id	sid	tid	token	lemma	pos
ejpam-100	1	1	european	european	PROPN
ejpam-100	1	2	journal	journal	PROPN
ejpam-100	1	3	of	of	ADP
ejpam-100	1	4	pure	pure	ADJ
ejpam-100	1	5	and	and	CCONJ
ejpam-100	1	6	applied	apply	VERB
ejpam-100	1	7	mathematics	mathematic	NOUN
ejpam-100	1	8	vol	vol	NOUN
ejpam-100	1	9	.	.	PROPN
ejpam-100	2	1	1	1	NUM
ejpam-100	2	2	,	,	PUNCT
ejpam-100	2	3	no	no	INTJ
ejpam-100	2	4	.	.	NOUN
ejpam-100	2	5	4	4	NUM
ejpam-100	2	6	,	,	PUNCT
ejpam-100	2	7	2008	2008	NUM
ejpam-100	2	8	,	,	PUNCT
ejpam-100	2	9	(	(	PUNCT
ejpam-100	2	10	56	56	NUM
ejpam-100	2	11	-	-	SYM
ejpam-100	2	12	71	71	NUM
ejpam-100	2	13	)	)	PUNCT
ejpam-100	2	14	issn	issn	PROPN
ejpam-100	2	15	1307	1307	NUM
ejpam-100	2	16	-	-	SYM
ejpam-100	2	17	5543	5543	NUM
ejpam-100	3	1	–	–	PUNCT
ejpam-100	3	2	www.ejpam.com	www.ejpam.com	X
ejpam-100	3	3	entropy	entropy	VERB
ejpam-100	3	4	solutions	solution	NOUN
ejpam-100	3	5	of	of	ADP
ejpam-100	3	6	nonlinear	nonlinear	ADJ
ejpam-100	3	7	elliptic	elliptic	ADJ
ejpam-100	3	8	equations	equation	NOUN
ejpam-100	3	9	with	with	ADP
ejpam-100	3	10	measurable	measurable	ADJ
ejpam-100	3	11	boundary	boundary	ADJ
ejpam-100	3	12	conditions	condition	NOUN
ejpam-100	3	13	and	and	CCONJ
ejpam-100	3	14	without	without	ADP
ejpam-100	3	15	strict	strict	ADJ
ejpam-100	3	16	monotonocity	monotonocity	NOUN
ejpam-100	3	17	conditions	condition	NOUN
ejpam-100	3	18	y.	y.	PROPN
ejpam-100	3	19	akdim1,∗	akdim1,∗	PROPN
ejpam-100	3	20	,	,	PUNCT
ejpam-100	3	21	e.	e.	PROPN
ejpam-100	3	22	azroul1	azroul1	PROPN
ejpam-100	3	23	,	,	PUNCT
ejpam-100	3	24	mohamed	mohamed	PROPN
ejpam-100	3	25	rhoudaf2	rhoudaf2	PROPN
ejpam-100	3	26	1	1	NUM
ejpam-100	3	27	faculté	faculté	PROPN
ejpam-100	3	28	poly	poly	NOUN
ejpam-100	3	29	-	-	PUNCT
ejpam-100	3	30	disciplinaire	disciplinaire	NOUN
ejpam-100	3	31	de	de	PROPN
ejpam-100	3	32	taza	taza	PROPN
ejpam-100	3	33	,	,	PUNCT
ejpam-100	3	34	b.p	b.p	PROPN
ejpam-100	3	35	638	638	NUM
ejpam-100	3	36	taza	taza	NOUN
ejpam-100	3	37	,	,	PUNCT
ejpam-100	3	38	maroc	maroc	PROPN
ejpam-100	3	39	2	2	NUM
ejpam-100	3	40	département	département	X
ejpam-100	3	41	de	de	X
ejpam-100	3	42	mathématiques	mathématiques	X
ejpam-100	3	43	et	et	PROPN
ejpam-100	3	44	informatique	informatique	PROPN
ejpam-100	3	45	faculté	faculté	PROPN
ejpam-100	3	46	des	des	PROPN
ejpam-100	3	47	sciences	sciences	PROPN
ejpam-100	3	48	dhar	dhar	PROPN
ejpam-100	3	49	-	-	PUNCT
ejpam-100	3	50	mahraz	mahraz	NOUN
ejpam-100	3	51	,	,	PUNCT
ejpam-100	3	52	b.p	b.p	PROPN
ejpam-100	3	53	1796	1796	NUM
ejpam-100	3	54	atlas	atlas	PROPN
ejpam-100	3	55	fès	fès	PROPN
ejpam-100	3	56	,	,	PUNCT
ejpam-100	3	57	morocco	morocco	PROPN
ejpam-100	3	58	abstract	abstract	NOUN
ejpam-100	3	59	.	.	PUNCT
ejpam-100	4	1	we	we	PRON
ejpam-100	4	2	prove	prove	VERB
ejpam-100	4	3	some	some	DET
ejpam-100	4	4	existence	existence	NOUN
ejpam-100	4	5	results	result	NOUN
ejpam-100	4	6	for	for	ADP
ejpam-100	4	7	nonlinear	nonlinear	ADJ
ejpam-100	4	8	degenerate	degenerate	ADJ
ejpam-100	4	9	elliptic	elliptic	ADJ
ejpam-100	4	10	problems	problem	NOUN
ejpam-100	4	11	of	of	ADP
ejpam-100	4	12	the	the	DET
ejpam-100	4	13	form	form	NOUN
ejpam-100	4	14	au+	au+	PROPN
ejpam-100	4	15	g(x	g(x	PROPN
ejpam-100	4	16	,	,	PUNCT
ejpam-100	4	17	u	u	NOUN
ejpam-100	4	18	)	)	PUNCT
ejpam-100	4	19	=	=	SYM
ejpam-100	4	20	f	f	PROPN
ejpam-100	4	21	−	−	PROPN
ejpam-100	4	22	divf	divf	NOUN
ejpam-100	4	23	,	,	PUNCT
ejpam-100	4	24	where	where	SCONJ
ejpam-100	4	25	a(u	a(u	X
ejpam-100	4	26	)	)	PUNCT
ejpam-100	5	1	=	=	SYM
ejpam-100	5	2	−diva(x	−diva(x	NOUN
ejpam-100	5	3	,	,	PUNCT
ejpam-100	5	4	u,∇u	u,∇u	PROPN
ejpam-100	5	5	)	)	PUNCT
ejpam-100	5	6	is	be	AUX
ejpam-100	5	7	a	a	DET
ejpam-100	5	8	leray	leray	ADJ
ejpam-100	5	9	-	-	PUNCT
ejpam-100	5	10	lions	lion	NOUN
ejpam-100	5	11	,	,	PUNCT
ejpam-100	5	12	operator	operator	NOUN
ejpam-100	5	13	defined	define	VERB
ejpam-100	5	14	form	form	NOUN
ejpam-100	5	15	the	the	DET
ejpam-100	5	16	weighted	weight	VERB
ejpam-100	5	17	sobolev	sobolev	PROPN
ejpam-100	5	18	space	space	PROPN
ejpam-100	5	19	w	w	PROPN
ejpam-100	5	20	1,p	1,p	PROPN
ejpam-100	5	21	0	0	SYM
ejpam-100	5	22	(	(	PUNCT
ejpam-100	5	23	ω	ω	PROPN
ejpam-100	5	24	,	,	PUNCT
ejpam-100	5	25	w	w	NOUN
ejpam-100	5	26	)	)	PUNCT
ejpam-100	5	27	into	into	ADP
ejpam-100	5	28	its	its	PRON
ejpam-100	5	29	dual	dual	NOUN
ejpam-100	5	30	.	.	PUNCT
ejpam-100	6	1	the	the	DET
ejpam-100	6	2	right	right	ADJ
ejpam-100	6	3	hand	hand	NOUN
ejpam-100	6	4	side	side	NOUN
ejpam-100	6	5	,	,	PUNCT
ejpam-100	6	6	f	f	PROPN
ejpam-100	6	7	∈	∈	PROPN
ejpam-100	6	8	l1(ω	l1(ω	PROPN
ejpam-100	6	9	)	)	PUNCT
ejpam-100	6	10	and	and	CCONJ
ejpam-100	6	11	f	f	PROPN
ejpam-100	6	12	∈	∈	PROPN
ejpam-100	6	13	n	n	CCONJ
ejpam-100	6	14	∏	∏	PROPN
ejpam-100	6	15	i=1	i=1	PROPN
ejpam-100	7	1	lp′(ω	lp′(ω	PROPN
ejpam-100	7	2	,	,	PUNCT
ejpam-100	7	3	w∗i	w∗i	PRON
ejpam-100	7	4	)	)	PUNCT
ejpam-100	7	5	.	.	PUNCT
ejpam-100	8	1	note	note	VERB
ejpam-100	8	2	that	that	SCONJ
ejpam-100	8	3	the	the	DET
ejpam-100	8	4	carathéodory	carathéodory	ADJ
ejpam-100	8	5	function	function	NOUN
ejpam-100	8	6	a(x	a(x	PROPN
ejpam-100	8	7	,	,	PUNCT
ejpam-100	8	8	s	s	X
ejpam-100	8	9	,	,	PUNCT
ejpam-100	8	10	ξ	ξ	NOUN
ejpam-100	8	11	)	)	PUNCT
ejpam-100	8	12	satisfies	satisfie	NOUN
ejpam-100	8	13	only	only	ADV
ejpam-100	8	14	the	the	DET
ejpam-100	8	15	large	large	ADJ
ejpam-100	8	16	monotonicity	monotonicity	NOUN
ejpam-100	8	17	instead	instead	ADV
ejpam-100	8	18	of	of	ADP
ejpam-100	8	19	the	the	DET
ejpam-100	8	20	monotonicity	monotonicity	NOUN
ejpam-100	8	21	strict	strict	ADJ
ejpam-100	8	22	condition	condition	NOUN
ejpam-100	8	23	.	.	PUNCT
ejpam-100	9	1	we	we	PRON
ejpam-100	9	2	overcome	overcome	VERB
ejpam-100	9	3	this	this	DET
ejpam-100	9	4	difficulty	difficulty	NOUN
ejpam-100	9	5	by	by	ADP
ejpam-100	9	6	using	use	VERB
ejpam-100	9	7	the	the	DET
ejpam-100	9	8	l1	l1	PROPN
ejpam-100	9	9	-	-	PUNCT
ejpam-100	9	10	version	version	NOUN
ejpam-100	9	11	of	of	ADP
ejpam-100	9	12	minty	minty	PROPN
ejpam-100	9	13	’s	’s	PART
ejpam-100	9	14	lemma	lemma	PROPN
ejpam-100	9	15	.	.	PUNCT
ejpam-100	10	1	ams	ams	PROPN
ejpam-100	10	2	subject	subject	ADJ
ejpam-100	10	3	classifications	classification	NOUN
ejpam-100	10	4	:	:	PUNCT
ejpam-100	10	5	35j60	35j60	NUM
ejpam-100	10	6	.	.	PUNCT
ejpam-100	11	1	key	key	ADJ
ejpam-100	11	2	words	word	NOUN
ejpam-100	11	3	:	:	PUNCT
ejpam-100	11	4	entropy	entropy	NOUN
ejpam-100	11	5	solution	solution	NOUN
ejpam-100	11	6	,	,	PUNCT
ejpam-100	11	7	boundary	boundary	ADJ
ejpam-100	11	8	value	value	NOUN
ejpam-100	11	9	problems	problem	NOUN
ejpam-100	11	10	,	,	PUNCT
ejpam-100	11	11	truncations	truncation	NOUN
ejpam-100	11	12	,	,	PUNCT
ejpam-100	11	13	weighted	weight	VERB
ejpam-100	11	14	sobolev	sobolev	ADJ
ejpam-100	11	15	space	space	NOUN
ejpam-100	11	16	1	1	NUM
ejpam-100	11	17	.	.	PUNCT
ejpam-100	11	18	introduction	introduction	NOUN
ejpam-100	11	19	on	on	ADP
ejpam-100	11	20	a	a	DET
ejpam-100	11	21	bounded	bounded	ADJ
ejpam-100	11	22	open	open	ADJ
ejpam-100	11	23	domain	domain	NOUN
ejpam-100	11	24	ω	ω	PROPN
ejpam-100	11	25	of	of	ADP
ejpam-100	11	26	irn	irn	PROPN
ejpam-100	11	27	n	n	CCONJ
ejpam-100	11	28	≥	≥	NUM
ejpam-100	11	29	2	2	NUM
ejpam-100	11	30	we	we	PRON
ejpam-100	11	31	consider	consider	VERB
ejpam-100	11	32	the	the	DET
ejpam-100	11	33	dirichlet	dirichlet	PROPN
ejpam-100	11	34	problem	problem	NOUN
ejpam-100	11	35	for	for	SCONJ
ejpam-100	11	36	the	the	DET
ejpam-100	11	37	quasilinear	quasilinear	NOUN
ejpam-100	11	38	degenerated	degenerate	VERB
ejpam-100	11	39	elliptic	elliptic	ADJ
ejpam-100	11	40	equation	equation	NOUN
ejpam-100	11	41	,	,	PUNCT
ejpam-100	11	42	¨	¨	NOUN
ejpam-100	11	43	au+	au+	PROPN
ejpam-100	11	44	g(x	g(x	PROPN
ejpam-100	11	45	,	,	PUNCT
ejpam-100	11	46	u	u	NOUN
ejpam-100	11	47	)	)	PUNCT
ejpam-100	11	48	=	=	SYM
ejpam-100	11	49	µ	µ	X
ejpam-100	11	50	in	in	ADP
ejpam-100	11	51	ω	ω	NUM
ejpam-100	11	52	u=	u=	NOUN
ejpam-100	11	53	0	0	NUM
ejpam-100	11	54	on	on	ADP
ejpam-100	11	55	∂ω	∂ω	PROPN
ejpam-100	11	56	,	,	PUNCT
ejpam-100	11	57	(	(	PUNCT
ejpam-100	11	58	1.1	1.1	NUM
ejpam-100	11	59	)	)	PUNCT
ejpam-100	11	60	where	where	SCONJ
ejpam-100	11	61	au	au	ADV
ejpam-100	11	62	=	=	VERB
ejpam-100	11	63	−div(a(x	−div(a(x	NUM
ejpam-100	11	64	,	,	PUNCT
ejpam-100	11	65	u,∇u	u,∇u	PROPN
ejpam-100	11	66	)	)	PUNCT
ejpam-100	11	67	)	)	PUNCT
ejpam-100	11	68	is	be	AUX
ejpam-100	11	69	a	a	DET
ejpam-100	11	70	leray	leray	ADJ
ejpam-100	11	71	-	-	PUNCT
ejpam-100	11	72	lions	lion	NOUN
ejpam-100	11	73	operators	operator	NOUN
ejpam-100	11	74	defined	define	VERB
ejpam-100	11	75	from	from	ADP
ejpam-100	11	76	the	the	DET
ejpam-100	11	77	weighted	weight	VERB
ejpam-100	11	78	sobolev	sobolev	PROPN
ejpam-100	11	79	space	space	PROPN
ejpam-100	11	80	w	w	PROPN
ejpam-100	11	81	1,p	1,p	PROPN
ejpam-100	11	82	0	0	SYM
ejpam-100	11	83	(	(	PUNCT
ejpam-100	11	84	ω	ω	PROPN
ejpam-100	11	85	,	,	PUNCT
ejpam-100	11	86	w	w	NOUN
ejpam-100	11	87	)	)	PUNCT
ejpam-100	11	88	into	into	ADP
ejpam-100	11	89	its	its	PRON
ejpam-100	11	90	dual	dual	ADJ
ejpam-100	11	91	w−1,p′(ω	w−1,p′(ω	NOUN
ejpam-100	11	92	,	,	PUNCT
ejpam-100	11	93	w∗	w∗	PROPN
ejpam-100	11	94	)	)	PUNCT
ejpam-100	12	1	where	where	SCONJ
ejpam-100	12	2	w	w	NOUN
ejpam-100	12	3	=	=	SYM
ejpam-100	12	4	{	{	PUNCT
ejpam-100	12	5	wi	wi	PROPN
ejpam-100	12	6	,	,	PUNCT
ejpam-100	12	7	0	0	NUM
ejpam-100	12	8	≤	≤	NUM
ejpam-100	12	9	i	i	PRON
ejpam-100	12	10	≤	≤	NOUN
ejpam-100	12	11	n	n	CCONJ
ejpam-100	12	12	}	}	PUNCT
ejpam-100	12	13	is	be	AUX
ejpam-100	12	14	collection	collection	NOUN
ejpam-100	12	15	of	of	ADP
ejpam-100	12	16	weight	weight	NOUN
ejpam-100	12	17	functions	function	NOUN
ejpam-100	12	18	on	on	ADP
ejpam-100	12	19	ω	ω	NUM
ejpam-100	12	20	,	,	PUNCT
ejpam-100	12	21	1	1	NUM
ejpam-100	12	22	<	<	X
ejpam-100	12	23	p	p	X
ejpam-100	12	24	<	<	X
ejpam-100	12	25	∞	∞	NOUN
ejpam-100	12	26	and	and	CCONJ
ejpam-100	12	27	w∗	w∗	NOUN
ejpam-100	12	28	=	=	SYM
ejpam-100	12	29	{	{	PUNCT
ejpam-100	12	30	w1−p′	w1−p′	NOUN
ejpam-100	12	31	i	i	PRON
ejpam-100	12	32	,	,	PUNCT
ejpam-100	12	33	0≤	0≤	PUNCT
ejpam-100	12	34	i	i	NOUN
ejpam-100	12	35	≤	≤	NOUN
ejpam-100	12	36	n	n	CCONJ
ejpam-100	12	37	}	}	PUNCT
ejpam-100	12	38	.	.	PUNCT
ejpam-100	13	1	here	here	ADV
ejpam-100	13	2	a(x	a(x	PROPN
ejpam-100	13	3	,	,	PUNCT
ejpam-100	13	4	s	s	X
ejpam-100	13	5	,	,	PUNCT
ejpam-100	13	6	ξ	ξ	X
ejpam-100	13	7	)	)	PUNCT
ejpam-100	13	8	is	be	AUX
ejpam-100	13	9	a	a	DET
ejpam-100	13	10	carathéodory	carathéodory	ADJ
ejpam-100	13	11	function	function	NOUN
ejpam-100	13	12	defined	define	VERB
ejpam-100	13	13	on	on	ADP
ejpam-100	13	14	ω×	ω×	PROPN
ejpam-100	13	15	ir×	ir×	X
ejpam-100	13	16	irn	irn	PROPN
ejpam-100	13	17	and	and	CCONJ
ejpam-100	13	18	g(x	g(x	PROPN
ejpam-100	13	19	,	,	PUNCT
ejpam-100	13	20	u	u	NOUN
ejpam-100	13	21	)	)	PUNCT
ejpam-100	13	22	is	be	AUX
ejpam-100	13	23	a	a	DET
ejpam-100	13	24	nonlinear	nonlinear	ADJ
ejpam-100	13	25	term	term	NOUN
ejpam-100	13	26	which	which	PRON
ejpam-100	13	27	satisfy	satisfy	VERB
ejpam-100	13	28	some	some	DET
ejpam-100	13	29	suitable	suitable	ADJ
ejpam-100	13	30	conditions	condition	NOUN
ejpam-100	13	31	(	(	PUNCT
ejpam-100	13	32	h1)−	h1)−	PROPN
ejpam-100	13	33	(	(	PUNCT
ejpam-100	13	34	h2	h2	NOUN
ejpam-100	13	35	)	)	PUNCT
ejpam-100	13	36	below	below	ADV
ejpam-100	13	37	.	.	PUNCT
ejpam-100	14	1	the	the	DET
ejpam-100	14	2	second	second	ADJ
ejpam-100	14	3	member	member	NOUN
ejpam-100	14	4	µ	µ	PROPN
ejpam-100	14	5	is	be	AUX
ejpam-100	14	6	a	a	DET
ejpam-100	14	7	∗corresponding	∗corresponding	NOUN
ejpam-100	14	8	author	author	NOUN
ejpam-100	14	9	.	.	PUNCT
ejpam-100	15	1	email	email	NOUN
ejpam-100	15	2	addresses	address	NOUN
ejpam-100	15	3	:	:	PUNCT
ejpam-100	15	4	azroul−elhoussine@yahoo.fr	azroul−elhoussine@yahoo.fr	PROPN
ejpam-100	15	5	(	(	PUNCT
ejpam-100	15	6	e.	e.	PROPN
ejpam-100	15	7	azroul	azroul	PROPN
ejpam-100	15	8	)	)	PUNCT
ejpam-100	15	9	,	,	PUNCT
ejpam-100	15	10	rhoudaf−mohamed@yahoo.fr	rhoudaf−mohamed@yahoo.fr	PROPN
ejpam-100	15	11	(	(	PUNCT
ejpam-100	15	12	m.	m.	NOUN
ejpam-100	15	13	rhoudaf	rhoudaf	NOUN
ejpam-100	15	14	)	)	PUNCT
ejpam-100	15	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-100	16	1	56	56	NUM
ejpam-100	16	2	c	c	X
ejpam-100	16	3	©	©	PROPN
ejpam-100	16	4	2008	2008	NUM
ejpam-100	16	5	ejpam	ejpam	VERB
ejpam-100	16	6	all	all	DET
ejpam-100	16	7	rights	right	NOUN
ejpam-100	16	8	reserved	reserve	VERB
ejpam-100	16	9	.	.	PUNCT
ejpam-100	17	1	y.	y.	PROPN
ejpam-100	17	2	akdim	akdim	PROPN
ejpam-100	17	3	,	,	PUNCT
ejpam-100	17	4	e.	e.	PROPN
ejpam-100	17	5	azroul	azroul	PROPN
ejpam-100	17	6	,	,	PUNCT
ejpam-100	17	7	and	and	CCONJ
ejpam-100	17	8	m.	m.	NOUN
ejpam-100	17	9	rhoudaf	rhoudaf	PROPN
ejpam-100	17	10	/	/	SYM
ejpam-100	17	11	eur	eur	PROPN
ejpam-100	17	12	.	.	PUNCT
ejpam-100	18	1	j.	j.	PROPN
ejpam-100	18	2	pure	pure	PROPN
ejpam-100	18	3	appl	appl	PROPN
ejpam-100	18	4	.	.	PROPN
ejpam-100	18	5	math	math	PROPN
ejpam-100	18	6	,	,	PUNCT
ejpam-100	18	7	1	1	NUM
ejpam-100	18	8	(	(	PUNCT
ejpam-100	18	9	2008	2008	NUM
ejpam-100	18	10	)	)	PUNCT
ejpam-100	18	11	,	,	PUNCT
ejpam-100	18	12	(	(	PUNCT
ejpam-100	18	13	56	56	NUM
ejpam-100	18	14	-	-	SYM
ejpam-100	18	15	71	71	NUM
ejpam-100	18	16	)	)	PUNCT
ejpam-100	18	17	57	57	NUM
ejpam-100	18	18	measure	measure	NOUN
ejpam-100	18	19	which	which	PRON
ejpam-100	18	20	belongs	belong	VERB
ejpam-100	18	21	in	in	ADP
ejpam-100	18	22	l1(ω)+w−1,p′(ω	l1(ω)+w−1,p′(ω	PROPN
ejpam-100	18	23	,	,	PUNCT
ejpam-100	18	24	w∗	w∗	PROPN
ejpam-100	18	25	)	)	PUNCT
ejpam-100	18	26	.	.	PUNCT
ejpam-100	19	1	the	the	DET
ejpam-100	19	2	feature	feature	NOUN
ejpam-100	19	3	of	of	ADP
ejpam-100	19	4	this	this	DET
ejpam-100	19	5	paper	paper	NOUN
ejpam-100	19	6	,	,	PUNCT
ejpam-100	19	7	is	be	AUX
ejpam-100	19	8	to	to	PART
ejpam-100	19	9	treat	treat	VERB
ejpam-100	19	10	a	a	DET
ejpam-100	19	11	class	class	NOUN
ejpam-100	19	12	of	of	ADP
ejpam-100	19	13	problems	problem	NOUN
ejpam-100	19	14	for	for	ADP
ejpam-100	19	15	which	which	PRON
ejpam-100	19	16	the	the	DET
ejpam-100	19	17	classical	classical	ADJ
ejpam-100	19	18	monotone	monotone	ADJ
ejpam-100	19	19	operator	operator	NOUN
ejpam-100	19	20	methods	method	NOUN
ejpam-100	19	21	(	(	PUNCT
ejpam-100	19	22	developed	develop	VERB
ejpam-100	19	23	by	by	ADP
ejpam-100	19	24	visik	visik	NOUN
ejpam-100	19	25	[	[	X
ejpam-100	19	26	12	12	NUM
ejpam-100	19	27	]	]	PUNCT
ejpam-100	19	28	,	,	PUNCT
ejpam-100	19	29	minty	minty	ADJ
ejpam-100	19	30	[	[	X
ejpam-100	19	31	11	11	NUM
ejpam-100	19	32	]	]	PUNCT
ejpam-100	19	33	,	,	PUNCT
ejpam-100	19	34	browder	browder	NOUN
ejpam-100	19	35	[	[	X
ejpam-100	19	36	6	6	NUM
ejpam-100	19	37	]	]	PUNCT
ejpam-100	19	38	,	,	PUNCT
ejpam-100	19	39	brézis	brézi	NOUN
ejpam-100	19	40	[	[	X
ejpam-100	19	41	5	5	NUM
ejpam-100	19	42	]	]	PUNCT
ejpam-100	19	43	and	and	CCONJ
ejpam-100	19	44	lions	lion	NOUN
ejpam-100	19	45	[	[	X
ejpam-100	19	46	10	10	NUM
ejpam-100	19	47	]	]	PUNCT
ejpam-100	19	48	in	in	ADP
ejpam-100	19	49	non	non	NOUN
ejpam-100	19	50	weighted	weight	VERB
ejpam-100	19	51	case	case	NOUN
ejpam-100	19	52	and	and	CCONJ
ejpam-100	19	53	by	by	ADP
ejpam-100	19	54	akdim	akdim	NOUN
ejpam-100	19	55	-	-	PUNCT
ejpam-100	19	56	azroul	azroul	NOUN
ejpam-100	20	1	[	[	X
ejpam-100	20	2	2	2	NUM
ejpam-100	20	3	]	]	PUNCT
ejpam-100	20	4	in	in	ADP
ejpam-100	20	5	weighted	weighted	ADJ
ejpam-100	20	6	case	case	NOUN
ejpam-100	20	7	and	and	CCONJ
ejpam-100	20	8	others	other	NOUN
ejpam-100	20	9	)	)	PUNCT
ejpam-100	20	10	do	do	AUX
ejpam-100	20	11	not	not	PART
ejpam-100	20	12	apply	apply	VERB
ejpam-100	20	13	.	.	PUNCT
ejpam-100	21	1	the	the	DET
ejpam-100	21	2	reason	reason	NOUN
ejpam-100	21	3	for	for	ADP
ejpam-100	21	4	this	this	PRON
ejpam-100	21	5	,	,	PUNCT
ejpam-100	21	6	is	be	AUX
ejpam-100	21	7	that	that	PRON
ejpam-100	21	8	a	a	PRON
ejpam-100	21	9	(	(	PUNCT
ejpam-100	21	10	.	.	PUNCT
ejpam-100	21	11	)	)	PUNCT
ejpam-100	21	12	does	do	AUX
ejpam-100	21	13	not	not	PART
ejpam-100	21	14	need	need	VERB
ejpam-100	21	15	to	to	PART
ejpam-100	21	16	satisfy	satisfy	VERB
ejpam-100	21	17	the	the	DET
ejpam-100	21	18	strict	strict	ADJ
ejpam-100	21	19	monotonicity	monotonicity	NOUN
ejpam-100	21	20	condition	condition	NOUN
ejpam-100	21	21	that	that	PRON
ejpam-100	21	22	is	be	AUX
ejpam-100	21	23	,	,	PUNCT
ejpam-100	21	24	〈	〈	ADJ
ejpam-100	21	25	a(x	a(x	PROPN
ejpam-100	21	26	,	,	PUNCT
ejpam-100	21	27	s	s	PROPN
ejpam-100	21	28	,	,	PUNCT
ejpam-100	21	29	ξ)−	ξ)−	PROPN
ejpam-100	21	30	a(x	a(x	PROPN
ejpam-100	21	31	,	,	PUNCT
ejpam-100	21	32	s	s	X
ejpam-100	21	33	,	,	PUNCT
ejpam-100	21	34	η),ξ−η	η),ξ−η	X
ejpam-100	21	35	〉	〉	NOUN
ejpam-100	21	36	>	>	X
ejpam-100	21	37	0	0	NUM
ejpam-100	21	38	for	for	ADP
ejpam-100	21	39	all	all	DET
ejpam-100	21	40	ξ	ξ	PROPN
ejpam-100	21	41	6=	6=	ADP
ejpam-100	21	42	η	η	PROPN
ejpam-100	21	43	∈	∈	PROPN
ejpam-100	21	44	irn	irn	PROPN
ejpam-100	21	45	,	,	PUNCT
ejpam-100	21	46	(	(	PUNCT
ejpam-100	21	47	1.2	1.2	NUM
ejpam-100	21	48	)	)	PUNCT
ejpam-100	21	49	of	of	ADP
ejpam-100	21	50	a	a	DET
ejpam-100	21	51	typical	typical	ADJ
ejpam-100	21	52	leray	leray	ADJ
ejpam-100	21	53	-	-	PUNCT
ejpam-100	21	54	lions	lion	NOUN
ejpam-100	21	55	operator	operator	NOUN
ejpam-100	21	56	but	but	CCONJ
ejpam-100	21	57	only	only	ADV
ejpam-100	21	58	a	a	DET
ejpam-100	21	59	large	large	ADJ
ejpam-100	21	60	monotonicity	monotonicity	NOUN
ejpam-100	21	61	that	that	PRON
ejpam-100	21	62	is	be	AUX
ejpam-100	21	63	〈	〈	PRON
ejpam-100	21	64	a(x	a(x	PROPN
ejpam-100	21	65	,	,	PUNCT
ejpam-100	21	66	s	s	PROPN
ejpam-100	21	67	,	,	PUNCT
ejpam-100	21	68	ξ)−	ξ)−	PROPN
ejpam-100	21	69	a(x	a(x	PROPN
ejpam-100	21	70	,	,	PUNCT
ejpam-100	21	71	s	s	X
ejpam-100	21	72	,	,	PUNCT
ejpam-100	21	73	η),ξ−η	η),ξ−η	PROPN
ejpam-100	21	74	〉	〉	NOUN
ejpam-100	21	75	≥	≥	NUM
ejpam-100	21	76	0	0	NUM
ejpam-100	21	77	for	for	ADP
ejpam-100	21	78	all	all	DET
ejpam-100	21	79	(	(	PUNCT
ejpam-100	21	80	ξ	ξ	PROPN
ejpam-100	21	81	,	,	PUNCT
ejpam-100	21	82	η	η	NOUN
ejpam-100	21	83	)	)	PUNCT
ejpam-100	21	84	∈	∈	PROPN
ejpam-100	21	85	irn	irn	PROPN
ejpam-100	21	86	×	×	PROPN
ejpam-100	21	87	irn	irn	PROPN
ejpam-100	21	88	,	,	PUNCT
ejpam-100	21	89	(	(	PUNCT
ejpam-100	21	90	1.3	1.3	NUM
ejpam-100	21	91	)	)	PUNCT
ejpam-100	21	92	where	where	SCONJ
ejpam-100	21	93	〈	〈	NOUN
ejpam-100	21	94	,	,	PUNCT
ejpam-100	21	95	〉	〉	NOUN
ejpam-100	21	96	denotes	denote	VERB
ejpam-100	21	97	the	the	DET
ejpam-100	21	98	usual	usual	ADJ
ejpam-100	21	99	inner	inner	ADJ
ejpam-100	21	100	product	product	NOUN
ejpam-100	21	101	in	in	ADP
ejpam-100	21	102	irn	irn	PROPN
ejpam-100	21	103	.	.	PUNCT
ejpam-100	22	1	the	the	DET
ejpam-100	22	2	tool	tool	NOUN
ejpam-100	22	3	we	we	PRON
ejpam-100	22	4	use	use	VERB
ejpam-100	22	5	to	to	PART
ejpam-100	22	6	overcome	overcome	VERB
ejpam-100	22	7	the	the	DET
ejpam-100	22	8	difficulty	difficulty	NOUN
ejpam-100	22	9	of	of	ADP
ejpam-100	22	10	the	the	DET
ejpam-100	22	11	not	not	PART
ejpam-100	22	12	strict	strict	ADJ
ejpam-100	22	13	monotonicity	monotonicity	NOUN
ejpam-100	22	14	(	(	PUNCT
ejpam-100	22	15	which	which	PRON
ejpam-100	22	16	can	can	AUX
ejpam-100	22	17	not	not	PART
ejpam-100	22	18	guarantees	guarantee	VERB
ejpam-100	22	19	the	the	DET
ejpam-100	22	20	almost	almost	ADV
ejpam-100	22	21	every	every	PRON
ejpam-100	22	22	where	where	SCONJ
ejpam-100	22	23	convergence	convergence	NOUN
ejpam-100	22	24	of	of	ADP
ejpam-100	22	25	the	the	DET
ejpam-100	22	26	gradient	gradient	NOUN
ejpam-100	22	27	of	of	ADP
ejpam-100	22	28	approximation	approximation	NOUN
ejpam-100	22	29	solution	solution	NOUN
ejpam-100	22	30	)	)	PUNCT
ejpam-100	22	31	is	be	AUX
ejpam-100	22	32	to	to	PART
ejpam-100	22	33	investigate	investigate	VERB
ejpam-100	22	34	some	some	DET
ejpam-100	22	35	techniques	technique	NOUN
ejpam-100	22	36	induced	induce	VERB
ejpam-100	22	37	by	by	ADP
ejpam-100	22	38	minty	minty	PROPN
ejpam-100	22	39	’s	’s	PART
ejpam-100	22	40	lemma	lemma	PROPN
ejpam-100	22	41	.	.	PUNCT
ejpam-100	23	1	the	the	DET
ejpam-100	23	2	approach	approach	NOUN
ejpam-100	23	3	of	of	ADP
ejpam-100	23	4	pseudo	pseudo	NOUN
ejpam-100	23	5	-	-	NOUN
ejpam-100	23	6	monotonicity	monotonicity	NOUN
ejpam-100	23	7	can	can	AUX
ejpam-100	23	8	not	not	PART
ejpam-100	23	9	be	be	AUX
ejpam-100	23	10	used	use	VERB
ejpam-100	23	11	due	due	ADP
ejpam-100	23	12	to	to	ADP
ejpam-100	23	13	the	the	DET
ejpam-100	23	14	fact	fact	NOUN
ejpam-100	23	15	that	that	SCONJ
ejpam-100	23	16	f	f	PROPN
ejpam-100	23	17	∈	∈	PROPN
ejpam-100	23	18	l1(ω	l1(ω	PROPN
ejpam-100	23	19	)	)	PUNCT
ejpam-100	23	20	.	.	PUNCT
ejpam-100	24	1	in	in	ADP
ejpam-100	24	2	order	order	NOUN
ejpam-100	24	3	to	to	PART
ejpam-100	24	4	prove	prove	VERB
ejpam-100	24	5	the	the	DET
ejpam-100	24	6	a.e	a.e	PROPN
ejpam-100	24	7	.	.	PROPN
ejpam-100	24	8	convergence	convergence	NOUN
ejpam-100	24	9	of	of	ADP
ejpam-100	24	10	the	the	DET
ejpam-100	24	11	gradient	gradient	NOUN
ejpam-100	24	12	of	of	ADP
ejpam-100	24	13	the	the	DET
ejpam-100	24	14	approximate	approximate	ADJ
ejpam-100	24	15	solution	solution	NOUN
ejpam-100	24	16	un	un	PROPN
ejpam-100	24	17	,	,	PUNCT
ejpam-100	24	18	the	the	DET
ejpam-100	24	19	authors	author	NOUN
ejpam-100	24	20	in	in	ADP
ejpam-100	24	21	[	[	X
ejpam-100	24	22	4	4	X
ejpam-100	24	23	]	]	PUNCT
ejpam-100	24	24	have	have	AUX
ejpam-100	24	25	show	show	VERB
ejpam-100	24	26	that	that	SCONJ
ejpam-100	24	27	un	un	PROPN
ejpam-100	24	28	is	be	AUX
ejpam-100	24	29	bounded	bound	VERB
ejpam-100	24	30	in	in	ADP
ejpam-100	24	31	the	the	DET
ejpam-100	24	32	marcinkiewicz	marcinkiewicz	ADJ
ejpam-100	24	33	space	space	NOUN
ejpam-100	24	34	.	.	PUNCT
ejpam-100	25	1	while	while	SCONJ
ejpam-100	25	2	in	in	ADP
ejpam-100	25	3	our	our	PRON
ejpam-100	25	4	present	present	ADJ
ejpam-100	25	5	work	work	NOUN
ejpam-100	25	6	we	we	PRON
ejpam-100	25	7	prove	prove	VERB
ejpam-100	25	8	the	the	DET
ejpam-100	25	9	locally	locally	ADV
ejpam-100	25	10	converge	converge	NOUN
ejpam-100	25	11	in	in	ADP
ejpam-100	25	12	measure	measure	NOUN
ejpam-100	25	13	of	of	ADP
ejpam-100	25	14	un	un	PROPN
ejpam-100	25	15	(	(	PUNCT
ejpam-100	25	16	see	see	VERB
ejpam-100	25	17	step	step	NOUN
ejpam-100	25	18	2	2	NUM
ejpam-100	25	19	)	)	PUNCT
ejpam-100	25	20	.	.	PUNCT
ejpam-100	26	1	thus	thus	ADV
ejpam-100	26	2	our	our	PRON
ejpam-100	26	3	aim	aim	NOUN
ejpam-100	26	4	of	of	ADP
ejpam-100	26	5	this	this	DET
ejpam-100	26	6	paper	paper	NOUN
ejpam-100	26	7	,	,	PUNCT
ejpam-100	26	8	is	be	AUX
ejpam-100	26	9	then	then	ADV
ejpam-100	26	10	to	to	PART
ejpam-100	26	11	prove	prove	VERB
ejpam-100	26	12	an	an	DET
ejpam-100	26	13	existence	existence	NOUN
ejpam-100	26	14	of	of	ADP
ejpam-100	26	15	solution	solution	NOUN
ejpam-100	26	16	for	for	ADP
ejpam-100	26	17	the	the	DET
ejpam-100	26	18	following	following	ADJ
ejpam-100	26	19	problem	problem	NOUN
ejpam-100	26	20	,	,	PUNCT
ejpam-100	26	21	(	(	PUNCT
ejpam-100	26	22	p	p	NOUN
ejpam-100	26	23	)	)	PUNCT
ejpam-100	27	1	¨	¨	NOUN
ejpam-100	27	2	−diva(x	−diva(x	X
ejpam-100	27	3	,	,	PUNCT
ejpam-100	27	4	u,∇u	u,∇u	PROPN
ejpam-100	27	5	)	)	PUNCT
ejpam-100	28	1	+	+	CCONJ
ejpam-100	28	2	g(x	g(x	ADJ
ejpam-100	28	3	,	,	PUNCT
ejpam-100	28	4	u	u	NOUN
ejpam-100	28	5	)	)	PUNCT
ejpam-100	28	6	=	=	SYM
ejpam-100	28	7	µ	µ	X
ejpam-100	28	8	in	in	ADP
ejpam-100	28	9	ω	ω	NUM
ejpam-100	28	10	u=	u=	NOUN
ejpam-100	28	11	0	0	NUM
ejpam-100	28	12	on	on	ADP
ejpam-100	28	13	∂ω	∂ω	PROPN
ejpam-100	28	14	where	where	SCONJ
ejpam-100	28	15	µ	µ	X
ejpam-100	28	16	=	=	SYM
ejpam-100	28	17	f	f	PROPN
ejpam-100	28	18	−	−	PROPN
ejpam-100	28	19	divf	divf	NOUN
ejpam-100	28	20	with	with	ADP
ejpam-100	28	21	f	f	PROPN
ejpam-100	28	22	∈	∈	PROPN
ejpam-100	28	23	l1(ω	l1(ω	PROPN
ejpam-100	28	24	)	)	PUNCT
ejpam-100	28	25	and	and	CCONJ
ejpam-100	28	26	f	f	PROPN
ejpam-100	28	27	∈	∈	PROPN
ejpam-100	28	28	πn	πn	INTJ
ejpam-100	28	29	i=1	i=1	PROPN
ejpam-100	29	1	lp′(ω	lp′(ω	PROPN
ejpam-100	29	2	,	,	PUNCT
ejpam-100	29	3	w∗i	w∗i	PRON
ejpam-100	29	4	)	)	PUNCT
ejpam-100	29	5	.in	.in	PUNCT
ejpam-100	29	6	the	the	DET
ejpam-100	29	7	sense	sense	NOUN
ejpam-100	29	8	of	of	ADP
ejpam-100	29	9	entropy	entropy	NOUN
ejpam-100	29	10	solution	solution	NOUN
ejpam-100	29	11	(	(	PUNCT
ejpam-100	29	12	see	see	VERB
ejpam-100	29	13	definition	definition	NOUN
ejpam-100	29	14	2.1	2.1	NUM
ejpam-100	29	15	below	below	ADV
ejpam-100	29	16	)	)	PUNCT
ejpam-100	29	17	note	note	VERB
ejpam-100	29	18	that	that	SCONJ
ejpam-100	29	19	,	,	PUNCT
ejpam-100	29	20	the	the	DET
ejpam-100	29	21	existence	existence	NOUN
ejpam-100	29	22	of	of	ADP
ejpam-100	29	23	such	such	ADJ
ejpam-100	29	24	entropy	entropy	NOUN
ejpam-100	29	25	solution	solution	NOUN
ejpam-100	29	26	is	be	AUX
ejpam-100	29	27	proved	prove	VERB
ejpam-100	29	28	by	by	ADP
ejpam-100	29	29	using	use	VERB
ejpam-100	29	30	only	only	ADV
ejpam-100	29	31	the	the	DET
ejpam-100	29	32	large	large	ADJ
ejpam-100	29	33	monotonicity	monotonicity	NOUN
ejpam-100	29	34	(	(	PUNCT
ejpam-100	29	35	1.3	1.3	NUM
ejpam-100	29	36	)	)	PUNCT
ejpam-100	29	37	.	.	PUNCT
