id	sid	tid	token	lemma	pos
ejpam-3577	1	1	european	european	PROPN
ejpam-3577	1	2	journal	journal	PROPN
ejpam-3577	1	3	of	of	ADP
ejpam-3577	1	4	pure	pure	ADJ
ejpam-3577	1	5	and	and	CCONJ
ejpam-3577	1	6	applied	apply	VERB
ejpam-3577	1	7	mathematics	mathematic	NOUN
ejpam-3577	1	8	vol	vol	NOUN
ejpam-3577	1	9	.	.	PROPN
ejpam-3577	2	1	12	12	NUM
ejpam-3577	2	2	,	,	PUNCT
ejpam-3577	2	3	no	no	INTJ
ejpam-3577	2	4	.	.	NOUN
ejpam-3577	2	5	4	4	NUM
ejpam-3577	2	6	,	,	PUNCT
ejpam-3577	2	7	2019	2019	NUM
ejpam-3577	2	8	,	,	PUNCT
ejpam-3577	2	9	1595	1595	NUM
ejpam-3577	2	10	-	-	SYM
ejpam-3577	2	11	1601	1601	NUM
ejpam-3577	2	12	issn	issn	PROPN
ejpam-3577	2	13	1307	1307	NUM
ejpam-3577	2	14	-	-	SYM
ejpam-3577	2	15	5543	5543	NUM
ejpam-3577	2	16	–	–	PUNCT
ejpam-3577	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3577	2	18	published	publish	VERB
ejpam-3577	2	19	by	by	ADP
ejpam-3577	2	20	new	new	PROPN
ejpam-3577	2	21	york	york	PROPN
ejpam-3577	2	22	business	business	PROPN
ejpam-3577	2	23	global	global	ADJ
ejpam-3577	2	24	existence	existence	NOUN
ejpam-3577	2	25	of	of	ADP
ejpam-3577	2	26	optimal	optimal	ADJ
ejpam-3577	2	27	control	control	NOUN
ejpam-3577	2	28	for	for	ADP
ejpam-3577	2	29	a	a	DET
ejpam-3577	2	30	nonlinear	nonlinear	ADJ
ejpam-3577	2	31	partial	partial	ADJ
ejpam-3577	2	32	differential	differential	NOUN
ejpam-3577	2	33	equation	equation	NOUN
ejpam-3577	2	34	of	of	ADP
ejpam-3577	2	35	hyperbolic	hyperbolic	ADJ
ejpam-3577	2	36	-	-	PUNCT
ejpam-3577	2	37	type	type	NOUN
ejpam-3577	2	38	dieudonné	dieudonné	NOUN
ejpam-3577	2	39	ampini1,∗	ampini1,∗	NOUN
ejpam-3577	2	40	,	,	PUNCT
ejpam-3577	2	41	vital	vital	ADJ
ejpam-3577	2	42	delmas	delma	NOUN
ejpam-3577	2	43	mabonzo1	mabonzo1	PROPN
ejpam-3577	2	44	1	1	NUM
ejpam-3577	2	45	parcours	parcours	PROPN
ejpam-3577	2	46	mathématiques	mathématiques	PROPN
ejpam-3577	2	47	,	,	PUNCT
ejpam-3577	2	48	f.s.t	f.s.t	INTJ
ejpam-3577	2	49	,	,	PUNCT
ejpam-3577	2	50	université	université	NOUN
ejpam-3577	2	51	marien	marien	PROPN
ejpam-3577	2	52	ngouabi	ngouabi	PROPN
ejpam-3577	2	53	,	,	PUNCT
ejpam-3577	2	54	brazzaville	brazzaville	PROPN
ejpam-3577	2	55	,	,	PUNCT
ejpam-3577	2	56	congo	congo	PROPN
ejpam-3577	2	57	abstract	abstract	NOUN
ejpam-3577	2	58	.	.	PUNCT
ejpam-3577	3	1	in	in	ADP
ejpam-3577	3	2	this	this	DET
ejpam-3577	3	3	paper	paper	NOUN
ejpam-3577	3	4	,	,	PUNCT
ejpam-3577	3	5	we	we	PRON
ejpam-3577	3	6	prove	prove	VERB
ejpam-3577	3	7	the	the	DET
ejpam-3577	3	8	existence	existence	NOUN
ejpam-3577	3	9	of	of	ADP
ejpam-3577	3	10	an	an	DET
ejpam-3577	3	11	optimal	optimal	ADJ
ejpam-3577	3	12	control	control	NOUN
ejpam-3577	3	13	for	for	ADP
ejpam-3577	3	14	a	a	DET
ejpam-3577	3	15	nonlinear	nonlinear	ADJ
ejpam-3577	3	16	hyperbolic	hyperbolic	ADJ
ejpam-3577	3	17	problem	problem	NOUN
ejpam-3577	3	18	,	,	PUNCT
ejpam-3577	3	19	examined	examine	VERB
ejpam-3577	3	20	in	in	ADP
ejpam-3577	3	21	[	[	X
ejpam-3577	3	22	3	3	NUM
ejpam-3577	3	23	]	]	PUNCT
ejpam-3577	3	24	.	.	PUNCT
ejpam-3577	4	1	an	an	DET
ejpam-3577	4	2	estimation	estimation	NOUN
ejpam-3577	4	3	is	be	AUX
ejpam-3577	4	4	used	use	VERB
ejpam-3577	4	5	which	which	PRON
ejpam-3577	4	6	makes	make	VERB
ejpam-3577	4	7	it	it	PRON
ejpam-3577	4	8	possible	possible	ADJ
ejpam-3577	4	9	to	to	PART
ejpam-3577	4	10	extract	extract	VERB
ejpam-3577	4	11	from	from	ADP
ejpam-3577	4	12	a	a	DET
ejpam-3577	4	13	minimizable	minimizable	ADJ
ejpam-3577	4	14	sequence	sequence	NOUN
ejpam-3577	4	15	of	of	ADP
ejpam-3577	4	16	controls	control	NOUN
ejpam-3577	4	17	and	and	CCONJ
ejpam-3577	4	18	from	from	ADP
ejpam-3577	4	19	the	the	DET
ejpam-3577	4	20	sequence	sequence	NOUN
ejpam-3577	4	21	of	of	ADP
ejpam-3577	4	22	corresponding	corresponding	ADJ
ejpam-3577	4	23	solutions	solution	NOUN
ejpam-3577	4	24	weakly	weakly	ADV
ejpam-3577	4	25	convergent	convergent	ADJ
ejpam-3577	4	26	sub	sub	NOUN
ejpam-3577	4	27	sequences	sequence	NOUN
ejpam-3577	4	28	.	.	PUNCT
ejpam-3577	5	1	to	to	PART
ejpam-3577	5	2	prove	prove	VERB
ejpam-3577	5	3	the	the	DET
ejpam-3577	5	4	passage	passage	NOUN
ejpam-3577	5	5	to	to	ADP
ejpam-3577	5	6	the	the	DET
ejpam-3577	5	7	limit	limit	NOUN
ejpam-3577	5	8	in	in	ADP
ejpam-3577	5	9	a	a	DET
ejpam-3577	5	10	true	true	ADJ
ejpam-3577	5	11	equality	equality	NOUN
ejpam-3577	5	12	for	for	ADP
ejpam-3577	5	13	every	every	DET
ejpam-3577	5	14	element	element	NOUN
ejpam-3577	5	15	of	of	ADP
ejpam-3577	5	16	the	the	DET
ejpam-3577	5	17	minimizable	minimizable	ADJ
ejpam-3577	5	18	sequence	sequence	NOUN
ejpam-3577	5	19	,	,	PUNCT
ejpam-3577	5	20	lebesgue	lebesgue	PROPN
ejpam-3577	5	21	’s	’s	PART
ejpam-3577	5	22	theorem	theorem	NOUN
ejpam-3577	5	23	on	on	ADP
ejpam-3577	5	24	the	the	DET
ejpam-3577	5	25	passage	passage	NOUN
ejpam-3577	5	26	to	to	ADP
ejpam-3577	5	27	the	the	DET
ejpam-3577	5	28	limit	limit	NOUN
ejpam-3577	5	29	under	under	ADP
ejpam-3577	5	30	the	the	DET
ejpam-3577	5	31	integral	integral	ADJ
ejpam-3577	5	32	sign	sign	NOUN
ejpam-3577	5	33	and	and	CCONJ
ejpam-3577	5	34	the	the	DET
ejpam-3577	5	35	theorem	theorem	NOUN
ejpam-3577	5	36	of	of	ADP
ejpam-3577	5	37	immersion	immersion	NOUN
ejpam-3577	5	38	have	have	AUX
ejpam-3577	5	39	been	be	AUX
ejpam-3577	5	40	used	use	VERB
ejpam-3577	5	41	.	.	PUNCT
ejpam-3577	6	1	2010	2010	NUM
ejpam-3577	6	2	mathematics	mathematic	NOUN
ejpam-3577	6	3	subject	subject	NOUN
ejpam-3577	6	4	classifications	classification	NOUN
ejpam-3577	6	5	:	:	PUNCT
ejpam-3577	6	6	49j20	49j20	NUM
ejpam-3577	6	7	,	,	PUNCT
ejpam-3577	6	8	58j45	58j45	NUM
ejpam-3577	6	9	,	,	PUNCT
ejpam-3577	6	10	35l86	35l86	NUM
ejpam-3577	6	11	,	,	PUNCT
ejpam-3577	6	12	81t13	81t13	NUM
ejpam-3577	6	13	key	key	ADJ
ejpam-3577	6	14	words	word	NOUN
ejpam-3577	6	15	and	and	CCONJ
ejpam-3577	6	16	phrases	phrase	NOUN
ejpam-3577	6	17	:	:	PUNCT
ejpam-3577	6	18	optimal	optimal	ADJ
ejpam-3577	6	19	control	control	NOUN
ejpam-3577	6	20	,	,	PUNCT
ejpam-3577	6	21	hyperbolic	hyperbolic	ADJ
ejpam-3577	6	22	equation	equation	NOUN
ejpam-3577	6	23	,	,	PUNCT
ejpam-3577	6	24	functional	functional	ADJ
ejpam-3577	6	25	1	1	NUM
ejpam-3577	6	26	.	.	PUNCT
ejpam-3577	7	1	preliminaries	preliminary	NOUN
ejpam-3577	7	2	notions	notion	NOUN
ejpam-3577	7	3	before	before	ADP
ejpam-3577	7	4	proceeding	proceed	VERB
ejpam-3577	7	5	to	to	ADP
ejpam-3577	7	6	the	the	DET
ejpam-3577	7	7	formulation	formulation	NOUN
ejpam-3577	7	8	of	of	ADP
ejpam-3577	7	9	the	the	DET
ejpam-3577	7	10	problem	problem	NOUN
ejpam-3577	7	11	,	,	PUNCT
ejpam-3577	7	12	let	let	VERB
ejpam-3577	7	13	us	we	PRON
ejpam-3577	7	14	recall	recall	VERB
ejpam-3577	7	15	some	some	DET
ejpam-3577	7	16	fundamental	fundamental	ADJ
ejpam-3577	7	17	notions	notion	NOUN
ejpam-3577	7	18	of	of	ADP
ejpam-3577	7	19	[	[	X
ejpam-3577	7	20	2	2	NUM
ejpam-3577	7	21	]	]	PUNCT
ejpam-3577	7	22	.	.	PUNCT
ejpam-3577	8	1	1.1	1.1	NUM
ejpam-3577	8	2	.	.	PUNCT
ejpam-3577	8	3	definition	definition	NOUN
ejpam-3577	8	4	of	of	ADP
ejpam-3577	8	5	ck	ck	PROPN
ejpam-3577	8	6	,	,	PUNCT
ejpam-3577	8	7	λ,0(ω̄	λ,0(ω̄	NOUN
ejpam-3577	8	8	)	)	PUNCT
ejpam-3577	8	9	space	space	NOUN
ejpam-3577	8	10	:	:	PUNCT
ejpam-3577	8	11	(	(	PUNCT
ejpam-3577	8	12	see	see	VERB
ejpam-3577	8	13	[	[	X
ejpam-3577	8	14	4	4	NUM
ejpam-3577	8	15	]	]	PUNCT
ejpam-3577	8	16	)	)	PUNCT
ejpam-3577	8	17	let	let	VERB
ejpam-3577	8	18	ω	ω	PRON
ejpam-3577	8	19	be	be	AUX
ejpam-3577	8	20	a	a	DET
ejpam-3577	8	21	domain	domain	NOUN
ejpam-3577	8	22	of	of	ADP
ejpam-3577	8	23	rn	rn	PROPN
ejpam-3577	8	24	,	,	PUNCT
ejpam-3577	8	25	k	k	PROPN
ejpam-3577	8	26	∈	∈	PROPN
ejpam-3577	8	27	n0	n0	PROPN
ejpam-3577	8	28	and	and	CCONJ
ejpam-3577	8	29	λ	λ	NOUN
ejpam-3577	8	30	∈]0	∈]0	X
ejpam-3577	8	31	,	,	PUNCT
ejpam-3577	8	32	1	1	NUM
ejpam-3577	8	33	[	[	NOUN
ejpam-3577	8	34	.	.	PUNCT
ejpam-3577	9	1	we	we	PRON
ejpam-3577	9	2	call	call	VERB
ejpam-3577	9	3	ck	ck	PRON
ejpam-3577	9	4	,	,	PUNCT
ejpam-3577	9	5	λ,0(ω̄	λ,0(ω̄	NOUN
ejpam-3577	9	6	)	)	PUNCT
ejpam-3577	9	7	any	any	DET
ejpam-3577	9	8	subset	subset	NOUN
ejpam-3577	9	9	of	of	ADP
ejpam-3577	9	10	the	the	DET
ejpam-3577	9	11	functions	function	NOUN
ejpam-3577	9	12	u	u	NOUN
ejpam-3577	9	13	∈	∈	PROPN
ejpam-3577	9	14	ck	ck	PROPN
ejpam-3577	9	15	,	,	PUNCT
ejpam-3577	9	16	λ(ω̄	λ(ω̄	PROPN
ejpam-3577	9	17	)	)	PUNCT
ejpam-3577	9	18	for	for	ADP
ejpam-3577	9	19	which	which	PRON
ejpam-3577	9	20	the	the	DET
ejpam-3577	9	21	following	follow	VERB
ejpam-3577	9	22	condition	condition	NOUN
ejpam-3577	9	23	is	be	AUX
ejpam-3577	9	24	satisfied	satisfied	ADJ
ejpam-3577	9	25	∀ε	∀ε	X
ejpam-3577	9	26	>	>	X
ejpam-3577	9	27	0	0	NUM
ejpam-3577	9	28	,	,	PUNCT
ejpam-3577	9	29	∃δ	∃δ	PROPN
ejpam-3577	9	30	>	>	X
ejpam-3577	9	31	0	0	NUM
ejpam-3577	9	32	:	:	PUNCT
ejpam-3577	9	33	(	(	PUNCT
ejpam-3577	9	34	x	x	X
ejpam-3577	9	35	,	,	PUNCT
ejpam-3577	9	36	y	y	PROPN
ejpam-3577	9	37	∈	∈	PROPN
ejpam-3577	9	38	ω	ω	PROPN
ejpam-3577	9	39	,	,	PUNCT
ejpam-3577	9	40	0	0	NUM
ejpam-3577	9	41	<	<	X
ejpam-3577	9	42	|x−	|x−	NOUN
ejpam-3577	9	43	y|	y|	NOUN
ejpam-3577	9	44	<	<	X
ejpam-3577	9	45	δ	δ	PROPN
ejpam-3577	9	46	,	,	PUNCT
ejpam-3577	9	47	|α|	|α|	PROPN
ejpam-3577	9	48	=	=	SYM
ejpam-3577	9	49	k	k	NOUN
ejpam-3577	9	50	)	)	PUNCT
ejpam-3577	10	1	=	=	AUX
ejpam-3577	10	2	⇒	⇒	VERB
ejpam-3577	10	3	|dαu(x)−dαu(y)|	|dαu(x)−dαu(y)|	PROPN
ejpam-3577	10	4	·	·	PUNCT
ejpam-3577	10	5	|x−	|x−	PROPN
ejpam-3577	11	1	y|−λ	y|−λ	NOUN
ejpam-3577	11	2	<	<	X
ejpam-3577	11	3	ε	ε	PROPN
ejpam-3577	11	4	where	where	SCONJ
ejpam-3577	11	5	α	α	NOUN
ejpam-3577	11	6	=	=	SYM
ejpam-3577	11	7	(	(	PUNCT
ejpam-3577	11	8	α1	α1	PROPN
ejpam-3577	11	9	,	,	PUNCT
ejpam-3577	11	10	·	·	PUNCT
ejpam-3577	11	11	·	·	PUNCT
ejpam-3577	11	12	·	·	PUNCT
ejpam-3577	11	13	,	,	PUNCT
ejpam-3577	11	14	α2	α2	PROPN
ejpam-3577	11	15	)	)	PUNCT
ejpam-3577	11	16	is	be	AUX
ejpam-3577	11	17	the	the	DET
ejpam-3577	11	18	multi	multi	NOUN
ejpam-3577	11	19	-	-	NOUN
ejpam-3577	11	20	index	index	NOUN
ejpam-3577	11	21	.	.	PUNCT
ejpam-3577	12	1	the	the	DET
ejpam-3577	12	2	norm	norm	NOUN
ejpam-3577	12	3	of	of	ADP
ejpam-3577	12	4	the	the	DET
ejpam-3577	12	5	ck	ck	NOUN
ejpam-3577	12	6	,	,	PUNCT
ejpam-3577	12	7	λ,0(ω̄	λ,0(ω̄	NOUN
ejpam-3577	12	8	)	)	PUNCT
ejpam-3577	12	9	space	space	NOUN
ejpam-3577	12	10	is	be	AUX
ejpam-3577	12	11	deduced	deduce	VERB
ejpam-3577	12	12	from	from	ADP
ejpam-3577	12	13	ck	ck	PROPN
ejpam-3577	12	14	,	,	PUNCT
ejpam-3577	12	15	λ(ω̄	λ(ω̄	PROPN
ejpam-3577	12	16	)	)	PUNCT
ejpam-3577	12	17	,	,	PUNCT
ejpam-3577	12	18	namely	namely	ADV
ejpam-3577	12	19	‖u‖k	‖u‖k	ADJ
ejpam-3577	12	20	,	,	PUNCT
ejpam-3577	12	21	λ	λ	X
ejpam-3577	12	22	=	=	SYM
ejpam-3577	12	23	∑	∑	PUNCT
ejpam-3577	12	24	|α|6k	|α|6k	NOUN
ejpam-3577	12	25	sup	sup	NOUN
ejpam-3577	12	26	x∈ω	x∈ω	NOUN
ejpam-3577	12	27	|dαu(x)|+	|dαu(x)|+	NOUN
ejpam-3577	12	28	∑	∑	PROPN
ejpam-3577	12	29	|α|6k	|α|6k	NOUN
ejpam-3577	12	30	sup	sup	NOUN
ejpam-3577	12	31	x	x	SYM
ejpam-3577	12	32	6	6	NUM
ejpam-3577	12	33	=	=	SYM
ejpam-3577	12	34	y	y	PROPN
ejpam-3577	12	35	|dαu(x)−dαu(y)|	|dαu(x)−dαu(y)|	PROPN
ejpam-3577	12	36	·	·	PUNCT
ejpam-3577	12	37	|x−	|x−	PROPN
ejpam-3577	13	1	y|−λ	y|−λ	NOUN
ejpam-3577	13	2	.	.	PUNCT
ejpam-3577	13	3	∗corresponding	∗corresponde	VERB
ejpam-3577	13	4	author	author	NOUN
ejpam-3577	13	5	.	.	PUNCT
ejpam-3577	14	1	doi	doi	NOUN
ejpam-3577	14	2	:	:	PUNCT
ejpam-3577	14	3	https://doi.org/10.29020/nybg.ejpam.v12i4.3577	https://doi.org/10.29020/nybg.ejpam.v12i4.3577	PROPN
