	∈	∈	PROPN
ejpam-3877	161	5	l1(q	l1(q	CCONJ
ejpam-3877	161	6	)	)	PUNCT
ejpam-3877	161	7	,	,	PUNCT
ejpam-3877	161	8	g	g	PROPN
ejpam-3877	161	9	∈	∈	PROPN
ejpam-3877	161	10	[	[	PUNCT
ejpam-3877	161	11	l2(q	l2(q	PROPN
ejpam-3877	161	12	)	)	PUNCT
ejpam-3877	161	13	]	]	PUNCT
ejpam-3877	161	14	n	n	CCONJ
ejpam-3877	161	15	and	and	CCONJ
ejpam-3877	161	16	g	g	PROPN
ejpam-3877	161	17	∈	∈	PROPN
ejpam-3877	161	18	l2((0	l2((0	PROPN
ejpam-3877	161	19	,	,	PUNCT
ejpam-3877	161	20	t	t	PROPN
ejpam-3877	161	21	)	)	PUNCT
ejpam-3877	161	22	,	,	PUNCT
ejpam-3877	161	23	h1	h1	PROPN
ejpam-3877	161	24	0	0	NUM
ejpam-3877	161	25	(	(	PUNCT
ejpam-3877	161	26	ω	ω	NOUN
ejpam-3877	161	27	)	)	PUNCT
ejpam-3877	161	28	)	)	PUNCT
ejpam-3877	161	29	.	.	PUNCT
ejpam-3877	162	1	a	a	DET
ejpam-3877	162	2	measure	measure	NOUN
ejpam-3877	162	3	u	u	NOUN
ejpam-3877	162	4	is	be	AUX
ejpam-3877	162	5	called	call	VERB
ejpam-3877	162	6	very	very	ADV
ejpam-3877	162	7	weak	weak	ADJ
ejpam-3877	162	8	solutions	solution	NOUN
ejpam-3877	162	9	obtained	obtain	VERB
ejpam-3877	162	10	as	as	ADP
ejpam-3877	162	11	limit	limit	NOUN
ejpam-3877	162	12	of	of	ADP
ejpam-3877	162	13	approximation	approximation	NOUN
ejpam-3877	162	14	,	,	PUNCT
ejpam-3877	162	15	if	if	SCONJ
ejpam-3877	162	16	un	un	PROPN
ejpam-3877	162	17	∗	∗	NOUN
ejpam-3877	162	18	⇀	⇀	PUNCT
ejpam-3877	162	19	u	u	NOUN
ejpam-3877	162	20	in	in	ADP
ejpam-3877	162	21	m+(q	m+(q	PROPN
ejpam-3877	162	22	)	)	PUNCT
ejpam-3877	162	23	(	(	PUNCT
ejpam-3877	162	24	3.9	3.9	NUM
ejpam-3877	162	25	)	)	PUNCT
ejpam-3877	162	26	where	where	SCONJ
ejpam-3877	162	27	{	{	PUNCT
ejpam-3877	162	28	un	un	PROPN
ejpam-3877	162	29	}	}	PUNCT
ejpam-3877	162	30	⊆	⊆	NUM
ejpam-3877	162	31	l∞(q	l∞(q	NOUN
ejpam-3877	162	32	)	)	PUNCT
ejpam-3877	162	33	∩	∩	ADJ
ejpam-3877	162	34	l2((0	l2((0	PROPN
ejpam-3877	162	35	,	,	PUNCT
ejpam-3877	162	36	t	t	PROPN
ejpam-3877	162	37	)	)	PUNCT
ejpam-3877	162	38	,	,	PUNCT
ejpam-3877	162	39	h1	h1	PROPN
ejpam-3877	162	40	0	0	NUM
ejpam-3877	162	41	(	(	PUNCT
ejpam-3877	162	42	ω	ω	NOUN
ejpam-3877	162	43	)	)	PUNCT
ejpam-3877	162	44	)	)	PUNCT
ejpam-3877	162	45	is	be	AUX
ejpam-3877	162	46	a	a	DET
ejpam-3877	162	47	sequence	sequence	NOUN
ejpam-3877	162	48	of	of	ADP
ejpam-3877	162	49	weak	weak	ADJ
ejpam-3877	162	50	solutions	solution	NOUN
ejpam-3877	162	51	to	to	ADP
ejpam-3877	162	52	the	the	DET
ejpam-3877	162	53	problem	problem	NOUN
ejpam-3877	162	54	(	(	PUNCT
ejpam-3877	162	55	pn	pn	NOUN
ejpam-3877	162	56	)	)	PUNCT
ejpam-3877	162	57	and	and	CCONJ
ejpam-3877	162	58	satisfy	satisfy	VERB
ejpam-3877	162	59			NUM
ejpam-3877	162	60	µn	µn	PROPN
ejpam-3877	163	1	=	=	PUNCT
ejpam-3877	164	1	fn	fn	NOUN
ejpam-3877	165	1	−	−	PROPN
ejpam-3877	165	2	fn	fn	NOUN
ejpam-3877	166	1	+	+	CCONJ
ejpam-3877	166	2	gnt	gnt	PROPN
ejpam-3877	166	3	∈	∈	PROPN
ejpam-3877	166	4	c∞0	c∞0	PROPN
ejpam-3877	166	5	(	(	PUNCT
ejpam-3877	166	6	q	q	NOUN
ejpam-3877	166	7	)	)	PUNCT
ejpam-3877	166	8	,	,	PUNCT
ejpam-3877	166	9	u0n	u0n	PROPN
ejpam-3877	166	10	=	=	SYM
ejpam-3877	166	11	f0n	f0n	PROPN
ejpam-3877	166	12	−	−	PROPN
ejpam-3877	166	13	f0n	f0n	PROPN
ejpam-3877	166	14	∈	∈	PROPN
ejpam-3877	166	15	c∞0	c∞0	PROPN
ejpam-3877	166	16	(	(	PUNCT
ejpam-3877	166	17	ω	ω	PROPN
ejpam-3877	166	18	)	)	PUNCT
ejpam-3877	166	19	,	,	PUNCT
ejpam-3877	166	20	fn	fn	PROPN
ejpam-3877	166	21	→	→	SYM
ejpam-3877	166	22	f	f	PROPN
ejpam-3877	166	23	in	in	ADP
ejpam-3877	166	24	l1(q	l1(q	CCONJ
ejpam-3877	166	25	)	)	PUNCT
ejpam-3877	166	26	,	,	PUNCT
ejpam-3877	166	27	fn	fn	NOUN
ejpam-3877	166	28	→	→	SYM
ejpam-3877	166	29	divg	divg	NOUN
ejpam-3877	166	30	in	in	ADP
ejpam-3877	166	31	l2((0	l2((0	PROPN
ejpam-3877	166	32	,	,	PUNCT
ejpam-3877	166	33	t	t	PROPN
ejpam-3877	166	34	)	)	PUNCT
ejpam-3877	166	35	,	,	PUNCT
ejpam-3877	166	36	h−1(ω	h−1(ω	PROPN
ejpam-3877	166	37	)	)	PUNCT
ejpam-3877	166	38	)	)	PUNCT
ejpam-3877	166	39	,	,	PUNCT
ejpam-3877	166	40	gn	gn	PROPN
ejpam-3877	166	41	→	→	SYM
ejpam-3877	166	42	g	g	PROPN
ejpam-3877	166	43	in	in	ADP
ejpam-3877	166	44	l2((0	l2((0	PROPN
ejpam-3877	166	45	,	,	PUNCT
ejpam-3877	166	46	t	t	PROPN
ejpam-3877	166	47	)	)	PUNCT
ejpam-3877	166	48	,	,	PUNCT
ejpam-3877	166	49	h1	h1	PROPN
ejpam-3877	166	50	0	0	NUM
ejpam-3877	166	51	(	(	PUNCT
ejpam-3877	166	52	ω	ω	NOUN
ejpam-3877	166	53	)	)	PUNCT
ejpam-3877	166	54	)	)	PUNCT
ejpam-3877	166	55	,	,	PUNCT
ejpam-3877	166	56	f0n	f0n	VERB
ejpam-3877	166	57	→	→	SYM
ejpam-3877	166	58	divg0	divg0	X
ejpam-3877	166	59	in	in	ADP
ejpam-3877	166	60	h−1(ω	h−1(ω	PROPN
ejpam-3877	166	61	)	)	PUNCT
ejpam-3877	166	62	,	,	PUNCT
ejpam-3877	166	63	f0n	f0n	VERB
ejpam-3877	166	64	→	→	SYM
ejpam-3877	166	65	f0	f0	PROPN
ejpam-3877	166	66	in	in	ADP
ejpam-3877	166	67	l1(ω	l1(ω	PROPN
ejpam-3877	166	68	)	)	PUNCT
ejpam-3877	166	69	.	.	PUNCT
ejpam-3877	167	1	(	(	PUNCT
ejpam-3877	167	2	3.10	3.10	NUM
ejpam-3877	167	3	)	)	PUNCT
ejpam-3877	167	4	notice	notice	VERB
ejpam-3877	167	5	that	that	SCONJ
ejpam-3877	167	6	µn	µn	NOUN
ejpam-3877	167	7	∗	∗	NOUN
ejpam-3877	167	8	⇀	⇀	X
ejpam-3877	167	9	µ	µ	NOUN
ejpam-3877	167	10	in	in	ADP
ejpam-3877	167	11	m+(q	m+(q	NUM
ejpam-3877	167	12	)	)	PUNCT
ejpam-3877	167	13	and	and	CCONJ
ejpam-3877	167	14	u0n	u0n	PROPN
ejpam-3877	167	15	∗	∗	NOUN
ejpam-3877	167	16	⇀	⇀	NOUN
ejpam-3877	167	17	u0	u0	ADJ
ejpam-3877	167	18	in	in	ADP
ejpam-3877	167	19	m+(ω	m+(ω	PROPN
ejpam-3877	167	20	)	)	PUNCT
ejpam-3877	167	21	.	.	PUNCT
ejpam-3877	168	1	theorem	theorem	VERB
ejpam-3877	168	2	3.4	3.4	NUM
ejpam-3877	168	3	.	.	PUNCT
ejpam-3877	169	1	under	under	ADP
ejpam-3877	169	2	assumptions	assumption	NOUN
ejpam-3877	169	3	of	of	ADP
ejpam-3877	169	4	(	(	PUNCT
ejpam-3877	169	5	i	i	NOUN
ejpam-3877	169	6	)	)	PUNCT
ejpam-3877	169	7	and	and	CCONJ
ejpam-3877	169	8	(	(	PUNCT
ejpam-3877	169	9	j	j	NOUN
ejpam-3877	169	10	)	)	PUNCT
ejpam-3877	169	11	,	,	PUNCT
ejpam-3877	169	12	then	then	ADV
ejpam-3877	169	13	for	for	ADP
ejpam-3877	169	14	every	every	DET
ejpam-3877	169	15	µ	µ	PROPN
ejpam-3877	169	16	∈	∈	NOUN
ejpam-3877	169	17	m+	m+	NUM
ejpam-3877	169	18	d,2(q	d,2(q	NOUN
ejpam-3877	169	19	)	)	PUNCT
ejpam-3877	169	20	and	and	CCONJ
ejpam-3877	169	21	u0	u0	PROPN
ejpam-3877	169	22	∈	∈	PROPN
ejpam-3877	169	23	m+	m+	NUM
ejpam-3877	169	24	d,2(ω	d,2(ω	ADV
ejpam-3877	169	25	)	)	PUNCT
ejpam-3877	169	26	,	,	PUNCT
ejpam-3877	169	27	there	there	PRON
ejpam-3877	169	28	exists	exist	VERB
ejpam-3877	169	29	a	a	DET
ejpam-3877	169	30	unique	unique	ADJ
ejpam-3877	169	31	very	very	ADV
ejpam-3877	169	32	weak	weak	ADJ
ejpam-3877	169	33	solution	solution	NOUN
ejpam-3877	169	34	obtained	obtain	VERB
ejpam-3877	169	35	as	as	ADP
ejpam-3877	169	36	limit	limit	NOUN
ejpam-3877	169	37	of	of	ADP
ejpam-3877	169	38	approximation	approximation	NOUN
ejpam-3877	169	39	u	u	NOUN
ejpam-3877	169	40	of	of	ADP
ejpam-3877	169	41	the	the	DET
ejpam-3877	169	42	problem	problem	NOUN
ejpam-3877	169	43	(	(	PUNCT
ejpam-3877	169	44	p	p	NOUN
ejpam-3877	169	45	)	)	PUNCT
ejpam-3877	169	46	.	.	PUNCT
ejpam-3877	170	1	notice	notice	VERB
ejpam-3877	170	2	that	that	SCONJ
ejpam-3877	170	3	a	a	DET
ejpam-3877	170	4	very	very	ADV
ejpam-3877	170	5	weak	weak	ADJ
ejpam-3877	170	6	solution	solution	NOUN
ejpam-3877	170	7	is	be	AUX
ejpam-3877	170	8	also	also	ADV
ejpam-3877	170	9	weak	weak	ADJ
ejpam-3877	170	10	solution	solution	NOUN
ejpam-3877	170	11	to	to	ADP
ejpam-3877	170	12	the	the	DET
ejpam-3877	170	13	problem	problem	NOUN
ejpam-3877	170	14	(	(	PUNCT
ejpam-3877	170	15	p	p	NOUN
ejpam-3877	170	16	)	)	PUNCT
ejpam-3877	170	17	,	,	PUNCT
ejpam-3877	170	18	therefore	therefore	ADV
ejpam-3877	170	19	the	the	DET
ejpam-3877	170	20	problem	problem	NOUN
ejpam-3877	170	21	(	(	PUNCT
ejpam-3877	170	22	p	p	NOUN
ejpam-3877	170	23	)	)	PUNCT
ejpam-3877	170	24	possesses	possess	VERB
ejpam-3877	170	25	a	a	DET
ejpam-3877	170	26	unique	unique	ADJ
ejpam-3877	170	27	weak	weak	ADJ
ejpam-3877	170	28	solution	solution	NOUN
ejpam-3877	170	29	obtained	obtain	VERB
ejpam-3877	170	30	as	as	ADP
ejpam-3877	170	31	limit	limit	NOUN
ejpam-3877	170	32	of	of	ADP
ejpam-3877	170	33	approximation	approximation	NOUN
ejpam-3877	170	34	.	.	PUNCT
ejpam-3877	171	1	4	4	X
ejpam-3877	171	2	.	.	X
ejpam-3877	171	3	approximating	approximate	VERB
ejpam-3877	171	4	problems	problem	NOUN
ejpam-3877	171	5	and	and	CCONJ
ejpam-3877	171	6	the	the	DET
ejpam-3877	171	7	persistence	persistence	NOUN
ejpam-3877	171	8	now	now	ADV
ejpam-3877	171	9	we	we	PRON
ejpam-3877	171	10	establish	establish	VERB
ejpam-3877	171	11	some	some	DET
ejpam-3877	171	12	technical	technical	ADJ
ejpam-3877	171	13	statements	statement	NOUN
ejpam-3877	171	14	which	which	PRON
ejpam-3877	171	15	will	will	AUX
ejpam-3877	171	16	be	be	AUX
ejpam-3877	171	17	used	use	VERB
ejpam-3877	171	18	in	in	ADP
ejpam-3877	171	19	the	the	DET
ejpam-3877	171	20	proof	proof	NOUN
ejpam-3877	171	21	of	of	ADP
ejpam-3877	171	22	the	the	DET
ejpam-3877	171	23	existence	existence	NOUN
ejpam-3877	171	24	solution	solution	NOUN
ejpam-3877	171	25	.	.	PUNCT
ejpam-3877	172	1	lemma	lemma	PROPN
ejpam-3877	172	2	4.1	4.1	NUM
ejpam-3877	172	3	.	.	PUNCT
ejpam-3877	172	4	assume	assume	VERB
ejpam-3877	172	5	that	that	SCONJ
ejpam-3877	172	6	(	(	PUNCT
ejpam-3877	172	7	i	i	NOUN
ejpam-3877	172	8	)	)	PUNCT
ejpam-3877	172	9	and	and	CCONJ
ejpam-3877	172	10	(	(	PUNCT
ejpam-3877	172	11	j	j	NOUN
ejpam-3877	172	12	)	)	PUNCT
ejpam-3877	172	13	are	be	AUX
ejpam-3877	172	14	satisfied	satisfied	ADJ
ejpam-3877	172	15	and	and	CCONJ
ejpam-3877	172	16	un	un	PROPN
ejpam-3877	172	17	is	be	AUX
ejpam-3877	172	18	the	the	DET
ejpam-3877	172	19	solution	solution	NOUN
ejpam-3877	172	20	of	of	ADP
ejpam-3877	172	21	the	the	DET
ejpam-3877	172	22	approximation	approximation	NOUN
ejpam-3877	172	23	problem	problem	NOUN
ejpam-3877	172	24	(	(	PUNCT
ejpam-3877	172	25	pn	pn	NOUN
ejpam-3877	172	26	)	)	PUNCT
ejpam-3877	172	27	.	.	PUNCT
ejpam-3877	173	1	then	then	ADV
ejpam-3877	173	2	there	there	PRON
ejpam-3877	173	3	exists	exist	VERB
ejpam-3877	173	4	a	a	DET
ejpam-3877	173	5	zero	zero	NUM
ejpam-3877	173	6	lebesgue	lebesgue	NOUN
ejpam-3877	173	7	measure	measure	NOUN
ejpam-3877	173	8	set	set	VERB
ejpam-3877	173	9	f	f	PROPN
ejpam-3877	173	10	∗	∗	X
ejpam-3877	173	11	⊂	⊂	PROPN
ejpam-3877	173	12	(	(	PUNCT
ejpam-3877	173	13	0	0	NUM
ejpam-3877	173	14	,	,	PUNCT
ejpam-3877	173	15	t	t	NOUN
ejpam-3877	173	16	)	)	PUNCT
ejpam-3877	173	17	such	such	ADJ
ejpam-3877	173	18	that	that	PRON
ejpam-3877	173	19	‖	‖	PROPN
ejpam-3877	173	20	un	un	PROPN
ejpam-3877	173	21	(	(	PUNCT
ejpam-3877	173	22	·	·	PUNCT
ejpam-3877	173	23	,	,	PUNCT
ejpam-3877	173	24	t	t	PROPN
ejpam-3877	173	25	)	)	PUNCT
ejpam-3877	173	26	‖l1(ω)≤‖	‖l1(ω)≤‖	PROPN
ejpam-3877	173	27	u0	u0	ADJ
ejpam-3877	173	28	‖m+(ω	‖m+(ω	PROPN
ejpam-3877	173	29	)	)	PUNCT
ejpam-3877	173	30	)	)	PUNCT
ejpam-3877	174	1	+	+	CCONJ
ejpam-3877	174	2	‖	‖	PROPN
ejpam-3877	174	3	µ	µ	X
ejpam-3877	174	4	‖m+(q	‖m+(q	NOUN
ejpam-3877	174	5	)	)	PUNCT
ejpam-3877	174	6	(	(	PUNCT
ejpam-3877	174	7	4.1	4.1	NUM
ejpam-3877	174	8	)	)	PUNCT
ejpam-3877	174	9	quincy	quincy	PROPN
ejpam-3877	174	10	s.	s.	PROPN
ejpam-3877	174	11	nkombo	nkombo	PROPN
ejpam-3877	174	12	,	,	PUNCT
ejpam-3877	174	13	fengquan	fengquan	PROPN
ejpam-3877	174	14	li	li	PROPN
ejpam-3877	174	15	/	/	SYM
ejpam-3877	174	16	eur	eur	PROPN
ejpam-3877	174	17	.	.	PUNCT
ejpam-3877	175	1	j.	j.	PROPN
ejpam-3877	175	2	pure	pure	PROPN
ejpam-3877	175	3	appl	appl	PROPN
ejpam-3877	175	4	.	.	PROPN
ejpam-3877	175	5	math	math	PROPN
ejpam-3877	175	6	,	,	PUNCT
ejpam-3877	175	7	14	14	NUM
ejpam-3877	175	8	(	(	PUNCT
ejpam-3877	175	9	1	1	NUM
ejpam-3877	175	10	)	)	PUNCT
ejpam-3877	175	11	(	(	PUNCT
ejpam-3877	175	12	2021	2021	NUM
ejpam-3877	175	13	)	)	PUNCT
ejpam-3877	175	14	,	,	PUNCT
ejpam-3877	175	15	204	204	NUM
ejpam-3877	175	16	-	-	SYM
ejpam-3877	175	17	233	233	NUM
ejpam-3877	175	18	213	213	NUM
ejpam-3877	175	19	for	for	ADP
ejpam-3877	175	20	every	every	DET
ejpam-3877	175	21	t	t	NOUN
ejpam-3877	175	22	∈	∈	PROPN
ejpam-3877	175	23	(	(	PUNCT
ejpam-3877	175	24	0	0	NUM
ejpam-3877	175	25	,	,	PUNCT
ejpam-3877	175	26	t	t	NOUN
ejpam-3877	175	27	)	)	PUNCT
ejpam-3877	175	28	\	\	PROPN
ejpam-3877	176	1	f	f	PROPN
ejpam-3877	176	2	∗	∗	NOUN
ejpam-3877	176	3	and	and	CCONJ
ejpam-3877	176	4	n	n	CCONJ
ejpam-3877	176	5	∈	∈	PROPN
ejpam-3877	176	6	n.	n.	NOUN
ejpam-3877	176	7	proof	proof	NOUN
ejpam-3877	176	8	.	.	PUNCT
ejpam-3877	177	1	assuming	assume	VERB
ejpam-3877	177	2	that	that	SCONJ
ejpam-3877	177	3	any	any	DET
ejpam-3877	177	4	sequence	sequence	NOUN
ejpam-3877	177	5	{	{	PUNCT
ejpam-3877	177	6	ωj	ωj	ADP
ejpam-3877	177	7	}	}	PUNCT
ejpam-3877	177	8	of	of	ADP
ejpam-3877	177	9	smooth	smooth	ADJ
ejpam-3877	177	10	open	open	ADJ
ejpam-3877	177	11	sets	set	NOUN
ejpam-3877	177	12	such	such	ADJ
ejpam-3877	177	13	that	that	PRON
ejpam-3877	177	14	ωj	ωj	ADP
ejpam-3877	177	15	⊂	⊂	PRON
ejpam-3877	177	16	ωj+1	ωj+1	PUNCT
ejpam-3877	177	17	⊂	⊂	X
ejpam-3877	177	18	ωj+1	ωj+1	PROPN
ejpam-3877	177	19	⊂	⊂	PROPN
ejpam-3877	177	20	ω	ω	PROPN
ejpam-3877	177	21	,	,	PUNCT
ejpam-3877	177	22	ω	ω	PROPN
ejpam-3877	177	23	=	=	SYM
ejpam-3877	177	24	∞⋃	∞⋃	PROPN
ejpam-3877	177	25	j=1	j=1	PROPN
ejpam-3877	177	26	ωj	ωj	ADP
ejpam-3877	177	27	,	,	PUNCT
ejpam-3877	177	28	dist(ωj	dist(ωj	PROPN
ejpam-3877	177	29	,	,	PUNCT
ejpam-3877	177	30	∂ω	∂ω	ADJ
ejpam-3877	177	31	)	)	PUNCT
ejpam-3877	177	32	≤	≤	NUM
ejpam-3877	177	33	1	1	NUM
ejpam-3877	177	34	j	j	NOUN
ejpam-3877	177	35	.	.	PUNCT
ejpam-3877	178	1	let	let	VERB
ejpam-3877	178	2	{	{	PUNCT
ejpam-3877	178	3	ρj	ρj	NOUN
ejpam-3877	178	4	}	}	PUNCT
ejpam-3877	178	5	⊆	⊆	NUM
ejpam-3877	178	6	c∞c	c∞c	ADJ
ejpam-3877	178	7	(	(	PUNCT
ejpam-3877	178	8	ω	ω	NOUN
ejpam-3877	178	9	)	)	PUNCT
ejpam-3877	178	10	be	be	VERB
ejpam-3877	178	11	any	any	DET
ejpam-3877	178	12	function	function	NOUN
ejpam-3877	178	13	such	such	ADJ
ejpam-3877	178	14	that	that	SCONJ
ejpam-3877	178	15	0	0	NUM
ejpam-3877	178	16	≤	≤	NUM
ejpam-3877	178	17	ρj	ρj	NOUN
ejpam-3877	178	18	≤	≤	NUM
ejpam-3877	178	19	1	1	NUM
ejpam-3877	178	20	in	in	ADP
ejpam-3877	178	21	ω	ω	NUM
ejpam-3877	178	22	,	,	PUNCT
ejpam-3877	178	23	ρj	ρj	NOUN
ejpam-3877	178	24	=	=	NOUN
ejpam-3877	178	25	1	1	NUM
ejpam-3877	178	26	in	in	ADP
ejpam-3877	178	27	ωj	ωj	ADP
ejpam-3877	178	28	,	,	PUNCT
ejpam-3877	178	29	|	|	ADV
ejpam-3877	178	30	∇ρj	∇ρj	VERB
ejpam-3877	178	31	|≤	|≤	PROPN
ejpam-3877	178	32	j	j	PROPN
ejpam-3877	178	33	in	in	ADP
ejpam-3877	178	34	ω	ω	NUM
ejpam-3877	178	35	\	\	PROPN
ejpam-3877	178	36	ωj	ωj	ADP
ejpam-3877	178	37	.	.	PUNCT
ejpam-3877	179	1	then	then	ADV
ejpam-3877	179	2	for	for	SCONJ
ejpam-3877	179	3	any	any	DET
ejpam-3877	179	4	|	|	NOUN
ejpam-3877	179	5	∇ρj	∇ρj	VERB
ejpam-3877	179	6	|≤	|≤	ADJ
ejpam-3877	179	7	j	j	PROPN
ejpam-3877	179	8	≤	≤	ADV
ejpam-3877	179	9	1	1	NUM
ejpam-3877	179	10	d(x	d(x	NOUN
ejpam-3877	179	11	)	)	PUNCT
ejpam-3877	179	12	where	where	SCONJ
ejpam-3877	179	13	d(x	d(x	NOUN
ejpam-3877	179	14	)	)	PUNCT
ejpam-3877	180	1	:	:	PUNCT
ejpam-3877	180	2	=	=	SYM
ejpam-3877	180	3	dist(x	dist(x	X
ejpam-3877	180	4	,	,	PUNCT
ejpam-3877	180	5	∂ω	∂ω	ADJ
ejpam-3877	180	6	)	)	PUNCT
ejpam-3877	180	7	≤	≤	NOUN
ejpam-3877	180	8	dist(ωj	dist(ωj	NOUN
ejpam-3877	180	9	,	,	PUNCT
ejpam-3877	180	10	∂ω	∂ω	PROPN
ejpam-3877	180	11	)	)	PUNCT
ejpam-3877	180	12	(	(	PUNCT
ejpam-3877	180	13	see	see	VERB
ejpam-3877	180	14	[	[	X
ejpam-3877	180	15	24	24	NUM
ejpam-3877	180	16	]	]	PUNCT
ejpam-3877	180	17	)	)	PUNCT
ejpam-3877	180	18	.	.	PUNCT
ejpam-3877	181	1	let	let	VERB
ejpam-3877	181	2	us	we	PRON
ejpam-3877	181	3	consider	consider	VERB
ejpam-3877	181	4	the	the	DET
ejpam-3877	181	5	truncated	truncated	ADJ
ejpam-3877	181	6	function	function	NOUN
ejpam-3877	181	7	η	η	PROPN
ejpam-3877	181	8	such	such	ADJ
ejpam-3877	181	9	that	that	PRON
ejpam-3877	181	10	for	for	ADP
ejpam-3877	181	11	any	any	DET
ejpam-3877	181	12	0	0	NUM
ejpam-3877	181	13	≤	≤	NUM
ejpam-3877	181	14	t1	t1	NOUN
ejpam-3877	181	15	<	<	X
ejpam-3877	181	16	t2	t2	PROPN
ejpam-3877	181	17	≤	≤	X
ejpam-3877	181	18	t	t	NOUN
ejpam-3877	181	19	η(s	η(s	PROPN
ejpam-3877	181	20	)	)	PUNCT
ejpam-3877	182	1	=	=	SYM
ejpam-3877	183	1			NOUN
ejpam-3877	183	2	0	0	PUNCT
ejpam-3877	184	1	if	if	SCONJ
ejpam-3877	184	2	0	0	NUM
ejpam-3877	184	3	≤	≤	NUM
ejpam-3877	184	4	s	s	PART
ejpam-3877	184	5	≤	≤	NOUN
ejpam-3877	184	6	t1	t1	PROPN
ejpam-3877	184	7	,	,	PUNCT
ejpam-3877	184	8	1	1	NUM
ejpam-3877	184	9	if	if	SCONJ
ejpam-3877	184	10	t1	t1	VERB
ejpam-3877	184	11	<	<	X
ejpam-3877	184	12	s	s	X
ejpam-3877	184	13	<	<	X
ejpam-3877	184	14	t2	t2	NOUN
ejpam-3877	184	15	,	,	PUNCT
ejpam-3877	184	16	0	0	PUNCT
ejpam-3877	185	1	if	if	SCONJ
ejpam-3877	185	2	s	s	PRON
ejpam-3877	185	3	≥	≥	NOUN
ejpam-3877	185	4	t2	t2	NOUN
ejpam-3877	185	5	.	.	PUNCT
ejpam-3877	186	1	for	for	ADP
ejpam-3877	186	2	any	any	DET
ejpam-3877	186	3	fixed	fix	VERB
ejpam-3877	186	4	j	j	PROPN
ejpam-3877	186	5	∈	∈	PROPN
ejpam-3877	186	6	n	n	CCONJ
ejpam-3877	186	7	,	,	PUNCT
ejpam-3877	186	8	we	we	PRON
ejpam-3877	186	9	choose	choose	VERB
ejpam-3877	186	10	ξj(x	ξj(x	NOUN
ejpam-3877	186	11	,	,	PUNCT
ejpam-3877	186	12	s	s	PART
ejpam-3877	186	13	)	)	PUNCT
ejpam-3877	186	14	=	=	SYM
ejpam-3877	186	15	η(s)ρj(x	η(s)ρj(x	NOUN
ejpam-3877	186	16	)	)	PUNCT
ejpam-3877	186	17	as	as	ADP
ejpam-3877	186	18	a	a	DET
ejpam-3877	186	19	test	test	NOUN
ejpam-3877	186	20	function	function	NOUN
ejpam-3877	186	21	in	in	ADP
ejpam-3877	186	22	the	the	DET
ejpam-3877	186	23	problems	problem	NOUN
ejpam-3877	186	24	(	(	PUNCT
ejpam-3877	186	25	pn	pn	NOUN
ejpam-3877	186	26	)	)	PUNCT
ejpam-3877	186	27	gives∫	gives∫	PROPN
ejpam-3877	186	28	ω	ω	PROPN
ejpam-3877	186	29	un(x	un(x	PROPN
ejpam-3877	186	30	,	,	PUNCT
ejpam-3877	186	31	t2)ρj(x)dx−	t2)ρj(x)dx−	PROPN
ejpam-3877	186	32	∫	∫	PROPN
ejpam-3877	186	33	ω	ω	PROPN
ejpam-3877	186	34	un(x	un(x	PROPN
ejpam-3877	186	35	,	,	PUNCT
ejpam-3877	186	36	t1)ρj(x)dx	t1)ρj(x)dx	NUM
ejpam-3877	187	1	=	=	SYM
ejpam-3877	187	2	−	−	PROPN
ejpam-3877	187	3	∫	∫	PROPN
ejpam-3877	187	4	t2	t2	PROPN
ejpam-3877	187	5	t1	t1	PROPN
ejpam-3877	187	6	∫	∫	PROPN
ejpam-3877	187	7	ω	ω	NUM
ejpam-3877	187	8	η(s)∇ψ(un)∇ρj(x)dxds+	η(s)∇ψ(un)∇ρj(x)dxds+	PROPN
ejpam-3877	187	9	+	+	CCONJ
ejpam-3877	188	1	∫	∫	PROPN
ejpam-3877	188	2	t2	t2	PROPN
ejpam-3877	188	3	t1	t1	PROPN
ejpam-3877	188	4	∫	∫	PROPN
ejpam-3877	189	1	ω	ω	NUM
ejpam-3877	189	2	η(s)ρj(x)µn(x)dx	η(s)ρj(x)µn(x)dx	PROPN
ejpam-3877	189	3	.	.	PUNCT
ejpam-3877	190	1	(	(	PUNCT
ejpam-3877	190	2	4.2	4.2	NUM
ejpam-3877	190	3	)	)	PUNCT
ejpam-3877	190	4	it	it	PRON
ejpam-3877	190	5	is	be	AUX
ejpam-3877	190	6	worth	worth	ADJ
ejpam-3877	190	7	observing	observe	VERB
ejpam-3877	190	8	that∣∣∣∣∫	that∣∣∣∣∫	PROPN
ejpam-3877	190	9	ω	ω	NUM
ejpam-3877	190	10	∇ψ(un)∇ρj(x)dx	∇ψ(un)∇ρj(x)dx	VERB
ejpam-3877	190	11	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3877	190	12	≤|	≤|	NOUN
ejpam-3877	190	13	ω	ω	NUM
ejpam-3877	190	14	\	\	PROPN
ejpam-3877	190	15	ωj	ωj	ADP
ejpam-3877	190	16	|‖	|‖	PROPN
ejpam-3877	190	17	∇ψ(un	∇ψ(un	NUM
ejpam-3877	190	18	)	)	PUNCT
ejpam-3877	190	19	‖l2(ω	‖l2(ω	NOUN
ejpam-3877	190	20	)	)	PUNCT
ejpam-3877	190	21	.	.	PUNCT
ejpam-3877	191	1	by	by	ADP
ejpam-3877	191	2	letting	let	VERB
ejpam-3877	191	3	j	j	PROPN
ejpam-3877	191	4	to	to	PART
ejpam-3877	191	5	infinity	infinity	VERB
ejpam-3877	191	6	,	,	PUNCT
ejpam-3877	191	7	we	we	PRON
ejpam-3877	191	8	deduce	deduce	VERB
ejpam-3877	191	9	that	that	SCONJ
ejpam-3877	191	10	lim	lim	PROPN
ejpam-3877	192	1	j→∞	j→∞	NOUN
ejpam-3877	192	2	∫	∫	PROPN
ejpam-3877	192	3	ω	ω	X
ejpam-3877	192	4	∇ψ(un)∇ρj(x)dx	∇ψ(un)∇ρj(x)dx	PROPN
ejpam-3877	192	5	=	=	SYM
ejpam-3877	192	6	0	0	NUM
ejpam-3877	192	7	.	.	PUNCT
ejpam-3877	193	1	(	(	PUNCT
ejpam-3877	193	2	4.3	4.3	NUM
ejpam-3877	193	3	)	)	PUNCT
ejpam-3877	193	4	by	by	ADP
ejpam-3877	193	5	the	the	DET
ejpam-3877	193	6	properties	property	NOUN
ejpam-3877	193	7	of	of	ADP
ejpam-3877	193	8	the	the	DET
ejpam-3877	193	9	sequence	sequence	NOUN
ejpam-3877	193	10	functions	function	NOUN
ejpam-3877	193	11	{	{	PUNCT
ejpam-3877	193	12	ρj	ρj	NOUN
ejpam-3877	193	13	}	}	PUNCT
ejpam-3877	193	14	,	,	PUNCT
ejpam-3877	193	15	we	we	PRON
ejpam-3877	193	16	set	set	VERB
ejpam-3877	193	17	t2	t2	NOUN
ejpam-3877	193	18	=	=	SYM
ejpam-3877	193	19	t	t	PROPN
ejpam-3877	193	20	,	,	PUNCT
ejpam-3877	193	21	t1	t1	NOUN
ejpam-3877	193	22	=	=	PUNCT
ejpam-3877	193	23	0	0	PUNCT
ejpam-3877	194	1	and	and	CCONJ
ejpam-3877	194	2	then	then	ADV
ejpam-3877	194	3	combining	combine	VERB
ejpam-3877	194	4	together	together	ADP
ejpam-3877	194	5	(	(	PUNCT
ejpam-3877	194	6	4.2	4.2	NUM
ejpam-3877	194	7	)	)	PUNCT
ejpam-3877	194	8	with	with	ADP
ejpam-3877	194	9	(	(	PUNCT
ejpam-3877	194	10	4.3	4.3	NUM
ejpam-3877	194	11	)	)	PUNCT
ejpam-3877	194	12	,	,	PUNCT
ejpam-3877	194	13	there	there	PRON
ejpam-3877	194	14	holds∫	holds∫	VERB
ejpam-3877	194	15	ω	ω	NOUN
ejpam-3877	194	16	un(x	un(x	NOUN
ejpam-3877	194	17	,	,	PUNCT
ejpam-3877	194	18	t)dx	t)dx	PROPN
ejpam-3877	194	19	≤	≤	NUM
ejpam-3877	194	20	∫	∫	PROPN
ejpam-3877	194	21	ω	ω	PROPN
ejpam-3877	195	1	u0n(x)dx+	u0n(x)dx+	PROPN
ejpam-3877	195	2	∫	∫	PROPN
ejpam-3877	195	3	t	t	PROPN
ejpam-3877	195	4	0	0	NUM
ejpam-3877	195	5	∫	∫	PROPN
ejpam-3877	195	6	ω	ω	NUM
ejpam-3877	195	7	dµn	dµn	NOUN
ejpam-3877	195	8	.	.	PUNCT
ejpam-3877	196	1	(	(	PUNCT
ejpam-3877	196	2	4.4	4.4	NUM
ejpam-3877	196	3	)	)	PUNCT
ejpam-3877	196	4	hence	hence	ADV
ejpam-3877	196	5	the	the	DET
ejpam-3877	196	6	estimate	estimate	NOUN
ejpam-3877	196	7	(	(	PUNCT
ejpam-3877	196	8	4.1	4.1	NUM
ejpam-3877	196	9	)	)	PUNCT
ejpam-3877	196	10	follows	follow	VERB
ejpam-3877	196	11	.	.	PUNCT
ejpam-3877	197	1	�	�	PROPN
ejpam-3877	197	2	to	to	PART
ejpam-3877	197	3	show	show	VERB
ejpam-3877	197	4	the	the	DET
ejpam-3877	197	5	existence	existence	NOUN
ejpam-3877	197	6	of	of	ADP
ejpam-3877	197	7	the	the	DET
ejpam-3877	197	8	solutions	solution	NOUN
ejpam-3877	197	9	to	to	ADP
ejpam-3877	197	10	the	the	DET
ejpam-3877	197	11	problems	problem	NOUN
ejpam-3877	197	12	(	(	PUNCT
ejpam-3877	197	13	p	p	NOUN
ejpam-3877	197	14	)	)	PUNCT
ejpam-3877	197	15	we	we	PRON
ejpam-3877	197	16	need	need	VERB
ejpam-3877	197	17	a	a	DET
ejpam-3877	197	18	priori	priori	ADJ
ejpam-3877	197	19	estimates	estimate	NOUN
ejpam-3877	197	20	of	of	ADP
ejpam-3877	197	21	quincy	quincy	PROPN
ejpam-3877	197	22	s.	s.	PROPN
ejpam-3877	197	23	nkombo	nkombo	PROPN
ejpam-3877	197	24	,	,	PUNCT
ejpam-3877	197	25	fengquan	fengquan	PROPN
ejpam-3877	197	26	li	li	PROPN
ejpam-3877	197	27	/	/	SYM
ejpam-3877	197	28	eur	eur	PROPN
ejpam-3877	197	29	.	.	PUNCT
ejpam-3877	198	1	j.	j.	PROPN
ejpam-3877	198	2	pure	pure	PROPN
ejpam-3877	198	3	appl	appl	PROPN
ejpam-3877	198	4	.	.	PROPN
ejpam-3877	198	5	math	math	PROPN
ejpam-3877	198	6	,	,	PUNCT
ejpam-3877	198	7	14	14	NUM
ejpam-3877	198	8	(	(	PUNCT
ejpam-3877	198	9	1	1	NUM
ejpam-3877	198	10	)	)	PUNCT
ejpam-3877	198	11	(	(	PUNCT
ejpam-3877	198	12	2021	2021	NUM
ejpam-3877	198	13	)	)	PUNCT
ejpam-3877	198	14	,	,	PUNCT
ejpam-3877	198	15	204	204	NUM
ejpam-3877	198	16	-	-	SYM
ejpam-3877	198	17	233	233	NUM
ejpam-3877	198	18	214	214	NUM
ejpam-3877	198	19	sequences	sequence	NOUN
ejpam-3877	198	20	{	{	PUNCT
ejpam-3877	198	21	ψ(un	ψ(un	PROPN
ejpam-3877	198	22	)	)	PUNCT
ejpam-3877	198	23	}	}	PUNCT
ejpam-3877	198	24	.	.	PUNCT
ejpam-3877	199	1	proposition	proposition	NOUN
ejpam-3877	199	2	4.1	4.1	NUM
ejpam-3877	199	3	.	.	PUNCT
ejpam-3877	200	1	under	under	ADP
ejpam-3877	200	2	the	the	DET
ejpam-3877	200	3	assumptions	assumption	NOUN
ejpam-3877	200	4	of	of	ADP
ejpam-3877	200	5	(	(	PUNCT
ejpam-3877	200	6	i	i	NOUN
ejpam-3877	200	7	)	)	PUNCT
ejpam-3877	200	8	−	−	PROPN
ejpam-3877	201	1	(	(	PUNCT
ejpam-3877	201	2	j	j	NOUN
ejpam-3877	201	3	)	)	PUNCT
ejpam-3877	201	4	and	and	CCONJ
ejpam-3877	201	5	un	un	PROPN
ejpam-3877	201	6	be	be	AUX
ejpam-3877	201	7	the	the	DET
ejpam-3877	201	8	solution	solution	NOUN
ejpam-3877	201	9	of	of	ADP
ejpam-3877	201	10	the	the	DET
ejpam-3877	201	11	approximation	approximation	NOUN
ejpam-3877	201	12	problem	problem	NOUN
ejpam-3877	201	13	(	(	PUNCT
ejpam-3877	201	14	pn	pn	NOUN
ejpam-3877	201	15	)	)	PUNCT
ejpam-3877	201	16	.	.	PUNCT
ejpam-3877	202	1	then	then	ADV
ejpam-3877	202	2	we	we	PRON
ejpam-3877	202	3	obtain	obtain	VERB
ejpam-3877	202	4	‖	‖	ADJ
ejpam-3877	202	5	∇ψ(un	∇ψ(un	NOUN
ejpam-3877	202	6	)	)	PUNCT
ejpam-3877	202	7	‖l2(q)≤	‖l2(q)≤	PROPN
ejpam-3877	202	8	c.	c.	NOUN
ejpam-3877	202	9	(	(	PUNCT
ejpam-3877	202	10	4.5	4.5	NUM
ejpam-3877	202	11	)	)	PUNCT
ejpam-3877	202	12	‖	‖	PROPN
ejpam-3877	202	13	ψ(un	ψ(un	PROPN
ejpam-3877	202	14	)	)	PUNCT
ejpam-3877	202	15	‖l∞((0,t	‖l∞((0,t	NOUN
ejpam-3877	202	16	)	)	PUNCT
ejpam-3877	202	17	,	,	PUNCT
ejpam-3877	202	18	h1	h1	PROPN
ejpam-3877	202	19	0	0	NUM
ejpam-3877	202	20	(	(	PUNCT
ejpam-3877	202	21	ω))≤	ω))≤	PROPN
ejpam-3877	202	22	c.	c.	NOUN
ejpam-3877	202	23	(	(	PUNCT
ejpam-3877	202	24	4.6	4.6	NUM
ejpam-3877	202	25	)	)	PUNCT
ejpam-3877	202	26	proof	proof	NOUN
ejpam-3877	202	27	.	.	PUNCT
ejpam-3877	203	1	since	since	SCONJ
ejpam-3877	203	2	ψ(un	ψ(un	PROPN
ejpam-3877	203	3	)	)	PUNCT
ejpam-3877	203	4	≥	≥	NOUN
ejpam-3877	203	5	0	0	NUM
ejpam-3877	203	6	in	in	ADP
ejpam-3877	203	7	q	q	NOUN
ejpam-3877	203	8	and	and	CCONJ
ejpam-3877	203	9	ψ(un	ψ(un	PROPN
ejpam-3877	203	10	)	)	PUNCT
ejpam-3877	203	11	=	=	SYM
ejpam-3877	203	12	0	0	NUM
ejpam-3877	203	13	on	on	ADP
ejpam-3877	203	14	∂ω×	∂ω×	PROPN
ejpam-3877	203	15	(	(	PUNCT
ejpam-3877	203	16	0	0	NUM
ejpam-3877	203	17	,	,	PUNCT
ejpam-3877	203	18	t	t	PROPN
ejpam-3877	203	19	)	)	PUNCT
ejpam-3877	203	20	for	for	ADP
ejpam-3877	203	21	every	every	DET
ejpam-3877	203	22	t	t	NOUN
ejpam-3877	203	23	∈	∈	PROPN
ejpam-3877	203	24	(	(	PUNCT
ejpam-3877	203	25	0	0	NUM
ejpam-3877	203	26	,	,	PUNCT
ejpam-3877	203	27	t	t	NOUN
ejpam-3877	203	28	)	)	PUNCT
ejpam-3877	203	29	.	.	PUNCT
ejpam-3877	204	1	the	the	DET
ejpam-3877	204	2	fact	fact	NOUN
ejpam-3877	204	3	that	that	SCONJ
ejpam-3877	204	4	un	un	PROPN
ejpam-3877	204	5	=	=	PROPN
ejpam-3877	204	6	ψ(ψ−1(un	ψ(ψ−1(un	NOUN
ejpam-3877	204	7	)	)	PUNCT
ejpam-3877	204	8	)	)	PUNCT
ejpam-3877	205	1	∈	∈	PROPN
ejpam-3877	205	2	c1([0	c1([0	PROPN
ejpam-3877	205	3	,	,	PUNCT
ejpam-3877	205	4	t	t	X
ejpam-3877	205	5	]	]	PUNCT
ejpam-3877	205	6	,	,	PUNCT
ejpam-3877	205	7	h1	h1	PROPN
ejpam-3877	205	8	0	0	NUM
ejpam-3877	205	9	(	(	PUNCT
ejpam-3877	205	10	ω	ω	NOUN
ejpam-3877	205	11	)	)	PUNCT
ejpam-3877	205	12	)	)	PUNCT
ejpam-3877	205	13	.	.	PUNCT
ejpam-3877	206	1	take	take	VERB
ejpam-3877	206	2	ψ(un	ψ(un	PROPN
ejpam-3877	206	3	)	)	PUNCT
ejpam-3877	206	4	as	as	ADP
ejpam-3877	206	5	a	a	DET
ejpam-3877	206	6	test	test	NOUN
ejpam-3877	206	7	function	function	NOUN
ejpam-3877	206	8	in	in	ADP
ejpam-3877	206	9	(	(	PUNCT
ejpam-3877	206	10	pn	pn	NOUN
ejpam-3877	206	11	)	)	PUNCT
ejpam-3877	206	12	,	,	PUNCT
ejpam-3877	206	13	we	we	PRON
ejpam-3877	206	14	get∫	get∫	VERB
ejpam-3877	206	15	q	q	PUNCT
ejpam-3877	206	16	|	|	ADV
ejpam-3877	206	17	∇ψ(un	∇ψ(un	NOUN
ejpam-3877	206	18	)	)	PUNCT
ejpam-3877	206	19	|2	|2	NUM
ejpam-3877	206	20	dxdt	dxdt	NOUN
ejpam-3877	206	21	=	=	SYM
ejpam-3877	206	22	∫	∫	PROPN
ejpam-3877	206	23	ω	ω	PROPN
ejpam-3877	206	24	(	(	PUNCT
ejpam-3877	206	25	∫	∫	PROPN
ejpam-3877	206	26	u0n(x	u0n(x	PROPN
ejpam-3877	206	27	)	)	PUNCT
ejpam-3877	206	28	0	0	PUNCT
ejpam-3877	206	29	ψ(s)ds	ψ(s)ds	NOUN
ejpam-3877	206	30	)	)	PUNCT
ejpam-3877	207	1	dx−	dx−	NUM
ejpam-3877	207	2	∫	∫	PROPN
ejpam-3877	207	3	ω	ω	PROPN
ejpam-3877	207	4	(	(	PUNCT
ejpam-3877	207	5	∫	∫	PROPN
ejpam-3877	207	6	un(x	un(x	PROPN
ejpam-3877	207	7	,	,	PUNCT
ejpam-3877	207	8	t	t	PROPN
ejpam-3877	207	9	)	)	PUNCT
ejpam-3877	207	10	0	0	PUNCT
ejpam-3877	207	11	ψ(s)ds	ψ(s)ds	PRON
ejpam-3877	207	12	)	)	PUNCT
ejpam-3877	207	13	dx	dx	PROPN
ejpam-3877	208	1	+	+	CCONJ
ejpam-3877	208	2	∫	∫	PROPN
ejpam-3877	208	3	q	q	PROPN
ejpam-3877	209	1	µnψ(un)dxdt	µnψ(un)dxdt	PROPN
ejpam-3877	209	2	.	.	PUNCT
ejpam-3877	210	1	it	it	PRON
ejpam-3877	210	2	follows	follow	VERB
ejpam-3877	210	3	that∫	that∫	NOUN
ejpam-3877	210	4	q	q	PROPN
ejpam-3877	211	1	|	|	ADV
ejpam-3877	211	2	∇ψ(un	∇ψ(un	NOUN
ejpam-3877	211	3	)	)	PUNCT
ejpam-3877	211	4	|2	|2	NUM
ejpam-3877	211	5	dxdt	dxdt	NOUN
ejpam-3877	211	6	≤	≤	NUM
ejpam-3877	211	7	∫	∫	PROPN
ejpam-3877	211	8	ω	ω	PROPN
ejpam-3877	211	9	(	(	PUNCT
ejpam-3877	211	10	∫	∫	PROPN
ejpam-3877	211	11	u0n(x	u0n(x	PROPN
ejpam-3877	211	12	)	)	PUNCT
ejpam-3877	211	13	0	0	PUNCT
ejpam-3877	212	1	ψ(s)ds	ψ(s)ds	NOUN
ejpam-3877	212	2	)	)	PUNCT
ejpam-3877	212	3	dx+	dx+	NOUN
ejpam-3877	212	4	∫	∫	PROPN
ejpam-3877	212	5	q	q	PROPN
ejpam-3877	212	6	µnψ(un)dxdt	µnψ(un)dxdt	PROPN
ejpam-3877	212	7	.	.	PROPN
ejpam-3877	212	8	by	by	ADP
ejpam-3877	212	9	(	(	PUNCT
ejpam-3877	212	10	i)-(i	i)-(i	PROPN
ejpam-3877	212	11	)	)	PUNCT
ejpam-3877	212	12	and	and	CCONJ
ejpam-3877	212	13	the	the	DET
ejpam-3877	212	14	assumption	assumption	NOUN
ejpam-3877	212	15	(	(	PUNCT
ejpam-3877	212	16	3.3	3.3	NUM
ejpam-3877	212	17	)	)	PUNCT
ejpam-3877	212	18	,	,	PUNCT
ejpam-3877	212	19	there	there	PRON
ejpam-3877	212	20	exists	exist	VERB
ejpam-3877	212	21	a	a	DET
ejpam-3877	212	22	positive	positive	ADJ
ejpam-3877	212	23	constant	constant	ADJ
ejpam-3877	212	24	c	c	NOUN
ejpam-3877	212	25	such	such	ADJ
ejpam-3877	212	26	that	that	PRON
ejpam-3877	212	27	(	(	PUNCT
ejpam-3877	212	28	4.5	4.5	NUM
ejpam-3877	212	29	)	)	PUNCT
ejpam-3877	212	30	holds	hold	VERB
ejpam-3877	212	31	.	.	PUNCT
ejpam-3877	213	1	assume	assume	VERB
ejpam-3877	213	2	that	that	SCONJ
ejpam-3877	213	3	{	{	PUNCT
ejpam-3877	213	4	ηj	ηj	NOUN
ejpam-3877	213	5	}	}	PUNCT
ejpam-3877	213	6	a	a	DET
ejpam-3877	213	7	sequence	sequence	NOUN
ejpam-3877	213	8	such	such	ADJ
ejpam-3877	213	9	that	that	SCONJ
ejpam-3877	213	10	‖	‖	PROPN
ejpam-3877	213	11	ηj	ηj	ADP
ejpam-3877	213	12	‖l1(ω)≤	‖l1(ω)≤	PROPN
ejpam-3877	213	13	c	c	PROPN
ejpam-3877	213	14	and	and	CCONJ
ejpam-3877	213	15	ηj	ηj	ADP
ejpam-3877	213	16	∗	∗	NOUN
ejpam-3877	213	17	⇀	⇀	PROPN
ejpam-3877	214	1	δt0(t	δt0(t	PROPN
ejpam-3877	214	2	)	)	PUNCT
ejpam-3877	214	3	in	in	ADP
ejpam-3877	214	4	m+(0	m+(0	PROPN
ejpam-3877	214	5	,	,	PUNCT
ejpam-3877	214	6	t	t	PROPN
ejpam-3877	214	7	)	)	PUNCT
ejpam-3877	214	8	.	.	PUNCT
ejpam-3877	214	9	suppose	suppose	VERB
ejpam-3877	214	10	that	that	SCONJ
ejpam-3877	214	11	ξ(x	ξ(x	NOUN
ejpam-3877	214	12	,	,	PUNCT
ejpam-3877	214	13	t	t	PROPN
ejpam-3877	214	14	)	)	PUNCT
ejpam-3877	214	15	=	=	SYM
ejpam-3877	215	1	ψ(un)(t	ψ(un)(t	PROPN
ejpam-3877	215	2	−	−	PROPN
ejpam-3877	215	3	t)α	t)α	NOUN
ejpam-3877	215	4	∫	∫	PROPN
ejpam-3877	215	5	t	t	PROPN
ejpam-3877	215	6	t	t	PROPN
ejpam-3877	215	7	ηj(s)ds	ηj(s)ds	NOUN
ejpam-3877	215	8	(	(	PUNCT
ejpam-3877	215	9	1	1	NUM
ejpam-3877	215	10	<	<	X
ejpam-3877	215	11	t	t	PROPN
ejpam-3877	216	1	−	−	PROPN
ejpam-3877	216	2	t	t	PROPN
ejpam-3877	216	3	<	<	X
ejpam-3877	216	4	τ	τ	PROPN
ejpam-3877	216	5	,	,	PUNCT
ejpam-3877	216	6	α	α	PROPN
ejpam-3877	216	7	>	>	X
ejpam-3877	216	8	1	1	NUM
ejpam-3877	216	9	)	)	PUNCT
ejpam-3877	216	10	as	as	ADP
ejpam-3877	216	11	a	a	DET
ejpam-3877	216	12	test	test	NOUN
ejpam-3877	216	13	function	function	NOUN
ejpam-3877	216	14	in	in	ADP
ejpam-3877	216	15	the	the	DET
ejpam-3877	216	16	approximating	approximate	VERB
ejpam-3877	216	17	problem	problem	NOUN
ejpam-3877	216	18	(	(	PUNCT
ejpam-3877	216	19	pn	pn	NOUN
ejpam-3877	216	20	)	)	PUNCT
ejpam-3877	216	21	,	,	PUNCT
ejpam-3877	216	22	there	there	PRON
ejpam-3877	216	23	holds	hold	VERB
ejpam-3877	216	24	−	−	PROPN
ejpam-3877	216	25	∫	∫	PROPN
ejpam-3877	216	26	ω	ω	PROPN
ejpam-3877	216	27	(	(	PUNCT
ejpam-3877	216	28	∫	∫	PROPN
ejpam-3877	216	29	u0n(x	u0n(x	PROPN
ejpam-3877	216	30	)	)	PUNCT
ejpam-3877	216	31	0	0	PUNCT
ejpam-3877	216	32	ψ(s)ds	ψ(s)ds	NOUN
ejpam-3877	216	33	)	)	PUNCT
ejpam-3877	217	1	tα	tα	PROPN
ejpam-3877	217	2	∫	∫	PROPN
ejpam-3877	218	1	t	t	PROPN
ejpam-3877	218	2	0	0	NUM
ejpam-3877	218	3	ηj(s)ds+	ηj(s)ds+	PROPN
ejpam-3877	218	4	+	+	NUM
ejpam-3877	218	5	∫	∫	PROPN
ejpam-3877	218	6	ω	ω	PROPN
ejpam-3877	218	7	(	(	PUNCT
ejpam-3877	218	8	∫	∫	PROPN
ejpam-3877	218	9	un(x	un(x	X
ejpam-3877	218	10	,	,	PUNCT
ejpam-3877	218	11	t	t	PROPN
ejpam-3877	218	12	)	)	PUNCT
ejpam-3877	218	13	0	0	PUNCT
ejpam-3877	218	14	ψ(s)ds	ψ(s)ds	NOUN
ejpam-3877	218	15	)	)	PUNCT
ejpam-3877	218	16	{	{	PUNCT
ejpam-3877	218	17	(	(	PUNCT
ejpam-3877	218	18	t	t	PROPN
ejpam-3877	218	19	−	−	PROPN
ejpam-3877	218	20	t)α	t)α	X
ejpam-3877	218	21	∫	∫	PROPN
ejpam-3877	219	1	t	t	PROPN
ejpam-3877	219	2	0	0	NUM
ejpam-3877	219	3	ηj(s)ds+	ηj(s)ds+	ADJ
ejpam-3877	219	4	∫	∫	PROPN
ejpam-3877	219	5	t	t	PROPN
ejpam-3877	219	6	0	0	NUM
ejpam-3877	219	7	ηj(s)(t	ηj(s)(t	PROPN
ejpam-3877	219	8	−	−	PROPN
ejpam-3877	219	9	t)αdt	t)αdt	PROPN
ejpam-3877	219	10	}	}	PUNCT
ejpam-3877	219	11	=	=	PUNCT
ejpam-3877	220	1	=	=	SYM
ejpam-3877	220	2	1	1	NUM
ejpam-3877	220	3	1	1	NUM
ejpam-3877	220	4	+	+	CCONJ
ejpam-3877	221	1	α	α	NOUN
ejpam-3877	221	2	∫	∫	PROPN
ejpam-3877	221	3	ω	ω	NUM
ejpam-3877	221	4	|	|	CCONJ
ejpam-3877	221	5	∇ψ(un	∇ψ(un	NOUN
ejpam-3877	221	6	)	)	PUNCT
ejpam-3877	221	7	|2	|2	NUM
ejpam-3877	221	8	dx	dx	PROPN
ejpam-3877	221	9	(	(	PUNCT
ejpam-3877	221	10	∫	∫	PROPN
ejpam-3877	221	11	t	t	PROPN
ejpam-3877	221	12	0	0	PROPN
ejpam-3877	221	13	ηj(s)χ(0,t	ηj(s)χ(0,t	NOUN
ejpam-3877	221	14	)	)	PUNCT
ejpam-3877	221	15	(	(	PUNCT
ejpam-3877	221	16	s)ds	s)ds	PROPN
ejpam-3877	221	17	)	)	PUNCT
ejpam-3877	221	18	(	(	PUNCT
ejpam-3877	221	19	t−t)α−	t−t)α−	NOUN
ejpam-3877	221	20	∫	∫	PROPN
ejpam-3877	221	21	q	q	PROPN
ejpam-3877	221	22	µnψ(un)(t−t)α	µnψ(un)(t−t)α	PROPN
ejpam-3877	221	23	∫	∫	PROPN
ejpam-3877	221	24	t	t	PROPN
ejpam-3877	221	25	t	t	PROPN
ejpam-3877	221	26	ηj(s)ds	ηj(s)ds	PROPN
ejpam-3877	221	27	.	.	PUNCT
ejpam-3877	222	1	(	(	PUNCT
ejpam-3877	222	2	4.7	4.7	NUM
ejpam-3877	222	3	)	)	PUNCT
ejpam-3877	222	4	this	this	PRON
ejpam-3877	222	5	leads	lead	VERB
ejpam-3877	222	6	to	to	ADP
ejpam-3877	222	7	the	the	DET
ejpam-3877	222	8	following	follow	VERB
ejpam-3877	222	9	result(∫	result(∫	ADP
ejpam-3877	222	10	t	t	NOUN
ejpam-3877	222	11	0	0	NUM
ejpam-3877	222	12	ηj(s)χ(0,t	ηj(s)χ(0,t	NOUN
ejpam-3877	222	13	)	)	PUNCT
ejpam-3877	222	14	(	(	PUNCT
ejpam-3877	223	1	s)ds	s)ds	PROPN
ejpam-3877	223	2	)	)	PUNCT
ejpam-3877	223	3	∫	∫	PROPN
ejpam-3877	223	4	ω	ω	NUM
ejpam-3877	223	5	|	|	CCONJ
ejpam-3877	223	6	∇ψ(un	∇ψ(un	NOUN
ejpam-3877	223	7	)	)	PUNCT
ejpam-3877	223	8	|2	|2	NUM
ejpam-3877	224	1	dx	dx	PROPN
ejpam-3877	224	2	≤	≤	PROPN
ejpam-3877	224	3	c	c	X
ejpam-3877	224	4	(	(	PUNCT
ejpam-3877	224	5	‖	‖	PROPN
ejpam-3877	224	6	u0	u0	ADJ
ejpam-3877	224	7	‖m+(ω	‖m+(ω	PROPN
ejpam-3877	224	8	)	)	PUNCT
ejpam-3877	224	9	+	+	CCONJ
ejpam-3877	224	10	‖	‖	PROPN
ejpam-3877	224	11	µ	µ	X
ejpam-3877	224	12	‖m+(q	‖m+(q	NOUN
ejpam-3877	224	13	)	)	PUNCT
ejpam-3877	224	14	)	)	PUNCT
ejpam-3877	225	1	quincy	quincy	PROPN
ejpam-3877	225	2	s.	s.	PROPN
ejpam-3877	225	3	nkombo	nkombo	PROPN
ejpam-3877	225	4	,	,	PUNCT
ejpam-3877	225	5	fengquan	fengquan	PROPN
ejpam-3877	225	6	li	li	PROPN
ejpam-3877	225	7	/	/	SYM
ejpam-3877	225	8	eur	eur	PROPN
ejpam-3877	225	9	.	.	PUNCT
ejpam-3877	226	1	j.	j.	PROPN
ejpam-3877	226	2	pure	pure	PROPN
ejpam-3877	226	3	appl	appl	PROPN
ejpam-3877	226	4	.	.	PROPN
ejpam-3877	226	5	math	math	PROPN
ejpam-3877	226	6	,	,	PUNCT
ejpam-3877	226	7	14	14	NUM
ejpam-3877	226	8	(	(	PUNCT
ejpam-3877	226	9	1	1	NUM
ejpam-3877	226	10	)	)	PUNCT
ejpam-3877	226	11	(	(	PUNCT
ejpam-3877	226	12	2021	2021	NUM
ejpam-3877	226	13	)	)	PUNCT
ejpam-3877	226	14	,	,	PUNCT
ejpam-3877	226	15	204	204	NUM
ejpam-3877	226	16	-	-	SYM
ejpam-3877	226	17	233	233	NUM
ejpam-3877	226	18	215	215	NUM
ejpam-3877	226	19	letting	let	VERB
ejpam-3877	226	20	j	j	PROPN
ejpam-3877	226	21	→	→	SYM
ejpam-3877	226	22	+	+	NUM
ejpam-3877	226	23	∞	∞	PROPN
ejpam-3877	226	24	the	the	DET
ejpam-3877	226	25	assertion	assertion	NOUN
ejpam-3877	226	26	(	(	PUNCT
ejpam-3877	226	27	4.6	4.6	NUM
ejpam-3877	226	28	)	)	PUNCT
ejpam-3877	226	29	holds	hold	VERB
ejpam-3877	226	30	true	true	ADJ
ejpam-3877	226	31	.	.	PUNCT
ejpam-3877	227	1	�	�	PROPN
ejpam-3877	227	2	proposition	proposition	NOUN
ejpam-3877	227	3	4.2	4.2	NUM
ejpam-3877	227	4	.	.	PUNCT
ejpam-3877	227	5	suppose	suppose	VERB
ejpam-3877	227	6	that	that	SCONJ
ejpam-3877	227	7	(	(	PUNCT
ejpam-3877	227	8	i	i	NOUN
ejpam-3877	227	9	)	)	PUNCT
ejpam-3877	227	10	−	−	PROPN
ejpam-3877	228	1	(	(	PUNCT
ejpam-3877	228	2	j	j	NOUN
ejpam-3877	228	3	)	)	PUNCT
ejpam-3877	228	4	and	and	CCONJ
ejpam-3877	228	5	(	(	PUNCT
ejpam-3877	228	6	1.1	1.1	NUM
ejpam-3877	228	7	)	)	PUNCT
ejpam-3877	228	8	hold	hold	VERB
ejpam-3877	228	9	.	.	PUNCT
ejpam-3877	229	1	let	let	VERB
ejpam-3877	229	2	un	un	PROPN
ejpam-3877	229	3	be	be	AUX
ejpam-3877	229	4	the	the	DET
ejpam-3877	229	5	solution	solution	NOUN
ejpam-3877	229	6	of	of	ADP
ejpam-3877	229	7	the	the	DET
ejpam-3877	229	8	problem	problem	NOUN
ejpam-3877	229	9	(	(	PUNCT
ejpam-3877	229	10	pn	pn	NOUN
ejpam-3877	229	11	)	)	PUNCT
ejpam-3877	229	12	and	and	CCONJ
ejpam-3877	229	13	φ	φ	PROPN
ejpam-3877	229	14	∈	∈	PROPN
ejpam-3877	229	15	c1(r+	c1(r+	PROPN
ejpam-3877	229	16	)	)	PUNCT
ejpam-3877	229	17	be	be	VERB
ejpam-3877	229	18	the	the	DET
ejpam-3877	229	19	function	function	NOUN
ejpam-3877	229	20	defined	define	VERB
ejpam-3877	229	21	by	by	ADP
ejpam-3877	229	22	φ(s	φ(	VERB
ejpam-3877	229	23	)	)	PUNCT
ejpam-3877	230	1	=	=	SYM
ejpam-3877	231	1	∫	∫	PROPN
ejpam-3877	231	2	s	s	PART
ejpam-3877	231	3	0	0	NUM
ejpam-3877	231	4	ψ(z)dz	ψ(z)dz	NOUN
ejpam-3877	231	5	.	.	PUNCT
ejpam-3877	232	1	(	(	PUNCT
ejpam-3877	232	2	4.8	4.8	NUM
ejpam-3877	232	3	)	)	PUNCT
ejpam-3877	232	4	then	then	ADV
ejpam-3877	232	5	the	the	DET
ejpam-3877	232	6	sequence	sequence	NOUN
ejpam-3877	233	1	[	[	X
ejpam-3877	233	2	φ(tk(ψ(un))]t	φ(tk(ψ(un))]t	PROPN
ejpam-3877	233	3	is	be	AUX
ejpam-3877	233	4	bounded	bound	VERB
ejpam-3877	233	5	in	in	ADP
ejpam-3877	233	6	l2((0	l2((0	PROPN
ejpam-3877	233	7	,	,	PUNCT
ejpam-3877	233	8	t	t	PROPN
ejpam-3877	233	9	)	)	PUNCT
ejpam-3877	233	10	,	,	PUNCT
ejpam-3877	233	11	h−1(ω	h−1(ω	PROPN
ejpam-3877	233	12	)	)	PUNCT
ejpam-3877	233	13	)	)	PUNCT
ejpam-3877	234	1	+	+	PUNCT
ejpam-3877	234	2	l1(q	l1(q	ADV
ejpam-3877	234	3	)	)	PUNCT
ejpam-3877	234	4	.	.	PUNCT
ejpam-3877	235	1	where	where	SCONJ
ejpam-3877	235	2	tk(s	tk(s	ADP
ejpam-3877	235	3	)	)	PUNCT
ejpam-3877	235	4	=	=	SYM
ejpam-3877	235	5	min{s	min{s	PROPN
ejpam-3877	235	6	,	,	PUNCT
ejpam-3877	235	7	k	k	NOUN
ejpam-3877	235	8	}	}	PUNCT
ejpam-3877	235	9	.	.	PUNCT
ejpam-3877	236	1	proof	proof	NOUN
ejpam-3877	236	2	.	.	PUNCT
ejpam-3877	237	1	we	we	PRON
ejpam-3877	237	2	choose	choose	VERB
ejpam-3877	237	3	ψ(un)ϕ	ψ(un)ϕ	NOUN
ejpam-3877	237	4	as	as	ADP
ejpam-3877	237	5	a	a	DET
ejpam-3877	237	6	test	test	NOUN
ejpam-3877	237	7	function	function	NOUN
ejpam-3877	237	8	in	in	ADP
ejpam-3877	237	9	(	(	PUNCT
ejpam-3877	237	10	pn	pn	NOUN
ejpam-3877	237	11	)	)	PUNCT
ejpam-3877	237	12	,	,	PUNCT
ejpam-3877	237	13	with	with	ADP
ejpam-3877	237	14	ϕ	ϕ	PROPN
ejpam-3877	237	15	∈	∈	PROPN
ejpam-3877	237	16	c2,1	c2,1	PROPN
ejpam-3877	237	17	c	c	NOUN
ejpam-3877	237	18	(	(	PUNCT
ejpam-3877	237	19	q	q	NOUN
ejpam-3877	237	20	)	)	PUNCT
ejpam-3877	237	21	,	,	PUNCT
ejpam-3877	237	22	there	there	PRON
ejpam-3877	237	23	holds	hold	VERB
ejpam-3877	237	24	[	[	X
ejpam-3877	237	25	φ(tk(ψ(un))]t−div	φ(tk(ψ(un))]t−div	X
ejpam-3877	237	26	[	[	X
ejpam-3877	237	27	ψ(tk(ψ(un)))∇ψ(tk(ψ(un	ψ(tk(ψ(un)))∇ψ(tk(ψ(un	NOUN
ejpam-3877	237	28	)	)	PUNCT
