id	sid	tid	token	lemma	pos
ejpam-1563	1	1	european	european	PROPN
ejpam-1563	1	2	journal	journal	PROPN
ejpam-1563	1	3	of	of	ADP
ejpam-1563	1	4	pure	pure	ADJ
ejpam-1563	1	5	and	and	CCONJ
ejpam-1563	1	6	applied	apply	VERB
ejpam-1563	1	7	mathematics	mathematic	NOUN
ejpam-1563	1	8	vol	vol	NOUN
ejpam-1563	1	9	.	.	PROPN
ejpam-1563	2	1	6	6	NUM
ejpam-1563	2	2	,	,	PUNCT
ejpam-1563	2	3	no	no	INTJ
ejpam-1563	2	4	.	.	NOUN
ejpam-1563	2	5	3	3	NUM
ejpam-1563	2	6	,	,	PUNCT
ejpam-1563	2	7	2013	2013	NUM
ejpam-1563	2	8	,	,	PUNCT
ejpam-1563	2	9	365	365	NUM
ejpam-1563	2	10	-	-	SYM
ejpam-1563	2	11	376	376	NUM
ejpam-1563	2	12	issn	issn	PROPN
ejpam-1563	2	13	1307	1307	NUM
ejpam-1563	2	14	-	-	SYM
ejpam-1563	2	15	5543	5543	NUM
ejpam-1563	2	16	–	–	PUNCT
ejpam-1563	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1563	2	18	existence	existence	NOUN
ejpam-1563	2	19	results	result	VERB
ejpam-1563	2	20	for	for	ADP
ejpam-1563	2	21	generalized	generalized	ADJ
ejpam-1563	2	22	vector	vector	NOUN
ejpam-1563	2	23	equilibrium	equilibrium	NOUN
ejpam-1563	2	24	problems	problem	NOUN
ejpam-1563	2	25	on	on	ADP
ejpam-1563	2	26	unbounded	unbounded	ADJ
ejpam-1563	2	27	sets	set	NOUN
ejpam-1563	2	28	e.	e.	PROPN
ejpam-1563	2	29	allevi1,∗	allevi1,∗	PROPN
ejpam-1563	2	30	,	,	PUNCT
ejpam-1563	2	31	i.	i.	PROPN
ejpam-1563	2	32	v.	v.	PROPN
ejpam-1563	2	33	konnov	konnov	PROPN
ejpam-1563	2	34	2	2	NUM
ejpam-1563	2	35	,	,	PUNCT
ejpam-1563	2	36	m.	m.	NOUN
ejpam-1563	2	37	rocco3	rocco3	NOUN
ejpam-1563	2	38	1	1	NUM
ejpam-1563	2	39	department	department	NOUN
ejpam-1563	2	40	of	of	ADP
ejpam-1563	2	41	economics	economic	NOUN
ejpam-1563	2	42	and	and	CCONJ
ejpam-1563	2	43	management	management	NOUN
ejpam-1563	2	44	,	,	PUNCT
ejpam-1563	2	45	university	university	NOUN
ejpam-1563	2	46	of	of	ADP
ejpam-1563	2	47	brescia	brescia	PROPN
ejpam-1563	2	48	,	,	PUNCT
ejpam-1563	2	49	via	via	ADP
ejpam-1563	2	50	san	san	PROPN
ejpam-1563	2	51	faustino	faustino	PROPN
ejpam-1563	2	52	74	74	NUM
ejpam-1563	2	53	/	/	SYM
ejpam-1563	2	54	b	b	NOUN
ejpam-1563	2	55	,	,	PUNCT
ejpam-1563	2	56	25124	25124	NUM
ejpam-1563	2	57	,	,	PUNCT
ejpam-1563	2	58	brescia	brescia	PROPN
ejpam-1563	2	59	,	,	PUNCT
ejpam-1563	2	60	italy	italy	PROPN
ejpam-1563	2	61	2	2	NUM
ejpam-1563	2	62	department	department	NOUN
ejpam-1563	2	63	of	of	ADP
ejpam-1563	2	64	system	system	NOUN
ejpam-1563	2	65	analysis	analysis	NOUN
ejpam-1563	2	66	and	and	CCONJ
ejpam-1563	2	67	information	information	NOUN
ejpam-1563	2	68	technologies	technology	NOUN
ejpam-1563	2	69	,	,	PUNCT
ejpam-1563	2	70	kazan	kazan	PROPN
ejpam-1563	2	71	federal	federal	PROPN
ejpam-1563	2	72	university	university	PROPN
ejpam-1563	2	73	,	,	PUNCT
ejpam-1563	2	74	ul	ul	INTJ
ejpam-1563	2	75	.	.	PUNCT
ejpam-1563	3	1	kremlevskaya	kremlevskaya	PROPN
ejpam-1563	3	2	,	,	PUNCT
ejpam-1563	3	3	18	18	NUM
ejpam-1563	3	4	,	,	PUNCT
ejpam-1563	3	5	420008	420008	NUM
ejpam-1563	3	6	kazan	kazan	PROPN
ejpam-1563	3	7	,	,	PUNCT
ejpam-1563	3	8	russia	russia	PROPN
ejpam-1563	3	9	3	3	NUM
ejpam-1563	3	10	financial	financial	ADJ
ejpam-1563	3	11	stability	stability	NOUN
ejpam-1563	3	12	unit	unit	NOUN
ejpam-1563	3	13	,	,	PUNCT
ejpam-1563	3	14	bank	bank	PROPN
ejpam-1563	3	15	of	of	ADP
ejpam-1563	3	16	italy	italy	PROPN
ejpam-1563	3	17	,	,	PUNCT
ejpam-1563	3	18	via	via	ADP
ejpam-1563	3	19	nazionale	nazionale	PROPN
ejpam-1563	3	20	91	91	NUM
ejpam-1563	3	21	,	,	PUNCT
ejpam-1563	3	22	00184	00184	NUM
ejpam-1563	3	23	roma	roma	PROPN
ejpam-1563	3	24	,	,	PUNCT
ejpam-1563	3	25	italy	italy	PROPN
ejpam-1563	3	26	abstract	abstract	NOUN
ejpam-1563	3	27	.	.	PUNCT
ejpam-1563	4	1	we	we	PRON
ejpam-1563	4	2	provide	provide	VERB
ejpam-1563	4	3	existence	existence	NOUN
ejpam-1563	4	4	results	result	NOUN
ejpam-1563	4	5	for	for	ADP
ejpam-1563	4	6	generalized	generalized	ADJ
ejpam-1563	4	7	(	(	PUNCT
ejpam-1563	4	8	set	set	NOUN
ejpam-1563	4	9	-	-	PUNCT
ejpam-1563	4	10	valued	value	VERB
ejpam-1563	4	11	)	)	PUNCT
ejpam-1563	4	12	vector	vector	NOUN
ejpam-1563	4	13	equilibrium	equilibrium	NOUN
ejpam-1563	4	14	problems	problem	NOUN
ejpam-1563	4	15	on	on	ADP
ejpam-1563	4	16	unbounded	unbounded	ADJ
ejpam-1563	4	17	sets	set	NOUN
ejpam-1563	4	18	,	,	PUNCT
ejpam-1563	4	19	based	base	VERB
ejpam-1563	4	20	on	on	ADP
ejpam-1563	4	21	a	a	DET
ejpam-1563	4	22	coercivity	coercivity	NOUN
ejpam-1563	4	23	condition	condition	NOUN
ejpam-1563	4	24	recently	recently	ADV
ejpam-1563	4	25	proposed	propose	VERB
ejpam-1563	4	26	for	for	ADP
ejpam-1563	4	27	the	the	DET
ejpam-1563	4	28	scalar	scalar	ADJ
ejpam-1563	4	29	and	and	CCONJ
ejpam-1563	4	30	vector	vector	NOUN
ejpam-1563	4	31	cases	case	NOUN
ejpam-1563	4	32	.	.	PUNCT
ejpam-1563	5	1	several	several	ADJ
ejpam-1563	5	2	formulations	formulation	NOUN
ejpam-1563	5	3	of	of	ADP
ejpam-1563	5	4	the	the	DET
ejpam-1563	5	5	generalized	generalize	VERB
ejpam-1563	5	6	vector	vector	NOUN
ejpam-1563	5	7	equilibrium	equilibrium	NOUN
ejpam-1563	5	8	problem	problem	NOUN
ejpam-1563	5	9	are	be	AUX
ejpam-1563	5	10	taken	take	VERB
ejpam-1563	5	11	into	into	ADP
ejpam-1563	5	12	account	account	NOUN
ejpam-1563	5	13	,	,	PUNCT
ejpam-1563	5	14	thus	thus	ADV
ejpam-1563	5	15	covering	cover	VERB
ejpam-1563	5	16	most	most	ADJ
ejpam-1563	5	17	cases	case	NOUN
ejpam-1563	5	18	considered	consider	VERB
ejpam-1563	5	19	in	in	ADP
ejpam-1563	5	20	the	the	DET
ejpam-1563	5	21	literature	literature	NOUN
ejpam-1563	5	22	.	.	PUNCT
ejpam-1563	6	1	2010	2010	NUM
ejpam-1563	6	2	mathematics	mathematic	NOUN
ejpam-1563	6	3	subject	subject	NOUN
ejpam-1563	6	4	classifications	classification	NOUN
ejpam-1563	6	5	:	:	PUNCT
ejpam-1563	6	6	90c33	90c33	NUM
ejpam-1563	6	7	,	,	PUNCT
ejpam-1563	6	8	47j20	47j20	NUM
ejpam-1563	6	9	,	,	PUNCT
ejpam-1563	6	10	49j40	49j40	DET
ejpam-1563	6	11	key	key	ADJ
ejpam-1563	6	12	words	word	NOUN
ejpam-1563	6	13	and	and	CCONJ
ejpam-1563	6	14	phrases	phrase	NOUN
ejpam-1563	6	15	:	:	PUNCT
ejpam-1563	6	16	generalized	generalize	VERB
ejpam-1563	6	17	vector	vector	NOUN
ejpam-1563	6	18	equilibrium	equilibrium	NOUN
ejpam-1563	6	19	problems	problem	NOUN
ejpam-1563	6	20	,	,	PUNCT
ejpam-1563	6	21	set	set	NOUN
ejpam-1563	6	22	-	-	PUNCT
ejpam-1563	6	23	valued	value	VERB
ejpam-1563	6	24	bifunctions	bifunction	NOUN
ejpam-1563	6	25	,	,	PUNCT
ejpam-1563	6	26	coercivity	coercivity	NOUN
ejpam-1563	6	27	condition	condition	NOUN
ejpam-1563	7	1	,	,	PUNCT
ejpam-1563	7	2	existence	existence	NOUN
ejpam-1563	7	3	results	result	VERB
ejpam-1563	7	4	1	1	NUM
ejpam-1563	7	5	.	.	PUNCT
ejpam-1563	8	1	introduction	introduction	NOUN
ejpam-1563	8	2	many	many	ADJ
ejpam-1563	8	3	problems	problem	NOUN
ejpam-1563	8	4	of	of	ADP
ejpam-1563	8	5	practical	practical	ADJ
ejpam-1563	8	6	interest	interest	NOUN
ejpam-1563	8	7	in	in	ADP
ejpam-1563	8	8	optimization	optimization	NOUN
ejpam-1563	8	9	,	,	PUNCT
ejpam-1563	8	10	economics	economic	NOUN
ejpam-1563	8	11	and	and	CCONJ
ejpam-1563	8	12	engineering	engineering	NOUN
ejpam-1563	8	13	involve	involve	VERB
ejpam-1563	8	14	equilibrium	equilibrium	NOUN
ejpam-1563	8	15	in	in	ADP
ejpam-1563	8	16	their	their	PRON
ejpam-1563	8	17	description	description	NOUN
ejpam-1563	8	18	;	;	PUNCT
ejpam-1563	8	19	this	this	DET
ejpam-1563	8	20	fact	fact	NOUN
ejpam-1563	8	21	has	have	AUX
ejpam-1563	8	22	motivated	motivated	ADJ
ejpam-1563	8	23	researchers	researcher	NOUN
ejpam-1563	8	24	to	to	PART
ejpam-1563	8	25	establish	establish	VERB
ejpam-1563	8	26	general	general	ADJ
ejpam-1563	8	27	results	result	NOUN
ejpam-1563	8	28	on	on	ADP
ejpam-1563	8	29	the	the	DET
ejpam-1563	8	30	existence	existence	NOUN
ejpam-1563	8	31	of	of	ADP
ejpam-1563	8	32	solutions	solution	NOUN
ejpam-1563	8	33	for	for	ADP
ejpam-1563	8	34	equilibrium	equilibrium	NOUN
ejpam-1563	8	35	problems	problem	NOUN
ejpam-1563	8	36	,	,	PUNCT
ejpam-1563	8	37	see	see	VERB
ejpam-1563	8	38	e.g.	e.g.	ADV
ejpam-1563	8	39	[	[	X
ejpam-1563	8	40	2	2	NUM
ejpam-1563	8	41	,	,	PUNCT
ejpam-1563	8	42	3	3	NUM
ejpam-1563	8	43	]	]	PUNCT
ejpam-1563	8	44	.	.	PUNCT
ejpam-1563	9	1	indeed	indeed	ADV
ejpam-1563	9	2	there	there	PRON
ejpam-1563	9	3	is	be	VERB
ejpam-1563	9	4	a	a	DET
ejpam-1563	9	5	vast	vast	ADJ
ejpam-1563	9	6	literature	literature	NOUN
ejpam-1563	9	7	on	on	ADP
ejpam-1563	9	8	equilibrium	equilibrium	NOUN
ejpam-1563	9	9	problems	problem	NOUN
ejpam-1563	9	10	and	and	CCONJ
ejpam-1563	9	11	their	their	PRON
ejpam-1563	9	12	treatment	treatment	NOUN
ejpam-1563	9	13	in	in	ADP
ejpam-1563	9	14	optimization	optimization	NOUN
ejpam-1563	9	15	,	,	PUNCT
ejpam-1563	9	16	variational	variational	ADJ
ejpam-1563	9	17	and	and	CCONJ
ejpam-1563	9	18	quasivariational	quasivariational	ADJ
ejpam-1563	9	19	inequalities	inequality	NOUN
ejpam-1563	9	20	,	,	PUNCT
ejpam-1563	9	21	and	and	CCONJ
ejpam-1563	9	22	complementarity	complementarity	NOUN
ejpam-1563	9	23	problems	problem	NOUN
ejpam-1563	9	24	.	.	PUNCT
ejpam-1563	10	1	many	many	ADJ
ejpam-1563	10	2	authors	author	NOUN
ejpam-1563	10	3	investigated	investigate	VERB
ejpam-1563	10	4	different	different	ADJ
ejpam-1563	10	5	equilibrium	equilibrium	NOUN
ejpam-1563	10	6	models	model	NOUN
ejpam-1563	10	7	,	,	PUNCT
ejpam-1563	10	8	extending	extend	VERB
ejpam-1563	10	9	scalar	scalar	ADJ
ejpam-1563	10	10	equilibrium	equilibrium	NOUN
ejpam-1563	10	11	problems	problem	NOUN
ejpam-1563	10	12	to	to	ADP
ejpam-1563	10	13	the	the	DET
ejpam-1563	10	14	vector	vector	NOUN
ejpam-1563	10	15	-	-	PUNCT
ejpam-1563	10	16	valued	value	VERB
ejpam-1563	10	17	and	and	CCONJ
ejpam-1563	10	18	set	set	NOUN
ejpam-1563	10	19	-	-	PUNCT
ejpam-1563	10	20	valued	value	VERB
ejpam-1563	10	21	cases	case	NOUN
ejpam-1563	10	22	,	,	PUNCT
ejpam-1563	10	23	see	see	VERB
ejpam-1563	11	1	e.g.	e.g.	ADV
ejpam-1563	11	2	[	[	X
ejpam-1563	11	3	4	4	NUM
ejpam-1563	11	4	,	,	PUNCT
ejpam-1563	11	5	11–13	11–13	NUM
ejpam-1563	11	6	]	]	PUNCT
ejpam-1563	11	7	.	.	PUNCT
ejpam-1563	12	1	in	in	ADP
ejpam-1563	12	2	the	the	DET
ejpam-1563	12	3	case	case	NOUN
ejpam-1563	12	4	of	of	ADP
ejpam-1563	12	5	a	a	DET
ejpam-1563	12	6	set	set	NOUN
ejpam-1563	12	7	-	-	PUNCT
ejpam-1563	12	8	valued	value	VERB
ejpam-1563	12	9	bifunction	bifunction	NOUN
ejpam-1563	12	10	,	,	PUNCT
ejpam-1563	12	11	the	the	DET
ejpam-1563	12	12	general	general	ADJ
ejpam-1563	12	13	equilibrium	equilibrium	NOUN
ejpam-1563	12	14	problem	problem	NOUN
ejpam-1563	12	15	can	can	AUX
ejpam-1563	12	16	be	be	AUX
ejpam-1563	12	17	formulated	formulate	VERB
ejpam-1563	12	18	in	in	ADP
ejpam-1563	12	19	several	several	ADJ
ejpam-1563	12	20	(	(	PUNCT
ejpam-1563	12	21	non	non	X
ejpam-1563	12	22	equivalent	equivalent	ADJ
ejpam-1563	12	23	)	)	PUNCT
ejpam-1563	12	24	ways	way	NOUN
ejpam-1563	12	25	.	.	PUNCT
ejpam-1563	13	1	our	our	PRON
ejpam-1563	13	2	results	result	NOUN
ejpam-1563	13	3	will	will	AUX
ejpam-1563	13	4	cover	cover	VERB
ejpam-1563	13	5	the	the	DET
ejpam-1563	13	6	following	following	ADJ
ejpam-1563	13	7	cases	case	NOUN
ejpam-1563	13	8	.	.	PUNCT
ejpam-1563	14	1	given	give	VERB
ejpam-1563	14	2	topological	topological	ADJ
ejpam-1563	14	3	vector	vector	NOUN
ejpam-1563	14	4	spaces	space	NOUN
ejpam-1563	14	5	x	x	X
ejpam-1563	14	6	,	,	PUNCT
ejpam-1563	14	7	y	y	PROPN
ejpam-1563	14	8	,	,	PUNCT
ejpam-1563	14	9	a	a	DET
ejpam-1563	14	10	nonempty	nonempty	ADJ
ejpam-1563	14	11	,	,	PUNCT
ejpam-1563	14	12	closed	closed	ADJ
ejpam-1563	14	13	and	and	CCONJ
ejpam-1563	14	14	convex	convex	PROPN
ejpam-1563	14	15	set	set	VERB
ejpam-1563	14	16	k	k	PROPN
ejpam-1563	14	17	⊆	⊆	NUM
ejpam-1563	14	18	x	x	SYM
ejpam-1563	14	19	,	,	PUNCT
ejpam-1563	14	20	a	a	DET
ejpam-1563	14	21	set	set	NOUN
ejpam-1563	14	22	-	-	PUNCT
ejpam-1563	14	23	valued	value	VERB
ejpam-1563	14	24	mapping	mapping	NOUN
ejpam-1563	14	25	v	v	ADP
ejpam-1563	14	26	:	:	PUNCT
ejpam-1563	14	27	k	k	PROPN
ejpam-1563	14	28	→	→	SYM
ejpam-1563	14	29	π(y	π(y	PROPN
ejpam-1563	14	30	)	)	PUNCT
ejpam-1563	14	31	that	that	PRON
ejpam-1563	14	32	maps	map	VERB
ejpam-1563	14	33	each	each	DET
ejpam-1563	14	34	x	x	SYM
ejpam-1563	14	35	∈	∈	PROPN
ejpam-1563	14	36	k	k	PROPN
ejpam-1563	14	37	to	to	ADP
ejpam-1563	14	38	a	a	DET
ejpam-1563	14	39	nonempty	nonempty	ADV
ejpam-1563	14	40	set	set	VERB
ejpam-1563	14	41	v	v	NOUN
ejpam-1563	14	42	(	(	PUNCT
ejpam-1563	14	43	x	x	NOUN
ejpam-1563	14	44	)	)	PUNCT
ejpam-1563	14	45	⊆	⊆	NUM
ejpam-1563	14	46	y	y	PROPN
ejpam-1563	14	47	(	(	PUNCT
ejpam-1563	14	48	π(y	π(y	PROPN
ejpam-1563	14	49	)	)	PUNCT
ejpam-1563	14	50	denotes	denote	VERB
ejpam-1563	14	51	the	the	DET
ejpam-1563	14	52	power	power	NOUN
ejpam-1563	14	53	set	set	NOUN
ejpam-1563	14	54	of	of	ADP
ejpam-1563	14	55	y	y	PROPN
ejpam-1563	14	56	)	)	PUNCT
ejpam-1563	14	57	and	and	CCONJ
ejpam-1563	14	58	a	a	DET
ejpam-1563	14	59	set	set	NOUN
ejpam-1563	14	60	-	-	PUNCT
ejpam-1563	14	61	valued	value	VERB
ejpam-1563	14	62	bifunction	bifunction	NOUN
ejpam-1563	15	1	φ	φ	NOUN
ejpam-1563	15	2	:	:	PUNCT
ejpam-1563	16	1	k	k	PROPN
ejpam-1563	16	2	×	×	PROPN
ejpam-1563	16	3	k	k	X
ejpam-1563	16	4	→	→	SYM
ejpam-1563	16	5	π(y	π(y	PROPN
ejpam-1563	16	6	)	)	PUNCT
ejpam-1563	16	7	,	,	PUNCT
ejpam-1563	16	8	we	we	PRON
ejpam-1563	16	9	consider	consider	VERB
ejpam-1563	16	10	two	two	NUM
ejpam-1563	16	11	main	main	ADJ
ejpam-1563	16	12	formulations	formulation	NOUN
ejpam-1563	16	13	∗corresponding	∗corresponde	VERB
ejpam-1563	16	14	author	author	NOUN
ejpam-1563	16	15	.	.	PUNCT
ejpam-1563	17	1	email	email	NOUN
ejpam-1563	17	2	addresses	address	NOUN
ejpam-1563	17	3	:	:	PUNCT
ejpam-1563	17	4	allevi@eco.unibs.it	allevi@eco.unibs.it	PROPN
ejpam-1563	17	5	(	(	PUNCT
ejpam-1563	17	6	e.	e.	PROPN
ejpam-1563	17	7	allevi	allevi	PROPN
ejpam-1563	17	8	)	)	PUNCT
ejpam-1563	17	9	,	,	PUNCT
ejpam-1563	17	10	konn-igor@yandex.ru	konn-igor@yandex.ru	PROPN
ejpam-1563	17	11	(	(	PUNCT
ejpam-1563	17	12	i.	i.	PROPN
ejpam-1563	17	13	konnov	konnov	PROPN
ejpam-1563	17	14	)	)	PUNCT
ejpam-1563	17	15	,	,	PUNCT
ejpam-1563	17	16	marco.rocco@bancaditalia.it	marco.rocco@bancaditalia.it	X
ejpam-1563	17	17	(	(	PUNCT
ejpam-1563	17	18	m.	m.	NOUN
ejpam-1563	17	19	rocco	rocco	NOUN
ejpam-1563	17	20	)	)	PUNCT
ejpam-1563	17	21	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1563	18	1	365	365	NUM
ejpam-1563	18	2	c	c	X
ejpam-1563	18	3	©	©	PROPN
ejpam-1563	18	4	2013	2013	NUM
ejpam-1563	18	5	ejpam	ejpam	NOUN
ejpam-1563	18	6	all	all	DET
ejpam-1563	18	7	rights	right	NOUN
ejpam-1563	18	8	reserved	reserve	VERB
ejpam-1563	18	9	.	.	PUNCT
ejpam-1563	19	1	e.	e.	PROPN
ejpam-1563	19	2	allevi	allevi	PROPN
ejpam-1563	19	3	,	,	PUNCT
ejpam-1563	19	4	i.	i.	PROPN
ejpam-1563	19	5	konnov	konnov	PROPN
ejpam-1563	19	6	,	,	PUNCT
ejpam-1563	19	7	m.	m.	NOUN
ejpam-1563	19	8	rocco	rocco	NOUN
ejpam-1563	19	9	/	/	SYM
ejpam-1563	19	10	eur	eur	PROPN
ejpam-1563	19	11	.	.	PUNCT
ejpam-1563	20	1	j.	j.	PROPN
ejpam-1563	20	2	pure	pure	PROPN
ejpam-1563	20	3	appl	appl	PROPN
ejpam-1563	20	4	.	.	PROPN
ejpam-1563	20	5	math	math	PROPN
ejpam-1563	20	6	,	,	PUNCT
ejpam-1563	20	7	6	6	NUM
ejpam-1563	20	8	(	(	PUNCT
ejpam-1563	20	9	2013	2013	NUM
ejpam-1563	20	10	)	)	PUNCT
ejpam-1563	20	11	,	,	PUNCT
ejpam-1563	20	12	365	365	NUM
ejpam-1563	20	13	-	-	SYM
ejpam-1563	20	14	376	376	NUM
ejpam-1563	20	15	366	366	NUM
ejpam-1563	20	16	of	of	ADP
ejpam-1563	20	17	the	the	DET
ejpam-1563	20	18	generalized	generalize	VERB
ejpam-1563	20	19	vector	vector	NOUN
ejpam-1563	20	20	equilibrium	equilibrium	NOUN
ejpam-1563	20	21	problem	problem	NOUN
ejpam-1563	20	22	,	,	PUNCT
ejpam-1563	20	23	namely	namely	ADV
ejpam-1563	20	24	the	the	DET
ejpam-1563	20	25	problems	problem	NOUN
ejpam-1563	20	26	of	of	ADP
ejpam-1563	20	27	finding	find	VERB
ejpam-1563	20	28	x	x	PUNCT
ejpam-1563	20	29	∈	∈	PROPN
ejpam-1563	20	30	k	k	NOUN
ejpam-1563	20	31	such	such	ADJ
ejpam-1563	20	32	that	that	PRON
ejpam-1563	20	33	(	(	PUNCT
ejpam-1563	20	34	gvep1	gvep1	NOUN
ejpam-1563	20	35	)	)	PUNCT
ejpam-1563	21	1	φ(x	φ(x	PROPN
ejpam-1563	21	2	,	,	PUNCT
ejpam-1563	21	3	y	y	PROPN
ejpam-1563	21	4	)	)	PUNCT
ejpam-1563	21	5	6⊆	6⊆	PROPN
ejpam-1563	21	6	v	v	SYM
ejpam-1563	21	7	(	(	PUNCT
ejpam-1563	21	8	x	x	NOUN
ejpam-1563	21	9	)	)	PUNCT
ejpam-1563	21	10	,	,	PUNCT
ejpam-1563	21	11	∀y	∀y	PROPN
ejpam-1563	21	12	∈	∈	PROPN
ejpam-1563	21	13	k	k	NOUN
ejpam-1563	21	14	;	;	PUNCT
ejpam-1563	21	15	(	(	PUNCT
ejpam-1563	21	16	gvep2	gvep2	PROPN
ejpam-1563	21	17	)	)	PUNCT
ejpam-1563	21	18	φ(x	φ(x	PROPN
ejpam-1563	21	19	,	,	PUNCT
ejpam-1563	21	20	y)∩	y)∩	PROPN
ejpam-1563	21	21	v	v	PROPN
ejpam-1563	21	22	(	(	PUNCT
ejpam-1563	21	23	x	x	NOUN
ejpam-1563	21	24	)	)	PUNCT
ejpam-1563	21	25	=	=	SYM
ejpam-1563	21	26	;	;	PUNCT
ejpam-1563	21	27	,	,	PUNCT
ejpam-1563	21	28	∀y	∀y	PROPN
ejpam-1563	21	29	∈	∈	PROPN
ejpam-1563	21	30	k	k	X
ejpam-1563	21	31	.	.	PUNCT
ejpam-1563	22	1	in	in	ADP
ejpam-1563	22	2	particular	particular	ADJ
ejpam-1563	22	3	,	,	PUNCT
ejpam-1563	22	4	given	give	VERB
ejpam-1563	22	5	a	a	DET
ejpam-1563	22	6	set	set	NOUN
ejpam-1563	22	7	-	-	PUNCT
ejpam-1563	22	8	valued	value	VERB
ejpam-1563	22	9	mapping	mapping	NOUN
ejpam-1563	22	10	c	c	NOUN
ejpam-1563	22	11	:	:	PUNCT
ejpam-1563	22	12	k	k	X
ejpam-1563	22	13	→	→	PUNCT
ejpam-1563	22	14	π(y	π(y	PROPN
ejpam-1563	22	15	)	)	PUNCT
ejpam-1563	22	16	that	that	PRON
ejpam-1563	22	17	maps	map	VERB
ejpam-1563	22	18	each	each	DET
ejpam-1563	22	19	x	x	SYM
ejpam-1563	22	20	∈	∈	PROPN
ejpam-1563	22	21	k	k	PROPN
ejpam-1563	22	22	to	to	ADP
ejpam-1563	22	23	a	a	DET
ejpam-1563	22	24	pointed	pointed	ADJ
ejpam-1563	22	25	(	(	PUNCT
ejpam-1563	22	26	and	and	CCONJ
ejpam-1563	22	27	solid	solid	ADJ
ejpam-1563	22	28	,	,	PUNCT
ejpam-1563	22	29	if	if	SCONJ
ejpam-1563	22	30	necessary	necessary	ADJ
ejpam-1563	22	31	)	)	PUNCT
ejpam-1563	22	32	cone	cone	NOUN
ejpam-1563	22	33	c(x)⊆	c(x)⊆	NOUN
ejpam-1563	22	34	y	y	PROPN
ejpam-1563	22	35	,	,	PUNCT
ejpam-1563	22	36	we	we	PRON
ejpam-1563	22	37	can	can	AUX
ejpam-1563	22	38	recover	recover	VERB
ejpam-1563	22	39	the	the	DET
ejpam-1563	22	40	main	main	ADJ
ejpam-1563	22	41	formulations	formulation	NOUN
ejpam-1563	22	42	of	of	ADP
ejpam-1563	22	43	the	the	DET
ejpam-1563	22	44	generalized	generalize	VERB
ejpam-1563	22	45	vector	vector	NOUN
ejpam-1563	22	46	equilibrium	equilibrium	NOUN
ejpam-1563	22	47	problem	problem	NOUN
ejpam-1563	22	48	that	that	PRON
ejpam-1563	22	49	have	have	AUX
ejpam-1563	22	50	been	be	AUX
ejpam-1563	22	51	considered	consider	VERB
ejpam-1563	22	52	in	in	ADP
ejpam-1563	22	53	the	the	DET
ejpam-1563	22	54	literature	literature	NOUN
ejpam-1563	22	55	[	[	X
ejpam-1563	22	56	1	1	NUM
ejpam-1563	22	57	,	,	PUNCT
ejpam-1563	22	58	6	6	NUM
ejpam-1563	22	59	,	,	PUNCT
ejpam-1563	22	60	9	9	NUM
ejpam-1563	22	61	–	–	PUNCT
ejpam-1563	22	62	13	13	NUM
ejpam-1563	22	63	]	]	PUNCT
ejpam-1563	22	64	,	,	PUNCT
ejpam-1563	22	65	namely	namely	ADV
ejpam-1563	22	66	,	,	PUNCT
ejpam-1563	22	67	(	(	PUNCT
ejpam-1563	22	68	gvep1a	gvep1a	X
ejpam-1563	22	69	)	)	PUNCT
ejpam-1563	22	70	φ(x	φ(x	PROPN
ejpam-1563	22	71	,	,	PUNCT
ejpam-1563	22	72	y	y	PROPN
ejpam-1563	22	73	)	)	PUNCT
ejpam-1563	22	74	6⊆	6⊆	NOUN
ejpam-1563	22	75	−int	−int	ADP
ejpam-1563	22	76	c(x	c(x	NOUN
ejpam-1563	22	77	)	)	PUNCT
ejpam-1563	22	78	,	,	PUNCT
ejpam-1563	22	79	∀y	∀y	PROPN
ejpam-1563	22	80	∈	∈	PROPN
ejpam-1563	22	81	k	k	NOUN
ejpam-1563	22	82	;	;	PUNCT
ejpam-1563	22	83	(	(	PUNCT
ejpam-1563	22	84	gvep1b	gvep1b	NOUN
ejpam-1563	22	85	)	)	PUNCT
ejpam-1563	22	86	φ(x	φ(x	PROPN
ejpam-1563	22	87	,	,	PUNCT
ejpam-1563	22	88	y	y	PROPN
ejpam-1563	22	89	)	)	PUNCT
ejpam-1563	22	90	6⊆	6⊆	NOUN
ejpam-1563	22	91	−c(x)\{0	−c(x)\{0	PROPN
ejpam-1563	22	92	}	}	PUNCT
ejpam-1563	22	93	,	,	PUNCT
ejpam-1563	22	94	∀y	∀y	PROPN
ejpam-1563	22	95	∈	∈	PROPN
ejpam-1563	22	96	k	k	NOUN
ejpam-1563	22	97	;	;	PUNCT
ejpam-1563	22	98	(	(	PUNCT
ejpam-1563	22	99	gvep2a	gvep2a	ADJ
ejpam-1563	22	100	)	)	PUNCT
ejpam-1563	22	101	φ(x	φ(x	PROPN
ejpam-1563	22	102	,	,	PUNCT
ejpam-1563	22	103	y)∩−int	y)∩−int	NUM
ejpam-1563	22	104	c(x	c(x	NOUN
ejpam-1563	22	105	)	)	PUNCT
ejpam-1563	22	106	=	=	PUNCT
ejpam-1563	23	1	;	;	PUNCT
ejpam-1563	23	2	,	,	PUNCT
ejpam-1563	23	3	∀y	∀y	PROPN
ejpam-1563	23	4	∈	∈	PROPN
ejpam-1563	23	5	k	k	NOUN
ejpam-1563	23	6	;	;	PUNCT
ejpam-1563	23	7	(	(	PUNCT
ejpam-1563	23	8	gvep2b	gvep2b	NOUN
ejpam-1563	23	9	)	)	PUNCT
ejpam-1563	23	10	φ(x	φ(x	PROPN
ejpam-1563	23	11	,	,	PUNCT
ejpam-1563	23	12	y)∩	y)∩	PROPN
ejpam-1563	23	13	(	(	PUNCT
ejpam-1563	23	14	−c(x)\{0	−c(x)\{0	NOUN
ejpam-1563	23	15	}	}	PUNCT
ejpam-1563	23	16	)	)	PUNCT
ejpam-1563	23	17	=	=	SYM
ejpam-1563	23	18	;	;	PUNCT
ejpam-1563	23	19	,	,	PUNCT
ejpam-1563	23	20	∀y	∀y	PROPN
ejpam-1563	23	21	∈	∈	PROPN
ejpam-1563	23	22	k	k	X
ejpam-1563	23	23	.	.	PUNCT
ejpam-1563	24	1	for	for	ADP
ejpam-1563	24	2	i	i	PRON
ejpam-1563	24	3	=	=	SYM
ejpam-1563	24	4	1,2	1,2	NUM
ejpam-1563	24	5	,	,	PUNCT
ejpam-1563	24	6	or	or	CCONJ
ejpam-1563	24	7	,	,	PUNCT
ejpam-1563	24	8	more	more	ADV
ejpam-1563	24	9	specifically	specifically	ADV
ejpam-1563	24	10	,	,	PUNCT
ejpam-1563	24	11	i	i	PRON
ejpam-1563	24	12	=	=	SYM
ejpam-1563	24	13	1a	1a	NOUN
ejpam-1563	24	14	,	,	PUNCT
ejpam-1563	24	15	1b	1b	NUM
ejpam-1563	24	16	,	,	PUNCT
ejpam-1563	24	17	2a	2a	NUM
ejpam-1563	24	18	,	,	PUNCT
ejpam-1563	24	19	2b	2b	NUM
ejpam-1563	24	20	,	,	PUNCT
ejpam-1563	24	21	we	we	PRON
ejpam-1563	24	22	will	will	AUX
ejpam-1563	24	23	denote	denote	VERB
ejpam-1563	24	24	by	by	ADP
ejpam-1563	24	25	s	s	PROPN
ejpam-1563	25	1	i	i	PRON
ejpam-1563	25	2	k	k	PROPN
ejpam-1563	26	1	the	the	DET
ejpam-1563	26	2	set	set	NOUN
ejpam-1563	26	3	of	of	ADP
ejpam-1563	26	4	solutions	solution	NOUN
ejpam-1563	26	5	to	to	ADP
ejpam-1563	26	6	problem	problem	NOUN
ejpam-1563	26	7	(	(	PUNCT
ejpam-1563	26	8	gvepi	gvepi	NOUN
ejpam-1563	26	9	)	)	PUNCT
ejpam-1563	26	10	.	.	PUNCT
ejpam-1563	27	1	remark	remark	PROPN
ejpam-1563	27	2	1	1	NUM
ejpam-1563	27	3	.	.	PUNCT
ejpam-1563	28	1	for	for	ADP
ejpam-1563	28	2	convenience	convenience	NOUN
ejpam-1563	28	3	,	,	PUNCT
ejpam-1563	28	4	we	we	PRON
ejpam-1563	28	5	will	will	AUX
ejpam-1563	28	6	also	also	ADV
ejpam-1563	28	7	denote	denote	VERB
ejpam-1563	28	8	by	by	ADP
ejpam-1563	28	9	s	s	NOUN
ejpam-1563	29	1	i	i	PRON
ejpam-1563	29	2	h	h	VERB
ejpam-1563	29	3	the	the	DET
ejpam-1563	29	4	set	set	NOUN
ejpam-1563	29	5	of	of	ADP
ejpam-1563	29	6	solutions	solution	NOUN
ejpam-1563	29	7	to	to	ADP
ejpam-1563	29	8	problem	problem	NOUN
ejpam-1563	29	9	(	(	PUNCT
ejpam-1563	29	10	gvepi	gvepi	NOUN
ejpam-1563	29	11	)	)	PUNCT
ejpam-1563	29	12	,	,	PUNCT
ejpam-1563	29	13	with	with	ADP
ejpam-1563	29	14	k	k	PROPN
ejpam-1563	29	15	replaced	replace	VERB
ejpam-1563	29	16	by	by	ADP
ejpam-1563	29	17	a	a	DET
ejpam-1563	29	18	nonempty	nonempty	ADJ
ejpam-1563	29	19	,	,	PUNCT
ejpam-1563	29	20	closed	closed	ADJ
ejpam-1563	29	21	and	and	CCONJ
ejpam-1563	29	22	convex	convex	VERB
ejpam-1563	29	23	set	set	VERB
ejpam-1563	29	24	h	h	NOUN
ejpam-1563	29	25	⊆	⊆	NUM
ejpam-1563	29	26	k	k	PROPN
ejpam-1563	29	27	and	and	CCONJ
ejpam-1563	29	28	with	with	ADP
ejpam-1563	29	29	φ	φ	PROPN
ejpam-1563	29	30	and	and	CCONJ
ejpam-1563	29	31	c	c	AUX
ejpam-1563	29	32	being	be	AUX
ejpam-1563	29	33	replaced	replace	VERB
ejpam-1563	29	34	by	by	ADP
ejpam-1563	29	35	their	their	PRON
ejpam-1563	29	36	restrictions	restriction	NOUN
ejpam-1563	29	37	to	to	ADP
ejpam-1563	29	38	h	h	VERB
ejpam-1563	29	39	×h	×h	PROPN
ejpam-1563	29	40	and	and	CCONJ
ejpam-1563	29	41	h	h	NOUN
ejpam-1563	29	42	,	,	PUNCT
ejpam-1563	29	43	respectively	respectively	ADV
ejpam-1563	29	44	.	.	PUNCT
ejpam-1563	30	1	note	note	VERB
ejpam-1563	30	2	that	that	SCONJ
ejpam-1563	30	3	,	,	PUNCT
ejpam-1563	30	4	if	if	SCONJ
ejpam-1563	30	5	c(x	c(x	NOUN
ejpam-1563	30	6	)	)	PUNCT
ejpam-1563	30	7	has	have	AUX
ejpam-1563	30	8	nonempty	nonempty	VERB
ejpam-1563	30	9	interior	interior	ADJ
ejpam-1563	30	10	for	for	ADP
ejpam-1563	30	11	all	all	DET
ejpam-1563	30	12	x	x	SYM
ejpam-1563	30	13	∈	∈	PROPN
ejpam-1563	30	14	k	k	NOUN
ejpam-1563	30	15	,	,	PUNCT
ejpam-1563	30	16	then	then	ADV
ejpam-1563	30	17	the	the	DET
ejpam-1563	30	18	following	follow	VERB
ejpam-1563	30	19	inclusions	inclusion	NOUN
ejpam-1563	30	20	hold	hold	VERB
ejpam-1563	30	21	s2b	s2b	NOUN
ejpam-1563	30	22	k	k	NOUN
ejpam-1563	30	23	⊆	⊆	NUM
ejpam-1563	30	24	s1b	s1b	NOUN
ejpam-1563	30	25	k	k	NOUN
ejpam-1563	30	26	|∩	|∩	NOUN
ejpam-1563	30	27	|∩	|∩	NUM
ejpam-1563	30	28	s2a	s2a	NOUN
ejpam-1563	30	29	k	k	PROPN
ejpam-1563	30	30	⊆	⊆	NUM
ejpam-1563	30	31	s1a	s1a	NOUN
ejpam-1563	30	32	k	k	X
ejpam-1563	30	33	anyway	anyway	ADV
ejpam-1563	30	34	,	,	PUNCT
ejpam-1563	30	35	in	in	ADP
ejpam-1563	30	36	infinite	infinite	ADJ
ejpam-1563	30	37	dimensional	dimensional	ADJ
ejpam-1563	30	38	spaces	space	NOUN
ejpam-1563	30	39	the	the	DET
ejpam-1563	30	40	condition	condition	NOUN
ejpam-1563	30	41	int	int	NOUN
ejpam-1563	30	42	c(x	c(x	NOUN
ejpam-1563	30	43	)	)	PUNCT
ejpam-1563	30	44	6=	6=	NUM
ejpam-1563	30	45	;	;	PUNCT
ejpam-1563	30	46	can	can	AUX
ejpam-1563	30	47	be	be	AUX
ejpam-1563	30	48	a	a	DET
ejpam-1563	30	49	restrictive	restrictive	ADJ
ejpam-1563	30	50	assumption	assumption	NOUN
ejpam-1563	30	51	(	(	PUNCT
ejpam-1563	30	52	for	for	ADP
ejpam-1563	30	53	instance	instance	NOUN
ejpam-1563	30	54	,	,	PUNCT
ejpam-1563	30	55	in	in	ADP
ejpam-1563	30	56	the	the	DET
ejpam-1563	30	57	lebesgue	lebesgue	NOUN
ejpam-1563	30	58	space	space	NOUN
ejpam-1563	30	59	l2	l2	NOUN
ejpam-1563	30	60	,	,	PUNCT
ejpam-1563	30	61	the	the	DET
ejpam-1563	30	62	cone	cone	NOUN
ejpam-1563	30	63	of	of	ADP
ejpam-1563	30	64	functions	function	NOUN
ejpam-1563	30	65	that	that	PRON
ejpam-1563	30	66	are	be	AUX
ejpam-1563	30	67	nonnegative	nonnegative	ADJ
ejpam-1563	30	68	almost	almost	ADV
ejpam-1563	30	69	everywhere	everywhere	ADV
ejpam-1563	30	70	is	be	AUX
ejpam-1563	30	71	closed	close	VERB
ejpam-1563	30	72	and	and	CCONJ
ejpam-1563	30	73	convex	convex	ADJ
ejpam-1563	30	74	,	,	PUNCT
ejpam-1563	30	75	but	but	CCONJ
ejpam-1563	30	76	with	with	ADP
ejpam-1563	30	77	empty	empty	ADJ
ejpam-1563	30	78	interior	interior	NOUN
ejpam-1563	30	79	)	)	PUNCT
ejpam-1563	30	80	.	.	PUNCT
ejpam-1563	31	1	this	this	PRON
ejpam-1563	31	2	justifies	justify	VERB
ejpam-1563	31	3	our	our	PRON
ejpam-1563	31	4	interest	interest	NOUN
ejpam-1563	31	5	in	in	ADP
ejpam-1563	31	6	problems	problem	NOUN
ejpam-1563	31	7	(	(	PUNCT
ejpam-1563	31	8	gvep1b	gvep1b	NOUN
ejpam-1563	31	9	)	)	PUNCT
ejpam-1563	31	10	and	and	CCONJ
ejpam-1563	31	11	(	(	PUNCT
ejpam-1563	31	12	gvep2b	gvep2b	PROPN
ejpam-1563	31	13	)	)	PUNCT
ejpam-1563	31	14	,	,	PUNCT
ejpam-1563	31	15	as	as	SCONJ
ejpam-1563	31	16	they	they	PRON
ejpam-1563	31	17	may	may	AUX
ejpam-1563	31	18	have	have	VERB
ejpam-1563	31	19	a	a	DET
ejpam-1563	31	20	solution	solution	NOUN
ejpam-1563	31	21	even	even	ADV
ejpam-1563	31	22	in	in	ADP
ejpam-1563	31	23	this	this	DET
ejpam-1563	31	24	case	case	NOUN
ejpam-1563	31	25	.	.	PUNCT
ejpam-1563	32	1	in	in	ADP
ejpam-1563	32	2	most	most	ADJ