ejpam-3577	14	4	email	email	NOUN
ejpam-3577	14	5	addresses	address	NOUN
ejpam-3577	14	6	:	:	PUNCT
ejpam-3577	14	7	dieudonne.ampini@gmail.com	dieudonne.ampini@gmail.com	X
ejpam-3577	14	8	(	(	PUNCT
ejpam-3577	14	9	d.	d.	PROPN
ejpam-3577	14	10	ampini	ampini	PROPN
ejpam-3577	14	11	)	)	PUNCT
ejpam-3577	14	12	,	,	PUNCT
ejpam-3577	14	13	vitalm28@gmail.com	vitalm28@gmail.com	X
ejpam-3577	14	14	(	(	PUNCT
ejpam-3577	14	15	v.	v.	ADP
ejpam-3577	14	16	d.	d.	PROPN
ejpam-3577	14	17	mabonzo	mabonzo	PROPN
ejpam-3577	14	18	)	)	PUNCT
ejpam-3577	14	19	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3577	15	1	1595	1595	NUM
ejpam-3577	16	1	c	c	X
ejpam-3577	16	2	©	©	PROPN
ejpam-3577	16	3	2019	2019	NUM
ejpam-3577	16	4	ejpam	ejpam	NOUN
ejpam-3577	16	5	all	all	DET
ejpam-3577	16	6	rights	right	NOUN
ejpam-3577	16	7	reserved	reserve	VERB
ejpam-3577	16	8	.	.	PUNCT
ejpam-3577	17	1	d.	d.	PROPN
ejpam-3577	17	2	ampini	ampini	PROPN
ejpam-3577	17	3	,	,	PUNCT
ejpam-3577	17	4	v.	v.	PROPN
ejpam-3577	17	5	d.	d.	PROPN
ejpam-3577	17	6	mabonzo	mabonzo	PROPN
ejpam-3577	17	7	/	/	SYM
ejpam-3577	17	8	eur	eur	PROPN
ejpam-3577	17	9	.	.	PUNCT
ejpam-3577	18	1	j.	j.	PROPN
ejpam-3577	18	2	pure	pure	PROPN
ejpam-3577	18	3	appl	appl	PROPN
ejpam-3577	18	4	.	.	PROPN
ejpam-3577	18	5	math	math	PROPN
ejpam-3577	18	6	,	,	PUNCT
ejpam-3577	18	7	12	12	NUM
ejpam-3577	18	8	(	(	PUNCT
ejpam-3577	18	9	4	4	NUM
ejpam-3577	18	10	)	)	PUNCT
ejpam-3577	18	11	(	(	PUNCT
ejpam-3577	18	12	2019	2019	NUM
ejpam-3577	18	13	)	)	PUNCT
ejpam-3577	18	14	,	,	PUNCT
ejpam-3577	18	15	1595	1595	NUM
ejpam-3577	18	16	-	-	SYM
ejpam-3577	18	17	1601	1601	NUM
ejpam-3577	18	18	1596	1596	NUM
ejpam-3577	18	19	theorem	theorem	NOUN
ejpam-3577	18	20	1	1	NUM
ejpam-3577	18	21	(	(	PUNCT
ejpam-3577	18	22	[	[	X
ejpam-3577	18	23	2	2	NUM
ejpam-3577	18	24	]	]	PUNCT
ejpam-3577	18	25	,	,	PUNCT
ejpam-3577	18	26	p.11	p.11	PROPN
ejpam-3577	18	27	)	)	PUNCT
ejpam-3577	18	28	.	.	PUNCT
ejpam-3577	19	1	let	let	VERB
ejpam-3577	19	2	ω	ω	PRON
ejpam-3577	19	3	be	be	AUX
ejpam-3577	19	4	a	a	DET
ejpam-3577	19	5	bounded	bounded	ADJ
ejpam-3577	19	6	domain	domain	NOUN
ejpam-3577	19	7	of	of	ADP
ejpam-3577	19	8	rn	rn	PROPN
ejpam-3577	19	9	,	,	PUNCT
ejpam-3577	19	10	0	0	PUNCT
ejpam-3577	19	11	<	<	X
ejpam-3577	19	12	λ	λ	X
ejpam-3577	19	13	<	<	X
ejpam-3577	19	14	1	1	NUM
ejpam-3577	19	15	f	f	NOUN
ejpam-3577	19	16	:	:	PUNCT
ejpam-3577	20	1	r×	r×	VERB
ejpam-3577	20	2	ω̄	ω̄	ADP
ejpam-3577	20	3	−→	−→	ADJ
ejpam-3577	20	4	r	r	NOUN
ejpam-3577	20	5	,	,	PUNCT
ejpam-3577	20	6	(	(	PUNCT
ejpam-3577	20	7	u	u	NOUN
ejpam-3577	20	8	,	,	PUNCT
ejpam-3577	20	9	x	x	NOUN
ejpam-3577	20	10	)	)	PUNCT
ejpam-3577	20	11	7−→	7−→	NOUN
ejpam-3577	20	12	f	f	X
ejpam-3577	20	13	(	(	PUNCT
ejpam-3577	20	14	u	u	NOUN
ejpam-3577	20	15	,	,	PUNCT
ejpam-3577	20	16	x	x	X
ejpam-3577	20	17	)	)	PUNCT
ejpam-3577	20	18	a	a	DET
ejpam-3577	20	19	continuous	continuous	ADJ
ejpam-3577	20	20	function	function	NOUN
ejpam-3577	20	21	defined	define	VERB
ejpam-3577	20	22	on	on	ADP
ejpam-3577	20	23	r×	r×	NOUN
ejpam-3577	20	24	ω̄	ω̄	NOUN
ejpam-3577	20	25	,	,	PUNCT
ejpam-3577	20	26	differentiable	differentiable	VERB
ejpam-3577	20	27	with	with	ADP
ejpam-3577	20	28	respect	respect	NOUN
ejpam-3577	20	29	to	to	ADP
ejpam-3577	20	30	u	u	NOUN
ejpam-3577	20	31	on	on	ADP
ejpam-3577	20	32	r	r	NOUN
ejpam-3577	20	33	for	for	ADP
ejpam-3577	20	34	all	all	DET
ejpam-3577	20	35	x	x	SYM
ejpam-3577	20	36	∈	∈	NOUN
ejpam-3577	20	37	ω̄	ω̄	ADV
ejpam-3577	21	1	and	and	CCONJ
ejpam-3577	21	2	also	also	ADV
ejpam-3577	21	3	f	f	PROPN
ejpam-3577	21	4	′u	′u	PROPN
ejpam-3577	21	5	:	:	PUNCT
ejpam-3577	21	6	ω̄×r	ω̄×r	PUNCT
ejpam-3577	21	7	−→	−→	NOUN
ejpam-3577	21	8	r	r	NOUN
ejpam-3577	21	9	a	a	DET
ejpam-3577	21	10	continuous	continuous	ADJ
ejpam-3577	21	11	function	function	NOUN
ejpam-3577	21	12	on	on	ADP
ejpam-3577	21	13	ω̄×	ω̄×	ADJ
ejpam-3577	21	14	r	r	NOUN
ejpam-3577	21	15	satisfied	satisfy	VERB
ejpam-3577	21	16	|f	|f	ADP
ejpam-3577	21	17	′u(u	′u(u	NOUN
ejpam-3577	21	18	,	,	PUNCT
ejpam-3577	21	19	y)−	y)−	PROPN
ejpam-3577	21	20	f	f	PROPN
ejpam-3577	21	21	′u(v	′u(v	PROPN
ejpam-3577	21	22	,	,	PUNCT
ejpam-3577	21	23	z)|	z)|	PRON
ejpam-3577	21	24	6	6	NUM
ejpam-3577	21	25	q1|u−	q1|u−	VERB
ejpam-3577	21	26	v|+q2|y	v|+q2|y	NOUN
ejpam-3577	21	27	−	−	PROPN
ejpam-3577	21	28	z|λ	z|λ	PROPN
ejpam-3577	21	29	and	and	CCONJ
ejpam-3577	21	30	|f	|f	PROPN
ejpam-3577	21	31	(	(	PUNCT
ejpam-3577	21	32	u	u	NOUN
ejpam-3577	21	33	,	,	PUNCT
ejpam-3577	21	34	y)−	y)−	PROPN
ejpam-3577	21	35	f	f	PROPN
ejpam-3577	21	36	(	(	PUNCT
ejpam-3577	21	37	v	v	NOUN
ejpam-3577	21	38	,	,	PUNCT
ejpam-3577	21	39	z)|	z)|	ADP
ejpam-3577	21	40	6	6	NUM
ejpam-3577	21	41	c1|u−	c1|u−	PROPN
ejpam-3577	21	42	v|+	v|+	PROPN
ejpam-3577	21	43	c2(y	c2(y	PROPN
ejpam-3577	21	44	,	,	PUNCT
ejpam-3577	21	45	z)|y	z)|y	NOUN
ejpam-3577	21	46	−	−	PROPN
ejpam-3577	21	47	z|λ	z|λ	X
ejpam-3577	21	48	where	where	SCONJ
ejpam-3577	21	49	q1	q1	PROPN
ejpam-3577	21	50	,	,	PUNCT
ejpam-3577	21	51	q2	q2	PROPN
ejpam-3577	21	52	,	,	PUNCT
ejpam-3577	21	53	c1	c1	PROPN
ejpam-3577	21	54	are	be	AUX
ejpam-3577	21	55	the	the	DET
ejpam-3577	21	56	constants	constant	NOUN
ejpam-3577	21	57	and	and	CCONJ
ejpam-3577	21	58	c2	c2	PROPN
ejpam-3577	21	59	a	a	DET
ejpam-3577	21	60	bounded	bound	VERB
ejpam-3577	21	61	function	function	NOUN
ejpam-3577	21	62	which	which	PRON
ejpam-3577	21	63	verifies	verify	VERB
ejpam-3577	21	64	the	the	DET
ejpam-3577	21	65	condition	condition	NOUN
ejpam-3577	21	66	∀	∀	X
ejpam-3577	21	67	ε	ε	X
ejpam-3577	21	68	>	>	X
ejpam-3577	21	69	0,∃	0,∃	NUM
ejpam-3577	21	70	δ	δ	X
ejpam-3577	21	71	>	>	X
ejpam-3577	21	72	0	0	NUM
ejpam-3577	21	73	:	:	PUNCT
ejpam-3577	21	74	(	(	PUNCT
ejpam-3577	21	75	|y	|y	NOUN
ejpam-3577	21	76	−	−	X
ejpam-3577	21	77	z|	z|	PROPN
ejpam-3577	21	78	<	<	X
ejpam-3577	21	79	δ	δ	PROPN
ejpam-3577	21	80	)	)	PUNCT
ejpam-3577	21	81	=	=	VERB
ejpam-3577	21	82	⇒	⇒	NOUN
ejpam-3577	21	83	c2(y	c2(y	PROPN
ejpam-3577	21	84	,	,	PUNCT
ejpam-3577	21	85	z	z	NOUN
ejpam-3577	21	86	)	)	PUNCT
ejpam-3577	21	87	<	<	X
ejpam-3577	21	88	ε	ε	PROPN
ejpam-3577	21	89	.	.	PUNCT
ejpam-3577	22	1	then	then	ADV
ejpam-3577	22	2	the	the	DET
ejpam-3577	22	3	ϕ(x	ϕ(x	NOUN
ejpam-3577	22	4	)	)	PUNCT
ejpam-3577	22	5	7−→	7−→	PROPN
ejpam-3577	22	6	f	f	NOUN
ejpam-3577	22	7	(	(	PUNCT
ejpam-3577	22	8	ϕ(x	ϕ(x	NOUN
ejpam-3577	22	9	)	)	PUNCT
ejpam-3577	22	10	,	,	PUNCT
ejpam-3577	22	11	x	x	X
ejpam-3577	22	12	)	)	PUNCT
ejpam-3577	22	13	mapping	mapping	NOUN
ejpam-3577	22	14	is	be	AUX
ejpam-3577	22	15	defined	define	VERB
ejpam-3577	22	16	from	from	ADP
ejpam-3577	22	17	c0,λ,0(ω̄	c0,λ,0(ω̄	NOUN
ejpam-3577	22	18	)	)	PUNCT
ejpam-3577	22	19	to	to	ADP
ejpam-3577	22	20	c0,λ,0(ω̄	c0,λ,0(ω̄	PROPN
ejpam-3577	22	21	)	)	PUNCT
ejpam-3577	22	22	and	and	CCONJ
ejpam-3577	22	23	is	be	AUX
ejpam-3577	22	24	weakly	weakly	ADV
ejpam-3577	22	25	sequentially	sequentially	ADV
ejpam-3577	22	26	continuous	continuous	ADJ
ejpam-3577	22	27	.	.	PUNCT
ejpam-3577	23	1	theorem	theorem	ADJ
ejpam-3577	23	2	2	2	NUM
ejpam-3577	23	3	(	(	PUNCT
ejpam-3577	23	4	[	[	X
ejpam-3577	23	5	2	2	NUM
ejpam-3577	23	6	]	]	PUNCT
ejpam-3577	23	7	,	,	PUNCT
ejpam-3577	23	8	p.13	p.13	NOUN
ejpam-3577	23	9	)	)	PUNCT
ejpam-3577	23	10	.	.	PUNCT
ejpam-3577	24	1	let	let	VERB
ejpam-3577	24	2	ω	ω	PRON
ejpam-3577	24	3	be	be	AUX
ejpam-3577	24	4	a	a	DET
ejpam-3577	24	5	bounded	bounded	ADJ
ejpam-3577	24	6	domain	domain	NOUN
ejpam-3577	24	7	of	of	ADP
ejpam-3577	24	8	rn	rn	PROPN
ejpam-3577	24	9	,	,	PUNCT
ejpam-3577	24	10	0	0	PUNCT
ejpam-3577	24	11	<	<	X
ejpam-3577	24	12	λ	λ	X
ejpam-3577	24	13	<	<	X
ejpam-3577	24	14	1	1	NUM
ejpam-3577	24	15	k	k	NOUN
ejpam-3577	24	16	:	:	PUNCT
ejpam-3577	24	17	r×r	r×r	NUM
ejpam-3577	24	18	,	,	PUNCT
ejpam-3577	24	19	(	(	PUNCT
ejpam-3577	24	20	x	x	X
ejpam-3577	24	21	,	,	PUNCT
ejpam-3577	24	22	y	y	PROPN
ejpam-3577	24	23	,	,	PUNCT
ejpam-3577	24	24	u	u	NOUN
ejpam-3577	24	25	)	)	PUNCT
ejpam-3577	24	26	7−→	7−→	PROPN
ejpam-3577	24	27	k(x	k(x	PROPN
ejpam-3577	24	28	,	,	PUNCT
ejpam-3577	24	29	y	y	PROPN
ejpam-3577	24	30	,	,	PUNCT
ejpam-3577	24	31	u	u	NOUN
ejpam-3577	24	32	)	)	PUNCT
ejpam-3577	24	33	a	a	DET
ejpam-3577	24	34	continuous	continuous	ADJ
ejpam-3577	24	35	function	function	NOUN
ejpam-3577	24	36	on	on	ADP
ejpam-3577	24	37	r×	r×	PROPN
ejpam-3577	24	38	ω̄2	ω̄2	X
ejpam-3577	24	39	,	,	PUNCT
ejpam-3577	24	40	differentiable	differentiable	VERB
ejpam-3577	24	41	with	with	ADP
ejpam-3577	24	42	respect	respect	NOUN
ejpam-3577	24	43	to	to	ADP
ejpam-3577	24	44	u	u	NOUN
ejpam-3577	24	45	on	on	ADP
ejpam-3577	24	46	r	r	NOUN
ejpam-3577	24	47	for	for	ADP
ejpam-3577	24	48	all	all	DET
ejpam-3577	24	49	(	(	PUNCT
ejpam-3577	24	50	x	x	NOUN
ejpam-3577	24	51	,	,	PUNCT
ejpam-3577	24	52	y	y	NOUN
ejpam-3577	24	53	)	)	PUNCT
ejpam-3577	24	54	∈	∈	PROPN
ejpam-3577	24	55	ω̄2	ω̄2	NUM
ejpam-3577	24	56	and	and	CCONJ
ejpam-3577	24	57	also	also	ADV
ejpam-3577	24	58	k	k	PROPN
ejpam-3577	24	59	′u	′u	PROPN
ejpam-3577	24	60	:	:	PUNCT
ejpam-3577	24	61	ω̄2×r	ω̄2×r	NOUN
ejpam-3577	24	62	−→	−→	NOUN
ejpam-3577	24	63	r	r	NOUN
ejpam-3577	24	64	a	a	DET
ejpam-3577	24	65	continuous	continuous	ADJ
ejpam-3577	24	66	function	function	NOUN
ejpam-3577	24	67	on	on	ADP
ejpam-3577	24	68	ω̄2	ω̄2	NUM
ejpam-3577	24	69	×	×	NOUN
ejpam-3577	24	70	r	r	NOUN
ejpam-3577	24	71	verifying	verifying	NOUN
ejpam-3577	24	72	|k	|k	PROPN
ejpam-3577	24	73	′u(t	′u(t	PROPN
ejpam-3577	24	74	,	,	PUNCT
ejpam-3577	24	75	y	y	PROPN
ejpam-3577	24	76	,	,	PUNCT
ejpam-3577	24	77	u)−k	u)−k	PROPN
ejpam-3577	24	78	′u(s	′u(s	PROPN
ejpam-3577	24	79	,	,	PUNCT
ejpam-3577	24	80	y	y	NOUN
ejpam-3577	24	81	,	,	PUNCT
ejpam-3577	24	82	u)|	u)|	NOUN
ejpam-3577	24	83	6	6	NUM
ejpam-3577	24	84	qr|t−	qr|t−	NOUN
ejpam-3577	24	85	s|λ	s|λ	NOUN
ejpam-3577	24	86	,	,	PUNCT
ejpam-3577	24	87	|u|	|u|	ADV
ejpam-3577	24	88	6	6	NUM
ejpam-3577	24	89	r	r	NOUN
ejpam-3577	24	90	and	and	CCONJ
ejpam-3577	24	91	|k(t	|k(t	PROPN
ejpam-3577	24	92	,	,	PUNCT
ejpam-3577	24	93	y	y	PROPN
ejpam-3577	24	94	,	,	PUNCT
ejpam-3577	24	95	u)−k(s	u)−k(s	PROPN
ejpam-3577	24	96	,	,	PUNCT
ejpam-3577	24	97	y	y	NOUN
ejpam-3577	24	98	,	,	PUNCT
ejpam-3577	24	99	u)|	u)|	NOUN
ejpam-3577	24	100	6	6	NUM
ejpam-3577	24	101	ar(t	ar(t	NOUN
ejpam-3577	24	102	,	,	PUNCT
ejpam-3577	24	103	s	s	X
ejpam-3577	24	104	,	,	PUNCT
ejpam-3577	24	105	y	y	PROPN
ejpam-3577	24	106	)	)	PUNCT
ejpam-3577	24	107	,	,	PUNCT
ejpam-3577	24	108	|u|	|u|	ADV
ejpam-3577	24	109	6	6	NUM
ejpam-3577	24	110	r	r	NOUN
ejpam-3577	24	111	with	with	ADP
ejpam-3577	24	112	ar	ar	NOUN
ejpam-3577	24	113	a	a	DET
ejpam-3577	24	114	measurable	measurable	ADJ
ejpam-3577	24	115	function,∫	function,∫	PROPN
ejpam-3577	24	116	ω	ω	NOUN
ejpam-3577	24	117	ar(t	ar(t	NOUN
ejpam-3577	24	118	,	,	PUNCT
ejpam-3577	24	119	s	s	X
ejpam-3577	24	120	,	,	PUNCT
ejpam-3577	24	121	y)dy	y)dy	PROPN
ejpam-3577	24	122	6	6	NUM
ejpam-3577	24	123	br(t	br(t	NOUN
ejpam-3577	24	124	,	,	PUNCT
ejpam-3577	24	125	s	s	X
ejpam-3577	24	126	)	)	PUNCT
ejpam-3577	24	127	·	·	PUNCT
ejpam-3577	24	128	|t−	|t−	PROPN
ejpam-3577	24	129	s|λ	s|λ	NOUN
ejpam-3577	24	130	,	,	PUNCT
ejpam-3577	24	131	and	and	CCONJ
ejpam-3577	24	132	br	br	INTJ
ejpam-3577	24	133	:	:	PUNCT
ejpam-3577	24	134	q̄2	q̄2	PROPN
ejpam-3577	24	135	t	t	NOUN
ejpam-3577	24	136	−→	−→	NOUN
ejpam-3577	24	137	r	r	NOUN
ejpam-3577	24	138	satisfied	satisfy	VERB
ejpam-3577	24	139	the	the	DET