ejpam-3877	237	29	)	)	PUNCT
ejpam-3877	237	30	)	)	PUNCT
ejpam-3877	237	31	]	]	PUNCT
ejpam-3877	238	1	+	+	CCONJ
ejpam-3877	238	2	|	|	ADV
ejpam-3877	238	3	∇ψ(tk(ψ(un	∇ψ(tk(ψ(un	PROPN
ejpam-3877	238	4	)	)	PUNCT
ejpam-3877	238	5	)	)	PUNCT
ejpam-3877	238	6	)	)	PUNCT
ejpam-3877	239	1	|2=	|2=	PROPN
ejpam-3877	239	2	ψ(tk(ψ(un)))µn	ψ(tk(ψ(un)))µn	PROPN
ejpam-3877	239	3	.	.	PUNCT
ejpam-3877	240	1	it	it	PRON
ejpam-3877	240	2	follows	follow	VERB
ejpam-3877	240	3	that	that	SCONJ
ejpam-3877	240	4	‖	‖	PROPN
ejpam-3877	241	1	[	[	X
ejpam-3877	241	2	φ(tk(ψ(un)))]t	φ(tk(ψ(un)))]t	X
ejpam-3877	241	3	‖l2((0,t	‖l2((0,t	NOUN
ejpam-3877	241	4	)	)	PUNCT
ejpam-3877	241	5	,	,	PUNCT
ejpam-3877	241	6	h−1(ω))+l1(q	h−1(ω))+l1(q	NUM
ejpam-3877	241	7	)	)	PUNCT
ejpam-3877	241	8	≤‖	≤‖	PROPN
ejpam-3877	241	9	ψ(tk(ψ(un)))∇ψ(tk(ψ(un	ψ(tk(ψ(un)))∇ψ(tk(ψ(un	NOUN
ejpam-3877	241	10	)	)	PUNCT
ejpam-3877	241	11	)	)	PUNCT
ejpam-3877	241	12	)	)	PUNCT
ejpam-3877	242	1	‖l2(q	‖l2(q	PROPN
ejpam-3877	242	2	)	)	PUNCT
ejpam-3877	243	1	+	+	CCONJ
ejpam-3877	243	2	‖	‖	ADJ
ejpam-3877	243	3	∇ψ(tk(ψ(un	∇ψ(tk(ψ(un	PROPN
ejpam-3877	243	4	)	)	PUNCT
ejpam-3877	243	5	)	)	PUNCT
ejpam-3877	243	6	)	)	PUNCT
ejpam-3877	244	1	‖2l1(q	‖2l1(q	X
ejpam-3877	244	2	)	)	PUNCT
ejpam-3877	245	1	+	+	CCONJ
ejpam-3877	245	2	‖	‖	ADJ
ejpam-3877	245	3	ψ(tk(ψ(un)))µn	ψ(tk(ψ(un)))µn	PROPN
ejpam-3877	245	4	‖l1(q	‖l1(q	NUM
ejpam-3877	245	5	)	)	PUNCT
ejpam-3877	245	6	.	.	PUNCT
ejpam-3877	246	1	by	by	ADP
ejpam-3877	246	2	the	the	DET
ejpam-3877	246	3	condition	condition	NOUN
ejpam-3877	246	4	(	(	PUNCT
ejpam-3877	246	5	i	i	NOUN
ejpam-3877	246	6	)	)	PUNCT
ejpam-3877	246	7	,	,	PUNCT
ejpam-3877	246	8	we	we	PRON
ejpam-3877	246	9	obtain	obtain	VERB
ejpam-3877	246	10	the	the	DET
ejpam-3877	246	11	sequence	sequence	NOUN
ejpam-3877	246	12	{	{	PUNCT
ejpam-3877	246	13	[	[	X
ejpam-3877	246	14	φ(tk(ψ(un))]t	φ(tk(ψ(un))]t	X
ejpam-3877	246	15	}	}	PUNCT
ejpam-3877	246	16	is	be	AUX
ejpam-3877	246	17	bounded	bound	VERB
ejpam-3877	246	18	in	in	ADP
ejpam-3877	246	19	l2((0	l2((0	PROPN
ejpam-3877	246	20	,	,	PUNCT
ejpam-3877	246	21	t	t	PROPN
ejpam-3877	246	22	)	)	PUNCT
ejpam-3877	246	23	,	,	PUNCT
ejpam-3877	246	24	h−1(ω))+	h−1(ω))+	VERB
ejpam-3877	246	25	l1(q	l1(q	ADV
ejpam-3877	246	26	)	)	PUNCT
ejpam-3877	246	27	.	.	PUNCT
ejpam-3877	247	1	�	�	PROPN
ejpam-3877	247	2	proof	proof	NOUN
ejpam-3877	247	3	of	of	ADP
ejpam-3877	247	4	theorem	theorem	NOUN
ejpam-3877	247	5	3.1	3.1	NUM
ejpam-3877	247	6	.	.	PUNCT
ejpam-3877	248	1	this	this	DET
ejpam-3877	248	2	proof	proof	NOUN
ejpam-3877	248	3	is	be	AUX
ejpam-3877	248	4	similar	similar	ADJ
ejpam-3877	248	5	to	to	ADP
ejpam-3877	248	6	(	(	PUNCT
ejpam-3877	248	7	[	[	X
ejpam-3877	248	8	21	21	NUM
ejpam-3877	248	9	,	,	PUNCT
ejpam-3877	248	10	theorem	theorem	VERB
ejpam-3877	248	11	1.1	1.1	NUM
ejpam-3877	248	12	]	]	PUNCT
ejpam-3877	248	13	)	)	PUNCT
ejpam-3877	248	14	.	.	PUNCT
ejpam-3877	249	1	as	as	ADP
ejpam-3877	249	2	in	in	ADP
ejpam-3877	249	3	(	(	PUNCT
ejpam-3877	249	4	[	[	X
ejpam-3877	249	5	27	27	NUM
ejpam-3877	249	6	,	,	PUNCT
ejpam-3877	249	7	proposition	proposition	NOUN
ejpam-3877	249	8	3.1	3.1	NUM
ejpam-3877	249	9	]	]	PUNCT
ejpam-3877	249	10	)	)	PUNCT
ejpam-3877	249	11	,	,	PUNCT
ejpam-3877	249	12	it	it	PRON
ejpam-3877	249	13	is	be	AUX
ejpam-3877	249	14	enough	enough	ADJ
ejpam-3877	249	15	to	to	PART
ejpam-3877	249	16	show	show	VERB
ejpam-3877	249	17	that	that	SCONJ
ejpam-3877	249	18	for	for	ADP
ejpam-3877	249	19	any	any	DET
ejpam-3877	249	20	compact	compact	NOUN
ejpam-3877	250	1	k	k	PROPN
ejpam-3877	250	2	⊂	⊂	PROPN
ejpam-3877	250	3	q	q	X
ejpam-3877	251	1	such	such	ADJ
ejpam-3877	251	2	that	that	SCONJ
ejpam-3877	251	3	µ−(k	µ−(k	NOUN
ejpam-3877	251	4	)	)	PUNCT
ejpam-3877	251	5	=	=	SYM
ejpam-3877	251	6	0	0	NUM
ejpam-3877	251	7	,	,	PUNCT
ejpam-3877	251	8	(	(	PUNCT
ejpam-3877	251	9	u−0	u−0	PROPN
ejpam-3877	251	10	⊗	⊗	PROPN
ejpam-3877	251	11	δ{t=0	δ{t=0	PROPN
ejpam-3877	251	12	}	}	PUNCT
ejpam-3877	251	13	)	)	PUNCT
ejpam-3877	251	14	(	(	PUNCT
ejpam-3877	251	15	k	k	X
ejpam-3877	251	16	)	)	PUNCT
ejpam-3877	251	17	=	=	SYM
ejpam-3877	251	18	0	0	NUM
ejpam-3877	251	19	and	and	CCONJ
ejpam-3877	251	20	cap(k	cap(k	PROPN
ejpam-3877	251	21	)	)	PUNCT
ejpam-3877	251	22	=	=	SYM
ejpam-3877	252	1	0	0	NUM
ejpam-3877	252	2	,	,	PUNCT
ejpam-3877	252	3	then	then	ADV
ejpam-3877	252	4	µ+(k	µ+(k	PROPN
ejpam-3877	252	5	)	)	PUNCT
ejpam-3877	252	6	=	=	SYM
ejpam-3877	252	7	0	0	PUNCT
ejpam-3877	253	1	and	and	CCONJ
ejpam-3877	253	2	(	(	PUNCT
ejpam-3877	253	3	u+	u+	NUM
ejpam-3877	253	4	0	0	NUM
ejpam-3877	253	5	⊗	⊗	PROPN
ejpam-3877	253	6	δ{t=0	δ{t=0	PROPN
ejpam-3877	253	7	}	}	PUNCT
ejpam-3877	253	8	)	)	PUNCT
ejpam-3877	253	9	(	(	PUNCT
ejpam-3877	253	10	k	k	X
ejpam-3877	253	11	)	)	PUNCT
ejpam-3877	253	12	=	=	SYM
ejpam-3877	254	1	0	0	X
ejpam-3877	254	2	.	.	PUNCT
ejpam-3877	255	1	by	by	ADP
ejpam-3877	255	2	the	the	DET
ejpam-3877	255	3	equivalence	equivalence	NOUN
ejpam-3877	255	4	of	of	ADP
ejpam-3877	255	5	the	the	DET
ejpam-3877	255	6	capacity	capacity	NOUN
ejpam-3877	255	7	,	,	PUNCT
ejpam-3877	255	8	we	we	PRON
ejpam-3877	255	9	have	have	VERB
ejpam-3877	255	10	cap(e	cap(e	PROPN
ejpam-3877	255	11	×	×	NOUN
ejpam-3877	255	12	{	{	PUNCT
ejpam-3877	255	13	t	t	NOUN
ejpam-3877	255	14	=	=	SYM
ejpam-3877	255	15	0	0	NUM
ejpam-3877	255	16	}	}	PUNCT
ejpam-3877	255	17	)	)	PUNCT
ejpam-3877	256	1	=	=	SYM
ejpam-3877	256	2	0	0	NUM
ejpam-3877	256	3	,	,	PUNCT
ejpam-3877	256	4	where	where	SCONJ
ejpam-3877	256	5	e	e	PROPN
ejpam-3877	256	6	a	a	DET
ejpam-3877	256	7	compact	compact	ADJ
ejpam-3877	256	8	set	set	NOUN
ejpam-3877	256	9	of	of	ADP
ejpam-3877	256	10	ω	ω	PROPN
ejpam-3877	256	11	with	with	ADP
ejpam-3877	256	12	u−0	u−0	PROPN
ejpam-3877	256	13	(	(	PUNCT
ejpam-3877	256	14	e	e	NOUN
ejpam-3877	256	15	)	)	PUNCT
ejpam-3877	256	16	=	=	SYM
ejpam-3877	256	17	0	0	X
ejpam-3877	256	18	.	.	PUNCT
ejpam-3877	257	1	let	let	VERB
ejpam-3877	257	2	ε	ε	PROPN
ejpam-3877	257	3	>	>	X
ejpam-3877	257	4	0	0	PUNCT
ejpam-3877	258	1	and	and	CCONJ
ejpam-3877	258	2	we	we	PRON
ejpam-3877	258	3	choose	choose	VERB
ejpam-3877	258	4	an	an	DET
ejpam-3877	258	5	open	open	ADJ
ejpam-3877	258	6	set	set	NOUN
ejpam-3877	258	7	u	u	PRON
ejpam-3877	258	8	such	such	ADJ
ejpam-3877	258	9	that	that	SCONJ
ejpam-3877	258	10	(	(	PUNCT
ejpam-3877	258	11	|	|	ADV
ejpam-3877	258	12	µ	µ	X
ejpam-3877	258	13	|	|	NOUN
ejpam-3877	259	1	+	+	CCONJ
ejpam-3877	259	2	|	|	ADV
ejpam-3877	259	3	u0	u0	ADJ
ejpam-3877	259	4	|	|	NOUN
ejpam-3877	259	5	⊗δ{t=0	⊗δ{t=0	VERB
ejpam-3877	259	6	}	}	PUNCT
ejpam-3877	259	7	)	)	PUNCT
ejpam-3877	260	1	(	(	PUNCT
ejpam-3877	260	2	u	u	NOUN
ejpam-3877	260	3	\	\	PROPN
ejpam-3877	260	4	k	k	PROPN
ejpam-3877	260	5	)	)	PUNCT
ejpam-3877	260	6	<	<	X
ejpam-3877	260	7	ε	ε	PROPN
ejpam-3877	260	8	and	and	CCONJ
ejpam-3877	260	9	k	k	PROPN
ejpam-3877	260	10	⊂	⊂	PROPN
ejpam-3877	260	11	u	u	PROPN
ejpam-3877	260	12	⊂	⊂	PROPN
ejpam-3877	260	13	q.	q.	PROPN
ejpam-3877	260	14	then	then	ADV
ejpam-3877	260	15	there	there	PRON
ejpam-3877	260	16	exists	exist	VERB
ejpam-3877	260	17	a	a	DET
ejpam-3877	260	18	sequence	sequence	NOUN
ejpam-3877	260	19	{	{	PUNCT
ejpam-3877	260	20	ϕn	ϕn	NOUN
ejpam-3877	260	21	}	}	PUNCT
ejpam-3877	260	22	⊆	⊆	NUM
ejpam-3877	260	23	c∞0	c∞0	PROPN
ejpam-3877	260	24	(	(	PUNCT
ejpam-3877	260	25	q	q	X
ejpam-3877	260	26	)	)	PUNCT
ejpam-3877	260	27	such	such	ADJ
ejpam-3877	260	28	that	that	SCONJ
ejpam-3877	260	29	(	(	PUNCT
ejpam-3877	260	30	i	i	NOUN
ejpam-3877	260	31	)	)	PUNCT
ejpam-3877	260	32	0	0	NUM
ejpam-3877	261	1	≤	≤	NUM
ejpam-3877	261	2	ϕn	ϕn	VERB
ejpam-3877	261	3	≤	≤	ADJ
ejpam-3877	261	4	1	1	NUM
ejpam-3877	261	5	in	in	ADP
ejpam-3877	261	6	q	q	PROPN
ejpam-3877	261	7	,	,	PUNCT
ejpam-3877	261	8	ϕn	ϕn	ADP
ejpam-3877	261	9	≡	≡	PROPN
ejpam-3877	261	10	1	1	NUM
ejpam-3877	261	11	in	in	ADP
ejpam-3877	261	12	k.	k.	PROPN
ejpam-3877	261	13	(	(	PUNCT
ejpam-3877	261	14	ii	ii	PROPN
ejpam-3877	261	15	)	)	PUNCT
ejpam-3877	261	16	‖	‖	PROPN
ejpam-3877	261	17	∆ϕn	∆ϕn	X
ejpam-3877	261	18	‖l1(q)→	‖l1(q)→	PUNCT
ejpam-3877	261	19	0	0	PUNCT
ejpam-3877	261	20	as	as	ADP
ejpam-3877	261	21	n→∞.	n→∞.	ADJ
ejpam-3877	261	22	in	in	ADP
ejpam-3877	261	23	particular	particular	ADJ
ejpam-3877	261	24	,	,	PUNCT
ejpam-3877	261	25	ϕn	ϕn	X
ejpam-3877	261	26	→	→	X
ejpam-3877	261	27	0	0	NUM
ejpam-3877	261	28	in	in	ADP
ejpam-3877	261	29	w	w	PROPN
ejpam-3877	261	30	,	,	PUNCT
ejpam-3877	261	31	indeed∫	indeed∫	PROPN
ejpam-3877	261	32	q	q	NOUN
ejpam-3877	262	1	|	|	ADV
ejpam-3877	262	2	∇ϕn	∇ϕn	ADJ
ejpam-3877	262	3	|2	|2	NUM
ejpam-3877	262	4	dxdt	dxdt	NOUN
ejpam-3877	262	5	=	=	PUNCT
ejpam-3877	263	1	−	−	PROPN
ejpam-3877	263	2	∫	∫	PROPN
ejpam-3877	263	3	q	q	PROPN
ejpam-3877	264	1	ϕn∆ϕndxdt	ϕn∆ϕndxdt	PROPN
ejpam-3877	264	2	≤	≤	NUM
ejpam-3877	265	1	∫	∫	PROPN
ejpam-3877	265	2	q	q	PROPN
ejpam-3877	266	1	|	|	NOUN
ejpam-3877	266	2	∆ϕn	∆ϕn	NOUN
ejpam-3877	266	3	|	|	NOUN
ejpam-3877	266	4	dxdt	dxdt	NOUN
ejpam-3877	266	5	.	.	PUNCT
ejpam-3877	267	1	let	let	VERB
ejpam-3877	267	2	us	we	PRON
ejpam-3877	267	3	consider	consider	VERB
ejpam-3877	267	4	ϕn	ϕn	PRON
ejpam-3877	267	5	as	as	ADP
ejpam-3877	267	6	a	a	DET
ejpam-3877	267	7	test	test	NOUN
ejpam-3877	267	8	function	function	NOUN
ejpam-3877	267	9	in	in	ADP
ejpam-3877	267	10	(	(	PUNCT
ejpam-3877	267	11	p	p	NOUN
ejpam-3877	267	12	)	)	PUNCT
ejpam-3877	267	13	,	,	PUNCT
ejpam-3877	267	14	there	there	PRON
ejpam-3877	267	15	holds∫	holds∫	VERB
ejpam-3877	267	16	q	q	PROPN
ejpam-3877	268	1	ϕndµ+	ϕndµ+	NUM
ejpam-3877	268	2	∫	∫	PROPN
ejpam-3877	269	1	ω	ω	NUM
ejpam-3877	269	2	ϕn(0)du0	ϕn(0)du0	NOUN
ejpam-3877	269	3	=	=	PUNCT
ejpam-3877	269	4	−	−	PROPN
ejpam-3877	269	5	∫	∫	PROPN
ejpam-3877	269	6	q	q	PROPN
ejpam-3877	269	7	ψ(ur)∆ϕndxdt	ψ(ur)∆ϕndxdt	PROPN
ejpam-3877	269	8	.	.	PROPN
ejpam-3877	269	9	(	(	PUNCT
ejpam-3877	269	10	4.9	4.9	NUM
ejpam-3877	269	11	)	)	PUNCT
ejpam-3877	269	12	on	on	ADP
ejpam-3877	269	13	the	the	DET
ejpam-3877	269	14	other	other	ADJ
ejpam-3877	269	15	hand	hand	NOUN
ejpam-3877	269	16	,	,	PUNCT
ejpam-3877	269	17	we	we	PRON
ejpam-3877	269	18	get∫	get∫	VERB
ejpam-3877	269	19	q	q	NOUN
ejpam-3877	270	1	ϕndµ+	ϕndµ+	NUM
ejpam-3877	270	2	∫	∫	PROPN
ejpam-3877	271	1	ω	ω	NUM
ejpam-3877	271	2	ϕn(0)du0	ϕn(0)du0	PROPN
ejpam-3877	271	3	≥	≥	PROPN
ejpam-3877	271	4	µ+(k	µ+(k	PROPN
ejpam-3877	271	5	)	)	PUNCT
ejpam-3877	272	1	+	+	CCONJ
ejpam-3877	272	2	(	(	PUNCT
ejpam-3877	272	3	u+	u+	NUM
ejpam-3877	272	4	0	0	NUM
ejpam-3877	272	5	⊗	⊗	PROPN
ejpam-3877	272	6	δ{t=0	δ{t=0	PROPN
ejpam-3877	272	7	}	}	PUNCT
ejpam-3877	272	8	)	)	PUNCT
ejpam-3877	272	9	(	(	PUNCT
ejpam-3877	272	10	k	k	X
ejpam-3877	272	11	)	)	PUNCT
ejpam-3877	272	12	quincy	quincy	PROPN
ejpam-3877	272	13	s.	s.	PROPN
ejpam-3877	272	14	nkombo	nkombo	PROPN
ejpam-3877	272	15	,	,	PUNCT
ejpam-3877	272	16	fengquan	fengquan	PROPN
ejpam-3877	272	17	li	li	PROPN
ejpam-3877	272	18	/	/	SYM
ejpam-3877	272	19	eur	eur	PROPN
ejpam-3877	272	20	.	.	PUNCT
ejpam-3877	273	1	j.	j.	PROPN
ejpam-3877	273	2	pure	pure	PROPN
ejpam-3877	273	3	appl	appl	PROPN
ejpam-3877	273	4	.	.	PROPN
ejpam-3877	273	5	math	math	PROPN
ejpam-3877	273	6	,	,	PUNCT
ejpam-3877	273	7	14	14	NUM
ejpam-3877	273	8	(	(	PUNCT
ejpam-3877	273	9	1	1	NUM
ejpam-3877	273	10	)	)	PUNCT
ejpam-3877	273	11	(	(	PUNCT
ejpam-3877	273	12	2021	2021	NUM
ejpam-3877	273	13	)	)	PUNCT
ejpam-3877	273	14	,	,	PUNCT
ejpam-3877	273	15	204	204	NUM
ejpam-3877	273	16	-	-	SYM
ejpam-3877	273	17	233	233	NUM
ejpam-3877	273	18	216	216	NUM
ejpam-3877	273	19	−	−	PROPN
ejpam-3877	273	20	(	(	PUNCT
ejpam-3877	273	21	|	|	ADV
ejpam-3877	273	22	µ	µ	X
ejpam-3877	274	1	|	|	NOUN
ejpam-3877	275	1	+	+	CCONJ
ejpam-3877	275	2	|	|	ADV
ejpam-3877	275	3	u0	u0	ADJ
ejpam-3877	275	4	|	|	NOUN
ejpam-3877	275	5	⊗δ{t=0	⊗δ{t=0	VERB
ejpam-3877	275	6	}	}	PUNCT
ejpam-3877	275	7	)	)	PUNCT
ejpam-3877	276	1	(	(	PUNCT
ejpam-3877	276	2	u	u	NOUN
ejpam-3877	276	3	\k	\k	NOUN
ejpam-3877	276	4	)	)	PUNCT
ejpam-3877	276	5	.	.	PUNCT
ejpam-3877	277	1	it	it	PRON
ejpam-3877	277	2	follows	follow	VERB
ejpam-3877	277	3	that	that	SCONJ
ejpam-3877	277	4	∫	∫	PROPN
ejpam-3877	277	5	q	q	PROPN
ejpam-3877	278	1	ϕndµ+	ϕndµ+	X
ejpam-3877	278	2	∫	∫	PROPN
ejpam-3877	279	1	ω	ω	NUM
ejpam-3877	279	2	ϕn(0)du0	ϕn(0)du0	PROPN
ejpam-3877	279	3	≥	≥	PROPN
ejpam-3877	279	4	µ+(k	µ+(k	PROPN
ejpam-3877	279	5	)	)	PUNCT
ejpam-3877	280	1	+	+	CCONJ
ejpam-3877	280	2	(	(	PUNCT
ejpam-3877	280	3	u+	u+	NUM
ejpam-3877	280	4	0	0	NUM
ejpam-3877	280	5	⊗	⊗	PROPN
ejpam-3877	280	6	δ{t=0	δ{t=0	PROPN
ejpam-3877	280	7	}	}	PUNCT
ejpam-3877	280	8	)	)	PUNCT
ejpam-3877	280	9	(	(	PUNCT
ejpam-3877	280	10	k)−	k)−	PROPN
ejpam-3877	280	11	ε	ε	PROPN
ejpam-3877	280	12	.	.	PUNCT
ejpam-3877	281	1	(	(	PUNCT
ejpam-3877	281	2	4.10	4.10	NUM
ejpam-3877	281	3	)	)	PUNCT
ejpam-3877	281	4	combining	combine	VERB
ejpam-3877	281	5	(	(	PUNCT
ejpam-3877	281	6	4.11	4.11	NUM
ejpam-3877	281	7	)	)	PUNCT
ejpam-3877	281	8	with	with	ADP
ejpam-3877	281	9	(	(	PUNCT
ejpam-3877	281	10	4.12	4.12	NUM
ejpam-3877	281	11	)	)	PUNCT
ejpam-3877	281	12	,	,	PUNCT
ejpam-3877	281	13	we	we	PRON
ejpam-3877	281	14	obtain	obtain	VERB
ejpam-3877	281	15	that	that	DET
ejpam-3877	281	16	µ+(k	µ+(k	PROPN
ejpam-3877	281	17	)	)	PUNCT
ejpam-3877	282	1	+	+	CCONJ
ejpam-3877	282	2	(	(	PUNCT
ejpam-3877	282	3	u+	u+	NUM
ejpam-3877	282	4	0	0	NUM
ejpam-3877	282	5	⊗	⊗	PROPN
ejpam-3877	282	6	δ{t=0	δ{t=0	PROPN
ejpam-3877	282	7	}	}	PUNCT
ejpam-3877	282	8	)	)	PUNCT
ejpam-3877	282	9	(	(	PUNCT
ejpam-3877	282	10	k	k	X
ejpam-3877	282	11	)	)	PUNCT
ejpam-3877	282	12	≤‖	≤‖	PROPN
ejpam-3877	282	13	ψ	ψ	ADP
ejpam-3877	282	14	‖l∞(q)‖	‖l∞(q)‖	ADJ
ejpam-3877	282	15	∆ϕn	∆ϕn	NOUN
ejpam-3877	282	16	‖l1(q	‖l1(q	NOUN
ejpam-3877	282	17	)	)	PUNCT
ejpam-3877	282	18	+	+	PROPN
ejpam-3877	282	19	ε	ε	PROPN
ejpam-3877	282	20	.	.	PUNCT
ejpam-3877	282	21	letting	let	VERB
ejpam-3877	282	22	n	n	PART
ejpam-3877	282	23	to	to	PART
ejpam-3877	282	24	infinity	infinity	NOUN
ejpam-3877	282	25	,	,	PUNCT
ejpam-3877	282	26	we	we	PRON
ejpam-3877	282	27	infer	infer	VERB
ejpam-3877	282	28	that	that	SCONJ
ejpam-3877	282	29	µ+(k	µ+(k	PROPN
ejpam-3877	282	30	)	)	PUNCT
ejpam-3877	283	1	=	=	PUNCT
ejpam-3877	283	2	(	(	PUNCT
ejpam-3877	283	3	u+	u+	NUM
ejpam-3877	283	4	0	0	NUM
ejpam-3877	283	5	⊗	⊗	PROPN
ejpam-3877	283	6	δ{t=0	δ{t=0	PROPN
ejpam-3877	283	7	}	}	PUNCT
ejpam-3877	283	8	)	)	PUNCT
ejpam-3877	283	9	(	(	PUNCT
ejpam-3877	283	10	k	k	X
ejpam-3877	283	11	)	)	PUNCT
ejpam-3877	283	12	=	=	SYM
ejpam-3877	283	13	0	0	X
ejpam-3877	283	14	.	.	PUNCT
ejpam-3877	283	15	�	�	PROPN
ejpam-3877	283	16	proof	proof	NOUN
ejpam-3877	283	17	of	of	ADP
ejpam-3877	283	18	theorem	theorem	NOUN
ejpam-3877	283	19	3.2	3.2	NUM
ejpam-3877	283	20	.	.	PUNCT
ejpam-3877	284	1	let	let	VERB
ejpam-3877	284	2	k	k	PROPN
ejpam-3877	284	3	⊆	⊆	NUM
ejpam-3877	284	4	ω	ω	NUM
ejpam-3877	284	5	be	be	AUX
ejpam-3877	284	6	any	any	DET
ejpam-3877	284	7	compact	compact	ADJ
ejpam-3877	284	8	set	set	NOUN
ejpam-3877	284	9	such	such	ADJ
ejpam-3877	284	10	that	that	SCONJ
ejpam-3877	284	11	c2(k	c2(k	PROPN
ejpam-3877	284	12	)	)	PUNCT
ejpam-3877	284	13	=	=	SYM
ejpam-3877	284	14	0	0	NUM
ejpam-3877	284	15	,	,	PUNCT
ejpam-3877	284	16	there	there	PRON
ejpam-3877	284	17	exists	exist	VERB
ejpam-3877	284	18	a	a	DET
ejpam-3877	284	19	sequence	sequence	NOUN
ejpam-3877	284	20	{	{	PUNCT
ejpam-3877	284	21	φn	φn	NOUN
ejpam-3877	284	22	}	}	PUNCT
ejpam-3877	284	23	⊆	⊆	NUM
ejpam-3877	284	24	c∞c	c∞c	ADJ
ejpam-3877	284	25	(	(	PUNCT
ejpam-3877	284	26	ω	ω	NOUN
ejpam-3877	284	27	)	)	PUNCT
ejpam-3877	284	28	satisfying	satisfying	NOUN
ejpam-3877	284	29	(	(	PUNCT
ejpam-3877	284	30	iv	iv	X
ejpam-3877	284	31	)	)	PUNCT
ejpam-3877	284	32	and	and	CCONJ
ejpam-3877	284	33	(	(	PUNCT
ejpam-3877	284	34	viii	viii	NOUN
ejpam-3877	284	35	)	)	PUNCT
ejpam-3877	284	36	as	as	SCONJ
ejpam-3877	284	37	stated	state	VERB
ejpam-3877	284	38	in	in	ADP
ejpam-3877	284	39	preliminaries	preliminary	NOUN
ejpam-3877	284	40	,	,	PUNCT
ejpam-3877	284	41	section	section	NOUN
ejpam-3877	284	42	2	2	NUM
ejpam-3877	284	43	.	.	PUNCT
ejpam-3877	285	1	furthermore	furthermore	ADV
ejpam-3877	285	2	,	,	PUNCT
ejpam-3877	285	3	ρv	ρv	ADP
ejpam-3877	285	4	∈	∈	PROPN
ejpam-3877	285	5	c∞c	c∞c	ADJ
ejpam-3877	285	6	(	(	PUNCT
ejpam-3877	285	7	v	v	NOUN
ejpam-3877	285	8	)	)	PUNCT
ejpam-3877	285	9	be	be	AUX
ejpam-3877	285	10	any	any	DET
ejpam-3877	285	11	smooth	smooth	ADJ
ejpam-3877	285	12	function	function	NOUN
ejpam-3877	285	13	such	such	ADJ
ejpam-3877	285	14	that	that	SCONJ
ejpam-3877	285	15	(	(	PUNCT
ejpam-3877	285	16	iii	iii	NOUN
ejpam-3877	285	17	)	)	PUNCT
ejpam-3877	285	18	0	0	NUM
ejpam-3877	285	19	≤	≤	NUM
ejpam-3877	285	20	ρv	ρv	ADP
ejpam-3877	285	21	≤	≤	NUM
ejpam-3877	285	22	1	1	NUM
ejpam-3877	285	23	in	in	ADP
ejpam-3877	285	24	ω	ω	NUM
ejpam-3877	285	25	,	,	PUNCT
ejpam-3877	285	26	ρv	ρv	ADP
ejpam-3877	285	27	≡	≡	PROPN
ejpam-3877	285	28	1	1	NUM
ejpam-3877	285	29	in	in	ADP
ejpam-3877	285	30	k.	k.	PROPN
ejpam-3877	285	31	by	by	ADP
ejpam-3877	285	32	standard	standard	ADJ
ejpam-3877	285	33	regularization	regularization	NOUN
ejpam-3877	285	34	argument	argument	NOUN
ejpam-3877	285	35	,	,	PUNCT
ejpam-3877	285	36	we	we	PRON
ejpam-3877	285	37	consider	consider	VERB
ejpam-3877	285	38	φτ	φτ	NOUN
ejpam-3877	285	39	(	(	PUNCT
ejpam-3877	285	40	x	x	NOUN
ejpam-3877	285	41	,	,	PUNCT
ejpam-3877	285	42	s	s	PART
ejpam-3877	285	43	)	)	PUNCT
ejpam-3877	285	44	=	=	SYM
ejpam-3877	285	45	ρ(x)ητ	ρ(x)ητ	PROPN
ejpam-3877	285	46	(	(	PUNCT
ejpam-3877	285	47	s	s	NOUN
ejpam-3877	285	48	)	)	PUNCT
ejpam-3877	285	49	as	as	ADP
ejpam-3877	285	50	a	a	DET
ejpam-3877	285	51	test	test	NOUN
ejpam-3877	285	52	function	function	NOUN
ejpam-3877	285	53	in	in	ADP
ejpam-3877	285	54	(	(	PUNCT
ejpam-3877	285	55	3.8	3.8	NUM
ejpam-3877	285	56	)	)	PUNCT
ejpam-3877	285	57	,	,	PUNCT
ejpam-3877	285	58	where	where	SCONJ
ejpam-3877	285	59	ητ	ητ	PROPN
ejpam-3877	285	60	(	(	PUNCT
ejpam-3877	285	61	s	s	NOUN
ejpam-3877	285	62	)	)	PUNCT
ejpam-3877	285	63	=	=	SYM
ejpam-3877	286	1			NOUN
ejpam-3877	286	2	1	1	NUM
ejpam-3877	286	3	if	if	SCONJ
ejpam-3877	286	4	0	0	NUM
ejpam-3877	286	5	≤	≤	NUM
ejpam-3877	286	6	s	s	PART
ejpam-3877	286	7	≤	≤	NUM
ejpam-3877	286	8	t	t	PROPN
ejpam-3877	286	9	,	,	PUNCT
ejpam-3877	286	10	1	1	NUM
ejpam-3877	286	11	τ	τ	X
ejpam-3877	286	12	(	(	PUNCT
ejpam-3877	286	13	t+	t+	NOUN
ejpam-3877	286	14	τ	τ	PROPN
ejpam-3877	286	15	−	−	PROPN
ejpam-3877	286	16	s	s	PART
ejpam-3877	286	17	)	)	PUNCT
ejpam-3877	286	18	if	if	SCONJ
ejpam-3877	286	19	t	t	PROPN
ejpam-3877	286	20	≤	≤	NOUN
ejpam-3877	286	21	s	s	PART
ejpam-3877	286	22	≤	≤	NOUN
ejpam-3877	286	23	t+	t+	X
ejpam-3877	286	24	τ	τ	PROPN
ejpam-3877	286	25	,	,	PUNCT
ejpam-3877	286	26	0	0	PUNCT
ejpam-3877	287	1	if	if	SCONJ
ejpam-3877	287	2	s	s	PRON
ejpam-3877	287	3	≥	≥	NOUN
ejpam-3877	287	4	t+	t+	PUNCT
ejpam-3877	287	5	τ	τ	X
ejpam-3877	287	6	,	,	PUNCT
ejpam-3877	287	7	for	for	ADP
ejpam-3877	287	8	any	any	DET
ejpam-3877	287	9	ρ	ρ	PROPN
ejpam-3877	287	10	∈	∈	PROPN
ejpam-3877	287	11	c2	c2	PROPN
ejpam-3877	287	12	0	0	NUM
ejpam-3877	287	13	(	(	PUNCT
ejpam-3877	287	14	ω	ω	NOUN
ejpam-3877	287	15	)	)	PUNCT
ejpam-3877	287	16	and	and	CCONJ
ejpam-3877	287	17	τ	τ	X
ejpam-3877	287	18	>	>	X
ejpam-3877	287	19	0	0	X
ejpam-3877	287	20	.	.	PUNCT
ejpam-3877	288	1	there	there	PRON
ejpam-3877	288	2	holds	hold	VERB
ejpam-3877	288	3	1	1	NUM
ejpam-3877	288	4	τ	τ	PROPN
ejpam-3877	288	5	∫	∫	PROPN
ejpam-3877	288	6	t+τ	t+τ	NUM
ejpam-3877	288	7	t	t	PROPN
ejpam-3877	288	8	〈	〈	PROPN
ejpam-3877	288	9	u(s	u(s	NUM
ejpam-3877	288	10	)	)	PUNCT
ejpam-3877	288	11	,	,	PUNCT
ejpam-3877	288	12	ρ〉ω	ρ〉ω	PROPN
ejpam-3877	288	13	ds−	ds−	PROPN
ejpam-3877	288	14	〈	〈	NOUN
ejpam-3877	288	15	u0	u0	ADJ
ejpam-3877	288	16	,	,	PUNCT
ejpam-3877	288	17	ρ〉ω	ρ〉ω	PROPN
ejpam-3877	288	18	=	=	SYM
ejpam-3877	288	19	∫	∫	PROPN
ejpam-3877	288	20	t	t	PROPN
ejpam-3877	288	21	0	0	NUM
ejpam-3877	288	22	ητ	ητ	PROPN
ejpam-3877	288	23	(	(	PUNCT
ejpam-3877	288	24	s)ds	s)ds	PROPN
ejpam-3877	288	25	∫	∫	PROPN
ejpam-3877	288	26	ω	ω	PROPN
ejpam-3877	288	27	ψ(ur)∆ρdx+	ψ(ur)∆ρdx+	NUM
ejpam-3877	288	28	∫	∫	PROPN
ejpam-3877	288	29	t	t	PROPN
ejpam-3877	288	30	0	0	NUM
ejpam-3877	288	31	ητ	ητ	PROPN
ejpam-3877	288	32	(	(	PUNCT
ejpam-3877	288	33	s	s	NOUN
ejpam-3877	288	34	)	)	PUNCT
ejpam-3877	288	35	∫	∫	PROPN
ejpam-3877	288	36	ω	ω	NUM
ejpam-3877	288	37	ρdµ.	ρdµ.	NOUN
ejpam-3877	288	38	since	since	SCONJ
ejpam-3877	288	39	ητ	ητ	PROPN
ejpam-3877	288	40	(	(	PUNCT
ejpam-3877	288	41	s	s	NOUN
ejpam-3877	288	42	)	)	PUNCT
ejpam-3877	288	43	→	→	X
ejpam-3877	288	44	χ(0,t	χ(0,t	NOUN
ejpam-3877	288	45	]	]	PUNCT
ejpam-3877	288	46	for	for	ADP
ejpam-3877	288	47	every	every	DET
ejpam-3877	288	48	s	s	X
ejpam-3877	288	49	∈	∈	PROPN
ejpam-3877	288	50	(	(	PUNCT
ejpam-3877	288	51	0	0	NUM
ejpam-3877	288	52	,	,	PUNCT
ejpam-3877	288	53	t	t	PROPN
ejpam-3877	288	54	)	)	PUNCT
ejpam-3877	288	55	as	as	ADP
ejpam-3877	288	56	τ	τ	PROPN
ejpam-3877	288	57	→	→	SYM
ejpam-3877	288	58	0	0	NUM
ejpam-3877	288	59	and	and	CCONJ
ejpam-3877	288	60	we	we	PRON
ejpam-3877	288	61	replace	replace	VERB
ejpam-3877	288	62	the	the	DET
ejpam-3877	288	63	test	test	NOUN
ejpam-3877	288	64	function	function	NOUN
ejpam-3877	288	65	ρ	ρ	PROPN
ejpam-3877	288	66	by	by	ADP
ejpam-3877	288	67	φn(x)ρv	φn(x)ρv	PROPN
ejpam-3877	288	68	(	(	PUNCT
ejpam-3877	288	69	x	x	NOUN
ejpam-3877	288	70	)	)	PUNCT
ejpam-3877	288	71	.	.	PUNCT
ejpam-3877	289	1	then	then	ADV
ejpam-3877	289	2	we	we	PRON
ejpam-3877	289	3	infer	infer	VERB
ejpam-3877	289	4	that	that	SCONJ
ejpam-3877	289	5	〈	〈	PROPN
ejpam-3877	289	6	u	u	PRON
ejpam-3877	289	7	(	(	PUNCT
ejpam-3877	289	8	·	·	PROPN
ejpam-3877	289	9	,	,	PUNCT
ejpam-3877	289	10	t	t	PROPN
ejpam-3877	289	11	)	)	PUNCT
ejpam-3877	289	12	,	,	PUNCT
ejpam-3877	289	13	φnρv	φnρv	VERB
ejpam-3877	289	14	〉	〉	PROPN
ejpam-3877	289	15	ω	ω	NUM
ejpam-3877	289	16	−	−	NOUN
ejpam-3877	289	17	〈	〈	PROPN
ejpam-3877	289	18	u0	u0	PROPN
ejpam-3877	289	19	,	,	PUNCT
ejpam-3877	289	20	φnρv	φnρv	VERB
ejpam-3877	289	21	〉	〉	PROPN
ejpam-3877	289	22	ω	ω	PROPN
ejpam-3877	289	23	=	=	SYM
ejpam-3877	289	24	∫	∫	PROPN
ejpam-3877	289	25	t	t	PROPN
ejpam-3877	289	26	0	0	NUM
ejpam-3877	289	27	∫	∫	PROPN
ejpam-3877	289	28	ω	ω	PROPN
ejpam-3877	289	29	ψ(ur)∆(φnρv	ψ(ur)∆(φnρv	PROPN
ejpam-3877	289	30	)	)	PUNCT
ejpam-3877	289	31	dxds+	dxds+	PROPN
ejpam-3877	290	1	∫	∫	PROPN
ejpam-3877	290	2	t	t	PROPN
ejpam-3877	290	3	0	0	NUM
ejpam-3877	290	4	∫	∫	PROPN
ejpam-3877	290	5	ω	ω	PROPN
ejpam-3877	290	6	(	(	PUNCT
ejpam-3877	290	7	φnρv	φnρv	ADJ
ejpam-3877	290	8	)	)	PUNCT
ejpam-3877	290	9	dµ.	dµ.	VERB
ejpam-3877	290	10	by	by	ADP
ejpam-3877	290	11	(	(	PUNCT
ejpam-3877	290	12	[	[	X
ejpam-3877	290	13	14	14	NUM
ejpam-3877	290	14	,	,	PUNCT
ejpam-3877	290	15	theorem	theorem	VERB
ejpam-3877	290	16	8	8	NUM
ejpam-3877	290	17	,	,	PUNCT
ejpam-3877	290	18	p.85	p.85	ADP
ejpam-3877	290	19	]	]	PUNCT
ejpam-3877	290	20	)	)	PUNCT
ejpam-3877	290	21	,	,	PUNCT
ejpam-3877	290	22	the	the	DET
ejpam-3877	290	23	measure	measure	NOUN
ejpam-3877	290	24	µ	µ	PRON
ejpam-3877	290	25	∈m+(q	∈m+(q	NOUN
ejpam-3877	290	26	)	)	PUNCT
ejpam-3877	290	27	can	can	AUX
ejpam-3877	290	28	be	be	AUX
ejpam-3877	290	29	decomposed	decompose	VERB
ejpam-3877	290	30	as	as	ADP
ejpam-3877	290	31	λ	λ	PROPN
ejpam-3877	290	32	∈m+(0	∈m+(0	PROPN
ejpam-3877	290	33	,	,	PUNCT
ejpam-3877	290	34	t	t	PROPN
ejpam-3877	290	35	)	)	PUNCT
ejpam-3877	290	36	and	and	CCONJ
ejpam-3877	290	37	νt	νt	PROPN
ejpam-3877	290	38	∈m+(ω	∈m+(ω	NOUN
ejpam-3877	290	39	)	)	PUNCT
ejpam-3877	290	40	such	such	ADJ
ejpam-3877	290	41	that	that	PRON
ejpam-3877	290	42	for	for	ADP
ejpam-3877	290	43	φnρv	φnρv	ADJ
ejpam-3877	290	44	∈	∈	PROPN
ejpam-3877	290	45	c(ω	c(ω	PROPN
ejpam-3877	290	46	)	)	PUNCT
ejpam-3877	290	47	,	,	PUNCT
ejpam-3877	290	48	there	there	PRON
ejpam-3877	290	49	holds	hold	VERB
ejpam-3877	290	50	〈	〈	PROPN
ejpam-3877	290	51	µ	µ	NUM
ejpam-3877	290	52	,	,	PUNCT
ejpam-3877	290	53	φnρv	φnρv	ADJ
ejpam-3877	290	54	〉	〉	NOUN
ejpam-3877	290	55	q	q	NOUN
ejpam-3877	290	56	=	=	PRON
ejpam-3877	290	57	∫	∫	PROPN
ejpam-3877	290	58	(	(	PUNCT
ejpam-3877	290	59	0,t	0,t	PROPN
ejpam-3877	290	60	)	)	PUNCT
ejpam-3877	290	61	dλ(s	dλ(s	PROPN
ejpam-3877	290	62	)	)	PUNCT
ejpam-3877	291	1	∫	∫	PROPN
ejpam-3877	291	2	ω	ω	PROPN
ejpam-3877	291	3	φnρv	φnρv	PROPN
ejpam-3877	291	4	dν	dν	PROPN
ejpam-3877	291	5	t	t	PROPN
ejpam-3877	291	6	with	with	ADP
ejpam-3877	291	7	λ(s	λ(s	PROPN
ejpam-3877	291	8	)	)	PUNCT
ejpam-3877	291	9	:	:	PUNCT
ejpam-3877	291	10	=	=	SYM
ejpam-3877	291	11	δ(0,t	δ(0,t	NOUN
ejpam-3877	291	12	)	)	PUNCT
ejpam-3877	291	13	(	(	PUNCT
ejpam-3877	291	14	s	s	NOUN
ejpam-3877	291	15	)	)	PUNCT
ejpam-3877	291	16	,	,	PUNCT
ejpam-3877	291	17	where	where	SCONJ
ejpam-3877	291	18	δ(0,t	δ(0,t	NOUN
ejpam-3877	291	19	)	)	PUNCT
ejpam-3877	291	20	a	a	DET
ejpam-3877	291	21	dirac	dirac	NOUN
ejpam-3877	291	22	measure	measure	NOUN
ejpam-3877	291	23	on	on	ADP
ejpam-3877	291	24	(	(	PUNCT
ejpam-3877	291	25	0,t	0,t	PROPN
ejpam-3877	291	26	)	)	PUNCT
ejpam-3877	291	27	.	.	PUNCT
ejpam-3877	292	1	therefore	therefore	ADV
ejpam-3877	292	2	,	,	PUNCT
ejpam-3877	292	3	〈	〈	PROPN
ejpam-3877	292	4	[	[	X
ejpam-3877	292	5	u	u	NOUN
ejpam-3877	292	6	(	(	PUNCT
ejpam-3877	292	7	·	·	PUNCT
ejpam-3877	292	8	,	,	PUNCT
ejpam-3877	292	9	t)]c,2	t)]c,2	PROPN
ejpam-3877	292	10	,	,	PUNCT
ejpam-3877	292	11	φnρv	φnρv	VERB
ejpam-3877	292	12	〉	〉	PROPN
ejpam-3877	292	13	ω	ω	PROPN
ejpam-3877	292	14	+	+	CCONJ
ejpam-3877	292	15	〈	〈	PROPN
ejpam-3877	292	16	[	[	X
ejpam-3877	292	17	u	u	NOUN
ejpam-3877	292	18	(	(	PUNCT
ejpam-3877	292	19	·	·	PUNCT
ejpam-3877	292	20	,	,	PUNCT
ejpam-3877	292	21	t)]d,2	t)]d,2	NOUN
ejpam-3877	292	22	,	,	PUNCT
ejpam-3877	292	23	φnρv	φnρv	VERB
ejpam-3877	292	24	〉	〉	PROPN
ejpam-3877	292	25	ω	ω	PROPN
ejpam-3877	292	26	=	=	PROPN
ejpam-3877	292	27	quincy	quincy	PROPN
ejpam-3877	292	28	s.	s.	PROPN
ejpam-3877	292	29	nkombo	nkombo	PROPN
ejpam-3877	292	30	,	,	PUNCT
ejpam-3877	292	31	fengquan	fengquan	PROPN
ejpam-3877	292	32	li	li	PROPN
ejpam-3877	292	33	/	/	SYM
ejpam-3877	292	34	eur	eur	PROPN
ejpam-3877	292	35	.	.	PUNCT
ejpam-3877	293	1	j.	j.	PROPN
ejpam-3877	293	2	pure	pure	PROPN
ejpam-3877	293	3	appl	appl	PROPN
ejpam-3877	293	4	.	.	PROPN
ejpam-3877	293	5	math	math	PROPN
ejpam-3877	293	6	,	,	PUNCT
ejpam-3877	293	7	14	14	NUM
ejpam-3877	293	8	(	(	PUNCT
ejpam-3877	293	9	1	1	NUM
ejpam-3877	293	10	)	)	PUNCT
ejpam-3877	293	11	(	(	PUNCT
ejpam-3877	293	12	2021	2021	NUM
ejpam-3877	293	13	)	)	PUNCT
ejpam-3877	293	14	,	,	PUNCT
ejpam-3877	293	15	204	204	NUM
ejpam-3877	293	16	-	-	SYM
ejpam-3877	293	17	233	233	NUM
ejpam-3877	293	18	217	217	NUM
ejpam-3877	293	19	=	=	SYM
ejpam-3877	293	20	∫	∫	PROPN
ejpam-3877	293	21	t	t	PROPN
ejpam-3877	293	22	0	0	NUM
ejpam-3877	294	1	∫	∫	PROPN
ejpam-3877	294	2	ω	ω	PROPN
ejpam-3877	294	3	ψ(ur)∆(φnρv	ψ(ur)∆(φnρv	PROPN
ejpam-3877	294	4	)	)	PUNCT
ejpam-3877	294	5	dxds+	dxds+	PROPN
ejpam-3877	295	1	〈	〈	PROPN
ejpam-3877	296	1	[	[	X
ejpam-3877	296	2	νt]c,2	νt]c,2	PROPN
ejpam-3877	296	3	,	,	PUNCT
ejpam-3877	296	4	φnρv	φnρv	ADJ
ejpam-3877	296	5	〉	〉	NOUN
ejpam-3877	296	6	ω	ω	PROPN
ejpam-3877	296	7	+	+	CCONJ
ejpam-3877	296	8	+	+	CCONJ
ejpam-3877	296	9	〈	〈	PROPN
ejpam-3877	296	10	[	[	X
ejpam-3877	296	11	νt]d,2	νt]d,2	NUM
ejpam-3877	296	12	,	,	PUNCT
ejpam-3877	296	13	φnρv	φnρv	ADJ
ejpam-3877	296	14	〉	〉	NOUN
ejpam-3877	296	15	ω	ω	PROPN
ejpam-3877	297	1	+	+	CCONJ
ejpam-3877	297	2	〈	〈	PROPN
ejpam-3877	297	3	[	[	X
ejpam-3877	297	4	u0]c,2	u0]c,2	PROPN
ejpam-3877	297	5	,	,	PUNCT
ejpam-3877	297	6	φnρv	φnρv	ADJ
ejpam-3877	297	7	〉	〉	PROPN
ejpam-3877	297	8	ω	ω	PROPN
ejpam-3877	297	9	+	+	X
ejpam-3877	298	1	〈	〈	PROPN
ejpam-3877	298	2	[	[	NOUN
ejpam-3877	298	3	u0]d,2	u0]d,2	NOUN
ejpam-3877	298	4	,	,	PUNCT
ejpam-3877	298	5	φnρv	φnρv	ADJ
ejpam-3877	298	6	〉	〉	PROPN
ejpam-3877	298	7	ω	ω	PROPN
ejpam-3877	298	8	.	.	PUNCT
ejpam-3877	299	1	(	(	PUNCT
ejpam-3877	299	2	4.11	4.11	NUM
ejpam-3877	299	3	)	)	PUNCT
ejpam-3877	299	4	by	by	ADP
ejpam-3877	299	5	the	the	DET
ejpam-3877	299	6	assumptions	assumption	NOUN
ejpam-3877	299	7	stated	state	VERB
ejpam-3877	299	8	above	above	ADV
ejpam-3877	299	9	,	,	PUNCT
ejpam-3877	299	10	we	we	PRON
ejpam-3877	299	11	infer	infer	VERB
ejpam-3877	299	12	that	that	SCONJ
ejpam-3877	299	13	lim	lim	PROPN
ejpam-3877	299	14	n→∞	n→∞	PRON
ejpam-3877	300	1	∫	∫	PROPN
ejpam-3877	300	2	t	t	PROPN
ejpam-3877	300	3	0	0	NUM
ejpam-3877	300	4	∫	∫	PROPN
ejpam-3877	300	5	ω	ω	PROPN
ejpam-3877	300	6	ψ(ur)∆(φnρv	ψ(ur)∆(φnρv	PROPN
ejpam-3877	300	7	)	)	PUNCT
ejpam-3877	300	8	dxds	dxds	NOUN
ejpam-3877	300	9	=	=	SYM
ejpam-3877	300	10	0	0	X
ejpam-3877	300	11	.	.	PUNCT
ejpam-3877	301	1	moreover	moreover	ADV
ejpam-3877	301	2	,	,	PUNCT
ejpam-3877	301	3	since	since	SCONJ
ejpam-3877	301	4	[	[	X
ejpam-3877	301	5	u	u	X
ejpam-3877	301	6	(	(	PUNCT
ejpam-3877	301	7	·	·	PUNCT
ejpam-3877	301	8	,	,	PUNCT
ejpam-3877	301	9	t)]d,2	t)]d,2	NOUN
ejpam-3877	301	10	,	,	PUNCT
ejpam-3877	301	11	[	[	X
ejpam-3877	301	12	νt]d,2	νt]d,2	X
ejpam-3877	301	13	,	,	PUNCT
ejpam-3877	301	14	[	[	X
ejpam-3877	301	15	u0]d,2	u0]d,2	NOUN
ejpam-3877	301	16	belong	belong	VERB
ejpam-3877	301	17	to	to	ADP
ejpam-3877	301	18	l1(ω)+h−1(ω	l1(ω)+h−1(ω	NOUN
ejpam-3877	301	19	)	)	PUNCT
ejpam-3877	301	20	and	and	CCONJ
ejpam-3877	301	21	φn	φn	ADP
ejpam-3877	301	22	∗	∗	NOUN
ejpam-3877	301	23	⇀	⇀	NOUN
ejpam-3877	301	24	0	0	PUNCT
ejpam-3877	302	1	in	in	ADP
ejpam-3877	302	2	l∞(ω	l∞(ω	ADJ
ejpam-3877	302	3	)	)	PUNCT
ejpam-3877	302	4	,	,	PUNCT
ejpam-3877	302	5	φn	φn	ADP
ejpam-3877	302	6	→	→	SYM
ejpam-3877	302	7	0	0	NUM
ejpam-3877	302	8	in	in	ADP
ejpam-3877	302	9	h1	h1	PROPN
ejpam-3877	302	10	0	0	NUM
ejpam-3877	302	11	(	(	PUNCT
ejpam-3877	302	12	ω	ω	NOUN
ejpam-3877	302	13	)	)	PUNCT
ejpam-3877	303	1	so	so	SCONJ
ejpam-3877	303	2	that	that	SCONJ
ejpam-3877	303	3	lim	lim	PROPN
ejpam-3877	303	4	n→∞	n→∞	PRON
ejpam-3877	304	1	〈	〈	PROPN
ejpam-3877	304	2	[	[	X
ejpam-3877	304	3	u	u	NOUN
ejpam-3877	304	4	(	(	PUNCT
ejpam-3877	304	5	·	·	PUNCT
ejpam-3877	304	6	,	,	PUNCT
ejpam-3877	304	7	t)]d,2	t)]d,2	NOUN
ejpam-3877	304	8	,	,	PUNCT
ejpam-3877	304	9	φnρv	φnρv	VERB
ejpam-3877	304	10	〉	〉	PROPN
ejpam-3877	304	11	ω	ω	PROPN
ejpam-3877	304	12	=	=	PUNCT
ejpam-3877	304	13	lim	lim	PROPN
ejpam-3877	304	14	n→∞	n→∞	PRON
ejpam-3877	304	15	〈	〈	PROPN
ejpam-3877	305	1	[	[	X
ejpam-3877	305	2	νt]d,2	νt]d,2	NUM
ejpam-3877	305	3	,	,	PUNCT
ejpam-3877	305	4	φnρv	φnρv	ADJ
ejpam-3877	305	5	〉	〉	NOUN
ejpam-3877	305	6	ω	ω	X
ejpam-3877	305	7	=	=	PROPN
ejpam-3877	305	8	lim	lim	PROPN
ejpam-3877	305	9	n→∞	n→∞	X
ejpam-3877	306	1	〈	〈	PROPN
ejpam-3877	306	2	[	[	X
ejpam-3877	306	3	u0]d,2	u0]d,2	NOUN
ejpam-3877	306	4	,	,	PUNCT
ejpam-3877	306	5	φnρv	φnρv	ADJ
ejpam-3877	306	6	〉	〉	PROPN
ejpam-3877	306	7	ω	ω	NOUN
ejpam-3877	306	8	=	=	NOUN
ejpam-3877	306	9	0	0	PROPN
ejpam-3877	306	10	.	.	PUNCT
ejpam-3877	307	1	it	it	PRON
ejpam-3877	307	2	follows	follow	VERB
ejpam-3877	307	3	that	that	SCONJ
ejpam-3877	307	4	(	(	PUNCT
ejpam-3877	307	5	4.11	4.11	NUM
ejpam-3877	307	6	)	)	PUNCT
ejpam-3877	307	7	can	can	AUX
ejpam-3877	307	8	be	be	AUX
ejpam-3877	307	9	rewritten	rewrite	VERB
ejpam-3877	307	10	as	as	ADP
ejpam-3877	307	11	〈	〈	PROPN
ejpam-3877	307	12	[	[	X
ejpam-3877	307	13	u	u	NOUN
ejpam-3877	307	14	(	(	PUNCT
ejpam-3877	307	15	·	·	PUNCT
ejpam-3877	307	16	,	,	PUNCT
ejpam-3877	307	17	t)]c,2	t)]c,2	PROPN
ejpam-3877	307	18	,	,	PUNCT
ejpam-3877	307	19	φnρv	φnρv	VERB
ejpam-3877	307	20	〉	〉	PROPN
ejpam-3877	307	21	ω	ω	NOUN
ejpam-3877	307	22	=	=	SYM
ejpam-3877	308	1	〈	〈	PROPN
ejpam-3877	308	2	[	[	X
ejpam-3877	308	3	νt]c,2	νt]c,2	PROPN
ejpam-3877	308	4	,	,	PUNCT
ejpam-3877	308	5	φnρv	φnρv	ADJ
ejpam-3877	308	6	〉	〉	NOUN
ejpam-3877	308	7	ω	ω	PROPN
ejpam-3877	308	8	+	+	CCONJ
ejpam-3877	309	1	〈	〈	PROPN
ejpam-3877	309	2	[	[	X
ejpam-3877	309	3	u0]c,2	u0]c,2	PROPN
ejpam-3877	309	4	,	,	PUNCT
ejpam-3877	309	5	φnρv	φnρv	ADJ
ejpam-3877	309	6	〉	〉	PROPN
ejpam-3877	309	7	ω	ω	PROPN
ejpam-3877	309	8	.	.	PUNCT
ejpam-3877	310	1	(	(	PUNCT
ejpam-3877	310	2	4.12	4.12	NUM
ejpam-3877	310	3	)	)	PUNCT
ejpam-3877	310	4	since	since	SCONJ
ejpam-3877	310	5	k	k	PROPN
ejpam-3877	310	6	is	be	AUX
ejpam-3877	310	7	a	a	DET
ejpam-3877	310	8	subset	subset	ADJ
ejpam-3877	310	9	compact	compact	NOUN
ejpam-3877	310	10	of	of	ADP
ejpam-3877	310	11	ω	ω	PROPN
ejpam-3877	310	12	,	,	PUNCT
ejpam-3877	310	13	then	then	ADV
ejpam-3877	310	14	[	[	X
ejpam-3877	310	15	u	u	X
ejpam-3877	310	16	(	(	PUNCT
ejpam-3877	310	17	·	·	PUNCT
ejpam-3877	310	18	,	,	PUNCT
ejpam-3877	310	19	t)−	t)−	PROPN
ejpam-3877	310	20	u0]c,2	u0]c,2	ADJ
ejpam-3877	310	21	(	(	PUNCT
ejpam-3877	310	22	k	k	NOUN
ejpam-3877	310	23	)	)	PUNCT
ejpam-3877	310	24	≤	≤	NOUN
ejpam-3877	310	25	lim	lim	PROPN
ejpam-3877	310	26	sup	sup	VERB
ejpam-3877	310	27	n→∞	n→∞	NUM
ejpam-3877	311	1	〈	〈	PROPN
ejpam-3877	311	2	[	[	X
ejpam-3877	311	3	u	u	NOUN
ejpam-3877	311	4	(	(	PUNCT
ejpam-3877	311	5	·	·	PUNCT
ejpam-3877	311	6	,	,	PUNCT
ejpam-3877	311	7	t)−	t)−	PROPN
ejpam-3877	311	8	u0]c,2	u0]c,2	PROPN
ejpam-3877	311	9	,	,	PUNCT
ejpam-3877	311	10	φnρv	φnρv	VERB
ejpam-3877	311	11	〉	〉	PROPN
ejpam-3877	311	12	ω	ω	PROPN
ejpam-3877	311	13	=	=	PROPN
ejpam-3877	311	14	lim	lim	PROPN
ejpam-3877	311	15	sup	sup	VERB
ejpam-3877	311	16	n→∞	n→∞	NUM
ejpam-3877	311	17	〈	〈	PROPN
ejpam-3877	311	18	[	[	X
ejpam-3877	311	19	νt]c,2	νt]c,2	PROPN
ejpam-3877	311	20	,	,	PUNCT
ejpam-3877	311	21	φnρv	φnρv	VERB
ejpam-3877	311	22	〉	〉	NOUN
ejpam-3877	311	23	ω	ω	NUM
ejpam-3877	311	24	≤	≤	PROPN
ejpam-3877	311	25	[	[	PUNCT
ejpam-3877	311	26	νt	νt	X
ejpam-3877	311	27	]	]	PUNCT
ejpam-3877	311	28	c,2	c,2	VERB
ejpam-3877	311	29	(	(	PUNCT
ejpam-3877	311	30	k	k	NOUN
ejpam-3877	311	31	)	)	PUNCT
ejpam-3877	311	32	.	.	PUNCT
ejpam-3877	312	1	on	on	ADP
ejpam-3877	312	2	the	the	DET
ejpam-3877	312	3	other	other	ADJ
ejpam-3877	312	4	hand	hand	NOUN
ejpam-3877	312	5	,	,	PUNCT
ejpam-3877	312	6	we	we	PRON
ejpam-3877	312	7	get	get	VERB
ejpam-3877	312	8	[	[	PUNCT
ejpam-3877	312	9	νt	νt	X
ejpam-3877	312	10	]	]	PUNCT
ejpam-3877	312	11	c,2	c,2	VERB
ejpam-3877	312	12	(	(	PUNCT
ejpam-3877	312	13	k	k	NOUN
ejpam-3877	312	14	)	)	PUNCT
ejpam-3877	312	15	≤	≤	NOUN
ejpam-3877	312	16	lim	lim	PROPN
ejpam-3877	312	17	sup	sup	VERB
ejpam-3877	312	18	n→∞	n→∞	NUM
ejpam-3877	312	19	〈	〈	PROPN
ejpam-3877	312	20	[	[	X
ejpam-3877	312	21	νt]c,2	νt]c,2	PROPN
ejpam-3877	312	22	,	,	PUNCT
ejpam-3877	312	23	φnρv	φnρv	ADJ
ejpam-3877	312	24	〉	〉	NOUN
ejpam-3877	312	25	ω	ω	PROPN
ejpam-3877	313	1	=	=	SYM
ejpam-3877	313	2	lim	lim	PROPN
ejpam-3877	313	3	sup	sup	VERB
ejpam-3877	313	4	n→∞	n→∞	NUM
ejpam-3877	314	1	〈	〈	PROPN
ejpam-3877	314	2	[	[	X
ejpam-3877	314	3	u	u	X
ejpam-3877	314	4	(	(	PUNCT
ejpam-3877	314	5	.	.	PUNCT
ejpam-3877	314	6	,	,	PUNCT
ejpam-3877	314	7	t)−	t)−	PROPN
ejpam-3877	314	8	u0]c,2	u0]c,2	PROPN
ejpam-3877	314	9	,	,	PUNCT
ejpam-3877	314	10	φnρv	φnρv	VERB
ejpam-3877	314	11	〉	〉	PROPN
ejpam-3877	314	12	ω	ω	NOUN
ejpam-3877	314	13	≤	≤	NOUN
ejpam-3877	315	1	[	[	X
ejpam-3877	315	2	u	u	NOUN
ejpam-3877	315	3	(	(	PUNCT
ejpam-3877	315	4	.	.	PUNCT
ejpam-3877	315	5	,	,	PUNCT
ejpam-3877	315	6	t)−	t)−	PROPN
ejpam-3877	315	7	u0]c,2	u0]c,2	ADJ
ejpam-3877	315	8	(	(	PUNCT
ejpam-3877	315	9	k	k	NOUN
ejpam-3877	315	10	)	)	PUNCT
ejpam-3877	315	11	.	.	PUNCT
ejpam-3877	316	1	the	the	DET
ejpam-3877	316	2	above	above	ADJ
ejpam-3877	316	3	inequality	inequality	NOUN
ejpam-3877	316	4	implies	imply	VERB
ejpam-3877	316	5	that	that	SCONJ
ejpam-3877	316	6	[	[	X
ejpam-3877	316	7	u	u	X
ejpam-3877	316	8	(	(	PUNCT
ejpam-3877	316	9	·	·	PUNCT
ejpam-3877	316	10	,	,	PUNCT
ejpam-3877	316	11	t)−	t)−	PROPN
ejpam-3877	316	12	u0]c,2	u0]c,2	ADJ
ejpam-3877	316	13	(	(	PUNCT
ejpam-3877	316	14	k	k	NOUN
ejpam-3877	316	15	)	)	PUNCT
ejpam-3877	316	16	≤	≤	NOUN
ejpam-3877	316	17	inf	inf	NOUN
ejpam-3877	316	18	{	{	PUNCT
ejpam-3877	316	19	[	[	PUNCT
ejpam-3877	316	20	νt	νt	X
ejpam-3877	316	21	]	]	PUNCT
ejpam-3877	316	22	c,2	c,2	VERB
ejpam-3877	316	23	(	(	PUNCT
ejpam-3877	316	24	v	v	NOUN
ejpam-3877	316	25	)	)	PUNCT
ejpam-3877	316	26	|	|	ADV
ejpam-3877	316	27	k	k	PROPN
ejpam-3877	316	28	⊂	⊂	PROPN
ejpam-3877	316	29	v	v	PROPN
ejpam-3877	316	30	,	,	PUNCT
ejpam-3877	316	31	open	open	ADJ
ejpam-3877	316	32	}	}	PUNCT
ejpam-3877	316	33	=	=	PUNCT
ejpam-3877	316	34	[	[	PUNCT
ejpam-3877	316	35	νt	νt	X
ejpam-3877	316	36	]	]	PUNCT
ejpam-3877	316	37	c,2	c,2	VERB
ejpam-3877	316	38	(	(	PUNCT
ejpam-3877	316	39	k	k	NOUN
ejpam-3877	316	40	)	)	PUNCT
ejpam-3877	316	41	.	.	PUNCT
ejpam-3877	317	1	similarly	similarly	ADV
ejpam-3877	317	2	,	,	PUNCT
ejpam-3877	317	3	we	we	PRON
ejpam-3877	317	4	have	have	VERB
ejpam-3877	317	5	[	[	PUNCT
ejpam-3877	317	6	νt	νt	X
ejpam-3877	317	7	]	]	PUNCT
ejpam-3877	317	8	c,2	c,2	VERB
ejpam-3877	317	9	(	(	PUNCT
ejpam-3877	317	10	k	k	NOUN
ejpam-3877	317	11	)	)	PUNCT
ejpam-3877	317	12	≤	≤	NUM
ejpam-3877	317	13	inf	inf	NOUN
ejpam-3877	317	14	{	{	PUNCT
ejpam-3877	318	1	[	[	X
ejpam-3877	318	2	u	u	X
ejpam-3877	318	3	(	(	PUNCT
ejpam-3877	318	4	·	·	PUNCT
ejpam-3877	318	5	,	,	PUNCT
ejpam-3877	318	6	t)−	t)−	PROPN
ejpam-3877	318	7	u0]c,2	u0]c,2	ADJ
ejpam-3877	318	8	(	(	PUNCT
ejpam-3877	318	9	v	v	NOUN
ejpam-3877	318	10	)	)	PUNCT
ejpam-3877	319	1	|	|	ADV
ejpam-3877	319	2	k	k	PROPN
ejpam-3877	319	3	⊂	⊂	PROPN
ejpam-3877	319	4	v	v	PROPN
ejpam-3877	319	5	,	,	PUNCT
ejpam-3877	319	6	open	open	ADJ
ejpam-3877	319	7	}	}	PUNCT
ejpam-3877	319	8	=	=	PUNCT
ejpam-3877	320	1	[	[	X
ejpam-3877	320	2	u	u	X
ejpam-3877	320	3	(	(	PUNCT
ejpam-3877	320	4	.	.	PUNCT
ejpam-3877	320	5	,	,	PUNCT
ejpam-3877	320	6	t)−	t)−	PROPN
ejpam-3877	320	7	u0]c,2	u0]c,2	ADJ
ejpam-3877	320	8	(	(	PUNCT
ejpam-3877	320	9	k	k	NOUN
ejpam-3877	320	10	)	)	PUNCT
ejpam-3877	320	11	.	.	PUNCT
ejpam-3877	321	1	whence	whence	NOUN
ejpam-3877	321	2	,	,	PUNCT
ejpam-3877	321	3	the	the	DET
ejpam-3877	321	4	following	follow	VERB
ejpam-3877	321	5	statement	statement	NOUN
ejpam-3877	321	6	[	[	PUNCT
ejpam-3877	321	7	νt	νt	X
ejpam-3877	321	8	]	]	PUNCT
ejpam-3877	321	9	c,2	c,2	VERB
ejpam-3877	321	10	(	(	PUNCT
ejpam-3877	321	11	k	k	NOUN
ejpam-3877	321	12	)	)	PUNCT
ejpam-3877	321	13	=	=	PUNCT
ejpam-3877	322	1	[	[	X
ejpam-3877	322	2	u	u	X
ejpam-3877	322	3	(	(	PUNCT
ejpam-3877	322	4	·	·	PUNCT
ejpam-3877	322	5	,	,	PUNCT
ejpam-3877	322	6	t)−	t)−	PROPN
ejpam-3877	322	7	u0]c,2	u0]c,2	ADJ
ejpam-3877	322	8	(	(	PUNCT
ejpam-3877	322	9	k	k	NOUN
ejpam-3877	322	10	)	)	PUNCT
ejpam-3877	322	11	(	(	PUNCT
ejpam-3877	322	12	4.13	4.13	NUM
ejpam-3877	322	13	)	)	PUNCT
ejpam-3877	322	14	holds	hold	VERB
ejpam-3877	322	15	true	true	ADJ
ejpam-3877	322	16	.	.	PUNCT
ejpam-3877	323	1	according	accord	VERB
ejpam-3877	323	2	to	to	ADP
ejpam-3877	323	3	the	the	DET
ejpam-3877	323	4	arbitrariness	arbitrariness	NOUN
ejpam-3877	323	5	of	of	ADP
ejpam-3877	323	6	k	k	PROPN
ejpam-3877	323	7	,	,	PUNCT
ejpam-3877	323	8	(	(	PUNCT
ejpam-3877	323	9	4.13	4.13	NUM
ejpam-3877	323	10	)	)	PUNCT
ejpam-3877	323	11	is	be	AUX
ejpam-3877	323	12	satisfied	satisfied	ADJ
ejpam-3877	323	13	for	for	SCONJ
ejpam-3877	323	14	every	every	DET
ejpam-3877	323	15	borel	borel	NOUN
ejpam-3877	323	16	set	set	VERB
ejpam-3877	323	17	e	e	PROPN
ejpam-3877	323	18	⊆	⊆	NUM
ejpam-3877	323	19	ω	ω	NOUN
ejpam-3877	323	20	with	with	ADP
ejpam-3877	323	21	c2(e	c2(e	NOUN
ejpam-3877	323	22	)	)	PUNCT
ejpam-3877	323	23	=	=	SYM
ejpam-3877	323	24	0	0	X