ejpam-100	30	1	this	this	DET
ejpam-100	30	2	paper	paper	NOUN
ejpam-100	30	3	is	be	AUX
ejpam-100	30	4	organized	organize	VERB
ejpam-100	30	5	as	as	SCONJ
ejpam-100	30	6	follows	follow	VERB
ejpam-100	30	7	,	,	PUNCT
ejpam-100	30	8	section	section	NOUN
ejpam-100	30	9	2	2	NUM
ejpam-100	30	10	contains	contain	VERB
ejpam-100	30	11	some	some	DET
ejpam-100	30	12	preliminaries	preliminary	NOUN
ejpam-100	30	13	and	and	CCONJ
ejpam-100	30	14	basic	basic	ADJ
ejpam-100	30	15	assumptions	assumption	NOUN
ejpam-100	30	16	.	.	PUNCT
ejpam-100	31	1	in	in	ADP
ejpam-100	31	2	section	section	NOUN
ejpam-100	31	3	3	3	NUM
ejpam-100	31	4	we	we	PRON
ejpam-100	31	5	give	give	VERB
ejpam-100	31	6	our	our	PRON
ejpam-100	31	7	main	main	ADJ
ejpam-100	31	8	general	general	ADJ
ejpam-100	31	9	result	result	NOUN
ejpam-100	31	10	which	which	PRON
ejpam-100	31	11	is	be	AUX
ejpam-100	31	12	proved	prove	VERB
ejpam-100	31	13	in	in	ADP
ejpam-100	31	14	section	section	NOUN
ejpam-100	31	15	4	4	NUM
ejpam-100	31	16	.	.	PUNCT
ejpam-100	31	17	section	section	NOUN
ejpam-100	31	18	5	5	NUM
ejpam-100	31	19	is	be	AUX
ejpam-100	31	20	devoted	devote	VERB
ejpam-100	31	21	to	to	ADP
ejpam-100	31	22	an	an	DET
ejpam-100	31	23	example	example	NOUN
ejpam-100	31	24	which	which	PRON
ejpam-100	31	25	illustrated	illustrate	VERB
ejpam-100	31	26	our	our	PRON
ejpam-100	31	27	abstract	abstract	ADJ
ejpam-100	31	28	hypotheses	hypothesis	NOUN
ejpam-100	31	29	.	.	PUNCT
ejpam-100	32	1	2	2	X
ejpam-100	32	2	.	.	X
ejpam-100	32	3	basic	basic	ADJ
ejpam-100	32	4	assumptions	assumption	NOUN
ejpam-100	32	5	let	let	VERB
ejpam-100	32	6	ω	ω	NOUN
ejpam-100	32	7	be	be	AUX
ejpam-100	32	8	a	a	DET
ejpam-100	32	9	bounded	bounded	ADJ
ejpam-100	32	10	open	open	ADJ
ejpam-100	32	11	set	set	NOUN
ejpam-100	32	12	of	of	ADP
ejpam-100	32	13	irn	irn	PROPN
ejpam-100	32	14	,	,	PUNCT
ejpam-100	32	15	p	p	NOUN
ejpam-100	32	16	be	be	AUX
ejpam-100	32	17	a	a	DET
ejpam-100	32	18	real	real	ADJ
ejpam-100	32	19	number	number	NOUN
ejpam-100	32	20	such	such	ADJ
ejpam-100	33	1	that	that	SCONJ
ejpam-100	33	2	1	1	NUM
ejpam-100	33	3	<	<	X
ejpam-100	33	4	p	p	X
ejpam-100	33	5	<	<	X
ejpam-100	33	6	∞	∞	PROPN
ejpam-100	33	7	and	and	CCONJ
ejpam-100	33	8	w	w	NOUN
ejpam-100	33	9	=	=	PUNCT
ejpam-100	33	10	{	{	PUNCT
ejpam-100	33	11	wi(x	wi(x	NOUN
ejpam-100	33	12	)	)	PUNCT
ejpam-100	33	13	,	,	PUNCT
ejpam-100	33	14	0	0	NUM
ejpam-100	33	15	≤	≤	NUM
ejpam-100	33	16	i	i	PRON
ejpam-100	33	17	≤	≤	PROPN
ejpam-100	33	18	n	n	CCONJ
ejpam-100	33	19	}	}	PUNCT
ejpam-100	33	20	be	be	AUX
ejpam-100	33	21	a	a	DET
ejpam-100	33	22	vector	vector	NOUN
ejpam-100	33	23	of	of	ADP
ejpam-100	33	24	weight	weight	NOUN
ejpam-100	33	25	functions	function	NOUN
ejpam-100	33	26	,	,	PUNCT
ejpam-100	33	27	i.e.	i.e.	X
ejpam-100	33	28	every	every	DET
ejpam-100	33	29	component	component	NOUN
ejpam-100	33	30	wi(x	wi(x	NOUN
ejpam-100	33	31	)	)	PUNCT
ejpam-100	33	32	is	be	AUX
ejpam-100	33	33	a	a	DET
ejpam-100	33	34	measurable	measurable	ADJ
ejpam-100	33	35	function	function	NOUN
ejpam-100	33	36	which	which	PRON
ejpam-100	33	37	is	be	AUX
ejpam-100	33	38	positive	positive	ADJ
ejpam-100	33	39	a.e	a.e	NOUN
ejpam-100	33	40	.	.	PROPN
ejpam-100	33	41	in	in	ADP
ejpam-100	33	42	ω	ω	PROPN
ejpam-100	33	43	.	.	PUNCT
ejpam-100	34	1	further	far	ADV
ejpam-100	34	2	,	,	PUNCT
ejpam-100	34	3	we	we	PRON
ejpam-100	34	4	suppose	suppose	VERB
ejpam-100	34	5	in	in	ADP
ejpam-100	34	6	all	all	DET
ejpam-100	34	7	our	our	PRON
ejpam-100	34	8	considerations	consideration	NOUN
ejpam-100	34	9	that	that	PRON
ejpam-100	34	10	wi	wi	PROPN
ejpam-100	34	11	∈	∈	PROPN
ejpam-100	34	12	l1	l1	PROPN
ejpam-100	34	13	loc(ω	loc(ω	PROPN
ejpam-100	34	14	)	)	PUNCT
ejpam-100	34	15	,	,	PUNCT
ejpam-100	34	16	(	(	PUNCT
ejpam-100	34	17	2.1	2.1	NUM
ejpam-100	34	18	)	)	PUNCT
ejpam-100	34	19	and	and	CCONJ
ejpam-100	34	20	w	w	ADP
ejpam-100	34	21	−1	−1	NOUN
ejpam-100	34	22	p−1	p−1	PROPN
ejpam-100	34	23	i	i	PROPN
ejpam-100	34	24	∈	∈	PROPN
ejpam-100	34	25	l1	l1	PROPN
ejpam-100	34	26	loc(ω	loc(ω	PROPN
ejpam-100	34	27	)	)	PUNCT
ejpam-100	34	28	,	,	PUNCT
ejpam-100	34	29	(	(	PUNCT
ejpam-100	34	30	2.2	2.2	NUM
ejpam-100	34	31	)	)	PUNCT
ejpam-100	34	32	for	for	ADP
ejpam-100	34	33	any	any	DET
ejpam-100	34	34	0≤	0≤	ADJ
ejpam-100	34	35	i	i	NOUN
ejpam-100	34	36	≤	≤	ADJ
ejpam-100	34	37	n	n	X
ejpam-100	34	38	.	.	PUNCT
ejpam-100	35	1	y.	y.	PROPN
ejpam-100	35	2	akdim	akdim	PROPN
ejpam-100	35	3	,	,	PUNCT
ejpam-100	35	4	e.	e.	PROPN
ejpam-100	35	5	azroul	azroul	PROPN
ejpam-100	35	6	,	,	PUNCT
ejpam-100	35	7	and	and	CCONJ
ejpam-100	35	8	m.	m.	NOUN
ejpam-100	35	9	rhoudaf	rhoudaf	PROPN
ejpam-100	35	10	/	/	SYM
ejpam-100	35	11	eur	eur	PROPN
ejpam-100	35	12	.	.	PUNCT
ejpam-100	36	1	j.	j.	PROPN
ejpam-100	36	2	pure	pure	PROPN
ejpam-100	36	3	appl	appl	PROPN
ejpam-100	36	4	.	.	PROPN
ejpam-100	36	5	math	math	PROPN
ejpam-100	36	6	,	,	PUNCT
ejpam-100	36	7	1	1	NUM
ejpam-100	36	8	(	(	PUNCT
ejpam-100	36	9	2008	2008	NUM
ejpam-100	36	10	)	)	PUNCT
ejpam-100	36	11	,	,	PUNCT
ejpam-100	36	12	(	(	PUNCT
ejpam-100	36	13	56	56	NUM
ejpam-100	36	14	-	-	SYM
ejpam-100	36	15	71	71	NUM
ejpam-100	36	16	)	)	PUNCT
ejpam-100	36	17	58	58	NUM
ejpam-100	36	18	we	we	PRON
ejpam-100	36	19	denote	denote	VERB
ejpam-100	36	20	by	by	ADP
ejpam-100	36	21	w	w	PROPN
ejpam-100	36	22	1,p(ω	1,p(ω	PROPN
ejpam-100	36	23	,	,	PUNCT
ejpam-100	36	24	w	w	PROPN
ejpam-100	36	25	)	)	PUNCT
ejpam-100	36	26	the	the	DET
ejpam-100	36	27	space	space	NOUN
ejpam-100	36	28	of	of	ADP
ejpam-100	36	29	all	all	DET
ejpam-100	36	30	real	real	ADV
ejpam-100	36	31	-	-	PUNCT
ejpam-100	36	32	valued	value	VERB
ejpam-100	36	33	functions	function	NOUN
ejpam-100	36	34	u	u	X
ejpam-100	36	35	∈	∈	PROPN
ejpam-100	36	36	lp(ω	lp(ω	X
ejpam-100	36	37	,	,	PUNCT
ejpam-100	36	38	w0	w0	PROPN
ejpam-100	36	39	)	)	PUNCT
ejpam-100	36	40	such	such	ADJ
ejpam-100	36	41	that	that	SCONJ
ejpam-100	36	42	the	the	DET
ejpam-100	36	43	derivatives	derivative	NOUN
ejpam-100	36	44	in	in	ADP
ejpam-100	36	45	the	the	DET
ejpam-100	36	46	sense	sense	NOUN
ejpam-100	36	47	of	of	ADP
ejpam-100	36	48	distributions	distribution	NOUN
ejpam-100	36	49	fulfil	fulfil	PROPN
ejpam-100	36	50	∂	∂	NUM
ejpam-100	36	51	u	u	NOUN
ejpam-100	36	52	∂	∂	NOUN
ejpam-100	36	53	x	x	NOUN
ejpam-100	36	54	i	i	PRON
ejpam-100	36	55	∈	∈	PROPN
ejpam-100	36	56	lp(ω	lp(ω	PROPN
ejpam-100	36	57	,	,	PUNCT
ejpam-100	36	58	wi	wi	PROPN
ejpam-100	36	59	)	)	PUNCT
ejpam-100	36	60	for	for	ADP
ejpam-100	36	61	all	all	PRON
ejpam-100	36	62	i	i	PRON
ejpam-100	36	63	=	=	NOUN
ejpam-100	36	64	1	1	NUM
ejpam-100	36	65	,	,	PUNCT
ejpam-100	36	66	...	...	PUNCT
ejpam-100	36	67	,	,	PUNCT
ejpam-100	36	68	n	n	X
ejpam-100	36	69	,	,	PUNCT
ejpam-100	36	70	which	which	PRON
ejpam-100	36	71	is	be	AUX
ejpam-100	36	72	a	a	DET
ejpam-100	36	73	banach	banach	NOUN
ejpam-100	36	74	space	space	NOUN
ejpam-100	36	75	under	under	ADP
ejpam-100	36	76	the	the	DET
ejpam-100	36	77	norm	norm	NOUN
ejpam-100	36	78	‖u‖1,p	‖u‖1,p	PROPN
ejpam-100	36	79	,	,	PUNCT
ejpam-100	36	80	w	w	PROPN
ejpam-100	36	81	=	=	PROPN
ejpam-100	36	82			PROPN
ejpam-100	36	83			X
ejpam-100	36	84	∫	∫	PROPN
ejpam-100	36	85	ω	ω	PROPN
ejpam-100	36	86	|u(x)|pw0(x	|u(x)|pw0(x	PROPN
ejpam-100	36	87	)	)	PUNCT
ejpam-100	37	1	d	d	NOUN
ejpam-100	37	2	x	x	PUNCT
ejpam-100	38	1	+	+	NUM
ejpam-100	38	2	n	n	CCONJ
ejpam-100	38	3	∑	∑	PROPN
ejpam-100	38	4	i=1	i=1	PROPN
ejpam-100	38	5	∫	∫	PROPN
ejpam-100	38	6	ω	ω	NUM
ejpam-100	38	7	|	|	NOUN
ejpam-100	38	8	∂	∂	NUM
ejpam-100	38	9	u(x	u(x	NOUN
ejpam-100	38	10	)	)	PUNCT
ejpam-100	38	11	∂	∂	NOUN
ejpam-100	38	12	x	x	NOUN
ejpam-100	38	13	i	i	PRON
ejpam-100	38	14	|pwi(x	|pwi(x	ADJ
ejpam-100	38	15	)	)	PUNCT
ejpam-100	39	1	d	d	NOUN
ejpam-100	39	2	x	x	PUNCT
ejpam-100	39	3			PROPN
ejpam-100	39	4			PROPN
ejpam-100	39	5	1	1	NUM
ejpam-100	39	6	p	p	NOUN
ejpam-100	39	7	.	.	PUNCT
ejpam-100	40	1	(	(	PUNCT
ejpam-100	40	2	2.3	2.3	NUM
ejpam-100	40	3	)	)	PUNCT
ejpam-100	40	4	the	the	DET
ejpam-100	40	5	condition	condition	NOUN
ejpam-100	40	6	(	(	PUNCT
ejpam-100	40	7	2.1	2.1	NUM
ejpam-100	40	8	)	)	PUNCT
ejpam-100	40	9	implies	imply	VERB
ejpam-100	40	10	that	that	SCONJ
ejpam-100	40	11	c∞0	c∞0	PROPN
ejpam-100	40	12	(	(	PUNCT
ejpam-100	40	13	ω	ω	NOUN
ejpam-100	40	14	)	)	PUNCT
ejpam-100	40	15	is	be	AUX
ejpam-100	40	16	a	a	DET
ejpam-100	40	17	subspace	subspace	NOUN
ejpam-100	40	18	of	of	ADP
ejpam-100	40	19	w	w	PROPN
ejpam-100	40	20	1,p(ω	1,p(ω	PROPN
ejpam-100	40	21	,	,	PUNCT
ejpam-100	40	22	w	w	NOUN
ejpam-100	40	23	)	)	PUNCT
ejpam-100	40	24	and	and	CCONJ
ejpam-100	40	25	consequently	consequently	ADV
ejpam-100	40	26	,	,	PUNCT
ejpam-100	40	27	we	we	PRON
ejpam-100	40	28	can	can	AUX
ejpam-100	40	29	introduce	introduce	VERB
ejpam-100	40	30	the	the	DET
ejpam-100	40	31	subspace	subspace	NOUN
ejpam-100	40	32	w	w	PROPN
ejpam-100	40	33	1,p	1,p	PROPN
ejpam-100	40	34	0	0	NUM
ejpam-100	40	35	(	(	PUNCT
ejpam-100	40	36	ω	ω	PROPN
ejpam-100	40	37	,	,	PUNCT
ejpam-100	40	38	w	w	NOUN
ejpam-100	40	39	)	)	PUNCT
ejpam-100	40	40	of	of	ADP
ejpam-100	40	41	w	w	PROPN
ejpam-100	40	42	1,p(ω	1,p(ω	PROPN
ejpam-100	40	43	,	,	PUNCT
ejpam-100	40	44	w	w	NOUN
ejpam-100	40	45	)	)	PUNCT
ejpam-100	40	46	as	as	ADP
ejpam-100	40	47	the	the	DET
ejpam-100	40	48	closure	closure	NOUN
ejpam-100	40	49	of	of	ADP
ejpam-100	40	50	c∞0	c∞0	PROPN
ejpam-100	40	51	(	(	PUNCT
ejpam-100	40	52	ω	ω	NOUN
ejpam-100	40	53	)	)	PUNCT
ejpam-100	40	54	with	with	ADP
ejpam-100	40	55	respect	respect	NOUN
ejpam-100	40	56	to	to	ADP
ejpam-100	40	57	the	the	DET
ejpam-100	40	58	norm	norm	NOUN
ejpam-100	40	59	(	(	PUNCT
ejpam-100	40	60	2.3	2.3	NUM
ejpam-100	40	61	)	)	PUNCT
ejpam-100	40	62	.	.	PUNCT
ejpam-100	41	1	moreover	moreover	ADV
ejpam-100	41	2	,	,	PUNCT
ejpam-100	41	3	the	the	DET
ejpam-100	41	4	condition	condition	NOUN
ejpam-100	41	5	(	(	PUNCT
ejpam-100	41	6	2.2	2.2	NUM
ejpam-100	41	7	)	)	PUNCT
ejpam-100	41	8	implies	imply	VERB
ejpam-100	41	9	that	that	SCONJ
ejpam-100	41	10	w	w	PROPN
ejpam-100	41	11	1,p(ω	1,p(ω	NUM
ejpam-100	41	12	,	,	PUNCT
ejpam-100	41	13	w	w	NOUN
ejpam-100	41	14	)	)	PUNCT
ejpam-100	41	15	as	as	ADV
ejpam-100	41	16	well	well	ADV
ejpam-100	41	17	as	as	ADP
ejpam-100	41	18	w	w	PROPN
ejpam-100	41	19	1,p	1,p	PROPN
ejpam-100	41	20	0	0	SYM
ejpam-100	41	21	(	(	PUNCT
ejpam-100	41	22	ω	ω	PROPN
ejpam-100	41	23	,	,	PUNCT
ejpam-100	41	24	w	w	NOUN
ejpam-100	41	25	)	)	PUNCT
ejpam-100	41	26	are	be	AUX
ejpam-100	41	27	reflexive	reflexive	ADJ
ejpam-100	41	28	banach	banach	NOUN
ejpam-100	41	29	spaces	space	NOUN
ejpam-100	41	30	.	.	PUNCT
ejpam-100	42	1	we	we	PRON
ejpam-100	42	2	recall	recall	VERB
ejpam-100	42	3	that	that	SCONJ
ejpam-100	42	4	the	the	DET
ejpam-100	42	5	dual	dual	ADJ
ejpam-100	42	6	space	space	NOUN
ejpam-100	42	7	of	of	ADP
ejpam-100	42	8	weighted	weight	VERB
ejpam-100	42	9	sobolev	sobolev	NOUN
ejpam-100	42	10	spaces	space	VERB
ejpam-100	42	11	w	w	PROPN
ejpam-100	42	12	1,p	1,p	PROPN
ejpam-100	42	13	0	0	SYM
ejpam-100	42	14	(	(	PUNCT
ejpam-100	42	15	ω	ω	PROPN
ejpam-100	42	16	,	,	PUNCT
ejpam-100	42	17	w	w	NOUN
ejpam-100	42	18	)	)	PUNCT
ejpam-100	42	19	is	be	AUX
ejpam-100	42	20	equivalent	equivalent	ADJ
ejpam-100	42	21	to	to	ADP
ejpam-100	42	22	w−1,p′(ω	w−1,p′(ω	PROPN
ejpam-100	42	23	,	,	PUNCT
ejpam-100	42	24	w∗	w∗	PROPN
ejpam-100	42	25	)	)	PUNCT
ejpam-100	42	26	,	,	PUNCT
ejpam-100	42	27	where	where	SCONJ
ejpam-100	42	28	w∗	w∗	NOUN
ejpam-100	42	29	=	=	SYM
ejpam-100	42	30	{	{	PUNCT
ejpam-100	42	31	w∗i	w∗i	X
ejpam-100	42	32	=	=	PUNCT
ejpam-100	42	33	w1−p′	w1−p′	PROPN
ejpam-100	42	34	i	i	PRON
ejpam-100	42	35	,	,	PUNCT
ejpam-100	42	36	i	i	PRON
ejpam-100	42	37	=	=	NOUN
ejpam-100	42	38	1	1	NUM
ejpam-100	42	39	,	,	PUNCT
ejpam-100	42	40	...	...	PUNCT
ejpam-100	42	41	,	,	PUNCT
ejpam-100	42	42	n	n	CCONJ
ejpam-100	42	43	}	}	PUNCT
ejpam-100	42	44	and	and	CCONJ
ejpam-100	42	45	p′	p′	NOUN
ejpam-100	42	46	is	be	AUX
ejpam-100	42	47	the	the	DET
ejpam-100	42	48	conjugate	conjugate	NOUN
ejpam-100	42	49	of	of	ADP
ejpam-100	42	50	p	p	NOUN
ejpam-100	42	51	i.e.	i.e.	X
ejpam-100	42	52	p′	p′	X
ejpam-100	43	1	=	=	SYM
ejpam-100	43	2	p	p	PROPN
ejpam-100	43	3	p−1	p−1	PROPN
ejpam-100	43	4	(	(	PUNCT
ejpam-100	43	5	for	for	ADP
ejpam-100	43	6	more	more	ADJ
ejpam-100	43	7	details	detail	NOUN
ejpam-100	43	8	we	we	PRON
ejpam-100	43	9	refer	refer	VERB
ejpam-100	43	10	to	to	ADP
ejpam-100	43	11	[	[	X
ejpam-100	43	12	8	8	NUM
ejpam-100	43	13	]	]	NUM
ejpam-100	43	14	)	)	PUNCT
ejpam-100	43	15	.	.	PUNCT
ejpam-100	44	1	assumption(a1	assumption(a1	PROPN
ejpam-100	44	2	)	)	PUNCT
ejpam-100	45	1	we	we	PRON
ejpam-100	45	2	assume	assume	VERB
ejpam-100	45	3	that	that	SCONJ
ejpam-100	45	4	the	the	DET
ejpam-100	45	5	norm	norm	NOUN
ejpam-100	45	6	:	:	PUNCT
ejpam-100	45	7	‖|u‖|=	‖|u‖|=	VERB
ejpam-100	45	8	n	n	ADV
ejpam-100	45	9	∑	∑	PROPN
ejpam-100	45	10	i=1	i=1	PROPN
ejpam-100	45	11	∫	∫	PROPN
ejpam-100	46	1	ω	ω	NUM
ejpam-100	46	2	|	|	NOUN
ejpam-100	46	3	∂	∂	NUM
ejpam-100	46	4	u	u	NOUN
ejpam-100	46	5	∂	∂	NOUN
ejpam-100	46	6	x	x	NOUN
ejpam-100	46	7	i	i	PRON
ejpam-100	46	8	|pwi(x	|pwi(x	ADJ
ejpam-100	46	9	)	)	PUNCT
ejpam-100	47	1	d	d	NOUN
ejpam-100	47	2	x	x	X
ejpam-100	47	3	!	!	PUNCT
ejpam-100	48	1	1	1	NUM
ejpam-100	48	2	p	p	NOUN
ejpam-100	48	3	,	,	PUNCT
ejpam-100	48	4	(	(	PUNCT
ejpam-100	48	5	2.4	2.4	NUM
ejpam-100	48	6	)	)	PUNCT
ejpam-100	48	7	is	be	AUX
ejpam-100	48	8	equivalent	equivalent	ADJ
ejpam-100	48	9	to	to	ADP
ejpam-100	48	10	the	the	DET
ejpam-100	48	11	usual	usual	ADJ
ejpam-100	48	12	norm	norm	NOUN
ejpam-100	48	13	(	(	PUNCT
ejpam-100	48	14	2.3	2.3	NUM
ejpam-100	48	15	)	)	PUNCT
ejpam-100	48	16	,	,	PUNCT
ejpam-100	48	17	and	and	CCONJ
ejpam-100	48	18	there	there	PRON
ejpam-100	48	19	exists	exist	VERB
ejpam-100	48	20	a	a	DET
ejpam-100	48	21	weight	weight	NOUN
ejpam-100	48	22	function	function	NOUN
ejpam-100	48	23	σ(x	σ(x	PROPN
ejpam-100	48	24	)	)	PUNCT
ejpam-100	48	25	on	on	ADP
ejpam-100	48	26	ω	ω	PROPN
ejpam-100	48	27	and	and	CCONJ
ejpam-100	48	28	a	a	DET
ejpam-100	48	29	parameter	parameter	NOUN
ejpam-100	48	30	q	q	NOUN
ejpam-100	48	31	,	,	PUNCT
ejpam-100	48	32	1	1	NUM
ejpam-100	48	33	<	<	X
ejpam-100	48	34	q	q	X
ejpam-100	48	35	<	<	X
ejpam-100	48	36	∞	∞	NUM
ejpam-100	48	37	such	such	ADJ
ejpam-100	48	38	that	that	SCONJ
ejpam-100	48	39	the	the	DET
ejpam-100	48	40	hardy	hardy	ADJ
ejpam-100	48	41	inequality	inequality	NOUN
ejpam-100	48	42	,	,	PUNCT
ejpam-100	48	43	�	�	PROPN
ejpam-100	48	44	∫	∫	PROPN
ejpam-100	48	45	ω	ω	PROPN
ejpam-100	48	46	|u(x)|qσ(x	|u(x)|qσ(x	NUM
ejpam-100	48	47	)	)	PUNCT
ejpam-100	49	1	d	d	NOUN
ejpam-100	49	2	x	x	SYM
ejpam-100	49	3	�	�	PROPN
ejpam-100	49	4	1	1	NUM
ejpam-100	49	5	q	q	PROPN
ejpam-100	49	6	≤	≤	PROPN
ejpam-100	49	7	c	c	NOUN
ejpam-100	49	8	n	n	PROPN
ejpam-100	49	9	∑	∑	PROPN
ejpam-100	49	10	i=1	i=1	PROPN
ejpam-100	49	11	∫	∫	PROPN
ejpam-100	49	12	ω	ω	NUM
ejpam-100	49	13	|	|	NOUN
ejpam-100	49	14	∂	∂	NUM
ejpam-100	49	15	u	u	NOUN
ejpam-100	49	16	∂	∂	NOUN
ejpam-100	49	17	x	x	NOUN
ejpam-100	49	18	i	i	PRON
ejpam-100	49	19	|pwi(x	|pwi(x	ADJ
ejpam-100	49	20	)	)	PUNCT
ejpam-100	50	1	d	d	NOUN
ejpam-100	50	2	x	x	X
ejpam-100	50	3	!	!	PUNCT
ejpam-100	50	4	1	1	NUM
ejpam-100	51	1	p	p	NOUN
ejpam-100	51	2	holds	hold	VERB
ejpam-100	51	3	for	for	SCONJ
ejpam-100	51	4	every	every	DET
ejpam-100	51	5	u	u	NOUN
ejpam-100	51	6	∈w	∈w	VERB
ejpam-100	51	7	1,p	1,p	PROPN
ejpam-100	51	8	0	0	SYM
ejpam-100	51	9	(	(	PUNCT
ejpam-100	51	10	ω	ω	PROPN
ejpam-100	51	11	,	,	PUNCT
ejpam-100	51	12	w	w	NOUN
ejpam-100	51	13	)	)	PUNCT
ejpam-100	51	14	with	with	ADP
ejpam-100	51	15	a	a	DET
ejpam-100	51	16	constant	constant	ADJ
ejpam-100	51	17	c	c	NOUN
ejpam-100	51	18	>	>	X
ejpam-100	51	19	0	0	PROPN
ejpam-100	51	20	independent	independent	ADJ
ejpam-100	51	21	of	of	ADP
ejpam-100	51	22	u.	u.	PROPN
ejpam-100	51	23	moreover	moreover	ADV
ejpam-100	51	24	,	,	PUNCT
ejpam-100	51	25	the	the	DET
ejpam-100	51	26	imbedding	imbedding	NOUN
ejpam-100	51	27	,	,	PUNCT
ejpam-100	51	28	w	w	PROPN
ejpam-100	51	29	1,p	1,p	PROPN
ejpam-100	51	30	0	0	SYM
ejpam-100	51	31	(	(	PUNCT
ejpam-100	51	32	ω	ω	PROPN
ejpam-100	51	33	,	,	PUNCT
ejpam-100	51	34	w	w	PROPN
ejpam-100	51	35	)	)	PUNCT
ejpam-100	51	36	,	,	PUNCT
ejpam-100	51	37	→,→	→,→	PROPN
ejpam-100	51	38	lq(ω	lq(ω	PROPN
ejpam-100	51	39	,	,	PUNCT
ejpam-100	51	40	σ	σ	PROPN
ejpam-100	51	41	)	)	PUNCT
ejpam-100	51	42	,	,	PUNCT
ejpam-100	51	43	(	(	PUNCT
ejpam-100	51	44	2.5	2.5	NUM
ejpam-100	51	45	)	)	PUNCT
ejpam-100	51	46	is	be	AUX
ejpam-100	51	47	compact	compact	ADJ
ejpam-100	51	48	.	.	PUNCT
ejpam-100	52	1	let	let	VERB
ejpam-100	52	2	a	a	PRON
ejpam-100	52	3	be	be	AUX
ejpam-100	52	4	a	a	DET
ejpam-100	52	5	nonlinear	nonlinear	ADJ
ejpam-100	52	6	operator	operator	NOUN
ejpam-100	52	7	from	from	ADP
ejpam-100	52	8	w	w	PROPN
ejpam-100	52	9	1,p	1,p	PROPN
ejpam-100	52	10	0	0	NUM
ejpam-100	53	1	(	(	PUNCT
ejpam-100	53	2	ω	ω	PROPN
ejpam-100	53	3	,	,	PUNCT
ejpam-100	53	4	w	w	NOUN
ejpam-100	53	5	)	)	PUNCT
ejpam-100	53	6	into	into	ADP
ejpam-100	53	7	its	its	PRON
ejpam-100	53	8	dual	dual	ADJ
ejpam-100	53	9	w−1,p′(ω	w−1,p′(ω	NOUN
ejpam-100	53	10	,	,	PUNCT
ejpam-100	53	11	w∗	w∗	PROPN
ejpam-100	53	12	)	)	PUNCT
ejpam-100	53	13	defined	define	VERB
ejpam-100	53	14	as	as	ADP
ejpam-100	53	15	a(u	a(u	NOUN
ejpam-100	53	16	)	)	PUNCT
ejpam-100	54	1	=	=	NOUN
ejpam-100	54	2	−div(a(x	−div(a(x	NUM
ejpam-100	54	3	,	,	PUNCT
ejpam-100	54	4	u,∇u	u,∇u	PROPN
ejpam-100	54	5	)	)	PUNCT
ejpam-100	54	6	)	)	PUNCT
ejpam-100	54	7	where	where	SCONJ
ejpam-100	54	8	a(x	a(x	NOUN
ejpam-100	54	9	,	,	PUNCT
ejpam-100	54	10	s	s	X
ejpam-100	54	11	,	,	PUNCT
ejpam-100	54	12	ξ	ξ	NOUN
ejpam-100	54	13	)	)	PUNCT
ejpam-100	54	14	:	:	PUNCT
ejpam-100	54	15	ω×	ω×	X
ejpam-100	54	16	ir×	ir×	X
ejpam-100	54	17	irn	irn	PROPN
ejpam-100	54	18	→	→	SYM
ejpam-100	54	19	irn	irn	PROPN
ejpam-100	54	20	is	be	AUX
ejpam-100	54	21	a	a	DET
ejpam-100	54	22	caradhéodory	caradhéodory	NOUN
ejpam-100	54	23	vector	vector	NOUN
ejpam-100	54	24	-	-	PUNCT
ejpam-100	54	25	valued	value	VERB
ejpam-100	54	26	function	function	NOUN
ejpam-100	54	27	satisfies	satisfy	VERB
ejpam-100	54	28	the	the	DET
ejpam-100	54	29	following	following	ADJ
ejpam-100	54	30	assumption	assumption	NOUN
ejpam-100	54	31	.	.	PUNCT
ejpam-100	55	1	y.	y.	PROPN
ejpam-100	55	2	akdim	akdim	PROPN
ejpam-100	55	3	,	,	PUNCT
ejpam-100	55	4	e.	e.	PROPN
ejpam-100	55	5	azroul	azroul	PROPN
ejpam-100	55	6	,	,	PUNCT
ejpam-100	55	7	and	and	CCONJ
ejpam-100	55	8	m.	m.	NOUN
ejpam-100	55	9	rhoudaf	rhoudaf	PROPN
ejpam-100	55	10	/	/	SYM
ejpam-100	55	11	eur	eur	PROPN
ejpam-100	55	12	.	.	PUNCT
ejpam-100	56	1	j.	j.	PROPN
ejpam-100	56	2	pure	pure	PROPN
ejpam-100	56	3	appl	appl	PROPN
ejpam-100	56	4	.	.	PROPN
ejpam-100	56	5	math	math	PROPN
ejpam-100	56	6	,	,	PUNCT
ejpam-100	56	7	1	1	NUM
ejpam-100	56	8	(	(	PUNCT
ejpam-100	56	9	2008	2008	NUM
ejpam-100	56	10	)	)	PUNCT
ejpam-100	56	11	,	,	PUNCT
ejpam-100	56	12	(	(	PUNCT
ejpam-100	56	13	56	56	NUM
ejpam-100	56	14	-	-	SYM
ejpam-100	56	15	71	71	NUM
ejpam-100	56	16	)	)	PUNCT
ejpam-100	56	17	59	59	NUM
ejpam-100	56	18	assumption(a2	assumption(a2	NOUN
ejpam-100	56	19	)	)	PUNCT
ejpam-100	56	20	for	for	ADP
ejpam-100	56	21	i	i	PROPN
ejpam-100	56	22	=	=	NOUN
ejpam-100	56	23	1	1	NUM
ejpam-100	56	24	,	,	PUNCT
ejpam-100	56	25	...	...	PUNCT
ejpam-100	56	26	,	,	PUNCT
ejpam-100	56	27	n	n	PROPN
ejpam-100	56	28	|ai(x	|ai(x	NUM
ejpam-100	56	29	,	,	PUNCT
ejpam-100	56	30	s	s	X
ejpam-100	56	31	,	,	PUNCT
ejpam-100	56	32	ξ)|	ξ)|	ADJ
ejpam-100	56	33	≤	≤	NOUN
ejpam-100	56	34	βw	βw	ADP
ejpam-100	56	35	1	1	NUM
ejpam-100	56	36	p	p	NOUN
ejpam-100	56	37	i	i	PRON
ejpam-100	56	38	(	(	PUNCT
ejpam-100	56	39	x	x	X
ejpam-100	56	40	)	)	PUNCT
ejpam-100	57	1	[	[	X
ejpam-100	57	2	k(x	k(x	X
ejpam-100	57	3	)	)	PUNCT
ejpam-100	58	1	+	+	NOUN
ejpam-100	58	2	σ	σ	PROPN
ejpam-100	58	3	1	1	NUM
ejpam-100	58	4	p′	p′	NOUN
ejpam-100	58	5	|s|	|s|	PROPN
ejpam-100	58	6	q	q	PROPN
ejpam-100	58	7	p′	p′	NOUN
ejpam-100	58	8	+	+	CCONJ
ejpam-100	58	9	n	n	CCONJ
ejpam-100	58	10	∑	∑	PROPN
ejpam-100	58	11	j=1	j=1	PROPN
ejpam-100	58	12	w	w	PROPN
ejpam-100	58	13	1	1	NUM
ejpam-100	58	14	p′	p′	NUM
ejpam-100	58	15	j	j	PROPN
ejpam-100	58	16	(	(	PUNCT
ejpam-100	58	17	x)|ξ	x)|ξ	PROPN
ejpam-100	58	18	j|p−1	j|p−1	PROPN
ejpam-100	58	19	]	]	X
ejpam-100	58	20	,	,	PUNCT
ejpam-100	58	21	(	(	PUNCT
ejpam-100	58	22	2.6	2.6	NUM
ejpam-100	58	23	)	)	PUNCT
ejpam-100	58	24	for	for	ADP
ejpam-100	58	25	a.e	a.e	PROPN
ejpam-100	58	26	.	.	PROPN
ejpam-100	58	27	,	,	PUNCT
ejpam-100	58	28	x	x	X
ejpam-100	58	29	∈	∈	PROPN
ejpam-100	58	30	ω	ω	PROPN
ejpam-100	58	31	,	,	PUNCT
ejpam-100	58	32	all	all	PRON
ejpam-100	58	33	(	(	PUNCT
ejpam-100	58	34	s	s	PROPN
ejpam-100	58	35	,	,	PUNCT
ejpam-100	58	36	ξ	ξ	NOUN
ejpam-100	58	37	)	)	PUNCT
ejpam-100	58	38	∈	∈	PROPN
ejpam-100	59	1	ir×	ir×	ADJ
ejpam-100	59	2	irn	irn	PROPN
ejpam-100	59	3	,	,	PUNCT
ejpam-100	59	4	some	some	DET
ejpam-100	59	5	function	function	NOUN
ejpam-100	59	6	k(x	k(x	PROPN
ejpam-100	59	7	)	)	PUNCT
ejpam-100	59	8	∈	∈	PROPN
ejpam-100	59	9	lp′(ω	lp′(ω	PROPN
ejpam-100	59	10	)	)	PUNCT
ejpam-100	59	11	(	(	PUNCT
ejpam-100	59	12	1	1	NUM
ejpam-100	59	13	p	p	NOUN
ejpam-100	59	14	+	+	NOUN
ejpam-100	59	15	1	1	NUM
ejpam-100	59	16	p′	p′	NOUN
ejpam-100	59	17	=	=	SYM
ejpam-100	59	18	1	1	NUM
ejpam-100	59	19	)	)	PUNCT
ejpam-100	59	20	and	and	CCONJ
ejpam-100	59	21	β	β	X
ejpam-100	59	22	>	>	X
ejpam-100	59	23	0	0	X
ejpam-100	59	24	.	.	PUNCT
ejpam-100	60	1	here	here	ADV
ejpam-100	60	2	σ	σ	PROPN
ejpam-100	60	3	and	and	CCONJ
ejpam-100	60	4	q	q	NOUN
ejpam-100	60	5	are	be	AUX
ejpam-100	60	6	as	as	ADP
ejpam-100	60	7	in	in	ADP
ejpam-100	60	8	(	(	PUNCT
ejpam-100	60	9	a1	a1	NOUN
ejpam-100	60	10	)	)	PUNCT
ejpam-100	60	11	.	.	PUNCT
ejpam-100	61	1	〈	〈	NOUN
ejpam-100	61	2	a(x	a(x	PROPN
ejpam-100	61	3	,	,	PUNCT
ejpam-100	61	4	s	s	PROPN
ejpam-100	61	5	,	,	PUNCT
ejpam-100	61	6	ξ)−	ξ)−	PROPN
ejpam-100	61	7	a(x	a(x	PROPN
ejpam-100	61	8	,	,	PUNCT
ejpam-100	61	9	s	s	X
ejpam-100	61	10	,	,	PUNCT
ejpam-100	61	11	η),ξ−η	η),ξ−η	PROPN
ejpam-100	61	12	〉	〉	NOUN
ejpam-100	61	13	≥	≥	NUM
ejpam-100	61	14	0	0	NUM
ejpam-100	61	15	for	for	ADP
ejpam-100	61	16	all	all	DET
ejpam-100	61	17	(	(	PUNCT
ejpam-100	61	18	ξ	ξ	PROPN
ejpam-100	61	19	,	,	PUNCT
ejpam-100	61	20	η	η	NOUN
ejpam-100	61	21	)	)	PUNCT
ejpam-100	61	22	∈	∈	PROPN
ejpam-100	61	23	irn	irn	PROPN
ejpam-100	61	24	×	×	PROPN
ejpam-100	61	25	irn	irn	PROPN
ejpam-100	61	26	,	,	PUNCT
ejpam-100	61	27	(	(	PUNCT
ejpam-100	61	28	2.7	2.7	NUM
ejpam-100	61	29	)	)	PUNCT
ejpam-100	61	30	〈	〈	NOUN
ejpam-100	61	31	a(x	a(x	NOUN
ejpam-100	61	32	,	,	PUNCT
ejpam-100	61	33	s	s	X
ejpam-100	61	34	,	,	PUNCT
ejpam-100	61	35	ξ),ξ	ξ),ξ	PROPN
ejpam-100	61	36	〉	〉	X
ejpam-100	61	37	≥	≥	NUM
ejpam-100	61	38	α	α	PROPN
ejpam-100	61	39	n	n	PROPN
ejpam-100	61	40	∑	∑	PROPN
ejpam-100	61	41	i=1	i=1	PROPN
ejpam-100	61	42	wi|ξi|p	wi|ξi|p	NOUN
ejpam-100	61	43	,	,	PUNCT
ejpam-100	61	44	(	(	PUNCT
ejpam-100	61	45	2.8	2.8	NUM
ejpam-100	61	46	)	)	PUNCT
ejpam-100	61	47	where	where	SCONJ
ejpam-100	61	48	α	α	NOUN
ejpam-100	61	49	is	be	AUX
ejpam-100	61	50	strictly	strictly	ADV
ejpam-100	61	51	positive	positive	ADJ
ejpam-100	61	52	constant	constant	ADJ
ejpam-100	61	53	.	.	PUNCT
ejpam-100	62	1	moreover	moreover	ADV
ejpam-100	62	2	,	,	PUNCT
ejpam-100	62	3	the	the	DET
ejpam-100	62	4	function	function	NOUN
ejpam-100	62	5	g(x	g(x	PROPN
ejpam-100	62	6	,	,	PUNCT
ejpam-100	62	7	s	s	X
ejpam-100	62	8	)	)	PUNCT
ejpam-100	62	9	is	be	AUX
ejpam-100	62	10	a	a	DET
ejpam-100	62	11	carathéodory	carathéodory	ADJ
ejpam-100	62	12	function	function	NOUN
ejpam-100	62	13	satisfying	satisfy	VERB
ejpam-100	62	14	g(x	g(x	PROPN
ejpam-100	62	15	,	,	PUNCT
ejpam-100	62	16	s)s	s)s	X
ejpam-100	62	17	≥	≥	NOUN
ejpam-100	62	18	0	0	NUM
ejpam-100	62	19	.	.	PUNCT
ejpam-100	63	1	(	(	PUNCT
ejpam-100	63	2	2.9	2.9	NUM
ejpam-100	63	3	)	)	PUNCT
ejpam-100	63	4	sup	sup	NOUN
ejpam-100	63	5	|s|≤n	|s|≤n	PROPN
ejpam-100	63	6	|g(x	|g(x	PROPN
ejpam-100	63	7	,	,	PUNCT
ejpam-100	63	8	s)|=	s)|=	PROPN
ejpam-100	63	9	hn(x	hn(x	NUM
ejpam-100	63	10	)	)	PUNCT
ejpam-100	63	11	∈	∈	PROPN
ejpam-100	63	12	l1(ω	l1(ω	PROPN
ejpam-100	63	13	)	)	PUNCT
ejpam-100	63	14	(	(	PUNCT
ejpam-100	63	15	2.10	2.10	NUM
ejpam-100	63	16	)	)	PUNCT
ejpam-100	63	17	we	we	PRON
ejpam-100	63	18	recall	recall	VERB
ejpam-100	63	19	that	that	SCONJ
ejpam-100	63	20	,	,	PUNCT
ejpam-100	63	21	for	for	ADP
ejpam-100	63	22	k	k	PROPN
ejpam-100	63	23	>	>	X
ejpam-100	63	24	1	1	NUM
ejpam-100	63	25	and	and	CCONJ
ejpam-100	63	26	s	s	X
ejpam-100	63	27	in	in	ADP
ejpam-100	63	28	ir	ir	PROPN
ejpam-100	63	29	,	,	PUNCT
ejpam-100	63	30	the	the	DET
ejpam-100	63	31	truncation	truncation	NOUN
ejpam-100	63	32	is	be	AUX
ejpam-100	63	33	defined	define	VERB
ejpam-100	63	34	as	as	ADP
ejpam-100	63	35	tk(s	tk(s	PRON
ejpam-100	63	36	)	)	PUNCT
ejpam-100	63	37	=	=	PUNCT
ejpam-100	64	1	¨	¨	NOUN
ejpam-100	64	2	s	s	X
ejpam-100	64	3	if	if	SCONJ
ejpam-100	64	4	|s|	|s|	NOUN
ejpam-100	64	5	≤	≤	NUM
ejpam-100	64	6	k	k	X
ejpam-100	64	7	k	k	PROPN
ejpam-100	64	8	s	s	PROPN