ejpam-3577	24	140	following	following	ADJ
ejpam-3577	24	141	conditions	condition	NOUN
ejpam-3577	24	142	:	:	PUNCT
ejpam-3577	24	143	br	br	PROPN
ejpam-3577	24	144	is	be	AUX
ejpam-3577	24	145	bounded	bound	VERB
ejpam-3577	24	146	and	and	CCONJ
ejpam-3577	24	147	∀ε	∀ε	X
ejpam-3577	24	148	>	>	X
ejpam-3577	24	149	0	0	PROPN
ejpam-3577	24	150	,	,	PUNCT
ejpam-3577	24	151	∃δ	∃δ	PROPN
ejpam-3577	24	152	>	>	X
ejpam-3577	24	153	0	0	NUM
ejpam-3577	24	154	:	:	PUNCT
ejpam-3577	24	155	(	(	PUNCT
ejpam-3577	24	156	|t−	|t−	PROPN
ejpam-3577	24	157	s|	s|	VERB
ejpam-3577	24	158	<	<	X
ejpam-3577	24	159	δ	δ	X
ejpam-3577	24	160	)	)	PUNCT
ejpam-3577	25	1	=	=	VERB
ejpam-3577	25	2	⇒	⇒	NOUN
ejpam-3577	25	3	br(t	br(t	NOUN
ejpam-3577	25	4	,	,	PUNCT
ejpam-3577	25	5	s	s	X
ejpam-3577	25	6	)	)	PUNCT
ejpam-3577	25	7	<	<	X
ejpam-3577	25	8	ε	ε	PROPN
ejpam-3577	25	9	then	then	ADV
ejpam-3577	25	10	the	the	DET
ejpam-3577	25	11	mapping	mapping	NOUN
ejpam-3577	25	12	g	g	NOUN
ejpam-3577	25	13	:	:	PUNCT
ejpam-3577	26	1	[	[	X
ejpam-3577	26	2	u(x	u(x	NOUN
ejpam-3577	26	3	)	)	PUNCT
ejpam-3577	26	4	]	]	PUNCT
ejpam-3577	27	1	7−→	7−→	NOUN
ejpam-3577	27	2	∫	∫	PROPN
ejpam-3577	27	3	ω	ω	PROPN
ejpam-3577	27	4	k(x	k(x	PROPN
ejpam-3577	27	5	,	,	PUNCT
ejpam-3577	27	6	y	y	PROPN
ejpam-3577	27	7	,	,	PUNCT
ejpam-3577	27	8	u(y))dy	u(y))dy	NOUN
ejpam-3577	27	9	is	be	AUX
ejpam-3577	27	10	defined	define	VERB
ejpam-3577	27	11	from	from	ADP
ejpam-3577	27	12	c0,λ,0(ω̄	c0,λ,0(ω̄	NOUN
ejpam-3577	27	13	)	)	PUNCT
ejpam-3577	27	14	to	to	ADP
ejpam-3577	27	15	c0,λ,0(ω̄	c0,λ,0(ω̄	PROPN
ejpam-3577	27	16	)	)	PUNCT
ejpam-3577	27	17	and	and	CCONJ
ejpam-3577	27	18	weakly	weakly	ADJ
ejpam-3577	27	19	sequentially	sequentially	ADV
ejpam-3577	27	20	continuous	continuous	ADJ
ejpam-3577	27	21	.	.	PUNCT
ejpam-3577	28	1	2	2	X
ejpam-3577	28	2	.	.	X
ejpam-3577	28	3	main	main	ADJ
ejpam-3577	28	4	operators	operator	NOUN
ejpam-3577	28	5	we	we	PRON
ejpam-3577	28	6	shall	shall	AUX
ejpam-3577	28	7	consider	consider	VERB
ejpam-3577	28	8	the	the	DET
ejpam-3577	28	9	following	follow	VERB
ejpam-3577	28	10	problem	problem	NOUN
ejpam-3577	28	11	∂2u	∂2u	PROPN
ejpam-3577	28	12	∂t2	∂t2	PROPN
ejpam-3577	28	13	−∆u+	−∆u+	NOUN
ejpam-3577	28	14	|u|ρu	|u|ρu	NOUN
ejpam-3577	28	15	=	=	SYM
ejpam-3577	28	16	f(x	f(x	PROPN
ejpam-3577	28	17	,	,	PUNCT
ejpam-3577	28	18	t	t	PROPN
ejpam-3577	28	19	)	)	PUNCT
ejpam-3577	28	20	,	,	PUNCT
ejpam-3577	28	21	ρ	ρ	PROPN
ejpam-3577	28	22	>	>	X
ejpam-3577	28	23	0	0	NUM
ejpam-3577	28	24	,	,	PUNCT
ejpam-3577	28	25	(	(	PUNCT
ejpam-3577	28	26	1	1	X
ejpam-3577	28	27	)	)	PUNCT
ejpam-3577	28	28	∂u	∂u	PROPN
ejpam-3577	29	1	∂~n	∂~n	PROPN
ejpam-3577	29	2	(	(	PUNCT
ejpam-3577	29	3	x	x	X
ejpam-3577	29	4	,	,	PUNCT
ejpam-3577	29	5	t)|∂ω	t)|∂ω	PROPN
ejpam-3577	29	6	=	=	SYM
ejpam-3577	29	7	0	0	NUM
ejpam-3577	29	8	,	,	PUNCT
ejpam-3577	29	9	t	t	PROPN
ejpam-3577	29	10	∈	∈	PROPN
ejpam-3577	29	11	(	(	PUNCT
ejpam-3577	29	12	0	0	NUM
ejpam-3577	29	13	,	,	PUNCT
ejpam-3577	29	14	t	t	NOUN
ejpam-3577	29	15	)	)	PUNCT
ejpam-3577	29	16	(	(	PUNCT
ejpam-3577	29	17	2	2	X
ejpam-3577	29	18	)	)	PUNCT
ejpam-3577	29	19	d.	d.	NOUN
ejpam-3577	29	20	ampini	ampini	PROPN
ejpam-3577	29	21	,	,	PUNCT
ejpam-3577	29	22	v.	v.	PROPN
ejpam-3577	29	23	d.	d.	PROPN
ejpam-3577	29	24	mabonzo	mabonzo	PROPN
ejpam-3577	29	25	/	/	SYM
ejpam-3577	29	26	eur	eur	PROPN
ejpam-3577	29	27	.	.	PUNCT
ejpam-3577	30	1	j.	j.	PROPN
ejpam-3577	30	2	pure	pure	PROPN
ejpam-3577	30	3	appl	appl	PROPN
ejpam-3577	30	4	.	.	PROPN
ejpam-3577	30	5	math	math	PROPN
ejpam-3577	30	6	,	,	PUNCT
ejpam-3577	30	7	12	12	NUM
ejpam-3577	30	8	(	(	PUNCT
ejpam-3577	30	9	4	4	NUM
ejpam-3577	30	10	)	)	PUNCT
ejpam-3577	30	11	(	(	PUNCT
ejpam-3577	30	12	2019	2019	NUM
ejpam-3577	30	13	)	)	PUNCT
ejpam-3577	30	14	,	,	PUNCT
ejpam-3577	30	15	1595	1595	NUM
ejpam-3577	30	16	-	-	SYM
ejpam-3577	30	17	1601	1601	NUM
ejpam-3577	30	18	1597	1597	NUM
ejpam-3577	30	19	u(x	u(x	NOUN
ejpam-3577	30	20	,	,	PUNCT
ejpam-3577	30	21	t)|t=0	t)|t=0	NOUN
ejpam-3577	30	22	=	=	SYM
ejpam-3577	30	23	ϕ(x	ϕ(x	PROPN
ejpam-3577	30	24	)	)	PUNCT
ejpam-3577	30	25	,	,	PUNCT
ejpam-3577	30	26	x	x	PUNCT
ejpam-3577	30	27	∈	∈	PROPN
ejpam-3577	30	28	ω	ω	PROPN
ejpam-3577	30	29	,	,	PUNCT
ejpam-3577	30	30	∂u	∂u	PROPN
ejpam-3577	30	31	∂t	∂t	PROPN
ejpam-3577	30	32	(	(	PUNCT
ejpam-3577	30	33	x	x	NOUN
ejpam-3577	30	34	,	,	PUNCT
ejpam-3577	30	35	t)|t=0	t)|t=0	NOUN
ejpam-3577	30	36	=	=	SYM
ejpam-3577	30	37	ψ(x	ψ(x	PROPN
ejpam-3577	30	38	)	)	PUNCT
ejpam-3577	30	39	,	,	PUNCT
ejpam-3577	30	40	x	x	PUNCT
ejpam-3577	30	41	∈	∈	PROPN
ejpam-3577	30	42	ω	ω	X
ejpam-3577	30	43	(	(	PUNCT
ejpam-3577	30	44	3	3	NUM
ejpam-3577	30	45	)	)	PUNCT
ejpam-3577	30	46	in	in	ADP
ejpam-3577	30	47	the	the	DET
ejpam-3577	30	48	cylinder	cylinder	NOUN
ejpam-3577	30	49	qt	qt	NOUN
ejpam-3577	30	50	=	=	SYM
ejpam-3577	30	51	{	{	PUNCT
ejpam-3577	30	52	x	x	PROPN
ejpam-3577	30	53	,	,	PUNCT
ejpam-3577	30	54	t	t	NOUN
ejpam-3577	30	55	:	:	PUNCT
ejpam-3577	30	56	x	x	SYM
ejpam-3577	30	57	∈	∈	PROPN
ejpam-3577	30	58	ω	ω	NUM
ejpam-3577	30	59	⊂	⊂	PROPN
ejpam-3577	30	60	rn	rn	PROPN
ejpam-3577	30	61	,	,	PUNCT
ejpam-3577	30	62	0	0	PUNCT
ejpam-3577	30	63	<	<	X
ejpam-3577	30	64	t	t	PROPN
ejpam-3577	30	65	6	6	NUM
ejpam-3577	30	66	t	t	NOUN
ejpam-3577	30	67	<	<	X
ejpam-3577	30	68	∞	∞	PROPN
ejpam-3577	30	69	}	}	PUNCT
ejpam-3577	30	70	,	,	PUNCT
ejpam-3577	30	71	where	where	SCONJ
ejpam-3577	30	72	ω	ω	PROPN
ejpam-3577	30	73	is	be	AUX
ejpam-3577	30	74	a	a	DET
ejpam-3577	30	75	bounded	bounded	ADJ
ejpam-3577	30	76	domain	domain	NOUN
ejpam-3577	30	77	of	of	ADP
ejpam-3577	30	78	rn	rn	PROPN
ejpam-3577	30	79	with	with	ADP
ejpam-3577	30	80	differentiable	differentiable	ADJ
ejpam-3577	30	81	boundary	boundary	NOUN
ejpam-3577	30	82	∂ω	∂ω	PROPN
ejpam-3577	30	83	,	,	PUNCT
ejpam-3577	30	84	~n	~n	NUM
ejpam-3577	30	85	designates	designate	VERB
ejpam-3577	30	86	the	the	DET
ejpam-3577	30	87	outer	outer	ADJ
ejpam-3577	30	88	normal	normal	ADJ
ejpam-3577	30	89	to	to	ADP
ejpam-3577	30	90	∂ω	∂ω	PROPN
ejpam-3577	30	91	and	and	CCONJ
ejpam-3577	30	92	∆u	∆u	PROPN
ejpam-3577	30	93	=	=	SYM
ejpam-3577	30	94	n∑	n∑	PROPN
ejpam-3577	30	95	i=1	i=1	PROPN
ejpam-3577	31	1	∂2u	∂2u	PROPN
ejpam-3577	32	1	∂x2	∂x2	PROPN
ejpam-3577	33	1	i	i	PRON
ejpam-3577	33	2	.	.	PUNCT
ejpam-3577	34	1	let	let	VERB
ejpam-3577	34	2	h1(ω	h1(ω	PRON
ejpam-3577	34	3	)	)	PUNCT
ejpam-3577	34	4	=	=	PRON
ejpam-3577	34	5	{	{	PUNCT
ejpam-3577	34	6	v	v	NOUN
ejpam-3577	34	7	/	/	SYM
ejpam-3577	34	8	v	v	NOUN
ejpam-3577	34	9	∈	∈	NOUN
ejpam-3577	34	10	l2(ω	l2(ω	NOUN
ejpam-3577	34	11	)	)	PUNCT
ejpam-3577	34	12	,	,	PUNCT
ejpam-3577	34	13	∂v	∂v	PROPN
ejpam-3577	34	14	∂xi	∂xi	PROPN
ejpam-3577	34	15	∈	∈	PROPN
ejpam-3577	34	16	l2(ω	l2(ω	PROPN
ejpam-3577	34	17	)	)	PUNCT
ejpam-3577	34	18	,	,	PUNCT
ejpam-3577	34	19	i	i	NOUN
ejpam-3577	34	20	=	=	NOUN
ejpam-3577	34	21	1	1	NUM
ejpam-3577	34	22	,	,	PUNCT
ejpam-3577	34	23	·	·	PUNCT
ejpam-3577	34	24	·	·	PUNCT
ejpam-3577	34	25	·	·	PUNCT
ejpam-3577	34	26	,	,	PUNCT
ejpam-3577	34	27	n	n	CCONJ
ejpam-3577	34	28	}	}	PUNCT
ejpam-3577	34	29	with	with	ADP
ejpam-3577	34	30	associated	associated	ADJ
ejpam-3577	34	31	norm	norm	NOUN
ejpam-3577	34	32	‖v‖h1(ω	‖v‖h1(ω	NOUN
ejpam-3577	34	33	)	)	PUNCT
ejpam-3577	34	34	=	=	SYM
ejpam-3577	35	1	(	(	PUNCT
ejpam-3577	35	2	∫	∫	PROPN
ejpam-3577	35	3	ω	ω	PROPN
ejpam-3577	35	4	[	[	PUNCT
ejpam-3577	35	5	|v|2	|v|2	PROPN
ejpam-3577	35	6	+	+	PROPN
ejpam-3577	35	7	n∑	n∑	PROPN
ejpam-3577	35	8	i=1	i=1	PROPN
ejpam-3577	36	1	|	|	ADV
ejpam-3577	36	2	∂v	∂v	PROPN
ejpam-3577	36	3	∂xi	∂xi	PROPN
ejpam-3577	36	4	|2	|2	NUM
ejpam-3577	36	5	]	]	PUNCT
ejpam-3577	36	6	dx	dx	PROPN
ejpam-3577	36	7	)	)	PUNCT
ejpam-3577	36	8	1	1	NUM
ejpam-3577	36	9	2	2	NUM
ejpam-3577	36	10	.	.	PUNCT
ejpam-3577	36	11	assume	assume	VERB
ejpam-3577	36	12	that	that	SCONJ
ejpam-3577	36	13	the	the	DET
ejpam-3577	36	14	functions	function	NOUN
ejpam-3577	36	15	f(x	f(x	PROPN
ejpam-3577	36	16	,	,	PUNCT
ejpam-3577	36	17	t	t	PROPN
ejpam-3577	36	18	)	)	PUNCT
ejpam-3577	36	19	,	,	PUNCT
ejpam-3577	36	20	ϕ(x	ϕ(x	X
ejpam-3577	36	21	)	)	PUNCT
ejpam-3577	36	22	,	,	PUNCT
ejpam-3577	36	23	ψ(x	ψ(x	NOUN
ejpam-3577	36	24	)	)	PUNCT
ejpam-3577	36	25	are	be	AUX
ejpam-3577	36	26	the	the	DET
ejpam-3577	36	27	control	control	NOUN
ejpam-3577	36	28	and	and	CCONJ
ejpam-3577	36	29	then	then	ADV
ejpam-3577	36	30	f(x	f(x	PROPN
ejpam-3577	36	31	,	,	PUNCT
ejpam-3577	36	32	t	t	PROPN
ejpam-3577	36	33	)	)	PUNCT
ejpam-3577	36	34	∈	∈	PROPN
ejpam-3577	36	35	y	y	PROPN
ejpam-3577	36	36	⊂	⊂	PROPN
ejpam-3577	36	37	l2(qt	l2(qt	PROPN
ejpam-3577	36	38	)	)	PUNCT
ejpam-3577	36	39	,	,	PUNCT
ejpam-3577	36	40	ϕ(x	ϕ(x	X
ejpam-3577	36	41	)	)	PUNCT
ejpam-3577	36	42	∈	∈	PROPN
ejpam-3577	36	43	x	x	X
ejpam-3577	36	44	⊂	⊂	PROPN
ejpam-3577	36	45	h1(ω	h1(ω	PROPN
ejpam-3577	36	46	)	)	PUNCT
ejpam-3577	36	47	,	,	PUNCT
ejpam-3577	36	48	ψ(x	ψ(x	NUM
ejpam-3577	36	49	)	)	PUNCT
ejpam-3577	36	50	∈w	∈w	VERB
ejpam-3577	36	51	⊂	⊂	PRON
ejpam-3577	36	52	l2(ω	l2(ω	NUM
ejpam-3577	36	53	)	)	PUNCT
ejpam-3577	36	54	(	(	PUNCT
ejpam-3577	36	55	4	4	X
ejpam-3577	36	56	)	)	PUNCT
ejpam-3577	36	57	where	where	SCONJ
ejpam-3577	36	58	y	y	PROPN
ejpam-3577	36	59	,	,	PUNCT
ejpam-3577	36	60	x	x	NOUN
ejpam-3577	36	61	,	,	PUNCT
ejpam-3577	36	62	w	w	PROPN
ejpam-3577	36	63	are	be	AUX
ejpam-3577	36	64	respectively	respectively	ADV
ejpam-3577	36	65	the	the	DET
ejpam-3577	36	66	convex	convex	NOUN
ejpam-3577	36	67	sets	set	NOUN
ejpam-3577	36	68	,	,	PUNCT
ejpam-3577	36	69	bounded	bound	VERB
ejpam-3577	36	70	and	and	CCONJ
ejpam-3577	36	71	closed	close	VERB
ejpam-3577	36	72	of	of	ADP
ejpam-3577	36	73	l2(qt	l2(qt	PROPN
ejpam-3577	36	74	)	)	PUNCT
ejpam-3577	36	75	,	,	PUNCT
ejpam-3577	36	76	h1(ω	h1(ω	PROPN
ejpam-3577	36	77	)	)	PUNCT
ejpam-3577	36	78	and	and	CCONJ
ejpam-3577	36	79	l2(ω	l2(ω	NOUN
ejpam-3577	36	80	)	)	PUNCT
ejpam-3577	36	81	.	.	PUNCT
ejpam-3577	37	1	let	let	AUX
ejpam-3577	37	2	consider	consider	VERB
ejpam-3577	37	3	the	the	DET
ejpam-3577	37	4	operator	operator	NOUN
ejpam-3577	37	5	:	:	PUNCT
ejpam-3577	37	6	a	a	PRON
ejpam-3577	37	7	:	:	PUNCT
ejpam-3577	37	8	l2(qt	l2(qt	PROPN
ejpam-3577	37	9	)	)	PUNCT
ejpam-3577	37	10	×h1(ω)×	×h1(ω)×	PROPN
ejpam-3577	37	11	l2(ω	l2(ω	NOUN
ejpam-3577	37	12	)	)	PUNCT
ejpam-3577	37	13	−→	−→	NOUN
ejpam-3577	37	14	c0,λ,0(q̄t	c0,λ,0(q̄t	NOUN
ejpam-3577	37	15	)	)	PUNCT
ejpam-3577	38	1	[	[	X
ejpam-3577	38	2	a(f	a(f	PROPN
ejpam-3577	38	3	,	,	PUNCT
ejpam-3577	38	4	ϕ	ϕ	NOUN
ejpam-3577	38	5	,	,	PUNCT
ejpam-3577	38	6	ψ)](x	ψ)](x	NOUN
ejpam-3577	38	7	,	,	PUNCT
ejpam-3577	38	8	t	t	PROPN
ejpam-3577	38	9	)	)	PUNCT
ejpam-3577	38	10	=	=	SYM
ejpam-3577	38	11	∫	∫	PROPN
ejpam-3577	39	1	ω	ω	PROPN
ejpam-3577	39	2	k1(x	k1(x	PROPN
ejpam-3577	39	3	,	,	PUNCT
ejpam-3577	39	4	t	t	PROPN
ejpam-3577	39	5	,	,	PUNCT
ejpam-3577	39	6	x′	x′	NUM
ejpam-3577	39	7	,	,	PUNCT
ejpam-3577	39	8	t′)f(x′	t′)f(x′	PROPN
ejpam-3577	39	9	,	,	PUNCT
ejpam-3577	39	10	t′)dx′dt′+	t′)dx′dt′+	PROPN
ejpam-3577	39	11	∫	∫	PROPN
ejpam-3577	39	12	ω	ω	PROPN
ejpam-3577	39	13	k2(x	k2(x	PROPN
ejpam-3577	39	14	,	,	PUNCT
ejpam-3577	39	15	x′)ϕ(x′)dx′+	x′)ϕ(x′)dx′+	PROPN
ejpam-3577	39	16	∫	∫	PROPN
ejpam-3577	39	17	ω	ω	PROPN
ejpam-3577	39	18	k3(x	k3(x	PROPN
ejpam-3577	39	19	,	,	PUNCT
ejpam-3577	39	20	x′)ψ(x)dx′	x′)ψ(x)dx′	VERB
ejpam-3577	39	21	where	where	SCONJ
ejpam-3577	39	22	k1,k2,k3	k1,k2,k3	VERB