ejpam-3877	323	25	.	.	PUNCT
ejpam-3877	324	1	by	by	ADP
ejpam-3877	324	2	the	the	DET
ejpam-3877	324	3	definition	definition	NOUN
ejpam-3877	324	4	of	of	ADP
ejpam-3877	324	5	concentrated	concentrated	ADJ
ejpam-3877	324	6	measure	measure	NOUN
ejpam-3877	324	7	with	with	ADP
ejpam-3877	324	8	respect	respect	NOUN
ejpam-3877	324	9	to	to	ADP
ejpam-3877	324	10	the	the	DET
ejpam-3877	324	11	newtonian	newtonian	ADJ
ejpam-3877	324	12	capacity	capacity	NOUN
ejpam-3877	324	13	,	,	PUNCT
ejpam-3877	324	14	we	we	PRON
ejpam-3877	324	15	have	have	VERB
ejpam-3877	324	16	for	for	ADP
ejpam-3877	324	17	any	any	DET
ejpam-3877	324	18	t	t	NOUN
ejpam-3877	324	19	∈	∈	PROPN
ejpam-3877	324	20	(	(	PUNCT
ejpam-3877	324	21	0	0	NUM
ejpam-3877	324	22	,	,	PUNCT
ejpam-3877	324	23	t	t	NOUN
ejpam-3877	324	24	)	)	PUNCT
ejpam-3877	324	25	\	\	PROPN
ejpam-3877	325	1	f	f	X
ejpam-3877	325	2	,	,	PUNCT
ejpam-3877	325	3	[	[	X
ejpam-3877	325	4	u	u	X
ejpam-3877	325	5	(	(	PUNCT
ejpam-3877	325	6	·	·	PUNCT
ejpam-3877	325	7	,	,	PUNCT
ejpam-3877	325	8	t)]c,2	t)]c,2	X
ejpam-3877	325	9	=	=	PUNCT
ejpam-3877	326	1	[	[	X
ejpam-3877	326	2	u	u	X
ejpam-3877	326	3	(	(	PUNCT
ejpam-3877	326	4	·	·	PUNCT
ejpam-3877	326	5	,	,	PUNCT
ejpam-3877	326	6	t)]c,2	t)]c,2	PRON
ejpam-3877	326	7	xb1(t	xb1(t	PROPN
ejpam-3877	326	8	)	)	PUNCT
ejpam-3877	326	9	,	,	PUNCT
ejpam-3877	326	10	[	[	PUNCT
ejpam-3877	326	11	νt	νt	X
ejpam-3877	326	12	]	]	PUNCT
ejpam-3877	326	13	c,2	c,2	VERB
ejpam-3877	326	14	=	=	SYM
ejpam-3877	326	15	[	[	PUNCT
ejpam-3877	326	16	νt	νt	X
ejpam-3877	326	17	]	]	PUNCT
ejpam-3877	326	18	xb2(t	xb2(t	PROPN
ejpam-3877	326	19	)	)	PUNCT
ejpam-3877	326	20	and	and	CCONJ
ejpam-3877	327	1	[	[	X
ejpam-3877	327	2	u0]c,2	u0]c,2	ADJ
ejpam-3877	327	3	=	=	SYM
ejpam-3877	327	4	[	[	PUNCT
ejpam-3877	327	5	u0]c,2	u0]c,2	NOUN
ejpam-3877	327	6	xa	xa	PROPN
ejpam-3877	327	7	for	for	ADP
ejpam-3877	327	8	some	some	DET
ejpam-3877	327	9	borel	borel	NOUN
ejpam-3877	327	10	sets	set	VERB
ejpam-3877	327	11	b1(t	b1(t	PROPN
ejpam-3877	327	12	)	)	PUNCT
ejpam-3877	327	13	,	,	PUNCT
ejpam-3877	327	14	b2(t	b2(t	PROPN
ejpam-3877	327	15	)	)	PUNCT
ejpam-3877	327	16	,	,	PUNCT
ejpam-3877	327	17	and	and	CCONJ
ejpam-3877	327	18	a	a	PRON
ejpam-3877	327	19	is	be	AUX
ejpam-3877	327	20	a	a	DET
ejpam-3877	327	21	zero	zero	NUM
ejpam-3877	327	22	newtonian	newtonian	ADJ
ejpam-3877	327	23	capacity	capacity	NOUN
ejpam-3877	327	24	,	,	PUNCT
ejpam-3877	327	25	then	then	ADV
ejpam-3877	327	26	(	(	PUNCT
ejpam-3877	327	27	4.13	4.13	X
ejpam-3877	327	28	)	)	PUNCT
ejpam-3877	327	29	yields	yield	NOUN
ejpam-3877	328	1	[	[	X
ejpam-3877	328	2	u	u	X
ejpam-3877	328	3	(	(	PUNCT
ejpam-3877	328	4	·	·	PUNCT
ejpam-3877	328	5	,	,	PUNCT
ejpam-3877	328	6	t)]c,2	t)]c,2	X
ejpam-3877	328	7	(	(	PUNCT
ejpam-3877	328	8	(	(	PUNCT
ejpam-3877	328	9	b1(t	b1(t	SYM
ejpam-3877	328	10	)	)	PUNCT
ejpam-3877	328	11	∪b2(t	∪b2(t	NOUN
ejpam-3877	328	12	)	)	PUNCT
ejpam-3877	328	13	)	)	PUNCT
ejpam-3877	328	14	\a	\a	NUM
ejpam-3877	328	15	)	)	PUNCT
ejpam-3877	329	1	=	=	PRON
ejpam-3877	329	2	[	[	PUNCT
ejpam-3877	329	3	νt	νt	X
ejpam-3877	329	4	]	]	PUNCT
ejpam-3877	329	5	c,2	c,2	VERB
ejpam-3877	329	6	(	(	PUNCT
ejpam-3877	329	7	(	(	PUNCT
ejpam-3877	329	8	b1(t	b1(t	SYM
ejpam-3877	329	9	)	)	PUNCT
ejpam-3877	329	10	∪b2(t	∪b2(t	NOUN
ejpam-3877	329	11	)	)	PUNCT
ejpam-3877	329	12	)	)	PUNCT
ejpam-3877	329	13	\a	\a	NUM
ejpam-3877	329	14	)	)	PUNCT
ejpam-3877	330	1	=	=	SYM
ejpam-3877	330	2	quincy	quincy	PROPN
ejpam-3877	330	3	s.	s.	PROPN
ejpam-3877	330	4	nkombo	nkombo	PROPN
ejpam-3877	330	5	,	,	PUNCT
ejpam-3877	330	6	fengquan	fengquan	PROPN
ejpam-3877	330	7	li	li	PROPN
ejpam-3877	330	8	/	/	SYM
ejpam-3877	330	9	eur	eur	PROPN
ejpam-3877	330	10	.	.	PUNCT
ejpam-3877	331	1	j.	j.	PROPN
ejpam-3877	331	2	pure	pure	PROPN
ejpam-3877	331	3	appl	appl	PROPN
ejpam-3877	331	4	.	.	PROPN
ejpam-3877	331	5	math	math	PROPN
ejpam-3877	331	6	,	,	PUNCT
ejpam-3877	331	7	14	14	NUM
ejpam-3877	331	8	(	(	PUNCT
ejpam-3877	331	9	1	1	NUM
ejpam-3877	331	10	)	)	PUNCT
ejpam-3877	331	11	(	(	PUNCT
ejpam-3877	331	12	2021	2021	NUM
ejpam-3877	331	13	)	)	PUNCT
ejpam-3877	331	14	,	,	PUNCT
ejpam-3877	331	15	204	204	NUM
ejpam-3877	331	16	-	-	SYM
ejpam-3877	331	17	233	233	NUM
ejpam-3877	331	18	218	218	NUM
ejpam-3877	331	19	=	=	PUNCT
ejpam-3877	332	1	[	[	PUNCT
ejpam-3877	332	2	u0]c,2	u0]c,2	ADJ
ejpam-3877	332	3	(	(	PUNCT
ejpam-3877	332	4	(	(	PUNCT
ejpam-3877	332	5	b1(t	b1(t	ADJ
ejpam-3877	332	6	)	)	PUNCT
ejpam-3877	332	7	∪b2(t	∪b2(t	NOUN
ejpam-3877	332	8	)	)	PUNCT
ejpam-3877	332	9	)	)	PUNCT
ejpam-3877	332	10	\a	\a	NUM
ejpam-3877	332	11	)	)	PUNCT
ejpam-3877	333	1	=	=	SYM
ejpam-3877	333	2	0	0	X
ejpam-3877	333	3	.	.	PUNCT
ejpam-3877	334	1	therefore	therefore	ADV
ejpam-3877	334	2	for	for	ADP
ejpam-3877	334	3	every	every	DET
ejpam-3877	334	4	t	t	NOUN
ejpam-3877	334	5	∈	∈	PROPN
ejpam-3877	334	6	(	(	PUNCT
ejpam-3877	334	7	0	0	NUM
ejpam-3877	334	8	,	,	PUNCT
ejpam-3877	334	9	t	t	NOUN
ejpam-3877	334	10	)	)	PUNCT
ejpam-3877	334	11	\f	\f	PUNCT
ejpam-3877	334	12	,	,	PUNCT
ejpam-3877	334	13	[	[	X
ejpam-3877	334	14	u	u	X
ejpam-3877	334	15	(	(	PUNCT
ejpam-3877	334	16	·	·	PUNCT
ejpam-3877	334	17	,	,	PUNCT
ejpam-3877	334	18	t)]c,2	t)]c,2	X
ejpam-3877	334	19	,	,	PUNCT
ejpam-3877	334	20	[	[	PUNCT
ejpam-3877	334	21	νt	νt	X
ejpam-3877	334	22	]	]	PUNCT
ejpam-3877	334	23	c,2	c,2	VERB
ejpam-3877	334	24	,	,	PUNCT
ejpam-3877	334	25	[	[	X
ejpam-3877	334	26	u0]c,2	u0]c,2	NOUN
ejpam-3877	334	27	are	be	AUX
ejpam-3877	334	28	concentrated	concentrate	VERB
ejpam-3877	334	29	measures	measure	NOUN
ejpam-3877	334	30	on	on	ADP
ejpam-3877	334	31	the	the	DET
ejpam-3877	334	32	set	set	NOUN
ejpam-3877	334	33	b∗(t	b∗(t	NOUN
ejpam-3877	334	34	)	)	PUNCT
ejpam-3877	334	35	such	such	ADJ
ejpam-3877	334	36	that	that	SCONJ
ejpam-3877	334	37	b∗(t	b∗(t	NOUN
ejpam-3877	334	38	)	)	PUNCT
ejpam-3877	335	1	=	=	SYM
ejpam-3877	335	2	(	(	PUNCT
ejpam-3877	335	3	b1(t)∩a)∪	b1(t)∩a)∪	PRON
ejpam-3877	335	4	(	(	PUNCT
ejpam-3877	335	5	b2(t)∩a	b2(t)∩a	NOUN
ejpam-3877	335	6	)	)	PUNCT
ejpam-3877	335	7	.	.	PUNCT
ejpam-3877	336	1	therefore	therefore	ADV
ejpam-3877	336	2	,	,	PUNCT
ejpam-3877	336	3	for	for	ADP
ejpam-3877	336	4	every	every	DET
ejpam-3877	336	5	set	set	NOUN
ejpam-3877	336	6	e	e	NOUN
ejpam-3877	336	7	⊆	⊆	NUM
ejpam-3877	336	8	ω	ω	NUM
ejpam-3877	336	9	and	and	CCONJ
ejpam-3877	336	10	t	t	PROPN
ejpam-3877	336	11	∈	∈	PROPN
ejpam-3877	336	12	(	(	PUNCT
ejpam-3877	336	13	0	0	NUM
ejpam-3877	336	14	,	,	PUNCT
ejpam-3877	336	15	t	t	NOUN
ejpam-3877	336	16	)	)	PUNCT
ejpam-3877	336	17	\	\	PROPN
ejpam-3877	336	18	f	f	PROPN
ejpam-3877	336	19	,	,	PUNCT
ejpam-3877	336	20	there	there	PRON
ejpam-3877	336	21	holds	hold	VERB
ejpam-3877	336	22	[	[	X
ejpam-3877	336	23	u	u	NOUN
ejpam-3877	336	24	(	(	PUNCT
ejpam-3877	336	25	·	·	PUNCT
ejpam-3877	336	26	,	,	PUNCT
ejpam-3877	336	27	t)−	t)−	PROPN
ejpam-3877	336	28	u0]c,2	u0]c,2	ADJ
ejpam-3877	336	29	(	(	PUNCT
ejpam-3877	336	30	e	e	NOUN
ejpam-3877	336	31	)	)	PUNCT
ejpam-3877	336	32	=	=	SYM
ejpam-3877	336	33	(	(	PUNCT
ejpam-3877	336	34	[	[	X
ejpam-3877	336	35	u	u	X
ejpam-3877	336	36	(	(	PUNCT
ejpam-3877	336	37	·	·	PUNCT
ejpam-3877	336	38	,	,	PUNCT
ejpam-3877	336	39	t)−	t)−	PROPN
ejpam-3877	336	40	u0]c,2	u0]c,2	ADJ
ejpam-3877	336	41	xb	xb	ADJ
ejpam-3877	336	42	∗(t	∗(t	NOUN
ejpam-3877	336	43	)	)	PUNCT
ejpam-3877	336	44	)	)	PUNCT
ejpam-3877	336	45	(	(	PUNCT
ejpam-3877	336	46	e	e	X
ejpam-3877	336	47	)	)	PUNCT
ejpam-3877	336	48	=	=	PUNCT
ejpam-3877	337	1	[	[	X
ejpam-3877	337	2	u	u	X
ejpam-3877	337	3	(	(	PUNCT
ejpam-3877	337	4	·	·	PUNCT
ejpam-3877	337	5	,	,	PUNCT
ejpam-3877	337	6	t)−	t)−	PROPN
ejpam-3877	337	7	u0]c,2	u0]c,2	PROPN
ejpam-3877	337	8	x(b	x(b	PROPN
ejpam-3877	337	9	∗(t	∗(t	NOUN
ejpam-3877	337	10	)	)	PUNCT
ejpam-3877	337	11	∩	∩	NOUN
ejpam-3877	337	12	e	e	NOUN
ejpam-3877	337	13	)	)	PUNCT
ejpam-3877	337	14	=	=	SYM
ejpam-3877	338	1	=	=	PUNCT
ejpam-3877	338	2	[	[	PUNCT
ejpam-3877	338	3	νt	νt	X
ejpam-3877	338	4	]	]	PUNCT
ejpam-3877	338	5	c	c	PROPN
ejpam-3877	338	6	x(b∗(t	x(b∗(t	PROPN
ejpam-3877	338	7	)	)	PUNCT
ejpam-3877	338	8	∩	∩	NOUN
ejpam-3877	338	9	e	e	NOUN
ejpam-3877	338	10	)	)	PUNCT
ejpam-3877	338	11	=	=	SYM
ejpam-3877	338	12	(	(	PUNCT
ejpam-3877	338	13	[	[	PUNCT
ejpam-3877	338	14	νt	νt	X
ejpam-3877	338	15	]	]	PUNCT
ejpam-3877	338	16	c,2	c,2	VERB
ejpam-3877	338	17	xb∗(t	xb∗(t	NOUN
ejpam-3877	338	18	)	)	PUNCT
ejpam-3877	338	19	)	)	PUNCT
ejpam-3877	339	1	(	(	PUNCT
ejpam-3877	339	2	e	e	NOUN
ejpam-3877	339	3	)	)	PUNCT
ejpam-3877	339	4	.	.	PUNCT
ejpam-3877	340	1	hence	hence	ADV
ejpam-3877	340	2	,	,	PUNCT
ejpam-3877	340	3	the	the	DET
ejpam-3877	340	4	proof	proof	NOUN
ejpam-3877	340	5	is	be	AUX
ejpam-3877	340	6	achieved	achieve	VERB
ejpam-3877	340	7	.	.	PUNCT
ejpam-3877	341	1	�	�	PROPN
ejpam-3877	341	2	5	5	NUM
ejpam-3877	341	3	.	.	PUNCT
ejpam-3877	342	1	existence	existence	NOUN
ejpam-3877	342	2	results	result	NOUN
ejpam-3877	342	3	we	we	PRON
ejpam-3877	342	4	prove	prove	VERB
ejpam-3877	342	5	the	the	DET
ejpam-3877	342	6	existence	existence	NOUN
ejpam-3877	342	7	result	result	NOUN
ejpam-3877	342	8	of	of	ADP
ejpam-3877	342	9	the	the	DET
ejpam-3877	342	10	problem	problem	NOUN
ejpam-3877	342	11	(	(	PUNCT
ejpam-3877	342	12	p	p	NOUN
ejpam-3877	342	13	)	)	PUNCT
ejpam-3877	342	14	.	.	PUNCT
ejpam-3877	343	1	proposition	proposition	NOUN
ejpam-3877	343	2	5.1	5.1	NUM
ejpam-3877	343	3	.	.	PUNCT
ejpam-3877	344	1	assume	assume	VERB
ejpam-3877	344	2	that	that	SCONJ
ejpam-3877	344	3	(	(	PUNCT
ejpam-3877	344	4	i	i	NOUN
ejpam-3877	344	5	)	)	PUNCT
ejpam-3877	344	6	and	and	CCONJ
ejpam-3877	344	7	(	(	PUNCT
ejpam-3877	344	8	j	j	NOUN
ejpam-3877	344	9	)	)	PUNCT
ejpam-3877	344	10	hold	hold	VERB
ejpam-3877	344	11	.	.	PUNCT
ejpam-3877	345	1	let	let	VERB
ejpam-3877	345	2	un	un	PROPN
ejpam-3877	345	3	be	be	AUX
ejpam-3877	345	4	the	the	DET
ejpam-3877	345	5	solution	solution	NOUN
ejpam-3877	345	6	to	to	ADP
ejpam-3877	345	7	the	the	DET
ejpam-3877	345	8	approximation	approximation	NOUN
ejpam-3877	345	9	problem	problem	NOUN
ejpam-3877	345	10	(	(	PUNCT
ejpam-3877	345	11	pn	pn	NOUN
ejpam-3877	345	12	)	)	PUNCT
ejpam-3877	345	13	,	,	PUNCT
ejpam-3877	345	14	then	then	ADV
ejpam-3877	345	15	there	there	PRON
ejpam-3877	345	16	exist	exist	VERB
ejpam-3877	345	17	a	a	DET
ejpam-3877	345	18	subsequence	subsequence	NOUN
ejpam-3877	345	19	{	{	PUNCT
ejpam-3877	345	20	unj	unj	NOUN
ejpam-3877	345	21	}	}	PUNCT
ejpam-3877	345	22	⊆	⊆	NUM
ejpam-3877	345	23	{	{	PUNCT
ejpam-3877	345	24	un	un	NOUN
ejpam-3877	345	25	}	}	PUNCT
ejpam-3877	345	26	and	and	CCONJ
ejpam-3877	345	27	v	v	ADP
ejpam-3877	345	28	∈	∈	PROPN
ejpam-3877	345	29	l2((0	l2((0	PROPN
ejpam-3877	345	30	,	,	PUNCT
ejpam-3877	345	31	t	t	PROPN
ejpam-3877	345	32	)	)	PUNCT
ejpam-3877	345	33	,	,	PUNCT
ejpam-3877	345	34	h1	h1	PROPN
ejpam-3877	345	35	0	0	NUM
ejpam-3877	345	36	(	(	PUNCT
ejpam-3877	345	37	ω))∩	ω))∩	X
ejpam-3877	345	38	l∞((0	l∞((0	PROPN
ejpam-3877	345	39	,	,	PUNCT
ejpam-3877	345	40	t	t	PROPN
ejpam-3877	345	41	)	)	PUNCT
ejpam-3877	345	42	,	,	PUNCT
ejpam-3877	345	43	h1	h1	PROPN
ejpam-3877	345	44	0	0	NUM
ejpam-3877	345	45	(	(	PUNCT
ejpam-3877	345	46	ω	ω	NOUN
ejpam-3877	345	47	)	)	PUNCT
ejpam-3877	345	48	)	)	PUNCT
ejpam-3877	345	49	∩	∩	NOUN
ejpam-3877	345	50	l∞(q	l∞(q	NOUN
ejpam-3877	345	51	)	)	PUNCT
ejpam-3877	345	52	with	with	ADP
ejpam-3877	345	53	0	0	NUM
ejpam-3877	345	54	≤	≤	NUM
ejpam-3877	345	55	v	v	ADJ
ejpam-3877	345	56	≤	≤	NUM
ejpam-3877	345	57	γ	γ	NOUN
ejpam-3877	345	58	in	in	ADP
ejpam-3877	345	59	q	q	PROPN
ejpam-3877	345	60	such	such	ADJ
ejpam-3877	345	61	that	that	PRON
ejpam-3877	345	62	ψ(unj	ψ(unj	PROPN
ejpam-3877	345	63	)	)	PUNCT
ejpam-3877	345	64	∗	∗	NOUN
ejpam-3877	345	65	⇀	⇀	NUM
ejpam-3877	345	66	v	v	NOUN
ejpam-3877	345	67	in	in	ADP
ejpam-3877	345	68	l∞(q	l∞(q	NOUN
ejpam-3877	345	69	)	)	PUNCT
ejpam-3877	345	70	.	.	PUNCT
ejpam-3877	346	1	(	(	PUNCT
ejpam-3877	346	2	5.1	5.1	NUM
ejpam-3877	346	3	)	)	PUNCT
ejpam-3877	346	4	∇ψ(unj	∇ψ(unj	NOUN
ejpam-3877	346	5	)	)	PUNCT
ejpam-3877	347	1	⇀	⇀	INTJ
ejpam-3877	348	1	∇v	∇v	ADV
ejpam-3877	348	2	in	in	ADP
ejpam-3877	348	3	[	[	PUNCT
ejpam-3877	348	4	l2(q	l2(q	PROPN
ejpam-3877	348	5	)	)	PUNCT
ejpam-3877	348	6	]	]	PUNCT
ejpam-3877	348	7	n	n	X
ejpam-3877	348	8	.	.	PUNCT
ejpam-3877	349	1	(	(	PUNCT
ejpam-3877	349	2	5.2	5.2	NUM
ejpam-3877	349	3	)	)	PUNCT
ejpam-3877	349	4	ψ(unj	ψ(unj	PROPN
ejpam-3877	349	5	)	)	PUNCT
ejpam-3877	349	6	→	→	SYM
ejpam-3877	349	7	v	v	X
ejpam-3877	349	8	a.e	a.e	PROPN
ejpam-3877	349	9	in	in	ADP
ejpam-3877	349	10	q.	q.	PROPN
ejpam-3877	349	11	(	(	PUNCT
ejpam-3877	349	12	5.3	5.3	NUM
ejpam-3877	349	13	)	)	PUNCT
ejpam-3877	349	14	proof	proof	NOUN
ejpam-3877	349	15	.	.	PUNCT
ejpam-3877	350	1	by	by	ADP
ejpam-3877	350	2	the	the	DET
ejpam-3877	350	3	assumption	assumption	NOUN
ejpam-3877	350	4	(	(	PUNCT
ejpam-3877	350	5	i)-(ii	i)-(ii	PROPN
ejpam-3877	350	6	)	)	PUNCT
ejpam-3877	350	7	,	,	PUNCT
ejpam-3877	350	8	the	the	DET
ejpam-3877	350	9	sequence	sequence	NOUN
ejpam-3877	350	10	{	{	PUNCT
ejpam-3877	350	11	ψ(un	ψ(un	PROPN
ejpam-3877	350	12	)	)	PUNCT
ejpam-3877	350	13	}	}	PUNCT
ejpam-3877	350	14	is	be	AUX
ejpam-3877	350	15	uniformly	uniformly	ADV
ejpam-3877	350	16	bounded	bound	VERB
ejpam-3877	350	17	in	in	ADP
ejpam-3877	350	18	l∞(q	l∞(q	NOUN
ejpam-3877	350	19	)	)	PUNCT
ejpam-3877	350	20	,	,	PUNCT
ejpam-3877	350	21	then	then	ADV
ejpam-3877	350	22	from	from	ADP
ejpam-3877	350	23	[	[	X
ejpam-3877	350	24	5	5	NUM
ejpam-3877	350	25	]	]	PUNCT
ejpam-3877	350	26	there	there	PRON
ejpam-3877	350	27	exists	exist	VERB
ejpam-3877	350	28	a	a	DET
ejpam-3877	350	29	function	function	NOUN
ejpam-3877	350	30	v	v	ADP
ejpam-3877	350	31	∈	∈	PROPN
ejpam-3877	350	32	l∞(q	l∞(q	NOUN
ejpam-3877	350	33	)	)	PUNCT
ejpam-3877	350	34	such	such	ADJ
ejpam-3877	350	35	that	that	SCONJ
ejpam-3877	350	36	the	the	DET
ejpam-3877	350	37	convergence	convergence	NOUN
ejpam-3877	350	38	in	in	ADP
ejpam-3877	350	39	(	(	PUNCT
ejpam-3877	350	40	5.1	5.1	NUM
ejpam-3877	350	41	)	)	PUNCT
ejpam-3877	350	42	holds	hold	VERB
ejpam-3877	350	43	true	true	ADJ
ejpam-3877	350	44	.	.	PUNCT
ejpam-3877	351	1	furthermore	furthermore	ADV
ejpam-3877	351	2	,	,	PUNCT
ejpam-3877	351	3	the	the	DET
ejpam-3877	351	4	convergence	convergence	NOUN
ejpam-3877	351	5	(	(	PUNCT
ejpam-3877	351	6	5.2	5.2	NUM
ejpam-3877	351	7	)	)	PUNCT
ejpam-3877	351	8	stems	stem	VERB
ejpam-3877	351	9	from	from	ADP
ejpam-3877	351	10	estimate	estimate	NOUN
ejpam-3877	351	11	(	(	PUNCT
ejpam-3877	351	12	4.5	4.5	NUM
ejpam-3877	351	13	)	)	PUNCT
ejpam-3877	351	14	.	.	PUNCT
ejpam-3877	352	1	by	by	ADP
ejpam-3877	352	2	(	(	PUNCT
ejpam-3877	352	3	4.6	4.6	NUM
ejpam-3877	352	4	)	)	PUNCT
ejpam-3877	352	5	,	,	PUNCT
ejpam-3877	352	6	we	we	PRON
ejpam-3877	352	7	have	have	VERB
ejpam-3877	352	8	|	|	ADV
ejpam-3877	352	9	∇φ(tk(ψ(un	∇φ(tk(ψ(un	NOUN
ejpam-3877	352	10	)	)	PUNCT
ejpam-3877	352	11	)	)	PUNCT
ejpam-3877	352	12	)	)	PUNCT
ejpam-3877	353	1	|=|	|=|	PROPN
ejpam-3877	353	2	∇tk(ψ(un	∇tk(ψ(un	PROPN
ejpam-3877	353	3	)	)	PUNCT
ejpam-3877	353	4	)	)	PUNCT
ejpam-3877	353	5	||	||	PUNCT
ejpam-3877	354	1	ψ(tk(ψ(un	ψ(tk(ψ(un	NOUN
ejpam-3877	354	2	)	)	PUNCT
ejpam-3877	354	3	)	)	PUNCT
ejpam-3877	354	4	)	)	PUNCT
ejpam-3877	355	1	|	|	ADV
ejpam-3877	355	2	≤	≤	NUM
ejpam-3877	355	3	γ	γ	PROPN
ejpam-3877	355	4	|	|	NOUN
ejpam-3877	355	5	∇tk(ψ(un	∇tk(ψ(un	PROPN
ejpam-3877	355	6	)	)	PUNCT
ejpam-3877	355	7	)	)	PUNCT
ejpam-3877	356	1	|	|	ADV
ejpam-3877	356	2	.	.	PUNCT
ejpam-3877	357	1	(	(	PUNCT
ejpam-3877	357	2	5.4	5.4	NUM
ejpam-3877	357	3	)	)	PUNCT
ejpam-3877	357	4	it	it	PRON
ejpam-3877	357	5	follows	follow	VERB
ejpam-3877	357	6	that,∫	that,∫	PROPN
ejpam-3877	357	7	q	q	PROPN
ejpam-3877	357	8	|	|	ADV
ejpam-3877	357	9	∇φ(tk(ψ(un	∇φ(tk(ψ(un	NOUN
ejpam-3877	357	10	)	)	PUNCT
ejpam-3877	357	11	)	)	PUNCT
ejpam-3877	357	12	)	)	PUNCT
ejpam-3877	358	1	|	|	ADV
ejpam-3877	358	2	dxdt	dxdt	VERB
ejpam-3877	358	3	≤	≤	NOUN
ejpam-3877	358	4	γ	γ	NOUN
ejpam-3877	358	5	|	|	ADV
ejpam-3877	358	6	q	q	NOUN
ejpam-3877	359	1	|	|	NOUN
ejpam-3877	360	1	[	[	X
ejpam-3877	360	2	∫	∫	X
ejpam-3877	360	3	q	q	X
ejpam-3877	360	4	|	|	PROPN
ejpam-3877	360	5	∇tk(ψ(un	∇tk(ψ(un	PROPN
ejpam-3877	360	6	)	)	PUNCT
ejpam-3877	360	7	)	)	PUNCT
ejpam-3877	360	8	|2	|2	NUM
ejpam-3877	360	9	dxdt	dxdt	NOUN
ejpam-3877	360	10	]	]	PUNCT
ejpam-3877	360	11	1	1	NUM
ejpam-3877	360	12	2	2	NUM
ejpam-3877	360	13	.	.	PUNCT
ejpam-3877	361	1	since	since	SCONJ
ejpam-3877	361	2	tk(ψ(un	tk(ψ(un	PROPN
ejpam-3877	361	3	)	)	PUNCT
ejpam-3877	361	4	)	)	PUNCT
ejpam-3877	361	5	∈	∈	PROPN
ejpam-3877	361	6	l2((0	l2((0	PROPN
ejpam-3877	361	7	,	,	PUNCT
ejpam-3877	361	8	t	t	PROPN
ejpam-3877	361	9	)	)	PUNCT
ejpam-3877	361	10	,	,	PUNCT
ejpam-3877	361	11	h1	h1	PROPN
ejpam-3877	361	12	0	0	NUM
ejpam-3877	361	13	(	(	PUNCT
ejpam-3877	361	14	ω	ω	NOUN
ejpam-3877	361	15	)	)	PUNCT
ejpam-3877	361	16	)	)	PUNCT
ejpam-3877	361	17	then	then	ADV
ejpam-3877	361	18	there	there	PRON
ejpam-3877	361	19	exists	exist	VERB
ejpam-3877	361	20	a	a	DET
ejpam-3877	361	21	positive	positive	ADJ
ejpam-3877	361	22	constant	constant	ADJ
ejpam-3877	361	23	c	c	NOUN
ejpam-3877	361	24	such	such	ADJ
ejpam-3877	361	25	that∫	that∫	NOUN
ejpam-3877	361	26	q	q	NOUN
ejpam-3877	361	27	|	|	NOUN
ejpam-3877	361	28	∇φ(tk(ψ(un	∇φ(tk(ψ(un	NOUN
ejpam-3877	361	29	)	)	PUNCT
ejpam-3877	361	30	)	)	PUNCT
ejpam-3877	362	1	|	|	ADV
ejpam-3877	362	2	dxdt	dxdt	VERB
ejpam-3877	362	3	≤	≤	ADJ
ejpam-3877	362	4	c.	c.	NOUN
ejpam-3877	362	5	(	(	PUNCT
ejpam-3877	362	6	5.5	5.5	NUM
ejpam-3877	362	7	)	)	PUNCT
ejpam-3877	362	8	by	by	ADP
ejpam-3877	362	9	proposition	proposition	NOUN
ejpam-3877	362	10	4.2	4.2	NUM
ejpam-3877	362	11	,	,	PUNCT
ejpam-3877	362	12	the	the	DET
ejpam-3877	362	13	sequence	sequence	NOUN
ejpam-3877	362	14	[	[	X
ejpam-3877	362	15	φ(tk(ψ(un)))]t	φ(tk(ψ(un)))]t	NOUN
ejpam-3877	362	16	is	be	AUX
ejpam-3877	362	17	bounded	bound	VERB
ejpam-3877	362	18	in	in	ADP
ejpam-3877	362	19	l2((0	l2((0	PROPN
ejpam-3877	362	20	,	,	PUNCT
ejpam-3877	362	21	t	t	PROPN
ejpam-3877	362	22	)	)	PUNCT
ejpam-3877	362	23	,	,	PUNCT
ejpam-3877	362	24	h−1(ω	h−1(ω	PROPN
ejpam-3877	362	25	)	)	PUNCT
ejpam-3877	362	26	)	)	PUNCT
ejpam-3877	363	1	+	+	PUNCT
ejpam-3877	363	2	l1(q	l1(q	ADV
ejpam-3877	363	3	)	)	PUNCT
ejpam-3877	363	4	.	.	PUNCT
ejpam-3877	364	1	according	accord	VERB
ejpam-3877	364	2	to	to	ADP
ejpam-3877	364	3	the	the	DET
ejpam-3877	364	4	compactness	compactness	NOUN
ejpam-3877	364	5	theorem	theorem	NOUN
ejpam-3877	364	6	in	in	ADP
ejpam-3877	364	7	[	[	X
ejpam-3877	364	8	29	29	NUM
ejpam-3877	364	9	]	]	PUNCT
ejpam-3877	364	10	,	,	PUNCT
ejpam-3877	364	11	then	then	ADV
ejpam-3877	364	12	there	there	ADV
ejpam-3877	364	13	quincy	quincy	PROPN
ejpam-3877	364	14	s.	s.	PROPN
ejpam-3877	364	15	nkombo	nkombo	PROPN
ejpam-3877	364	16	,	,	PUNCT
ejpam-3877	364	17	fengquan	fengquan	PROPN
ejpam-3877	364	18	li	li	PROPN
ejpam-3877	364	19	/	/	SYM
ejpam-3877	364	20	eur	eur	PROPN
ejpam-3877	364	21	.	.	PUNCT
ejpam-3877	365	1	j.	j.	PROPN
ejpam-3877	365	2	pure	pure	PROPN
ejpam-3877	365	3	appl	appl	PROPN
ejpam-3877	365	4	.	.	PROPN
ejpam-3877	365	5	math	math	PROPN
ejpam-3877	365	6	,	,	PUNCT
ejpam-3877	365	7	14	14	NUM
ejpam-3877	365	8	(	(	PUNCT
ejpam-3877	365	9	1	1	NUM
ejpam-3877	365	10	)	)	PUNCT
ejpam-3877	365	11	(	(	PUNCT
ejpam-3877	365	12	2021	2021	NUM
ejpam-3877	365	13	)	)	PUNCT
ejpam-3877	365	14	,	,	PUNCT
ejpam-3877	365	15	204	204	NUM
ejpam-3877	365	16	-	-	SYM
ejpam-3877	365	17	233	233	NUM
ejpam-3877	365	18	219	219	NUM
ejpam-3877	365	19	exists	exist	VERB
ejpam-3877	365	20	a	a	DET
ejpam-3877	365	21	subsequence	subsequence	NOUN
ejpam-3877	365	22	denoted	denote	VERB
ejpam-3877	365	23	again	again	ADV
ejpam-3877	365	24	{	{	PUNCT
ejpam-3877	365	25	ψ(unj	ψ(unj	PROPN
ejpam-3877	365	26	)	)	PUNCT
ejpam-3877	365	27	}	}	PUNCT
ejpam-3877	365	28	(	(	PUNCT
ejpam-3877	365	29	possibly	possibly	ADV
ejpam-3877	365	30	for	for	ADP
ejpam-3877	365	31	k	k	PROPN
ejpam-3877	365	32	>	>	X
ejpam-3877	365	33	0	0	PROPN
ejpam-3877	365	34	,	,	PUNCT
ejpam-3877	365	35	tk(ψ(un	tk(ψ(un	PROPN
ejpam-3877	365	36	)	)	PUNCT
ejpam-3877	365	37	)	)	PUNCT
ejpam-3877	366	1	=	=	SYM
ejpam-3877	366	2	ψ(unj	ψ(unj	PROPN
ejpam-3877	366	3	)	)	PUNCT
ejpam-3877	366	4	and	and	CCONJ
ejpam-3877	366	5	|	|	ADV
ejpam-3877	366	6	ψ(unj	ψ(unj	PROPN
ejpam-3877	366	7	)	)	PUNCT
ejpam-3877	367	1	|≤	|≤	PROPN
ejpam-3877	367	2	k	k	PROPN
ejpam-3877	367	3	)	)	PUNCT
ejpam-3877	367	4	and	and	CCONJ
ejpam-3877	367	5	a	a	DET
ejpam-3877	367	6	function	function	NOUN
ejpam-3877	367	7	v	v	ADP
ejpam-3877	367	8	∈	∈	PROPN
ejpam-3877	367	9	l1((0	l1((0	NOUN
ejpam-3877	367	10	,	,	PUNCT
ejpam-3877	367	11	t	t	PROPN
ejpam-3877	367	12	)	)	PUNCT
ejpam-3877	367	13	,	,	PUNCT
ejpam-3877	367	14	w	w	PROPN
ejpam-3877	367	15	1,1	1,1	NUM
ejpam-3877	367	16	0	0	NUM
ejpam-3877	367	17	(	(	PUNCT
ejpam-3877	367	18	ω	ω	NOUN
ejpam-3877	367	19	)	)	PUNCT
ejpam-3877	367	20	)	)	PUNCT
ejpam-3877	367	21	∩	∩	NOUN
ejpam-3877	367	22	l1(q	l1(q	CCONJ
ejpam-3877	367	23	)	)	PUNCT
ejpam-3877	367	24	such	such	ADJ
ejpam-3877	367	25	that	that	SCONJ
ejpam-3877	367	26	φ(ψ(unj	φ(ψ(unj	PROPN
ejpam-3877	367	27	)	)	PUNCT
ejpam-3877	367	28	)	)	PUNCT
ejpam-3877	367	29	→	→	SYM
ejpam-3877	368	1	v	v	X
ejpam-3877	368	2	a.e	a.e	PROPN
ejpam-3877	368	3	in	in	ADP
ejpam-3877	368	4	q.	q.	PROPN
ejpam-3877	368	5	(	(	PUNCT
ejpam-3877	368	6	5.6	5.6	NUM
ejpam-3877	368	7	)	)	PUNCT
ejpam-3877	368	8	therefore	therefore	ADV
ejpam-3877	368	9	,	,	PUNCT
ejpam-3877	368	10	we	we	PRON
ejpam-3877	368	11	get	get	VERB
ejpam-3877	368	12	ψ(unj	ψ(unj	X
ejpam-3877	368	13	)	)	PUNCT
ejpam-3877	368	14	→	→	SYM
ejpam-3877	368	15	φ−1(v	φ−1(v	PROPN
ejpam-3877	368	16	)	)	PUNCT
ejpam-3877	369	1	a.e	a.e	PROPN
ejpam-3877	369	2	in	in	ADP
ejpam-3877	369	3	q.	q.	PROPN
ejpam-3877	369	4	(	(	PUNCT
ejpam-3877	369	5	5.7	5.7	NUM
ejpam-3877	369	6	)	)	PUNCT
ejpam-3877	369	7	combining	combine	VERB
ejpam-3877	369	8	(	(	PUNCT
ejpam-3877	369	9	5.6	5.6	NUM
ejpam-3877	369	10	)	)	PUNCT
ejpam-3877	369	11	with	with	ADP
ejpam-3877	369	12	(	(	PUNCT
ejpam-3877	369	13	5.1	5.1	NUM
ejpam-3877	369	14	)	)	PUNCT
ejpam-3877	369	15	gives	give	VERB
ejpam-3877	369	16	φ−1(v	φ−1(v	PROPN
ejpam-3877	369	17	)	)	PUNCT
ejpam-3877	369	18	=	=	SYM
ejpam-3877	369	19	v	v	NOUN
ejpam-3877	369	20	,	,	PUNCT
ejpam-3877	369	21	this	this	PRON
ejpam-3877	369	22	proves	prove	VERB
ejpam-3877	369	23	(	(	PUNCT
ejpam-3877	369	24	5.3	5.3	NUM
ejpam-3877	369	25	)	)	PUNCT
ejpam-3877	369	26	.	.	PUNCT
ejpam-3877	370	1	�	�	PROPN
ejpam-3877	370	2	we	we	PRON
ejpam-3877	370	3	recall	recall	VERB
ejpam-3877	370	4	the	the	DET
ejpam-3877	370	5	following	follow	VERB
ejpam-3877	370	6	sclicing	sclice	VERB
ejpam-3877	370	7	property	property	NOUN
ejpam-3877	370	8	of	of	ADP
ejpam-3877	370	9	the	the	DET
ejpam-3877	370	10	bounded	bounded	ADJ
ejpam-3877	370	11	radon	radon	PROPN
ejpam-3877	370	12	measure	measure	NOUN
ejpam-3877	370	13	u	u	PROPN
ejpam-3877	370	14	∈	∈	PROPN
ejpam-3877	370	15	m(q	m(q	PROPN
ejpam-3877	370	16	)	)	PUNCT
ejpam-3877	370	17	.	.	PUNCT
ejpam-3877	371	1	the	the	DET
ejpam-3877	371	2	proof	proof	NOUN
ejpam-3877	371	3	is	be	AUX
ejpam-3877	371	4	omitted	omit	VERB
ejpam-3877	371	5	since	since	SCONJ
ejpam-3877	371	6	it	it	PRON
ejpam-3877	371	7	follows	follow	VERB
ejpam-3877	371	8	from	from	ADP
ejpam-3877	371	9	the	the	DET
ejpam-3877	371	10	more	more	ADV
ejpam-3877	371	11	general	general	ADJ
ejpam-3877	371	12	result	result	NOUN
ejpam-3877	371	13	in	in	ADP
ejpam-3877	371	14	(	(	PUNCT
ejpam-3877	371	15	[	[	X
ejpam-3877	371	16	14	14	NUM
ejpam-3877	371	17	,	,	PUNCT
ejpam-3877	371	18	theorem	theorem	VERB
ejpam-3877	371	19	8	8	NUM
ejpam-3877	371	20	,	,	PUNCT
ejpam-3877	371	21	p.35	p.35	NOUN
ejpam-3877	371	22	]	]	PUNCT
ejpam-3877	371	23	)	)	PUNCT
ejpam-3877	371	24	.	.	PUNCT
ejpam-3877	372	1	proposition	proposition	NOUN
ejpam-3877	372	2	5.2	5.2	NUM
ejpam-3877	372	3	.	.	PUNCT
ejpam-3877	373	1	assume	assume	VERB
ejpam-3877	373	2	that	that	SCONJ
ejpam-3877	373	3	µ	µ	NOUN
ejpam-3877	373	4	∈m+(q	∈m+(q	NOUN
ejpam-3877	373	5	)	)	PUNCT
ejpam-3877	373	6	.	.	PUNCT
ejpam-3877	374	1	then	then	ADV
ejpam-3877	374	2	there	there	PRON
ejpam-3877	374	3	exists	exist	VERB
ejpam-3877	374	4	a	a	DET
ejpam-3877	374	5	measure	measure	NOUN
ejpam-3877	374	6	λ	λ	PROPN
ejpam-3877	374	7	∈m+(0	∈m+(0	PROPN
ejpam-3877	374	8	,	,	PUNCT
ejpam-3877	374	9	t	t	PROPN
ejpam-3877	374	10	)	)	PUNCT
ejpam-3877	374	11	and	and	CCONJ
ejpam-3877	374	12	for	for	ADP
ejpam-3877	374	13	λ	λ	PROPN
ejpam-3877	374	14	almost	almost	ADV
ejpam-3877	374	15	everywhere	everywhere	ADV
ejpam-3877	374	16	t	t	PROPN
ejpam-3877	374	17	∈	∈	PROPN
ejpam-3877	374	18	(	(	PUNCT
ejpam-3877	374	19	0	0	NUM
ejpam-3877	374	20	,	,	PUNCT
ejpam-3877	374	21	t	t	PROPN
ejpam-3877	374	22	)	)	PUNCT
ejpam-3877	374	23	,	,	PUNCT
ejpam-3877	374	24	there	there	PRON
ejpam-3877	374	25	exists	exist	VERB
ejpam-3877	374	26	a	a	DET
ejpam-3877	374	27	probability	probability	NOUN
ejpam-3877	374	28	νt	νt	X
ejpam-3877	374	29	∈	∈	NOUN
ejpam-3877	374	30	m+(ω	m+(ω	NOUN
ejpam-3877	374	31	)	)	PUNCT
ejpam-3877	374	32	with	with	ADP
ejpam-3877	374	33	the	the	DET
ejpam-3877	374	34	following	follow	VERB
ejpam-3877	374	35	properties	property	NOUN
ejpam-3877	374	36	(	(	PUNCT
ejpam-3877	374	37	i	i	NOUN
ejpam-3877	374	38	)	)	PUNCT
ejpam-3877	374	39	for	for	ADP
ejpam-3877	374	40	any	any	DET
ejpam-3877	374	41	borel	borel	NOUN
ejpam-3877	374	42	set	set	VERB
ejpam-3877	374	43	e	e	PROPN
ejpam-3877	374	44	⊆	⊆	NUM
ejpam-3877	374	45	q	q	PROPN
ejpam-3877	374	46	µ(e	µ(e	PROPN
ejpam-3877	374	47	)	)	PUNCT
ejpam-3877	375	1	=	=	SYM
ejpam-3877	375	2	∫	∫	PROPN
ejpam-3877	375	3	(	(	PUNCT
ejpam-3877	375	4	0,t	0,t	PROPN
ejpam-3877	375	5	)	)	PUNCT
ejpam-3877	375	6	νt(et)dλ(t	νt(et)dλ(t	PROPN
ejpam-3877	375	7	)	)	PUNCT
ejpam-3877	375	8	(	(	PUNCT
ejpam-3877	375	9	5.8	5.8	NUM
ejpam-3877	375	10	)	)	PUNCT
ejpam-3877	375	11	where	where	SCONJ
ejpam-3877	375	12	et	et	NOUN
ejpam-3877	375	13	=	=	PUNCT
ejpam-3877	375	14	{	{	PUNCT
ejpam-3877	375	15	x	x	PUNCT
ejpam-3877	375	16	∈	∈	NOUN
ejpam-3877	375	17	ω/(x	ω/(x	NOUN
ejpam-3877	375	18	,	,	PUNCT
ejpam-3877	375	19	t	t	PROPN
ejpam-3877	375	20	)	)	PUNCT
ejpam-3877	375	21	∈	∈	PROPN
ejpam-3877	375	22	e	e	X
ejpam-3877	375	23	}	}	PUNCT
ejpam-3877	375	24	(	(	PUNCT
ejpam-3877	375	25	ii	ii	NOUN
ejpam-3877	375	26	)	)	PUNCT
ejpam-3877	375	27	for	for	ADP
ejpam-3877	375	28	every	every	DET
ejpam-3877	375	29	ξ	ξ	PROPN
ejpam-3877	375	30	∈	∈	PROPN
ejpam-3877	375	31	c(q	c(q	PROPN
ejpam-3877	375	32	)	)	PUNCT
ejpam-3877	376	1	〈	〈	PROPN
ejpam-3877	376	2	µ	µ	PRON
ejpam-3877	376	3	,	,	PUNCT
ejpam-3877	376	4	ξ〉q	ξ〉q	PROPN
ejpam-3877	376	5	=	=	SYM
ejpam-3877	376	6	∫	∫	PROPN
ejpam-3877	376	7	(	(	PUNCT
ejpam-3877	376	8	0,t	0,t	PROPN
ejpam-3877	376	9	)	)	PUNCT
ejpam-3877	376	10	dλ(t	dλ(t	PUNCT
ejpam-3877	376	11	)	)	PUNCT
ejpam-3877	376	12	∫	∫	PROPN
ejpam-3877	377	1	ω	ω	NUM
ejpam-3877	377	2	ξ(x	ξ(x	PROPN
ejpam-3877	377	3	,	,	PUNCT
ejpam-3877	377	4	t)dνt(x	t)dνt(x	NUM
ejpam-3877	377	5	)	)	PUNCT
ejpam-3877	377	6	.	.	PUNCT
ejpam-3877	378	1	(	(	PUNCT
ejpam-3877	378	2	5.9	5.9	NUM
ejpam-3877	378	3	)	)	PUNCT
ejpam-3877	378	4	proposition	proposition	NOUN
ejpam-3877	378	5	5.3	5.3	NUM
ejpam-3877	378	6	.	.	PUNCT
ejpam-3877	379	1	let	let	VERB
ejpam-3877	379	2	{	{	PUNCT
ejpam-3877	379	3	unj	unj	VERB
ejpam-3877	379	4	}	}	PUNCT
ejpam-3877	379	5	and	and	CCONJ
ejpam-3877	379	6	v	v	NOUN
ejpam-3877	379	7	as	as	ADP
ejpam-3877	379	8	in	in	ADP
ejpam-3877	379	9	proposition	proposition	NOUN
ejpam-3877	379	10	5.1	5.1	NUM
ejpam-3877	379	11	.	.	PUNCT
ejpam-3877	380	1	then	then	ADV
ejpam-3877	380	2	the	the	DET
ejpam-3877	380	3	following	follow	VERB
ejpam-3877	380	4	assertions	assertion	NOUN
ejpam-3877	380	5	hold	hold	VERB
ejpam-3877	380	6	(	(	PUNCT
ejpam-3877	380	7	i	i	NOUN
ejpam-3877	380	8	)	)	PUNCT
ejpam-3877	380	9	ψ−1(unj	ψ−1(unj	PART
ejpam-3877	380	10	)	)	PUNCT
ejpam-3877	380	11	∈	∈	PROPN
ejpam-3877	380	12	l1(q	l1(q	CCONJ
ejpam-3877	380	13	)	)	PUNCT
ejpam-3877	380	14	and	and	CCONJ
ejpam-3877	380	15	we	we	PRON
ejpam-3877	380	16	have	have	VERB
ejpam-3877	380	17	unj	unj	VERB
ejpam-3877	380	18	(	(	PUNCT
ejpam-3877	380	19	x	x	NOUN
ejpam-3877	380	20	,	,	PUNCT
ejpam-3877	380	21	t)→	t)→	PROPN
ejpam-3877	381	1	[	[	X
ejpam-3877	381	2	ψ−1(v)](x	ψ−1(v)](x	X
ejpam-3877	381	3	,	,	PUNCT
ejpam-3877	381	4	t	t	X
ejpam-3877	381	5	)	)	PUNCT
ejpam-3877	381	6	a.e	a.e	PROPN
ejpam-3877	381	7	(	(	PUNCT
ejpam-3877	381	8	x	x	NOUN
ejpam-3877	381	9	,	,	PUNCT
ejpam-3877	381	10	t	t	PROPN
ejpam-3877	381	11	)	)	PUNCT
ejpam-3877	381	12	∈	∈	PROPN
ejpam-3877	381	13	q.	q.	NOUN
ejpam-3877	381	14	(	(	PUNCT
ejpam-3877	381	15	5.10	5.10	NUM
ejpam-3877	381	16	)	)	PUNCT
ejpam-3877	381	17	(	(	PUNCT
ejpam-3877	381	18	ii	ii	NOUN
ejpam-3877	381	19	)	)	PUNCT
ejpam-3877	381	20	there	there	PRON
ejpam-3877	381	21	exist	exist	VERB
ejpam-3877	381	22	λ1	λ1	ADJ
ejpam-3877	381	23	,	,	PUNCT
ejpam-3877	381	24	λ2	λ2	PROPN
ejpam-3877	381	25	∈	∈	PROPN
ejpam-3877	381	26	l∞((0	l∞((0	PROPN
ejpam-3877	381	27	,	,	PUNCT
ejpam-3877	381	28	t	t	NOUN
ejpam-3877	381	29	)	)	PUNCT
ejpam-3877	381	30	,	,	PUNCT
ejpam-3877	381	31	m+(ω	m+(ω	NOUN
ejpam-3877	381	32	)	)	PUNCT
ejpam-3877	381	33	)	)	PUNCT
ejpam-3877	381	34	)	)	PUNCT
ejpam-3877	382	1	and	and	CCONJ
ejpam-3877	382	2	we	we	PRON
ejpam-3877	382	3	can	can	AUX
ejpam-3877	382	4	extract	extract	VERB
ejpam-3877	382	5	a	a	DET
ejpam-3877	382	6	subsequence	subsequence	NOUN
ejpam-3877	382	7	still	still	ADV
ejpam-3877	382	8	denoted	denote	VERB
ejpam-3877	382	9	{	{	PUNCT
ejpam-3877	382	10	unj	unj	NOUN
ejpam-3877	382	11	}	}	PUNCT
ejpam-3877	382	12	such	such	ADJ
ejpam-3877	382	13	that	that	SCONJ
ejpam-3877	382	14	u+	u+	NOUN
ejpam-3877	382	15	nj	nj	PROPN
ejpam-3877	382	16	∗	∗	NOUN
ejpam-3877	382	17	⇀	⇀	PUNCT
ejpam-3877	383	1	[	[	X
ejpam-3877	383	2	ψ−1(v)]+	ψ−1(v)]+	X
ejpam-3877	383	3	+	+	X
ejpam-3877	383	4	λ1	λ1	PROPN
ejpam-3877	383	5	in	in	ADP
ejpam-3877	383	6	m+(q	m+(q	PROPN
ejpam-3877	383	7	)	)	PUNCT
ejpam-3877	383	8	,	,	PUNCT
ejpam-3877	383	9	(	(	PUNCT
ejpam-3877	383	10	5.11	5.11	NUM
ejpam-3877	383	11	)	)	PUNCT
ejpam-3877	384	1	u−nj	u−nj	ADJ
ejpam-3877	384	2	∗	∗	NOUN
ejpam-3877	384	3	⇀	⇀	PUNCT
ejpam-3877	385	1	[	[	X
ejpam-3877	385	2	ψ−1(v)]−	ψ−1(v)]−	NOUN
ejpam-3877	385	3	+	+	NUM
ejpam-3877	385	4	λ2	λ2	NOUN
ejpam-3877	385	5	in	in	ADP
ejpam-3877	385	6	m+(q	m+(q	PROPN
ejpam-3877	385	7	)	)	PUNCT
ejpam-3877	385	8	,	,	PUNCT
ejpam-3877	385	9	(	(	PUNCT
ejpam-3877	385	10	5.12	5.12	NUM
ejpam-3877	385	11	)	)	PUNCT
ejpam-3877	385	12	unj	unj	NOUN
ejpam-3877	385	13	∗	∗	NOUN
ejpam-3877	385	14	⇀	⇀	PUNCT
ejpam-3877	386	1	[	[	X
ejpam-3877	386	2	ψ−1(v	ψ−1(v	NOUN
ejpam-3877	386	3	)	)	PUNCT
ejpam-3877	386	4	]	]	PUNCT
ejpam-3877	387	1	+	+	CCONJ
ejpam-3877	387	2	λ	λ	NOUN
ejpam-3877	387	3	in	in	ADP
ejpam-3877	387	4	m+(q	m+(q	NUM
ejpam-3877	387	5	)	)	PUNCT
ejpam-3877	387	6	,	,	PUNCT
ejpam-3877	387	7	(	(	PUNCT
ejpam-3877	387	8	5.13	5.13	NUM
ejpam-3877	387	9	)	)	PUNCT
ejpam-3877	387	10	where	where	SCONJ
ejpam-3877	387	11	λ	λ	X
ejpam-3877	387	12	:	:	PUNCT
ejpam-3877	387	13	=	=	SYM
ejpam-3877	387	14	λ1	λ1	ADJ
ejpam-3877	387	15	−	−	PROPN
ejpam-3877	387	16	λ2	λ2	PROPN
ejpam-3877	387	17	in	in	ADP
ejpam-3877	387	18	l∞((0	l∞((0	PROPN
ejpam-3877	387	19	,	,	PUNCT
ejpam-3877	387	20	t	t	PROPN
ejpam-3877	387	21	)	)	PUNCT
ejpam-3877	387	22	,	,	PUNCT
ejpam-3877	387	23	m+(ω	m+(ω	NOUN
ejpam-3877	387	24	)	)	PUNCT
ejpam-3877	387	25	)	)	PUNCT
ejpam-3877	387	26	.	.	PUNCT
ejpam-3877	388	1	proof	proof	NOUN
ejpam-3877	388	2	.	.	PUNCT
ejpam-3877	389	1	from	from	ADP
ejpam-3877	389	2	(	(	PUNCT
ejpam-3877	389	3	5.3	5.3	NUM
ejpam-3877	389	4	)	)	PUNCT
ejpam-3877	389	5	,	,	PUNCT
ejpam-3877	389	6	(	(	PUNCT
ejpam-3877	389	7	4.1	4.1	NUM
ejpam-3877	389	8	)	)	PUNCT
ejpam-3877	389	9	and	and	CCONJ
ejpam-3877	389	10	ψ−1(unj	ψ−1(unj	X
ejpam-3877	389	11	)	)	PUNCT
ejpam-3877	389	12	∈	∈	PROPN
ejpam-3877	389	13	l1(q	l1(q	CCONJ
ejpam-3877	389	14	)	)	PUNCT
ejpam-3877	389	15	,	,	PUNCT
ejpam-3877	389	16	then	then	ADV
ejpam-3877	389	17	by	by	ADP
ejpam-3877	389	18	fatou	fatou	NOUN
ejpam-3877	389	19	’s	’s	PART
ejpam-3877	389	20	lemma	lemma	PROPN
ejpam-3877	389	21	,	,	PUNCT
ejpam-3877	389	22	we	we	PRON
ejpam-3877	389	23	get∫	get∫	VERB
ejpam-3877	389	24	q	q	X
ejpam-3877	390	1	[	[	X
ejpam-3877	390	2	ψ−1(v)](x	ψ−1(v)](x	X
ejpam-3877	390	3	,	,	PUNCT
ejpam-3877	390	4	t)dxdt	t)dxdt	NOUN
ejpam-3877	390	5	≤	≤	PROPN
ejpam-3877	390	6	lim	lim	PROPN
ejpam-3877	390	7	inf	inf	PROPN
ejpam-3877	390	8	j→∞	j→∞	NUM
ejpam-3877	390	9	∫	∫	PROPN
ejpam-3877	390	10	q	q	PROPN
ejpam-3877	390	11	unj	unj	PROPN
ejpam-3877	390	12	(	(	PUNCT
ejpam-3877	390	13	x	x	NOUN
ejpam-3877	390	14	,	,	PUNCT
ejpam-3877	390	15	t)dxdt	t)dxdt	PROPN
ejpam-3877	390	16	.	.	PUNCT
ejpam-3877	391	1	(	(	PUNCT
ejpam-3877	391	2	5.14	5.14	NUM
ejpam-3877	391	3	)	)	PUNCT
ejpam-3877	391	4	quincy	quincy	PROPN
ejpam-3877	391	5	s.	s.	PROPN
ejpam-3877	391	6	nkombo	nkombo	PROPN
ejpam-3877	391	7	,	,	PUNCT
ejpam-3877	391	8	fengquan	fengquan	PROPN
ejpam-3877	391	9	li	li	PROPN
ejpam-3877	391	10	/	/	SYM
ejpam-3877	391	11	eur	eur	PROPN
ejpam-3877	391	12	.	.	PUNCT
ejpam-3877	392	1	j.	j.	PROPN
ejpam-3877	392	2	pure	pure	PROPN
ejpam-3877	392	3	appl	appl	PROPN
ejpam-3877	392	4	.	.	PROPN
ejpam-3877	392	5	math	math	PROPN
ejpam-3877	392	6	,	,	PUNCT
ejpam-3877	392	7	14	14	NUM
ejpam-3877	392	8	(	(	PUNCT
ejpam-3877	392	9	1	1	NUM
ejpam-3877	392	10	)	)	PUNCT
ejpam-3877	392	11	(	(	PUNCT
ejpam-3877	392	12	2021	2021	NUM
ejpam-3877	392	13	)	)	PUNCT
ejpam-3877	392	14	,	,	PUNCT
ejpam-3877	392	15	204	204	NUM
ejpam-3877	392	16	-	-	SYM
ejpam-3877	392	17	233	233	NUM
ejpam-3877	392	18	220	220	NUM
ejpam-3877	392	19	by	by	ADP
ejpam-3877	392	20	(	(	PUNCT
ejpam-3877	392	21	5.3	5.3	NUM
ejpam-3877	392	22	)	)	PUNCT
ejpam-3877	392	23	the	the	DET
ejpam-3877	392	24	convergence	convergence	NOUN
ejpam-3877	392	25	(	(	PUNCT
ejpam-3877	392	26	5.11	5.11	NUM
ejpam-3877	392	27	)	)	PUNCT
ejpam-3877	392	28	is	be	AUX
ejpam-3877	392	29	satisfied	satisfied	ADJ
ejpam-3877	392	30	.	.	PUNCT
ejpam-3877	393	1	since	since	SCONJ
ejpam-3877	393	2	the	the	DET
ejpam-3877	393	3	sequence	sequence	NOUN
ejpam-3877	393	4	{	{	PUNCT
ejpam-3877	393	5	unj	unj	PROPN
ejpam-3877	393	6	}	}	PUNCT
ejpam-3877	393	7	is	be	AUX
ejpam-3877	393	8	uniformly	uniformly	ADV
ejpam-3877	393	9	bounded	bound	VERB
ejpam-3877	393	10	in	in	ADP
ejpam-3877	393	11	l1(q	l1(q	CCONJ
ejpam-3877	393	12	)	)	PUNCT
ejpam-3877	393	13	and	and	CCONJ
ejpam-3877	393	14	by	by	ADP
ejpam-3877	393	15	(	(	PUNCT
ejpam-3877	393	16	4.6	4.6	NUM
ejpam-3877	393	17	)	)	PUNCT
ejpam-3877	393	18	,	,	PUNCT
ejpam-3877	393	19	there	there	PRON
ejpam-3877	393	20	exist	exist	VERB
ejpam-3877	393	21	a	a	DET
ejpam-3877	393	22	subsequence	subsequence	NOUN
ejpam-3877	393	23	{	{	PUNCT
ejpam-3877	393	24	unj	unj	NOUN
ejpam-3877	393	25	}	}	PUNCT
ejpam-3877	393	26	which	which	PRON
ejpam-3877	393	27	still	still	ADV
ejpam-3877	393	28	denote	denote	VERB
ejpam-3877	393	29	{	{	PUNCT
ejpam-3877	393	30	unj	unj	NOUN
ejpam-3877	393	31	}	}	PUNCT
ejpam-3877	393	32	and	and	CCONJ
ejpam-3877	393	33	radon	radon	NOUN
ejpam-3877	393	34	-	-	PUNCT
ejpam-3877	393	35	measures	measure	NOUN
ejpam-3877	393	36	u	u	NOUN
ejpam-3877	393	37	,	,	PUNCT
ejpam-3877	393	38	ũ	ũ	PROPN
ejpam-3877	393	39	∈m+(q	∈m+(q	NOUN
ejpam-3877	393	40	)	)	PUNCT
ejpam-3877	393	41	such	such	ADJ
ejpam-3877	393	42	that	that	SCONJ
ejpam-3877	393	43	u+	u+	NOUN
ejpam-3877	394	1	nj	nj	PROPN
ejpam-3877	394	2	∗	∗	NOUN
ejpam-3877	394	3	⇀	⇀	PUNCT
ejpam-3877	394	4	u	u	NOUN
ejpam-3877	394	5	in	in	ADP
ejpam-3877	394	6	m+(q	m+(q	NUM
ejpam-3877	394	7	)	)	PUNCT
ejpam-3877	394	8	.	.	PUNCT
ejpam-3877	395	1	(	(	PUNCT
ejpam-3877	395	2	5.15	5.15	NUM
ejpam-3877	395	3	)	)	PUNCT
ejpam-3877	395	4	u−nj	u−nj	ADJ
ejpam-3877	395	5	∗	∗	NOUN
ejpam-3877	395	6	⇀	⇀	PUNCT
ejpam-3877	396	1	ũ	ũ	PROPN
ejpam-3877	396	2	in	in	ADP
ejpam-3877	396	3	m+(q	m+(q	NUM
ejpam-3877	396	4	)	)	PUNCT
ejpam-3877	396	5	.	.	PUNCT
ejpam-3877	397	1	(	(	PUNCT
ejpam-3877	397	2	5.16	5.16	NUM
ejpam-3877	397	3	)	)	PUNCT
ejpam-3877	397	4	let	let	VERB
ejpam-3877	397	5	us	we	PRON
ejpam-3877	397	6	prove	prove	VERB
ejpam-3877	397	7	that	that	SCONJ
ejpam-3877	397	8	u	u	PROPN
ejpam-3877	397	9	,	,	PUNCT
ejpam-3877	397	10	ũ	ũ	PROPN
ejpam-3877	397	11	∈	∈	PROPN
ejpam-3877	397	12	l∞((0	l∞((0	PROPN
ejpam-3877	397	13	,	,	PUNCT
ejpam-3877	397	14	t	t	PROPN
ejpam-3877	397	15	)	)	PUNCT
ejpam-3877	397	16	,	,	PUNCT
ejpam-3877	397	17	m+(ω	m+(ω	NOUN
ejpam-3877	397	18	)	)	PUNCT
ejpam-3877	397	19	)	)	PUNCT
ejpam-3877	397	20	.	.	PUNCT
ejpam-3877	398	1	to	to	PART
ejpam-3877	398	2	prove	prove	VERB
ejpam-3877	398	3	this	this	PRON
ejpam-3877	398	4	,	,	PUNCT
ejpam-3877	398	5	we	we	PRON
ejpam-3877	398	6	consider	consider	VERB
ejpam-3877	398	7	λi	λi	PRON
ejpam-3877	398	8	∈	∈	PROPN
ejpam-3877	398	9	m+(0	m+(0	PROPN
ejpam-3877	398	10	,	,	PUNCT
ejpam-3877	398	11	t	t	PROPN
ejpam-3877	398	12	)	)	PUNCT
ejpam-3877	398	13	and	and	CCONJ
ejpam-3877	398	14	λi	λi	NOUN
ejpam-3877	398	15	-	-	ADJ
ejpam-3877	398	16	a.e	a.e	NOUN
ejpam-3877	398	17	t	t	NOUN
ejpam-3877	398	18	∈	∈	PROPN
ejpam-3877	398	19	(	(	PUNCT
ejpam-3877	398	20	0	0	NUM
ejpam-3877	398	21	,	,	PUNCT
ejpam-3877	398	22	t	t	NOUN
ejpam-3877	398	23	)	)	PUNCT
ejpam-3877	398	24	.	.	PUNCT
ejpam-3877	399	1	let	let	VERB
ejpam-3877	399	2	νti	νti	PROPN
ejpam-3877	399	3	∈	∈	PROPN
ejpam-3877	399	4	m+(ω	m+(ω	NOUN
ejpam-3877	399	5	)	)	PUNCT
ejpam-3877	399	6	be	be	VERB
ejpam-3877	399	7	the	the	DET
ejpam-3877	399	8	measure	measure	NOUN
ejpam-3877	399	9	given	give	VERB
ejpam-3877	399	10	by	by	ADP
ejpam-3877	399	11	proposition	proposition	NOUN
ejpam-3877	399	12	5.2	5.2	NUM
ejpam-3877	399	13	in	in	ADP
ejpam-3877	399	14	correspondence	correspondence	NOUN
ejpam-3877	399	15	with	with	ADP
ejpam-3877	399	16	each	each	DET
ejpam-3877	399	17	u	u	NOUN
ejpam-3877	399	18	,	,	PUNCT
ejpam-3877	399	19	ũ.	ũ.	PROPN
ejpam-3877	399	20	let	let	VERB
ejpam-3877	399	21	us	we	PRON
ejpam-3877	399	22	show	show	VERB
ejpam-3877	399	23	that	that	SCONJ
ejpam-3877	399	24	the	the	DET
ejpam-3877	399	25	measures	measure	NOUN
ejpam-3877	399	26	λi	λi	ADP
ejpam-3877	399	27	∈	∈	PROPN
ejpam-3877	399	28	m+(0	m+(0	PROPN
ejpam-3877	399	29	,	,	PUNCT
ejpam-3877	399	30	t	t	PROPN
ejpam-3877	399	31	)	)	PUNCT
ejpam-3877	399	32	are	be	AUX
ejpam-3877	399	33	absolutely	absolutely	ADV
ejpam-3877	399	34	continuous	continuous	ADJ
ejpam-3877	399	35	with	with	ADP
ejpam-3877	399	36	respect	respect	NOUN
ejpam-3877	399	37	to	to	ADP
ejpam-3877	399	38	the	the	DET
ejpam-3877	399	39	lebesgue	lebesgue	ADJ
ejpam-3877	399	40	measure	measure	NOUN
ejpam-3877	399	41	over	over	ADP
ejpam-3877	399	42	(	(	PUNCT
ejpam-3877	399	43	0	0	NUM
ejpam-3877	399	44	,	,	PUNCT
ejpam-3877	399	45	t	t	NOUN
ejpam-3877	399	46	)	)	PUNCT
ejpam-3877	399	47	.	.	PUNCT
ejpam-3877	400	1	in	in	ADP
ejpam-3877	400	2	this	this	DET
ejpam-3877	400	3	direction	direction	NOUN
ejpam-3877	400	4	,	,	PUNCT
ejpam-3877	400	5	fix	fix	NOUN
ejpam-3877	400	6	arbitrarily	arbitrarily	ADV
ejpam-3877	400	7	t	t	X
ejpam-3877	400	8	∈	∈	PROPN
ejpam-3877	400	9	(	(	PUNCT
ejpam-3877	400	10	0	0	NUM
ejpam-3877	400	11	,	,	PUNCT
ejpam-3877	400	12	t	t	NOUN
ejpam-3877	400	13	)	)	PUNCT
ejpam-3877	400	14	and	and	CCONJ
ejpam-3877	400	15	choose	choose	VERB