ejpam-100	64	9	|s|	|s|	PROPN
ejpam-100	64	10	if	if	SCONJ
ejpam-100	64	11	|s|	|s|	PROPN
ejpam-100	64	12	>	>	PROPN
ejpam-100	64	13	k.	k.	PROPN
ejpam-100	64	14	lemma	lemma	PROPN
ejpam-100	64	15	2.1	2.1	NUM
ejpam-100	64	16	.	.	PUNCT
ejpam-100	65	1	(	(	PUNCT
ejpam-100	65	2	cf	cf	NOUN
ejpam-100	65	3	.	.	PUNCT
ejpam-100	66	1	[	[	X
ejpam-100	66	2	1	1	NUM
ejpam-100	66	3	]	]	PUNCT
ejpam-100	66	4	)	)	PUNCT
ejpam-100	66	5	assume	assume	VERB
ejpam-100	66	6	that	that	SCONJ
ejpam-100	66	7	(	(	PUNCT
ejpam-100	66	8	a1	a1	NOUN
ejpam-100	66	9	)	)	PUNCT
ejpam-100	66	10	holds	hold	VERB
ejpam-100	66	11	.	.	PUNCT
ejpam-100	67	1	let	let	AUX
ejpam-100	67	2	(	(	PUNCT
ejpam-100	67	3	un	un	VERB
ejpam-100	67	4	)	)	PUNCT
ejpam-100	67	5	be	be	VERB
ejpam-100	67	6	a	a	DET
ejpam-100	67	7	sequence	sequence	NOUN
ejpam-100	67	8	of	of	ADP
ejpam-100	67	9	w	w	PROPN
ejpam-100	67	10	1,p	1,p	PROPN
ejpam-100	67	11	0	0	NUM
ejpam-100	67	12	(	(	PUNCT
ejpam-100	67	13	ω	ω	PROPN
ejpam-100	67	14	,	,	PUNCT
ejpam-100	67	15	w	w	NOUN
ejpam-100	67	16	)	)	PUNCT
ejpam-100	67	17	such	such	ADJ
ejpam-100	67	18	that	that	SCONJ
ejpam-100	67	19	un	un	PROPN
ejpam-100	67	20	*	*	PUNCT
ejpam-100	67	21	u	u	PROPN
ejpam-100	67	22	weakly	weakly	ADV
ejpam-100	67	23	in	in	ADP
ejpam-100	67	24	w	w	PROPN
ejpam-100	67	25	1,p	1,p	PROPN
ejpam-100	67	26	0	0	NUM
ejpam-100	67	27	(	(	PUNCT
ejpam-100	67	28	ω	ω	PROPN
ejpam-100	67	29	,	,	PUNCT
ejpam-100	67	30	w	w	PROPN
ejpam-100	67	31	)	)	PUNCT
ejpam-100	67	32	.	.	PUNCT
ejpam-100	68	1	then	then	ADV
ejpam-100	68	2	tk(un	tk(un	VERB
ejpam-100	68	3	)	)	PUNCT
ejpam-100	68	4	*	*	PUNCT
ejpam-100	68	5	tk(u	tk(u	NOUN
ejpam-100	68	6	)	)	PUNCT
ejpam-100	68	7	weakly	weakly	ADV
ejpam-100	68	8	in	in	ADP
ejpam-100	68	9	w	w	PROPN
ejpam-100	68	10	1,p	1,p	PROPN
ejpam-100	68	11	0	0	NUM
ejpam-100	68	12	(	(	PUNCT
ejpam-100	68	13	ω	ω	PROPN
ejpam-100	68	14	,	,	PUNCT
ejpam-100	68	15	w	w	NOUN
ejpam-100	68	16	)	)	PUNCT
ejpam-100	68	17	.	.	PUNCT
ejpam-100	69	1	3	3	X
ejpam-100	69	2	.	.	X
ejpam-100	69	3	main	main	ADJ
ejpam-100	69	4	existence	existence	NOUN
ejpam-100	69	5	theorem	theorem	NOUN
ejpam-100	69	6	consider	consider	VERB
ejpam-100	69	7	the	the	DET
ejpam-100	69	8	following	follow	VERB
ejpam-100	69	9	problem	problem	NOUN
ejpam-100	69	10	:	:	PUNCT
ejpam-100	69	11	(	(	PUNCT
ejpam-100	69	12	p	p	NOUN
ejpam-100	69	13	)	)	PUNCT
ejpam-100	69	14	¨	¨	NOUN
ejpam-100	69	15	−diva(x	−diva(x	X
ejpam-100	69	16	,	,	PUNCT
ejpam-100	69	17	u,∇u	u,∇u	PROPN
ejpam-100	69	18	)	)	PUNCT
ejpam-100	70	1	+	+	CCONJ
ejpam-100	70	2	g(x	g(x	ADJ
ejpam-100	70	3	,	,	PUNCT
ejpam-100	70	4	u	u	NOUN
ejpam-100	70	5	)	)	PUNCT
ejpam-100	70	6	=	=	SYM
ejpam-100	71	1	f	f	PROPN
ejpam-100	71	2	−	−	PROPN
ejpam-100	71	3	div(f	div(f	PROPN
ejpam-100	71	4	)	)	PUNCT
ejpam-100	71	5	in	in	ADP
ejpam-100	71	6	ω	ω	NUM
ejpam-100	71	7	u=	u=	NOUN
ejpam-100	71	8	0	0	NUM
ejpam-100	71	9	on	on	ADP
ejpam-100	71	10	∂ω	∂ω	PROPN
ejpam-100	72	1	where	where	SCONJ
ejpam-100	72	2	f	f	PROPN
ejpam-100	72	3	∈	∈	PROPN
ejpam-100	72	4	l1(ω	l1(ω	PROPN
ejpam-100	72	5	)	)	PUNCT
ejpam-100	72	6	and	and	CCONJ
ejpam-100	72	7	f	f	PROPN
ejpam-100	72	8	∈	∈	PROPN
ejpam-100	72	9	n	n	CCONJ
ejpam-100	72	10	∏	∏	PROPN
ejpam-100	72	11	i=1	i=1	PROPN
ejpam-100	73	1	lp′(ω	lp′(ω	PROPN
ejpam-100	73	2	,	,	PUNCT
ejpam-100	73	3	w∗i	w∗i	PRON
ejpam-100	73	4	)	)	PUNCT
ejpam-100	73	5	.	.	PUNCT
ejpam-100	74	1	definition	definition	NOUN
ejpam-100	74	2	3.1	3.1	NUM
ejpam-100	74	3	.	.	PUNCT
ejpam-100	74	4	.	.	PUNCT
ejpam-100	75	1	an	an	DET
ejpam-100	75	2	entropy	entropy	NOUN
ejpam-100	75	3	solution	solution	NOUN
ejpam-100	75	4	of	of	ADP
ejpam-100	75	5	(	(	PUNCT
ejpam-100	75	6	p	p	NOUN
ejpam-100	75	7	)	)	PUNCT
ejpam-100	75	8	is	be	AUX
ejpam-100	75	9	a	a	DET
ejpam-100	75	10	measurable	measurable	ADJ
ejpam-100	75	11	function	function	NOUN
ejpam-100	75	12	u	u	NOUN
ejpam-100	75	13	such	such	ADJ
ejpam-100	75	14	that	that	SCONJ
ejpam-100	75	15	tk(u	tk(u	NUM
ejpam-100	75	16	)	)	PUNCT
ejpam-100	75	17	belongs	belong	VERB
ejpam-100	75	18	to	to	ADP
ejpam-100	75	19	w	w	PROPN
ejpam-100	75	20	1,p	1,p	PROPN
ejpam-100	75	21	0	0	NUM
ejpam-100	75	22	(	(	PUNCT
ejpam-100	75	23	ω	ω	PROPN
ejpam-100	75	24	,	,	PUNCT
ejpam-100	75	25	w	w	NOUN
ejpam-100	75	26	)	)	PUNCT
ejpam-100	75	27	for	for	ADP
ejpam-100	75	28	every	every	DET
ejpam-100	75	29	k	k	PROPN
ejpam-100	75	30	>	>	X
ejpam-100	75	31	0	0	PUNCT
ejpam-100	75	32	and	and	CCONJ
ejpam-100	75	33	such	such	ADJ
ejpam-100	76	1	that	that	DET
ejpam-100	76	2	∫	∫	PROPN
ejpam-100	76	3	ω	ω	PROPN
ejpam-100	76	4	〈	〈	NOUN
ejpam-100	76	5	a(x	a(x	PROPN
ejpam-100	76	6	,	,	PUNCT
ejpam-100	76	7	u,∇u),∇tk[u−ϕ	u,∇u),∇tk[u−ϕ	NOUN
ejpam-100	76	8	]	]	X
ejpam-100	76	9	〉	〉	NOUN
ejpam-100	76	10	d	d	NOUN
ejpam-100	76	11	x+	x+	PROPN
ejpam-100	76	12	∫	∫	PROPN
ejpam-100	76	13	ω	ω	NUM
ejpam-100	76	14	g(x	g(x	PROPN
ejpam-100	76	15	,	,	PUNCT
ejpam-100	76	16	u)tk[u−ϕ	u)tk[u−ϕ	VERB
ejpam-100	76	17	]	]	X
ejpam-100	77	1	d	d	NOUN
ejpam-100	77	2	x	x	SYM
ejpam-100	77	3	=	=	SYM
ejpam-100	77	4	∫	∫	PROPN
ejpam-100	77	5	ω	ω	PROPN
ejpam-100	77	6	f	f	PROPN
ejpam-100	77	7	tk[u−ϕ	tk[u−ϕ	PROPN
ejpam-100	77	8	]	]	X
ejpam-100	78	1	d	d	X
ejpam-100	78	2	x+	x+	SYM
ejpam-100	78	3	∫	∫	PROPN
ejpam-100	78	4	ω	ω	PROPN
ejpam-100	78	5	〈	〈	PROPN
ejpam-100	78	6	f,∇tk[u−ϕ	f,∇tk[u−ϕ	PROPN
ejpam-100	78	7	]	]	SYM
ejpam-100	78	8	〉	〉	NOUN
ejpam-100	78	9	d	d	NOUN
ejpam-100	78	10	x	x	PUNCT
ejpam-100	78	11	for	for	ADP
ejpam-100	78	12	every	every	DET
ejpam-100	78	13	ϕ	ϕ	NOUN
ejpam-100	78	14	∈w	∈w	PROPN
ejpam-100	78	15	1,p	1,p	PROPN
ejpam-100	78	16	0	0	SYM
ejpam-100	78	17	(	(	PUNCT
ejpam-100	78	18	ω	ω	PROPN
ejpam-100	78	19	,	,	PUNCT
ejpam-100	78	20	w)∩	w)∩	X
ejpam-100	78	21	l∞(ω	l∞(ω	ADJ
ejpam-100	78	22	)	)	PUNCT
ejpam-100	78	23	.	.	PUNCT
ejpam-100	79	1	y.	y.	PROPN
ejpam-100	79	2	akdim	akdim	PROPN
ejpam-100	79	3	,	,	PUNCT
ejpam-100	79	4	e.	e.	PROPN
ejpam-100	79	5	azroul	azroul	PROPN
ejpam-100	79	6	,	,	PUNCT
ejpam-100	79	7	and	and	CCONJ
ejpam-100	79	8	m.	m.	NOUN
ejpam-100	79	9	rhoudaf	rhoudaf	PROPN
ejpam-100	79	10	/	/	SYM
ejpam-100	79	11	eur	eur	PROPN
ejpam-100	79	12	.	.	PUNCT
ejpam-100	80	1	j.	j.	PROPN
ejpam-100	80	2	pure	pure	PROPN
ejpam-100	80	3	appl	appl	PROPN
ejpam-100	80	4	.	.	PROPN
ejpam-100	80	5	math	math	PROPN
ejpam-100	80	6	,	,	PUNCT
ejpam-100	80	7	1	1	NUM
ejpam-100	80	8	(	(	PUNCT
ejpam-100	80	9	2008	2008	NUM
ejpam-100	80	10	)	)	PUNCT
ejpam-100	80	11	,	,	PUNCT
ejpam-100	80	12	(	(	PUNCT
ejpam-100	80	13	56	56	NUM
ejpam-100	80	14	-	-	SYM
ejpam-100	80	15	71	71	NUM
ejpam-100	80	16	)	)	PUNCT
ejpam-100	80	17	60	60	NUM
ejpam-100	80	18	theorem	theorem	VERB
ejpam-100	80	19	3.1	3.1	NUM
ejpam-100	80	20	.	.	PUNCT
ejpam-100	81	1	under	under	ADP
ejpam-100	81	2	the	the	DET
ejpam-100	81	3	assumptions	assumption	NOUN
ejpam-100	81	4	(	(	PUNCT
ejpam-100	81	5	a1	a1	NOUN
ejpam-100	81	6	)	)	PUNCT
ejpam-100	81	7	and	and	CCONJ
ejpam-100	81	8	(	(	PUNCT
ejpam-100	81	9	a2	a2	PROPN
ejpam-100	81	10	)	)	PUNCT
ejpam-100	81	11	there	there	PRON
ejpam-100	81	12	exist	exist	VERB
ejpam-100	81	13	an	an	DET
ejpam-100	81	14	entropy	entropy	NOUN
ejpam-100	81	15	solution	solution	NOUN
ejpam-100	81	16	u	u	NOUN
ejpam-100	81	17	of	of	ADP
ejpam-100	81	18	the	the	DET
ejpam-100	81	19	problem	problem	NOUN
ejpam-100	81	20	(	(	PUNCT
ejpam-100	81	21	p	p	NOUN
ejpam-100	81	22	)	)	PUNCT
ejpam-100	81	23	.	.	PUNCT
ejpam-100	82	1	i.e.	i.e.	X
ejpam-100	82	2	u	u	NOUN
ejpam-100	82	3	is	be	AUX
ejpam-100	82	4	a	a	DET
ejpam-100	82	5	solution	solution	NOUN
ejpam-100	82	6	of	of	ADP
ejpam-100	82	7	(	(	PUNCT
ejpam-100	82	8	p	p	NOUN
ejpam-100	82	9	)	)	PUNCT
ejpam-100	82	10	in	in	ADP
ejpam-100	82	11	the	the	DET
ejpam-100	82	12	following	follow	VERB
ejpam-100	82	13	sense	sense	NOUN
ejpam-100	82	14	.	.	PUNCT
ejpam-100	83	1	∫	∫	PROPN
ejpam-100	83	2	ω	ω	PROPN
ejpam-100	83	3	〈	〈	NOUN
ejpam-100	83	4	a(x	a(x	PROPN
ejpam-100	83	5	,	,	PUNCT
ejpam-100	83	6	u,∇u),∇tk[u−ϕ	u,∇u),∇tk[u−ϕ	NOUN
ejpam-100	83	7	]	]	X
ejpam-100	83	8	〉	〉	NOUN
ejpam-100	84	1	d	d	NOUN
ejpam-100	84	2	x+	x+	PROPN
ejpam-100	84	3	∫	∫	PROPN
ejpam-100	84	4	ω	ω	NUM
ejpam-100	84	5	g(x	g(x	PROPN
ejpam-100	84	6	,	,	PUNCT
ejpam-100	84	7	u)tk[u−ϕ	u)tk[u−ϕ	VERB
ejpam-100	84	8	]	]	X
ejpam-100	85	1	d	d	NOUN
ejpam-100	85	2	x	x	SYM
ejpam-100	85	3	=	=	SYM
ejpam-100	85	4	∫	∫	PROPN
ejpam-100	85	5	ω	ω	PROPN
ejpam-100	85	6	f	f	PROPN
ejpam-100	85	7	tk[u−ϕ	tk[u−ϕ	PROPN
ejpam-100	85	8	]	]	X
ejpam-100	86	1	d	d	X
ejpam-100	86	2	x+	x+	SYM
ejpam-100	86	3	∫	∫	PROPN
ejpam-100	86	4	ω	ω	PROPN
ejpam-100	86	5	〈	〈	PROPN
ejpam-100	86	6	f,∇tk[u−ϕ	f,∇tk[u−ϕ	PROPN
ejpam-100	86	7	]	]	SYM
ejpam-100	86	8	〉	〉	NOUN
ejpam-100	86	9	d	d	NOUN
ejpam-100	86	10	x	x	PUNCT
ejpam-100	86	11	for	for	ADP
ejpam-100	86	12	every	every	DET
ejpam-100	86	13	ϕ	ϕ	NOUN
ejpam-100	86	14	∈w	∈w	PROPN
ejpam-100	86	15	1,p	1,p	PROPN
ejpam-100	86	16	0	0	SYM
ejpam-100	86	17	(	(	PUNCT
ejpam-100	86	18	ω	ω	PROPN
ejpam-100	86	19	,	,	PUNCT
ejpam-100	86	20	w)∩	w)∩	X
ejpam-100	86	21	l∞(ω	l∞(ω	ADJ
ejpam-100	86	22	)	)	PUNCT
ejpam-100	86	23	,	,	PUNCT
ejpam-100	86	24	for	for	ADP
ejpam-100	86	25	every	every	DET
ejpam-100	86	26	k	k	PROPN
ejpam-100	86	27	>	>	X
ejpam-100	86	28	0	0	X
ejpam-100	86	29	.	.	PUNCT
ejpam-100	86	30	remark	remark	PROPN
ejpam-100	86	31	3.1	3.1	NUM
ejpam-100	86	32	.	.	PUNCT
ejpam-100	87	1	the	the	DET
ejpam-100	87	2	statement	statement	NOUN
ejpam-100	87	3	of	of	ADP
ejpam-100	87	4	theorem	theorem	ADJ
ejpam-100	87	5	3.1	3.1	NUM
ejpam-100	87	6	generalizes	generalize	NOUN
ejpam-100	87	7	in	in	ADP
ejpam-100	87	8	weighted	weighted	ADJ
ejpam-100	87	9	case	case	NOUN
ejpam-100	87	10	the	the	DET
ejpam-100	87	11	analogous	analogous	ADJ
ejpam-100	87	12	in	in	ADP
ejpam-100	87	13	[	[	X
ejpam-100	87	14	4	4	NUM
ejpam-100	87	15	]	]	PUNCT
ejpam-100	87	16	and	and	CCONJ
ejpam-100	87	17	[	[	X
ejpam-100	87	18	3](with	3](with	NUM
ejpam-100	87	19	g	g	PROPN
ejpam-100	87	20	≡	≡	PROPN
ejpam-100	87	21	0	0	NUM
ejpam-100	87	22	)	)	PUNCT
ejpam-100	87	23	.	.	PUNCT
ejpam-100	88	1	4	4	X
ejpam-100	88	2	.	.	X
ejpam-100	88	3	proof	proof	NOUN
ejpam-100	88	4	of	of	ADP
ejpam-100	88	5	existence	existence	NOUN
ejpam-100	88	6	theorem	theorem	VERB
ejpam-100	88	7	4.1	4.1	NUM
ejpam-100	88	8	.	.	PUNCT
ejpam-100	89	1	main	main	ADJ
ejpam-100	89	2	lemma	lemma	PROPN
ejpam-100	89	3	lemma	lemma	PROPN
ejpam-100	89	4	4.1	4.1	NUM
ejpam-100	89	5	.	.	PUNCT
ejpam-100	90	1	let	let	VERB
ejpam-100	90	2	u	u	PRON
ejpam-100	90	3	be	be	AUX
ejpam-100	90	4	a	a	DET
ejpam-100	90	5	measurable	measurable	ADJ
ejpam-100	90	6	function	function	NOUN
ejpam-100	90	7	such	such	ADJ
ejpam-100	90	8	that	that	SCONJ
ejpam-100	90	9	tk(u	tk(u	NUM
ejpam-100	90	10	)	)	PUNCT
ejpam-100	90	11	belongs	belong	VERB
ejpam-100	90	12	to	to	ADP
ejpam-100	90	13	w	w	PROPN
ejpam-100	90	14	1,p	1,p	PROPN
ejpam-100	90	15	0	0	NUM
ejpam-100	90	16	(	(	PUNCT
ejpam-100	90	17	ω	ω	PROPN
ejpam-100	90	18	,	,	PUNCT
ejpam-100	90	19	w	w	NOUN
ejpam-100	90	20	)	)	PUNCT
ejpam-100	90	21	for	for	ADP
ejpam-100	90	22	every	every	DET
ejpam-100	90	23	k	k	PROPN
ejpam-100	90	24	>	>	X
ejpam-100	91	1	0	0	X
ejpam-100	91	2	.	.	PUNCT
ejpam-100	92	1	then	then	ADV
ejpam-100	92	2	∫	∫	PROPN
ejpam-100	92	3	ω	ω	PROPN
ejpam-100	92	4	〈	〈	NOUN
ejpam-100	92	5	a(x	a(x	PROPN
ejpam-100	92	6	,	,	PUNCT
ejpam-100	92	7	u,∇ϕ),∇tk[u−ϕ	u,∇ϕ),∇tk[u−ϕ	ADJ
ejpam-100	92	8	]	]	X
ejpam-100	92	9	〉	〉	NOUN
ejpam-100	92	10	d	d	NOUN
ejpam-100	92	11	x	x	SYM
ejpam-100	92	12	≤	≤	NUM
ejpam-100	92	13	∫	∫	PROPN
ejpam-100	92	14	ω	ω	PROPN
ejpam-100	92	15	f	f	PROPN
ejpam-100	92	16	tk[u−ϕ	tk[u−ϕ	PROPN
ejpam-100	92	17	]	]	PUNCT
ejpam-100	93	1	d	d	X
ejpam-100	93	2	x	x	SYM
ejpam-100	93	3	+	+	NUM
ejpam-100	93	4	∫	∫	PROPN
ejpam-100	93	5	ω	ω	NUM
ejpam-100	93	6	〈	〈	PROPN
ejpam-100	93	7	f,∇tk[u−ϕ	f,∇tk[u−ϕ	PROPN
ejpam-100	93	8	]	]	SYM
ejpam-100	93	9	〉	〉	NOUN
ejpam-100	93	10	d	d	NOUN
ejpam-100	93	11	x	x	PROPN
ejpam-100	93	12	.	.	PUNCT
ejpam-100	94	1	(	(	PUNCT
ejpam-100	94	2	4.1	4.1	NUM
ejpam-100	94	3	)	)	PUNCT
ejpam-100	94	4	is	be	AUX
ejpam-100	94	5	equivalent	equivalent	ADJ
ejpam-100	94	6	to	to	ADP
ejpam-100	94	7	∫	∫	PROPN
ejpam-100	94	8	ω	ω	PROPN
ejpam-100	94	9	〈	〈	PROPN
ejpam-100	94	10	a(x	a(x	PROPN
ejpam-100	94	11	,	,	PUNCT
ejpam-100	94	12	u,∇u),∇tk[u−ϕ	u,∇u),∇tk[u−ϕ	NOUN
ejpam-100	94	13	]	]	X
ejpam-100	94	14	〉	〉	NOUN
ejpam-100	94	15	d	d	NOUN
ejpam-100	94	16	x+	x+	PROPN
ejpam-100	94	17	∫	∫	PROPN
ejpam-100	94	18	ω	ω	NUM
ejpam-100	94	19	g(x	g(x	PROPN
ejpam-100	94	20	,	,	PUNCT
ejpam-100	94	21	u)tk[u−ϕ	u)tk[u−ϕ	VERB
ejpam-100	94	22	]	]	X
ejpam-100	95	1	d	d	NOUN
ejpam-100	95	2	x	x	SYM
ejpam-100	95	3	=	=	SYM
ejpam-100	95	4	∫	∫	PROPN
ejpam-100	95	5	ω	ω	PROPN
ejpam-100	95	6	f	f	PROPN
ejpam-100	95	7	tk[u−ϕ	tk[u−ϕ	PROPN
ejpam-100	95	8	]	]	X
ejpam-100	96	1	d	d	X
ejpam-100	96	2	x+	x+	SYM
ejpam-100	96	3	∫	∫	PROPN
ejpam-100	96	4	ω	ω	PROPN
ejpam-100	96	5	〈	〈	PROPN
ejpam-100	96	6	f,∇tk[u−ϕ	f,∇tk[u−ϕ	PROPN
ejpam-100	96	7	]	]	SYM
ejpam-100	96	8	〉	〉	NOUN
ejpam-100	96	9	d	d	NOUN
ejpam-100	96	10	x	x	PROPN
ejpam-100	96	11	.	.	PUNCT
ejpam-100	97	1	(	(	PUNCT
ejpam-100	97	2	4.2	4.2	NUM
ejpam-100	97	3	)	)	PUNCT
ejpam-100	97	4	for	for	ADP
ejpam-100	97	5	every	every	DET
ejpam-100	97	6	ϕ	ϕ	NOUN
ejpam-100	97	7	in	in	ADP
ejpam-100	97	8	w	w	PROPN
ejpam-100	97	9	1,p	1,p	PROPN
ejpam-100	97	10	0	0	NUM
ejpam-100	97	11	(	(	PUNCT
ejpam-100	97	12	ω	ω	PROPN
ejpam-100	97	13	,	,	PUNCT
ejpam-100	97	14	w)∩	w)∩	X
ejpam-100	97	15	l∞(ω	l∞(ω	ADJ
ejpam-100	97	16	)	)	PUNCT
ejpam-100	97	17	,	,	PUNCT
ejpam-100	97	18	and	and	CCONJ
ejpam-100	97	19	for	for	ADP
ejpam-100	97	20	every	every	DET
ejpam-100	97	21	k	k	PROPN
ejpam-100	97	22	>	>	X
ejpam-100	97	23	0	0	X
ejpam-100	97	24	.	.	PUNCT
ejpam-100	98	1	proof	proof	NOUN
ejpam-100	98	2	in	in	ADP
ejpam-100	98	3	fact	fact	NOUN
ejpam-100	98	4	(	(	PUNCT
ejpam-100	98	5	4.2	4.2	NUM
ejpam-100	98	6	)	)	PUNCT
ejpam-100	98	7	implies	imply	VERB
ejpam-100	98	8	(	(	PUNCT
ejpam-100	98	9	4.1	4.1	NUM
ejpam-100	98	10	)	)	PUNCT
ejpam-100	98	11	is	be	AUX
ejpam-100	98	12	easily	easily	ADV
ejpam-100	98	13	proved	prove	VERB
ejpam-100	98	14	adding	add	VERB
ejpam-100	98	15	and	and	CCONJ
ejpam-100	98	16	subtracting	subtract	VERB
ejpam-100	98	17	∫	∫	PROPN
ejpam-100	98	18	ω	ω	PROPN
ejpam-100	98	19	〈	〈	NOUN
ejpam-100	98	20	a(x	a(x	PROPN
ejpam-100	98	21	,	,	PUNCT
ejpam-100	98	22	u,∇ϕ),∇tk[u−ϕ	u,∇ϕ),∇tk[u−ϕ	ADJ
ejpam-100	98	23	]	]	X
ejpam-100	98	24	〉	〉	ADJ
ejpam-100	98	25	d	d	NOUN
ejpam-100	98	26	x	x	X
ejpam-100	98	27	and	and	CCONJ
ejpam-100	98	28	then	then	ADV
ejpam-100	98	29	using	use	VERB
ejpam-100	98	30	assumption	assumption	NOUN
ejpam-100	98	31	(	(	PUNCT
ejpam-100	98	32	2.7	2.7	NUM
ejpam-100	98	33	)	)	PUNCT
ejpam-100	98	34	.	.	PUNCT
ejpam-100	99	1	thus	thus	ADV
ejpam-100	99	2	,	,	PUNCT
ejpam-100	99	3	it	it	PRON
ejpam-100	99	4	remains	remain	VERB
ejpam-100	99	5	to	to	PART
ejpam-100	99	6	prove	prove	VERB
ejpam-100	99	7	that	that	SCONJ
ejpam-100	99	8	(	(	PUNCT
ejpam-100	99	9	4.1	4.1	NUM
ejpam-100	99	10	)	)	PUNCT
ejpam-100	99	11	implies	imply	VERB
ejpam-100	99	12	(	(	PUNCT
ejpam-100	99	13	4.2	4.2	NUM
ejpam-100	99	14	)	)	PUNCT
ejpam-100	99	15	.	.	PUNCT
ejpam-100	100	1	let	let	VERB
ejpam-100	100	2	h	h	NOUN
ejpam-100	100	3	and	and	CCONJ
ejpam-100	100	4	k	k	PROPN
ejpam-100	100	5	be	be	AUX
ejpam-100	100	6	positive	positive	ADJ
ejpam-100	100	7	real	real	ADJ
ejpam-100	100	8	numbers	number	NOUN
ejpam-100	100	9	,	,	PUNCT
ejpam-100	100	10	let	let	VERB
ejpam-100	100	11	λ	λ	X
ejpam-100	100	12	∈	∈	PROPN
ejpam-100	100	13	]	]	PUNCT
ejpam-100	100	14	−	−	PROPN
ejpam-100	100	15	1	1	NUM
ejpam-100	100	16	,	,	PUNCT
ejpam-100	100	17	1	1	NUM
ejpam-100	100	18	[	[	PUNCT
ejpam-100	100	19	and	and	CCONJ
ejpam-100	100	20	ψ	ψ	ADP
ejpam-100	100	21	∈w	∈w	VERB
ejpam-100	100	22	1,p	1,p	PROPN
ejpam-100	100	23	0	0	SYM
ejpam-100	100	24	(	(	PUNCT
ejpam-100	100	25	ω	ω	PROPN
ejpam-100	100	26	,	,	PUNCT
ejpam-100	100	27	w)∩	w)∩	X
ejpam-100	100	28	l∞(ω	l∞(ω	ADJ
ejpam-100	100	29	)	)	PUNCT
ejpam-100	100	30	.	.	PUNCT
ejpam-100	101	1	choose	choose	VERB
ejpam-100	101	2	,	,	PUNCT
ejpam-100	101	3	ϕ	ϕ	X
ejpam-100	101	4	=	=	PUNCT
ejpam-100	101	5	th(u−λtk(u−ψ	th(u−λtk(u−ψ	NOUN
ejpam-100	101	6	)	)	PUNCT
ejpam-100	101	7	)	)	PUNCT
ejpam-100	102	1	∈w	∈w	VERB
ejpam-100	102	2	1,p	1,p	PROPN
ejpam-100	102	3	0	0	SYM
ejpam-100	102	4	(	(	PUNCT
ejpam-100	102	5	ω	ω	PROPN
ejpam-100	102	6	,	,	PUNCT
ejpam-100	102	7	w)∩	w)∩	X
ejpam-100	102	8	l∞(ω	l∞(ω	ADJ
ejpam-100	102	9	)	)	PUNCT
ejpam-100	102	10	as	as	ADP
ejpam-100	102	11	test	test	NOUN
ejpam-100	102	12	function	function	NOUN
ejpam-100	102	13	in	in	ADP
ejpam-100	102	14	(	(	PUNCT
ejpam-100	102	15	4.1	4.1	NUM
ejpam-100	102	16	)	)	PUNCT
ejpam-100	102	17	,	,	PUNCT
ejpam-100	102	18	we	we	PRON
ejpam-100	102	19	have	have	VERB
ejpam-100	102	20	:	:	PUNCT
ejpam-100	102	21	ihk	ihk	NOUN
ejpam-100	102	22	≤	≤	PROPN
ejpam-100	102	23	jhk	jhk	NOUN
ejpam-100	102	24	(	(	PUNCT
ejpam-100	102	25	4.3	4.3	NUM
ejpam-100	102	26	)	)	PUNCT
ejpam-100	102	27	with	with	ADP
ejpam-100	102	28	ihk	ihk	NOUN
ejpam-100	102	29	=	=	SYM
ejpam-100	102	30	∫	∫	PROPN
ejpam-100	102	31	ω	ω	PROPN
ejpam-100	102	32	〈	〈	NOUN
ejpam-100	102	33	a(x	a(x	PROPN
ejpam-100	102	34	,	,	PUNCT
ejpam-100	102	35	u,∇th(u−λtk(u−ψ))),∇tk(u−	u,∇th(u−λtk(u−ψ))),∇tk(u−	ADJ
ejpam-100	102	36	th(u−λtk(u−ψ	th(u−λtk(u−ψ	NOUN
ejpam-100	102	37	)	)	PUNCT
ejpam-100	102	38	)	)	PUNCT
ejpam-100	102	39	)	)	PUNCT
ejpam-100	102	40	〉	〉	NOUN
ejpam-100	103	1	d	d	NOUN
ejpam-100	103	2	x	x	SYM
ejpam-100	104	1	+	+	NUM
ejpam-100	104	2	∫	∫	PROPN
ejpam-100	104	3	ω	ω	NUM
ejpam-100	104	4	g(x	g(x	PROPN
ejpam-100	104	5	,	,	PUNCT
ejpam-100	104	6	u)tk(u−	u)tk(u−	PRON
ejpam-100	104	7	th(u−λtk(u−ψ	th(u−λtk(u−ψ	NOUN
ejpam-100	104	8	)	)	PUNCT
ejpam-100	104	9	)	)	PUNCT
ejpam-100	104	10	)	)	PUNCT
ejpam-100	105	1	d	d	X
ejpam-100	105	2	x	x	X
ejpam-100	105	3	=	=	NOUN
ejpam-100	105	4	i	i	PRON
ejpam-100	105	5	′hk	′hk	VERB
ejpam-100	106	1	+	+	CCONJ
ejpam-100	106	2	i	i	PRON
ejpam-100	106	3	′′hk	′′hk	PROPN
ejpam-100	106	4	y.	y.	PROPN
ejpam-100	106	5	akdim	akdim	PROPN
ejpam-100	106	6	,	,	PUNCT
ejpam-100	106	7	e.	e.	PROPN
ejpam-100	106	8	azroul	azroul	PROPN
ejpam-100	106	9	,	,	PUNCT
ejpam-100	106	10	and	and	CCONJ
ejpam-100	106	11	m.	m.	NOUN
ejpam-100	106	12	rhoudaf	rhoudaf	PROPN
ejpam-100	106	13	/	/	SYM
ejpam-100	106	14	eur	eur	PROPN
ejpam-100	106	15	.	.	PUNCT
ejpam-100	107	1	j.	j.	PROPN
ejpam-100	107	2	pure	pure	PROPN
ejpam-100	107	3	appl	appl	PROPN
ejpam-100	107	4	.	.	PROPN
ejpam-100	107	5	math	math	PROPN
ejpam-100	107	6	,	,	PUNCT
ejpam-100	107	7	1	1	NUM
ejpam-100	107	8	(	(	PUNCT
ejpam-100	107	9	2008	2008	NUM
ejpam-100	107	10	)	)	PUNCT
ejpam-100	107	11	,	,	PUNCT
ejpam-100	107	12	(	(	PUNCT
ejpam-100	107	13	56	56	NUM
ejpam-100	107	14	-	-	SYM
ejpam-100	107	15	71	71	NUM
ejpam-100	107	16	)	)	PUNCT
ejpam-100	107	17	61	61	NUM
ejpam-100	107	18	and	and	CCONJ
ejpam-100	107	19	jhk	jhk	NOUN
ejpam-100	107	20	=	=	SYM
ejpam-100	108	1	∫	∫	PROPN
ejpam-100	108	2	ω	ω	PROPN
ejpam-100	108	3	f	f	PROPN
ejpam-100	108	4	tk(u−	tk(u−	NUM
ejpam-100	108	5	th(u−λtk(u−ψ	th(u−λtk(u−ψ	NOUN
ejpam-100	108	6	)	)	PUNCT
ejpam-100	108	7	)	)	PUNCT
ejpam-100	108	8	)	)	PUNCT
ejpam-100	109	1	d	d	X
ejpam-100	109	2	x	x	PUNCT
ejpam-100	110	1	+	+	NUM
ejpam-100	110	2	∫	∫	PROPN
ejpam-100	110	3	ω	ω	NUM
ejpam-100	110	4	〈	〈	PROPN
ejpam-100	110	5	f,∇tk(u−	f,∇tk(u−	PROPN
ejpam-100	110	6	th(u−λtk(u−ψ	th(u−λtk(u−ψ	NOUN
ejpam-100	110	7	)	)	PUNCT
ejpam-100	110	8	)	)	PUNCT
ejpam-100	110	9	)	)	PUNCT
ejpam-100	110	10	〉	〉	NOUN
ejpam-100	111	1	d	d	NOUN
ejpam-100	111	2	x	x	X
ejpam-100	111	3	.	.	PUNCT
ejpam-100	112	1	put	put	VERB
ejpam-100	112	2	ahk	ahk	NOUN
ejpam-100	112	3	=	=	PUNCT
ejpam-100	112	4	{	{	PUNCT
ejpam-100	112	5	x	x	PROPN
ejpam-100	112	6	∈	∈	PROPN
ejpam-100	112	7	ω	ω	PROPN
ejpam-100	112	8	,	,	PUNCT
ejpam-100	112	9	|u−	|u−	NOUN
ejpam-100	112	10	th(u−λtk(u−ψ))|	th(u−λtk(u−ψ))|	VERB
ejpam-100	112	11	≤	≤	NUM
ejpam-100	113	1	k	k	NOUN
ejpam-100	113	2	}	}	PUNCT
ejpam-100	113	3	and	and	CCONJ
ejpam-100	113	4	bhk	bhk	X
ejpam-100	113	5	=	=	PUNCT
ejpam-100	113	6	{	{	PUNCT
ejpam-100	113	7	x	x	SYM
ejpam-100	113	8	∈	∈	PROPN
ejpam-100	113	9	ω	ω	PROPN
ejpam-100	113	10	,	,	PUNCT
ejpam-100	113	11	|u−λtk(u−ψ)|	|u−λtk(u−ψ)|	ADJ
ejpam-100	113	12	≤	≤	ADJ
ejpam-100	113	13	h	h	NOUN
ejpam-100	113	14	}	}	PUNCT
ejpam-100	113	15	.	.	PUNCT
ejpam-100	114	1	then	then	ADV
ejpam-100	114	2	,	,	PUNCT
ejpam-100	114	3	we	we	PRON
ejpam-100	114	4	obtain	obtain	VERB
ejpam-100	114	5	i	i	PRON
ejpam-100	114	6	′hk	′hk	NOUN
ejpam-100	114	7	=	=	SYM
ejpam-100	114	8	∫	∫	PROPN
ejpam-100	114	9	akh∩bhk	akh∩bhk	X
ejpam-100	115	1	〈	〈	X
ejpam-100	115	2	a(x	a(x	PROPN
ejpam-100	115	3	,	,	PUNCT
ejpam-100	115	4	u,∇th(u−λtk(u−ψ))),∇tk(u−	u,∇th(u−λtk(u−ψ))),∇tk(u−	ADJ
ejpam-100	115	5	th(u−λtk(u−ψ	th(u−λtk(u−ψ	NOUN
ejpam-100	115	6	)	)	PUNCT
ejpam-100	115	7	)	)	PUNCT
ejpam-100	115	8	)	)	PUNCT
ejpam-100	115	9	〉	〉	NOUN
ejpam-100	116	1	d	d	NOUN
ejpam-100	116	2	x	x	SYM
ejpam-100	117	1	+	+	NUM
ejpam-100	117	2	∫	∫	PROPN
ejpam-100	117	3	akh∩bc	akh∩bc	PROPN
ejpam-100	117	4	hk	hk	PROPN
ejpam-100	118	1	〈	〈	NOUN
ejpam-100	118	2	a(x	a(x	PROPN
ejpam-100	118	3	,	,	PUNCT
ejpam-100	118	4	u,∇th(u−λtk(u−ψ))),∇tk(u−	u,∇th(u−λtk(u−ψ))),∇tk(u−	ADJ
ejpam-100	118	5	th(u−λtk(u−ψ	th(u−λtk(u−ψ	NOUN
ejpam-100	118	6	)	)	PUNCT
ejpam-100	118	7	)	)	PUNCT
ejpam-100	118	8	)	)	PUNCT
ejpam-100	118	9	〉	〉	NOUN
ejpam-100	119	1	d	d	NOUN
ejpam-100	119	2	x	x	SYM
ejpam-100	120	1	+	+	NUM
ejpam-100	121	1	∫	∫	PROPN
ejpam-100	121	2	ac	ac	PROPN
ejpam-100	121	3	kh	kh	PROPN
ejpam-100	121	4	〈	〈	PROPN
ejpam-100	121	5	a(x	a(x	PROPN
ejpam-100	121	6	,	,	PUNCT
ejpam-100	121	7	u,∇th(u−λtk(u−ψ))),∇tk(u−	u,∇th(u−λtk(u−ψ))),∇tk(u−	ADJ
ejpam-100	121	8	th(u−λtk(u−ψ	th(u−λtk(u−ψ	NOUN
ejpam-100	121	9	)	)	PUNCT
ejpam-100	121	10	)	)	PUNCT
ejpam-100	121	11	)	)	PUNCT
ejpam-100	121	12	〉	〉	NOUN
ejpam-100	122	1	d	d	NOUN
ejpam-100	122	2	x	x	X
ejpam-100	122	3	.	.	PUNCT
ejpam-100	123	1	since	since	SCONJ
ejpam-100	123	2	∇tk(u−	∇tk(u−	NUM
ejpam-100	123	3	th(u−λtk(u−ψ	th(u−λtk(u−ψ	NOUN
ejpam-100	123	4	)	)	PUNCT
ejpam-100	123	5	)	)	PUNCT
ejpam-100	123	6	)	)	PUNCT
ejpam-100	123	7	is	be	AUX
ejpam-100	123	8	different	different	ADJ
ejpam-100	123	9	to	to	ADP
ejpam-100	123	10	zero	zero	NUM
ejpam-100	123	11	only	only	ADV
ejpam-100	123	12	on	on	ADP
ejpam-100	123	13	akh	akh	NOUN
ejpam-100	123	14	,	,	PUNCT
ejpam-100	123	15	we	we	PRON
ejpam-100	123	16	have	have	VERB
ejpam-100	123	17	∫	∫	PROPN
ejpam-100	123	18	ac	ac	PROPN
ejpam-100	123	19	kh	kh	PROPN
ejpam-100	123	20	〈	〈	PROPN
ejpam-100	123	21	a(x	a(x	PROPN
ejpam-100	123	22	,	,	PUNCT
ejpam-100	123	23	u,∇th(u−λtk(u−ψ))),∇tk(u−	u,∇th(u−λtk(u−ψ))),∇tk(u−	ADJ
ejpam-100	123	24	th(u−λtk(u−ψ	th(u−λtk(u−ψ	NOUN
ejpam-100	123	25	)	)	PUNCT
ejpam-100	123	26	)	)	PUNCT
ejpam-100	123	27	)	)	PUNCT
ejpam-100	123	28	〉	〉	NOUN
ejpam-100	124	1	d	d	NOUN
ejpam-100	124	2	x	x	SYM
ejpam-100	124	3	=	=	NOUN
ejpam-100	124	4	0	0	NUM
ejpam-100	124	5	.	.	PUNCT
ejpam-100	125	1	(	(	PUNCT
ejpam-100	125	2	4.4	4.4	NUM
ejpam-100	125	3	)	)	PUNCT
ejpam-100	125	4	moreover	moreover	ADV
ejpam-100	125	5	,	,	PUNCT
ejpam-100	125	6	if	if	SCONJ
ejpam-100	125	7	x	x	PROPN
ejpam-100	125	8	∈	∈	PROPN
ejpam-100	125	9	bc	bc	PROPN
ejpam-100	125	10	hk	hk	PROPN
ejpam-100	125	11	,	,	PUNCT
ejpam-100	125	12	we	we	PRON
ejpam-100	125	13	have	have	VERB
ejpam-100	125	14	∇th(u−λtk(u−ψ	∇th(u−λtk(u−ψ	NOUN
ejpam-100	125	15	)	)	PUNCT
ejpam-100	125	16	)	)	PUNCT
ejpam-100	126	1	=	=	SYM
ejpam-100	126	2	0	0	PUNCT
ejpam-100	127	1	and	and	CCONJ
ejpam-100	127	2	using	use	VERB
ejpam-100	127	3	(	(	PUNCT
ejpam-100	127	4	2.8	2.8	NUM
ejpam-100	127	5	)	)	PUNCT
ejpam-100	127	6	,	,	PUNCT
ejpam-100	127	7	we	we	PRON
ejpam-100	127	8	deduce	deduce	VERB
ejpam-100	127	9	that	that	PRON
ejpam-100	127	10	,	,	PUNCT
ejpam-100	127	11	∫	∫	PROPN
ejpam-100	127	12	akh∩bc	akh∩bc	PROPN
ejpam-100	127	13	hk	hk	PROPN
ejpam-100	128	1	〈	〈	NOUN
ejpam-100	128	2	a(x	a(x	PROPN
ejpam-100	128	3	,	,	PUNCT
ejpam-100	128	4	u,∇th(u−λtk(u−ψ))),∇tk(u−	u,∇th(u−λtk(u−ψ))),∇tk(u−	ADJ
ejpam-100	128	5	th(u−λtk(u−ψ	th(u−λtk(u−ψ	NOUN
ejpam-100	128	6	)	)	PUNCT
ejpam-100	128	7	)	)	PUNCT
ejpam-100	128	8	)	)	PUNCT
ejpam-100	128	9	〉	〉	NOUN
ejpam-100	129	1	d	d	NOUN
ejpam-100	129	2	x	x	SYM
ejpam-100	129	3	=	=	SYM
ejpam-100	129	4	∫	∫	PROPN
ejpam-100	130	1	akh∩bc	akh∩bc	PROPN
ejpam-100	130	2	hk	hk	PROPN
ejpam-100	131	1	〈	〈	NOUN
ejpam-100	131	2	a(x	a(x	PROPN
ejpam-100	131	3	,	,	PUNCT
ejpam-100	131	4	u	u	NOUN
ejpam-100	131	5	,	,	PUNCT
ejpam-100	131	6	0),∇tk(u−	0),∇tk(u−	NUM
ejpam-100	131	7	th(u−λtk(u−ψ	th(u−λtk(u−ψ	NOUN
ejpam-100	131	8	)	)	PUNCT
ejpam-100	131	9	)	)	PUNCT
ejpam-100	131	10	)	)	PUNCT
ejpam-100	131	11	〉	〉	NOUN
ejpam-100	132	1	d	d	NOUN
ejpam-100	132	2	x	x	SYM
ejpam-100	132	3	=	=	NOUN
ejpam-100	132	4	0	0	NUM
ejpam-100	132	5	.	.	PUNCT
ejpam-100	133	1	(	(	PUNCT
ejpam-100	133	2	4.5	4.5	NUM
ejpam-100	133	3	)	)	PUNCT
ejpam-100	133	4	from	from	ADP
ejpam-100	133	5	(	(	PUNCT
ejpam-100	133	6	4.4	4.4	NUM