ejpam-3577	39	23	verify	verify	VERB
ejpam-3577	39	24	the	the	DET
ejpam-3577	39	25	condition	condition	NOUN
ejpam-3577	39	26	of	of	ADP
ejpam-3577	39	27	hölder	hölder	NOUN
ejpam-3577	39	28	:	:	PUNCT
ejpam-3577	39	29	λ+	λ+	NUM
ejpam-3577	39	30	λ′	λ′	NUM
ejpam-3577	39	31	,	,	PUNCT
ejpam-3577	39	32	0	0	PUNCT
ejpam-3577	39	33	<	<	X
ejpam-3577	39	34	λ′	λ′	X
ejpam-3577	39	35	<	<	X
ejpam-3577	39	36	λ	λ	PROPN
ejpam-3577	39	37	,	,	PUNCT
ejpam-3577	39	38	λ+	λ+	PUNCT
ejpam-3577	39	39	λ′	λ′	X
ejpam-3577	39	40	<	<	X
ejpam-3577	39	41	1	1	NUM
ejpam-3577	39	42	respectively	respectively	ADV
ejpam-3577	39	43	in	in	ADP
ejpam-3577	39	44	(	(	PUNCT
ejpam-3577	39	45	x	x	NOUN
ejpam-3577	39	46	,	,	PUNCT
ejpam-3577	39	47	t	t	PROPN
ejpam-3577	39	48	)	)	PUNCT
ejpam-3577	39	49	,	,	PUNCT
ejpam-3577	39	50	x	x	X
ejpam-3577	39	51	,	,	PUNCT
ejpam-3577	39	52	x′	x′	PROPN
ejpam-3577	39	53	and	and	CCONJ
ejpam-3577	39	54	|k1(x	|k1(x	PROPN
ejpam-3577	39	55	,	,	PUNCT
ejpam-3577	39	56	t	t	PROPN
ejpam-3577	39	57	,	,	PUNCT
ejpam-3577	39	58	x′	x′	NUM
ejpam-3577	39	59	,	,	PUNCT
ejpam-3577	39	60	t′)−k1(x̃	t′)−k1(x̃	PROPN
ejpam-3577	39	61	,	,	PUNCT
ejpam-3577	39	62	t̃	t̃	PROPN
ejpam-3577	39	63	,	,	PUNCT
ejpam-3577	39	64	x′	x′	NUM
ejpam-3577	39	65	,	,	PUNCT
ejpam-3577	39	66	t′)|	t′)|	PROPN
ejpam-3577	39	67	6	6	NUM
ejpam-3577	39	68	c3(x′	c3(x′	ADP
ejpam-3577	39	69	,	,	PUNCT
ejpam-3577	39	70	t′)|(x	t′)|(x	ADP
ejpam-3577	39	71	,	,	PUNCT
ejpam-3577	39	72	t)−	t)−	PROPN
ejpam-3577	39	73	(	(	PUNCT
ejpam-3577	39	74	x̃	x̃	PROPN
ejpam-3577	39	75	,	,	PUNCT
ejpam-3577	39	76	t̃)|λ+λ′	t̃)|λ+λ′	NOUN
ejpam-3577	39	77	,	,	PUNCT
ejpam-3577	39	78	|k2(x	|k2(x	PROPN
ejpam-3577	39	79	,	,	PUNCT
ejpam-3577	39	80	x′)−k2(x̃	x′)−k2(x̃	PROPN
ejpam-3577	39	81	,	,	PUNCT
ejpam-3577	39	82	x′)|	x′)|	PROPN
ejpam-3577	39	83	6	6	NUM
ejpam-3577	39	84	c4(x′)|x−	c4(x′)|x−	PROPN
ejpam-3577	39	85	x̃|λ+λ′	x̃|λ+λ′	PROPN
ejpam-3577	39	86	,	,	PUNCT
ejpam-3577	39	87	|k3(x	|k3(x	PROPN
ejpam-3577	39	88	,	,	PUNCT
ejpam-3577	39	89	x′)−k3(x̃	x′)−k3(x̃	PROPN
ejpam-3577	39	90	,	,	PUNCT
ejpam-3577	39	91	x′)|	x′)|	PROPN
ejpam-3577	39	92	6	6	NUM
ejpam-3577	39	93	c5(x′)|x−	c5(x′)|x−	PROPN
ejpam-3577	39	94	x̃|λ+λ′	x̃|λ+λ′	PROPN
ejpam-3577	39	95	,	,	PUNCT
ejpam-3577	39	96	sup	sup	PROPN
ejpam-3577	39	97	(	(	PUNCT
ejpam-3577	39	98	x	x	X
ejpam-3577	39	99	,	,	PUNCT
ejpam-3577	39	100	t)∈qt	t)∈qt	PROPN
ejpam-3577	39	101	∫	∫	PROPN
ejpam-3577	39	102	qt	qt	PROPN
ejpam-3577	39	103	k2	k2	PROPN
ejpam-3577	39	104	1	1	NUM
ejpam-3577	39	105	(	(	PUNCT
ejpam-3577	39	106	x	x	PROPN
ejpam-3577	39	107	,	,	PUNCT
ejpam-3577	39	108	t	t	PROPN
ejpam-3577	39	109	,	,	PUNCT
ejpam-3577	39	110	x′	x′	NUM
ejpam-3577	39	111	,	,	PUNCT
ejpam-3577	39	112	t′)dx′dt′	t′)dx′dt′	NOUN
ejpam-3577	39	113	=	=	PROPN
ejpam-3577	39	114	c6	c6	PROPN
ejpam-3577	39	115	<	<	X
ejpam-3577	39	116	∞	∞	PROPN
ejpam-3577	39	117	,	,	PUNCT
ejpam-3577	39	118	sup	sup	NOUN
ejpam-3577	39	119	x∈ω̄	x∈ω̄	PROPN
ejpam-3577	39	120	∫	∫	PROPN
ejpam-3577	39	121	qt	qt	PROPN
ejpam-3577	39	122	k2	k2	PROPN
ejpam-3577	39	123	2	2	NUM
ejpam-3577	39	124	(	(	PUNCT
ejpam-3577	39	125	x	x	NOUN
ejpam-3577	39	126	,	,	PUNCT
ejpam-3577	39	127	x′)dx′	x′)dx′	PROPN
ejpam-3577	39	128	=	=	SYM
ejpam-3577	39	129	c7	c7	PROPN
ejpam-3577	39	130	<	<	X
ejpam-3577	39	131	∞	∞	PROPN
ejpam-3577	39	132	,	,	PUNCT
ejpam-3577	39	133	sup	sup	NOUN
ejpam-3577	39	134	x∈ω̄	x∈ω̄	PROPN
ejpam-3577	39	135	∫	∫	PROPN
ejpam-3577	39	136	qt	qt	PROPN
ejpam-3577	39	137	k2	k2	PROPN
ejpam-3577	39	138	3	3	NUM
ejpam-3577	39	139	(	(	PUNCT
ejpam-3577	39	140	x	x	NOUN
ejpam-3577	39	141	,	,	PUNCT
ejpam-3577	39	142	x′)dx′	x′)dx′	PROPN
ejpam-3577	39	143	=	=	PUNCT
ejpam-3577	39	144	c8	c8	PROPN
ejpam-3577	39	145	<	<	X
ejpam-3577	39	146	∞.	∞.	PROPN
ejpam-3577	39	147	with	with	ADP
ejpam-3577	39	148	c3(x′	c3(x′	ADP
ejpam-3577	39	149	,	,	PUNCT
ejpam-3577	39	150	t′	t′	NUM
ejpam-3577	39	151	)	)	PUNCT
ejpam-3577	39	152	∈	∈	PROPN
ejpam-3577	39	153	l2(qt	l2(qt	PROPN
ejpam-3577	39	154	)	)	PUNCT
ejpam-3577	39	155	,	,	PUNCT
ejpam-3577	39	156	c4(x′	c4(x′	PROPN
ejpam-3577	39	157	)	)	PUNCT
ejpam-3577	39	158	,	,	PUNCT
ejpam-3577	39	159	c5(x′	c5(x′	X
ejpam-3577	39	160	)	)	PUNCT
ejpam-3577	39	161	∈	∈	PROPN
ejpam-3577	39	162	l2(ω	l2(ω	PROPN
ejpam-3577	39	163	)	)	PUNCT
ejpam-3577	39	164	.	.	PUNCT
ejpam-3577	40	1	d.	d.	PROPN
ejpam-3577	40	2	ampini	ampini	PROPN
ejpam-3577	40	3	,	,	PUNCT
ejpam-3577	40	4	v.	v.	PROPN
ejpam-3577	40	5	d.	d.	PROPN
ejpam-3577	40	6	mabonzo	mabonzo	PROPN
ejpam-3577	40	7	/	/	SYM
ejpam-3577	40	8	eur	eur	PROPN
ejpam-3577	40	9	.	.	PUNCT
ejpam-3577	41	1	j.	j.	PROPN
ejpam-3577	41	2	pure	pure	PROPN
ejpam-3577	41	3	appl	appl	PROPN
ejpam-3577	41	4	.	.	PROPN
ejpam-3577	41	5	math	math	PROPN
ejpam-3577	41	6	,	,	PUNCT
ejpam-3577	41	7	12	12	NUM
ejpam-3577	41	8	(	(	PUNCT
ejpam-3577	41	9	4	4	NUM
ejpam-3577	41	10	)	)	PUNCT
ejpam-3577	41	11	(	(	PUNCT
ejpam-3577	41	12	2019	2019	NUM
ejpam-3577	41	13	)	)	PUNCT
ejpam-3577	41	14	,	,	PUNCT
ejpam-3577	41	15	1595	1595	NUM
ejpam-3577	41	16	-	-	SYM
ejpam-3577	41	17	1601	1601	NUM
ejpam-3577	41	18	1598	1598	NUM
ejpam-3577	41	19	note	note	NOUN
ejpam-3577	41	20	that	that	SCONJ
ejpam-3577	41	21	this	this	DET
ejpam-3577	41	22	operator	operator	NOUN
ejpam-3577	41	23	is	be	AUX
ejpam-3577	41	24	linear	linear	ADJ
ejpam-3577	41	25	,	,	PUNCT
ejpam-3577	41	26	continuous	continuous	ADJ
ejpam-3577	41	27	and	and	CCONJ
ejpam-3577	41	28	therefore	therefore	ADV
ejpam-3577	41	29	it	it	PRON
ejpam-3577	41	30	is	be	AUX
ejpam-3577	41	31	weakly	weakly	ADV
ejpam-3577	41	32	sequentially	sequentially	ADV
ejpam-3577	41	33	continuous	continuous	ADJ
ejpam-3577	41	34	(	(	PUNCT
ejpam-3577	41	35	by	by	ADP
ejpam-3577	41	36	theorem	theorem	NOUN
ejpam-3577	41	37	1	1	NUM
ejpam-3577	41	38	)	)	PUNCT
ejpam-3577	41	39	.	.	PUNCT
ejpam-3577	42	1	let	let	AUX
ejpam-3577	42	2	consider	consider	VERB
ejpam-3577	42	3	then	then	ADV
ejpam-3577	42	4	the	the	DET
ejpam-3577	42	5	operator	operator	NOUN
ejpam-3577	42	6	[	[	X
ejpam-3577	42	7	b(f	b(f	PROPN
ejpam-3577	42	8	,	,	PUNCT
ejpam-3577	42	9	ϕ	ϕ	NOUN
ejpam-3577	42	10	,	,	PUNCT
ejpam-3577	42	11	ψ)](x	ψ)](x	NOUN
ejpam-3577	42	12	,	,	PUNCT
ejpam-3577	42	13	t	t	PROPN
ejpam-3577	42	14	)	)	PUNCT
ejpam-3577	43	1	=	=	SYM
ejpam-3577	43	2	∫	∫	PROPN
ejpam-3577	43	3	qt	qt	PROPN
ejpam-3577	43	4	k(x	k(x	PROPN
ejpam-3577	43	5	,	,	PUNCT
ejpam-3577	43	6	t	t	PROPN
ejpam-3577	43	7	,	,	PUNCT
ejpam-3577	43	8	x′	x′	NUM
ejpam-3577	43	9	,	,	PUNCT
ejpam-3577	43	10	t′	t′	NUM
ejpam-3577	43	11	,	,	PUNCT
ejpam-3577	43	12	[	[	X
ejpam-3577	43	13	a(f	a(f	PROPN
ejpam-3577	43	14	,	,	PUNCT
ejpam-3577	43	15	ϕ	ϕ	NOUN
ejpam-3577	43	16	,	,	PUNCT
ejpam-3577	43	17	ψ)](x′	ψ)](x′	NUM
ejpam-3577	43	18	,	,	PUNCT
ejpam-3577	43	19	t′)dx′dt′	t′)dx′dt′	NOUN
ejpam-3577	43	20	where	where	SCONJ
ejpam-3577	43	21	•	•	ADP
ejpam-3577	43	22	the	the	DET
ejpam-3577	43	23	function	function	NOUN
ejpam-3577	43	24	k	k	PROPN
ejpam-3577	43	25	:	:	PUNCT
ejpam-3577	43	26	q̄2	q̄2	PROPN
ejpam-3577	44	1	t	t	NOUN
ejpam-3577	44	2	×	×	NOUN
ejpam-3577	44	3	r	r	NOUN
ejpam-3577	44	4	−→	−→	NOUN
ejpam-3577	44	5	r	r	NOUN
ejpam-3577	44	6	,	,	PUNCT
ejpam-3577	44	7	k	k	NOUN
ejpam-3577	44	8	:	:	PUNCT
ejpam-3577	44	9	(	(	PUNCT
ejpam-3577	44	10	x	x	X
ejpam-3577	44	11	,	,	PUNCT
ejpam-3577	44	12	t	t	PROPN
ejpam-3577	44	13	,	,	PUNCT
ejpam-3577	44	14	x′	x′	NUM
ejpam-3577	44	15	,	,	PUNCT
ejpam-3577	44	16	ξ	ξ	X
ejpam-3577	44	17	)	)	PUNCT
ejpam-3577	44	18	−→	−→	ADJ
ejpam-3577	44	19	k(x	k(x	PROPN
ejpam-3577	44	20	,	,	PUNCT
ejpam-3577	44	21	t	t	PROPN
ejpam-3577	44	22	,	,	PUNCT
ejpam-3577	44	23	x′	x′	NUM
ejpam-3577	44	24	,	,	PUNCT
ejpam-3577	44	25	t′	t′	NUM
ejpam-3577	44	26	,	,	PUNCT
ejpam-3577	44	27	ξ	ξ	X
ejpam-3577	44	28	)	)	PUNCT
ejpam-3577	44	29	is	be	AUX
ejpam-3577	44	30	continuous	continuous	ADJ
ejpam-3577	44	31	on	on	ADP
ejpam-3577	44	32	q̄2	q̄2	X
ejpam-3577	44	33	t	t	PROPN
ejpam-3577	44	34	×	×	PROPN
ejpam-3577	44	35	r	r	NOUN
ejpam-3577	44	36	,	,	PUNCT
ejpam-3577	44	37	differentiable	differentiable	ADJ
ejpam-3577	44	38	with	with	ADP
ejpam-3577	44	39	respect	respect	NOUN
ejpam-3577	44	40	to	to	ADP
ejpam-3577	44	41	ξ	ξ	PROPN
ejpam-3577	44	42	on	on	ADP
ejpam-3577	44	43	r	r	NOUN
ejpam-3577	44	44	for	for	ADP
ejpam-3577	44	45	all	all	PRON
ejpam-3577	44	46	(	(	PUNCT
ejpam-3577	44	47	x	x	NOUN
ejpam-3577	44	48	,	,	PUNCT
ejpam-3577	44	49	t	t	PROPN
ejpam-3577	44	50	,	,	PUNCT
ejpam-3577	44	51	x′	x′	NUM
ejpam-3577	44	52	,	,	PUNCT
ejpam-3577	44	53	t′	t′	NUM
ejpam-3577	44	54	)	)	PUNCT
ejpam-3577	44	55	∈	∈	PROPN
ejpam-3577	44	56	q̄2	q̄2	X
ejpam-3577	44	57	t	t	NOUN
ejpam-3577	44	58	;	;	PUNCT
ejpam-3577	44	59	•	•	ADP
ejpam-3577	44	60	the	the	DET
ejpam-3577	44	61	derived	derive	VERB
ejpam-3577	44	62	function	function	NOUN
ejpam-3577	44	63	k	k	PROPN
ejpam-3577	44	64	′ξ	′ξ	PROPN
ejpam-3577	44	65	:	:	PUNCT
ejpam-3577	44	66	q̄2	q̄2	PROPN
ejpam-3577	44	67	t	t	NOUN
ejpam-3577	44	68	×	×	NOUN
ejpam-3577	44	69	r	r	NOUN
ejpam-3577	44	70	−→	−→	NOUN
ejpam-3577	44	71	r	r	NOUN
ejpam-3577	44	72	is	be	AUX
ejpam-3577	44	73	also	also	ADV
ejpam-3577	44	74	continuous	continuous	ADJ
ejpam-3577	44	75	on	on	ADP
ejpam-3577	44	76	q̄2	q̄2	X
ejpam-3577	44	77	t	t	PROPN
ejpam-3577	44	78	×	×	PROPN
ejpam-3577	44	79	r	r	NOUN
ejpam-3577	44	80	,	,	PUNCT
ejpam-3577	44	81	and	and	CCONJ
ejpam-3577	44	82	|k	|k	NOUN
ejpam-3577	44	83	′ξ(x	′ξ(x	NOUN
ejpam-3577	44	84	,	,	PUNCT
ejpam-3577	44	85	t	t	PROPN
ejpam-3577	44	86	,	,	PUNCT
ejpam-3577	44	87	x′	x′	NUM
ejpam-3577	44	88	,	,	PUNCT
ejpam-3577	44	89	t′	t′	NUM
ejpam-3577	44	90	,	,	PUNCT
ejpam-3577	44	91	ξ)−k	ξ)−k	NUM
ejpam-3577	44	92	′ξ(x̃	′ξ(x̃	NOUN
ejpam-3577	44	93	,	,	PUNCT
ejpam-3577	44	94	t̃	t̃	PROPN
ejpam-3577	44	95	,	,	PUNCT
ejpam-3577	44	96	x′	x′	NUM
ejpam-3577	44	97	,	,	PUNCT
ejpam-3577	44	98	t′	t′	NUM
ejpam-3577	44	99	,	,	PUNCT
ejpam-3577	44	100	ξ)|	ξ)|	VERB
ejpam-3577	44	101	6	6	NUM
ejpam-3577	44	102	qt	qt	NOUN
ejpam-3577	44	103	|(x	|(x	ADP
ejpam-3577	44	104	,	,	PUNCT
ejpam-3577	45	1	t)−	t)−	PROPN
ejpam-3577	45	2	(	(	PUNCT
ejpam-3577	45	3	x̃	x̃	PROPN
ejpam-3577	45	4	,	,	PUNCT
ejpam-3577	45	5	t̃)|λ+λ′	t̃)|λ+λ′	NOUN
ejpam-3577	45	6	,	,	PUNCT
ejpam-3577	45	7	|ξ|	|ξ|	PROPN
ejpam-3577	45	8	6	6	NUM
ejpam-3577	45	9	r	r	NOUN
ejpam-3577	45	10	|k	|k	NOUN
ejpam-3577	45	11	′ξ(x	′ξ(x	NOUN
ejpam-3577	45	12	,	,	PUNCT
ejpam-3577	45	13	t	t	PROPN
ejpam-3577	45	14	,	,	PUNCT
ejpam-3577	45	15	x′	x′	NUM
ejpam-3577	45	16	,	,	PUNCT
ejpam-3577	45	17	t′	t′	NUM
ejpam-3577	45	18	,	,	PUNCT
ejpam-3577	45	19	ξ)−k(x̃	ξ)−k(x̃	NOUN
ejpam-3577	45	20	,	,	PUNCT
ejpam-3577	45	21	t̃	t̃	PROPN
ejpam-3577	45	22	,	,	PUNCT
ejpam-3577	45	23	x′	x′	NUM
ejpam-3577	45	24	,	,	PUNCT
ejpam-3577	45	25	t′	t′	NUM
ejpam-3577	45	26	,	,	PUNCT
ejpam-3577	45	27	ξ)|	ξ)|	NOUN
ejpam-3577	45	28	6	6	NUM
ejpam-3577	45	29	ar(x	ar(x	NOUN
ejpam-3577	45	30	,	,	PUNCT
ejpam-3577	45	31	t	t	PROPN
ejpam-3577	45	32	,	,	PUNCT
ejpam-3577	45	33	x̃	x̃	PROPN
ejpam-3577	45	34	,	,	PUNCT
ejpam-3577	45	35	t̃	t̃	PROPN
ejpam-3577	45	36	,	,	PUNCT
ejpam-3577	45	37	x	x	NOUN
ejpam-3577	45	38	′	′	NUM
ejpam-3577	45	39	,	,	PUNCT
ejpam-3577	45	40	t′	t′	NUM
ejpam-3577	45	41	)	)	PUNCT
ejpam-3577	45	42	,	,	PUNCT
ejpam-3577	45	43	|ξ|	|ξ|	NOUN
ejpam-3577	45	44	6	6	NUM
ejpam-3577	45	45	r	r	NOUN
ejpam-3577	45	46	here	here	ADV
ejpam-3577	45	47	ar	ar	PROPN
ejpam-3577	45	48	is	be	AUX
ejpam-3577	45	49	a	a	DET