ejpam-3877	400	16	r	r	NOUN
ejpam-3877	400	17	,	,	PUNCT
ejpam-3877	400	18	s	s	PART
ejpam-3877	400	19	>	>	X
ejpam-3877	400	20	0	0	NUM
ejpam-3877	400	21	such	such	ADJ
ejpam-3877	400	22	that	that	SCONJ
ejpam-3877	400	23	jr	jr	PROPN
ejpam-3877	400	24	,	,	PUNCT
ejpam-3877	400	25	s	s	PART
ejpam-3877	400	26	≡	≡	PROPN
ejpam-3877	400	27	(	(	PUNCT
ejpam-3877	400	28	t−r−2s	t−r−2s	NOUN
ejpam-3877	400	29	,	,	PUNCT
ejpam-3877	400	30	t+r+2s	t+r+2s	NUM
ejpam-3877	400	31	)	)	PUNCT
ejpam-3877	400	32	⊆	⊆	NUM
ejpam-3877	400	33	(	(	PUNCT
ejpam-3877	400	34	0	0	NUM
ejpam-3877	400	35	,	,	PUNCT
ejpam-3877	400	36	t	t	NOUN
ejpam-3877	400	37	)	)	PUNCT
ejpam-3877	400	38	.	.	PUNCT
ejpam-3877	401	1	then	then	ADV
ejpam-3877	401	2	for	for	ADP
ejpam-3877	401	3	every	every	DET
ejpam-3877	401	4	function	function	NOUN
ejpam-3877	401	5	ηr	ηr	NOUN
ejpam-3877	401	6	,	,	PUNCT
ejpam-3877	401	7	s	s	PART
ejpam-3877	401	8	∈	∈	PROPN
ejpam-3877	401	9	c1	c1	NOUN
ejpam-3877	401	10	c	c	PROPN
ejpam-3877	401	11	(	(	PUNCT
ejpam-3877	401	12	0	0	NUM
ejpam-3877	401	13	,	,	PUNCT
ejpam-3877	401	14	t	t	NOUN
ejpam-3877	401	15	)	)	PUNCT
ejpam-3877	401	16	such	such	ADJ
ejpam-3877	401	17	that	that	SCONJ
ejpam-3877	401	18	ηr	ηr	NOUN
ejpam-3877	401	19	,	,	PUNCT
ejpam-3877	401	20	s	s	PART
ejpam-3877	401	21	≡	≡	PROPN
ejpam-3877	401	22	1	1	NUM
ejpam-3877	401	23	in	in	ADP
ejpam-3877	401	24	[	[	PUNCT
ejpam-3877	401	25	t−	t−	PROPN
ejpam-3877	401	26	r	r	NOUN
ejpam-3877	401	27	−	−	NOUN
ejpam-3877	401	28	2s	2s	NUM
ejpam-3877	401	29	,	,	PUNCT
ejpam-3877	401	30	t+	t+	ADP
ejpam-3877	401	31	r	r	NOUN
ejpam-3877	401	32	+	+	X
ejpam-3877	401	33	2s	2s	NOUN
ejpam-3877	401	34	]	]	X
ejpam-3877	401	35	,	,	PUNCT
ejpam-3877	401	36	0	0	NUM
ejpam-3877	401	37	≤	≤	NUM
ejpam-3877	401	38	ηr	ηr	NOUN
ejpam-3877	401	39	,	,	PUNCT
ejpam-3877	401	40	s	s	PART
ejpam-3877	401	41	≤	≤	NUM
ejpam-3877	401	42	1	1	NUM
ejpam-3877	401	43	,	,	PUNCT
ejpam-3877	401	44	suppηr	suppηr	VERB
ejpam-3877	401	45	,	,	PUNCT
ejpam-3877	401	46	s	s	PART
ejpam-3877	401	47	⊆	⊆	NUM
ejpam-3877	401	48	jr	jr	PROPN
ejpam-3877	401	49	,	,	PUNCT
ejpam-3877	401	50	s.	s.	PROPN
ejpam-3877	401	51	by	by	ADP
ejpam-3877	401	52	the	the	DET
ejpam-3877	401	53	estimate	estimate	NOUN
ejpam-3877	401	54	(	(	PUNCT
ejpam-3877	401	55	4.1	4.1	NUM
ejpam-3877	401	56	)	)	PUNCT
ejpam-3877	401	57	,	,	PUNCT
ejpam-3877	401	58	we	we	PRON
ejpam-3877	401	59	have∫	have∫	VERB
ejpam-3877	401	60	q	q	ADJ
ejpam-3877	401	61	u±nj	u±nj	PROPN
ejpam-3877	401	62	ηr	ηr	NOUN
ejpam-3877	401	63	,	,	PUNCT
ejpam-3877	401	64	s(t)dxdt	s(t)dxdt	NOUN
ejpam-3877	401	65	≤	≤	NOUN
ejpam-3877	401	66	2(r	2(r	NUM
ejpam-3877	402	1	+	+	CCONJ
ejpam-3877	402	2	2s	2s	X
ejpam-3877	402	3	)	)	PUNCT
ejpam-3877	402	4	‖	‖	PROPN
ejpam-3877	402	5	µ	µ	X
ejpam-3877	402	6	‖m+(q	‖m+(q	NOUN
ejpam-3877	402	7	)	)	PUNCT
ejpam-3877	402	8	+2(r	+2(r	PROPN
ejpam-3877	403	1	+	+	CCONJ
ejpam-3877	403	2	2s	2s	X
ejpam-3877	403	3	)	)	PUNCT
ejpam-3877	403	4	‖	‖	PROPN
ejpam-3877	403	5	u0	u0	NOUN
ejpam-3877	403	6	‖m+(ω	‖m+(ω	PROPN
ejpam-3877	403	7	)	)	PUNCT
ejpam-3877	403	8	.	.	PUNCT
ejpam-3877	404	1	(	(	PUNCT
ejpam-3877	404	2	5.17	5.17	NUM
ejpam-3877	404	3	)	)	PUNCT
ejpam-3877	404	4	by	by	ADP
ejpam-3877	404	5	(	(	PUNCT
ejpam-3877	404	6	5.15	5.15	NUM
ejpam-3877	404	7	)	)	PUNCT
ejpam-3877	404	8	,	,	PUNCT
ejpam-3877	404	9	(	(	PUNCT
ejpam-3877	404	10	5.16	5.16	NUM
ejpam-3877	404	11	)	)	PUNCT
ejpam-3877	404	12	and	and	CCONJ
ejpam-3877	404	13	(	(	PUNCT
ejpam-3877	404	14	5.17	5.17	NUM
ejpam-3877	404	15	)	)	PUNCT
ejpam-3877	404	16	,	,	PUNCT
ejpam-3877	404	17	there	there	PRON
ejpam-3877	404	18	holds∫	holds∫	VERB
ejpam-3877	404	19	[	[	X
ejpam-3877	404	20	t−r	t−r	NOUN
ejpam-3877	404	21	,	,	PUNCT
ejpam-3877	404	22	t+r	t+r	ADP
ejpam-3877	404	23	]	]	X
ejpam-3877	404	24	dλi(t	dλi(t	NOUN
ejpam-3877	404	25	)	)	PUNCT
ejpam-3877	404	26	≤	≤	NUM
ejpam-3877	404	27	∫	∫	PROPN
ejpam-3877	404	28	(	(	PUNCT
ejpam-3877	404	29	t−r−2s	t−r−2s	NOUN
ejpam-3877	404	30	,	,	PUNCT
ejpam-3877	404	31	t+r+2s	t+r+2s	NUM
ejpam-3877	404	32	)	)	PUNCT
ejpam-3877	404	33	νti	νti	NOUN
ejpam-3877	404	34	(	(	PUNCT
ejpam-3877	404	35	ω)dλi(t	ω)dλi(t	NOUN
ejpam-3877	404	36	)	)	PUNCT
ejpam-3877	404	37	≤	≤	NOUN
ejpam-3877	404	38	lim	lim	PROPN
ejpam-3877	404	39	inf	inf	PROPN
ejpam-3877	404	40	k→∞	k→∞	PROPN
ejpam-3877	404	41	∫	∫	PROPN
ejpam-3877	404	42	q	q	PROPN
ejpam-3877	404	43	u±nj	u±nj	PROPN
ejpam-3877	404	44	(	(	PUNCT
ejpam-3877	404	45	x	x	X
ejpam-3877	404	46	,	,	PUNCT
ejpam-3877	404	47	t)ηr	t)ηr	PROPN
ejpam-3877	404	48	,	,	PUNCT
ejpam-3877	404	49	s(t)dxdt	s(t)dxdt	NOUN
ejpam-3877	404	50	.	.	PUNCT
ejpam-3877	405	1	thus	thus	ADV
ejpam-3877	405	2	∫	∫	X
ejpam-3877	406	1	[	[	X
ejpam-3877	406	2	t−r	t−r	NOUN
ejpam-3877	406	3	,	,	PUNCT
ejpam-3877	406	4	t+r	t+r	ADP
ejpam-3877	406	5	]	]	X
ejpam-3877	406	6	dλi(t	dλi(t	NOUN
ejpam-3877	406	7	)	)	PUNCT
ejpam-3877	406	8	≤	≤	NOUN
ejpam-3877	406	9	2(r	2(r	NUM
ejpam-3877	407	1	+	+	CCONJ
ejpam-3877	407	2	2s	2s	X
ejpam-3877	407	3	)	)	PUNCT
ejpam-3877	407	4	‖	‖	PROPN
ejpam-3877	407	5	µ	µ	X
ejpam-3877	407	6	‖m+(q	‖m+(q	NOUN
ejpam-3877	407	7	)	)	PUNCT
ejpam-3877	407	8	+2(r	+2(r	PROPN
ejpam-3877	408	1	+	+	CCONJ
ejpam-3877	408	2	2s	2s	X
ejpam-3877	408	3	)	)	PUNCT
ejpam-3877	408	4	‖	‖	PROPN
ejpam-3877	408	5	u0	u0	NOUN
ejpam-3877	408	6	‖m+(ω	‖m+(ω	PROPN
ejpam-3877	408	7	)	)	PUNCT
ejpam-3877	408	8	.	.	PUNCT
ejpam-3877	409	1	noting	note	VERB
ejpam-3877	409	2	s	s	VERB
ejpam-3877	409	3	is	be	AUX
ejpam-3877	409	4	arbitrary	arbitrary	ADJ
ejpam-3877	409	5	,	,	PUNCT
ejpam-3877	409	6	thus	thus	ADV
ejpam-3877	409	7	we	we	PRON
ejpam-3877	409	8	divide	divide	VERB
ejpam-3877	409	9	both	both	DET
ejpam-3877	409	10	sides	side	NOUN
ejpam-3877	409	11	of	of	ADP
ejpam-3877	409	12	the	the	DET
ejpam-3877	409	13	above	above	ADJ
ejpam-3877	409	14	inequality	inequality	NOUN
ejpam-3877	409	15	by	by	ADP
ejpam-3877	409	16	2r	2r	NUM
ejpam-3877	409	17	,	,	PUNCT
ejpam-3877	409	18	we	we	PRON
ejpam-3877	409	19	obtain	obtain	VERB
ejpam-3877	409	20	1	1	NUM
ejpam-3877	409	21	2r	2r	NUM
ejpam-3877	409	22	∫	∫	PROPN
ejpam-3877	410	1	[	[	X
ejpam-3877	410	2	t−r	t−r	PROPN
ejpam-3877	410	3	,	,	PUNCT
ejpam-3877	410	4	t+r	t+r	ADP
ejpam-3877	410	5	]	]	X
ejpam-3877	410	6	dλi(t	dλi(t	NOUN
ejpam-3877	410	7	)	)	PUNCT
ejpam-3877	410	8	≤‖	≤‖	PROPN
ejpam-3877	410	9	µ	µ	X
ejpam-3877	410	10	‖m+(q	‖m+(q	NOUN
ejpam-3877	410	11	)	)	PUNCT
ejpam-3877	410	12	+	+	CCONJ
ejpam-3877	410	13	‖	‖	ADJ
ejpam-3877	410	14	u0	u0	ADJ
ejpam-3877	410	15	‖m+(ω	‖m+(ω	PROPN
ejpam-3877	410	16	)	)	PUNCT
ejpam-3877	410	17	.	.	PUNCT
ejpam-3877	411	1	therefore	therefore	ADV
ejpam-3877	411	2	there	there	PRON
ejpam-3877	411	3	exists	exist	VERB
ejpam-3877	411	4	hi	hi	PROPN
ejpam-3877	411	5	∈	∈	PROPN
ejpam-3877	411	6	l1(0	l1(0	PROPN
ejpam-3877	411	7	,	,	PUNCT
ejpam-3877	411	8	t	t	PROPN
ejpam-3877	411	9	)	)	PUNCT
ejpam-3877	411	10	,	,	PUNCT
ejpam-3877	411	11	hi	hi	INTJ
ejpam-3877	411	12	≥	≥	NOUN
ejpam-3877	411	13	0	0	NUM
ejpam-3877	411	14	such	such	ADJ
ejpam-3877	411	15	that	that	DET
ejpam-3877	411	16	dλi(t	dλi(t	NOUN
ejpam-3877	411	17	)	)	PUNCT
ejpam-3877	411	18	=	=	PUNCT
ejpam-3877	411	19	hi(t)dt	hi(t)dt	NOUN
ejpam-3877	411	20	,	,	PUNCT
ejpam-3877	411	21	this	this	PRON
ejpam-3877	411	22	means	mean	VERB
ejpam-3877	411	23	that	that	SCONJ
ejpam-3877	411	24	the	the	DET
ejpam-3877	411	25	radon	radon	ADJ
ejpam-3877	411	26	-	-	PUNCT
ejpam-3877	411	27	measure	measure	NOUN
ejpam-3877	411	28	m+(0	m+(0	PROPN
ejpam-3877	411	29	,	,	PUNCT
ejpam-3877	411	30	t	t	PROPN
ejpam-3877	411	31	)	)	PUNCT
ejpam-3877	411	32	is	be	AUX
ejpam-3877	411	33	regular	regular	ADJ
ejpam-3877	411	34	(	(	PUNCT
ejpam-3877	411	35	e.g	e.g	NOUN
ejpam-3877	411	36	,	,	PUNCT
ejpam-3877	411	37	[	[	X
ejpam-3877	411	38	9	9	NUM
ejpam-3877	411	39	]	]	PUNCT
ejpam-3877	411	40	)	)	PUNCT
ejpam-3877	411	41	.	.	PUNCT
ejpam-3877	412	1	since	since	SCONJ
ejpam-3877	412	2	u	u	PRON
ejpam-3877	412	3	,	,	PUNCT
ejpam-3877	412	4	ũ	ũ	PROPN
ejpam-3877	412	5	∈	∈	NOUN
ejpam-3877	412	6	m+(q	m+(q	NUM
ejpam-3877	412	7	)	)	PUNCT
ejpam-3877	412	8	are	be	AUX
ejpam-3877	412	9	nonnegative	nonnegative	ADJ
ejpam-3877	412	10	radon	radon	NOUN
ejpam-3877	412	11	-	-	PUNCT
ejpam-3877	412	12	measures	measure	NOUN
ejpam-3877	412	13	,	,	PUNCT
ejpam-3877	412	14	letting	let	VERB
ejpam-3877	412	15	r	r	NOUN
ejpam-3877	412	16	→	→	SYM
ejpam-3877	412	17	0	0	NUM
ejpam-3877	412	18	in	in	ADP
ejpam-3877	412	19	the	the	DET
ejpam-3877	412	20	previous	previous	ADJ
ejpam-3877	412	21	inequality	inequality	NOUN
ejpam-3877	412	22	yields	yield	VERB
ejpam-3877	412	23	0	0	NUM
ejpam-3877	412	24	≤	≤	NUM
ejpam-3877	412	25	hi(t	hi(t	NOUN
ejpam-3877	412	26	)	)	PUNCT
ejpam-3877	413	1	≤	≤	NUM
ejpam-3877	413	2	c	c	X
ejpam-3877	413	3	(	(	PUNCT
ejpam-3877	413	4	‖	‖	PROPN
ejpam-3877	413	5	µ	µ	X
ejpam-3877	413	6	‖m+(q	‖m+(q	NOUN
ejpam-3877	413	7	)	)	PUNCT
ejpam-3877	413	8	+	+	CCONJ
ejpam-3877	413	9	‖	‖	ADJ
ejpam-3877	413	10	u0	u0	ADJ
ejpam-3877	413	11	‖m+(ω	‖m+(ω	PROPN
ejpam-3877	413	12	)	)	PUNCT
ejpam-3877	413	13	)	)	PUNCT
ejpam-3877	413	14	for	for	ADP
ejpam-3877	413	15	almost	almost	ADV
ejpam-3877	413	16	every	every	PRON
ejpam-3877	413	17	t	t	NOUN
ejpam-3877	413	18	∈	∈	PROPN
ejpam-3877	413	19	(	(	PUNCT
ejpam-3877	413	20	0	0	NUM
ejpam-3877	413	21	,	,	PUNCT
ejpam-3877	413	22	t	t	NOUN
ejpam-3877	413	23	)	)	PUNCT
ejpam-3877	413	24	.	.	PUNCT
ejpam-3877	414	1	finally	finally	ADV
ejpam-3877	414	2	,	,	PUNCT
ejpam-3877	414	3	defining	define	VERB
ejpam-3877	414	4	u(t	u(t	NOUN
ejpam-3877	414	5	)	)	PUNCT
ejpam-3877	414	6	=	=	SYM
ejpam-3877	414	7	h1(t)νt1	h1(t)νt1	NOUN
ejpam-3877	414	8	and	and	CCONJ
ejpam-3877	414	9	ũ(t	ũ(t	PROPN
ejpam-3877	414	10	)	)	PUNCT
ejpam-3877	414	11	=	=	PUNCT
ejpam-3877	414	12	h2(t)νt2	h2(t)νt2	NOUN
ejpam-3877	414	13	for	for	ADP
ejpam-3877	414	14	almost	almost	ADV
ejpam-3877	414	15	everywhere	everywhere	ADV
ejpam-3877	414	16	t	t	PROPN
ejpam-3877	414	17	∈	∈	PROPN
ejpam-3877	414	18	(	(	PUNCT
ejpam-3877	414	19	0	0	NUM
ejpam-3877	414	20	,	,	PUNCT
ejpam-3877	414	21	t	t	NOUN
ejpam-3877	414	22	)	)	PUNCT
ejpam-3877	414	23	.	.	PUNCT
ejpam-3877	415	1	from	from	ADP
ejpam-3877	415	2	(	(	PUNCT
ejpam-3877	415	3	5.7	5.7	NUM
ejpam-3877	415	4	)	)	PUNCT
ejpam-3877	415	5	and	and	CCONJ
ejpam-3877	415	6	(	(	PUNCT
ejpam-3877	415	7	5.8	5.8	X
ejpam-3877	415	8	)	)	PUNCT
ejpam-3877	415	9	we	we	PRON
ejpam-3877	415	10	obtain	obtain	VERB
ejpam-3877	415	11	that	that	DET
ejpam-3877	415	12	u	u	NOUN
ejpam-3877	415	13	,	,	PUNCT
ejpam-3877	415	14	ũ	ũ	PROPN
ejpam-3877	415	15	∈	∈	PROPN
ejpam-3877	415	16	l∞((0	l∞((0	PROPN
ejpam-3877	415	17	,	,	PUNCT
ejpam-3877	415	18	t	t	PROPN
ejpam-3877	415	19	)	)	PUNCT
ejpam-3877	415	20	,	,	PUNCT
ejpam-3877	415	21	m+(ω	m+(ω	NOUN
ejpam-3877	415	22	)	)	PUNCT
ejpam-3877	415	23	)	)	PUNCT
ejpam-3877	415	24	.	.	PUNCT
ejpam-3877	416	1	since	since	SCONJ
ejpam-3877	416	2	unj	unj	NOUN
ejpam-3877	416	3	→	→	SYM
ejpam-3877	416	4	ψ−1(v	ψ−1(v	VERB
ejpam-3877	416	5	)	)	PUNCT
ejpam-3877	416	6	almost	almost	ADV
ejpam-3877	416	7	everywhere	everywhere	ADV
ejpam-3877	416	8	in	in	ADP
ejpam-3877	416	9	q	q	NOUN
ejpam-3877	416	10	,	,	PUNCT
ejpam-3877	416	11	then	then	ADV
ejpam-3877	416	12	u±nj	u±nj	PROPN
ejpam-3877	416	13	→	→	PUNCT
ejpam-3877	416	14	[	[	X
ejpam-3877	416	15	ψ−1(v)]±	ψ−1(v)]±	NOUN
ejpam-3877	416	16	almost	almost	ADV
ejpam-3877	416	17	everywhere	everywhere	ADV
ejpam-3877	416	18	in	in	ADP
ejpam-3877	416	19	quincy	quincy	PROPN
ejpam-3877	416	20	s.	s.	PROPN
ejpam-3877	416	21	nkombo	nkombo	PROPN
ejpam-3877	416	22	,	,	PUNCT
ejpam-3877	416	23	fengquan	fengquan	PROPN
ejpam-3877	416	24	li	li	PROPN
ejpam-3877	416	25	/	/	SYM
ejpam-3877	416	26	eur	eur	PROPN
ejpam-3877	416	27	.	.	PUNCT
ejpam-3877	417	1	j.	j.	PROPN
ejpam-3877	417	2	pure	pure	PROPN
ejpam-3877	417	3	appl	appl	PROPN
ejpam-3877	417	4	.	.	PROPN
ejpam-3877	417	5	math	math	PROPN
ejpam-3877	417	6	,	,	PUNCT
ejpam-3877	417	7	14	14	NUM
ejpam-3877	417	8	(	(	PUNCT
ejpam-3877	417	9	1	1	NUM
ejpam-3877	417	10	)	)	PUNCT
ejpam-3877	417	11	(	(	PUNCT
ejpam-3877	417	12	2021	2021	NUM
ejpam-3877	417	13	)	)	PUNCT
ejpam-3877	417	14	,	,	PUNCT
ejpam-3877	417	15	204	204	NUM
ejpam-3877	417	16	-	-	SYM
ejpam-3877	417	17	233	233	NUM
ejpam-3877	417	18	221	221	NUM
ejpam-3877	417	19	q.	q.	NOUN
ejpam-3877	417	20	by	by	ADP
ejpam-3877	417	21	(	(	PUNCT
ejpam-3877	417	22	5.14	5.14	NUM
ejpam-3877	417	23	)	)	PUNCT
ejpam-3877	417	24	and	and	CCONJ
ejpam-3877	417	25	(	(	PUNCT
ejpam-3877	417	26	5.16	5.16	NUM
ejpam-3877	417	27	)	)	PUNCT
ejpam-3877	418	1	,	,	PUNCT
ejpam-3877	418	2	then	then	ADV
ejpam-3877	418	3	we	we	PRON
ejpam-3877	418	4	infer	infer	VERB
ejpam-3877	418	5	from	from	ADP
ejpam-3877	418	6	fatou	fatou	NOUN
ejpam-3877	418	7	’s	’s	PART
ejpam-3877	418	8	lemma∫	lemma∫	PROPN
ejpam-3877	418	9	q	q	PUNCT
ejpam-3877	419	1	[	[	X
ejpam-3877	419	2	ψ−1(v)]+ξ(x	ψ−1(v)]+ξ(x	NOUN
ejpam-3877	419	3	,	,	PUNCT
ejpam-3877	419	4	t)dxdt	t)dxdt	NOUN
ejpam-3877	419	5	≤	≤	PROPN
ejpam-3877	419	6	lim	lim	PROPN
ejpam-3877	419	7	inf	inf	PROPN
ejpam-3877	419	8	j→∞	j→∞	NUM
ejpam-3877	419	9	∫	∫	PROPN
ejpam-3877	419	10	q	q	PROPN
ejpam-3877	419	11	u+	u+	PROPN
ejpam-3877	419	12	nj	nj	PROPN
ejpam-3877	419	13	ξ(x	ξ(x	NOUN
ejpam-3877	419	14	,	,	PUNCT
ejpam-3877	419	15	t)dxdt	t)dxdt	NOUN
ejpam-3877	419	16	≤	≤	VERB
ejpam-3877	419	17	〈	〈	PROPN
ejpam-3877	419	18	u	u	NOUN
ejpam-3877	419	19	,	,	PUNCT
ejpam-3877	419	20	ξ〉q	ξ〉q	PROPN
ejpam-3877	419	21	.	.	PUNCT
ejpam-3877	420	1	similarly	similarly	ADV
ejpam-3877	420	2	,	,	PUNCT
ejpam-3877	420	3	we	we	PRON
ejpam-3877	420	4	have∫	have∫	VERB
ejpam-3877	420	5	q	q	X
ejpam-3877	421	1	[	[	X
ejpam-3877	421	2	ψ−1(v)]−ξ(x	ψ−1(v)]−ξ(x	NOUN
ejpam-3877	421	3	,	,	PUNCT
ejpam-3877	421	4	t)dxdt	t)dxdt	NOUN
ejpam-3877	421	5	≤	≤	PROPN
ejpam-3877	421	6	lim	lim	PROPN
ejpam-3877	421	7	inf	inf	PROPN
ejpam-3877	421	8	j→∞	j→∞	NUM
ejpam-3877	421	9	∫	∫	PROPN
ejpam-3877	421	10	q	q	PROPN
ejpam-3877	421	11	u−nj	u−nj	PROPN
ejpam-3877	421	12	ξ(x	ξ(x	NOUN
ejpam-3877	421	13	,	,	PUNCT
ejpam-3877	421	14	t)dxdt	t)dxdt	NOUN
ejpam-3877	421	15	≤	≤	PUNCT
ejpam-3877	421	16	〈	〈	PROPN
ejpam-3877	421	17	ũ	ũ	PROPN
ejpam-3877	421	18	,	,	PUNCT
ejpam-3877	421	19	ξ〉q	ξ〉q	PROPN
ejpam-3877	421	20	for	for	ADP
ejpam-3877	421	21	every	every	DET
ejpam-3877	421	22	ξ	ξ	PROPN
ejpam-3877	421	23	∈	∈	PROPN
ejpam-3877	421	24	cc(q	cc(q	NOUN
ejpam-3877	421	25	)	)	PUNCT
ejpam-3877	421	26	,	,	PUNCT
ejpam-3877	421	27	ξ	ξ	X
ejpam-3877	421	28	≥	≥	NOUN
ejpam-3877	421	29	0	0	NUM
ejpam-3877	421	30	,	,	PUNCT
ejpam-3877	421	31	thus	thus	ADV
ejpam-3877	421	32	defining	define	VERB
ejpam-3877	421	33	λ1	λ1	PROPN
ejpam-3877	421	34	=	=	SYM
ejpam-3877	421	35	u−	u−	PROPN
ejpam-3877	422	1	[	[	X
ejpam-3877	422	2	ψ−1(v)]+	ψ−1(v)]+	PROPN
ejpam-3877	422	3	and	and	CCONJ
ejpam-3877	422	4	λ2	λ2	NOUN
ejpam-3877	422	5	=	=	NOUN
ejpam-3877	422	6	ũ−	ũ−	NOUN
ejpam-3877	423	1	[	[	X
ejpam-3877	423	2	ψ−1(v)]−.	ψ−1(v)]−.	X
ejpam-3877	423	3	hence	hence	ADV
ejpam-3877	423	4	,	,	PUNCT
ejpam-3877	423	5	λ1	λ1	ADJ
ejpam-3877	423	6	,	,	PUNCT
ejpam-3877	423	7	λ2	λ2	PROPN
ejpam-3877	423	8	∈	∈	PROPN
ejpam-3877	423	9	l∞((0	l∞((0	PROPN
ejpam-3877	423	10	,	,	PUNCT
ejpam-3877	423	11	t	t	NOUN
ejpam-3877	423	12	)	)	PUNCT
ejpam-3877	423	13	,	,	PUNCT
ejpam-3877	423	14	m+(ω	m+(ω	NOUN
ejpam-3877	423	15	)	)	PUNCT
ejpam-3877	423	16	)	)	PUNCT
ejpam-3877	423	17	hods	hod	VERB
ejpam-3877	423	18	true	true	ADJ
ejpam-3877	423	19	.	.	PUNCT
ejpam-3877	424	1	�	�	PROPN
ejpam-3877	424	2	proposition	proposition	NOUN
ejpam-3877	424	3	5.4	5.4	NUM
ejpam-3877	424	4	.	.	PUNCT
ejpam-3877	425	1	let	let	VERB
ejpam-3877	425	2	u	u	PRON
ejpam-3877	425	3	and	and	CCONJ
ejpam-3877	425	4	v	v	NOUN
ejpam-3877	425	5	be	be	AUX
ejpam-3877	425	6	in	in	ADP
ejpam-3877	425	7	proposition	proposition	NOUN
ejpam-3877	425	8	5.3	5.3	NUM
ejpam-3877	425	9	and	and	CCONJ
ejpam-3877	425	10	proposition	proposition	NOUN
ejpam-3877	425	11	5.1	5.1	NUM
ejpam-3877	425	12	.	.	PUNCT
ejpam-3877	426	1	then	then	ADV
ejpam-3877	426	2	for	for	ADP
ejpam-3877	426	3	almost	almost	ADV
ejpam-3877	426	4	every	every	PRON
ejpam-3877	426	5	t	t	NOUN
ejpam-3877	426	6	∈	∈	PROPN
ejpam-3877	426	7	(	(	PUNCT
ejpam-3877	426	8	0	0	NUM
ejpam-3877	426	9	,	,	PUNCT
ejpam-3877	426	10	t	t	PROPN
ejpam-3877	426	11	)	)	PUNCT
ejpam-3877	426	12	,	,	PUNCT
ejpam-3877	426	13	we	we	PRON
ejpam-3877	426	14	have	have	VERB
ejpam-3877	426	15	unj	unj	VERB
ejpam-3877	426	16	(	(	PUNCT
ejpam-3877	426	17	·	·	PUNCT
ejpam-3877	426	18	,	,	PUNCT
ejpam-3877	426	19	t)→	t)→	PROPN
ejpam-3877	427	1	[	[	X
ejpam-3877	427	2	ψ−1(v	ψ−1(v	NOUN
ejpam-3877	427	3	)	)	PUNCT
ejpam-3877	427	4	]	]	X
ejpam-3877	427	5	(	(	PUNCT
ejpam-3877	427	6	·	·	PUNCT
ejpam-3877	427	7	,	,	PUNCT
ejpam-3877	427	8	t	t	X
ejpam-3877	427	9	)	)	PUNCT
ejpam-3877	427	10	a.e	a.e	PROPN
ejpam-3877	427	11	in	in	ADP
ejpam-3877	427	12	ω	ω	PROPN
ejpam-3877	427	13	.	.	PUNCT
ejpam-3877	428	1	(	(	PUNCT
ejpam-3877	428	2	5.18	5.18	NUM
ejpam-3877	428	3	)	)	PUNCT
ejpam-3877	428	4	u+	u+	NOUN
ejpam-3877	428	5	nj	nj	PROPN
ejpam-3877	428	6	(	(	PUNCT
ejpam-3877	428	7	t	t	PROPN
ejpam-3877	428	8	)	)	PUNCT
ejpam-3877	428	9	∗	∗	NOUN
ejpam-3877	428	10	⇀	⇀	PUNCT
ejpam-3877	429	1	[	[	X
ejpam-3877	429	2	ψ−1(v)]+	ψ−1(v)]+	PROPN
ejpam-3877	429	3	(	(	PUNCT
ejpam-3877	429	4	·	·	PUNCT
ejpam-3877	429	5	,	,	PUNCT
ejpam-3877	429	6	t	t	PROPN
ejpam-3877	429	7	)	)	PUNCT
ejpam-3877	429	8	+	+	SYM
ejpam-3877	429	9	λ1	λ1	ADJ
ejpam-3877	429	10	(	(	PUNCT
ejpam-3877	429	11	·	·	PUNCT
ejpam-3877	429	12	,	,	PUNCT
ejpam-3877	429	13	t	t	PROPN
ejpam-3877	429	14	)	)	PUNCT
ejpam-3877	429	15	in	in	ADP
ejpam-3877	429	16	m+(ω	m+(ω	PROPN
ejpam-3877	429	17	)	)	PUNCT
ejpam-3877	429	18	.	.	PUNCT
ejpam-3877	430	1	(	(	PUNCT
ejpam-3877	430	2	5.19	5.19	NUM
ejpam-3877	430	3	)	)	PUNCT
ejpam-3877	430	4	u−nj	u−nj	PROPN
ejpam-3877	430	5	(	(	PUNCT
ejpam-3877	430	6	·	·	PROPN
ejpam-3877	430	7	,	,	PUNCT
ejpam-3877	430	8	t	t	NOUN
ejpam-3877	430	9	)	)	PUNCT
ejpam-3877	430	10	∗	∗	NOUN
ejpam-3877	430	11	⇀	⇀	PROPN
ejpam-3877	431	1	[	[	X
ejpam-3877	431	2	ψ−1(v)]−	ψ−1(v)]−	NOUN
ejpam-3877	431	3	(	(	PUNCT
ejpam-3877	431	4	·	·	PUNCT
ejpam-3877	431	5	,	,	PUNCT
ejpam-3877	431	6	t	t	PROPN
ejpam-3877	431	7	)	)	PUNCT
ejpam-3877	431	8	+	+	CCONJ
ejpam-3877	431	9	λ2	λ2	NOUN
ejpam-3877	431	10	(	(	PUNCT
ejpam-3877	431	11	·	·	NUM
ejpam-3877	431	12	,	,	PUNCT
ejpam-3877	431	13	t	t	PROPN
ejpam-3877	431	14	)	)	PUNCT
ejpam-3877	431	15	in	in	ADP
ejpam-3877	431	16	m+(ω	m+(ω	PROPN
ejpam-3877	431	17	)	)	PUNCT
ejpam-3877	431	18	.	.	PUNCT
ejpam-3877	432	1	(	(	PUNCT
ejpam-3877	432	2	5.20	5.20	NUM
ejpam-3877	432	3	)	)	PUNCT
ejpam-3877	432	4	unj	unj	NOUN
ejpam-3877	432	5	(	(	PUNCT
ejpam-3877	432	6	·	·	PUNCT
ejpam-3877	432	7	,	,	PUNCT
ejpam-3877	432	8	t	t	PROPN
ejpam-3877	432	9	)	)	PUNCT
ejpam-3877	432	10	∗	∗	NOUN
ejpam-3877	432	11	⇀	⇀	PUNCT
ejpam-3877	433	1	[	[	X
ejpam-3877	433	2	ψ−1(v	ψ−1(v	X
ejpam-3877	433	3	)	)	PUNCT
ejpam-3877	433	4	]	]	X
ejpam-3877	433	5	(	(	PUNCT
ejpam-3877	433	6	·	·	PUNCT
ejpam-3877	433	7	,	,	PUNCT
ejpam-3877	433	8	t	t	PROPN
ejpam-3877	433	9	)	)	PUNCT
ejpam-3877	433	10	+	+	SYM
ejpam-3877	433	11	λ	λ	PROPN
ejpam-3877	433	12	(	(	PUNCT
ejpam-3877	433	13	·	·	PUNCT
ejpam-3877	433	14	,	,	PUNCT
ejpam-3877	433	15	t	t	PROPN
ejpam-3877	433	16	)	)	PUNCT
ejpam-3877	433	17	in	in	ADP
ejpam-3877	433	18	m+(ω	m+(ω	NOUN
ejpam-3877	433	19	)	)	PUNCT
ejpam-3877	433	20	.	.	PUNCT
ejpam-3877	434	1	(	(	PUNCT
ejpam-3877	434	2	5.21	5.21	NUM
ejpam-3877	434	3	)	)	PUNCT
ejpam-3877	434	4	proof	proof	NOUN
ejpam-3877	434	5	.	.	PUNCT
ejpam-3877	435	1	this	this	DET
ejpam-3877	435	2	proof	proof	NOUN
ejpam-3877	435	3	is	be	AUX
ejpam-3877	435	4	similar	similar	ADJ
ejpam-3877	435	5	to	to	ADP
ejpam-3877	435	6	that	that	PRON
ejpam-3877	435	7	given	give	VERB
ejpam-3877	435	8	in	in	ADP
ejpam-3877	435	9	[	[	X
ejpam-3877	435	10	18	18	NUM
ejpam-3877	435	11	,	,	PUNCT
ejpam-3877	435	12	24	24	NUM
ejpam-3877	435	13	]	]	PUNCT
ejpam-3877	435	14	.	.	PUNCT
ejpam-3877	436	1	let	let	VERB
ejpam-3877	436	2	us	we	PRON
ejpam-3877	436	3	recall	recall	VERB
ejpam-3877	436	4	the	the	DET
ejpam-3877	436	5	statement	statement	NOUN
ejpam-3877	436	6	of	of	ADP
ejpam-3877	436	7	the	the	DET
ejpam-3877	436	8	function	function	NOUN
ejpam-3877	436	9	f	f	PROPN
ejpam-3877	436	10	which	which	PRON
ejpam-3877	436	11	belongs	belong	VERB
ejpam-3877	436	12	to	to	ADP
ejpam-3877	436	13	c2(r+	c2(r+	NOUN
ejpam-3877	436	14	)	)	PUNCT
ejpam-3877	436	15	(	(	PUNCT
ejpam-3877	436	16	see	see	VERB
ejpam-3877	436	17	[	[	X
ejpam-3877	436	18	18	18	NUM
ejpam-3877	436	19	,	,	PUNCT
ejpam-3877	436	20	proposition	proposition	NOUN
ejpam-3877	436	21	4.3	4.3	NUM
ejpam-3877	436	22	]	]	PUNCT
ejpam-3877	436	23	.	.	PUNCT
ejpam-3877	437	1	let	let	VERB
ejpam-3877	437	2	un	un	PROPN
ejpam-3877	437	3	be	be	AUX
ejpam-3877	437	4	the	the	DET
ejpam-3877	437	5	solution	solution	NOUN
ejpam-3877	437	6	of	of	ADP
ejpam-3877	437	7	the	the	DET
ejpam-3877	437	8	problem	problem	NOUN
ejpam-3877	437	9	(	(	PUNCT
ejpam-3877	437	10	pn	pn	NOUN
ejpam-3877	437	11	)	)	PUNCT
ejpam-3877	437	12	,	,	PUNCT
ejpam-3877	437	13	and	and	CCONJ
ejpam-3877	437	14	f	f	PROPN
ejpam-3877	437	15	∈	∈	PROPN
ejpam-3877	437	16	c2(r+	c2(r+	PROPN
ejpam-3877	437	17	)	)	PUNCT
ejpam-3877	437	18	,	,	PUNCT
ejpam-3877	437	19	then	then	ADV
ejpam-3877	437	20	for	for	ADP
ejpam-3877	437	21	any	any	DET
ejpam-3877	437	22	ρ	ρ	PROPN
ejpam-3877	437	23	∈	∈	PROPN
ejpam-3877	437	24	c1	c1	PROPN
ejpam-3877	437	25	c	c	PROPN
ejpam-3877	437	26	(	(	PUNCT
ejpam-3877	437	27	ω	ω	NOUN
ejpam-3877	437	28	)	)	PUNCT
ejpam-3877	437	29	,	,	PUNCT
ejpam-3877	437	30	ρ(x	ρ(x	PROPN
ejpam-3877	437	31	)	)	PUNCT
ejpam-3877	437	32	≥	≥	NOUN
ejpam-3877	437	33	0	0	NUM
ejpam-3877	438	1	and	and	CCONJ
ejpam-3877	438	2	there	there	PRON
ejpam-3877	438	3	exists	exist	VERB
ejpam-3877	438	4	a	a	DET
ejpam-3877	438	5	zero	zero	NUM
ejpam-3877	438	6	lebesgue	lebesgue	NOUN
ejpam-3877	438	7	measure	measure	NOUN
ejpam-3877	438	8	set	set	VERB
ejpam-3877	438	9	h	h	NOUN
ejpam-3877	438	10	such	such	ADJ
ejpam-3877	438	11	that	that	SCONJ
ejpam-3877	438	12	(	(	PUNCT
ejpam-3877	438	13	0	0	NUM
ejpam-3877	438	14	,	,	PUNCT
ejpam-3877	438	15	t	t	NOUN
ejpam-3877	438	16	)	)	PUNCT
ejpam-3877	438	17	\h	\h	PROPN
ejpam-3877	438	18	,	,	PUNCT
ejpam-3877	438	19	the	the	DET
ejpam-3877	438	20	following	follow	VERB
ejpam-3877	438	21	identity	identity	NOUN
ejpam-3877	438	22	is	be	AUX
ejpam-3877	438	23	satisfied∫	satisfied∫	VERB
ejpam-3877	438	24	ω	ω	NUM
ejpam-3877	438	25	f(un)(x	f(un)(x	NOUN
ejpam-3877	438	26	,	,	PUNCT
ejpam-3877	438	27	t)ρ(x)dx−	t)ρ(x)dx−	NOUN
ejpam-3877	438	28	∫	∫	PROPN
ejpam-3877	438	29	ω	ω	NUM
ejpam-3877	438	30	f(un)(x	f(un)(x	PROPN
ejpam-3877	438	31	,	,	PUNCT
ejpam-3877	438	32	0)ρ(x)dx	0)ρ(x)dx	NOUN
ejpam-3877	438	33	=	=	PUNCT
ejpam-3877	439	1	=	=	SYM
ejpam-3877	439	2	∫	∫	PROPN
ejpam-3877	439	3	t	t	PROPN
ejpam-3877	439	4	0	0	NUM
ejpam-3877	439	5	∫	∫	PROPN
ejpam-3877	439	6	ω	ω	PROPN
ejpam-3877	439	7	{	{	PUNCT
ejpam-3877	439	8	−f	−f	PROPN
ejpam-3877	439	9	′(un)∇ψ(un)∇ρdx−	′(un)∇ψ(un)∇ρdx−	PROPN
ejpam-3877	439	10	f	f	PROPN
ejpam-3877	439	11	′′(un	′′(un	PROPN
ejpam-3877	439	12	)	)	PUNCT
ejpam-3877	439	13	ψ′(un	ψ′(un	NOUN
ejpam-3877	439	14	)	)	PUNCT
ejpam-3877	439	15	|	|	ADV
ejpam-3877	439	16	∇ψ(un	∇ψ(un	NOUN
ejpam-3877	439	17	)	)	PUNCT
ejpam-3877	439	18	|2	|2	NUM
ejpam-3877	439	19	ρ	ρ	NOUN
ejpam-3877	439	20	}	}	PUNCT
ejpam-3877	439	21	dxdt+	dxdt+	X
ejpam-3877	440	1	+	+	NUM
ejpam-3877	440	2	∫	∫	PROPN
ejpam-3877	440	3	t	t	PROPN
ejpam-3877	440	4	0	0	NUM
ejpam-3877	440	5	∫	∫	PROPN
ejpam-3877	440	6	ω	ω	NUM
ejpam-3877	440	7	µnf	µnf	PROPN
ejpam-3877	440	8	′(un)ρdxdt	′(un)ρdxdt	PROPN
ejpam-3877	440	9	.	.	PUNCT
ejpam-3877	441	1	(	(	PUNCT
ejpam-3877	441	2	5.22	5.22	NUM
ejpam-3877	441	3	)	)	PUNCT
ejpam-3877	441	4	the	the	DET
ejpam-3877	441	5	convergence	convergence	NOUN
ejpam-3877	441	6	(	(	PUNCT
ejpam-3877	441	7	5.18	5.18	NUM
ejpam-3877	441	8	)	)	PUNCT
ejpam-3877	441	9	immediately	immediately	ADV
ejpam-3877	441	10	follows	follow	VERB
ejpam-3877	441	11	from	from	ADP
ejpam-3877	441	12	(	(	PUNCT
ejpam-3877	441	13	5.3	5.3	NUM
ejpam-3877	441	14	)	)	PUNCT
ejpam-3877	441	15	.	.	PUNCT
ejpam-3877	442	1	next	next	ADV
ejpam-3877	442	2	let	let	VERB
ejpam-3877	442	3	us	we	PRON
ejpam-3877	442	4	fix	fix	VERB
ejpam-3877	442	5	j	j	PROPN
ejpam-3877	442	6	>	>	X
ejpam-3877	442	7	1	1	NUM
ejpam-3877	442	8	and	and	CCONJ
ejpam-3877	442	9	we	we	PRON
ejpam-3877	442	10	consider	consider	VERB
ejpam-3877	442	11	the	the	DET
ejpam-3877	442	12	functions	function	NOUN
ejpam-3877	442	13	fj	fj	INTJ
ejpam-3877	442	14	,	,	PUNCT
ejpam-3877	442	15	rj	rj	PROPN
ejpam-3877	442	16	∈	∈	PROPN
ejpam-3877	442	17	c2(r+	c2(r+	PROPN
ejpam-3877	442	18	)	)	PUNCT
ejpam-3877	442	19	defined	define	VERB
ejpam-3877	442	20	as	as	ADP
ejpam-3877	442	21	follows	follow	VERB
ejpam-3877	442	22	fj(s	fj(s	PUNCT
ejpam-3877	442	23	)	)	PUNCT
ejpam-3877	443	1	=	=	SYM
ejpam-3877	443	2			NOUN
ejpam-3877	443	3	0	0	PUNCT
ejpam-3877	444	1	if	if	SCONJ
ejpam-3877	444	2	0	0	NUM
ejpam-3877	444	3	≤	≤	NUM
ejpam-3877	444	4	s	s	PART
ejpam-3877	444	5	≤	≤	PROPN
ejpam-3877	444	6	j	j	PROPN
ejpam-3877	444	7	,	,	PUNCT
ejpam-3877	444	8	s−	s−	PROPN
ejpam-3877	444	9	j	j	PROPN
ejpam-3877	445	1	if	if	SCONJ
ejpam-3877	445	2	j	j	PROPN
ejpam-3877	445	3	≤	≤	PROPN
ejpam-3877	445	4	s	s	PART
ejpam-3877	445	5	≤	≤	PROPN
ejpam-3877	445	6	j	j	NOUN
ejpam-3877	445	7	+	+	CCONJ
ejpam-3877	445	8	1	1	NUM
ejpam-3877	445	9	,	,	PUNCT
ejpam-3877	445	10	s−	s−	PROPN
ejpam-3877	445	11	j	j	PROPN
ejpam-3877	446	1	if	if	SCONJ
ejpam-3877	446	2	s	s	VERB
ejpam-3877	446	3	≥	≥	PROPN
ejpam-3877	446	4	j	j	NOUN
ejpam-3877	447	1	+	+	CCONJ
ejpam-3877	447	2	1	1	NUM
ejpam-3877	447	3	,	,	PUNCT
ejpam-3877	447	4	quincy	quincy	PROPN
ejpam-3877	447	5	s.	s.	PROPN
ejpam-3877	447	6	nkombo	nkombo	PROPN
ejpam-3877	447	7	,	,	PUNCT
ejpam-3877	447	8	fengquan	fengquan	PROPN
ejpam-3877	447	9	li	li	PROPN
ejpam-3877	447	10	/	/	SYM
ejpam-3877	447	11	eur	eur	PROPN
ejpam-3877	447	12	.	.	PUNCT
ejpam-3877	448	1	j.	j.	PROPN
ejpam-3877	448	2	pure	pure	PROPN
ejpam-3877	448	3	appl	appl	PROPN
ejpam-3877	448	4	.	.	PROPN
ejpam-3877	448	5	math	math	PROPN
ejpam-3877	448	6	,	,	PUNCT
ejpam-3877	448	7	14	14	NUM
ejpam-3877	448	8	(	(	PUNCT
ejpam-3877	448	9	1	1	NUM
ejpam-3877	448	10	)	)	PUNCT
ejpam-3877	448	11	(	(	PUNCT
ejpam-3877	448	12	2021	2021	NUM
ejpam-3877	448	13	)	)	PUNCT
ejpam-3877	448	14	,	,	PUNCT
ejpam-3877	448	15	204	204	NUM
ejpam-3877	448	16	-	-	SYM
ejpam-3877	448	17	233	233	NUM
ejpam-3877	448	18	222	222	NUM
ejpam-3877	448	19	and	and	CCONJ
ejpam-3877	448	20	rj(s	rj(s	NUM
ejpam-3877	448	21	)	)	PUNCT
ejpam-3877	448	22	=	=	SYM
ejpam-3877	448	23	s−fj(s	s−fj(s	NOUN
ejpam-3877	448	24	)	)	PUNCT
ejpam-3877	448	25	(	(	PUNCT
ejpam-3877	448	26	s	s	NOUN
ejpam-3877	448	27	∈	∈	NOUN
ejpam-3877	448	28	r+	r+	X
ejpam-3877	448	29	)	)	PUNCT
ejpam-3877	448	30	and	and	CCONJ
ejpam-3877	448	31	rj(s)χ{s≥j+1	rj(s)χ{s≥j+1	ADJ
ejpam-3877	448	32	}	}	PUNCT
ejpam-3877	448	33	=	=	SYM
ejpam-3877	448	34	j	j	PROPN
ejpam-3877	448	35	.	.	PUNCT
ejpam-3877	449	1	let	let	VERB
ejpam-3877	449	2	us	we	PRON
ejpam-3877	449	3	consider	consider	VERB
ejpam-3877	449	4	the	the	DET
ejpam-3877	449	5	function	function	NOUN
ejpam-3877	449	6	hn	hn	PROPN
ejpam-3877	449	7	belongs	belong	VERB
ejpam-3877	449	8	to	to	ADP
ejpam-3877	449	9	c1(r+	c1(r+	NOUN
ejpam-3877	449	10	)	)	PUNCT
ejpam-3877	449	11	by	by	ADP
ejpam-3877	449	12	setting	set	VERB
ejpam-3877	449	13	hn	hn	PRON
ejpam-3877	449	14	,	,	PUNCT
ejpam-3877	449	15	ρ(t	ρ(t	NUM
ejpam-3877	449	16	)	)	PUNCT
ejpam-3877	450	1	=	=	SYM
ejpam-3877	450	2	∫	∫	PROPN
ejpam-3877	450	3	ω	ω	X
ejpam-3877	450	4	fj(un(x	fj(un(x	X
ejpam-3877	450	5	,	,	PUNCT
ejpam-3877	450	6	t))ρ(x)dx	t))ρ(x)dx	PROPN
ejpam-3877	450	7	.	.	PUNCT
ejpam-3877	451	1	by	by	ADP
ejpam-3877	451	2	(	(	PUNCT
ejpam-3877	451	3	4.1	4.1	NUM
ejpam-3877	451	4	)	)	PUNCT
ejpam-3877	451	5	,	,	PUNCT
ejpam-3877	451	6	there	there	PRON
ejpam-3877	451	7	exists	exist	VERB
ejpam-3877	451	8	a	a	DET
ejpam-3877	451	9	positive	positive	ADJ
ejpam-3877	451	10	constant	constant	ADJ
ejpam-3877	451	11	c	c	NOUN
ejpam-3877	451	12	such	such	ADJ
ejpam-3877	451	13	that∫	that∫	NOUN
ejpam-3877	451	14	t	t	NOUN
ejpam-3877	451	15	0	0	NUM
ejpam-3877	452	1	|	|	ADV
ejpam-3877	452	2	hn	hn	NOUN
ejpam-3877	452	3	,	,	PUNCT
ejpam-3877	452	4	ρ(t	ρ(t	NUM
ejpam-3877	452	5	)	)	PUNCT
ejpam-3877	453	1	|	|	ADV
ejpam-3877	453	2	dt	dt	X
ejpam-3877	453	3	≤‖	≤‖	PROPN
ejpam-3877	453	4	ρ	ρ	PROPN
ejpam-3877	453	5	‖l∞(ω	‖l∞(ω	PROPN
ejpam-3877	453	6	)	)	PUNCT
ejpam-3877	453	7	∫	∫	PROPN
ejpam-3877	453	8	t	t	PROPN
ejpam-3877	453	9	0	0	NUM
ejpam-3877	453	10	∫	∫	PROPN
ejpam-3877	453	11	ω	ω	PROPN
ejpam-3877	453	12	u+	u+	PROPN
ejpam-3877	453	13	n	n	PROPN
ejpam-3877	453	14	(	(	PUNCT
ejpam-3877	453	15	x	x	NOUN
ejpam-3877	453	16	,	,	PUNCT
ejpam-3877	453	17	t)dxdt	t)dxdt	NOUN
ejpam-3877	453	18	≤	≤	NOUN
ejpam-3877	453	19	c	c	NOUN
ejpam-3877	453	20	where	where	SCONJ
ejpam-3877	453	21	c	c	NOUN
ejpam-3877	453	22	=	=	SYM
ejpam-3877	453	23	c	c	PROPN
ejpam-3877	453	24	[	[	PUNCT
ejpam-3877	453	25	t	t	PROPN
ejpam-3877	453	26	,	,	PUNCT
ejpam-3877	453	27	‖	‖	PROPN
ejpam-3877	453	28	ρ	ρ	PROPN
ejpam-3877	453	29	‖l∞(ω	‖l∞(ω	NOUN
ejpam-3877	453	30	)	)	PUNCT
ejpam-3877	453	31	,	,	PUNCT
ejpam-3877	453	32	‖	‖	PROPN
ejpam-3877	453	33	u0	u0	PROPN
ejpam-3877	453	34	‖m+(ω	‖m+(ω	PROPN
ejpam-3877	453	35	)	)	PUNCT
ejpam-3877	453	36	,	,	PUNCT
ejpam-3877	453	37	‖	‖	PROPN
ejpam-3877	453	38	µ	µ	X
ejpam-3877	453	39	‖m+(q	‖m+(q	NOUN
ejpam-3877	453	40	)	)	PUNCT
ejpam-3877	453	41	]	]	PUNCT
ejpam-3877	454	1	>	>	X
ejpam-3877	454	2	0	0	X
ejpam-3877	454	3	.	.	PUNCT
ejpam-3877	455	1	thus	thus	ADV
ejpam-3877	455	2	hn	hn	PROPN
ejpam-3877	455	3	,	,	PUNCT
ejpam-3877	455	4	ρ	ρ	PROPN
ejpam-3877	455	5	∈	∈	PROPN
ejpam-3877	455	6	l1(0	l1(0	PROPN
ejpam-3877	455	7	,	,	PUNCT
ejpam-3877	455	8	t	t	PROPN
ejpam-3877	455	9	)	)	PUNCT
ejpam-3877	455	10	for	for	ADP
ejpam-3877	455	11	every	every	DET
ejpam-3877	455	12	ρ	ρ	PROPN
ejpam-3877	455	13	∈	∈	PROPN
ejpam-3877	455	14	c1	c1	PROPN
ejpam-3877	455	15	c	c	PROPN
ejpam-3877	455	16	(	(	PUNCT
ejpam-3877	455	17	ω	ω	NOUN
ejpam-3877	455	18	)	)	PUNCT
ejpam-3877	455	19	.	.	PUNCT
ejpam-3877	456	1	furthermore	furthermore	ADV
ejpam-3877	456	2	by	by	ADP
ejpam-3877	456	3	(	(	PUNCT
ejpam-3877	456	4	5.22	5.22	NUM
ejpam-3877	456	5	)	)	PUNCT
ejpam-3877	456	6	yields∫	yields∫	PROPN
ejpam-3877	456	7	t	t	PROPN
ejpam-3877	456	8	0	0	NUM
ejpam-3877	456	9	∣∣∣∣dhn	∣∣∣∣dhn	PROPN
ejpam-3877	456	10	,	,	PUNCT
ejpam-3877	456	11	ρ(t)dt	ρ(t)dt	PART
ejpam-3877	456	12	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3877	456	13	dt	dt	PUNCT
ejpam-3877	456	14	≤	≤	NUM
ejpam-3877	456	15	∫	∫	PROPN
ejpam-3877	456	16	t	t	PROPN
ejpam-3877	456	17	0	0	NUM
ejpam-3877	456	18	∫	∫	PROPN
ejpam-3877	457	1	ω	ω	PROPN
ejpam-3877	457	2	f	f	PROPN
ejpam-3877	457	3	′j(un	′j(un	PROPN
ejpam-3877	457	4	)	)	PUNCT
ejpam-3877	457	5	|	|	ADV
ejpam-3877	457	6	∇ψ(un	∇ψ(un	NOUN
ejpam-3877	457	7	)	)	PUNCT
ejpam-3877	457	8	|2|	|2|	PROPN
ejpam-3877	457	9	∇ρ	∇ρ	NOUN
ejpam-3877	458	1	|	|	ADV
ejpam-3877	458	2	dxdt+	dxdt+	X
ejpam-3877	459	1	+	+	CCONJ
ejpam-3877	459	2	∫	∫	PROPN
ejpam-3877	459	3	t	t	PROPN
ejpam-3877	459	4	0	0	NUM
ejpam-3877	460	1	∫	∫	PROPN
ejpam-3877	460	2	ω	ω	PROPN
ejpam-3877	460	3	f	f	PROPN
ejpam-3877	460	4	′′(un	′′(un	PROPN
ejpam-3877	460	5	)	)	PUNCT
ejpam-3877	460	6	ψ′(un	ψ′(un	NOUN
ejpam-3877	460	7	)	)	PUNCT
ejpam-3877	460	8	|	|	ADV
ejpam-3877	460	9	∇ψ(un	∇ψ(un	NOUN
ejpam-3877	460	10	)	)	PUNCT
ejpam-3877	460	11	|2	|2	NUM
ejpam-3877	461	1	ρdxdt+	ρdxdt+	NUM
ejpam-3877	462	1	∫	∫	PROPN
ejpam-3877	462	2	t	t	PROPN
ejpam-3877	462	3	0	0	NUM
ejpam-3877	462	4	∫	∫	PROPN
ejpam-3877	462	5	ω	ω	NUM
ejpam-3877	462	6	µnf	µnf	PROPN
ejpam-3877	462	7	′(un)ρdxdt	′(un)ρdxdt	PROPN
ejpam-3877	462	8	.	.	PUNCT
ejpam-3877	463	1	(	(	PUNCT
ejpam-3877	463	2	5.23	5.23	NUM
ejpam-3877	463	3	)	)	PUNCT
ejpam-3877	463	4	by	by	ADP
ejpam-3877	463	5	properties	property	NOUN
ejpam-3877	463	6	of	of	ADP
ejpam-3877	463	7	sequence	sequence	NOUN
ejpam-3877	463	8	{	{	PUNCT
ejpam-3877	463	9	fj(un)}j>1	fj(un)}j>1	PROPN
ejpam-3877	463	10	mentioned	mention	VERB
ejpam-3877	463	11	above	above	ADV
ejpam-3877	463	12	and	and	CCONJ
ejpam-3877	463	13	ρ	ρ	PROPN
ejpam-3877	463	14	∈	∈	PROPN
ejpam-3877	463	15	c1	c1	PROPN
ejpam-3877	463	16	c	c	PROPN
ejpam-3877	463	17	(	(	PUNCT
ejpam-3877	463	18	ω	ω	NOUN
ejpam-3877	463	19	)	)	PUNCT
ejpam-3877	463	20	,	,	PUNCT
ejpam-3877	463	21	there	there	PRON
ejpam-3877	463	22	exists	exist	VERB
ejpam-3877	463	23	a	a	DET
ejpam-3877	463	24	positive	positive	ADJ
ejpam-3877	463	25	constant	constant	ADJ
ejpam-3877	463	26	c	c	NOUN
ejpam-3877	463	27	=	=	SYM
ejpam-3877	463	28	c	c	PROPN
ejpam-3877	463	29	[	[	PUNCT
ejpam-3877	463	30	‖	‖	PROPN
ejpam-3877	463	31	ρ	ρ	PROPN
ejpam-3877	463	32	‖l∞(ω	‖l∞(ω	NOUN
ejpam-3877	463	33	)	)	PUNCT
ejpam-3877	463	34	,	,	PUNCT
ejpam-3877	463	35	‖	‖	PROPN
ejpam-3877	463	36	u0	u0	PROPN
ejpam-3877	463	37	‖m+(ω	‖m+(ω	PROPN
ejpam-3877	463	38	)	)	PUNCT
ejpam-3877	463	39	,	,	PUNCT
ejpam-3877	463	40	‖	‖	PROPN
ejpam-3877	463	41	µ	µ	X
ejpam-3877	463	42	‖m+(q	‖m+(q	NOUN
ejpam-3877	463	43	)	)	PUNCT
ejpam-3877	463	44	]	]	PUNCT
ejpam-3877	464	1	>	>	X
ejpam-3877	464	2	0	0	PUNCT
ejpam-3877	465	1	such	such	ADJ
ejpam-3877	465	2	that∫	that∫	NOUN
ejpam-3877	465	3	t	t	NOUN
ejpam-3877	465	4	0	0	NUM
ejpam-3877	466	1	∣∣∣∣dhn	∣∣∣∣dhn	PROPN
ejpam-3877	466	2	,	,	PUNCT
ejpam-3877	466	3	ρ(t)dt	ρ(t)dt	PART
ejpam-3877	466	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3877	466	5	dt	dt	PUNCT
ejpam-3877	466	6	≤	≤	PROPN
ejpam-3877	466	7	c.	c.	NOUN
ejpam-3877	466	8	thus	thus	ADV
ejpam-3877	466	9	the	the	DET
ejpam-3877	466	10	family	family	NOUN
ejpam-3877	466	11	hn	hn	PROPN
ejpam-3877	466	12	,	,	PUNCT
ejpam-3877	466	13	ρ	ρ	PROPN
ejpam-3877	466	14	is	be	AUX
ejpam-3877	466	15	uniformly	uniformly	ADV
ejpam-3877	466	16	bounded	bound	VERB
ejpam-3877	466	17	in	in	ADP
ejpam-3877	466	18	w	w	PROPN
ejpam-3877	466	19	1,1(0	1,1(0	PROPN
ejpam-3877	466	20	,	,	PUNCT
ejpam-3877	466	21	t	t	PROPN
ejpam-3877	466	22	)	)	PUNCT
ejpam-3877	466	23	.	.	PUNCT
ejpam-3877	467	1	hence	hence	ADV
ejpam-3877	467	2	there	there	PRON
ejpam-3877	467	3	exist	exist	VERB
ejpam-3877	467	4	a	a	DET
ejpam-3877	467	5	subsequence	subsequence	NOUN
ejpam-3877	467	6	{	{	PUNCT
ejpam-3877	467	7	hnj	hnj	NOUN
ejpam-3877	467	8	,	,	PUNCT
ejpam-3877	467	9	ρ	ρ	PROPN
ejpam-3877	467	10	}	}	PUNCT
ejpam-3877	467	11	⊆	⊆	NUM
ejpam-3877	467	12	{	{	PUNCT
ejpam-3877	467	13	hn	hn	PROPN
ejpam-3877	467	14	,	,	PUNCT
ejpam-3877	467	15	ρ	ρ	PROPN
ejpam-3877	467	16	}	}	PUNCT
ejpam-3877	467	17	and	and	CCONJ
ejpam-3877	467	18	a	a	DET
ejpam-3877	467	19	function	function	NOUN
ejpam-3877	467	20	hρ	hρ	PROPN
ejpam-3877	467	21	∈	∈	PROPN
ejpam-3877	467	22	l1(0	l1(0	PROPN
ejpam-3877	467	23	,	,	PUNCT
ejpam-3877	467	24	t	t	PROPN
ejpam-3877	467	25	)	)	PUNCT
ejpam-3877	467	26	such	such	ADJ
ejpam-3877	467	27	that	that	DET
ejpam-3877	467	28	hnj	hnj	NOUN
ejpam-3877	467	29	,	,	PUNCT
ejpam-3877	467	30	ρ	ρ	PROPN
ejpam-3877	467	31	→	→	SYM
ejpam-3877	467	32	hρ	hρ	PROPN
ejpam-3877	467	33	in	in	ADP
ejpam-3877	467	34	l1(0	l1(0	PROPN
ejpam-3877	467	35	,	,	PUNCT
ejpam-3877	467	36	t	t	PROPN
ejpam-3877	467	37	)	)	PUNCT
ejpam-3877	467	38	.	.	PUNCT
ejpam-3877	468	1	(	(	PUNCT
ejpam-3877	468	2	5.24	5.24	NUM
ejpam-3877	468	3	)	)	PUNCT
ejpam-3877	468	4	by	by	ADP
ejpam-3877	468	5	the	the	DET
ejpam-3877	468	6	properties	property	NOUN
ejpam-3877	468	7	of	of	ADP
ejpam-3877	468	8	the	the	DET
ejpam-3877	468	9	function	function	NOUN
ejpam-3877	468	10	fj	fj	PROPN
ejpam-3877	468	11	,	,	PUNCT
ejpam-3877	468	12	the	the	DET
ejpam-3877	468	13	function	function	NOUN
ejpam-3877	468	14	rj	rj	PROPN
ejpam-3877	468	15	is	be	AUX
ejpam-3877	468	16	continuous	continuous	ADJ
ejpam-3877	468	17	and	and	CCONJ
ejpam-3877	468	18	bounded	bound	VERB
ejpam-3877	468	19	in	in	ADP
ejpam-3877	468	20	r+	r+	X
ejpam-3877	468	21	,	,	PUNCT
ejpam-3877	468	22	then	then	ADV
ejpam-3877	468	23	the	the	DET
ejpam-3877	468	24	convergence	convergence	NOUN
ejpam-3877	468	25	(	(	PUNCT
ejpam-3877	468	26	5.10	5.10	NUM
ejpam-3877	468	27	)	)	PUNCT
ejpam-3877	468	28	and	and	CCONJ
ejpam-3877	468	29	the	the	DET
ejpam-3877	468	30	dominated	dominate	VERB
ejpam-3877	468	31	convergence	convergence	NOUN
ejpam-3877	468	32	theorem	theorem	VERB
ejpam-3877	468	33	imply	imply	VERB
ejpam-3877	468	34	that	that	PRON
ejpam-3877	468	35	rj(unj	rj(unj	NOUN
ejpam-3877	468	36	)	)	PUNCT
ejpam-3877	468	37	→	→	SYM
ejpam-3877	468	38	rj	rj	PROPN
ejpam-3877	468	39	(	(	PUNCT
ejpam-3877	468	40	ψ−1(v	ψ−1(v	NOUN
ejpam-3877	468	41	)	)	PUNCT
ejpam-3877	468	42	)	)	PUNCT
ejpam-3877	468	43	in	in	ADP
ejpam-3877	468	44	l1(q	l1(q	ADV
ejpam-3877	468	45	)	)	PUNCT
ejpam-3877	468	46	.	.	PUNCT
ejpam-3877	469	1	(	(	PUNCT
ejpam-3877	469	2	5.25	5.25	NUM
ejpam-3877	469	3	)	)	PUNCT
ejpam-3877	469	4	by	by	ADP
ejpam-3877	469	5	(	(	PUNCT
ejpam-3877	469	6	5.10	5.10	NUM
ejpam-3877	469	7	)	)	PUNCT
ejpam-3877	469	8	,	,	PUNCT
ejpam-3877	469	9	(	(	PUNCT
ejpam-3877	469	10	5.11	5.11	NUM
ejpam-3877	469	11	)	)	PUNCT
ejpam-3877	469	12	and	and	CCONJ
ejpam-3877	469	13	the	the	DET
ejpam-3877	469	14	definition	definition	NOUN
ejpam-3877	469	15	of	of	ADP
ejpam-3877	469	16	rj	rj	PROPN
ejpam-3877	469	17	,	,	PUNCT
ejpam-3877	469	18	we	we	PRON
ejpam-3877	469	19	have	have	VERB
ejpam-3877	469	20	fj(unj	fj(unj	NOUN
ejpam-3877	469	21	)	)	PUNCT
ejpam-3877	470	1	=	=	SYM
ejpam-3877	470	2	u+	u+	NUM
ejpam-3877	470	3	nj	nj	PROPN
ejpam-3877	470	4	−rj(unj	−rj(unj	PROPN
ejpam-3877	470	5	)	)	PUNCT
ejpam-3877	471	1	∗	∗	NOUN
ejpam-3877	471	2	⇀	⇀	PROPN
ejpam-3877	472	1	[	[	PUNCT
ejpam-3877	472	2	ψ−1(v	ψ−1(v	NOUN
ejpam-3877	472	3	)	)	PUNCT
ejpam-3877	472	4	]	]	PUNCT
ejpam-3877	473	1	+	+	PUNCT
ejpam-3877	473	2	+	+	ADJ
ejpam-3877	473	3	λ1−rj	λ1−rj	X
ejpam-3877	473	4	(	(	PUNCT
ejpam-3877	473	5	ψ−1(v	ψ−1(v	NOUN
ejpam-3877	473	6	)	)	PUNCT
ejpam-3877	473	7	)	)	PUNCT
ejpam-3877	474	1	=	=	SYM
ejpam-3877	474	2	fj	fj	PROPN
ejpam-3877	474	3	(	(	PUNCT
ejpam-3877	474	4	ψ−1(v	ψ−1(v	NOUN
ejpam-3877	474	5	)	)	PUNCT
ejpam-3877	474	6	)	)	PUNCT
ejpam-3877	475	1	+	+	ADV
ejpam-3877	475	2	λ1	λ1	ADJ
ejpam-3877	475	3	in	in	ADP
ejpam-3877	475	4	m+(q	m+(q	PROPN
ejpam-3877	475	5	)	)	PUNCT
ejpam-3877	475	6	.	.	PUNCT
ejpam-3877	476	1	(	(	PUNCT
ejpam-3877	476	2	5.26	5.26	NUM
ejpam-3877	476	3	)	)	PUNCT
ejpam-3877	476	4	in	in	ADP
ejpam-3877	476	5	view	view	NOUN
ejpam-3877	476	6	of	of	ADP
ejpam-3877	476	7	(	(	PUNCT
ejpam-3877	476	8	5.24	5.24	NUM
ejpam-3877	476	9	)	)	PUNCT
ejpam-3877	476	10	and	and	CCONJ
ejpam-3877	476	11	(	(	PUNCT
ejpam-3877	476	12	5.26	5.26	NUM
ejpam-3877	476	13	)	)	PUNCT
ejpam-3877	476	14	,	,	PUNCT
ejpam-3877	476	15	for	for	ADP
ejpam-3877	476	16	any	any	DET
ejpam-3877	476	17	h	h	NOUN
ejpam-3877	476	18	∈	∈	PROPN
ejpam-3877	476	19	cc(0	cc(0	PROPN
ejpam-3877	476	20	,	,	PUNCT
ejpam-3877	476	21	t	t	PROPN
ejpam-3877	476	22	)	)	PUNCT
ejpam-3877	476	23	and	and	CCONJ
ejpam-3877	476	24	ρ	ρ	PROPN
ejpam-3877	476	25	∈	∈	PROPN
ejpam-3877	476	26	c1	c1	PROPN
ejpam-3877	476	27	c	c	PROPN
ejpam-3877	476	28	(	(	PUNCT
ejpam-3877	476	29	ω	ω	INTJ
ejpam-3877	476	30	)	)	PUNCT
ejpam-3877	476	31	we	we	PRON
ejpam-3877	476	32	get∫	get∫	PROPN