ejpam-1563	32	3	of	of	ADP
ejpam-1563	32	4	the	the	DET
ejpam-1563	32	5	papers	paper	NOUN
ejpam-1563	32	6	on	on	ADP
ejpam-1563	32	7	the	the	DET
ejpam-1563	32	8	existence	existence	NOUN
ejpam-1563	32	9	of	of	ADP
ejpam-1563	32	10	solutions	solution	NOUN
ejpam-1563	32	11	of	of	ADP
ejpam-1563	32	12	gveps	gvep	NOUN
ejpam-1563	32	13	,	,	PUNCT
ejpam-1563	32	14	either	either	CCONJ
ejpam-1563	32	15	boundedness	boundedness	NOUN
ejpam-1563	32	16	of	of	ADP
ejpam-1563	32	17	the	the	DET
ejpam-1563	32	18	feasible	feasible	ADJ
ejpam-1563	32	19	set	set	NOUN
ejpam-1563	32	20	or	or	CCONJ
ejpam-1563	32	21	a	a	DET
ejpam-1563	32	22	certain	certain	ADJ
ejpam-1563	32	23	coercivity	coercivity	NOUN
ejpam-1563	32	24	condition	condition	NOUN
ejpam-1563	32	25	is	be	AUX
ejpam-1563	32	26	assumed	assume	VERB
ejpam-1563	32	27	.	.	PUNCT
ejpam-1563	33	1	the	the	DET
ejpam-1563	33	2	purpose	purpose	NOUN
ejpam-1563	33	3	of	of	ADP
ejpam-1563	33	4	the	the	DET
ejpam-1563	33	5	present	present	ADJ
ejpam-1563	33	6	paper	paper	NOUN
ejpam-1563	33	7	is	be	AUX
ejpam-1563	33	8	to	to	PART
ejpam-1563	33	9	provide	provide	VERB
ejpam-1563	33	10	some	some	DET
ejpam-1563	33	11	existence	existence	NOUN
ejpam-1563	33	12	theorems	theorem	NOUN
ejpam-1563	33	13	concerning	concern	VERB
ejpam-1563	33	14	solutions	solution	NOUN
ejpam-1563	33	15	of	of	ADP
ejpam-1563	33	16	generalized	generalized	ADJ
ejpam-1563	33	17	vector	vector	NOUN
ejpam-1563	33	18	equilibrium	equilibrium	NOUN
ejpam-1563	33	19	problems	problem	NOUN
ejpam-1563	33	20	on	on	ADP
ejpam-1563	33	21	an	an	DET
ejpam-1563	33	22	unbounded	unbounded	ADJ
ejpam-1563	33	23	set	set	NOUN
ejpam-1563	33	24	with	with	ADP
ejpam-1563	33	25	set	set	NOUN
ejpam-1563	33	26	-	-	PUNCT
ejpam-1563	33	27	valued	value	VERB
ejpam-1563	33	28	maps	map	NOUN
ejpam-1563	33	29	defined	define	VERB
ejpam-1563	33	30	on	on	ADP
ejpam-1563	33	31	reflexive	reflexive	ADJ
ejpam-1563	33	32	banach	banach	NOUN
ejpam-1563	33	33	spaces	space	NOUN
ejpam-1563	33	34	,	,	PUNCT
ejpam-1563	33	35	exploiting	exploit	VERB
ejpam-1563	33	36	a	a	DET
ejpam-1563	33	37	new	new	ADJ
ejpam-1563	33	38	coercivity	coercivity	NOUN
ejpam-1563	33	39	condition	condition	NOUN
ejpam-1563	33	40	,	,	PUNCT
ejpam-1563	33	41	which	which	PRON
ejpam-1563	33	42	was	be	AUX
ejpam-1563	33	43	introduced	introduce	VERB
ejpam-1563	33	44	in	in	ADP
ejpam-1563	33	45	[	[	X
ejpam-1563	33	46	7	7	NUM
ejpam-1563	33	47	]	]	PUNCT
ejpam-1563	33	48	for	for	ADP
ejpam-1563	33	49	scalar	scalar	ADJ
ejpam-1563	33	50	bifunctions	bifunction	NOUN
ejpam-1563	33	51	and	and	CCONJ
ejpam-1563	33	52	in	in	ADP
ejpam-1563	33	53	[	[	X
ejpam-1563	33	54	8	8	NUM
ejpam-1563	33	55	]	]	PUNCT
ejpam-1563	33	56	for	for	ADP
ejpam-1563	33	57	vector	vector	NOUN
ejpam-1563	33	58	-	-	PUNCT
ejpam-1563	33	59	valued	value	VERB
ejpam-1563	33	60	functions	function	NOUN
ejpam-1563	33	61	.	.	PUNCT
ejpam-1563	34	1	in	in	ADP
ejpam-1563	34	2	[	[	X
ejpam-1563	34	3	7	7	NUM
ejpam-1563	34	4	]	]	PUNCT
ejpam-1563	34	5	,	,	PUNCT
ejpam-1563	34	6	in	in	ADP
ejpam-1563	34	7	particular	particular	ADJ
ejpam-1563	34	8	,	,	PUNCT
ejpam-1563	34	9	it	it	PRON
ejpam-1563	34	10	is	be	AUX
ejpam-1563	34	11	shown	show	VERB
ejpam-1563	34	12	how	how	SCONJ
ejpam-1563	34	13	several	several	ADJ
ejpam-1563	34	14	coercivity	coercivity	NOUN
ejpam-1563	34	15	conditions	condition	NOUN
ejpam-1563	34	16	proposed	propose	VERB
ejpam-1563	34	17	in	in	ADP
ejpam-1563	34	18	the	the	DET
ejpam-1563	34	19	literature	literature	NOUN
ejpam-1563	34	20	are	be	AUX
ejpam-1563	34	21	stronger	strong	ADJ
ejpam-1563	34	22	than	than	ADP
ejpam-1563	34	23	this	this	DET
ejpam-1563	34	24	new	new	ADJ
ejpam-1563	34	25	condition	condition	NOUN
ejpam-1563	34	26	,	,	PUNCT
ejpam-1563	34	27	in	in	ADP
ejpam-1563	34	28	the	the	DET
ejpam-1563	34	29	sense	sense	NOUN
ejpam-1563	34	30	that	that	SCONJ
ejpam-1563	34	31	,	,	PUNCT
ejpam-1563	34	32	if	if	SCONJ
ejpam-1563	34	33	the	the	DET
ejpam-1563	34	34	former	former	ADJ
ejpam-1563	34	35	hold	hold	NOUN
ejpam-1563	34	36	,	,	PUNCT
ejpam-1563	34	37	then	then	ADV
ejpam-1563	34	38	the	the	DET
ejpam-1563	34	39	latter	latter	ADJ
ejpam-1563	34	40	holds	hold	VERB
ejpam-1563	34	41	as	as	ADV
ejpam-1563	34	42	well	well	ADV
ejpam-1563	34	43	.	.	PUNCT
ejpam-1563	35	1	thus	thus	ADV
ejpam-1563	35	2	,	,	PUNCT
ejpam-1563	35	3	employing	employ	VERB
ejpam-1563	35	4	this	this	DET
ejpam-1563	35	5	weak	weak	ADJ
ejpam-1563	35	6	coercivity	coercivity	NOUN
ejpam-1563	35	7	condition	condition	NOUN
ejpam-1563	35	8	can	can	AUX
ejpam-1563	35	9	yield	yield	VERB
ejpam-1563	35	10	more	more	ADJ
ejpam-1563	35	11	general	general	ADJ
ejpam-1563	35	12	results	result	NOUN
ejpam-1563	35	13	in	in	ADP
ejpam-1563	35	14	the	the	DET
ejpam-1563	35	15	field	field	NOUN
ejpam-1563	35	16	of	of	ADP
ejpam-1563	35	17	equilibrium	equilibrium	NOUN
ejpam-1563	35	18	problems	problem	NOUN
ejpam-1563	35	19	.	.	PUNCT
ejpam-1563	36	1	e.	e.	PROPN
ejpam-1563	36	2	allevi	allevi	PROPN
ejpam-1563	36	3	,	,	PUNCT
ejpam-1563	36	4	i.	i.	PROPN
ejpam-1563	36	5	konnov	konnov	PROPN
ejpam-1563	36	6	,	,	PUNCT
ejpam-1563	36	7	m.	m.	NOUN
ejpam-1563	36	8	rocco	rocco	NOUN
ejpam-1563	36	9	/	/	SYM
ejpam-1563	36	10	eur	eur	PROPN
ejpam-1563	36	11	.	.	PUNCT
ejpam-1563	37	1	j.	j.	PROPN
ejpam-1563	37	2	pure	pure	PROPN
ejpam-1563	37	3	appl	appl	PROPN
ejpam-1563	37	4	.	.	PROPN
ejpam-1563	37	5	math	math	PROPN
ejpam-1563	37	6	,	,	PUNCT
ejpam-1563	37	7	6	6	NUM
ejpam-1563	37	8	(	(	PUNCT
ejpam-1563	37	9	2013	2013	NUM
ejpam-1563	37	10	)	)	PUNCT
ejpam-1563	37	11	,	,	PUNCT
ejpam-1563	37	12	365	365	NUM
ejpam-1563	37	13	-	-	SYM
ejpam-1563	37	14	376	376	NUM
ejpam-1563	37	15	367	367	NUM
ejpam-1563	37	16	2	2	NUM
ejpam-1563	37	17	.	.	PUNCT
ejpam-1563	37	18	preliminaries	preliminary	NOUN
ejpam-1563	37	19	in	in	ADP
ejpam-1563	37	20	this	this	DET
ejpam-1563	37	21	paper	paper	NOUN
ejpam-1563	37	22	we	we	PRON
ejpam-1563	37	23	will	will	AUX
ejpam-1563	37	24	consider	consider	VERB
ejpam-1563	37	25	partial	partial	ADJ
ejpam-1563	37	26	orderings	ordering	NOUN
ejpam-1563	37	27	on	on	ADP
ejpam-1563	37	28	vector	vector	NOUN
ejpam-1563	37	29	spaces	space	NOUN
ejpam-1563	37	30	induced	induce	VERB
ejpam-1563	37	31	by	by	ADP
ejpam-1563	37	32	cones	cone	NOUN
ejpam-1563	37	33	.	.	PUNCT
ejpam-1563	38	1	we	we	PRON
ejpam-1563	38	2	agree	agree	VERB
ejpam-1563	38	3	that	that	SCONJ
ejpam-1563	38	4	any	any	DET
ejpam-1563	38	5	cone	cone	NOUN
ejpam-1563	38	6	contains	contain	VERB
ejpam-1563	38	7	the	the	DET
ejpam-1563	38	8	origin	origin	NOUN
ejpam-1563	38	9	,	,	PUNCT
ejpam-1563	38	10	according	accord	VERB
ejpam-1563	38	11	to	to	ADP
ejpam-1563	38	12	the	the	DET
ejpam-1563	38	13	following	follow	VERB
ejpam-1563	38	14	definition	definition	NOUN
ejpam-1563	38	15	.	.	PUNCT
ejpam-1563	39	1	definition	definition	NOUN
ejpam-1563	39	2	1	1	NUM
ejpam-1563	39	3	.	.	PUNCT
ejpam-1563	40	1	let	let	VERB
ejpam-1563	40	2	x	x	PRON
ejpam-1563	40	3	be	be	AUX
ejpam-1563	40	4	a	a	DET
ejpam-1563	40	5	vector	vector	NOUN
ejpam-1563	40	6	space	space	NOUN
ejpam-1563	40	7	and	and	CCONJ
ejpam-1563	40	8	c	c	NOUN
ejpam-1563	40	9	⊆	⊆	NUM
ejpam-1563	40	10	x	x	PUNCT
ejpam-1563	40	11	be	be	AUX
ejpam-1563	40	12	nonempty	nonempty	ADJ
ejpam-1563	40	13	.	.	PUNCT
ejpam-1563	41	1	c	c	NOUN
ejpam-1563	41	2	is	be	AUX
ejpam-1563	41	3	a	a	DET
ejpam-1563	41	4	cone	cone	NOUN
ejpam-1563	41	5	if	if	SCONJ
ejpam-1563	41	6	,	,	PUNCT
ejpam-1563	41	7	for	for	ADP
ejpam-1563	41	8	all	all	DET
ejpam-1563	41	9	k	k	PROPN
ejpam-1563	41	10	∈	∈	PROPN
ejpam-1563	41	11	c	c	NOUN
ejpam-1563	41	12	and	and	CCONJ
ejpam-1563	41	13	λ≥	λ≥	PROPN
ejpam-1563	41	14	0	0	NUM
ejpam-1563	41	15	,	,	PUNCT
ejpam-1563	41	16	λk	λk	PROPN
ejpam-1563	41	17	∈	∈	PROPN
ejpam-1563	41	18	c.	c.	NOUN
ejpam-1563	41	19	if	if	SCONJ
ejpam-1563	41	20	−c	−c	NOUN
ejpam-1563	41	21	∩	∩	NOUN
ejpam-1563	41	22	c	c	NOUN
ejpam-1563	41	23	=	=	SYM
ejpam-1563	41	24	{	{	PUNCT
ejpam-1563	41	25	0	0	NUM
ejpam-1563	41	26	}	}	PUNCT
ejpam-1563	41	27	,	,	PUNCT
ejpam-1563	41	28	then	then	ADV
ejpam-1563	41	29	the	the	DET
ejpam-1563	41	30	cone	cone	NOUN
ejpam-1563	41	31	c	c	NOUN
ejpam-1563	41	32	is	be	AUX
ejpam-1563	41	33	pointed	point	VERB
ejpam-1563	41	34	,	,	PUNCT
ejpam-1563	41	35	while	while	SCONJ
ejpam-1563	41	36	it	it	PRON
ejpam-1563	41	37	is	be	AUX
ejpam-1563	41	38	solid	solid	ADJ
ejpam-1563	41	39	if	if	SCONJ
ejpam-1563	41	40	int	int	NOUN
ejpam-1563	41	41	c	c	NOUN
ejpam-1563	41	42	6=	6=	PROPN
ejpam-1563	41	43	;	;	PUNCT
ejpam-1563	41	44	.	.	PUNCT
ejpam-1563	42	1	in	in	ADP
ejpam-1563	42	2	the	the	DET
ejpam-1563	42	3	next	next	ADJ
ejpam-1563	42	4	section	section	NOUN
ejpam-1563	42	5	we	we	PRON
ejpam-1563	42	6	will	will	AUX
ejpam-1563	42	7	need	need	VERB
ejpam-1563	42	8	existence	existence	NOUN
ejpam-1563	42	9	results	result	NOUN
ejpam-1563	42	10	for	for	ADP
ejpam-1563	42	11	generalized	generalized	ADJ
ejpam-1563	42	12	vector	vector	NOUN
ejpam-1563	42	13	equilibrium	equilibrium	NOUN
ejpam-1563	42	14	problems	problem	NOUN
ejpam-1563	42	15	defined	define	VERB
ejpam-1563	42	16	on	on	ADP
ejpam-1563	42	17	compact	compact	ADJ
ejpam-1563	42	18	sets	set	NOUN
ejpam-1563	42	19	.	.	PUNCT
ejpam-1563	43	1	these	these	DET
ejpam-1563	43	2	results	result	NOUN
ejpam-1563	43	3	can	can	AUX
ejpam-1563	43	4	be	be	AUX
ejpam-1563	43	5	based	base	VERB
ejpam-1563	43	6	on	on	ADP
ejpam-1563	43	7	the	the	DET
ejpam-1563	43	8	following	follow	VERB
ejpam-1563	43	9	lemma	lemma	PROPN
ejpam-1563	43	10	,	,	PUNCT
ejpam-1563	43	11	which	which	PRON
ejpam-1563	43	12	is	be	AUX
ejpam-1563	43	13	an	an	DET
ejpam-1563	43	14	easy	easy	ADJ
ejpam-1563	43	15	adaptation	adaptation	NOUN
ejpam-1563	43	16	of	of	ADP
ejpam-1563	43	17	[	[	X
ejpam-1563	43	18	5	5	NUM
ejpam-1563	43	19	,	,	PUNCT
ejpam-1563	43	20	lemma	lemma	PROPN
ejpam-1563	43	21	4	4	NUM
ejpam-1563	43	22	]	]	PUNCT
ejpam-1563	43	23	,	,	PUNCT
ejpam-1563	43	24	a	a	DET
ejpam-1563	43	25	consequence	consequence	NOUN
ejpam-1563	43	26	of	of	ADP
ejpam-1563	43	27	the	the	DET
ejpam-1563	43	28	well	well	ADV
ejpam-1563	43	29	-	-	PUNCT
ejpam-1563	43	30	known	know	VERB
ejpam-1563	43	31	ky	ky	PROPN
ejpam-1563	43	32	fan	fan	PROPN
ejpam-1563	43	33	’s	’s	PART
ejpam-1563	43	34	lemma	lemma	PROPN
ejpam-1563	44	1	[	[	X
ejpam-1563	44	2	5	5	NUM
ejpam-1563	44	3	,	,	PUNCT
ejpam-1563	44	4	lemma	lemma	PROPN
ejpam-1563	44	5	1	1	NUM
ejpam-1563	44	6	]	]	PUNCT
ejpam-1563	44	7	.	.	PUNCT
ejpam-1563	45	1	in	in	ADP
ejpam-1563	45	2	the	the	DET
ejpam-1563	45	3	following	following	NOUN
ejpam-1563	45	4	,	,	PUNCT
ejpam-1563	45	5	given	give	VERB
ejpam-1563	45	6	a	a	DET
ejpam-1563	45	7	set	set	NOUN
ejpam-1563	45	8	s	s	PART
ejpam-1563	45	9	,	,	PUNCT
ejpam-1563	45	10	we	we	PRON
ejpam-1563	45	11	denote	denote	VERB
ejpam-1563	45	12	by	by	ADP
ejpam-1563	45	13	π(s	π(s	PROPN
ejpam-1563	45	14	)	)	PUNCT
ejpam-1563	45	15	the	the	DET
ejpam-1563	45	16	power	power	NOUN
ejpam-1563	45	17	set	set	NOUN
ejpam-1563	45	18	of	of	ADP
ejpam-1563	45	19	s.	s.	PROPN
ejpam-1563	45	20	lemma	lemma	PROPN
ejpam-1563	46	1	1	1	X
ejpam-1563	46	2	.	.	PUNCT
ejpam-1563	46	3	let	let	VERB
ejpam-1563	46	4	k	k	PRON
ejpam-1563	46	5	be	be	AUX
ejpam-1563	46	6	a	a	DET
ejpam-1563	46	7	nonempty	nonempty	ADJ
ejpam-1563	46	8	compact	compact	ADJ
ejpam-1563	46	9	convex	convex	NOUN
ejpam-1563	46	10	set	set	VERB
ejpam-1563	46	11	in	in	ADP
ejpam-1563	46	12	a	a	DET
ejpam-1563	46	13	topological	topological	ADJ
ejpam-1563	46	14	vector	vector	NOUN
ejpam-1563	46	15	space	space	NOUN
ejpam-1563	46	16	and	and	CCONJ
ejpam-1563	46	17	let	let	VERB
ejpam-1563	46	18	a	a	PRON
ejpam-1563	46	19	:	:	PUNCT
ejpam-1563	46	20	k	k	X
ejpam-1563	46	21	→	→	PROPN
ejpam-1563	46	22	π(k	π(k	PROPN
ejpam-1563	46	23	×	×	PROPN
ejpam-1563	46	24	k	k	NOUN
ejpam-1563	46	25	)	)	PUNCT
ejpam-1563	46	26	be	be	VERB
ejpam-1563	46	27	such	such	ADJ
ejpam-1563	46	28	that	that	SCONJ
ejpam-1563	46	29	:	:	PUNCT
ejpam-1563	46	30	(	(	PUNCT
ejpam-1563	46	31	i	i	NOUN
ejpam-1563	46	32	)	)	PUNCT
ejpam-1563	46	33	(	(	PUNCT
ejpam-1563	46	34	x	x	X
ejpam-1563	46	35	,	,	PUNCT
ejpam-1563	46	36	x	x	NOUN
ejpam-1563	46	37	)	)	PUNCT
ejpam-1563	46	38	/∈	/∈	PUNCT
ejpam-1563	47	1	a(x	a(x	NOUN
ejpam-1563	47	2	)	)	PUNCT
ejpam-1563	47	3	for	for	ADP
ejpam-1563	47	4	all	all	DET
ejpam-1563	47	5	x	x	SYM
ejpam-1563	47	6	∈	∈	PROPN
ejpam-1563	47	7	k	k	NOUN
ejpam-1563	47	8	;	;	PUNCT
ejpam-1563	47	9	(	(	PUNCT
ejpam-1563	47	10	ii	ii	NOUN
ejpam-1563	47	11	)	)	PUNCT
ejpam-1563	47	12	for	for	ADP
ejpam-1563	47	13	any	any	DET
ejpam-1563	47	14	fixed	fix	VERB
ejpam-1563	47	15	x	x	SYM
ejpam-1563	47	16	∈	∈	PROPN
ejpam-1563	47	17	k	k	NOUN
ejpam-1563	47	18	,	,	PUNCT
ejpam-1563	47	19	the	the	DET
ejpam-1563	47	20	set	set	NOUN
ejpam-1563	47	21	{	{	PUNCT
ejpam-1563	47	22	y	y	PROPN
ejpam-1563	47	23	∈	∈	PROPN
ejpam-1563	47	24	k	k	NOUN
ejpam-1563	47	25	:	:	PUNCT
ejpam-1563	47	26	(	(	PUNCT
ejpam-1563	47	27	x	x	X
ejpam-1563	47	28	,	,	PUNCT
ejpam-1563	47	29	y	y	PROPN
ejpam-1563	47	30	)	)	PUNCT
ejpam-1563	47	31	∈	∈	PROPN
ejpam-1563	47	32	a(x	a(x	NOUN
ejpam-1563	47	33	)	)	PUNCT
ejpam-1563	47	34	}	}	PUNCT
ejpam-1563	47	35	is	be	AUX
ejpam-1563	47	36	convex	convex	ADJ
ejpam-1563	47	37	;	;	PUNCT
ejpam-1563	47	38	(	(	PUNCT
ejpam-1563	47	39	iii	iii	NOUN
ejpam-1563	47	40	)	)	PUNCT
ejpam-1563	47	41	for	for	ADP
ejpam-1563	47	42	any	any	DET
ejpam-1563	47	43	fixed	fix	VERB
ejpam-1563	47	44	y	y	PROPN
ejpam-1563	47	45	∈	∈	PROPN
ejpam-1563	47	46	k	k	PROPN
ejpam-1563	47	47	,	,	PUNCT
ejpam-1563	47	48	the	the	DET
ejpam-1563	47	49	set	set	NOUN
ejpam-1563	47	50	{	{	PUNCT
ejpam-1563	47	51	x	x	SYM
ejpam-1563	47	52	∈	∈	PROPN
ejpam-1563	47	53	k	k	NOUN
ejpam-1563	47	54	:	:	PUNCT
ejpam-1563	47	55	(	(	PUNCT
ejpam-1563	47	56	x	x	X
ejpam-1563	47	57	,	,	PUNCT
ejpam-1563	47	58	y	y	PROPN
ejpam-1563	47	59	)	)	PUNCT
ejpam-1563	47	60	/∈	/∈	PUNCT
ejpam-1563	48	1	a(x	a(x	NOUN
ejpam-1563	48	2	)	)	PUNCT
ejpam-1563	48	3	}	}	PUNCT
ejpam-1563	48	4	is	be	AUX
ejpam-1563	48	5	closed	closed	ADJ
ejpam-1563	48	6	.	.	PUNCT
ejpam-1563	49	1	then	then	ADV
ejpam-1563	49	2	there	there	PRON
ejpam-1563	49	3	exists	exist	VERB
ejpam-1563	49	4	a	a	DET
ejpam-1563	49	5	point	point	NOUN
ejpam-1563	49	6	x	x	X
ejpam-1563	49	7	∈	∈	PROPN
ejpam-1563	49	8	k	k	ADJ
ejpam-1563	49	9	such	such	ADJ
ejpam-1563	49	10	that	that	PRON
ejpam-1563	49	11	(	(	PUNCT
ejpam-1563	49	12	x	x	X
ejpam-1563	49	13	,	,	PUNCT
ejpam-1563	49	14	y	y	PROPN
ejpam-1563	49	15	)	)	PUNCT
ejpam-1563	49	16	/∈	/∈	PUNCT
ejpam-1563	50	1	a(x	a(x	NOUN
ejpam-1563	50	2	)	)	PUNCT
ejpam-1563	50	3	for	for	ADP
ejpam-1563	50	4	all	all	DET
ejpam-1563	50	5	y	y	PROPN
ejpam-1563	50	6	∈	∈	PROPN
ejpam-1563	50	7	k.	k.	NOUN
ejpam-1563	50	8	proof	proof	NOUN
ejpam-1563	50	9	.	.	PUNCT
ejpam-1563	51	1	by	by	ADP
ejpam-1563	51	2	(	(	PUNCT
ejpam-1563	51	3	iii	iii	NOUN
ejpam-1563	51	4	)	)	PUNCT
ejpam-1563	51	5	,	,	PUNCT
ejpam-1563	51	6	for	for	ADP
ejpam-1563	51	7	any	any	DET
ejpam-1563	51	8	fixed	fix	VERB
ejpam-1563	51	9	y	y	PROPN
ejpam-1563	51	10	∈	∈	PROPN
ejpam-1563	51	11	k	k	PROPN
ejpam-1563	51	12	the	the	DET
ejpam-1563	51	13	set	set	NOUN
ejpam-1563	51	14	f(y	f(y	NOUN
ejpam-1563	51	15	)	)	PUNCT
ejpam-1563	51	16	=	=	PRON
ejpam-1563	51	17	{	{	PUNCT
ejpam-1563	51	18	x	x	PUNCT
ejpam-1563	51	19	∈	∈	PROPN
ejpam-1563	51	20	k	k	NOUN
ejpam-1563	51	21	:	:	PUNCT
ejpam-1563	51	22	(	(	PUNCT
ejpam-1563	51	23	x	x	X
ejpam-1563	51	24	,	,	PUNCT
ejpam-1563	51	25	y	y	PROPN
ejpam-1563	51	26	)	)	PUNCT
ejpam-1563	51	27	/∈	/∈	PUNCT
ejpam-1563	52	1	a(x	a(x	NOUN
ejpam-1563	52	2	)	)	PUNCT
ejpam-1563	52	3	}	}	PUNCT
ejpam-1563	52	4	is	be	AUX
ejpam-1563	52	5	closed	close	VERB
ejpam-1563	52	6	in	in	ADP
ejpam-1563	52	7	k	k	PROPN
ejpam-1563	52	8	,	,	PUNCT
ejpam-1563	52	9	hence	hence	ADV
ejpam-1563	52	10	compact	compact	ADJ
ejpam-1563	52	11	.	.	PUNCT
ejpam-1563	53	1	moreover	moreover	ADV
ejpam-1563	53	2	,	,	PUNCT
ejpam-1563	53	3	f	f	PROPN
ejpam-1563	53	4	is	be	AUX
ejpam-1563	53	5	a	a	DET
ejpam-1563	53	6	kkm	kkm	PROPN
ejpam-1563	53	7	-	-	PUNCT
ejpam-1563	53	8	map	map	NOUN
ejpam-1563	53	9	,	,	PUNCT
ejpam-1563	53	10	i.e.	i.e.	X
ejpam-1563	53	11	such	such	ADJ
ejpam-1563	53	12	that	that	SCONJ
ejpam-1563	53	13	the	the	DET
ejpam-1563	53	14	convex	convex	PROPN
ejpam-1563	53	15	hull	hull	NOUN
ejpam-1563	53	16	of	of	ADP
ejpam-1563	53	17	any	any	DET
ejpam-1563	53	18	finite	finite	NOUN
ejpam-1563	53	19	subset	subset	NOUN
ejpam-1563	53	20	{	{	PUNCT
ejpam-1563	53	21	y1	y1	NOUN
ejpam-1563	53	22	,	,	PUNCT
ejpam-1563	53	23	·	·	PUNCT
ejpam-1563	53	24	·	·	PUNCT
ejpam-1563	53	25	·	·	PUNCT
ejpam-1563	53	26	,	,	PUNCT
ejpam-1563	53	27	yn	yn	PROPN
ejpam-1563	53	28	}	}	PUNCT
ejpam-1563	53	29	of	of	ADP
ejpam-1563	53	30	k	k	PROPN
ejpam-1563	53	31	is	be	AUX
ejpam-1563	53	32	contained	contain	VERB
ejpam-1563	53	33	in	in	ADP
ejpam-1563	53	34	⋃n	⋃n	NOUN
ejpam-1563	53	35	i=1	i=1	PROPN
ejpam-1563	53	36	f(yi	f(yi	PROPN
ejpam-1563	53	37	)	)	PUNCT
ejpam-1563	53	38	.	.	PUNCT
ejpam-1563	54	1	indeed	indeed	ADV
ejpam-1563	54	2	,	,	PUNCT
ejpam-1563	54	3	suppose	suppose	VERB
ejpam-1563	54	4	by	by	ADP
ejpam-1563	54	5	contradiction	contradiction	NOUN
ejpam-1563	54	6	that	that	SCONJ
ejpam-1563	54	7	there	there	PRON
ejpam-1563	54	8	exist	exist	VERB
ejpam-1563	54	9	(	(	PUNCT
ejpam-1563	54	10	λ1	λ1	ADJ
ejpam-1563	54	11	,	,	PUNCT
ejpam-1563	54	12	·	·	PUNCT
ejpam-1563	54	13	·	·	PUNCT
ejpam-1563	54	14	·	·	PUNCT
ejpam-1563	54	15	,	,	PUNCT
ejpam-1563	54	16	λn	λn	NOUN
ejpam-1563	54	17	)	)	PUNCT
ejpam-1563	54	18	∈	∈	PROPN
ejpam-1563	55	1	[	[	X
ejpam-1563	55	2	0,1]n	0,1]n	NOUN
ejpam-1563	55	3	such	such	ADJ
ejpam-1563	55	4	that	that	SCONJ
ejpam-1563	55	5	λ1	λ1	PROPN
ejpam-1563	55	6	+	+	X
ejpam-1563	55	7	·	·	PUNCT
ejpam-1563	55	8	·	·	PUNCT
ejpam-1563	55	9	·	·	PUNCT
ejpam-1563	55	10	+	+	NOUN
ejpam-1563	55	11	λn	λn	NOUN
ejpam-1563	55	12	=	=	SYM
ejpam-1563	55	13	1	1	NUM
ejpam-1563	55	14	and	and	CCONJ
ejpam-1563	55	15			NOUN
ejpam-1563	55	16			NOUN
ejpam-1563	55	17			NOUN
ejpam-1563	55	18	n	n	CCONJ
ejpam-1563	55	19	∑	∑	PUNCT
ejpam-1563	55	20	j=1	j=1	PROPN
ejpam-1563	55	21	λ	λ	X
ejpam-1563	55	22	j	j	PROPN
ejpam-1563	55	23	y	y	PROPN
ejpam-1563	55	24	j	j	PROPN
ejpam-1563	55	25	,	,	PUNCT
ejpam-1563	55	26	yi	yi	PROPN
ejpam-1563	55	27			PROPN
ejpam-1563	55	28			VERB
ejpam-1563	55	29			PUNCT
ejpam-1563	56	1	∈	∈	VERB
ejpam-1563	56	2	a	a	DET
ejpam-1563	56	3			NOUN
ejpam-1563	56	4			NOUN
ejpam-1563	56	5			NOUN
ejpam-1563	56	6	n	n	CCONJ
ejpam-1563	56	7	∑	∑	PUNCT
ejpam-1563	56	8	j=1	j=1	PROPN
ejpam-1563	56	9	λ	λ	X
ejpam-1563	56	10	j	j	PROPN
ejpam-1563	56	11	y	y	PROPN
ejpam-1563	56	12	j	j	PROPN
ejpam-1563	56	13			PROPN
ejpam-1563	56	14			VERB
ejpam-1563	56	15			X
ejpam-1563	56	16	,	,	PUNCT
ejpam-1563	56	17	∀i	∀i	NOUN
ejpam-1563	56	18	=	=	SYM
ejpam-1563	56	19	1	1	NUM
ejpam-1563	56	20	,	,	PUNCT
ejpam-1563	56	21	·	·	PUNCT
ejpam-1563	56	22	·	·	PUNCT
ejpam-1563	56	23	·	·	PUNCT
ejpam-1563	56	24	,	,	PUNCT
ejpam-1563	56	25	n	n	CCONJ
ejpam-1563	56	26	,	,	PUNCT
ejpam-1563	56	27	i.e.	i.e.	X
ejpam-1563	56	28	yi	yi	X
ejpam-1563	56	29	∈	∈	PROPN
ejpam-1563	56	30	{	{	PUNCT
ejpam-1563	56	31	y	y	PROPN
ejpam-1563	56	32	∈	∈	PROPN
ejpam-1563	56	33	k	k	NOUN
ejpam-1563	56	34	:	:	PUNCT
ejpam-1563	56	35	(	(	PUNCT
ejpam-1563	56	36	∑n	∑n	PROPN
ejpam-1563	56	37	j=1λ	j=1λ	PROPN
ejpam-1563	56	38	j	j	PROPN
ejpam-1563	56	39	y	y	PROPN
ejpam-1563	56	40	j	j	PROPN
ejpam-1563	56	41	,	,	PUNCT
ejpam-1563	56	42	y	y	PROPN
ejpam-1563	56	43	)	)	PUNCT
ejpam-1563	56	44	∈	∈	PROPN
ejpam-1563	57	1	a	a	PRON
ejpam-1563	57	2	(	(	PUNCT
ejpam-1563	57	3	∑n	∑n	PROPN
ejpam-1563	57	4	j=1λ	j=1λ	PROPN
ejpam-1563	57	5	j	j	PROPN
ejpam-1563	57	6	y	y	PROPN
ejpam-1563	57	7	j	j	PROPN
ejpam-1563	57	8	)	)	PUNCT
ejpam-1563	57	9	}	}	PUNCT
ejpam-1563	57	10	.	.	PUNCT
ejpam-1563	58	1	then	then	ADV
ejpam-1563	58	2	,	,	PUNCT
ejpam-1563	58	3	by	by	ADP
ejpam-1563	58	4	(	(	PUNCT
ejpam-1563	58	5	ii	ii	NOUN
ejpam-1563	58	6	)	)	PUNCT
ejpam-1563	58	7	,	,	PUNCT
ejpam-1563	58	8	∑n	∑n	PROPN
ejpam-1563	58	9	j=1λ	j=1λ	PROPN
ejpam-1563	58	10	j	j	PROPN
ejpam-1563	58	11	y	y	PROPN
ejpam-1563	58	12	j	j	PROPN
ejpam-1563	58	13	belongs	belong	VERB
ejpam-1563	58	14	to	to	ADP
ejpam-1563	58	15	the	the	DET
ejpam-1563	58	16	same	same	ADJ
ejpam-1563	58	17	set	set	NOUN
ejpam-1563	58	18	,	,	PUNCT
ejpam-1563	58	19	so	so	SCONJ
ejpam-1563	58	20	that	that	SCONJ
ejpam-1563	58	21			VERB
ejpam-1563	58	22			NOUN
ejpam-1563	58	23			NOUN
ejpam-1563	58	24	n	n	CCONJ
ejpam-1563	58	25	∑	∑	PUNCT
ejpam-1563	58	26	j=1	j=1	PROPN
ejpam-1563	58	27	λ	λ	X
ejpam-1563	58	28	j	j	PROPN
ejpam-1563	58	29	y	y	PROPN
ejpam-1563	58	30	j	j	PROPN
ejpam-1563	58	31	,	,	PUNCT
ejpam-1563	58	32	n	n	CCONJ
ejpam-1563	58	33	∑	∑	ADP
ejpam-1563	59	1	j=1	j=1	PROPN
ejpam-1563	59	2	λ	λ	X
ejpam-1563	59	3	j	j	PROPN
ejpam-1563	59	4	y	y	PROPN
ejpam-1563	59	5	j	j	PROPN
ejpam-1563	59	6			PROPN
ejpam-1563	59	7			VERB
ejpam-1563	59	8			PUNCT
ejpam-1563	60	1	∈	∈	VERB
ejpam-1563	60	2	a	a	DET
ejpam-1563	60	3			NOUN
ejpam-1563	60	4			NOUN
ejpam-1563	60	5			NOUN
ejpam-1563	60	6	n	n	CCONJ
ejpam-1563	60	7	∑	∑	PUNCT
ejpam-1563	60	8	j=1	j=1	PROPN
ejpam-1563	60	9	λ	λ	X
ejpam-1563	60	10	j	j	PROPN
ejpam-1563	60	11	y	y	PROPN
ejpam-1563	60	12	j	j	PROPN
ejpam-1563	60	13			PROPN
ejpam-1563	60	14			VERB
ejpam-1563	60	15			PUNCT
ejpam-1563	61	1	,	,	PUNCT
ejpam-1563	61	2	a	a	DET
ejpam-1563	61	3	contradiction	contradiction	NOUN
ejpam-1563	61	4	to	to	ADP
ejpam-1563	61	5	(	(	PUNCT
ejpam-1563	61	6	i	i	NOUN
ejpam-1563	61	7	)	)	PUNCT
ejpam-1563	61	8	.	.	PUNCT
ejpam-1563	62	1	therefore	therefore	ADV
ejpam-1563	62	2	,	,	PUNCT
ejpam-1563	62	3	it	it	PRON
ejpam-1563	62	4	follows	follow	VERB
ejpam-1563	62	5	from	from	ADP
ejpam-1563	62	6	[	[	X
ejpam-1563	62	7	5	5	NUM
ejpam-1563	62	8	,	,	PUNCT
ejpam-1563	62	9	lemma	lemma	PROPN
ejpam-1563	62	10	1	1	NUM
ejpam-1563	62	11	]	]	PUNCT
ejpam-1563	62	12	that	that	SCONJ
ejpam-1563	62	13	⋂	⋂	PROPN
ejpam-1563	62	14	y∈k	y∈k	PROPN
ejpam-1563	62	15	f(y	f(y	NOUN
ejpam-1563	62	16	)	)	PUNCT
ejpam-1563	62	17	6=	6=	NUM
ejpam-1563	62	18	;	;	CCONJ
ejpam-1563	62	19	,	,	PUNCT
ejpam-1563	62	20	i.e.	i.e.	X
ejpam-1563	62	21	,	,	PUNCT
ejpam-1563	62	22	there	there	PRON
ejpam-1563	62	23	exists	exist	VERB
ejpam-1563	62	24	x	x	X
ejpam-1563	62	25	∈	∈	PROPN
ejpam-1563	62	26	k	k	NOUN
ejpam-1563	62	27	such	such	ADJ
ejpam-1563	62	28	that	that	PRON
ejpam-1563	62	29	(	(	PUNCT
ejpam-1563	62	30	x	x	X
ejpam-1563	62	31	,	,	PUNCT
ejpam-1563	62	32	y	y	PROPN
ejpam-1563	62	33	)	)	PUNCT
ejpam-1563	62	34	/∈	/∈	PUNCT
ejpam-1563	63	1	a(x	a(x	NOUN
ejpam-1563	63	2	)	)	PUNCT
ejpam-1563	63	3	for	for	ADP
ejpam-1563	63	4	all	all	DET
ejpam-1563	63	5	y	y	PROPN
ejpam-1563	63	6	∈	∈	PROPN
ejpam-1563	63	7	k	k	PROPN
ejpam-1563	63	8	.	.	PUNCT
ejpam-1563	64	1	e.	e.	PROPN
ejpam-1563	64	2	allevi	allevi	PROPN
ejpam-1563	64	3	,	,	PUNCT
ejpam-1563	64	4	i.	i.	PROPN
ejpam-1563	64	5	konnov	konnov	PROPN
ejpam-1563	64	6	,	,	PUNCT
ejpam-1563	64	7	m.	m.	NOUN
ejpam-1563	64	8	rocco	rocco	NOUN
ejpam-1563	64	9	/	/	SYM
ejpam-1563	64	10	eur	eur	PROPN
ejpam-1563	64	11	.	.	PUNCT
ejpam-1563	65	1	j.	j.	PROPN
ejpam-1563	65	2	pure	pure	PROPN
ejpam-1563	65	3	appl	appl	PROPN
ejpam-1563	65	4	.	.	PROPN
ejpam-1563	65	5	math	math	PROPN
ejpam-1563	65	6	,	,	PUNCT
ejpam-1563	65	7	6	6	NUM
ejpam-1563	65	8	(	(	PUNCT
ejpam-1563	65	9	2013	2013	NUM
ejpam-1563	65	10	)	)	PUNCT
ejpam-1563	65	11	,	,	PUNCT
ejpam-1563	65	12	365	365	NUM
ejpam-1563	65	13	-	-	SYM
ejpam-1563	65	14	376	376	NUM
ejpam-1563	65	15	368	368	NUM
ejpam-1563	65	16	as	as	ADP
ejpam-1563	65	17	an	an	DET
ejpam-1563	65	18	immediate	immediate	ADJ
ejpam-1563	65	19	consequence	consequence	NOUN
ejpam-1563	65	20	of	of	ADP
ejpam-1563	65	21	the	the	DET
ejpam-1563	65	22	preceding	precede	VERB
ejpam-1563	65	23	lemma	lemma	PROPN
ejpam-1563	65	24	,	,	PUNCT
ejpam-1563	65	25	one	one	NOUN
ejpam-1563	65	26	obtains	obtain	VERB
ejpam-1563	65	27	the	the	DET
ejpam-1563	65	28	following	follow	VERB
ejpam-1563	65	29	existence	existence	NOUN
ejpam-1563	65	30	results	result	VERB
ejpam-1563	65	31	for	for	ADP
ejpam-1563	65	32	generalized	generalized	ADJ
ejpam-1563	65	33	vector	vector	NOUN
ejpam-1563	65	34	equilibrium	equilibrium	NOUN
ejpam-1563	65	35	problems	problem	NOUN
ejpam-1563	65	36	(	(	PUNCT
ejpam-1563	65	37	gvep1	gvep1	NOUN
ejpam-1563	65	38	)	)	PUNCT
ejpam-1563	65	39	and	and	CCONJ
ejpam-1563	65	40	(	(	PUNCT
ejpam-1563	65	41	gvep2	gvep2	PROPN
ejpam-1563	65	42	)	)	PUNCT
ejpam-1563	65	43	on	on	ADP
ejpam-1563	65	44	a	a	DET
ejpam-1563	65	45	compact	compact	ADJ
ejpam-1563	65	46	set	set	NOUN
ejpam-1563	65	47	k	k	PROPN
ejpam-1563	65	48	.	.	PUNCT
ejpam-1563	66	1	the	the	DET
ejpam-1563	66	2	proofs	proof	NOUN
ejpam-1563	66	3	are	be	AUX
ejpam-1563	66	4	based	base	VERB
ejpam-1563	66	5	on	on	ADP
ejpam-1563	66	6	lemma	lemma	PROPN
ejpam-1563	66	7	1	1	NUM
ejpam-1563	66	8	,	,	PUNCT
ejpam-1563	66	9	with	with	ADP
ejpam-1563	66	10	a(x	a(x	NOUN
ejpam-1563	66	11	)	)	PUNCT
ejpam-1563	66	12	=	=	PUNCT
ejpam-1563	66	13	φ+(v	φ+(v	NOUN
ejpam-1563	66	14	(	(	PUNCT
ejpam-1563	66	15	x	x	NOUN
ejpam-1563	66	16	)	)	PUNCT
ejpam-1563	66	17	)	)	PUNCT
ejpam-1563	66	18	and	and	CCONJ
ejpam-1563	66	19	a(x	a(x	PROPN
ejpam-1563	66	20	)	)	PUNCT
ejpam-1563	66	21	=	=	SYM
ejpam-1563	66	22	φ−(v	φ−(v	NOUN
ejpam-1563	66	23	(	(	PUNCT
ejpam-1563	66	24	x	x	NOUN
ejpam-1563	66	25	)	)	PUNCT
ejpam-1563	66	26	)	)	PUNCT
ejpam-1563	66	27	for	for	ADP
ejpam-1563	66	28	all	all	DET
ejpam-1563	66	29	x	x	SYM
ejpam-1563	66	30	∈	∈	PROPN
ejpam-1563	66	31	k	k	PROPN
ejpam-1563	66	32	,	,	PUNCT
ejpam-1563	66	33	respectively	respectively	ADV
ejpam-1563	66	34	,	,	PUNCT
ejpam-1563	66	35	where	where	SCONJ
ejpam-1563	66	36	the	the	DET
ejpam-1563	66	37	upper	upper	ADJ
ejpam-1563	66	38	and	and	CCONJ
ejpam-1563	66	39	lower	low	ADJ
ejpam-1563	66	40	inverse	inverse	NOUN
ejpam-1563	66	41	mappings	mapping	NOUN
ejpam-1563	66	42	of	of	ADP
ejpam-1563	66	43	φ	φ	PROPN
ejpam-1563	66	44	are	be	AUX
ejpam-1563	66	45	defined	define	VERB
ejpam-1563	66	46	as	as	ADP
ejpam-1563	66	47	φ+(z	φ+(z	NOUN
ejpam-1563	66	48	)	)	PUNCT
ejpam-1563	66	49	=	=	SYM
ejpam-1563	67	1	{	{	PUNCT
ejpam-1563	67	2	(	(	PUNCT
ejpam-1563	67	3	x	x	INTJ
ejpam-1563	67	4	,	,	PUNCT
ejpam-1563	67	5	y	y	PROPN
ejpam-1563	67	6	)	)	PUNCT
ejpam-1563	67	7	∈	∈	PROPN
ejpam-1563	68	1	k	k	NOUN
ejpam-1563	68	2	×	×	PROPN
ejpam-1563	68	3	k	k	NOUN
ejpam-1563	68	4	:	:	PUNCT
ejpam-1563	68	5	φ(x	φ(x	PROPN
ejpam-1563	68	6	,	,	PUNCT
ejpam-1563	68	7	y)⊆	y)⊆	PROPN
ejpam-1563	68	8	z	z	NOUN
ejpam-1563	68	9	}	}	PUNCT
ejpam-1563	68	10	,	,	PUNCT
ejpam-1563	68	11	φ−(z	φ−(z	PROPN
ejpam-1563	68	12	)	)	PUNCT
ejpam-1563	68	13	=	=	PRON
ejpam-1563	68	14	{	{	PUNCT
ejpam-1563	68	15	(	(	PUNCT
ejpam-1563	68	16	x	x	INTJ
ejpam-1563	68	17	,	,	PUNCT
ejpam-1563	68	18	y	y	PROPN
ejpam-1563	68	19	)	)	PUNCT
ejpam-1563	68	20	∈	∈	PROPN
ejpam-1563	69	1	k	k	NOUN
ejpam-1563	69	2	×	×	PROPN