ejpam-3577	45	50	measurable	measurable	ADJ
ejpam-3577	45	51	function	function	NOUN
ejpam-3577	45	52	verifying∫	verifying∫	NOUN
ejpam-3577	45	53	qt	qt	PROPN
ejpam-3577	45	54	ar(x	ar(x	PROPN
ejpam-3577	45	55	,	,	PUNCT
ejpam-3577	45	56	t	t	PROPN
ejpam-3577	45	57	,	,	PUNCT
ejpam-3577	45	58	x̃	x̃	PROPN
ejpam-3577	45	59	,	,	PUNCT
ejpam-3577	45	60	t̃	t̃	PROPN
ejpam-3577	45	61	,	,	PUNCT
ejpam-3577	45	62	x	x	NOUN
ejpam-3577	45	63	′	′	NUM
ejpam-3577	45	64	,	,	PUNCT
ejpam-3577	45	65	t′)dx′dt′	t′)dx′dt′	NOUN
ejpam-3577	45	66	6	6	NUM
ejpam-3577	45	67	br(x	br(x	NOUN
ejpam-3577	45	68	,	,	PUNCT
ejpam-3577	45	69	t	t	PROPN
ejpam-3577	45	70	,	,	PUNCT
ejpam-3577	45	71	x̃	x̃	PROPN
ejpam-3577	45	72	,	,	PUNCT
ejpam-3577	45	73	t̃	t̃	PROPN
ejpam-3577	45	74	)	)	PUNCT
ejpam-3577	45	75	·	·	PUNCT
ejpam-3577	46	1	|(x	|(x	ADP
ejpam-3577	46	2	,	,	PUNCT
ejpam-3577	46	3	t)−	t)−	PROPN
ejpam-3577	46	4	(	(	PUNCT
ejpam-3577	46	5	x̃	x̃	PROPN
ejpam-3577	46	6	,	,	PUNCT
ejpam-3577	46	7	t̃)|λ+λ′	t̃)|λ+λ′	NOUN
ejpam-3577	46	8	and	and	CCONJ
ejpam-3577	46	9	br	br	PROPN
ejpam-3577	46	10	:	:	PUNCT
ejpam-3577	46	11	q̄2	q̄2	PROPN
ejpam-3577	46	12	t	t	NOUN
ejpam-3577	46	13	−→	−→	NOUN
ejpam-3577	46	14	r	r	NOUN
ejpam-3577	46	15	satisfying	satisfy	VERB
ejpam-3577	46	16	the	the	DET
ejpam-3577	46	17	following	following	ADJ
ejpam-3577	46	18	conditions	condition	NOUN
ejpam-3577	46	19	:	:	PUNCT
ejpam-3577	46	20	br	br	PROPN
ejpam-3577	46	21	is	be	AUX
ejpam-3577	46	22	bounded	bound	VERB
ejpam-3577	46	23	and	and	CCONJ
ejpam-3577	46	24	∀ε	∀ε	X
ejpam-3577	46	25	>	>	X
ejpam-3577	46	26	0,∃δ	0,∃δ	NUM
ejpam-3577	47	1	>	>	X
ejpam-3577	47	2	0	0	NUM
ejpam-3577	47	3	:	:	PUNCT
ejpam-3577	47	4	(	(	PUNCT
ejpam-3577	47	5	|(x	|(x	ADP
ejpam-3577	47	6	,	,	PUNCT
ejpam-3577	47	7	t)−	t)−	PROPN
ejpam-3577	47	8	(	(	PUNCT
ejpam-3577	47	9	x̃	x̃	PROPN
ejpam-3577	47	10	,	,	PUNCT
ejpam-3577	47	11	t̃)|	t̃)|	PROPN
ejpam-3577	47	12	<	<	X
ejpam-3577	47	13	δ	δ	X
ejpam-3577	47	14	)	)	PUNCT
ejpam-3577	47	15	=	=	VERB
ejpam-3577	47	16	⇒	⇒	NOUN
ejpam-3577	47	17	br(x	br(x	PROPN
ejpam-3577	47	18	,	,	PUNCT
ejpam-3577	47	19	t	t	PROPN
ejpam-3577	47	20	,	,	PUNCT
ejpam-3577	47	21	x̃	x̃	PROPN
ejpam-3577	47	22	,	,	PUNCT
ejpam-3577	47	23	t̃	t̃	PROPN
ejpam-3577	47	24	)	)	PUNCT
ejpam-3577	47	25	<	<	X
ejpam-3577	47	26	ε	ε	PROPN
ejpam-3577	47	27	.	.	PUNCT
ejpam-3577	48	1	this	this	DET
ejpam-3577	48	2	operation	operation	NOUN
ejpam-3577	48	3	is	be	AUX
ejpam-3577	48	4	a	a	DET
ejpam-3577	48	5	mapping	mapping	NOUN
ejpam-3577	48	6	defined	define	VERB
ejpam-3577	48	7	from	from	ADP
ejpam-3577	48	8	l2(qt	l2(qt	PROPN
ejpam-3577	48	9	)	)	PUNCT
ejpam-3577	48	10	×h1(ω)×	×h1(ω)×	PROPN
ejpam-3577	48	11	l2(ω	l2(ω	NOUN
ejpam-3577	48	12	)	)	PUNCT
ejpam-3577	48	13	to	to	ADP
ejpam-3577	48	14	c0,λ,0(q̄t	c0,λ,0(q̄t	PROPN
ejpam-3577	48	15	)	)	PUNCT
ejpam-3577	48	16	and	and	CCONJ
ejpam-3577	48	17	it	it	PRON
ejpam-3577	48	18	is	be	AUX
ejpam-3577	48	19	weakly	weakly	ADV
ejpam-3577	48	20	sequentially	sequentially	ADV
ejpam-3577	48	21	continuous	continuous	ADJ
ejpam-3577	48	22	(	(	PUNCT
ejpam-3577	48	23	by	by	ADP
ejpam-3577	48	24	theorem	theorem	NOUN
ejpam-3577	48	25	2	2	NUM
ejpam-3577	48	26	)	)	PUNCT
ejpam-3577	48	27	.	.	PUNCT
ejpam-3577	49	1	let	let	VERB
ejpam-3577	49	2	e	e	X
ejpam-3577	49	3	∈	∈	PROPN
ejpam-3577	49	4	(	(	PUNCT
ejpam-3577	49	5	c0,λ,0(q̄t	c0,λ,0(q̄t	NOUN
ejpam-3577	49	6	)	)	PUNCT
ejpam-3577	49	7	)	)	PUNCT
ejpam-3577	49	8	′.	′.	NOUN
ejpam-3577	49	9	remember	remember	VERB
ejpam-3577	49	10	(	(	PUNCT
ejpam-3577	49	11	[	[	X
ejpam-3577	49	12	2],p.5	2],p.5	NUM
ejpam-3577	49	13	)	)	PUNCT
ejpam-3577	49	14	that	that	SCONJ
ejpam-3577	49	15	there	there	PRON
ejpam-3577	49	16	exists	exist	VERB
ejpam-3577	49	17	such	such	ADJ
ejpam-3577	49	18	borelian	borelian	ADJ
ejpam-3577	49	19	measures	measure	NOUN
ejpam-3577	49	20	(	(	PUNCT
ejpam-3577	49	21	definite	definite	ADJ
ejpam-3577	49	22	positive	positive	ADJ
ejpam-3577	49	23	)	)	PUNCT
ejpam-3577	49	24	µ1	µ1	NOUN
ejpam-3577	49	25	and	and	CCONJ
ejpam-3577	49	26	µ2	µ2	PROPN
ejpam-3577	49	27	with	with	ADP
ejpam-3577	49	28	bounded	bounded	ADJ
ejpam-3577	49	29	variation	variation	NOUN
ejpam-3577	49	30	on	on	ADP
ejpam-3577	49	31	q̄t	q̄t	PROPN
ejpam-3577	49	32	and	and	CCONJ
ejpam-3577	49	33	q̄2	q̄2	PROPN
ejpam-3577	49	34	t	t	PROPN
ejpam-3577	49	35	respectively	respectively	ADV
ejpam-3577	49	36	for	for	ADP
ejpam-3577	49	37	which	which	PRON
ejpam-3577	49	38	〈	〈	PROPN
ejpam-3577	49	39	e	e	PROPN
ejpam-3577	49	40	,	,	PUNCT
ejpam-3577	49	41	u	u	NOUN
ejpam-3577	49	42	〉	〉	NUM
ejpam-3577	49	43	=	=	SYM
ejpam-3577	49	44	∫	∫	PROPN
ejpam-3577	49	45	qt	qt	NOUN
ejpam-3577	49	46	u(x	u(x	NOUN
ejpam-3577	49	47	,	,	PUNCT
ejpam-3577	49	48	t)dµ1(x	t)dµ1(x	PROPN
ejpam-3577	49	49	,	,	PUNCT
ejpam-3577	49	50	t	t	PROPN
ejpam-3577	49	51	)	)	PUNCT
ejpam-3577	50	1	+	+	CCONJ
ejpam-3577	50	2	∫	∫	PROPN
ejpam-3577	50	3	2	2	NUM
ejpam-3577	50	4	qt	qt	NOUN
ejpam-3577	50	5	(	(	PUNCT
ejpam-3577	50	6	u(x	u(x	PROPN
ejpam-3577	50	7	,	,	PUNCT
ejpam-3577	50	8	t)−	t)−	PROPN
ejpam-3577	50	9	u(x̃	u(x̃	PROPN
ejpam-3577	50	10	,	,	PUNCT
ejpam-3577	50	11	t̃	t̃	PROPN
ejpam-3577	50	12	)	)	PUNCT
ejpam-3577	50	13	)	)	PUNCT
ejpam-3577	50	14	·	·	PUNCT
ejpam-3577	51	1	|(x	|(x	ADP
ejpam-3577	51	2	,	,	PUNCT
ejpam-3577	51	3	t)−	t)−	PROPN
ejpam-3577	51	4	(	(	PUNCT
ejpam-3577	51	5	x̃	x̃	PROPN
ejpam-3577	51	6	,	,	PUNCT
ejpam-3577	51	7	t̃)|−λdµ2(x	t̃)|−λdµ2(x	PROPN
ejpam-3577	51	8	,	,	PUNCT
ejpam-3577	51	9	t	t	PROPN
ejpam-3577	51	10	,	,	PUNCT
ejpam-3577	51	11	x̃	x̃	PROPN
ejpam-3577	51	12	,	,	PUNCT
ejpam-3577	51	13	t̃	t̃	PROPN
ejpam-3577	51	14	)	)	PUNCT
ejpam-3577	51	15	for	for	ADP
ejpam-3577	51	16	u	u	PROPN
ejpam-3577	51	17	∈	∈	PROPN
ejpam-3577	51	18	c0,λ,0(q̄t	c0,λ,0(q̄t	PROPN
ejpam-3577	51	19	)	)	PUNCT
ejpam-3577	51	20	.	.	PUNCT
ejpam-3577	52	1	in	in	ADP
ejpam-3577	52	2	this	this	DET
ejpam-3577	52	3	case	case	NOUN
ejpam-3577	52	4	,	,	PUNCT
ejpam-3577	52	5	the	the	DET
ejpam-3577	52	6	functionals	functional	NOUN
ejpam-3577	52	7	of	of	ADP
ejpam-3577	52	8	the	the	DET
ejpam-3577	52	9	form	form	NOUN
ejpam-3577	53	1	f	f	X
ejpam-3577	54	1	i	i	PRON
ejpam-3577	54	2	:	:	PUNCT
ejpam-3577	54	3	l2(qt	l2(qt	PROPN
ejpam-3577	54	4	)	)	PUNCT
ejpam-3577	54	5	×h1(ω)×	×h1(ω)×	PROPN
ejpam-3577	54	6	l2(ω	l2(ω	NOUN
ejpam-3577	54	7	)	)	PUNCT
ejpam-3577	54	8	−→	−→	NOUN
ejpam-3577	54	9	r	r	NOUN
ejpam-3577	54	10	f	f	PROPN
ejpam-3577	55	1	i(f	i(f	PROPN
ejpam-3577	55	2	,	,	PUNCT
ejpam-3577	55	3	ϕ	ϕ	NOUN
ejpam-3577	55	4	,	,	PUNCT
ejpam-3577	55	5	ψ	ψ	NOUN
ejpam-3577	55	6	)	)	PUNCT
ejpam-3577	55	7	=	=	SYM
ejpam-3577	56	1	〈	〈	PROPN
ejpam-3577	56	2	ei	ei	PROPN
ejpam-3577	56	3	,	,	PUNCT
ejpam-3577	56	4	bi(f	bi(f	PROPN
ejpam-3577	56	5	,	,	PUNCT
ejpam-3577	56	6	ϕ	ϕ	NOUN
ejpam-3577	56	7	,	,	PUNCT
ejpam-3577	56	8	ψ	ψ	NOUN
ejpam-3577	56	9	)	)	PUNCT
ejpam-3577	56	10	〉	〉	PROPN
ejpam-3577	56	11	,	,	PUNCT
ejpam-3577	56	12	i	i	PRON
ejpam-3577	56	13	=	=	NOUN
ejpam-3577	56	14	0	0	NUM
ejpam-3577	56	15	,	,	PUNCT
ejpam-3577	56	16	s1	s1	PROPN
ejpam-3577	56	17	+	+	CCONJ
ejpam-3577	56	18	s2	s2	PROPN
ejpam-3577	56	19	,	,	PUNCT
ejpam-3577	56	20	are	be	AUX
ejpam-3577	56	21	also	also	ADV
ejpam-3577	56	22	weakly	weakly	ADV
ejpam-3577	56	23	sequentially	sequentially	ADV
ejpam-3577	56	24	continuous	continuous	ADJ
ejpam-3577	56	25	.	.	PUNCT
ejpam-3577	57	1	d.	d.	PROPN
ejpam-3577	57	2	ampini	ampini	PROPN
ejpam-3577	57	3	,	,	PUNCT
ejpam-3577	57	4	v.	v.	PROPN
ejpam-3577	57	5	d.	d.	PROPN
ejpam-3577	57	6	mabonzo	mabonzo	PROPN
ejpam-3577	57	7	/	/	SYM
ejpam-3577	57	8	eur	eur	PROPN
ejpam-3577	57	9	.	.	PUNCT
ejpam-3577	58	1	j.	j.	PROPN
ejpam-3577	58	2	pure	pure	PROPN
ejpam-3577	58	3	appl	appl	PROPN
ejpam-3577	58	4	.	.	PROPN
ejpam-3577	58	5	math	math	PROPN
ejpam-3577	58	6	,	,	PUNCT
ejpam-3577	58	7	12	12	NUM
ejpam-3577	58	8	(	(	PUNCT
ejpam-3577	58	9	4	4	NUM
ejpam-3577	58	10	)	)	PUNCT
ejpam-3577	58	11	(	(	PUNCT
ejpam-3577	58	12	2019	2019	NUM
ejpam-3577	58	13	)	)	PUNCT
ejpam-3577	58	14	,	,	PUNCT
ejpam-3577	58	15	1595	1595	NUM
ejpam-3577	58	16	-	-	SYM
ejpam-3577	58	17	1601	1601	NUM
ejpam-3577	58	18	1599	1599	NUM
ejpam-3577	58	19	3	3	NUM
ejpam-3577	58	20	.	.	PUNCT
ejpam-3577	59	1	formulation	formulation	NOUN
ejpam-3577	59	2	of	of	ADP
ejpam-3577	59	3	the	the	DET
ejpam-3577	59	4	problem	problem	NOUN
ejpam-3577	59	5	consider	consider	VERB
ejpam-3577	59	6	the	the	DET
ejpam-3577	59	7	problem	problem	NOUN
ejpam-3577	59	8	(	(	PUNCT
ejpam-3577	59	9	1)-(3	1)-(3	NUM
ejpam-3577	59	10	)	)	PUNCT
ejpam-3577	59	11	with	with	ADP
ejpam-3577	59	12	the	the	DET
ejpam-3577	59	13	propositions	proposition	NOUN
ejpam-3577	59	14	(	(	PUNCT
ejpam-3577	59	15	4	4	NUM
ejpam-3577	59	16	)	)	PUNCT
ejpam-3577	59	17	.	.	PUNCT
ejpam-3577	60	1	then	then	ADV
ejpam-3577	60	2	consider	consider	VERB
ejpam-3577	60	3	the	the	DET
ejpam-3577	60	4	functional	functional	ADJ
ejpam-3577	60	5	of	of	ADP
ejpam-3577	60	6	the	the	DET
ejpam-3577	60	7	form	form	NOUN
ejpam-3577	60	8	ji(f	ji(f	PROPN
ejpam-3577	60	9	,	,	PUNCT
ejpam-3577	60	10	ϕ	ϕ	NOUN
ejpam-3577	60	11	,	,	PUNCT
ejpam-3577	60	12	ψ	ψ	NOUN
ejpam-3577	60	13	)	)	PUNCT
ejpam-3577	60	14	=	=	SYM
ejpam-3577	60	15	∫	∫	PROPN
ejpam-3577	60	16	q̄t	q̄t	PROPN
ejpam-3577	60	17	vi(x	vi(x	PROPN
ejpam-3577	60	18	,	,	PUNCT
ejpam-3577	60	19	t	t	PROPN
ejpam-3577	60	20	,	,	PUNCT
ejpam-3577	60	21	u(x	u(x	PROPN
ejpam-3577	60	22	,	,	PUNCT
ejpam-3577	60	23	t))dxdt+	t))dxdt+	ADP
ejpam-3577	60	24	f	f	X
ejpam-3577	61	1	i(f	i(f	PROPN
ejpam-3577	61	2	,	,	PUNCT
ejpam-3577	61	3	ϕ	ϕ	NOUN
ejpam-3577	61	4	,	,	PUNCT
ejpam-3577	61	5	ψ	ψ	NOUN
ejpam-3577	61	6	)	)	PUNCT
ejpam-3577	61	7	,	,	PUNCT
ejpam-3577	61	8	(	(	PUNCT
ejpam-3577	61	9	5	5	X
ejpam-3577	61	10	)	)	PUNCT
ejpam-3577	61	11	i	i	NOUN
ejpam-3577	61	12	=	=	NOUN
ejpam-3577	61	13	0	0	NUM
ejpam-3577	61	14	,	,	PUNCT
ejpam-3577	61	15	s1	s1	NOUN
ejpam-3577	61	16	+	+	CCONJ
ejpam-3577	61	17	s2	s2	VERB
ejpam-3577	61	18	where	where	SCONJ
ejpam-3577	61	19	the	the	DET
ejpam-3577	61	20	functions	function	NOUN
ejpam-3577	61	21	vi(x	vi(x	NUM
ejpam-3577	61	22	,	,	PUNCT
ejpam-3577	61	23	t	t	PROPN
ejpam-3577	61	24	,	,	PUNCT
ejpam-3577	61	25	ξ	ξ	X
ejpam-3577	61	26	)	)	PUNCT
ejpam-3577	61	27	verify	verify	VERB
ejpam-3577	61	28	the	the	DET
ejpam-3577	61	29	following	follow	VERB
ejpam-3577	61	30	conditions	condition	NOUN
ejpam-3577	61	31	:	:	PUNCT
ejpam-3577	61	32	a	a	X
ejpam-3577	61	33	)	)	PUNCT
ejpam-3577	61	34	the	the	DET
ejpam-3577	61	35	functions	function	NOUN
ejpam-3577	61	36	vi(x	vi(x	NUM
ejpam-3577	61	37	,	,	PUNCT
ejpam-3577	61	38	t	t	PROPN
ejpam-3577	61	39	,	,	PUNCT
ejpam-3577	61	40	ξ	ξ	X
ejpam-3577	61	41	)	)	PUNCT
ejpam-3577	61	42	are	be	AUX
ejpam-3577	61	43	measurable	measurable	ADJ
ejpam-3577	61	44	on	on	ADP
ejpam-3577	61	45	qt	qt	NOUN
ejpam-3577	61	46	×	×	PROPN
ejpam-3577	61	47	r	r	NOUN
ejpam-3577	61	48	,	,	PUNCT
ejpam-3577	61	49	b	b	NOUN
ejpam-3577	61	50	)	)	PUNCT
ejpam-3577	61	51	almost	almost	ADV
ejpam-3577	61	52	for	for	ADP
ejpam-3577	61	53	each	each	DET
ejpam-3577	61	54	(	(	PUNCT
ejpam-3577	61	55	x	x	PROPN
ejpam-3577	61	56	,	,	PUNCT
ejpam-3577	61	57	t	t	PROPN
ejpam-3577	61	58	)	)	PUNCT
ejpam-3577	61	59	∈	∈	PROPN
ejpam-3577	61	60	qt	qt	NOUN
ejpam-3577	61	61	,	,	PUNCT
ejpam-3577	61	62	the	the	DET
ejpam-3577	61	63	functions	function	NOUN
ejpam-3577	61	64	vi(x	vi(x	NUM
ejpam-3577	61	65	,	,	PUNCT
ejpam-3577	61	66	t	t	PROPN
ejpam-3577	61	67	,	,	PUNCT