ejpam-3877	476	33	t	t	PROPN
ejpam-3877	476	34	0	0	NUM
ejpam-3877	476	35	hρ(t)h(t)dt	hρ(t)h(t)dt	PROPN
ejpam-3877	476	36	=	=	SYM
ejpam-3877	476	37	lim	lim	PROPN
ejpam-3877	476	38	j→∞	j→∞	NOUN
ejpam-3877	476	39	∫	∫	PROPN
ejpam-3877	476	40	t	t	PROPN
ejpam-3877	476	41	0	0	NUM
ejpam-3877	476	42	hnj	hnj	PROPN
ejpam-3877	476	43	,	,	PUNCT
ejpam-3877	476	44	ρ(t)h(t)dt	ρ(t)h(t)dt	NOUN
ejpam-3877	476	45	=	=	PROPN
ejpam-3877	476	46	lim	lim	PROPN
ejpam-3877	476	47	j→∞	j→∞	PROPN
ejpam-3877	476	48	∫	∫	PROPN
ejpam-3877	476	49	q	q	PROPN
ejpam-3877	476	50	fj(unj	fj(unj	PROPN
ejpam-3877	476	51	)	)	PUNCT
ejpam-3877	476	52	ρ(x)h(t)dxdt	ρ(x)h(t)dxdt	NOUN
ejpam-3877	476	53	=	=	PUNCT
ejpam-3877	477	1	=	=	SYM
ejpam-3877	477	2	∫	∫	PROPN
ejpam-3877	477	3	t	t	PROPN
ejpam-3877	477	4	0	0	NUM
ejpam-3877	477	5	h(t	h(t	PROPN
ejpam-3877	477	6	)	)	PUNCT
ejpam-3877	478	1	〈	〈	PROPN
ejpam-3877	478	2	fj	fj	PROPN
ejpam-3877	478	3	(	(	PUNCT
ejpam-3877	478	4	ψ−1(v	ψ−1(v	PROPN
ejpam-3877	478	5	)	)	PUNCT
ejpam-3877	478	6	(	(	PUNCT
ejpam-3877	478	7	·	·	PUNCT
ejpam-3877	478	8	,	,	PUNCT
ejpam-3877	478	9	t	t	PROPN
ejpam-3877	478	10	)	)	PUNCT
ejpam-3877	478	11	)	)	PUNCT
ejpam-3877	479	1	+	+	CCONJ
ejpam-3877	480	1	λ1	λ1	ADJ
ejpam-3877	480	2	(	(	PUNCT
ejpam-3877	480	3	·	·	PUNCT
ejpam-3877	480	4	,	,	PUNCT
ejpam-3877	480	5	t	t	PROPN
ejpam-3877	480	6	)	)	PUNCT
ejpam-3877	480	7	,	,	PUNCT
ejpam-3877	480	8	ρ	ρ	NUM
ejpam-3877	480	9	〉	〉	NOUN
ejpam-3877	480	10	ω	ω	NUM
ejpam-3877	480	11	dt	dt	PROPN
ejpam-3877	480	12	.	.	PUNCT
ejpam-3877	481	1	quincy	quincy	PROPN
ejpam-3877	481	2	s.	s.	PROPN
ejpam-3877	481	3	nkombo	nkombo	PROPN
ejpam-3877	481	4	,	,	PUNCT
ejpam-3877	481	5	fengquan	fengquan	PROPN
ejpam-3877	481	6	li	li	PROPN
ejpam-3877	481	7	/	/	SYM
ejpam-3877	481	8	eur	eur	PROPN
ejpam-3877	481	9	.	.	PUNCT
ejpam-3877	482	1	j.	j.	PROPN
ejpam-3877	482	2	pure	pure	PROPN
ejpam-3877	482	3	appl	appl	PROPN
ejpam-3877	482	4	.	.	PROPN
ejpam-3877	482	5	math	math	PROPN
ejpam-3877	482	6	,	,	PUNCT
ejpam-3877	482	7	14	14	NUM
ejpam-3877	482	8	(	(	PUNCT
ejpam-3877	482	9	1	1	NUM
ejpam-3877	482	10	)	)	PUNCT
ejpam-3877	482	11	(	(	PUNCT
ejpam-3877	482	12	2021	2021	NUM
ejpam-3877	482	13	)	)	PUNCT
ejpam-3877	482	14	,	,	PUNCT
ejpam-3877	482	15	204	204	NUM
ejpam-3877	482	16	-	-	SYM
ejpam-3877	482	17	233	233	NUM
ejpam-3877	482	18	223	223	NUM
ejpam-3877	482	19	then	then	ADV
ejpam-3877	482	20	by	by	ADP
ejpam-3877	482	21	the	the	DET
ejpam-3877	482	22	above	above	ADJ
ejpam-3877	482	23	equality	equality	NOUN
ejpam-3877	483	1	,	,	PUNCT
ejpam-3877	483	2	we	we	PRON
ejpam-3877	483	3	deduce	deduce	VERB
ejpam-3877	483	4	that	that	PRON
ejpam-3877	483	5	hρ(t	hρ(t	PUNCT
ejpam-3877	483	6	)	)	PUNCT
ejpam-3877	484	1	=	=	SYM
ejpam-3877	485	1	〈	〈	PROPN
ejpam-3877	485	2	fj	fj	PROPN
ejpam-3877	485	3	(	(	PUNCT
ejpam-3877	485	4	ψ−1(v	ψ−1(v	PROPN
ejpam-3877	485	5	)	)	PUNCT
ejpam-3877	485	6	(	(	PUNCT
ejpam-3877	485	7	·	·	PUNCT
ejpam-3877	485	8	,	,	PUNCT
ejpam-3877	485	9	t	t	PROPN
ejpam-3877	485	10	)	)	PUNCT
ejpam-3877	485	11	)	)	PUNCT
ejpam-3877	486	1	+	+	CCONJ
ejpam-3877	487	1	λ1	λ1	ADJ
ejpam-3877	487	2	(	(	PUNCT
ejpam-3877	487	3	·	·	PUNCT
ejpam-3877	487	4	,	,	PUNCT
ejpam-3877	487	5	t	t	PROPN
ejpam-3877	487	6	)	)	PUNCT
ejpam-3877	487	7	,	,	PUNCT
ejpam-3877	487	8	ρ	ρ	NUM
ejpam-3877	487	9	〉	〉	NOUN
ejpam-3877	487	10	ω	ω	NOUN
ejpam-3877	487	11	for	for	ADP
ejpam-3877	487	12	almost	almost	ADV
ejpam-3877	487	13	every	every	PRON
ejpam-3877	487	14	t	t	NOUN
ejpam-3877	487	15	∈	∈	PROPN
ejpam-3877	487	16	(	(	PUNCT
ejpam-3877	487	17	0	0	NUM
ejpam-3877	487	18	,	,	PUNCT
ejpam-3877	487	19	t	t	PROPN
ejpam-3877	487	20	)	)	PUNCT
ejpam-3877	487	21	and	and	CCONJ
ejpam-3877	487	22	hj	hj	PROPN
ejpam-3877	487	23	,	,	PUNCT
ejpam-3877	487	24	ρ	ρ	PROPN
ejpam-3877	487	25	→	→	SYM
ejpam-3877	487	26	〈	〈	PROPN
ejpam-3877	487	27	fj	fj	PROPN
ejpam-3877	487	28	(	(	PUNCT
ejpam-3877	487	29	ψ−1(v	ψ−1(v	PROPN
ejpam-3877	487	30	)	)	PUNCT
ejpam-3877	487	31	(	(	PUNCT
ejpam-3877	487	32	·	·	PUNCT
ejpam-3877	487	33	,	,	PUNCT
ejpam-3877	487	34	t	t	PROPN
ejpam-3877	487	35	)	)	PUNCT
ejpam-3877	487	36	)	)	PUNCT
ejpam-3877	488	1	+	+	CCONJ
ejpam-3877	489	1	λ1	λ1	ADJ
ejpam-3877	489	2	(	(	PUNCT
ejpam-3877	489	3	·	·	PUNCT
ejpam-3877	489	4	,	,	PUNCT
ejpam-3877	489	5	t	t	PROPN
ejpam-3877	489	6	)	)	PUNCT
ejpam-3877	489	7	,	,	PUNCT
ejpam-3877	489	8	ρ	ρ	NUM
ejpam-3877	489	9	〉	〉	NOUN
ejpam-3877	489	10	ω	ω	PROPN
ejpam-3877	489	11	in	in	ADP
ejpam-3877	489	12	l1(0	l1(0	PROPN
ejpam-3877	489	13	,	,	PUNCT
ejpam-3877	489	14	t	t	PROPN
ejpam-3877	489	15	)	)	PUNCT
ejpam-3877	489	16	for	for	ADP
ejpam-3877	489	17	any	any	DET
ejpam-3877	489	18	ρ	ρ	PROPN
ejpam-3877	489	19	∈	∈	PROPN
ejpam-3877	489	20	c1	c1	PROPN
ejpam-3877	489	21	c	c	PROPN
ejpam-3877	489	22	(	(	PUNCT
ejpam-3877	489	23	ω	ω	NOUN
ejpam-3877	489	24	)	)	PUNCT
ejpam-3877	489	25	.	.	PUNCT
ejpam-3877	490	1	�	�	PROPN
ejpam-3877	490	2	proof	proof	NOUN
ejpam-3877	490	3	of	of	ADP
ejpam-3877	490	4	theorem	theorem	ADJ
ejpam-3877	490	5	3.3	3.3	NUM
ejpam-3877	490	6	.	.	PUNCT
ejpam-3877	491	1	let	let	VERB
ejpam-3877	491	2	us	we	PRON
ejpam-3877	491	3	show	show	VERB
ejpam-3877	491	4	that	that	SCONJ
ejpam-3877	491	5	for	for	ADP
ejpam-3877	491	6	every	every	DET
ejpam-3877	491	7	ρ	ρ	PROPN
ejpam-3877	491	8	∈	∈	PROPN
ejpam-3877	491	9	c1	c1	PROPN
ejpam-3877	491	10	c	c	PROPN
ejpam-3877	491	11	(	(	PUNCT
ejpam-3877	491	12	ω	ω	NOUN
ejpam-3877	491	13	)	)	PUNCT
ejpam-3877	491	14	,	,	PUNCT
ejpam-3877	491	15	ρ	ρ	PROPN
ejpam-3877	491	16	≥	≥	NOUN
ejpam-3877	491	17	0	0	NUM
ejpam-3877	491	18	and	and	CCONJ
ejpam-3877	491	19	for	for	ADP
ejpam-3877	491	20	almost	almost	ADV
ejpam-3877	491	21	every	every	PRON
ejpam-3877	491	22	τ	τ	PROPN
ejpam-3877	491	23	∈	∈	PROPN
ejpam-3877	491	24	(	(	PUNCT
ejpam-3877	491	25	0	0	NUM
ejpam-3877	491	26	,	,	PUNCT
ejpam-3877	491	27	t	t	PROPN
ejpam-3877	491	28	)	)	PUNCT
ejpam-3877	491	29	,	,	PUNCT
ejpam-3877	491	30	there	there	PRON
ejpam-3877	491	31	exists	exist	VERB
ejpam-3877	491	32	a	a	DET
ejpam-3877	491	33	radon	radon	ADJ
ejpam-3877	491	34	measure	measure	NOUN
ejpam-3877	491	35	ντ	ντ	PROPN
ejpam-3877	491	36	∈m+(ω	∈m+(ω	NOUN
ejpam-3877	491	37	)	)	PUNCT
ejpam-3877	491	38	such	such	ADJ
ejpam-3877	491	39	that	that	SCONJ
ejpam-3877	491	40	〈	〈	PROPN
ejpam-3877	491	41	λ1(τ	λ1(τ	PROPN
ejpam-3877	491	42	)	)	PUNCT
ejpam-3877	491	43	,	,	PUNCT
ejpam-3877	491	44	ρ〉ω	ρ〉ω	PROPN
ejpam-3877	491	45	≤	≤	PROPN
ejpam-3877	491	46	〈	〈	PROPN
ejpam-3877	492	1	[	[	X
ejpam-3877	492	2	u0s	u0s	X
ejpam-3877	492	3	]	]	PUNCT
ejpam-3877	493	1	+	+	PUNCT
ejpam-3877	493	2	+	+	PUNCT
ejpam-3877	493	3	[	[	X
ejpam-3877	493	4	ντs	ντs	NOUN
ejpam-3877	493	5	]	]	X
ejpam-3877	493	6	+	+	ADJ
ejpam-3877	493	7	,	,	PUNCT
ejpam-3877	493	8	ρ	ρ	NUM
ejpam-3877	493	9	〉	〉	NOUN
ejpam-3877	493	10	ω	ω	PROPN
ejpam-3877	493	11	,	,	PUNCT
ejpam-3877	493	12	(	(	PUNCT
ejpam-3877	493	13	5.27	5.27	NUM
ejpam-3877	493	14	)	)	PUNCT
ejpam-3877	493	15	〈	〈	PROPN
ejpam-3877	493	16	λ2(τ	λ2(τ	PROPN
ejpam-3877	493	17	)	)	PUNCT
ejpam-3877	493	18	,	,	PUNCT
ejpam-3877	493	19	ρ〉ω	ρ〉ω	PROPN
ejpam-3877	493	20	≤	≤	PROPN
ejpam-3877	493	21	〈	〈	PROPN
ejpam-3877	494	1	[	[	X
ejpam-3877	494	2	u0s	u0s	X
ejpam-3877	494	3	]	]	PUNCT
ejpam-3877	494	4	−	−	PROPN
ejpam-3877	495	1	+	+	CCONJ
ejpam-3877	496	1	[	[	X
ejpam-3877	496	2	ντs	ντs	NOUN
ejpam-3877	496	3	]	]	X
ejpam-3877	496	4	−	−	NOUN
ejpam-3877	496	5	,	,	PUNCT
ejpam-3877	496	6	ρ	ρ	NUM
ejpam-3877	496	7	〉	〉	NOUN
ejpam-3877	496	8	ω	ω	NOUN
ejpam-3877	496	9	.	.	PUNCT
ejpam-3877	497	1	(	(	PUNCT
ejpam-3877	497	2	5.28	5.28	NUM
ejpam-3877	497	3	)	)	PUNCT
ejpam-3877	497	4	we	we	PRON
ejpam-3877	497	5	prove	prove	VERB
ejpam-3877	497	6	the	the	DET
ejpam-3877	497	7	first	first	ADJ
ejpam-3877	497	8	inequality	inequality	NOUN
ejpam-3877	497	9	(	(	PUNCT
ejpam-3877	497	10	5.27	5.27	NUM
ejpam-3877	497	11	)	)	PUNCT
ejpam-3877	497	12	and	and	CCONJ
ejpam-3877	497	13	the	the	DET
ejpam-3877	497	14	second	second	ADJ
ejpam-3877	497	15	one	one	NOUN
ejpam-3877	497	16	follows	follow	VERB
ejpam-3877	497	17	by	by	ADP
ejpam-3877	497	18	similar	similar	ADJ
ejpam-3877	497	19	argument	argument	NOUN
ejpam-3877	497	20	.	.	PUNCT
ejpam-3877	498	1	fix	fix	VERB
ejpam-3877	498	2	any	any	DET
ejpam-3877	498	3	ρ	ρ	PROPN
ejpam-3877	498	4	∈	∈	PROPN
ejpam-3877	498	5	c1	c1	PROPN
ejpam-3877	498	6	c	c	PROPN
ejpam-3877	498	7	(	(	PUNCT
ejpam-3877	498	8	ω	ω	NOUN
ejpam-3877	498	9	)	)	PUNCT
ejpam-3877	498	10	,	,	PUNCT
ejpam-3877	498	11	ρ	ρ	PROPN
ejpam-3877	498	12	≥	≥	NOUN
ejpam-3877	498	13	0	0	NUM
ejpam-3877	499	1	and	and	CCONJ
ejpam-3877	499	2	we	we	PRON
ejpam-3877	499	3	consider	consider	VERB
ejpam-3877	499	4	the	the	DET
ejpam-3877	499	5	sequence	sequence	NOUN
ejpam-3877	499	6	{	{	PUNCT
ejpam-3877	499	7	fj(un	fj(un	PROPN
ejpam-3877	499	8	)	)	PUNCT
ejpam-3877	499	9	}	}	PUNCT
ejpam-3877	499	10	as	as	SCONJ
ejpam-3877	499	11	mentioned	mention	VERB
ejpam-3877	499	12	above	above	ADV
ejpam-3877	499	13	and	and	CCONJ
ejpam-3877	499	14	we	we	PRON
ejpam-3877	499	15	use	use	VERB
ejpam-3877	499	16	it	it	PRON
ejpam-3877	499	17	in	in	ADP
ejpam-3877	499	18	(	(	PUNCT
ejpam-3877	499	19	5.22	5.22	NUM
ejpam-3877	499	20	)	)	PUNCT
ejpam-3877	499	21	,	,	PUNCT
ejpam-3877	499	22	then	then	ADV
ejpam-3877	499	23	we	we	PRON
ejpam-3877	499	24	obtain	obtain	VERB
ejpam-3877	499	25	for	for	ADP
ejpam-3877	499	26	every	every	DET
ejpam-3877	499	27	τ	τ	PROPN
ejpam-3877	499	28	∈	∈	PROPN
ejpam-3877	499	29	(	(	PUNCT
ejpam-3877	499	30	0	0	NUM
ejpam-3877	499	31	,	,	PUNCT
ejpam-3877	499	32	t	t	NOUN
ejpam-3877	499	33	)	)	PUNCT
ejpam-3877	499	34	∫	∫	PROPN
ejpam-3877	500	1	ω	ω	NUM
ejpam-3877	500	2	fj(un)(x	fj(un)(x	PROPN
ejpam-3877	500	3	,	,	PUNCT
ejpam-3877	500	4	τ)ρ(x)dx−	τ)ρ(x)dx−	PROPN
ejpam-3877	500	5	∫	∫	PROPN
ejpam-3877	500	6	ω	ω	PROPN
ejpam-3877	500	7	fj(u0n)(x)ρ(x)dx	fj(u0n)(x)ρ(x)dx	PROPN
ejpam-3877	500	8	≤	≤	NOUN
ejpam-3877	500	9	−	−	ADP
ejpam-3877	500	10	∫	∫	PROPN
ejpam-3877	500	11	τ	τ	X
ejpam-3877	500	12	0	0	NUM
ejpam-3877	500	13	∫	∫	PROPN
ejpam-3877	501	1	ω	ω	NUM
ejpam-3877	501	2	f	f	PROPN
ejpam-3877	501	3	′j(un)∇ψ(un)∇ρdxdt+	′j(un)∇ψ(un)∇ρdxdt+	SYM
ejpam-3877	501	4	∫	∫	PROPN
ejpam-3877	501	5	τ	τ	X
ejpam-3877	501	6	0	0	NUM
ejpam-3877	501	7	∫	∫	PROPN
ejpam-3877	501	8	ω	ω	NUM
ejpam-3877	501	9	µnf	µnf	PROPN
ejpam-3877	501	10	′j(un)ρdxdt	′j(un)ρdxdt	PROPN
ejpam-3877	501	11	.	.	PROPN
ejpam-3877	502	1	(	(	PUNCT
ejpam-3877	502	2	5.29	5.29	NUM
ejpam-3877	502	3	)	)	PUNCT
ejpam-3877	502	4	let	let	VERB
ejpam-3877	502	5	us	we	PRON
ejpam-3877	502	6	consider	consider	VERB
ejpam-3877	502	7	{	{	PUNCT
ejpam-3877	502	8	unj	unj	NOUN
ejpam-3877	502	9	}	}	PUNCT
ejpam-3877	502	10	the	the	DET
ejpam-3877	502	11	sequence	sequence	NOUN
ejpam-3877	502	12	given	give	VERB
ejpam-3877	502	13	in	in	ADP
ejpam-3877	502	14	proposition	proposition	NOUN
ejpam-3877	502	15	5.1	5.1	NUM
ejpam-3877	502	16	and	and	CCONJ
ejpam-3877	502	17	proposition	proposition	VERB
ejpam-3877	502	18	5.2	5.2	NUM
ejpam-3877	502	19	and	and	CCONJ
ejpam-3877	502	20	let	let	VERB
ejpam-3877	502	21	us	we	PRON
ejpam-3877	502	22	take	take	VERB
ejpam-3877	502	23	the	the	DET
ejpam-3877	502	24	limit	limit	NOUN
ejpam-3877	502	25	as	as	SCONJ
ejpam-3877	502	26	j	j	PROPN
ejpam-3877	502	27	tends	tend	VERB
ejpam-3877	502	28	to	to	PART
ejpam-3877	502	29	infinity	infinity	VERB
ejpam-3877	502	30	in	in	ADP
ejpam-3877	502	31	(	(	PUNCT
ejpam-3877	502	32	5.29	5.29	NUM
ejpam-3877	502	33	)	)	PUNCT
ejpam-3877	502	34	(	(	PUNCT
ejpam-3877	502	35	with	with	ADP
ejpam-3877	502	36	n	n	PROPN
ejpam-3877	502	37	=	=	SYM
ejpam-3877	502	38	nj	nj	PROPN
ejpam-3877	502	39	)	)	PUNCT
ejpam-3877	502	40	.	.	PUNCT
ejpam-3877	503	1	by	by	ADP
ejpam-3877	503	2	(	(	PUNCT
ejpam-3877	503	3	5.2	5.2	NUM
ejpam-3877	503	4	)	)	PUNCT
ejpam-3877	503	5	,	,	PUNCT
ejpam-3877	503	6	(	(	PUNCT
ejpam-3877	503	7	5.3	5.3	NUM
ejpam-3877	503	8	)	)	PUNCT
ejpam-3877	503	9	and	and	CCONJ
ejpam-3877	503	10	the	the	DET
ejpam-3877	503	11	fact	fact	NOUN
ejpam-3877	503	12	that	that	SCONJ
ejpam-3877	503	13	{	{	PUNCT
ejpam-3877	503	14	f	f	NOUN
ejpam-3877	503	15	′j(unj	′j(unj	NUM
ejpam-3877	503	16	)	)	PUNCT
ejpam-3877	503	17	}	}	PUNCT
ejpam-3877	503	18	is	be	AUX
ejpam-3877	503	19	bounded	bound	VERB
ejpam-3877	503	20	in	in	ADP
ejpam-3877	503	21	l∞(q	l∞(q	NOUN
ejpam-3877	503	22	)	)	PUNCT
ejpam-3877	503	23	,	,	PUNCT
ejpam-3877	503	24	there	there	PRON
ejpam-3877	503	25	holds	hold	VERB
ejpam-3877	503	26	lim	lim	PROPN
ejpam-3877	503	27	j→∞	j→∞	PROPN
ejpam-3877	503	28	∫	∫	PROPN
ejpam-3877	503	29	τ	τ	PROPN
ejpam-3877	503	30	0	0	NUM
ejpam-3877	503	31	∫	∫	PROPN
ejpam-3877	503	32	ω	ω	PROPN
ejpam-3877	503	33	f	f	PROPN
ejpam-3877	503	34	′j(unj	′j(unj	NUM
ejpam-3877	503	35	)	)	PUNCT
ejpam-3877	503	36	∇ψ(unj	∇ψ(unj	X
ejpam-3877	503	37	)	)	PUNCT
ejpam-3877	503	38	∇ρdxdt	∇ρdxdt	NOUN
ejpam-3877	503	39	=	=	SYM
ejpam-3877	503	40	∫	∫	PROPN
ejpam-3877	503	41	τ	τ	PROPN
ejpam-3877	503	42	0	0	NUM
ejpam-3877	503	43	∫	∫	PROPN
ejpam-3877	503	44	ω	ω	PROPN
ejpam-3877	503	45	f	f	PROPN
ejpam-3877	503	46	′j(ψ−1(v))∇v∇ρdxdt	′j(ψ−1(v))∇v∇ρdxdt	PROPN
ejpam-3877	503	47	.	.	PUNCT
ejpam-3877	504	1	in	in	ADP
ejpam-3877	504	2	view	view	NOUN
ejpam-3877	504	3	of	of	ADP
ejpam-3877	504	4	the	the	DET
ejpam-3877	504	5	definition	definition	NOUN
ejpam-3877	504	6	of	of	ADP
ejpam-3877	504	7	the	the	DET
ejpam-3877	504	8	sequence	sequence	NOUN
ejpam-3877	504	9	{	{	PUNCT
ejpam-3877	504	10	f	f	PROPN
ejpam-3877	504	11	′j(unj	′j(unj	NUM
ejpam-3877	504	12	)	)	PUNCT
ejpam-3877	504	13	}	}	PUNCT
ejpam-3877	504	14	,	,	PUNCT
ejpam-3877	504	15	yields	yield	NOUN
ejpam-3877	504	16	0	0	NUM
ejpam-3877	504	17	≤	≤	NUM
ejpam-3877	504	18	f	f	NOUN
ejpam-3877	504	19	′j(unj	′j(unj	NUM
ejpam-3877	504	20	)	)	PUNCT
ejpam-3877	504	21	≤	≤	NUM
ejpam-3877	504	22	1	1	NUM
ejpam-3877	504	23	,	,	PUNCT
ejpam-3877	504	24	f	f	PROPN
ejpam-3877	504	25	′j(unj	′j(unj	NUM
ejpam-3877	504	26	)	)	PUNCT
ejpam-3877	504	27	→	→	SYM
ejpam-3877	504	28	0	0	PUNCT
ejpam-3877	504	29	as	as	ADP
ejpam-3877	504	30	j	j	PROPN
ejpam-3877	504	31	→∞	→∞	PROPN
ejpam-3877	504	32	and	and	CCONJ
ejpam-3877	504	33	ψ−1(v	ψ−1(v	NOUN
ejpam-3877	504	34	)	)	PUNCT
ejpam-3877	504	35	∈	∈	PROPN
ejpam-3877	504	36	l1(q	l1(q	CCONJ
ejpam-3877	504	37	)	)	PUNCT
ejpam-3877	504	38	.	.	PUNCT
ejpam-3877	505	1	it	it	PRON
ejpam-3877	505	2	follows	follow	VERB
ejpam-3877	505	3	that	that	SCONJ
ejpam-3877	505	4	lim	lim	PROPN
ejpam-3877	505	5	j→∞	j→∞	PROPN
ejpam-3877	505	6	lim	lim	PROPN
ejpam-3877	506	1	j→∞	j→∞	PROPN
ejpam-3877	506	2	∫	∫	PROPN
ejpam-3877	506	3	τ	τ	PROPN
ejpam-3877	506	4	0	0	NUM
ejpam-3877	506	5	∫	∫	PROPN
ejpam-3877	507	1	ω	ω	NUM
ejpam-3877	507	2	f	f	PROPN
ejpam-3877	507	3	′j(ψ−1(v))∇v∇ρdxdt	′j(ψ−1(v))∇v∇ρdxdt	PUNCT
ejpam-3877	507	4	=	=	NOUN
ejpam-3877	507	5	0	0	X
ejpam-3877	507	6	.	.	PUNCT
ejpam-3877	508	1	(	(	PUNCT
ejpam-3877	508	2	5.30	5.30	NUM
ejpam-3877	508	3	)	)	PUNCT
ejpam-3877	508	4	on	on	ADP
ejpam-3877	508	5	the	the	DET
ejpam-3877	508	6	other	other	ADJ
ejpam-3877	508	7	hand	hand	NOUN
ejpam-3877	508	8	,	,	PUNCT
ejpam-3877	508	9	by	by	ADP
ejpam-3877	508	10	(	(	PUNCT
ejpam-3877	508	11	5.26	5.26	NUM
ejpam-3877	508	12	)	)	PUNCT
ejpam-3877	508	13	one	one	NOUN
ejpam-3877	508	14	has	have	VERB
ejpam-3877	508	15	lim	lim	PROPN
ejpam-3877	509	1	j→∞	j→∞	PROPN
ejpam-3877	509	2	∫	∫	PROPN
ejpam-3877	509	3	ω	ω	NUM
ejpam-3877	509	4	fj(unj	fj(unj	INTJ
ejpam-3877	509	5	(	(	PUNCT
ejpam-3877	509	6	x	x	NOUN
ejpam-3877	509	7	,	,	PUNCT
ejpam-3877	509	8	τ))ρ(x)dx	τ))ρ(x)dx	NOUN
ejpam-3877	509	9	=	=	SYM
ejpam-3877	509	10	∫	∫	PROPN
ejpam-3877	509	11	ω	ω	NUM
ejpam-3877	509	12	fj(ψ−1(v))(x	fj(ψ−1(v))(x	PROPN
ejpam-3877	509	13	,	,	PUNCT
ejpam-3877	509	14	τ)dx+	τ)dx+	X
ejpam-3877	509	15	〈	〈	PROPN
ejpam-3877	509	16	λ1(τ	λ1(τ	PROPN
ejpam-3877	509	17	)	)	PUNCT
ejpam-3877	509	18	,	,	PUNCT
ejpam-3877	509	19	ρ〉ω	ρ〉ω	PROPN
ejpam-3877	509	20	.	.	PUNCT
ejpam-3877	510	1	referring	refer	VERB
ejpam-3877	510	2	to	to	ADP
ejpam-3877	510	3	the	the	DET
ejpam-3877	510	4	definition	definition	NOUN
ejpam-3877	510	5	of	of	ADP
ejpam-3877	510	6	the	the	DET
ejpam-3877	510	7	sequence	sequence	NOUN
ejpam-3877	510	8	{	{	PUNCT
ejpam-3877	510	9	fj(un)}j>1	fj(un)}j>1	PROPN
ejpam-3877	510	10	,	,	PUNCT
ejpam-3877	510	11	we	we	PRON
ejpam-3877	510	12	infer	infer	VERB
ejpam-3877	510	13	that	that	SCONJ
ejpam-3877	510	14	0	0	NUM
ejpam-3877	510	15	≤	≤	NUM
ejpam-3877	510	16	fj(unj	fj(unj	NOUN
ejpam-3877	510	17	)	)	PUNCT
ejpam-3877	510	18	≤	≤	NUM
ejpam-3877	510	19	1	1	NUM
ejpam-3877	510	20	,	,	PUNCT
ejpam-3877	510	21	fj(unj	fj(unj	NOUN
ejpam-3877	510	22	)	)	PUNCT
ejpam-3877	510	23	→	→	SYM
ejpam-3877	510	24	0	0	PUNCT
ejpam-3877	511	1	as	as	ADP
ejpam-3877	511	2	j	j	PROPN
ejpam-3877	511	3	→∞	→∞	PROPN
ejpam-3877	511	4	and	and	CCONJ
ejpam-3877	511	5	ψ−1(v	ψ−1(v	NOUN
ejpam-3877	511	6	)	)	PUNCT
ejpam-3877	511	7	∈	∈	PROPN
ejpam-3877	511	8	l1(q	l1(q	CCONJ
ejpam-3877	511	9	)	)	PUNCT
ejpam-3877	511	10	.	.	PUNCT
ejpam-3877	512	1	quincy	quincy	PROPN
ejpam-3877	512	2	s.	s.	PROPN
ejpam-3877	512	3	nkombo	nkombo	PROPN
ejpam-3877	512	4	,	,	PUNCT
ejpam-3877	512	5	fengquan	fengquan	PROPN
ejpam-3877	512	6	li	li	PROPN
ejpam-3877	512	7	/	/	SYM
ejpam-3877	512	8	eur	eur	PROPN
ejpam-3877	512	9	.	.	PUNCT
ejpam-3877	513	1	j.	j.	PROPN
ejpam-3877	513	2	pure	pure	PROPN
ejpam-3877	513	3	appl	appl	PROPN
ejpam-3877	513	4	.	.	PROPN
ejpam-3877	513	5	math	math	PROPN
ejpam-3877	513	6	,	,	PUNCT
ejpam-3877	513	7	14	14	NUM
ejpam-3877	513	8	(	(	PUNCT
ejpam-3877	513	9	1	1	NUM
ejpam-3877	513	10	)	)	PUNCT
ejpam-3877	513	11	(	(	PUNCT
ejpam-3877	513	12	2021	2021	NUM
ejpam-3877	513	13	)	)	PUNCT
ejpam-3877	513	14	,	,	PUNCT
ejpam-3877	513	15	204	204	NUM
ejpam-3877	513	16	-	-	SYM
ejpam-3877	513	17	233	233	NUM
ejpam-3877	513	18	224	224	NUM
ejpam-3877	513	19	then	then	ADV
ejpam-3877	513	20	we	we	PRON
ejpam-3877	513	21	obtain	obtain	VERB
ejpam-3877	513	22	lim	lim	PROPN
ejpam-3877	513	23	j→∞	j→∞	PROPN
ejpam-3877	513	24	lim	lim	PROPN
ejpam-3877	513	25	j→∞	j→∞	PROPN
ejpam-3877	513	26	∫	∫	PROPN
ejpam-3877	513	27	ω	ω	PROPN
ejpam-3877	513	28	fj(un(τ))ρ(x)dx	fj(un(τ))ρ(x)dx	X
ejpam-3877	513	29	=	=	PUNCT
ejpam-3877	513	30	〈	〈	PROPN
ejpam-3877	513	31	λ1(τ	λ1(τ	PROPN
ejpam-3877	513	32	)	)	PUNCT
ejpam-3877	513	33	,	,	PUNCT
ejpam-3877	513	34	ρ〉ω	ρ〉ω	PROPN
ejpam-3877	513	35	.	.	PUNCT
ejpam-3877	514	1	(	(	PUNCT
ejpam-3877	514	2	5.31	5.31	NUM
ejpam-3877	514	3	)	)	PUNCT
ejpam-3877	514	4	let	let	VERB
ejpam-3877	514	5	us	we	PRON
ejpam-3877	514	6	consider	consider	VERB
ejpam-3877	514	7	the	the	DET
ejpam-3877	514	8	sequence	sequence	NOUN
ejpam-3877	514	9	{	{	PUNCT
ejpam-3877	514	10	u0n(x	u0n(x	PROPN
ejpam-3877	514	11	)	)	PUNCT
ejpam-3877	514	12	}	}	PUNCT
ejpam-3877	514	13	satisfies	satisfie	NOUN
ejpam-3877	514	14	(	(	PUNCT
ejpam-3877	514	15	3.3	3.3	NUM
ejpam-3877	514	16	)	)	PUNCT
ejpam-3877	514	17	,	,	PUNCT
ejpam-3877	514	18	then	then	ADV
ejpam-3877	514	19	fj(u0nj	fj(u0nj	PROPN
ejpam-3877	514	20	)	)	PUNCT
ejpam-3877	515	1	=	=	PUNCT
ejpam-3877	516	1	[	[	X
ejpam-3877	516	2	u0nj	u0nj	PUNCT
ejpam-3877	516	3	]	]	PUNCT
ejpam-3877	517	1	+	+	NUM
ejpam-3877	517	2	−rj(u0nj	−rj(u0nj	NOUN
ejpam-3877	517	3	)	)	PUNCT
ejpam-3877	517	4	≤	≤	NOUN
ejpam-3877	518	1	[	[	X
ejpam-3877	518	2	u0rnj	u0rnj	X
ejpam-3877	518	3	]	]	PUNCT
ejpam-3877	519	1	+	+	PUNCT
ejpam-3877	519	2	+	+	NOUN
ejpam-3877	519	3	[	[	X
ejpam-3877	519	4	u0sn]+	u0sn]+	NOUN
ejpam-3877	519	5	−rj(u0nj	−rj(u0nj	PROPN
ejpam-3877	519	6	)	)	PUNCT
ejpam-3877	519	7	.	.	PUNCT
ejpam-3877	520	1	since	since	SCONJ
ejpam-3877	520	2	u0rnj	u0rnj	NOUN
ejpam-3877	520	3	→	→	SYM
ejpam-3877	520	4	u0r	u0r	PROPN
ejpam-3877	520	5	in	in	ADP
ejpam-3877	520	6	l1(ω	l1(ω	PROPN
ejpam-3877	520	7	)	)	PUNCT
ejpam-3877	520	8	and	and	CCONJ
ejpam-3877	520	9	the	the	DET
ejpam-3877	520	10	sequence	sequence	NOUN
ejpam-3877	520	11	{	{	PUNCT
ejpam-3877	520	12	rj(u0rnj	rj(u0rnj	NOUN
ejpam-3877	520	13	)	)	PUNCT
ejpam-3877	520	14	}	}	PUNCT
ejpam-3877	520	15	is	be	AUX
ejpam-3877	520	16	bounded	bound	VERB
ejpam-3877	520	17	in	in	ADP
ejpam-3877	520	18	l∞(ω	l∞(ω	NOUN
ejpam-3877	520	19	)	)	PUNCT
ejpam-3877	520	20	,	,	PUNCT
ejpam-3877	520	21	we	we	PRON
ejpam-3877	520	22	obtain	obtain	VERB
ejpam-3877	520	23	[	[	X
ejpam-3877	520	24	u0rnj	u0rnj	X
ejpam-3877	520	25	]	]	PUNCT
ejpam-3877	521	1	+	+	CCONJ
ejpam-3877	521	2	−rj(u0nj	−rj(u0nj	NOUN
ejpam-3877	521	3	)	)	PUNCT
ejpam-3877	521	4	→	→	PUNCT
ejpam-3877	522	1	[	[	X
ejpam-3877	522	2	u0r	u0r	NOUN
ejpam-3877	522	3	]	]	X
ejpam-3877	522	4	+	+	CCONJ
ejpam-3877	522	5	−rj(u0r	−rj(u0r	PROPN
ejpam-3877	522	6	)	)	PUNCT
ejpam-3877	522	7	=	=	SYM
ejpam-3877	522	8	fj(u0r	fj(u0r	NOUN
ejpam-3877	522	9	)	)	PUNCT
ejpam-3877	522	10	in	in	ADP
ejpam-3877	522	11	l1(ω	l1(ω	PROPN
ejpam-3877	522	12	)	)	PUNCT
ejpam-3877	522	13	which	which	PRON
ejpam-3877	522	14	leads	lead	VERB
ejpam-3877	522	15	to	to	ADP
ejpam-3877	522	16	lim	lim	PROPN
ejpam-3877	522	17	j→∞	j→∞	PROPN
ejpam-3877	522	18	lim	lim	PROPN
ejpam-3877	522	19	sup	sup	PROPN
ejpam-3877	522	20	j→∞	j→∞	NUM
ejpam-3877	522	21	∫	∫	PROPN
ejpam-3877	522	22	ω	ω	PROPN
ejpam-3877	522	23	fj(u0nj	fj(u0nj	PROPN
ejpam-3877	522	24	)	)	PUNCT
ejpam-3877	522	25	ρ(x)dx	ρ(x)dx	ADP
ejpam-3877	522	26	≤	≤	NUM
ejpam-3877	522	27	〈	〈	PROPN
ejpam-3877	522	28	[	[	X
ejpam-3877	522	29	u0s	u0s	X
ejpam-3877	522	30	]	]	X
ejpam-3877	522	31	+	+	X
ejpam-3877	522	32	,	,	PUNCT
ejpam-3877	522	33	ρ	ρ	NUM
ejpam-3877	522	34	〉	〉	NOUN
ejpam-3877	522	35	ω	ω	NOUN
ejpam-3877	522	36	.	.	PUNCT
ejpam-3877	523	1	(	(	PUNCT
ejpam-3877	523	2	5.32	5.32	NUM
ejpam-3877	523	3	)	)	PUNCT
ejpam-3877	523	4	let	let	VERB
ejpam-3877	523	5	us	we	PRON
ejpam-3877	523	6	now	now	ADV
ejpam-3877	523	7	consider	consider	VERB
ejpam-3877	523	8	the	the	DET
ejpam-3877	523	9	function	function	NOUN
ejpam-3877	523	10	ηr	ηr	NOUN
ejpam-3877	523	11	,	,	PUNCT
ejpam-3877	523	12	s	s	PART
ejpam-3877	523	13	constructs	construct	NOUN
ejpam-3877	523	14	from	from	ADP
ejpam-3877	523	15	the	the	DET
ejpam-3877	523	16	function	function	NOUN
ejpam-3877	523	17	ηr	ηr	NOUN
ejpam-3877	523	18	,	,	PUNCT
ejpam-3877	523	19	s	s	AUX
ejpam-3877	523	20	given	give	VERB
ejpam-3877	523	21	in	in	ADP
ejpam-3877	523	22	proposition	proposition	NOUN
ejpam-3877	523	23	5.2	5.2	NUM
ejpam-3877	523	24	as	as	SCONJ
ejpam-3877	523	25	follows	follow	VERB
ejpam-3877	523	26	ηr	ηr	PROPN
ejpam-3877	523	27	,	,	PUNCT
ejpam-3877	523	28	s(t	s(t	PROPN
ejpam-3877	523	29	)	)	PUNCT
ejpam-3877	523	30	=	=	PUNCT
ejpam-3877	523	31	∫	∫	PROPN
ejpam-3877	523	32	t	t	PROPN
ejpam-3877	523	33	t+r+2s	t+r+2s	PUNCT
ejpam-3877	523	34	ηr	ηr	NOUN
ejpam-3877	523	35	,	,	PUNCT
ejpam-3877	523	36	s(θ)dθ	s(θ)dθ	ADP
ejpam-3877	523	37	for	for	ADP
ejpam-3877	523	38	every	every	DET
ejpam-3877	523	39	θ	θ	PROPN
ejpam-3877	523	40	∈	∈	PROPN
ejpam-3877	523	41	(	(	PUNCT
ejpam-3877	523	42	0	0	NUM
ejpam-3877	523	43	,	,	PUNCT
ejpam-3877	523	44	t	t	NOUN
ejpam-3877	523	45	)	)	PUNCT
ejpam-3877	523	46	we	we	PRON
ejpam-3877	523	47	deduce	deduce	VERB
ejpam-3877	523	48	that∫	that∫	NOUN
ejpam-3877	524	1	τ	τ	PROPN
ejpam-3877	524	2	0	0	NUM
ejpam-3877	524	3	∫	∫	PROPN
ejpam-3877	524	4	ω	ω	PROPN
ejpam-3877	524	5	µnjf	µnjf	VERB
ejpam-3877	524	6	′j(unj	′j(unj	NUM
ejpam-3877	524	7	)	)	PUNCT
ejpam-3877	524	8	ρdxdt	ρdxdt	NOUN
ejpam-3877	524	9	=	=	SYM
ejpam-3877	524	10	∫	∫	PROPN
ejpam-3877	524	11	τ	τ	PROPN
ejpam-3877	524	12	0	0	NUM
ejpam-3877	524	13	∫	∫	PROPN
ejpam-3877	524	14	ω	ω	PROPN
ejpam-3877	524	15	µnj	µnj	PROPN
ejpam-3877	524	16	(	(	PUNCT
ejpam-3877	524	17	1−	1−	NUM
ejpam-3877	524	18	ηr	ηr	NOUN
ejpam-3877	524	19	,	,	PUNCT
ejpam-3877	524	20	s(t	s(t	PROPN
ejpam-3877	524	21	)	)	PUNCT
ejpam-3877	524	22	)	)	PUNCT
ejpam-3877	525	1	f	f	PROPN
ejpam-3877	525	2	′j(unj	′j(unj	NUM
ejpam-3877	525	3	)	)	PUNCT
ejpam-3877	526	1	ρdxdt+	ρdxdt+	X
ejpam-3877	527	1	+	+	NUM
ejpam-3877	527	2	∫	∫	PROPN
ejpam-3877	527	3	τ	τ	PROPN
ejpam-3877	527	4	0	0	NUM
ejpam-3877	527	5	∫	∫	PROPN
ejpam-3877	527	6	ω	ω	X
ejpam-3877	527	7	µnjηr	µnjηr	NOUN
ejpam-3877	527	8	,	,	PUNCT
ejpam-3877	527	9	s(t)f	s(t)f	PROPN
ejpam-3877	527	10	′j(unj	′j(unj	NUM
ejpam-3877	527	11	)	)	PUNCT
ejpam-3877	527	12	ρdxdt	ρdxdt	NOUN
ejpam-3877	527	13	.	.	PUNCT
ejpam-3877	528	1	(	(	PUNCT
ejpam-3877	528	2	5.33	5.33	NUM
ejpam-3877	528	3	)	)	PUNCT
ejpam-3877	528	4	since	since	SCONJ
ejpam-3877	528	5	{	{	PUNCT
ejpam-3877	528	6	µnj	µnj	PROPN
ejpam-3877	528	7	}	}	PUNCT
ejpam-3877	528	8	is	be	AUX
ejpam-3877	528	9	a	a	DET
ejpam-3877	528	10	nonnegative	nonnegative	ADJ
ejpam-3877	528	11	bounded	bounded	ADJ
ejpam-3877	528	12	radon	radon	NOUN
ejpam-3877	528	13	-	-	PUNCT
ejpam-3877	528	14	measure	measure	NOUN
ejpam-3877	528	15	,	,	PUNCT
ejpam-3877	528	16	and	and	CCONJ
ejpam-3877	528	17	the	the	DET
ejpam-3877	528	18	function	function	NOUN
ejpam-3877	528	19	1−	1−	NUM
ejpam-3877	528	20	ηr	ηr	NOUN
ejpam-3877	528	21	,	,	PUNCT
ejpam-3877	528	22	s(t	s(t	PROPN
ejpam-3877	528	23	)	)	PUNCT
ejpam-3877	528	24	is	be	AUX
ejpam-3877	528	25	bounded	bound	VERB
ejpam-3877	528	26	in	in	ADP
ejpam-3877	528	27	r+	r+	NOUN
ejpam-3877	528	28	,	,	PUNCT
ejpam-3877	528	29	there	there	PRON
ejpam-3877	528	30	holds	hold	VERB
ejpam-3877	528	31	lim	lim	PROPN
ejpam-3877	528	32	sup	sup	PROPN
ejpam-3877	528	33	j→∞	j→∞	NUM
ejpam-3877	528	34	∫	∫	PROPN
ejpam-3877	528	35	τ	τ	PROPN
ejpam-3877	528	36	0	0	NUM
ejpam-3877	528	37	∫	∫	PROPN
ejpam-3877	528	38	ω	ω	PROPN
ejpam-3877	528	39	µnj	µnj	PROPN
ejpam-3877	528	40	(	(	PUNCT
ejpam-3877	528	41	1−	1−	NUM
ejpam-3877	528	42	ηr	ηr	NOUN
ejpam-3877	528	43	,	,	PUNCT
ejpam-3877	528	44	s(t	s(t	PROPN
ejpam-3877	528	45	)	)	PUNCT
ejpam-3877	528	46	)	)	PUNCT
ejpam-3877	529	1	f	f	PROPN
ejpam-3877	529	2	′j(unj	′j(unj	NUM
ejpam-3877	529	3	)	)	PUNCT
ejpam-3877	529	4	ρdxdt	ρdxdt	NOUN
ejpam-3877	529	5	≤	≤	X
ejpam-3877	529	6	∫	∫	PROPN
ejpam-3877	529	7	τ	τ	PROPN
ejpam-3877	529	8	0	0	NUM
ejpam-3877	529	9	〈	〈	PROPN
ejpam-3877	529	10	µ	µ	X
ejpam-3877	529	11	,	,	PUNCT
ejpam-3877	529	12	ρfj(ψ−1(v	ρfj(ψ−1(v	PROPN
ejpam-3877	529	13	)	)	PUNCT
ejpam-3877	529	14	)	)	PUNCT
ejpam-3877	530	1	(	(	PUNCT
ejpam-3877	530	2	1−	1−	NUM
ejpam-3877	530	3	ηr	ηr	NOUN
ejpam-3877	530	4	,	,	PUNCT
ejpam-3877	530	5	s(t	s(t	PROPN
ejpam-3877	530	6	)	)	PUNCT
ejpam-3877	530	7	)	)	PUNCT
ejpam-3877	530	8	〉	〉	NOUN
ejpam-3877	531	1	dt	dt	PROPN
ejpam-3877	531	2	.	.	PUNCT
ejpam-3877	532	1	letting	let	VERB
ejpam-3877	532	2	j	j	PROPN
ejpam-3877	532	3	to	to	PART
ejpam-3877	532	4	infinity	infinity	VERB
ejpam-3877	532	5	,	,	PUNCT
ejpam-3877	532	6	we	we	PRON
ejpam-3877	532	7	obtain	obtain	VERB
ejpam-3877	532	8	lim	lim	PROPN
ejpam-3877	532	9	j→∞	j→∞	PROPN
ejpam-3877	532	10	lim	lim	PROPN
ejpam-3877	533	1	sup	sup	PROPN
ejpam-3877	533	2	j→∞	j→∞	NUM
ejpam-3877	533	3	∫	∫	PROPN
ejpam-3877	533	4	τ	τ	PROPN
ejpam-3877	533	5	0	0	NUM
ejpam-3877	533	6	∫	∫	PROPN
ejpam-3877	533	7	ω	ω	PROPN
ejpam-3877	533	8	µnj	µnj	PROPN
ejpam-3877	533	9	(	(	PUNCT
ejpam-3877	533	10	1−	1−	NUM
ejpam-3877	533	11	ηr	ηr	NOUN
ejpam-3877	533	12	,	,	PUNCT
ejpam-3877	533	13	s(t	s(t	PROPN
ejpam-3877	533	14	)	)	PUNCT
ejpam-3877	533	15	)	)	PUNCT
ejpam-3877	534	1	f	f	PROPN
ejpam-3877	534	2	′j(unj	′j(unj	NUM
ejpam-3877	534	3	)	)	PUNCT
ejpam-3877	534	4	ρdxdt	ρdxdt	NOUN
ejpam-3877	534	5	=	=	NOUN
ejpam-3877	534	6	0	0	PROPN
ejpam-3877	534	7	.	.	PUNCT
ejpam-3877	535	1	(	(	PUNCT
ejpam-3877	535	2	5.34	5.34	NUM
ejpam-3877	535	3	)	)	PUNCT
ejpam-3877	535	4	by	by	ADP
ejpam-3877	535	5	[	[	X
ejpam-3877	535	6	11	11	NUM
ejpam-3877	535	7	,	,	PUNCT
ejpam-3877	535	8	theorem	theorem	VERB
ejpam-3877	535	9	8	8	NUM
ejpam-3877	535	10	,	,	PUNCT
ejpam-3877	535	11	p.85	p.85	ADP
ejpam-3877	535	12	]	]	PUNCT
ejpam-3877	535	13	,	,	PUNCT
ejpam-3877	535	14	there	there	PRON
ejpam-3877	535	15	exist	exist	VERB
ejpam-3877	535	16	νtnj	νtnj	ADJ
ejpam-3877	535	17	∈m+(ω	∈m+(ω	NOUN
ejpam-3877	535	18	)	)	PUNCT
ejpam-3877	535	19	and	and	CCONJ
ejpam-3877	535	20	δ0	δ0	PROPN
ejpam-3877	535	21	∈m+(0	∈m+(0	PROPN
ejpam-3877	535	22	,	,	PUNCT
ejpam-3877	535	23	t	t	PROPN
ejpam-3877	535	24	)	)	PUNCT
ejpam-3877	535	25	for	for	ADP
ejpam-3877	535	26	µnj	µnj	PROPN
ejpam-3877	535	27	∈m+(q	∈m+(q	PROPN
ejpam-3877	535	28	)	)	PUNCT
ejpam-3877	536	1	such	such	ADJ
ejpam-3877	536	2	that	that	SCONJ
ejpam-3877	536	3	(	(	PUNCT
ejpam-3877	536	4	5.33	5.33	NUM
ejpam-3877	536	5	)	)	PUNCT
ejpam-3877	536	6	,	,	PUNCT
ejpam-3877	536	7	becomes∫	becomes∫	X
ejpam-3877	536	8	τ	τ	PROPN
ejpam-3877	536	9	0	0	NUM
ejpam-3877	536	10	∫	∫	PROPN
ejpam-3877	536	11	ω	ω	X
ejpam-3877	536	12	µnjηr	µnjηr	NOUN
ejpam-3877	536	13	,	,	PUNCT
ejpam-3877	536	14	s(t)f	s(t)f	ADP
ejpam-3877	536	15	′j(unk	′j(unk	NOUN
ejpam-3877	536	16	)	)	PUNCT
ejpam-3877	536	17	ρdxdt	ρdxdt	NOUN
ejpam-3877	536	18	≤	≤	PROPN
ejpam-3877	536	19	ηr	ηr	PROPN
ejpam-3877	536	20	,	,	PUNCT
ejpam-3877	536	21	s(0	s(0	PROPN
ejpam-3877	536	22	)	)	PUNCT
ejpam-3877	536	23	∫	∫	PROPN
ejpam-3877	537	1	ω	ω	PROPN
ejpam-3877	537	2	ντnj	ντnj	PROPN
ejpam-3877	537	3	fj(unj	fj(unj	PROPN
ejpam-3877	537	4	)	)	PUNCT
ejpam-3877	537	5	ρdx	ρdx	PROPN
ejpam-3877	537	6	≤	≤	NOUN
ejpam-3877	537	7	(	(	PUNCT
ejpam-3877	537	8	4r	4r	NOUN
ejpam-3877	537	9	+	+	CCONJ
ejpam-3877	538	1	2s	2s	X
ejpam-3877	538	2	)	)	PUNCT
ejpam-3877	538	3	∫	∫	PROPN
ejpam-3877	538	4	ω	ω	PROPN
ejpam-3877	538	5	ντnj	ντnj	PROPN
ejpam-3877	538	6	fj(unj	fj(unj	PROPN
ejpam-3877	538	7	)	)	PUNCT
ejpam-3877	538	8	ρdx	ρdx	VERB
ejpam-3877	538	9	.	.	PUNCT
ejpam-3877	539	1	setting	set	VERB
ejpam-3877	539	2	r	r	NOUN
ejpam-3877	539	3	=	=	SYM
ejpam-3877	539	4	1	1	NUM
ejpam-3877	539	5	8	8	NUM
ejpam-3877	539	6	and	and	CCONJ
ejpam-3877	539	7	s	s	NOUN
ejpam-3877	539	8	=	=	SYM
ejpam-3877	539	9	1	1	NUM
ejpam-3877	539	10	4	4	NUM
ejpam-3877	539	11	,	,	PUNCT
ejpam-3877	539	12	then∫	then∫	NOUN
ejpam-3877	539	13	τ	τ	PROPN
ejpam-3877	539	14	0	0	NUM
ejpam-3877	539	15	∫	∫	PROPN
ejpam-3877	539	16	ω	ω	X
ejpam-3877	539	17	µnjηr	µnjηr	NOUN
ejpam-3877	539	18	,	,	PUNCT
ejpam-3877	539	19	s(t)f	s(t)f	PROPN
ejpam-3877	539	20	′j(unj	′j(unj	NUM
ejpam-3877	539	21	)	)	PUNCT
ejpam-3877	539	22	ρdxdt	ρdxdt	NOUN
ejpam-3877	539	23	≤	≤	PUNCT
ejpam-3877	540	1	∫	∫	PROPN
ejpam-3877	540	2	ω	ω	PROPN
ejpam-3877	541	1	[	[	X
ejpam-3877	541	2	ντs	ντs	NOUN
ejpam-3877	541	3	]	]	X
ejpam-3877	541	4	+	+	NOUN
ejpam-3877	541	5	nj	nj	PROPN
ejpam-3877	541	6	ρdx+	ρdx+	ADJ
ejpam-3877	541	7	∫	∫	PROPN
ejpam-3877	541	8	ω	ω	PROPN
ejpam-3877	542	1	[	[	X
ejpam-3877	542	2	ντr	ντr	X
ejpam-3877	542	3	]	]	X
ejpam-3877	542	4	+	+	NOUN
ejpam-3877	542	5	nj	nj	PROPN
ejpam-3877	542	6	fj(unj	fj(unj	NOUN
ejpam-3877	542	7	)	)	PUNCT
ejpam-3877	542	8	ρdx	ρdx	PROPN
ejpam-3877	542	9	.	.	PUNCT
ejpam-3877	543	1	quincy	quincy	PROPN
ejpam-3877	543	2	s.	s.	PROPN
ejpam-3877	543	3	nkombo	nkombo	PROPN
ejpam-3877	543	4	,	,	PUNCT
ejpam-3877	543	5	fengquan	fengquan	PROPN
ejpam-3877	543	6	li	li	PROPN
ejpam-3877	543	7	/	/	SYM
ejpam-3877	543	8	eur	eur	PROPN
ejpam-3877	543	9	.	.	PUNCT
ejpam-3877	544	1	j.	j.	PROPN
ejpam-3877	544	2	pure	pure	PROPN
ejpam-3877	544	3	appl	appl	PROPN
ejpam-3877	544	4	.	.	PROPN
ejpam-3877	544	5	math	math	PROPN
ejpam-3877	544	6	,	,	PUNCT
ejpam-3877	544	7	14	14	NUM
ejpam-3877	544	8	(	(	PUNCT
ejpam-3877	544	9	1	1	NUM
ejpam-3877	544	10	)	)	PUNCT
ejpam-3877	544	11	(	(	PUNCT
ejpam-3877	544	12	2021	2021	NUM
ejpam-3877	544	13	)	)	PUNCT
ejpam-3877	544	14	,	,	PUNCT
ejpam-3877	544	15	204	204	NUM
ejpam-3877	544	16	-	-	SYM
ejpam-3877	544	17	233	233	NUM
ejpam-3877	544	18	225	225	NUM
ejpam-3877	544	19	therefore	therefore	ADV
ejpam-3877	544	20	,	,	PUNCT
ejpam-3877	544	21	lim	lim	PROPN
ejpam-3877	544	22	j→∞	j→∞	NUM
ejpam-3877	544	23	lim	lim	PROPN
ejpam-3877	544	24	sup	sup	PROPN
ejpam-3877	544	25	j→∞	j→∞	NUM
ejpam-3877	544	26	∫	∫	PROPN
ejpam-3877	544	27	τ	τ	PROPN
ejpam-3877	544	28	0	0	NUM
ejpam-3877	544	29	∫	∫	PROPN
ejpam-3877	544	30	ω	ω	PROPN
ejpam-3877	544	31	µnjf	µnjf	VERB
ejpam-3877	544	32	′j(unj	′j(unj	NUM
ejpam-3877	544	33	)	)	PUNCT
ejpam-3877	544	34	ρdxdt	ρdxdt	NOUN
ejpam-3877	544	35	≤	≤	PUNCT
ejpam-3877	544	36	〈	〈	PROPN
ejpam-3877	545	1	[	[	X
ejpam-3877	545	2	ντs	ντs	NOUN
ejpam-3877	545	3	]	]	X
ejpam-3877	545	4	+	+	ADJ
ejpam-3877	545	5	,	,	PUNCT
ejpam-3877	545	6	ρ	ρ	NUM
ejpam-3877	545	7	〉	〉	NOUN
ejpam-3877	545	8	ω	ω	NOUN
ejpam-3877	545	9	.	.	PUNCT
ejpam-3877	546	1	(	(	PUNCT
ejpam-3877	546	2	5.35	5.35	NUM
ejpam-3877	546	3	)	)	PUNCT
ejpam-3877	546	4	combining	combine	VERB
ejpam-3877	546	5	(	(	PUNCT
ejpam-3877	546	6	5.30	5.30	NUM
ejpam-3877	546	7	)	)	PUNCT
ejpam-3877	546	8	,	,	PUNCT
ejpam-3877	546	9	(	(	PUNCT
ejpam-3877	546	10	5.31	5.31	NUM
ejpam-3877	546	11	)	)	PUNCT
ejpam-3877	546	12	,	,	PUNCT
ejpam-3877	546	13	(	(	PUNCT
ejpam-3877	546	14	5.32	5.32	NUM
ejpam-3877	546	15	)	)	PUNCT
ejpam-3877	546	16	,	,	PUNCT
ejpam-3877	546	17	(	(	PUNCT
ejpam-3877	546	18	5.34	5.34	NUM
ejpam-3877	546	19	)	)	PUNCT
ejpam-3877	546	20	and	and	CCONJ
ejpam-3877	546	21	(	(	PUNCT
ejpam-3877	546	22	5.35	5.35	NUM
ejpam-3877	546	23	)	)	PUNCT
ejpam-3877	546	24	together	together	ADV
ejpam-3877	546	25	.	.	PUNCT
ejpam-3877	547	1	hence	hence	ADV
ejpam-3877	547	2	(	(	PUNCT
ejpam-3877	547	3	5.27	5.27	NUM
ejpam-3877	547	4	)	)	PUNCT
ejpam-3877	547	5	holds	hold	VERB
ejpam-3877	547	6	true	true	ADJ
ejpam-3877	547	7	.	.	PUNCT
ejpam-3877	548	1	�	�	PROPN
ejpam-3877	548	2	remark	remark	VERB
ejpam-3877	548	3	5.1	5.1	NUM
ejpam-3877	548	4	.	.	PUNCT
ejpam-3877	549	1	by	by	ADP
ejpam-3877	549	2	the	the	DET
ejpam-3877	549	3	assumptions	assumption	NOUN
ejpam-3877	549	4	(	(	PUNCT
ejpam-3877	549	5	i	i	NOUN
ejpam-3877	549	6	)	)	PUNCT
ejpam-3877	549	7	and	and	CCONJ
ejpam-3877	549	8	(	(	PUNCT
ejpam-3877	549	9	j	j	NOUN
ejpam-3877	549	10	)	)	PUNCT
ejpam-3877	549	11	,	,	PUNCT
ejpam-3877	549	12	it	it	PRON
ejpam-3877	549	13	has	have	AUX
ejpam-3877	549	14	been	be	AUX
ejpam-3877	549	15	proved	prove	VERB
ejpam-3877	549	16	that	that	SCONJ
ejpam-3877	549	17	(	(	PUNCT
ejpam-3877	549	18	i	i	NOUN
ejpam-3877	549	19	)	)	PUNCT
ejpam-3877	549	20	the	the	DET
ejpam-3877	549	21	set	set	NOUN
ejpam-3877	549	22	s̃	s̃	PROPN
ejpam-3877	549	23	=	=	PUNCT
ejpam-3877	549	24	{	{	PUNCT
ejpam-3877	549	25	(	(	PUNCT
ejpam-3877	549	26	x	x	NOUN
ejpam-3877	549	27	,	,	PUNCT
ejpam-3877	549	28	t	t	PROPN
ejpam-3877	549	29	)	)	PUNCT
ejpam-3877	549	30	∈	∈	PROPN
ejpam-3877	549	31	ω	ω	PROPN
ejpam-3877	549	32	/	/	SYM
ejpam-3877	549	33	ψ(ur)(x	ψ(ur)(x	PROPN
ejpam-3877	549	34	,	,	PUNCT
ejpam-3877	549	35	t	t	PROPN
ejpam-3877	549	36	)	)	PUNCT
ejpam-3877	549	37	=	=	PUNCT
ejpam-3877	550	1	γ	γ	X
ejpam-3877	550	2	}	}	PUNCT
ejpam-3877	550	3	has	have	VERB
ejpam-3877	550	4	zero	zero	NUM
ejpam-3877	550	5	lebesgue	lebesgue	NOUN
ejpam-3877	550	6	measure	measure	NOUN
ejpam-3877	550	7	(	(	PUNCT
ejpam-3877	550	8	see	see	VERB
ejpam-3877	550	9	[	[	X
ejpam-3877	550	10	23	23	NUM
ejpam-3877	550	11	,	,	PUNCT
ejpam-3877	550	12	proposition	proposition	NOUN
ejpam-3877	550	13	5.2	5.2	NUM
ejpam-3877	550	14	]	]	PUNCT
ejpam-3877	550	15	)	)	PUNCT
ejpam-3877	550	16	.	.	PUNCT
ejpam-3877	551	1	(	(	PUNCT
ejpam-3877	551	2	ii	ii	X
ejpam-3877	551	3	)	)	PUNCT
ejpam-3877	551	4	there	there	PRON
ejpam-3877	551	5	hold	hold	VERB
ejpam-3877	551	6	supp(u(x	supp(u(x	PROPN
ejpam-3877	551	7	,	,	PUNCT
ejpam-3877	551	8	t	t	PROPN
ejpam-3877	551	9	)	)	PUNCT
ejpam-3877	551	10	)	)	PUNCT
ejpam-3877	552	1	⊆	⊆	NUM
ejpam-3877	552	2	s̃	s̃	PROPN
ejpam-3877	552	3	and	and	CCONJ
ejpam-3877	552	4	ur	ur	NOUN
ejpam-3877	552	5	=	=	NOUN
ejpam-3877	552	6	ψ−1(v	ψ−1(v	NOUN
ejpam-3877	552	7	)	)	PUNCT
ejpam-3877	553	1	a.e	a.e	NOUN
ejpam-3877	553	2	in	in	ADP
ejpam-3877	553	3	q	q	NOUN
ejpam-3877	553	4	\	\	PROPN
ejpam-3877	553	5	s̃	s̃	PROPN
ejpam-3877	553	6	(	(	PUNCT
ejpam-3877	553	7	see	see	VERB
ejpam-3877	553	8	[	[	X
ejpam-3877	553	9	30	30	NUM
ejpam-3877	553	10	,	,	PUNCT
ejpam-3877	553	11	proposition	proposition	NOUN
ejpam-3877	553	12	4.1	4.1	NUM
ejpam-3877	553	13	]	]	PUNCT
ejpam-3877	553	14	)	)	PUNCT
ejpam-3877	553	15	.	.	PUNCT
ejpam-3877	554	1	6	6	X
ejpam-3877	554	2	.	.	X
ejpam-3877	554	3	monotonicity	monotonicity	NOUN
ejpam-3877	554	4	and	and	CCONJ
ejpam-3877	554	5	uniqueness	uniqueness	PROPN
ejpam-3877	554	6	results	result	NOUN
ejpam-3877	554	7	lemma	lemma	PROPN
ejpam-3877	554	8	6.1	6.1	NUM
ejpam-3877	554	9	.	.	PUNCT
ejpam-3877	555	1	under	under	ADP
ejpam-3877	555	2	assumption	assumption	NOUN
ejpam-3877	555	3	(	(	PUNCT
ejpam-3877	555	4	i	i	NOUN
ejpam-3877	555	5	)	)	PUNCT
ejpam-3877	555	6	.	.	PUNCT
ejpam-3877	556	1	if	if	SCONJ
ejpam-3877	556	2	u	u	NOUN
ejpam-3877	556	3	is	be	AUX
ejpam-3877	556	4	a	a	DET
ejpam-3877	556	5	weak	weak	ADJ
ejpam-3877	556	6	solution	solution	NOUN
ejpam-3877	556	7	of	of	ADP
ejpam-3877	556	8	the	the	DET
ejpam-3877	556	9	problem	problem	NOUN
ejpam-3877	556	10	(	(	PUNCT
ejpam-3877	556	11	p	p	NOUN
ejpam-3877	556	12	)	)	PUNCT
ejpam-3877	556	13	.	.	PUNCT
ejpam-3877	557	1	then	then	ADV
ejpam-3877	557	2	(	(	PUNCT
ejpam-3877	557	3	i	i	NOUN
ejpam-3877	557	4	)	)	PUNCT
ejpam-3877	557	5	there	there	PRON
ejpam-3877	557	6	exist	exist	VERB
ejpam-3877	557	7	a	a	DET
ejpam-3877	557	8	zero	zero	NUM
ejpam-3877	557	9	lebesgue	lebesgue	NOUN
ejpam-3877	557	10	measure	measure	NOUN
ejpam-3877	557	11	set	set	VERB
ejpam-3877	557	12	d	d	PROPN
ejpam-3877	557	13	⊆	⊆	NUM
ejpam-3877	557	14	(	(	PUNCT
ejpam-3877	557	15	0	0	NUM
ejpam-3877	557	16	,	,	PUNCT
ejpam-3877	557	17	t	t	PROPN
ejpam-3877	557	18	)	)	PUNCT
ejpam-3877	557	19	and	and	CCONJ
ejpam-3877	557	20	a	a	DET
ejpam-3877	557	21	positive	positive	ADJ
ejpam-3877	557	22	constant	constant	ADJ
ejpam-3877	557	23	c	c	NOUN
ejpam-3877	557	24	such	such	ADJ
ejpam-3877	557	25	that	that	SCONJ
ejpam-3877	557	26	ess	ess	PROPN
ejpam-3877	557	27	lim	lim	PROPN
ejpam-3877	557	28	t→0	t→0	PROPN
ejpam-3877	558	1	+	+	CCONJ
ejpam-3877	558	2	∫	∫	PROPN
ejpam-3877	558	3	ω	ω	NUM
ejpam-3877	558	4	u	u	PROPN
ejpam-3877	558	5	(	(	PUNCT
ejpam-3877	558	6	·	·	PUNCT
ejpam-3877	558	7	,	,	PUNCT
ejpam-3877	558	8	t)dx	t)dx	NOUN
ejpam-3877	558	9	=	=	PUNCT
ejpam-3877	558	10	c	c	X
ejpam-3877	558	11	(	(	PUNCT
ejpam-3877	558	12	6.1	6.1	NUM
ejpam-3877	558	13	)	)	PUNCT
ejpam-3877	558	14	(	(	PUNCT
ejpam-3877	558	15	ii	ii	NOUN
ejpam-3877	558	16	)	)	PUNCT
ejpam-3877	558	17	for	for	ADP
ejpam-3877	558	18	any	any	DET
ejpam-3877	558	19	ρ	ρ	PROPN
ejpam-3877	558	20	∈	∈	PROPN
ejpam-3877	558	21	c2	c2	PROPN
ejpam-3877	558	22	0	0	NUM
ejpam-3877	558	23	(	(	PUNCT
ejpam-3877	558	24	ω	ω	NOUN
ejpam-3877	558	25	)	)	PUNCT
ejpam-3877	558	26	,	,	PUNCT
ejpam-3877	558	27	ρ	ρ	PROPN
ejpam-3877	558	28	≥	≥	NOUN
ejpam-3877	558	29	0	0	NUM
ejpam-3877	558	30	,	,	PUNCT
ejpam-3877	558	31	there	there	PRON
ejpam-3877	558	32	holds	hold	VERB
ejpam-3877	558	33	ess	ess	PROPN
ejpam-3877	558	34	lim	lim	PROPN
ejpam-3877	558	35	t→0	t→0	PROPN
ejpam-3877	558	36	+	+	CCONJ
ejpam-3877	558	37	〈	〈	PROPN
ejpam-3877	558	38	u	u	NOUN
ejpam-3877	558	39	(	(	PUNCT
ejpam-3877	558	40	·	·	PROPN
ejpam-3877	558	41	,	,	PUNCT
ejpam-3877	558	42	t	t	PROPN
ejpam-3877	558	43	)	)	PUNCT
ejpam-3877	558	44	,	,	PUNCT
ejpam-3877	558	45	ρ〉ω	ρ〉ω	PROPN
ejpam-3877	559	1	=	=	SYM
ejpam-3877	560	1	〈	〈	PROPN
ejpam-3877	560	2	u0	u0	ADJ
ejpam-3877	560	3	,	,	PUNCT
ejpam-3877	560	4	ρ〉ω	ρ〉ω	PROPN
ejpam-3877	560	5	(	(	PUNCT
ejpam-3877	560	6	6.2	6.2	NUM
ejpam-3877	560	7	)	)	PUNCT
ejpam-3877	560	8	for	for	ADP
ejpam-3877	560	9	almost	almost	ADV
ejpam-3877	560	10	every	every	PRON
ejpam-3877	560	11	t	t	NOUN
ejpam-3877	560	12	∈	∈	PROPN
ejpam-3877	560	13	(	(	PUNCT