ejpam-100	133	7	)	)	PUNCT
ejpam-100	133	8	and	and	CCONJ
ejpam-100	133	9	(	(	PUNCT
ejpam-100	133	10	4.5	4.5	NUM
ejpam-100	133	11	)	)	PUNCT
ejpam-100	133	12	,	,	PUNCT
ejpam-100	133	13	we	we	PRON
ejpam-100	133	14	obtain	obtain	VERB
ejpam-100	133	15	i	i	PRON
ejpam-100	133	16	′hk	′hk	NOUN
ejpam-100	133	17	=	=	SYM
ejpam-100	133	18	∫	∫	PROPN
ejpam-100	133	19	akh∩bhk	akh∩bhk	X
ejpam-100	134	1	〈	〈	X
ejpam-100	134	2	a(x	a(x	PROPN
ejpam-100	134	3	,	,	PUNCT
ejpam-100	134	4	u,∇th(u−λtk(u−ψ))),∇tk(u−	u,∇th(u−λtk(u−ψ))),∇tk(u−	ADJ
ejpam-100	134	5	th(u−λtk(u−ψ	th(u−λtk(u−ψ	NOUN
ejpam-100	134	6	)	)	PUNCT
ejpam-100	134	7	)	)	PUNCT
ejpam-100	134	8	)	)	PUNCT
ejpam-100	134	9	〉	〉	NOUN
ejpam-100	135	1	d	d	NOUN
ejpam-100	135	2	x	x	X
ejpam-100	135	3	.	.	PUNCT
ejpam-100	136	1	letting	let	VERB
ejpam-100	136	2	h→+∞	h→+∞	VERB
ejpam-100	136	3	,	,	PUNCT
ejpam-100	136	4	and	and	CCONJ
ejpam-100	136	5	|λ|	|λ|	NOUN
ejpam-100	136	6	≤	≤	NOUN
ejpam-100	136	7	1	1	NUM
ejpam-100	136	8	,	,	PUNCT
ejpam-100	136	9	we	we	PRON
ejpam-100	136	10	have	have	VERB
ejpam-100	136	11	akh→	akh→	NOUN
ejpam-100	136	12	{	{	PUNCT
ejpam-100	136	13	x	x	NOUN
ejpam-100	136	14	,	,	PUNCT
ejpam-100	136	15	|λ||tk(u−ψ)|	|λ||tk(u−ψ)|	PROPN
ejpam-100	136	16	≤	≤	PROPN
ejpam-100	137	1	k}=	k}=	PROPN
ejpam-100	137	2	ω	ω	PROPN
ejpam-100	137	3	,	,	PUNCT
ejpam-100	137	4	(	(	PUNCT
ejpam-100	137	5	4.6	4.6	NUM
ejpam-100	137	6	)	)	PUNCT
ejpam-100	137	7	bhk→	bhk→	NOUN
ejpam-100	137	8	ω	ω	NOUN
ejpam-100	137	9	which	which	PRON
ejpam-100	137	10	implies	imply	VERB
ejpam-100	137	11	akh	akh	PROPN
ejpam-100	137	12	∩	∩	PROPN
ejpam-100	137	13	bhk→	bhk→	PROPN
ejpam-100	137	14	ω	ω	X
ejpam-100	137	15	.	.	PUNCT
ejpam-100	138	1	(	(	PUNCT
ejpam-100	138	2	4.7	4.7	NUM
ejpam-100	138	3	)	)	PUNCT
ejpam-100	138	4	y.	y.	PROPN
ejpam-100	138	5	akdim	akdim	PROPN
ejpam-100	138	6	,	,	PUNCT
ejpam-100	138	7	e.	e.	PROPN
ejpam-100	138	8	azroul	azroul	PROPN
ejpam-100	138	9	,	,	PUNCT
ejpam-100	138	10	and	and	CCONJ
ejpam-100	138	11	m.	m.	NOUN
ejpam-100	138	12	rhoudaf	rhoudaf	PROPN
ejpam-100	138	13	/	/	SYM
ejpam-100	138	14	eur	eur	PROPN
ejpam-100	138	15	.	.	PUNCT
ejpam-100	139	1	j.	j.	PROPN
ejpam-100	139	2	pure	pure	PROPN
ejpam-100	139	3	appl	appl	PROPN
ejpam-100	139	4	.	.	PROPN
ejpam-100	139	5	math	math	PROPN
ejpam-100	139	6	,	,	PUNCT
ejpam-100	139	7	1	1	NUM
ejpam-100	139	8	(	(	PUNCT
ejpam-100	139	9	2008	2008	NUM
ejpam-100	139	10	)	)	PUNCT
ejpam-100	139	11	,	,	PUNCT
ejpam-100	139	12	(	(	PUNCT
ejpam-100	139	13	56	56	NUM
ejpam-100	139	14	-	-	SYM
ejpam-100	139	15	71	71	NUM
ejpam-100	139	16	)	)	PUNCT
ejpam-100	139	17	62	62	NUM
ejpam-100	139	18	which	which	PRON
ejpam-100	139	19	and	and	CCONJ
ejpam-100	139	20	using	use	VERB
ejpam-100	139	21	lebesgue	lebesgue	NOUN
ejpam-100	139	22	theorem	theorem	PROPN
ejpam-100	139	23	,	,	PUNCT
ejpam-100	139	24	we	we	PRON
ejpam-100	139	25	conclude	conclude	VERB
ejpam-100	139	26	that	that	SCONJ
ejpam-100	139	27	lim	lim	PROPN
ejpam-100	139	28	h→+∞	h→+∞	PROPN
ejpam-100	139	29	∫	∫	PROPN
ejpam-100	139	30	akh∩bhk	akh∩bhk	X
ejpam-100	140	1	〈	〈	X
ejpam-100	140	2	a(x	a(x	PROPN
ejpam-100	140	3	,	,	PUNCT
ejpam-100	140	4	u,∇th(u−λtk(u−ψ))),∇tk(u−	u,∇th(u−λtk(u−ψ))),∇tk(u−	ADJ
ejpam-100	140	5	th(u−λtk(u−ψ	th(u−λtk(u−ψ	NOUN
ejpam-100	140	6	)	)	PUNCT
ejpam-100	140	7	)	)	PUNCT
ejpam-100	140	8	)	)	PUNCT
ejpam-100	140	9	〉	〉	NOUN
ejpam-100	141	1	d	d	NOUN
ejpam-100	141	2	x	x	SYM
ejpam-100	141	3	=	=	SYM
ejpam-100	141	4	λ	λ	X
ejpam-100	141	5	∫	∫	PROPN
ejpam-100	141	6	ω	ω	PROPN
ejpam-100	141	7	〈	〈	NOUN
ejpam-100	141	8	a(x	a(x	PROPN
ejpam-100	141	9	,	,	PUNCT
ejpam-100	141	10	u,∇(u−λtk(u−ψ)),∇tk(u−ψ	u,∇(u−λtk(u−ψ)),∇tk(u−ψ	NOUN
ejpam-100	141	11	)	)	PUNCT
ejpam-100	141	12	〉	〉	NOUN
ejpam-100	141	13	d	d	NOUN
ejpam-100	141	14	x	x	X
ejpam-100	141	15	.	.	PUNCT
ejpam-100	142	1	(	(	PUNCT
ejpam-100	142	2	4.8	4.8	NUM
ejpam-100	142	3	)	)	PUNCT
ejpam-100	142	4	i.e.	i.e.	X
ejpam-100	142	5	,	,	PUNCT
ejpam-100	142	6	lim	lim	PROPN
ejpam-100	142	7	h→+∞	h→+∞	PROPN
ejpam-100	142	8	i	i	PRON
ejpam-100	142	9	′hk	′hk	NOUN
ejpam-100	142	10	=	=	SYM
ejpam-100	143	1	λ	λ	PROPN
ejpam-100	143	2	∫	∫	PROPN
ejpam-100	143	3	ω	ω	PROPN
ejpam-100	143	4	〈	〈	NOUN
ejpam-100	143	5	a(x	a(x	PROPN
ejpam-100	143	6	,	,	PUNCT
ejpam-100	143	7	u,∇(u−λtk(u−ψ)),∇tk(u−ψ	u,∇(u−λtk(u−ψ)),∇tk(u−ψ	NOUN
ejpam-100	143	8	)	)	PUNCT
ejpam-100	143	9	〉	〉	NOUN
ejpam-100	144	1	d	d	NOUN
ejpam-100	144	2	x	x	X
ejpam-100	144	3	.	.	PUNCT
ejpam-100	145	1	(	(	PUNCT
ejpam-100	145	2	4.9	4.9	NUM
ejpam-100	145	3	)	)	PUNCT
ejpam-100	145	4	moreover	moreover	ADV
ejpam-100	145	5	it	it	PRON
ejpam-100	145	6	is	be	AUX
ejpam-100	145	7	easy	easy	ADJ
ejpam-100	145	8	to	to	PART
ejpam-100	145	9	see	see	VERB
ejpam-100	145	10	that	that	PRON
ejpam-100	145	11	,	,	PUNCT
ejpam-100	145	12	lim	lim	PROPN
ejpam-100	145	13	h→+∞	h→+∞	PROPN
ejpam-100	145	14	∫	∫	PROPN
ejpam-100	145	15	ω	ω	NUM
ejpam-100	145	16	g(x	g(x	PROPN
ejpam-100	145	17	,	,	PUNCT
ejpam-100	145	18	u)tk(u−	u)tk(u−	PRON
ejpam-100	145	19	th(u−λtk(u−ψ	th(u−λtk(u−ψ	NOUN
ejpam-100	145	20	)	)	PUNCT
ejpam-100	145	21	)	)	PUNCT
ejpam-100	145	22	)	)	PUNCT
ejpam-100	146	1	d	d	X
ejpam-100	146	2	x	x	X
ejpam-100	146	3	=	=	SYM
ejpam-100	146	4	λ	λ	X
ejpam-100	146	5	∫	∫	PROPN
ejpam-100	146	6	ω	ω	NUM
ejpam-100	146	7	g(x	g(x	PROPN
ejpam-100	146	8	,	,	PUNCT
ejpam-100	146	9	u)tk[u−ψ	u)tk[u−ψ	PROPN
ejpam-100	146	10	]	]	PUNCT
ejpam-100	147	1	d	d	X
ejpam-100	147	2	x	x	PRON
ejpam-100	147	3	thus	thus	ADV
ejpam-100	147	4	implies	imply	VERB
ejpam-100	147	5	that	that	SCONJ
ejpam-100	147	6	,	,	PUNCT
ejpam-100	148	1	lim	lim	PROPN
ejpam-100	148	2	h→+∞	h→+∞	PROPN
ejpam-100	148	3	ihk	ihk	NOUN
ejpam-100	148	4	=	=	PROPN
ejpam-100	148	5	λ	λ	PROPN
ejpam-100	148	6	∫	∫	PROPN
ejpam-100	148	7	ω	ω	PROPN
ejpam-100	148	8	〈	〈	NOUN
ejpam-100	148	9	a(x	a(x	PROPN
ejpam-100	148	10	,	,	PUNCT
ejpam-100	148	11	u,∇(u−λtk(u−ψ)),∇tk(u−ψ	u,∇(u−λtk(u−ψ)),∇tk(u−ψ	NOUN
ejpam-100	148	12	)	)	PUNCT
ejpam-100	148	13	〉	〉	NOUN
ejpam-100	149	1	d	d	NOUN
ejpam-100	149	2	x+λ	x+λ	PROPN
ejpam-100	149	3	∫	∫	PROPN
ejpam-100	150	1	ω	ω	NUM
ejpam-100	150	2	g(x	g(x	PROPN
ejpam-100	150	3	,	,	PUNCT
ejpam-100	150	4	u)tk[u−ψ	u)tk[u−ψ	PROPN
ejpam-100	150	5	]	]	PUNCT
ejpam-100	151	1	d	d	X
ejpam-100	151	2	x	x	X
ejpam-100	151	3	(	(	PUNCT
ejpam-100	151	4	4.10	4.10	NUM
ejpam-100	151	5	)	)	PUNCT
ejpam-100	151	6	on	on	ADP
ejpam-100	151	7	the	the	DET
ejpam-100	151	8	other	other	ADJ
ejpam-100	151	9	hand	hand	NOUN
ejpam-100	151	10	,	,	PUNCT
ejpam-100	151	11	we	we	PRON
ejpam-100	151	12	have	have	VERB
ejpam-100	151	13	,	,	PUNCT
ejpam-100	151	14	jhk	jhk	VERB
ejpam-100	151	15	=	=	SYM
ejpam-100	152	1	∫	∫	PROPN
ejpam-100	152	2	ω	ω	PROPN
ejpam-100	152	3	f	f	PROPN
ejpam-100	152	4	tk(u−	tk(u−	NUM
ejpam-100	152	5	th(u−λtk(u−ψ	th(u−λtk(u−ψ	NOUN
ejpam-100	152	6	)	)	PUNCT
ejpam-100	152	7	)	)	PUNCT
ejpam-100	152	8	)	)	PUNCT
ejpam-100	153	1	d	d	X
ejpam-100	153	2	x	x	PUNCT
ejpam-100	154	1	+	+	NUM
ejpam-100	154	2	∫	∫	PROPN
ejpam-100	154	3	ω	ω	NUM
ejpam-100	154	4	〈	〈	PROPN
ejpam-100	154	5	f,∇tk(u−	f,∇tk(u−	PROPN
ejpam-100	154	6	th(u−λtk(u−ψ	th(u−λtk(u−ψ	NOUN
ejpam-100	154	7	)	)	PUNCT
ejpam-100	154	8	)	)	PUNCT
ejpam-100	154	9	)	)	PUNCT
ejpam-100	154	10	〉	〉	NOUN
ejpam-100	155	1	d	d	NOUN
ejpam-100	155	2	x	x	X
ejpam-100	155	3	.	.	PUNCT
ejpam-100	156	1	then	then	ADV
ejpam-100	156	2	lim	lim	PROPN
ejpam-100	156	3	h→+∞	h→+∞	PROPN
ejpam-100	156	4	∫	∫	PROPN
ejpam-100	156	5	ω	ω	PROPN
ejpam-100	156	6	f	f	PROPN
ejpam-100	156	7	tk(u−	tk(u−	NUM
ejpam-100	156	8	th(u−λtk(u−ψ	th(u−λtk(u−ψ	NOUN
ejpam-100	156	9	)	)	PUNCT
ejpam-100	156	10	)	)	PUNCT
ejpam-100	156	11	)	)	PUNCT
ejpam-100	157	1	d	d	X
ejpam-100	157	2	x	x	PUNCT
ejpam-100	158	1	+	+	NUM
ejpam-100	158	2	∫	∫	PROPN
ejpam-100	158	3	ω	ω	NUM
ejpam-100	158	4	〈	〈	PROPN
ejpam-100	158	5	f,∇tk(u−	f,∇tk(u−	PROPN
ejpam-100	158	6	th(u−λtk(u−ψ	th(u−λtk(u−ψ	NOUN
ejpam-100	158	7	)	)	PUNCT
ejpam-100	158	8	)	)	PUNCT
ejpam-100	158	9	)	)	PUNCT
ejpam-100	158	10	〉	〉	NOUN
ejpam-100	159	1	d	d	NOUN
ejpam-100	159	2	x	x	SYM
ejpam-100	159	3	=	=	SYM
ejpam-100	159	4	λ	λ	X
ejpam-100	159	5	∫	∫	PROPN
ejpam-100	159	6	ω	ω	PROPN
ejpam-100	159	7	f	f	PROPN
ejpam-100	159	8	tk[u−ψ	tk[u−ψ	PROPN
ejpam-100	159	9	]	]	X
ejpam-100	160	1	d	d	X
ejpam-100	160	2	x	x	PUNCT
ejpam-100	160	3	+	+	PUNCT
ejpam-100	160	4	λ	λ	X
ejpam-100	160	5	∫	∫	PROPN
ejpam-100	160	6	ω	ω	PROPN
ejpam-100	160	7	〈	〈	PROPN
ejpam-100	160	8	f,∇tk[u−ψ	f,∇tk[u−ψ	NOUN
ejpam-100	160	9	]	]	SYM
ejpam-100	160	10	〉	〉	NOUN
ejpam-100	160	11	d	d	NOUN
ejpam-100	160	12	x	x	X
ejpam-100	160	13	i.e.	i.e.	X
ejpam-100	160	14	,	,	PUNCT
ejpam-100	160	15	lim	lim	PROPN
ejpam-100	160	16	h→+∞	h→+∞	ADJ
ejpam-100	160	17	jhk	jhk	NOUN
ejpam-100	160	18	=	=	SYM
ejpam-100	160	19	λ	λ	PROPN
ejpam-100	160	20	∫	∫	PROPN
ejpam-100	160	21	ω	ω	PROPN
ejpam-100	160	22	f	f	PROPN
ejpam-100	160	23	tk[u−ψ	tk[u−ψ	PROPN
ejpam-100	160	24	]	]	X
ejpam-100	160	25	d	d	X
ejpam-100	160	26	x	x	PUNCT
ejpam-100	161	1	+	+	PUNCT
ejpam-100	161	2	λ	λ	X
ejpam-100	161	3	∫	∫	PROPN
ejpam-100	161	4	ω	ω	PROPN
ejpam-100	161	5	〈	〈	PROPN
ejpam-100	161	6	f,∇tk[u−ψ	f,∇tk[u−ψ	NOUN
ejpam-100	161	7	]	]	SYM
ejpam-100	161	8	〉	〉	NOUN
ejpam-100	161	9	d	d	NOUN
ejpam-100	161	10	x	x	PROPN
ejpam-100	161	11	.	.	PUNCT
ejpam-100	162	1	(	(	PUNCT
ejpam-100	162	2	4.11	4.11	NUM
ejpam-100	162	3	)	)	PUNCT
ejpam-100	162	4	together	together	ADV
ejpam-100	162	5	(	(	PUNCT
ejpam-100	162	6	4.10	4.10	NUM
ejpam-100	162	7	)	)	PUNCT
ejpam-100	162	8	,	,	PUNCT
ejpam-100	162	9	(	(	PUNCT
ejpam-100	162	10	4.11	4.11	NUM
ejpam-100	162	11	)	)	PUNCT
ejpam-100	162	12	and	and	CCONJ
ejpam-100	162	13	passing	pass	VERB
ejpam-100	162	14	to	to	ADP
ejpam-100	162	15	the	the	DET
ejpam-100	162	16	limit	limit	NOUN
ejpam-100	162	17	in	in	ADP
ejpam-100	162	18	(	(	PUNCT
ejpam-100	162	19	4.3	4.3	NUM
ejpam-100	162	20	)	)	PUNCT
ejpam-100	162	21	,	,	PUNCT
ejpam-100	162	22	we	we	PRON
ejpam-100	162	23	obtain	obtain	VERB
ejpam-100	162	24	,	,	PUNCT
ejpam-100	162	25	λ	λ	PROPN
ejpam-100	162	26	�	�	PROPN
ejpam-100	162	27	∫	∫	PROPN
ejpam-100	162	28	ω	ω	PROPN
ejpam-100	162	29	〈	〈	PROPN
ejpam-100	162	30	a(x	a(x	PROPN
ejpam-100	162	31	,	,	PUNCT
ejpam-100	162	32	u,∇(u−λtk(u−ψ),∇tk(u−ψ	u,∇(u−λtk(u−ψ),∇tk(u−ψ	PROPN
ejpam-100	162	33	)	)	PUNCT
ejpam-100	162	34	〉	〉	NOUN
ejpam-100	163	1	d	d	NOUN
ejpam-100	163	2	x	x	SYM
ejpam-100	164	1	+	+	NUM
ejpam-100	164	2	∫	∫	PROPN
ejpam-100	164	3	ω	ω	NUM
ejpam-100	164	4	g(x	g(x	PROPN
ejpam-100	164	5	,	,	PUNCT
ejpam-100	164	6	u)tk[u−ψ	u)tk[u−ψ	PROPN
ejpam-100	164	7	]	]	PUNCT
ejpam-100	165	1	d	d	X
ejpam-100	165	2	x	x	SYM
ejpam-100	165	3	�	�	PROPN
ejpam-100	165	4	≤	≤	PROPN
ejpam-100	165	5	λ	λ	PROPN
ejpam-100	165	6	�	�	PROPN
ejpam-100	165	7	∫	∫	PROPN
ejpam-100	165	8	ω	ω	PROPN
ejpam-100	165	9	f	f	PROPN
ejpam-100	165	10	tk[u−ψ	tk[u−ψ	PROPN
ejpam-100	165	11	]	]	X
ejpam-100	166	1	d	d	NOUN
ejpam-100	166	2	x	x	SYM
ejpam-100	166	3	+	+	NUM
ejpam-100	166	4	∫	∫	PROPN
ejpam-100	166	5	ω	ω	NUM
ejpam-100	166	6	〈	〈	NOUN
ejpam-100	166	7	f,∇tk[u−ψ	f,∇tk[u−ψ	NOUN
ejpam-100	166	8	]	]	SYM
ejpam-100	166	9	〉	〉	NOUN
ejpam-100	166	10	d	d	NOUN
ejpam-100	166	11	x	x	SYM
ejpam-100	166	12	�	�	PROPN
ejpam-100	166	13	y.	y.	PROPN
ejpam-100	166	14	akdim	akdim	PROPN
ejpam-100	166	15	,	,	PUNCT
ejpam-100	166	16	e.	e.	PROPN
ejpam-100	166	17	azroul	azroul	PROPN
ejpam-100	166	18	,	,	PUNCT
ejpam-100	166	19	and	and	CCONJ
ejpam-100	166	20	m.	m.	NOUN
ejpam-100	166	21	rhoudaf	rhoudaf	PROPN
ejpam-100	166	22	/	/	SYM
ejpam-100	166	23	eur	eur	PROPN
ejpam-100	166	24	.	.	PUNCT
ejpam-100	167	1	j.	j.	PROPN
ejpam-100	167	2	pure	pure	PROPN
ejpam-100	167	3	appl	appl	PROPN
ejpam-100	167	4	.	.	PROPN
ejpam-100	167	5	math	math	PROPN
ejpam-100	167	6	,	,	PUNCT
ejpam-100	167	7	1	1	NUM
ejpam-100	167	8	(	(	PUNCT
ejpam-100	167	9	2008	2008	NUM
ejpam-100	167	10	)	)	PUNCT
ejpam-100	167	11	,	,	PUNCT
ejpam-100	167	12	(	(	PUNCT
ejpam-100	167	13	56	56	NUM
ejpam-100	167	14	-	-	SYM
ejpam-100	167	15	71	71	NUM
ejpam-100	167	16	)	)	PUNCT
ejpam-100	167	17	63	63	NUM
ejpam-100	167	18	for	for	ADP
ejpam-100	167	19	every	every	DET
ejpam-100	167	20	ψ	ψ	X
ejpam-100	167	21	∈	∈	PROPN
ejpam-100	167	22	w	w	PROPN
ejpam-100	167	23	1,p	1,p	PROPN
ejpam-100	167	24	0	0	NUM
ejpam-100	167	25	(	(	PUNCT
ejpam-100	167	26	ω	ω	PROPN
ejpam-100	167	27	,	,	PUNCT
ejpam-100	167	28	w	w	NOUN
ejpam-100	167	29	)	)	PUNCT
ejpam-100	167	30	∩	∩	NOUN
ejpam-100	167	31	l∞(ω	l∞(ω	NOUN
ejpam-100	167	32	)	)	PUNCT
ejpam-100	167	33	,	,	PUNCT
ejpam-100	167	34	and	and	CCONJ
ejpam-100	167	35	for	for	ADP
ejpam-100	167	36	k	k	PROPN
ejpam-100	167	37	>	>	X
ejpam-100	167	38	0	0	X
ejpam-100	167	39	.	.	PUNCT
ejpam-100	168	1	choosing	choose	VERB
ejpam-100	168	2	λ	λ	PROPN
ejpam-100	168	3	>	>	X
ejpam-100	168	4	0	0	PUNCT
ejpam-100	168	5	dividing	divide	VERB
ejpam-100	168	6	by	by	ADP
ejpam-100	168	7	λ	λ	NOUN
ejpam-100	168	8	,	,	PUNCT
ejpam-100	168	9	and	and	CCONJ
ejpam-100	168	10	then	then	ADV
ejpam-100	168	11	letting	let	VERB
ejpam-100	168	12	λ	λ	NOUN
ejpam-100	168	13	tend	tend	VERB
ejpam-100	168	14	to	to	ADP
ejpam-100	168	15	zero	zero	NUM
ejpam-100	168	16	,	,	PUNCT
ejpam-100	168	17	we	we	PRON
ejpam-100	168	18	obtain	obtain	VERB
ejpam-100	168	19	∫	∫	PROPN
ejpam-100	168	20	ω	ω	PROPN
ejpam-100	168	21	〈	〈	NOUN
ejpam-100	168	22	a(x	a(x	PROPN
ejpam-100	168	23	,	,	PUNCT
ejpam-100	168	24	u,∇u),∇tk[u−ϕ	u,∇u),∇tk[u−ϕ	NOUN
ejpam-100	168	25	]	]	X
ejpam-100	168	26	〉	〉	NOUN
ejpam-100	168	27	d	d	NOUN
ejpam-100	168	28	x+	x+	PROPN
ejpam-100	168	29	∫	∫	PROPN
ejpam-100	168	30	ω	ω	NUM
ejpam-100	168	31	g(x	g(x	PROPN
ejpam-100	168	32	,	,	PUNCT
ejpam-100	168	33	u)tk[u−ψ	u)tk[u−ψ	PROPN
ejpam-100	168	34	]	]	PUNCT
ejpam-100	169	1	d	d	X
ejpam-100	169	2	x	x	SYM
ejpam-100	169	3	≤	≤	NUM
ejpam-100	169	4	∫	∫	PROPN
ejpam-100	169	5	ω	ω	PROPN
ejpam-100	169	6	f	f	PROPN
ejpam-100	169	7	tk[u−ϕ	tk[u−ϕ	PROPN
ejpam-100	169	8	]	]	X
ejpam-100	170	1	d	d	X
ejpam-100	170	2	x+	x+	SYM
ejpam-100	170	3	∫	∫	PROPN
ejpam-100	170	4	ω	ω	PROPN
ejpam-100	170	5	〈	〈	PROPN
ejpam-100	170	6	f,∇tk[u−ϕ	f,∇tk[u−ϕ	PROPN
ejpam-100	170	7	]	]	SYM
ejpam-100	170	8	〉	〉	NOUN
ejpam-100	170	9	d	d	NOUN
ejpam-100	170	10	x	x	PROPN
ejpam-100	170	11	.	.	PUNCT
ejpam-100	171	1	(	(	PUNCT
ejpam-100	171	2	4.12	4.12	NUM
ejpam-100	171	3	)	)	PUNCT
ejpam-100	171	4	for	for	ADP
ejpam-100	171	5	λ	λ	PROPN
ejpam-100	171	6	<	<	X
ejpam-100	171	7	0	0	NUM
ejpam-100	171	8	,	,	PUNCT
ejpam-100	171	9	dividing	divide	VERB
ejpam-100	171	10	by	by	ADP
ejpam-100	171	11	λ	λ	NOUN
ejpam-100	171	12	,	,	PUNCT
ejpam-100	171	13	and	and	CCONJ
ejpam-100	171	14	then	then	ADV
ejpam-100	171	15	letting	let	VERB
ejpam-100	171	16	λ	λ	NOUN
ejpam-100	171	17	tend	tend	VERB
ejpam-100	171	18	to	to	ADP
ejpam-100	171	19	zero	zero	NUM
ejpam-100	171	20	,	,	PUNCT
ejpam-100	171	21	we	we	PRON
ejpam-100	171	22	obtain	obtain	VERB
ejpam-100	171	23	∫	∫	PROPN
ejpam-100	171	24	ω	ω	PROPN
ejpam-100	171	25	〈	〈	NOUN
ejpam-100	171	26	a(x	a(x	PROPN
ejpam-100	171	27	,	,	PUNCT
ejpam-100	171	28	u,∇u),∇tk[u−ϕ	u,∇u),∇tk[u−ϕ	NOUN
ejpam-100	171	29	]	]	X
ejpam-100	171	30	〉	〉	NOUN
ejpam-100	171	31	d	d	NOUN
ejpam-100	171	32	x+	x+	PROPN
ejpam-100	171	33	∫	∫	PROPN
ejpam-100	171	34	ω	ω	NUM
ejpam-100	171	35	g(x	g(x	PROPN
ejpam-100	171	36	,	,	PUNCT
ejpam-100	171	37	u)tk[u−ψ	u)tk[u−ψ	PROPN
ejpam-100	171	38	]	]	PUNCT
ejpam-100	172	1	d	d	X
ejpam-100	172	2	x	x	SYM
ejpam-100	172	3	≥	≥	NUM
ejpam-100	172	4	∫	∫	PROPN
ejpam-100	172	5	ω	ω	PROPN
ejpam-100	172	6	f	f	PROPN
ejpam-100	172	7	tk[u−ϕ	tk[u−ϕ	PROPN
ejpam-100	172	8	]	]	X
ejpam-100	173	1	d	d	X
ejpam-100	173	2	x+	x+	SYM
ejpam-100	173	3	∫	∫	PROPN
ejpam-100	173	4	ω	ω	PROPN
ejpam-100	173	5	〈	〈	PROPN
ejpam-100	173	6	f,∇tk[u−ϕ	f,∇tk[u−ϕ	PROPN
ejpam-100	173	7	]	]	SYM
ejpam-100	173	8	〉	〉	NOUN
ejpam-100	173	9	d	d	NOUN
ejpam-100	173	10	x	x	PROPN
ejpam-100	173	11	.	.	PUNCT
ejpam-100	174	1	(	(	PUNCT
ejpam-100	174	2	4.13	4.13	X
ejpam-100	174	3	)	)	PUNCT
ejpam-100	174	4	combining	combine	VERB
ejpam-100	174	5	(	(	PUNCT
ejpam-100	174	6	4.12	4.12	NUM
ejpam-100	174	7	)	)	PUNCT
ejpam-100	174	8	and	and	CCONJ
ejpam-100	174	9	(	(	PUNCT
ejpam-100	174	10	4.13	4.13	NUM
ejpam-100	174	11	)	)	PUNCT
ejpam-100	174	12	,	,	PUNCT
ejpam-100	174	13	we	we	PRON
ejpam-100	174	14	conclude	conclude	VERB
ejpam-100	174	15	the	the	DET
ejpam-100	174	16	following	follow	VERB
ejpam-100	174	17	equality	equality	NOUN
ejpam-100	174	18	:	:	PUNCT
ejpam-100	174	19	∫	∫	PROPN
ejpam-100	174	20	ω	ω	PROPN
ejpam-100	174	21	〈	〈	NOUN
ejpam-100	174	22	a(x	a(x	PROPN
ejpam-100	174	23	,	,	PUNCT
ejpam-100	174	24	u,∇u),∇tk[u−ϕ	u,∇u),∇tk[u−ϕ	NOUN
ejpam-100	174	25	]	]	X
ejpam-100	174	26	〉	〉	NOUN
ejpam-100	174	27	d	d	NOUN
ejpam-100	174	28	x+	x+	PROPN
ejpam-100	174	29	∫	∫	PROPN
ejpam-100	174	30	ω	ω	NUM
ejpam-100	174	31	g(x	g(x	PROPN
ejpam-100	174	32	,	,	PUNCT
ejpam-100	174	33	u)tk[u−ψ	u)tk[u−ψ	PROPN
ejpam-100	174	34	]	]	PUNCT
ejpam-100	175	1	d	d	NOUN
ejpam-100	175	2	x	x	SYM
ejpam-100	175	3	=	=	SYM
ejpam-100	175	4	∫	∫	PROPN
ejpam-100	175	5	ω	ω	PROPN
ejpam-100	175	6	f	f	PROPN
ejpam-100	175	7	tk[u−ϕ	tk[u−ϕ	PROPN
ejpam-100	175	8	]	]	X
ejpam-100	176	1	d	d	X
ejpam-100	176	2	x+	x+	SYM
ejpam-100	176	3	∫	∫	PROPN
ejpam-100	176	4	ω	ω	PROPN
ejpam-100	176	5	〈	〈	PROPN
ejpam-100	176	6	f,∇tk[u−ϕ	f,∇tk[u−ϕ	PROPN
ejpam-100	176	7	]	]	SYM
ejpam-100	176	8	〉	〉	NOUN
ejpam-100	176	9	d	d	NOUN
ejpam-100	176	10	x	x	PROPN
ejpam-100	176	11	.	.	PUNCT
ejpam-100	177	1	(	(	PUNCT
ejpam-100	177	2	4.14	4.14	NUM
ejpam-100	177	3	)	)	PUNCT
ejpam-100	177	4	this	this	PRON
ejpam-100	177	5	completes	complete	VERB
ejpam-100	177	6	the	the	DET
ejpam-100	177	7	proof	proof	NOUN
ejpam-100	177	8	of	of	ADP
ejpam-100	177	9	lemma	lemma	PROPN
ejpam-100	177	10	4.1	4.1	NUM
ejpam-100	177	11	.	.	PUNCT
ejpam-100	177	12	4.2	4.2	NUM
ejpam-100	177	13	.	.	PUNCT
ejpam-100	178	1	proof	proof	NOUN
ejpam-100	178	2	of	of	ADP
ejpam-100	178	3	theorem	theorem	ADJ
ejpam-100	178	4	3.1	3.1	NUM
ejpam-100	178	5	1	1	NUM
ejpam-100	178	6	.	.	NOUN
ejpam-100	178	7	approximate	approximate	ADJ
ejpam-100	178	8	problem	problem	NOUN
ejpam-100	178	9	and	and	CCONJ
ejpam-100	178	10	a	a	DET
ejpam-100	178	11	priori	priori	ADJ
ejpam-100	178	12	estimate	estimate	NOUN
ejpam-100	178	13	let	let	VERB
ejpam-100	178	14	fn	fn	PRON
ejpam-100	178	15	be	be	AUX
ejpam-100	178	16	a	a	DET
ejpam-100	178	17	sequence	sequence	NOUN
ejpam-100	178	18	function	function	NOUN
ejpam-100	178	19	of	of	ADP
ejpam-100	178	20	l∞(ω	l∞(ω	NOUN
ejpam-100	178	21	)	)	PUNCT
ejpam-100	178	22	which	which	PRON
ejpam-100	178	23	is	be	AUX
ejpam-100	178	24	strongly	strongly	ADV
ejpam-100	178	25	convergent	convergent	ADJ
ejpam-100	178	26	to	to	ADP
ejpam-100	178	27	f	f	PROPN
ejpam-100	178	28	in	in	ADP
ejpam-100	178	29	l1(ω	l1(ω	PROPN
ejpam-100	178	30	)	)	PUNCT
ejpam-100	179	1	such	such	ADJ
ejpam-100	179	2	that	that	SCONJ
ejpam-100	179	3	‖	‖	PROPN
ejpam-100	179	4	fn‖l1	fn‖l1	PROPN
ejpam-100	179	5	≤	≤	NUM
ejpam-100	179	6	‖	‖	PROPN
ejpam-100	179	7	f	f	PROPN
ejpam-100	179	8	‖l1	‖l1	PROPN
ejpam-100	179	9	,	,	PUNCT
ejpam-100	179	10	and	and	CCONJ
ejpam-100	179	11	let	let	VERB
ejpam-100	179	12	un	un	PROPN
ejpam-100	179	13	be	be	AUX
ejpam-100	179	14	a	a	DET
ejpam-100	179	15	solution	solution	NOUN
ejpam-100	179	16	in	in	ADP
ejpam-100	179	17	w	w	PROPN
ejpam-100	179	18	1,p	1,p	PROPN
ejpam-100	179	19	0	0	NUM
ejpam-100	179	20	(	(	PUNCT
ejpam-100	179	21	ω	ω	PROPN
ejpam-100	179	22	,	,	PUNCT
ejpam-100	179	23	w	w	NOUN
ejpam-100	179	24	)	)	PUNCT
ejpam-100	179	25	of	of	ADP
ejpam-100	179	26	the	the	DET
ejpam-100	179	27	problem	problem	NOUN
ejpam-100	179	28	¨	¨	NOUN
ejpam-100	179	29	−diva(x	−diva(x	X
ejpam-100	179	30	,	,	PUNCT
ejpam-100	179	31	un,∇un	un,∇un	NUM
ejpam-100	179	32	)	)	PUNCT
ejpam-100	179	33	+	+	CCONJ
ejpam-100	179	34	gn(x	gn(x	INTJ
ejpam-100	179	35	,	,	PUNCT
ejpam-100	179	36	un	un	PROPN
ejpam-100	179	37	)	)	PUNCT
ejpam-100	179	38	=	=	SYM
ejpam-100	179	39	fn−	fn−	NUM
ejpam-100	179	40	div(f	div(f	PROPN
ejpam-100	179	41	)	)	PUNCT
ejpam-100	179	42	in	in	ADP
ejpam-100	179	43	ω	ω	PROPN
ejpam-100	179	44	un	un	PROPN
ejpam-100	179	45	=	=	NOUN
ejpam-100	179	46	0	0	NUM
ejpam-100	179	47	on	on	ADP
ejpam-100	179	48	∂ω	∂ω	PROPN
ejpam-100	179	49	(	(	PUNCT
ejpam-100	179	50	4.15	4.15	NUM
ejpam-100	179	51	)	)	PUNCT
ejpam-100	179	52	where	where	SCONJ
ejpam-100	179	53	gn(x	gn(x	X
ejpam-100	179	54	,	,	PUNCT
ejpam-100	179	55	s	s	X
ejpam-100	179	56	)	)	PUNCT
ejpam-100	179	57	=	=	SYM
ejpam-100	180	1	g(x	g(x	X
ejpam-100	180	2	,	,	PUNCT
ejpam-100	180	3	s	s	X
ejpam-100	180	4	)	)	PUNCT
ejpam-100	180	5	1	1	NUM
ejpam-100	180	6	+	+	SYM
ejpam-100	180	7	1	1	NUM
ejpam-100	180	8	n	n	PRON
ejpam-100	180	9	|g(x	|g(x	NOUN
ejpam-100	180	10	,	,	PUNCT
ejpam-100	180	11	s)|	s)|	NOUN
ejpam-100	180	12	θn(x	θn(x	PUNCT
ejpam-100	180	13	)	)	PUNCT
ejpam-100	180	14	and	and	CCONJ
ejpam-100	180	15	θn(x	θn(x	NUM
ejpam-100	180	16	)	)	PUNCT
ejpam-100	180	17	=	=	SYM
ejpam-100	180	18	t	t	PROPN
ejpam-100	180	19	1	1	NUM
ejpam-100	180	20	n	n	PROPN
ejpam-100	180	21	(	(	PUNCT
ejpam-100	180	22	σ	σ	PROPN
ejpam-100	180	23	1	1	NUM
ejpam-100	180	24	q	q	NOUN
ejpam-100	180	25	(	(	PUNCT
ejpam-100	180	26	x	x	NOUN
ejpam-100	180	27	)	)	PUNCT
ejpam-100	180	28	)	)	PUNCT
ejpam-100	180	29	which	which	PRON
ejpam-100	180	30	exists	exist	VERB
ejpam-100	180	31	thanks	thank	NOUN
ejpam-100	180	32	to	to	ADP
ejpam-100	180	33	[	[	X
ejpam-100	180	34	7	7	NUM
ejpam-100	180	35	]	]	PUNCT
ejpam-100	180	36	.	.	PUNCT
ejpam-100	181	1	choosing	choose	VERB
ejpam-100	181	2	tk(un	tk(un	PROPN
ejpam-100	181	3	)	)	PUNCT
ejpam-100	181	4	as	as	ADP
ejpam-100	181	5	test	test	NOUN
ejpam-100	181	6	function	function	NOUN
ejpam-100	181	7	in	in	ADP
ejpam-100	181	8	(	(	PUNCT
ejpam-100	181	9	4.15	4.15	NUM
ejpam-100	181	10	)	)	PUNCT
ejpam-100	181	11	,	,	PUNCT
ejpam-100	181	12	we	we	PRON
ejpam-100	181	13	have	have	VERB
ejpam-100	181	14	∫	∫	PROPN
ejpam-100	181	15	ω	ω	PROPN
ejpam-100	181	16	〈	〈	PROPN
ejpam-100	181	17	a(x	a(x	PROPN
ejpam-100	181	18	,	,	PUNCT
ejpam-100	181	19	un,∇un),∇tk(un	un,∇un),∇tk(un	ADJ
ejpam-100	181	20	)	)	PUNCT
ejpam-100	181	21	〉	〉	NOUN
ejpam-100	181	22	d	d	NOUN
ejpam-100	181	23	x+	x+	PROPN
ejpam-100	181	24	∫	∫	PROPN
ejpam-100	181	25	ω	ω	PROPN
ejpam-100	181	26	gn(x	gn(x	X
ejpam-100	181	27	,	,	PUNCT
ejpam-100	181	28	un)tk(un	un)tk(un	PROPN
ejpam-100	181	29	)	)	PUNCT
ejpam-100	182	1	d	d	NOUN
ejpam-100	182	2	x	x	SYM
ejpam-100	182	3	=	=	SYM
ejpam-100	182	4	∫	∫	PROPN
ejpam-100	182	5	ω	ω	PROPN
ejpam-100	182	6	fntk(un	fntk(un	PROPN
ejpam-100	182	7	)	)	PUNCT
ejpam-100	182	8	d	d	X
ejpam-100	182	9	x+	x+	PROPN
ejpam-100	182	10	∫	∫	PROPN
ejpam-100	182	11	ω	ω	PROPN
ejpam-100	183	1	〈	〈	PROPN
ejpam-100	183	2	f,∇tk(un	f,∇tk(un	PROPN
ejpam-100	183	3	)	)	PUNCT
ejpam-100	183	4	〉	〉	NOUN
ejpam-100	184	1	d	d	NOUN
ejpam-100	184	2	x	x	SYM
ejpam-100	184	3	using	use	VERB
ejpam-100	184	4	∇tk(un	∇tk(un	PROPN
ejpam-100	184	5	)	)	PUNCT
ejpam-100	184	6	=	=	X
ejpam-100	184	7	∇unχ{|un|≤k	∇unχ{|un|≤k	PROPN
ejpam-100	184	8	}	}	PUNCT
ejpam-100	184	9	and	and	CCONJ
ejpam-100	184	10	thanks	thank	NOUN
ejpam-100	184	11	to	to	ADP
ejpam-100	184	12	assumption	assumption	NOUN
ejpam-100	184	13	(	(	PUNCT
ejpam-100	184	14	2.8	2.8	NUM
ejpam-100	184	15	)	)	PUNCT
ejpam-100	184	16	,	,	PUNCT
ejpam-100	184	17	we	we	PRON
ejpam-100	184	18	obtain	obtain	VERB
ejpam-100	184	19	∫	∫	PROPN
ejpam-100	184	20	ω	ω	PROPN
ejpam-100	184	21	〈	〈	NOUN
ejpam-100	184	22	a(x	a(x	PROPN
ejpam-100	184	23	,	,	PUNCT
ejpam-100	184	24	un,∇un),∇tk(un	un,∇un),∇tk(un	ADJ
ejpam-100	184	25	)	)	PUNCT
ejpam-100	184	26	〉	〉	NOUN
ejpam-100	185	1	d	d	NOUN
ejpam-100	185	2	x	x	SYM
ejpam-100	185	3	≥	≥	PROPN
ejpam-100	185	4	α	α	NOUN
ejpam-100	185	5	n	n	NOUN
ejpam-100	185	6	∑	∑	PROPN
ejpam-100	185	7	i=1	i=1	PROPN
ejpam-100	185	8	∫	∫	PROPN
ejpam-100	185	9	ω	ω	PROPN
ejpam-100	186	1	wi|	wi|	PROPN
ejpam-100	186	2	∂	∂	NUM
ejpam-100	186	3	tk(un	tk(un	PROPN
ejpam-100	186	4	)	)	PUNCT
ejpam-100	186	5	∂	∂	NOUN
ejpam-100	187	1	x	x	NOUN
ejpam-100	187	2	i	i	PRON
ejpam-100	187	3	|p	|p	VERB
ejpam-100	188	1	d	d	X
ejpam-100	188	2	x	x	X
ejpam-100	188	3	then	then	ADV
ejpam-100	188	4	since	since	SCONJ
ejpam-100	188	5	gn(x	gn(x	X
ejpam-100	188	6	,	,	PUNCT
ejpam-100	188	7	un)tk(un)≥	un)tk(un)≥	NUM
ejpam-100	188	8	0	0	NUM
ejpam-100	188	9	we	we	PRON
ejpam-100	188	10	have	have	VERB
ejpam-100	188	11	,	,	PUNCT
ejpam-100	188	12	α	α	PROPN
ejpam-100	188	13	n	n	NOUN
ejpam-100	188	14	∑	∑	PROPN
ejpam-100	188	15	i=1	i=1	PROPN
ejpam-100	188	16	∫	∫	PROPN
ejpam-100	188	17	ω	ω	PROPN
ejpam-100	188	18	wi|	wi|	PROPN
ejpam-100	188	19	∂	∂	NUM
ejpam-100	188	20	tk(un	tk(un	PROPN
ejpam-100	188	21	)	)	PUNCT
ejpam-100	188	22	∂	∂	NOUN
ejpam-100	188	23	x	x	NOUN
ejpam-100	188	24	i	i	PRON
ejpam-100	188	25	|p	|p	VERB
ejpam-100	188	26	d	d	X
ejpam-100	188	27	x	x	SYM
ejpam-100	188	28	≤	≤	X
ejpam-100	188	29	k‖	k‖	X
ejpam-100	188	30	f	f	PROPN
ejpam-100	188	31	‖l1	‖l1	PROPN
ejpam-100	189	1	+	+	CCONJ
ejpam-100	189	2	n	n	CCONJ
ejpam-100	189	3	∑	∑	PROPN
ejpam-100	189	4	i=1	i=1	PROPN
ejpam-100	189	5	∫	∫	PROPN
ejpam-100	189	6	ω	ω	NUM