ejpam-1563	69	3	k	k	NOUN
ejpam-1563	69	4	:	:	PUNCT
ejpam-1563	69	5	φ(x	φ(x	PROPN
ejpam-1563	69	6	,	,	PUNCT
ejpam-1563	69	7	y)∩	y)∩	PROPN
ejpam-1563	69	8	z	z	PROPN
ejpam-1563	69	9	6=	6=	NUM
ejpam-1563	69	10	;	;	PUNCT
ejpam-1563	69	11	}	}	PUNCT
ejpam-1563	69	12	,	,	PUNCT
ejpam-1563	69	13	for	for	ADP
ejpam-1563	69	14	all	all	DET
ejpam-1563	69	15	z	z	NOUN
ejpam-1563	69	16	⊆	⊆	NUM
ejpam-1563	69	17	y	y	PROPN
ejpam-1563	69	18	.	.	PUNCT
ejpam-1563	70	1	theorem	theorem	NOUN
ejpam-1563	70	2	1	1	X
ejpam-1563	70	3	.	.	PUNCT
ejpam-1563	71	1	let	let	VERB
ejpam-1563	71	2	x	x	PRON
ejpam-1563	71	3	be	be	AUX
ejpam-1563	71	4	a	a	DET
ejpam-1563	71	5	reflexive	reflexive	ADJ
ejpam-1563	71	6	banach	banach	NOUN
ejpam-1563	71	7	space	space	NOUN
ejpam-1563	71	8	,	,	PUNCT
ejpam-1563	71	9	y	y	PROPN
ejpam-1563	71	10	be	be	AUX
ejpam-1563	71	11	a	a	DET
ejpam-1563	71	12	banach	banach	NOUN
ejpam-1563	71	13	space	space	NOUN
ejpam-1563	71	14	,	,	PUNCT
ejpam-1563	71	15	k	k	X
ejpam-1563	71	16	be	be	AUX
ejpam-1563	71	17	a	a	DET
ejpam-1563	71	18	nonempty	nonempty	ADJ
ejpam-1563	71	19	,	,	PUNCT
ejpam-1563	71	20	closed	closed	ADJ
ejpam-1563	71	21	,	,	PUNCT
ejpam-1563	71	22	convex	convex	NOUN
ejpam-1563	71	23	and	and	CCONJ
ejpam-1563	71	24	bounded	bound	VERB
ejpam-1563	71	25	subset	subset	NOUN
ejpam-1563	71	26	of	of	ADP
ejpam-1563	71	27	x	x	PUNCT
ejpam-1563	71	28	and	and	CCONJ
ejpam-1563	71	29	let	let	VERB
ejpam-1563	71	30	v	v	X
ejpam-1563	71	31	:	:	PUNCT
ejpam-1563	71	32	k	k	PROPN
ejpam-1563	71	33	→	→	SYM
ejpam-1563	71	34	π(y	π(y	PROPN
ejpam-1563	71	35	)	)	PUNCT
ejpam-1563	71	36	map	map	VERB
ejpam-1563	71	37	any	any	DET
ejpam-1563	71	38	x	x	SYM
ejpam-1563	71	39	∈	∈	PROPN
ejpam-1563	71	40	k	k	NOUN
ejpam-1563	71	41	to	to	ADP
ejpam-1563	71	42	a	a	DET
ejpam-1563	71	43	nonempty	nonempty	ADV
ejpam-1563	71	44	set	set	VERB
ejpam-1563	71	45	v	v	NOUN
ejpam-1563	71	46	(	(	PUNCT
ejpam-1563	71	47	x)⊆	x)⊆	PROPN
ejpam-1563	71	48	y	y	PROPN
ejpam-1563	71	49	such	such	ADJ
ejpam-1563	71	50	that	that	PRON
ejpam-1563	71	51	0	0	NUM
ejpam-1563	71	52	/∈	/∈	SYM
ejpam-1563	71	53	v	v	ADJ
ejpam-1563	71	54	(	(	PUNCT
ejpam-1563	71	55	x	x	NOUN
ejpam-1563	71	56	)	)	PUNCT
ejpam-1563	71	57	.	.	PUNCT
ejpam-1563	72	1	moreover	moreover	ADV
ejpam-1563	72	2	,	,	PUNCT
ejpam-1563	72	3	let	let	VERB
ejpam-1563	72	4	φ	φ	NOUN
ejpam-1563	72	5	:	:	PUNCT
ejpam-1563	73	1	k	k	PROPN
ejpam-1563	73	2	×	×	PROPN
ejpam-1563	73	3	k	k	PROPN
ejpam-1563	73	4	→	→	SYM
ejpam-1563	73	5	π(y	π(y	PROPN
ejpam-1563	73	6	)	)	PUNCT
ejpam-1563	73	7	be	be	AUX
ejpam-1563	73	8	such	such	ADJ
ejpam-1563	73	9	that	that	PRON
ejpam-1563	73	10	:	:	PUNCT
ejpam-1563	73	11	(	(	PUNCT
ejpam-1563	73	12	i	i	NOUN
ejpam-1563	73	13	)	)	PUNCT
ejpam-1563	73	14	φ(x	φ(x	PROPN
ejpam-1563	73	15	,	,	PUNCT
ejpam-1563	73	16	x	x	X
ejpam-1563	73	17	)	)	PUNCT
ejpam-1563	73	18	=	=	SYM
ejpam-1563	73	19	{	{	PUNCT
ejpam-1563	73	20	0	0	NUM
ejpam-1563	73	21	}	}	PUNCT
ejpam-1563	73	22	,	,	PUNCT
ejpam-1563	73	23	for	for	ADP
ejpam-1563	73	24	all	all	DET
ejpam-1563	73	25	x	x	SYM
ejpam-1563	73	26	∈	∈	PROPN
ejpam-1563	73	27	k	k	NOUN
ejpam-1563	73	28	;	;	PUNCT
ejpam-1563	73	29	(	(	PUNCT
ejpam-1563	73	30	ii	ii	NOUN
ejpam-1563	73	31	)	)	PUNCT
ejpam-1563	73	32	for	for	ADP
ejpam-1563	73	33	any	any	DET
ejpam-1563	73	34	fixed	fix	VERB
ejpam-1563	73	35	x	x	SYM
ejpam-1563	73	36	∈	∈	PROPN
ejpam-1563	73	37	k	k	NOUN
ejpam-1563	73	38	,	,	PUNCT
ejpam-1563	73	39	the	the	DET
ejpam-1563	73	40	set	set	NOUN
ejpam-1563	73	41	{	{	PUNCT
ejpam-1563	73	42	y	y	PROPN
ejpam-1563	73	43	∈	∈	PROPN
ejpam-1563	73	44	k	k	NOUN
ejpam-1563	73	45	:	:	PUNCT
ejpam-1563	73	46	φ(x	φ(x	PROPN
ejpam-1563	73	47	,	,	PUNCT
ejpam-1563	73	48	y)⊆	y)⊆	PROPN
ejpam-1563	73	49	v	v	X
ejpam-1563	73	50	(	(	PUNCT
ejpam-1563	73	51	x	x	NOUN
ejpam-1563	73	52	)	)	PUNCT
ejpam-1563	73	53	}	}	PUNCT
ejpam-1563	73	54	is	be	AUX
ejpam-1563	73	55	convex	convex	ADJ
ejpam-1563	73	56	;	;	PUNCT
ejpam-1563	73	57	(	(	PUNCT
ejpam-1563	73	58	iii	iii	NOUN
ejpam-1563	73	59	)	)	PUNCT
ejpam-1563	73	60	for	for	ADP
ejpam-1563	73	61	any	any	DET
ejpam-1563	73	62	fixed	fix	VERB
ejpam-1563	73	63	y	y	PROPN
ejpam-1563	73	64	∈	∈	PROPN
ejpam-1563	73	65	k	k	PROPN
ejpam-1563	73	66	,	,	PUNCT
ejpam-1563	73	67	the	the	DET
ejpam-1563	73	68	set	set	NOUN
ejpam-1563	73	69	{	{	PUNCT
ejpam-1563	73	70	x	x	SYM
ejpam-1563	73	71	∈	∈	PROPN
ejpam-1563	73	72	k	k	NOUN
ejpam-1563	73	73	:	:	PUNCT
ejpam-1563	73	74	φ(x	φ(x	PROPN
ejpam-1563	73	75	,	,	PUNCT
ejpam-1563	73	76	y	y	PROPN
ejpam-1563	73	77	)	)	PUNCT
ejpam-1563	73	78	6⊆	6⊆	PROPN
ejpam-1563	73	79	v	v	SYM
ejpam-1563	73	80	(	(	PUNCT
ejpam-1563	73	81	x	x	NOUN
ejpam-1563	73	82	)	)	PUNCT
ejpam-1563	73	83	}	}	PUNCT
ejpam-1563	73	84	is	be	AUX
ejpam-1563	73	85	closed	close	VERB
ejpam-1563	73	86	with	with	ADP
ejpam-1563	73	87	respect	respect	NOUN
ejpam-1563	73	88	to	to	ADP
ejpam-1563	73	89	the	the	DET
ejpam-1563	73	90	topology	topology	NOUN
ejpam-1563	73	91	induced	induce	VERB
ejpam-1563	73	92	on	on	ADP
ejpam-1563	73	93	k	k	X
ejpam-1563	73	94	by	by	ADP
ejpam-1563	73	95	the	the	DET
ejpam-1563	73	96	weak	weak	ADJ
ejpam-1563	73	97	topology	topology	NOUN
ejpam-1563	73	98	of	of	ADP
ejpam-1563	73	99	x	x	X
ejpam-1563	73	100	.	.	PUNCT
ejpam-1563	74	1	then	then	ADV
ejpam-1563	74	2	,	,	PUNCT
ejpam-1563	74	3	s1	s1	PROPN
ejpam-1563	74	4	k	k	PROPN
ejpam-1563	74	5	6=	6=	PROPN
ejpam-1563	74	6	;	;	PUNCT
ejpam-1563	74	7	.	.	PUNCT
ejpam-1563	75	1	proof	proof	NOUN
ejpam-1563	75	2	.	.	PUNCT
ejpam-1563	76	1	let	let	VERB
ejpam-1563	76	2	a	a	PRON
ejpam-1563	76	3	:	:	PUNCT
ejpam-1563	76	4	k	k	X
ejpam-1563	76	5	→	→	PROPN
ejpam-1563	76	6	π(k	π(k	PROPN
ejpam-1563	76	7	×	×	PROPN
ejpam-1563	76	8	k	k	NOUN
ejpam-1563	76	9	)	)	PUNCT
ejpam-1563	76	10	be	be	AUX
ejpam-1563	76	11	defined	define	VERB
ejpam-1563	76	12	as	as	ADP
ejpam-1563	76	13	a(x	a(x	NOUN
ejpam-1563	76	14	)	)	PUNCT
ejpam-1563	76	15	=	=	PUNCT
ejpam-1563	76	16	φ+(v	φ+(v	NOUN
ejpam-1563	76	17	(	(	PUNCT
ejpam-1563	76	18	x	x	NOUN
ejpam-1563	76	19	)	)	PUNCT
ejpam-1563	76	20	)	)	PUNCT
ejpam-1563	76	21	for	for	ADP
ejpam-1563	76	22	all	all	DET
ejpam-1563	76	23	x	x	SYM
ejpam-1563	76	24	∈	∈	PROPN
ejpam-1563	76	25	k	k	X
ejpam-1563	76	26	.	.	PUNCT
ejpam-1563	77	1	by	by	ADP
ejpam-1563	77	2	(	(	PUNCT
ejpam-1563	77	3	i	i	NOUN
ejpam-1563	77	4	)	)	PUNCT
ejpam-1563	77	5	,	,	PUNCT
ejpam-1563	77	6	φ(x	φ(x	PROPN
ejpam-1563	77	7	,	,	PUNCT
ejpam-1563	77	8	x	x	X
ejpam-1563	77	9	)	)	PUNCT
ejpam-1563	77	10	6⊆	6⊆	NUM
ejpam-1563	77	11	v	v	SYM
ejpam-1563	77	12	(	(	PUNCT
ejpam-1563	77	13	x	x	NOUN
ejpam-1563	77	14	)	)	PUNCT
ejpam-1563	77	15	,	,	PUNCT
ejpam-1563	77	16	i.e.	i.e.	X
ejpam-1563	77	17	(	(	PUNCT
ejpam-1563	77	18	x	x	INTJ
ejpam-1563	77	19	,	,	PUNCT
ejpam-1563	77	20	x	x	NOUN
ejpam-1563	77	21	)	)	PUNCT
ejpam-1563	77	22	/∈	/∈	PUNCT
ejpam-1563	77	23	a(x	a(x	NOUN
ejpam-1563	77	24	)	)	PUNCT
ejpam-1563	77	25	.	.	PUNCT
ejpam-1563	78	1	by	by	ADP
ejpam-1563	78	2	(	(	PUNCT
ejpam-1563	78	3	ii	ii	NOUN
ejpam-1563	78	4	)	)	PUNCT
ejpam-1563	78	5	,	,	PUNCT
ejpam-1563	78	6	the	the	DET
ejpam-1563	78	7	set	set	NOUN
ejpam-1563	78	8	{	{	PUNCT
ejpam-1563	78	9	y	y	PROPN
ejpam-1563	78	10	∈	∈	PROPN
ejpam-1563	78	11	k	k	NOUN
ejpam-1563	78	12	:	:	PUNCT
ejpam-1563	78	13	(	(	PUNCT
ejpam-1563	78	14	x	x	X
ejpam-1563	78	15	,	,	PUNCT
ejpam-1563	78	16	y	y	PROPN
ejpam-1563	78	17	)	)	PUNCT
ejpam-1563	78	18	∈	∈	PROPN
ejpam-1563	78	19	a(x	a(x	NOUN
ejpam-1563	78	20	)	)	PUNCT
ejpam-1563	78	21	}	}	PUNCT
ejpam-1563	78	22	is	be	AUX
ejpam-1563	78	23	convex	convex	ADJ
ejpam-1563	78	24	for	for	ADP
ejpam-1563	78	25	all	all	DET
ejpam-1563	78	26	x	x	SYM
ejpam-1563	78	27	∈	∈	PROPN
ejpam-1563	78	28	k	k	NOUN
ejpam-1563	78	29	,	,	PUNCT
ejpam-1563	78	30	while	while	SCONJ
ejpam-1563	78	31	,	,	PUNCT
ejpam-1563	78	32	by	by	ADP
ejpam-1563	78	33	(	(	PUNCT
ejpam-1563	78	34	iii	iii	NOUN
ejpam-1563	78	35	)	)	PUNCT
ejpam-1563	78	36	,	,	PUNCT
ejpam-1563	78	37	{	{	PUNCT
ejpam-1563	78	38	x	x	PUNCT
ejpam-1563	78	39	∈	∈	PROPN
ejpam-1563	78	40	k	k	NOUN
ejpam-1563	78	41	:	:	PUNCT
ejpam-1563	78	42	(	(	PUNCT
ejpam-1563	78	43	x	x	X
ejpam-1563	78	44	,	,	PUNCT
ejpam-1563	78	45	y	y	PROPN
ejpam-1563	78	46	)	)	PUNCT
ejpam-1563	78	47	/∈	/∈	PUNCT
ejpam-1563	79	1	a(x	a(x	NOUN
ejpam-1563	79	2	)	)	PUNCT
ejpam-1563	79	3	}	}	PUNCT
ejpam-1563	79	4	is	be	AUX
ejpam-1563	79	5	closed	close	VERB
ejpam-1563	79	6	for	for	ADP
ejpam-1563	79	7	all	all	DET
ejpam-1563	79	8	y	y	PROPN
ejpam-1563	79	9	∈	∈	PROPN
ejpam-1563	79	10	k	k	X
ejpam-1563	79	11	.	.	PUNCT
ejpam-1563	80	1	then	then	ADV
ejpam-1563	80	2	,	,	PUNCT
ejpam-1563	80	3	by	by	ADP
ejpam-1563	80	4	lemma	lemma	PROPN
ejpam-1563	80	5	1	1	NUM
ejpam-1563	80	6	,	,	PUNCT
ejpam-1563	80	7	there	there	PRON
ejpam-1563	80	8	exists	exist	VERB
ejpam-1563	80	9	x	x	X
ejpam-1563	80	10	∈	∈	PROPN
ejpam-1563	80	11	k	k	NOUN
ejpam-1563	80	12	such	such	ADJ
ejpam-1563	80	13	that	that	SCONJ
ejpam-1563	80	14	φ(x	φ(x	PROPN
ejpam-1563	80	15	,	,	PUNCT
ejpam-1563	80	16	y	y	PROPN
ejpam-1563	80	17	)	)	PUNCT
ejpam-1563	80	18	6⊆	6⊆	PROPN
ejpam-1563	80	19	v	v	SYM
ejpam-1563	80	20	(	(	PUNCT
ejpam-1563	80	21	x	x	NOUN
ejpam-1563	80	22	)	)	PUNCT
ejpam-1563	80	23	for	for	ADP
ejpam-1563	80	24	all	all	DET
ejpam-1563	80	25	y	y	PROPN
ejpam-1563	80	26	∈	∈	PROPN
ejpam-1563	80	27	k	k	X
ejpam-1563	80	28	.	.	PUNCT
ejpam-1563	81	1	theorem	theorem	PROPN
ejpam-1563	81	2	2	2	NUM
ejpam-1563	81	3	.	.	PUNCT
ejpam-1563	82	1	let	let	VERB
ejpam-1563	82	2	x	x	PRON
ejpam-1563	82	3	be	be	AUX
ejpam-1563	82	4	a	a	DET
ejpam-1563	82	5	reflexive	reflexive	ADJ
ejpam-1563	82	6	banach	banach	NOUN
ejpam-1563	82	7	space	space	NOUN
ejpam-1563	82	8	,	,	PUNCT
ejpam-1563	82	9	y	y	PROPN
ejpam-1563	82	10	be	be	AUX
ejpam-1563	82	11	a	a	DET
ejpam-1563	82	12	banach	banach	NOUN
ejpam-1563	82	13	space	space	NOUN
ejpam-1563	82	14	,	,	PUNCT
ejpam-1563	82	15	k	k	X
ejpam-1563	82	16	be	be	AUX
ejpam-1563	82	17	a	a	DET
ejpam-1563	82	18	nonempty	nonempty	ADJ
ejpam-1563	82	19	,	,	PUNCT
ejpam-1563	82	20	closed	closed	ADJ
ejpam-1563	82	21	,	,	PUNCT
ejpam-1563	82	22	convex	convex	NOUN
ejpam-1563	82	23	and	and	CCONJ
ejpam-1563	82	24	bounded	bound	VERB
ejpam-1563	82	25	subset	subset	NOUN
ejpam-1563	82	26	of	of	ADP
ejpam-1563	82	27	x	x	PUNCT
ejpam-1563	82	28	and	and	CCONJ
ejpam-1563	82	29	let	let	VERB
ejpam-1563	82	30	v	v	X
ejpam-1563	82	31	:	:	PUNCT
ejpam-1563	82	32	k	k	PROPN
ejpam-1563	82	33	→	→	SYM
ejpam-1563	82	34	π(y	π(y	PROPN
ejpam-1563	82	35	)	)	PUNCT
ejpam-1563	82	36	map	map	VERB
ejpam-1563	82	37	any	any	DET
ejpam-1563	82	38	x	x	SYM
ejpam-1563	82	39	∈	∈	PROPN
ejpam-1563	82	40	k	k	PROPN
ejpam-1563	82	41	to	to	ADP
ejpam-1563	82	42	a	a	DET
ejpam-1563	82	43	set	set	NOUN
ejpam-1563	82	44	v	v	NOUN
ejpam-1563	82	45	(	(	PUNCT
ejpam-1563	82	46	x	x	NOUN
ejpam-1563	82	47	)	)	PUNCT
ejpam-1563	82	48	⊆	⊆	NUM
ejpam-1563	82	49	y	y	NUM
ejpam-1563	82	50	such	such	ADJ
ejpam-1563	82	51	that	that	PRON
ejpam-1563	82	52	0	0	NUM
ejpam-1563	82	53	/∈	/∈	SYM
ejpam-1563	83	1	v	v	ADJ
ejpam-1563	83	2	(	(	PUNCT
ejpam-1563	83	3	x	x	NOUN
ejpam-1563	83	4	)	)	PUNCT
ejpam-1563	83	5	.	.	PUNCT
ejpam-1563	84	1	moreover	moreover	ADV
ejpam-1563	84	2	,	,	PUNCT
ejpam-1563	84	3	let	let	VERB
ejpam-1563	84	4	φ	φ	NOUN
ejpam-1563	84	5	:	:	PUNCT
ejpam-1563	85	1	k	k	PROPN
ejpam-1563	85	2	×	×	PROPN
ejpam-1563	85	3	k	k	PROPN
ejpam-1563	85	4	→	→	SYM
ejpam-1563	85	5	π(y	π(y	PROPN
ejpam-1563	85	6	)	)	PUNCT
ejpam-1563	85	7	be	be	AUX
ejpam-1563	85	8	such	such	ADJ
ejpam-1563	85	9	that	that	PRON
ejpam-1563	85	10	:	:	PUNCT
ejpam-1563	85	11	(	(	PUNCT
ejpam-1563	85	12	i	i	NOUN
ejpam-1563	85	13	)	)	PUNCT
ejpam-1563	85	14	φ(x	φ(x	PROPN
ejpam-1563	85	15	,	,	PUNCT
ejpam-1563	85	16	x	x	X
ejpam-1563	85	17	)	)	PUNCT
ejpam-1563	85	18	=	=	SYM
ejpam-1563	85	19	{	{	PUNCT
ejpam-1563	85	20	0	0	NUM
ejpam-1563	85	21	}	}	PUNCT
ejpam-1563	85	22	,	,	PUNCT
ejpam-1563	85	23	for	for	ADP
ejpam-1563	85	24	all	all	DET
ejpam-1563	85	25	x	x	SYM
ejpam-1563	85	26	∈	∈	PROPN
ejpam-1563	85	27	k	k	NOUN
ejpam-1563	85	28	;	;	PUNCT
ejpam-1563	85	29	(	(	PUNCT
ejpam-1563	85	30	ii	ii	NOUN
ejpam-1563	85	31	)	)	PUNCT
ejpam-1563	85	32	for	for	ADP
ejpam-1563	85	33	any	any	DET
ejpam-1563	85	34	fixed	fix	VERB
ejpam-1563	85	35	x	x	SYM
ejpam-1563	85	36	∈	∈	PROPN
ejpam-1563	85	37	k	k	NOUN
ejpam-1563	85	38	,	,	PUNCT
ejpam-1563	85	39	the	the	DET
ejpam-1563	85	40	set	set	NOUN
ejpam-1563	85	41	{	{	PUNCT
ejpam-1563	85	42	y	y	PROPN
ejpam-1563	85	43	∈	∈	PROPN
ejpam-1563	85	44	k	k	NOUN
ejpam-1563	85	45	:	:	PUNCT
ejpam-1563	85	46	φ(x	φ(x	PROPN
ejpam-1563	85	47	,	,	PUNCT
ejpam-1563	85	48	y)∩	y)∩	PROPN
ejpam-1563	85	49	v	v	PROPN
ejpam-1563	85	50	(	(	PUNCT
ejpam-1563	85	51	x	x	X
ejpam-1563	85	52	)	)	PUNCT
ejpam-1563	85	53	6=	6=	NUM
ejpam-1563	85	54	;	;	PUNCT
ejpam-1563	85	55	}	}	PUNCT
ejpam-1563	85	56	is	be	AUX
ejpam-1563	85	57	convex	convex	ADJ
ejpam-1563	85	58	;	;	PUNCT
ejpam-1563	85	59	(	(	PUNCT
ejpam-1563	85	60	iii	iii	NOUN
ejpam-1563	85	61	)	)	PUNCT
ejpam-1563	85	62	for	for	ADP
ejpam-1563	85	63	any	any	DET
ejpam-1563	85	64	fixed	fix	VERB
ejpam-1563	85	65	y	y	PROPN
ejpam-1563	85	66	∈	∈	PROPN
ejpam-1563	85	67	k	k	PROPN
ejpam-1563	85	68	,	,	PUNCT
ejpam-1563	85	69	the	the	DET
ejpam-1563	85	70	set	set	NOUN
ejpam-1563	85	71	{	{	PUNCT
ejpam-1563	85	72	x	x	SYM
ejpam-1563	85	73	∈	∈	PROPN
ejpam-1563	85	74	k	k	NOUN
ejpam-1563	85	75	:	:	PUNCT
ejpam-1563	85	76	φ(x	φ(x	PROPN
ejpam-1563	85	77	,	,	PUNCT
ejpam-1563	85	78	y	y	NOUN
ejpam-1563	85	79	)	)	PUNCT
ejpam-1563	85	80	∩	∩	ADJ
ejpam-1563	85	81	v	v	X
ejpam-1563	85	82	(	(	PUNCT
ejpam-1563	85	83	x	x	NOUN
ejpam-1563	85	84	)	)	PUNCT
ejpam-1563	85	85	=	=	SYM
ejpam-1563	85	86	;	;	PUNCT
ejpam-1563	85	87	}	}	PUNCT
ejpam-1563	85	88	is	be	AUX
ejpam-1563	85	89	closed	close	VERB
ejpam-1563	85	90	with	with	ADP
ejpam-1563	85	91	respect	respect	NOUN
ejpam-1563	85	92	to	to	ADP
ejpam-1563	85	93	the	the	DET
ejpam-1563	85	94	topology	topology	NOUN
ejpam-1563	85	95	induced	induce	VERB
ejpam-1563	85	96	on	on	ADP
ejpam-1563	85	97	k	k	X
ejpam-1563	85	98	by	by	ADP
ejpam-1563	85	99	the	the	DET
ejpam-1563	85	100	weak	weak	ADJ
ejpam-1563	85	101	topology	topology	NOUN
ejpam-1563	85	102	of	of	ADP
ejpam-1563	85	103	x	x	X
ejpam-1563	85	104	.	.	PUNCT
ejpam-1563	86	1	then	then	ADV
ejpam-1563	86	2	,	,	PUNCT
ejpam-1563	86	3	s2	s2	PROPN
ejpam-1563	86	4	k	k	PROPN
ejpam-1563	86	5	6=	6=	PROPN
ejpam-1563	86	6	;	;	PUNCT
ejpam-1563	86	7	.	.	PUNCT
ejpam-1563	87	1	proof	proof	NOUN
ejpam-1563	87	2	.	.	PUNCT
ejpam-1563	88	1	let	let	VERB
ejpam-1563	88	2	a	a	PRON
ejpam-1563	88	3	:	:	PUNCT
ejpam-1563	88	4	k	k	X
ejpam-1563	88	5	→	→	PROPN
ejpam-1563	88	6	π(k	π(k	PROPN
ejpam-1563	88	7	×	×	PROPN
ejpam-1563	88	8	k	k	NOUN
ejpam-1563	88	9	)	)	PUNCT
ejpam-1563	88	10	be	be	AUX
ejpam-1563	88	11	defined	define	VERB
ejpam-1563	88	12	as	as	ADP
ejpam-1563	88	13	a(x	a(x	NOUN
ejpam-1563	88	14	)	)	PUNCT
ejpam-1563	88	15	=	=	SYM
ejpam-1563	88	16	φ−(v	φ−(v	NOUN
ejpam-1563	88	17	(	(	PUNCT
ejpam-1563	88	18	x	x	NOUN
ejpam-1563	88	19	)	)	PUNCT
ejpam-1563	88	20	)	)	PUNCT
ejpam-1563	88	21	for	for	ADP
ejpam-1563	88	22	all	all	PRON
ejpam-1563	88	23	x	x	SYM
ejpam-1563	88	24	∈	∈	PROPN
ejpam-1563	88	25	k	k	X
ejpam-1563	88	26	.	.	PUNCT
ejpam-1563	89	1	by	by	ADP
ejpam-1563	89	2	(	(	PUNCT
ejpam-1563	89	3	i	i	NOUN
ejpam-1563	89	4	)	)	PUNCT
ejpam-1563	89	5	,	,	PUNCT
ejpam-1563	89	6	φ(x	φ(x	PROPN
ejpam-1563	89	7	,	,	PUNCT
ejpam-1563	89	8	x)∩	x)∩	PROPN
ejpam-1563	89	9	v	v	X
ejpam-1563	89	10	(	(	PUNCT
ejpam-1563	89	11	x	x	NOUN
ejpam-1563	89	12	)	)	PUNCT
ejpam-1563	89	13	=	=	SYM
ejpam-1563	89	14	;	;	PUNCT
ejpam-1563	89	15	,	,	PUNCT
ejpam-1563	89	16	i.e.	i.e.	X
ejpam-1563	89	17	(	(	PUNCT
ejpam-1563	89	18	x	x	INTJ
ejpam-1563	89	19	,	,	PUNCT
ejpam-1563	89	20	x	x	NOUN
ejpam-1563	89	21	)	)	PUNCT
ejpam-1563	89	22	/∈	/∈	PUNCT
ejpam-1563	89	23	a(x	a(x	NOUN
ejpam-1563	89	24	)	)	PUNCT
ejpam-1563	89	25	.	.	PUNCT
ejpam-1563	90	1	by	by	ADP
ejpam-1563	90	2	(	(	PUNCT
ejpam-1563	90	3	ii	ii	NOUN
ejpam-1563	90	4	)	)	PUNCT
ejpam-1563	90	5	,	,	PUNCT
ejpam-1563	90	6	the	the	DET
ejpam-1563	90	7	set	set	NOUN
ejpam-1563	90	8	{	{	PUNCT
ejpam-1563	90	9	y	y	PROPN
ejpam-1563	90	10	∈	∈	PROPN
ejpam-1563	90	11	k	k	NOUN
ejpam-1563	90	12	:	:	PUNCT
ejpam-1563	90	13	(	(	PUNCT
ejpam-1563	90	14	x	x	X
ejpam-1563	90	15	,	,	PUNCT
ejpam-1563	90	16	y	y	PROPN
ejpam-1563	90	17	)	)	PUNCT
ejpam-1563	90	18	∈	∈	PROPN
ejpam-1563	90	19	a(x	a(x	NOUN
ejpam-1563	90	20	)	)	PUNCT
ejpam-1563	90	21	}	}	PUNCT
ejpam-1563	90	22	is	be	AUX
ejpam-1563	90	23	convex	convex	ADJ
ejpam-1563	90	24	for	for	ADP
ejpam-1563	90	25	all	all	DET
ejpam-1563	90	26	x	x	SYM
ejpam-1563	90	27	∈	∈	PROPN
ejpam-1563	90	28	k	k	NOUN
ejpam-1563	90	29	,	,	PUNCT
ejpam-1563	90	30	while	while	SCONJ
ejpam-1563	90	31	,	,	PUNCT
ejpam-1563	90	32	by	by	ADP
ejpam-1563	90	33	(	(	PUNCT
ejpam-1563	90	34	iii	iii	NOUN
ejpam-1563	90	35	)	)	PUNCT
ejpam-1563	90	36	,	,	PUNCT
ejpam-1563	90	37	{	{	PUNCT
ejpam-1563	90	38	x	x	PUNCT
ejpam-1563	90	39	∈	∈	PROPN
ejpam-1563	90	40	k	k	NOUN
ejpam-1563	90	41	:	:	PUNCT
ejpam-1563	90	42	(	(	PUNCT
ejpam-1563	90	43	x	x	X
ejpam-1563	90	44	,	,	PUNCT
ejpam-1563	90	45	y	y	PROPN
ejpam-1563	90	46	)	)	PUNCT
ejpam-1563	90	47	/∈	/∈	PUNCT
ejpam-1563	91	1	a(x	a(x	NOUN
ejpam-1563	91	2	)	)	PUNCT
ejpam-1563	91	3	}	}	PUNCT
ejpam-1563	91	4	is	be	AUX
ejpam-1563	91	5	closed	close	VERB
ejpam-1563	91	6	for	for	ADP
ejpam-1563	91	7	all	all	DET
ejpam-1563	91	8	y	y	PROPN
ejpam-1563	91	9	∈	∈	PROPN
ejpam-1563	91	10	k	k	X
ejpam-1563	91	11	.	.	PUNCT
ejpam-1563	92	1	then	then	ADV
ejpam-1563	92	2	,	,	PUNCT
ejpam-1563	92	3	by	by	ADP
ejpam-1563	92	4	lemma	lemma	PROPN
ejpam-1563	92	5	1	1	NUM
ejpam-1563	92	6	,	,	PUNCT
ejpam-1563	92	7	there	there	PRON
ejpam-1563	92	8	exists	exist	VERB
ejpam-1563	92	9	x	x	X
ejpam-1563	92	10	∈	∈	PROPN
ejpam-1563	92	11	k	k	NOUN
ejpam-1563	92	12	such	such	ADJ
ejpam-1563	92	13	that	that	SCONJ
ejpam-1563	92	14	φ(x	φ(x	PROPN
ejpam-1563	92	15	,	,	PUNCT
ejpam-1563	92	16	y)∩	y)∩	PROPN
ejpam-1563	92	17	v	v	PROPN
ejpam-1563	92	18	(	(	PUNCT
ejpam-1563	92	19	x	x	NOUN
ejpam-1563	92	20	)	)	PUNCT
ejpam-1563	92	21	=	=	SYM
ejpam-1563	92	22	;	;	PUNCT
ejpam-1563	92	23	for	for	ADP
ejpam-1563	92	24	all	all	DET
ejpam-1563	92	25	y	y	PROPN
ejpam-1563	92	26	∈	∈	PROPN
ejpam-1563	92	27	k	k	PROPN
ejpam-1563	92	28	.	.	PUNCT
ejpam-1563	93	1	e.	e.	PROPN
ejpam-1563	93	2	allevi	allevi	PROPN
ejpam-1563	93	3	,	,	PUNCT
ejpam-1563	93	4	i.	i.	PROPN
ejpam-1563	93	5	konnov	konnov	PROPN
ejpam-1563	93	6	,	,	PUNCT
ejpam-1563	93	7	m.	m.	NOUN
ejpam-1563	93	8	rocco	rocco	NOUN
ejpam-1563	93	9	/	/	SYM
ejpam-1563	93	10	eur	eur	PROPN
ejpam-1563	93	11	.	.	PUNCT
ejpam-1563	94	1	j.	j.	PROPN
ejpam-1563	94	2	pure	pure	PROPN
ejpam-1563	94	3	appl	appl	PROPN
ejpam-1563	94	4	.	.	PROPN
ejpam-1563	94	5	math	math	PROPN
ejpam-1563	94	6	,	,	PUNCT
ejpam-1563	94	7	6	6	NUM
ejpam-1563	94	8	(	(	PUNCT
ejpam-1563	94	9	2013	2013	NUM
ejpam-1563	94	10	)	)	PUNCT
ejpam-1563	94	11	,	,	PUNCT
ejpam-1563	94	12	365	365	NUM
ejpam-1563	94	13	-	-	SYM
ejpam-1563	94	14	376	376	NUM
ejpam-1563	94	15	369	369	NUM
ejpam-1563	94	16	remark	remark	NOUN
ejpam-1563	94	17	2	2	NUM
ejpam-1563	94	18	.	.	PUNCT
ejpam-1563	95	1	ky	ky	PROPN
ejpam-1563	95	2	fan	fan	PROPN
ejpam-1563	95	3	’s	’s	PART
ejpam-1563	95	4	lemma	lemma	PROPN
ejpam-1563	95	5	[	[	X
ejpam-1563	95	6	5	5	NUM
ejpam-1563	95	7	,	,	PUNCT
ejpam-1563	95	8	lemma	lemma	PROPN
ejpam-1563	95	9	1	1	NUM
ejpam-1563	95	10	]	]	PUNCT
ejpam-1563	95	11	is	be	AUX
ejpam-1563	95	12	the	the	DET
ejpam-1563	95	13	standard	standard	ADJ
ejpam-1563	95	14	tool	tool	NOUN
ejpam-1563	95	15	to	to	PART
ejpam-1563	95	16	derive	derive	VERB
ejpam-1563	95	17	existence	existence	NOUN
ejpam-1563	95	18	results	result	NOUN
ejpam-1563	95	19	for	for	ADP
ejpam-1563	95	20	equilibrium	equilibrium	NOUN
ejpam-1563	95	21	problems	problem	NOUN
ejpam-1563	95	22	on	on	ADP
ejpam-1563	95	23	bounded	bounded	ADJ
ejpam-1563	95	24	sets	set	NOUN
ejpam-1563	95	25	(	(	PUNCT
ejpam-1563	95	26	see	see	VERB
ejpam-1563	95	27	e.g.	e.g.	ADV
ejpam-1563	95	28	[	[	X
ejpam-1563	95	29	9	9	NUM
ejpam-1563	95	30	]	]	PUNCT
ejpam-1563	95	31	and	and	CCONJ
ejpam-1563	95	32	[	[	X
ejpam-1563	95	33	10	10	NUM
ejpam-1563	95	34	]	]	NUM
ejpam-1563	95	35	)	)	PUNCT
ejpam-1563	95	36	.	.	PUNCT
ejpam-1563	96	1	while	while	SCONJ
ejpam-1563	96	2	in	in	SCONJ
ejpam-1563	96	3	[	[	PUNCT
ejpam-1563	96	4	9	9	NUM
ejpam-1563	96	5	]	]	PUNCT
ejpam-1563	96	6	existence	existence	NOUN
ejpam-1563	96	7	of	of	ADP
ejpam-1563	96	8	solutions	solution	NOUN
ejpam-1563	96	9	is	be	AUX
ejpam-1563	96	10	obtained	obtain	VERB
ejpam-1563	96	11	based	base	VERB
ejpam-1563	96	12	on	on	ADP
ejpam-1563	96	13	a	a	DET
ejpam-1563	96	14	duality	duality	NOUN
ejpam-1563	96	15	approach	approach	NOUN
ejpam-1563	96	16	and	and	CCONJ
ejpam-1563	96	17	generalized	generalized	ADJ
ejpam-1563	96	18	monotonicity	monotonicity	NOUN
ejpam-1563	96	19	properties	property	NOUN
ejpam-1563	96	20	,	,	PUNCT
ejpam-1563	96	21	adapting	adapt	VERB
ejpam-1563	96	22	[	[	X
ejpam-1563	96	23	5	5	NUM
ejpam-1563	96	24	,	,	PUNCT
ejpam-1563	96	25	lemma	lemma	PROPN
ejpam-1563	96	26	4	4	NUM
ejpam-1563	96	27	]	]	PUNCT
ejpam-1563	96	28	enables	enable	VERB
ejpam-1563	96	29	us	we	PRON
ejpam-1563	96	30	to	to	PART
ejpam-1563	96	31	follow	follow	VERB
ejpam-1563	96	32	a	a	DET
ejpam-1563	96	33	more	more	ADV
ejpam-1563	96	34	direct	direct	ADJ
ejpam-1563	96	35	reasoning	reasoning	NOUN
ejpam-1563	96	36	,	,	PUNCT
ejpam-1563	96	37	that	that	PRON
ejpam-1563	96	38	avoids	avoid	VERB
ejpam-1563	96	39	both	both	DET
ejpam-1563	96	40	duality	duality	NOUN
ejpam-1563	96	41	and	and	CCONJ
ejpam-1563	96	42	monotonicity	monotonicity	NOUN
ejpam-1563	96	43	.	.	PUNCT
ejpam-1563	97	1	our	our	PRON
ejpam-1563	97	2	approach	approach	NOUN
ejpam-1563	97	3	in	in	ADP
ejpam-1563	97	4	formulating	formulate	VERB
ejpam-1563	97	5	the	the	DET
ejpam-1563	97	6	preceding	precede	VERB
ejpam-1563	97	7	theorems	theorem	NOUN
ejpam-1563	97	8	is	be	AUX
ejpam-1563	97	9	more	more	ADJ
ejpam-1563	97	10	in	in	ADP
ejpam-1563	97	11	the	the	DET
ejpam-1563	97	12	spirit	spirit	NOUN
ejpam-1563	97	13	of	of	ADP
ejpam-1563	97	14	[	[	X
ejpam-1563	97	15	10	10	NUM
ejpam-1563	97	16	]	]	PUNCT
ejpam-1563	97	17	.	.	PUNCT
ejpam-1563	98	1	anyway	anyway	INTJ
ejpam-1563	98	2	,	,	PUNCT
ejpam-1563	98	3	[	[	X
ejpam-1563	98	4	10	10	NUM
ejpam-1563	98	5	]	]	PUNCT
ejpam-1563	98	6	directly	directly	ADV
ejpam-1563	98	7	extends	extend	VERB
ejpam-1563	98	8	existence	existence	NOUN
ejpam-1563	98	9	results	result	NOUN
ejpam-1563	98	10	for	for	ADP
ejpam-1563	98	11	generalized	generalized	ADJ
ejpam-1563	98	12	vector	vector	NOUN
ejpam-1563	98	13	equilibrium	equilibrium	NOUN
ejpam-1563	98	14	problems	problem	NOUN
ejpam-1563	98	15	to	to	ADP
ejpam-1563	98	16	the	the	DET
ejpam-1563	98	17	case	case	NOUN
ejpam-1563	98	18	in	in	ADP
ejpam-1563	98	19	which	which	PRON
ejpam-1563	98	20	the	the	DET
ejpam-1563	98	21	set	set	NOUN
ejpam-1563	98	22	k	k	PROPN
ejpam-1563	98	23	is	be	AUX
ejpam-1563	98	24	unbounded	unbounded	ADJ
ejpam-1563	98	25	,	,	PUNCT
ejpam-1563	98	26	while	while	SCONJ
ejpam-1563	98	27	we	we	PRON
ejpam-1563	98	28	will	will	AUX
ejpam-1563	98	29	pursue	pursue	VERB
ejpam-1563	98	30	this	this	DET
ejpam-1563	98	31	task	task	NOUN
ejpam-1563	98	32	separately	separately	ADV
ejpam-1563	98	33	in	in	ADP
ejpam-1563	98	34	the	the	DET
ejpam-1563	98	35	following	follow	VERB
ejpam-1563	98	36	sections	section	NOUN
ejpam-1563	98	37	by	by	ADP
ejpam-1563	98	38	means	mean	NOUN
ejpam-1563	98	39	of	of	ADP
ejpam-1563	98	40	an	an	DET
ejpam-1563	98	41	apt	apt	ADJ
ejpam-1563	98	42	coercivity	coercivity	NOUN
ejpam-1563	98	43	condition	condition	NOUN
ejpam-1563	98	44	.	.	PUNCT
ejpam-1563	99	1	3	3	X
ejpam-1563	99	2	.	.	X
ejpam-1563	99	3	existence	existence	NOUN
ejpam-1563	99	4	results	result	VERB
ejpam-1563	99	5	for	for	ADP
ejpam-1563	99	6	(	(	PUNCT
ejpam-1563	99	7	gvep1a	gvep1a	X
ejpam-1563	99	8	)	)	PUNCT
ejpam-1563	99	9	and	and	CCONJ
ejpam-1563	99	10	(	(	PUNCT
ejpam-1563	99	11	gvep1b	gvep1b	PROPN
ejpam-1563	99	12	)	)	PUNCT
ejpam-1563	99	13	the	the	DET
ejpam-1563	99	14	main	main	ADJ
ejpam-1563	99	15	goal	goal	NOUN
ejpam-1563	99	16	of	of	ADP
ejpam-1563	99	17	this	this	DET
ejpam-1563	99	18	section	section	NOUN
ejpam-1563	99	19	is	be	AUX
ejpam-1563	99	20	to	to	PART
ejpam-1563	99	21	prove	prove	VERB
ejpam-1563	99	22	an	an	DET
ejpam-1563	99	23	existence	existence	NOUN
ejpam-1563	99	24	result	result	NOUN
ejpam-1563	99	25	for	for	ADP
ejpam-1563	99	26	the	the	DET
ejpam-1563	99	27	generalized	generalize	VERB
ejpam-1563	99	28	vector	vector	NOUN
ejpam-1563	99	29	equilibrium	equilibrium	NOUN
ejpam-1563	99	30	problem	problem	NOUN
ejpam-1563	99	31	(	(	PUNCT
ejpam-1563	99	32	gvep1a	gvep1a	X
ejpam-1563	99	33	)	)	PUNCT
ejpam-1563	99	34	on	on	ADP
ejpam-1563	99	35	unbounded	unbounded	ADJ
ejpam-1563	99	36	sets	set	NOUN
ejpam-1563	99	37	,	,	PUNCT
ejpam-1563	99	38	conditional	conditional	ADJ
ejpam-1563	99	39	on	on	ADP
ejpam-1563	99	40	available	available	ADJ
ejpam-1563	99	41	results	result	NOUN
ejpam-1563	99	42	for	for	ADP
ejpam-1563	99	43	the	the	DET
ejpam-1563	99	44	existence	existence	NOUN
ejpam-1563	99	45	of	of	ADP
ejpam-1563	99	46	solutions	solution	NOUN
ejpam-1563	99	47	to	to	ADP
ejpam-1563	99	48	the	the	DET
ejpam-1563	99	49	same	same	ADJ
ejpam-1563	99	50	problem	problem	NOUN
ejpam-1563	99	51	on	on	ADP
ejpam-1563	99	52	closed	closed	ADJ
ejpam-1563	99	53	,	,	PUNCT
ejpam-1563	99	54	convex	convex	ADJ
ejpam-1563	99	55	and	and	CCONJ
ejpam-1563	99	56	bounded	bound	VERB
ejpam-1563	99	57	sets	set	NOUN
ejpam-1563	99	58	.	.	PUNCT
ejpam-1563	100	1	this	this	DET
ejpam-1563	100	2	task	task	NOUN
ejpam-1563	100	3	is	be	AUX
ejpam-1563	100	4	pursued	pursue	VERB
ejpam-1563	100	5	in	in	ADP
ejpam-1563	100	6	theorem	theorem	NOUN
ejpam-1563	100	7	3	3	NUM
ejpam-1563	100	8	below	below	ADV
ejpam-1563	100	9	,	,	PUNCT
ejpam-1563	100	10	which	which	PRON
ejpam-1563	100	11	generalizes	generalize	VERB
ejpam-1563	100	12	similar	similar	ADJ
ejpam-1563	100	13	results	result	NOUN
ejpam-1563	100	14	of	of	ADP
ejpam-1563	100	15	[	[	X
ejpam-1563	100	16	7	7	NUM
ejpam-1563	100	17	,	,	PUNCT
ejpam-1563	100	18	8	8	NUM
ejpam-1563	100	19	]	]	PUNCT
ejpam-1563	100	20	to	to	PART
ejpam-1563	100	21	set	set	VERB
ejpam-1563	100	22	-	-	PUNCT
ejpam-1563	100	23	valued	value	VERB
ejpam-1563	100	24	bifunctions	bifunction	NOUN
ejpam-1563	100	25	,	,	PUNCT
ejpam-1563	100	26	while	while	SCONJ
ejpam-1563	100	27	corollary	corollary	ADJ
ejpam-1563	100	28	1	1	NUM
ejpam-1563	100	29	combines	combine	VERB
ejpam-1563	100	30	this	this	DET
ejpam-1563	100	31	theorem	theorem	NOUN
ejpam-1563	100	32	with	with	ADP
ejpam-1563	100	33	theorem	theorem	NOUN
ejpam-1563	100	34	1	1	NUM
ejpam-1563	100	35	.	.	PUNCT
ejpam-1563	101	1	the	the	DET