ejpam-3877	560	14	0	0	NUM
ejpam-3877	560	15	,	,	PUNCT
ejpam-3877	560	16	t	t	NOUN
ejpam-3877	560	17	)	)	PUNCT
ejpam-3877	560	18	\d	\d	NOUN
ejpam-3877	560	19	.	.	PUNCT
ejpam-3877	561	1	proof	proof	NOUN
ejpam-3877	561	2	.	.	PUNCT
ejpam-3877	562	1	let	let	VERB
ejpam-3877	562	2	us	we	PRON
ejpam-3877	562	3	consider	consider	VERB
ejpam-3877	562	4	for	for	ADP
ejpam-3877	562	5	every	every	PRON
ejpam-3877	562	6	τ	τ	PROPN
ejpam-3877	562	7	>	>	X
ejpam-3877	562	8	0	0	PROPN
ejpam-3877	562	9	,	,	PUNCT
ejpam-3877	562	10	the	the	DET
ejpam-3877	562	11	smooth	smooth	ADJ
ejpam-3877	562	12	function	function	NOUN
ejpam-3877	562	13	ητ	ητ	PROPN
ejpam-3877	562	14	∈	∈	PROPN
ejpam-3877	562	15	c1	c1	PROPN
ejpam-3877	562	16	0	0	NUM
ejpam-3877	563	1	(	(	PUNCT
ejpam-3877	563	2	0	0	NUM
ejpam-3877	563	3	,	,	PUNCT
ejpam-3877	563	4	t	t	NOUN
ejpam-3877	563	5	)	)	PUNCT
ejpam-3877	563	6	,	,	PUNCT
ejpam-3877	563	7	0	0	NUM
ejpam-3877	563	8	≤	≤	NUM
ejpam-3877	563	9	ητ	ητ	VERB
ejpam-3877	563	10	≤	≤	NUM
ejpam-3877	563	11	1	1	NUM
ejpam-3877	564	1	such	such	ADJ
ejpam-3877	564	2	that	that	DET
ejpam-3877	564	3	ητ	ητ	PROPN
ejpam-3877	564	4	(	(	PUNCT
ejpam-3877	564	5	t	t	PROPN
ejpam-3877	564	6	)	)	PUNCT
ejpam-3877	564	7	=	=	PUNCT
ejpam-3877	565	1			NUM
ejpam-3877	565	2	0	0	PUNCT
ejpam-3877	566	1	if	if	SCONJ
ejpam-3877	566	2	0	0	NUM
ejpam-3877	566	3	≤	≤	NUM
ejpam-3877	566	4	t	t	PROPN
ejpam-3877	566	5	≤	≤	NUM
ejpam-3877	566	6	t1	t1	NOUN
ejpam-3877	566	7	−	−	PROPN
ejpam-3877	566	8	τ	τ	PROPN
ejpam-3877	566	9	,	,	PUNCT
ejpam-3877	566	10	1	1	NUM
ejpam-3877	566	11	τ	τ	X
ejpam-3877	566	12	(	(	PUNCT
ejpam-3877	566	13	t+	t+	NOUN
ejpam-3877	566	14	τ	τ	PROPN
ejpam-3877	566	15	−	−	PROPN
ejpam-3877	566	16	t1	t1	PROPN
ejpam-3877	566	17	)	)	PUNCT
ejpam-3877	566	18	if	if	SCONJ
ejpam-3877	566	19	t1	t1	NOUN
ejpam-3877	566	20	−	−	PROPN
ejpam-3877	566	21	τ	τ	PROPN
ejpam-3877	566	22	≤	≤	PROPN
ejpam-3877	566	23	t	t	PROPN
ejpam-3877	566	24	≤	≤	NUM
ejpam-3877	566	25	t1	t1	PROPN
ejpam-3877	566	26	,	,	PUNCT
ejpam-3877	566	27	1	1	NUM
ejpam-3877	566	28	if	if	SCONJ
ejpam-3877	566	29	t1	t1	NOUN
ejpam-3877	566	30	≤	≤	X
ejpam-3877	566	31	t	t	PROPN
ejpam-3877	566	32	≤	≤	NOUN
ejpam-3877	566	33	t2	t2	NOUN
ejpam-3877	566	34	,	,	PUNCT
ejpam-3877	566	35	1	1	NUM
ejpam-3877	566	36	τ	τ	X
ejpam-3877	566	37	(	(	PUNCT
ejpam-3877	566	38	−t+	−t+	ADJ
ejpam-3877	566	39	τ	τ	PROPN
ejpam-3877	566	40	+	+	CCONJ
ejpam-3877	566	41	t2	t2	NOUN
ejpam-3877	566	42	)	)	PUNCT
ejpam-3877	566	43	if	if	SCONJ
ejpam-3877	566	44	t2	t2	NOUN
ejpam-3877	566	45	≤	≤	X
ejpam-3877	566	46	t	t	NOUN
ejpam-3877	566	47	≤	≤	NOUN
ejpam-3877	566	48	t2	t2	NOUN
ejpam-3877	566	49	+	+	CCONJ
ejpam-3877	566	50	τ	τ	PROPN
ejpam-3877	566	51	,	,	PUNCT
ejpam-3877	566	52	0	0	PUNCT
ejpam-3877	566	53	if	if	SCONJ
ejpam-3877	566	54	t2	t2	PROPN
ejpam-3877	566	55	+	+	CCONJ
ejpam-3877	566	56	τ	τ	PROPN
ejpam-3877	566	57	≤	≤	PROPN
ejpam-3877	566	58	t	t	PROPN
ejpam-3877	566	59	≤	≤	NOUN
ejpam-3877	566	60	t.	t.	PROPN
ejpam-3877	566	61	let	let	VERB
ejpam-3877	566	62	us	we	PRON
ejpam-3877	566	63	choose	choose	VERB
ejpam-3877	566	64	ρj(x)ητ	ρj(x)ητ	PROPN
ejpam-3877	566	65	(	(	PUNCT
ejpam-3877	566	66	t	t	PROPN
ejpam-3877	566	67	)	)	PUNCT
ejpam-3877	566	68	as	as	ADP
ejpam-3877	566	69	a	a	DET
ejpam-3877	566	70	test	test	NOUN
ejpam-3877	566	71	function	function	NOUN
ejpam-3877	566	72	in	in	ADP
ejpam-3877	566	73	(	(	PUNCT
ejpam-3877	566	74	p	p	NOUN
ejpam-3877	566	75	)	)	PUNCT
ejpam-3877	566	76	,	,	PUNCT
ejpam-3877	566	77	there	there	PRON
ejpam-3877	566	78	holds∫	holds∫	VERB
ejpam-3877	566	79	t	t	PROPN
ejpam-3877	566	80	0	0	NUM
ejpam-3877	566	81	∫	∫	PROPN
ejpam-3877	566	82	ω	ω	PROPN
ejpam-3877	566	83	{	{	PUNCT
ejpam-3877	566	84	−uρj(x)η′τ	−uρj(x)η′τ	PROPN
ejpam-3877	566	85	(	(	PUNCT
ejpam-3877	566	86	t)−	t)−	PROPN
ejpam-3877	566	87	ψ(ur)ητ	ψ(ur)ητ	PROPN
ejpam-3877	566	88	(	(	PUNCT
ejpam-3877	566	89	t)∆ρj(x	t)∆ρj(x	PROPN
ejpam-3877	566	90	)	)	PUNCT
ejpam-3877	566	91	}	}	PUNCT
ejpam-3877	566	92	dxdt	dxdt	NOUN
ejpam-3877	566	93	=	=	SYM
ejpam-3877	567	1	∫	∫	PROPN
ejpam-3877	567	2	t	t	PROPN
ejpam-3877	567	3	0	0	NUM
ejpam-3877	568	1	∫	∫	PROPN
ejpam-3877	568	2	ω	ω	PROPN
ejpam-3877	568	3	µρj(x)ητ	µρj(x)ητ	X
ejpam-3877	568	4	(	(	PUNCT
ejpam-3877	568	5	t)dxdt	t)dxdt	NOUN
ejpam-3877	568	6	.	.	PUNCT
ejpam-3877	569	1	it	it	PRON
ejpam-3877	569	2	is	be	AUX
ejpam-3877	569	3	worth	worth	ADJ
ejpam-3877	569	4	observing	observe	VERB
ejpam-3877	569	5	that	that	SCONJ
ejpam-3877	569	6	the	the	DET
ejpam-3877	569	7	first	first	ADJ
ejpam-3877	569	8	term	term	NOUN
ejpam-3877	569	9	of	of	ADP
ejpam-3877	569	10	the	the	DET
ejpam-3877	569	11	left	left	ADJ
ejpam-3877	569	12	hand	hand	NOUN
ejpam-3877	569	13	side	side	NOUN
ejpam-3877	569	14	of	of	ADP
ejpam-3877	569	15	the	the	DET
ejpam-3877	569	16	above	above	ADJ
ejpam-3877	569	17	equality	equality	NOUN
ejpam-3877	569	18	becomes∫	becomes∫	X
ejpam-3877	569	19	t	t	PROPN
ejpam-3877	569	20	0	0	NUM
ejpam-3877	569	21	∫	∫	PROPN
ejpam-3877	570	1	ω	ω	PROPN
ejpam-3877	570	2	−uρj(x)η′τ	−uρj(x)η′τ	PROPN
ejpam-3877	570	3	(	(	PUNCT
ejpam-3877	570	4	t)dxdt	t)dxdt	NOUN
ejpam-3877	570	5	=	=	SYM
ejpam-3877	570	6	−1	−1	NOUN
ejpam-3877	570	7	τ	τ	PROPN
ejpam-3877	570	8	∫	∫	PROPN
ejpam-3877	570	9	t1	t1	NOUN
ejpam-3877	571	1	t1−τ	t1−τ	PROPN
ejpam-3877	571	2	∫	∫	PROPN
ejpam-3877	571	3	ω	ω	NUM
ejpam-3877	571	4	u(x	u(x	PROPN
ejpam-3877	571	5	,	,	PUNCT
ejpam-3877	571	6	t)ρj(x)dxdt+	t)ρj(x)dxdt+	PROPN
ejpam-3877	571	7	1	1	NUM
ejpam-3877	571	8	τ	τ	NUM
ejpam-3877	571	9	∫	∫	NOUN
ejpam-3877	571	10	t2+τ	t2+τ	ADP
ejpam-3877	571	11	t2	t2	PROPN
ejpam-3877	571	12	∫	∫	PROPN
ejpam-3877	571	13	ω	ω	PROPN
ejpam-3877	571	14	u(x	u(x	PROPN
ejpam-3877	571	15	,	,	PUNCT
ejpam-3877	571	16	t)ρj(x)dxdt	t)ρj(x)dxdt	PROPN
ejpam-3877	571	17	.	.	PUNCT
ejpam-3877	572	1	let	let	VERB
ejpam-3877	572	2	us	we	PRON
ejpam-3877	572	3	consider	consider	VERB
ejpam-3877	572	4	a	a	DET
ejpam-3877	572	5	zero	zero	NUM
ejpam-3877	572	6	lebesgue	lebesgue	NOUN
ejpam-3877	572	7	measure	measure	NOUN
ejpam-3877	572	8	set	set	VERB
ejpam-3877	572	9	dj	dj	NOUN
ejpam-3877	572	10	in	in	ADP
ejpam-3877	572	11	(	(	PUNCT
ejpam-3877	572	12	0	0	NUM
ejpam-3877	572	13	,	,	PUNCT
ejpam-3877	572	14	t	t	NOUN
ejpam-3877	572	15	)	)	PUNCT
ejpam-3877	572	16	such	such	ADJ
ejpam-3877	572	17	that	that	PRON
ejpam-3877	572	18	for	for	ADP
ejpam-3877	572	19	any	any	DET
ejpam-3877	572	20	t1	t1	NOUN
ejpam-3877	572	21	,	,	PUNCT
ejpam-3877	572	22	t2	t2	PROPN
ejpam-3877	572	23	∈	∈	PROPN
ejpam-3877	572	24	(	(	PUNCT
ejpam-3877	572	25	0	0	NUM
ejpam-3877	572	26	,	,	PUNCT
ejpam-3877	572	27	t	t	NOUN
ejpam-3877	572	28	)	)	PUNCT
ejpam-3877	572	29	\dj	\dj	PROPN
ejpam-3877	572	30	,	,	PUNCT
ejpam-3877	572	31	one	one	NUM
ejpam-3877	572	32	has	have	VERB
ejpam-3877	572	33	lim	lim	PROPN
ejpam-3877	572	34	τ→0	τ→0	PUNCT
ejpam-3877	573	1	∫	∫	PROPN
ejpam-3877	573	2	t	t	PROPN
ejpam-3877	573	3	0	0	NUM
ejpam-3877	574	1	∫	∫	PROPN
ejpam-3877	574	2	ω	ω	PROPN
ejpam-3877	574	3	−uρj(x)η′τ	−uρj(x)η′τ	PROPN
ejpam-3877	574	4	(	(	PUNCT
ejpam-3877	574	5	x	x	NOUN
ejpam-3877	574	6	,	,	PUNCT
ejpam-3877	574	7	t)dxdt	t)dxdt	NOUN
ejpam-3877	574	8	=	=	SYM
ejpam-3877	574	9	−	−	PROPN
ejpam-3877	574	10	∫	∫	PROPN
ejpam-3877	574	11	ω	ω	NUM
ejpam-3877	574	12	u(x	u(x	PROPN
ejpam-3877	574	13	,	,	PUNCT
ejpam-3877	574	14	t1)ρj(x)dx+	t1)ρj(x)dx+	NOUN
ejpam-3877	574	15	∫	∫	PROPN
ejpam-3877	574	16	ω	ω	NUM
ejpam-3877	574	17	u(x	u(x	PROPN
ejpam-3877	574	18	,	,	PUNCT
ejpam-3877	574	19	t2)ρj(x)dx	t2)ρj(x)dx	NUM
ejpam-3877	574	20	.	.	PUNCT
ejpam-3877	575	1	quincy	quincy	PROPN
ejpam-3877	575	2	s.	s.	PROPN
ejpam-3877	575	3	nkombo	nkombo	PROPN
ejpam-3877	575	4	,	,	PUNCT
ejpam-3877	575	5	fengquan	fengquan	PROPN
ejpam-3877	575	6	li	li	PROPN
ejpam-3877	575	7	/	/	SYM
ejpam-3877	575	8	eur	eur	PROPN
ejpam-3877	575	9	.	.	PUNCT
ejpam-3877	576	1	j.	j.	PROPN
ejpam-3877	576	2	pure	pure	PROPN
ejpam-3877	576	3	appl	appl	PROPN
ejpam-3877	576	4	.	.	PROPN
ejpam-3877	576	5	math	math	PROPN
ejpam-3877	576	6	,	,	PUNCT
ejpam-3877	576	7	14	14	NUM
ejpam-3877	576	8	(	(	PUNCT
ejpam-3877	576	9	1	1	NUM
ejpam-3877	576	10	)	)	PUNCT
ejpam-3877	576	11	(	(	PUNCT
ejpam-3877	576	12	2021	2021	NUM
ejpam-3877	576	13	)	)	PUNCT
ejpam-3877	576	14	,	,	PUNCT
ejpam-3877	576	15	204	204	NUM
ejpam-3877	576	16	-	-	SYM
ejpam-3877	576	17	233	233	NUM
ejpam-3877	576	18	226	226	NUM
ejpam-3877	576	19	we	we	PRON
ejpam-3877	576	20	use	use	VERB
ejpam-3877	576	21	a	a	DET
ejpam-3877	576	22	sequence	sequence	NOUN
ejpam-3877	576	23	{	{	PUNCT
ejpam-3877	576	24	ρj(x)}j∈n	ρj(x)}j∈n	NUM
ejpam-3877	576	25	of	of	ADP
ejpam-3877	576	26	test	test	NOUN
ejpam-3877	576	27	functions	function	NOUN
ejpam-3877	576	28	in	in	ADP
ejpam-3877	576	29	ω	ω	NUM
ejpam-3877	577	1	such	such	ADJ
ejpam-3877	577	2	that	that	SCONJ
ejpam-3877	577	3	ρj(x	ρj(x	ADJ
ejpam-3877	577	4	)	)	PUNCT
ejpam-3877	577	5	∈	∈	PROPN
ejpam-3877	577	6	c2	c2	PROPN
ejpam-3877	577	7	0	0	NUM
ejpam-3877	577	8	(	(	PUNCT
ejpam-3877	577	9	ω	ω	NOUN
ejpam-3877	577	10	)	)	PUNCT
ejpam-3877	577	11	,	,	PUNCT
ejpam-3877	577	12	0	0	NUM
ejpam-3877	577	13	≤	≤	NUM
ejpam-3877	577	14	ρj(x	ρj(x	NOUN
ejpam-3877	577	15	)	)	PUNCT
ejpam-3877	577	16	≤	≤	NUM
ejpam-3877	577	17	1	1	NUM
ejpam-3877	577	18	,	,	PUNCT
ejpam-3877	577	19	ρj(x	ρj(x	X
ejpam-3877	577	20	)	)	PUNCT
ejpam-3877	577	21	→	→	SYM
ejpam-3877	577	22	1	1	NUM
ejpam-3877	577	23	in	in	ADP
ejpam-3877	577	24	ω	ω	NUM
ejpam-3877	577	25	and	and	CCONJ
ejpam-3877	577	26	−∆ρj(x	−∆ρj(x	NUM
ejpam-3877	577	27	)	)	PUNCT
ejpam-3877	577	28	≥	≥	X
ejpam-3877	577	29	0	0	PUNCT
ejpam-3877	577	30	(	(	PUNCT
ejpam-3877	577	31	for	for	ADP
ejpam-3877	577	32	instance	instance	NOUN
ejpam-3877	577	33	,	,	PUNCT
ejpam-3877	577	34	ρj(x	ρj(x	X
ejpam-3877	577	35	)	)	PUNCT
ejpam-3877	577	36	=	=	SYM
ejpam-3877	577	37	1−(1−	1−(1−	NUM
ejpam-3877	577	38	φ)j	φ)j	X
ejpam-3877	577	39	,	,	PUNCT
ejpam-3877	577	40	where	where	SCONJ
ejpam-3877	577	41	φ	φ	PROPN
ejpam-3877	577	42	is	be	AUX
ejpam-3877	577	43	the	the	DET
ejpam-3877	577	44	first	first	ADJ
ejpam-3877	577	45	eigenfunction	eigenfunction	NOUN
ejpam-3877	577	46	of	of	ADP
ejpam-3877	577	47	−∆	−∆	NOUN
ejpam-3877	577	48	in	in	ADP
ejpam-3877	577	49	h1	h1	PROPN
ejpam-3877	577	50	0	0	NUM
ejpam-3877	577	51	(	(	PUNCT
ejpam-3877	577	52	ω	ω	NOUN
ejpam-3877	577	53	)	)	PUNCT
ejpam-3877	577	54	,	,	PUNCT
ejpam-3877	578	1	with	with	ADP
ejpam-3877	578	2	normalization	normalization	NOUN
ejpam-3877	578	3	maxφ	maxφ	PROPN
ejpam-3877	579	1	=	=	SYM
ejpam-3877	580	1	1)(see	1)(see	NOUN
ejpam-3877	581	1	[	[	X
ejpam-3877	581	2	6	6	NUM
ejpam-3877	581	3	]	]	PUNCT
ejpam-3877	581	4	reference	reference	NOUN
ejpam-3877	581	5	therein	therein	ADV
ejpam-3877	581	6	)	)	PUNCT
ejpam-3877	581	7	.	.	PUNCT
ejpam-3877	582	1	for	for	ADP
ejpam-3877	582	2	every	every	DET
ejpam-3877	582	3	s	s	X
ejpam-3877	582	4	∈	∈	PROPN
ejpam-3877	582	5	(	(	PUNCT
ejpam-3877	582	6	0	0	NUM
ejpam-3877	582	7	,	,	PUNCT
ejpam-3877	582	8	t	t	NOUN
ejpam-3877	582	9	)	)	PUNCT
ejpam-3877	582	10	\dj	\dj	PROPN
ejpam-3877	582	11	,	,	PUNCT
ejpam-3877	582	12	there	there	PRON
ejpam-3877	582	13	holds∫	holds∫	VERB
ejpam-3877	582	14	ω	ω	NUM
ejpam-3877	582	15	u(x	u(x	NOUN
ejpam-3877	582	16	,	,	PUNCT
ejpam-3877	582	17	t)ρj(x)dx−	t)ρj(x)dx−	PROPN
ejpam-3877	582	18	∫	∫	PROPN
ejpam-3877	582	19	qt	qt	X
ejpam-3877	582	20	ψ(ur)∆ρj(x)dxds	ψ(ur)∆ρj(x)dxds	PROPN
ejpam-3877	582	21	=	=	SYM
ejpam-3877	582	22	∫	∫	PROPN
ejpam-3877	582	23	qt	qt	PROPN
ejpam-3877	582	24	ρj(x)dµ+	ρj(x)dµ+	PROPN
ejpam-3877	582	25	∫	∫	PROPN
ejpam-3877	582	26	ω	ω	PROPN
ejpam-3877	582	27	ρj(x)du0	ρj(x)du0	NOUN
ejpam-3877	582	28	.	.	PUNCT
ejpam-3877	583	1	let	let	VERB
ejpam-3877	583	2	j	j	PROPN
ejpam-3877	583	3	goes	go	VERB
ejpam-3877	583	4	to	to	ADP
ejpam-3877	583	5	infinity	infinity	NOUN
ejpam-3877	583	6	,	,	PUNCT
ejpam-3877	583	7	then	then	ADV
ejpam-3877	583	8	we	we	PRON
ejpam-3877	583	9	get	get	VERB
ejpam-3877	583	10	that	that	PRON
ejpam-3877	583	11	d	d	PROPN
ejpam-3877	583	12	≡	≡	PROPN
ejpam-3877	583	13	⋃	⋃	NOUN
ejpam-3877	583	14	j∈n	j∈n	NOUN
ejpam-3877	583	15	dj	dj	NOUN
ejpam-3877	583	16	which	which	PRON
ejpam-3877	583	17	leads	lead	VERB
ejpam-3877	583	18	to	to	ADP
ejpam-3877	583	19	∫	∫	PROPN
ejpam-3877	583	20	ω	ω	PROPN
ejpam-3877	583	21	u(x	u(x	PROPN
ejpam-3877	583	22	,	,	PUNCT
ejpam-3877	583	23	t)dx	t)dx	PROPN
ejpam-3877	583	24	≤	≤	NUM
ejpam-3877	583	25	∫	∫	PROPN
ejpam-3877	583	26	qt	qt	PROPN
ejpam-3877	583	27	dµ+	dµ+	PROPN
ejpam-3877	583	28	∫	∫	PROPN
ejpam-3877	583	29	ω	ω	PROPN
ejpam-3877	583	30	du0	du0	PROPN
ejpam-3877	583	31	.	.	PUNCT
ejpam-3877	584	1	now	now	ADV
ejpam-3877	584	2	let	let	VERB
ejpam-3877	584	3	us	we	PRON
ejpam-3877	584	4	consider	consider	VERB
ejpam-3877	584	5	{	{	PUNCT
ejpam-3877	584	6	φk	φk	PART
ejpam-3877	584	7	}	}	PUNCT
ejpam-3877	584	8	be	be	AUX
ejpam-3877	584	9	a	a	DET
ejpam-3877	584	10	sequence	sequence	NOUN
ejpam-3877	584	11	of	of	ADP
ejpam-3877	584	12	c0(ω	c0(ω	NOUN
ejpam-3877	584	13	)	)	PUNCT
ejpam-3877	584	14	functions	function	NOUN
ejpam-3877	584	15	such	such	ADJ
ejpam-3877	584	16	that	that	SCONJ
ejpam-3877	584	17	0	0	NUM
ejpam-3877	584	18	≤	≤	NUM
ejpam-3877	584	19	φj	φj	ADP
ejpam-3877	584	20	≤	≤	NUM
ejpam-3877	584	21	1	1	NUM
ejpam-3877	584	22	,	,	PUNCT
ejpam-3877	584	23	φk	φk	ADP
ejpam-3877	584	24	→	→	SYM
ejpam-3877	584	25	1	1	NUM
ejpam-3877	584	26	as	as	ADP
ejpam-3877	584	27	j	j	PROPN
ejpam-3877	584	28	→∞.	→∞.	PUNCT
ejpam-3877	584	29	by	by	ADP
ejpam-3877	584	30	[	[	X
ejpam-3877	584	31	12	12	NUM
ejpam-3877	584	32	,	,	PUNCT
ejpam-3877	584	33	lemma	lemma	PROPN
ejpam-3877	584	34	5.1	5.1	NUM
ejpam-3877	584	35	]	]	PUNCT
ejpam-3877	584	36	,	,	PUNCT
ejpam-3877	584	37	the	the	DET
ejpam-3877	584	38	following	follow	VERB
ejpam-3877	584	39	statement	statement	NOUN
ejpam-3877	584	40	hold∫	hold∫	NOUN
ejpam-3877	584	41	ω	ω	NUM
ejpam-3877	584	42	φjdu0	φjdu0	NOUN
ejpam-3877	584	43	≤	≤	NUM
ejpam-3877	584	44	1	1	NUM
ejpam-3877	584	45	j	j	NOUN
ejpam-3877	584	46	and	and	CCONJ
ejpam-3877	584	47	∫	∫	PROPN
ejpam-3877	584	48	qt	qt	PROPN
ejpam-3877	584	49	φjdµ	φjdµ	VERB
ejpam-3877	584	50	≤	≤	NUM
ejpam-3877	584	51	1	1	NUM
ejpam-3877	585	1	j	j	NOUN
ejpam-3877	585	2	then∫	then∫	NOUN
ejpam-3877	585	3	qt	qt	PROPN
ejpam-3877	586	1	dµ+	dµ+	PROPN
ejpam-3877	586	2	∫	∫	PROPN
ejpam-3877	586	3	ω	ω	PROPN
ejpam-3877	586	4	du0−	du0−	PROPN
ejpam-3877	586	5	∫	∫	PROPN
ejpam-3877	586	6	ω	ω	PROPN
ejpam-3877	586	7	u(x	u(x	PROPN
ejpam-3877	586	8	,	,	PUNCT
ejpam-3877	586	9	t)dx	t)dx	PROPN
ejpam-3877	586	10	=	=	SYM
ejpam-3877	586	11	∫	∫	PROPN
ejpam-3877	586	12	qt	qt	PROPN
ejpam-3877	586	13	(	(	PUNCT
ejpam-3877	586	14	1−	1−	NUM
ejpam-3877	586	15	φj	φj	NOUN
ejpam-3877	586	16	)	)	PUNCT
ejpam-3877	586	17	dµ+	dµ+	NOUN
ejpam-3877	586	18	∫	∫	PROPN
ejpam-3877	587	1	qt	qt	PROPN
ejpam-3877	587	2	φjdµ+	φjdµ+	X
ejpam-3877	587	3	∫	∫	PROPN
ejpam-3877	587	4	ω	ω	PROPN
ejpam-3877	587	5	(	(	PUNCT
ejpam-3877	587	6	1−	1−	NUM
ejpam-3877	587	7	φj	φj	NOUN
ejpam-3877	587	8	)	)	PUNCT
ejpam-3877	587	9	du0	du0	NOUN
ejpam-3877	587	10	+	+	CCONJ
ejpam-3877	587	11	∫	∫	PROPN
ejpam-3877	587	12	ω	ω	NUM
ejpam-3877	587	13	φjdu0−	φjdu0−	NOUN
ejpam-3877	587	14	−	−	PROPN
ejpam-3877	587	15	∫	∫	PROPN
ejpam-3877	587	16	ω	ω	PROPN
ejpam-3877	587	17	u(x	u(x	PROPN
ejpam-3877	587	18	,	,	PUNCT
ejpam-3877	587	19	t)φjdx+	t)φjdx+	PROPN
ejpam-3877	587	20	∫	∫	PROPN
ejpam-3877	587	21	ω	ω	PROPN
ejpam-3877	587	22	u(x	u(x	PROPN
ejpam-3877	587	23	,	,	PUNCT
ejpam-3877	587	24	t	t	PROPN
ejpam-3877	587	25	)	)	PUNCT
ejpam-3877	587	26	(	(	PUNCT
ejpam-3877	587	27	φj	φj	ADP
ejpam-3877	587	28	−	−	NUM
ejpam-3877	587	29	1	1	NUM
ejpam-3877	587	30	)	)	PUNCT
ejpam-3877	587	31	dx	dx	PROPN
ejpam-3877	587	32	.	.	PUNCT
ejpam-3877	588	1	since	since	SCONJ
ejpam-3877	588	2	φj	φj	ADP
ejpam-3877	588	3	≤	≤	NUM
ejpam-3877	588	4	1	1	NUM
ejpam-3877	588	5	yields∫	yields∫	PROPN
ejpam-3877	588	6	qt	qt	PROPN
ejpam-3877	588	7	dµ+	dµ+	PROPN
ejpam-3877	588	8	∫	∫	PROPN
ejpam-3877	588	9	ω	ω	PROPN
ejpam-3877	588	10	du0	du0	PROPN
ejpam-3877	588	11	−	−	PROPN
ejpam-3877	588	12	∫	∫	PROPN
ejpam-3877	588	13	ω	ω	PROPN
ejpam-3877	588	14	u(x	u(x	PROPN
ejpam-3877	588	15	,	,	PUNCT
ejpam-3877	588	16	t)dx	t)dx	PROPN
ejpam-3877	588	17	≤	≤	NUM
ejpam-3877	588	18	∫	∫	NOUN
ejpam-3877	588	19	qt	qt	PROPN
ejpam-3877	588	20	(	(	PUNCT
ejpam-3877	588	21	1−	1−	NUM
ejpam-3877	588	22	φj	φj	NOUN
ejpam-3877	588	23	)	)	PUNCT
ejpam-3877	588	24	dµ+	dµ+	NOUN
ejpam-3877	588	25	∫	∫	PROPN
ejpam-3877	588	26	ω	ω	PROPN
ejpam-3877	589	1	(	(	PUNCT
ejpam-3877	589	2	1−	1−	NUM
ejpam-3877	589	3	φj	φj	NOUN
ejpam-3877	589	4	)	)	PUNCT
ejpam-3877	589	5	du0	du0	NOUN
ejpam-3877	589	6	−	−	PROPN
ejpam-3877	589	7	∫	∫	PROPN
ejpam-3877	589	8	ω	ω	PROPN
ejpam-3877	589	9	u(x	u(x	PROPN
ejpam-3877	589	10	,	,	PUNCT
ejpam-3877	589	11	t)φjdx+	t)φjdx+	NOUN
ejpam-3877	589	12	2	2	NUM
ejpam-3877	589	13	j	j	PROPN
ejpam-3877	589	14	.	.	PUNCT
ejpam-3877	590	1	since	since	SCONJ
ejpam-3877	590	2	u(x	u(x	PROPN
ejpam-3877	590	3	,	,	PUNCT
ejpam-3877	590	4	t	t	PROPN
ejpam-3877	590	5	)	)	PUNCT
ejpam-3877	590	6	converges	converge	NOUN
ejpam-3877	590	7	to	to	PART
ejpam-3877	590	8	δx	δx	VERB
ejpam-3877	590	9	,	,	PUNCT
ejpam-3877	590	10	we	we	PRON
ejpam-3877	590	11	get	get	VERB
ejpam-3877	590	12	lim	lim	PROPN
ejpam-3877	590	13	sup	sup	PROPN
ejpam-3877	590	14	t→0	t→0	PROPN
ejpam-3877	591	1	+	+	NUM
ejpam-3877	592	1	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-3877	593	1	ω	ω	NOUN
ejpam-3877	593	2	du0	du0	NOUN
ejpam-3877	593	3	−	−	PROPN
ejpam-3877	593	4	∫	∫	PROPN
ejpam-3877	593	5	ω	ω	PROPN
ejpam-3877	593	6	u(x	u(x	PROPN
ejpam-3877	593	7	,	,	PUNCT
ejpam-3877	593	8	t)dx	t)dx	PROPN
ejpam-3877	593	9	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3877	593	10	≤	≤	NUM
ejpam-3877	593	11	∫	∫	PROPN
ejpam-3877	593	12	ω	ω	PROPN
ejpam-3877	593	13	(	(	PUNCT
ejpam-3877	593	14	1−	1−	NUM
ejpam-3877	593	15	φj	φj	NOUN
ejpam-3877	593	16	)	)	PUNCT
ejpam-3877	594	1	du0	du0	NOUN
ejpam-3877	594	2	+	+	NOUN
ejpam-3877	594	3	2	2	NUM
ejpam-3877	594	4	j	j	NOUN
ejpam-3877	594	5	.	.	PUNCT
ejpam-3877	595	1	let	let	VERB
ejpam-3877	595	2	j	j	PROPN
ejpam-3877	595	3	to	to	PART
ejpam-3877	595	4	infinity	infinity	VERB
ejpam-3877	595	5	,	,	PUNCT
ejpam-3877	595	6	there	there	PRON
ejpam-3877	595	7	exists	exist	VERB
ejpam-3877	595	8	a	a	DET
ejpam-3877	595	9	positive	positive	ADJ
ejpam-3877	595	10	constant	constant	ADJ
ejpam-3877	595	11	c	c	NOUN
ejpam-3877	595	12	such	such	ADJ
ejpam-3877	595	13	that	that	SCONJ
ejpam-3877	595	14	(	(	PUNCT
ejpam-3877	595	15	6.1	6.1	NUM
ejpam-3877	595	16	)	)	PUNCT
ejpam-3877	595	17	holds	hold	VERB
ejpam-3877	595	18	.	.	PUNCT
ejpam-3877	596	1	using	use	VERB
ejpam-3877	596	2	the	the	DET
ejpam-3877	596	3	same	same	ADJ
ejpam-3877	596	4	method	method	NOUN
ejpam-3877	596	5	as	as	ADP
ejpam-3877	596	6	the	the	DET
ejpam-3877	596	7	previous	previous	ADJ
ejpam-3877	596	8	,	,	PUNCT
ejpam-3877	596	9	it	it	PRON
ejpam-3877	596	10	is	be	AUX
ejpam-3877	596	11	obvious	obvious	ADJ
ejpam-3877	596	12	that	that	SCONJ
ejpam-3877	596	13	for	for	ADP
ejpam-3877	596	14	every	every	DET
ejpam-3877	596	15	ρ	ρ	PROPN
ejpam-3877	596	16	∈	∈	PROPN
ejpam-3877	596	17	c2	c2	PROPN
ejpam-3877	596	18	0	0	NUM
ejpam-3877	596	19	(	(	PUNCT
ejpam-3877	596	20	ω	ω	NOUN
ejpam-3877	596	21	)	)	PUNCT
ejpam-3877	596	22	ess	ess	PROPN
ejpam-3877	596	23	lim	lim	PROPN
ejpam-3877	596	24	t→0	t→0	PROPN
ejpam-3877	596	25	+	+	CCONJ
ejpam-3877	596	26	〈	〈	PROPN
ejpam-3877	596	27	u(x	u(x	NOUN
ejpam-3877	596	28	,	,	PUNCT
ejpam-3877	596	29	t	t	PROPN
ejpam-3877	596	30	)	)	PUNCT
ejpam-3877	596	31	,	,	PUNCT
ejpam-3877	596	32	ρ〉ω	ρ〉ω	PROPN
ejpam-3877	596	33	=	=	SYM
ejpam-3877	596	34	〈	〈	PROPN
ejpam-3877	596	35	u0	u0	NOUN
ejpam-3877	596	36	,	,	PUNCT
ejpam-3877	596	37	ρ〉ω	ρ〉ω	PROPN
ejpam-3877	596	38	.	.	PUNCT
ejpam-3877	597	1	quincy	quincy	PROPN
ejpam-3877	597	2	s.	s.	PROPN
ejpam-3877	597	3	nkombo	nkombo	PROPN
ejpam-3877	597	4	,	,	PUNCT
ejpam-3877	597	5	fengquan	fengquan	PROPN
ejpam-3877	597	6	li	li	PROPN
ejpam-3877	597	7	/	/	SYM
ejpam-3877	597	8	eur	eur	PROPN
ejpam-3877	597	9	.	.	PUNCT
ejpam-3877	598	1	j.	j.	PROPN
ejpam-3877	598	2	pure	pure	PROPN
ejpam-3877	598	3	appl	appl	PROPN
ejpam-3877	598	4	.	.	PROPN
ejpam-3877	598	5	math	math	PROPN
ejpam-3877	598	6	,	,	PUNCT
ejpam-3877	598	7	14	14	NUM
ejpam-3877	598	8	(	(	PUNCT
ejpam-3877	598	9	1	1	NUM
ejpam-3877	598	10	)	)	PUNCT
ejpam-3877	598	11	(	(	PUNCT
ejpam-3877	598	12	2021	2021	NUM
ejpam-3877	598	13	)	)	PUNCT
ejpam-3877	598	14	,	,	PUNCT
ejpam-3877	598	15	204	204	NUM
ejpam-3877	598	16	-	-	SYM
ejpam-3877	598	17	233	233	NUM
ejpam-3877	598	18	227	227	NUM
ejpam-3877	598	19	hence	hence	ADV
ejpam-3877	598	20	(	(	PUNCT
ejpam-3877	598	21	6.2	6.2	NUM
ejpam-3877	598	22	)	)	PUNCT
ejpam-3877	598	23	is	be	AUX
ejpam-3877	598	24	satisfied	satisfied	ADJ
ejpam-3877	598	25	.	.	PUNCT
ejpam-3877	599	1	�	�	PROPN
ejpam-3877	599	2	for	for	ADP
ejpam-3877	599	3	every	every	DET
ejpam-3877	599	4	g	g	PROPN
ejpam-3877	599	5	∈	∈	PROPN
ejpam-3877	599	6	c1(r	c1(r	PROPN
ejpam-3877	599	7	)	)	PUNCT
ejpam-3877	599	8	g(s	g(s	NOUN
ejpam-3877	599	9	)	)	PUNCT
ejpam-3877	599	10	=	=	SYM
ejpam-3877	600	1	∫	∫	PROPN
ejpam-3877	600	2	s	s	PART
ejpam-3877	600	3	0	0	NUM
ejpam-3877	600	4	g(ψ(z))dz	g(ψ(z))dz	NOUN
ejpam-3877	600	5	.	.	PUNCT
ejpam-3877	601	1	(	(	PUNCT
ejpam-3877	601	2	6.3	6.3	NUM
ejpam-3877	601	3	)	)	PUNCT
ejpam-3877	601	4	assuming	assume	VERB
ejpam-3877	601	5	(	(	PUNCT
ejpam-3877	601	6	i	i	NOUN
ejpam-3877	601	7	)	)	PUNCT
ejpam-3877	601	8	holds	hold	VERB
ejpam-3877	601	9	.	.	PUNCT
ejpam-3877	602	1	let	let	VERB
ejpam-3877	602	2	us	we	PRON
ejpam-3877	602	3	state	state	VERB
ejpam-3877	602	4	the	the	DET
ejpam-3877	602	5	following	follow	VERB
ejpam-3877	602	6	definition	definition	NOUN
ejpam-3877	602	7	.	.	PUNCT
ejpam-3877	603	1	definition	definition	NOUN
ejpam-3877	603	2	6.1	6.1	NUM
ejpam-3877	603	3	.	.	PUNCT
ejpam-3877	604	1	for	for	ADP
ejpam-3877	604	2	any	any	DET
ejpam-3877	604	3	µ	µ	PROPN
ejpam-3877	604	4	∈	∈	NOUN
ejpam-3877	604	5	m+	m+	NUM
ejpam-3877	604	6	d,2(q	d,2(q	NOUN
ejpam-3877	604	7	)	)	PUNCT
ejpam-3877	604	8	and	and	CCONJ
ejpam-3877	604	9	u0	u0	PROPN
ejpam-3877	604	10	∈	∈	PROPN
ejpam-3877	604	11	m+	m+	NUM
ejpam-3877	604	12	d,2(ω	d,2(ω	PROPN
ejpam-3877	604	13	)	)	PUNCT
ejpam-3877	604	14	,	,	PUNCT
ejpam-3877	604	15	a	a	DET
ejpam-3877	604	16	measure	measure	NOUN
ejpam-3877	604	17	u	u	NOUN
ejpam-3877	604	18	is	be	AUX
ejpam-3877	604	19	called	call	VERB
ejpam-3877	604	20	a	a	DET
ejpam-3877	604	21	weak	weak	ADJ
ejpam-3877	604	22	entropy	entropy	NOUN
ejpam-3877	604	23	solution	solution	NOUN
ejpam-3877	604	24	,	,	PUNCT
ejpam-3877	604	25	if	if	SCONJ
ejpam-3877	604	26	u	u	NOUN
ejpam-3877	604	27	is	be	AUX
ejpam-3877	604	28	a	a	DET
ejpam-3877	604	29	weak	weak	ADJ
ejpam-3877	604	30	solution	solution	NOUN
ejpam-3877	604	31	of	of	ADP
ejpam-3877	604	32	(	(	PUNCT
ejpam-3877	604	33	p	p	NOUN
ejpam-3877	604	34	)	)	PUNCT
ejpam-3877	604	35	such	such	ADJ
ejpam-3877	604	36	that	that	PRON
ejpam-3877	604	37	for	for	ADP
ejpam-3877	604	38	every	every	DET
ejpam-3877	604	39	g	g	PROPN
ejpam-3877	604	40	∈	∈	PROPN
ejpam-3877	604	41	c1(r	c1(r	PROPN
ejpam-3877	604	42	)	)	PUNCT
ejpam-3877	604	43	,	,	PUNCT
ejpam-3877	604	44	g′	g′	NOUN
ejpam-3877	604	45	≥	≥	NOUN
ejpam-3877	604	46	0	0	NUM
ejpam-3877	604	47	,	,	PUNCT
ejpam-3877	604	48	g(γ	g(γ	PROPN
ejpam-3877	604	49	)	)	PUNCT
ejpam-3877	604	50	=	=	SYM
ejpam-3877	604	51	0	0	NUM
ejpam-3877	604	52	,	,	PUNCT
ejpam-3877	604	53	the	the	DET
ejpam-3877	604	54	inequality	inequality	NOUN
ejpam-3877	604	55	holds∫	holds∫	VERB
ejpam-3877	604	56	q	q	NOUN
ejpam-3877	604	57	{	{	PUNCT
ejpam-3877	604	58	g′(ψ(ur	g′(ψ(ur	PROPN
ejpam-3877	604	59	)	)	PUNCT
ejpam-3877	604	60	)	)	PUNCT
ejpam-3877	605	1	|	|	ADV
ejpam-3877	605	2	∇ψ(ur	∇ψ(ur	NOUN
ejpam-3877	605	3	)	)	PUNCT
ejpam-3877	605	4	|2	|2	NUM
ejpam-3877	605	5	φ+	φ+	NOUN
ejpam-3877	605	6	g(ψ(ur))∇ψ(ur)∇φ−g(ur)φt	g(ψ(ur))∇ψ(ur)∇φ−g(ur)φt	PROPN
ejpam-3877	605	7	}	}	PUNCT
ejpam-3877	605	8	dxdt	dxdt	NOUN
ejpam-3877	605	9	≤	≤	NUM
ejpam-3877	605	10	∫	∫	PROPN
ejpam-3877	606	1	q	q	PROPN
ejpam-3877	606	2	g(ψ(ur))φdµ+	g(ψ(ur))φdµ+	PROPN
ejpam-3877	606	3	∫	∫	PROPN
ejpam-3877	606	4	ω	ω	PROPN
ejpam-3877	606	5	g(u0r)φ(0)dx	g(u0r)φ(0)dx	NOUN
ejpam-3877	606	6	(	(	PUNCT
ejpam-3877	606	7	6.4	6.4	NUM
ejpam-3877	606	8	)	)	PUNCT
ejpam-3877	606	9	for	for	ADP
ejpam-3877	606	10	every	every	DET
ejpam-3877	606	11	φ	φ	PROPN
ejpam-3877	606	12	∈	∈	PROPN
ejpam-3877	606	13	c1([0	c1([0	PROPN
ejpam-3877	606	14	,	,	PUNCT
ejpam-3877	606	15	t	t	X
ejpam-3877	606	16	]	]	PUNCT
ejpam-3877	606	17	,	,	PUNCT
ejpam-3877	606	18	c1	c1	PROPN
ejpam-3877	606	19	0	0	NUM
ejpam-3877	606	20	(	(	PUNCT
ejpam-3877	606	21	ω	ω	NOUN
ejpam-3877	606	22	)	)	PUNCT
ejpam-3877	606	23	)	)	PUNCT
ejpam-3877	606	24	,	,	PUNCT
ejpam-3877	606	25	φ	φ	PROPN
ejpam-3877	606	26	(	(	PUNCT
ejpam-3877	606	27	.	.	PROPN
ejpam-3877	606	28	,	,	PUNCT
ejpam-3877	606	29	t	t	NOUN
ejpam-3877	606	30	)	)	PUNCT
ejpam-3877	606	31	=	=	SYM
ejpam-3877	606	32	0	0	NUM
ejpam-3877	606	33	in	in	ADP
ejpam-3877	606	34	ω	ω	PROPN
ejpam-3877	606	35	and	and	CCONJ
ejpam-3877	606	36	φ	φ	PROPN
ejpam-3877	606	37	≥	≥	PROPN
ejpam-3877	606	38	0	0	NUM
ejpam-3877	606	39	.	.	PUNCT
ejpam-3877	607	1	by	by	ADP
ejpam-3877	607	2	the	the	DET
ejpam-3877	607	3	definition	definition	NOUN
ejpam-3877	607	4	6.1	6.1	NUM
ejpam-3877	607	5	,	,	PUNCT
ejpam-3877	607	6	the	the	DET
ejpam-3877	607	7	existence	existence	NOUN
ejpam-3877	607	8	of	of	ADP
ejpam-3877	607	9	weak	weak	ADJ
ejpam-3877	607	10	entropy	entropy	NOUN
ejpam-3877	607	11	solutions	solution	NOUN
ejpam-3877	607	12	of	of	ADP
ejpam-3877	607	13	problem	problem	NOUN
ejpam-3877	607	14	(	(	PUNCT
ejpam-3877	607	15	p	p	NOUN
ejpam-3877	607	16	)	)	PUNCT
ejpam-3877	607	17	is	be	AUX
ejpam-3877	607	18	the	the	DET
ejpam-3877	607	19	same	same	ADJ
ejpam-3877	607	20	as	as	SCONJ
ejpam-3877	607	21	stated	state	VERB
ejpam-3877	607	22	in	in	ADP
ejpam-3877	607	23	[	[	X
ejpam-3877	607	24	23	23	NUM
ejpam-3877	607	25	,	,	PUNCT
ejpam-3877	607	26	theorem	theorem	VERB
ejpam-3877	607	27	2.8	2.8	NUM
ejpam-3877	607	28	]	]	PUNCT
ejpam-3877	607	29	.	.	PUNCT
ejpam-3877	608	1	for	for	ADP
ejpam-3877	608	2	that	that	PRON
ejpam-3877	608	3	we	we	PRON
ejpam-3877	608	4	use	use	VERB
ejpam-3877	608	5	entropy	entropy	NOUN
ejpam-3877	608	6	inequality	inequality	NOUN
ejpam-3877	608	7	to	to	PART
ejpam-3877	608	8	prove	prove	VERB
ejpam-3877	608	9	the	the	DET
ejpam-3877	608	10	monotonicity	monotonicity	NOUN
ejpam-3877	608	11	of	of	ADP
ejpam-3877	608	12	solutions	solution	NOUN
ejpam-3877	608	13	given	give	VERB
ejpam-3877	608	14	by	by	ADP
ejpam-3877	608	15	the	the	DET
ejpam-3877	608	16	following	follow	VERB
ejpam-3877	608	17	proposition	proposition	NOUN
ejpam-3877	608	18	.	.	PUNCT
ejpam-3877	609	1	proposition	proposition	NOUN
ejpam-3877	609	2	6.1	6.1	NUM
ejpam-3877	609	3	.	.	PUNCT
ejpam-3877	609	4	suppose	suppose	VERB
ejpam-3877	609	5	that	that	SCONJ
ejpam-3877	609	6	the	the	DET
ejpam-3877	609	7	assumption	assumption	NOUN
ejpam-3877	609	8	(	(	PUNCT
ejpam-3877	609	9	i	i	NOUN
ejpam-3877	609	10	)	)	PUNCT
ejpam-3877	609	11	holds	hold	VERB
ejpam-3877	609	12	.	.	PUNCT
ejpam-3877	610	1	let	let	VERB
ejpam-3877	610	2	u	u	PRON
ejpam-3877	610	3	be	be	AUX
ejpam-3877	610	4	a	a	DET
ejpam-3877	610	5	weak	weak	ADJ
ejpam-3877	610	6	entropy	entropy	NOUN
ejpam-3877	610	7	solution	solution	NOUN
ejpam-3877	610	8	to	to	ADP
ejpam-3877	610	9	the	the	DET
ejpam-3877	610	10	problem	problem	NOUN
ejpam-3877	610	11	(	(	PUNCT
ejpam-3877	610	12	p	p	NOUN
ejpam-3877	610	13	)	)	PUNCT
ejpam-3877	610	14	.	.	PUNCT
ejpam-3877	611	1	for	for	ADP
ejpam-3877	611	2	any	any	DET
ejpam-3877	611	3	ρ	ρ	PROPN
ejpam-3877	611	4	∈	∈	PROPN
ejpam-3877	611	5	h1	h1	NOUN
ejpam-3877	611	6	0	0	NUM
ejpam-3877	611	7	(	(	PUNCT
ejpam-3877	611	8	ω	ω	NOUN
ejpam-3877	611	9	)	)	PUNCT
ejpam-3877	611	10	,	,	PUNCT
ejpam-3877	611	11	ρ	ρ	PROPN
ejpam-3877	611	12	≥	≥	NOUN
ejpam-3877	611	13	0	0	NUM
ejpam-3877	611	14	,	,	PUNCT
ejpam-3877	611	15	then	then	ADV
ejpam-3877	611	16	〈	〈	PROPN
ejpam-3877	611	17	us	we	PRON
ejpam-3877	611	18	(	(	PUNCT
ejpam-3877	611	19	·	·	PROPN
ejpam-3877	611	20	,	,	PUNCT
ejpam-3877	611	21	t2	t2	NOUN
ejpam-3877	611	22	)	)	PUNCT
ejpam-3877	611	23	,	,	PUNCT
ejpam-3877	611	24	ρ〉ω	ρ〉ω	PROPN
ejpam-3877	611	25	≤	≤	PROPN
ejpam-3877	611	26	〈	〈	PROPN
ejpam-3877	611	27	us	we	PRON
ejpam-3877	611	28	(	(	PUNCT
ejpam-3877	611	29	·	·	PUNCT
ejpam-3877	611	30	,	,	PUNCT
ejpam-3877	611	31	t1	t1	NOUN
ejpam-3877	611	32	)	)	PUNCT
ejpam-3877	611	33	,	,	PUNCT
ejpam-3877	611	34	ρ〉ω	ρ〉ω	PROPN
ejpam-3877	611	35	≤	≤	PROPN
ejpam-3877	611	36	〈	〈	PROPN
ejpam-3877	611	37	u0s	u0s	PART
ejpam-3877	611	38	,	,	PUNCT
ejpam-3877	611	39	ρ〉ω	ρ〉ω	PROPN
ejpam-3877	611	40	(	(	PUNCT
ejpam-3877	611	41	6.5	6.5	NUM
ejpam-3877	611	42	)	)	PUNCT
ejpam-3877	611	43	hols	hol	NOUN
ejpam-3877	611	44	,	,	PUNCT
ejpam-3877	611	45	for	for	ADP
ejpam-3877	611	46	almost	almost	ADV
ejpam-3877	611	47	every	every	PRON
ejpam-3877	611	48	t1	t1	NOUN
ejpam-3877	611	49	,	,	PUNCT
ejpam-3877	611	50	t2	t2	PROPN
ejpam-3877	611	51	∈	∈	PROPN
ejpam-3877	611	52	(	(	PUNCT
ejpam-3877	611	53	0	0	NUM
ejpam-3877	611	54	,	,	PUNCT
ejpam-3877	611	55	t	t	PROPN
ejpam-3877	611	56	)	)	PUNCT
ejpam-3877	611	57	;	;	PUNCT
ejpam-3877	611	58	t1	t1	NOUN
ejpam-3877	611	59	<	<	X
ejpam-3877	611	60	t2	t2	PROPN
ejpam-3877	611	61	.	.	PUNCT
ejpam-3877	612	1	proof	proof	NOUN
ejpam-3877	612	2	.	.	PUNCT
ejpam-3877	613	1	let	let	VERB
ejpam-3877	613	2	gj	gj	NOUN
ejpam-3877	613	3	be	be	AUX
ejpam-3877	613	4	the	the	DET
ejpam-3877	613	5	function	function	NOUN
ejpam-3877	613	6	given	give	VERB
ejpam-3877	613	7	in	in	ADP
ejpam-3877	613	8	(	(	PUNCT
ejpam-3877	613	9	6.3	6.3	NUM
ejpam-3877	613	10	)	)	PUNCT
ejpam-3877	613	11	and	and	CCONJ
ejpam-3877	613	12	we	we	PRON
ejpam-3877	613	13	take	take	VERB
ejpam-3877	613	14	g	g	NOUN
ejpam-3877	613	15	=	=	PUNCT
ejpam-3877	613	16	gj	gj	PROPN
ejpam-3877	613	17	for	for	ADP
ejpam-3877	613	18	any	any	DET
ejpam-3877	613	19	j	j	PROPN
ejpam-3877	613	20	∈	∈	PROPN
ejpam-3877	613	21	n.	n.	NOUN
ejpam-3877	613	22	by	by	ADP
ejpam-3877	613	23	the	the	DET
ejpam-3877	613	24	definition	definition	NOUN
ejpam-3877	613	25	6.1	6.1	NUM
ejpam-3877	613	26	,	,	PUNCT
ejpam-3877	613	27	we	we	PRON
ejpam-3877	613	28	obtain∫	obtain∫	VERB
ejpam-3877	613	29	q	q	X
ejpam-3877	613	30	{	{	PUNCT
ejpam-3877	613	31	g′j(ψ(ur	g′j(ψ(ur	PROPN
ejpam-3877	613	32	)	)	PUNCT
ejpam-3877	613	33	)	)	PUNCT
ejpam-3877	614	1	|	|	ADV
ejpam-3877	614	2	∇ψ(ur	∇ψ(ur	NOUN
ejpam-3877	614	3	)	)	PUNCT
ejpam-3877	614	4	|2	|2	NUM
ejpam-3877	614	5	φ+	φ+	NOUN
ejpam-3877	614	6	gj(ψ(ur))∇ψ(ur)∇φ−gj(ur)φt	gj(ψ(ur))∇ψ(ur)∇φ−gj(ur)φt	PROPN
ejpam-3877	614	7	}	}	PUNCT
ejpam-3877	614	8	dxdt	dxdt	NOUN
ejpam-3877	614	9	≤	≤	NUM
ejpam-3877	614	10	∫	∫	PROPN
ejpam-3877	614	11	q	q	PROPN
ejpam-3877	614	12	gj(ψ(ur))φdµ+	gj(ψ(ur))φdµ+	PUNCT
ejpam-3877	614	13	∫	∫	PROPN
ejpam-3877	614	14	ω	ω	NUM
ejpam-3877	614	15	gj(u0r)φ(0)dx	gj(u0r)φ(0)dx	NOUN
ejpam-3877	614	16	(	(	PUNCT
ejpam-3877	614	17	6.6	6.6	NUM
ejpam-3877	614	18	)	)	PUNCT
ejpam-3877	614	19	for	for	ADP
ejpam-3877	614	20	every	every	DET
ejpam-3877	614	21	φ	φ	PROPN
ejpam-3877	614	22	∈	∈	PROPN
ejpam-3877	614	23	c1([0	c1([0	PROPN
ejpam-3877	614	24	,	,	PUNCT
ejpam-3877	614	25	t	t	X
ejpam-3877	614	26	]	]	PUNCT
ejpam-3877	614	27	,	,	PUNCT
ejpam-3877	614	28	c1	c1	PROPN
ejpam-3877	614	29	0	0	NUM
ejpam-3877	614	30	(	(	PUNCT
ejpam-3877	614	31	ω	ω	NOUN
ejpam-3877	614	32	)	)	PUNCT
ejpam-3877	614	33	)	)	PUNCT
ejpam-3877	614	34	,	,	PUNCT
ejpam-3877	614	35	φ	φ	X
ejpam-3877	614	36	(	(	PUNCT
ejpam-3877	614	37	·	·	PUNCT
ejpam-3877	614	38	,	,	PUNCT
ejpam-3877	614	39	t	t	NOUN
ejpam-3877	614	40	)	)	PUNCT
ejpam-3877	614	41	=	=	SYM
ejpam-3877	614	42	0	0	NUM
ejpam-3877	615	1	in	in	ADP
ejpam-3877	615	2	ω	ω	PROPN
ejpam-3877	615	3	and	and	CCONJ
ejpam-3877	615	4	φ	φ	PROPN
ejpam-3877	615	5	≥	≥	PROPN
ejpam-3877	615	6	0	0	NUM
ejpam-3877	615	7	,	,	PUNCT
ejpam-3877	615	8	where	where	SCONJ
ejpam-3877	615	9	gj(s	gj(s	PUNCT
ejpam-3877	615	10	)	)	PUNCT
ejpam-3877	615	11	=	=	PUNCT
ejpam-3877	616	1			PRON
ejpam-3877	616	2	−1	−1	ADV
ejpam-3877	616	3	if	if	SCONJ
ejpam-3877	616	4	s	s	VERB
ejpam-3877	616	5	≤	≤	NUM
ejpam-3877	616	6	γ	γ	NOUN
ejpam-3877	616	7	−	−	PROPN
ejpam-3877	616	8	1	1	NUM
ejpam-3877	616	9	j	j	PROPN
ejpam-3877	616	10	,	,	PUNCT
ejpam-3877	616	11	j(s−	j(s−	PROPN
ejpam-3877	616	12	γ	γ	PROPN
ejpam-3877	616	13	)	)	PUNCT
ejpam-3877	616	14	if	if	SCONJ
ejpam-3877	616	15	γ	γ	PROPN
ejpam-3877	616	16	−	−	PROPN
ejpam-3877	616	17	1	1	NUM
ejpam-3877	616	18	j	j	PROPN
ejpam-3877	616	19	≤	≤	PROPN
ejpam-3877	616	20	s	s	PART
ejpam-3877	616	21	≤	≤	NUM
ejpam-3877	616	22	γ	γ	X
ejpam-3877	616	23	,	,	PUNCT
ejpam-3877	616	24	0	0	PUNCT
ejpam-3877	616	25	if	if	SCONJ
ejpam-3877	616	26	s	s	PRON
ejpam-3877	616	27	≥	≥	PROPN
ejpam-3877	616	28	γ	γ	X
ejpam-3877	616	29	.	.	PROPN
ejpam-3877	616	30	to	to	PART
ejpam-3877	616	31	avoid	avoid	VERB
ejpam-3877	616	32	repeating	repeat	VERB
ejpam-3877	616	33	the	the	DET
ejpam-3877	616	34	same	same	ADJ
ejpam-3877	616	35	calculation	calculation	NOUN
ejpam-3877	616	36	we	we	PRON
ejpam-3877	616	37	refer	refer	VERB
ejpam-3877	616	38	to	to	ADP
ejpam-3877	616	39	the	the	DET
ejpam-3877	616	40	proof	proof	NOUN
ejpam-3877	616	41	of	of	ADP
ejpam-3877	616	42	[	[	X
ejpam-3877	616	43	23	23	NUM
ejpam-3877	616	44	,	,	PUNCT
ejpam-3877	616	45	theorem	theorem	VERB
ejpam-3877	616	46	2.9	2.9	NUM
ejpam-3877	616	47	]	]	PUNCT
ejpam-3877	616	48	.	.	PUNCT
ejpam-3877	617	1	then	then	ADV
ejpam-3877	617	2	by	by	ADP
ejpam-3877	617	3	letting	let	VERB
ejpam-3877	617	4	j	j	PROPN
ejpam-3877	617	5	to	to	PART
ejpam-3877	617	6	infinity	infinity	VERB
ejpam-3877	617	7	,	,	PUNCT
ejpam-3877	617	8	we	we	PRON
ejpam-3877	617	9	get∫	get∫	VERB
ejpam-3877	617	10	q	q	X
ejpam-3877	617	11	{	{	PUNCT
ejpam-3877	617	12	urφt	urφt	NOUN
ejpam-3877	617	13	−∇ψ(ur)∇φ	−∇ψ(ur)∇φ	ADV
ejpam-3877	617	14	}	}	PUNCT
ejpam-3877	617	15	dxdt	dxdt	VERB
ejpam-3877	617	16	≤	≤	NUM
ejpam-3877	617	17	−	−	ADP
ejpam-3877	617	18	∫	∫	PROPN
ejpam-3877	617	19	q	q	PROPN
ejpam-3877	617	20	φdµ−	φdµ−	PROPN
ejpam-3877	617	21	∫	∫	PROPN
ejpam-3877	617	22	ω	ω	PROPN
ejpam-3877	617	23	u0rφ(0)dx	u0rφ(0)dx	PROPN
ejpam-3877	617	24	.	.	PUNCT
ejpam-3877	618	1	(	(	PUNCT
ejpam-3877	618	2	6.7	6.7	NUM
ejpam-3877	618	3	)	)	PUNCT
ejpam-3877	618	4	quincy	quincy	PROPN
ejpam-3877	618	5	s.	s.	PROPN
ejpam-3877	618	6	nkombo	nkombo	PROPN
ejpam-3877	618	7	,	,	PUNCT
ejpam-3877	618	8	fengquan	fengquan	PROPN
ejpam-3877	618	9	li	li	PROPN
ejpam-3877	618	10	/	/	SYM
ejpam-3877	618	11	eur	eur	PROPN
ejpam-3877	618	12	.	.	PUNCT
ejpam-3877	619	1	j.	j.	PROPN
ejpam-3877	619	2	pure	pure	PROPN
ejpam-3877	619	3	appl	appl	PROPN
ejpam-3877	619	4	.	.	PROPN
ejpam-3877	619	5	math	math	PROPN
ejpam-3877	619	6	,	,	PUNCT
ejpam-3877	619	7	14	14	NUM
ejpam-3877	619	8	(	(	PUNCT
ejpam-3877	619	9	1	1	NUM
ejpam-3877	619	10	)	)	PUNCT
ejpam-3877	619	11	(	(	PUNCT
ejpam-3877	619	12	2021	2021	NUM
ejpam-3877	619	13	)	)	PUNCT
ejpam-3877	619	14	,	,	PUNCT
ejpam-3877	619	15	204	204	NUM
ejpam-3877	619	16	-	-	SYM
ejpam-3877	619	17	233	233	NUM
ejpam-3877	619	18	228	228	NUM
ejpam-3877	619	19	combining	combine	VERB
ejpam-3877	619	20	(	(	PUNCT
ejpam-3877	619	21	6.7	6.7	NUM
ejpam-3877	619	22	)	)	PUNCT
ejpam-3877	619	23	with	with	ADP
ejpam-3877	619	24	(	(	PUNCT
ejpam-3877	619	25	3.1	3.1	NUM
ejpam-3877	619	26	)	)	PUNCT
ejpam-3877	620	1	,	,	PUNCT
ejpam-3877	620	2	we	we	PRON
ejpam-3877	620	3	have	have	VERB
ejpam-3877	620	4	−	−	PROPN
ejpam-3877	620	5	∫	∫	PROPN
ejpam-3877	620	6	t	t	PROPN
ejpam-3877	620	7	0	0	PUNCT
ejpam-3877	621	1	〈	〈	PROPN
ejpam-3877	621	2	us	we	PRON
ejpam-3877	621	3	(	(	PUNCT
ejpam-3877	621	4	·	·	PROPN
ejpam-3877	621	5	,	,	PUNCT
ejpam-3877	621	6	t	t	PROPN
ejpam-3877	621	7	)	)	PUNCT
ejpam-3877	621	8	,	,	PUNCT
ejpam-3877	621	9	φt〉ω	φt〉ω	NOUN
ejpam-3877	621	10	dt	dt	X
ejpam-3877	621	11	≤	≤	PUNCT
ejpam-3877	621	12	〈	〈	PROPN
ejpam-3877	621	13	u0s	u0s	PROPN
ejpam-3877	621	14	,	,	PUNCT
ejpam-3877	621	15	φ(0)〉ω	φ(0)〉ω	NOUN
ejpam-3877	621	16	.	.	PUNCT
ejpam-3877	622	1	(	(	PUNCT
ejpam-3877	622	2	6.8	6.8	NUM
ejpam-3877	622	3	)	)	PUNCT
ejpam-3877	622	4	for	for	ADP
ejpam-3877	622	5	any	any	DET
ejpam-3877	622	6	fix	fix	NOUN
ejpam-3877	622	7	0	0	NUM
ejpam-3877	622	8	≤	≤	NUM
ejpam-3877	622	9	t1	t1	NOUN
ejpam-3877	622	10	<	<	X
ejpam-3877	622	11	t2	t2	PROPN
ejpam-3877	622	12	≤	≤	X
ejpam-3877	622	13	t	t	PROPN
ejpam-3877	622	14	.	.	PUNCT
ejpam-3877	623	1	we	we	PRON
ejpam-3877	623	2	consider	consider	VERB
ejpam-3877	623	3	χr(t	χr(t	NOUN
ejpam-3877	623	4	)	)	PUNCT
ejpam-3877	623	5	=	=	PUNCT
ejpam-3877	624	1			NOUN
ejpam-3877	624	2	1	1	NUM
ejpam-3877	624	3	r	r	NOUN
ejpam-3877	624	4	(	(	PUNCT
ejpam-3877	624	5	t−	t−	PROPN
ejpam-3877	624	6	t1	t1	NOUN
ejpam-3877	624	7	+	+	CCONJ
ejpam-3877	624	8	r	r	NOUN
ejpam-3877	624	9	2	2	NUM
ejpam-3877	624	10	)	)	PUNCT
ejpam-3877	624	11	if	if	SCONJ
ejpam-3877	624	12	t1	t1	NOUN
ejpam-3877	624	13	−	−	NOUN
ejpam-3877	625	1	r	r	NOUN
ejpam-3877	625	2	2	2	NUM
ejpam-3877	625	3	<	<	X
ejpam-3877	625	4	t	t	X
ejpam-3877	625	5	<	<	X
ejpam-3877	625	6	t1	t1	NOUN
ejpam-3877	625	7	+	+	CCONJ
ejpam-3877	625	8	r	r	NOUN
ejpam-3877	625	9	2	2	NUM
ejpam-3877	625	10	,	,	PUNCT
ejpam-3877	625	11	1	1	NUM
ejpam-3877	625	12	if	if	SCONJ
ejpam-3877	625	13	t1	t1	NOUN
ejpam-3877	625	14	+	+	CCONJ
ejpam-3877	625	15	r	r	NOUN
ejpam-3877	625	16	2	2	NUM
ejpam-3877	625	17	<	<	X
ejpam-3877	625	18	t	t	X
ejpam-3877	625	19	<	<	X
ejpam-3877	625	20	t2	t2	PROPN
ejpam-3877	626	1	−	−	PROPN
ejpam-3877	626	2	r	r	NOUN
ejpam-3877	626	3	2	2	NUM
ejpam-3877	626	4	,	,	PUNCT
ejpam-3877	626	5	−1	−1	NOUN
ejpam-3877	626	6	r	r	NOUN
ejpam-3877	626	7	(	(	PUNCT
ejpam-3877	626	8	t−	t−	PROPN
ejpam-3877	626	9	t2	t2	NOUN
ejpam-3877	626	10	−	−	NOUN
ejpam-3877	626	11	r	r	NOUN
ejpam-3877	626	12	2	2	NUM
ejpam-3877	626	13	)	)	PUNCT
ejpam-3877	626	14	if	if	SCONJ
ejpam-3877	626	15	t2	t2	NOUN
ejpam-3877	626	16	−	−	NOUN
ejpam-3877	626	17	r	r	NOUN
ejpam-3877	626	18	2	2	NUM
ejpam-3877	626	19	<	<	X
ejpam-3877	626	20	t	t	X
ejpam-3877	626	21	<	<	X
ejpam-3877	626	22	t2	t2	PROPN
ejpam-3877	626	23	+	+	CCONJ
ejpam-3877	626	24	r	r	NOUN
ejpam-3877	626	25	2	2	NUM
ejpam-3877	626	26	,	,	PUNCT
ejpam-3877	626	27	0	0	NUM
ejpam-3877	626	28	otherwise	otherwise	ADV
ejpam-3877	626	29	,	,	PUNCT
ejpam-3877	626	30	where	where	SCONJ
ejpam-3877	626	31	0	0	NUM
ejpam-3877	626	32	<	<	X
ejpam-3877	626	33	r	r	X
ejpam-3877	626	34	<	<	X
ejpam-3877	626	35	t2	t2	PROPN
ejpam-3877	626	36	−	−	PROPN
ejpam-3877	626	37	t1	t1	PROPN
ejpam-3877	626	38	,	,	PUNCT
ejpam-3877	626	39	such	such	ADJ
ejpam-3877	626	40	that	that	SCONJ
ejpam-3877	627	1	[	[	X
ejpam-3877	627	2	t1	t1	NOUN
ejpam-3877	627	3	−	−	NOUN
ejpam-3877	627	4	r	r	NOUN
ejpam-3877	627	5	2	2	NUM
ejpam-3877	627	6	,	,	PUNCT
ejpam-3877	627	7	t2	t2	NOUN
ejpam-3877	627	8	+	+	CCONJ
ejpam-3877	627	9	r	r	NOUN
ejpam-3877	627	10	2	2	NUM
ejpam-3877	627	11	]	]	PUNCT
ejpam-3877	627	12	⊂	⊂	X
ejpam-3877	627	13	(	(	PUNCT
ejpam-3877	627	14	0	0	NUM
ejpam-3877	627	15	,	,	PUNCT
ejpam-3877	627	16	t	t	NOUN
ejpam-3877	627	17	)	)	PUNCT
ejpam-3877	627	18	(	(	PUNCT
ejpam-3877	627	19	see	see	VERB
ejpam-3877	627	20	[	[	X
ejpam-3877	627	21	30	30	NUM
ejpam-3877	627	22	,	,	PUNCT