ejpam-100	189	7	fi|	fi|	PROPN
ejpam-100	189	8	∂	∂	NUM
ejpam-100	189	9	tk(un	tk(un	NOUN
ejpam-100	189	10	)	)	PUNCT
ejpam-100	189	11	∂	∂	NOUN
ejpam-100	190	1	x	x	NOUN
ejpam-100	191	1	i	i	PRON
ejpam-100	191	2	|	|	ADV
ejpam-100	192	1	d	d	X
ejpam-100	192	2	x	x	PROPN
ejpam-100	192	3	y.	y.	PROPN
ejpam-100	192	4	akdim	akdim	PROPN
ejpam-100	192	5	,	,	PUNCT
ejpam-100	192	6	e.	e.	PROPN
ejpam-100	192	7	azroul	azroul	PROPN
ejpam-100	192	8	,	,	PUNCT
ejpam-100	192	9	and	and	CCONJ
ejpam-100	192	10	m.	m.	NOUN
ejpam-100	192	11	rhoudaf	rhoudaf	PROPN
ejpam-100	192	12	/	/	SYM
ejpam-100	192	13	eur	eur	PROPN
ejpam-100	192	14	.	.	PUNCT
ejpam-100	193	1	j.	j.	PROPN
ejpam-100	193	2	pure	pure	PROPN
ejpam-100	193	3	appl	appl	PROPN
ejpam-100	193	4	.	.	PROPN
ejpam-100	193	5	math	math	PROPN
ejpam-100	193	6	,	,	PUNCT
ejpam-100	193	7	1	1	NUM
ejpam-100	193	8	(	(	PUNCT
ejpam-100	193	9	2008	2008	NUM
ejpam-100	193	10	)	)	PUNCT
ejpam-100	193	11	,	,	PUNCT
ejpam-100	193	12	(	(	PUNCT
ejpam-100	193	13	56	56	NUM
ejpam-100	193	14	-	-	SYM
ejpam-100	193	15	71	71	NUM
ejpam-100	193	16	)	)	PUNCT
ejpam-100	193	17	64	64	NUM
ejpam-100	193	18	≤	≤	NOUN
ejpam-100	193	19	k‖	k‖	X
ejpam-100	193	20	f	f	PROPN
ejpam-100	193	21	‖l1	‖l1	PROPN
ejpam-100	194	1	+	+	CCONJ
ejpam-100	194	2	n	n	CCONJ
ejpam-100	194	3	∑	∑	PROPN
ejpam-100	194	4	i=1	i=1	PROPN
ejpam-100	194	5	∫	∫	PROPN
ejpam-100	194	6	ω	ω	NUM
ejpam-100	194	7	fiw	fiw	PROPN
ejpam-100	194	8	−1	−1	NOUN
ejpam-100	194	9	p	p	PROPN
ejpam-100	195	1	i	i	PRON
ejpam-100	195	2	(	(	PUNCT
ejpam-100	195	3	α	α	NOUN
ejpam-100	195	4	2	2	NUM
ejpam-100	195	5	)	)	PUNCT
ejpam-100	195	6	−1	−1	NOUN
ejpam-100	195	7	p	p	NOUN
ejpam-100	195	8	|	|	NOUN
ejpam-100	195	9	∂	∂	NUM
ejpam-100	195	10	tk(un	tk(un	NOUN
ejpam-100	195	11	)	)	PUNCT
ejpam-100	195	12	∂	∂	NOUN
ejpam-100	195	13	x	x	NOUN
ejpam-100	196	1	i	i	PRON
ejpam-100	196	2	|w	|w	VERB
ejpam-100	196	3	1	1	NUM
ejpam-100	197	1	p	p	NOUN
ejpam-100	197	2	i	i	PRON
ejpam-100	197	3	(	(	PUNCT
ejpam-100	197	4	α	α	PROPN
ejpam-100	197	5	2	2	NUM
ejpam-100	197	6	)	)	PUNCT
ejpam-100	197	7	1	1	NUM
ejpam-100	197	8	p	p	NOUN
ejpam-100	197	9	d	d	X
ejpam-100	197	10	x	x	PUNCT
ejpam-100	197	11	by	by	ADP
ejpam-100	197	12	young	young	PROPN
ejpam-100	197	13	’s	’s	PART
ejpam-100	197	14	inequality	inequality	NOUN
ejpam-100	197	15	,	,	PUNCT
ejpam-100	197	16	we	we	PRON
ejpam-100	197	17	obtain	obtain	VERB
ejpam-100	197	18	α	α	PROPN
ejpam-100	197	19	n	n	ADV
ejpam-100	197	20	∑	∑	PROPN
ejpam-100	197	21	i=1	i=1	PROPN
ejpam-100	197	22	∫	∫	PROPN
ejpam-100	198	1	ω	ω	PROPN
ejpam-100	199	1	wi|	wi|	PROPN
ejpam-100	199	2	∂	∂	NUM
ejpam-100	199	3	tk(un	tk(un	PROPN
ejpam-100	199	4	)	)	PUNCT
ejpam-100	199	5	∂	∂	NOUN
ejpam-100	200	1	x	x	NOUN
ejpam-100	200	2	i	i	PRON
ejpam-100	200	3	|p	|p	VERB
ejpam-100	200	4	d	d	X
ejpam-100	200	5	x	x	SYM
ejpam-100	200	6	≤	≤	X
ejpam-100	200	7	k‖	k‖	X
ejpam-100	200	8	f	f	PROPN
ejpam-100	200	9	‖l1	‖l1	PROPN
ejpam-100	200	10	+	+	PROPN
ejpam-100	200	11	c(α	c(α	NOUN
ejpam-100	200	12	)	)	PUNCT
ejpam-100	200	13	p′	p′	NOUN
ejpam-100	200	14	|f‖∏	|f‖∏	ADJ
ejpam-100	200	15	lp′	lp′	PROPN
ejpam-100	200	16	(	(	PUNCT
ejpam-100	200	17	ω	ω	NOUN
ejpam-100	200	18	,	,	PUNCT
ejpam-100	200	19	w∗i	w∗i	PRON
ejpam-100	200	20	)	)	PUNCT
ejpam-100	201	1	+	+	CCONJ
ejpam-100	201	2	α	α	SYM
ejpam-100	201	3	2	2	NUM
ejpam-100	201	4	n	n	NOUN
ejpam-100	201	5	∑	∑	PROPN
ejpam-100	201	6	i=1	i=1	PROPN
ejpam-100	201	7	∫	∫	PROPN
ejpam-100	201	8	ω	ω	PROPN
ejpam-100	201	9	wi|	wi|	PROPN
ejpam-100	201	10	∂	∂	NUM
ejpam-100	201	11	tk(un	tk(un	PROPN
ejpam-100	201	12	)	)	PUNCT
ejpam-100	201	13	∂	∂	NOUN
ejpam-100	201	14	x	x	NOUN
ejpam-100	201	15	i	i	PRON
ejpam-100	201	16	|p	|p	VERB
ejpam-100	201	17	d	d	NOUN
ejpam-100	201	18	x	x	X
ejpam-100	201	19	.	.	PUNCT
ejpam-100	202	1	then	then	ADV
ejpam-100	202	2	,	,	PUNCT
ejpam-100	202	3	α	α	PROPN
ejpam-100	202	4	2	2	NUM
ejpam-100	202	5	n	n	NOUN
ejpam-100	202	6	∑	∑	PROPN
ejpam-100	202	7	i=1	i=1	PROPN
ejpam-100	202	8	∫	∫	PROPN
ejpam-100	202	9	ω	ω	PROPN
ejpam-100	202	10	wi|	wi|	PROPN
ejpam-100	202	11	∂	∂	NUM
ejpam-100	202	12	tk(un	tk(un	PROPN
ejpam-100	202	13	)	)	PUNCT
ejpam-100	202	14	∂	∂	NOUN
ejpam-100	202	15	x	x	NOUN
ejpam-100	203	1	i	i	PRON
ejpam-100	203	2	|p	|p	VERB
ejpam-100	203	3	d	d	X
ejpam-100	203	4	x	x	X
ejpam-100	203	5	≤	≤	ADV
ejpam-100	204	1	k(‖	k(‖	PUNCT
ejpam-100	204	2	f	f	X
ejpam-100	204	3	‖l1	‖l1	PROPN
ejpam-100	205	1	+	+	CCONJ
ejpam-100	205	2	c(α	c(α	PROPN
ejpam-100	205	3	)	)	PUNCT
ejpam-100	205	4	p′	p′	NOUN
ejpam-100	205	5	‖f‖∏	‖f‖∏	NOUN
ejpam-100	205	6	lp′	lp′	NOUN
ejpam-100	205	7	(	(	PUNCT
ejpam-100	205	8	ω	ω	NOUN
ejpam-100	205	9	,	,	PUNCT
ejpam-100	205	10	w∗i	w∗i	PRON
ejpam-100	205	11	)	)	PUNCT
ejpam-100	205	12	for	for	ADP
ejpam-100	205	13	k	k	PROPN
ejpam-100	205	14	>	>	X
ejpam-100	205	15	1	1	NUM
ejpam-100	205	16	,	,	PUNCT
ejpam-100	205	17	which	which	PRON
ejpam-100	205	18	implies	imply	VERB
ejpam-100	205	19	that	that	SCONJ
ejpam-100	205	20	n	n	AUX
ejpam-100	205	21	∑	∑	PROPN
ejpam-100	205	22	i=1	i=1	PROPN
ejpam-100	205	23	∫	∫	PROPN
ejpam-100	205	24	ω	ω	NUM
ejpam-100	205	25	|	|	NOUN
ejpam-100	205	26	∂	∂	NUM
ejpam-100	205	27	tk(un	tk(un	NOUN
ejpam-100	205	28	)	)	PUNCT
ejpam-100	205	29	∂	∂	NOUN
ejpam-100	205	30	x	x	NOUN
ejpam-100	205	31	i	i	PRON
ejpam-100	205	32	|pwi(x)d	|pwi(x)d	PROPN
ejpam-100	205	33	x	x	X
ejpam-100	205	34	!	!	PUNCT
ejpam-100	205	35	1	1	NUM
ejpam-100	205	36	p	p	NOUN
ejpam-100	205	37	≤	≤	NUM
ejpam-100	206	1	ck	ck	INTJ
ejpam-100	206	2	1	1	NUM
ejpam-100	206	3	p	p	NOUN
ejpam-100	206	4	∀k	∀k	NOUN
ejpam-100	206	5	>	>	X
ejpam-100	206	6	1	1	NUM
ejpam-100	206	7	.	.	PUNCT
ejpam-100	207	1	(	(	PUNCT
ejpam-100	207	2	4.16	4.16	NUM
ejpam-100	207	3	)	)	PUNCT
ejpam-100	207	4	2	2	NUM
ejpam-100	207	5	:	:	PUNCT
ejpam-100	207	6	locally	locally	ADV
ejpam-100	207	7	convergence	convergence	NOUN
ejpam-100	207	8	of	of	ADP
ejpam-100	207	9	un	un	PROPN
ejpam-100	207	10	in	in	ADP
ejpam-100	207	11	measure	measure	NOUN
ejpam-100	207	12	we	we	PRON
ejpam-100	207	13	prove	prove	VERB
ejpam-100	207	14	that	that	SCONJ
ejpam-100	207	15	un	un	PROPN
ejpam-100	207	16	converges	converge	VERB
ejpam-100	207	17	to	to	ADP
ejpam-100	207	18	some	some	DET
ejpam-100	207	19	function	function	NOUN
ejpam-100	207	20	u	u	NOUN
ejpam-100	207	21	locally	locally	ADV
ejpam-100	207	22	in	in	ADP
ejpam-100	207	23	measure	measure	NOUN
ejpam-100	207	24	(	(	PUNCT
ejpam-100	207	25	and	and	CCONJ
ejpam-100	207	26	therefore	therefore	ADV
ejpam-100	207	27	,	,	PUNCT
ejpam-100	207	28	we	we	PRON
ejpam-100	207	29	can	can	AUX
ejpam-100	207	30	always	always	ADV
ejpam-100	207	31	assume	assume	VERB
ejpam-100	207	32	that	that	SCONJ
ejpam-100	207	33	the	the	DET
ejpam-100	207	34	convergence	convergence	NOUN
ejpam-100	207	35	is	be	AUX
ejpam-100	207	36	a.e	a.e	PROPN
ejpam-100	207	37	.	.	PROPN
ejpam-100	207	38	after	after	ADP
ejpam-100	207	39	passing	pass	VERB
ejpam-100	207	40	to	to	ADP
ejpam-100	207	41	a	a	DET
ejpam-100	207	42	suitable	suitable	ADJ
ejpam-100	207	43	subsequence	subsequence	NOUN
ejpam-100	207	44	)	)	PUNCT
ejpam-100	207	45	,	,	PUNCT
ejpam-100	207	46	we	we	PRON
ejpam-100	207	47	shall	shall	AUX
ejpam-100	207	48	show	show	VERB
ejpam-100	207	49	that	that	SCONJ
ejpam-100	207	50	un	un	PROPN
ejpam-100	207	51	is	be	AUX
ejpam-100	207	52	a	a	DET
ejpam-100	207	53	cauchy	cauchy	ADJ
ejpam-100	207	54	sequence	sequence	NOUN
ejpam-100	207	55	in	in	ADP
ejpam-100	207	56	measure	measure	NOUN
ejpam-100	207	57	in	in	ADP
ejpam-100	207	58	any	any	DET
ejpam-100	207	59	ball	ball	NOUN
ejpam-100	207	60	br	br	NOUN
ejpam-100	207	61	.	.	PUNCT
ejpam-100	208	1	let	let	VERB
ejpam-100	208	2	k	k	PRON
ejpam-100	208	3	>	>	X
ejpam-100	208	4	0	0	PUNCT
ejpam-100	209	1	large	large	ADJ
ejpam-100	209	2	enough	enough	ADV
ejpam-100	209	3	,	,	PUNCT
ejpam-100	209	4	by	by	ADP
ejpam-100	209	5	using	use	VERB
ejpam-100	209	6	(	(	PUNCT
ejpam-100	209	7	2.5	2.5	NUM
ejpam-100	209	8	)	)	PUNCT
ejpam-100	209	9	,	,	PUNCT
ejpam-100	209	10	we	we	PRON
ejpam-100	209	11	have	have	VERB
ejpam-100	209	12	k	k	PROPN
ejpam-100	209	13	meas({|un|	meas({|un|	X
ejpam-100	209	14	>	>	X
ejpam-100	209	15	k	k	ADJ
ejpam-100	209	16	}	}	PUNCT
ejpam-100	209	17	∩	∩	ADJ
ejpam-100	209	18	br	br	NOUN
ejpam-100	209	19	)	)	PUNCT
ejpam-100	209	20	=	=	SYM
ejpam-100	209	21	∫	∫	PROPN
ejpam-100	209	22	{	{	PUNCT
ejpam-100	209	23	|un|>k}∩br	|un|>k}∩br	PROPN
ejpam-100	209	24	|tk(un)|	|tk(un)|	NOUN
ejpam-100	210	1	d	d	X
ejpam-100	210	2	x	x	SYM
ejpam-100	210	3	≤	≤	NUM
ejpam-100	210	4	∫	∫	PROPN
ejpam-100	210	5	br	br	PROPN
ejpam-100	210	6	|tk(un)|	|tk(un)|	PROPN
ejpam-100	210	7	d	d	X
ejpam-100	210	8	x	x	SYM
ejpam-100	210	9	≤	≤	PROPN
ejpam-100	210	10	�	�	PROPN
ejpam-100	210	11	∫	∫	PROPN
ejpam-100	210	12	ω	ω	PROPN
ejpam-100	210	13	|tk(un)|pw0	|tk(un)|pw0	NOUN
ejpam-100	211	1	d	d	X
ejpam-100	211	2	x	x	SYM
ejpam-100	211	3	�	�	PROPN
ejpam-100	211	4	1	1	NUM
ejpam-100	211	5	p	p	NOUN
ejpam-100	211	6	.	.	PUNCT
ejpam-100	212	1	∫	∫	PROPN
ejpam-100	213	1	br	br	PROPN
ejpam-100	214	1	w1−p′	w1−p′	PROPN
ejpam-100	214	2	0	0	NUM
ejpam-100	215	1	d	d	NOUN
ejpam-100	215	2	x	x	X
ejpam-100	215	3	!	!	PUNCT
ejpam-100	216	1	1	1	NUM
ejpam-100	216	2	q′	q′	NOUN
ejpam-100	216	3	≤	≤	NUM
ejpam-100	216	4	cr	cr	PROPN
ejpam-100	216	5	∫	∫	PROPN
ejpam-100	216	6	ω	ω	PROPN
ejpam-100	217	1	n	n	PROPN
ejpam-100	217	2	∑	∑	PROPN
ejpam-100	217	3	i=1	i=1	PROPN
ejpam-100	217	4	|	|	ADV
ejpam-100	217	5	∂	∂	NUM
ejpam-100	217	6	tk(un	tk(un	NOUN
ejpam-100	217	7	)	)	PUNCT
ejpam-100	217	8	∂	∂	NOUN
ejpam-100	217	9	x	x	NOUN
ejpam-100	217	10	i	i	PRON
ejpam-100	217	11	|pwi(x	|pwi(x	ADJ
ejpam-100	217	12	)	)	PUNCT
ejpam-100	218	1	d	d	NOUN
ejpam-100	218	2	x	x	X
ejpam-100	218	3	!	!	PUNCT
ejpam-100	218	4	1	1	NUM
ejpam-100	218	5	p	p	NOUN
ejpam-100	218	6	≤	≤	NUM
ejpam-100	218	7	c1k	c1k	VERB
ejpam-100	218	8	1	1	NUM
ejpam-100	218	9	p	p	NOUN
ejpam-100	218	10	.	.	PUNCT
ejpam-100	219	1	which	which	PRON
ejpam-100	219	2	implies	imply	VERB
ejpam-100	219	3	meas({|un|	meas({|un|	NOUN
ejpam-100	219	4	>	>	X
ejpam-100	219	5	k	k	ADJ
ejpam-100	219	6	}	}	PUNCT
ejpam-100	219	7	∩	∩	NOUN
ejpam-100	219	8	br)≤	br)≤	VERB
ejpam-100	219	9	c1	c1	PROPN
ejpam-100	219	10	k1−	k1−	PROPN
ejpam-100	219	11	1	1	NUM
ejpam-100	219	12	p	p	VERB
ejpam-100	219	13	∀k	∀k	NOUN
ejpam-100	219	14	>	>	X
ejpam-100	219	15	1	1	NUM
ejpam-100	219	16	.	.	PUNCT
ejpam-100	220	1	(	(	PUNCT
ejpam-100	220	2	4.17	4.17	NUM
ejpam-100	220	3	)	)	PUNCT
ejpam-100	220	4	we	we	PRON
ejpam-100	220	5	have	have	AUX
ejpam-100	220	6	,	,	PUNCT
ejpam-100	220	7	for	for	ADP
ejpam-100	220	8	every	every	DET
ejpam-100	220	9	δ	δ	PROPN
ejpam-100	220	10	>	>	X
ejpam-100	220	11	0	0	PROPN
ejpam-100	220	12	,	,	PUNCT
ejpam-100	220	13	meas({|un−	meas({|un−	PROPN
ejpam-100	220	14	um|	um|	PROPN
ejpam-100	220	15	>	>	PART
ejpam-100	220	16	δ	δ	PROPN
ejpam-100	220	17	}	}	PUNCT
ejpam-100	220	18	∩	∩	ADJ
ejpam-100	220	19	br	br	NOUN
ejpam-100	220	20	)	)	PUNCT
ejpam-100	220	21	≤	≤	NOUN
ejpam-100	220	22	meas({|un|	meas({|un|	NOUN
ejpam-100	220	23	>	>	X
ejpam-100	220	24	k	k	NOUN
ejpam-100	220	25	}	}	PUNCT
ejpam-100	220	26	∩	∩	ADJ
ejpam-100	220	27	br	br	X
ejpam-100	220	28	)	)	PUNCT
ejpam-100	220	29	+	+	NOUN
ejpam-100	220	30	meas({|um|	meas({|um|	NOUN
ejpam-100	220	31	>	>	X
ejpam-100	220	32	k	k	PROPN
ejpam-100	220	33	}	}	PUNCT
ejpam-100	220	34	∩	∩	ADJ
ejpam-100	220	35	br	br	X
ejpam-100	220	36	)	)	PUNCT
ejpam-100	220	37	+	+	PROPN
ejpam-100	220	38	meas{|tk(un)−	meas{|tk(un)−	PROPN
ejpam-100	220	39	tk(um)|	tk(um)|	PROPN
ejpam-100	220	40	>	>	SYM
ejpam-100	220	41	δ	δ	PROPN
ejpam-100	220	42	}	}	PUNCT
ejpam-100	220	43	.	.	PUNCT
ejpam-100	221	1	(	(	PUNCT
ejpam-100	221	2	4.18	4.18	NUM
ejpam-100	221	3	)	)	PUNCT
ejpam-100	221	4	since	since	SCONJ
ejpam-100	221	5	tk(un	tk(un	PROPN
ejpam-100	221	6	)	)	PUNCT
ejpam-100	221	7	is	be	AUX
ejpam-100	221	8	bounded	bound	VERB
ejpam-100	221	9	in	in	ADP
ejpam-100	221	10	w	w	PROPN
ejpam-100	221	11	1,p	1,p	PROPN
ejpam-100	221	12	0	0	NUM
ejpam-100	221	13	(	(	PUNCT
ejpam-100	221	14	ω	ω	PROPN
ejpam-100	221	15	,	,	PUNCT
ejpam-100	221	16	w	w	PROPN
ejpam-100	221	17	)	)	PUNCT
ejpam-100	221	18	,	,	PUNCT
ejpam-100	221	19	there	there	PRON
ejpam-100	221	20	exists	exist	VERB
ejpam-100	221	21	some	some	DET
ejpam-100	221	22	vk	vk	NOUN
ejpam-100	221	23	∈w	∈w	PROPN
ejpam-100	221	24	1,p	1,p	PROPN
ejpam-100	221	25	0	0	SYM
ejpam-100	221	26	(	(	PUNCT
ejpam-100	221	27	ω	ω	PROPN
ejpam-100	221	28	,	,	PUNCT
ejpam-100	221	29	w	w	PROPN
ejpam-100	221	30	)	)	PUNCT
ejpam-100	221	31	,	,	PUNCT
ejpam-100	221	32	such	such	ADJ
ejpam-100	221	33	that	that	DET
ejpam-100	221	34	tk(un	tk(un	PROPN
ejpam-100	221	35	)	)	PUNCT
ejpam-100	221	36	*	*	PUNCT
ejpam-100	222	1	vk	vk	ADP
ejpam-100	222	2	weakly	weakly	ADV
ejpam-100	222	3	in	in	ADP
ejpam-100	222	4	w	w	PROPN
ejpam-100	222	5	1,p	1,p	PROPN
ejpam-100	222	6	0	0	NUM
ejpam-100	222	7	(	(	PUNCT
ejpam-100	222	8	ω	ω	PROPN
ejpam-100	222	9	,	,	PUNCT
ejpam-100	222	10	w	w	NOUN
ejpam-100	222	11	)	)	PUNCT
ejpam-100	222	12	tk(un)→	tk(un)→	PROPN
ejpam-100	222	13	vk	vk	NOUN
ejpam-100	222	14	strongly	strongly	ADV
ejpam-100	222	15	in	in	ADP
ejpam-100	222	16	lq(ω	lq(ω	PROPN
ejpam-100	222	17	,	,	PUNCT
ejpam-100	222	18	σ	σ	PROPN
ejpam-100	222	19	)	)	PUNCT
ejpam-100	222	20	and	and	CCONJ
ejpam-100	222	21	a.e	a.e	PROPN
ejpam-100	222	22	.	.	PROPN
ejpam-100	223	1	in	in	ADP
ejpam-100	223	2	ω	ω	PROPN
ejpam-100	223	3	.	.	PUNCT
ejpam-100	224	1	y.	y.	PROPN
ejpam-100	224	2	akdim	akdim	PROPN
ejpam-100	224	3	,	,	PUNCT
ejpam-100	224	4	e.	e.	PROPN
ejpam-100	224	5	azroul	azroul	PROPN
ejpam-100	224	6	,	,	PUNCT
ejpam-100	224	7	and	and	CCONJ
ejpam-100	224	8	m.	m.	NOUN
ejpam-100	224	9	rhoudaf	rhoudaf	PROPN
ejpam-100	224	10	/	/	SYM
ejpam-100	224	11	eur	eur	PROPN
ejpam-100	224	12	.	.	PUNCT
ejpam-100	225	1	j.	j.	PROPN
ejpam-100	225	2	pure	pure	PROPN
ejpam-100	225	3	appl	appl	PROPN
ejpam-100	225	4	.	.	PROPN
ejpam-100	225	5	math	math	PROPN
ejpam-100	225	6	,	,	PUNCT
ejpam-100	225	7	1	1	NUM
ejpam-100	225	8	(	(	PUNCT
ejpam-100	225	9	2008	2008	NUM
ejpam-100	225	10	)	)	PUNCT
ejpam-100	225	11	,	,	PUNCT
ejpam-100	225	12	(	(	PUNCT
ejpam-100	225	13	56	56	NUM
ejpam-100	225	14	-	-	SYM
ejpam-100	225	15	71	71	NUM
ejpam-100	225	16	)	)	PUNCT
ejpam-100	225	17	65	65	NUM
ejpam-100	226	1	consequently	consequently	ADV
ejpam-100	226	2	,	,	PUNCT
ejpam-100	226	3	we	we	PRON
ejpam-100	226	4	can	can	AUX
ejpam-100	226	5	assume	assume	VERB
ejpam-100	226	6	that	that	SCONJ
ejpam-100	226	7	tk(un	tk(un	PROPN
ejpam-100	226	8	)	)	PUNCT
ejpam-100	226	9	is	be	AUX
ejpam-100	226	10	a	a	DET
ejpam-100	226	11	cauchy	cauchy	ADJ
ejpam-100	226	12	sequence	sequence	NOUN
ejpam-100	226	13	in	in	ADP
ejpam-100	226	14	measure	measure	NOUN
ejpam-100	226	15	in	in	ADP
ejpam-100	226	16	ω	ω	PROPN
ejpam-100	226	17	.	.	PUNCT
ejpam-100	227	1	let	let	VERB
ejpam-100	227	2	ε	ε	PROPN
ejpam-100	227	3	>	>	X
ejpam-100	227	4	0	0	PROPN
ejpam-100	227	5	,	,	PUNCT
ejpam-100	227	6	then	then	ADV
ejpam-100	227	7	by	by	ADP
ejpam-100	227	8	(	(	PUNCT
ejpam-100	227	9	4.17	4.17	NUM
ejpam-100	227	10	)	)	PUNCT
ejpam-100	227	11	and	and	CCONJ
ejpam-100	227	12	(	(	PUNCT
ejpam-100	227	13	4.18	4.18	NUM
ejpam-100	227	14	)	)	PUNCT
ejpam-100	227	15	,	,	PUNCT
ejpam-100	227	16	there	there	PRON
ejpam-100	227	17	exists	exist	VERB
ejpam-100	227	18	some	some	DET
ejpam-100	227	19	k(ε	k(ε	PROPN
ejpam-100	227	20	)	)	PUNCT
ejpam-100	227	21	>	>	X
ejpam-100	227	22	0	0	NUM
ejpam-100	228	1	such	such	ADJ
ejpam-100	228	2	that	that	SCONJ
ejpam-100	228	3	meas({|un	meas({|un	PROPN
ejpam-100	228	4	−	−	PUNCT
ejpam-100	229	1	um|	um|	ADJ
ejpam-100	229	2	>	>	SYM
ejpam-100	229	3	δ	δ	PROPN
ejpam-100	229	4	}	}	PUNCT
ejpam-100	229	5	∩	∩	ADJ
ejpam-100	229	6	br	br	NOUN
ejpam-100	229	7	)	)	PUNCT
ejpam-100	229	8	<	<	X
ejpam-100	229	9	ε	ε	PROPN
ejpam-100	229	10	for	for	ADP
ejpam-100	229	11	all	all	DET
ejpam-100	229	12	n	n	CCONJ
ejpam-100	229	13	,	,	PUNCT
ejpam-100	229	14	m	m	PROPN
ejpam-100	229	15	≥	≥	NOUN
ejpam-100	229	16	n0(k(ε),δ	n0(k(ε),δ	NUM
ejpam-100	229	17	,	,	PUNCT
ejpam-100	229	18	r	r	NOUN
ejpam-100	229	19	)	)	PUNCT
ejpam-100	229	20	.	.	PUNCT
ejpam-100	230	1	this	this	PRON
ejpam-100	230	2	proves	prove	VERB
ejpam-100	230	3	that	that	SCONJ
ejpam-100	230	4	(	(	PUNCT
ejpam-100	230	5	un	un	PROPN
ejpam-100	230	6	)	)	PUNCT
ejpam-100	230	7	is	be	AUX
ejpam-100	230	8	a	a	DET
ejpam-100	230	9	cauchy	cauchy	ADJ
ejpam-100	230	10	sequence	sequence	NOUN
ejpam-100	230	11	in	in	ADP
ejpam-100	230	12	measure	measure	NOUN
ejpam-100	230	13	in	in	ADP
ejpam-100	230	14	br	br	NOUN
ejpam-100	230	15	,	,	PUNCT
ejpam-100	230	16	thus	thus	ADV
ejpam-100	230	17	converges	converge	VERB
ejpam-100	230	18	almost	almost	ADV
ejpam-100	230	19	everywhere	everywhere	ADV
ejpam-100	230	20	to	to	ADP
ejpam-100	230	21	some	some	DET
ejpam-100	230	22	measurable	measurable	ADJ
ejpam-100	230	23	function	function	NOUN
ejpam-100	230	24	u.	u.	PROPN
ejpam-100	230	25	then	then	ADV
ejpam-100	230	26	tk(un	tk(un	VERB
ejpam-100	230	27	)	)	PUNCT
ejpam-100	230	28	*	*	PUNCT
ejpam-100	230	29	tk(u	tk(u	NOUN
ejpam-100	230	30	)	)	PUNCT
ejpam-100	230	31	weakly	weakly	ADV
ejpam-100	230	32	in	in	ADP
ejpam-100	230	33	w	w	PROPN
ejpam-100	230	34	1,p	1,p	PROPN
ejpam-100	230	35	0	0	NUM
ejpam-100	230	36	(	(	PUNCT
ejpam-100	230	37	ω	ω	PROPN
ejpam-100	230	38	,	,	PUNCT
ejpam-100	230	39	w	w	PROPN
ejpam-100	230	40	)	)	PUNCT
ejpam-100	230	41	,	,	PUNCT
ejpam-100	230	42	tk(un)→	tk(un)→	PROPN
ejpam-100	230	43	tk(u	tk(u	PUNCT
ejpam-100	230	44	)	)	PUNCT
ejpam-100	230	45	strongly	strongly	ADV
ejpam-100	230	46	in	in	ADP
ejpam-100	230	47	lq(ω	lq(ω	PROPN
ejpam-100	230	48	,	,	PUNCT
ejpam-100	230	49	σ	σ	PROPN
ejpam-100	230	50	)	)	PUNCT
ejpam-100	230	51	and	and	CCONJ
ejpam-100	230	52	a.e	a.e	PROPN
ejpam-100	230	53	in	in	ADP
ejpam-100	230	54	ω	ω	NUM
ejpam-100	230	55	.	.	PUNCT
ejpam-100	231	1	(	(	PUNCT
ejpam-100	231	2	4.19	4.19	NUM
ejpam-100	231	3	)	)	PUNCT
ejpam-100	231	4	3	3	NUM
ejpam-100	231	5	.	.	PUNCT
ejpam-100	232	1	equi	equi	NOUN
ejpam-100	232	2	-	-	PUNCT
ejpam-100	232	3	integrability	integrability	NOUN
ejpam-100	232	4	of	of	ADP
ejpam-100	232	5	nonlinearities	nonlinearitie	NOUN
ejpam-100	232	6	we	we	PRON
ejpam-100	232	7	need	need	VERB
ejpam-100	232	8	to	to	PART
ejpam-100	232	9	prove	prove	VERB
ejpam-100	232	10	that	that	SCONJ
ejpam-100	232	11	gn(x	gn(x	X
ejpam-100	232	12	,	,	PUNCT
ejpam-100	232	13	un)→	un)→	ADP
ejpam-100	232	14	g(x	g(x	PROPN
ejpam-100	232	15	,	,	PUNCT
ejpam-100	232	16	u	u	NOUN
ejpam-100	232	17	)	)	PUNCT
ejpam-100	232	18	strongly	strongly	ADV
ejpam-100	232	19	in	in	ADP
ejpam-100	232	20	l1(ω	l1(ω	PROPN
ejpam-100	232	21	)	)	PUNCT
ejpam-100	232	22	(	(	PUNCT
ejpam-100	232	23	4.20	4.20	NUM
ejpam-100	232	24	)	)	PUNCT
ejpam-100	232	25	in	in	ADP
ejpam-100	232	26	particular	particular	ADJ
ejpam-100	232	27	it	it	PRON
ejpam-100	232	28	is	be	AUX
ejpam-100	232	29	enough	enough	ADJ
ejpam-100	232	30	to	to	PART
ejpam-100	232	31	prove	prove	VERB
ejpam-100	232	32	the	the	DET
ejpam-100	232	33	equi	equi	NOUN
ejpam-100	232	34	-	-	PUNCT
ejpam-100	232	35	integrable	integrable	ADJ
ejpam-100	232	36	of	of	ADP
ejpam-100	232	37	gn(x	gn(x	X
ejpam-100	232	38	,	,	PUNCT
ejpam-100	232	39	un	un	PROPN
ejpam-100	232	40	)	)	PUNCT
ejpam-100	232	41	to	to	ADP
ejpam-100	232	42	this	this	DET
ejpam-100	232	43	purpose	purpose	NOUN
ejpam-100	232	44	.	.	PUNCT
ejpam-100	233	1	we	we	PRON
ejpam-100	233	2	take	take	VERB
ejpam-100	233	3	tl+1(un)−	tl+1(un)−	PROPN
ejpam-100	233	4	tl(un	tl(un	PROPN
ejpam-100	233	5	)	)	PUNCT
ejpam-100	233	6	as	as	ADP
ejpam-100	233	7	test	test	NOUN
ejpam-100	233	8	function	function	NOUN
ejpam-100	233	9	in	in	ADP
ejpam-100	233	10	(	(	PUNCT
ejpam-100	233	11	4.15	4.15	NUM
ejpam-100	233	12	)	)	PUNCT
ejpam-100	233	13	,	,	PUNCT
ejpam-100	233	14	we	we	PRON
ejpam-100	233	15	obtain	obtain	VERB
ejpam-100	233	16	∫	∫	PROPN
ejpam-100	233	17	ω	ω	PROPN
ejpam-100	233	18	〈	〈	NOUN
ejpam-100	233	19	a(x	a(x	PROPN
ejpam-100	233	20	,	,	PUNCT
ejpam-100	233	21	un,∇un),∇(tl+1(un)−	un,∇un),∇(tl+1(un)−	PROPN
ejpam-100	233	22	tl(un	tl(un	PROPN
ejpam-100	233	23	)	)	PUNCT
ejpam-100	233	24	)	)	PUNCT
ejpam-100	233	25	〉	〉	NOUN
ejpam-100	234	1	d	d	NOUN
ejpam-100	234	2	x	x	SYM
ejpam-100	235	1	+	+	NUM
ejpam-100	235	2	∫	∫	PROPN
ejpam-100	235	3	ω	ω	NUM
ejpam-100	235	4	gn(x	gn(x	X
ejpam-100	235	5	,	,	PUNCT
ejpam-100	235	6	un)(tl+1(un)−	un)(tl+1(un)−	PROPN
ejpam-100	235	7	tl(un	tl(un	PROPN
ejpam-100	235	8	)	)	PUNCT
ejpam-100	235	9	)	)	PUNCT
ejpam-100	236	1	d	d	NOUN
ejpam-100	236	2	x	x	X
ejpam-100	236	3	=	=	SYM
ejpam-100	237	1	∫	∫	PROPN
ejpam-100	237	2	ω	ω	NUM
ejpam-100	237	3	f	f	PROPN
ejpam-100	237	4	(	(	PUNCT
ejpam-100	237	5	tl+1(un)−	tl+1(un)−	PROPN
ejpam-100	237	6	tl(un	tl(un	PROPN
ejpam-100	237	7	)	)	PUNCT
ejpam-100	237	8	)	)	PUNCT
ejpam-100	238	1	d	d	X
ejpam-100	238	2	x	x	PUNCT
ejpam-100	239	1	+	+	NUM
ejpam-100	239	2	n	n	CCONJ
ejpam-100	239	3	∑	∑	PROPN
ejpam-100	239	4	i=1	i=1	PROPN
ejpam-100	239	5	∫	∫	PROPN
ejpam-100	239	6	ω	ω	PROPN
ejpam-100	239	7	fi∇(tl+1(un)−	fi∇(tl+1(un)−	PROPN
ejpam-100	239	8	tl(un	tl(un	PROPN
ejpam-100	239	9	)	)	PUNCT
ejpam-100	239	10	)	)	PUNCT
ejpam-100	240	1	d	d	X
ejpam-100	240	2	x	x	X
ejpam-100	240	3	which	which	PRON
ejpam-100	240	4	implies	imply	VERB
ejpam-100	240	5	that	that	PRON
ejpam-100	240	6	,	,	PUNCT
ejpam-100	240	7	∫	∫	PROPN
ejpam-100	240	8	{	{	PUNCT
ejpam-100	240	9	l≤|un|≤l+1	l≤|un|≤l+1	PROPN
ejpam-100	240	10	}	}	PUNCT
ejpam-100	240	11	〈	〈	NOUN
ejpam-100	240	12	a(x	a(x	NOUN
ejpam-100	240	13	,	,	PUNCT
ejpam-100	240	14	un,∇un),∇un	un,∇un),∇un	SYM
ejpam-100	240	15	〉	〉	NOUN
ejpam-100	240	16	d	d	NOUN
ejpam-100	240	17	x	x	SYM
ejpam-100	241	1	+	+	NUM
ejpam-100	241	2	∫	∫	PROPN
ejpam-100	241	3	{	{	PUNCT
ejpam-100	241	4	|un|≥l+1	|un|≥l+1	PROPN
ejpam-100	241	5	}	}	PUNCT
ejpam-100	241	6	|gn(x	|gn(x	X
ejpam-100	241	7	,	,	PUNCT
ejpam-100	241	8	un)|	un)|	PROPN
ejpam-100	241	9	d	d	NOUN
ejpam-100	241	10	x	x	SYM
ejpam-100	241	11	≤	≤	PROPN
ejpam-100	241	12	c	c	NOUN
ejpam-100	241	13	∫	∫	PROPN
ejpam-100	241	14	{	{	PUNCT
ejpam-100	241	15	|un|≥l	|un|≥l	NOUN
ejpam-100	241	16	}	}	PUNCT
ejpam-100	242	1	|	|	NOUN
ejpam-100	242	2	f	f	NOUN
ejpam-100	243	1	|	|	NOUN
ejpam-100	243	2	d	d	NOUN
ejpam-100	243	3	x	x	X
ejpam-100	244	1	+	+	NUM
ejpam-100	244	2	n	n	CCONJ
ejpam-100	244	3	∑	∑	PROPN
ejpam-100	244	4	i=1	i=1	PROPN
ejpam-100	244	5	∫	∫	PROPN
ejpam-100	244	6	{	{	PUNCT
ejpam-100	244	7	l≤|un|≤l+1	l≤|un|≤l+1	PROPN
ejpam-100	244	8	}	}	PUNCT
ejpam-100	244	9	fiw	fiw	VERB
ejpam-100	244	10	−1	−1	ADP
ejpam-100	244	11	p	p	X
ejpam-100	245	1	i	i	PRON
ejpam-100	245	2	(	(	PUNCT
ejpam-100	245	3	α	α	NOUN
ejpam-100	245	4	2	2	NUM
ejpam-100	245	5	)	)	PUNCT
ejpam-100	245	6	−1	−1	NOUN
ejpam-100	245	7	p	p	NOUN
ejpam-100	245	8	|∇un|	|∇un|	NOUN
ejpam-100	245	9	(	(	PUNCT
ejpam-100	245	10	α	α	NOUN
ejpam-100	245	11	2	2	NUM
ejpam-100	245	12	)	)	PUNCT
ejpam-100	245	13	1	1	NUM
ejpam-100	245	14	p	p	NOUN
ejpam-100	245	15	d	d	X
ejpam-100	245	16	x	x	PUNCT
ejpam-100	245	17	by	by	ADP
ejpam-100	245	18	young	young	PROPN
ejpam-100	245	19	’s	’s	PART
ejpam-100	245	20	inequality	inequality	NOUN
ejpam-100	245	21	,	,	PUNCT
ejpam-100	245	22	we	we	PRON
ejpam-100	245	23	obtain	obtain	VERB
ejpam-100	245	24	∫	∫	PROPN
ejpam-100	245	25	{	{	PUNCT
ejpam-100	245	26	l≤|un|≤l+1	l≤|un|≤l+1	PROPN
ejpam-100	245	27	}	}	PUNCT
ejpam-100	245	28	〈	〈	NOUN
ejpam-100	245	29	a(x	a(x	NOUN
ejpam-100	245	30	,	,	PUNCT
ejpam-100	245	31	un,∇un),∇un	un,∇un),∇un	SYM
ejpam-100	245	32	〉	〉	NOUN
ejpam-100	246	1	d	d	NOUN
ejpam-100	247	1	x	x	SYM
ejpam-100	248	1	+	+	NUM
ejpam-100	248	2	∫	∫	PROPN
ejpam-100	248	3	{	{	PUNCT
ejpam-100	248	4	|un|≥l+1	|un|≥l+1	PROPN
ejpam-100	248	5	}	}	PUNCT
ejpam-100	248	6	|gn(x	|gn(x	X
ejpam-100	248	7	,	,	PUNCT
ejpam-100	248	8	un)|	un)|	PROPN
ejpam-100	248	9	d	d	NOUN
ejpam-100	248	10	x	x	SYM
ejpam-100	248	11	≤	≤	PROPN
ejpam-100	248	12	c	c	NOUN
ejpam-100	248	13	∫	∫	PROPN
ejpam-100	248	14	{	{	PUNCT
ejpam-100	248	15	|un|≥l	|un|≥l	NOUN
ejpam-100	248	16	}	}	PUNCT
ejpam-100	249	1	|	|	NOUN
ejpam-100	249	2	f	f	NOUN
ejpam-100	250	1	|	|	NOUN
ejpam-100	250	2	d	d	NOUN
ejpam-100	250	3	x	x	X
ejpam-100	250	4	+	+	X
ejpam-100	250	5	c(α	c(α	NOUN
ejpam-100	250	6	)	)	PUNCT
ejpam-100	250	7	p′	p′	NOUN
ejpam-100	251	1	n	n	CCONJ
ejpam-100	251	2	∑	∑	PROPN
ejpam-100	251	3	i=1	i=1	PROPN
ejpam-100	251	4	∫	∫	PROPN
ejpam-100	251	5	{	{	PUNCT
ejpam-100	251	6	|un|≥l	|un|≥l	NOUN
ejpam-100	251	7	}	}	PUNCT
ejpam-100	251	8	|fi|p	|fi|p	PROPN
ejpam-100	251	9	′	′	NUM
ejpam-100	251	10	w1−p′	w1−p′	NOUN
ejpam-100	252	1	i	i	PRON
ejpam-100	252	2	d	d	NOUN
ejpam-100	252	3	x	x	X
ejpam-100	253	1	+	+	NOUN
ejpam-100	253	2	α	α	NOUN
ejpam-100	253	3	2	2	NUM
ejpam-100	253	4	n	n	NOUN
ejpam-100	253	5	∑	∑	PROPN
ejpam-100	253	6	i=1	i=1	PROPN
ejpam-100	253	7	∫	∫	PROPN
ejpam-100	253	8	{	{	PUNCT
ejpam-100	253	9	l≤|un|≤l+1	l≤|un|≤l+1	PROPN
ejpam-100	253	10	}	}	PUNCT
ejpam-100	253	11	|∇un|pwi	|∇un|pwi	NOUN
ejpam-100	253	12	d	d	NOUN
ejpam-100	253	13	x	x	PUNCT
ejpam-100	253	14	thus	thus	ADV