ejpam-1563	101	2	main	main	ADJ
ejpam-1563	101	3	tool	tool	NOUN
ejpam-1563	101	4	in	in	ADP
ejpam-1563	101	5	our	our	PRON
ejpam-1563	101	6	proof	proof	NOUN
ejpam-1563	101	7	will	will	AUX
ejpam-1563	101	8	be	be	AUX
ejpam-1563	101	9	a	a	DET
ejpam-1563	101	10	new	new	ADJ
ejpam-1563	101	11	coercivity	coercivity	NOUN
ejpam-1563	101	12	condition	condition	NOUN
ejpam-1563	101	13	introduced	introduce	VERB
ejpam-1563	101	14	in	in	ADP
ejpam-1563	101	15	[	[	X
ejpam-1563	101	16	7	7	NUM
ejpam-1563	101	17	,	,	PUNCT
ejpam-1563	101	18	8	8	NUM
ejpam-1563	101	19	]	]	PUNCT
ejpam-1563	101	20	for	for	ADP
ejpam-1563	101	21	scalar	scalar	ADJ
ejpam-1563	101	22	and	and	CCONJ
ejpam-1563	101	23	vector	vector	NOUN
ejpam-1563	101	24	equilibrium	equilibrium	NOUN
ejpam-1563	101	25	problems	problem	NOUN
ejpam-1563	101	26	,	,	PUNCT
ejpam-1563	101	27	which	which	PRON
ejpam-1563	101	28	is	be	AUX
ejpam-1563	101	29	weaker	weak	ADJ
ejpam-1563	101	30	than	than	ADP
ejpam-1563	101	31	standard	standard	ADJ
ejpam-1563	101	32	coercivity	coercivity	NOUN
ejpam-1563	101	33	conditions	condition	NOUN
ejpam-1563	101	34	in	in	ADP
ejpam-1563	101	35	the	the	DET
ejpam-1563	101	36	literature	literature	NOUN
ejpam-1563	101	37	.	.	PUNCT
ejpam-1563	102	1	given	give	VERB
ejpam-1563	102	2	a	a	DET
ejpam-1563	102	3	metric	metric	ADJ
ejpam-1563	102	4	space	space	NOUN
ejpam-1563	102	5	x	x	X
ejpam-1563	102	6	,	,	PUNCT
ejpam-1563	102	7	k	k	PROPN
ejpam-1563	102	8	⊆	⊆	NUM
ejpam-1563	102	9	x	x	PUNCT
ejpam-1563	102	10	and	and	CCONJ
ejpam-1563	102	11	a	a	DET
ejpam-1563	102	12	function	function	NOUN
ejpam-1563	102	13	µ	µ	NOUN
ejpam-1563	102	14	:	:	PUNCT
ejpam-1563	102	15	x	x	SYM
ejpam-1563	102	16	→	→	SYM
ejpam-1563	102	17	r	r	NOUN
ejpam-1563	102	18	,	,	PUNCT
ejpam-1563	102	19	we	we	PRON
ejpam-1563	102	20	will	will	AUX
ejpam-1563	102	21	use	use	VERB
ejpam-1563	102	22	the	the	DET
ejpam-1563	102	23	following	following	ADJ
ejpam-1563	102	24	notation	notation	NOUN
ejpam-1563	102	25	for	for	ADP
ejpam-1563	102	26	lower	low	ADJ
ejpam-1563	102	27	level	level	NOUN
ejpam-1563	102	28	sets	set	NOUN
ejpam-1563	102	29	of	of	ADP
ejpam-1563	102	30	µ	µ	PRON
ejpam-1563	102	31	restricted	restrict	VERB
ejpam-1563	102	32	to	to	ADP
ejpam-1563	102	33	k	k	PROPN
ejpam-1563	102	34	.	.	PUNCT
ejpam-1563	103	1	for	for	ADP
ejpam-1563	103	2	any	any	DET
ejpam-1563	103	3	r	r	NOUN
ejpam-1563	103	4	∈	∈	NOUN
ejpam-1563	103	5	r	r	NOUN
ejpam-1563	103	6	,	,	PUNCT
ejpam-1563	103	7	wr	wr	NOUN
ejpam-1563	103	8	:	:	PUNCT
ejpam-1563	103	9	=	=	SYM
ejpam-1563	103	10	{	{	PUNCT
ejpam-1563	103	11	x	x	PUNCT
ejpam-1563	103	12	∈	∈	PROPN
ejpam-1563	103	13	k	k	NOUN
ejpam-1563	103	14	:	:	PUNCT
ejpam-1563	103	15	µ(x)≤	µ(x)≤	X
ejpam-1563	103	16	r	r	NOUN
ejpam-1563	103	17	}	}	PUNCT
ejpam-1563	103	18	and	and	CCONJ
ejpam-1563	103	19	ur	ur	INTJ
ejpam-1563	103	20	:	:	PUNCT
ejpam-1563	103	21	=	=	SYM
ejpam-1563	103	22	{	{	PUNCT
ejpam-1563	103	23	x	x	PUNCT
ejpam-1563	103	24	∈	∈	PROPN
ejpam-1563	103	25	k	k	NOUN
ejpam-1563	103	26	:	:	PUNCT
ejpam-1563	103	27	µ(x	µ(x	X
ejpam-1563	103	28	)	)	PUNCT
ejpam-1563	103	29	<	<	X
ejpam-1563	103	30	r	r	NOUN
ejpam-1563	103	31	}	}	PUNCT
ejpam-1563	103	32	.	.	PUNCT
ejpam-1563	104	1	definition	definition	NOUN
ejpam-1563	104	2	2	2	NUM
ejpam-1563	104	3	.	.	PUNCT
ejpam-1563	105	1	let	let	VERB
ejpam-1563	105	2	x	x	PRON
ejpam-1563	105	3	be	be	AUX
ejpam-1563	105	4	a	a	DET
ejpam-1563	105	5	set	set	NOUN
ejpam-1563	105	6	and	and	CCONJ
ejpam-1563	105	7	k	k	NOUN
ejpam-1563	105	8	⊆	⊆	X
ejpam-1563	105	9	x	x	PUNCT
ejpam-1563	105	10	be	be	AUX
ejpam-1563	105	11	nonempty	nonempty	ADJ
ejpam-1563	105	12	.	.	PUNCT
ejpam-1563	106	1	a	a	DET
ejpam-1563	106	2	function	function	NOUN
ejpam-1563	106	3	µ	µ	NOUN
ejpam-1563	106	4	:	:	PUNCT
ejpam-1563	106	5	x	x	SYM
ejpam-1563	106	6	→	→	SYM
ejpam-1563	106	7	r	r	NOUN
ejpam-1563	106	8	is	be	AUX
ejpam-1563	106	9	weakly	weakly	ADV
ejpam-1563	106	10	coercive	coercive	ADJ
ejpam-1563	106	11	with	with	ADP
ejpam-1563	106	12	respect	respect	NOUN
ejpam-1563	106	13	to	to	ADP
ejpam-1563	106	14	the	the	DET
ejpam-1563	106	15	set	set	NOUN
ejpam-1563	106	16	k	k	PROPN
ejpam-1563	106	17	if	if	SCONJ
ejpam-1563	106	18	there	there	PRON
ejpam-1563	106	19	exists	exist	VERB
ejpam-1563	106	20	r	r	NOUN
ejpam-1563	106	21	∈	∈	PROPN
ejpam-1563	106	22	r	r	NOUN
ejpam-1563	106	23	such	such	ADJ
ejpam-1563	106	24	that	that	DET
ejpam-1563	106	25	wr	wr	PROPN
ejpam-1563	106	26	is	be	AUX
ejpam-1563	106	27	nonempty	nonempty	ADJ
ejpam-1563	106	28	and	and	CCONJ
ejpam-1563	106	29	bounded	bound	VERB
ejpam-1563	106	30	.	.	PUNCT
ejpam-1563	107	1	remark	remark	PROPN
ejpam-1563	107	2	3	3	NUM
ejpam-1563	107	3	.	.	PUNCT
ejpam-1563	108	1	if	if	SCONJ
ejpam-1563	108	2	a	a	DET
ejpam-1563	108	3	function	function	NOUN
ejpam-1563	108	4	µ	µ	NOUN
ejpam-1563	108	5	is	be	AUX
ejpam-1563	108	6	lower	low	ADJ
ejpam-1563	108	7	semicontinuous	semicontinuous	ADJ
ejpam-1563	108	8	and	and	CCONJ
ejpam-1563	108	9	strongly	strongly	ADV
ejpam-1563	108	10	convex	convex	ADJ
ejpam-1563	108	11	,	,	PUNCT
ejpam-1563	108	12	or	or	CCONJ
ejpam-1563	108	13	it	it	PRON
ejpam-1563	108	14	is	be	AUX
ejpam-1563	108	15	coercive	coercive	ADJ
ejpam-1563	108	16	in	in	ADP
ejpam-1563	108	17	the	the	DET
ejpam-1563	108	18	usual	usual	ADJ
ejpam-1563	108	19	sense	sense	NOUN
ejpam-1563	108	20	(	(	PUNCT
ejpam-1563	108	21	i.e.	i.e.	X
ejpam-1563	108	22	,	,	PUNCT
ejpam-1563	108	23	µ(x	µ(x	ADJ
ejpam-1563	108	24	)	)	PUNCT
ejpam-1563	108	25	→	→	PUNCT
ejpam-1563	108	26	+	+	NUM
ejpam-1563	108	27	∞	∞	NUM
ejpam-1563	108	28	as	as	ADP
ejpam-1563	108	29	‖x‖	‖x‖	PROPN
ejpam-1563	108	30	→	→	SYM
ejpam-1563	108	31	+	+	NOUN
ejpam-1563	108	32	∞	∞	NUM
ejpam-1563	108	33	)	)	PUNCT
ejpam-1563	108	34	,	,	PUNCT
ejpam-1563	108	35	then	then	ADV
ejpam-1563	108	36	µ	µ	NOUN
ejpam-1563	108	37	is	be	AUX
ejpam-1563	108	38	weakly	weakly	ADV
ejpam-1563	108	39	coercive	coercive	ADJ
ejpam-1563	108	40	with	with	ADP
ejpam-1563	108	41	respect	respect	NOUN
ejpam-1563	108	42	to	to	ADP
ejpam-1563	108	43	any	any	DET
ejpam-1563	108	44	nonempty	nonempty	ADV
ejpam-1563	108	45	set	set	VERB
ejpam-1563	108	46	.	.	PUNCT
ejpam-1563	109	1	moreover	moreover	ADV
ejpam-1563	109	2	,	,	PUNCT
ejpam-1563	109	3	if	if	SCONJ
ejpam-1563	109	4	µ	µ	NOUN
ejpam-1563	109	5	is	be	AUX
ejpam-1563	109	6	convex	convex	ADJ
ejpam-1563	109	7	and	and	CCONJ
ejpam-1563	109	8	weakly	weakly	ADV
ejpam-1563	109	9	coercive	coercive	ADJ
ejpam-1563	109	10	,	,	PUNCT
ejpam-1563	109	11	then	then	ADV
ejpam-1563	109	12	w%	w%	NOUN
ejpam-1563	109	13	is	be	AUX
ejpam-1563	109	14	bounded	bound	VERB
ejpam-1563	109	15	for	for	ADP
ejpam-1563	109	16	each	each	DET
ejpam-1563	109	17	%	%	NOUN
ejpam-1563	109	18	∈	∈	PROPN
ejpam-1563	109	19	r	r	NOUN
ejpam-1563	109	20	[	[	X
ejpam-1563	109	21	14	14	NUM
ejpam-1563	109	22	,	,	PUNCT
ejpam-1563	109	23	chapter	chapter	NOUN
ejpam-1563	109	24	3	3	NUM
ejpam-1563	109	25	,	,	PUNCT
ejpam-1563	109	26	theorem	theorem	VERB
ejpam-1563	109	27	3.14	3.14	NUM
ejpam-1563	109	28	]	]	PUNCT
ejpam-1563	109	29	.	.	PUNCT
ejpam-1563	110	1	in	in	ADP
ejpam-1563	110	2	theorem	theorem	NOUN
ejpam-1563	110	3	3	3	NUM
ejpam-1563	110	4	,	,	PUNCT
ejpam-1563	110	5	we	we	PRON
ejpam-1563	110	6	will	will	AUX
ejpam-1563	110	7	assume	assume	VERB
ejpam-1563	110	8	the	the	DET
ejpam-1563	110	9	following	follow	VERB
ejpam-1563	110	10	coercivity	coercivity	NOUN
ejpam-1563	110	11	condition	condition	NOUN
ejpam-1563	110	12	,	,	PUNCT
ejpam-1563	110	13	which	which	PRON
ejpam-1563	110	14	extends	extend	VERB
ejpam-1563	110	15	that	that	PRON
ejpam-1563	110	16	of	of	ADP
ejpam-1563	110	17	[	[	X
ejpam-1563	110	18	7	7	NUM
ejpam-1563	110	19	,	,	PUNCT
ejpam-1563	110	20	8	8	NUM
ejpam-1563	110	21	]	]	PUNCT
ejpam-1563	110	22	to	to	ADP
ejpam-1563	110	23	the	the	DET
ejpam-1563	110	24	case	case	NOUN
ejpam-1563	110	25	of	of	ADP
ejpam-1563	110	26	set	set	NOUN
ejpam-1563	110	27	-	-	PUNCT
ejpam-1563	110	28	valued	value	VERB
ejpam-1563	110	29	bifunctions	bifunction	NOUN
ejpam-1563	110	30	.	.	PUNCT
ejpam-1563	111	1	(	(	PUNCT
ejpam-1563	111	2	g1a	g1a	NOUN
ejpam-1563	111	3	)	)	PUNCT
ejpam-1563	111	4	there	there	PRON
ejpam-1563	111	5	exist	exist	VERB
ejpam-1563	111	6	a	a	DET
ejpam-1563	111	7	convex	convex	NOUN
ejpam-1563	111	8	and	and	CCONJ
ejpam-1563	111	9	lower	low	ADJ
ejpam-1563	111	10	semicontinuous	semicontinuous	ADJ
ejpam-1563	111	11	function	function	NOUN
ejpam-1563	111	12	µ	µ	NOUN
ejpam-1563	111	13	:	:	PUNCT
ejpam-1563	111	14	x	x	SYM
ejpam-1563	111	15	→	→	SYM
ejpam-1563	111	16	r	r	NOUN
ejpam-1563	111	17	,	,	PUNCT
ejpam-1563	111	18	which	which	PRON
ejpam-1563	111	19	is	be	AUX
ejpam-1563	111	20	weakly	weakly	ADV
ejpam-1563	111	21	coercive	coercive	ADJ
ejpam-1563	111	22	with	with	ADP
ejpam-1563	111	23	respect	respect	NOUN
ejpam-1563	111	24	to	to	ADP
ejpam-1563	111	25	the	the	DET
ejpam-1563	111	26	set	set	NOUN
ejpam-1563	111	27	k	k	NOUN
ejpam-1563	111	28	,	,	PUNCT
ejpam-1563	111	29	and	and	CCONJ
ejpam-1563	111	30	a	a	DET
ejpam-1563	111	31	number	number	NOUN
ejpam-1563	111	32	r	r	NOUN
ejpam-1563	111	33	such	such	ADJ
ejpam-1563	111	34	that	that	PRON
ejpam-1563	111	35	for	for	ADP
ejpam-1563	111	36	any	any	DET
ejpam-1563	111	37	point	point	NOUN
ejpam-1563	111	38	x	x	X
ejpam-1563	111	39	∈	∈	PROPN
ejpam-1563	111	40	k\wr	k\wr	PROPN
ejpam-1563	111	41	with	with	ADP
ejpam-1563	111	42	φ	φ	PROPN
ejpam-1563	111	43	�	�	PROPN
ejpam-1563	111	44	x	x	SYM
ejpam-1563	111	45	,	,	PUNCT
ejpam-1563	111	46	y	y	PROPN
ejpam-1563	111	47	�	�	PROPN
ejpam-1563	111	48	6⊆	6⊆	PROPN
ejpam-1563	111	49	−int	−int	ADP
ejpam-1563	111	50	c(x	c(x	NOUN
ejpam-1563	111	51	)	)	PUNCT
ejpam-1563	111	52	,	,	PUNCT
ejpam-1563	111	53	∀y	∀y	PROPN
ejpam-1563	111	54	∈wr	∈wr	NUM
ejpam-1563	111	55	,	,	PUNCT
ejpam-1563	111	56	(	(	PUNCT
ejpam-1563	111	57	1	1	X
ejpam-1563	111	58	)	)	PUNCT
ejpam-1563	111	59	there	there	PRON
ejpam-1563	111	60	is	be	VERB
ejpam-1563	111	61	a	a	DET
ejpam-1563	111	62	point	point	NOUN
ejpam-1563	111	63	z	z	NOUN
ejpam-1563	111	64	∈	∈	PROPN
ejpam-1563	111	65	k	k	NOUN
ejpam-1563	111	66	,	,	PUNCT
ejpam-1563	111	67	µ(z	µ(z	PROPN
ejpam-1563	111	68	)	)	PUNCT
ejpam-1563	111	69	<	<	X
ejpam-1563	111	70	µ(x	µ(x	NOUN
ejpam-1563	111	71	)	)	PUNCT
ejpam-1563	111	72	,	,	PUNCT
ejpam-1563	111	73	such	such	ADJ
ejpam-1563	111	74	that	that	SCONJ
ejpam-1563	111	75	φ(x	φ(x	PROPN
ejpam-1563	111	76	,	,	PUNCT
ejpam-1563	111	77	z)⊆−c(x	z)⊆−c(x	NOUN
ejpam-1563	111	78	)	)	PUNCT
ejpam-1563	111	79	.	.	PUNCT
ejpam-1563	112	1	remark	remark	PROPN
ejpam-1563	112	2	4	4	NUM
ejpam-1563	112	3	.	.	PUNCT
ejpam-1563	112	4	notice	notice	VERB
ejpam-1563	112	5	that	that	SCONJ
ejpam-1563	112	6	,	,	PUNCT
ejpam-1563	112	7	when	when	SCONJ
ejpam-1563	112	8	x	x	PRON
ejpam-1563	112	9	is	be	AUX
ejpam-1563	112	10	a	a	DET
ejpam-1563	112	11	reflexive	reflexive	ADJ
ejpam-1563	112	12	banach	banach	NOUN
ejpam-1563	112	13	space	space	NOUN
ejpam-1563	112	14	,	,	PUNCT
ejpam-1563	112	15	wr	wr	PROPN
ejpam-1563	112	16	in	in	ADP
ejpam-1563	112	17	(	(	PUNCT
ejpam-1563	112	18	g1a	g1a	NOUN
ejpam-1563	112	19	)	)	PUNCT
ejpam-1563	112	20	must	must	AUX
ejpam-1563	112	21	be	be	AUX
ejpam-1563	112	22	nonempty	nonempty	ADJ
ejpam-1563	112	23	.	.	PUNCT
ejpam-1563	113	1	indeed	indeed	ADV
ejpam-1563	113	2	,	,	PUNCT
ejpam-1563	113	3	otherwise	otherwise	ADV
ejpam-1563	113	4	we	we	PRON
ejpam-1563	113	5	can	can	AUX
ejpam-1563	113	6	take	take	VERB
ejpam-1563	113	7	x	x	PUNCT
ejpam-1563	113	8	∈	∈	NOUN
ejpam-1563	113	9	k	k	NOUN
ejpam-1563	114	1	=	=	SYM
ejpam-1563	114	2	k	k	PROPN
ejpam-1563	114	3	\wr	\wr	PROPN
ejpam-1563	114	4	such	such	ADJ
ejpam-1563	114	5	that	that	SCONJ
ejpam-1563	114	6	,	,	PUNCT
ejpam-1563	114	7	by	by	ADP
ejpam-1563	114	8	weierstrass	weierstrass	NOUN
ejpam-1563	114	9	’	'	PUNCT
ejpam-1563	114	10	theorem	theorem	NOUN
ejpam-1563	114	11	(	(	PUNCT
ejpam-1563	114	12	µ	µ	X
ejpam-1563	114	13	is	be	AUX
ejpam-1563	114	14	convex	convex	ADJ
ejpam-1563	114	15	and	and	CCONJ
ejpam-1563	114	16	lower	low	ADJ
ejpam-1563	114	17	semicontinuous	semicontinuous	ADJ
ejpam-1563	114	18	,	,	PUNCT
ejpam-1563	114	19	hence	hence	ADV
ejpam-1563	114	20	lower	low	ADJ
ejpam-1563	114	21	semicontinuous	semicontinuous	ADJ
ejpam-1563	114	22	with	with	ADP
ejpam-1563	114	23	respect	respect	NOUN
ejpam-1563	114	24	to	to	ADP
ejpam-1563	114	25	the	the	DET
ejpam-1563	114	26	weak	weak	ADJ
ejpam-1563	114	27	topology	topology	NOUN
ejpam-1563	114	28	;	;	PUNCT
ejpam-1563	114	29	moreover	moreover	ADV
ejpam-1563	114	30	,	,	PUNCT
ejpam-1563	114	31	e.	e.	PROPN
ejpam-1563	114	32	allevi	allevi	PROPN
ejpam-1563	114	33	,	,	PUNCT
ejpam-1563	114	34	i.	i.	PROPN
ejpam-1563	114	35	konnov	konnov	PROPN
ejpam-1563	114	36	,	,	PUNCT
ejpam-1563	114	37	m.	m.	NOUN
ejpam-1563	114	38	rocco	rocco	NOUN
ejpam-1563	114	39	/	/	SYM
ejpam-1563	114	40	eur	eur	PROPN
ejpam-1563	114	41	.	.	PUNCT
ejpam-1563	115	1	j.	j.	PROPN
ejpam-1563	115	2	pure	pure	PROPN
ejpam-1563	115	3	appl	appl	PROPN
ejpam-1563	115	4	.	.	PROPN
ejpam-1563	115	5	math	math	PROPN
ejpam-1563	115	6	,	,	PUNCT
ejpam-1563	115	7	6	6	NUM
ejpam-1563	115	8	(	(	PUNCT
ejpam-1563	115	9	2013	2013	NUM
ejpam-1563	115	10	)	)	PUNCT
ejpam-1563	115	11	,	,	PUNCT
ejpam-1563	115	12	365	365	NUM
ejpam-1563	115	13	-	-	SYM
ejpam-1563	115	14	376	376	NUM
ejpam-1563	115	15	370	370	NUM
ejpam-1563	115	16	since	since	SCONJ
ejpam-1563	115	17	it	it	PRON
ejpam-1563	115	18	is	be	AUX
ejpam-1563	115	19	weakly	weakly	ADV
ejpam-1563	115	20	coercive	coercive	ADJ
ejpam-1563	115	21	,	,	PUNCT
ejpam-1563	115	22	there	there	PRON
ejpam-1563	115	23	exists	exist	VERB
ejpam-1563	115	24	r̄	r̄	NOUN
ejpam-1563	115	25	∈	∈	NOUN
ejpam-1563	115	26	r	r	NOUN
ejpam-1563	115	27	such	such	ADJ
ejpam-1563	115	28	that	that	SCONJ
ejpam-1563	115	29	wr̄	wr̄	PROPN
ejpam-1563	115	30	is	be	AUX
ejpam-1563	115	31	nonempty	nonempty	ADJ
ejpam-1563	115	32	and	and	CCONJ
ejpam-1563	115	33	bounded	bound	VERB
ejpam-1563	115	34	,	,	PUNCT
ejpam-1563	115	35	hence	hence	ADV
ejpam-1563	115	36	compact	compact	ADJ
ejpam-1563	115	37	in	in	ADP
ejpam-1563	115	38	the	the	DET
ejpam-1563	115	39	weak	weak	ADJ
ejpam-1563	115	40	topology	topology	NOUN
ejpam-1563	115	41	)	)	PUNCT
ejpam-1563	115	42	,	,	PUNCT
ejpam-1563	115	43	µ(x	µ(x	NOUN
ejpam-1563	115	44	)	)	PUNCT
ejpam-1563	115	45	=	=	SYM
ejpam-1563	115	46	min	min	NOUN
ejpam-1563	115	47	x∈wr̄	x∈wr̄	PROPN
ejpam-1563	115	48	µ(x	µ(x	X
ejpam-1563	115	49	)	)	PUNCT
ejpam-1563	115	50	=	=	SYM
ejpam-1563	116	1	r	r	NOUN
ejpam-1563	116	2	′	′	NUM
ejpam-1563	116	3	>	>	PUNCT
ejpam-1563	116	4	r	r	NOUN
ejpam-1563	116	5	,	,	PUNCT
ejpam-1563	116	6	but	but	CCONJ
ejpam-1563	116	7	then	then	ADV
ejpam-1563	116	8	there	there	PRON
ejpam-1563	116	9	exists	exist	VERB
ejpam-1563	116	10	z	z	PROPN
ejpam-1563	116	11	∈	∈	PROPN
ejpam-1563	116	12	k	k	PROPN
ejpam-1563	116	13	,	,	PUNCT
ejpam-1563	116	14	µ(z	µ(z	PROPN
ejpam-1563	116	15	)	)	PUNCT
ejpam-1563	116	16	<	<	X
ejpam-1563	116	17	µ(x	µ(x	ADJ
ejpam-1563	116	18	)	)	PUNCT
ejpam-1563	116	19	=	=	SYM
ejpam-1563	116	20	r	r	NOUN
ejpam-1563	116	21	′	′	NOUN
ejpam-1563	116	22	,	,	PUNCT
ejpam-1563	116	23	a	a	DET
ejpam-1563	116	24	contradiction	contradiction	NOUN
ejpam-1563	116	25	.	.	PUNCT
ejpam-1563	117	1	remark	remark	NOUN
ejpam-1563	117	2	5	5	NUM
ejpam-1563	117	3	.	.	PUNCT
ejpam-1563	118	1	in	in	ADP
ejpam-1563	118	2	what	what	PRON
ejpam-1563	118	3	follows	follow	VERB
ejpam-1563	118	4	,	,	PUNCT
ejpam-1563	118	5	we	we	PRON
ejpam-1563	118	6	will	will	AUX
ejpam-1563	118	7	assume	assume	VERB
ejpam-1563	118	8	that	that	SCONJ
ejpam-1563	118	9	x	x	PROPN
ejpam-1563	118	10	and	and	CCONJ
ejpam-1563	118	11	y	y	PROPN
ejpam-1563	118	12	are	be	AUX
ejpam-1563	118	13	banach	banach	NOUN
ejpam-1563	118	14	spaces	space	NOUN
ejpam-1563	118	15	and	and	CCONJ
ejpam-1563	118	16	that	that	SCONJ
ejpam-1563	118	17	x	x	PRON
ejpam-1563	118	18	is	be	AUX
ejpam-1563	118	19	reflexive	reflexive	ADJ
ejpam-1563	118	20	(	(	PUNCT
ejpam-1563	118	21	in	in	ADP
ejpam-1563	118	22	order	order	NOUN
ejpam-1563	118	23	to	to	PART
ejpam-1563	118	24	easily	easily	ADV
ejpam-1563	118	25	fulfill	fulfill	VERB
ejpam-1563	118	26	the	the	DET
ejpam-1563	118	27	assumptions	assumption	NOUN
ejpam-1563	118	28	of	of	ADP
ejpam-1563	118	29	compactness	compactness	NOUN
ejpam-1563	118	30	)	)	PUNCT
ejpam-1563	118	31	,	,	PUNCT
ejpam-1563	118	32	though	though	SCONJ
ejpam-1563	118	33	lemma	lemma	PROPN
ejpam-1563	118	34	2	2	NUM
ejpam-1563	118	35	and	and	CCONJ
ejpam-1563	118	36	theorem	theorem	VERB
ejpam-1563	118	37	3	3	NUM
ejpam-1563	118	38	could	could	AUX
ejpam-1563	118	39	also	also	ADV
ejpam-1563	118	40	be	be	AUX
ejpam-1563	118	41	stated	state	VERB
ejpam-1563	118	42	in	in	ADP
ejpam-1563	118	43	a	a	DET
ejpam-1563	118	44	more	more	ADV
ejpam-1563	118	45	general	general	ADJ
ejpam-1563	118	46	setting	setting	NOUN
ejpam-1563	118	47	.	.	PUNCT
ejpam-1563	119	1	similarly	similarly	ADV
ejpam-1563	119	2	,	,	PUNCT
ejpam-1563	119	3	the	the	DET
ejpam-1563	119	4	assumptions	assumption	NOUN
ejpam-1563	119	5	on	on	ADP
ejpam-1563	119	6	c	c	NOUN
ejpam-1563	119	7	could	could	AUX
ejpam-1563	119	8	be	be	AUX
ejpam-1563	119	9	weakened	weaken	VERB
ejpam-1563	119	10	.	.	PUNCT
ejpam-1563	120	1	a	a	DET
ejpam-1563	120	2	similar	similar	ADJ
ejpam-1563	120	3	remark	remark	NOUN
ejpam-1563	120	4	holds	hold	VERB
ejpam-1563	120	5	for	for	ADP
ejpam-1563	120	6	the	the	DET
ejpam-1563	120	7	results	result	NOUN
ejpam-1563	120	8	presented	present	VERB
ejpam-1563	120	9	in	in	ADP
ejpam-1563	120	10	the	the	DET
ejpam-1563	120	11	following	follow	VERB
ejpam-1563	120	12	sections	section	NOUN
ejpam-1563	120	13	.	.	PUNCT
ejpam-1563	121	1	in	in	ADP
ejpam-1563	121	2	order	order	NOUN
ejpam-1563	121	3	to	to	PART
ejpam-1563	121	4	prove	prove	VERB
ejpam-1563	121	5	the	the	DET
ejpam-1563	121	6	main	main	ADJ
ejpam-1563	121	7	result	result	NOUN
ejpam-1563	121	8	of	of	ADP
ejpam-1563	121	9	this	this	DET
ejpam-1563	121	10	section	section	NOUN
ejpam-1563	121	11	,	,	PUNCT
ejpam-1563	121	12	we	we	PRON
ejpam-1563	121	13	state	state	VERB
ejpam-1563	121	14	the	the	DET
ejpam-1563	121	15	following	follow	VERB
ejpam-1563	121	16	lemma	lemma	PROPN
ejpam-1563	121	17	first	first	ADV
ejpam-1563	121	18	.	.	PUNCT
ejpam-1563	122	1	lemma	lemma	PROPN
ejpam-1563	122	2	2	2	X
ejpam-1563	122	3	.	.	PUNCT
ejpam-1563	123	1	let	let	VERB
ejpam-1563	123	2	x	x	PRON
ejpam-1563	123	3	be	be	AUX
ejpam-1563	123	4	a	a	DET
ejpam-1563	123	5	reflexive	reflexive	ADJ
ejpam-1563	123	6	banach	banach	NOUN
ejpam-1563	123	7	space	space	NOUN
ejpam-1563	123	8	,	,	PUNCT
ejpam-1563	123	9	y	y	PROPN
ejpam-1563	123	10	be	be	AUX
ejpam-1563	123	11	a	a	DET
ejpam-1563	123	12	banach	banach	NOUN
ejpam-1563	123	13	space	space	NOUN
ejpam-1563	123	14	,	,	PUNCT
ejpam-1563	123	15	k	k	PROPN
ejpam-1563	123	16	⊆	⊆	NUM
ejpam-1563	123	17	x	x	PUNCT
ejpam-1563	123	18	be	be	AUX
ejpam-1563	123	19	nonempty	nonempty	ADJ
ejpam-1563	123	20	,	,	PUNCT
ejpam-1563	123	21	closed	closed	ADJ
ejpam-1563	123	22	and	and	CCONJ
ejpam-1563	123	23	convex	convex	PROPN
ejpam-1563	123	24	,	,	PUNCT
ejpam-1563	123	25	c	c	NOUN
ejpam-1563	123	26	:	:	PUNCT
ejpam-1563	123	27	k	k	X
ejpam-1563	123	28	→	→	PUNCT
ejpam-1563	123	29	π(y	π(y	PROPN
ejpam-1563	123	30	)	)	PUNCT
ejpam-1563	123	31	be	be	AUX
ejpam-1563	123	32	a	a	DET
ejpam-1563	123	33	set	set	NOUN
ejpam-1563	123	34	-	-	PUNCT
ejpam-1563	123	35	valued	value	VERB
ejpam-1563	123	36	mapping	mapping	NOUN
ejpam-1563	123	37	that	that	PRON
ejpam-1563	123	38	maps	map	VERB
ejpam-1563	123	39	any	any	DET
ejpam-1563	123	40	x	x	SYM
ejpam-1563	123	41	∈	∈	PROPN
ejpam-1563	123	42	k	k	PROPN
ejpam-1563	123	43	to	to	ADP
ejpam-1563	123	44	a	a	DET
ejpam-1563	123	45	convex	convex	NOUN
ejpam-1563	123	46	,	,	PUNCT
ejpam-1563	123	47	solid	solid	ADJ
ejpam-1563	123	48	and	and	CCONJ
ejpam-1563	123	49	pointed	point	VERB
ejpam-1563	123	50	cone	cone	NOUN
ejpam-1563	123	51	of	of	ADP
ejpam-1563	123	52	y	y	PROPN
ejpam-1563	123	53	and	and	CCONJ
ejpam-1563	123	54	φ	φ	NUM
ejpam-1563	123	55	:	:	PUNCT
ejpam-1563	124	1	k	k	PROPN
ejpam-1563	124	2	×	×	PROPN
ejpam-1563	124	3	k	k	PROPN
ejpam-1563	124	4	→	→	SYM
ejpam-1563	124	5	π(y	π(y	PROPN
ejpam-1563	124	6	)	)	PUNCT
ejpam-1563	124	7	be	be	AUX
ejpam-1563	124	8	such	such	ADJ
ejpam-1563	124	9	that	that	DET
ejpam-1563	124	10	c1	c1	NOUN
ejpam-1563	124	11	)	)	PUNCT
ejpam-1563	124	12	for	for	ADP
ejpam-1563	124	13	all	all	DET
ejpam-1563	124	14	x	x	SYM
ejpam-1563	124	15	,	,	PUNCT
ejpam-1563	124	16	y	y	PROPN
ejpam-1563	124	17	′	′	NOUN
ejpam-1563	124	18	,	,	PUNCT
ejpam-1563	124	19	y	y	PROPN
ejpam-1563	124	20	′′	′′	PROPN
ejpam-1563	124	21	∈	∈	PROPN
ejpam-1563	124	22	k	k	NOUN
ejpam-1563	124	23	,	,	PUNCT
ejpam-1563	124	24	if	if	SCONJ
ejpam-1563	124	25	φ(x	φ(x	PROPN
ejpam-1563	124	26	,	,	PUNCT
ejpam-1563	124	27	y	y	PROPN
ejpam-1563	124	28	′)⊆−c(x	′)⊆−c(x	NOUN
ejpam-1563	124	29	)	)	PUNCT
ejpam-1563	124	30	and	and	CCONJ
ejpam-1563	124	31	φ(x	φ(x	PROPN
ejpam-1563	124	32	,	,	PUNCT
ejpam-1563	124	33	y	y	PROPN
ejpam-1563	124	34	′′)⊆−int	′′)⊆−int	PROPN
ejpam-1563	124	35	c(x	c(x	NOUN
ejpam-1563	124	36	)	)	PUNCT
ejpam-1563	124	37	,	,	PUNCT
ejpam-1563	124	38	then	then	ADV
ejpam-1563	124	39	φ(x	φ(x	PROPN
ejpam-1563	124	40	,	,	PUNCT
ejpam-1563	124	41	αy	αy	X
ejpam-1563	124	42	′+	′+	PUNCT
ejpam-1563	124	43	(	(	PUNCT
ejpam-1563	124	44	1−α)y	1−α)y	NUM
ejpam-1563	124	45	′′)⊆−int	′′)⊆−int	ADJ
ejpam-1563	124	46	c(x	c(x	NOUN
ejpam-1563	124	47	)	)	PUNCT
ejpam-1563	124	48	for	for	ADP
ejpam-1563	124	49	all	all	DET
ejpam-1563	124	50	α	α	NOUN
ejpam-1563	124	51	∈	∈	NOUN
ejpam-1563	124	52	]	]	X
ejpam-1563	124	53	0	0	NUM
ejpam-1563	124	54	,	,	PUNCT
ejpam-1563	124	55	1	1	NUM
ejpam-1563	124	56	[	[	NOUN
ejpam-1563	124	57	.	.	PUNCT
ejpam-1563	125	1	if	if	SCONJ
ejpam-1563	125	2	there	there	PRON
ejpam-1563	125	3	exist	exist	VERB
ejpam-1563	125	4	%	%	NOUN
ejpam-1563	125	5	∈	∈	PROPN
ejpam-1563	125	6	r	r	NOUN
ejpam-1563	125	7	,	,	PUNCT
ejpam-1563	125	8	x%	x%	X
ejpam-1563	125	9	∈	∈	PROPN
ejpam-1563	126	1	k	k	PROPN
ejpam-1563	126	2	such	such	ADJ
ejpam-1563	126	3	that	that	SCONJ
ejpam-1563	126	4	φ	φ	PROPN
ejpam-1563	126	5	�	�	PROPN
ejpam-1563	126	6	x%	x%	PROPN
ejpam-1563	126	7	,	,	PUNCT
ejpam-1563	126	8	y	y	PROPN
ejpam-1563	126	9	�	�	PROPN
ejpam-1563	126	10	6⊆	6⊆	PROPN
ejpam-1563	126	11	−int	−int	ADP
ejpam-1563	126	12	c(x%	c(x%	PROPN
ejpam-1563	126	13	)	)	PUNCT
ejpam-1563	126	14	,	,	PUNCT
ejpam-1563	126	15	∀y	∀y	NUM
ejpam-1563	126	16	∈w%	∈w%	NOUN
ejpam-1563	126	17	(	(	PUNCT
ejpam-1563	126	18	2	2	NUM
ejpam-1563	126	19	)	)	PUNCT
ejpam-1563	126	20	and	and	CCONJ
ejpam-1563	126	21	z	z	NOUN
ejpam-1563	126	22	∈	∈	PROPN
ejpam-1563	126	23	u%	u%	NOUN
ejpam-1563	126	24	such	such	ADJ
ejpam-1563	126	25	that	that	SCONJ
ejpam-1563	126	26	φ(x%	φ(x%	PROPN
ejpam-1563	126	27	,	,	PUNCT
ejpam-1563	126	28	z)⊆−c(x%	z)⊆−c(x%	NOUN
ejpam-1563	126	29	)	)	PUNCT
ejpam-1563	126	30	,	,	PUNCT
ejpam-1563	126	31	then	then	ADV
ejpam-1563	126	32	x%	x%	PUNCT
ejpam-1563	126	33	∈	∈	PROPN
ejpam-1563	126	34	s1a	s1a	PROPN
ejpam-1563	126	35	k	k	X
ejpam-1563	126	36	.	.	PUNCT
ejpam-1563	127	1	proof	proof	NOUN
ejpam-1563	127	2	.	.	PUNCT
ejpam-1563	128	1	suppose	suppose	VERB
ejpam-1563	128	2	by	by	ADP
ejpam-1563	128	3	contradiction	contradiction	NOUN
ejpam-1563	128	4	that	that	SCONJ
ejpam-1563	128	5	there	there	PRON
ejpam-1563	128	6	exists	exist	VERB
ejpam-1563	128	7	y	y	NOUN
ejpam-1563	128	8	′	′	NOUN
ejpam-1563	128	9	∈	∈	PROPN
ejpam-1563	128	10	k\w%	k\w%	PROPN
ejpam-1563	128	11	such	such	ADJ
ejpam-1563	128	12	that	that	SCONJ
ejpam-1563	128	13	φ	φ	PROPN
ejpam-1563	128	14	�	�	PROPN
ejpam-1563	128	15	x%	x%	PROPN
ejpam-1563	128	16	,	,	PUNCT
ejpam-1563	128	17	y	y	PROPN
ejpam-1563	128	18	′	′	NUM
ejpam-1563	128	19	�	�	PROPN
ejpam-1563	128	20	⊆−int	⊆−int	PROPN
ejpam-1563	128	21	c(x%	c(x%	PROPN
ejpam-1563	128	22	)	)	PUNCT
ejpam-1563	128	23	.	.	PUNCT
ejpam-1563	129	1	since	since	SCONJ
ejpam-1563	129	2	k	k	PROPN
ejpam-1563	129	3	is	be	AUX
ejpam-1563	129	4	a	a	DET
ejpam-1563	129	5	convex	convex	NOUN
ejpam-1563	129	6	set	set	NOUN
ejpam-1563	129	7	,	,	PUNCT
ejpam-1563	129	8	µ	µ	X
ejpam-1563	129	9	is	be	AUX
ejpam-1563	129	10	a	a	DET
ejpam-1563	129	11	convex	convex	NOUN
ejpam-1563	129	12	function	function	NOUN
ejpam-1563	129	13	and	and	CCONJ
ejpam-1563	129	14	z	z	NOUN
ejpam-1563	129	15	∈	∈	PROPN
ejpam-1563	129	16	u%	u%	NOUN
ejpam-1563	129	17	,	,	PUNCT
ejpam-1563	129	18	it	it	PRON
ejpam-1563	129	19	is	be	AUX
ejpam-1563	129	20	easy	easy	ADJ
ejpam-1563	129	21	to	to	PART
ejpam-1563	129	22	prove	prove	VERB
ejpam-1563	129	23	that	that	SCONJ
ejpam-1563	129	24	there	there	PRON
ejpam-1563	129	25	exists	exist	VERB
ejpam-1563	129	26	α̂	α̂	X
ejpam-1563	129	27	∈	∈	PROPN
ejpam-1563	129	28	]	]	X
ejpam-1563	129	29	0	0	NUM
ejpam-1563	129	30	,	,	PUNCT
ejpam-1563	129	31	1	1	NUM
ejpam-1563	129	32	[	[	PUNCT
ejpam-1563	129	33	such	such	ADJ
ejpam-1563	129	34	that	that	DET
ejpam-1563	129	35	y(α̂	y(α̂	PROPN
ejpam-1563	129	36	)	)	PUNCT
ejpam-1563	129	37	:	:	PUNCT
ejpam-1563	130	1	=	=	SYM
ejpam-1563	130	2	α̂z+	α̂z+	INTJ
ejpam-1563	130	3	(	(	PUNCT
ejpam-1563	130	4	1−	1−	NUM
ejpam-1563	130	5	α̂)y	α̂)y	NUM
ejpam-1563	130	6	′	′	NUM
ejpam-1563	130	7	∈w%	∈w%	NOUN
ejpam-1563	130	8	.	.	PUNCT
ejpam-1563	131	1	therefore	therefore	ADV
ejpam-1563	131	2	,	,	PUNCT
ejpam-1563	131	3	by	by	ADP
ejpam-1563	131	4	hypothesis	hypothesis	NOUN
ejpam-1563	131	5	,	,	PUNCT
ejpam-1563	131	6	we	we	PRON
ejpam-1563	131	7	obtain	obtain	VERB
ejpam-1563	131	8	φ	φ	PROPN
ejpam-1563	131	9	�	�	PROPN
ejpam-1563	131	10	x%	x%	PROPN
ejpam-1563	131	11	,	,	PUNCT
ejpam-1563	131	12	y(α̂	y(α̂	PROPN
ejpam-1563	131	13	)	)	PUNCT
ejpam-1563	131	14	�	�	PROPN
ejpam-1563	131	15	⊆−int	⊆−int	PROPN
ejpam-1563	131	16	c(x%	c(x%	PROPN
ejpam-1563	131	17	)	)	PUNCT
ejpam-1563	131	18	,	,	PUNCT
ejpam-1563	131	19	a	a	DET
ejpam-1563	131	20	contradiction	contradiction	NOUN
ejpam-1563	131	21	to	to	ADP
ejpam-1563	131	22	(	(	PUNCT
ejpam-1563	131	23	2	2	NUM
ejpam-1563	131	24	)	)	PUNCT
ejpam-1563	131	25	.	.	PUNCT
ejpam-1563	132	1	as	as	SCONJ
ejpam-1563	132	2	we	we	PRON
ejpam-1563	132	3	anticipated	anticipate	VERB
ejpam-1563	132	4	,	,	PUNCT
ejpam-1563	132	5	the	the	DET
ejpam-1563	132	6	following	follow	VERB
ejpam-1563	132	7	theorem	theorem	NOUN
ejpam-1563	132	8	provides	provide	VERB
ejpam-1563	132	9	a	a	DET
ejpam-1563	132	10	general	general	ADJ
ejpam-1563	132	11	scheme	scheme	NOUN
ejpam-1563	132	12	to	to	PART
ejpam-1563	132	13	obtain	obtain	VERB
ejpam-1563	132	14	existence	existence	NOUN
ejpam-1563	132	15	results	result	NOUN
ejpam-1563	132	16	for	for	ADP
ejpam-1563	132	17	the	the	DET
ejpam-1563	132	18	generalized	generalize	VERB
ejpam-1563	132	19	vector	vector	NOUN
ejpam-1563	132	20	equilibrium	equilibrium	NOUN
ejpam-1563	132	21	problem	problem	NOUN
ejpam-1563	132	22	(	(	PUNCT
ejpam-1563	132	23	gvep1a	gvep1a	X