ejpam-3577	61	68	ξ	ξ	X
ejpam-3577	61	69	)	)	PUNCT
ejpam-3577	61	70	are	be	AUX
ejpam-3577	61	71	continuous	continuous	ADJ
ejpam-3577	61	72	at	at	ADP
ejpam-3577	61	73	ξ	ξ	PROPN
ejpam-3577	61	74	on	on	ADP
ejpam-3577	61	75	r	r	NOUN
ejpam-3577	61	76	and	and	CCONJ
ejpam-3577	61	77	|vi(x	|vi(x	NUM
ejpam-3577	61	78	,	,	PUNCT
ejpam-3577	61	79	t	t	PROPN
ejpam-3577	61	80	,	,	PUNCT
ejpam-3577	61	81	ξ)|	ξ)|	ADJ
ejpam-3577	61	82	6	6	NUM
ejpam-3577	61	83	c9	c9	NOUN
ejpam-3577	61	84	+	+	CCONJ
ejpam-3577	61	85	c10|ξ|2	c10|ξ|2	ADJ
ejpam-3577	61	86	.	.	PUNCT
ejpam-3577	62	1	(	(	PUNCT
ejpam-3577	62	2	6	6	X
ejpam-3577	62	3	)	)	PUNCT
ejpam-3577	62	4	note	note	NOUN
ejpam-3577	62	5	that	that	SCONJ
ejpam-3577	62	6	the	the	DET
ejpam-3577	62	7	functions	function	NOUN
ejpam-3577	62	8	ji(f	ji(f	PROPN
ejpam-3577	62	9	,	,	PUNCT
ejpam-3577	62	10	ϕ	ϕ	NOUN
ejpam-3577	62	11	,	,	PUNCT
ejpam-3577	62	12	ψ	ψ	NOUN
ejpam-3577	62	13	)	)	PUNCT
ejpam-3577	62	14	are	be	AUX
ejpam-3577	62	15	weakly	weakly	ADV
ejpam-3577	62	16	sequentially	sequentially	ADV
ejpam-3577	62	17	continuous	continuous	ADJ
ejpam-3577	62	18	by	by	ADP
ejpam-3577	62	19	virtue	virtue	NOUN
ejpam-3577	62	20	of	of	ADP
ejpam-3577	62	21	the	the	DET
ejpam-3577	62	22	immersion	immersion	NOUN
ejpam-3577	63	1	theorem	theorem	NOUN
ejpam-3577	63	2	h1(qt	h1(qt	PROPN
ejpam-3577	63	3	)	)	PUNCT
ejpam-3577	63	4	⊂	⊂	PROPN
ejpam-3577	63	5	l2(qt	l2(qt	PROPN
ejpam-3577	63	6	)	)	PUNCT
ejpam-3577	63	7	,	,	PUNCT
ejpam-3577	63	8	of	of	ADP
ejpam-3577	63	9	inequality	inequality	NOUN
ejpam-3577	63	10	‖u‖h1(qt	‖u‖h1(qt	PROPN
ejpam-3577	63	11	)	)	PUNCT
ejpam-3577	63	12	6	6	NUM
ejpam-3577	63	13	c(t	c(t	PROPN
ejpam-3577	63	14	)	)	PUNCT
ejpam-3577	63	15	(	(	PUNCT
ejpam-3577	63	16	‖f‖l2(qt	‖f‖l2(qt	NOUN
ejpam-3577	63	17	)	)	PUNCT
ejpam-3577	63	18	+	+	CCONJ
ejpam-3577	63	19	‖ϕ‖h1(ω	‖ϕ‖h1(ω	X
ejpam-3577	63	20	)	)	PUNCT
ejpam-3577	63	21	+	+	NUM
ejpam-3577	63	22	‖ψ‖l2(ω	‖ψ‖l2(ω	ADV
ejpam-3577	63	23	)	)	PUNCT
ejpam-3577	63	24	)	)	PUNCT
ejpam-3577	64	1	[	[	X
ejpam-3577	64	2	1	1	NUM
ejpam-3577	64	3	]	]	PUNCT
ejpam-3577	64	4	,	,	PUNCT
ejpam-3577	64	5	and	and	CCONJ
ejpam-3577	64	6	the	the	DET
ejpam-3577	64	7	continuity	continuity	NOUN
ejpam-3577	64	8	of	of	ADP
ejpam-3577	64	9	the	the	DET
ejpam-3577	64	10	functional	functional	ADJ
ejpam-3577	64	11	u	u	NOUN
ejpam-3577	64	12	7−→	7−→	PROPN
ejpam-3577	64	13	∫	∫	PROPN
ejpam-3577	64	14	qt	qt	PROPN
ejpam-3577	64	15	vi(x	vi(x	PROPN
ejpam-3577	64	16	,	,	PUNCT
ejpam-3577	64	17	t	t	PROPN
ejpam-3577	64	18	,	,	PUNCT
ejpam-3577	64	19	u(x	u(x	PROPN
ejpam-3577	64	20	,	,	PUNCT
ejpam-3577	64	21	t))dxdt	t))dxdt	NOUN
ejpam-3577	64	22	from	from	ADP
ejpam-3577	64	23	l2(qt	l2(qt	PROPN
ejpam-3577	64	24	)	)	PUNCT
ejpam-3577	64	25	into	into	ADP
ejpam-3577	64	26	r.	r.	NOUN
ejpam-3577	64	27	we	we	PRON
ejpam-3577	64	28	thus	thus	ADV
ejpam-3577	64	29	pose	pose	VERB
ejpam-3577	64	30	the	the	DET
ejpam-3577	64	31	following	following	ADJ
ejpam-3577	64	32	problem	problem	NOUN
ejpam-3577	64	33	:	:	PUNCT
ejpam-3577	64	34	to	to	PART
ejpam-3577	64	35	find	find	VERB
ejpam-3577	64	36	out	out	ADP
ejpam-3577	64	37	such	such	ADJ
ejpam-3577	64	38	measurable	measurable	ADJ
ejpam-3577	64	39	functions	function	NOUN
ejpam-3577	64	40	f0(x	f0(x	PROPN
ejpam-3577	64	41	,	,	PUNCT
ejpam-3577	64	42	t	t	PROPN
ejpam-3577	64	43	)	)	PUNCT
ejpam-3577	64	44	∈	∈	PROPN
ejpam-3577	64	45	y	y	PROPN
ejpam-3577	64	46	,	,	PUNCT
ejpam-3577	64	47	ϕ0(x	ϕ0(x	NOUN
ejpam-3577	64	48	)	)	PUNCT
ejpam-3577	64	49	∈	∈	PROPN
ejpam-3577	64	50	x	x	SYM
ejpam-3577	64	51	,	,	PUNCT
ejpam-3577	64	52	ψ0(x	ψ0(x	SYM
ejpam-3577	64	53	)	)	PUNCT
ejpam-3577	64	54	∈	∈	PROPN
ejpam-3577	64	55	w	w	NOUN
ejpam-3577	64	56	in	in	ADP
ejpam-3577	64	57	such	such	DET
ejpam-3577	64	58	a	a	DET
ejpam-3577	64	59	way	way	NOUN
ejpam-3577	64	60	that	that	PRON
ejpam-3577	64	61	,	,	PUNCT
ejpam-3577	64	62	for	for	ADP
ejpam-3577	64	63	the	the	DET
ejpam-3577	64	64	solution	solution	NOUN
ejpam-3577	64	65	u0(x	u0(x	SYM
ejpam-3577	64	66	,	,	PUNCT
ejpam-3577	64	67	t	t	PROPN
ejpam-3577	64	68	)	)	PUNCT
ejpam-3577	64	69	of	of	ADP
ejpam-3577	64	70	the	the	DET
ejpam-3577	64	71	problem	problem	NOUN
ejpam-3577	64	72	(	(	PUNCT
ejpam-3577	64	73	1)-(3	1)-(3	NOUN
ejpam-3577	64	74	)	)	PUNCT
ejpam-3577	64	75	corresponding	correspond	VERB
ejpam-3577	64	76	to	to	ADP
ejpam-3577	64	77	(	(	PUNCT
ejpam-3577	64	78	f0	f0	PROPN
ejpam-3577	64	79	,	,	PUNCT
ejpam-3577	64	80	ϕ0	ϕ0	NOUN
ejpam-3577	64	81	,	,	PUNCT
ejpam-3577	64	82	ψ0	ψ0	ADJ
ejpam-3577	64	83	)	)	PUNCT
ejpam-3577	64	84	,	,	PUNCT
ejpam-3577	64	85	inequality	inequality	NOUN
ejpam-3577	64	86	-	-	PUNCT
ejpam-3577	64	87	type	type	NOUN
ejpam-3577	64	88	constraints	constraint	NOUN
ejpam-3577	64	89	are	be	AUX
ejpam-3577	64	90	verified	verify	VERB
ejpam-3577	64	91	,	,	PUNCT
ejpam-3577	64	92	ji(f	ji(f	PROPN
ejpam-3577	64	93	,	,	PUNCT
ejpam-3577	64	94	ϕ	ϕ	NOUN
ejpam-3577	64	95	,	,	PUNCT
ejpam-3577	64	96	ψ	ψ	NOUN
ejpam-3577	64	97	)	)	PUNCT
ejpam-3577	64	98	6	6	NUM
ejpam-3577	64	99	0	0	NUM
ejpam-3577	64	100	,	,	PUNCT
ejpam-3577	64	101	i	i	PRON
ejpam-3577	64	102	=	=	NOUN
ejpam-3577	64	103	1	1	NUM
ejpam-3577	64	104	,	,	PUNCT
ejpam-3577	64	105	s1	s1	NOUN
ejpam-3577	64	106	,	,	PUNCT
ejpam-3577	64	107	(	(	PUNCT
ejpam-3577	64	108	7	7	X
ejpam-3577	64	109	)	)	PUNCT
ejpam-3577	64	110	equality	equality	NOUN
ejpam-3577	64	111	-	-	PUNCT
ejpam-3577	64	112	type	type	NOUN
ejpam-3577	64	113	constraints	constraint	NOUN
ejpam-3577	64	114	,	,	PUNCT
ejpam-3577	64	115	ji(f	ji(f	PROPN
ejpam-3577	64	116	,	,	PUNCT
ejpam-3577	64	117	ϕ	ϕ	NOUN
ejpam-3577	64	118	,	,	PUNCT
ejpam-3577	64	119	ψ	ψ	NOUN
ejpam-3577	64	120	)	)	PUNCT
ejpam-3577	64	121	=	=	SYM
ejpam-3577	64	122	0	0	NUM
ejpam-3577	64	123	,	,	PUNCT
ejpam-3577	64	124	i	i	PRON
ejpam-3577	64	125	=	=	SYM
ejpam-3577	64	126	s1	s1	PROPN
ejpam-3577	64	127	+	+	CCONJ
ejpam-3577	64	128	1	1	NUM
ejpam-3577	64	129	,	,	PUNCT
ejpam-3577	64	130	s1	s1	PROPN
ejpam-3577	64	131	+	+	CCONJ
ejpam-3577	64	132	s2	s2	PROPN
ejpam-3577	64	133	(	(	PUNCT
ejpam-3577	64	134	8)	8)	NUM
ejpam-3577	64	135	and	and	CCONJ
ejpam-3577	64	136	with	with	ADP
ejpam-3577	64	137	that	that	DET
ejpam-3577	64	138	j0(f0	j0(f0	NOUN
ejpam-3577	64	139	,	,	PUNCT
ejpam-3577	64	140	ϕ0	ϕ0	NOUN
ejpam-3577	64	141	,	,	PUNCT
ejpam-3577	64	142	ψ0	ψ0	ADJ
ejpam-3577	64	143	)	)	PUNCT
ejpam-3577	64	144	=	=	SYM
ejpam-3577	64	145	inf	inf	NOUN
ejpam-3577	64	146	y×x×w	y×x×w	ADP
ejpam-3577	64	147	j0(f	j0(f	PROPN
ejpam-3577	64	148	,	,	PUNCT
ejpam-3577	64	149	ϕ	ϕ	PROPN
ejpam-3577	64	150	,	,	PUNCT
ejpam-3577	64	151	ψ	ψ	NOUN
ejpam-3577	64	152	)	)	PUNCT
ejpam-3577	64	153	(	(	PUNCT
ejpam-3577	64	154	9	9	NUM
ejpam-3577	64	155	)	)	SYM
ejpam-3577	64	156	4	4	NUM
ejpam-3577	64	157	.	.	PUNCT
ejpam-3577	65	1	existence	existence	NOUN
ejpam-3577	65	2	of	of	ADP
ejpam-3577	65	3	an	an	DET
ejpam-3577	65	4	optimal	optimal	ADJ
ejpam-3577	65	5	control	control	NOUN
ejpam-3577	65	6	theorem	theorem	VERB
ejpam-3577	65	7	3	3	X
ejpam-3577	65	8	.	.	PUNCT
ejpam-3577	66	1	we	we	PRON
ejpam-3577	66	2	suppose	suppose	VERB
ejpam-3577	66	3	there	there	PRON
ejpam-3577	66	4	is	be	VERB
ejpam-3577	66	5	a	a	DET
ejpam-3577	66	6	control	control	NOUN
ejpam-3577	66	7	of	of	ADP
ejpam-3577	66	8	the	the	DET
ejpam-3577	66	9	above	above	ADJ
ejpam-3577	66	10	indicated	indicate	VERB
ejpam-3577	66	11	class	class	NOUN
ejpam-3577	66	12	and	and	CCONJ
ejpam-3577	66	13	inf	inf	PROPN
ejpam-3577	66	14	y×x×w	y×x×w	ADP
ejpam-3577	66	15	ji(f	ji(f	PROPN
ejpam-3577	66	16	,	,	PUNCT
ejpam-3577	66	17	ϕ	ϕ	NOUN
ejpam-3577	66	18	,	,	PUNCT
ejpam-3577	66	19	ψ	ψ	NOUN
ejpam-3577	66	20	)	)	PUNCT
ejpam-3577	66	21	>	>	X
ejpam-3577	66	22	−∞.	−∞.	PROPN
ejpam-3577	66	23	then	then	ADV
ejpam-3577	66	24	there	there	PRON
ejpam-3577	66	25	exists	exist	VERB
ejpam-3577	66	26	an	an	DET
ejpam-3577	66	27	optimal	optimal	ADJ
ejpam-3577	66	28	control	control	NOUN
ejpam-3577	66	29	f̂0(x	f̂0(x	NOUN
ejpam-3577	66	30	,	,	PUNCT
ejpam-3577	66	31	t	t	PROPN
ejpam-3577	66	32	)	)	PUNCT
ejpam-3577	66	33	,	,	PUNCT
ejpam-3577	66	34	ϕ̂0(x	ϕ̂0(x	PROPN
ejpam-3577	66	35	)	)	PUNCT
ejpam-3577	66	36	,	,	PUNCT
ejpam-3577	66	37	ψ̂0(x	ψ̂0(x	NOUN
ejpam-3577	66	38	)	)	PUNCT
ejpam-3577	66	39	.	.	PUNCT
ejpam-3577	67	1	proof	proof	NOUN
ejpam-3577	67	2	.	.	PUNCT
ejpam-3577	68	1	white	white	ADJ
ejpam-3577	68	2	.	.	PUNCT
ejpam-3577	69	1	let	let	VERB
ejpam-3577	69	2	{	{	PUNCT
ejpam-3577	69	3	fm(x	fm(x	PROPN
ejpam-3577	69	4	,	,	PUNCT
ejpam-3577	69	5	t)}m>1	t)}m>1	PROPN
ejpam-3577	69	6	,	,	PUNCT
ejpam-3577	69	7	{	{	PUNCT
ejpam-3577	69	8	ϕm(x)}m>1	ϕm(x)}m>1	ADJ
ejpam-3577	69	9	,	,	PUNCT
ejpam-3577	69	10	{	{	PUNCT
ejpam-3577	69	11	ψm(x)}m>1	ψm(x)}m>1	VERB
ejpam-3577	69	12	be	be	AUX
ejpam-3577	69	13	minimizable	minimizable	ADJ
ejpam-3577	69	14	sequences	sequence	NOUN
ejpam-3577	69	15	of	of	ADP
ejpam-3577	69	16	controls	control	NOUN
ejpam-3577	69	17	and	and	CCONJ
ejpam-3577	69	18	{	{	PUNCT
ejpam-3577	69	19	um(x	um(x	PROPN
ejpam-3577	69	20	,	,	PUNCT
ejpam-3577	69	21	t)}m>1	t)}m>1	VERB
ejpam-3577	69	22	their	their	PRON
ejpam-3577	69	23	corresponding	correspond	VERB
ejpam-3577	69	24	sequence	sequence	NOUN
ejpam-3577	69	25	of	of	ADP
ejpam-3577	69	26	solution	solution	NOUN
ejpam-3577	69	27	of	of	ADP
ejpam-3577	69	28	the	the	DET
ejpam-3577	69	29	problem	problem	NOUN
ejpam-3577	69	30	(	(	PUNCT
ejpam-3577	69	31	1)-(3	1)-(3	NUM
ejpam-3577	69	32	)	)	PUNCT
ejpam-3577	69	33	.	.	PUNCT
ejpam-3577	70	1	from	from	ADP
ejpam-3577	70	2	the	the	DET
ejpam-3577	70	3	inequality	inequality	NOUN
ejpam-3577	70	4	‖um(x	‖um(x	ADP
ejpam-3577	70	5	,	,	PUNCT
ejpam-3577	70	6	t)‖h1(qt	t)‖h1(qt	NOUN
ejpam-3577	70	7	)	)	PUNCT
ejpam-3577	70	8	+	+	CCONJ
ejpam-3577	70	9	‖um(x	‖um(x	NUM
ejpam-3577	70	10	,	,	PUNCT
ejpam-3577	70	11	t)‖lp(qt	t)‖lp(qt	NOUN
ejpam-3577	70	12	)	)	PUNCT
ejpam-3577	70	13	6	6	NUM
ejpam-3577	70	14	const	const	PROPN
ejpam-3577	70	15	d.	d.	PROPN
ejpam-3577	70	16	ampini	ampini	PROPN
ejpam-3577	70	17	,	,	PUNCT
ejpam-3577	70	18	v.	v.	PROPN
ejpam-3577	70	19	d.	d.	PROPN
ejpam-3577	70	20	mabonzo	mabonzo	PROPN
ejpam-3577	70	21	/	/	SYM
ejpam-3577	70	22	eur	eur	PROPN
ejpam-3577	70	23	.	.	PUNCT
ejpam-3577	71	1	j.	j.	PROPN
ejpam-3577	71	2	pure	pure	PROPN
ejpam-3577	71	3	appl	appl	PROPN
ejpam-3577	71	4	.	.	PROPN
ejpam-3577	71	5	math	math	PROPN
ejpam-3577	71	6	,	,	PUNCT
ejpam-3577	71	7	12	12	NUM
ejpam-3577	71	8	(	(	PUNCT
ejpam-3577	71	9	4	4	NUM
ejpam-3577	71	10	)	)	PUNCT
ejpam-3577	71	11	(	(	PUNCT
ejpam-3577	71	12	2019	2019	NUM
ejpam-3577	71	13	)	)	PUNCT
ejpam-3577	71	14	,	,	PUNCT
ejpam-3577	71	15	1595	1595	NUM
ejpam-3577	71	16	-	-	SYM
ejpam-3577	71	17	1601	1601	NUM
ejpam-3577	71	18	1600	1600	NUM
ejpam-3577	72	1	[	[	X
ejpam-3577	72	2	3	3	NUM
ejpam-3577	72	3	]	]	PUNCT
ejpam-3577	72	4	,	,	PUNCT
ejpam-3577	72	5	where	where	SCONJ
ejpam-3577	72	6	p	p	NOUN
ejpam-3577	72	7	=	=	NOUN
ejpam-3577	72	8	ρ	ρ	PROPN
ejpam-3577	73	1	+	+	NOUN
ejpam-3577	73	2	2	2	NUM
ejpam-3577	73	3	,	,	PUNCT
ejpam-3577	73	4	it	it	PRON
ejpam-3577	73	5	follows	follow	VERB
ejpam-3577	73	6	that	that	SCONJ
ejpam-3577	73	7	the	the	DET
ejpam-3577	73	8	{	{	PUNCT
ejpam-3577	73	9	um(x	um(x	PROPN
ejpam-3577	73	10	,	,	PUNCT
ejpam-3577	73	11	t)}m>1	t)}m>1	VERB
ejpam-3577	73	12	sequence	sequence	NOUN
ejpam-3577	73	13	is	be	AUX
ejpam-3577	73	14	uniformly	uniformly	ADV
ejpam-3577	73	15	bounded	bound	VERB