ejpam-100	253	15	by	by	ADP
ejpam-100	253	16	(	(	PUNCT
ejpam-100	253	17	2.8	2.8	NUM
ejpam-100	253	18	)	)	PUNCT
ejpam-100	253	19	,	,	PUNCT
ejpam-100	253	20	we	we	PRON
ejpam-100	253	21	have	have	VERB
ejpam-100	253	22	∫	∫	PROPN
ejpam-100	253	23	{	{	PUNCT
ejpam-100	253	24	|un|≥l+1	|un|≥l+1	PROPN
ejpam-100	253	25	}	}	PUNCT
ejpam-100	253	26	|gn(x	|gn(x	X
ejpam-100	253	27	,	,	PUNCT
ejpam-100	253	28	un)|	un)|	PROPN
ejpam-100	253	29	d	d	NOUN
ejpam-100	253	30	x	x	SYM
ejpam-100	253	31	≤	≤	PROPN
ejpam-100	253	32	c	c	NOUN
ejpam-100	253	33	∫	∫	PROPN
ejpam-100	253	34	{	{	PUNCT
ejpam-100	253	35	|un|≥l	|un|≥l	NOUN
ejpam-100	253	36	}	}	PUNCT
ejpam-100	253	37	|	|	ADV
ejpam-100	253	38	fn|	fn|	VERB
ejpam-100	253	39	d	d	NOUN
ejpam-100	253	40	x	x	SYM
ejpam-100	253	41	+	+	X
ejpam-100	253	42	c(α	c(α	NOUN
ejpam-100	253	43	)	)	PUNCT
ejpam-100	253	44	p′	p′	NOUN
ejpam-100	253	45	n	n	CCONJ
ejpam-100	253	46	∑	∑	PROPN
ejpam-100	253	47	i=1	i=1	PROPN
ejpam-100	253	48	∫	∫	PROPN
ejpam-100	253	49	{	{	PUNCT
ejpam-100	253	50	|un|≥l	|un|≥l	NOUN
ejpam-100	253	51	}	}	PUNCT
ejpam-100	253	52	|fi|p	|fi|p	PROPN
ejpam-100	253	53	′	′	NUM
ejpam-100	254	1	w1−p′	w1−p′	NOUN
ejpam-100	255	1	i	i	PRON
ejpam-100	255	2	d	d	NOUN
ejpam-100	255	3	x	x	X
ejpam-100	255	4	.	.	PUNCT
ejpam-100	256	1	y.	y.	PROPN
ejpam-100	256	2	akdim	akdim	PROPN
ejpam-100	256	3	,	,	PUNCT
ejpam-100	256	4	e.	e.	PROPN
ejpam-100	256	5	azroul	azroul	PROPN
ejpam-100	256	6	,	,	PUNCT
ejpam-100	256	7	and	and	CCONJ
ejpam-100	256	8	m.	m.	NOUN
ejpam-100	256	9	rhoudaf	rhoudaf	PROPN
ejpam-100	256	10	/	/	SYM
ejpam-100	256	11	eur	eur	PROPN
ejpam-100	256	12	.	.	PUNCT
ejpam-100	257	1	j.	j.	PROPN
ejpam-100	257	2	pure	pure	PROPN
ejpam-100	257	3	appl	appl	PROPN
ejpam-100	257	4	.	.	PROPN
ejpam-100	257	5	math	math	PROPN
ejpam-100	257	6	,	,	PUNCT
ejpam-100	257	7	1	1	NUM
ejpam-100	257	8	(	(	PUNCT
ejpam-100	257	9	2008	2008	NUM
ejpam-100	257	10	)	)	PUNCT
ejpam-100	257	11	,	,	PUNCT
ejpam-100	257	12	(	(	PUNCT
ejpam-100	257	13	56	56	NUM
ejpam-100	257	14	-	-	SYM
ejpam-100	257	15	71	71	NUM
ejpam-100	257	16	)	)	PUNCT
ejpam-100	257	17	66	66	NUM
ejpam-100	257	18	let	let	VERB
ejpam-100	257	19	ε	ε	PROPN
ejpam-100	257	20	>	>	X
ejpam-100	257	21	0	0	PROPN
ejpam-100	257	22	,	,	PUNCT
ejpam-100	257	23	then	then	ADV
ejpam-100	257	24	there	there	PRON
ejpam-100	257	25	exist	exist	VERB
ejpam-100	257	26	l(ε)≥	l(ε)≥	NOUN
ejpam-100	257	27	1	1	NUM
ejpam-100	257	28	such	such	ADJ
ejpam-100	257	29	that	that	DET
ejpam-100	257	30	∫	∫	PROPN
ejpam-100	257	31	{	{	PUNCT
ejpam-100	257	32	|un|>l(ε	|un|>l(ε	PROPN
ejpam-100	257	33	)	)	PUNCT
ejpam-100	257	34	}	}	PUNCT
ejpam-100	257	35	|gn(x	|gn(x	X
ejpam-100	257	36	,	,	PUNCT
ejpam-100	257	37	un)|	un)|	PROPN
ejpam-100	257	38	d	d	NOUN
ejpam-100	257	39	x	x	SYM
ejpam-100	257	40	≤	≤	NUM
ejpam-100	257	41	ε	ε	PROPN
ejpam-100	257	42	2	2	NUM
ejpam-100	257	43	.	.	PUNCT
ejpam-100	258	1	(	(	PUNCT
ejpam-100	258	2	4.21	4.21	NUM
ejpam-100	258	3	)	)	PUNCT
ejpam-100	258	4	for	for	ADP
ejpam-100	258	5	any	any	DET
ejpam-100	258	6	measurable	measurable	ADJ
ejpam-100	258	7	subset	subset	NOUN
ejpam-100	258	8	e	e	PROPN
ejpam-100	258	9	⊂	⊂	PROPN
ejpam-100	258	10	ω	ω	PROPN
ejpam-100	258	11	,	,	PUNCT
ejpam-100	258	12	we	we	PRON
ejpam-100	258	13	have	have	VERB
ejpam-100	258	14	∫	∫	PROPN
ejpam-100	258	15	e	e	X
ejpam-100	258	16	|gn(x	|gn(x	X
ejpam-100	258	17	,	,	PUNCT
ejpam-100	258	18	un)|	un)|	PROPN
ejpam-100	258	19	d	d	NOUN
ejpam-100	258	20	x	x	SYM
ejpam-100	258	21	≤	≤	NUM
ejpam-100	258	22	∫	∫	NOUN
ejpam-100	258	23	e∩{|un|≤l(ε	e∩{|un|≤l(ε	NOUN
ejpam-100	258	24	)	)	PUNCT
ejpam-100	258	25	}	}	PUNCT
ejpam-100	258	26	|gn(x	|gn(x	X
ejpam-100	258	27	,	,	PUNCT
ejpam-100	258	28	un)|	un)|	PROPN
ejpam-100	258	29	d	d	NOUN
ejpam-100	258	30	x	x	PROPN
ejpam-100	259	1	+	+	NUM
ejpam-100	259	2	∫	∫	PROPN
ejpam-100	259	3	e∩{|un|>l(ε	e∩{|un|>l(ε	PROPN
ejpam-100	259	4	)	)	PUNCT
ejpam-100	259	5	}	}	PUNCT
ejpam-100	259	6	|gn(x	|gn(x	X
ejpam-100	259	7	,	,	PUNCT
ejpam-100	259	8	un)|	un)|	PROPN
ejpam-100	259	9	d	d	NOUN
ejpam-100	259	10	x	x	SYM
ejpam-100	259	11	≤	≤	NUM
ejpam-100	259	12	∫	∫	PROPN
ejpam-100	259	13	e	e	NOUN
ejpam-100	259	14	|hl(ε)(x)|	|hl(ε)(x)|	VERB
ejpam-100	259	15	d	d	NOUN
ejpam-100	259	16	x	x	SYM
ejpam-100	260	1	+	+	NUM
ejpam-100	260	2	∫	∫	PROPN
ejpam-100	260	3	e∩{|un|>l(ε	e∩{|un|>l(ε	PROPN
ejpam-100	260	4	)	)	PUNCT
ejpam-100	260	5	}	}	PUNCT
ejpam-100	261	1	|gn(x	|gn(x	X
ejpam-100	261	2	,	,	PUNCT
ejpam-100	261	3	un)|	un)|	PROPN
ejpam-100	261	4	d	d	NOUN
ejpam-100	261	5	x	x	X
ejpam-100	261	6	.	.	PUNCT
ejpam-100	262	1	in	in	ADP
ejpam-100	262	2	view	view	NOUN
ejpam-100	262	3	to	to	ADP
ejpam-100	262	4	(	(	PUNCT
ejpam-100	262	5	2.10	2.10	NUM
ejpam-100	262	6	)	)	PUNCT
ejpam-100	262	7	there	there	PRON
ejpam-100	262	8	exist	exist	VERB
ejpam-100	262	9	η(ε	η(ε	NOUN
ejpam-100	262	10	)	)	PUNCT
ejpam-100	262	11	>	>	X
ejpam-100	262	12	0	0	NUM
ejpam-100	263	1	such	such	ADJ
ejpam-100	263	2	that	that	SCONJ
ejpam-100	263	3	∫	∫	PROPN
ejpam-100	263	4	e	e	NOUN
ejpam-100	263	5	|hl(ε)(x)|	|hl(ε)(x)|	VERB
ejpam-100	263	6	d	d	X
ejpam-100	263	7	x	x	SYM
ejpam-100	263	8	≤	≤	NUM
ejpam-100	263	9	ε	ε	PROPN
ejpam-100	263	10	2	2	NUM
ejpam-100	263	11	(	(	PUNCT
ejpam-100	263	12	4.22	4.22	NUM
ejpam-100	263	13	)	)	PUNCT
ejpam-100	263	14	for	for	ADP
ejpam-100	263	15	all	all	DET
ejpam-100	263	16	e	e	NOUN
ejpam-100	263	17	such	such	ADJ
ejpam-100	263	18	that	that	DET
ejpam-100	263	19	meas(e	meas(e	PROPN
ejpam-100	263	20	)	)	PUNCT
ejpam-100	263	21	<	<	X
ejpam-100	263	22	η(ε	η(ε	NOUN
ejpam-100	263	23	)	)	PUNCT
ejpam-100	263	24	.	.	PUNCT
ejpam-100	264	1	finally	finally	ADV
ejpam-100	264	2	,	,	PUNCT
ejpam-100	264	3	by	by	ADP
ejpam-100	264	4	combining	combine	VERB
ejpam-100	264	5	(	(	PUNCT
ejpam-100	264	6	4.21	4.21	NUM
ejpam-100	264	7	)	)	PUNCT
ejpam-100	264	8	and	and	CCONJ
ejpam-100	264	9	(	(	PUNCT
ejpam-100	264	10	4.22	4.22	NUM
ejpam-100	264	11	)	)	PUNCT
ejpam-100	264	12	one	one	NOUN
ejpam-100	264	13	easily	easily	ADV
ejpam-100	264	14	has	have	VERB
ejpam-100	264	15	∫	∫	PROPN
ejpam-100	264	16	e	e	X
ejpam-100	264	17	|gn(x	|gn(x	X
ejpam-100	264	18	,	,	PUNCT
ejpam-100	264	19	un)|	un)|	PROPN
ejpam-100	264	20	d	d	NOUN
ejpam-100	264	21	x	x	SYM
ejpam-100	264	22	≤	≤	PROPN
ejpam-100	264	23	ε	ε	PROPN
ejpam-100	264	24	,	,	PUNCT
ejpam-100	264	25	for	for	ADP
ejpam-100	264	26	all	all	DET
ejpam-100	264	27	e	e	ADP
ejpam-100	264	28	such	such	ADJ
ejpam-100	264	29	that	that	DET
ejpam-100	264	30	meas(e	meas(e	PROPN
ejpam-100	264	31	)	)	PUNCT
ejpam-100	264	32	<	<	X
ejpam-100	264	33	η(ε	η(ε	NOUN
ejpam-100	264	34	)	)	PUNCT
ejpam-100	264	35	.	.	PUNCT
ejpam-100	265	1	4	4	X
ejpam-100	265	2	.	.	X
ejpam-100	265	3	an	an	DET
ejpam-100	265	4	intermediate	intermediate	ADJ
ejpam-100	265	5	inequality	inequality	NOUN
ejpam-100	265	6	in	in	ADP
ejpam-100	265	7	this	this	DET
ejpam-100	265	8	step	step	NOUN
ejpam-100	265	9	,	,	PUNCT
ejpam-100	265	10	we	we	PRON
ejpam-100	265	11	shall	shall	AUX
ejpam-100	265	12	prove	prove	VERB
ejpam-100	265	13	that	that	SCONJ
ejpam-100	265	14	for	for	ADP
ejpam-100	265	15	ϕ	ϕ	PROPN
ejpam-100	265	16	∈w	∈w	PROPN
ejpam-100	265	17	1,p	1,p	PROPN
ejpam-100	265	18	0	0	SYM
ejpam-100	265	19	(	(	PUNCT
ejpam-100	265	20	ω	ω	PROPN
ejpam-100	265	21	,	,	PUNCT
ejpam-100	265	22	w)∩	w)∩	X
ejpam-100	265	23	l∞(ω	l∞(ω	X
ejpam-100	265	24	)	)	PUNCT
ejpam-100	265	25	,	,	PUNCT
ejpam-100	265	26	we	we	PRON
ejpam-100	265	27	have	have	VERB
ejpam-100	265	28	∫	∫	PROPN
ejpam-100	265	29	ω	ω	PROPN
ejpam-100	265	30	〈	〈	NOUN
ejpam-100	265	31	a(x	a(x	PROPN
ejpam-100	265	32	,	,	PUNCT
ejpam-100	265	33	un,∇ϕ),∇tk[un−ϕ	un,∇ϕ),∇tk[un−ϕ	NOUN
ejpam-100	265	34	]	]	X
ejpam-100	265	35	〉	〉	NOUN
ejpam-100	265	36	d	d	NOUN
ejpam-100	265	37	x	x	SYM
ejpam-100	266	1	+	+	NUM
ejpam-100	266	2	∫	∫	PROPN
ejpam-100	266	3	ω	ω	NUM
ejpam-100	266	4	gn(x	gn(x	X
ejpam-100	266	5	,	,	PUNCT
ejpam-100	266	6	un)tk[un−ϕ	un)tk[un−ϕ	NOUN
ejpam-100	266	7	]	]	X
ejpam-100	266	8	d	d	X
ejpam-100	266	9	x	x	SYM
ejpam-100	266	10	≤	≤	NUM
ejpam-100	266	11	∫	∫	PROPN
ejpam-100	266	12	ω	ω	PROPN
ejpam-100	266	13	fntk[un−ϕ	fntk[un−ϕ	PROPN
ejpam-100	266	14	]	]	X
ejpam-100	267	1	d	d	X
ejpam-100	267	2	x	x	SYM
ejpam-100	267	3	+	+	NUM
ejpam-100	267	4	∫	∫	PROPN
ejpam-100	267	5	ω	ω	NUM
ejpam-100	267	6	〈	〈	PROPN
ejpam-100	267	7	f,∇tk[un−ϕ	f,∇tk[un−ϕ	PROPN
ejpam-100	267	8	]	]	SYM
ejpam-100	267	9	〉	〉	NOUN
ejpam-100	267	10	d	d	NOUN
ejpam-100	267	11	x	x	PROPN
ejpam-100	267	12	.	.	PUNCT
ejpam-100	268	1	(	(	PUNCT
ejpam-100	268	2	4.23	4.23	NUM
ejpam-100	268	3	)	)	PUNCT
ejpam-100	268	4	we	we	PRON
ejpam-100	268	5	choose	choose	VERB
ejpam-100	268	6	now	now	ADV
ejpam-100	268	7	tk(un−ϕ	tk(un−ϕ	NOUN
ejpam-100	268	8	)	)	PUNCT
ejpam-100	268	9	as	as	ADP
ejpam-100	268	10	test	test	NOUN
ejpam-100	268	11	function	function	NOUN
ejpam-100	268	12	in	in	ADP
ejpam-100	268	13	(	(	PUNCT
ejpam-100	268	14	4.15	4.15	NUM
ejpam-100	268	15	)	)	PUNCT
ejpam-100	268	16	,	,	PUNCT
ejpam-100	268	17	with	with	ADP
ejpam-100	268	18	ϕ	ϕ	NOUN
ejpam-100	268	19	in	in	ADP
ejpam-100	268	20	w	w	PROPN
ejpam-100	268	21	1,p	1,p	PROPN
ejpam-100	268	22	0	0	NUM
ejpam-100	268	23	(	(	PUNCT
ejpam-100	268	24	ω	ω	PROPN
ejpam-100	268	25	,	,	PUNCT
ejpam-100	268	26	w)∩	w)∩	X
ejpam-100	268	27	l∞(ω	l∞(ω	X
ejpam-100	268	28	)	)	PUNCT
ejpam-100	268	29	,	,	PUNCT
ejpam-100	268	30	we	we	PRON
ejpam-100	268	31	obtain	obtain	VERB
ejpam-100	268	32	∫	∫	PROPN
ejpam-100	268	33	ω	ω	PROPN
ejpam-100	268	34	〈	〈	NOUN
ejpam-100	268	35	a(x	a(x	PROPN
ejpam-100	268	36	,	,	PUNCT
ejpam-100	268	37	un,∇un),∇tk[un−ϕ	un,∇un),∇tk[un−ϕ	PROPN
ejpam-100	268	38	]	]	X
ejpam-100	268	39	〉	〉	NOUN
ejpam-100	268	40	d	d	NOUN
ejpam-100	268	41	x	x	SYM
ejpam-100	269	1	+	+	NUM
ejpam-100	269	2	∫	∫	PROPN
ejpam-100	269	3	ω	ω	NUM
ejpam-100	269	4	gn(x	gn(x	X
ejpam-100	269	5	,	,	PUNCT
ejpam-100	269	6	un)tk[un−ϕ	un)tk[un−ϕ	NOUN
ejpam-100	269	7	]	]	X
ejpam-100	270	1	d	d	NOUN
ejpam-100	270	2	x	x	SYM
ejpam-100	270	3	=	=	SYM
ejpam-100	270	4	∫	∫	PROPN
ejpam-100	270	5	ω	ω	PROPN
ejpam-100	270	6	fntk[un−ϕ	fntk[un−ϕ	PROPN
ejpam-100	270	7	]	]	X
ejpam-100	271	1	d	d	X
ejpam-100	271	2	x	x	SYM
ejpam-100	271	3	+	+	NUM
ejpam-100	271	4	∫	∫	PROPN
ejpam-100	271	5	ω	ω	NUM
ejpam-100	271	6	〈	〈	PROPN
ejpam-100	271	7	f,∇tk[un−ϕ	f,∇tk[un−ϕ	PROPN
ejpam-100	271	8	]	]	SYM
ejpam-100	271	9	〉	〉	NOUN
ejpam-100	271	10	d	d	NOUN
ejpam-100	271	11	x	x	PUNCT
ejpam-100	271	12	.	.	PUNCT
ejpam-100	272	1	adding	add	VERB
ejpam-100	272	2	and	and	CCONJ
ejpam-100	272	3	subtracting	subtract	VERB
ejpam-100	272	4	the	the	DET
ejpam-100	272	5	term	term	NOUN
ejpam-100	272	6	∫	∫	PROPN
ejpam-100	272	7	ω	ω	PROPN
ejpam-100	272	8	〈	〈	NOUN
ejpam-100	272	9	a(x	a(x	PROPN
ejpam-100	272	10	,	,	PUNCT
ejpam-100	272	11	un,∇ϕ),∇tk[un−ϕ	un,∇ϕ),∇tk[un−ϕ	NOUN
ejpam-100	272	12	]	]	X
ejpam-100	272	13	〉	〉	ADJ
ejpam-100	272	14	d	d	NOUN
ejpam-100	272	15	x	x	X
ejpam-100	272	16	i.e.	i.e.	X
ejpam-100	272	17	,	,	PUNCT
ejpam-100	272	18	∫	∫	PROPN
ejpam-100	272	19	ω	ω	NUM
ejpam-100	272	20	〈	〈	NOUN
ejpam-100	272	21	a(x	a(x	PROPN
ejpam-100	272	22	,	,	PUNCT
ejpam-100	272	23	un,∇un),∇tk[un−ϕ	un,∇un),∇tk[un−ϕ	PROPN
ejpam-100	272	24	]	]	X
ejpam-100	272	25	〉	〉	NOUN
ejpam-100	272	26	d	d	NOUN
ejpam-100	272	27	x	x	SYM
ejpam-100	273	1	+	+	NUM
ejpam-100	273	2	∫	∫	PROPN
ejpam-100	273	3	ω	ω	NUM
ejpam-100	273	4	〈	〈	NOUN
ejpam-100	273	5	a(x	a(x	PROPN
ejpam-100	273	6	,	,	PUNCT
ejpam-100	273	7	un,∇ϕ),∇tk[un−ϕ	un,∇ϕ),∇tk[un−ϕ	NOUN
ejpam-100	273	8	]	]	X
ejpam-100	273	9	〉	〉	ADJ
ejpam-100	273	10	d	d	NOUN
ejpam-100	273	11	x	x	SYM
ejpam-100	274	1	−	−	PROPN
ejpam-100	274	2	∫	∫	PROPN
ejpam-100	274	3	ω	ω	NUM
ejpam-100	274	4	〈	〈	NOUN
ejpam-100	274	5	a(x	a(x	PROPN
ejpam-100	274	6	,	,	PUNCT
ejpam-100	274	7	un,∇ϕ),∇tk[un−ϕ	un,∇ϕ),∇tk[un−ϕ	NOUN
ejpam-100	274	8	]	]	X
ejpam-100	274	9	〉	〉	NOUN
ejpam-100	274	10	d	d	NOUN
ejpam-100	274	11	x	x	SYM
ejpam-100	274	12	+	+	NUM
ejpam-100	274	13	∫	∫	PROPN
ejpam-100	274	14	ω	ω	NUM
ejpam-100	274	15	gn(x	gn(x	X
ejpam-100	274	16	,	,	PUNCT
ejpam-100	274	17	un)tk[un−ϕ	un)tk[un−ϕ	NOUN
ejpam-100	274	18	]	]	X
ejpam-100	274	19	d	d	NOUN
ejpam-100	274	20	x	x	SYM
ejpam-100	274	21	=	=	SYM
ejpam-100	274	22	∫	∫	PROPN
ejpam-100	274	23	ω	ω	PROPN
ejpam-100	274	24	fntk[un−ϕ	fntk[un−ϕ	PROPN
ejpam-100	274	25	]	]	X
ejpam-100	275	1	d	d	X
ejpam-100	275	2	x	x	SYM
ejpam-100	275	3	+	+	NUM
ejpam-100	275	4	∫	∫	PROPN
ejpam-100	275	5	ω	ω	NUM
ejpam-100	275	6	〈	〈	PROPN
ejpam-100	275	7	f,∇tk[un−ϕ	f,∇tk[un−ϕ	PROPN
ejpam-100	275	8	]	]	SYM
ejpam-100	275	9	〉	〉	NOUN
ejpam-100	275	10	d	d	NOUN
ejpam-100	275	11	x	x	X
ejpam-100	275	12	(	(	PUNCT
ejpam-100	275	13	4.24	4.24	NUM
ejpam-100	275	14	)	)	PUNCT
ejpam-100	275	15	y.	y.	PROPN
ejpam-100	275	16	akdim	akdim	PROPN
ejpam-100	275	17	,	,	PUNCT
ejpam-100	275	18	e.	e.	PROPN
ejpam-100	275	19	azroul	azroul	PROPN
ejpam-100	275	20	,	,	PUNCT
ejpam-100	275	21	and	and	CCONJ
ejpam-100	275	22	m.	m.	NOUN
ejpam-100	275	23	rhoudaf	rhoudaf	PROPN
ejpam-100	275	24	/	/	SYM
ejpam-100	275	25	eur	eur	PROPN
ejpam-100	275	26	.	.	PUNCT
ejpam-100	276	1	j.	j.	PROPN
ejpam-100	276	2	pure	pure	PROPN
ejpam-100	276	3	appl	appl	PROPN
ejpam-100	276	4	.	.	PROPN
ejpam-100	276	5	math	math	PROPN
ejpam-100	276	6	,	,	PUNCT
ejpam-100	276	7	1	1	NUM
ejpam-100	276	8	(	(	PUNCT
ejpam-100	276	9	2008	2008	NUM
ejpam-100	276	10	)	)	PUNCT
ejpam-100	276	11	,	,	PUNCT
ejpam-100	276	12	(	(	PUNCT
ejpam-100	276	13	56	56	NUM
ejpam-100	276	14	-	-	SYM
ejpam-100	276	15	71	71	NUM
ejpam-100	276	16	)	)	PUNCT
ejpam-100	276	17	67	67	NUM
ejpam-100	276	18	thanks	thank	NOUN
ejpam-100	276	19	to	to	ADP
ejpam-100	276	20	assumption	assumption	NOUN
ejpam-100	276	21	(	(	PUNCT
ejpam-100	276	22	2.7	2.7	NUM
ejpam-100	276	23	)	)	PUNCT
ejpam-100	276	24	and	and	CCONJ
ejpam-100	276	25	the	the	DET
ejpam-100	276	26	definition	definition	NOUN
ejpam-100	276	27	of	of	ADP
ejpam-100	276	28	truncation	truncation	NOUN
ejpam-100	276	29	function	function	NOUN
ejpam-100	276	30	,	,	PUNCT
ejpam-100	276	31	we	we	PRON
ejpam-100	276	32	have	have	VERB
ejpam-100	276	33	∫	∫	PROPN
ejpam-100	276	34	ω	ω	PROPN
ejpam-100	277	1	[	[	X
ejpam-100	277	2	a(x	a(x	NOUN
ejpam-100	277	3	,	,	PUNCT
ejpam-100	277	4	un,∇un)−	un,∇un)−	NOUN
ejpam-100	277	5	a(x	a(x	NOUN
ejpam-100	277	6	,	,	PUNCT
ejpam-100	277	7	un,∇ϕ	un,∇ϕ	PROPN
ejpam-100	277	8	)	)	PUNCT
ejpam-100	277	9	�	�	PROPN
ejpam-100	277	10	,	,	PUNCT
ejpam-100	277	11	∇tk[un−ϕ	∇tk[un−ϕ	PROPN
ejpam-100	277	12	]	]	PUNCT
ejpam-100	277	13	〉	〉	NOUN
ejpam-100	277	14	d	d	NOUN
ejpam-100	277	15	x	x	X
ejpam-100	277	16	≥	≥	NOUN
ejpam-100	277	17	0	0	NUM
ejpam-100	277	18	(	(	PUNCT
ejpam-100	277	19	4.25	4.25	NUM
ejpam-100	277	20	)	)	PUNCT
ejpam-100	277	21	combining	combine	VERB
ejpam-100	277	22	(	(	PUNCT
ejpam-100	277	23	4.24	4.24	NUM
ejpam-100	277	24	)	)	PUNCT
ejpam-100	277	25	and	and	CCONJ
ejpam-100	277	26	(	(	PUNCT
ejpam-100	277	27	4.25	4.25	NUM
ejpam-100	277	28	)	)	PUNCT
ejpam-100	277	29	,	,	PUNCT
ejpam-100	277	30	we	we	PRON
ejpam-100	277	31	obtain	obtain	VERB
ejpam-100	277	32	(	(	PUNCT
ejpam-100	277	33	4.23	4.23	NUM
ejpam-100	277	34	)	)	PUNCT
ejpam-100	277	35	.	.	PUNCT
ejpam-100	278	1	5	5	X
ejpam-100	278	2	.	.	X
ejpam-100	278	3	passing	pass	VERB
ejpam-100	278	4	to	to	ADP
ejpam-100	278	5	the	the	DET
ejpam-100	278	6	limit	limit	NOUN
ejpam-100	278	7	we	we	PRON
ejpam-100	278	8	shall	shall	AUX
ejpam-100	278	9	prove	prove	VERB
ejpam-100	278	10	that	that	SCONJ
ejpam-100	278	11	for	for	ADP
ejpam-100	278	12	ϕ	ϕ	PROPN
ejpam-100	278	13	∈w	∈w	PROPN
ejpam-100	278	14	1,p	1,p	PROPN
ejpam-100	278	15	0	0	SYM
ejpam-100	278	16	(	(	PUNCT
ejpam-100	278	17	ω	ω	PROPN
ejpam-100	278	18	,	,	PUNCT
ejpam-100	278	19	w)∩	w)∩	X
ejpam-100	278	20	l∞(ω	l∞(ω	X
ejpam-100	278	21	)	)	PUNCT
ejpam-100	278	22	,	,	PUNCT
ejpam-100	278	23	we	we	PRON
ejpam-100	278	24	have	have	VERB
ejpam-100	278	25	∫	∫	PROPN
ejpam-100	278	26	ω	ω	PROPN
ejpam-100	278	27	〈	〈	NOUN
ejpam-100	278	28	a(x	a(x	PROPN
ejpam-100	278	29	,	,	PUNCT
ejpam-100	278	30	u,∇ϕ),∇tk[u−ϕ	u,∇ϕ),∇tk[u−ϕ	ADJ
ejpam-100	278	31	]	]	X
ejpam-100	278	32	〉	〉	ADJ
ejpam-100	278	33	d	d	NOUN
ejpam-100	278	34	x+	x+	PROPN
ejpam-100	278	35	∫	∫	PROPN
ejpam-100	278	36	ω	ω	NUM
ejpam-100	278	37	g(x	g(x	PROPN
ejpam-100	278	38	,	,	PUNCT
ejpam-100	278	39	u)tk[u−ϕ	u)tk[u−ϕ	NOUN
ejpam-100	278	40	]	]	X
ejpam-100	279	1	d	d	X
ejpam-100	279	2	x	x	SYM
ejpam-100	279	3	≤	≤	NUM
ejpam-100	279	4	∫	∫	PROPN
ejpam-100	279	5	ω	ω	PROPN
ejpam-100	279	6	f	f	PROPN
ejpam-100	279	7	tk[u−ϕ	tk[u−ϕ	PROPN
ejpam-100	279	8	]	]	X
ejpam-100	280	1	d	d	X
ejpam-100	280	2	x+	x+	SYM
ejpam-100	280	3	∫	∫	PROPN
ejpam-100	280	4	ω	ω	PROPN
ejpam-100	280	5	〈	〈	PROPN
ejpam-100	280	6	f,∇tk[u−ϕ	f,∇tk[u−ϕ	PROPN
ejpam-100	280	7	]	]	SYM
ejpam-100	280	8	〉	〉	NOUN
ejpam-100	280	9	d	d	NOUN
ejpam-100	280	10	x	x	X
ejpam-100	280	11	.	.	PUNCT
ejpam-100	281	1	firstly	firstly	ADV
ejpam-100	281	2	,	,	PUNCT
ejpam-100	281	3	we	we	PRON
ejpam-100	281	4	claim	claim	VERB
ejpam-100	281	5	that	that	SCONJ
ejpam-100	281	6	∫	∫	PROPN
ejpam-100	281	7	ω	ω	PROPN
ejpam-100	281	8	〈	〈	NOUN
ejpam-100	281	9	a(x	a(x	PROPN
ejpam-100	281	10	,	,	PUNCT
ejpam-100	281	11	un,∇ϕ),∇tk[un−ϕ	un,∇ϕ),∇tk[un−ϕ	NOUN
ejpam-100	281	12	]	]	X
ejpam-100	281	13	〉	〉	NOUN
ejpam-100	282	1	d	d	NOUN
ejpam-100	282	2	x	x	PROPN
ejpam-100	282	3	→	→	SYM
ejpam-100	282	4	∫	∫	PROPN
ejpam-100	282	5	ω	ω	NUM
ejpam-100	282	6	〈	〈	NOUN
ejpam-100	282	7	a(x	a(x	PROPN
ejpam-100	282	8	,	,	PUNCT
ejpam-100	282	9	u,∇ϕ),∇tk[u−ϕ	u,∇ϕ),∇tk[u−ϕ	ADJ
ejpam-100	282	10	]	]	X
ejpam-100	282	11	〉	〉	NOUN
ejpam-100	282	12	d	d	NOUN
ejpam-100	282	13	x	x	PUNCT
ejpam-100	282	14	as	as	ADP
ejpam-100	282	15	n→+∞.	n→+∞.	NOUN
ejpam-100	282	16	since	since	SCONJ
ejpam-100	282	17	tm	tm	PROPN
ejpam-100	282	18	(	(	PUNCT
ejpam-100	282	19	un	un	PROPN
ejpam-100	282	20	)	)	PUNCT
ejpam-100	282	21	*	*	PUNCT
ejpam-100	282	22	tm	tm	PROPN
ejpam-100	282	23	(	(	PUNCT
ejpam-100	282	24	u	u	NOUN
ejpam-100	282	25	)	)	PUNCT
ejpam-100	282	26	weakly	weakly	ADV
ejpam-100	282	27	in	in	ADP
ejpam-100	282	28	w	w	PROPN
ejpam-100	282	29	1,p	1,p	PROPN
ejpam-100	282	30	0	0	NUM
ejpam-100	282	31	(	(	PUNCT
ejpam-100	282	32	ω	ω	NOUN
ejpam-100	282	33	,	,	PUNCT
ejpam-100	282	34	w),with	w),with	ADP
ejpam-100	282	35	m	m	PROPN
ejpam-100	282	36	=	=	SYM
ejpam-100	282	37	k	k	PROPN
ejpam-100	283	1	+	+	PROPN
ejpam-100	283	2	‖ϕ‖∞	‖ϕ‖∞	PROPN
ejpam-100	283	3	,	,	PUNCT
ejpam-100	283	4	then	then	ADV
ejpam-100	283	5	by	by	ADP
ejpam-100	283	6	lemma	lemma	PROPN
ejpam-100	283	7	2.1	2.1	NUM
ejpam-100	283	8	,	,	PUNCT
ejpam-100	283	9	we	we	PRON
ejpam-100	283	10	have	have	VERB
ejpam-100	283	11	tk(un−ϕ	tk(un−ϕ	NOUN
ejpam-100	283	12	)	)	PUNCT
ejpam-100	283	13	*	*	PUNCT
ejpam-100	284	1	tk(u−ϕ	tk(u−ϕ	NUM
ejpam-100	284	2	)	)	PUNCT
ejpam-100	284	3	in	in	ADP
ejpam-100	284	4	w	w	NOUN
ejpam-100	284	5	1.p	1.p	NUM
ejpam-100	284	6	0	0	NUM
ejpam-100	284	7	(	(	PUNCT
ejpam-100	284	8	ω	ω	PROPN
ejpam-100	284	9	,	,	PUNCT
ejpam-100	284	10	w	w	PROPN
ejpam-100	284	11	)	)	PUNCT
ejpam-100	284	12	,	,	PUNCT
ejpam-100	284	13	(	(	PUNCT
ejpam-100	284	14	4.26	4.26	NUM
ejpam-100	284	15	)	)	PUNCT
ejpam-100	284	16	which	which	PRON
ejpam-100	284	17	gives	give	VERB
ejpam-100	284	18	∂	∂	NUM
ejpam-100	284	19	tk	tk	PROPN
ejpam-100	284	20	∂	∂	NOUN
ejpam-100	284	21	x	x	X
ejpam-100	285	1	i	i	PRON
ejpam-100	285	2	(	(	PUNCT
ejpam-100	285	3	un−ϕ	un−ϕ	NOUN
ejpam-100	285	4	)	)	PUNCT
ejpam-100	285	5	*	*	SYM
ejpam-100	285	6	∂	∂	NUM
ejpam-100	285	7	tk	tk	PROPN
ejpam-100	285	8	∂	∂	NOUN
ejpam-100	285	9	x	x	VERB
ejpam-100	285	10	i	i	PROPN
ejpam-100	285	11	(	(	PUNCT
ejpam-100	285	12	u−ϕ	u−ϕ	PROPN
ejpam-100	285	13	)	)	PUNCT
ejpam-100	285	14	weakly	weakly	ADV
ejpam-100	285	15	in	in	ADP
ejpam-100	285	16	lp(ω	lp(ω	PROPN
ejpam-100	285	17	,	,	PUNCT
ejpam-100	285	18	wi	wi	PROPN
ejpam-100	285	19	)	)	PUNCT
ejpam-100	285	20	∀i	∀i	NOUN
ejpam-100	285	21	=	=	SYM
ejpam-100	285	22	1	1	NUM
ejpam-100	285	23	,	,	PUNCT
ejpam-100	285	24	..	..	PUNCT
ejpam-100	285	25	,	,	PUNCT
ejpam-100	285	26	n	n	X
ejpam-100	285	27	.	.	PUNCT
ejpam-100	286	1	(	(	PUNCT
ejpam-100	286	2	4.27	4.27	NUM
ejpam-100	286	3	)	)	PUNCT
ejpam-100	286	4	show	show	VERB
ejpam-100	286	5	that	that	PRON
ejpam-100	286	6	ai(x	ai(x	NOUN
ejpam-100	286	7	,	,	PUNCT
ejpam-100	286	8	tm	tm	PROPN
ejpam-100	286	9	(	(	PUNCT
ejpam-100	286	10	un),∇ϕ)→	un),∇ϕ)→	PROPN
ejpam-100	286	11	ai(x	ai(x	NOUN
ejpam-100	286	12	,	,	PUNCT
ejpam-100	286	13	tm	tm	PROPN
ejpam-100	286	14	(	(	PUNCT
ejpam-100	286	15	u),∇ϕ	u),∇ϕ	ADV
ejpam-100	286	16	)	)	PUNCT
ejpam-100	286	17	strongly	strongly	ADV
ejpam-100	286	18	in	in	ADP
ejpam-100	286	19	lp′(ω	lp′(ω	PROPN
ejpam-100	286	20	,	,	PUNCT
ejpam-100	286	21	w∗i	w∗i	PRON
ejpam-100	286	22	)	)	PUNCT
ejpam-100	286	23	thanks	thank	NOUN
ejpam-100	286	24	to	to	ADP
ejpam-100	286	25	assumption	assumption	NOUN
ejpam-100	286	26	(	(	PUNCT
ejpam-100	286	27	2.6	2.6	NUM
ejpam-100	286	28	)	)	PUNCT
ejpam-100	286	29	,	,	PUNCT
ejpam-100	286	30	we	we	PRON
ejpam-100	286	31	obtain	obtain	VERB
ejpam-100	286	32	|ai(x	|ai(x	X
ejpam-100	286	33	,	,	PUNCT
ejpam-100	286	34	tm	tm	PROPN
ejpam-100	286	35	(	(	PUNCT
ejpam-100	286	36	un),∇ϕ)|p	un),∇ϕ)|p	PROPN
ejpam-100	286	37	′	′	NUM
ejpam-100	286	38	w	w	NOUN
ejpam-100	286	39	−p′	−p′	INTJ
ejpam-100	286	40	p	p	X
ejpam-100	286	41	i	i	PRON
ejpam-100	286	42	≤	≤	NUM
ejpam-100	286	43	β[k(x	β[k(x	VERB
ejpam-100	286	44	)	)	PUNCT
ejpam-100	287	1	+	+	CCONJ
ejpam-100	287	2	|tm	|tm	X
ejpam-100	287	3	(	(	PUNCT
ejpam-100	287	4	un)|	un)|	PROPN
ejpam-100	287	5	q	q	PROPN
ejpam-100	287	6	p′σ	p′σ	PROPN
ejpam-100	287	7	1	1	NUM
ejpam-100	287	8	p′	p′	NOUN
ejpam-100	287	9	+	+	CCONJ
ejpam-100	287	10	n	n	CCONJ
ejpam-100	287	11	∑	∑	ADP
ejpam-100	287	12	j=1	j=1	PROPN
ejpam-100	287	13	|	|	ADV
ejpam-100	287	14	∂	∂	PROPN
ejpam-100	287	15	ϕ	ϕ	NOUN
ejpam-100	287	16	∂	∂	NOUN
ejpam-100	287	17	x	x	VERB
ejpam-100	287	18	i	i	PRON
ejpam-100	287	19	|p−1w	|p−1w	VERB
ejpam-100	287	20	1	1	NUM
ejpam-100	287	21	p′	p′	NOUN
ejpam-100	287	22	i	i	PRON
ejpam-100	287	23	]	]	PUNCT
ejpam-100	287	24	p′	p′	PROPN
ejpam-100	287	25	≤	≤	NOUN
ejpam-100	287	26	γ[k(x)p	γ[k(x)p	NOUN
ejpam-100	287	27	′	′	NUM
ejpam-100	288	1	+	+	CCONJ
ejpam-100	288	2	|tm	|tm	X
ejpam-100	288	3	(	(	PUNCT
ejpam-100	288	4	un)|qσ+	un)|qσ+	PROPN
ejpam-100	288	5	n	n	PROPN
ejpam-100	288	6	∑	∑	PROPN
ejpam-100	288	7	j=1	j=1	PROPN
ejpam-100	288	8	|	|	ADV
ejpam-100	288	9	∂	∂	PROPN
ejpam-100	288	10	ϕ	ϕ	NOUN
ejpam-100	288	11	∂	∂	NOUN
ejpam-100	288	12	x	x	X
ejpam-100	288	13	i	i	PRON
ejpam-100	288	14	|pwi	|pwi	PROPN
ejpam-100	288	15	]	]	PUNCT
ejpam-100	288	16	,	,	PUNCT
ejpam-100	288	17	(	(	PUNCT
ejpam-100	288	18	4.28	4.28	NUM
ejpam-100	288	19	)	)	PUNCT
ejpam-100	288	20	with	with	ADP
ejpam-100	288	21	β	β	PRON
ejpam-100	288	22	and	and	CCONJ
ejpam-100	288	23	γ	γ	NOUN
ejpam-100	288	24	are	be	AUX
ejpam-100	288	25	positive	positive	ADJ
ejpam-100	288	26	constants	constant	NOUN
ejpam-100	288	27	.	.	PUNCT
ejpam-100	289	1	since	since	SCONJ
ejpam-100	289	2	tm	tm	PROPN
ejpam-100	289	3	(	(	PUNCT
ejpam-100	289	4	un	un	PROPN
ejpam-100	289	5	)	)	PUNCT
ejpam-100	289	6	*	*	PROPN
ejpam-100	289	7	tm	tm	PROPN
ejpam-100	289	8	(	(	PUNCT
ejpam-100	289	9	u	u	NOUN
ejpam-100	289	10	)	)	PUNCT
ejpam-100	289	11	weakly	weakly	ADV
ejpam-100	289	12	in	in	ADP
ejpam-100	289	13	w	w	PROPN
ejpam-100	289	14	1,p	1,p	PROPN
ejpam-100	289	15	0	0	NUM
ejpam-100	289	16	(	(	PUNCT
ejpam-100	289	17	ω	ω	PROPN
ejpam-100	289	18	,	,	PUNCT
ejpam-100	289	19	w	w	NOUN
ejpam-100	289	20	)	)	PUNCT
ejpam-100	289	21	and	and	CCONJ
ejpam-100	289	22	w	w	PROPN
ejpam-100	289	23	1,p	1,p	PROPN
ejpam-100	289	24	0	0	NUM
ejpam-100	289	25	(	(	PUNCT
ejpam-100	289	26	ω	ω	PROPN
ejpam-100	289	27	,	,	PUNCT
ejpam-100	289	28	w	w	PROPN
ejpam-100	289	29	)	)	PUNCT
ejpam-100	289	30	,	,	PUNCT
ejpam-100	289	31	→,→	→,→	PROPN
ejpam-100	289	32	lq(ω	lq(ω	PROPN
ejpam-100	289	33	,	,	PUNCT
ejpam-100	289	34	σ	σ	PROPN
ejpam-100	289	35	)	)	PUNCT
ejpam-100	289	36	,	,	PUNCT
ejpam-100	289	37	then	then	ADV
ejpam-100	289	38	tm	tm	PROPN
ejpam-100	289	39	(	(	PUNCT
ejpam-100	289	40	un	un	PROPN
ejpam-100	289	41	)	)	PUNCT
ejpam-100	289	42	→	→	SYM
ejpam-100	289	43	tm	tm	PROPN
ejpam-100	289	44	(	(	PUNCT
ejpam-100	289	45	u	u	NOUN
ejpam-100	289	46	)	)	PUNCT
ejpam-100	289	47	strongly	strongly	ADV
ejpam-100	289	48	in	in	ADP
ejpam-100	289	49	lq(ω	lq(ω	PROPN
ejpam-100	289	50	,	,	PUNCT
ejpam-100	289	51	σ	σ	PROPN
ejpam-100	289	52	)	)	PUNCT
ejpam-100	289	53	and	and	CCONJ
ejpam-100	289	54	a.e	a.e	PROPN
ejpam-100	289	55	.	.	PROPN
ejpam-100	289	56	in	in	ADP
ejpam-100	289	57	ω	ω	NUM
ejpam-100	289	58	,	,	PUNCT
ejpam-100	289	59	hence	hence	ADV
ejpam-100	289	60	|ai(x	|ai(x	NUM
ejpam-100	289	61	,	,	PUNCT
ejpam-100	289	62	tm	tm	PROPN
ejpam-100	289	63	(	(	PUNCT
ejpam-100	289	64	un),∇ϕ)|p	un),∇ϕ)|p	PROPN
ejpam-100	289	65	′	′	NUM
ejpam-100	289	66	w∗i	w∗i	PRON
ejpam-100	289	67	→	→	SYM
ejpam-100	289	68	|ai(x	|ai(x	PROPN
ejpam-100	289	69	,	,	PUNCT
ejpam-100	289	70	tm	tm	PROPN
ejpam-100	289	71	(	(	PUNCT
ejpam-100	289	72	u),∇ϕ)|p	u),∇ϕ)|p	PROPN
ejpam-100	289	73	′	′	NOUN