ejpam-1563	132	24	)	)	PUNCT
ejpam-1563	132	25	on	on	ADP
ejpam-1563	132	26	an	an	DET
ejpam-1563	132	27	unbounded	unbounded	ADJ
ejpam-1563	132	28	set	set	NOUN
ejpam-1563	132	29	,	,	PUNCT
ejpam-1563	132	30	given	give	VERB
ejpam-1563	132	31	coercivity	coercivity	NOUN
ejpam-1563	132	32	condition	condition	NOUN
ejpam-1563	132	33	(	(	PUNCT
ejpam-1563	132	34	g1a	g1a	PROPN
ejpam-1563	132	35	)	)	PUNCT
ejpam-1563	132	36	and	and	CCONJ
ejpam-1563	132	37	any	any	DET
ejpam-1563	132	38	arbitrary	arbitrary	ADJ
ejpam-1563	132	39	existence	existence	NOUN
ejpam-1563	132	40	result	result	NOUN
ejpam-1563	132	41	for	for	ADP
ejpam-1563	132	42	problem	problem	NOUN
ejpam-1563	132	43	(	(	PUNCT
ejpam-1563	132	44	gvep1a	gvep1a	X
ejpam-1563	132	45	)	)	PUNCT
ejpam-1563	132	46	on	on	ADP
ejpam-1563	132	47	a	a	DET
ejpam-1563	132	48	closed	closed	ADJ
ejpam-1563	132	49	,	,	PUNCT
ejpam-1563	132	50	convex	convex	ADJ
ejpam-1563	132	51	and	and	CCONJ
ejpam-1563	132	52	bounded	bound	VERB
ejpam-1563	132	53	set	set	PROPN
ejpam-1563	132	54	.	.	PUNCT
ejpam-1563	133	1	theorem	theorem	VERB
ejpam-1563	133	2	3	3	X
ejpam-1563	133	3	.	.	PUNCT
ejpam-1563	134	1	let	let	VERB
ejpam-1563	134	2	x	x	PRON
ejpam-1563	134	3	be	be	AUX
ejpam-1563	134	4	a	a	DET
ejpam-1563	134	5	reflexive	reflexive	ADJ
ejpam-1563	134	6	banach	banach	NOUN
ejpam-1563	134	7	space	space	NOUN
ejpam-1563	134	8	,	,	PUNCT
ejpam-1563	134	9	y	y	PROPN
ejpam-1563	134	10	be	be	AUX
ejpam-1563	134	11	a	a	DET
ejpam-1563	134	12	banach	banach	NOUN
ejpam-1563	134	13	space	space	NOUN
ejpam-1563	134	14	,	,	PUNCT
ejpam-1563	134	15	k	k	PROPN
ejpam-1563	134	16	⊆	⊆	NUM
ejpam-1563	134	17	x	x	PUNCT
ejpam-1563	134	18	be	be	AUX
ejpam-1563	134	19	nonempty	nonempty	ADJ
ejpam-1563	134	20	,	,	PUNCT
ejpam-1563	134	21	closed	closed	ADJ
ejpam-1563	134	22	and	and	CCONJ
ejpam-1563	134	23	convex	convex	PROPN
ejpam-1563	134	24	,	,	PUNCT
ejpam-1563	134	25	c	c	NOUN
ejpam-1563	134	26	:	:	PUNCT
ejpam-1563	134	27	k	k	X
ejpam-1563	134	28	→	→	PUNCT
ejpam-1563	134	29	π(y	π(y	PROPN
ejpam-1563	134	30	)	)	PUNCT
ejpam-1563	134	31	be	be	AUX
ejpam-1563	134	32	a	a	DET
ejpam-1563	134	33	set	set	NOUN
ejpam-1563	134	34	-	-	PUNCT
ejpam-1563	134	35	valued	value	VERB
ejpam-1563	134	36	mapping	mapping	NOUN
ejpam-1563	134	37	that	that	PRON
ejpam-1563	134	38	maps	map	VERB
ejpam-1563	134	39	any	any	DET
ejpam-1563	134	40	x	x	SYM
ejpam-1563	134	41	∈	∈	PROPN
ejpam-1563	134	42	k	k	PROPN
ejpam-1563	134	43	to	to	ADP
ejpam-1563	134	44	a	a	DET
ejpam-1563	134	45	convex	convex	NOUN
ejpam-1563	134	46	,	,	PUNCT
ejpam-1563	134	47	solid	solid	ADJ
ejpam-1563	134	48	and	and	CCONJ
ejpam-1563	134	49	pointed	point	VERB
ejpam-1563	134	50	cone	cone	NOUN
ejpam-1563	134	51	of	of	ADP
ejpam-1563	134	52	y	y	PROPN
ejpam-1563	134	53	and	and	CCONJ
ejpam-1563	134	54	φ	φ	NUM
ejpam-1563	134	55	:	:	PUNCT
ejpam-1563	135	1	k	k	PROPN
ejpam-1563	135	2	×	×	PROPN
ejpam-1563	135	3	k	k	PROPN
ejpam-1563	135	4	→	→	SYM
ejpam-1563	135	5	π(y	π(y	PROPN
ejpam-1563	135	6	)	)	PUNCT
ejpam-1563	135	7	be	be	AUX
ejpam-1563	135	8	such	such	ADJ
ejpam-1563	135	9	that	that	PRON
ejpam-1563	135	10	:	:	PUNCT
ejpam-1563	135	11	(	(	PUNCT
ejpam-1563	135	12	i	i	NOUN
ejpam-1563	135	13	)	)	PUNCT
ejpam-1563	135	14	φ(x	φ(x	PROPN
ejpam-1563	135	15	,	,	PUNCT
ejpam-1563	135	16	x	x	X
ejpam-1563	135	17	)	)	PUNCT
ejpam-1563	135	18	=	=	SYM
ejpam-1563	135	19	{	{	PUNCT
ejpam-1563	135	20	0	0	NUM
ejpam-1563	135	21	}	}	PUNCT
ejpam-1563	135	22	,	,	PUNCT
ejpam-1563	135	23	for	for	ADP
ejpam-1563	135	24	all	all	DET
ejpam-1563	135	25	x	x	SYM
ejpam-1563	135	26	∈	∈	PROPN
ejpam-1563	135	27	k	k	NOUN
ejpam-1563	135	28	;	;	PUNCT
ejpam-1563	135	29	e.	e.	PROPN
ejpam-1563	135	30	allevi	allevi	PROPN
ejpam-1563	135	31	,	,	PUNCT
ejpam-1563	135	32	i.	i.	PROPN
ejpam-1563	135	33	konnov	konnov	PROPN
ejpam-1563	135	34	,	,	PUNCT
ejpam-1563	135	35	m.	m.	NOUN
ejpam-1563	135	36	rocco	rocco	NOUN
ejpam-1563	135	37	/	/	SYM
ejpam-1563	135	38	eur	eur	PROPN
ejpam-1563	135	39	.	.	PUNCT
ejpam-1563	136	1	j.	j.	PROPN
ejpam-1563	136	2	pure	pure	PROPN
ejpam-1563	136	3	appl	appl	PROPN
ejpam-1563	136	4	.	.	PROPN
ejpam-1563	136	5	math	math	PROPN
ejpam-1563	136	6	,	,	PUNCT
ejpam-1563	136	7	6	6	NUM
ejpam-1563	136	8	(	(	PUNCT
ejpam-1563	136	9	2013	2013	NUM
ejpam-1563	136	10	)	)	PUNCT
ejpam-1563	136	11	,	,	PUNCT
ejpam-1563	136	12	365	365	NUM
ejpam-1563	136	13	-	-	SYM
ejpam-1563	136	14	376	376	NUM
ejpam-1563	136	15	371	371	NUM
ejpam-1563	136	16	(	(	PUNCT
ejpam-1563	136	17	ii	ii	NOUN
ejpam-1563	136	18	)	)	PUNCT
ejpam-1563	136	19	for	for	ADP
ejpam-1563	136	20	all	all	DET
ejpam-1563	136	21	x	x	SYM
ejpam-1563	136	22	,	,	PUNCT
ejpam-1563	136	23	y	y	PROPN
ejpam-1563	136	24	′	′	NOUN
ejpam-1563	136	25	,	,	PUNCT
ejpam-1563	137	1	y	y	PROPN
ejpam-1563	137	2	′′	′′	PROPN
ejpam-1563	137	3	∈	∈	PROPN
ejpam-1563	137	4	k	k	NOUN
ejpam-1563	137	5	,	,	PUNCT
ejpam-1563	137	6	if	if	SCONJ
ejpam-1563	137	7	φ(x	φ(x	PROPN
ejpam-1563	137	8	,	,	PUNCT
ejpam-1563	137	9	y	y	PROPN
ejpam-1563	137	10	′)⊆−c(x	′)⊆−c(x	NOUN
ejpam-1563	137	11	)	)	PUNCT
ejpam-1563	137	12	and	and	CCONJ
ejpam-1563	137	13	φ(x	φ(x	PROPN
ejpam-1563	137	14	,	,	PUNCT
ejpam-1563	137	15	y	y	PROPN
ejpam-1563	137	16	′′)⊆−int	′′)⊆−int	PROPN
ejpam-1563	137	17	c(x	c(x	NOUN
ejpam-1563	137	18	)	)	PUNCT
ejpam-1563	137	19	,	,	PUNCT
ejpam-1563	137	20	then	then	ADV
ejpam-1563	137	21	φ(x	φ(x	PROPN
ejpam-1563	137	22	,	,	PUNCT
ejpam-1563	137	23	αy	αy	X
ejpam-1563	137	24	′+	′+	PUNCT
ejpam-1563	137	25	(	(	PUNCT
ejpam-1563	137	26	1−α)y	1−α)y	NUM
ejpam-1563	137	27	′′)⊆−int	′′)⊆−int	ADJ
ejpam-1563	137	28	c(x	c(x	NOUN
ejpam-1563	137	29	)	)	PUNCT
ejpam-1563	137	30	,	,	PUNCT
ejpam-1563	137	31	for	for	ADP
ejpam-1563	137	32	all	all	DET
ejpam-1563	137	33	α	α	NOUN
ejpam-1563	137	34	∈	∈	NOUN
ejpam-1563	137	35	]	]	X
ejpam-1563	137	36	0,1	0,1	NUM
ejpam-1563	137	37	[	[	X
ejpam-1563	137	38	.	.	PUNCT
ejpam-1563	137	39	suppose	suppose	VERB
ejpam-1563	137	40	that	that	SCONJ
ejpam-1563	137	41	s1a	s1a	PROPN
ejpam-1563	137	42	h	h	PROPN
ejpam-1563	137	43	6=	6=	NOUN
ejpam-1563	137	44	;	;	PUNCT
ejpam-1563	137	45	whenever	whenever	SCONJ
ejpam-1563	137	46	h	h	NOUN
ejpam-1563	137	47	is	be	AUX
ejpam-1563	137	48	a	a	DET
ejpam-1563	137	49	nonempty	nonempty	ADJ
ejpam-1563	137	50	,	,	PUNCT
ejpam-1563	137	51	closed	closed	ADJ
ejpam-1563	137	52	,	,	PUNCT
ejpam-1563	137	53	convex	convex	NOUN
ejpam-1563	137	54	and	and	CCONJ
ejpam-1563	137	55	bounded	bound	VERB
ejpam-1563	137	56	subset	subset	NOUN
ejpam-1563	137	57	of	of	ADP
ejpam-1563	137	58	k.	k.	PROPN
ejpam-1563	137	59	if	if	SCONJ
ejpam-1563	137	60	(	(	PUNCT
ejpam-1563	137	61	g1a	g1a	NOUN
ejpam-1563	137	62	)	)	PUNCT
ejpam-1563	137	63	holds	hold	VERB
ejpam-1563	137	64	,	,	PUNCT
ejpam-1563	137	65	then	then	ADV
ejpam-1563	137	66	s1a	s1a	PROPN
ejpam-1563	137	67	k	k	PROPN
ejpam-1563	137	68	6=	6=	PROPN
ejpam-1563	137	69	;	;	PUNCT
ejpam-1563	137	70	.	.	PUNCT
ejpam-1563	138	1	proof	proof	NOUN
ejpam-1563	138	2	.	.	PUNCT
ejpam-1563	139	1	let	let	VERB
ejpam-1563	139	2	r	r	PRON
ejpam-1563	139	3	∈	∈	NOUN
ejpam-1563	139	4	r	r	NOUN
ejpam-1563	139	5	be	be	VERB
ejpam-1563	139	6	as	as	ADP
ejpam-1563	139	7	in	in	ADP
ejpam-1563	139	8	(	(	PUNCT
ejpam-1563	139	9	g1a	g1a	NOUN
ejpam-1563	139	10	)	)	PUNCT
ejpam-1563	139	11	and	and	CCONJ
ejpam-1563	139	12	take	take	VERB
ejpam-1563	139	13	%	%	NOUN
ejpam-1563	139	14	>	>	X
ejpam-1563	139	15	r.	r.	PROPN
ejpam-1563	139	16	by	by	ADP
ejpam-1563	139	17	remarks	remark	NOUN
ejpam-1563	139	18	4	4	NUM
ejpam-1563	139	19	and	and	CCONJ
ejpam-1563	139	20	3	3	NUM
ejpam-1563	139	21	,	,	PUNCT
ejpam-1563	139	22	w%	w%	NOUN
ejpam-1563	139	23	is	be	AUX
ejpam-1563	139	24	nonempty	nonempty	ADJ
ejpam-1563	139	25	and	and	CCONJ
ejpam-1563	139	26	bounded	bound	VERB
ejpam-1563	139	27	;	;	PUNCT
ejpam-1563	139	28	furthermore	furthermore	ADV
ejpam-1563	139	29	,	,	PUNCT
ejpam-1563	139	30	it	it	PRON
ejpam-1563	139	31	is	be	AUX
ejpam-1563	139	32	closed	closed	ADJ
ejpam-1563	139	33	and	and	CCONJ
ejpam-1563	139	34	convex	convex	ADJ
ejpam-1563	139	35	,	,	PUNCT
ejpam-1563	139	36	since	since	SCONJ
ejpam-1563	139	37	k	k	PROPN
ejpam-1563	139	38	is	be	AUX
ejpam-1563	139	39	closed	closed	ADJ
ejpam-1563	139	40	and	and	CCONJ
ejpam-1563	139	41	convex	convex	ADJ
ejpam-1563	139	42	and	and	CCONJ
ejpam-1563	139	43	µ	µ	NOUN
ejpam-1563	139	44	is	be	AUX
ejpam-1563	139	45	lower	low	ADJ
ejpam-1563	139	46	semicontinuous	semicontinuous	ADJ
ejpam-1563	139	47	and	and	CCONJ
ejpam-1563	139	48	convex	convex	NOUN
ejpam-1563	139	49	.	.	PUNCT
ejpam-1563	140	1	therefore	therefore	ADV
ejpam-1563	140	2	,	,	PUNCT
ejpam-1563	140	3	by	by	ADP
ejpam-1563	140	4	hypothesis	hypothesis	NOUN
ejpam-1563	140	5	,	,	PUNCT
ejpam-1563	140	6	there	there	PRON
ejpam-1563	140	7	exists	exist	VERB
ejpam-1563	140	8	x%	x%	X
ejpam-1563	140	9	∈	∈	PROPN
ejpam-1563	140	10	s1a	s1a	PROPN
ejpam-1563	140	11	w%	w%	NOUN
ejpam-1563	140	12	,	,	PUNCT
ejpam-1563	140	13	i.e.	i.e.	X
ejpam-1563	140	14	x%	x%	X
ejpam-1563	140	15	∈	∈	PROPN
ejpam-1563	140	16	w%	w%	NOUN
ejpam-1563	140	17	satisfying	satisfy	VERB
ejpam-1563	140	18	(	(	PUNCT
ejpam-1563	140	19	2	2	NUM
ejpam-1563	140	20	)	)	PUNCT
ejpam-1563	140	21	.	.	PUNCT
ejpam-1563	141	1	if	if	SCONJ
ejpam-1563	141	2	x%	x%	SYM
ejpam-1563	141	3	∈	∈	PROPN
ejpam-1563	141	4	w%\wr	w%\wr	NOUN
ejpam-1563	141	5	,	,	PUNCT
ejpam-1563	141	6	then	then	ADV
ejpam-1563	141	7	by	by	ADP
ejpam-1563	141	8	(	(	PUNCT
ejpam-1563	141	9	g1a	g1a	NOUN
ejpam-1563	141	10	)	)	PUNCT
ejpam-1563	141	11	there	there	PRON
ejpam-1563	141	12	exists	exist	VERB
ejpam-1563	141	13	z	z	PROPN
ejpam-1563	141	14	∈	∈	PROPN
ejpam-1563	142	1	k	k	NOUN
ejpam-1563	143	1	such	such	ADJ
ejpam-1563	143	2	that	that	SCONJ
ejpam-1563	143	3	µ(z	µ(z	NOUN
ejpam-1563	143	4	)	)	PUNCT
ejpam-1563	143	5	<	<	X
ejpam-1563	143	6	µ(x%	µ(x%	PROPN
ejpam-1563	143	7	)	)	PUNCT
ejpam-1563	143	8	,	,	PUNCT
ejpam-1563	143	9	i.e.	i.e.	X
ejpam-1563	143	10	z	z	X
ejpam-1563	143	11	∈	∈	PROPN
ejpam-1563	143	12	u%	u%	NOUN
ejpam-1563	143	13	,	,	PUNCT
ejpam-1563	143	14	and	and	CCONJ
ejpam-1563	143	15	φ(x%	φ(x%	PROPN
ejpam-1563	143	16	,	,	PUNCT
ejpam-1563	143	17	z	z	NOUN
ejpam-1563	143	18	)	)	PUNCT
ejpam-1563	143	19	⊆	⊆	NUM
ejpam-1563	143	20	−c(x%	−c(x%	NOUN
ejpam-1563	143	21	)	)	PUNCT
ejpam-1563	143	22	.	.	PUNCT
ejpam-1563	144	1	on	on	ADP
ejpam-1563	144	2	the	the	DET
ejpam-1563	144	3	other	other	ADJ
ejpam-1563	144	4	hand	hand	NOUN
ejpam-1563	144	5	,	,	PUNCT
ejpam-1563	144	6	if	if	SCONJ
ejpam-1563	144	7	x%	x%	X
ejpam-1563	144	8	∈wr	∈wr	PROPN
ejpam-1563	144	9	,	,	PUNCT
ejpam-1563	144	10	setting	set	VERB
ejpam-1563	144	11	z	z	NOUN
ejpam-1563	144	12	:	:	PUNCT
ejpam-1563	144	13	=	=	SYM
ejpam-1563	144	14	x%	x%	NOUN
ejpam-1563	144	15	,	,	PUNCT
ejpam-1563	144	16	one	one	PRON
ejpam-1563	144	17	obtains	obtain	VERB
ejpam-1563	144	18	φ(x%	φ(x%	PROPN
ejpam-1563	144	19	,	,	PUNCT
ejpam-1563	144	20	z	z	NOUN
ejpam-1563	144	21	)	)	PUNCT
ejpam-1563	144	22	=	=	PRON
ejpam-1563	144	23	{	{	PUNCT
ejpam-1563	144	24	0	0	NUM
ejpam-1563	144	25	}	}	PUNCT
ejpam-1563	144	26	⊆	⊆	NUM
ejpam-1563	144	27	−c(x%	−c(x%	NOUN
ejpam-1563	144	28	)	)	PUNCT
ejpam-1563	144	29	.	.	PUNCT
ejpam-1563	145	1	in	in	ADP
ejpam-1563	145	2	both	both	DET
ejpam-1563	145	3	cases	case	NOUN
ejpam-1563	145	4	,	,	PUNCT
ejpam-1563	145	5	the	the	DET
ejpam-1563	145	6	result	result	NOUN
ejpam-1563	145	7	follows	follow	VERB
ejpam-1563	145	8	from	from	ADP
ejpam-1563	145	9	lemma	lemma	PROPN
ejpam-1563	145	10	2	2	NUM
ejpam-1563	145	11	.	.	PUNCT
ejpam-1563	146	1	the	the	DET
ejpam-1563	146	2	existence	existence	NOUN
ejpam-1563	146	3	of	of	ADP
ejpam-1563	146	4	solutions	solution	NOUN
ejpam-1563	146	5	to	to	ADP
ejpam-1563	146	6	problem	problem	NOUN
ejpam-1563	146	7	(	(	PUNCT
ejpam-1563	146	8	gvep1a	gvep1a	X
ejpam-1563	146	9	)	)	PUNCT
ejpam-1563	146	10	on	on	ADP
ejpam-1563	146	11	nonempty	nonempty	NOUN
ejpam-1563	146	12	,	,	PUNCT
ejpam-1563	146	13	bounded	bound	VERB
ejpam-1563	146	14	,	,	PUNCT
ejpam-1563	146	15	closed	closed	ADJ
ejpam-1563	146	16	and	and	CCONJ
ejpam-1563	146	17	convex	convex	ADJ
ejpam-1563	146	18	subsets	subset	NOUN
ejpam-1563	146	19	of	of	ADP
ejpam-1563	146	20	k	k	PROPN
ejpam-1563	146	21	is	be	AUX
ejpam-1563	146	22	guaranteed	guarantee	VERB
ejpam-1563	146	23	,	,	PUNCT
ejpam-1563	146	24	for	for	ADP
ejpam-1563	146	25	instance	instance	NOUN
ejpam-1563	146	26	,	,	PUNCT
ejpam-1563	146	27	by	by	ADP
ejpam-1563	146	28	theorem	theorem	NOUN
ejpam-1563	146	29	1	1	NUM
ejpam-1563	146	30	.	.	PUNCT
ejpam-1563	146	31	corollary	corollary	ADJ
ejpam-1563	147	1	1	1	NUM
ejpam-1563	147	2	.	.	PUNCT
ejpam-1563	148	1	let	let	VERB
ejpam-1563	148	2	x	x	PRON
ejpam-1563	148	3	be	be	AUX
ejpam-1563	148	4	a	a	DET
ejpam-1563	148	5	reflexive	reflexive	ADJ
ejpam-1563	148	6	banach	banach	NOUN
ejpam-1563	148	7	space	space	NOUN
ejpam-1563	148	8	,	,	PUNCT
ejpam-1563	148	9	y	y	PROPN
ejpam-1563	148	10	be	be	AUX
ejpam-1563	148	11	a	a	DET
ejpam-1563	148	12	banach	banach	NOUN
ejpam-1563	148	13	space	space	NOUN
ejpam-1563	148	14	,	,	PUNCT
ejpam-1563	148	15	k	k	X
ejpam-1563	148	16	be	be	AUX
ejpam-1563	148	17	a	a	DET
ejpam-1563	148	18	nonempty	nonempty	ADJ
ejpam-1563	148	19	,	,	PUNCT
ejpam-1563	148	20	closed	closed	ADJ
ejpam-1563	148	21	and	and	CCONJ
ejpam-1563	148	22	convex	convex	NOUN
ejpam-1563	148	23	subset	subset	NOUN
ejpam-1563	148	24	of	of	ADP
ejpam-1563	148	25	x	x	PUNCT
ejpam-1563	148	26	and	and	CCONJ
ejpam-1563	148	27	let	let	VERB
ejpam-1563	148	28	c	c	NOUN
ejpam-1563	148	29	:	:	PUNCT
ejpam-1563	148	30	k	k	PROPN
ejpam-1563	148	31	→	→	PUNCT
ejpam-1563	148	32	π(y	π(y	PROPN
ejpam-1563	148	33	)	)	PUNCT
ejpam-1563	148	34	map	map	VERB
ejpam-1563	148	35	any	any	DET
ejpam-1563	148	36	x	x	SYM
ejpam-1563	148	37	∈	∈	PROPN
ejpam-1563	148	38	k	k	PROPN
ejpam-1563	148	39	to	to	ADP
ejpam-1563	148	40	a	a	DET
ejpam-1563	148	41	convex	convex	NOUN
ejpam-1563	148	42	,	,	PUNCT
ejpam-1563	148	43	solid	solid	ADJ
ejpam-1563	148	44	and	and	CCONJ
ejpam-1563	148	45	pointed	point	VERB
ejpam-1563	148	46	cone	cone	NOUN
ejpam-1563	148	47	c(x)⊆	c(x)⊆	PROPN
ejpam-1563	148	48	y	y	PROPN
ejpam-1563	148	49	.	.	PUNCT
ejpam-1563	149	1	moreover	moreover	ADV
ejpam-1563	149	2	,	,	PUNCT
ejpam-1563	149	3	let	let	VERB
ejpam-1563	149	4	φ	φ	NOUN
ejpam-1563	149	5	:	:	PUNCT
ejpam-1563	150	1	k	k	PROPN
ejpam-1563	150	2	×	×	PROPN
ejpam-1563	150	3	k	k	PROPN
ejpam-1563	150	4	→	→	SYM
ejpam-1563	150	5	π(y	π(y	PROPN
ejpam-1563	150	6	)	)	PUNCT
ejpam-1563	150	7	be	be	AUX
ejpam-1563	150	8	such	such	ADJ
ejpam-1563	150	9	that	that	PRON
ejpam-1563	150	10	:	:	PUNCT
ejpam-1563	150	11	(	(	PUNCT
ejpam-1563	150	12	i	i	NOUN
ejpam-1563	150	13	)	)	PUNCT
ejpam-1563	150	14	φ(x	φ(x	PROPN
ejpam-1563	150	15	,	,	PUNCT
ejpam-1563	150	16	x	x	X
ejpam-1563	150	17	)	)	PUNCT
ejpam-1563	150	18	=	=	SYM
ejpam-1563	150	19	{	{	PUNCT
ejpam-1563	150	20	0	0	NUM
ejpam-1563	150	21	}	}	PUNCT
ejpam-1563	150	22	,	,	PUNCT
ejpam-1563	150	23	for	for	ADP
ejpam-1563	150	24	all	all	DET
ejpam-1563	150	25	x	x	SYM
ejpam-1563	150	26	∈	∈	PROPN
ejpam-1563	150	27	k	k	NOUN
ejpam-1563	150	28	;	;	PUNCT
ejpam-1563	150	29	(	(	PUNCT
ejpam-1563	150	30	ii	ii	NOUN
ejpam-1563	150	31	)	)	PUNCT
ejpam-1563	150	32	for	for	ADP
ejpam-1563	150	33	all	all	DET
ejpam-1563	150	34	x	x	SYM
ejpam-1563	150	35	,	,	PUNCT
ejpam-1563	150	36	y	y	PROPN
ejpam-1563	150	37	′	′	NOUN
ejpam-1563	150	38	,	,	PUNCT
ejpam-1563	151	1	y	y	PROPN
ejpam-1563	151	2	′′	′′	PROPN
ejpam-1563	151	3	∈	∈	PROPN
ejpam-1563	151	4	k	k	NOUN
ejpam-1563	151	5	,	,	PUNCT
ejpam-1563	151	6	if	if	SCONJ
ejpam-1563	151	7	φ(x	φ(x	PROPN
ejpam-1563	151	8	,	,	PUNCT
ejpam-1563	151	9	y	y	PROPN
ejpam-1563	151	10	′)⊆−c(x	′)⊆−c(x	NOUN
ejpam-1563	151	11	)	)	PUNCT
ejpam-1563	151	12	and	and	CCONJ
ejpam-1563	151	13	φ(x	φ(x	PROPN
ejpam-1563	151	14	,	,	PUNCT
ejpam-1563	151	15	y	y	PROPN
ejpam-1563	151	16	′′)⊆−int	′′)⊆−int	PROPN
ejpam-1563	151	17	c(x	c(x	NOUN
ejpam-1563	151	18	)	)	PUNCT
ejpam-1563	151	19	,	,	PUNCT
ejpam-1563	151	20	then	then	ADV
ejpam-1563	151	21	φ(x	φ(x	PROPN
ejpam-1563	151	22	,	,	PUNCT
ejpam-1563	151	23	αy	αy	X
ejpam-1563	151	24	′+	′+	PUNCT
ejpam-1563	151	25	(	(	PUNCT
ejpam-1563	151	26	1−α)y	1−α)y	NUM
ejpam-1563	151	27	′′)⊆−int	′′)⊆−int	ADJ
ejpam-1563	151	28	c(x	c(x	NOUN
ejpam-1563	151	29	)	)	PUNCT
ejpam-1563	151	30	,	,	PUNCT
ejpam-1563	151	31	for	for	ADP
ejpam-1563	151	32	all	all	DET
ejpam-1563	151	33	α	α	NOUN
ejpam-1563	151	34	∈	∈	NOUN
ejpam-1563	151	35	]	]	X
ejpam-1563	151	36	0,1	0,1	NUM
ejpam-1563	151	37	[	[	X
ejpam-1563	151	38	;	;	PUNCT
ejpam-1563	151	39	(	(	PUNCT
ejpam-1563	151	40	iii	iii	NOUN
ejpam-1563	151	41	)	)	PUNCT
ejpam-1563	151	42	for	for	ADP
ejpam-1563	151	43	any	any	DET
ejpam-1563	151	44	fixed	fix	VERB
ejpam-1563	151	45	y	y	PROPN
ejpam-1563	151	46	∈	∈	PROPN
ejpam-1563	151	47	k	k	PROPN
ejpam-1563	151	48	,	,	PUNCT
ejpam-1563	151	49	the	the	DET
ejpam-1563	151	50	set	set	NOUN
ejpam-1563	151	51	{	{	PUNCT
ejpam-1563	151	52	x	x	SYM
ejpam-1563	151	53	∈	∈	PROPN
ejpam-1563	151	54	k	k	NOUN
ejpam-1563	151	55	:	:	PUNCT
ejpam-1563	151	56	φ(x	φ(x	PROPN
ejpam-1563	151	57	,	,	PUNCT
ejpam-1563	151	58	y	y	PROPN
ejpam-1563	151	59	)	)	PUNCT
ejpam-1563	151	60	6⊆	6⊆	NOUN
ejpam-1563	151	61	−int	−int	ADP
ejpam-1563	151	62	c(x	c(x	NOUN
ejpam-1563	151	63	)	)	PUNCT
ejpam-1563	151	64	}	}	PUNCT
ejpam-1563	151	65	is	be	AUX
ejpam-1563	151	66	closed	close	VERB
ejpam-1563	151	67	with	with	ADP
ejpam-1563	151	68	respect	respect	NOUN
ejpam-1563	151	69	to	to	ADP
ejpam-1563	151	70	the	the	DET
ejpam-1563	151	71	topology	topology	NOUN
ejpam-1563	151	72	induced	induce	VERB
ejpam-1563	151	73	on	on	ADP
ejpam-1563	151	74	k	k	X
ejpam-1563	151	75	by	by	ADP
ejpam-1563	151	76	the	the	DET
ejpam-1563	151	77	weak	weak	ADJ
ejpam-1563	151	78	topology	topology	NOUN
ejpam-1563	151	79	of	of	ADP
ejpam-1563	151	80	x	x	X
ejpam-1563	151	81	.	.	PUNCT
ejpam-1563	152	1	if	if	SCONJ
ejpam-1563	152	2	(	(	PUNCT
ejpam-1563	152	3	g1a	g1a	NOUN
ejpam-1563	152	4	)	)	PUNCT
ejpam-1563	152	5	holds	hold	VERB
ejpam-1563	152	6	,	,	PUNCT
ejpam-1563	152	7	then	then	ADV
ejpam-1563	152	8	s1a	s1a	PROPN
ejpam-1563	152	9	k	k	PROPN
ejpam-1563	152	10	6=	6=	PROPN
ejpam-1563	152	11	;	;	PUNCT
ejpam-1563	152	12	.	.	PUNCT
ejpam-1563	153	1	proof	proof	NOUN
ejpam-1563	153	2	.	.	PUNCT
ejpam-1563	154	1	observe	observe	VERB
ejpam-1563	154	2	that	that	PRON
ejpam-1563	154	3	assumption	assumption	NOUN
ejpam-1563	154	4	(	(	PUNCT
ejpam-1563	154	5	ii	ii	NOUN
ejpam-1563	154	6	)	)	PUNCT
ejpam-1563	154	7	implies	imply	VERB
ejpam-1563	154	8	that	that	SCONJ
ejpam-1563	154	9	for	for	ADP
ejpam-1563	154	10	any	any	DET
ejpam-1563	154	11	fixed	fix	VERB
ejpam-1563	154	12	x	x	SYM
ejpam-1563	154	13	∈	∈	PROPN
ejpam-1563	154	14	k	k	PROPN
ejpam-1563	154	15	,	,	PUNCT
ejpam-1563	154	16	the	the	DET
ejpam-1563	154	17	set	set	NOUN
ejpam-1563	154	18	{	{	PUNCT
ejpam-1563	154	19	y	y	PROPN
ejpam-1563	154	20	∈	∈	PROPN
ejpam-1563	154	21	k	k	NOUN
ejpam-1563	154	22	:	:	PUNCT
ejpam-1563	154	23	φ(x	φ(x	PROPN
ejpam-1563	154	24	,	,	PUNCT
ejpam-1563	154	25	y	y	PROPN
ejpam-1563	154	26	)	)	PUNCT
ejpam-1563	154	27	⊆	⊆	NUM
ejpam-1563	154	28	−int	−int	ADP
ejpam-1563	154	29	c(x	c(x	NOUN
ejpam-1563	154	30	)	)	PUNCT
ejpam-1563	154	31	}	}	PUNCT
ejpam-1563	154	32	is	be	AUX
ejpam-1563	154	33	convex	convex	ADJ
ejpam-1563	154	34	.	.	PUNCT
ejpam-1563	155	1	hence	hence	ADV
ejpam-1563	155	2	,	,	PUNCT
ejpam-1563	155	3	for	for	ADP
ejpam-1563	155	4	any	any	DET
ejpam-1563	155	5	nonempty	nonempty	ADJ
ejpam-1563	155	6	,	,	PUNCT
ejpam-1563	155	7	closed	closed	ADJ
ejpam-1563	155	8	,	,	PUNCT
ejpam-1563	155	9	convex	convex	VERB
ejpam-1563	155	10	and	and	CCONJ
ejpam-1563	155	11	bounded	bound	VERB
ejpam-1563	155	12	set	set	VERB
ejpam-1563	155	13	h	h	NOUN
ejpam-1563	155	14	⊆	⊆	NUM
ejpam-1563	155	15	k	k	PROPN
ejpam-1563	155	16	,	,	PUNCT
ejpam-1563	155	17	assumptions	assumption	NOUN
ejpam-1563	155	18	(	(	PUNCT
ejpam-1563	155	19	i)-(iii	i)-(iii	NOUN
ejpam-1563	155	20	)	)	PUNCT
ejpam-1563	155	21	of	of	ADP
ejpam-1563	155	22	theorem	theorem	ADJ
ejpam-1563	155	23	1	1	NUM
ejpam-1563	155	24	hold	hold	NOUN
ejpam-1563	155	25	(	(	PUNCT
ejpam-1563	155	26	with	with	ADP
ejpam-1563	155	27	k	k	PROPN
ejpam-1563	155	28	replaced	replace	VERB
ejpam-1563	155	29	by	by	ADP
ejpam-1563	155	30	h	h	NOUN
ejpam-1563	155	31	and	and	CCONJ
ejpam-1563	155	32	v	v	NOUN
ejpam-1563	155	33	(	(	PUNCT
ejpam-1563	155	34	x	x	NOUN
ejpam-1563	155	35	)	)	PUNCT
ejpam-1563	155	36	=	=	SYM
ejpam-1563	155	37	−int	−int	ADP
ejpam-1563	155	38	c(x	c(x	NOUN
ejpam-1563	155	39	)	)	PUNCT
ejpam-1563	155	40	)	)	PUNCT
ejpam-1563	155	41	for	for	ADP
ejpam-1563	155	42	φ	φ	NUM
ejpam-1563	155	43	restricted	restrict	VERB
ejpam-1563	155	44	to	to	ADP
ejpam-1563	155	45	h	h	PROPN
ejpam-1563	155	46	×	×	PROPN
ejpam-1563	155	47	h.	h.	PROPN
ejpam-1563	155	48	then	then	ADV
ejpam-1563	155	49	,	,	PUNCT
ejpam-1563	155	50	by	by	ADP
ejpam-1563	155	51	theorem	theorem	NOUN
ejpam-1563	155	52	1	1	NUM
ejpam-1563	155	53	,	,	PUNCT
ejpam-1563	155	54	s1a	s1a	PROPN
ejpam-1563	155	55	h	h	NOUN
ejpam-1563	155	56	6=	6=	PROPN
ejpam-1563	155	57	;	;	PUNCT
ejpam-1563	155	58	.	.	PUNCT
ejpam-1563	156	1	hence	hence	ADV
ejpam-1563	156	2	,	,	PUNCT
ejpam-1563	156	3	the	the	DET
ejpam-1563	156	4	conclusion	conclusion	NOUN
ejpam-1563	156	5	follows	follow	VERB
ejpam-1563	156	6	from	from	ADP
ejpam-1563	156	7	theorem	theorem	ADJ
ejpam-1563	156	8	3	3	X
ejpam-1563	156	9	.	.	PUNCT
ejpam-1563	156	10	finally	finally	ADV
ejpam-1563	156	11	,	,	PUNCT
ejpam-1563	156	12	reasoning	reason	VERB
ejpam-1563	156	13	on	on	ADP
ejpam-1563	156	14	the	the	DET
ejpam-1563	156	15	same	same	ADJ
ejpam-1563	156	16	lines	line	NOUN
ejpam-1563	156	17	,	,	PUNCT
ejpam-1563	156	18	one	one	PRON
ejpam-1563	156	19	can	can	AUX
ejpam-1563	156	20	prove	prove	VERB
ejpam-1563	156	21	analogous	analogous	ADJ
ejpam-1563	156	22	results	result	NOUN
ejpam-1563	156	23	for	for	ADP
ejpam-1563	156	24	problem	problem	NOUN
ejpam-1563	156	25	(	(	PUNCT
ejpam-1563	156	26	gvep1b	gvep1b	NOUN
ejpam-1563	156	27	)	)	PUNCT
ejpam-1563	156	28	.	.	PUNCT
ejpam-1563	157	1	to	to	ADP
ejpam-1563	157	2	this	this	DET
ejpam-1563	157	3	end	end	NOUN
ejpam-1563	157	4	,	,	PUNCT
ejpam-1563	157	5	it	it	PRON
ejpam-1563	157	6	basically	basically	ADV
ejpam-1563	157	7	suffices	suffice	VERB
ejpam-1563	157	8	to	to	ADP
ejpam-1563	157	9	substitute	substitute	NOUN
ejpam-1563	157	10	c(x)\{0	c(x)\{0	NOUN
ejpam-1563	157	11	}	}	PUNCT
ejpam-1563	157	12	for	for	ADP
ejpam-1563	157	13	int	int	NOUN
ejpam-1563	157	14	c(x	c(x	NOUN
ejpam-1563	157	15	)	)	PUNCT
ejpam-1563	157	16	(	(	PUNCT
ejpam-1563	157	17	in	in	ADP
ejpam-1563	157	18	this	this	DET
ejpam-1563	157	19	case	case	NOUN
ejpam-1563	157	20	,	,	PUNCT
ejpam-1563	157	21	c	c	PROPN
ejpam-1563	157	22	does	do	AUX
ejpam-1563	157	23	not	not	PART
ejpam-1563	157	24	need	need	VERB
ejpam-1563	157	25	to	to	PART
ejpam-1563	157	26	be	be	AUX
ejpam-1563	157	27	solid	solid	ADJ
ejpam-1563	157	28	)	)	PUNCT
ejpam-1563	157	29	.	.	PUNCT
ejpam-1563	158	1	for	for	ADP
ejpam-1563	158	2	instance	instance	NOUN
ejpam-1563	158	3	,	,	PUNCT
ejpam-1563	158	4	corollary	corollary	ADJ
ejpam-1563	158	5	1	1	NUM
ejpam-1563	158	6	reads	read	NOUN
ejpam-1563	158	7	as	as	ADP
ejpam-1563	158	8	in	in	ADP
ejpam-1563	158	9	the	the	DET
ejpam-1563	158	10	following	following	NOUN
ejpam-1563	158	11	,	,	PUNCT
ejpam-1563	158	12	where	where	SCONJ
ejpam-1563	158	13	the	the	DET
ejpam-1563	158	14	coercivity	coercivity	NOUN
ejpam-1563	158	15	assumption	assumption	NOUN
ejpam-1563	158	16	(	(	PUNCT
ejpam-1563	158	17	g1a	g1a	NOUN
ejpam-1563	158	18	)	)	PUNCT
ejpam-1563	158	19	is	be	AUX
ejpam-1563	158	20	replaced	replace	VERB
ejpam-1563	158	21	by	by	ADP
ejpam-1563	158	22	(	(	PUNCT
ejpam-1563	158	23	g1b	g1b	ADJ
ejpam-1563	158	24	)	)	PUNCT
ejpam-1563	158	25	there	there	PRON
ejpam-1563	158	26	exist	exist	VERB
ejpam-1563	158	27	a	a	DET
ejpam-1563	158	28	convex	convex	NOUN
ejpam-1563	158	29	lower	low	ADJ
ejpam-1563	158	30	semicontinuous	semicontinuous	ADJ
ejpam-1563	158	31	function	function	NOUN
ejpam-1563	158	32	µ	µ	NOUN
ejpam-1563	158	33	:	:	PUNCT
ejpam-1563	158	34	x	x	SYM
ejpam-1563	158	35	→	→	SYM
ejpam-1563	158	36	r	r	NOUN
ejpam-1563	158	37	,	,	PUNCT
ejpam-1563	158	38	which	which	PRON
ejpam-1563	158	39	is	be	AUX
ejpam-1563	158	40	weakly	weakly	ADV
ejpam-1563	158	41	coercive	coercive	ADJ
ejpam-1563	158	42	with	with	ADP
ejpam-1563	158	43	respect	respect	NOUN
ejpam-1563	158	44	to	to	ADP
ejpam-1563	158	45	the	the	DET
ejpam-1563	158	46	set	set	NOUN
ejpam-1563	158	47	k	k	NOUN
ejpam-1563	158	48	,	,	PUNCT
ejpam-1563	158	49	and	and	CCONJ
ejpam-1563	158	50	a	a	DET
ejpam-1563	158	51	number	number	NOUN
ejpam-1563	158	52	r	r	NOUN
ejpam-1563	158	53	such	such	ADJ
ejpam-1563	158	54	that	that	PRON
ejpam-1563	158	55	for	for	ADP
ejpam-1563	158	56	any	any	DET
ejpam-1563	158	57	point	point	NOUN
ejpam-1563	158	58	x	x	X
ejpam-1563	158	59	∈	∈	PROPN
ejpam-1563	158	60	k\wr	k\wr	PROPN
ejpam-1563	158	61	with	with	ADP
ejpam-1563	158	62	φ	φ	PROPN
ejpam-1563	158	63	�	�	PROPN
ejpam-1563	158	64	x	x	SYM
ejpam-1563	158	65	,	,	PUNCT
ejpam-1563	158	66	y	y	PROPN
ejpam-1563	158	67	�	�	PROPN
ejpam-1563	158	68	6⊆	6⊆	PROPN
ejpam-1563	158	69	−c(x)\{0	−c(x)\{0	PROPN
ejpam-1563	158	70	}	}	PUNCT
ejpam-1563	158	71	,	,	PUNCT
ejpam-1563	158	72	∀y	∀y	PROPN
ejpam-1563	158	73	∈wr	∈wr	NUM
ejpam-1563	158	74	,	,	PUNCT
ejpam-1563	158	75	(	(	PUNCT
ejpam-1563	158	76	3	3	X
ejpam-1563	158	77	)	)	PUNCT
ejpam-1563	158	78	there	there	PRON
ejpam-1563	158	79	is	be	VERB
ejpam-1563	158	80	a	a	DET
ejpam-1563	158	81	point	point	NOUN
ejpam-1563	158	82	z	z	NOUN
ejpam-1563	158	83	∈	∈	PROPN
ejpam-1563	158	84	k	k	NOUN
ejpam-1563	158	85	,	,	PUNCT
ejpam-1563	158	86	µ(z	µ(z	PROPN
ejpam-1563	158	87	)	)	PUNCT
ejpam-1563	158	88	<	<	X
ejpam-1563	158	89	µ(x	µ(x	NOUN
ejpam-1563	158	90	)	)	PUNCT
ejpam-1563	158	91	,	,	PUNCT
ejpam-1563	158	92	such	such	ADJ
ejpam-1563	158	93	that	that	SCONJ
ejpam-1563	158	94	φ(x	φ(x	PROPN
ejpam-1563	158	95	,	,	PUNCT
ejpam-1563	158	96	z)⊆−c(x	z)⊆−c(x	NOUN
ejpam-1563	158	97	)	)	PUNCT
ejpam-1563	158	98	.	.	PUNCT
ejpam-1563	159	1	e.	e.	PROPN
ejpam-1563	159	2	allevi	allevi	PROPN
ejpam-1563	159	3	,	,	PUNCT
ejpam-1563	159	4	i.	i.	PROPN
ejpam-1563	159	5	konnov	konnov	PROPN
ejpam-1563	159	6	,	,	PUNCT
ejpam-1563	159	7	m.	m.	NOUN
ejpam-1563	159	8	rocco	rocco	NOUN
ejpam-1563	159	9	/	/	SYM
ejpam-1563	159	10	eur	eur	PROPN
ejpam-1563	159	11	.	.	PUNCT
ejpam-1563	160	1	j.	j.	PROPN
ejpam-1563	160	2	pure	pure	PROPN
ejpam-1563	160	3	appl	appl	PROPN
ejpam-1563	160	4	.	.	PROPN
ejpam-1563	160	5	math	math	PROPN
ejpam-1563	160	6	,	,	PUNCT
ejpam-1563	160	7	6	6	NUM
ejpam-1563	160	8	(	(	PUNCT
ejpam-1563	160	9	2013	2013	NUM
ejpam-1563	160	10	)	)	PUNCT
ejpam-1563	160	11	,	,	PUNCT
ejpam-1563	160	12	365	365	NUM