ejpam-3577	73	16	into	into	ADP
ejpam-3577	73	17	h1(qt	h1(qt	PROPN
ejpam-3577	73	18	)	)	PUNCT
ejpam-3577	73	19	;	;	PUNCT
ejpam-3577	73	20	which	which	PRON
ejpam-3577	73	21	allows	allow	VERB
ejpam-3577	73	22	to	to	PART
ejpam-3577	73	23	subtract	subtract	VERB
ejpam-3577	73	24	a	a	DET
ejpam-3577	73	25	sub	sub	NOUN
ejpam-3577	73	26	-	-	NOUN
ejpam-3577	73	27	sequence	sequence	NOUN
ejpam-3577	73	28	of	of	ADP
ejpam-3577	73	29	solutions	solution	NOUN
ejpam-3577	73	30	{	{	PUNCT
ejpam-3577	73	31	umk	umk	INTJ
ejpam-3577	73	32	(	(	PUNCT
ejpam-3577	73	33	x	x	X
ejpam-3577	73	34	,	,	PUNCT
ejpam-3577	73	35	t)}∞k=1	t)}∞k=1	INTJ
ejpam-3577	73	36	that	that	PRON
ejpam-3577	73	37	converge	converge	VERB
ejpam-3577	73	38	weakly	weakly	ADV
ejpam-3577	73	39	to	to	ADP
ejpam-3577	73	40	u(x	u(x	NOUN
ejpam-3577	73	41	,	,	PUNCT
ejpam-3577	73	42	t	t	PROPN
ejpam-3577	73	43	)	)	PUNCT
ejpam-3577	73	44	into	into	ADP
ejpam-3577	73	45	h1(qt	h1(qt	PROPN
ejpam-3577	73	46	)	)	PUNCT
ejpam-3577	73	47	and	and	CCONJ
ejpam-3577	73	48	fmk	fmk	PROPN
ejpam-3577	73	49	(	(	PUNCT
ejpam-3577	73	50	x	x	PROPN
ejpam-3577	73	51	,	,	PUNCT
ejpam-3577	73	52	t	t	PROPN
ejpam-3577	73	53	)	)	PUNCT
ejpam-3577	73	54	,	,	PUNCT
ejpam-3577	73	55	ϕmk	ϕmk	X
ejpam-3577	73	56	(	(	PUNCT
ejpam-3577	73	57	x	x	NOUN
ejpam-3577	73	58	)	)	PUNCT
ejpam-3577	73	59	,	,	PUNCT
ejpam-3577	73	60	ψmk	ψmk	PRON
ejpam-3577	73	61	(	(	PUNCT
ejpam-3577	73	62	x	x	X
ejpam-3577	73	63	)	)	PUNCT
ejpam-3577	73	64	converge	converge	VERB
ejpam-3577	73	65	weakly	weakly	ADV
ejpam-3577	73	66	in	in	ADP
ejpam-3577	73	67	the	the	DET
ejpam-3577	73	68	spaces	space	NOUN
ejpam-3577	73	69	l2(qt	l2(qt	PROPN
ejpam-3577	73	70	)	)	PUNCT
ejpam-3577	73	71	,	,	PUNCT
ejpam-3577	73	72	h1(ω	h1(ω	PROPN
ejpam-3577	73	73	)	)	PUNCT
ejpam-3577	73	74	,	,	PUNCT
ejpam-3577	73	75	l2(ω	l2(ω	NOUN
ejpam-3577	73	76	)	)	PUNCT
ejpam-3577	73	77	to	to	ADP
ejpam-3577	73	78	f0(x	f0(x	PROPN
ejpam-3577	73	79	,	,	PUNCT
ejpam-3577	73	80	t	t	PROPN
ejpam-3577	73	81	)	)	PUNCT
ejpam-3577	73	82	∈	∈	PROPN
ejpam-3577	73	83	y	y	PROPN
ejpam-3577	73	84	,	,	PUNCT
ejpam-3577	73	85	ϕ0(x	ϕ0(x	NOUN
ejpam-3577	73	86	)	)	PUNCT
ejpam-3577	73	87	∈	∈	PROPN
ejpam-3577	73	88	x	x	SYM
ejpam-3577	73	89	,	,	PUNCT
ejpam-3577	73	90	ψ0(x	ψ0(x	SYM
ejpam-3577	73	91	)	)	PUNCT
ejpam-3577	73	92	∈w	∈w	NOUN
ejpam-3577	73	93	.	.	PUNCT
ejpam-3577	74	1	from	from	ADP
ejpam-3577	74	2	the	the	DET
ejpam-3577	74	3	weak	weak	ADJ
ejpam-3577	74	4	converge	converge	NOUN
ejpam-3577	74	5	in	in	ADP
ejpam-3577	74	6	h1(qt	h1(qt	PROPN
ejpam-3577	74	7	)	)	PUNCT
ejpam-3577	74	8	of	of	ADP
ejpam-3577	74	9	the	the	DET
ejpam-3577	74	10	sequence	sequence	NOUN
ejpam-3577	74	11	umk	umk	NOUN
ejpam-3577	74	12	(	(	PUNCT
ejpam-3577	74	13	x	x	NOUN
ejpam-3577	74	14	,	,	PUNCT
ejpam-3577	74	15	t	t	PROPN
ejpam-3577	74	16	)	)	PUNCT
ejpam-3577	74	17	to	to	ADP
ejpam-3577	74	18	u(x	u(x	PROPN
ejpam-3577	74	19	,	,	PUNCT
ejpam-3577	74	20	t	t	PROPN
ejpam-3577	74	21	)	)	PUNCT
ejpam-3577	74	22	and	and	CCONJ
ejpam-3577	74	23	by	by	ADP
ejpam-3577	74	24	virtue	virtue	NOUN
ejpam-3577	74	25	of	of	ADP
ejpam-3577	74	26	the	the	DET
ejpam-3577	74	27	complete	complete	ADJ
ejpam-3577	74	28	continuity	continuity	NOUN
ejpam-3577	74	29	of	of	ADP
ejpam-3577	74	30	the	the	DET
ejpam-3577	74	31	operator	operator	NOUN
ejpam-3577	74	32	h1(qt	h1(qt	PROPN
ejpam-3577	74	33	)	)	PUNCT
ejpam-3577	74	34	into	into	ADP
ejpam-3577	74	35	l2(qt	l2(qt	PROPN
ejpam-3577	74	36	)	)	PUNCT
ejpam-3577	74	37	,	,	PUNCT
ejpam-3577	74	38	result	result	VERB
ejpam-3577	74	39	the	the	DET
ejpam-3577	74	40	weak	weak	ADJ
ejpam-3577	74	41	convergence	convergence	NOUN
ejpam-3577	74	42	into	into	ADP
ejpam-3577	74	43	l2(qt	l2(qt	PROPN
ejpam-3577	74	44	)	)	PUNCT
ejpam-3577	74	45	of	of	ADP
ejpam-3577	74	46	the	the	DET
ejpam-3577	74	47	sequence	sequence	NOUN
ejpam-3577	74	48	umk	umk	NOUN
ejpam-3577	74	49	(	(	PUNCT
ejpam-3577	74	50	x	x	NOUN
ejpam-3577	74	51	,	,	PUNCT
ejpam-3577	74	52	t	t	PROPN
ejpam-3577	74	53	)	)	PUNCT
ejpam-3577	74	54	to	to	ADP
ejpam-3577	74	55	u(x	u(x	PROPN
ejpam-3577	74	56	,	,	PUNCT
ejpam-3577	74	57	t	t	PROPN
ejpam-3577	74	58	)	)	PUNCT
ejpam-3577	74	59	.	.	PUNCT
ejpam-3577	75	1	h1(qt	h1(qt	PROPN
ejpam-3577	75	2	)	)	PUNCT
ejpam-3577	75	3	⊂	⊂	PROPN
ejpam-3577	75	4	l2(qt	l2(qt	PROPN
ejpam-3577	75	5	)	)	PUNCT
ejpam-3577	75	6	∀{um(x	∀{um(x	PROPN
ejpam-3577	75	7	,	,	PUNCT
ejpam-3577	75	8	t	t	PROPN
ejpam-3577	75	9	)	)	PUNCT
ejpam-3577	75	10	}	}	PUNCT
ejpam-3577	76	1	⊂	⊂	PROPN
ejpam-3577	76	2	h1(qt	h1(qt	PROPN
ejpam-3577	76	3	)	)	PUNCT
ejpam-3577	76	4	:	:	PUNCT
ejpam-3577	76	5	‖um(x	‖um(x	NUM
ejpam-3577	76	6	,	,	PUNCT
ejpam-3577	76	7	t)‖h1(qt	t)‖h1(qt	NOUN
ejpam-3577	76	8	)	)	PUNCT
ejpam-3577	76	9	6	6	NUM
ejpam-3577	76	10	c11	c11	NOUN
ejpam-3577	76	11	∃	∃	PROPN
ejpam-3577	76	12	{	{	PUNCT
ejpam-3577	76	13	umk	umk	PROPN
ejpam-3577	76	14	(	(	PUNCT
ejpam-3577	76	15	x	x	NOUN
ejpam-3577	76	16	,	,	PUNCT
ejpam-3577	76	17	t	t	PROPN
ejpam-3577	76	18	)	)	PUNCT
ejpam-3577	76	19	}	}	PUNCT
ejpam-3577	77	1	⊂	⊂	PRON
ejpam-3577	77	2	{	{	PUNCT
ejpam-3577	77	3	um(x	um(x	PROPN
ejpam-3577	77	4	,	,	PUNCT
ejpam-3577	77	5	t	t	PROPN
ejpam-3577	77	6	)	)	PUNCT
ejpam-3577	77	7	}	}	PUNCT
ejpam-3577	77	8	which	which	PRON
ejpam-3577	77	9	is	be	AUX
ejpam-3577	77	10	fundamental	fundamental	ADJ
ejpam-3577	77	11	in	in	ADP
ejpam-3577	77	12	l2(qt	l2(qt	PROPN
ejpam-3577	77	13	)	)	PUNCT
ejpam-3577	77	14	.	.	PUNCT
ejpam-3577	78	1	as	as	ADP
ejpam-3577	78	2	l2(qt	l2(qt	PROPN
ejpam-3577	78	3	)	)	PUNCT
ejpam-3577	78	4	is	be	AUX
ejpam-3577	78	5	complete	complete	ADJ
ejpam-3577	78	6	then	then	ADV
ejpam-3577	78	7	∃	∃	PROPN
ejpam-3577	78	8	x∗(x	x∗(x	PROPN
ejpam-3577	78	9	,	,	PUNCT
ejpam-3577	78	10	t	t	PROPN
ejpam-3577	78	11	)	)	PUNCT
ejpam-3577	78	12	∈	∈	PROPN
ejpam-3577	78	13	l2(qt	l2(qt	PROPN
ejpam-3577	78	14	)	)	PUNCT
ejpam-3577	78	15	:	:	PUNCT
ejpam-3577	79	1	umk	umk	INTJ
ejpam-3577	79	2	(	(	PUNCT
ejpam-3577	79	3	x	x	NOUN
ejpam-3577	79	4	,	,	PUNCT
ejpam-3577	79	5	t	t	PROPN
ejpam-3577	79	6	)	)	PUNCT
ejpam-3577	79	7	−→	−→	NOUN
ejpam-3577	79	8	u∗	u∗	NOUN
ejpam-3577	79	9	converge	converge	NOUN
ejpam-3577	79	10	strongly	strongly	ADV
ejpam-3577	79	11	into	into	ADP
ejpam-3577	79	12	l2(qt	l2(qt	PROPN
ejpam-3577	79	13	)	)	PUNCT
ejpam-3577	79	14	.	.	PUNCT
ejpam-3577	80	1	by	by	ADP
ejpam-3577	80	2	virtue	virtue	NOUN
ejpam-3577	80	3	of	of	ADP
ejpam-3577	80	4	the	the	DET
ejpam-3577	80	5	separation	separation	NOUN
ejpam-3577	80	6	of	of	ADP
ejpam-3577	80	7	l2(qt	l2(qt	PROPN
ejpam-3577	80	8	)	)	PUNCT
ejpam-3577	80	9	,	,	PUNCT
ejpam-3577	80	10	we	we	PRON
ejpam-3577	80	11	have	have	VERB
ejpam-3577	80	12	u	u	NOUN
ejpam-3577	80	13	=	=	NOUN
ejpam-3577	80	14	u∗.	u∗.	PROPN
ejpam-3577	80	15	we	we	PRON
ejpam-3577	80	16	can	can	AUX
ejpam-3577	80	17	consider	consider	VERB
ejpam-3577	80	18	that	that	PRON
ejpam-3577	80	19	(	(	PUNCT
ejpam-3577	80	20	[	[	X
ejpam-3577	80	21	5],p.162	5],p.162	NUM
ejpam-3577	80	22	)	)	PUNCT
ejpam-3577	80	23	|umk	|umk	NOUN
ejpam-3577	80	24	(	(	PUNCT
ejpam-3577	80	25	x	x	NOUN
ejpam-3577	80	26	,	,	PUNCT
ejpam-3577	80	27	t)|	t)|	ADV
ejpam-3577	80	28	6	6	NUM
ejpam-3577	80	29	z(x	z(x	NUM
ejpam-3577	80	30	,	,	PUNCT
ejpam-3577	80	31	t	t	PROPN
ejpam-3577	80	32	)	)	PUNCT
ejpam-3577	80	33	∈	∈	PROPN
ejpam-3577	80	34	l2(qt	l2(qt	PROPN
ejpam-3577	80	35	)	)	PUNCT
ejpam-3577	80	36	.	.	PUNCT
ejpam-3577	81	1	then	then	ADV
ejpam-3577	81	2	from	from	ADP
ejpam-3577	81	3	the	the	DET
ejpam-3577	81	4	inequality	inequality	NOUN
ejpam-3577	81	5	(	(	PUNCT
ejpam-3577	81	6	6	6	NUM
ejpam-3577	81	7	)	)	PUNCT
ejpam-3577	81	8	,	,	PUNCT
ejpam-3577	81	9	we	we	PRON
ejpam-3577	81	10	obtain	obtain	VERB
ejpam-3577	81	11	|vi(x	|vi(x	NUM
ejpam-3577	81	12	,	,	PUNCT
ejpam-3577	81	13	t	t	PROPN
ejpam-3577	81	14	,	,	PUNCT
ejpam-3577	81	15	umk	umk	PROPN
ejpam-3577	81	16	)	)	PUNCT
ejpam-3577	81	17	|	|	ADV
ejpam-3577	81	18	6	6	NUM
ejpam-3577	81	19	c9	c9	NOUN
ejpam-3577	81	20	+	+	CCONJ
ejpam-3577	81	21	c10z	c10z	NOUN
ejpam-3577	81	22	2(x	2(x	NUM
ejpam-3577	81	23	,	,	PUNCT
ejpam-3577	81	24	t	t	PROPN
ejpam-3577	81	25	)	)	PUNCT
ejpam-3577	81	26	∈	∈	PROPN
ejpam-3577	81	27	l1(qt	l1(qt	PROPN
ejpam-3577	81	28	)	)	PUNCT
ejpam-3577	81	29	.	.	PUNCT
ejpam-3577	82	1	by	by	ADP
ejpam-3577	82	2	using	use	VERB
ejpam-3577	82	3	the	the	DET
ejpam-3577	82	4	formula	formula	NOUN
ejpam-3577	82	5	of	of	ADP
ejpam-3577	82	6	the	the	DET
ejpam-3577	82	7	functional	functional	ADJ
ejpam-3577	82	8	ji(f	ji(f	PROPN
ejpam-3577	82	9	,	,	PUNCT
ejpam-3577	82	10	ϕ	ϕ	NOUN
ejpam-3577	82	11	,	,	PUNCT
ejpam-3577	82	12	ψ	ψ	NOUN
ejpam-3577	82	13	)	)	PUNCT
ejpam-3577	82	14	for	for	ADP
ejpam-3577	82	15	umk	umk	NOUN
ejpam-3577	82	16	(	(	PUNCT
ejpam-3577	82	17	x	x	NOUN
ejpam-3577	82	18	,	,	PUNCT
ejpam-3577	82	19	t	t	PROPN
ejpam-3577	82	20	)	)	PUNCT
ejpam-3577	82	21	,	,	PUNCT
ejpam-3577	82	22	we	we	PRON
ejpam-3577	82	23	have	have	VERB
ejpam-3577	82	24	ji(fmk	ji(fmk	ADV
ejpam-3577	82	25	,	,	PUNCT
ejpam-3577	82	26	ϕmk	ϕmk	INTJ
ejpam-3577	82	27	,	,	PUNCT
ejpam-3577	82	28	ψmk	ψmk	PRON
ejpam-3577	82	29	)	)	PUNCT
ejpam-3577	83	1	=	=	SYM
ejpam-3577	83	2	∫	∫	PROPN
ejpam-3577	83	3	qt	qt	PROPN
ejpam-3577	83	4	vi(x	vi(x	PROPN
ejpam-3577	83	5	,	,	PUNCT
ejpam-3577	83	6	t	t	PROPN
ejpam-3577	83	7	,	,	PUNCT
ejpam-3577	83	8	umk	umk	PROPN
ejpam-3577	83	9	)	)	PUNCT
ejpam-3577	83	10	dxdt+	dxdt+	PROPN
ejpam-3577	83	11	f	f	PROPN
ejpam-3577	83	12	i(fmk	i(fmk	PROPN
ejpam-3577	83	13	,	,	PUNCT
ejpam-3577	83	14	ϕmk	ϕmk	INTJ
ejpam-3577	83	15	,	,	PUNCT
ejpam-3577	83	16	ψmk	ψmk	NUM
ejpam-3577	83	17	)	)	PUNCT
ejpam-3577	84	1	i	i	PRON
ejpam-3577	84	2	=	=	NOUN
ejpam-3577	84	3	0	0	NUM
ejpam-3577	84	4	,	,	PUNCT
ejpam-3577	84	5	s1	s1	PROPN
ejpam-3577	84	6	+	+	CCONJ
ejpam-3577	84	7	s2	s2	PROPN
ejpam-3577	84	8	according	accord	VERB
ejpam-3577	84	9	to	to	ADP
ejpam-3577	84	10	the	the	DET
ejpam-3577	84	11	lebesgue	lebesgue	NOUN
ejpam-3577	84	12	theorem	theorem	PROPN
ejpam-3577	84	13	,	,	PUNCT
ejpam-3577	84	14	we	we	PRON
ejpam-3577	84	15	obtain	obtain	VERB
ejpam-3577	84	16	ji(f̂	ji(f̂	PROPN
ejpam-3577	84	17	0	0	NUM
ejpam-3577	84	18	,	,	PUNCT
ejpam-3577	84	19	ϕ̂0	ϕ̂0	X
ejpam-3577	84	20	,	,	PUNCT
ejpam-3577	84	21	ψ̂0	ψ̂0	X
ejpam-3577	84	22	)	)	PUNCT
ejpam-3577	85	1	=	=	SYM
ejpam-3577	85	2	∫	∫	PROPN
ejpam-3577	85	3	qt	qt	PROPN
ejpam-3577	85	4	vi(x	vi(x	PROPN
ejpam-3577	85	5	,	,	PUNCT
ejpam-3577	85	6	t	t	PROPN
ejpam-3577	85	7	,	,	PUNCT
ejpam-3577	85	8	u(x	u(x	PROPN
ejpam-3577	85	9	,	,	PUNCT
ejpam-3577	85	10	t))dxdt+	t))dxdt+	ADP
ejpam-3577	85	11	f	f	PROPN
ejpam-3577	85	12	i(f̂0	i(f̂0	PROPN
ejpam-3577	85	13	,	,	PUNCT
ejpam-3577	85	14	ϕ̂0	ϕ̂0	PROPN
ejpam-3577	85	15	,	,	PUNCT
ejpam-3577	85	16	ψ̂0	ψ̂0	PROPN
ejpam-3577	85	17	)	)	PUNCT
ejpam-3577	85	18	(	(	PUNCT
ejpam-3577	85	19	10	10	NUM
ejpam-3577	85	20	)	)	PUNCT
ejpam-3577	86	1	i	i	NOUN
ejpam-3577	86	2	=	=	NOUN
ejpam-3577	86	3	0	0	NUM
ejpam-3577	86	4	,	,	PUNCT
ejpam-3577	86	5	s1	s1	PROPN
ejpam-3577	86	6	+	+	CCONJ
ejpam-3577	86	7	s2	s2	PROPN
ejpam-3577	86	8	as	as	ADP
ejpam-3577	86	9	the	the	DET
ejpam-3577	86	10	functions	function	NOUN
ejpam-3577	86	11	fm(x	fm(x	PUNCT
ejpam-3577	86	12	,	,	PUNCT
ejpam-3577	86	13	t	t	PROPN
ejpam-3577	86	14	)	)	PUNCT
ejpam-3577	86	15	,	,	PUNCT
ejpam-3577	86	16	ϕm(x	ϕm(x	NUM
ejpam-3577	86	17	)	)	PUNCT
ejpam-3577	86	18	,	,	PUNCT
ejpam-3577	86	19	ψm(x	ψm(x	NUM
ejpam-3577	86	20	)	)	PUNCT
ejpam-3577	86	21	are	be	AUX