ejpam-100	289	74	w∗i	w∗i	PRON
ejpam-100	289	75	a.e.in	a.e.in	X
ejpam-100	289	76	ω	ω	X
ejpam-100	289	77	.	.	PUNCT
ejpam-100	289	78	and	and	CCONJ
ejpam-100	289	79	γ	γ	PROPN
ejpam-100	289	80			PROPN
ejpam-100	289	81			NOUN
ejpam-100	289	82			NUM
ejpam-100	289	83	k(x)p	k(x)p	NOUN
ejpam-100	290	1	′	′	NUM
ejpam-100	291	1	+	+	CCONJ
ejpam-100	291	2	|tm	|tm	X
ejpam-100	291	3	(	(	PUNCT
ejpam-100	291	4	un)|qσ+	un)|qσ+	PROPN
ejpam-100	291	5	n	n	PROPN
ejpam-100	291	6	∑	∑	PROPN
ejpam-100	291	7	j=1	j=1	PROPN
ejpam-100	291	8	|	|	ADV
ejpam-100	291	9	∂	∂	PROPN
ejpam-100	291	10	ϕ	ϕ	NOUN
ejpam-100	291	11	∂	∂	NOUN
ejpam-100	291	12	x	x	SYM
ejpam-100	291	13	i	i	PRON
ejpam-100	291	14	|pwi	|pwi	NOUN
ejpam-100	291	15			PROPN
ejpam-100	291	16			PROPN
ejpam-100	291	17			PROPN
ejpam-100	291	18	→	→	SYM
ejpam-100	291	19	γ	γ	X
ejpam-100	291	20			NOUN
ejpam-100	291	21			NOUN
ejpam-100	291	22			X
ejpam-100	292	1	k(x)p	k(x)p	NOUN
ejpam-100	292	2	′	′	NUM
ejpam-100	293	1	+	+	CCONJ
ejpam-100	293	2	|tm	|tm	X
ejpam-100	293	3	(	(	PUNCT
ejpam-100	293	4	u)|qσ+	u)|qσ+	NUM
ejpam-100	293	5	n	n	CCONJ
ejpam-100	293	6	∑	∑	PROPN
ejpam-100	293	7	j=1	j=1	PROPN
ejpam-100	293	8	|	|	ADV
ejpam-100	293	9	∂	∂	PROPN
ejpam-100	293	10	ϕ	ϕ	NOUN
ejpam-100	293	11	∂	∂	NOUN
ejpam-100	293	12	x	x	SYM
ejpam-100	293	13	i	i	PRON
ejpam-100	293	14	|pwi	|pwi	NOUN
ejpam-100	293	15			PROPN
ejpam-100	293	16			PROPN
ejpam-100	293	17			PROPN
ejpam-100	293	18	a.e	a.e	PROPN
ejpam-100	293	19	.	.	PROPN
ejpam-100	293	20	in	in	ADP
ejpam-100	293	21	ω	ω	PROPN
ejpam-100	293	22	.	.	PUNCT
ejpam-100	294	1	y.	y.	PROPN
ejpam-100	294	2	akdim	akdim	PROPN
ejpam-100	294	3	,	,	PUNCT
ejpam-100	294	4	e.	e.	PROPN
ejpam-100	294	5	azroul	azroul	PROPN
ejpam-100	294	6	,	,	PUNCT
ejpam-100	294	7	and	and	CCONJ
ejpam-100	294	8	m.	m.	NOUN
ejpam-100	294	9	rhoudaf	rhoudaf	PROPN
ejpam-100	294	10	/	/	SYM
ejpam-100	294	11	eur	eur	PROPN
ejpam-100	294	12	.	.	PUNCT
ejpam-100	295	1	j.	j.	PROPN
ejpam-100	295	2	pure	pure	PROPN
ejpam-100	295	3	appl	appl	PROPN
ejpam-100	295	4	.	.	PROPN
ejpam-100	295	5	math	math	PROPN
ejpam-100	295	6	,	,	PUNCT
ejpam-100	295	7	1	1	NUM
ejpam-100	295	8	(	(	PUNCT
ejpam-100	295	9	2008	2008	NUM
ejpam-100	295	10	)	)	PUNCT
ejpam-100	295	11	,	,	PUNCT
ejpam-100	295	12	(	(	PUNCT
ejpam-100	295	13	56	56	NUM
ejpam-100	295	14	-	-	SYM
ejpam-100	295	15	71	71	NUM
ejpam-100	295	16	)	)	PUNCT
ejpam-100	295	17	68	68	NUM
ejpam-100	295	18	then	then	ADV
ejpam-100	295	19	,	,	PUNCT
ejpam-100	295	20	by	by	ADP
ejpam-100	295	21	vitali	vitali	PROPN
ejpam-100	295	22	’s	’s	PART
ejpam-100	295	23	theorem	theorem	PROPN
ejpam-100	295	24	,	,	PUNCT
ejpam-100	295	25	we	we	PRON
ejpam-100	295	26	deduce	deduce	VERB
ejpam-100	295	27	that	that	PRON
ejpam-100	295	28	ai(x	ai(x	NOUN
ejpam-100	295	29	,	,	PUNCT
ejpam-100	295	30	tm	tm	PROPN
ejpam-100	295	31	(	(	PUNCT
ejpam-100	295	32	un),∇ϕ)→	un),∇ϕ)→	PROPN
ejpam-100	295	33	ai(x	ai(x	NOUN
ejpam-100	295	34	,	,	PUNCT
ejpam-100	295	35	tm	tm	PROPN
ejpam-100	295	36	(	(	PUNCT
ejpam-100	295	37	u),∇ϕ	u),∇ϕ	ADV
ejpam-100	295	38	)	)	PUNCT
ejpam-100	295	39	strongly	strongly	ADV
ejpam-100	295	40	in	in	ADP
ejpam-100	295	41	lp′(ω	lp′(ω	PROPN
ejpam-100	295	42	,	,	PUNCT
ejpam-100	295	43	w∗i	w∗i	PRON
ejpam-100	295	44	)	)	PUNCT
ejpam-100	295	45	,	,	PUNCT
ejpam-100	295	46	as	as	ADP
ejpam-100	295	47	n→+∞.	n→+∞.	X
ejpam-100	295	48	(	(	PUNCT
ejpam-100	295	49	4.29	4.29	NUM
ejpam-100	295	50	)	)	PUNCT
ejpam-100	295	51	combining	combine	VERB
ejpam-100	295	52	(	(	PUNCT
ejpam-100	295	53	4.27	4.27	NUM
ejpam-100	295	54	)	)	PUNCT
ejpam-100	295	55	and	and	CCONJ
ejpam-100	295	56	(	(	PUNCT
ejpam-100	295	57	4.29	4.29	NUM
ejpam-100	295	58	)	)	PUNCT
ejpam-100	295	59	,	,	PUNCT
ejpam-100	295	60	we	we	PRON
ejpam-100	295	61	obtain	obtain	VERB
ejpam-100	295	62	∫	∫	PROPN
ejpam-100	295	63	ω	ω	PROPN
ejpam-100	295	64	〈	〈	NOUN
ejpam-100	295	65	a(x	a(x	PROPN
ejpam-100	295	66	,	,	PUNCT
ejpam-100	295	67	un,∇ϕ),∇tk[un−ϕ	un,∇ϕ),∇tk[un−ϕ	NOUN
ejpam-100	295	68	]	]	X
ejpam-100	295	69	〉	〉	NOUN
ejpam-100	296	1	d	d	NOUN
ejpam-100	296	2	x	x	PROPN
ejpam-100	296	3	→	→	SYM
ejpam-100	296	4	∫	∫	PROPN
ejpam-100	296	5	ω	ω	NUM
ejpam-100	296	6	〈	〈	NOUN
ejpam-100	296	7	a(x	a(x	PROPN
ejpam-100	296	8	,	,	PUNCT
ejpam-100	296	9	u,∇ϕ),∇tk[u−ϕ	u,∇ϕ),∇tk[u−ϕ	ADJ
ejpam-100	296	10	]	]	X
ejpam-100	296	11	〉	〉	NOUN
ejpam-100	296	12	d	d	NOUN
ejpam-100	296	13	x	x	X
ejpam-100	296	14	,	,	PUNCT
ejpam-100	296	15	as	as	ADP
ejpam-100	296	16	n→+∞.	n→+∞.	X
ejpam-100	296	17	(	(	PUNCT
ejpam-100	296	18	4.30	4.30	NUM
ejpam-100	296	19	)	)	PUNCT
ejpam-100	296	20	secondly	secondly	ADV
ejpam-100	296	21	,	,	PUNCT
ejpam-100	296	22	we	we	PRON
ejpam-100	296	23	show	show	VERB
ejpam-100	296	24	that	that	SCONJ
ejpam-100	296	25	∫	∫	PROPN
ejpam-100	296	26	ω	ω	PROPN
ejpam-100	296	27	fntk[un−ϕ	fntk[un−ϕ	PROPN
ejpam-100	296	28	]	]	X
ejpam-100	296	29	d	d	X
ejpam-100	296	30	x	x	X
ejpam-100	296	31	→	→	SYM
ejpam-100	296	32	∫	∫	PROPN
ejpam-100	296	33	ω	ω	PROPN
ejpam-100	296	34	f	f	PROPN
ejpam-100	296	35	tk[u−ϕ	tk[u−ϕ	PROPN
ejpam-100	296	36	]	]	PUNCT
ejpam-100	297	1	d	d	NOUN
ejpam-100	297	2	x	x	X
ejpam-100	297	3	.	.	PUNCT
ejpam-100	298	1	(	(	PUNCT
ejpam-100	298	2	4.31	4.31	NUM
ejpam-100	298	3	)	)	PUNCT
ejpam-100	298	4	we	we	PRON
ejpam-100	298	5	have	have	VERB
ejpam-100	298	6	fntk[un	fntk[un	PROPN
ejpam-100	298	7	−ϕ]→	−ϕ]→	ADP
ejpam-100	298	8	f	f	PROPN
ejpam-100	298	9	tk[u−ϕ	tk[u−ϕ	PROPN
ejpam-100	298	10	]	]	PUNCT
ejpam-100	298	11	a.e	a.e	PROPN
ejpam-100	298	12	.	.	PROPN
ejpam-100	299	1	in	in	ADP
ejpam-100	299	2	ω	ω	PROPN
ejpam-100	299	3	and	and	CCONJ
ejpam-100	299	4	|	|	ADV
ejpam-100	299	5	fntk[un	fntk[un	PROPN
ejpam-100	299	6	−ϕ]|	−ϕ]|	VERB
ejpam-100	299	7	≤	≤	NUM
ejpam-100	299	8	k|	k|	NOUN
ejpam-100	299	9	fn|	fn|	NOUN
ejpam-100	299	10	and	and	CCONJ
ejpam-100	299	11	k|	k|	NOUN
ejpam-100	299	12	fn|	fn|	NOUN
ejpam-100	299	13	→	→	SYM
ejpam-100	299	14	k|	k|	NOUN
ejpam-100	299	15	f	f	NOUN
ejpam-100	299	16	|	|	ADV
ejpam-100	299	17	in	in	ADP
ejpam-100	299	18	l1(ω	l1(ω	PROPN
ejpam-100	299	19	)	)	PUNCT
ejpam-100	299	20	,	,	PUNCT
ejpam-100	299	21	then	then	ADV
ejpam-100	299	22	by	by	ADP
ejpam-100	299	23	using	use	VERB
ejpam-100	299	24	vitali	vitali	PROPN
ejpam-100	299	25	’s	’s	PART
ejpam-100	299	26	theorem	theorem	PROPN
ejpam-100	299	27	,	,	PUNCT
ejpam-100	299	28	we	we	PRON
ejpam-100	299	29	obtain	obtain	VERB
ejpam-100	299	30	(	(	PUNCT
ejpam-100	299	31	4.31	4.31	NUM
ejpam-100	299	32	)	)	PUNCT
ejpam-100	299	33	.	.	PUNCT
ejpam-100	300	1	similarly	similarly	ADV
ejpam-100	300	2	thanks	thank	NOUN
ejpam-100	300	3	to	to	ADP
ejpam-100	300	4	(	(	PUNCT
ejpam-100	300	5	4.20	4.20	NUM
ejpam-100	300	6	)	)	PUNCT
ejpam-100	300	7	we	we	PRON
ejpam-100	300	8	can	can	AUX
ejpam-100	300	9	show	show	VERB
ejpam-100	300	10	that	that	SCONJ
ejpam-100	300	11	∫	∫	PROPN
ejpam-100	300	12	ω	ω	PROPN
ejpam-100	300	13	gn(x	gn(x	X
ejpam-100	300	14	,	,	PUNCT
ejpam-100	300	15	un)tk[un−ϕ	un)tk[un−ϕ	NOUN
ejpam-100	300	16	]	]	X
ejpam-100	300	17	d	d	NOUN
ejpam-100	300	18	x	x	X
ejpam-100	300	19	→	→	SYM
ejpam-100	300	20	∫	∫	PROPN
ejpam-100	300	21	ω	ω	NUM
ejpam-100	300	22	g(x	g(x	PROPN
ejpam-100	300	23	,	,	PUNCT
ejpam-100	300	24	u)tk[u−ϕ	u)tk[u−ϕ	NOUN
ejpam-100	300	25	]	]	X
ejpam-100	301	1	d	d	NOUN
ejpam-100	301	2	x	x	PUNCT
ejpam-100	301	3	as	as	ADP
ejpam-100	301	4	n→∞.	n→∞.	PROPN
ejpam-100	301	5	(	(	PUNCT
ejpam-100	301	6	4.32	4.32	NUM
ejpam-100	301	7	)	)	PUNCT
ejpam-100	301	8	show	show	VERB
ejpam-100	301	9	that	that	SCONJ
ejpam-100	301	10	:	:	PUNCT
ejpam-100	301	11	∫	∫	PROPN
ejpam-100	301	12	ω	ω	PROPN
ejpam-100	301	13	〈	〈	PROPN
ejpam-100	301	14	f,∇tk[un−ϕ	f,∇tk[un−ϕ	PROPN
ejpam-100	301	15	]	]	SYM
ejpam-100	301	16	〉	〉	NOUN
ejpam-100	301	17	d	d	NOUN
ejpam-100	301	18	x	x	PROPN
ejpam-100	301	19	→	→	SYM
ejpam-100	301	20	∫	∫	PROPN
ejpam-100	301	21	ω	ω	PROPN
ejpam-100	301	22	〈	〈	PROPN
ejpam-100	301	23	f,∇tk[u−ϕ	f,∇tk[u−ϕ	PROPN
ejpam-100	301	24	]	]	SYM
ejpam-100	301	25	〉	〉	NOUN
ejpam-100	301	26	d	d	NOUN
ejpam-100	301	27	x	x	X
ejpam-100	301	28	.	.	PUNCT
ejpam-100	302	1	(	(	PUNCT
ejpam-100	302	2	4.33	4.33	NUM
ejpam-100	302	3	)	)	PUNCT
ejpam-100	302	4	in	in	ADP
ejpam-100	302	5	view	view	NOUN
ejpam-100	302	6	of	of	ADP
ejpam-100	302	7	(	(	PUNCT
ejpam-100	302	8	4.27	4.27	NUM
ejpam-100	302	9	)	)	PUNCT
ejpam-100	302	10	and	and	CCONJ
ejpam-100	302	11	since	since	SCONJ
ejpam-100	302	12	f	f	PROPN
ejpam-100	302	13	∈	∈	PROPN
ejpam-100	302	14	n	n	CCONJ
ejpam-100	302	15	∏	∏	PROPN
ejpam-100	302	16	i=1	i=1	PROPN
ejpam-100	302	17	lp′(ω	lp′(ω	PROPN
ejpam-100	302	18	,	,	PUNCT
ejpam-100	302	19	w∗i	w∗i	PRON
ejpam-100	302	20	)	)	PUNCT
ejpam-100	302	21	,	,	PUNCT
ejpam-100	302	22	we	we	PRON
ejpam-100	302	23	obtain	obtain	VERB
ejpam-100	302	24	(	(	PUNCT
ejpam-100	302	25	4.33	4.33	NUM
ejpam-100	302	26	)	)	PUNCT
ejpam-100	302	27	.	.	PUNCT
ejpam-100	303	1	thanks	thank	NOUN
ejpam-100	303	2	to	to	ADP
ejpam-100	303	3	(	(	PUNCT
ejpam-100	303	4	4.30	4.30	NUM
ejpam-100	303	5	)	)	PUNCT
ejpam-100	303	6	,	,	PUNCT
ejpam-100	303	7	(	(	PUNCT
ejpam-100	303	8	4.31	4.31	NUM
ejpam-100	303	9	)	)	PUNCT
ejpam-100	303	10	and	and	CCONJ
ejpam-100	303	11	(	(	PUNCT
ejpam-100	303	12	4.33	4.33	NUM
ejpam-100	303	13	)	)	PUNCT
ejpam-100	303	14	allow	allow	VERB
ejpam-100	303	15	to	to	PART
ejpam-100	303	16	pass	pass	VERB
ejpam-100	303	17	to	to	ADP
ejpam-100	303	18	the	the	DET
ejpam-100	303	19	limit	limit	NOUN
ejpam-100	303	20	in	in	ADP
ejpam-100	303	21	the	the	DET
ejpam-100	303	22	inequality	inequality	NOUN
ejpam-100	303	23	(	(	PUNCT
ejpam-100	303	24	4.23	4.23	NUM
ejpam-100	303	25	)	)	PUNCT
ejpam-100	303	26	,	,	PUNCT
ejpam-100	303	27	so	so	SCONJ
ejpam-100	303	28	that	that	SCONJ
ejpam-100	303	29	∀ϕ	∀ϕ	PROPN
ejpam-100	303	30	∈w	∈w	VERB
ejpam-100	303	31	1,p	1,p	PROPN
ejpam-100	303	32	0	0	SYM
ejpam-100	303	33	(	(	PUNCT
ejpam-100	303	34	ω	ω	PROPN
ejpam-100	303	35	,	,	PUNCT
ejpam-100	303	36	w)∩	w)∩	X
ejpam-100	303	37	l∞(ω	l∞(ω	X
ejpam-100	303	38	)	)	PUNCT
ejpam-100	303	39	,	,	PUNCT
ejpam-100	303	40	we	we	PRON
ejpam-100	303	41	deduce	deduce	VERB
ejpam-100	303	42	∫	∫	PROPN
ejpam-100	303	43	ω	ω	PROPN
ejpam-100	303	44	〈	〈	NOUN
ejpam-100	303	45	a(x	a(x	PROPN
ejpam-100	303	46	,	,	PUNCT
ejpam-100	303	47	u,∇ϕ),∇tk[u−ϕ	u,∇ϕ),∇tk[u−ϕ	ADJ
ejpam-100	303	48	]	]	X
ejpam-100	303	49	〉	〉	NOUN
ejpam-100	303	50	d	d	NOUN
ejpam-100	303	51	x	x	SYM
ejpam-100	303	52	≤	≤	NUM
ejpam-100	303	53	∫	∫	PROPN
ejpam-100	303	54	ω	ω	PROPN
ejpam-100	303	55	f	f	PROPN
ejpam-100	303	56	tk[u−ϕ	tk[u−ϕ	PROPN
ejpam-100	303	57	]	]	PUNCT
ejpam-100	304	1	d	d	X
ejpam-100	304	2	x	x	SYM
ejpam-100	304	3	+	+	NUM
ejpam-100	304	4	∫	∫	PROPN
ejpam-100	304	5	ω	ω	NUM
ejpam-100	304	6	〈	〈	PROPN
ejpam-100	304	7	f,∇tk[u−ϕ	f,∇tk[u−ϕ	PROPN
ejpam-100	304	8	]	]	SYM
ejpam-100	304	9	〉	〉	NOUN
ejpam-100	304	10	d	d	NOUN
ejpam-100	304	11	x	x	X
ejpam-100	304	12	.	.	PUNCT
ejpam-100	305	1	in	in	ADP
ejpam-100	305	2	view	view	NOUN
ejpam-100	305	3	of	of	ADP
ejpam-100	305	4	main	main	ADJ
ejpam-100	305	5	lemma	lemma	NOUN
ejpam-100	305	6	,	,	PUNCT
ejpam-100	305	7	we	we	PRON
ejpam-100	305	8	can	can	AUX
ejpam-100	305	9	deduce	deduce	VERB
ejpam-100	305	10	that	that	SCONJ
ejpam-100	305	11	u	u	NOUN
ejpam-100	305	12	is	be	AUX
ejpam-100	305	13	an	an	DET
ejpam-100	305	14	entropy	entropy	NOUN
ejpam-100	305	15	solution	solution	NOUN
ejpam-100	305	16	of	of	ADP
ejpam-100	305	17	the	the	DET
ejpam-100	305	18	problem	problem	NOUN
ejpam-100	305	19	(	(	PUNCT
ejpam-100	305	20	p	p	NOUN
ejpam-100	305	21	)	)	PUNCT
ejpam-100	305	22	.	.	PUNCT
ejpam-100	306	1	this	this	PRON
ejpam-100	306	2	completes	complete	VERB
ejpam-100	306	3	the	the	DET
ejpam-100	306	4	proof	proof	NOUN
ejpam-100	306	5	of	of	ADP
ejpam-100	306	6	theorem	theorem	ADJ
ejpam-100	306	7	3.1	3.1	NUM
ejpam-100	306	8	.	.	PUNCT
ejpam-100	306	9	remark	remark	NOUN
ejpam-100	306	10	4.1	4.1	NUM
ejpam-100	306	11	.	.	PUNCT
ejpam-100	307	1	in	in	ADP
ejpam-100	307	2	the	the	DET
ejpam-100	307	3	case	case	NOUN
ejpam-100	307	4	where	where	SCONJ
ejpam-100	307	5	f	f	PROPN
ejpam-100	307	6	≡	≡	PROPN
ejpam-100	307	7	0	0	NUM
ejpam-100	307	8	,	,	PUNCT
ejpam-100	307	9	if	if	SCONJ
ejpam-100	307	10	we	we	PRON
ejpam-100	307	11	suppose	suppose	VERB
ejpam-100	307	12	that	that	SCONJ
ejpam-100	307	13	the	the	DET
ejpam-100	307	14	second	second	ADJ
ejpam-100	307	15	member	member	NOUN
ejpam-100	307	16	are	be	AUX
ejpam-100	307	17	nonnegative	nonnegative	ADJ
ejpam-100	307	18	,	,	PUNCT
ejpam-100	307	19	then	then	ADV
ejpam-100	307	20	we	we	PRON
ejpam-100	307	21	obtain	obtain	VERB
ejpam-100	307	22	a	a	DET
ejpam-100	307	23	nonnegative	nonnegative	ADJ
ejpam-100	307	24	solution	solution	NOUN
ejpam-100	307	25	.	.	PUNCT
ejpam-100	308	1	indeed	indeed	ADV
ejpam-100	308	2	,	,	PUNCT
ejpam-100	308	3	if	if	SCONJ
ejpam-100	308	4	we	we	PRON
ejpam-100	308	5	take	take	VERB
ejpam-100	308	6	v	v	NOUN
ejpam-100	308	7	=	=	SYM
ejpam-100	308	8	th(u+	th(u+	PROPN
ejpam-100	308	9	)	)	PUNCT
ejpam-100	308	10	in	in	ADP
ejpam-100	308	11	(	(	PUNCT
ejpam-100	308	12	p	p	NOUN
ejpam-100	308	13	)	)	PUNCT
ejpam-100	308	14	,	,	PUNCT
ejpam-100	308	15	we	we	PRON
ejpam-100	308	16	have	have	VERB
ejpam-100	308	17	∫	∫	PROPN
ejpam-100	308	18	ω	ω	PROPN
ejpam-100	308	19	〈	〈	PROPN
ejpam-100	308	20	a(x	a(x	PROPN
ejpam-100	308	21	,	,	PUNCT
ejpam-100	308	22	u,∇u),∇tk(u−	u,∇u),∇tk(u−	PROPN
ejpam-100	308	23	th(u	th(u	X
ejpam-100	308	24	+	+	ADJ
ejpam-100	308	25	)	)	PUNCT
ejpam-100	308	26	)	)	PUNCT
ejpam-100	308	27	〉	〉	NOUN
ejpam-100	309	1	d	d	NOUN
ejpam-100	309	2	x	x	SYM
ejpam-100	310	1	+	+	NUM
ejpam-100	310	2	∫	∫	PROPN
ejpam-100	310	3	ω	ω	NUM
ejpam-100	310	4	g(x	g(x	PROPN
ejpam-100	310	5	,	,	PUNCT
ejpam-100	310	6	u)tk(u−	u)tk(u−	PRON
ejpam-100	310	7	th(u	th(u	X
ejpam-100	310	8	+	+	ADJ
ejpam-100	310	9	)	)	PUNCT
ejpam-100	310	10	)	)	PUNCT
ejpam-100	311	1	d	d	X
ejpam-100	311	2	x	x	SYM
ejpam-100	311	3	≤	≤	NUM
ejpam-100	311	4	∫	∫	PROPN
ejpam-100	311	5	ω	ω	PROPN
ejpam-100	311	6	f	f	PROPN
ejpam-100	311	7	tk(u−	tk(u−	PRON
ejpam-100	311	8	th(u	th(u	X
ejpam-100	311	9	+	+	NOUN
ejpam-100	311	10	)	)	PUNCT
ejpam-100	311	11	)	)	PUNCT
ejpam-100	312	1	d	d	NOUN
ejpam-100	312	2	x	x	X
ejpam-100	312	3	.	.	PUNCT
ejpam-100	313	1	y.	y.	PROPN
ejpam-100	313	2	akdim	akdim	PROPN
ejpam-100	313	3	,	,	PUNCT
ejpam-100	313	4	e.	e.	PROPN
ejpam-100	313	5	azroul	azroul	PROPN
ejpam-100	313	6	,	,	PUNCT
ejpam-100	313	7	and	and	CCONJ
ejpam-100	313	8	m.	m.	NOUN
ejpam-100	313	9	rhoudaf	rhoudaf	PROPN
ejpam-100	313	10	/	/	SYM
ejpam-100	313	11	eur	eur	PROPN
ejpam-100	313	12	.	.	PUNCT
ejpam-100	314	1	j.	j.	PROPN
ejpam-100	314	2	pure	pure	PROPN
ejpam-100	314	3	appl	appl	PROPN
ejpam-100	314	4	.	.	PROPN
ejpam-100	314	5	math	math	PROPN
ejpam-100	314	6	,	,	PUNCT
ejpam-100	314	7	1	1	NUM
ejpam-100	314	8	(	(	PUNCT
ejpam-100	314	9	2008	2008	NUM
ejpam-100	314	10	)	)	PUNCT
ejpam-100	314	11	,	,	PUNCT
ejpam-100	314	12	(	(	PUNCT
ejpam-100	314	13	56	56	NUM
ejpam-100	314	14	-	-	SYM
ejpam-100	314	15	71	71	NUM
ejpam-100	314	16	)	)	PUNCT
ejpam-100	314	17	69	69	NUM
ejpam-100	314	18	since	since	SCONJ
ejpam-100	314	19	g(x	g(x	PROPN
ejpam-100	314	20	,	,	PUNCT
ejpam-100	314	21	u)tk(u−	u)tk(u−	CCONJ
ejpam-100	314	22	th(u+))≥	th(u+))≥	PROPN
ejpam-100	314	23	0	0	NUM
ejpam-100	314	24	,	,	PUNCT
ejpam-100	314	25	we	we	PRON
ejpam-100	314	26	deduce	deduce	VERB
ejpam-100	314	27	∫	∫	PROPN
ejpam-100	314	28	ω	ω	PROPN
ejpam-100	314	29	〈	〈	NOUN
ejpam-100	314	30	a(x	a(x	PROPN
ejpam-100	314	31	,	,	PUNCT
ejpam-100	314	32	u,∇u),∇tk(u−	u,∇u),∇tk(u−	PROPN
ejpam-100	314	33	th(u	th(u	X
ejpam-100	314	34	+	+	ADJ
ejpam-100	314	35	)	)	PUNCT
ejpam-100	314	36	)	)	PUNCT
ejpam-100	314	37	〉	〉	NOUN
ejpam-100	315	1	d	d	NOUN
ejpam-100	315	2	x	x	SYM
ejpam-100	315	3	≤	≤	NUM
ejpam-100	315	4	∫	∫	PROPN
ejpam-100	315	5	ω	ω	PROPN
ejpam-100	315	6	f	f	PROPN
ejpam-100	315	7	tk(u−	tk(u−	PRON
ejpam-100	315	8	th(u	th(u	X
ejpam-100	315	9	+	+	NOUN
ejpam-100	315	10	)	)	PUNCT
ejpam-100	315	11	)	)	PUNCT
ejpam-100	316	1	d	d	NOUN
ejpam-100	316	2	x	x	X
ejpam-100	316	3	,	,	PUNCT
ejpam-100	316	4	we	we	PRON
ejpam-100	316	5	remark	remark	VERB
ejpam-100	316	6	also	also	ADV
ejpam-100	316	7	,	,	PUNCT
ejpam-100	316	8	by	by	ADP
ejpam-100	316	9	using	use	VERB
ejpam-100	316	10	f	f	PROPN
ejpam-100	316	11	≥	≥	NUM
ejpam-100	316	12	0	0	NUM
ejpam-100	316	13	∫	∫	PROPN
ejpam-100	317	1	ω	ω	PROPN
ejpam-100	317	2	f	f	PROPN
ejpam-100	317	3	tk(u−	tk(u−	PRON
ejpam-100	317	4	th(u	th(u	X
ejpam-100	317	5	+	+	NOUN
ejpam-100	317	6	)	)	PUNCT
ejpam-100	317	7	)	)	PUNCT
ejpam-100	318	1	d	d	X
ejpam-100	318	2	x	x	SYM
ejpam-100	318	3	≤	≤	NUM
ejpam-100	318	4	∫	∫	PROPN
ejpam-100	318	5	{	{	PUNCT
ejpam-100	318	6	u≥h	u≥h	PROPN
ejpam-100	318	7	}	}	PUNCT
ejpam-100	318	8	f	f	PROPN
ejpam-100	318	9	tk(u−	tk(u−	NUM
ejpam-100	318	10	th(u	th(u	NUM
ejpam-100	318	11	)	)	PUNCT
ejpam-100	318	12	)	)	PUNCT
ejpam-100	319	1	d	d	NOUN
ejpam-100	319	2	x	x	X
ejpam-100	319	3	.	.	PUNCT
ejpam-100	320	1	on	on	ADP
ejpam-100	320	2	the	the	DET
ejpam-100	320	3	other	other	ADJ
ejpam-100	320	4	hand	hand	NOUN
ejpam-100	320	5	,	,	PUNCT
ejpam-100	320	6	thanks	thank	NOUN
ejpam-100	320	7	to	to	ADP
ejpam-100	320	8	(	(	PUNCT
ejpam-100	320	9	2.8	2.8	NUM
ejpam-100	320	10	)	)	PUNCT
ejpam-100	320	11	,	,	PUNCT
ejpam-100	320	12	we	we	PRON
ejpam-100	320	13	conclude	conclude	VERB
ejpam-100	320	14	α	α	PRON
ejpam-100	320	15	∫	∫	PROPN
ejpam-100	320	16	ω	ω	PROPN
ejpam-100	320	17	n	n	PROPN
ejpam-100	320	18	∑	∑	PROPN
ejpam-100	320	19	i=1	i=1	PROPN
ejpam-100	320	20	|	|	ADV
ejpam-100	320	21	∂	∂	NUM
ejpam-100	320	22	tk(u−	tk(u−	NUM
ejpam-100	320	23	)	)	PUNCT
ejpam-100	320	24	∂	∂	NOUN
ejpam-100	320	25	x	x	NOUN
ejpam-100	321	1	i	i	NOUN
ejpam-100	321	2	|pwi	|pwi	PROPN
ejpam-100	321	3	d	d	X
ejpam-100	321	4	x	x	SYM
ejpam-100	321	5	≤	≤	NUM
ejpam-100	321	6	∫	∫	PROPN
ejpam-100	321	7	{	{	PUNCT
ejpam-100	321	8	u≥h	u≥h	PROPN
ejpam-100	321	9	}	}	PUNCT
ejpam-100	321	10	f	f	PROPN
ejpam-100	321	11	tk(u−	tk(u−	NUM
ejpam-100	321	12	th(u	th(u	NUM
ejpam-100	321	13	)	)	PUNCT
ejpam-100	321	14	)	)	PUNCT
ejpam-100	322	1	d	d	NOUN
ejpam-100	322	2	x	x	X
ejpam-100	322	3	.	.	PUNCT
ejpam-100	323	1	letting	let	VERB
ejpam-100	323	2	h	h	NOUN
ejpam-100	323	3	tend	tend	VERB
ejpam-100	323	4	to	to	PART
ejpam-100	323	5	infinity	infinity	VERB
ejpam-100	323	6	,	,	PUNCT
ejpam-100	323	7	we	we	PRON
ejpam-100	323	8	can	can	AUX
ejpam-100	323	9	easily	easily	ADV
ejpam-100	323	10	deduce	deduce	VERB
ejpam-100	323	11	tk(u	tk(u	NOUN
ejpam-100	323	12	−	−	NUM
ejpam-100	323	13	)	)	PUNCT
ejpam-100	323	14	=	=	SYM
ejpam-100	323	15	0	0	NUM
ejpam-100	323	16	,	,	PUNCT
ejpam-100	323	17	∀k	∀k	NOUN
ejpam-100	323	18	>	>	X
ejpam-100	323	19	0	0	NUM
ejpam-100	323	20	,	,	PUNCT
ejpam-100	323	21	which	which	PRON
ejpam-100	323	22	implies	imply	VERB
ejpam-100	323	23	that	that	SCONJ
ejpam-100	323	24	u≥	u≥	PROPN
ejpam-100	323	25	0	0	NUM
ejpam-100	323	26	.	.	PROPN
ejpam-100	323	27	5	5	NUM
ejpam-100	323	28	.	.	X
ejpam-100	323	29	example	example	NOUN
ejpam-100	323	30	let	let	VERB
ejpam-100	323	31	us	we	PRON
ejpam-100	323	32	consider	consider	VERB
ejpam-100	323	33	the	the	DET
ejpam-100	323	34	following	follow	VERB
ejpam-100	323	35	special	special	ADJ
ejpam-100	323	36	case	case	NOUN
ejpam-100	323	37	:	:	PUNCT
ejpam-100	323	38	ai(x	ai(x	NUM
ejpam-100	323	39	,	,	PUNCT
ejpam-100	323	40	η	η	PROPN
ejpam-100	323	41	,	,	PUNCT
ejpam-100	323	42	ξ	ξ	NOUN
ejpam-100	323	43	)	)	PUNCT
ejpam-100	323	44	=	=	PUNCT
ejpam-100	324	1	wi(x)|ξi|p−1sgn(ξi	wi(x)|ξi|p−1sgn(ξi	ADP
ejpam-100	324	2	)	)	PUNCT
ejpam-100	324	3	i	i	NOUN
ejpam-100	324	4	=	=	NOUN
ejpam-100	324	5	1	1	NUM
ejpam-100	324	6	,	,	PUNCT
ejpam-100	324	7	...	...	PUNCT
ejpam-100	324	8	,	,	PUNCT
ejpam-100	324	9	n	n	X
ejpam-100	324	10	,	,	PUNCT
ejpam-100	324	11	g(x	g(x	PROPN
ejpam-100	324	12	,	,	PUNCT
ejpam-100	324	13	s	s	X
ejpam-100	324	14	)	)	PUNCT
ejpam-100	324	15	=	=	SYM
ejpam-100	324	16	ρs|s|r	ρs|s|r	PROPN
ejpam-100	324	17	ρ	ρ	X
ejpam-100	324	18	>	>	X
ejpam-100	324	19	0	0	PUNCT
ejpam-100	325	1	and	and	CCONJ
ejpam-100	325	2	r	r	X
ejpam-100	325	3	>	>	X
ejpam-100	325	4	0	0	PUNCT
ejpam-100	325	5	with	with	ADP
ejpam-100	325	6	wi(x	wi(x	NOUN
ejpam-100	325	7	)	)	PUNCT
ejpam-100	325	8	is	be	AUX
ejpam-100	325	9	a	a	DET
ejpam-100	325	10	weight	weight	NOUN
ejpam-100	325	11	function	function	NOUN
ejpam-100	325	12	(	(	PUNCT
ejpam-100	325	13	i	i	NOUN
ejpam-100	325	14	=	=	NOUN
ejpam-100	325	15	1	1	NUM
ejpam-100	325	16	,	,	PUNCT
ejpam-100	325	17	...	...	PUNCT
ejpam-100	325	18	,	,	PUNCT
ejpam-100	325	19	n	n	CCONJ
ejpam-100	325	20	)	)	PUNCT
ejpam-100	325	21	.	.	PUNCT
ejpam-100	326	1	for	for	ADP
ejpam-100	326	2	simplicity	simplicity	NOUN
ejpam-100	326	3	,	,	PUNCT
ejpam-100	326	4	we	we	PRON
ejpam-100	326	5	shall	shall	AUX
ejpam-100	326	6	suppose	suppose	VERB
ejpam-100	326	7	that	that	SCONJ
ejpam-100	326	8	:	:	PUNCT
ejpam-100	326	9	wi(x	wi(x	X
ejpam-100	326	10	)	)	PUNCT
ejpam-100	326	11	=	=	SYM
ejpam-100	326	12	w(x	w(x	NOUN
ejpam-100	326	13	)	)	PUNCT
ejpam-100	326	14	for	for	ADP
ejpam-100	326	15	i	i	PROPN
ejpam-100	326	16	=	=	NOUN
ejpam-100	326	17	1	1	NUM
ejpam-100	326	18	,	,	PUNCT
ejpam-100	326	19	...	...	PUNCT
ejpam-100	326	20	,	,	PUNCT
ejpam-100	326	21	n	n	CCONJ
ejpam-100	326	22	−	−	PROPN
ejpam-100	326	23	1	1	NUM
ejpam-100	326	24	,	,	PUNCT
ejpam-100	326	25	wn	wn	PROPN
ejpam-100	326	26	(	(	PUNCT
ejpam-100	326	27	x)≡	x)≡	PROPN
ejpam-100	326	28	0	0	NUM
ejpam-100	327	1	it	it	PRON
ejpam-100	327	2	is	be	AUX
ejpam-100	327	3	easy	easy	ADJ
ejpam-100	327	4	to	to	PART
ejpam-100	327	5	show	show	VERB
ejpam-100	327	6	that	that	DET
ejpam-100	327	7	ai(x	ai(x	NOUN
ejpam-100	327	8	,	,	PUNCT
ejpam-100	327	9	s	s	X
ejpam-100	327	10	,	,	PUNCT
ejpam-100	327	11	ξ	ξ	NOUN
ejpam-100	327	12	)	)	PUNCT
ejpam-100	327	13	are	be	AUX
ejpam-100	327	14	caracthéodory	caracthéodory	NOUN
ejpam-100	327	15	function	function	NOUN
ejpam-100	327	16	satisfying	satisfy	VERB
ejpam-100	327	17	the	the	DET
ejpam-100	327	18	growth	growth	NOUN
ejpam-100	327	19	condition	condition	NOUN
ejpam-100	327	20	(	(	PUNCT
ejpam-100	327	21	2.6	2.6	NUM
ejpam-100	327	22	)	)	PUNCT
ejpam-100	327	23	and	and	CCONJ
ejpam-100	327	24	the	the	DET
ejpam-100	327	25	coercivity	coercivity	NOUN
ejpam-100	327	26	(	(	PUNCT
ejpam-100	327	27	2.8	2.8	NUM
ejpam-100	327	28	)	)	PUNCT
ejpam-100	327	29	.	.	PUNCT
ejpam-100	328	1	on	on	ADP
ejpam-100	328	2	the	the	DET
ejpam-100	328	3	other	other	ADJ
ejpam-100	328	4	hand	hand	NOUN
ejpam-100	328	5	,	,	PUNCT
ejpam-100	328	6	the	the	DET
ejpam-100	328	7	monotonicity	monotonicity	NOUN
ejpam-100	328	8	condition	condition	NOUN
ejpam-100	328	9	is	be	AUX
ejpam-100	328	10	verified	verify	VERB
ejpam-100	328	11	.	.	PUNCT
ejpam-100	329	1	in	in	ADP
ejpam-100	329	2	fact	fact	NOUN
ejpam-100	329	3	,	,	PUNCT
ejpam-100	329	4	n	n	CCONJ
ejpam-100	329	5	∑	∑	PROPN
ejpam-100	329	6	i=1	i=1	PROPN
ejpam-100	329	7	(	(	PUNCT
ejpam-100	329	8	ai(x	ai(x	NOUN
ejpam-100	329	9	,	,	PUNCT
ejpam-100	329	10	s	s	X
ejpam-100	329	11	,	,	PUNCT
ejpam-100	329	12	ξ)−	ξ)−	PROPN
ejpam-100	329	13	ai(x	ai(x	NOUN
ejpam-100	329	14	,	,	PUNCT
ejpam-100	329	15	s	s	AUX
ejpam-100	329	16	,	,	PUNCT
ejpam-100	329	17	ξ̂))(ξi	ξ̂))(ξi	NUM
ejpam-100	329	18	−	−	NOUN
ejpam-100	329	19	ξ̂i	ξ̂i	NUM
ejpam-100	329	20	)	)	PUNCT
ejpam-100	329	21	=	=	SYM
ejpam-100	329	22	w(x	w(x	NOUN
ejpam-100	329	23	)	)	PUNCT
ejpam-100	330	1	n−1	n−1	PROPN
ejpam-100	330	2	∑	∑	PUNCT
ejpam-100	330	3	i=1	i=1	PROPN
ejpam-100	330	4	(	(	PUNCT
ejpam-100	330	5	|ξi|p−1sgn(ξi)−	|ξi|p−1sgn(ξi)−	NUM
ejpam-100	330	6	|ξ̂i|p−1sgn(ξ̂i))(ξi	|ξ̂i|p−1sgn(ξ̂i))(ξi	PROPN
ejpam-100	330	7	−	−	PROPN
ejpam-100	330	8	ξ̂i)≥	ξ̂i)≥	NOUN
ejpam-100	330	9	0	0	PUNCT
ejpam-100	330	10	for	for	ADP
ejpam-100	330	11	almost	almost	ADV
ejpam-100	330	12	all	all	PRON
ejpam-100	330	13	x	x	SYM
ejpam-100	330	14	∈	∈	PROPN
ejpam-100	330	15	ω	ω	NOUN
ejpam-100	330	16	and	and	CCONJ
ejpam-100	330	17	for	for	ADP
ejpam-100	330	18	all	all	DET
ejpam-100	330	19	ξ	ξ	PROPN
ejpam-100	330	20	,	,	PUNCT
ejpam-100	330	21	ξ̂	ξ̂	NUM
ejpam-100	330	22	∈	∈	PROPN
ejpam-100	330	23	irn	irn	PROPN
ejpam-100	330	24	.	.	PUNCT
ejpam-100	331	1	this	this	DET
ejpam-100	331	2	last	last	ADJ
ejpam-100	331	3	inequality	inequality	NOUN
ejpam-100	331	4	can	can	AUX
ejpam-100	331	5	not	not	PART
ejpam-100	331	6	be	be	AUX
ejpam-100	331	7	strict	strict	ADJ
ejpam-100	331	8	,	,	PUNCT
ejpam-100	331	9	since	since	SCONJ
ejpam-100	331	10	for	for	ADP
ejpam-100	331	11	ξ	ξ	PROPN
ejpam-100	331	12	6=	6=	ADP
ejpam-100	331	13	ξ̂	ξ̂	NOUN
ejpam-100	331	14	with	with	ADP
ejpam-100	331	15	ξn	ξn	PROPN
ejpam-100	331	16	6=	6=	NUM
ejpam-100	331	17	ξ̂n	ξ̂n	PROPN
ejpam-100	331	18	and	and	CCONJ
ejpam-100	331	19	ξi	ξi	NOUN
ejpam-100	331	20	=	=	SYM
ejpam-100	332	1	ξ̂i	ξ̂i	NUM
ejpam-100	332	2	,	,	PUNCT
ejpam-100	332	3	i	i	PRON
ejpam-100	332	4	=	=	NOUN
ejpam-100	332	5	1	1	NUM
ejpam-100	332	6	,	,	PUNCT
ejpam-100	332	7	...	...	PUNCT
ejpam-100	332	8	,	,	PUNCT
ejpam-100	332	9	n	n	CCONJ
ejpam-100	332	10	−	−	PROPN
ejpam-100	332	11	1	1	NUM
ejpam-100	332	12	.	.	PUNCT
ejpam-100	333	1	the	the	DET