ejpam-1563	160	13	-	-	SYM
ejpam-1563	160	14	376	376	NUM
ejpam-1563	160	15	372	372	NUM
ejpam-1563	160	16	corollary	corollary	NOUN
ejpam-1563	160	17	2	2	NUM
ejpam-1563	160	18	.	.	PUNCT
ejpam-1563	161	1	let	let	VERB
ejpam-1563	161	2	x	x	PRON
ejpam-1563	161	3	be	be	AUX
ejpam-1563	161	4	a	a	DET
ejpam-1563	161	5	reflexive	reflexive	ADJ
ejpam-1563	161	6	banach	banach	NOUN
ejpam-1563	161	7	space	space	NOUN
ejpam-1563	161	8	,	,	PUNCT
ejpam-1563	161	9	y	y	PROPN
ejpam-1563	161	10	be	be	AUX
ejpam-1563	161	11	a	a	DET
ejpam-1563	161	12	banach	banach	NOUN
ejpam-1563	161	13	space	space	NOUN
ejpam-1563	161	14	,	,	PUNCT
ejpam-1563	161	15	k	k	X
ejpam-1563	161	16	be	be	AUX
ejpam-1563	161	17	a	a	DET
ejpam-1563	161	18	nonempty	nonempty	ADJ
ejpam-1563	161	19	,	,	PUNCT
ejpam-1563	161	20	closed	closed	ADJ
ejpam-1563	161	21	and	and	CCONJ
ejpam-1563	161	22	convex	convex	NOUN
ejpam-1563	161	23	subset	subset	NOUN
ejpam-1563	161	24	of	of	ADP
ejpam-1563	161	25	x	x	PUNCT
ejpam-1563	161	26	and	and	CCONJ
ejpam-1563	161	27	let	let	VERB
ejpam-1563	161	28	c	c	NOUN
ejpam-1563	161	29	:	:	PUNCT
ejpam-1563	161	30	k	k	PROPN
ejpam-1563	161	31	→	→	PUNCT
ejpam-1563	161	32	π(y	π(y	PROPN
ejpam-1563	161	33	)	)	PUNCT
ejpam-1563	161	34	map	map	VERB
ejpam-1563	161	35	any	any	DET
ejpam-1563	161	36	x	x	SYM
ejpam-1563	161	37	∈	∈	PROPN
ejpam-1563	161	38	k	k	NOUN
ejpam-1563	161	39	to	to	ADP
ejpam-1563	161	40	a	a	DET
ejpam-1563	161	41	convex	convex	NOUN
ejpam-1563	161	42	and	and	CCONJ
ejpam-1563	161	43	pointed	point	VERB
ejpam-1563	161	44	cone	cone	NOUN
ejpam-1563	161	45	c(x)⊆	c(x)⊆	PROPN
ejpam-1563	161	46	y	y	PROPN
ejpam-1563	161	47	.	.	PUNCT
ejpam-1563	162	1	moreover	moreover	ADV
ejpam-1563	162	2	,	,	PUNCT
ejpam-1563	162	3	let	let	VERB
ejpam-1563	162	4	φ	φ	NOUN
ejpam-1563	162	5	:	:	PUNCT
ejpam-1563	163	1	k	k	PROPN
ejpam-1563	163	2	×	×	PROPN
ejpam-1563	163	3	k	k	PROPN
ejpam-1563	163	4	→	→	SYM
ejpam-1563	163	5	π(y	π(y	PROPN
ejpam-1563	163	6	)	)	PUNCT
ejpam-1563	163	7	be	be	AUX
ejpam-1563	163	8	such	such	ADJ
ejpam-1563	163	9	that	that	PRON
ejpam-1563	163	10	:	:	PUNCT
ejpam-1563	163	11	(	(	PUNCT
ejpam-1563	163	12	i	i	NOUN
ejpam-1563	163	13	)	)	PUNCT
ejpam-1563	163	14	φ(x	φ(x	PROPN
ejpam-1563	163	15	,	,	PUNCT
ejpam-1563	163	16	x	x	X
ejpam-1563	163	17	)	)	PUNCT
ejpam-1563	163	18	=	=	SYM
ejpam-1563	163	19	{	{	PUNCT
ejpam-1563	163	20	0	0	NUM
ejpam-1563	163	21	}	}	PUNCT
ejpam-1563	163	22	,	,	PUNCT
ejpam-1563	163	23	for	for	ADP
ejpam-1563	163	24	all	all	DET
ejpam-1563	163	25	x	x	SYM
ejpam-1563	163	26	∈	∈	PROPN
ejpam-1563	163	27	k	k	NOUN
ejpam-1563	163	28	;	;	PUNCT
ejpam-1563	163	29	(	(	PUNCT
ejpam-1563	163	30	ii	ii	NOUN
ejpam-1563	163	31	)	)	PUNCT
ejpam-1563	163	32	for	for	ADP
ejpam-1563	163	33	all	all	DET
ejpam-1563	163	34	x	x	SYM
ejpam-1563	163	35	,	,	PUNCT
ejpam-1563	163	36	y	y	PROPN
ejpam-1563	163	37	′	′	NOUN
ejpam-1563	163	38	,	,	PUNCT
ejpam-1563	164	1	y	y	PROPN
ejpam-1563	164	2	′′	′′	PROPN
ejpam-1563	164	3	∈	∈	PROPN
ejpam-1563	164	4	k	k	NOUN
ejpam-1563	164	5	,	,	PUNCT
ejpam-1563	164	6	if	if	SCONJ
ejpam-1563	164	7	φ(x	φ(x	PROPN
ejpam-1563	164	8	,	,	PUNCT
ejpam-1563	164	9	y	y	PROPN
ejpam-1563	164	10	′)⊆−c(x	′)⊆−c(x	NOUN
ejpam-1563	164	11	)	)	PUNCT
ejpam-1563	164	12	and	and	CCONJ
ejpam-1563	164	13	φ(x	φ(x	PROPN
ejpam-1563	164	14	,	,	PUNCT
ejpam-1563	164	15	y	y	PROPN
ejpam-1563	164	16	′′)⊆−c(x)\{0	′′)⊆−c(x)\{0	PROPN
ejpam-1563	164	17	}	}	PUNCT
ejpam-1563	164	18	,	,	PUNCT
ejpam-1563	164	19	then	then	ADV
ejpam-1563	164	20	φ(x	φ(x	PROPN
ejpam-1563	164	21	,	,	PUNCT
ejpam-1563	164	22	αy	αy	X
ejpam-1563	164	23	′+	′+	PUNCT
ejpam-1563	164	24	(	(	PUNCT
ejpam-1563	164	25	1−α)y	1−α)y	NUM
ejpam-1563	164	26	′′)⊆−c(x)\{0	′′)⊆−c(x)\{0	PROPN
ejpam-1563	164	27	}	}	PUNCT
ejpam-1563	164	28	,	,	PUNCT
ejpam-1563	164	29	for	for	ADP
ejpam-1563	164	30	all	all	DET
ejpam-1563	164	31	α	α	NOUN
ejpam-1563	164	32	∈	∈	NOUN
ejpam-1563	164	33	]	]	X
ejpam-1563	164	34	0,1	0,1	NUM
ejpam-1563	164	35	[	[	X
ejpam-1563	164	36	;	;	PUNCT
ejpam-1563	164	37	(	(	PUNCT
ejpam-1563	164	38	iii	iii	NOUN
ejpam-1563	164	39	)	)	PUNCT
ejpam-1563	164	40	for	for	ADP
ejpam-1563	164	41	any	any	DET
ejpam-1563	164	42	fixed	fix	VERB
ejpam-1563	164	43	y	y	PROPN
ejpam-1563	164	44	∈	∈	PROPN
ejpam-1563	164	45	k	k	PROPN
ejpam-1563	164	46	,	,	PUNCT
ejpam-1563	164	47	the	the	DET
ejpam-1563	164	48	set	set	NOUN
ejpam-1563	164	49	{	{	PUNCT
ejpam-1563	164	50	x	x	SYM
ejpam-1563	164	51	∈	∈	PROPN
ejpam-1563	164	52	k	k	NOUN
ejpam-1563	164	53	:	:	PUNCT
ejpam-1563	164	54	φ(x	φ(x	PROPN
ejpam-1563	164	55	,	,	PUNCT
ejpam-1563	164	56	y	y	PROPN
ejpam-1563	164	57	)	)	PUNCT
ejpam-1563	164	58	6⊆	6⊆	PROPN
ejpam-1563	164	59	−c(x)\{0	−c(x)\{0	PROPN
ejpam-1563	164	60	}	}	PUNCT
ejpam-1563	164	61	}	}	PUNCT
ejpam-1563	164	62	is	be	AUX
ejpam-1563	164	63	closed	close	VERB
ejpam-1563	164	64	with	with	ADP
ejpam-1563	164	65	respect	respect	NOUN
ejpam-1563	164	66	to	to	ADP
ejpam-1563	164	67	the	the	DET
ejpam-1563	164	68	topology	topology	NOUN
ejpam-1563	164	69	induced	induce	VERB
ejpam-1563	164	70	on	on	ADP
ejpam-1563	164	71	k	k	X
ejpam-1563	164	72	by	by	ADP
ejpam-1563	164	73	the	the	DET
ejpam-1563	164	74	weak	weak	ADJ
ejpam-1563	164	75	topology	topology	NOUN
ejpam-1563	164	76	of	of	ADP
ejpam-1563	164	77	x	x	X
ejpam-1563	164	78	.	.	PUNCT
ejpam-1563	165	1	if	if	SCONJ
ejpam-1563	165	2	(	(	PUNCT
ejpam-1563	165	3	g1b	g1b	ADJ
ejpam-1563	165	4	)	)	PUNCT
ejpam-1563	165	5	holds	hold	NOUN
ejpam-1563	165	6	,	,	PUNCT
ejpam-1563	165	7	then	then	ADV
ejpam-1563	165	8	s1b	s1b	VERB
ejpam-1563	165	9	k	k	PROPN
ejpam-1563	165	10	6=	6=	PROPN
ejpam-1563	165	11	;	;	PUNCT
ejpam-1563	165	12	.	.	PUNCT
ejpam-1563	166	1	4	4	X
ejpam-1563	166	2	.	.	X
ejpam-1563	166	3	existence	existence	NOUN
ejpam-1563	166	4	results	result	VERB
ejpam-1563	166	5	for	for	ADP
ejpam-1563	166	6	(	(	PUNCT
ejpam-1563	166	7	gvep2a	gvep2a	ADJ
ejpam-1563	166	8	)	)	PUNCT
ejpam-1563	166	9	and	and	CCONJ
ejpam-1563	166	10	(	(	PUNCT
ejpam-1563	166	11	gvep2b	gvep2b	PROPN
ejpam-1563	166	12	)	)	PUNCT
ejpam-1563	166	13	the	the	DET
ejpam-1563	166	14	goal	goal	NOUN
ejpam-1563	166	15	of	of	ADP
ejpam-1563	166	16	this	this	DET
ejpam-1563	166	17	section	section	NOUN
ejpam-1563	166	18	is	be	AUX
ejpam-1563	166	19	to	to	PART
ejpam-1563	166	20	briefly	briefly	ADV
ejpam-1563	166	21	explain	explain	VERB
ejpam-1563	166	22	how	how	SCONJ
ejpam-1563	166	23	to	to	PART
ejpam-1563	166	24	obtain	obtain	VERB
ejpam-1563	166	25	existence	existence	NOUN
ejpam-1563	166	26	results	result	NOUN
ejpam-1563	166	27	for	for	ADP
ejpam-1563	166	28	problems	problem	NOUN
ejpam-1563	166	29	(	(	PUNCT
ejpam-1563	166	30	gvep2a	gvep2a	ADJ
ejpam-1563	166	31	)	)	PUNCT
ejpam-1563	166	32	and	and	CCONJ
ejpam-1563	166	33	(	(	PUNCT
ejpam-1563	166	34	gvep2b	gvep2b	PROPN
ejpam-1563	166	35	)	)	PUNCT
ejpam-1563	166	36	on	on	ADP
ejpam-1563	166	37	unbounded	unbounded	ADJ
ejpam-1563	166	38	sets	set	NOUN
ejpam-1563	166	39	,	,	PUNCT
ejpam-1563	166	40	analogous	analogous	ADJ
ejpam-1563	166	41	to	to	ADP
ejpam-1563	166	42	corollaries	corollary	NOUN
ejpam-1563	166	43	1	1	NUM
ejpam-1563	166	44	and	and	CCONJ
ejpam-1563	166	45	2	2	NUM
ejpam-1563	166	46	.	.	PUNCT
ejpam-1563	167	1	the	the	DET
ejpam-1563	167	2	proofs	proof	NOUN
ejpam-1563	167	3	are	be	AUX
ejpam-1563	167	4	on	on	ADP
ejpam-1563	167	5	the	the	DET
ejpam-1563	167	6	same	same	ADJ
ejpam-1563	167	7	lines	line	NOUN
ejpam-1563	167	8	and	and	CCONJ
ejpam-1563	167	9	we	we	PRON
ejpam-1563	167	10	will	will	AUX
ejpam-1563	167	11	explicitly	explicitly	ADV
ejpam-1563	167	12	propose	propose	VERB
ejpam-1563	167	13	only	only	ADV
ejpam-1563	167	14	those	those	PRON
ejpam-1563	167	15	related	relate	VERB
ejpam-1563	167	16	to	to	ADP
ejpam-1563	167	17	problem	problem	NOUN
ejpam-1563	167	18	(	(	PUNCT
ejpam-1563	167	19	gvep2a	gvep2a	ADJ
ejpam-1563	167	20	)	)	PUNCT
ejpam-1563	167	21	.	.	PUNCT
ejpam-1563	168	1	in	in	ADP
ejpam-1563	168	2	this	this	DET
ejpam-1563	168	3	case	case	NOUN
ejpam-1563	168	4	,	,	PUNCT
ejpam-1563	168	5	the	the	DET
ejpam-1563	168	6	coercivity	coercivity	NOUN
ejpam-1563	168	7	assumption	assumption	NOUN
ejpam-1563	168	8	is	be	AUX
ejpam-1563	168	9	modified	modify	VERB
ejpam-1563	168	10	in	in	ADP
ejpam-1563	168	11	the	the	DET
ejpam-1563	168	12	following	follow	VERB
ejpam-1563	168	13	natural	natural	ADJ
ejpam-1563	168	14	way	way	NOUN
ejpam-1563	168	15	.	.	PUNCT
ejpam-1563	169	1	(	(	PUNCT
ejpam-1563	169	2	g2a	g2a	NOUN
ejpam-1563	169	3	)	)	PUNCT
ejpam-1563	169	4	there	there	PRON
ejpam-1563	169	5	exist	exist	VERB
ejpam-1563	169	6	a	a	DET
ejpam-1563	169	7	convex	convex	NOUN
ejpam-1563	169	8	lower	low	ADJ
ejpam-1563	169	9	semicontinuous	semicontinuous	ADJ
ejpam-1563	169	10	function	function	NOUN
ejpam-1563	169	11	µ	µ	NOUN
ejpam-1563	169	12	:	:	PUNCT
ejpam-1563	169	13	x	x	SYM
ejpam-1563	169	14	→	→	SYM
ejpam-1563	169	15	r	r	NOUN
ejpam-1563	169	16	,	,	PUNCT
ejpam-1563	169	17	which	which	PRON
ejpam-1563	169	18	is	be	AUX
ejpam-1563	169	19	weakly	weakly	ADV
ejpam-1563	169	20	coercive	coercive	ADJ
ejpam-1563	169	21	with	with	ADP
ejpam-1563	169	22	respect	respect	NOUN
ejpam-1563	169	23	to	to	ADP
ejpam-1563	169	24	the	the	DET
ejpam-1563	169	25	set	set	NOUN
ejpam-1563	169	26	k	k	NOUN
ejpam-1563	169	27	,	,	PUNCT
ejpam-1563	169	28	and	and	CCONJ
ejpam-1563	169	29	a	a	DET
ejpam-1563	169	30	number	number	NOUN
ejpam-1563	169	31	r	r	NOUN
ejpam-1563	169	32	such	such	ADJ
ejpam-1563	169	33	that	that	PRON
ejpam-1563	169	34	for	for	ADP
ejpam-1563	169	35	any	any	DET
ejpam-1563	169	36	point	point	NOUN
ejpam-1563	169	37	x	x	X
ejpam-1563	169	38	∈	∈	PROPN
ejpam-1563	169	39	k\wr	k\wr	PROPN
ejpam-1563	169	40	with	with	ADP
ejpam-1563	169	41	φ	φ	PROPN
ejpam-1563	169	42	�	�	PROPN
ejpam-1563	169	43	x	x	SYM
ejpam-1563	169	44	,	,	PUNCT
ejpam-1563	169	45	y	y	PROPN
ejpam-1563	169	46	�	�	PROPN
ejpam-1563	169	47	∩−int	∩−int	PROPN
ejpam-1563	169	48	c(x	c(x	NOUN
ejpam-1563	169	49	)	)	PUNCT
ejpam-1563	169	50	=	=	PUNCT
ejpam-1563	169	51	;	;	PUNCT
ejpam-1563	169	52	,	,	PUNCT
ejpam-1563	169	53	∀y	∀y	PROPN
ejpam-1563	169	54	∈wr	∈wr	NUM
ejpam-1563	169	55	,	,	PUNCT
ejpam-1563	169	56	(	(	PUNCT
ejpam-1563	169	57	4	4	X
ejpam-1563	169	58	)	)	PUNCT
ejpam-1563	169	59	there	there	PRON
ejpam-1563	169	60	is	be	VERB
ejpam-1563	169	61	a	a	DET
ejpam-1563	169	62	point	point	NOUN
ejpam-1563	169	63	z	z	NOUN
ejpam-1563	169	64	∈	∈	PROPN
ejpam-1563	169	65	k	k	NOUN
ejpam-1563	169	66	,	,	PUNCT
ejpam-1563	169	67	µ(z	µ(z	PROPN
ejpam-1563	169	68	)	)	PUNCT
ejpam-1563	169	69	<	<	X
ejpam-1563	169	70	µ(x	µ(x	NOUN
ejpam-1563	169	71	)	)	PUNCT
ejpam-1563	169	72	,	,	PUNCT
ejpam-1563	169	73	such	such	ADJ
ejpam-1563	169	74	that	that	SCONJ
ejpam-1563	169	75	φ(x	φ(x	PROPN
ejpam-1563	169	76	,	,	PUNCT
ejpam-1563	169	77	z)∩−c(x	z)∩−c(x	NOUN
ejpam-1563	169	78	)	)	PUNCT
ejpam-1563	169	79	6=	6=	NUM
ejpam-1563	169	80	;	;	PUNCT
ejpam-1563	169	81	.	.	PUNCT
ejpam-1563	170	1	again	again	ADV
ejpam-1563	170	2	,	,	PUNCT
ejpam-1563	170	3	as	as	ADP
ejpam-1563	170	4	in	in	ADP
ejpam-1563	170	5	(	(	PUNCT
ejpam-1563	170	6	g1a	g1a	NOUN
ejpam-1563	170	7	)	)	PUNCT
ejpam-1563	170	8	the	the	DET
ejpam-1563	170	9	set	set	NOUN
ejpam-1563	170	10	wr	wr	NOUN
ejpam-1563	170	11	in	in	ADP
ejpam-1563	170	12	(	(	PUNCT
ejpam-1563	170	13	g2a	g2a	PROPN
ejpam-1563	170	14	)	)	PUNCT
ejpam-1563	170	15	is	be	AUX
ejpam-1563	170	16	nonempty	nonempty	ADJ
ejpam-1563	170	17	and	and	CCONJ
ejpam-1563	170	18	bounded	bound	VERB
ejpam-1563	170	19	(	(	PUNCT
ejpam-1563	170	20	see	see	VERB
ejpam-1563	170	21	remarks	remark	NOUN
ejpam-1563	170	22	4	4	NUM
ejpam-1563	170	23	and	and	CCONJ
ejpam-1563	170	24	3	3	NUM
ejpam-1563	170	25	)	)	PUNCT
ejpam-1563	170	26	.	.	PUNCT
ejpam-1563	171	1	lemma	lemma	PROPN
ejpam-1563	171	2	3	3	X
ejpam-1563	171	3	.	.	PUNCT
ejpam-1563	172	1	let	let	VERB
ejpam-1563	172	2	x	x	PRON
ejpam-1563	172	3	be	be	AUX
ejpam-1563	172	4	a	a	DET
ejpam-1563	172	5	reflexive	reflexive	ADJ
ejpam-1563	172	6	banach	banach	NOUN
ejpam-1563	172	7	space	space	NOUN
ejpam-1563	172	8	,	,	PUNCT
ejpam-1563	172	9	y	y	PROPN
ejpam-1563	172	10	be	be	AUX
ejpam-1563	172	11	a	a	DET
ejpam-1563	172	12	banach	banach	NOUN
ejpam-1563	172	13	space	space	NOUN
ejpam-1563	172	14	,	,	PUNCT
ejpam-1563	172	15	k	k	PROPN
ejpam-1563	172	16	⊆	⊆	NUM
ejpam-1563	172	17	x	x	PUNCT
ejpam-1563	172	18	be	be	AUX
ejpam-1563	172	19	nonempty	nonempty	ADJ
ejpam-1563	172	20	,	,	PUNCT
ejpam-1563	172	21	closed	closed	ADJ
ejpam-1563	172	22	and	and	CCONJ
ejpam-1563	172	23	convex	convex	PROPN
ejpam-1563	172	24	,	,	PUNCT
ejpam-1563	172	25	c	c	NOUN
ejpam-1563	172	26	:	:	PUNCT
ejpam-1563	172	27	k	k	X
ejpam-1563	172	28	→	→	PUNCT
ejpam-1563	172	29	π(y	π(y	PROPN
ejpam-1563	172	30	)	)	PUNCT
ejpam-1563	172	31	be	be	AUX
ejpam-1563	172	32	a	a	DET
ejpam-1563	172	33	set	set	NOUN
ejpam-1563	172	34	-	-	PUNCT
ejpam-1563	172	35	valued	value	VERB
ejpam-1563	172	36	mapping	mapping	NOUN
ejpam-1563	172	37	that	that	PRON
ejpam-1563	172	38	maps	map	VERB
ejpam-1563	172	39	any	any	DET
ejpam-1563	172	40	x	x	SYM
ejpam-1563	172	41	∈	∈	PROPN
ejpam-1563	172	42	k	k	PROPN
ejpam-1563	172	43	to	to	ADP
ejpam-1563	172	44	a	a	DET
ejpam-1563	172	45	convex	convex	NOUN
ejpam-1563	172	46	,	,	PUNCT
ejpam-1563	172	47	solid	solid	ADJ
ejpam-1563	172	48	and	and	CCONJ
ejpam-1563	172	49	pointed	point	VERB
ejpam-1563	172	50	cone	cone	NOUN
ejpam-1563	172	51	of	of	ADP
ejpam-1563	172	52	y	y	PROPN
ejpam-1563	172	53	and	and	CCONJ
ejpam-1563	172	54	φ	φ	NUM
ejpam-1563	172	55	:	:	PUNCT
ejpam-1563	173	1	k	k	PROPN
ejpam-1563	173	2	×	×	PROPN
ejpam-1563	173	3	k	k	PROPN
ejpam-1563	173	4	→	→	SYM
ejpam-1563	173	5	π(y	π(y	PROPN
ejpam-1563	173	6	)	)	PUNCT
ejpam-1563	173	7	be	be	AUX
ejpam-1563	173	8	such	such	ADJ
ejpam-1563	173	9	that	that	DET
ejpam-1563	173	10	c2	c2	PROPN
ejpam-1563	173	11	)	)	PUNCT
ejpam-1563	173	12	for	for	ADP
ejpam-1563	173	13	all	all	DET
ejpam-1563	173	14	x	x	SYM
ejpam-1563	173	15	,	,	PUNCT
ejpam-1563	173	16	y	y	PROPN
ejpam-1563	173	17	′	′	NOUN
ejpam-1563	173	18	,	,	PUNCT
ejpam-1563	173	19	y	y	PROPN
ejpam-1563	173	20	′′	′′	PROPN
ejpam-1563	173	21	∈	∈	PROPN
ejpam-1563	174	1	k	k	PROPN
ejpam-1563	174	2	if	if	SCONJ
ejpam-1563	174	3	φ(x	φ(x	PROPN
ejpam-1563	174	4	,	,	PUNCT
ejpam-1563	174	5	y	y	PROPN
ejpam-1563	174	6	′)∩−c(x	′)∩−c(x	PROPN
ejpam-1563	174	7	)	)	PUNCT
ejpam-1563	174	8	6=	6=	NUM
ejpam-1563	174	9	;	;	PUNCT
ejpam-1563	174	10	and	and	CCONJ
ejpam-1563	174	11	φ(x	φ(x	PROPN
ejpam-1563	174	12	,	,	PUNCT
ejpam-1563	174	13	y	y	PROPN
ejpam-1563	174	14	′′)∩−int	′′)∩−int	NUM
ejpam-1563	174	15	c(x	c(x	NOUN
ejpam-1563	174	16	)	)	PUNCT
ejpam-1563	174	17	6=	6=	PUNCT
ejpam-1563	175	1	;	;	PUNCT
ejpam-1563	175	2	,	,	PUNCT
ejpam-1563	175	3	then	then	ADV
ejpam-1563	175	4	φ(x	φ(x	PROPN
ejpam-1563	175	5	,	,	PUNCT
ejpam-1563	175	6	αy	αy	X
ejpam-1563	175	7	′+	′+	PUNCT
ejpam-1563	175	8	(	(	PUNCT
ejpam-1563	175	9	1−α)y	1−α)y	NUM
ejpam-1563	175	10	′′)∩−int	′′)∩−int	NUM
ejpam-1563	175	11	c(x	c(x	NOUN
ejpam-1563	175	12	)	)	PUNCT
ejpam-1563	175	13	6=	6=	NUM
ejpam-1563	175	14	;	;	PUNCT
ejpam-1563	175	15	for	for	ADP
ejpam-1563	175	16	all	all	DET
ejpam-1563	175	17	α	α	NOUN
ejpam-1563	175	18	∈	∈	NOUN
ejpam-1563	175	19	]	]	X
ejpam-1563	175	20	0,1	0,1	NUM
ejpam-1563	175	21	[	[	NOUN
ejpam-1563	175	22	.	.	PUNCT
ejpam-1563	176	1	if	if	SCONJ
ejpam-1563	176	2	there	there	PRON
ejpam-1563	176	3	exist	exist	VERB
ejpam-1563	176	4	%	%	NOUN
ejpam-1563	176	5	∈	∈	PROPN
ejpam-1563	176	6	r	r	NOUN
ejpam-1563	176	7	,	,	PUNCT
ejpam-1563	176	8	x%	x%	X
ejpam-1563	176	9	∈	∈	PROPN
ejpam-1563	177	1	k	k	PROPN
ejpam-1563	177	2	such	such	ADJ
ejpam-1563	177	3	that	that	SCONJ
ejpam-1563	177	4	φ	φ	PROPN
ejpam-1563	177	5	�	�	PROPN
ejpam-1563	177	6	x%	x%	PROPN
ejpam-1563	177	7	,	,	PUNCT
ejpam-1563	177	8	y	y	PROPN
ejpam-1563	177	9	�	�	PROPN
ejpam-1563	177	10	∩−int	∩−int	PROPN
ejpam-1563	177	11	c(x%	c(x%	PROPN
ejpam-1563	177	12	)	)	PUNCT
ejpam-1563	177	13	=	=	PUNCT
ejpam-1563	177	14	;	;	PUNCT
ejpam-1563	177	15	,	,	PUNCT
ejpam-1563	177	16	∀y	∀y	NUM
ejpam-1563	177	17	∈w%	∈w%	NOUN
ejpam-1563	177	18	(	(	PUNCT
ejpam-1563	177	19	5	5	NUM
ejpam-1563	177	20	)	)	PUNCT
ejpam-1563	177	21	and	and	CCONJ
ejpam-1563	177	22	z	z	NOUN
ejpam-1563	177	23	∈	∈	PROPN
ejpam-1563	177	24	u%	u%	NOUN
ejpam-1563	177	25	such	such	ADJ
ejpam-1563	177	26	that	that	SCONJ
ejpam-1563	177	27	φ(x%	φ(x%	PROPN
ejpam-1563	177	28	,	,	PUNCT
ejpam-1563	177	29	z)∩−c(x%	z)∩−c(x%	PROPN
ejpam-1563	177	30	)	)	PUNCT
ejpam-1563	177	31	6=	6=	NUM
ejpam-1563	177	32	;	;	PUNCT
ejpam-1563	177	33	,	,	PUNCT
ejpam-1563	177	34	then	then	ADV
ejpam-1563	177	35	x%	x%	PUNCT
ejpam-1563	177	36	∈	∈	PROPN
ejpam-1563	177	37	s2a	s2a	NOUN
ejpam-1563	177	38	k	k	PROPN
ejpam-1563	177	39	.	.	PUNCT
ejpam-1563	178	1	proof	proof	NOUN
ejpam-1563	178	2	.	.	PUNCT
ejpam-1563	179	1	suppose	suppose	VERB
ejpam-1563	179	2	by	by	ADP
ejpam-1563	179	3	contradiction	contradiction	NOUN
ejpam-1563	179	4	that	that	SCONJ
ejpam-1563	179	5	there	there	PRON
ejpam-1563	179	6	exists	exist	VERB
ejpam-1563	179	7	y	y	NOUN
ejpam-1563	179	8	′	′	NOUN
ejpam-1563	179	9	∈	∈	PROPN
ejpam-1563	179	10	k\w%	k\w%	PROPN
ejpam-1563	179	11	such	such	ADJ
ejpam-1563	179	12	that	that	SCONJ
ejpam-1563	179	13	φ	φ	PROPN
ejpam-1563	179	14	�	�	PROPN
ejpam-1563	179	15	x%	x%	PROPN
ejpam-1563	179	16	,	,	PUNCT
ejpam-1563	179	17	y	y	PROPN
ejpam-1563	179	18	′	′	PROPN
ejpam-1563	179	19	�	�	PROPN
ejpam-1563	179	20	∩−int	∩−int	PROPN
ejpam-1563	179	21	c(x%	c(x%	PROPN
ejpam-1563	179	22	)	)	PUNCT
ejpam-1563	179	23	6=	6=	NUM
ejpam-1563	179	24	;	;	PUNCT
ejpam-1563	179	25	.	.	PUNCT
ejpam-1563	180	1	e.	e.	PROPN
ejpam-1563	180	2	allevi	allevi	PROPN
ejpam-1563	180	3	,	,	PUNCT
ejpam-1563	180	4	i.	i.	PROPN
ejpam-1563	180	5	konnov	konnov	PROPN
ejpam-1563	180	6	,	,	PUNCT
ejpam-1563	180	7	m.	m.	NOUN
ejpam-1563	180	8	rocco	rocco	NOUN
ejpam-1563	180	9	/	/	SYM
ejpam-1563	180	10	eur	eur	PROPN
ejpam-1563	180	11	.	.	PUNCT
ejpam-1563	181	1	j.	j.	PROPN
ejpam-1563	181	2	pure	pure	PROPN
ejpam-1563	181	3	appl	appl	PROPN
ejpam-1563	181	4	.	.	PROPN
ejpam-1563	181	5	math	math	PROPN
ejpam-1563	181	6	,	,	PUNCT
ejpam-1563	181	7	6	6	NUM
ejpam-1563	181	8	(	(	PUNCT
ejpam-1563	181	9	2013	2013	NUM
ejpam-1563	181	10	)	)	PUNCT
ejpam-1563	181	11	,	,	PUNCT
ejpam-1563	181	12	365	365	NUM
ejpam-1563	181	13	-	-	SYM
ejpam-1563	181	14	376	376	NUM
ejpam-1563	181	15	373	373	NUM
ejpam-1563	181	16	since	since	SCONJ
ejpam-1563	181	17	k	k	PROPN
ejpam-1563	181	18	is	be	AUX
ejpam-1563	181	19	a	a	DET
ejpam-1563	181	20	convex	convex	NOUN
ejpam-1563	181	21	set	set	NOUN
ejpam-1563	181	22	,	,	PUNCT
ejpam-1563	181	23	µ	µ	X
ejpam-1563	181	24	is	be	AUX
ejpam-1563	181	25	a	a	DET
ejpam-1563	181	26	convex	convex	NOUN
ejpam-1563	181	27	function	function	NOUN
ejpam-1563	181	28	and	and	CCONJ
ejpam-1563	181	29	z	z	NOUN
ejpam-1563	181	30	∈	∈	PROPN
ejpam-1563	181	31	u%	u%	NOUN
ejpam-1563	181	32	,	,	PUNCT
ejpam-1563	181	33	there	there	PRON
ejpam-1563	181	34	exists	exist	VERB
ejpam-1563	181	35	α̂	α̂	X
ejpam-1563	181	36	∈	∈	PROPN
ejpam-1563	181	37	]	]	X
ejpam-1563	181	38	0	0	NUM
ejpam-1563	181	39	,	,	PUNCT
ejpam-1563	181	40	1	1	NUM
ejpam-1563	181	41	[	[	PUNCT
ejpam-1563	181	42	such	such	ADJ
ejpam-1563	181	43	that	that	DET
ejpam-1563	181	44	y(α̂	y(α̂	PROPN
ejpam-1563	181	45	)	)	PUNCT
ejpam-1563	181	46	:	:	PUNCT
ejpam-1563	182	1	=	=	SYM
ejpam-1563	182	2	α̂z+	α̂z+	INTJ
ejpam-1563	182	3	(	(	PUNCT
ejpam-1563	182	4	1−	1−	NUM
ejpam-1563	182	5	α̂)y	α̂)y	NUM
ejpam-1563	182	6	′	′	NUM
ejpam-1563	182	7	∈w%	∈w%	NOUN
ejpam-1563	182	8	.	.	PUNCT
ejpam-1563	183	1	therefore	therefore	ADV
ejpam-1563	183	2	,	,	PUNCT
ejpam-1563	183	3	by	by	ADP
ejpam-1563	183	4	hypothesis	hypothesis	NOUN
ejpam-1563	183	5	,	,	PUNCT
ejpam-1563	183	6	we	we	PRON
ejpam-1563	183	7	obtain	obtain	VERB
ejpam-1563	183	8	φ	φ	PROPN
ejpam-1563	183	9	�	�	PROPN
ejpam-1563	183	10	x%	x%	PROPN
ejpam-1563	183	11	,	,	PUNCT
ejpam-1563	183	12	y(α̂	y(α̂	PROPN
ejpam-1563	183	13	)	)	PUNCT
ejpam-1563	183	14	�	�	PROPN
ejpam-1563	183	15	∩−int	∩−int	PROPN
ejpam-1563	183	16	c(x%	c(x%	PROPN
ejpam-1563	183	17	)	)	PUNCT
ejpam-1563	183	18	6=	6=	NUM
ejpam-1563	183	19	;	;	PUNCT
ejpam-1563	183	20	,	,	PUNCT
ejpam-1563	183	21	a	a	DET
ejpam-1563	183	22	contradiction	contradiction	NOUN
ejpam-1563	183	23	to	to	ADP
ejpam-1563	183	24	(	(	PUNCT
ejpam-1563	183	25	5	5	NUM
ejpam-1563	183	26	)	)	PUNCT
ejpam-1563	183	27	.	.	PUNCT
ejpam-1563	184	1	the	the	DET
ejpam-1563	184	2	following	follow	VERB
ejpam-1563	184	3	theorem	theorem	NOUN
ejpam-1563	184	4	provides	provide	VERB
ejpam-1563	184	5	a	a	DET
ejpam-1563	184	6	general	general	ADJ
ejpam-1563	184	7	scheme	scheme	NOUN
ejpam-1563	184	8	to	to	PART
ejpam-1563	184	9	obtain	obtain	VERB
ejpam-1563	184	10	existence	existence	NOUN
ejpam-1563	184	11	results	result	NOUN
ejpam-1563	184	12	for	for	ADP
ejpam-1563	184	13	the	the	DET
ejpam-1563	184	14	generalized	generalize	VERB
ejpam-1563	184	15	vector	vector	NOUN
ejpam-1563	184	16	equilibrium	equilibrium	NOUN
ejpam-1563	184	17	problem	problem	NOUN
ejpam-1563	184	18	(	(	PUNCT
ejpam-1563	184	19	gvep2a	gvep2a	ADJ
ejpam-1563	184	20	)	)	PUNCT
ejpam-1563	184	21	on	on	ADP
ejpam-1563	184	22	an	an	DET
ejpam-1563	184	23	unbounded	unbounded	ADJ
ejpam-1563	184	24	set	set	NOUN
ejpam-1563	184	25	,	,	PUNCT
ejpam-1563	184	26	given	give	VERB
ejpam-1563	184	27	coercivity	coercivity	NOUN
ejpam-1563	184	28	condition	condition	NOUN
ejpam-1563	184	29	(	(	PUNCT
ejpam-1563	184	30	g2a	g2a	NOUN
ejpam-1563	184	31	)	)	PUNCT
ejpam-1563	184	32	and	and	CCONJ
ejpam-1563	184	33	any	any	DET
ejpam-1563	184	34	arbitrary	arbitrary	ADJ
ejpam-1563	184	35	existence	existence	NOUN
ejpam-1563	184	36	result	result	NOUN
ejpam-1563	184	37	for	for	ADP
ejpam-1563	184	38	problem	problem	NOUN
ejpam-1563	184	39	(	(	PUNCT
ejpam-1563	184	40	gvep2a	gvep2a	ADJ
ejpam-1563	184	41	)	)	PUNCT
ejpam-1563	184	42	on	on	ADP
ejpam-1563	184	43	a	a	DET
ejpam-1563	184	44	closed	closed	ADJ
ejpam-1563	184	45	,	,	PUNCT
ejpam-1563	184	46	convex	convex	ADJ
ejpam-1563	184	47	and	and	CCONJ
ejpam-1563	184	48	bounded	bound	VERB
ejpam-1563	184	49	set	set	PROPN
ejpam-1563	184	50	.	.	PUNCT
ejpam-1563	185	1	theorem	theorem	VERB
ejpam-1563	185	2	4	4	NUM
ejpam-1563	185	3	.	.	PUNCT
ejpam-1563	186	1	let	let	VERB
ejpam-1563	186	2	x	x	PRON
ejpam-1563	186	3	be	be	AUX
ejpam-1563	186	4	a	a	DET
ejpam-1563	186	5	reflexive	reflexive	ADJ
ejpam-1563	186	6	banach	banach	NOUN
ejpam-1563	186	7	space	space	NOUN
ejpam-1563	186	8	,	,	PUNCT
ejpam-1563	186	9	y	y	PROPN
ejpam-1563	186	10	be	be	AUX
ejpam-1563	186	11	a	a	DET
ejpam-1563	186	12	banach	banach	NOUN
ejpam-1563	186	13	space	space	NOUN
ejpam-1563	186	14	,	,	PUNCT
ejpam-1563	186	15	k	k	PROPN
ejpam-1563	186	16	⊆	⊆	NUM
ejpam-1563	186	17	x	x	PUNCT
ejpam-1563	186	18	be	be	AUX
ejpam-1563	186	19	nonempty	nonempty	ADJ
ejpam-1563	186	20	,	,	PUNCT
ejpam-1563	186	21	closed	closed	ADJ
ejpam-1563	186	22	and	and	CCONJ
ejpam-1563	186	23	convex	convex	PROPN
ejpam-1563	186	24	,	,	PUNCT
ejpam-1563	186	25	c	c	NOUN
ejpam-1563	186	26	:	:	PUNCT
ejpam-1563	186	27	k	k	X
ejpam-1563	186	28	→	→	PUNCT
ejpam-1563	186	29	π(y	π(y	PROPN
ejpam-1563	186	30	)	)	PUNCT
ejpam-1563	186	31	be	be	AUX
ejpam-1563	186	32	a	a	DET
ejpam-1563	186	33	set	set	NOUN
ejpam-1563	186	34	-	-	PUNCT
ejpam-1563	186	35	valued	value	VERB
ejpam-1563	186	36	mapping	mapping	NOUN
ejpam-1563	186	37	that	that	PRON
ejpam-1563	186	38	maps	map	VERB
ejpam-1563	186	39	any	any	DET
ejpam-1563	186	40	x	x	SYM
ejpam-1563	186	41	∈	∈	PROPN
ejpam-1563	186	42	k	k	PROPN
ejpam-1563	186	43	to	to	ADP
ejpam-1563	186	44	a	a	DET
ejpam-1563	186	45	convex	convex	NOUN
ejpam-1563	186	46	,	,	PUNCT
ejpam-1563	186	47	solid	solid	ADJ
ejpam-1563	186	48	and	and	CCONJ
ejpam-1563	186	49	pointed	point	VERB
ejpam-1563	186	50	cone	cone	NOUN
ejpam-1563	186	51	of	of	ADP
ejpam-1563	186	52	y	y	PROPN
ejpam-1563	186	53	and	and	CCONJ
ejpam-1563	186	54	φ	φ	NUM
ejpam-1563	186	55	:	:	PUNCT
ejpam-1563	187	1	k	k	PROPN
ejpam-1563	187	2	×	×	PROPN
ejpam-1563	187	3	k	k	PROPN
ejpam-1563	187	4	→	→	SYM
ejpam-1563	187	5	π(y	π(y	PROPN
ejpam-1563	187	6	)	)	PUNCT
ejpam-1563	187	7	be	be	AUX
ejpam-1563	187	8	such	such	ADJ
ejpam-1563	187	9	that	that	PRON
ejpam-1563	187	10	:	:	PUNCT
ejpam-1563	187	11	(	(	PUNCT
ejpam-1563	187	12	i	i	NOUN
ejpam-1563	187	13	)	)	PUNCT
ejpam-1563	187	14	φ(x	φ(x	PROPN
ejpam-1563	187	15	,	,	PUNCT
ejpam-1563	187	16	x	x	X
ejpam-1563	187	17	)	)	PUNCT
ejpam-1563	187	18	=	=	SYM
ejpam-1563	187	19	{	{	PUNCT
ejpam-1563	187	20	0	0	NUM
ejpam-1563	187	21	}	}	PUNCT
ejpam-1563	187	22	,	,	PUNCT
ejpam-1563	187	23	for	for	ADP
ejpam-1563	187	24	all	all	DET
ejpam-1563	187	25	x	x	SYM
ejpam-1563	187	26	∈	∈	PROPN
ejpam-1563	187	27	k	k	NOUN
ejpam-1563	187	28	;	;	PUNCT
ejpam-1563	187	29	(	(	PUNCT
ejpam-1563	187	30	ii	ii	NOUN
ejpam-1563	187	31	)	)	PUNCT
ejpam-1563	187	32	for	for	ADP
ejpam-1563	187	33	all	all	DET
ejpam-1563	187	34	x	x	SYM
ejpam-1563	187	35	,	,	PUNCT
ejpam-1563	187	36	y	y	PROPN
ejpam-1563	187	37	′	′	NOUN
ejpam-1563	187	38	,	,	PUNCT
ejpam-1563	188	1	y	y	PROPN
ejpam-1563	188	2	′′	′′	PROPN
ejpam-1563	188	3	∈	∈	PROPN
ejpam-1563	188	4	k	k	NOUN
ejpam-1563	188	5	,	,	PUNCT
ejpam-1563	188	6	if	if	SCONJ
ejpam-1563	188	7	φ(x	φ(x	PROPN
ejpam-1563	188	8	,	,	PUNCT
ejpam-1563	188	9	y	y	PROPN
ejpam-1563	188	10	′	′	NOUN
ejpam-1563	188	11	)	)	PUNCT
ejpam-1563	188	12	∩	∩	ADJ
ejpam-1563	188	13	−c(x	−c(x	NOUN
ejpam-1563	188	14	)	)	PUNCT
ejpam-1563	188	15	6=	6=	NUM
ejpam-1563	188	16	;	;	PUNCT
ejpam-1563	188	17	and	and	CCONJ
ejpam-1563	188	18	φ(x	φ(x	PROPN
ejpam-1563	188	19	,	,	PUNCT
ejpam-1563	188	20	y	y	PROPN
ejpam-1563	188	21	′′	′′	PROPN
ejpam-1563	188	22	)	)	PUNCT
ejpam-1563	188	23	∩	∩	NOUN
ejpam-1563	188	24	−int	−int	ADP
ejpam-1563	188	25	c(x	c(x	NOUN
ejpam-1563	188	26	)	)	PUNCT
ejpam-1563	188	27	6=	6=	PUNCT
ejpam-1563	188	28	;	;	PUNCT
ejpam-1563	188	29	,	,	PUNCT
ejpam-1563	188	30	then	then	ADV
ejpam-1563	188	31	φ(x	φ(x	PROPN
ejpam-1563	188	32	,	,	PUNCT
ejpam-1563	188	33	αy	αy	X
ejpam-1563	188	34	′+	′+	PUNCT
ejpam-1563	188	35	(	(	PUNCT
ejpam-1563	188	36	1−α)y	1−α)y	NUM
ejpam-1563	188	37	′′)∩−int	′′)∩−int	NUM
ejpam-1563	188	38	c(x	c(x	NOUN
ejpam-1563	188	39	)	)	PUNCT
ejpam-1563	188	40	6=	6=	NUM
ejpam-1563	188	41	;	;	CCONJ
ejpam-1563	188	42	,	,	PUNCT
ejpam-1563	188	43	for	for	ADP
ejpam-1563	188	44	all	all	DET
ejpam-1563	188	45	α	α	NOUN
ejpam-1563	188	46	∈	∈	NOUN
ejpam-1563	188	47	]	]	X
ejpam-1563	188	48	0,1	0,1	NUM
ejpam-1563	188	49	[	[	X
ejpam-1563	188	50	.	.	PUNCT
ejpam-1563	188	51	suppose	suppose	VERB
ejpam-1563	188	52	that	that	SCONJ
ejpam-1563	188	53	s2a	s2a	NOUN
ejpam-1563	188	54	h	h	NOUN
ejpam-1563	188	55	6=	6=	NUM
ejpam-1563	188	56	;	;	PUNCT
ejpam-1563	188	57	whenever	whenever	SCONJ
ejpam-1563	188	58	h	h	NOUN
ejpam-1563	188	59	is	be	AUX
ejpam-1563	188	60	a	a	DET