ejpam-3877	627	23	theorem	theorem	VERB
ejpam-3877	627	24	2.5	2.5	NUM
ejpam-3877	627	25	]	]	PUNCT
ejpam-3877	627	26	.	.	PUNCT
ejpam-3877	628	1	for	for	ADP
ejpam-3877	628	2	any	any	DET
ejpam-3877	628	3	φ	φ	PROPN
ejpam-3877	628	4	∈	∈	PROPN
ejpam-3877	628	5	c1	c1	PROPN
ejpam-3877	628	6	0	0	NUM
ejpam-3877	629	1	(	(	PUNCT
ejpam-3877	629	2	ω	ω	NOUN
ejpam-3877	629	3	)	)	PUNCT
ejpam-3877	629	4	,	,	PUNCT
ejpam-3877	629	5	ρ	ρ	PROPN
ejpam-3877	629	6	≥	≥	NOUN
ejpam-3877	629	7	0	0	NUM
ejpam-3877	629	8	we	we	PRON
ejpam-3877	629	9	choose	choose	VERB
ejpam-3877	629	10	φ(x	φ(x	PROPN
ejpam-3877	629	11	,	,	PUNCT
ejpam-3877	629	12	t	t	NOUN
ejpam-3877	629	13	)	)	PUNCT
ejpam-3877	630	1	=	=	SYM
ejpam-3877	630	2	ρ(x)χr(t	ρ(x)χr(t	X
ejpam-3877	630	3	)	)	PUNCT
ejpam-3877	630	4	as	as	ADP
ejpam-3877	630	5	a	a	DET
ejpam-3877	630	6	test	test	NOUN
ejpam-3877	630	7	function	function	NOUN
ejpam-3877	630	8	in	in	ADP
ejpam-3877	630	9	(	(	PUNCT
ejpam-3877	630	10	6.8	6.8	NUM
ejpam-3877	630	11	)	)	PUNCT
ejpam-3877	630	12	,	,	PUNCT
ejpam-3877	630	13	one	one	PRON
ejpam-3877	630	14	has	have	VERB
ejpam-3877	630	15	−1	−1	NOUN
ejpam-3877	630	16	r	r	NOUN
ejpam-3877	630	17	∫	∫	PROPN
ejpam-3877	630	18	t1	t1	NOUN
ejpam-3877	630	19	+	+	X
ejpam-3877	630	20	r	r	NOUN
ejpam-3877	630	21	2	2	NUM
ejpam-3877	630	22	t1−	t1−	NOUN
ejpam-3877	630	23	r	r	NOUN
ejpam-3877	630	24	1	1	NUM
ejpam-3877	630	25	〈	〈	PROPN
ejpam-3877	630	26	us(t	us(t	NOUN
ejpam-3877	630	27	)	)	PUNCT
ejpam-3877	630	28	,	,	PUNCT
ejpam-3877	630	29	ρ〉ω	ρ〉ω	NOUN
ejpam-3877	630	30	dt+	dt+	NOUN
ejpam-3877	630	31	1	1	NUM
ejpam-3877	630	32	r	r	NOUN
ejpam-3877	630	33	∫	∫	NOUN
ejpam-3877	630	34	t2	t2	NOUN
ejpam-3877	630	35	+	+	CCONJ
ejpam-3877	630	36	r	r	NOUN
ejpam-3877	630	37	2	2	NUM
ejpam-3877	630	38	t2−	t2−	NOUN
ejpam-3877	630	39	r	r	NOUN
ejpam-3877	630	40	2	2	NUM
ejpam-3877	630	41	〈	〈	NOUN
ejpam-3877	630	42	us(t	us(t	NOUN
ejpam-3877	630	43	)	)	PUNCT
ejpam-3877	630	44	,	,	PUNCT
ejpam-3877	630	45	ρ〉ω	ρ〉ω	PROPN
ejpam-3877	630	46	dt	dt	NOUN
ejpam-3877	630	47	≤	≤	ADV
ejpam-3877	630	48	0	0	NUM
ejpam-3877	630	49	for	for	ADP
ejpam-3877	630	50	almost	almost	ADV
ejpam-3877	630	51	every	every	DET
ejpam-3877	630	52	0	0	NUM
ejpam-3877	630	53	<	<	X
ejpam-3877	630	54	t1	t1	NOUN
ejpam-3877	630	55	<	<	X
ejpam-3877	630	56	t2	t2	PROPN
ejpam-3877	630	57	<	<	X
ejpam-3877	630	58	t	t	PROPN
ejpam-3877	630	59	and	and	CCONJ
ejpam-3877	630	60	letting	let	VERB
ejpam-3877	630	61	r	r	NOUN
ejpam-3877	630	62	→	→	SYM
ejpam-3877	630	63	0	0	NUM
ejpam-3877	630	64	in	in	ADP
ejpam-3877	630	65	the	the	DET
ejpam-3877	630	66	above	above	ADJ
ejpam-3877	630	67	inequality	inequality	NOUN
ejpam-3877	630	68	,	,	PUNCT
ejpam-3877	630	69	there	there	PRON
ejpam-3877	630	70	holds	hold	VERB
ejpam-3877	630	71	〈	〈	PROPN
ejpam-3877	630	72	us	we	PRON
ejpam-3877	630	73	(	(	PUNCT
ejpam-3877	630	74	·	·	PROPN
ejpam-3877	630	75	,	,	PUNCT
ejpam-3877	630	76	t2	t2	NOUN
ejpam-3877	630	77	)	)	PUNCT
ejpam-3877	630	78	,	,	PUNCT
ejpam-3877	630	79	ρ〉ω	ρ〉ω	PROPN
ejpam-3877	630	80	≤	≤	PROPN
ejpam-3877	630	81	〈	〈	PROPN
ejpam-3877	630	82	us	we	PRON
ejpam-3877	630	83	(	(	PUNCT
ejpam-3877	630	84	·	·	PUNCT
ejpam-3877	630	85	,	,	PUNCT
ejpam-3877	630	86	t1	t1	NOUN
ejpam-3877	630	87	)	)	PUNCT
ejpam-3877	630	88	,	,	PUNCT
ejpam-3877	630	89	ρ〉ω	ρ〉ω	PROPN
ejpam-3877	630	90	.	.	PUNCT
ejpam-3877	631	1	similarly	similarly	ADV
ejpam-3877	631	2	,	,	PUNCT
ejpam-3877	631	3	let	let	VERB
ejpam-3877	631	4	us	we	PRON
ejpam-3877	631	5	consider	consider	VERB
ejpam-3877	631	6	for	for	ADP
ejpam-3877	631	7	every	every	DET
ejpam-3877	631	8	fixed	fix	VERB
ejpam-3877	631	9	t1	t1	NOUN
ejpam-3877	631	10	∈	∈	PROPN
ejpam-3877	631	11	(	(	PUNCT
ejpam-3877	631	12	0	0	NUM
ejpam-3877	631	13	,	,	PUNCT
ejpam-3877	631	14	t	t	NOUN
ejpam-3877	631	15	)	)	PUNCT
ejpam-3877	631	16	χr(t	χr(t	NOUN
ejpam-3877	631	17	)	)	PUNCT
ejpam-3877	632	1	=	=	SYM
ejpam-3877	632	2			NOUN
ejpam-3877	632	3	1	1	NUM
ejpam-3877	632	4	if	if	SCONJ
ejpam-3877	632	5	0	0	NUM
ejpam-3877	632	6	≤	≤	NUM
ejpam-3877	632	7	t	t	PROPN
ejpam-3877	632	8	≤	≤	NUM
ejpam-3877	632	9	t1	t1	PROPN
ejpam-3877	632	10	,	,	PUNCT
ejpam-3877	632	11	−1	−1	NOUN
ejpam-3877	632	12	r	r	NOUN
ejpam-3877	632	13	(	(	PUNCT
ejpam-3877	632	14	t−	t−	PROPN
ejpam-3877	632	15	t1	t1	NOUN
ejpam-3877	632	16	−	−	NOUN
ejpam-3877	632	17	r	r	NOUN
ejpam-3877	632	18	)	)	PUNCT
ejpam-3877	632	19	if	if	SCONJ
ejpam-3877	632	20	t1	t1	PROPN
ejpam-3877	632	21	≤	≤	X
ejpam-3877	632	22	t	t	PROPN
ejpam-3877	632	23	≤	≤	NUM
ejpam-3877	632	24	t1	t1	NOUN
ejpam-3877	632	25	+	+	CCONJ
ejpam-3877	632	26	r	r	NOUN
ejpam-3877	632	27	,	,	PUNCT
ejpam-3877	632	28	0	0	NUM
ejpam-3877	632	29	if	if	SCONJ
ejpam-3877	632	30	t	t	PROPN
ejpam-3877	632	31	≥	≥	PROPN
ejpam-3877	632	32	t1	t1	NOUN
ejpam-3877	632	33	+	+	CCONJ
ejpam-3877	632	34	r.	r.	PROPN
ejpam-3877	632	35	therefore	therefore	ADV
ejpam-3877	632	36	,	,	PUNCT
ejpam-3877	632	37	we	we	PRON
ejpam-3877	632	38	can	can	AUX
ejpam-3877	632	39	deduce	deduce	VERB
ejpam-3877	632	40	that	that	DET
ejpam-3877	632	41	1	1	NUM
ejpam-3877	632	42	r	r	NOUN
ejpam-3877	632	43	∫	∫	PROPN
ejpam-3877	632	44	t1+r	t1+r	PROPN
ejpam-3877	632	45	t1	t1	NOUN
ejpam-3877	632	46	〈	〈	PROPN
ejpam-3877	632	47	us	we	PRON
ejpam-3877	632	48	(	(	PUNCT
ejpam-3877	632	49	·	·	PROPN
ejpam-3877	632	50	,	,	PUNCT
ejpam-3877	632	51	t	t	PROPN
ejpam-3877	632	52	)	)	PUNCT
ejpam-3877	632	53	,	,	PUNCT
ejpam-3877	632	54	ρ〉ω	ρ〉ω	PROPN
ejpam-3877	632	55	dt	dt	NOUN
ejpam-3877	632	56	≤	≤	PUNCT
ejpam-3877	632	57	〈	〈	PROPN
ejpam-3877	632	58	u0s	u0s	PROPN
ejpam-3877	632	59	,	,	PUNCT
ejpam-3877	632	60	ρ〉ω	ρ〉ω	PROPN
ejpam-3877	632	61	.	.	PUNCT
ejpam-3877	633	1	hence	hence	ADV
ejpam-3877	633	2	the	the	DET
ejpam-3877	633	3	estimate	estimate	NOUN
ejpam-3877	633	4	(	(	PUNCT
ejpam-3877	633	5	6.5	6.5	NUM
ejpam-3877	633	6	)	)	PUNCT
ejpam-3877	633	7	holds	hold	VERB
ejpam-3877	633	8	true	true	ADJ
ejpam-3877	633	9	.	.	PUNCT
ejpam-3877	634	1	�	�	PROPN
ejpam-3877	634	2	proof	proof	NOUN
ejpam-3877	634	3	of	of	ADP
ejpam-3877	634	4	theorem	theorem	ADJ
ejpam-3877	634	5	3.4	3.4	NUM
ejpam-3877	634	6	.	.	PUNCT
ejpam-3877	635	1	let	let	VERB
ejpam-3877	635	2	u1	u1	NOUN
ejpam-3877	635	3	,	,	PUNCT
ejpam-3877	635	4	u2	u2	PROPN
ejpam-3877	635	5	be	be	AUX
ejpam-3877	635	6	two	two	NUM
ejpam-3877	635	7	very	very	ADV
ejpam-3877	635	8	weak	weak	ADJ
ejpam-3877	635	9	solutions	solution	NOUN
ejpam-3877	635	10	obtained	obtain	VERB
ejpam-3877	635	11	as	as	ADP
ejpam-3877	635	12	limit	limit	NOUN
ejpam-3877	635	13	of	of	ADP
ejpam-3877	635	14	approximation	approximation	NOUN
ejpam-3877	635	15	of	of	ADP
ejpam-3877	635	16	(	(	PUNCT
ejpam-3877	635	17	p	p	NOUN
ejpam-3877	635	18	)	)	PUNCT
ejpam-3877	635	19	with	with	ADP
ejpam-3877	635	20	initial	initial	ADJ
ejpam-3877	635	21	data	datum	NOUN
ejpam-3877	635	22	u01n	u01n	NOUN
ejpam-3877	635	23	and	and	CCONJ
ejpam-3877	635	24	u02n	u02n	NOUN
ejpam-3877	635	25	respectively	respectively	ADV
ejpam-3877	635	26	.	.	PUNCT
ejpam-3877	636	1	let	let	VERB
ejpam-3877	636	2	{	{	PUNCT
ejpam-3877	636	3	u1n	u1n	NOUN
ejpam-3877	636	4	}	}	PUNCT
ejpam-3877	636	5	,	,	PUNCT
ejpam-3877	636	6	{	{	PUNCT
ejpam-3877	636	7	u2n	u2n	NOUN
ejpam-3877	636	8	}	}	PUNCT
ejpam-3877	636	9	⊆	⊆	NUM
ejpam-3877	636	10	l∞(q	l∞(q	NOUN
ejpam-3877	636	11	)	)	PUNCT
ejpam-3877	636	12	∩	∩	ADJ
ejpam-3877	636	13	l2((0	l2((0	PROPN
ejpam-3877	636	14	,	,	PUNCT
ejpam-3877	636	15	t	t	PROPN
ejpam-3877	636	16	)	)	PUNCT
ejpam-3877	636	17	,	,	PUNCT
ejpam-3877	636	18	h1	h1	PROPN
ejpam-3877	636	19	0	0	NUM
ejpam-3877	636	20	(	(	PUNCT
ejpam-3877	636	21	ω	ω	NOUN
ejpam-3877	636	22	)	)	PUNCT
ejpam-3877	636	23	)	)	PUNCT
ejpam-3877	636	24	be	be	AUX
ejpam-3877	636	25	two	two	NUM
ejpam-3877	636	26	approximating	approximate	VERB
ejpam-3877	636	27	sequences	sequence	NOUN
ejpam-3877	636	28	of	of	ADP
ejpam-3877	636	29	solutions	solution	NOUN
ejpam-3877	636	30	to	to	ADP
ejpam-3877	636	31	the	the	DET
ejpam-3877	636	32	approximation	approximation	NOUN
ejpam-3877	636	33	problem	problem	NOUN
ejpam-3877	636	34	(	(	PUNCT
ejpam-3877	636	35	pn	pn	NOUN
ejpam-3877	636	36	)	)	PUNCT
ejpam-3877	636	37	and	and	CCONJ
ejpam-3877	636	38	satisfying	satisfy	VERB
ejpam-3877	636	39	the	the	DET
ejpam-3877	636	40	assumption	assumption	NOUN
ejpam-3877	636	41	(	(	PUNCT
ejpam-3877	636	42	3.9	3.9	NUM
ejpam-3877	636	43	)	)	PUNCT
ejpam-3877	636	44	.	.	PUNCT
ejpam-3877	637	1	for	for	ADP
ejpam-3877	637	2	every	every	DET
ejpam-3877	637	3	ξ	ξ	PROPN
ejpam-3877	637	4	∈	∈	PROPN
ejpam-3877	637	5	c2,1(q	c2,1(q	NOUN
ejpam-3877	637	6	)	)	PUNCT
ejpam-3877	637	7	vanishing	vanish	VERB
ejpam-3877	637	8	on	on	ADP
ejpam-3877	637	9	∂ω×	∂ω×	PROPN
ejpam-3877	637	10	(	(	PUNCT
ejpam-3877	637	11	0	0	NUM
ejpam-3877	637	12	,	,	PUNCT
ejpam-3877	637	13	t	t	PROPN
ejpam-3877	637	14	)	)	PUNCT
ejpam-3877	637	15	and	and	CCONJ
ejpam-3877	637	16	ξ	ξ	X
ejpam-3877	637	17	(	(	PUNCT
ejpam-3877	637	18	·	·	PUNCT
ejpam-3877	637	19	,	,	PUNCT
ejpam-3877	637	20	t	t	NOUN
ejpam-3877	637	21	)	)	PUNCT
ejpam-3877	637	22	=	=	SYM
ejpam-3877	637	23	0	0	NUM
ejpam-3877	637	24	in	in	ADP
ejpam-3877	637	25	ω	ω	NUM
ejpam-3877	637	26	,	,	PUNCT
ejpam-3877	637	27	there	there	PRON
ejpam-3877	637	28	holds∫	holds∫	VERB
ejpam-3877	637	29	q	q	NOUN
ejpam-3877	637	30	(	(	PUNCT
ejpam-3877	637	31	u1n	u1n	NOUN
ejpam-3877	637	32	−	−	PROPN
ejpam-3877	637	33	u2n	u2n	NOUN
ejpam-3877	637	34	)	)	PUNCT
ejpam-3877	637	35	ξtdxdt	ξtdxdt	NOUN
ejpam-3877	637	36	=	=	PUNCT
ejpam-3877	638	1	−	−	PROPN
ejpam-3877	638	2	∫	∫	PROPN
ejpam-3877	638	3	q	q	PROPN
ejpam-3877	638	4	(	(	PUNCT
ejpam-3877	638	5	ψ(u1n)−	ψ(u1n)−	X
ejpam-3877	638	6	ψ(u2n	ψ(u2n	ADV
ejpam-3877	638	7	)	)	PUNCT
ejpam-3877	638	8	)	)	PUNCT
ejpam-3877	639	1	∆ξdxdt−	∆ξdxdt−	PROPN
ejpam-3877	639	2	−	−	PROPN
ejpam-3877	639	3	∫	∫	PROPN
ejpam-3877	639	4	q	q	PROPN
ejpam-3877	639	5	(	(	PUNCT
ejpam-3877	639	6	µ1n	µ1n	NOUN
ejpam-3877	639	7	−	−	PROPN
ejpam-3877	639	8	µ2n	µ2n	NOUN
ejpam-3877	639	9	)	)	PUNCT
ejpam-3877	639	10	ξdxdt−	ξdxdt−	ADP
ejpam-3877	639	11	∫	∫	PROPN
ejpam-3877	639	12	ω	ω	PROPN
ejpam-3877	639	13	(	(	PUNCT
ejpam-3877	639	14	u01n	u01n	NOUN
ejpam-3877	639	15	−	−	NOUN
ejpam-3877	639	16	u02n	u02n	NOUN
ejpam-3877	639	17	)	)	PUNCT
ejpam-3877	639	18	ξ(x	ξ(x	NOUN
ejpam-3877	639	19	,	,	PUNCT
ejpam-3877	639	20	0)dx	0)dx	PROPN
ejpam-3877	639	21	,	,	PUNCT
ejpam-3877	639	22	(	(	PUNCT
ejpam-3877	639	23	6.9	6.9	NUM
ejpam-3877	639	24	)	)	PUNCT
ejpam-3877	639	25	quincy	quincy	PROPN
ejpam-3877	639	26	s.	s.	PROPN
ejpam-3877	639	27	nkombo	nkombo	PROPN
ejpam-3877	639	28	,	,	PUNCT
ejpam-3877	639	29	fengquan	fengquan	PROPN
ejpam-3877	639	30	li	li	PROPN
ejpam-3877	639	31	/	/	SYM
ejpam-3877	639	32	eur	eur	PROPN
ejpam-3877	639	33	.	.	PUNCT
ejpam-3877	640	1	j.	j.	PROPN
ejpam-3877	640	2	pure	pure	PROPN
ejpam-3877	640	3	appl	appl	PROPN
ejpam-3877	640	4	.	.	PROPN
ejpam-3877	640	5	math	math	PROPN
ejpam-3877	640	6	,	,	PUNCT
ejpam-3877	640	7	14	14	NUM
ejpam-3877	640	8	(	(	PUNCT
ejpam-3877	640	9	1	1	NUM
ejpam-3877	640	10	)	)	PUNCT
ejpam-3877	640	11	(	(	PUNCT
ejpam-3877	640	12	2021	2021	NUM
ejpam-3877	640	13	)	)	PUNCT
ejpam-3877	640	14	,	,	PUNCT
ejpam-3877	640	15	204	204	NUM
ejpam-3877	640	16	-	-	SYM
ejpam-3877	640	17	233	233	NUM
ejpam-3877	640	18	229	229	NUM
ejpam-3877	640	19	where	where	SCONJ
ejpam-3877	640	20	{	{	PUNCT
ejpam-3877	640	21	µ1n	µ1n	NOUN
ejpam-3877	640	22	}	}	PUNCT
ejpam-3877	640	23	,	,	PUNCT
ejpam-3877	640	24	{	{	PUNCT
ejpam-3877	640	25	µ2n	µ2n	NOUN
ejpam-3877	640	26	}	}	PUNCT
ejpam-3877	640	27	,	,	PUNCT
ejpam-3877	640	28	{	{	PUNCT
ejpam-3877	640	29	u01n	u01n	NOUN
ejpam-3877	640	30	}	}	PUNCT
ejpam-3877	640	31	,	,	PUNCT
ejpam-3877	640	32	and	and	CCONJ
ejpam-3877	640	33	{	{	PUNCT
ejpam-3877	640	34	u02n	u02n	AUX
ejpam-3877	640	35	}	}	PUNCT
ejpam-3877	640	36	are	be	AUX
ejpam-3877	640	37	approximating	approximate	VERB
ejpam-3877	640	38	radon	radon	NOUN
ejpam-3877	640	39	measures	measure	NOUN
ejpam-3877	640	40	satisfying	satisfy	VERB
ejpam-3877	640	41	(	(	PUNCT
ejpam-3877	640	42	3.10	3.10	NUM
ejpam-3877	640	43	)	)	PUNCT
ejpam-3877	640	44	.	.	PUNCT
ejpam-3877	641	1	for	for	ADP
ejpam-3877	641	2	almost	almost	ADV
ejpam-3877	641	3	every	every	DET
ejpam-3877	641	4	(	(	PUNCT
ejpam-3877	641	5	x	x	NOUN
ejpam-3877	641	6	,	,	PUNCT
ejpam-3877	641	7	t	t	PROPN
ejpam-3877	641	8	)	)	PUNCT
ejpam-3877	641	9	∈	∈	PROPN
ejpam-3877	642	1	q	q	NOUN
ejpam-3877	642	2	,	,	PUNCT
ejpam-3877	642	3	we	we	PRON
ejpam-3877	642	4	consider	consider	VERB
ejpam-3877	642	5	the	the	DET
ejpam-3877	642	6	function	function	NOUN
ejpam-3877	642	7	an(x	an(x	X
ejpam-3877	642	8	,	,	PUNCT
ejpam-3877	642	9	t	t	PROPN
ejpam-3877	642	10	)	)	PUNCT
ejpam-3877	642	11	defined	define	VERB
ejpam-3877	642	12	by	by	ADP
ejpam-3877	642	13	an(x	an(x	NUM
ejpam-3877	642	14	,	,	PUNCT
ejpam-3877	642	15	t	t	PROPN
ejpam-3877	642	16	)	)	PUNCT
ejpam-3877	642	17	=	=	PRON
ejpam-3877	642	18	{	{	PUNCT
ejpam-3877	642	19	ψ(u1n(x	ψ(u1n(x	PROPN
ejpam-3877	642	20	,	,	PUNCT
ejpam-3877	642	21	t))−ψ(u2n(x	t))−ψ(u2n(x	PROPN
ejpam-3877	642	22	,	,	PUNCT
ejpam-3877	642	23	t	t	PROPN
ejpam-3877	642	24	)	)	PUNCT
ejpam-3877	642	25	)	)	PUNCT
ejpam-3877	643	1	u1n(x	u1n(x	PROPN
ejpam-3877	643	2	,	,	PUNCT
ejpam-3877	643	3	t)−u2n(x	t)−u2n(x	ADP
ejpam-3877	643	4	,	,	PUNCT
ejpam-3877	643	5	t	t	PROPN
ejpam-3877	643	6	)	)	PUNCT
ejpam-3877	643	7	if	if	SCONJ
ejpam-3877	643	8	u1n(x	u1n(x	PROPN
ejpam-3877	643	9	,	,	PUNCT
ejpam-3877	643	10	t	t	PROPN
ejpam-3877	643	11	)	)	PUNCT
ejpam-3877	643	12	6=	6=	PUNCT
ejpam-3877	644	1	u2n(x	u2n(x	PROPN
ejpam-3877	644	2	,	,	PUNCT
ejpam-3877	644	3	t	t	PROPN
ejpam-3877	644	4	)	)	PUNCT
ejpam-3877	644	5	,	,	PUNCT
ejpam-3877	644	6	ψ′(u1n(x	ψ′(u1n(x	NOUN
ejpam-3877	644	7	,	,	PUNCT
ejpam-3877	644	8	t	t	PROPN
ejpam-3877	644	9	)	)	PUNCT
ejpam-3877	644	10	)	)	PUNCT
ejpam-3877	645	1	if	if	SCONJ
ejpam-3877	645	2	u1n(x	u1n(x	PROPN
ejpam-3877	645	3	,	,	PUNCT
ejpam-3877	645	4	t	t	PROPN
ejpam-3877	645	5	)	)	PUNCT
ejpam-3877	645	6	=	=	SYM
ejpam-3877	646	1	u2n(x	u2n(x	PROPN
ejpam-3877	646	2	,	,	PUNCT
ejpam-3877	646	3	t	t	PROPN
ejpam-3877	646	4	)	)	PUNCT
ejpam-3877	646	5	.	.	PUNCT
ejpam-3877	647	1	(	(	PUNCT
ejpam-3877	647	2	6.10	6.10	NUM
ejpam-3877	647	3	)	)	PUNCT
ejpam-3877	647	4	obviously	obviously	ADV
ejpam-3877	647	5	an	an	DET
ejpam-3877	647	6	∈	∈	PROPN
ejpam-3877	647	7	l∞(q	l∞(q	NOUN
ejpam-3877	647	8	)	)	PUNCT
ejpam-3877	647	9	and	and	CCONJ
ejpam-3877	647	10	for	for	ADP
ejpam-3877	647	11	every	every	DET
ejpam-3877	647	12	n	n	PRON
ejpam-3877	647	13	∈	∈	PRON
ejpam-3877	647	14	n	n	CCONJ
ejpam-3877	647	15	there	there	PRON
ejpam-3877	647	16	exists	exist	VERB
ejpam-3877	647	17	a	a	DET
ejpam-3877	647	18	positive	positive	ADJ
ejpam-3877	647	19	constant	constant	ADJ
ejpam-3877	647	20	cn	cn	NOUN
ejpam-3877	647	21	such	such	ADJ
ejpam-3877	647	22	that	that	SCONJ
ejpam-3877	647	23	ess	ess	PROPN
ejpam-3877	647	24	inf	inf	PROPN
ejpam-3877	647	25	(	(	PUNCT
ejpam-3877	647	26	x	x	X
ejpam-3877	647	27	,	,	PUNCT
ejpam-3877	647	28	t)∈q	t)∈q	NUM
ejpam-3877	647	29	an(x	an(x	NUM
ejpam-3877	647	30	,	,	PUNCT
ejpam-3877	647	31	t	t	PROPN
ejpam-3877	647	32	)	)	PUNCT
ejpam-3877	647	33	≥	≥	NOUN
ejpam-3877	647	34	cn	cn	X
ejpam-3877	647	35	>	>	X
ejpam-3877	647	36	0	0	X
ejpam-3877	647	37	.	.	PUNCT
ejpam-3877	648	1	this	this	PRON
ejpam-3877	648	2	ensures	ensure	VERB
ejpam-3877	648	3	that	that	SCONJ
ejpam-3877	648	4	for	for	ADP
ejpam-3877	648	5	every	every	DET
ejpam-3877	648	6	z	z	PROPN
ejpam-3877	648	7	∈	∈	PROPN
ejpam-3877	648	8	c2	c2	PROPN
ejpam-3877	648	9	c	c	PROPN
ejpam-3877	648	10	(	(	PUNCT
ejpam-3877	648	11	q	q	NOUN
ejpam-3877	648	12	)	)	PUNCT
ejpam-3877	648	13	,	,	PUNCT
ejpam-3877	648	14	the	the	DET
ejpam-3877	648	15	problem	problem	NUM
ejpam-3877	648	16	ξnt	ξnt	NOUN
ejpam-3877	648	17	+	+	CCONJ
ejpam-3877	648	18	an∆ξn	an∆ξn	ADJ
ejpam-3877	649	1	+	+	PUNCT
ejpam-3877	649	2	z	z	NOUN
ejpam-3877	649	3	=	=	SYM
ejpam-3877	649	4	0	0	NUM
ejpam-3877	649	5	in	in	ADP
ejpam-3877	649	6	q	q	PROPN
ejpam-3877	649	7	ξn	ξn	PROPN
ejpam-3877	649	8	=	=	NOUN
ejpam-3877	649	9	0	0	NUM
ejpam-3877	649	10	on	on	ADP
ejpam-3877	649	11	∂ω×	∂ω×	PROPN
ejpam-3877	649	12	(	(	PUNCT
ejpam-3877	649	13	0	0	NUM
ejpam-3877	649	14	,	,	PUNCT
ejpam-3877	649	15	t	t	NOUN
ejpam-3877	649	16	)	)	PUNCT
ejpam-3877	649	17	ξn	ξn	PROPN
ejpam-3877	649	18	(	(	PUNCT
ejpam-3877	649	19	·	·	PUNCT
ejpam-3877	649	20	,	,	PUNCT
ejpam-3877	649	21	t	t	NOUN
ejpam-3877	649	22	)	)	PUNCT
ejpam-3877	650	1	=	=	SYM
ejpam-3877	650	2	0	0	NUM
ejpam-3877	651	1	in	in	ADP
ejpam-3877	651	2	ω	ω	PROPN
ejpam-3877	651	3	(	(	PUNCT
ejpam-3877	651	4	6.11	6.11	NUM
ejpam-3877	651	5	)	)	PUNCT
ejpam-3877	651	6	has	have	VERB
ejpam-3877	651	7	a	a	DET
ejpam-3877	651	8	unique	unique	ADJ
ejpam-3877	651	9	solution	solution	NOUN
ejpam-3877	651	10	ξn	ξn	PROPN
ejpam-3877	651	11	∈	∈	PROPN
ejpam-3877	651	12	l∞((0	l∞((0	PROPN
ejpam-3877	651	13	,	,	PUNCT
ejpam-3877	651	14	t	t	PROPN
ejpam-3877	651	15	)	)	PUNCT
ejpam-3877	651	16	,	,	PUNCT
ejpam-3877	651	17	h2(ω	h2(ω	NOUN
ejpam-3877	651	18	)	)	PUNCT
ejpam-3877	651	19	)	)	PUNCT
ejpam-3877	651	20	∩	∩	PROPN
ejpam-3877	651	21	l2((0	l2((0	PROPN
ejpam-3877	651	22	,	,	PUNCT
ejpam-3877	651	23	t	t	PROPN
ejpam-3877	651	24	)	)	PUNCT
ejpam-3877	651	25	,	,	PUNCT
ejpam-3877	651	26	h1	h1	PROPN
ejpam-3877	651	27	0	0	NUM
ejpam-3877	651	28	(	(	PUNCT
ejpam-3877	651	29	ω	ω	NOUN
ejpam-3877	651	30	)	)	PUNCT
ejpam-3877	651	31	)	)	PUNCT
ejpam-3877	651	32	with	with	ADP
ejpam-3877	651	33	ξnt	ξnt	NOUN
ejpam-3877	651	34	∈	∈	PROPN
ejpam-3877	651	35	l2(q	l2(q	PROPN
ejpam-3877	651	36	)	)	PUNCT
ejpam-3877	651	37	(	(	PUNCT
ejpam-3877	651	38	see	see	VERB
ejpam-3877	651	39	[	[	X
ejpam-3877	651	40	8	8	NUM
ejpam-3877	651	41	,	,	PUNCT
ejpam-3877	651	42	19	19	NUM
ejpam-3877	651	43	]	]	NUM
ejpam-3877	651	44	)	)	PUNCT
ejpam-3877	651	45	.	.	PUNCT
ejpam-3877	652	1	moreover	moreover	ADV
ejpam-3877	652	2	,	,	PUNCT
ejpam-3877	652	3	it	it	PRON
ejpam-3877	652	4	can	can	AUX
ejpam-3877	652	5	be	be	AUX
ejpam-3877	652	6	seen	see	VERB
ejpam-3877	652	7	that	that	SCONJ
ejpam-3877	652	8	|	|	ADV
ejpam-3877	652	9	ξn(x	ξn(x	ADJ
ejpam-3877	652	10	,	,	PUNCT
ejpam-3877	652	11	t	t	PROPN
ejpam-3877	652	12	)	)	PUNCT
ejpam-3877	652	13	|≤	|≤	PROPN
ejpam-3877	652	14	(	(	PUNCT
ejpam-3877	652	15	t	t	PROPN
ejpam-3877	652	16	−	−	PROPN
ejpam-3877	652	17	t	t	PROPN
ejpam-3877	652	18	)	)	PUNCT
ejpam-3877	652	19	‖	‖	PROPN
ejpam-3877	652	20	z	z	PROPN
ejpam-3877	652	21	‖l∞(q	‖l∞(q	NOUN
ejpam-3877	652	22	)	)	PUNCT
ejpam-3877	652	23	.	.	PUNCT
ejpam-3877	653	1	(	(	PUNCT
ejpam-3877	653	2	6.12	6.12	NUM
ejpam-3877	653	3	)	)	PUNCT
ejpam-3877	653	4	let	let	VERB
ejpam-3877	653	5	us	we	PRON
ejpam-3877	653	6	consider	consider	VERB
ejpam-3877	653	7	the	the	DET
ejpam-3877	653	8	function	function	NOUN
ejpam-3877	653	9	η	η	PROPN
ejpam-3877	653	10	such	such	ADJ
ejpam-3877	653	11	that	that	PRON
ejpam-3877	653	12	for	for	ADP
ejpam-3877	653	13	any	any	DET
ejpam-3877	653	14	t1	t1	NOUN
ejpam-3877	653	15	+	+	CCONJ
ejpam-3877	653	16	1	1	NUM
ejpam-3877	653	17	<	<	X
ejpam-3877	653	18	t2	t2	PROPN
ejpam-3877	653	19	and	and	CCONJ
ejpam-3877	653	20	t1	t1	NOUN
ejpam-3877	653	21	,	,	PUNCT
ejpam-3877	653	22	t2	t2	PROPN
ejpam-3877	653	23	∈	∈	PROPN
ejpam-3877	653	24	(	(	PUNCT
ejpam-3877	653	25	0	0	NUM
ejpam-3877	653	26	,	,	PUNCT
ejpam-3877	653	27	t	t	NOUN
ejpam-3877	653	28	)	)	PUNCT
ejpam-3877	653	29	η(t	η(t	NOUN
ejpam-3877	653	30	)	)	PUNCT
ejpam-3877	654	1	=	=	SYM
ejpam-3877	655	1			NOUN
ejpam-3877	655	2	0	0	PUNCT
ejpam-3877	656	1	if	if	SCONJ
ejpam-3877	656	2	0	0	NUM
ejpam-3877	656	3	≤	≤	NUM
ejpam-3877	656	4	t	t	PROPN
ejpam-3877	656	5	≤	≤	NUM
ejpam-3877	656	6	t1	t1	PROPN
ejpam-3877	656	7	,	,	PUNCT
ejpam-3877	656	8	t−	t−	PROPN
ejpam-3877	656	9	t1	t1	NOUN
ejpam-3877	657	1	if	if	SCONJ
ejpam-3877	657	2	t1	t1	PROPN
ejpam-3877	657	3	<	<	X
ejpam-3877	657	4	t	t	X
ejpam-3877	657	5	<	<	X
ejpam-3877	657	6	t2	t2	PROPN
ejpam-3877	657	7	,	,	PUNCT
ejpam-3877	657	8	t2	t2	PROPN
ejpam-3877	657	9	−	−	PROPN
ejpam-3877	657	10	t1	t1	NOUN
ejpam-3877	657	11	if	if	SCONJ
ejpam-3877	657	12	t	t	PROPN
ejpam-3877	657	13	≥	≥	PROPN
ejpam-3877	657	14	t2	t2	PROPN
ejpam-3877	657	15	.	.	PUNCT
ejpam-3877	658	1	choosing	choose	VERB
ejpam-3877	658	2	η∆ξn	η∆ξn	PROPN
ejpam-3877	658	3	as	as	ADP
ejpam-3877	658	4	a	a	DET
ejpam-3877	658	5	test	test	NOUN
ejpam-3877	658	6	function	function	NOUN
ejpam-3877	658	7	in	in	ADP
ejpam-3877	658	8	(	(	PUNCT
ejpam-3877	658	9	6.11	6.11	NUM
ejpam-3877	658	10	)	)	PUNCT
ejpam-3877	658	11	,	,	PUNCT
ejpam-3877	658	12	then	then	ADV
ejpam-3877	658	13	we	we	PRON
ejpam-3877	658	14	obtain∫	obtain∫	VERB
ejpam-3877	658	15	q	q	PUNCT
ejpam-3877	658	16	ξntη(t)∆ξndxdt+	ξntη(t)∆ξndxdt+	ADP
ejpam-3877	658	17	∫	∫	PROPN
ejpam-3877	658	18	q	q	X
ejpam-3877	658	19	η(t)an(x	η(t)an(x	NOUN
ejpam-3877	658	20	,	,	PUNCT
ejpam-3877	658	21	t)[∆ξn]2dxdt+	t)[∆ξn]2dxdt+	NOUN
ejpam-3877	658	22	∫	∫	PROPN
ejpam-3877	658	23	q	q	PROPN
ejpam-3877	658	24	zη(t)∆ξndxdt	zη(t)∆ξndxdt	PROPN
ejpam-3877	658	25	=	=	SYM
ejpam-3877	658	26	0	0	NUM
ejpam-3877	658	27	.	.	PUNCT
ejpam-3877	659	1	(	(	PUNCT
ejpam-3877	659	2	6.13	6.13	NUM
ejpam-3877	659	3	)	)	PUNCT
ejpam-3877	659	4	it	it	PRON
ejpam-3877	659	5	follows	follow	VERB
ejpam-3877	659	6	that	that	SCONJ
ejpam-3877	659	7	1	1	NUM
ejpam-3877	659	8	2	2	NUM
ejpam-3877	659	9	∫	∫	NOUN
ejpam-3877	659	10	q	q	NOUN
ejpam-3877	660	1	|	|	ADV
ejpam-3877	660	2	∇ξn	∇ξn	PROPN
ejpam-3877	660	3	|2	|2	NUM
ejpam-3877	660	4	dxdt+	dxdt+	X
ejpam-3877	660	5	∫	∫	PROPN
ejpam-3877	660	6	q	q	NOUN
ejpam-3877	660	7	an(x	an(x	PROPN
ejpam-3877	660	8	,	,	PUNCT
ejpam-3877	660	9	t)[∆ξn]2dxdt	t)[∆ξn]2dxdt	VERB
ejpam-3877	660	10	≤	≤	NUM
ejpam-3877	660	11	c0(t	c0(t	PROPN
ejpam-3877	660	12	,	,	PUNCT
ejpam-3877	660	13	z	z	NOUN
ejpam-3877	660	14	)	)	PUNCT
ejpam-3877	660	15	(	(	PUNCT
ejpam-3877	660	16	6.14	6.14	NUM
ejpam-3877	660	17	)	)	PUNCT
ejpam-3877	660	18	holds	hold	VERB
ejpam-3877	660	19	,	,	PUNCT
ejpam-3877	660	20	for	for	ADP
ejpam-3877	660	21	some	some	DET
ejpam-3877	660	22	constant	constant	ADJ
ejpam-3877	660	23	c0(t	c0(t	NOUN
ejpam-3877	660	24	,	,	PUNCT
ejpam-3877	660	25	z	z	NOUN
ejpam-3877	660	26	)	)	PUNCT
ejpam-3877	660	27	independent	independent	ADJ
ejpam-3877	660	28	on	on	ADP
ejpam-3877	660	29	n.	n.	NOUN
ejpam-3877	660	30	from	from	ADP
ejpam-3877	660	31	(	(	PUNCT
ejpam-3877	660	32	6.12	6.12	NUM
ejpam-3877	660	33	)	)	PUNCT
ejpam-3877	660	34	and	and	CCONJ
ejpam-3877	660	35	(	(	PUNCT
ejpam-3877	660	36	6.14	6.14	NUM
ejpam-3877	660	37	)	)	PUNCT
ejpam-3877	660	38	,	,	PUNCT
ejpam-3877	660	39	there	there	PRON
ejpam-3877	660	40	exists	exist	VERB
ejpam-3877	660	41	a	a	DET
ejpam-3877	660	42	constant	constant	ADJ
ejpam-3877	660	43	c1(t	c1(t	NOUN
ejpam-3877	660	44	,	,	PUNCT
ejpam-3877	660	45	z	z	NOUN
ejpam-3877	660	46	)	)	PUNCT
ejpam-3877	660	47	such	such	ADJ
ejpam-3877	660	48	that	that	SCONJ
ejpam-3877	660	49	‖	‖	PROPN
ejpam-3877	660	50	ξn	ξn	PROPN
ejpam-3877	660	51	‖l2((0,t	‖l2((0,t	NOUN
ejpam-3877	660	52	)	)	PUNCT
ejpam-3877	660	53	,	,	PUNCT
ejpam-3877	660	54	h1	h1	PROPN
ejpam-3877	660	55	0	0	NUM
ejpam-3877	660	56	(	(	PUNCT
ejpam-3877	660	57	ω	ω	NOUN
ejpam-3877	660	58	)	)	PUNCT
ejpam-3877	660	59	)	)	PUNCT
ejpam-3877	661	1	+	+	CCONJ
ejpam-3877	661	2	‖	‖	ADJ
ejpam-3877	661	3	√	√	INTJ
ejpam-3877	661	4	an∆ξn	an∆ξn	ADJ
ejpam-3877	661	5	‖l2(q)≤	‖l2(q)≤	NUM
ejpam-3877	661	6	c1(t	c1(t	PROPN
ejpam-3877	661	7	,	,	PUNCT
ejpam-3877	661	8	z	z	NOUN
ejpam-3877	661	9	)	)	PUNCT
ejpam-3877	661	10	.	.	PUNCT
ejpam-3877	662	1	(	(	PUNCT
ejpam-3877	662	2	6.15	6.15	NUM
ejpam-3877	662	3	)	)	PUNCT
ejpam-3877	662	4	on	on	ADP
ejpam-3877	662	5	the	the	DET
ejpam-3877	662	6	other	other	ADJ
ejpam-3877	662	7	hand	hand	NOUN
ejpam-3877	662	8	,	,	PUNCT
ejpam-3877	662	9	multiplying	multiply	VERB
ejpam-3877	662	10	(	(	PUNCT
ejpam-3877	662	11	6.11	6.11	NUM
ejpam-3877	662	12	)	)	PUNCT
ejpam-3877	662	13	by	by	ADP
ejpam-3877	662	14	∆ξn	∆ξn	PROPN
ejpam-3877	662	15	,	,	PUNCT
ejpam-3877	662	16	we	we	PRON
ejpam-3877	662	17	obtain	obtain	VERB
ejpam-3877	662	18	−	−	PROPN
ejpam-3877	662	19	∫	∫	PROPN
ejpam-3877	662	20	q	q	PROPN
ejpam-3877	662	21	∇ξn∇ξnt	∇ξn∇ξnt	PROPN
ejpam-3877	662	22	+	+	CCONJ
ejpam-3877	662	23	∫	∫	PROPN
ejpam-3877	663	1	q	q	PROPN
ejpam-3877	663	2	an[∆ξn]2dxdt	an[∆ξn]2dxdt	PROPN
ejpam-3877	663	3	=	=	PUNCT
ejpam-3877	663	4	−	−	PROPN
ejpam-3877	663	5	∫	∫	PROPN
ejpam-3877	663	6	q	q	PROPN
ejpam-3877	663	7	ξn∆zdxdt	ξn∆zdxdt	PROPN
ejpam-3877	663	8	quincy	quincy	PROPN
ejpam-3877	663	9	s.	s.	PROPN
ejpam-3877	663	10	nkombo	nkombo	PROPN
ejpam-3877	663	11	,	,	PUNCT
ejpam-3877	663	12	fengquan	fengquan	PROPN
ejpam-3877	663	13	li	li	PROPN
ejpam-3877	663	14	/	/	SYM
ejpam-3877	663	15	eur	eur	PROPN
ejpam-3877	663	16	.	.	PUNCT
ejpam-3877	664	1	j.	j.	PROPN
ejpam-3877	664	2	pure	pure	PROPN
ejpam-3877	664	3	appl	appl	PROPN
ejpam-3877	664	4	.	.	PROPN
ejpam-3877	664	5	math	math	PROPN
ejpam-3877	664	6	,	,	PUNCT
ejpam-3877	664	7	14	14	NUM
ejpam-3877	664	8	(	(	PUNCT
ejpam-3877	664	9	1	1	NUM
ejpam-3877	664	10	)	)	PUNCT
ejpam-3877	664	11	(	(	PUNCT
ejpam-3877	664	12	2021	2021	NUM
ejpam-3877	664	13	)	)	PUNCT
ejpam-3877	664	14	,	,	PUNCT
ejpam-3877	664	15	204	204	NUM
ejpam-3877	664	16	-	-	SYM
ejpam-3877	664	17	233	233	NUM
ejpam-3877	664	18	230	230	NUM
ejpam-3877	664	19	which	which	PRON
ejpam-3877	664	20	leads	lead	VERB
ejpam-3877	664	21	to	to	ADP
ejpam-3877	664	22	1	1	NUM
ejpam-3877	664	23	2	2	NUM
ejpam-3877	664	24	∫	∫	NOUN
ejpam-3877	664	25	ω	ω	NUM
ejpam-3877	664	26	|	|	PROPN
ejpam-3877	664	27	∇ξn	∇ξn	PROPN
ejpam-3877	664	28	|2	|2	NUM
ejpam-3877	664	29	(	(	PUNCT
ejpam-3877	664	30	x	x	NOUN
ejpam-3877	664	31	,	,	PUNCT
ejpam-3877	664	32	0)dx+	0)dx+	NOUN
ejpam-3877	664	33	∫	∫	PROPN
ejpam-3877	664	34	q	q	PROPN
ejpam-3877	664	35	an[∆ξn]2dxdt	an[∆ξn]2dxdt	PROPN
ejpam-3877	664	36	≤	≤	PROPN
ejpam-3877	664	37	c2(t	c2(t	PROPN
ejpam-3877	664	38	,	,	PUNCT
ejpam-3877	664	39	z	z	NOUN
ejpam-3877	664	40	)	)	PUNCT
ejpam-3877	664	41	,	,	PUNCT
ejpam-3877	664	42	(	(	PUNCT
ejpam-3877	664	43	6.16	6.16	NUM
ejpam-3877	664	44	)	)	PUNCT
ejpam-3877	664	45	where	where	SCONJ
ejpam-3877	664	46	c2(t	c2(t	PROPN
ejpam-3877	664	47	,	,	PUNCT
ejpam-3877	664	48	z	z	NOUN
ejpam-3877	664	49	)	)	PUNCT
ejpam-3877	665	1	=	=	NOUN
ejpam-3877	665	2	‖	‖	NOUN
ejpam-3877	665	3	ξn	ξn	NOUN
ejpam-3877	665	4	‖l∞(q)‖	‖l∞(q)‖	PROPN
ejpam-3877	665	5	z	z	NOUN
ejpam-3877	665	6	‖c2(q	‖c2(q	NOUN
ejpam-3877	665	7	)	)	PUNCT
ejpam-3877	665	8	.	.	PUNCT
ejpam-3877	666	1	therefore	therefore	ADV
ejpam-3877	666	2	,	,	PUNCT
ejpam-3877	666	3	we	we	PRON
ejpam-3877	666	4	get	get	VERB
ejpam-3877	666	5	‖	‖	PROPN
ejpam-3877	666	6	ξn	ξn	PROPN
ejpam-3877	666	7	(	(	PUNCT
ejpam-3877	666	8	.	.	PUNCT
ejpam-3877	666	9	,	,	PUNCT
ejpam-3877	666	10	0	0	NUM
ejpam-3877	666	11	)	)	PUNCT
ejpam-3877	666	12	‖h1	‖h1	NOUN
ejpam-3877	666	13	0	0	PUNCT
ejpam-3877	666	14	(	(	PUNCT
ejpam-3877	666	15	ω	ω	NOUN
ejpam-3877	666	16	)	)	PUNCT
ejpam-3877	666	17	+	+	CCONJ
ejpam-3877	666	18	‖	‖	ADJ
ejpam-3877	666	19	√	√	INTJ
ejpam-3877	666	20	an∆ξn	an∆ξn	ADJ
ejpam-3877	666	21	‖l2(q)≤	‖l2(q)≤	NUM
ejpam-3877	666	22	c2(t	c2(t	PROPN
ejpam-3877	666	23	,	,	PUNCT
ejpam-3877	666	24	z	z	NOUN
ejpam-3877	666	25	)	)	PUNCT
ejpam-3877	666	26	.	.	PUNCT
ejpam-3877	667	1	(	(	PUNCT
ejpam-3877	667	2	6.17	6.17	NUM
ejpam-3877	667	3	)	)	PUNCT
ejpam-3877	667	4	by	by	ADP
ejpam-3877	667	5	standard	standard	ADJ
ejpam-3877	667	6	density	density	NOUN
ejpam-3877	667	7	argument	argument	NOUN
ejpam-3877	667	8	and	and	CCONJ
ejpam-3877	667	9	for	for	ADP
ejpam-3877	667	10	ξ	ξ	PROPN
ejpam-3877	667	11	=	=	SYM
ejpam-3877	667	12	ξn	ξn	PROPN
ejpam-3877	667	13	a	a	DET
ejpam-3877	667	14	test	test	NOUN
ejpam-3877	667	15	function	function	NOUN
ejpam-3877	667	16	in	in	ADP
ejpam-3877	667	17	(	(	PUNCT
ejpam-3877	667	18	6.9	6.9	NUM
ejpam-3877	667	19	)	)	PUNCT
ejpam-3877	667	20	.	.	PUNCT
ejpam-3877	668	1	moreover	moreover	ADV
ejpam-3877	668	2	,	,	PUNCT
ejpam-3877	668	3	by	by	ADP
ejpam-3877	668	4	recalling	recall	VERB
ejpam-3877	668	5	(	(	PUNCT
ejpam-3877	668	6	6.10	6.10	NUM
ejpam-3877	668	7	)	)	PUNCT
ejpam-3877	668	8	and	and	CCONJ
ejpam-3877	668	9	(	(	PUNCT
ejpam-3877	668	10	6.9	6.9	NUM
ejpam-3877	668	11	)	)	PUNCT
ejpam-3877	668	12	,	,	PUNCT
ejpam-3877	668	13	there	there	PRON
ejpam-3877	668	14	holds∫	holds∫	VERB
ejpam-3877	668	15	q	q	NOUN
ejpam-3877	668	16	(	(	PUNCT
ejpam-3877	668	17	u1n	u1n	NOUN
ejpam-3877	668	18	−	−	PROPN
ejpam-3877	668	19	u2n	u2n	NOUN
ejpam-3877	668	20	)	)	PUNCT
ejpam-3877	668	21	zdxdt	zdxdt	NOUN
ejpam-3877	668	22	=	=	SYM
ejpam-3877	668	23	∫	∫	PROPN
ejpam-3877	668	24	q	q	PROPN
ejpam-3877	669	1	(	(	PUNCT
ejpam-3877	669	2	µ1n	µ1n	NOUN
ejpam-3877	669	3	−	−	PROPN
ejpam-3877	669	4	µ2n	µ2n	NOUN
ejpam-3877	669	5	)	)	PUNCT
ejpam-3877	669	6	ξ(x	ξ(x	PROPN
ejpam-3877	669	7	,	,	PUNCT
ejpam-3877	669	8	t)dxdt+	t)dxdt+	PROPN
ejpam-3877	669	9	∫	∫	PROPN
ejpam-3877	669	10	ω	ω	PROPN
ejpam-3877	669	11	(	(	PUNCT
ejpam-3877	669	12	u01n	u01n	NOUN
ejpam-3877	669	13	−	−	NOUN
ejpam-3877	669	14	u02n	u02n	NOUN
ejpam-3877	669	15	)	)	PUNCT
ejpam-3877	669	16	ξ(x	ξ(x	NOUN
ejpam-3877	669	17	,	,	PUNCT
ejpam-3877	669	18	0)dx	0)dx	NOUN
ejpam-3877	669	19	.	.	PUNCT
ejpam-3877	670	1	(	(	PUNCT
ejpam-3877	670	2	6.18	6.18	NUM
ejpam-3877	670	3	)	)	PUNCT
ejpam-3877	670	4	letting	let	VERB
ejpam-3877	670	5	n	n	PRON
ejpam-3877	670	6	to	to	PART
ejpam-3877	670	7	infinity	infinity	VERB
ejpam-3877	670	8	in	in	ADP
ejpam-3877	670	9	(	(	PUNCT
ejpam-3877	670	10	6.18	6.18	NUM
ejpam-3877	670	11	)	)	PUNCT
ejpam-3877	670	12	.	.	PUNCT
ejpam-3877	671	1	then	then	ADV
ejpam-3877	671	2	it	it	PRON
ejpam-3877	671	3	is	be	AUX
ejpam-3877	671	4	enough	enough	ADJ
ejpam-3877	671	5	to	to	PART
ejpam-3877	671	6	observe	observe	VERB
ejpam-3877	671	7	from	from	ADP
ejpam-3877	671	8	(	(	PUNCT
ejpam-3877	671	9	6.15	6.15	NUM
ejpam-3877	671	10	)	)	PUNCT
ejpam-3877	671	11	,	,	PUNCT
ejpam-3877	671	12	there	there	PRON
ejpam-3877	671	13	exists	exist	VERB
ejpam-3877	671	14	ξn	ξn	PROPN
ejpam-3877	671	15	∈	∈	PROPN
ejpam-3877	671	16	l∞((0	l∞((0	PROPN
ejpam-3877	671	17	,	,	PUNCT
ejpam-3877	671	18	t	t	PROPN
ejpam-3877	671	19	)	)	PUNCT
ejpam-3877	671	20	,	,	PUNCT
ejpam-3877	671	21	h2(ω))∩l2((0	h2(ω))∩l2((0	NOUN
ejpam-3877	671	22	,	,	PUNCT
ejpam-3877	671	23	t	t	PROPN
ejpam-3877	671	24	)	)	PUNCT
ejpam-3877	671	25	,	,	PUNCT
ejpam-3877	671	26	h1	h1	PROPN
ejpam-3877	671	27	0	0	NUM
ejpam-3877	671	28	(	(	PUNCT
ejpam-3877	671	29	ω	ω	NOUN
ejpam-3877	671	30	)	)	PUNCT
ejpam-3877	671	31	)	)	PUNCT
ejpam-3877	671	32	which	which	PRON
ejpam-3877	671	33	is	be	AUX
ejpam-3877	671	34	obtained	obtain	VERB
ejpam-3877	671	35	by	by	ADP
ejpam-3877	671	36	extracting	extract	VERB
ejpam-3877	671	37	the	the	DET
ejpam-3877	671	38	subsequence	subsequence	NOUN
ejpam-3877	671	39	of	of	ADP
ejpam-3877	671	40	the	the	DET
ejpam-3877	671	41	sequence	sequence	NOUN
ejpam-3877	671	42	{	{	PUNCT
ejpam-3877	671	43	ξn	ξn	PROPN
ejpam-3877	671	44	}	}	PUNCT
ejpam-3877	671	45	,	,	PUNCT
ejpam-3877	671	46	such	such	ADJ
ejpam-3877	671	47	that	that	SCONJ
ejpam-3877	671	48	ξn(x	ξn(x	ADJ
ejpam-3877	671	49	,	,	PUNCT
ejpam-3877	671	50	t	t	PROPN
ejpam-3877	671	51	)	)	PUNCT
ejpam-3877	671	52	∗	∗	NOUN
ejpam-3877	671	53	⇀	⇀	NUM
ejpam-3877	671	54	ξ(x	ξ(x	NOUN
ejpam-3877	671	55	,	,	PUNCT
ejpam-3877	671	56	t	t	PROPN
ejpam-3877	671	57	)	)	PUNCT
ejpam-3877	671	58	in	in	ADP
ejpam-3877	671	59	l∞(q	l∞(q	NOUN
ejpam-3877	671	60	)	)	PUNCT
ejpam-3877	671	61	.	.	PUNCT
ejpam-3877	672	1	(	(	PUNCT
ejpam-3877	672	2	6.19	6.19	NUM
ejpam-3877	672	3	)	)	PUNCT
ejpam-3877	672	4	∇ξn(x	∇ξn(x	PROPN
ejpam-3877	672	5	,	,	PUNCT
ejpam-3877	672	6	t	t	PROPN
ejpam-3877	672	7	)	)	PUNCT
ejpam-3877	672	8	⇀	⇀	PROPN
ejpam-3877	672	9	∇ξ(x	∇ξ(x	NOUN
ejpam-3877	672	10	,	,	PUNCT
ejpam-3877	672	11	t	t	PROPN
ejpam-3877	672	12	)	)	PUNCT
ejpam-3877	672	13	in	in	ADP
ejpam-3877	672	14	[	[	X
ejpam-3877	672	15	l2(q)]n	l2(q)]n	ADV
ejpam-3877	672	16	.	.	PUNCT
ejpam-3877	673	1	(	(	PUNCT
ejpam-3877	673	2	6.20	6.20	NUM
ejpam-3877	673	3	)	)	PUNCT
ejpam-3877	673	4	since	since	SCONJ
ejpam-3877	673	5	ξnt	ξnt	NOUN
ejpam-3877	673	6	∈	∈	PROPN
ejpam-3877	673	7	l2(q	l2(q	PROPN
ejpam-3877	673	8	)	)	PUNCT
ejpam-3877	673	9	,	,	PUNCT
ejpam-3877	673	10	as	as	SCONJ
ejpam-3877	673	11	stated	state	VERB
ejpam-3877	673	12	in	in	ADP
ejpam-3877	673	13	[	[	X
ejpam-3877	673	14	19	19	NUM
ejpam-3877	673	15	]	]	PUNCT
ejpam-3877	673	16	,	,	PUNCT
ejpam-3877	673	17	we	we	PRON
ejpam-3877	673	18	deduce	deduce	VERB
ejpam-3877	673	19	that	that	SCONJ
ejpam-3877	673	20	ξnt(x	ξnt(x	PROPN
ejpam-3877	673	21	,	,	PUNCT
ejpam-3877	673	22	t)→	t)→	NUM
ejpam-3877	673	23	ξt(x	ξt(x	PROPN
ejpam-3877	673	24	,	,	PUNCT
ejpam-3877	673	25	t	t	PROPN
ejpam-3877	673	26	)	)	PUNCT
ejpam-3877	673	27	in	in	ADP
ejpam-3877	673	28	l2(q	l2(q	PROPN
ejpam-3877	673	29	)	)	PUNCT
ejpam-3877	673	30	,	,	PUNCT
ejpam-3877	673	31	(	(	PUNCT
ejpam-3877	673	32	6.21	6.21	NUM
ejpam-3877	673	33	)	)	PUNCT
ejpam-3877	673	34	ξn(x	ξn(x	ADJ
ejpam-3877	673	35	,	,	PUNCT
ejpam-3877	673	36	t)→	t)→	NUM
ejpam-3877	673	37	ξ(x	ξ(x	NOUN
ejpam-3877	673	38	,	,	PUNCT
ejpam-3877	673	39	t	t	PROPN
ejpam-3877	673	40	)	)	PUNCT
ejpam-3877	673	41	a.e	a.e	PROPN
ejpam-3877	673	42	in	in	ADP
ejpam-3877	673	43	q.	q.	PROPN
ejpam-3877	673	44	(	(	PUNCT
ejpam-3877	673	45	6.22	6.22	NUM
ejpam-3877	673	46	)	)	PUNCT
ejpam-3877	673	47	on	on	ADP
ejpam-3877	673	48	one	one	NUM
ejpam-3877	673	49	hand	hand	NOUN
ejpam-3877	673	50	,	,	PUNCT
ejpam-3877	673	51	it	it	PRON
ejpam-3877	673	52	is	be	AUX
ejpam-3877	673	53	enough	enough	ADJ
ejpam-3877	673	54	to	to	PART
ejpam-3877	673	55	observe	observe	VERB
ejpam-3877	673	56	that	that	SCONJ
ejpam-3877	673	57	from	from	ADP
ejpam-3877	673	58	(	(	PUNCT
ejpam-3877	673	59	6.17	6.17	NUM
ejpam-3877	673	60	)	)	PUNCT
ejpam-3877	673	61	,	,	PUNCT
ejpam-3877	673	62	there	there	PRON
ejpam-3877	673	63	exists	exist	VERB
ejpam-3877	673	64	ξ	ξ	PROPN
ejpam-3877	673	65	(	(	PUNCT
ejpam-3877	673	66	·	·	PUNCT
ejpam-3877	673	67	,	,	PUNCT
ejpam-3877	673	68	0	0	NUM
ejpam-3877	673	69	)	)	PUNCT
ejpam-3877	673	70	∈	∈	NOUN
ejpam-3877	673	71	l∞(ω	l∞(ω	X
ejpam-3877	673	72	)	)	PUNCT
ejpam-3877	674	1	∩h1	∩h1	NOUN
ejpam-3877	674	2	0	0	SYM
ejpam-3877	674	3	(	(	PUNCT
ejpam-3877	674	4	ω	ω	NOUN
ejpam-3877	674	5	)	)	PUNCT
ejpam-3877	674	6	such	such	ADJ
ejpam-3877	674	7	that	that	SCONJ
ejpam-3877	674	8	the	the	DET
ejpam-3877	674	9	following	follow	VERB
ejpam-3877	674	10	statements	statement	NOUN
ejpam-3877	674	11	ξn(x	ξn(x	ADJ
ejpam-3877	674	12	,	,	PUNCT
ejpam-3877	674	13	0	0	NUM
ejpam-3877	674	14	)	)	PUNCT
ejpam-3877	674	15	∗	∗	NOUN
ejpam-3877	674	16	⇀	⇀	NUM
ejpam-3877	674	17	ξ(x	ξ(x	NOUN
ejpam-3877	674	18	,	,	PUNCT
ejpam-3877	674	19	0	0	NUM
ejpam-3877	674	20	)	)	PUNCT
ejpam-3877	674	21	in	in	ADP
ejpam-3877	674	22	l∞(ω	l∞(ω	ADJ
ejpam-3877	674	23	)	)	PUNCT
ejpam-3877	674	24	,	,	PUNCT
ejpam-3877	674	25	(	(	PUNCT
ejpam-3877	674	26	6.23	6.23	NUM
ejpam-3877	674	27	)	)	PUNCT
ejpam-3877	674	28	ξn(x	ξn(x	ADJ
ejpam-3877	674	29	,	,	PUNCT
ejpam-3877	674	30	0	0	NUM
ejpam-3877	674	31	)	)	PUNCT
ejpam-3877	674	32	⇀	⇀	PROPN
ejpam-3877	674	33	ξ(x	ξ(x	NOUN
ejpam-3877	674	34	,	,	PUNCT
ejpam-3877	674	35	0	0	NUM
ejpam-3877	674	36	)	)	PUNCT
ejpam-3877	674	37	in	in	ADP
ejpam-3877	674	38	h1	h1	PROPN
ejpam-3877	674	39	0	0	NUM
ejpam-3877	674	40	(	(	PUNCT
ejpam-3877	674	41	ω	ω	NOUN
ejpam-3877	674	42	)	)	PUNCT
ejpam-3877	674	43	,	,	PUNCT
ejpam-3877	674	44	(	(	PUNCT
ejpam-3877	674	45	6.24	6.24	NUM
ejpam-3877	674	46	)	)	PUNCT
ejpam-3877	674	47	holds	hold	VERB
ejpam-3877	674	48	true	true	ADJ
ejpam-3877	674	49	.	.	PUNCT
ejpam-3877	675	1	combining	combine	VERB
ejpam-3877	675	2	(	(	PUNCT
ejpam-3877	675	3	6.18)-(6.24	6.18)-(6.24	NUM
ejpam-3877	675	4	)	)	PUNCT
ejpam-3877	675	5	and	and	CCONJ
ejpam-3877	675	6	(	(	PUNCT
ejpam-3877	675	7	3.10	3.10	NUM
ejpam-3877	675	8	)	)	PUNCT
ejpam-3877	675	9	,	,	PUNCT
ejpam-3877	675	10	there	there	PRON
ejpam-3877	675	11	holds	hold	VERB
ejpam-3877	675	12	lim	lim	PROPN
ejpam-3877	675	13	n→∞	n→∞	NUM
ejpam-3877	675	14	∫	∫	PROPN
ejpam-3877	675	15	q	q	PROPN
ejpam-3877	676	1	(	(	PUNCT
ejpam-3877	676	2	u1n	u1n	NOUN
ejpam-3877	676	3	−	−	PROPN
ejpam-3877	676	4	u2n	u2n	NOUN
ejpam-3877	676	5	)	)	PUNCT
ejpam-3877	676	6	zdxdt	zdxdt	NOUN
ejpam-3877	676	7	=	=	PROPN
ejpam-3877	676	8	lim	lim	PROPN
ejpam-3877	676	9	n→∞	n→∞	NUM
ejpam-3877	676	10	∫	∫	PROPN
ejpam-3877	676	11	q	q	PROPN
ejpam-3877	677	1	(	(	PUNCT
ejpam-3877	677	2	f1n	f1n	PROPN
ejpam-3877	677	3	−	−	PROPN
ejpam-3877	677	4	f2n	f2n	PROPN
ejpam-3877	677	5	)	)	PUNCT
ejpam-3877	677	6	ξ(x	ξ(x	NOUN
ejpam-3877	677	7	,	,	PUNCT
ejpam-3877	677	8	t)dxdt+	t)dxdt+	PROPN
ejpam-3877	677	9	+	+	CCONJ
ejpam-3877	677	10	lim	lim	PROPN
ejpam-3877	677	11	n→∞	n→∞	NUM
ejpam-3877	677	12	∫	∫	PROPN
ejpam-3877	677	13	q	q	PROPN
ejpam-3877	678	1	(	(	PUNCT
ejpam-3877	678	2	f1n	f1n	PROPN
ejpam-3877	678	3	−	−	PROPN
ejpam-3877	678	4	f2n	f2n	PROPN
ejpam-3877	678	5	)	)	PUNCT
ejpam-3877	678	6	ξ(x	ξ(x	NOUN
ejpam-3877	678	7	,	,	PUNCT
ejpam-3877	678	8	t)dxdt−	t)dxdt−	PROPN
ejpam-3877	678	9	lim	lim	PROPN
ejpam-3877	678	10	n→∞	n→∞	NUM
ejpam-3877	678	11	∫	∫	PROPN
ejpam-3877	678	12	q	q	PROPN
ejpam-3877	678	13	(	(	PUNCT
ejpam-3877	678	14	g1n	g1n	INTJ
ejpam-3877	678	15	−	−	PROPN
ejpam-3877	678	16	g2n	g2n	NOUN
ejpam-3877	678	17	)	)	PUNCT
ejpam-3877	678	18	ξt(x	ξt(x	NOUN
ejpam-3877	678	19	,	,	PUNCT
ejpam-3877	678	20	t)dxdt+	t)dxdt+	PROPN
ejpam-3877	678	21	+	+	CCONJ
ejpam-3877	678	22	lim	lim	PROPN
ejpam-3877	678	23	n→∞	n→∞	NUM
ejpam-3877	679	1	∫	∫	PROPN
ejpam-3877	679	2	ω	ω	PROPN
ejpam-3877	679	3	(	(	PUNCT
ejpam-3877	679	4	g01n	g01n	PROPN
ejpam-3877	679	5	−	−	PROPN
ejpam-3877	679	6	g02n	g02n	NOUN
ejpam-3877	679	7	)	)	PUNCT
ejpam-3877	679	8	ξ(x	ξ(x	NOUN
ejpam-3877	679	9	,	,	PUNCT
ejpam-3877	679	10	0)dxdt+	0)dxdt+	NUM
ejpam-3877	679	11	lim	lim	PROPN
ejpam-3877	679	12	n→∞	n→∞	NUM
ejpam-3877	679	13	∫	∫	PROPN
ejpam-3877	679	14	ω	ω	PROPN
ejpam-3877	679	15	(	(	PUNCT
ejpam-3877	679	16	f01n	f01n	X
ejpam-3877	679	17	−	−	PRON
ejpam-3877	679	18	f02n	f02n	NOUN
ejpam-3877	679	19	)	)	PUNCT
ejpam-3877	679	20	ξ(x	ξ(x	NOUN
ejpam-3877	679	21	,	,	PUNCT
ejpam-3877	679	22	0)dx	0)dx	NOUN
ejpam-3877	679	23	=	=	NOUN
ejpam-3877	679	24	0	0	X
ejpam-3877	679	25	.	.	PUNCT
ejpam-3877	680	1	therefore	therefore	ADV
ejpam-3877	680	2	the	the	DET
ejpam-3877	680	3	following	follow	VERB
ejpam-3877	680	4	equality	equality	NOUN
ejpam-3877	680	5	holds	hold	VERB
ejpam-3877	680	6	〈	〈	PROPN
ejpam-3877	680	7	u1	u1	NOUN
ejpam-3877	680	8	−	−	PROPN
ejpam-3877	680	9	u2	u2	NOUN
ejpam-3877	680	10	,	,	PUNCT
ejpam-3877	680	11	z〉q	z〉q	NOUN
ejpam-3877	680	12	=	=	NOUN
ejpam-3877	680	13	0	0	X
ejpam-3877	680	14	.	.	PUNCT
ejpam-3877	681	1	as	as	SCONJ
ejpam-3877	681	2	we	we	PRON
ejpam-3877	681	3	stated	state	VERB
ejpam-3877	681	4	above	above	ADV
ejpam-3877	681	5	in	in	ADP
ejpam-3877	681	6	the	the	DET
ejpam-3877	681	7	previous	previous	ADJ
ejpam-3877	681	8	proof	proof	NOUN
ejpam-3877	681	9	u1n	u1n	NOUN
ejpam-3877	681	10	∗	∗	NOUN
ejpam-3877	681	11	⇀	⇀	PROPN
ejpam-3877	681	12	u1	u1	NOUN
ejpam-3877	681	13	in	in	ADP
ejpam-3877	681	14	m+(q	m+(q	PROPN
ejpam-3877	681	15	)	)	PUNCT
ejpam-3877	681	16	and	and	CCONJ
ejpam-3877	681	17	u2n	u2n	PROPN
ejpam-3877	681	18	∗	∗	NOUN
ejpam-3877	681	19	⇀	⇀	PROPN
ejpam-3877	681	20	u2	u2	NOUN
ejpam-3877	681	21	in	in	ADP