ejpam-3577	86	22	the	the	DET
ejpam-3577	86	23	minimizable	minimizable	ADJ
ejpam-3577	86	24	sequences	sequence	NOUN
ejpam-3577	86	25	,	,	PUNCT
ejpam-3577	86	26	then	then	ADV
ejpam-3577	86	27	j0(fm	j0(fm	PROPN
ejpam-3577	86	28	,	,	PUNCT
ejpam-3577	86	29	ϕm	ϕm	INTJ
ejpam-3577	86	30	,	,	PUNCT
ejpam-3577	86	31	ψm	ψm	ADJ
ejpam-3577	86	32	)	)	PUNCT
ejpam-3577	86	33	−→	−→	PROPN
ejpam-3577	86	34	inf	inf	PROPN
ejpam-3577	86	35	x×y×w	x×y×w	PROPN
ejpam-3577	87	1	j0(f	j0(f	PROPN
ejpam-3577	87	2	,	,	PUNCT
ejpam-3577	87	3	ϕ	ϕ	PROPN
ejpam-3577	87	4	,	,	PUNCT
ejpam-3577	87	5	ψ	ψ	NOUN
ejpam-3577	87	6	)	)	PUNCT
ejpam-3577	87	7	:	:	PUNCT
ejpam-3577	87	8	=	=	PUNCT
ejpam-3577	87	9	j∗	j∗	PROPN
ejpam-3577	87	10	(	(	PUNCT
ejpam-3577	87	11	11	11	NUM
ejpam-3577	87	12	)	)	PUNCT
ejpam-3577	87	13	under	under	ADP
ejpam-3577	87	14	the	the	DET
ejpam-3577	87	15	weak	weak	ADJ
ejpam-3577	87	16	sequential	sequential	ADJ
ejpam-3577	87	17	continuity	continuity	NOUN
ejpam-3577	87	18	,	,	PUNCT
ejpam-3577	87	19	we	we	PRON
ejpam-3577	87	20	have	have	VERB
ejpam-3577	87	21	j∗	j∗	PROPN
ejpam-3577	87	22	=	=	SYM
ejpam-3577	87	23	lim	lim	PROPN
ejpam-3577	87	24	m→∞	m→∞	NOUN
ejpam-3577	87	25	j0(fm	j0(fm	PROPN
ejpam-3577	87	26	,	,	PUNCT
ejpam-3577	87	27	ϕm	ϕm	INTJ
ejpam-3577	87	28	,	,	PUNCT
ejpam-3577	87	29	ψm	ψm	PROPN
ejpam-3577	87	30	)	)	PUNCT
ejpam-3577	87	31	=	=	SYM
ejpam-3577	88	1	j0(f̂0	j0(f̂0	PROPN
ejpam-3577	88	2	,	,	PUNCT
ejpam-3577	88	3	ϕ̂0	ϕ̂0	PROPN
ejpam-3577	88	4	,	,	PUNCT
ejpam-3577	88	5	ψ̂0	ψ̂0	PROPN
ejpam-3577	88	6	)	)	PUNCT
ejpam-3577	88	7	(	(	PUNCT
ejpam-3577	88	8	12	12	NUM
ejpam-3577	88	9	)	)	PUNCT
ejpam-3577	88	10	by	by	ADP
ejpam-3577	88	11	the	the	DET
ejpam-3577	88	12	same	same	ADJ
ejpam-3577	88	13	way	way	NOUN
ejpam-3577	88	14	,	,	PUNCT
ejpam-3577	88	15	we	we	PRON
ejpam-3577	88	16	have	have	VERB
ejpam-3577	88	17	lim	lim	PROPN
ejpam-3577	88	18	m→∞	m→∞	NUM
ejpam-3577	88	19	ji(fm	ji(fm	PROPN
ejpam-3577	88	20	,	,	PUNCT
ejpam-3577	88	21	ϕm	ϕm	INTJ
ejpam-3577	88	22	,	,	PUNCT
ejpam-3577	88	23	ψm	ψm	PROPN
ejpam-3577	88	24	)	)	PUNCT
ejpam-3577	88	25	=	=	SYM
ejpam-3577	88	26	ji(f̂	ji(f̂	PROPN
ejpam-3577	89	1	0	0	NUM
ejpam-3577	89	2	,	,	PUNCT
ejpam-3577	89	3	ϕ̂0	ϕ̂0	PROPN
ejpam-3577	89	4	,	,	PUNCT
ejpam-3577	89	5	ψ̂0	ψ̂0	PROPN
ejpam-3577	89	6	)	)	PUNCT
ejpam-3577	89	7	,	,	PUNCT
ejpam-3577	89	8	(	(	PUNCT
ejpam-3577	89	9	13	13	X
ejpam-3577	89	10	)	)	PUNCT
ejpam-3577	89	11	references	reference	NOUN
ejpam-3577	89	12	1601	1601	NUM
ejpam-3577	89	13	i	i	NOUN
ejpam-3577	89	14	=	=	SYM
ejpam-3577	89	15	1	1	NUM
ejpam-3577	89	16	,	,	PUNCT
ejpam-3577	89	17	s1	s1	NOUN
ejpam-3577	89	18	+	+	CCONJ
ejpam-3577	89	19	s2	s2	NOUN
ejpam-3577	89	20	in	in	ADP
ejpam-3577	89	21	addition	addition	NOUN
ejpam-3577	89	22	,	,	PUNCT
ejpam-3577	89	23	from	from	ADP
ejpam-3577	89	24	(	(	PUNCT
ejpam-3577	89	25	7	7	NUM
ejpam-3577	89	26	)	)	PUNCT
ejpam-3577	89	27	and	and	CCONJ
ejpam-3577	89	28	(	(	PUNCT
ejpam-3577	89	29	8)	8)	NUM
ejpam-3577	89	30	,	,	PUNCT
ejpam-3577	89	31	it	it	PRON
ejpam-3577	89	32	follows	follow	VERB
ejpam-3577	89	33	that	that	SCONJ
ejpam-3577	89	34	:	:	PUNCT
ejpam-3577	90	1	ji(fm	ji(fm	PROPN
ejpam-3577	90	2	,	,	PUNCT
ejpam-3577	90	3	ϕm	ϕm	INTJ
ejpam-3577	90	4	,	,	PUNCT
ejpam-3577	90	5	ψm	ψm	PROPN
ejpam-3577	90	6	)	)	PUNCT
ejpam-3577	90	7	6	6	NUM
ejpam-3577	90	8	0	0	NUM
ejpam-3577	90	9	,	,	PUNCT
ejpam-3577	90	10	i	i	PRON
ejpam-3577	90	11	=	=	NOUN
ejpam-3577	90	12	1	1	NUM
ejpam-3577	90	13	,	,	PUNCT
ejpam-3577	90	14	s1	s1	PROPN
ejpam-3577	90	15	ji(fm	ji(fm	PROPN
ejpam-3577	90	16	,	,	PUNCT
ejpam-3577	90	17	ϕm	ϕm	INTJ
ejpam-3577	90	18	,	,	PUNCT
ejpam-3577	90	19	ψm	ψm	PROPN
ejpam-3577	90	20	)	)	PUNCT
ejpam-3577	90	21	=	=	SYM
ejpam-3577	90	22	0	0	NUM
ejpam-3577	90	23	,	,	PUNCT
ejpam-3577	90	24	i	i	PRON
ejpam-3577	90	25	=	=	SYM
ejpam-3577	90	26	s1	s1	PROPN
ejpam-3577	90	27	+	+	CCONJ
ejpam-3577	90	28	1	1	NUM
ejpam-3577	90	29	,	,	PUNCT
ejpam-3577	90	30	s1	s1	NOUN
ejpam-3577	90	31	+	+	CCONJ
ejpam-3577	90	32	s2	s2	PROPN
ejpam-3577	90	33	and	and	CCONJ
ejpam-3577	90	34	from	from	ADP
ejpam-3577	90	35	this	this	PRON
ejpam-3577	90	36	,	,	PUNCT
ejpam-3577	90	37	it	it	PRON
ejpam-3577	90	38	follows	follow	VERB
ejpam-3577	90	39	that	that	SCONJ
ejpam-3577	90	40	:	:	PUNCT
ejpam-3577	90	41	ji(f̂	ji(f̂	PROPN
ejpam-3577	90	42	0	0	NUM
ejpam-3577	90	43	,	,	PUNCT
ejpam-3577	90	44	ϕ̂0	ϕ̂0	PROPN
ejpam-3577	90	45	,	,	PUNCT
ejpam-3577	90	46	ψ̂0	ψ̂0	PROPN
ejpam-3577	90	47	)	)	PUNCT
ejpam-3577	90	48	6	6	NUM
ejpam-3577	90	49	0	0	NUM
ejpam-3577	90	50	,	,	PUNCT
ejpam-3577	90	51	i	i	PRON
ejpam-3577	90	52	=	=	NOUN
ejpam-3577	90	53	1	1	NUM
ejpam-3577	90	54	,	,	PUNCT
ejpam-3577	90	55	s1	s1	NOUN
ejpam-3577	90	56	(	(	PUNCT
ejpam-3577	90	57	14	14	NUM
ejpam-3577	90	58	)	)	PUNCT
ejpam-3577	90	59	ji(f̂	ji(f̂	PROPN
ejpam-3577	90	60	0	0	NUM
ejpam-3577	90	61	,	,	PUNCT
ejpam-3577	90	62	ϕ̂0	ϕ̂0	PROPN
ejpam-3577	90	63	,	,	PUNCT
ejpam-3577	90	64	ψ̂0	ψ̂0	X
ejpam-3577	90	65	)	)	PUNCT
ejpam-3577	90	66	=	=	SYM
ejpam-3577	91	1	0	0	NUM
ejpam-3577	91	2	,	,	PUNCT
ejpam-3577	91	3	i	i	PRON
ejpam-3577	91	4	=	=	SYM
ejpam-3577	91	5	s1	s1	PROPN
ejpam-3577	91	6	+	+	CCONJ
ejpam-3577	91	7	1	1	NUM
ejpam-3577	91	8	,	,	PUNCT
ejpam-3577	91	9	s1	s1	PROPN
ejpam-3577	91	10	+	+	CCONJ
ejpam-3577	91	11	s2	s2	PROPN
ejpam-3577	91	12	.	.	PUNCT
ejpam-3577	92	1	(	(	PUNCT
ejpam-3577	92	2	15	15	NUM
ejpam-3577	92	3	)	)	PUNCT
ejpam-3577	92	4	from	from	ADP
ejpam-3577	92	5	(	(	PUNCT
ejpam-3577	92	6	12	12	NUM
ejpam-3577	92	7	)	)	PUNCT
ejpam-3577	92	8	,	,	PUNCT
ejpam-3577	92	9	(	(	PUNCT
ejpam-3577	92	10	14	14	NUM
ejpam-3577	92	11	)	)	PUNCT
ejpam-3577	92	12	,	,	PUNCT
ejpam-3577	92	13	(	(	PUNCT
ejpam-3577	92	14	15	15	NUM
ejpam-3577	92	15	)	)	PUNCT
ejpam-3577	92	16	,	,	PUNCT
ejpam-3577	92	17	it	it	PRON
ejpam-3577	92	18	follows	follow	VERB
ejpam-3577	92	19	that	that	SCONJ
ejpam-3577	92	20	f̂0	f̂0	NOUN
ejpam-3577	92	21	,	,	PUNCT
ejpam-3577	92	22	ϕ̂0	ϕ̂0	PROPN
ejpam-3577	92	23	,	,	PUNCT
ejpam-3577	92	24	ψ̂0	ψ̂0	PROPN
ejpam-3577	92	25	is	be	AUX
ejpam-3577	92	26	an	an	DET
ejpam-3577	92	27	optimal	optimal	ADJ
ejpam-3577	92	28	control	control	NOUN
ejpam-3577	92	29	.	.	PUNCT
ejpam-3577	93	1	acknowledgements	acknowledgement	NOUN
ejpam-3577	93	2	the	the	DET
ejpam-3577	93	3	authors	author	NOUN
ejpam-3577	93	4	thank	thank	VERB
ejpam-3577	93	5	the	the	DET
ejpam-3577	93	6	anonymous	anonymous	ADJ
ejpam-3577	93	7	referees	referee	NOUN
ejpam-3577	93	8	of	of	ADP
ejpam-3577	93	9	european	european	PROPN
ejpam-3577	93	10	journal	journal	PROPN
ejpam-3577	93	11	of	of	ADP
ejpam-3577	93	12	pure	pure	ADJ
ejpam-3577	93	13	and	and	CCONJ
ejpam-3577	93	14	applied	applied	ADJ
ejpam-3577	93	15	mathematics	mathematic	NOUN
ejpam-3577	93	16	,	,	PUNCT
ejpam-3577	93	17	for	for	ADP
ejpam-3577	93	18	their	their	PRON
ejpam-3577	93	19	valuable	valuable	ADJ
ejpam-3577	93	20	comments	comment	NOUN
ejpam-3577	93	21	and	and	CCONJ
ejpam-3577	93	22	suggestions	suggestion	NOUN
ejpam-3577	93	23	which	which	PRON
ejpam-3577	93	24	have	have	AUX
ejpam-3577	93	25	led	lead	VERB
ejpam-3577	93	26	to	to	ADP
ejpam-3577	93	27	an	an	DET
ejpam-3577	93	28	improvement	improvement	NOUN
ejpam-3577	93	29	of	of	ADP
ejpam-3577	93	30	the	the	DET
ejpam-3577	93	31	presentation	presentation	NOUN
ejpam-3577	93	32	.	.	PUNCT
ejpam-3577	94	1	references	reference	NOUN
ejpam-3577	94	2	[	[	X
ejpam-3577	94	3	1	1	NUM
ejpam-3577	94	4	]	]	X
ejpam-3577	94	5	o.a	o.a	PROPN
ejpam-3577	94	6	.	.	PROPN
ejpam-3577	94	7	ladyzhenskaya	ladyzhenskaya	PROPN
ejpam-3577	94	8	.	.	PUNCT
ejpam-3577	95	1	problèmes	problèmes	PROPN
ejpam-3577	95	2	aux	aux	PROPN
ejpam-3577	95	3	limites	limites	PROPN
ejpam-3577	95	4	de	de	X
ejpam-3577	95	5	la	la	X
ejpam-3577	95	6	physique	physique	PROPN
ejpam-3577	95	7	mathématique	mathématique	PROPN
ejpam-3577	95	8	.	.	PUNCT
ejpam-3577	96	1	nouvelle	nouvelle	PROPN
ejpam-3577	96	2	édition	édition	PROPN
ejpam-3577	96	3	moscou	moscou	PROPN
ejpam-3577	96	4	,	,	PUNCT
ejpam-3577	96	5	nanka	nanka	NOUN
ejpam-3577	96	6	,	,	PUNCT
ejpam-3577	96	7	1993	1993	NUM
ejpam-3577	96	8	.	.	PUNCT
ejpam-3577	97	1	[	[	X
ejpam-3577	97	2	2	2	X
ejpam-3577	97	3	]	]	X
ejpam-3577	97	4	n.v	n.v	PROPN
ejpam-3577	97	5	.	.	PROPN
ejpam-3577	97	6	lihito	lihito	PROPN
ejpam-3577	97	7	.	.	PUNCT
ejpam-3577	98	1	résolution	résolution	PROPN
ejpam-3577	98	2	des	des	PROPN
ejpam-3577	98	3	problèmes	problèmes	AUX
ejpam-3577	98	4	d’optimisation	d’optimisation	NOUN
ejpam-3577	98	5	pour	pour	VERB
ejpam-3577	98	6	les	les	PROPN
ejpam-3577	98	7	équations	équations	PROPN
ejpam-3577	98	8	intégrofonctionnelles	intégrofonctionnelles	PROPN
ejpam-3577	98	9	.	.	PUNCT
ejpam-3577	99	1	phd	phd	NOUN
ejpam-3577	99	2	thesis	thesis	NOUN
ejpam-3577	99	3	,	,	PUNCT
ejpam-3577	99	4	université	université	NOUN
ejpam-3577	99	5	d’amitié	d’amitié	VERB
ejpam-3577	99	6	des	de	NOUN
ejpam-3577	99	7	peuples	peuple	NOUN
ejpam-3577	99	8	,	,	PUNCT
ejpam-3577	99	9	1988	1988	NUM
ejpam-3577	99	10	.	.	PUNCT
ejpam-3577	100	1	[	[	X
ejpam-3577	100	2	3	3	X
ejpam-3577	100	3	]	]	X
ejpam-3577	100	4	j.l	j.l	PROPN
ejpam-3577	100	5	.	.	PROPN
ejpam-3577	100	6	lions	lion	NOUN
ejpam-3577	100	7	.	.	PUNCT
ejpam-3577	101	1	quelques	quelque	NOUN
ejpam-3577	101	2	méthodes	méthodes	PROPN
ejpam-3577	101	3	de	de	PROPN
ejpam-3577	101	4	résolutions	résolutions	PROPN
ejpam-3577	101	5	des	des	X
ejpam-3577	101	6	problèmes	problèmes	PROPN
ejpam-3577	101	7	aux	aux	PROPN
ejpam-3577	101	8	limites	limites	X
ejpam-3577	101	9	non	non	PROPN
ejpam-3577	101	10	linéaires	linéaire	NOUN
ejpam-3577	101	11	.	.	PUNCT
ejpam-3577	102	1	edition	edition	PROPN
ejpam-3577	102	2	mir	mir	PROPN
ejpam-3577	102	3	,	,	PUNCT
ejpam-3577	102	4	moscou	moscou	PROPN
ejpam-3577	102	5	,	,	PUNCT
ejpam-3577	102	6	1982	1982	NUM
ejpam-3577	102	7	.	.	PUNCT
ejpam-3577	103	1	[	[	X
ejpam-3577	103	2	4	4	NUM
ejpam-3577	103	3	]	]	PUNCT
ejpam-3577	103	4	a.	a.	NOUN
ejpam-3577	103	5	fufner	fufner	PROPN
ejpam-3577	103	6	s.	s.	PROPN
ejpam-3577	103	7	fucik	fucik	PROPN
ejpam-3577	103	8	,	,	PUNCT
ejpam-3577	103	9	o.	o.	PROPN
ejpam-3577	103	10	john	john	PROPN
ejpam-3577	103	11	.	.	PUNCT
ejpam-3577	104	1	function	function	PROPN
ejpam-3577	104	2	spaces	space	VERB
ejpam-3577	104	3	.	.	PUNCT
ejpam-3577	105	1	czechoslovak	czechoslovak	PROPN
ejpam-3577	105	2	academy	academy	PROPN
ejpam-3577	105	3	of	of	ADP
ejpam-3577	105	4	sciences	sciences	PROPN
ejpam-3577	105	5	,	,	PUNCT
ejpam-3577	105	6	prague	prague	NOUN
ejpam-3577	105	7	,	,	PUNCT
ejpam-3577	105	8	1987	1987	NUM
ejpam-3577	105	9	.	.	PUNCT
ejpam-3577	106	1	[	[	X
ejpam-3577	106	2	5	5	NUM
ejpam-3577	106	3	]	]	X
ejpam-3577	106	4	m.f	m.f	PROPN
ejpam-3577	106	5	.	.	PROPN
ejpam-3577	106	6	soukhinine	soukhinine	PROPN
ejpam-3577	106	7	.	.	PUNCT
ejpam-3577	107	1	elements	element	NOUN
ejpam-3577	107	2	d’analyse	d’analyse	PROPN
ejpam-3577	107	3	non	non	ADJ
ejpam-3577	107	4	linéaire	linéaire	PROPN
ejpam-3577	107	5	.	.	PROPN
ejpam-3577	107	6	edition	edition	PROPN
ejpam-3577	107	7	de	de	PROPN
ejpam-3577	107	8	l’université	l’université	PROPN
ejpam-3577	107	9	d’amitié	d’amitié	PROPN
ejpam-3577	107	10	des	des	PROPN
ejpam-3577	107	11	peuples	peuples	X
ejpam-3577	107	12	de	de	X
ejpam-3577	107	13	russie	russie	PROPN
ejpam-3577	107	14	,	,	PUNCT
ejpam-3577	107	15	moscou	moscou	PROPN
ejpam-3577	107	16	,	,	PUNCT
ejpam-3577	107	17	1992	1992	NUM
ejpam-3577	107	18	.	.	PUNCT