ejpam-1563	188	61	nonempty	nonempty	ADJ
ejpam-1563	188	62	,	,	PUNCT
ejpam-1563	188	63	closed	closed	ADJ
ejpam-1563	188	64	,	,	PUNCT
ejpam-1563	188	65	convex	convex	NOUN
ejpam-1563	188	66	and	and	CCONJ
ejpam-1563	188	67	bounded	bound	VERB
ejpam-1563	188	68	subset	subset	NOUN
ejpam-1563	188	69	of	of	ADP
ejpam-1563	188	70	k.	k.	PROPN
ejpam-1563	188	71	if	if	SCONJ
ejpam-1563	188	72	(	(	PUNCT
ejpam-1563	188	73	g2a	g2a	NOUN
ejpam-1563	188	74	)	)	PUNCT
ejpam-1563	188	75	holds	hold	VERB
ejpam-1563	188	76	,	,	PUNCT
ejpam-1563	188	77	then	then	ADV
ejpam-1563	188	78	s2a	s2a	VERB
ejpam-1563	188	79	k	k	PROPN
ejpam-1563	188	80	6=	6=	PROPN
ejpam-1563	188	81	;	;	PUNCT
ejpam-1563	188	82	.	.	PUNCT
ejpam-1563	189	1	proof	proof	NOUN
ejpam-1563	189	2	.	.	PUNCT
ejpam-1563	190	1	let	let	VERB
ejpam-1563	190	2	r	r	PRON
ejpam-1563	190	3	∈	∈	NOUN
ejpam-1563	190	4	r	r	NOUN
ejpam-1563	190	5	be	be	VERB
ejpam-1563	190	6	as	as	ADP
ejpam-1563	190	7	in	in	ADP
ejpam-1563	190	8	(	(	PUNCT
ejpam-1563	190	9	g2a	g2a	NOUN
ejpam-1563	190	10	)	)	PUNCT
ejpam-1563	190	11	and	and	CCONJ
ejpam-1563	190	12	take	take	VERB
ejpam-1563	190	13	%	%	NOUN
ejpam-1563	190	14	>	>	X
ejpam-1563	190	15	r.	r.	PROPN
ejpam-1563	190	16	w%	w%	NOUN
ejpam-1563	190	17	is	be	AUX
ejpam-1563	190	18	nonempty	nonempty	X
ejpam-1563	190	19	,	,	PUNCT
ejpam-1563	190	20	bounded	bound	VERB
ejpam-1563	190	21	,	,	PUNCT
ejpam-1563	190	22	closed	closed	ADJ
ejpam-1563	190	23	and	and	CCONJ
ejpam-1563	190	24	convex	convex	NOUN
ejpam-1563	190	25	.	.	PUNCT
ejpam-1563	191	1	thus	thus	ADV
ejpam-1563	191	2	,	,	PUNCT
ejpam-1563	191	3	by	by	ADP
ejpam-1563	191	4	hypothesis	hypothesis	NOUN
ejpam-1563	191	5	,	,	PUNCT
ejpam-1563	191	6	there	there	PRON
ejpam-1563	191	7	exists	exist	VERB
ejpam-1563	191	8	x%	x%	PUNCT
ejpam-1563	192	1	∈	∈	PROPN
ejpam-1563	192	2	s2a	s2a	NOUN
ejpam-1563	192	3	w%	w%	NOUN
ejpam-1563	192	4	,	,	PUNCT
ejpam-1563	192	5	i.e.	i.e.	X
ejpam-1563	192	6	x%	x%	X
ejpam-1563	192	7	∈	∈	PROPN
ejpam-1563	192	8	w%	w%	NOUN
ejpam-1563	192	9	satisfying	satisfy	VERB
ejpam-1563	192	10	(	(	PUNCT
ejpam-1563	192	11	5	5	NUM
ejpam-1563	192	12	)	)	PUNCT
ejpam-1563	192	13	.	.	PUNCT
ejpam-1563	193	1	if	if	SCONJ
ejpam-1563	193	2	x%	x%	SYM
ejpam-1563	193	3	∈	∈	PROPN
ejpam-1563	193	4	w%\wr	w%\wr	NOUN
ejpam-1563	193	5	,	,	PUNCT
ejpam-1563	193	6	then	then	ADV
ejpam-1563	193	7	by	by	ADP
ejpam-1563	193	8	(	(	PUNCT
ejpam-1563	193	9	g2a	g2a	PROPN
ejpam-1563	193	10	)	)	PUNCT
ejpam-1563	193	11	there	there	PRON
ejpam-1563	193	12	exists	exist	VERB
ejpam-1563	193	13	z	z	PROPN
ejpam-1563	193	14	∈	∈	PROPN
ejpam-1563	194	1	k	k	NOUN
ejpam-1563	195	1	such	such	ADJ
ejpam-1563	195	2	that	that	SCONJ
ejpam-1563	195	3	µ(z	µ(z	NOUN
ejpam-1563	195	4	)	)	PUNCT
ejpam-1563	195	5	<	<	X
ejpam-1563	195	6	µ(x%	µ(x%	PROPN
ejpam-1563	195	7	)	)	PUNCT
ejpam-1563	195	8	,	,	PUNCT
ejpam-1563	195	9	i.e.	i.e.	X
ejpam-1563	195	10	z	z	X
ejpam-1563	195	11	∈	∈	PROPN
ejpam-1563	195	12	u%	u%	NOUN
ejpam-1563	195	13	,	,	PUNCT
ejpam-1563	195	14	and	and	CCONJ
ejpam-1563	195	15	φ(x%	φ(x%	PROPN
ejpam-1563	195	16	,	,	PUNCT
ejpam-1563	195	17	z)∩−c(x%	z)∩−c(x%	PROPN
ejpam-1563	195	18	)	)	PUNCT
ejpam-1563	195	19	6=	6=	NUM
ejpam-1563	195	20	;	;	PUNCT
ejpam-1563	195	21	.	.	PUNCT
ejpam-1563	196	1	on	on	ADP
ejpam-1563	196	2	the	the	DET
ejpam-1563	196	3	other	other	ADJ
ejpam-1563	196	4	hand	hand	NOUN
ejpam-1563	196	5	,	,	PUNCT
ejpam-1563	196	6	if	if	SCONJ
ejpam-1563	196	7	x%	x%	X
ejpam-1563	196	8	∈wr	∈wr	PROPN
ejpam-1563	196	9	,	,	PUNCT
ejpam-1563	196	10	setting	set	VERB
ejpam-1563	196	11	z	z	NOUN
ejpam-1563	196	12	:	:	PUNCT
ejpam-1563	196	13	=	=	SYM
ejpam-1563	196	14	x%	x%	NOUN
ejpam-1563	196	15	,	,	PUNCT
ejpam-1563	196	16	one	one	PRON
ejpam-1563	196	17	obtains	obtain	VERB
ejpam-1563	196	18	φ(x%	φ(x%	PROPN
ejpam-1563	196	19	,	,	PUNCT
ejpam-1563	196	20	z)∩−c(x%	z)∩−c(x%	PROPN
ejpam-1563	196	21	)	)	PUNCT
ejpam-1563	196	22	=	=	SYM
ejpam-1563	196	23	{	{	PUNCT
ejpam-1563	196	24	0	0	NUM
ejpam-1563	196	25	}	}	PUNCT
ejpam-1563	196	26	∩−c(x%	∩−c(x%	NOUN
ejpam-1563	196	27	)	)	PUNCT
ejpam-1563	196	28	6=	6=	NUM
ejpam-1563	196	29	;	;	PUNCT
ejpam-1563	196	30	.	.	PUNCT
ejpam-1563	197	1	in	in	ADP
ejpam-1563	197	2	both	both	DET
ejpam-1563	197	3	cases	case	NOUN
ejpam-1563	197	4	,	,	PUNCT
ejpam-1563	197	5	the	the	DET
ejpam-1563	197	6	result	result	NOUN
ejpam-1563	197	7	follows	follow	VERB
ejpam-1563	197	8	from	from	ADP
ejpam-1563	197	9	lemma	lemma	PROPN
ejpam-1563	197	10	3	3	NUM
ejpam-1563	197	11	.	.	PUNCT
ejpam-1563	198	1	the	the	DET
ejpam-1563	198	2	existence	existence	NOUN
ejpam-1563	198	3	of	of	ADP
ejpam-1563	198	4	solutions	solution	NOUN
ejpam-1563	198	5	to	to	ADP
ejpam-1563	198	6	problem	problem	NOUN
ejpam-1563	198	7	(	(	PUNCT
ejpam-1563	198	8	gvep2a	gvep2a	ADJ
ejpam-1563	198	9	)	)	PUNCT
ejpam-1563	198	10	on	on	ADP
ejpam-1563	198	11	nonempty	nonempty	NOUN
ejpam-1563	198	12	,	,	PUNCT
ejpam-1563	198	13	bounded	bound	VERB
ejpam-1563	198	14	,	,	PUNCT
ejpam-1563	198	15	closed	closed	ADJ
ejpam-1563	198	16	and	and	CCONJ
ejpam-1563	198	17	convex	convex	ADJ
ejpam-1563	198	18	subsets	subset	NOUN
ejpam-1563	198	19	of	of	ADP
ejpam-1563	198	20	x	x	SYM
ejpam-1563	198	21	is	be	AUX
ejpam-1563	198	22	guaranteed	guarantee	VERB
ejpam-1563	198	23	,	,	PUNCT
ejpam-1563	198	24	for	for	ADP
ejpam-1563	198	25	instance	instance	NOUN
ejpam-1563	198	26	,	,	PUNCT
ejpam-1563	198	27	by	by	ADP
ejpam-1563	198	28	theorem	theorem	NOUN
ejpam-1563	198	29	2	2	NUM
ejpam-1563	198	30	.	.	PUNCT
ejpam-1563	198	31	corollary	corollary	ADJ
ejpam-1563	198	32	3	3	X
ejpam-1563	198	33	.	.	PUNCT
ejpam-1563	199	1	let	let	VERB
ejpam-1563	199	2	x	x	PRON
ejpam-1563	199	3	be	be	AUX
ejpam-1563	199	4	a	a	DET
ejpam-1563	199	5	reflexive	reflexive	ADJ
ejpam-1563	199	6	banach	banach	NOUN
ejpam-1563	199	7	space	space	NOUN
ejpam-1563	199	8	,	,	PUNCT
ejpam-1563	199	9	y	y	PROPN
ejpam-1563	199	10	be	be	AUX
ejpam-1563	199	11	a	a	DET
ejpam-1563	199	12	banach	banach	NOUN
ejpam-1563	199	13	space	space	NOUN
ejpam-1563	199	14	,	,	PUNCT
ejpam-1563	199	15	k	k	X
ejpam-1563	199	16	be	be	AUX
ejpam-1563	199	17	a	a	DET
ejpam-1563	199	18	nonempty	nonempty	ADJ
ejpam-1563	199	19	,	,	PUNCT
ejpam-1563	199	20	closed	closed	ADJ
ejpam-1563	199	21	and	and	CCONJ
ejpam-1563	199	22	convex	convex	NOUN
ejpam-1563	199	23	subset	subset	NOUN
ejpam-1563	199	24	of	of	ADP
ejpam-1563	199	25	x	x	PUNCT
ejpam-1563	199	26	and	and	CCONJ
ejpam-1563	199	27	let	let	VERB
ejpam-1563	199	28	c	c	NOUN
ejpam-1563	199	29	:	:	PUNCT
ejpam-1563	199	30	k	k	PROPN
ejpam-1563	199	31	→	→	PUNCT
ejpam-1563	199	32	π(y	π(y	PROPN
ejpam-1563	199	33	)	)	PUNCT
ejpam-1563	199	34	map	map	VERB
ejpam-1563	199	35	any	any	DET
ejpam-1563	199	36	x	x	SYM
ejpam-1563	199	37	∈	∈	PROPN
ejpam-1563	199	38	k	k	PROPN
ejpam-1563	199	39	to	to	ADP
ejpam-1563	199	40	a	a	DET
ejpam-1563	199	41	convex	convex	NOUN
ejpam-1563	199	42	,	,	PUNCT
ejpam-1563	199	43	solid	solid	ADJ
ejpam-1563	199	44	and	and	CCONJ
ejpam-1563	199	45	pointed	point	VERB
ejpam-1563	199	46	cone	cone	NOUN
ejpam-1563	199	47	c(x)⊆	c(x)⊆	PROPN
ejpam-1563	199	48	y	y	PROPN
ejpam-1563	199	49	.	.	PUNCT
ejpam-1563	200	1	moreover	moreover	ADV
ejpam-1563	200	2	,	,	PUNCT
ejpam-1563	200	3	let	let	VERB
ejpam-1563	200	4	φ	φ	NOUN
ejpam-1563	200	5	:	:	PUNCT
ejpam-1563	201	1	k	k	PROPN
ejpam-1563	201	2	×	×	PROPN
ejpam-1563	201	3	k	k	PROPN
ejpam-1563	201	4	→	→	SYM
ejpam-1563	201	5	π(y	π(y	PROPN
ejpam-1563	201	6	)	)	PUNCT
ejpam-1563	201	7	be	be	AUX
ejpam-1563	201	8	such	such	ADJ
ejpam-1563	201	9	that	that	PRON
ejpam-1563	201	10	:	:	PUNCT
ejpam-1563	201	11	(	(	PUNCT
ejpam-1563	201	12	i	i	NOUN
ejpam-1563	201	13	)	)	PUNCT
ejpam-1563	201	14	φ(x	φ(x	PROPN
ejpam-1563	201	15	,	,	PUNCT
ejpam-1563	201	16	x	x	X
ejpam-1563	201	17	)	)	PUNCT
ejpam-1563	201	18	=	=	SYM
ejpam-1563	201	19	{	{	PUNCT
ejpam-1563	201	20	0	0	NUM
ejpam-1563	201	21	}	}	PUNCT
ejpam-1563	201	22	,	,	PUNCT
ejpam-1563	201	23	for	for	ADP
ejpam-1563	201	24	all	all	DET
ejpam-1563	201	25	x	x	SYM
ejpam-1563	201	26	∈	∈	PROPN
ejpam-1563	201	27	k	k	NOUN
ejpam-1563	201	28	;	;	PUNCT
ejpam-1563	201	29	(	(	PUNCT
ejpam-1563	201	30	ii	ii	NOUN
ejpam-1563	201	31	)	)	PUNCT
ejpam-1563	201	32	for	for	ADP
ejpam-1563	201	33	all	all	DET
ejpam-1563	201	34	x	x	SYM
ejpam-1563	201	35	,	,	PUNCT
ejpam-1563	201	36	y	y	PROPN
ejpam-1563	201	37	′	′	NOUN
ejpam-1563	201	38	,	,	PUNCT
ejpam-1563	202	1	y	y	PROPN
ejpam-1563	202	2	′′	′′	PROPN
ejpam-1563	202	3	∈	∈	PROPN
ejpam-1563	202	4	k	k	NOUN
ejpam-1563	202	5	,	,	PUNCT
ejpam-1563	202	6	if	if	SCONJ
ejpam-1563	202	7	φ(x	φ(x	PROPN
ejpam-1563	202	8	,	,	PUNCT
ejpam-1563	202	9	y	y	PROPN
ejpam-1563	202	10	′	′	NOUN
ejpam-1563	202	11	)	)	PUNCT
ejpam-1563	202	12	∩	∩	ADJ
ejpam-1563	202	13	−c(x	−c(x	NOUN
ejpam-1563	202	14	)	)	PUNCT
ejpam-1563	202	15	6=	6=	NUM
ejpam-1563	202	16	;	;	PUNCT
ejpam-1563	202	17	and	and	CCONJ
ejpam-1563	202	18	φ(x	φ(x	PROPN
ejpam-1563	202	19	,	,	PUNCT
ejpam-1563	202	20	y	y	PROPN
ejpam-1563	202	21	′′	′′	PROPN
ejpam-1563	202	22	)	)	PUNCT
ejpam-1563	202	23	∩	∩	NOUN
ejpam-1563	202	24	−int	−int	ADP
ejpam-1563	202	25	c(x	c(x	NOUN
ejpam-1563	202	26	)	)	PUNCT
ejpam-1563	202	27	6=	6=	PUNCT
ejpam-1563	202	28	;	;	PUNCT
ejpam-1563	202	29	,	,	PUNCT
ejpam-1563	202	30	then	then	ADV
ejpam-1563	202	31	φ(x	φ(x	PROPN
ejpam-1563	202	32	,	,	PUNCT
ejpam-1563	202	33	αy	αy	X
ejpam-1563	202	34	′+	′+	PUNCT
ejpam-1563	202	35	(	(	PUNCT
ejpam-1563	202	36	1−α)y	1−α)y	NUM
ejpam-1563	202	37	′′)∩−int	′′)∩−int	NUM
ejpam-1563	202	38	c(x	c(x	NOUN
ejpam-1563	202	39	)	)	PUNCT
ejpam-1563	202	40	6=	6=	NUM
ejpam-1563	202	41	;	;	CCONJ
ejpam-1563	202	42	,	,	PUNCT
ejpam-1563	202	43	for	for	ADP
ejpam-1563	202	44	all	all	DET
ejpam-1563	202	45	α	α	NOUN
ejpam-1563	202	46	∈	∈	NOUN
ejpam-1563	202	47	]	]	X
ejpam-1563	202	48	0,1	0,1	NUM
ejpam-1563	202	49	[	[	X
ejpam-1563	202	50	;	;	PUNCT
ejpam-1563	202	51	(	(	PUNCT
ejpam-1563	202	52	iii	iii	NOUN
ejpam-1563	202	53	)	)	PUNCT
ejpam-1563	202	54	for	for	ADP
ejpam-1563	202	55	any	any	DET
ejpam-1563	202	56	fixed	fix	VERB
ejpam-1563	202	57	y	y	PROPN
ejpam-1563	202	58	∈	∈	PROPN
ejpam-1563	202	59	k	k	PROPN
ejpam-1563	202	60	,	,	PUNCT
ejpam-1563	202	61	the	the	DET
ejpam-1563	202	62	set	set	NOUN
ejpam-1563	202	63	{	{	PUNCT
ejpam-1563	202	64	x	x	SYM
ejpam-1563	202	65	∈	∈	PROPN
ejpam-1563	202	66	k	k	NOUN
ejpam-1563	202	67	:	:	PUNCT
ejpam-1563	202	68	φ(x	φ(x	PROPN
ejpam-1563	202	69	,	,	PUNCT
ejpam-1563	202	70	y)∩−int	y)∩−int	NUM
ejpam-1563	202	71	c(x	c(x	NOUN
ejpam-1563	202	72	)	)	PUNCT
ejpam-1563	202	73	=	=	PUNCT
ejpam-1563	202	74	;	;	PUNCT
ejpam-1563	202	75	}	}	PUNCT
ejpam-1563	202	76	is	be	AUX
ejpam-1563	202	77	closed	close	VERB
ejpam-1563	202	78	with	with	ADP
ejpam-1563	202	79	respect	respect	NOUN
ejpam-1563	202	80	to	to	ADP
ejpam-1563	202	81	the	the	DET
ejpam-1563	202	82	topology	topology	NOUN
ejpam-1563	202	83	induced	induce	VERB
ejpam-1563	202	84	on	on	ADP
ejpam-1563	202	85	k	k	X
ejpam-1563	202	86	by	by	ADP
ejpam-1563	202	87	the	the	DET
ejpam-1563	202	88	weak	weak	ADJ
ejpam-1563	202	89	topology	topology	NOUN
ejpam-1563	202	90	of	of	ADP
ejpam-1563	202	91	x	x	X
ejpam-1563	202	92	.	.	PUNCT
ejpam-1563	203	1	if	if	SCONJ
ejpam-1563	203	2	(	(	PUNCT
ejpam-1563	203	3	g2a	g2a	NOUN
ejpam-1563	203	4	)	)	PUNCT
ejpam-1563	203	5	holds	hold	VERB
ejpam-1563	203	6	,	,	PUNCT
ejpam-1563	203	7	then	then	ADV
ejpam-1563	203	8	s2a	s2a	VERB
ejpam-1563	203	9	k	k	PROPN
ejpam-1563	203	10	6=	6=	PROPN
ejpam-1563	203	11	;	;	PUNCT
ejpam-1563	203	12	.	.	PUNCT
ejpam-1563	204	1	e.	e.	PROPN
ejpam-1563	204	2	allevi	allevi	PROPN
ejpam-1563	204	3	,	,	PUNCT
ejpam-1563	204	4	i.	i.	PROPN
ejpam-1563	204	5	konnov	konnov	PROPN
ejpam-1563	204	6	,	,	PUNCT
ejpam-1563	204	7	m.	m.	NOUN
ejpam-1563	204	8	rocco	rocco	NOUN
ejpam-1563	204	9	/	/	SYM
ejpam-1563	204	10	eur	eur	PROPN
ejpam-1563	204	11	.	.	PUNCT
ejpam-1563	205	1	j.	j.	PROPN
ejpam-1563	205	2	pure	pure	PROPN
ejpam-1563	205	3	appl	appl	PROPN
ejpam-1563	205	4	.	.	PROPN
ejpam-1563	205	5	math	math	PROPN
ejpam-1563	205	6	,	,	PUNCT
ejpam-1563	205	7	6	6	NUM
ejpam-1563	205	8	(	(	PUNCT
ejpam-1563	205	9	2013	2013	NUM
ejpam-1563	205	10	)	)	PUNCT
ejpam-1563	205	11	,	,	PUNCT
ejpam-1563	205	12	365	365	NUM
ejpam-1563	205	13	-	-	SYM
ejpam-1563	205	14	376	376	NUM
ejpam-1563	205	15	374	374	NUM
ejpam-1563	205	16	proof	proof	NOUN
ejpam-1563	205	17	.	.	PUNCT
ejpam-1563	206	1	assumption	assumption	NOUN
ejpam-1563	206	2	(	(	PUNCT
ejpam-1563	206	3	ii	ii	NOUN
ejpam-1563	206	4	)	)	PUNCT
ejpam-1563	206	5	implies	imply	VERB
ejpam-1563	206	6	that	that	SCONJ
ejpam-1563	206	7	for	for	ADP
ejpam-1563	206	8	any	any	DET
ejpam-1563	206	9	fixed	fix	VERB
ejpam-1563	206	10	x	x	SYM
ejpam-1563	206	11	∈	∈	PROPN
ejpam-1563	206	12	k	k	PROPN
ejpam-1563	206	13	,	,	PUNCT
ejpam-1563	206	14	the	the	DET
ejpam-1563	206	15	set	set	NOUN
ejpam-1563	206	16	{	{	PUNCT
ejpam-1563	206	17	y	y	PROPN
ejpam-1563	206	18	∈	∈	PROPN
ejpam-1563	206	19	k	k	NOUN
ejpam-1563	206	20	:	:	PUNCT
ejpam-1563	206	21	φ(x	φ(x	PROPN
ejpam-1563	206	22	,	,	PUNCT
ejpam-1563	206	23	y	y	PROPN
ejpam-1563	206	24	)	)	PUNCT
ejpam-1563	206	25	∩−int	∩−int	NOUN
ejpam-1563	206	26	c(x	c(x	NOUN
ejpam-1563	206	27	)	)	PUNCT
ejpam-1563	206	28	6=	6=	NUM
ejpam-1563	206	29	;	;	PUNCT
ejpam-1563	206	30	}	}	PUNCT
ejpam-1563	206	31	is	be	AUX
ejpam-1563	206	32	convex	convex	ADJ
ejpam-1563	206	33	.	.	PUNCT
ejpam-1563	207	1	hence	hence	ADV
ejpam-1563	207	2	,	,	PUNCT
ejpam-1563	207	3	for	for	ADP
ejpam-1563	207	4	any	any	DET
ejpam-1563	207	5	nonempty	nonempty	ADJ
ejpam-1563	207	6	,	,	PUNCT
ejpam-1563	207	7	closed	closed	ADJ
ejpam-1563	207	8	,	,	PUNCT
ejpam-1563	207	9	convex	convex	VERB
ejpam-1563	207	10	and	and	CCONJ
ejpam-1563	207	11	bounded	bound	VERB
ejpam-1563	207	12	set	set	VERB
ejpam-1563	207	13	h	h	NOUN
ejpam-1563	207	14	⊆	⊆	NUM
ejpam-1563	207	15	k	k	PROPN
ejpam-1563	207	16	,	,	PUNCT
ejpam-1563	207	17	assumptions	assumption	NOUN
ejpam-1563	207	18	(	(	PUNCT
ejpam-1563	207	19	i)-(iii	i)-(iii	NOUN
ejpam-1563	207	20	)	)	PUNCT
ejpam-1563	207	21	of	of	ADP
ejpam-1563	207	22	theorem	theorem	ADJ
ejpam-1563	207	23	2	2	NUM
ejpam-1563	207	24	hold	hold	NOUN
ejpam-1563	207	25	(	(	PUNCT
ejpam-1563	207	26	with	with	ADP
ejpam-1563	207	27	k	k	PROPN
ejpam-1563	207	28	replaced	replace	VERB
ejpam-1563	207	29	by	by	ADP
ejpam-1563	207	30	h	h	NOUN
ejpam-1563	207	31	and	and	CCONJ
ejpam-1563	207	32	v	v	NOUN
ejpam-1563	207	33	(	(	PUNCT
ejpam-1563	207	34	x	x	NOUN
ejpam-1563	207	35	)	)	PUNCT
ejpam-1563	207	36	=	=	SYM
ejpam-1563	207	37	−int	−int	ADP
ejpam-1563	207	38	c(x	c(x	NOUN
ejpam-1563	207	39	)	)	PUNCT
ejpam-1563	207	40	)	)	PUNCT
ejpam-1563	207	41	for	for	ADP
ejpam-1563	207	42	φ	φ	NUM
ejpam-1563	207	43	restricted	restrict	VERB
ejpam-1563	207	44	to	to	ADP
ejpam-1563	207	45	h	h	PROPN
ejpam-1563	207	46	×	×	PROPN
ejpam-1563	207	47	h.	h.	PROPN
ejpam-1563	207	48	then	then	ADV
ejpam-1563	207	49	,	,	PUNCT
ejpam-1563	207	50	by	by	ADP
ejpam-1563	207	51	theorem	theorem	NOUN
ejpam-1563	207	52	2	2	NUM
ejpam-1563	207	53	,	,	PUNCT
ejpam-1563	207	54	s2a	s2a	VERB
ejpam-1563	207	55	h	h	NOUN
ejpam-1563	207	56	6=	6=	NUM
ejpam-1563	207	57	;	;	PUNCT
ejpam-1563	207	58	.	.	PUNCT
ejpam-1563	208	1	hence	hence	ADV
ejpam-1563	208	2	,	,	PUNCT
ejpam-1563	208	3	the	the	DET
ejpam-1563	208	4	conclusion	conclusion	NOUN
ejpam-1563	208	5	follows	follow	VERB
ejpam-1563	208	6	from	from	ADP
ejpam-1563	208	7	theorem	theorem	ADJ
ejpam-1563	208	8	4	4	NUM
ejpam-1563	208	9	.	.	NOUN
ejpam-1563	208	10	remark	remark	NOUN
ejpam-1563	208	11	6	6	NUM
ejpam-1563	208	12	.	.	PUNCT
ejpam-1563	208	13	with	with	ADP
ejpam-1563	208	14	a	a	DET
ejpam-1563	208	15	reasoning	reasoning	NOUN
ejpam-1563	208	16	analogous	analogous	ADJ
ejpam-1563	208	17	to	to	ADP
ejpam-1563	208	18	that	that	PRON
ejpam-1563	208	19	employed	employ	VERB
ejpam-1563	208	20	in	in	ADP
ejpam-1563	208	21	this	this	DET
ejpam-1563	208	22	section	section	NOUN
ejpam-1563	208	23	,	,	PUNCT
ejpam-1563	208	24	one	one	PRON
ejpam-1563	208	25	can	can	AUX
ejpam-1563	208	26	prove	prove	VERB
ejpam-1563	208	27	an	an	DET
ejpam-1563	208	28	existence	existence	NOUN
ejpam-1563	208	29	result	result	NOUN
ejpam-1563	208	30	for	for	ADP
ejpam-1563	208	31	problem	problem	NOUN
ejpam-1563	208	32	(	(	PUNCT
ejpam-1563	208	33	gvep2b	gvep2b	PROPN
ejpam-1563	208	34	)	)	PUNCT
ejpam-1563	208	35	as	as	ADV
ejpam-1563	208	36	well	well	ADV
ejpam-1563	208	37	.	.	PUNCT
ejpam-1563	209	1	to	to	ADP
ejpam-1563	209	2	this	this	DET
ejpam-1563	209	3	end	end	NOUN
ejpam-1563	209	4	,	,	PUNCT
ejpam-1563	209	5	it	it	PRON
ejpam-1563	209	6	suffices	suffice	VERB
ejpam-1563	209	7	to	to	PART
ejpam-1563	209	8	replace	replace	VERB
ejpam-1563	209	9	condition	condition	NOUN
ejpam-1563	209	10	c2	c2	PROPN
ejpam-1563	209	11	in	in	ADP
ejpam-1563	209	12	lemma	lemma	PROPN
ejpam-1563	209	13	3	3	NUM
ejpam-1563	209	14	(	(	PUNCT
ejpam-1563	209	15	and	and	CCONJ
ejpam-1563	209	16	,	,	PUNCT
ejpam-1563	209	17	consequently	consequently	ADV
ejpam-1563	209	18	,	,	PUNCT
ejpam-1563	209	19	condition	condition	NOUN
ejpam-1563	209	20	(	(	PUNCT
ejpam-1563	209	21	ii	ii	NOUN
ejpam-1563	209	22	)	)	PUNCT
ejpam-1563	209	23	of	of	ADP
ejpam-1563	209	24	theorem	theorem	ADJ
ejpam-1563	209	25	4	4	NUM
ejpam-1563	209	26	and	and	CCONJ
ejpam-1563	209	27	corollary	corollary	ADJ
ejpam-1563	209	28	3	3	NUM
ejpam-1563	209	29	)	)	PUNCT
ejpam-1563	209	30	by	by	ADP
ejpam-1563	209	31	c3	c3	PROPN
ejpam-1563	209	32	)	)	PUNCT
ejpam-1563	209	33	for	for	ADP
ejpam-1563	209	34	all	all	DET
ejpam-1563	209	35	x	x	SYM
ejpam-1563	209	36	,	,	PUNCT
ejpam-1563	209	37	y	y	PROPN
ejpam-1563	209	38	′	′	NOUN
ejpam-1563	209	39	,	,	PUNCT
ejpam-1563	210	1	y	y	PROPN
ejpam-1563	210	2	′′	′′	PROPN
ejpam-1563	210	3	∈	∈	PROPN
ejpam-1563	210	4	k	k	NOUN
ejpam-1563	210	5	,	,	PUNCT
ejpam-1563	210	6	if	if	SCONJ
ejpam-1563	210	7	φ(x	φ(x	PROPN
ejpam-1563	210	8	,	,	PUNCT
ejpam-1563	210	9	y	y	PROPN
ejpam-1563	210	10	′)∩−c(x	′)∩−c(x	PROPN
ejpam-1563	210	11	)	)	PUNCT
ejpam-1563	210	12	6=	6=	NUM
ejpam-1563	210	13	;	;	PUNCT
ejpam-1563	210	14	and	and	CCONJ
ejpam-1563	210	15	φ(x	φ(x	PROPN
ejpam-1563	210	16	,	,	PUNCT
ejpam-1563	210	17	y	y	PROPN
ejpam-1563	210	18	′′)∩	′′)∩	PROPN
ejpam-1563	210	19	(	(	PUNCT
ejpam-1563	210	20	−c(x)\{0	−c(x)\{0	PROPN
ejpam-1563	210	21	}	}	PUNCT
ejpam-1563	210	22	)	)	PUNCT
ejpam-1563	210	23	6=	6=	NUM
ejpam-1563	210	24	;	;	PUNCT
ejpam-1563	210	25	,	,	PUNCT
ejpam-1563	210	26	then	then	ADV
ejpam-1563	210	27	φ(x	φ(x	PROPN
ejpam-1563	210	28	,	,	PUNCT
ejpam-1563	210	29	αy	αy	X
ejpam-1563	210	30	′+	′+	PUNCT
ejpam-1563	210	31	(	(	PUNCT
ejpam-1563	210	32	1−α)y	1−α)y	NUM
ejpam-1563	210	33	′′)∩	′′)∩	NOUN
ejpam-1563	210	34	(	(	PUNCT
ejpam-1563	210	35	−c(x)\{0	−c(x)\{0	PROPN
ejpam-1563	210	36	}	}	PUNCT
ejpam-1563	210	37	)	)	PUNCT
ejpam-1563	210	38	6=	6=	NUM
ejpam-1563	210	39	;	;	PUNCT
ejpam-1563	210	40	for	for	ADP
ejpam-1563	210	41	all	all	DET
ejpam-1563	210	42	α	α	NOUN
ejpam-1563	210	43	∈	∈	NOUN
ejpam-1563	210	44	]	]	X
ejpam-1563	210	45	0,1	0,1	NUM
ejpam-1563	210	46	[	[	NOUN
ejpam-1563	210	47	,	,	PUNCT
ejpam-1563	210	48	and	and	CCONJ
ejpam-1563	210	49	to	to	PART
ejpam-1563	210	50	modify	modify	VERB
ejpam-1563	210	51	the	the	DET
ejpam-1563	210	52	coercivity	coercivity	NOUN
ejpam-1563	210	53	condition	condition	NOUN
ejpam-1563	210	54	(	(	PUNCT
ejpam-1563	210	55	g2a	g2a	NOUN
ejpam-1563	210	56	)	)	PUNCT
ejpam-1563	210	57	replacing	replace	VERB
ejpam-1563	210	58	(	(	PUNCT
ejpam-1563	210	59	4	4	NUM
ejpam-1563	210	60	)	)	PUNCT
ejpam-1563	210	61	by	by	ADP
ejpam-1563	210	62	φ	φ	PROPN
ejpam-1563	210	63	�	�	PROPN
ejpam-1563	210	64	x	x	SYM
ejpam-1563	210	65	,	,	PUNCT
ejpam-1563	210	66	y	y	PROPN
ejpam-1563	210	67	�	�	PROPN
ejpam-1563	210	68	∩−c(x)\{0}=	∩−c(x)\{0}=	PUNCT
ejpam-1563	210	69	;	;	PUNCT
ejpam-1563	210	70	,	,	PUNCT
ejpam-1563	210	71	∀y	∀y	PROPN
ejpam-1563	210	72	∈wr	∈wr	NUM
ejpam-1563	210	73	.	.	PUNCT
ejpam-1563	211	1	(	(	PUNCT
ejpam-1563	211	2	6	6	NUM
ejpam-1563	211	3	)	)	SYM
ejpam-1563	211	4	5	5	NUM
ejpam-1563	211	5	.	.	PUNCT
ejpam-1563	211	6	applications	application	NOUN
ejpam-1563	211	7	and	and	CCONJ
ejpam-1563	211	8	examples	example	NOUN
ejpam-1563	211	9	as	as	ADP
ejpam-1563	211	10	an	an	DET
ejpam-1563	211	11	application	application	NOUN
ejpam-1563	211	12	of	of	ADP
ejpam-1563	211	13	the	the	DET
ejpam-1563	211	14	theoretical	theoretical	ADJ
ejpam-1563	211	15	results	result	NOUN
ejpam-1563	211	16	obtained	obtain	VERB
ejpam-1563	211	17	in	in	ADP
ejpam-1563	211	18	the	the	DET
ejpam-1563	211	19	preceding	precede	VERB
ejpam-1563	211	20	section	section	NOUN
ejpam-1563	211	21	,	,	PUNCT
ejpam-1563	211	22	one	one	PRON
ejpam-1563	211	23	can	can	AUX
ejpam-1563	211	24	consider	consider	VERB
ejpam-1563	211	25	the	the	DET
ejpam-1563	211	26	case	case	NOUN
ejpam-1563	211	27	in	in	ADP
ejpam-1563	211	28	which	which	PRON
ejpam-1563	211	29	the	the	DET
ejpam-1563	211	30	order	order	NOUN
ejpam-1563	211	31	structure	structure	NOUN
ejpam-1563	211	32	in	in	ADP
ejpam-1563	211	33	y	y	PROPN
ejpam-1563	211	34	is	be	AUX
ejpam-1563	211	35	lexicographic	lexicographic	ADJ
ejpam-1563	211	36	.	.	PUNCT
ejpam-1563	212	1	in	in	ADP
ejpam-1563	212	2	this	this	DET
ejpam-1563	212	3	case	case	NOUN
ejpam-1563	212	4	,	,	PUNCT
ejpam-1563	212	5	y	y	PROPN
ejpam-1563	212	6	is	be	AUX
ejpam-1563	212	7	a	a	DET
ejpam-1563	212	8	finite	finite	ADJ
ejpam-1563	212	9	dimensional	dimensional	ADJ
ejpam-1563	212	10	vector	vector	NOUN
ejpam-1563	212	11	space	space	NOUN
ejpam-1563	212	12	,	,	PUNCT
ejpam-1563	212	13	which	which	PRON
ejpam-1563	212	14	we	we	PRON
ejpam-1563	212	15	will	will	AUX
ejpam-1563	212	16	identify	identify	VERB
ejpam-1563	212	17	with	with	ADP
ejpam-1563	212	18	rn	rn	PROPN
ejpam-1563	212	19	,	,	PUNCT
ejpam-1563	212	20	for	for	ADP
ejpam-1563	212	21	simplicity	simplicity	NOUN
ejpam-1563	212	22	,	,	PUNCT
ejpam-1563	212	23	and	and	CCONJ
ejpam-1563	212	24	the	the	DET
ejpam-1563	212	25	lexicographic	lexicographic	ADJ
ejpam-1563	212	26	order	order	NOUN
ejpam-1563	212	27	is	be	AUX
ejpam-1563	212	28	defined	define	VERB
ejpam-1563	212	29	by	by	ADP
ejpam-1563	212	30	considering	consider	VERB
ejpam-1563	212	31	the	the	DET
ejpam-1563	212	32	cone	cone	NOUN
ejpam-1563	212	33	clex	clex	NOUN
ejpam-1563	212	34	=	=	SYM
ejpam-1563	212	35	{	{	PUNCT
ejpam-1563	212	36	0	0	NUM
ejpam-1563	212	37	}	}	PUNCT
ejpam-1563	212	38	∪	∪	NOUN
ejpam-1563	212	39	{	{	PUNCT
ejpam-1563	212	40	x	x	SYM
ejpam-1563	212	41	∈	∈	PROPN
ejpam-1563	212	42	rn	rn	PROPN
ejpam-1563	212	43	:	:	PUNCT
ejpam-1563	212	44	∃i	∃i	PROPN
ejpam-1563	212	45	∈	∈	PROPN
ejpam-1563	212	46	in	in	ADP
ejpam-1563	212	47	x	x	PROPN
ejpam-1563	212	48	i	i	X
ejpam-1563	212	49	>	>	X
ejpam-1563	212	50	0,∀	0,∀	NUM
ejpam-1563	213	1	j	j	X
ejpam-1563	213	2	<	<	X
ejpam-1563	213	3	i	i	X
ejpam-1563	213	4	x	x	X
ejpam-1563	213	5	j	j	PROPN
ejpam-1563	213	6	=	=	NOUN
ejpam-1563	213	7	0	0	NUM
ejpam-1563	213	8	}	}	PUNCT
ejpam-1563	213	9	,	,	PUNCT
ejpam-1563	213	10	(	(	PUNCT
ejpam-1563	213	11	7	7	X
ejpam-1563	213	12	)	)	PUNCT
ejpam-1563	213	13	where	where	SCONJ
ejpam-1563	213	14	in	in	ADP
ejpam-1563	213	15	=	=	PUNCT
ejpam-1563	213	16	{	{	PUNCT
ejpam-1563	213	17	1	1	NUM
ejpam-1563	213	18	,	,	PUNCT
ejpam-1563	213	19	.	.	PUNCT
ejpam-1563	213	20	.	.	PUNCT
ejpam-1563	214	1	.	.	PUNCT
ejpam-1563	214	2	,	,	PUNCT
ejpam-1563	215	1	n	n	CCONJ
ejpam-1563	215	2	}	}	PUNCT
ejpam-1563	215	3	.	.	PUNCT
ejpam-1563	216	1	note	note	VERB
ejpam-1563	216	2	that	that	PRON
ejpam-1563	216	3	clex	clex	NOUN
ejpam-1563	216	4	is	be	AUX
ejpam-1563	216	5	convex	convex	PROPN
ejpam-1563	216	6	,	,	PUNCT
ejpam-1563	216	7	pointed	pointed	ADJ
ejpam-1563	216	8	and	and	CCONJ
ejpam-1563	216	9	solid	solid	ADJ
ejpam-1563	216	10	,	,	PUNCT
ejpam-1563	216	11	but	but	CCONJ
ejpam-1563	216	12	it	it	PRON
ejpam-1563	216	13	is	be	AUX
ejpam-1563	216	14	neither	neither	CCONJ
ejpam-1563	216	15	closed	closed	ADJ
ejpam-1563	216	16	,	,	PUNCT
ejpam-1563	216	17	nor	nor	CCONJ
ejpam-1563	216	18	open	open	ADJ
ejpam-1563	216	19	.	.	PUNCT
ejpam-1563	217	1	moreover	moreover	ADV
ejpam-1563	217	2	,	,	PUNCT
ejpam-1563	217	3	the	the	DET
ejpam-1563	217	4	order	order	NOUN
ejpam-1563	217	5	is	be	AUX
ejpam-1563	217	6	total	total	ADJ
ejpam-1563	217	7	,	,	PUNCT
ejpam-1563	217	8	since	since	SCONJ
ejpam-1563	217	9	−clex	−clex	PROPN
ejpam-1563	217	10	∪	∪	ADP
ejpam-1563	217	11	clex	clex	PROPN
ejpam-1563	217	12	=	=	SYM
ejpam-1563	217	13	rn	rn	PROPN
ejpam-1563	217	14	.	.	PROPN
ejpam-1563	217	15	though	though	SCONJ
ejpam-1563	217	16	clex	clex	NOUN
ejpam-1563	217	17	is	be	AUX
ejpam-1563	217	18	solid	solid	ADJ
ejpam-1563	217	19	,	,	PUNCT
ejpam-1563	217	20	in	in	ADP
ejpam-1563	217	21	this	this	DET
ejpam-1563	217	22	setting	setting	NOUN
ejpam-1563	217	23	it	it	PRON
ejpam-1563	217	24	is	be	AUX
ejpam-1563	217	25	worthwhile	worthwhile	ADJ
ejpam-1563	217	26	considering	consider	VERB
ejpam-1563	217	27	formulation	formulation	NOUN
ejpam-1563	217	28	(	(	PUNCT
ejpam-1563	217	29	gvep2b	gvep2b	PROPN
ejpam-1563	217	30	)	)	PUNCT
ejpam-1563	217	31	of	of	ADP
ejpam-1563	217	32	the	the	DET
ejpam-1563	217	33	generalized	generalize	VERB
ejpam-1563	217	34	vector	vector	NOUN
ejpam-1563	217	35	equilibrium	equilibrium	NOUN
ejpam-1563	217	36	problem	problem	NOUN
ejpam-1563	217	37	,	,	PUNCT
ejpam-1563	217	38	since	since	ADV
ejpam-1563	217	39	,	,	PUNCT
ejpam-1563	217	40	as	as	SCONJ
ejpam-1563	217	41	lexicographic	lexicographic	ADJ
ejpam-1563	217	42	order	order	NOUN
ejpam-1563	217	43	is	be	AUX
ejpam-1563	217	44	total	total	ADJ
ejpam-1563	217	45	,	,	PUNCT
ejpam-1563	217	46	it	it	PRON
ejpam-1563	217	47	coincides	coincide	VERB
ejpam-1563	217	48	with	with	ADP
ejpam-1563	217	49	the	the	DET
ejpam-1563	217	50	strong	strong	ADJ
ejpam-1563	217	51	formulation	formulation	NOUN
ejpam-1563	217	52	of	of	ADP
ejpam-1563	217	53	the	the	DET
ejpam-1563	217	54	problem	problem	NOUN
ejpam-1563	217	55	,	,	PUNCT
ejpam-1563	217	56	i.e.	i.e.	X
ejpam-1563	217	57	,	,	PUNCT
ejpam-1563	217	58	find	find	VERB
ejpam-1563	217	59	x	x	X
ejpam-1563	217	60	∈	∈	PROPN
ejpam-1563	217	61	k	k	NOUN
ejpam-1563	217	62	such	such	ADJ
ejpam-1563	217	63	that	that	SCONJ
ejpam-1563	217	64	φ(x	φ(x	PROPN
ejpam-1563	217	65	,	,	PUNCT
ejpam-1563	217	66	y)⊆	y)⊆	PROPN
ejpam-1563	217	67	clex	clex	NOUN
ejpam-1563	217	68	,	,	PUNCT
ejpam-1563	217	69	∀y	∀y	PROPN
ejpam-1563	217	70	∈	∈	PROPN
ejpam-1563	217	71	k	k	X
ejpam-1563	217	72	.	.	PUNCT
ejpam-1563	218	1	(	(	PUNCT
ejpam-1563	218	2	8)	8)	NUM
ejpam-1563	218	3	corollary	corollary	NOUN
ejpam-1563	218	4	2	2	NUM
ejpam-1563	218	5	,	,	PUNCT
ejpam-1563	218	6	with	with	ADP
ejpam-1563	218	7	y	y	PROPN
ejpam-1563	218	8	=	=	SYM
ejpam-1563	218	9	rn	rn	PROPN
ejpam-1563	218	10	and	and	CCONJ
ejpam-1563	218	11	c(x	c(x	NOUN
ejpam-1563	218	12	)	)	PUNCT
ejpam-1563	218	13	replaced	replace	VERB