ejpam-100	333	2	corresponding	corresponding	ADJ
ejpam-100	333	3	expression	expression	NOUN
ejpam-100	333	4	is	be	AUX
ejpam-100	333	5	zero	zero	NUM
ejpam-100	333	6	.	.	PUNCT
ejpam-100	334	1	references	reference	NOUN
ejpam-100	334	2	70	70	NUM
ejpam-100	334	3	in	in	ADP
ejpam-100	334	4	particular	particular	ADJ
ejpam-100	334	5	,	,	PUNCT
ejpam-100	334	6	let	let	VERB
ejpam-100	334	7	us	we	PRON
ejpam-100	334	8	use	use	VERB
ejpam-100	334	9	special	special	ADJ
ejpam-100	334	10	weight	weight	NOUN
ejpam-100	334	11	functions	function	NOUN
ejpam-100	334	12	w	w	PROPN
ejpam-100	334	13	and	and	CCONJ
ejpam-100	334	14	σ	σ	PROPN
ejpam-100	334	15	expressed	express	VERB
ejpam-100	334	16	in	in	ADP
ejpam-100	334	17	terms	term	NOUN
ejpam-100	334	18	of	of	ADP
ejpam-100	334	19	the	the	DET
ejpam-100	334	20	distance	distance	NOUN
ejpam-100	334	21	to	to	ADP
ejpam-100	334	22	the	the	DET
ejpam-100	334	23	bounded	bounded	ADJ
ejpam-100	334	24	∂ω	∂ω	PROPN
ejpam-100	334	25	.	.	PUNCT
ejpam-100	335	1	denote	denote	PROPN
ejpam-100	335	2	d(x	d(x	PROPN
ejpam-100	335	3	)	)	PUNCT
ejpam-100	336	1	=	=	SYM
ejpam-100	337	1	dist(x	dist(x	INTJ
ejpam-100	337	2	,	,	PUNCT
ejpam-100	337	3	∂ω	∂ω	ADJ
ejpam-100	337	4	)	)	PUNCT
ejpam-100	337	5	and	and	CCONJ
ejpam-100	337	6	set	set	VERB
ejpam-100	337	7	w(x	w(x	NOUN
ejpam-100	337	8	)	)	PUNCT
ejpam-100	337	9	=	=	SYM
ejpam-100	337	10	dλ(x	dλ(x	X
ejpam-100	337	11	)	)	PUNCT
ejpam-100	337	12	,	,	PUNCT
ejpam-100	337	13	σ(x	σ(x	PROPN
ejpam-100	337	14	)	)	PUNCT
ejpam-100	337	15	=	=	PUNCT
ejpam-100	337	16	dµ(x	dµ(x	PUNCT
ejpam-100	337	17	)	)	PUNCT
ejpam-100	337	18	.	.	PUNCT
ejpam-100	338	1	in	in	ADP
ejpam-100	338	2	this	this	DET
ejpam-100	338	3	case	case	NOUN
ejpam-100	338	4	,	,	PUNCT
ejpam-100	338	5	the	the	DET
ejpam-100	338	6	hardy	hardy	ADJ
ejpam-100	338	7	inequality	inequality	NOUN
ejpam-100	338	8	reads	read	VERB
ejpam-100	338	9	�	�	PROPN
ejpam-100	338	10	∫	∫	PROPN
ejpam-100	338	11	ω	ω	PROPN
ejpam-100	338	12	|u(x)|qdµ(x	|u(x)|qdµ(x	PROPN
ejpam-100	338	13	)	)	PUNCT
ejpam-100	338	14	d	d	NOUN
ejpam-100	338	15	x	x	SYM
ejpam-100	338	16	�	�	PROPN
ejpam-100	338	17	1	1	NUM
ejpam-100	338	18	q	q	PROPN
ejpam-100	338	19	≤	≤	PROPN
ejpam-100	338	20	c	c	NOUN
ejpam-100	338	21	n−1	n−1	PROPN
ejpam-100	338	22	∑	∑	PUNCT
ejpam-100	338	23	i=1	i=1	PROPN
ejpam-100	338	24	∫	∫	PROPN
ejpam-100	339	1	ω	ω	NUM
ejpam-100	339	2	|	|	NOUN
ejpam-100	339	3	∂	∂	NUM
ejpam-100	339	4	u	u	NOUN
ejpam-100	339	5	∂	∂	NOUN
ejpam-100	339	6	x	x	VERB
ejpam-100	339	7	i	i	PRON
ejpam-100	339	8	|pdλ(x	|pdλ(x	NOUN
ejpam-100	339	9	)	)	PUNCT
ejpam-100	340	1	d	d	X
ejpam-100	340	2	x	x	X
ejpam-100	340	3	!	!	PUNCT
ejpam-100	340	4	1	1	NUM
ejpam-100	340	5	p	p	NOUN
ejpam-100	340	6	.	.	PUNCT
ejpam-100	341	1	the	the	DET
ejpam-100	341	2	corresponding	corresponding	ADJ
ejpam-100	341	3	imbedding	imbedding	NOUN
ejpam-100	341	4	is	be	AUX
ejpam-100	341	5	compact	compact	ADJ
ejpam-100	341	6	if	if	SCONJ
ejpam-100	341	7	:	:	PUNCT
ejpam-100	341	8	(	(	PUNCT
ejpam-100	341	9	i	i	NOUN
ejpam-100	341	10	)	)	PUNCT
ejpam-100	341	11	for	for	ADP
ejpam-100	341	12	,	,	PUNCT
ejpam-100	341	13	1	1	NUM
ejpam-100	341	14	<	<	X
ejpam-100	341	15	p	p	X
ejpam-100	341	16	≤	≤	ADJ
ejpam-100	341	17	q	q	NOUN
ejpam-100	341	18	<	<	X
ejpam-100	341	19	∞	∞	PROPN
ejpam-100	341	20	,	,	PUNCT
ejpam-100	341	21	λ	λ	X
ejpam-100	341	22	<	<	X
ejpam-100	341	23	p−	p−	PROPN
ejpam-100	341	24	1	1	NUM
ejpam-100	341	25	,	,	PUNCT
ejpam-100	341	26	n	n	PRON
ejpam-100	341	27	q	q	NOUN
ejpam-100	341	28	−	−	PROPN
ejpam-100	341	29	n	n	PRON
ejpam-100	341	30	p	p	NOUN
ejpam-100	341	31	+	+	NUM
ejpam-100	341	32	1≥	1≥	NUM
ejpam-100	341	33	0	0	NUM
ejpam-100	341	34	,	,	PUNCT
ejpam-100	341	35	µ	µ	PRON
ejpam-100	341	36	q	q	NOUN
ejpam-100	341	37	−	−	PROPN
ejpam-100	342	1	λ	λ	X
ejpam-100	342	2	p	p	NOUN
ejpam-100	342	3	+	+	NOUN
ejpam-100	342	4	n	n	CCONJ
ejpam-100	342	5	q	q	NOUN
ejpam-100	342	6	−	−	PROPN
ejpam-100	343	1	n	n	PRON
ejpam-100	343	2	p	p	NOUN
ejpam-100	343	3	+	+	CCONJ
ejpam-100	343	4	1	1	NUM
ejpam-100	343	5	>	>	SYM
ejpam-100	343	6	0	0	NUM
ejpam-100	343	7	.	.	PUNCT
ejpam-100	344	1	(	(	PUNCT
ejpam-100	344	2	5.1	5.1	NUM
ejpam-100	344	3	)	)	PUNCT
ejpam-100	344	4	(	(	PUNCT
ejpam-100	344	5	ii	ii	NOUN
ejpam-100	344	6	)	)	PUNCT
ejpam-100	344	7	for	for	ADP
ejpam-100	344	8	1≤	1≤	NUM
ejpam-100	344	9	q	q	NOUN
ejpam-100	345	1	<	<	X
ejpam-100	345	2	p	p	X
ejpam-100	345	3	<	<	X
ejpam-100	345	4	∞	∞	PROPN
ejpam-100	345	5	,	,	PUNCT
ejpam-100	345	6	λ	λ	X
ejpam-100	345	7	<	<	X
ejpam-100	345	8	p−	p−	PROPN
ejpam-100	345	9	1	1	NUM
ejpam-100	345	10	,	,	PUNCT
ejpam-100	345	11	µ	µ	PRON
ejpam-100	345	12	q	q	NOUN
ejpam-100	346	1	−	−	PROPN
ejpam-100	346	2	λ	λ	X
ejpam-100	346	3	p	p	NOUN
ejpam-100	346	4	+	+	NOUN
ejpam-100	346	5	1	1	NUM
ejpam-100	346	6	q	q	NOUN
ejpam-100	346	7	−	−	PROPN
ejpam-100	346	8	1	1	NUM
ejpam-100	346	9	p	p	NOUN
ejpam-100	346	10	+	+	NOUN
ejpam-100	346	11	1	1	NUM
ejpam-100	346	12	>	>	SYM
ejpam-100	346	13	0	0	NUM
ejpam-100	346	14	.	.	PUNCT
ejpam-100	347	1	(	(	PUNCT
ejpam-100	347	2	5.2	5.2	NUM
ejpam-100	347	3	)	)	PUNCT
ejpam-100	347	4	remark	remark	NOUN
ejpam-100	347	5	5.1	5.1	NUM
ejpam-100	347	6	.	.	PUNCT
ejpam-100	348	1	1.condition	1.condition	NUM
ejpam-100	348	2	(	(	PUNCT
ejpam-100	348	3	5.1	5.1	NUM
ejpam-100	348	4	)	)	PUNCT
ejpam-100	348	5	or	or	CCONJ
ejpam-100	348	6	(	(	PUNCT
ejpam-100	348	7	5.2	5.2	NUM
ejpam-100	348	8	)	)	PUNCT
ejpam-100	348	9	are	be	AUX
ejpam-100	348	10	sufficient	sufficient	ADJ
ejpam-100	348	11	for	for	ADP
ejpam-100	348	12	the	the	DET
ejpam-100	348	13	compact	compact	ADJ
ejpam-100	348	14	imbedding	imbedding	NOUN
ejpam-100	348	15	(	(	PUNCT
ejpam-100	348	16	2.5	2.5	NUM
ejpam-100	348	17	)	)	PUNCT
ejpam-100	348	18	to	to	PART
ejpam-100	348	19	hold	hold	VERB
ejpam-100	348	20	;	;	PUNCT
ejpam-100	348	21	for	for	ADP
ejpam-100	348	22	example	example	NOUN
ejpam-100	348	23	[	[	PUNCT
ejpam-100	348	24	[	[	X
ejpam-100	348	25	7	7	NUM
ejpam-100	348	26	]	]	PUNCT
ejpam-100	348	27	,	,	PUNCT
ejpam-100	348	28	example	example	NOUN
ejpam-100	348	29	1	1	NUM
ejpam-100	348	30	,	,	PUNCT
ejpam-100	348	31	[	[	X
ejpam-100	348	32	8	8	X
ejpam-100	348	33	]	]	PUNCT
ejpam-100	348	34	example	example	NOUN
ejpam-100	348	35	1.5	1.5	NUM
ejpam-100	348	36	]	]	PUNCT
ejpam-100	348	37	,	,	PUNCT
ejpam-100	348	38	and	and	CCONJ
ejpam-100	349	1	[	[	X
ejpam-100	349	2	9	9	NUM
ejpam-100	349	3	]	]	PUNCT
ejpam-100	349	4	,	,	PUNCT
ejpam-100	349	5	theorems	theorem	VERB
ejpam-100	349	6	19.17	19.17	NUM
ejpam-100	349	7	,	,	PUNCT
ejpam-100	349	8	19.22	19.22	NUM
ejpam-100	349	9	]	]	PUNCT
ejpam-100	349	10	.	.	PUNCT
ejpam-100	350	1	finally	finally	ADV
ejpam-100	350	2	,	,	PUNCT
ejpam-100	350	3	the	the	DET
ejpam-100	350	4	hypotheses	hypothesis	NOUN
ejpam-100	350	5	of	of	ADP
ejpam-100	350	6	theorem	theorem	ADJ
ejpam-100	350	7	3.1	3.1	NUM
ejpam-100	350	8	are	be	AUX
ejpam-100	350	9	satisfied	satisfied	ADJ
ejpam-100	350	10	.	.	PUNCT
ejpam-100	351	1	therefor	therefor	ADP
ejpam-100	351	2	the	the	DET
ejpam-100	351	3	following	following	ADJ
ejpam-100	351	4	problem	problem	NOUN
ejpam-100	351	5			PROPN
ejpam-100	351	6			PROPN
ejpam-100	351	7			PROPN
ejpam-100	351	8			PROPN
ejpam-100	351	9			PROPN
ejpam-100	351	10			PROPN
ejpam-100	351	11			PROPN
ejpam-100	351	12			PROPN
ejpam-100	351	13			PROPN
ejpam-100	351	14			NOUN
ejpam-100	351	15			PROPN
ejpam-100	351	16			PROPN
ejpam-100	351	17			PROPN
ejpam-100	351	18			PROPN
ejpam-100	351	19			PROPN
ejpam-100	351	20			PROPN
ejpam-100	351	21			PROPN
ejpam-100	351	22			PROPN
ejpam-100	351	23			PROPN
ejpam-100	351	24	tk(u	tk(u	NOUN
ejpam-100	351	25	)	)	PUNCT
ejpam-100	351	26	∈w	∈w	VERB
ejpam-100	351	27	1,p	1,p	PROPN
ejpam-100	351	28	0	0	SYM
ejpam-100	351	29	(	(	PUNCT
ejpam-100	351	30	ω	ω	PROPN
ejpam-100	351	31	,	,	PUNCT
ejpam-100	351	32	w	w	PROPN
ejpam-100	351	33	)	)	PUNCT
ejpam-100	351	34	∫	∫	PROPN
ejpam-100	352	1	ω	ω	PROPN
ejpam-100	352	2	n	n	PROPN
ejpam-100	352	3	∑	∑	PROPN
ejpam-100	352	4	i=1	i=1	PROPN
ejpam-100	352	5	wi(x)|	wi(x)|	NOUN
ejpam-100	352	6	∂	∂	NUM
ejpam-100	352	7	u	u	NOUN
ejpam-100	352	8	∂	∂	NOUN
ejpam-100	352	9	x	x	X
ejpam-100	352	10	i	i	PRON
ejpam-100	352	11	|p−1sgn	|p−1sgn	VERB
ejpam-100	352	12	(	(	PUNCT
ejpam-100	352	13	∂	∂	NUM
ejpam-100	352	14	u	u	NOUN
ejpam-100	352	15	∂	∂	NOUN
ejpam-100	352	16	x	x	NOUN
ejpam-100	352	17	i	i	PROPN
ejpam-100	352	18	)	)	PUNCT
ejpam-100	352	19	∂	∂	NUM
ejpam-100	352	20	tk(u−ϕ	tk(u−ϕ	NUM
ejpam-100	352	21	)	)	PUNCT
ejpam-100	352	22	∂	∂	NOUN
ejpam-100	353	1	x	x	NOUN
ejpam-100	353	2	i	i	NOUN
ejpam-100	353	3	d	d	NOUN
ejpam-100	353	4	x	x	PUNCT
ejpam-100	354	1	+	+	NUM
ejpam-100	354	2	∫	∫	PROPN
ejpam-100	354	3	ω	ω	NUM
ejpam-100	354	4	uexp(u)tk(u−ϕ	uexp(u)tk(u−ϕ	NOUN
ejpam-100	354	5	)	)	PUNCT
ejpam-100	355	1	d	d	NOUN
ejpam-100	355	2	x	x	SYM
ejpam-100	355	3	=	=	SYM
ejpam-100	356	1	∫	∫	PROPN
ejpam-100	356	2	ω	ω	NUM
ejpam-100	356	3	f	f	PROPN
ejpam-100	356	4	tk(u−ϕ	tk(u−ϕ	NUM
ejpam-100	356	5	)	)	PUNCT
ejpam-100	357	1	d	d	NOUN
ejpam-100	357	2	x	x	PUNCT
ejpam-100	358	1	+	+	NUM
ejpam-100	358	2	∫	∫	PROPN
ejpam-100	358	3	ω	ω	NUM
ejpam-100	358	4	f∇tk(u−ϕ	f∇tk(u−ϕ	PROPN
ejpam-100	358	5	)	)	PUNCT
ejpam-100	359	1	d	d	NOUN
ejpam-100	359	2	x	x	PUNCT
ejpam-100	359	3	f	f	PROPN
ejpam-100	359	4	∈	∈	PROPN
ejpam-100	359	5	l1(ω	l1(ω	PROPN
ejpam-100	359	6	)	)	PUNCT
ejpam-100	359	7	,	,	PUNCT
ejpam-100	359	8	f	f	PROPN
ejpam-100	359	9	∈	∈	PROPN
ejpam-100	359	10	n	n	CCONJ
ejpam-100	359	11	∏	∏	PROPN
ejpam-100	359	12	i=1	i=1	PROPN
ejpam-100	360	1	lp′(ω	lp′(ω	PROPN
ejpam-100	360	2	,	,	PUNCT
ejpam-100	360	3	w∗i	w∗i	PRON
ejpam-100	360	4	)	)	PUNCT
ejpam-100	360	5	and	and	CCONJ
ejpam-100	360	6	∀ϕ	∀ϕ	NUM
ejpam-100	360	7	∈w	∈w	VERB
ejpam-100	360	8	1,p	1,p	PROPN
ejpam-100	360	9	0	0	SYM
ejpam-100	360	10	(	(	PUNCT
ejpam-100	360	11	ω	ω	PROPN
ejpam-100	360	12	,	,	PUNCT
ejpam-100	360	13	w)∩	w)∩	X
ejpam-100	360	14	l∞(ω	l∞(ω	X
ejpam-100	360	15	)	)	PUNCT
ejpam-100	360	16	has	have	VERB
ejpam-100	360	17	at	at	ADP
ejpam-100	360	18	last	last	ADJ
ejpam-100	360	19	one	one	NUM
ejpam-100	360	20	solution	solution	NOUN
ejpam-100	360	21	.	.	PUNCT
ejpam-100	361	1	references	reference	NOUN
ejpam-100	362	1	[	[	X
ejpam-100	362	2	1	1	NUM
ejpam-100	362	3	]	]	X
ejpam-100	362	4	y.	y.	PROPN
ejpam-100	362	5	akdim	akdim	PROPN
ejpam-100	362	6	,	,	PUNCT
ejpam-100	362	7	e.	e.	PROPN
ejpam-100	362	8	azroul	azroul	PROPN
ejpam-100	362	9	and	and	CCONJ
ejpam-100	362	10	a.	a.	PROPN
ejpam-100	362	11	benkirane	benkirane	PROPN
ejpam-100	362	12	,	,	PUNCT
ejpam-100	362	13	existence	existence	NOUN
ejpam-100	362	14	of	of	ADP
ejpam-100	362	15	solution	solution	NOUN
ejpam-100	362	16	for	for	ADP
ejpam-100	362	17	quasilinear	quasilinear	NOUN
ejpam-100	362	18	degenerated	degenerate	VERB
ejpam-100	362	19	elliptic	elliptic	ADJ
ejpam-100	362	20	equations	equation	NOUN
ejpam-100	362	21	,	,	PUNCT
ejpam-100	362	22	electronic	electronic	ADJ
ejpam-100	362	23	j.	j.	PROPN
ejpam-100	362	24	diff	diff	PROPN
ejpam-100	362	25	.	.	PUNCT
ejpam-100	363	1	equ	equ	PROPN
ejpam-100	363	2	.	.	PROPN
ejpam-100	363	3	,	,	PUNCT
ejpam-100	363	4	vol	vol	NOUN
ejpam-100	363	5	.	.	PROPN
ejpam-100	363	6	2001	2001	NUM
ejpam-100	363	7	,	,	PUNCT
ejpam-100	363	8	n	n	PROPN
ejpam-100	363	9	71	71	NUM
ejpam-100	363	10	,	,	PUNCT
ejpam-100	363	11	(	(	PUNCT
ejpam-100	363	12	2001	2001	NUM
ejpam-100	363	13	)	)	PUNCT
ejpam-100	363	14	pp	pp	ADP
ejpam-100	363	15	1	1	NUM
ejpam-100	363	16	-	-	SYM
ejpam-100	363	17	19	19	NUM
ejpam-100	363	18	.	.	PUNCT
ejpam-100	364	1	[	[	X
ejpam-100	364	2	2	2	X
ejpam-100	364	3	]	]	X
ejpam-100	364	4	y.	y.	PROPN
ejpam-100	364	5	akdim	akdim	PROPN
ejpam-100	364	6	,	,	PUNCT
ejpam-100	364	7	e.	e.	PROPN
ejpam-100	364	8	azroul	azroul	PROPN
ejpam-100	364	9	and	and	CCONJ
ejpam-100	364	10	a.	a.	PROPN
ejpam-100	364	11	benkirane	benkirane	PROPN
ejpam-100	364	12	,	,	PUNCT
ejpam-100	364	13	psudo	psudo	NOUN
ejpam-100	364	14	-	-	PUNCT
ejpam-100	364	15	monotonicity	monotonicity	ADJ
ejpam-100	364	16	and	and	CCONJ
ejpam-100	364	17	degenerated	degenerated	ADJ
ejpam-100	364	18	elliptic	elliptic	ADJ
ejpam-100	364	19	operator	operator	NOUN
ejpam-100	364	20	of	of	ADP
ejpam-100	364	21	second	second	ADJ
ejpam-100	364	22	order	order	NOUN
ejpam-100	364	23	,	,	PUNCT
ejpam-100	364	24	electronic	electronic	ADJ
ejpam-100	364	25	j.	j.	PROPN
ejpam-100	364	26	diff	diff	PROPN
ejpam-100	364	27	.	.	PUNCT
ejpam-100	365	1	equ	equ	PROPN
ejpam-100	365	2	.	.	PROPN
ejpam-100	365	3	,	,	PUNCT
ejpam-100	365	4	conference	conference	NOUN
ejpam-100	365	5	09	09	NUM
ejpam-100	365	6	,	,	PUNCT
ejpam-100	365	7	2003	2003	NUM
ejpam-100	365	8	,	,	PUNCT
ejpam-100	365	9	n	n	PROPN
ejpam-100	365	10	71	71	NUM
ejpam-100	365	11	,	,	PUNCT
ejpam-100	365	12	(	(	PUNCT
ejpam-100	365	13	2001	2001	NUM
ejpam-100	365	14	)	)	PUNCT
ejpam-100	365	15	pp	pp	ADP
ejpam-100	365	16	9	9	NUM
ejpam-100	365	17	-	-	SYM
ejpam-100	365	18	24	24	NUM
ejpam-100	365	19	.	.	PUNCT
ejpam-100	366	1	[	[	X
ejpam-100	366	2	3	3	X
ejpam-100	366	3	]	]	X
ejpam-100	366	4	l.	l.	PROPN
ejpam-100	366	5	boccardo	boccardo	PROPN
ejpam-100	366	6	,	,	PUNCT
ejpam-100	366	7	a	a	DET
ejpam-100	366	8	remark	remark	NOUN
ejpam-100	366	9	on	on	ADP
ejpam-100	366	10	some	some	DET
ejpam-100	366	11	nonlinear	nonlinear	ADJ
ejpam-100	366	12	elliptic	elliptic	ADJ
ejpam-100	366	13	problems	problem	NOUN
ejpam-100	366	14	,	,	PUNCT
ejpam-100	366	15	electron	electron	PROPN
ejpam-100	366	16	.	.	PUNCT
ejpam-100	367	1	j.	j.	PROPN
ejpam-100	367	2	diff	diff	PROPN
ejpam-100	367	3	.	.	PUNCT
ejpam-100	368	1	eqns	eqns	PROPN
ejpam-100	368	2	.	.	PUNCT
ejpam-100	369	1	conf	conf	PROPN
ejpam-100	369	2	.	.	PROPN
ejpam-100	370	1	08	08	NUM
ejpam-100	370	2	,	,	PUNCT
ejpam-100	370	3	2002	2002	NUM
ejpam-100	370	4	,	,	PUNCT
ejpam-100	370	5	pp	pp	ADJ
ejpam-100	370	6	.	.	PUNCT
ejpam-100	371	1	47	47	NUM
ejpam-100	371	2	-	-	SYM
ejpam-100	371	3	52	52	NUM
ejpam-100	371	4	.	.	PUNCT
ejpam-100	372	1	[	[	X
ejpam-100	372	2	4	4	NUM
ejpam-100	372	3	]	]	X
ejpam-100	372	4	l.	l.	PROPN
ejpam-100	372	5	boccardo	boccardo	PROPN
ejpam-100	372	6	,	,	PUNCT
ejpam-100	372	7	l.	l.	PROPN
ejpam-100	372	8	orsina	orsina	PROPN
ejpam-100	372	9	,	,	PUNCT
ejpam-100	372	10	existence	existence	NOUN
ejpam-100	372	11	results	result	VERB
ejpam-100	372	12	for	for	ADP
ejpam-100	372	13	dirichlet	dirichlet	PROPN
ejpam-100	372	14	problem	problem	NOUN
ejpam-100	372	15	in	in	ADP
ejpam-100	372	16	l1	l1	PROPN
ejpam-100	372	17	via	via	ADP
ejpam-100	372	18	minty	minty	PROPN
ejpam-100	372	19	’s	’s	PART
ejpam-100	372	20	lemma	lemma	PROPN
ejpam-100	372	21	,	,	PUNCT
ejpam-100	372	22	applicable	applicable	ADJ
ejpam-100	372	23	ana	ana	PROPN
ejpam-100	372	24	(	(	PUNCT
ejpam-100	372	25	1999	1999	NUM
ejpam-100	372	26	)	)	PUNCT
ejpam-100	372	27	pp	pp	ADP
ejpam-100	372	28	309	309	NUM
ejpam-100	372	29	-	-	SYM
ejpam-100	372	30	313	313	NUM
ejpam-100	372	31	.	.	PUNCT
ejpam-100	373	1	references	reference	NOUN
ejpam-100	373	2	71	71	NUM
ejpam-100	373	3	[	[	X
ejpam-100	373	4	5	5	NUM
ejpam-100	373	5	]	]	PUNCT
ejpam-100	373	6	h.	h.	NOUN
ejpam-100	373	7	brezis	brezis	PROPN
ejpam-100	373	8	,	,	PUNCT
ejpam-100	373	9	operateurs	operateur	VERB
ejpam-100	373	10	maximaux	maximaux	NOUN
ejpam-100	373	11	monotones	monotone	NOUN
ejpam-100	373	12	et	et	NOUN
ejpam-100	373	13	semi	semi	NOUN
ejpam-100	373	14	-	-	AUX
ejpam-100	373	15	groupes	groupe	NOUN
ejpam-100	373	16	de	de	X
ejpam-100	373	17	contractions	contraction	NOUN
ejpam-100	373	18	dans	dan	NOUN
ejpam-100	373	19	les	les	X
ejpam-100	373	20	espaces	espaces	X
ejpam-100	373	21	de	de	X
ejpam-100	373	22	hilbert	hilbert	PROPN
ejpam-100	373	23	,	,	PUNCT
ejpam-100	373	24	north	north	NOUN
ejpam-100	373	25	-	-	PUNCT
ejpam-100	373	26	holland	holland	PROPN
ejpam-100	373	27	mathematics	mathematics	PROPN
ejpam-100	373	28	studies	study	NOUN
ejpam-100	373	29	,	,	PUNCT
ejpam-100	373	30	no	no	INTJ
ejpam-100	373	31	.	.	NOUN
ejpam-100	373	32	5	5	NUM
ejpam-100	373	33	.	.	X
ejpam-100	373	34	notas	notas	PROPN
ejpam-100	373	35	de	de	PROPN
ejpam-100	373	36	matemática	matemática	PROPN
ejpam-100	373	37	(	(	PUNCT
ejpam-100	373	38	50	50	NUM
ejpam-100	373	39	)	)	PUNCT
ejpam-100	373	40	.	.	PUNCT
ejpam-100	374	1	north	north	NOUN
ejpam-100	374	2	-	-	PUNCT
ejpam-100	374	3	holland	holland	PROPN
ejpam-100	374	4	publishing	publishing	PROPN
ejpam-100	374	5	co.	co.	PROPN
ejpam-100	374	6	,	,	PUNCT
ejpam-100	374	7	amsterdam	amsterdam	PROPN
ejpam-100	374	8	-	-	PUNCT
ejpam-100	374	9	london	london	PROPN
ejpam-100	374	10	;	;	PUNCT
ejpam-100	374	11	american	american	PROPN
ejpam-100	374	12	elsevier	elsevier	PROPN
ejpam-100	374	13	publishing	publishing	PROPN
ejpam-100	374	14	co.	co.	PROPN
ejpam-100	374	15	,	,	PUNCT
ejpam-100	374	16	inc	inc	PROPN
ejpam-100	374	17	.	.	PROPN
ejpam-100	374	18	,	,	PUNCT
ejpam-100	374	19	new	new	PROPN
ejpam-100	374	20	york	york	PROPN
ejpam-100	374	21	,	,	PUNCT
ejpam-100	374	22	1973	1973	NUM
ejpam-100	374	23	,	,	PUNCT
ejpam-100	374	24	mr	mr	PROPN
ejpam-100	374	25	50	50	NUM
ejpam-100	374	26	6=	6=	SYM
ejpam-100	374	27	1060	1060	NUM
ejpam-100	374	28	zbl	zbl	PROPN
ejpam-100	374	29	252.47055	252.47055	NUM
ejpam-100	374	30	.	.	PUNCT
ejpam-100	375	1	[	[	X
ejpam-100	375	2	6	6	NUM
ejpam-100	375	3	]	]	PUNCT
ejpam-100	375	4	f.	f.	PROPN
ejpam-100	375	5	e.	e.	PROPN
ejpam-100	375	6	browder	browder	PROPN
ejpam-100	375	7	,	,	PUNCT
ejpam-100	375	8	existence	existence	NOUN
ejpam-100	375	9	theorems	theorem	VERB
ejpam-100	375	10	for	for	ADP
ejpam-100	375	11	nonlinear	nonlinear	ADJ
ejpam-100	375	12	partial	partial	ADJ
ejpam-100	375	13	differential	differential	NOUN
ejpam-100	375	14	equations	equation	NOUN
ejpam-100	375	15	,	,	PUNCT
ejpam-100	375	16	global	global	ADJ
ejpam-100	375	17	analysis	analysis	NOUN
ejpam-100	375	18	(	(	PUNCT
ejpam-100	375	19	berkeley	berkeley	NOUN
ejpam-100	375	20	,	,	PUNCT
ejpam-100	375	21	1968	1968	NUM
ejpam-100	375	22	)	)	PUNCT
ejpam-100	375	23	,	,	PUNCT
ejpam-100	375	24	proc	proc	NOUN
ejpam-100	375	25	.	.	PUNCT
ejpam-100	376	1	sympos	sympos	PROPN
ejpam-100	376	2	.	.	PUNCT
ejpam-100	377	1	pure	pure	ADJ
ejpam-100	377	2	math	math	NOUN
ejpam-100	377	3	.	.	PUNCT
ejpam-100	377	4	,	,	PUNCT
ejpam-100	378	1	no	no	INTJ
ejpam-100	378	2	.	.	PUNCT
ejpam-100	379	1	xvi	xvi	NOUN
ejpam-100	379	2	,	,	PUNCT
ejpam-100	379	3	ams	am	NOUN
ejpam-100	379	4	,	,	PUNCT
ejpam-100	379	5	providence	providence	NOUN
ejpam-100	379	6	,	,	PUNCT
ejpam-100	379	7	1970	1970	NUM
ejpam-100	379	8	,	,	PUNCT
ejpam-100	379	9	pp	pp	ADJ
ejpam-100	379	10	.	.	PUNCT
ejpam-100	380	1	1	1	NUM
ejpam-100	380	2	-	-	SYM
ejpam-100	380	3	60	60	NUM
ejpam-100	380	4	,	,	PUNCT
ejpam-100	380	5	mr	mr	PROPN
ejpam-100	380	6	42	42	NUM
ejpam-100	380	7	6=	6=	PROPN
ejpam-100	380	8	4855	4855	NUM
ejpam-100	380	9	.	.	PUNCT
ejpam-100	381	1	[	[	X
ejpam-100	381	2	7	7	X
ejpam-100	381	3	]	]	X
ejpam-100	381	4	p.	p.	NOUN
ejpam-100	381	5	drabek	drabek	PROPN
ejpam-100	381	6	,	,	PUNCT
ejpam-100	381	7	a.	a.	NOUN
ejpam-100	381	8	kufner	kufner	NOUN
ejpam-100	381	9	and	and	CCONJ
ejpam-100	381	10	v.	v.	ADP
ejpam-100	381	11	mustonen	mustonen	PROPN
ejpam-100	381	12	,	,	PUNCT
ejpam-100	381	13	pseudo	pseudo	NOUN
ejpam-100	381	14	-	-	ADJ
ejpam-100	381	15	monotonicity	monotonicity	ADJ
ejpam-100	381	16	and	and	CCONJ
ejpam-100	381	17	degenerated	degenerated	ADJ
ejpam-100	381	18	or	or	CCONJ
ejpam-100	381	19	singular	singular	ADJ
ejpam-100	381	20	elliptic	elliptic	ADJ
ejpam-100	381	21	operators	operator	NOUN
ejpam-100	381	22	,	,	PUNCT
ejpam-100	381	23	bull	bull	NOUN
ejpam-100	381	24	.	.	PUNCT
ejpam-100	382	1	austral	austral	PROPN
ejpam-100	382	2	.	.	PUNCT
ejpam-100	383	1	math	math	NOUN
ejpam-100	383	2	.	.	PUNCT
ejpam-100	384	1	soc	soc	PROPN
ejpam-100	384	2	.	.	PUNCT
ejpam-100	385	1	vol	vol	NOUN
ejpam-100	385	2	.	.	PUNCT
ejpam-100	386	1	58	58	NUM
ejpam-100	386	2	(	(	PUNCT
ejpam-100	386	3	1998	1998	NUM
ejpam-100	386	4	)	)	PUNCT
ejpam-100	386	5	,	,	PUNCT
ejpam-100	386	6	213	213	NUM
ejpam-100	386	7	-	-	SYM
ejpam-100	386	8	221	221	NUM
ejpam-100	386	9	.	.	PUNCT
ejpam-100	387	1	[	[	X
ejpam-100	387	2	8	8	NUM
ejpam-100	387	3	]	]	PUNCT
ejpam-100	387	4	p.	p.	NOUN
ejpam-100	387	5	drabek	drabek	PROPN
ejpam-100	387	6	,	,	PUNCT
ejpam-100	387	7	a.	a.	NOUN
ejpam-100	387	8	kufner	kufner	PROPN
ejpam-100	387	9	and	and	CCONJ
ejpam-100	387	10	f.	f.	PROPN
ejpam-100	387	11	nicolosi	nicolosi	PROPN
ejpam-100	387	12	,	,	PUNCT
ejpam-100	387	13	non	non	X
ejpam-100	387	14	linear	linear	PROPN
ejpam-100	387	15	elliptic	elliptic	ADJ
ejpam-100	387	16	equations	equation	NOUN
ejpam-100	387	17	,	,	PUNCT
ejpam-100	387	18	singular	singular	ADJ
ejpam-100	387	19	and	and	CCONJ
ejpam-100	387	20	degenerate	degenerate	ADJ
ejpam-100	387	21	cases	case	NOUN
ejpam-100	387	22	,	,	PUNCT
ejpam-100	387	23	university	university	NOUN
ejpam-100	387	24	of	of	ADP
ejpam-100	387	25	west	west	PROPN
ejpam-100	387	26	bohemia	bohemia	PROPN
ejpam-100	387	27	,	,	PUNCT
ejpam-100	387	28	(	(	PUNCT
ejpam-100	387	29	1996	1996	NUM
ejpam-100	387	30	)	)	PUNCT
ejpam-100	387	31	.	.	PUNCT
ejpam-100	388	1	[	[	X
ejpam-100	388	2	9	9	NUM
ejpam-100	388	3	]	]	PUNCT
ejpam-100	388	4	a.	a.	NOUN
ejpam-100	388	5	kufner	kufner	PROPN
ejpam-100	388	6	,	,	PUNCT
ejpam-100	388	7	weighted	weight	VERB
ejpam-100	388	8	sobolev	sobolev	NOUN
ejpam-100	388	9	spaces	space	NOUN
ejpam-100	388	10	,	,	PUNCT
ejpam-100	388	11	john	john	PROPN
ejpam-100	388	12	wiley	wiley	PROPN
ejpam-100	388	13	and	and	CCONJ
ejpam-100	388	14	sons	son	NOUN
ejpam-100	388	15	,	,	PUNCT
ejpam-100	388	16	(	(	PUNCT
ejpam-100	388	17	1985	1985	NUM
ejpam-100	388	18	)	)	PUNCT
ejpam-100	388	19	.	.	PUNCT
ejpam-100	389	1	[	[	X
ejpam-100	389	2	10	10	NUM
ejpam-100	389	3	]	]	X
ejpam-100	389	4	j.l	j.l	PROPN
ejpam-100	389	5	.	.	PROPN
ejpam-100	389	6	lions	lion	NOUN
ejpam-100	389	7	,	,	PUNCT
ejpam-100	389	8	quelques	quelques	PROPN
ejpam-100	389	9	méthodes	méthode	NOUN
ejpam-100	389	10	de	de	X
ejpam-100	389	11	résolution	résolution	PROPN
ejpam-100	389	12	des	des	X
ejpam-100	389	13	problèmes	problèmes	PROPN
ejpam-100	389	14	aux	aux	PROPN
ejpam-100	389	15	limites	limites	PROPN
ejpam-100	389	16	non	non	PROPN
ejpam-100	389	17	linéaires	linéaires	PROPN
ejpam-100	389	18	,	,	PUNCT
ejpam-100	389	19	dunod	dunod	PROPN
ejpam-100	389	20	,	,	PUNCT
ejpam-100	389	21	paris	paris	PROPN
ejpam-100	389	22	(	(	PUNCT
ejpam-100	389	23	1969	1969	NUM
ejpam-100	389	24	)	)	PUNCT
ejpam-100	389	25	.	.	PUNCT
ejpam-100	390	1	[	[	X
ejpam-100	390	2	11	11	NUM
ejpam-100	390	3	]	]	X
ejpam-100	390	4	g.	g.	PROPN
ejpam-100	390	5	j.	j.	PROPN
ejpam-100	390	6	minty	minty	PROPN
ejpam-100	390	7	,	,	PUNCT
ejpam-100	390	8	monotone	monotone	ADJ
ejpam-100	390	9	(	(	PUNCT
ejpam-100	390	10	nonlinear	nonlinear	ADJ
ejpam-100	390	11	)	)	PUNCT
ejpam-100	390	12	operators	operator	NOUN
ejpam-100	390	13	in	in	ADP
ejpam-100	390	14	hilbert	hilbert	PROPN
ejpam-100	390	15	space	space	NOUN
ejpam-100	390	16	,	,	PUNCT
ejpam-100	390	17	duke	duke	PROPN
ejpam-100	390	18	math	math	PROPN
ejpam-100	390	19	.	.	PUNCT
ejpam-100	391	1	j.	j.	PROPN
ejpam-100	391	2	29	29	NUM
ejpam-100	391	3	(	(	PUNCT
ejpam-100	391	4	1962	1962	NUM
ejpam-100	391	5	)	)	PUNCT
ejpam-100	391	6	,	,	PUNCT
ejpam-100	391	7	[	[	X
ejpam-100	391	8	12	12	NUM
ejpam-100	391	9	]	]	X
ejpam-100	391	10	m.l	m.l	PROPN
ejpam-100	391	11	.	.	PROPN
ejpam-100	391	12	visik	visik	PROPN
ejpam-100	391	13	,	,	PUNCT
ejpam-100	391	14	solvability	solvability	NOUN
ejpam-100	391	15	of	of	ADP
ejpam-100	391	16	the	the	DET
ejpam-100	391	17	first	first	ADJ
ejpam-100	391	18	boundary	boundary	ADJ
ejpam-100	391	19	value	value	NOUN
ejpam-100	391	20	problem	problem	NOUN
ejpam-100	391	21	for	for	ADP
ejpam-100	391	22	quasilinear	quasilinear	NOUN
ejpam-100	391	23	equations	equation	NOUN
ejpam-100	391	24	with	with	ADP
ejpam-100	391	25	rapidly	rapidly	ADV
ejpam-100	391	26	increasing	increase	VERB
ejpam-100	391	27	coefficients	coefficient	NOUN
ejpam-100	391	28	in	in	ADP
ejpam-100	391	29	orlicz	orlicz	ADJ
ejpam-100	391	30	classes	class	NOUN
ejpam-100	391	31	,	,	PUNCT
ejpam-100	391	32	dok1	dok1	PROPN
ejpam-100	391	33	.	.	PUNCT
ejpam-100	391	34	akad	akad	PROPN
ejpam-100	391	35	.	.	PUNCT
ejpam-100	392	1	nauk	nauk	PROPN
ejpam-100	392	2	sssr	sssr	NOUN
ejpam-100	392	3	151	151	NUM
ejpam-100	392	4	,	,	PUNCT
ejpam-100	392	5	1963	1963	NUM
ejpam-100	392	6	,	,	PUNCT
ejpam-100	392	7	pp	pp	ADJ
ejpam-100	392	8	.	.	PUNCT
ejpam-100	393	1	758	758	NUM
ejpam-100	393	2	-	-	SYM
ejpam-100	393	3	761	761	NUM
ejpam-100	393	4	=	=	NUM
ejpam-100	393	5	sovier	sovier	ADJ
ejpam-100	393	6	math	math	NOUN
ejpam-100	393	7	.	.	PUNCT
ejpam-100	394	1	dok1	dok1	PROPN
ejpam-100	394	2	.	.	PUNCT
ejpam-100	395	1	4	4	NUM
ejpam-100	395	2	(	(	PUNCT
ejpam-100	395	3	1963	1963	NUM
ejpam-100	395	4	)	)	PUNCT
ejpam-100	395	5	,	,	PUNCT
ejpam-100	395	6	1060	1060	NUM
ejpam-100	395	7	-	-	SYM
ejpam-100	395	8	1064	1064	NUM
ejpam-100	395	9	.	.	PUNCT
ejpam-100	396	1	mr	mr	PROPN
ejpam-100	396	2	27	27	NUM
ejpam-100	396	3	6=	6=	SYM
ejpam-100	396	4	5032	5032	NUM
ejpam-100	396	5	.	.	PUNCT