ejpam-3877	681	22	m+(q	m+(q	NUM
ejpam-3877	681	23	)	)	PUNCT
ejpam-3877	681	24	.	.	PUNCT
ejpam-3877	682	1	thus	thus	ADV
ejpam-3877	682	2	we	we	PRON
ejpam-3877	682	3	can	can	AUX
ejpam-3877	682	4	deduce	deduce	VERB
ejpam-3877	682	5	u1	u1	NOUN
ejpam-3877	682	6	=	=	SYM
ejpam-3877	682	7	u1	u1	NOUN
ejpam-3877	682	8	holds	hold	NOUN
ejpam-3877	682	9	.	.	PUNCT
ejpam-3877	683	1	�	�	PROPN
ejpam-3877	683	2	references	reference	VERB
ejpam-3877	683	3	231	231	NUM
ejpam-3877	683	4	acknowledgements	acknowledgement	NOUN
ejpam-3877	683	5	this	this	DET
ejpam-3877	683	6	work	work	NOUN
ejpam-3877	683	7	was	be	AUX
ejpam-3877	683	8	partially	partially	ADV
ejpam-3877	683	9	supported	support	VERB
ejpam-3877	683	10	by	by	ADP
ejpam-3877	683	11	national	national	ADJ
ejpam-3877	683	12	natural	natural	PROPN
ejpam-3877	683	13	sciences	sciences	PROPN
ejpam-3877	683	14	foundation	foundation	PROPN
ejpam-3877	683	15	of	of	ADP
ejpam-3877	683	16	china	china	PROPN
ejpam-3877	683	17	,	,	PUNCT
ejpam-3877	683	18	no	no	PRON
ejpam-3877	683	19	:	:	PUNCT
ejpam-3877	683	20	11571057	11571057	NUM
ejpam-3877	683	21	.	.	PUNCT
ejpam-3877	684	1	references	reference	NOUN
ejpam-3877	684	2	[	[	X
ejpam-3877	684	3	1	1	NUM
ejpam-3877	684	4	]	]	PUNCT
ejpam-3877	684	5	a.	a.	NOUN
ejpam-3877	684	6	mercaldo	mercaldo	PROPN
ejpam-3877	684	7	a.	a.	NOUN
ejpam-3877	684	8	fiorenza	fiorenza	PROPN
ejpam-3877	684	9	and	and	CCONJ
ejpam-3877	684	10	j.	j.	PROPN
ejpam-3877	684	11	m.	m.	PROPN
ejpam-3877	684	12	rakotoson	rakotoson	PROPN
ejpam-3877	684	13	.	.	PUNCT
ejpam-3877	685	1	regularity	regularity	NOUN
ejpam-3877	685	2	and	and	CCONJ
ejpam-3877	685	3	uniqueness	uniqueness	NOUN
ejpam-3877	685	4	results	result	NOUN
ejpam-3877	685	5	in	in	ADP
ejpam-3877	685	6	grand	grand	ADJ
ejpam-3877	685	7	sobolev	sobolev	NOUN
ejpam-3877	685	8	spaces	space	NOUN
ejpam-3877	685	9	for	for	ADP
ejpam-3877	685	10	parabolic	parabolic	ADJ
ejpam-3877	685	11	equations	equation	NOUN
ejpam-3877	685	12	with	with	ADP
ejpam-3877	685	13	measure	measure	NOUN
ejpam-3877	685	14	data	datum	NOUN
ejpam-3877	685	15	.	.	PUNCT
ejpam-3877	686	1	discrete	discrete	ADJ
ejpam-3877	686	2	contin	contin	NOUN
ejpam-3877	686	3	.	.	PUNCT
ejpam-3877	687	1	dyn	dyn	NOUN
ejpam-3877	687	2	.	.	PUNCT
ejpam-3877	688	1	syst	syst	PROPN
ejpam-3877	688	2	.	.	PROPN
ejpam-3877	688	3	,	,	PUNCT
ejpam-3877	688	4	8:893–906	8:893–906	NUM
ejpam-3877	688	5	,	,	PUNCT
ejpam-3877	688	6	2002	2002	NUM
ejpam-3877	688	7	.	.	PUNCT
ejpam-3877	689	1	[	[	X
ejpam-3877	689	2	2	2	NUM
ejpam-3877	689	3	]	]	PUNCT
ejpam-3877	689	4	c.	c.	PROPN
ejpam-3877	689	5	ponce	ponce	PROPN
ejpam-3877	689	6	augusto	augusto	PROPN
ejpam-3877	689	7	.	.	PUNCT
ejpam-3877	690	1	elliptic	elliptic	ADJ
ejpam-3877	690	2	pdes	pde	NOUN
ejpam-3877	690	3	,	,	PUNCT
ejpam-3877	690	4	measures	measure	NOUN
ejpam-3877	690	5	and	and	CCONJ
ejpam-3877	690	6	capacities	capacity	NOUN
ejpam-3877	690	7	.	.	PUNCT
ejpam-3877	691	1	from	from	ADP
ejpam-3877	691	2	the	the	DET
ejpam-3877	691	3	poisson	poisson	PROPN
ejpam-3877	691	4	equations	equation	NOUN
ejpam-3877	691	5	to	to	PART
ejpam-3877	691	6	nonlinear	nonlinear	VERB
ejpam-3877	691	7	thomas	thomas	PROPN
ejpam-3877	691	8	-	-	PUNCT
ejpam-3877	691	9	fermi	fermi	NOUN
ejpam-3877	691	10	problems	problem	NOUN
ejpam-3877	691	11	.	.	PUNCT
ejpam-3877	692	1	ems	ems	PROPN
ejpam-3877	692	2	tracts	tract	NOUN
ejpam-3877	692	3	in	in	ADP
ejpam-3877	692	4	mathematics	mathematic	NOUN
ejpam-3877	692	5	,	,	PUNCT
ejpam-3877	692	6	volume	volume	NOUN
ejpam-3877	692	7	23	23	NUM
ejpam-3877	692	8	.	.	PUNCT
ejpam-3877	693	1	zurich	zurich	PROPN
ejpam-3877	693	2	,	,	PUNCT
ejpam-3877	693	3	2016	2016	NUM
ejpam-3877	693	4	.	.	PUNCT
ejpam-3877	694	1	[	[	X
ejpam-3877	694	2	3	3	X
ejpam-3877	694	3	]	]	PUNCT
ejpam-3877	694	4	m.	m.	NOUN
ejpam-3877	694	5	bertsch	bertsch	PROPN
ejpam-3877	694	6	.	.	PUNCT
ejpam-3877	695	1	a	a	DET
ejpam-3877	695	2	class	class	NOUN
ejpam-3877	695	3	of	of	ADP
ejpam-3877	695	4	degenerate	degenerate	ADJ
ejpam-3877	695	5	diffusion	diffusion	NOUN
ejpam-3877	695	6	equations	equation	NOUN
ejpam-3877	695	7	with	with	ADP
ejpam-3877	695	8	a	a	DET
ejpam-3877	695	9	singular	singular	ADJ
ejpam-3877	695	10	nonlinear	nonlinear	ADJ
ejpam-3877	695	11	term	term	NOUN
ejpam-3877	695	12	.	.	PUNCT
ejpam-3877	696	1	nonlinear	nonlinear	ADJ
ejpam-3877	696	2	anal	anal	PROPN
ejpam-3877	696	3	.	.	PUNCT
ejpam-3877	696	4	,	,	PUNCT
ejpam-3877	697	1	7:117–127	7:117–127	NUM
ejpam-3877	697	2	,	,	PUNCT
ejpam-3877	697	3	1983	1983	NUM
ejpam-3877	697	4	.	.	PUNCT
ejpam-3877	698	1	[	[	X
ejpam-3877	698	2	4	4	NUM
ejpam-3877	698	3	]	]	X
ejpam-3877	698	4	l.	l.	PROPN
ejpam-3877	698	5	boccardo	boccardo	PROPN
ejpam-3877	698	6	and	and	CCONJ
ejpam-3877	698	7	m.	m.	NOUN
ejpam-3877	698	8	m.	m.	NOUN
ejpam-3877	698	9	porzio	porzio	PROPN
ejpam-3877	698	10	.	.	PUNCT
ejpam-3877	699	1	bounded	bound	VERB
ejpam-3877	699	2	solutions	solution	NOUN
ejpam-3877	699	3	for	for	ADP
ejpam-3877	699	4	a	a	DET
ejpam-3877	699	5	class	class	NOUN
ejpam-3877	699	6	of	of	ADP
ejpam-3877	699	7	quasi	quasi	ADJ
ejpam-3877	699	8	-	-	ADJ
ejpam-3877	699	9	linear	linear	ADJ
ejpam-3877	699	10	parabolic	parabolic	NOUN
ejpam-3877	699	11	problems	problem	NOUN
ejpam-3877	699	12	with	with	ADP
ejpam-3877	699	13	a	a	DET
ejpam-3877	699	14	quadratic	quadratic	ADJ
ejpam-3877	699	15	gradient	gradient	ADJ
ejpam-3877	699	16	term	term	NOUN
ejpam-3877	699	17	.	.	PUNCT
ejpam-3877	700	1	evolution	evolution	NOUN
ejpam-3877	700	2	equations	equation	NOUN
ejpam-3877	700	3	,	,	PUNCT
ejpam-3877	700	4	semigroups	semigroup	NOUN
ejpam-3877	700	5	and	and	CCONJ
ejpam-3877	700	6	functional	functional	ADJ
ejpam-3877	700	7	analysis	analysis	NOUN
ejpam-3877	700	8	(	(	PUNCT
ejpam-3877	700	9	milano	milano	PROPN
ejpam-3877	700	10	,	,	PUNCT
ejpam-3877	700	11	2000	2000	NUM
ejpam-3877	700	12	)	)	PUNCT
ejpam-3877	700	13	39	39	NUM
ejpam-3877	700	14	-	-	SYM
ejpam-3877	700	15	48	48	NUM
ejpam-3877	700	16	.	.	PUNCT
ejpam-3877	701	1	progr	progr	NOUN
ejpam-3877	701	2	.	.	PUNCT
ejpam-3877	702	1	nonlinear	nonlinear	ADJ
ejpam-3877	702	2	differential	differential	ADJ
ejpam-3877	702	3	equations	equation	NOUN
ejpam-3877	702	4	appl	appl	PROPN
ejpam-3877	702	5	.	.	PROPN
ejpam-3877	702	6	,	,	PUNCT
ejpam-3877	702	7	50	50	NUM
ejpam-3877	702	8	,	,	PUNCT
ejpam-3877	702	9	birkhauser	birkhauser	NOUN
ejpam-3877	702	10	,	,	PUNCT
ejpam-3877	702	11	basel	basel	PROPN
ejpam-3877	702	12	,	,	PUNCT
ejpam-3877	702	13	2002	2002	NUM
ejpam-3877	702	14	.	.	PUNCT
ejpam-3877	703	1	[	[	X
ejpam-3877	703	2	5	5	X
ejpam-3877	703	3	]	]	PUNCT
ejpam-3877	703	4	h.	h.	NOUN
ejpam-3877	703	5	brezis	brezis	PROPN
ejpam-3877	703	6	.	.	PUNCT
ejpam-3877	704	1	functional	functional	ADJ
ejpam-3877	704	2	analysis	analysis	NOUN
ejpam-3877	704	3	,	,	PUNCT
ejpam-3877	704	4	sobolev	sobolev	NOUN
ejpam-3877	704	5	spaces	space	NOUN
ejpam-3877	704	6	and	and	CCONJ
ejpam-3877	704	7	partial	partial	ADJ
ejpam-3877	704	8	differential	differential	ADJ
ejpam-3877	704	9	equations	equation	NOUN
ejpam-3877	704	10	.	.	PUNCT
ejpam-3877	705	1	springer	springer	NOUN
ejpam-3877	705	2	,	,	PUNCT
ejpam-3877	705	3	new	new	PROPN
ejpam-3877	705	4	york	york	PROPN
ejpam-3877	705	5	,	,	PUNCT
ejpam-3877	705	6	2011	2011	NUM
ejpam-3877	705	7	.	.	PUNCT
ejpam-3877	706	1	[	[	X
ejpam-3877	706	2	6	6	NUM
ejpam-3877	706	3	]	]	PUNCT
ejpam-3877	706	4	e.	e.	PROPN
ejpam-3877	706	5	chasseigne	chasseigne	PROPN
ejpam-3877	706	6	.	.	PUNCT
ejpam-3877	707	1	initial	initial	ADJ
ejpam-3877	707	2	trace	trace	NOUN
ejpam-3877	707	3	for	for	ADP
ejpam-3877	707	4	a	a	DET
ejpam-3877	707	5	porous	porous	ADJ
ejpam-3877	707	6	medium	medium	NOUN
ejpam-3877	707	7	equation	equation	NOUN
ejpam-3877	707	8	.	.	PUNCT
ejpam-3877	708	1	i.	i.	PROPN
ejpam-3877	708	2	the	the	DET
ejpam-3877	708	3	strong	strong	ADJ
ejpam-3877	708	4	absorption	absorption	NOUN
ejpam-3877	708	5	case	case	NOUN
ejpam-3877	708	6	.	.	PUNCT
ejpam-3877	709	1	ann	ann	PROPN
ejpam-3877	709	2	.	.	PUNCT
ejpam-3877	709	3	mat	mat	PROPN
ejpam-3877	709	4	.	.	PUNCT
ejpam-3877	709	5	pura	pura	NOUN
ejpam-3877	709	6	appl	appl	PROPN
ejpam-3877	709	7	.	.	PROPN
ejpam-3877	709	8	,	,	PUNCT
ejpam-3877	709	9	179:413–458	179:413–458	NUM
ejpam-3877	709	10	,	,	PUNCT
ejpam-3877	709	11	2001	2001	NUM
ejpam-3877	709	12	.	.	PUNCT
ejpam-3877	710	1	[	[	X
ejpam-3877	710	2	7	7	NUM
ejpam-3877	710	3	]	]	PUNCT
ejpam-3877	710	4	a.	a.	NOUN
ejpam-3877	710	5	dall’aglio	dall’aglio	PROPN
ejpam-3877	710	6	,	,	PUNCT
ejpam-3877	710	7	d.	d.	PROPN
ejpam-3877	710	8	giachetti	giachetti	PROPN
ejpam-3877	710	9	,	,	PUNCT
ejpam-3877	710	10	c.	c.	PROPN
ejpam-3877	710	11	leone	leone	PROPN
ejpam-3877	710	12	,	,	PUNCT
ejpam-3877	710	13	and	and	CCONJ
ejpam-3877	710	14	s.	s.	PROPN
ejpam-3877	710	15	segura	segura	PROPN
ejpam-3877	710	16	de	de	PROPN
ejpam-3877	710	17	léon	léon	PROPN
ejpam-3877	710	18	.	.	PUNCT
ejpam-3877	711	1	quasilinear	quasilinear	PROPN
ejpam-3877	711	2	parabolic	parabolic	PROPN
ejpam-3877	711	3	equations	equation	NOUN
ejpam-3877	711	4	with	with	ADP
ejpam-3877	711	5	degenerate	degenerate	ADJ
ejpam-3877	711	6	coercivity	coercivity	NOUN
ejpam-3877	711	7	having	have	VERB
ejpam-3877	711	8	a	a	DET
ejpam-3877	711	9	quadratic	quadratic	ADJ
ejpam-3877	711	10	gradient	gradient	ADJ
ejpam-3877	711	11	term	term	NOUN
ejpam-3877	711	12	.	.	PUNCT
ejpam-3877	712	1	ann	ann	PROPN
ejpam-3877	712	2	.	.	PROPN
ejpam-3877	712	3	inst	inst	PROPN
ejpam-3877	712	4	.	.	PUNCT
ejpam-3877	713	1	h.	h.	PROPN
ejpam-3877	713	2	poincare	poincare	PROPN
ejpam-3877	713	3	anal	anal	PROPN
ejpam-3877	713	4	.	.	PUNCT
ejpam-3877	714	1	non	non	PROPN
ejpam-3877	714	2	lineaire	lineaire	PROPN
ejpam-3877	714	3	,	,	PUNCT
ejpam-3877	714	4	23:97–126	23:97–126	NUM
ejpam-3877	714	5	,	,	PUNCT
ejpam-3877	714	6	2006	2006	NUM
ejpam-3877	714	7	.	.	PUNCT
ejpam-3877	715	1	[	[	X
ejpam-3877	715	2	8	8	NUM
ejpam-3877	715	3	]	]	X
ejpam-3877	715	4	l.	l.	PROPN
ejpam-3877	715	5	c.	c.	PROPN
ejpam-3877	715	6	evans	evans	PROPN
ejpam-3877	715	7	.	.	PUNCT
ejpam-3877	716	1	partial	partial	ADJ
ejpam-3877	716	2	differential	differential	PROPN
ejpam-3877	716	3	equations.second	equations.second	PROPN
ejpam-3877	716	4	edition	edition	NOUN
ejpam-3877	716	5	.	.	PUNCT
ejpam-3877	717	1	graduate	graduate	PROPN
ejpam-3877	717	2	studies	study	NOUN
ejpam-3877	717	3	in	in	ADP
ejpam-3877	717	4	mathematics	mathematic	NOUN
ejpam-3877	717	5	.	.	PUNCT
ejpam-3877	718	1	ams	am	NOUN
ejpam-3877	718	2	.	.	PUNCT
ejpam-3877	718	3	,	,	PUNCT
ejpam-3877	718	4	19	19	NUM
ejpam-3877	718	5	:	:	PUNCT
ejpam-3877	718	6	xxii+749	xxii+749	PROPN
ejpam-3877	718	7	pp	pp	ADP
ejpam-3877	718	8	,	,	PUNCT
ejpam-3877	718	9	2010	2010	NUM
ejpam-3877	718	10	.	.	PUNCT
ejpam-3877	719	1	[	[	X
ejpam-3877	719	2	9	9	NUM
ejpam-3877	719	3	]	]	SYM
ejpam-3877	719	4	l.	l.	PROPN
ejpam-3877	719	5	c.	c.	PROPN
ejpam-3877	719	6	evans	evans	PROPN
ejpam-3877	719	7	and	and	CCONJ
ejpam-3877	719	8	r.	r.	PROPN
ejpam-3877	719	9	f.	f.	PROPN
ejpam-3877	719	10	gariepy	gariepy	PROPN
ejpam-3877	719	11	.	.	PUNCT
ejpam-3877	720	1	measure	measure	NOUN
ejpam-3877	720	2	theory	theory	NOUN
ejpam-3877	720	3	and	and	CCONJ
ejpam-3877	720	4	fine	fine	ADJ
ejpam-3877	720	5	properties	property	NOUN
ejpam-3877	720	6	of	of	ADP
ejpam-3877	720	7	functions	function	NOUN
ejpam-3877	720	8	.	.	PUNCT
ejpam-3877	721	1	studies	study	NOUN
ejpam-3877	721	2	in	in	ADP
ejpam-3877	721	3	advanced	advanced	ADJ
ejpam-3877	721	4	mathematics	mathematic	NOUN
ejpam-3877	721	5	.	.	PUNCT
ejpam-3877	722	1	crc	crc	PROPN
ejpam-3877	722	2	press	press	PROPN
ejpam-3877	722	3	,	,	PUNCT
ejpam-3877	722	4	boca	boca	PROPN
ejpam-3877	722	5	raton	raton	PROPN
ejpam-3877	722	6	,	,	PUNCT
ejpam-3877	722	7	fl	fl	PROPN
ejpam-3877	722	8	,	,	PUNCT
ejpam-3877	722	9	pages	page	VERB
ejpam-3877	722	10	viii+268	viii+268	NOUN
ejpam-3877	722	11	pp	pp	ADP
ejpam-3877	722	12	,	,	PUNCT
ejpam-3877	722	13	1992	1992	NUM
ejpam-3877	722	14	.	.	PUNCT
ejpam-3877	723	1	[	[	X
ejpam-3877	723	2	10	10	NUM
ejpam-3877	723	3	]	]	PUNCT
ejpam-3877	723	4	a.	a.	NOUN
ejpam-3877	723	5	c.	c.	PROPN
ejpam-3877	723	6	ponce	ponce	PROPN
ejpam-3877	723	7	f.	f.	PROPN
ejpam-3877	723	8	petitta	petitta	PROPN
ejpam-3877	723	9	and	and	CCONJ
ejpam-3877	723	10	a.	a.	NOUN
ejpam-3877	723	11	porretta	porretta	PROPN
ejpam-3877	723	12	.	.	PUNCT
ejpam-3877	724	1	approximation	approximation	NOUN
ejpam-3877	724	2	of	of	ADP
ejpam-3877	724	3	diffuse	diffuse	ADJ
ejpam-3877	724	4	measures	measure	NOUN
ejpam-3877	724	5	for	for	ADP
ejpam-3877	724	6	parabolic	parabolic	ADJ
ejpam-3877	724	7	capacities	capacity	NOUN
ejpam-3877	724	8	.	.	PUNCT
ejpam-3877	725	1	c.	c.	PROPN
ejpam-3877	725	2	r.	r.	PROPN
ejpam-3877	725	3	math	math	PROPN
ejpam-3877	725	4	.	.	PUNCT
ejpam-3877	726	1	acad	acad	PROPN
ejpam-3877	726	2	.	.	PUNCT
ejpam-3877	727	1	sci	sci	PROPN
ejpam-3877	727	2	.	.	PROPN
ejpam-3877	727	3	paris	paris	PROPN
ejpam-3877	727	4	,	,	PUNCT
ejpam-3877	727	5	346:161–166	346:161–166	NUM
ejpam-3877	727	6	,	,	PUNCT
ejpam-3877	727	7	2008	2008	NUM
ejpam-3877	727	8	.	.	PUNCT
ejpam-3877	728	1	[	[	X
ejpam-3877	728	2	11	11	NUM
ejpam-3877	728	3	]	]	PUNCT
ejpam-3877	728	4	a.	a.	NOUN
ejpam-3877	728	5	c.	c.	PROPN
ejpam-3877	728	6	ponce	ponce	PROPN
ejpam-3877	728	7	f.	f.	PROPN
ejpam-3877	728	8	petitta	petitta	PROPN
ejpam-3877	728	9	and	and	CCONJ
ejpam-3877	728	10	a.	a.	NOUN
ejpam-3877	728	11	porretta	porretta	PROPN
ejpam-3877	728	12	.	.	PUNCT
ejpam-3877	729	1	diffuse	diffuse	VERB
ejpam-3877	729	2	measures	measure	NOUN
ejpam-3877	729	3	and	and	CCONJ
ejpam-3877	729	4	nonlinear	nonlinear	ADJ
ejpam-3877	729	5	parabolic	parabolic	ADJ
ejpam-3877	729	6	equations	equation	NOUN
ejpam-3877	729	7	.	.	PUNCT
ejpam-3877	730	1	j.	j.	PROPN
ejpam-3877	730	2	evol	evol	PROPN
ejpam-3877	730	3	.	.	PUNCT
ejpam-3877	731	1	equ	equ	PROPN
ejpam-3877	731	2	.	.	PROPN
ejpam-3877	731	3	,	,	PUNCT
ejpam-3877	731	4	11:861–905	11:861–905	PROPN
ejpam-3877	731	5	,	,	PUNCT
ejpam-3877	731	6	2011	2011	NUM
ejpam-3877	731	7	.	.	PUNCT
ejpam-3877	732	1	references	reference	NOUN
ejpam-3877	732	2	232	232	NUM
ejpam-3877	733	1	[	[	X
ejpam-3877	733	2	12	12	NUM
ejpam-3877	733	3	]	]	X
ejpam-3877	733	4	l.	l.	PROPN
ejpam-3877	733	5	orsina	orsina	PROPN
ejpam-3877	733	6	g.	g.	PROPN
ejpam-3877	733	7	dal	dal	PROPN
ejpam-3877	733	8	masso	masso	PROPN
ejpam-3877	733	9	,	,	PUNCT
ejpam-3877	733	10	f.	f.	PROPN
ejpam-3877	733	11	murat	murat	PROPN
ejpam-3877	733	12	and	and	CCONJ
ejpam-3877	733	13	a.	a.	NOUN
ejpam-3877	733	14	prignet	prignet	PROPN
ejpam-3877	733	15	.	.	PUNCT
ejpam-3877	734	1	renormalized	renormalize	VERB
ejpam-3877	734	2	solutions	solution	NOUN
ejpam-3877	734	3	of	of	ADP
ejpam-3877	734	4	elliptic	elliptic	ADJ
ejpam-3877	734	5	equations	equation	NOUN
ejpam-3877	734	6	with	with	ADP
ejpam-3877	734	7	general	general	ADJ
ejpam-3877	734	8	measure	measure	NOUN
ejpam-3877	734	9	data	datum	NOUN
ejpam-3877	734	10	.	.	PUNCT
ejpam-3877	735	1	ann	ann	PROPN
ejpam-3877	735	2	.	.	PUNCT
ejpam-3877	735	3	scuola	scuola	PROPN
ejpam-3877	735	4	norm	norm	NOUN
ejpam-3877	735	5	.	.	PUNCT
ejpam-3877	736	1	sup	sup	NOUN
ejpam-3877	736	2	.	.	PUNCT
ejpam-3877	736	3	pisa	pisa	PROPN
ejpam-3877	736	4	cl	cl	PROPN
ejpam-3877	736	5	.	.	PUNCT
ejpam-3877	737	1	sci	sci	PROPN
ejpam-3877	737	2	.	.	PROPN
ejpam-3877	737	3	,	,	PUNCT
ejpam-3877	737	4	28:741	28:741	NUM
ejpam-3877	737	5	–	–	PUNCT
ejpam-3877	737	6	808	808	NUM
ejpam-3877	737	7	,	,	PUNCT
ejpam-3877	737	8	1999	1999	NUM
ejpam-3877	737	9	.	.	PUNCT
ejpam-3877	738	1	[	[	X
ejpam-3877	738	2	13	13	NUM
ejpam-3877	738	3	]	]	X
ejpam-3877	738	4	u.	u.	NOUN
ejpam-3877	738	5	gianazza	gianazza	PROPN
ejpam-3877	738	6	.	.	PUNCT
ejpam-3877	739	1	degenerate	degenerate	ADJ
ejpam-3877	739	2	and	and	CCONJ
ejpam-3877	739	3	singular	singular	ADJ
ejpam-3877	739	4	porous	porous	ADJ
ejpam-3877	739	5	medium	medium	ADJ
ejpam-3877	739	6	type	type	NOUN
ejpam-3877	739	7	equations	equation	NOUN
ejpam-3877	739	8	with	with	ADP
ejpam-3877	739	9	measure	measure	NOUN
ejpam-3877	739	10	data	datum	NOUN
ejpam-3877	739	11	.	.	PUNCT
ejpam-3877	740	1	elliptic	elliptic	ADJ
ejpam-3877	740	2	and	and	CCONJ
ejpam-3877	740	3	parabolic	parabolic	ADJ
ejpam-3877	740	4	equation	equation	NOUN
ejpam-3877	740	5	,	,	PUNCT
ejpam-3877	740	6	139	139	NUM
ejpam-3877	740	7	-	-	SYM
ejpam-3877	740	8	158	158	NUM
ejpam-3877	740	9	.	.	PUNCT
ejpam-3877	741	1	springer	springer	NOUN
ejpam-3877	741	2	proc	proc	PROPN
ejpam-3877	741	3	.	.	PUNCT
ejpam-3877	742	1	math	math	NOUN
ejpam-3877	742	2	.	.	PUNCT
ejpam-3877	743	1	stat	stat	PROPN
ejpam-3877	743	2	.	.	PUNCT
ejpam-3877	743	3	,	,	PUNCT
ejpam-3877	743	4	119	119	NUM
ejpam-3877	743	5	,	,	PUNCT
ejpam-3877	743	6	2015	2015	NUM
ejpam-3877	743	7	.	.	PUNCT
ejpam-3877	744	1	[	[	X
ejpam-3877	744	2	14	14	NUM
ejpam-3877	744	3	]	]	PUNCT
ejpam-3877	744	4	m.	m.	NOUN
ejpam-3877	744	5	giaquinta	giaquinta	NOUN
ejpam-3877	744	6	,	,	PUNCT
ejpam-3877	744	7	g.	g.	PROPN
ejpam-3877	744	8	moadica	moadica	PROPN
ejpam-3877	744	9	,	,	PUNCT
ejpam-3877	744	10	and	and	CCONJ
ejpam-3877	744	11	j.	j.	PROPN
ejpam-3877	744	12	souček	souček	PROPN
ejpam-3877	744	13	.	.	PUNCT
ejpam-3877	745	1	cartesian	cartesian	ADJ
ejpam-3877	745	2	currents	current	NOUN
ejpam-3877	745	3	in	in	ADP
ejpam-3877	745	4	the	the	DET
ejpam-3877	745	5	calculus	calculus	NOUN
ejpam-3877	745	6	of	of	ADP
ejpam-3877	745	7	variations	variation	NOUN
ejpam-3877	745	8	.	.	PUNCT
ejpam-3877	746	1	i.	i.	PROPN
ejpam-3877	746	2	cartesian	cartesian	ADJ
ejpam-3877	746	3	currents	current	NOUN
ejpam-3877	746	4	.	.	PUNCT
ejpam-3877	747	1	springer	springer	NOUN
ejpam-3877	747	2	-	-	PUNCT
ejpam-3877	747	3	verlag	verlag	PROPN
ejpam-3877	747	4	,	,	PUNCT
ejpam-3877	747	5	berlin	berlin	PROPN
ejpam-3877	747	6	,	,	PUNCT
ejpam-3877	747	7	37	37	NUM
ejpam-3877	747	8	:	:	PUNCT
ejpam-3877	747	9	xxiv+711	xxiv+711	NOUN
ejpam-3877	747	10	pp	pp	ADP
ejpam-3877	747	11	,	,	PUNCT
ejpam-3877	747	12	1998	1998	NUM
ejpam-3877	747	13	.	.	PUNCT
ejpam-3877	748	1	[	[	X
ejpam-3877	748	2	15	15	NUM
ejpam-3877	748	3	]	]	PUNCT
ejpam-3877	748	4	m.	m.	NOUN
ejpam-3877	748	5	marcus	marcus	PROPN
ejpam-3877	748	6	h.	h.	PROPN
ejpam-3877	748	7	brezis	brezis	PROPN
ejpam-3877	748	8	and	and	CCONJ
ejpam-3877	748	9	a.	a.	PROPN
ejpam-3877	748	10	c.	c.	PROPN
ejpam-3877	748	11	ponce	ponce	PROPN
ejpam-3877	748	12	.	.	PUNCT
ejpam-3877	749	1	nonlinear	nonlinear	ADJ
ejpam-3877	749	2	elliptic	elliptic	ADJ
ejpam-3877	749	3	equations	equation	NOUN
ejpam-3877	749	4	with	with	ADP
ejpam-3877	749	5	measures	measure	NOUN
ejpam-3877	749	6	revisited	revisit	VERB
ejpam-3877	749	7	,	,	PUNCT
ejpam-3877	749	8	mathematics	mathematic	NOUN
ejpam-3877	749	9	aspects	aspect	NOUN
ejpam-3877	749	10	of	of	ADP
ejpam-3877	749	11	nonlinear	nonlinear	ADJ
ejpam-3877	749	12	dispersive	dispersive	ADJ
ejpam-3877	749	13	equations	equation	NOUN
ejpam-3877	749	14	,	,	PUNCT
ejpam-3877	749	15	55	55	NUM
ejpam-3877	749	16	-	-	SYM
ejpam-3877	749	17	109	109	NUM
ejpam-3877	749	18	.	.	PUNCT
ejpam-3877	750	1	ann	ann	PROPN
ejpam-3877	750	2	.	.	PROPN
ejpam-3877	750	3	of	of	ADP
ejpam-3877	750	4	math	math	NOUN
ejpam-3877	750	5	.	.	PUNCT
ejpam-3877	751	1	stud	stud	PROPN
ejpam-3877	751	2	.	.	PUNCT
ejpam-3877	752	1	,	,	PUNCT
ejpam-3877	752	2	163	163	NUM
ejpam-3877	752	3	,	,	PUNCT
ejpam-3877	752	4	princeton	princeton	PROPN
ejpam-3877	752	5	univ	univ	PROPN
ejpam-3877	752	6	.	.	PUNCT
ejpam-3877	753	1	press	press	PROPN
ejpam-3877	753	2	,	,	PUNCT
ejpam-3877	753	3	princeton	princeton	PROPN
ejpam-3877	753	4	,	,	PUNCT
ejpam-3877	753	5	nj	nj	PROPN
ejpam-3877	753	6	,	,	PUNCT
ejpam-3877	753	7	2007	2007	NUM
ejpam-3877	753	8	.	.	PUNCT
ejpam-3877	754	1	[	[	X
ejpam-3877	754	2	16	16	NUM
ejpam-3877	754	3	]	]	PUNCT
ejpam-3877	754	4	a.	a.	NOUN
ejpam-3877	754	5	porretta	porretta	PROPN
ejpam-3877	754	6	j.	j.	PROPN
ejpam-3877	754	7	droniou	droniou	PROPN
ejpam-3877	754	8	and	and	CCONJ
ejpam-3877	754	9	a.	a.	NOUN
ejpam-3877	754	10	prignet	prignet	PROPN
ejpam-3877	754	11	.	.	PUNCT
ejpam-3877	755	1	parabolic	parabolic	ADJ
ejpam-3877	755	2	capacity	capacity	NOUN
ejpam-3877	755	3	and	and	CCONJ
ejpam-3877	755	4	soft	soft	ADJ
ejpam-3877	755	5	measures	measure	NOUN
ejpam-3877	755	6	for	for	ADP
ejpam-3877	755	7	nonlinear	nonlinear	ADJ
ejpam-3877	755	8	equations	equation	NOUN
ejpam-3877	755	9	.	.	PUNCT
ejpam-3877	756	1	potential	potential	ADJ
ejpam-3877	756	2	anal	anal	NOUN
ejpam-3877	756	3	.	.	PUNCT
ejpam-3877	756	4	,	,	PUNCT
ejpam-3877	756	5	19:99–161	19:99–161	NUM
ejpam-3877	756	6	,	,	PUNCT
ejpam-3877	756	7	2003	2003	NUM
ejpam-3877	756	8	.	.	PUNCT
ejpam-3877	757	1	[	[	X
ejpam-3877	757	2	17	17	NUM
ejpam-3877	757	3	]	]	PUNCT
ejpam-3877	757	4	m.	m.	NOUN
ejpam-3877	757	5	rokyta	rokyta	NOUN
ejpam-3877	757	6	j.	j.	PROPN
ejpam-3877	757	7	málek	málek	PROPN
ejpam-3877	757	8	,	,	PUNCT
ejpam-3877	757	9	j.	j.	PROPN
ejpam-3877	757	10	nečas	nečas	PROPN
ejpam-3877	757	11	and	and	CCONJ
ejpam-3877	757	12	m.	m.	PROPN
ejpam-3877	757	13	ru̇žička	ru̇žička	PROPN
ejpam-3877	757	14	.	.	PUNCT
ejpam-3877	758	1	weak	weak	ADJ
ejpam-3877	758	2	and	and	CCONJ
ejpam-3877	758	3	measure	measure	NOUN
ejpam-3877	758	4	-	-	PUNCT
ejpam-3877	758	5	valued	value	VERB
ejpam-3877	758	6	solutions	solution	NOUN
ejpam-3877	758	7	to	to	ADP
ejpam-3877	758	8	evolutionary	evolutionary	ADJ
ejpam-3877	758	9	pdes	pde	NOUN
ejpam-3877	758	10	.	.	PUNCT
ejpam-3877	759	1	,	,	PUNCT
ejpam-3877	759	2	volume	volume	NOUN
ejpam-3877	759	3	13	13	NUM
ejpam-3877	759	4	.	.	PUNCT
ejpam-3877	760	1	chapman	chapman	PROPN
ejpam-3877	760	2	and	and	CCONJ
ejpam-3877	760	3	hall	hall	PROPN
ejpam-3877	760	4	,	,	PUNCT
ejpam-3877	760	5	london	london	PROPN
ejpam-3877	760	6	,	,	PUNCT
ejpam-3877	760	7	1996	1996	NUM
ejpam-3877	760	8	.	.	PUNCT
ejpam-3877	761	1	[	[	X
ejpam-3877	761	2	18	18	NUM
ejpam-3877	761	3	]	]	PUNCT
ejpam-3877	761	4	m.	m.	NOUN
ejpam-3877	761	5	porzio	porzio	PROPN
ejpam-3877	761	6	l.	l.	PROPN
ejpam-3877	761	7	orsina	orsina	PROPN
ejpam-3877	761	8	and	and	CCONJ
ejpam-3877	761	9	f.	f.	PROPN
ejpam-3877	761	10	smarrazzo	smarrazzo	PROPN
ejpam-3877	761	11	.	.	PUNCT
ejpam-3877	762	1	measure	measure	NOUN
ejpam-3877	762	2	-	-	PUNCT
ejpam-3877	762	3	valued	value	VERB
ejpam-3877	762	4	solutions	solution	NOUN
ejpam-3877	762	5	of	of	ADP
ejpam-3877	762	6	nonlinear	nonlinear	ADJ
ejpam-3877	762	7	parabolic	parabolic	ADJ
ejpam-3877	762	8	equations	equation	NOUN
ejpam-3877	762	9	with	with	ADP
ejpam-3877	762	10	logarithmic	logarithmic	ADJ
ejpam-3877	762	11	diffusion	diffusion	NOUN
ejpam-3877	762	12	.	.	PUNCT
ejpam-3877	763	1	j.	j.	PROPN
ejpam-3877	763	2	evol	evol	PROPN
ejpam-3877	763	3	.	.	PUNCT
ejpam-3877	764	1	equ	equ	PROPN
ejpam-3877	764	2	.	.	PROPN
ejpam-3877	764	3	,	,	PUNCT
ejpam-3877	764	4	15:609–645	15:609–645	NUM
ejpam-3877	764	5	,	,	PUNCT
ejpam-3877	764	6	2015	2015	NUM
ejpam-3877	764	7	.	.	PUNCT
ejpam-3877	765	1	[	[	X
ejpam-3877	765	2	19	19	NUM
ejpam-3877	765	3	]	]	X
ejpam-3877	765	4	j.	j.	PROPN
ejpam-3877	765	5	l.	l.	PROPN
ejpam-3877	765	6	lions	lions	PROPN
ejpam-3877	765	7	.	.	PUNCT
ejpam-3877	766	1	quelques	quelques	PROPN
ejpam-3877	766	2	methodes	methode	NOUN
ejpam-3877	766	3	de	de	PROPN
ejpam-3877	766	4	resolutions	resolution	NOUN
ejpam-3877	766	5	des	des	X
ejpam-3877	766	6	problemes	problemes	PROPN
ejpam-3877	766	7	aux	aux	PROPN
ejpam-3877	766	8	limites	limites	PROPN
ejpam-3877	766	9	non	non	PROPN
ejpam-3877	766	10	lineaires	lineaires	PROPN
ejpam-3877	766	11	(	(	PUNCT
ejpam-3877	766	12	french	french	PROPN
ejpam-3877	766	13	)	)	PUNCT
ejpam-3877	766	14	.	.	PUNCT
ejpam-3877	767	1	paris	paris	PROPN
ejpam-3877	767	2	,	,	PUNCT
ejpam-3877	767	3	gauthier	gauthier	PROPN
ejpam-3877	767	4	-	-	PUNCT
ejpam-3877	767	5	villars	villars	PROPN
ejpam-3877	767	6	,	,	PUNCT
ejpam-3877	767	7	dunod	dunod	PROPN
ejpam-3877	767	8	,	,	PUNCT
ejpam-3877	767	9	pages	page	NOUN
ejpam-3877	767	10	xx+554	xx+554	INTJ
ejpam-3877	767	11	pp	pp	PROPN
ejpam-3877	767	12	,	,	PUNCT
ejpam-3877	767	13	1969	1969	NUM
ejpam-3877	767	14	.	.	PUNCT
ejpam-3877	768	1	[	[	X
ejpam-3877	768	2	20	20	NUM
ejpam-3877	768	3	]	]	X
ejpam-3877	768	4	p	p	X
ejpam-3877	768	5	de	de	X
ejpam-3877	768	6	mottoni	mottoni	PROPN
ejpam-3877	768	7	m	m	VERB
ejpam-3877	768	8	bertsch	bertsch	VERB
ejpam-3877	768	9	and	and	CCONJ
ejpam-3877	768	10	l.	l.	PROPN
ejpam-3877	768	11	a.	a.	PROPN
ejpam-3877	768	12	peletier	peletier	PROPN
ejpam-3877	768	13	.	.	PUNCT
ejpam-3877	769	1	degenerate	degenerate	ADJ
ejpam-3877	769	2	diffusion	diffusion	NOUN
ejpam-3877	769	3	and	and	CCONJ
ejpam-3877	769	4	stefan	stefan	PROPN
ejpam-3877	769	5	problem	problem	PROPN
ejpam-3877	769	6	.	.	PUNCT
ejpam-3877	770	1	nonlinear	nonlinear	ADJ
ejpam-3877	770	2	anal	anal	PROPN
ejpam-3877	770	3	.	.	PUNCT
ejpam-3877	770	4	,	,	PUNCT
ejpam-3877	770	5	8:1311–1336	8:1311–1336	NUM
ejpam-3877	770	6	,	,	PUNCT
ejpam-3877	770	7	1984	1984	NUM
ejpam-3877	770	8	.	.	PUNCT
ejpam-3877	771	1	[	[	X
ejpam-3877	771	2	21	21	NUM
ejpam-3877	771	3	]	]	X
ejpam-3877	771	4	l.	l.	PROPN
ejpam-3877	771	5	veron	veron	PROPN
ejpam-3877	771	6	m.	m.	PROPN
ejpam-3877	771	7	francoise	francoise	PROPN
ejpam-3877	771	8	-	-	PUNCT
ejpam-3877	771	9	bidaut	bidaut	PROPN
ejpam-3877	771	10	and	and	CCONJ
ejpam-3877	771	11	quoc	quoc	PROPN
ejpam-3877	771	12	-	-	PROPN
ejpam-3877	771	13	h	h	NOUN
ejpam-3877	771	14	nguyen	nguyen	NOUN
ejpam-3877	771	15	.	.	PUNCT
ejpam-3877	772	1	pointwise	pointwise	NOUN
ejpam-3877	772	2	estimates	estimate	NOUN
ejpam-3877	772	3	and	and	CCONJ
ejpam-3877	772	4	existence	existence	NOUN
ejpam-3877	772	5	of	of	ADP
ejpam-3877	772	6	solutions	solution	NOUN
ejpam-3877	772	7	of	of	ADP
ejpam-3877	772	8	porous	porous	ADJ
ejpam-3877	772	9	pedium	pedium	NOUN
ejpam-3877	772	10	and	and	CCONJ
ejpam-3877	772	11	p	p	ADJ
ejpam-3877	772	12	-	-	PUNCT
ejpam-3877	772	13	laplacian	laplacian	ADJ
ejpam-3877	772	14	evolution	evolution	NOUN
ejpam-3877	772	15	equations	equation	NOUN
ejpam-3877	772	16	with	with	ADP
ejpam-3877	772	17	absorption	absorption	NOUN
ejpam-3877	772	18	and	and	CCONJ
ejpam-3877	772	19	measure	measure	NOUN
ejpam-3877	772	20	data	datum	NOUN
ejpam-3877	772	21	.	.	PUNCT
ejpam-3877	773	1	ann	ann	PROPN
ejpam-3877	773	2	.	.	PROPN
ejpam-3877	773	3	sc	sc	PROPN
ejpam-3877	773	4	.	.	PROPN
ejpam-3877	773	5	norm	norm	PROPN
ejpam-3877	773	6	.	.	PUNCT
ejpam-3877	774	1	super	super	ADJ
ejpam-3877	774	2	.	.	PUNCT
ejpam-3877	774	3	pisa	pisa	PROPN
ejpam-3877	774	4	cl	cl	PROPN
ejpam-3877	774	5	.	.	PUNCT
ejpam-3877	775	1	sci	sci	PROPN
ejpam-3877	775	2	.	.	PROPN
ejpam-3877	775	3	,	,	PUNCT
ejpam-3877	775	4	16:675–705	16:675–705	NUM
ejpam-3877	775	5	,	,	PUNCT
ejpam-3877	775	6	2016	2016	NUM
ejpam-3877	775	7	.	.	PUNCT
ejpam-3877	776	1	[	[	X
ejpam-3877	776	2	22	22	NUM
ejpam-3877	776	3	]	]	PUNCT
ejpam-3877	776	4	m.	m.	NOUN
ejpam-3877	776	5	porzio	porzio	NOUN
ejpam-3877	776	6	m.	m.	NOUN
ejpam-3877	776	7	papi	papi	NOUN
ejpam-3877	776	8	and	and	CCONJ
ejpam-3877	776	9	f.	f.	PROPN
ejpam-3877	776	10	smarrazzo	smarrazzo	PROPN
ejpam-3877	776	11	.	.	PUNCT
ejpam-3877	777	1	existence	existence	NOUN
ejpam-3877	777	2	of	of	ADP
ejpam-3877	777	3	solutions	solution	NOUN
ejpam-3877	777	4	to	to	ADP
ejpam-3877	777	5	a	a	DET
ejpam-3877	777	6	class	class	NOUN
ejpam-3877	777	7	of	of	ADP
ejpam-3877	777	8	weakly	weakly	ADJ
ejpam-3877	777	9	coercive	coercive	ADJ
ejpam-3877	777	10	diffusion	diffusion	NOUN
ejpam-3877	777	11	equations	equation	NOUN
ejpam-3877	777	12	with	with	ADP
ejpam-3877	777	13	singular	singular	PROPN
ejpam-3877	777	14	initial	initial	ADJ
ejpam-3877	777	15	data	datum	NOUN
ejpam-3877	777	16	.	.	PUNCT
ejpam-3877	778	1	adv	adv	PROPN
ejpam-3877	778	2	.	.	PUNCT
ejpam-3877	778	3	differential	differential	PROPN
ejpam-3877	778	4	equations	equation	NOUN
ejpam-3877	778	5	,	,	PUNCT
ejpam-3877	778	6	22:893–962	22:893–962	NUM
ejpam-3877	778	7	,	,	PUNCT
ejpam-3877	778	8	2017	2017	NUM
ejpam-3877	778	9	.	.	PUNCT
ejpam-3877	779	1	[	[	X
ejpam-3877	779	2	23	23	NUM
ejpam-3877	779	3	]	]	X
ejpam-3877	779	4	f.	f.	PROPN
ejpam-3877	779	5	smarrazzo	smarrazzo	PROPN
ejpam-3877	779	6	m.	m.	NOUN
ejpam-3877	779	7	porzio	porzio	PROPN
ejpam-3877	779	8	and	and	CCONJ
ejpam-3877	779	9	a.	a.	NOUN
ejpam-3877	779	10	tesei	tesei	PROPN
ejpam-3877	779	11	.	.	PUNCT
ejpam-3877	780	1	radon	radon	PROPN
ejpam-3877	780	2	measure	measure	NOUN
ejpam-3877	780	3	-	-	PUNCT
ejpam-3877	780	4	valued	value	VERB
ejpam-3877	780	5	solutions	solution	NOUN
ejpam-3877	780	6	for	for	ADP
ejpam-3877	780	7	a	a	DET
ejpam-3877	780	8	class	class	NOUN
ejpam-3877	780	9	of	of	ADP
ejpam-3877	780	10	quasilinear	quasilinear	PROPN
ejpam-3877	780	11	parabolic	parabolic	PROPN
ejpam-3877	780	12	equations	equation	NOUN
ejpam-3877	780	13	.	.	PUNCT
ejpam-3877	781	1	arch	arch	NOUN
ejpam-3877	781	2	.	.	PUNCT
ejpam-3877	782	1	ration	ration	NOUN
ejpam-3877	782	2	.	.	PUNCT
ejpam-3877	783	1	mech	mech	PROPN
ejpam-3877	783	2	.	.	PUNCT
ejpam-3877	784	1	anal	anal	PROPN
ejpam-3877	784	2	.	.	PROPN
ejpam-3877	784	3	,	,	PUNCT
ejpam-3877	784	4	210:713–772	210:713–772	NUM
ejpam-3877	784	5	,	,	PUNCT
ejpam-3877	784	6	2013	2013	NUM
ejpam-3877	784	7	.	.	PUNCT
ejpam-3877	785	1	[	[	X
ejpam-3877	785	2	24	24	NUM
ejpam-3877	785	3	]	]	X
ejpam-3877	785	4	f.	f.	PROPN
ejpam-3877	785	5	smarrazzo	smarrazzo	PROPN
ejpam-3877	785	6	m.	m.	NOUN
ejpam-3877	785	7	porzio	porzio	PROPN
ejpam-3877	785	8	and	and	CCONJ
ejpam-3877	785	9	a.	a.	NOUN
ejpam-3877	785	10	tesei	tesei	PROPN
ejpam-3877	785	11	.	.	PUNCT
ejpam-3877	786	1	radon	radon	PROPN
ejpam-3877	786	2	measure	measure	NOUN
ejpam-3877	786	3	-	-	PUNCT
ejpam-3877	786	4	valued	value	VERB
ejpam-3877	786	5	solutions	solution	NOUN
ejpam-3877	786	6	of	of	ADP
ejpam-3877	786	7	nonlinear	nonlinear	ADJ
ejpam-3877	786	8	strongly	strongly	ADV
ejpam-3877	786	9	degenerate	degenerate	ADJ
ejpam-3877	786	10	parabolic	parabolic	ADJ
ejpam-3877	786	11	equations	equation	NOUN
ejpam-3877	786	12	.	.	PUNCT
ejpam-3877	787	1	calc	calc	PROPN
ejpam-3877	787	2	.	.	PUNCT
ejpam-3877	788	1	var	var	PROPN
ejpam-3877	788	2	.	.	PUNCT
ejpam-3877	789	1	partial	partial	ADJ
ejpam-3877	789	2	differential	differential	NOUN
ejpam-3877	789	3	equations	equation	NOUN
ejpam-3877	789	4	,	,	PUNCT
ejpam-3877	789	5	51:401–437	51:401–437	NUM
ejpam-3877	789	6	,	,	PUNCT
ejpam-3877	789	7	2014	2014	NUM
ejpam-3877	789	8	.	.	PUNCT
ejpam-3877	790	1	[	[	X
ejpam-3877	790	2	25	25	NUM
ejpam-3877	790	3	]	]	PUNCT
ejpam-3877	790	4	m.	m.	NOUN
ejpam-3877	790	5	marcus	marcus	PROPN
ejpam-3877	790	6	and	and	CCONJ
ejpam-3877	790	7	l.	l.	PROPN
ejpam-3877	790	8	veron	veron	PROPN
ejpam-3877	790	9	.	.	PUNCT
ejpam-3877	791	1	nonlinear	nonlinear	ADJ
ejpam-3877	791	2	second	second	ADJ
ejpam-3877	791	3	order	order	NOUN
ejpam-3877	791	4	elliptic	elliptic	ADJ
ejpam-3877	791	5	equations	equation	NOUN
ejpam-3877	791	6	involving	involve	VERB
ejpam-3877	791	7	measures	measure	NOUN
ejpam-3877	791	8	,	,	PUNCT
ejpam-3877	791	9	volume	volume	NOUN
ejpam-3877	791	10	21	21	NUM
ejpam-3877	791	11	.	.	PUNCT
ejpam-3877	792	1	de	de	X
ejpam-3877	792	2	gruyter	gruyter	NOUN
ejpam-3877	792	3	,	,	PUNCT
ejpam-3877	792	4	berlin	berlin	PROPN
ejpam-3877	792	5	,	,	PUNCT
ejpam-3877	792	6	2014	2014	NUM
ejpam-3877	792	7	.	.	PUNCT
ejpam-3877	793	1	references	reference	NOUN
ejpam-3877	793	2	233	233	NUM
ejpam-3877	794	1	[	[	X
ejpam-3877	794	2	26	26	NUM
ejpam-3877	794	3	]	]	X
ejpam-3877	794	4	o.	o.	NOUN
ejpam-3877	794	5	a.	a.	NOUN
ejpam-3877	794	6	oleinik	oleinik	NOUN
ejpam-3877	794	7	and	and	CCONJ
ejpam-3877	794	8	s.	s.	PROPN
ejpam-3877	794	9	n.	n.	PROPN
ejpam-3877	794	10	kruzhkov	kruzhkov	PROPN
ejpam-3877	794	11	.	.	PUNCT
ejpam-3877	795	1	quasilinear	quasilinear	PROPN
ejpam-3877	795	2	second	second	ADJ
ejpam-3877	795	3	order	order	NOUN
ejpam-3877	795	4	parabolic	parabolic	NOUN
ejpam-3877	795	5	equations	equation	NOUN
ejpam-3877	795	6	with	with	ADP
ejpam-3877	795	7	many	many	ADJ
ejpam-3877	795	8	independent	independent	ADJ
ejpam-3877	795	9	variables	variable	NOUN
ejpam-3877	795	10	.	.	PUNCT
ejpam-3877	796	1	russ	russ	PROPN
ejpam-3877	796	2	.	.	PROPN
ejpam-3877	796	3	math	math	PROPN
ejpam-3877	796	4	.	.	PUNCT
ejpam-3877	797	1	surv	surv	PROPN
ejpam-3877	797	2	.	.	PUNCT
ejpam-3877	798	1	,	,	PUNCT
ejpam-3877	798	2	16:105–148	16:105–148	NUM
ejpam-3877	798	3	,	,	PUNCT
ejpam-3877	798	4	1961	1961	NUM
ejpam-3877	798	5	.	.	PUNCT
ejpam-3877	799	1	[	[	X
ejpam-3877	799	2	27	27	NUM
ejpam-3877	799	3	]	]	X
ejpam-3877	799	4	b.	b.	PROPN
ejpam-3877	799	5	pierre	pierre	PROPN
ejpam-3877	799	6	and	and	CCONJ
ejpam-3877	799	7	p.	p.	PROPN
ejpam-3877	799	8	michel	michel	PROPN
ejpam-3877	799	9	.	.	PUNCT
ejpam-3877	799	10	problemes	problemes	PROPN
ejpam-3877	799	11	paraboliques	parabolique	VERB
ejpam-3877	799	12	semi	semi	NOUN
ejpam-3877	799	13	-	-	NOUN
ejpam-3877	799	14	linaires	linaire	NOUN
ejpam-3877	799	15	avec	avec	PROPN
ejpam-3877	799	16	donnees	donnees	X
ejpam-3877	799	17	mesures	mesures	X
ejpam-3877	799	18	(	(	PUNCT
ejpam-3877	799	19	french	french	PROPN
ejpam-3877	799	20	)	)	PUNCT
ejpam-3877	799	21	.	.	PUNCT
ejpam-3877	800	1	applicable	applicable	ADJ
ejpam-3877	800	2	anal	anal	PROPN
ejpam-3877	800	3	.	.	PUNCT
ejpam-3877	800	4	,	,	PUNCT
ejpam-3877	800	5	18:111–149	18:111–149	NUM
ejpam-3877	800	6	,	,	PUNCT
ejpam-3877	800	7	1984	1984	NUM
ejpam-3877	800	8	.	.	PUNCT
ejpam-3877	801	1	[	[	X
ejpam-3877	801	2	28	28	NUM
ejpam-3877	801	3	]	]	X
ejpam-3877	801	4	m.	m.	NOUN
ejpam-3877	801	5	m.	m.	NOUN
ejpam-3877	801	6	porzio	porzio	PROPN
ejpam-3877	801	7	and	and	CCONJ
ejpam-3877	801	8	f.	f.	PROPN
ejpam-3877	801	9	smarrazzo	smarrazzo	PROPN
ejpam-3877	801	10	.	.	PUNCT
ejpam-3877	802	1	radon	radon	PROPN
ejpam-3877	802	2	measure	measure	NOUN
ejpam-3877	802	3	-	-	PUNCT
ejpam-3877	802	4	valued	value	VERB
ejpam-3877	802	5	solutions	solution	NOUN
ejpam-3877	802	6	for	for	ADP
ejpam-3877	802	7	some	some	DET
ejpam-3877	802	8	quasilinear	quasilinear	NOUN
ejpam-3877	802	9	degenerate	degenerate	ADJ
ejpam-3877	802	10	elliptic	elliptic	ADJ
ejpam-3877	802	11	equations	equation	NOUN
ejpam-3877	802	12	.	.	PUNCT
ejpam-3877	803	1	ann	ann	PROPN
ejpam-3877	803	2	.	.	PUNCT
ejpam-3877	803	3	mat	mat	PROPN
ejpam-3877	803	4	.	.	PUNCT
ejpam-3877	803	5	pura	pura	NOUN
ejpam-3877	803	6	appl	appl	PROPN
ejpam-3877	803	7	.	.	PROPN
ejpam-3877	803	8	,	,	PUNCT
ejpam-3877	803	9	194:495–532	194:495–532	NUM
ejpam-3877	803	10	,	,	PUNCT
ejpam-3877	803	11	2015	2015	NUM
ejpam-3877	803	12	.	.	PUNCT
ejpam-3877	804	1	[	[	X
ejpam-3877	804	2	29	29	NUM
ejpam-3877	804	3	]	]	PUNCT
ejpam-3877	804	4	j.	j.	PROPN
ejpam-3877	804	5	simon	simon	PROPN
ejpam-3877	804	6	.	.	PUNCT
ejpam-3877	805	1	compact	compact	ADJ
ejpam-3877	805	2	sets	set	NOUN
ejpam-3877	805	3	in	in	ADP
ejpam-3877	805	4	the	the	DET
ejpam-3877	805	5	space	space	NOUN
ejpam-3877	805	6	lp(0	lp(0	PROPN
ejpam-3877	805	7	,	,	PUNCT
ejpam-3877	805	8	t	t	PROPN
ejpam-3877	805	9	;	;	PUNCT
ejpam-3877	805	10	b	b	X
ejpam-3877	805	11	)	)	PUNCT
ejpam-3877	805	12	.	.	PUNCT
ejpam-3877	806	1	ann	ann	PROPN
ejpam-3877	806	2	.	.	PUNCT
ejpam-3877	806	3	mat	mat	PROPN
ejpam-3877	806	4	.	.	PUNCT
ejpam-3877	806	5	pura	pura	NOUN
ejpam-3877	806	6	appl	appl	PROPN
ejpam-3877	806	7	.	.	PROPN
ejpam-3877	806	8	,	,	PUNCT
ejpam-3877	806	9	146:65–96	146:65–96	NUM
ejpam-3877	806	10	,	,	PUNCT
ejpam-3877	806	11	1987	1987	NUM
ejpam-3877	806	12	.	.	PUNCT
ejpam-3877	807	1	[	[	X
ejpam-3877	807	2	30	30	NUM
ejpam-3877	807	3	]	]	X
ejpam-3877	807	4	f.	f.	PROPN
ejpam-3877	807	5	smarrazzo	smarrazzo	PROPN
ejpam-3877	807	6	and	and	CCONJ
ejpam-3877	807	7	a.	a.	PROPN
ejpam-3877	807	8	tesei	tesei	PROPN
ejpam-3877	807	9	.	.	PUNCT
ejpam-3877	808	1	degenerate	degenerate	ADJ
ejpam-3877	808	2	regularization	regularization	NOUN
ejpam-3877	808	3	of	of	ADP
ejpam-3877	808	4	forward	forward	ADJ
ejpam-3877	808	5	-	-	PUNCT
ejpam-3877	808	6	backward	backward	ADJ
ejpam-3877	808	7	parabolic	parabolic	ADJ
ejpam-3877	808	8	equations	equation	NOUN
ejpam-3877	808	9	:	:	PUNCT
ejpam-3877	808	10	the	the	DET
ejpam-3877	808	11	regularized	regularize	VERB
ejpam-3877	808	12	problem	problem	NOUN
ejpam-3877	808	13	.	.	PUNCT
ejpam-3877	809	1	arch	arch	NOUN
ejpam-3877	809	2	.	.	PUNCT
ejpam-3877	810	1	ration	ration	NOUN
ejpam-3877	810	2	.	.	PUNCT
ejpam-3877	811	1	mech	mech	PROPN
ejpam-3877	811	2	.	.	PUNCT
ejpam-3877	812	1	anal	anal	PROPN
ejpam-3877	812	2	.	.	PROPN
ejpam-3877	812	3	,	,	PUNCT
ejpam-3877	812	4	204:85–139	204:85–139	NUM
ejpam-3877	812	5	,	,	PUNCT
ejpam-3877	812	6	2012	2012	NUM
ejpam-3877	812	7	.	.	PUNCT
ejpam-3877	813	1	[	[	X
ejpam-3877	813	2	31	31	NUM
ejpam-3877	813	3	]	]	PUNCT
ejpam-3877	813	4	f.	f.	PROPN
ejpam-3877	813	5	smarrazzo	smarrazzo	PROPN
ejpam-3877	813	6	and	and	CCONJ
ejpam-3877	813	7	a.	a.	PROPN
ejpam-3877	813	8	tesei	tesei	PROPN
ejpam-3877	813	9	.	.	PUNCT
ejpam-3877	814	1	degenerate	degenerate	ADJ
ejpam-3877	814	2	regularization	regularization	NOUN
ejpam-3877	814	3	of	of	ADP
ejpam-3877	814	4	forward	forward	ADJ
ejpam-3877	814	5	-	-	PUNCT
ejpam-3877	814	6	backward	backward	ADJ
ejpam-3877	814	7	parabolic	parabolic	ADJ
ejpam-3877	814	8	equations	equation	NOUN
ejpam-3877	814	9	:	:	PUNCT
ejpam-3877	814	10	the	the	DET
ejpam-3877	814	11	vanishing	vanish	VERB
ejpam-3877	814	12	viscosity	viscosity	NOUN
ejpam-3877	814	13	limit	limit	NOUN
ejpam-3877	814	14	.	.	PUNCT
ejpam-3877	815	1	math	math	NOUN
ejpam-3877	815	2	.	.	PUNCT
ejpam-3877	816	1	ann	ann	PROPN
ejpam-3877	816	2	.	.	PROPN
ejpam-3877	816	3	,	,	PUNCT
ejpam-3877	816	4	355:551–584	355:551–584	NUM
ejpam-3877	816	5	,	,	PUNCT
ejpam-3877	816	6	2013	2013	NUM
ejpam-3877	816	7	.	.	PUNCT
ejpam-3877	817	1	[	[	X
ejpam-3877	817	2	32	32	NUM
ejpam-3877	817	3	]	]	PUNCT
ejpam-3877	817	4	f.	f.	NOUN
ejpam-3877	817	5	duzaar	duzaar	PROPN
ejpam-3877	817	6	v.	v.	ADP
ejpam-3877	817	7	bögelein	bögelein	PROPN
ejpam-3877	817	8	and	and	CCONJ
ejpam-3877	817	9	g.	g.	PROPN
ejpam-3877	817	10	ugo	ugo	PROPN
ejpam-3877	817	11	.	.	PROPN
ejpam-3877	817	12	porous	porous	ADJ
ejpam-3877	817	13	medium	medium	ADJ
ejpam-3877	817	14	equations	equation	NOUN
ejpam-3877	817	15	with	with	ADP
ejpam-3877	817	16	measure	measure	NOUN
ejpam-3877	817	17	data	datum	NOUN
ejpam-3877	817	18	and	and	CCONJ
ejpam-3877	817	19	potential	potential	ADJ
ejpam-3877	817	20	estimates	estimate	NOUN
ejpam-3877	817	21	.	.	PUNCT
ejpam-3877	818	1	math	math	NOUN
ejpam-3877	818	2	.	.	PUNCT
ejpam-3877	819	1	ann	ann	PROPN
ejpam-3877	819	2	.	.	PROPN
ejpam-3877	819	3	,	,	PUNCT
ejpam-3877	819	4	45:3283–3330	45:3283–3330	PROPN
ejpam-3877	819	5	,	,	PUNCT
ejpam-3877	819	6	2013	2013	NUM
ejpam-3877	819	7	.	.	PUNCT
ejpam-3877	820	1	[	[	X
ejpam-3877	820	2	33	33	NUM
ejpam-3877	820	3	]	]	PUNCT
ejpam-3877	820	4	j.	j.	PROPN
ejpam-3877	820	5	l.	l.	PROPN
ejpam-3877	820	6	vázquez	vázquez	PROPN
ejpam-3877	820	7	.	.	PROPN
ejpam-3877	821	1	the	the	DET
ejpam-3877	821	2	porous	porous	ADJ
ejpam-3877	821	3	meduim	meduim	ADJ
ejpam-3877	821	4	equation	equation	NOUN
ejpam-3877	821	5	.	.	PUNCT
ejpam-3877	822	1	mathematical	mathematical	ADJ
ejpam-3877	822	2	theory	theory	NOUN
ejpam-3877	822	3	.	.	PUNCT
ejpam-3877	823	1	oxford	oxford	PROPN
ejpam-3877	823	2	mathematical	mathematical	PROPN
ejpam-3877	823	3	monographs	monograph	NOUN
ejpam-3877	823	4	,	,	PUNCT
ejpam-3877	823	5	oxford	oxford	PROPN
ejpam-3877	823	6	,	,	PUNCT
ejpam-3877	823	7	2007	2007	NUM
ejpam-3877	823	8	.	.	PUNCT