ejpam-1563	218	14	by	by	ADP
ejpam-1563	218	15	clex	clex	NOUN
ejpam-1563	218	16	for	for	ADP
ejpam-1563	218	17	all	all	DET
ejpam-1563	218	18	x	x	SYM
ejpam-1563	218	19	∈	∈	PROPN
ejpam-1563	218	20	x	x	X
ejpam-1563	218	21	,	,	PUNCT
ejpam-1563	218	22	then	then	ADV
ejpam-1563	218	23	yields	yield	VERB
ejpam-1563	218	24	an	an	DET
ejpam-1563	218	25	existence	existence	NOUN
ejpam-1563	218	26	result	result	NOUN
ejpam-1563	218	27	for	for	ADP
ejpam-1563	218	28	the	the	DET
ejpam-1563	218	29	generalized	generalize	VERB
ejpam-1563	218	30	vector	vector	NOUN
ejpam-1563	218	31	equilibrium	equilibrium	NOUN
ejpam-1563	218	32	problem	problem	NOUN
ejpam-1563	218	33	(	(	PUNCT
ejpam-1563	218	34	gvep2b	gvep2b	PROPN
ejpam-1563	218	35	)	)	PUNCT
ejpam-1563	218	36	on	on	ADP
ejpam-1563	218	37	unbounded	unbounded	ADJ
ejpam-1563	218	38	sets	set	NOUN
ejpam-1563	218	39	.	.	PUNCT
ejpam-1563	219	1	finally	finally	ADV
ejpam-1563	219	2	,	,	PUNCT
ejpam-1563	219	3	we	we	PRON
ejpam-1563	219	4	provide	provide	VERB
ejpam-1563	219	5	a	a	DET
ejpam-1563	219	6	simple	simple	ADJ
ejpam-1563	219	7	numerical	numerical	ADJ
ejpam-1563	219	8	example	example	NOUN
ejpam-1563	219	9	instantiating	instantiate	VERB
ejpam-1563	219	10	the	the	DET
ejpam-1563	219	11	results	result	NOUN
ejpam-1563	219	12	presented	present	VERB
ejpam-1563	219	13	in	in	ADP
ejpam-1563	219	14	the	the	DET
ejpam-1563	219	15	previous	previous	ADJ
ejpam-1563	219	16	sections	section	NOUN
ejpam-1563	219	17	.	.	PUNCT
ejpam-1563	220	1	example	example	NOUN
ejpam-1563	221	1	1	1	NUM
ejpam-1563	221	2	.	.	PUNCT
ejpam-1563	221	3	let	let	VERB
ejpam-1563	221	4	x	x	PUNCT
ejpam-1563	221	5	=	=	SYM
ejpam-1563	221	6	r	r	NOUN
ejpam-1563	221	7	,	,	PUNCT
ejpam-1563	221	8	k	k	NOUN
ejpam-1563	221	9	=	=	PUNCT
ejpam-1563	222	1	[	[	X
ejpam-1563	222	2	0,+∞	0,+∞	NUM
ejpam-1563	222	3	[	[	X
ejpam-1563	222	4	,	,	PUNCT
ejpam-1563	222	5	y	y	PROPN
ejpam-1563	222	6	be	be	AUX
ejpam-1563	222	7	a	a	DET
ejpam-1563	222	8	banach	banach	NOUN
ejpam-1563	222	9	space	space	NOUN
ejpam-1563	222	10	,	,	PUNCT
ejpam-1563	222	11	c	c	PROPN
ejpam-1563	222	12	⊆	⊆	NUM
ejpam-1563	222	13	y	y	PROPN
ejpam-1563	222	14	be	be	AUX
ejpam-1563	222	15	a	a	DET
ejpam-1563	222	16	convex	convex	NOUN
ejpam-1563	222	17	,	,	PUNCT
ejpam-1563	222	18	solid	solid	ADJ
ejpam-1563	222	19	and	and	CCONJ
ejpam-1563	222	20	pointed	pointed	ADJ
ejpam-1563	222	21	cone	cone	NOUN
ejpam-1563	222	22	,	,	PUNCT
ejpam-1563	222	23	and	and	CCONJ
ejpam-1563	222	24	c	c	NOUN
ejpam-1563	222	25	:	:	PUNCT
ejpam-1563	223	1	k	k	X
ejpam-1563	223	2	→	→	PUNCT
ejpam-1563	223	3	π(y	π(y	PROPN
ejpam-1563	223	4	)	)	PUNCT
ejpam-1563	223	5	be	be	AUX
ejpam-1563	223	6	the	the	DET
ejpam-1563	223	7	constant	constant	ADJ
ejpam-1563	223	8	set	set	NOUN
ejpam-1563	223	9	-	-	PUNCT
ejpam-1563	223	10	valued	value	VERB
ejpam-1563	223	11	mapping	mapping	NOUN
ejpam-1563	223	12	defined	define	VERB
ejpam-1563	223	13	as	as	ADP
ejpam-1563	223	14	c(x	c(x	NOUN
ejpam-1563	223	15	)	)	PUNCT
ejpam-1563	223	16	=	=	SYM
ejpam-1563	224	1	c	c	NOUN
ejpam-1563	224	2	for	for	ADP
ejpam-1563	224	3	all	all	DET
ejpam-1563	224	4	x	x	SYM
ejpam-1563	224	5	∈	∈	PROPN
ejpam-1563	224	6	k.	k.	NOUN
ejpam-1563	224	7	then	then	ADV
ejpam-1563	224	8	,	,	PUNCT
ejpam-1563	224	9	the	the	DET
ejpam-1563	224	10	set	set	NOUN
ejpam-1563	224	11	-	-	PUNCT
ejpam-1563	224	12	valued	value	VERB
ejpam-1563	224	13	mapping	mapping	NOUN
ejpam-1563	224	14	φ	φ	NOUN
ejpam-1563	224	15	:	:	PUNCT
ejpam-1563	225	1	k	k	PROPN
ejpam-1563	225	2	×	×	PROPN
ejpam-1563	225	3	k	k	PROPN
ejpam-1563	225	4	→	→	SYM
ejpam-1563	225	5	π(y	π(y	PROPN
ejpam-1563	225	6	)	)	PUNCT
ejpam-1563	225	7	defined	define	VERB
ejpam-1563	225	8	as	as	ADP
ejpam-1563	225	9	φ(x	φ(x	PROPN
ejpam-1563	225	10	,	,	PUNCT
ejpam-1563	225	11	y	y	PROPN
ejpam-1563	225	12	)	)	PUNCT
ejpam-1563	225	13	=	=	PUNCT
ejpam-1563	226	1			PROPN
ejpam-1563	226	2			NOUN
ejpam-1563	226	3			PROPN
ejpam-1563	226	4	−int	−int	NOUN
ejpam-1563	226	5	c	c	NOUN
ejpam-1563	226	6	,	,	PUNCT
ejpam-1563	226	7	if	if	SCONJ
ejpam-1563	226	8	x	x	PROPN
ejpam-1563	226	9	>	>	X
ejpam-1563	226	10	y	y	PROPN
ejpam-1563	226	11	{	{	PUNCT
ejpam-1563	226	12	0	0	NUM
ejpam-1563	226	13	}	}	PUNCT
ejpam-1563	226	14	,	,	PUNCT
ejpam-1563	226	15	if	if	SCONJ
ejpam-1563	226	16	x	x	X
ejpam-1563	226	17	=	=	SYM
ejpam-1563	226	18	y	y	PROPN
ejpam-1563	226	19	int	int	NOUN
ejpam-1563	226	20	c	c	NOUN
ejpam-1563	226	21	,	,	PUNCT
ejpam-1563	226	22	if	if	SCONJ
ejpam-1563	226	23	x	x	X
ejpam-1563	226	24	<	<	X
ejpam-1563	226	25	y	y	PROPN
ejpam-1563	226	26	,	,	PUNCT
ejpam-1563	226	27	references	reference	VERB
ejpam-1563	226	28	375	375	NUM
ejpam-1563	226	29	for	for	ADP
ejpam-1563	226	30	all	all	DET
ejpam-1563	226	31	(	(	PUNCT
ejpam-1563	226	32	x	x	INTJ
ejpam-1563	226	33	,	,	PUNCT
ejpam-1563	226	34	y	y	PROPN
ejpam-1563	226	35	)	)	PUNCT
ejpam-1563	226	36	∈	∈	PROPN
ejpam-1563	226	37	k×k	k×k	PROPN
ejpam-1563	226	38	,	,	PUNCT
ejpam-1563	226	39	satisfies	satisfy	VERB
ejpam-1563	226	40	the	the	DET
ejpam-1563	226	41	assumptions	assumption	NOUN
ejpam-1563	226	42	of	of	ADP
ejpam-1563	226	43	corollaries	corollary	NOUN
ejpam-1563	226	44	1	1	NUM
ejpam-1563	226	45	and	and	CCONJ
ejpam-1563	226	46	3	3	NUM
ejpam-1563	226	47	.	.	X
ejpam-1563	227	1	we	we	PRON
ejpam-1563	227	2	prove	prove	VERB
ejpam-1563	227	3	it	it	PRON
ejpam-1563	227	4	for	for	ADP
ejpam-1563	227	5	corollary	corollary	ADJ
ejpam-1563	227	6	1	1	NUM
ejpam-1563	227	7	only	only	ADV
ejpam-1563	227	8	,	,	PUNCT
ejpam-1563	227	9	given	give	VERB
ejpam-1563	227	10	that	that	SCONJ
ejpam-1563	227	11	the	the	DET
ejpam-1563	227	12	proof	proof	NOUN
ejpam-1563	227	13	for	for	ADP
ejpam-1563	227	14	corollary	corollary	ADJ
ejpam-1563	227	15	3	3	NUM
ejpam-1563	227	16	is	be	AUX
ejpam-1563	227	17	similar	similar	ADJ
ejpam-1563	227	18	.	.	PUNCT
ejpam-1563	228	1	first	first	ADV
ejpam-1563	228	2	of	of	ADP
ejpam-1563	228	3	all	all	PRON
ejpam-1563	228	4	,	,	PUNCT
ejpam-1563	228	5	by	by	ADP
ejpam-1563	228	6	definition	definition	NOUN
ejpam-1563	228	7	of	of	ADP
ejpam-1563	228	8	φ	φ	PROPN
ejpam-1563	228	9	,	,	PUNCT
ejpam-1563	228	10	φ(x	φ(x	PROPN
ejpam-1563	228	11	,	,	PUNCT
ejpam-1563	228	12	x	x	X
ejpam-1563	228	13	)	)	PUNCT
ejpam-1563	228	14	=	=	SYM
ejpam-1563	228	15	{	{	PUNCT
ejpam-1563	228	16	0	0	NUM
ejpam-1563	228	17	}	}	PUNCT
ejpam-1563	228	18	for	for	ADP
ejpam-1563	228	19	all	all	DET
ejpam-1563	228	20	x	x	SYM
ejpam-1563	228	21	∈	∈	PROPN
ejpam-1563	229	1	[	[	X
ejpam-1563	229	2	0,+∞	0,+∞	NUM
ejpam-1563	229	3	[	[	X
ejpam-1563	229	4	.	.	PUNCT
ejpam-1563	230	1	next	next	ADV
ejpam-1563	230	2	,	,	PUNCT
ejpam-1563	230	3	given	give	VERB
ejpam-1563	230	4	a	a	DET
ejpam-1563	230	5	fixed	fix	VERB
ejpam-1563	230	6	y	y	PROPN
ejpam-1563	230	7	∈	∈	PROPN
ejpam-1563	230	8	[	[	X
ejpam-1563	230	9	0,+∞	0,+∞	PROPN
ejpam-1563	230	10	[	[	X
ejpam-1563	230	11	,	,	PUNCT
ejpam-1563	230	12	the	the	DET
ejpam-1563	230	13	set	set	NOUN
ejpam-1563	230	14	{	{	PUNCT
ejpam-1563	230	15	x	x	SYM
ejpam-1563	230	16	∈	∈	PROPN
ejpam-1563	231	1	[	[	X
ejpam-1563	231	2	0,+∞	0,+∞	X
ejpam-1563	231	3	[:	[:	X
ejpam-1563	231	4	φ(x	φ(x	PROPN
ejpam-1563	231	5	,	,	PUNCT
ejpam-1563	231	6	y	y	PROPN
ejpam-1563	231	7	)	)	PUNCT
ejpam-1563	231	8	6⊆	6⊆	NOUN
ejpam-1563	231	9	−int	−int	NOUN
ejpam-1563	231	10	c	c	X
ejpam-1563	231	11	}	}	PUNCT
ejpam-1563	231	12	is	be	AUX
ejpam-1563	231	13	the	the	DET
ejpam-1563	231	14	interval	interval	NOUN
ejpam-1563	231	15	[	[	X
ejpam-1563	231	16	0	0	NUM
ejpam-1563	231	17	,	,	PUNCT
ejpam-1563	231	18	y	y	PROPN
ejpam-1563	231	19	]	]	X
ejpam-1563	231	20	,	,	PUNCT
ejpam-1563	231	21	which	which	PRON
ejpam-1563	231	22	is	be	AUX
ejpam-1563	231	23	closed	close	VERB
ejpam-1563	231	24	.	.	PUNCT
ejpam-1563	232	1	finally	finally	ADV
ejpam-1563	232	2	,	,	PUNCT
ejpam-1563	232	3	given	give	VERB
ejpam-1563	232	4	arbitrary	arbitrary	ADJ
ejpam-1563	232	5	x	x	SYM
ejpam-1563	232	6	,	,	PUNCT
ejpam-1563	232	7	y	y	PROPN
ejpam-1563	232	8	′	′	NOUN
ejpam-1563	232	9	,	,	PUNCT
ejpam-1563	232	10	y	y	PROPN
ejpam-1563	232	11	′′	′′	PROPN
ejpam-1563	232	12	∈	∈	PROPN
ejpam-1563	233	1	[	[	X
ejpam-1563	233	2	0,+∞	0,+∞	NUM
ejpam-1563	233	3	[	[	PUNCT
ejpam-1563	233	4	such	such	ADJ
ejpam-1563	233	5	that	that	SCONJ
ejpam-1563	233	6	φ(x	φ(x	PROPN
ejpam-1563	233	7	,	,	PUNCT
ejpam-1563	233	8	y	y	PROPN
ejpam-1563	233	9	′)⊆−c	′)⊆−c	NOUN
ejpam-1563	233	10	and	and	CCONJ
ejpam-1563	233	11	φ(x	φ(x	PROPN
ejpam-1563	233	12	,	,	PUNCT
ejpam-1563	233	13	y	y	PROPN
ejpam-1563	233	14	′′)⊆−int	′′)⊆−int	PROPN
ejpam-1563	233	15	c	c	X
ejpam-1563	233	16	,	,	PUNCT
ejpam-1563	233	17	one	one	PRON
ejpam-1563	233	18	has	have	VERB
ejpam-1563	233	19	y	y	PROPN
ejpam-1563	233	20	′	′	NUM
ejpam-1563	233	21	∈	∈	PROPN
ejpam-1563	234	1	[	[	X
ejpam-1563	234	2	0	0	NUM
ejpam-1563	234	3	,	,	PUNCT
ejpam-1563	234	4	x	x	PRON
ejpam-1563	234	5	]	]	PUNCT
ejpam-1563	234	6	and	and	CCONJ
ejpam-1563	234	7	y	y	PROPN
ejpam-1563	234	8	′′	′′	PROPN
ejpam-1563	234	9	∈	∈	PROPN
ejpam-1563	235	1	[	[	X
ejpam-1563	235	2	0	0	NUM
ejpam-1563	235	3	,	,	PUNCT
ejpam-1563	235	4	x	x	X
ejpam-1563	236	1	[	[	X
ejpam-1563	236	2	.	.	PUNCT
ejpam-1563	237	1	then	then	ADV
ejpam-1563	237	2	,	,	PUNCT
ejpam-1563	237	3	for	for	ADP
ejpam-1563	237	4	any	any	DET
ejpam-1563	237	5	α	α	NOUN
ejpam-1563	237	6	∈	∈	NOUN
ejpam-1563	237	7	]	]	X
ejpam-1563	237	8	0	0	NUM
ejpam-1563	237	9	,	,	PUNCT
ejpam-1563	237	10	1	1	NUM
ejpam-1563	237	11	[	[	NOUN
ejpam-1563	237	12	,	,	PUNCT
ejpam-1563	237	13	αy	αy	NOUN
ejpam-1563	237	14	′+	′+	PUNCT
ejpam-1563	237	15	(	(	PUNCT
ejpam-1563	237	16	1−α)y	1−α)y	NUM
ejpam-1563	237	17	′′	′′	PROPN
ejpam-1563	237	18	belongs	belong	VERB
ejpam-1563	237	19	to	to	ADP
ejpam-1563	237	20	[	[	X
ejpam-1563	237	21	0	0	NUM
ejpam-1563	237	22	,	,	PUNCT
ejpam-1563	237	23	x	x	X
ejpam-1563	237	24	[	[	PUNCT
ejpam-1563	237	25	and	and	CCONJ
ejpam-1563	237	26	,	,	PUNCT
ejpam-1563	237	27	as	as	ADP
ejpam-1563	237	28	a	a	DET
ejpam-1563	237	29	consequence	consequence	NOUN
ejpam-1563	237	30	,	,	PUNCT
ejpam-1563	237	31	φ(x	φ(x	PROPN
ejpam-1563	237	32	,	,	PUNCT
ejpam-1563	237	33	αy	αy	X
ejpam-1563	237	34	′+	′+	PUNCT
ejpam-1563	237	35	(	(	PUNCT
ejpam-1563	237	36	1−α)y	1−α)y	NUM
ejpam-1563	237	37	′′)⊆−int	′′)⊆−int	PROPN
ejpam-1563	237	38	c.	c.	NOUN
ejpam-1563	237	39	an	an	DET
ejpam-1563	237	40	analogous	analogous	ADJ
ejpam-1563	237	41	example	example	NOUN
ejpam-1563	237	42	,	,	PUNCT
ejpam-1563	237	43	with	with	ADP
ejpam-1563	237	44	c	c	PROPN
ejpam-1563	237	45	a	a	DET
ejpam-1563	237	46	non	non	X
ejpam-1563	237	47	solid	solid	ADJ
ejpam-1563	237	48	cone	cone	NOUN
ejpam-1563	237	49	and	and	CCONJ
ejpam-1563	237	50	int	int	NOUN
ejpam-1563	237	51	c	c	PROPN
ejpam-1563	237	52	replaced	replace	VERB
ejpam-1563	237	53	by	by	ADP
ejpam-1563	237	54	c\{0	c\{0	PROPN
ejpam-1563	237	55	}	}	PUNCT
ejpam-1563	237	56	,	,	PUNCT
ejpam-1563	237	57	can	can	AUX
ejpam-1563	237	58	be	be	AUX
ejpam-1563	237	59	provided	provide	VERB
ejpam-1563	237	60	for	for	ADP
ejpam-1563	237	61	corollary	corollary	ADJ
ejpam-1563	237	62	2	2	NUM
ejpam-1563	237	63	.	.	PUNCT
ejpam-1563	238	1	as	as	ADP
ejpam-1563	238	2	a	a	DET
ejpam-1563	238	3	particular	particular	ADJ
ejpam-1563	238	4	case	case	NOUN
ejpam-1563	238	5	,	,	PUNCT
ejpam-1563	238	6	when	when	SCONJ
ejpam-1563	238	7	y	y	PROPN
ejpam-1563	238	8	=	=	SYM
ejpam-1563	238	9	r	r	PROPN
ejpam-1563	238	10	and	and	CCONJ
ejpam-1563	238	11	k	k	NOUN
ejpam-1563	239	1	=	=	PUNCT
ejpam-1563	239	2	c	c	NOUN
ejpam-1563	239	3	=	=	PUNCT
ejpam-1563	240	1	[	[	X
ejpam-1563	240	2	0,+∞	0,+∞	NUM
ejpam-1563	240	3	[	[	X
ejpam-1563	240	4	,	,	PUNCT
ejpam-1563	240	5	we	we	PRON
ejpam-1563	240	6	obtain	obtain	VERB
ejpam-1563	240	7	the	the	DET
ejpam-1563	240	8	set	set	NOUN
ejpam-1563	240	9	-	-	PUNCT
ejpam-1563	240	10	valued	value	VERB
ejpam-1563	240	11	mapping	mapping	NOUN
ejpam-1563	240	12	φ	φ	NOUN
ejpam-1563	240	13	:	:	PUNCT
ejpam-1563	241	1	k	k	PROPN
ejpam-1563	241	2	×	×	PROPN
ejpam-1563	241	3	k	k	PROPN
ejpam-1563	241	4	→	→	SYM
ejpam-1563	241	5	π(r	π(r	PROPN
ejpam-1563	241	6	)	)	PUNCT
ejpam-1563	241	7	defined	define	VERB
ejpam-1563	241	8	as	as	ADP
ejpam-1563	241	9	φ(x	φ(x	PROPN
ejpam-1563	241	10	,	,	PUNCT
ejpam-1563	241	11	y	y	PROPN
ejpam-1563	241	12	)	)	PUNCT
ejpam-1563	241	13	=	=	PUNCT
ejpam-1563	242	1			PROPN
ejpam-1563	242	2			PRON
ejpam-1563	242	3			PROPN
ejpam-1563	242	4	]	]	PUNCT
ejpam-1563	242	5	−∞	−∞	NOUN
ejpam-1563	242	6	,	,	PUNCT
ejpam-1563	242	7	0	0	PUNCT
ejpam-1563	243	1	[	[	X
ejpam-1563	243	2	,	,	PUNCT
ejpam-1563	243	3	if	if	SCONJ
ejpam-1563	243	4	x	x	PROPN
ejpam-1563	243	5	>	>	X
ejpam-1563	243	6	y	y	PROPN
ejpam-1563	243	7	{	{	PUNCT
ejpam-1563	243	8	0	0	NUM
ejpam-1563	243	9	}	}	PUNCT
ejpam-1563	243	10	,	,	PUNCT
ejpam-1563	243	11	if	if	SCONJ
ejpam-1563	243	12	x	x	X
ejpam-1563	243	13	=	=	SYM
ejpam-1563	243	14	y	y	PROPN
ejpam-1563	243	15	]	]	PUNCT
ejpam-1563	243	16	0,+∞	0,+∞	PROPN
ejpam-1563	244	1	[	[	X
ejpam-1563	244	2	,	,	PUNCT
ejpam-1563	244	3	if	if	SCONJ
ejpam-1563	244	4	x	x	PUNCT
ejpam-1563	244	5	<	<	X
ejpam-1563	244	6	y	y	PROPN
ejpam-1563	244	7	,	,	PUNCT
ejpam-1563	244	8	for	for	ADP
ejpam-1563	244	9	all	all	DET
ejpam-1563	244	10	(	(	PUNCT
ejpam-1563	244	11	x	x	INTJ
ejpam-1563	244	12	,	,	PUNCT
ejpam-1563	244	13	y	y	PROPN
ejpam-1563	244	14	)	)	PUNCT
ejpam-1563	244	15	∈	∈	PROPN
ejpam-1563	244	16	k	k	PROPN
ejpam-1563	244	17	×	×	PROPN
ejpam-1563	244	18	k	k	PROPN
ejpam-1563	244	19	,	,	PUNCT
ejpam-1563	244	20	which	which	PRON
ejpam-1563	244	21	satisfies	satisfy	VERB
ejpam-1563	244	22	the	the	DET
ejpam-1563	244	23	assumptions	assumption	NOUN
ejpam-1563	244	24	of	of	ADP
ejpam-1563	244	25	corollaries	corollary	NOUN
ejpam-1563	244	26	1	1	NUM
ejpam-1563	244	27	,	,	PUNCT
ejpam-1563	244	28	2	2	NUM
ejpam-1563	244	29	and	and	CCONJ
ejpam-1563	244	30	3	3	NUM
ejpam-1563	244	31	.	.	X
ejpam-1563	244	32	acknowledgements	acknowledgement	NOUN
ejpam-1563	244	33	in	in	ADP
ejpam-1563	244	34	this	this	DET
ejpam-1563	244	35	work	work	NOUN
ejpam-1563	244	36	,	,	PUNCT
ejpam-1563	244	37	the	the	DET
ejpam-1563	244	38	second	second	ADJ
ejpam-1563	244	39	author	author	NOUN
ejpam-1563	244	40	was	be	AUX
ejpam-1563	244	41	supported	support	VERB
ejpam-1563	244	42	in	in	ADP
ejpam-1563	244	43	part	part	NOUN
ejpam-1563	244	44	by	by	ADP
ejpam-1563	244	45	the	the	DET
ejpam-1563	244	46	rfbr	rfbr	ADJ
ejpam-1563	244	47	grant	grant	NOUN
ejpam-1563	244	48	,	,	PUNCT
ejpam-1563	244	49	project	project	VERB
ejpam-1563	244	50	no	no	NOUN
ejpam-1563	244	51	.	.	NOUN
ejpam-1563	244	52	13	13	NUM
ejpam-1563	244	53	-	-	PUNCT
ejpam-1563	244	54	01	01	NUM
ejpam-1563	244	55	-	-	PUNCT
ejpam-1563	244	56	00029a	00029a	NUM
ejpam-1563	244	57	.	.	PUNCT
ejpam-1563	245	1	the	the	DET
ejpam-1563	245	2	third	third	ADJ
ejpam-1563	245	3	author	author	NOUN
ejpam-1563	245	4	contributed	contribute	VERB
ejpam-1563	245	5	to	to	ADP
ejpam-1563	245	6	this	this	DET
ejpam-1563	245	7	work	work	NOUN
ejpam-1563	245	8	during	during	ADP
ejpam-1563	245	9	his	his	PRON
ejpam-1563	245	10	postdoc	postdoc	ADJ
ejpam-1563	245	11	fellowship	fellowship	NOUN
ejpam-1563	245	12	at	at	ADP
ejpam-1563	245	13	the	the	DET
ejpam-1563	245	14	university	university	NOUN
ejpam-1563	245	15	of	of	ADP
ejpam-1563	245	16	bergamo	bergamo	X
ejpam-1563	245	17	(	(	PUNCT
ejpam-1563	245	18	italy	italy	PROPN
ejpam-1563	245	19	)	)	PUNCT
ejpam-1563	245	20	,	,	PUNCT
ejpam-1563	245	21	department	department	NOUN
ejpam-1563	245	22	of	of	ADP
ejpam-1563	245	23	mathematics	mathematic	NOUN
ejpam-1563	245	24	,	,	PUNCT
ejpam-1563	245	25	statistics	statistic	NOUN
ejpam-1563	245	26	,	,	PUNCT
ejpam-1563	245	27	computing	computing	NOUN
ejpam-1563	245	28	and	and	CCONJ
ejpam-1563	245	29	applications	application	NOUN
ejpam-1563	245	30	.	.	PUNCT
ejpam-1563	246	1	references	reference	NOUN
ejpam-1563	246	2	[	[	X
ejpam-1563	246	3	1	1	NUM
ejpam-1563	246	4	]	]	PUNCT
ejpam-1563	246	5	q.	q.	PROPN
ejpam-1563	246	6	h.	h.	PROPN
ejpam-1563	246	7	ansari	ansari	PROPN
ejpam-1563	246	8	and	and	CCONJ
ejpam-1563	246	9	f.	f.	PROPN
ejpam-1563	246	10	flores	flores	PROPN
ejpam-1563	246	11	-	-	PUNCT
ejpam-1563	246	12	bazán	bazán	PROPN
ejpam-1563	246	13	.	.	PUNCT
ejpam-1563	247	1	recession	recession	NOUN
ejpam-1563	247	2	methods	method	NOUN
ejpam-1563	247	3	for	for	ADP
ejpam-1563	247	4	generalized	generalized	ADJ
ejpam-1563	247	5	vector	vector	NOUN
ejpam-1563	247	6	equilibrium	equilibrium	NOUN
ejpam-1563	247	7	problems	problem	NOUN
ejpam-1563	247	8	,	,	PUNCT
ejpam-1563	247	9	journal	journal	NOUN
ejpam-1563	247	10	of	of	ADP
ejpam-1563	247	11	mathematical	mathematical	ADJ
ejpam-1563	247	12	analysis	analysis	NOUN
ejpam-1563	247	13	and	and	CCONJ
ejpam-1563	247	14	applications	application	NOUN
ejpam-1563	247	15	,	,	PUNCT
ejpam-1563	247	16	321	321	NUM
ejpam-1563	247	17	,	,	PUNCT
ejpam-1563	247	18	132–146	132–146	NUM
ejpam-1563	247	19	,	,	PUNCT
ejpam-1563	247	20	2006	2006	NUM
ejpam-1563	247	21	.	.	PUNCT
ejpam-1563	248	1	[	[	X
ejpam-1563	248	2	2	2	NUM
ejpam-1563	248	3	]	]	PUNCT
ejpam-1563	248	4	c.	c.	PROPN
ejpam-1563	248	5	baiocchi	baiocchi	PROPN
ejpam-1563	248	6	and	and	CCONJ
ejpam-1563	248	7	a.	a.	NOUN
ejpam-1563	248	8	capelo	capelo	NOUN
ejpam-1563	248	9	.	.	PUNCT
ejpam-1563	249	1	variational	variational	ADJ
ejpam-1563	249	2	and	and	CCONJ
ejpam-1563	249	3	quasivariational	quasivariational	ADJ
ejpam-1563	249	4	inequalities	inequality	NOUN
ejpam-1563	249	5	.	.	PUNCT
ejpam-1563	250	1	applications	application	NOUN
ejpam-1563	250	2	to	to	PART
ejpam-1563	250	3	free	free	VERB
ejpam-1563	250	4	boundary	boundary	ADJ
ejpam-1563	250	5	problems	problem	NOUN
ejpam-1563	250	6	,	,	PUNCT
ejpam-1563	250	7	john	john	PROPN
ejpam-1563	250	8	wiley	wiley	PROPN
ejpam-1563	250	9	and	and	CCONJ
ejpam-1563	250	10	sons	son	NOUN
ejpam-1563	250	11	,	,	PUNCT
ejpam-1563	250	12	new	new	PROPN
ejpam-1563	250	13	york	york	PROPN
ejpam-1563	250	14	,	,	PUNCT
ejpam-1563	250	15	1984	1984	NUM
ejpam-1563	250	16	.	.	PUNCT
ejpam-1563	251	1	[	[	X
ejpam-1563	251	2	3	3	X
ejpam-1563	251	3	]	]	X
ejpam-1563	251	4	e.	e.	PROPN
ejpam-1563	251	5	blum	blum	PROPN
ejpam-1563	251	6	and	and	CCONJ
ejpam-1563	251	7	w.	w.	PROPN
ejpam-1563	251	8	oettli	oettli	PROPN
ejpam-1563	251	9	.	.	PUNCT
ejpam-1563	252	1	from	from	ADP
ejpam-1563	252	2	optimization	optimization	NOUN
ejpam-1563	252	3	and	and	CCONJ
ejpam-1563	252	4	variational	variational	ADJ
ejpam-1563	252	5	inequalities	inequality	NOUN
ejpam-1563	252	6	to	to	ADP
ejpam-1563	252	7	equilibrium	equilibrium	NOUN
ejpam-1563	252	8	problems	problem	NOUN
ejpam-1563	252	9	,	,	PUNCT
ejpam-1563	252	10	mathematics	mathematics	NOUN
ejpam-1563	252	11	student	student	NOUN
ejpam-1563	252	12	,	,	PUNCT
ejpam-1563	252	13	63	63	NUM
ejpam-1563	252	14	,	,	PUNCT
ejpam-1563	252	15	123–145	123–145	NUM
ejpam-1563	252	16	,	,	PUNCT
ejpam-1563	252	17	1994	1994	NUM
ejpam-1563	252	18	.	.	PUNCT
ejpam-1563	253	1	[	[	X
ejpam-1563	253	2	4	4	X
ejpam-1563	253	3	]	]	X
ejpam-1563	253	4	g.	g.	PROPN
ejpam-1563	253	5	y.	y.	PROPN
ejpam-1563	253	6	chen	chen	PROPN
ejpam-1563	253	7	.	.	PUNCT
ejpam-1563	254	1	existence	existence	NOUN
ejpam-1563	254	2	of	of	ADP
ejpam-1563	254	3	solutions	solution	NOUN
ejpam-1563	254	4	for	for	ADP
ejpam-1563	254	5	a	a	DET
ejpam-1563	254	6	vector	vector	NOUN
ejpam-1563	254	7	variational	variational	ADJ
ejpam-1563	254	8	inequality	inequality	NOUN
ejpam-1563	254	9	:	:	PUNCT
ejpam-1563	254	10	an	an	DET
ejpam-1563	254	11	extension	extension	NOUN
ejpam-1563	254	12	of	of	ADP
ejpam-1563	254	13	the	the	DET
ejpam-1563	254	14	hartmann	hartmann	PROPN
ejpam-1563	254	15	-	-	PUNCT
ejpam-1563	254	16	stampacchia	stampacchia	NOUN
ejpam-1563	254	17	theorem	theorem	ADJ
ejpam-1563	254	18	,	,	PUNCT
ejpam-1563	254	19	journal	journal	NOUN
ejpam-1563	254	20	of	of	ADP
ejpam-1563	254	21	optimization	optimization	NOUN
ejpam-1563	254	22	theory	theory	NOUN
ejpam-1563	254	23	and	and	CCONJ
ejpam-1563	254	24	applications	application	NOUN
ejpam-1563	254	25	,	,	PUNCT
ejpam-1563	254	26	74	74	NUM
ejpam-1563	254	27	,	,	PUNCT
ejpam-1563	254	28	445–456	445–456	NUM
ejpam-1563	254	29	,	,	PUNCT
ejpam-1563	254	30	1994	1994	NUM
ejpam-1563	254	31	.	.	PUNCT
ejpam-1563	255	1	[	[	X
ejpam-1563	255	2	5	5	X
ejpam-1563	255	3	]	]	PUNCT
ejpam-1563	255	4	k.	k.	PROPN
ejpam-1563	255	5	fan	fan	PROPN
ejpam-1563	255	6	.	.	PUNCT
ejpam-1563	256	1	a	a	DET
ejpam-1563	256	2	generalization	generalization	NOUN
ejpam-1563	256	3	of	of	ADP
ejpam-1563	256	4	tychonoff	tychonoff	NOUN
ejpam-1563	256	5	’s	’s	PART
ejpam-1563	256	6	fixed	fix	VERB
ejpam-1563	256	7	point	point	NOUN
ejpam-1563	256	8	theorem	theorem	ADJ
ejpam-1563	256	9	,	,	PUNCT
ejpam-1563	256	10	mathematische	mathematische	NOUN
ejpam-1563	256	11	annalen	annalen	PROPN
ejpam-1563	256	12	,	,	PUNCT
ejpam-1563	256	13	142	142	NUM
ejpam-1563	256	14	,	,	PUNCT
ejpam-1563	256	15	305–310	305–310	NUM
ejpam-1563	256	16	,	,	PUNCT
ejpam-1563	256	17	1961	1961	NUM
ejpam-1563	256	18	.	.	PUNCT
ejpam-1563	257	1	[	[	X
ejpam-1563	257	2	6	6	NUM
ejpam-1563	257	3	]	]	X
ejpam-1563	257	4	f.	f.	PROPN
ejpam-1563	257	5	flores	flores	PROPN
ejpam-1563	257	6	-	-	PUNCT
ejpam-1563	257	7	bazán	bazán	PROPN
ejpam-1563	257	8	and	and	CCONJ
ejpam-1563	257	9	f.	f.	PROPN
ejpam-1563	257	10	flores	flores	PROPN
ejpam-1563	257	11	-	-	PUNCT
ejpam-1563	257	12	bazán	bazán	NOUN
ejpam-1563	257	13	,	,	PUNCT
ejpam-1563	257	14	vector	vector	NOUN
ejpam-1563	257	15	equilibrium	equilibrium	NOUN
ejpam-1563	257	16	problems	problem	NOUN
ejpam-1563	257	17	under	under	ADP
ejpam-1563	257	18	asymptotic	asymptotic	ADJ
ejpam-1563	257	19	analysis	analysis	NOUN
ejpam-1563	257	20	,	,	PUNCT
ejpam-1563	257	21	journal	journal	NOUN
ejpam-1563	257	22	of	of	ADP
ejpam-1563	257	23	global	global	ADJ
ejpam-1563	257	24	optimization	optimization	NOUN
ejpam-1563	257	25	,	,	PUNCT
ejpam-1563	257	26	26	26	NUM
ejpam-1563	257	27	,	,	PUNCT
ejpam-1563	257	28	141–166	141–166	NUM
ejpam-1563	257	29	,	,	PUNCT
ejpam-1563	257	30	2003	2003	NUM
ejpam-1563	257	31	.	.	PUNCT
ejpam-1563	258	1	references	reference	NOUN
ejpam-1563	258	2	376	376	NUM
ejpam-1563	259	1	[	[	X
ejpam-1563	259	2	7	7	NUM
ejpam-1563	259	3	]	]	X
ejpam-1563	259	4	i.	i.	NOUN
ejpam-1563	259	5	v.	v.	ADP
ejpam-1563	259	6	konnov	konnov	PROPN
ejpam-1563	259	7	and	and	CCONJ
ejpam-1563	259	8	d.	d.	PROPN
ejpam-1563	259	9	a.	a.	NOUN
ejpam-1563	259	10	dyabilkin	dyabilkin	PROPN
ejpam-1563	259	11	.	.	PUNCT
ejpam-1563	260	1	nonmonotone	nonmonotone	PROPN
ejpam-1563	260	2	equilibrium	equilibrium	PROPN
ejpam-1563	260	3	problems	problem	NOUN
ejpam-1563	260	4	:	:	PUNCT
ejpam-1563	260	5	coercivity	coercivity	NOUN
ejpam-1563	260	6	conditions	condition	NOUN
ejpam-1563	260	7	and	and	CCONJ
ejpam-1563	260	8	weak	weak	ADJ
ejpam-1563	260	9	regularization	regularization	NOUN
ejpam-1563	260	10	,	,	PUNCT
ejpam-1563	260	11	journal	journal	NOUN
ejpam-1563	260	12	of	of	ADP
ejpam-1563	260	13	global	global	ADJ
ejpam-1563	260	14	optimization	optimization	NOUN
ejpam-1563	260	15	,	,	PUNCT
ejpam-1563	260	16	49(4	49(4	NOUN
ejpam-1563	260	17	)	)	PUNCT
ejpam-1563	260	18	,	,	PUNCT
ejpam-1563	260	19	575–587	575–587	NUM
ejpam-1563	260	20	,	,	PUNCT
ejpam-1563	260	21	2011	2011	NUM
ejpam-1563	260	22	.	.	PUNCT
ejpam-1563	261	1	[	[	X
ejpam-1563	261	2	8	8	NUM
ejpam-1563	261	3	]	]	X
ejpam-1563	261	4	i.	i.	PROPN
ejpam-1563	261	5	v.	v.	ADP
ejpam-1563	261	6	konnov	konnov	PROPN
ejpam-1563	261	7	and	and	CCONJ
ejpam-1563	261	8	z.	z.	PROPN
ejpam-1563	261	9	liu	liu	PROPN
ejpam-1563	261	10	.	.	PUNCT
ejpam-1563	262	1	vector	vector	PROPN
ejpam-1563	262	2	equilibrium	equilibrium	NOUN
ejpam-1563	262	3	problems	problem	NOUN
ejpam-1563	262	4	on	on	ADP
ejpam-1563	262	5	unbounded	unbounded	ADJ
ejpam-1563	262	6	sets	set	NOUN
ejpam-1563	262	7	,	,	PUNCT
ejpam-1563	262	8	lobachevskii	lobachevskii	ADJ
ejpam-1563	262	9	journal	journal	NOUN
ejpam-1563	262	10	of	of	ADP
ejpam-1563	262	11	mathematics	mathematic	NOUN
ejpam-1563	262	12	,	,	PUNCT
ejpam-1563	262	13	31(3	31(3	NUM
ejpam-1563	262	14	)	)	PUNCT
ejpam-1563	262	15	,	,	PUNCT
ejpam-1563	262	16	232–238	232–238	NUM
ejpam-1563	262	17	,	,	PUNCT
ejpam-1563	262	18	2010	2010	NUM
ejpam-1563	262	19	.	.	PUNCT
ejpam-1563	263	1	[	[	X
ejpam-1563	263	2	9	9	NUM
ejpam-1563	263	3	]	]	SYM
ejpam-1563	263	4	i.	i.	NOUN
ejpam-1563	263	5	v.	v.	ADP
ejpam-1563	263	6	konnov	konnov	PROPN
ejpam-1563	263	7	and	and	CCONJ
ejpam-1563	263	8	j.	j.	PROPN
ejpam-1563	263	9	c.	c.	PROPN
ejpam-1563	263	10	yao	yao	PROPN
ejpam-1563	263	11	.	.	PUNCT
ejpam-1563	264	1	existence	existence	NOUN
ejpam-1563	264	2	of	of	ADP
ejpam-1563	264	3	solutions	solution	NOUN
ejpam-1563	264	4	for	for	ADP
ejpam-1563	264	5	generalized	generalized	ADJ
ejpam-1563	264	6	vector	vector	NOUN
ejpam-1563	264	7	equilibrium	equilibrium	NOUN
ejpam-1563	264	8	problems	problem	NOUN
ejpam-1563	264	9	,	,	PUNCT
ejpam-1563	264	10	journal	journal	NOUN
ejpam-1563	264	11	of	of	ADP
ejpam-1563	264	12	mathematical	mathematical	ADJ
ejpam-1563	264	13	analysis	analysis	NOUN
ejpam-1563	264	14	and	and	CCONJ
ejpam-1563	264	15	applications	application	NOUN
ejpam-1563	264	16	,	,	PUNCT
ejpam-1563	264	17	233	233	NUM
ejpam-1563	264	18	,	,	PUNCT
ejpam-1563	264	19	328–335	328–335	NUM
ejpam-1563	264	20	,	,	PUNCT
ejpam-1563	264	21	1999	1999	NUM
ejpam-1563	264	22	.	.	PUNCT
ejpam-1563	265	1	[	[	X
ejpam-1563	265	2	10	10	NUM
ejpam-1563	265	3	]	]	X
ejpam-1563	265	4	z.	z.	PROPN
ejpam-1563	265	5	mitrovič	mitrovič	NOUN
ejpam-1563	265	6	and	and	CCONJ
ejpam-1563	265	7	m.	m.	NOUN
ejpam-1563	265	8	merkle	merkle	NOUN
ejpam-1563	265	9	.	.	PUNCT
ejpam-1563	266	1	on	on	ADP
ejpam-1563	266	2	generalized	generalized	ADJ
ejpam-1563	266	3	vector	vector	NOUN
ejpam-1563	266	4	equilibrium	equilibrium	NOUN
ejpam-1563	266	5	problems	problem	NOUN
ejpam-1563	266	6	with	with	ADP
ejpam-1563	266	7	bounds	bound	NOUN
ejpam-1563	266	8	,	,	PUNCT
ejpam-1563	266	9	applied	apply	VERB
ejpam-1563	266	10	mathematics	mathematics	NOUN
ejpam-1563	266	11	letters	letter	NOUN
ejpam-1563	266	12	,	,	PUNCT
ejpam-1563	266	13	23	23	NUM
ejpam-1563	266	14	,	,	PUNCT
ejpam-1563	266	15	783–787	783–787	NUM
ejpam-1563	266	16	,	,	PUNCT
ejpam-1563	266	17	2010	2010	NUM
ejpam-1563	266	18	.	.	PUNCT
ejpam-1563	267	1	[	[	X
ejpam-1563	267	2	11	11	NUM
ejpam-1563	267	3	]	]	X
ejpam-1563	267	4	w.	w.	PROPN
ejpam-1563	267	5	oettli	oettli	PROPN
ejpam-1563	267	6	and	and	CCONJ
ejpam-1563	267	7	d.	d.	PROPN
ejpam-1563	267	8	schläger	schläger	PROPN
ejpam-1563	267	9	.	.	PUNCT
ejpam-1563	268	1	generalized	generalize	VERB
ejpam-1563	268	2	vectorial	vectorial	ADJ
ejpam-1563	268	3	equilibria	equilibrium	NOUN
ejpam-1563	268	4	and	and	CCONJ
ejpam-1563	268	5	generalized	generalized	ADJ
ejpam-1563	268	6	monotonicity	monotonicity	NOUN
ejpam-1563	268	7	,	,	PUNCT
ejpam-1563	268	8	m.	m.	NOUN
ejpam-1563	268	9	brokate	brokate	NOUN
ejpam-1563	268	10	,	,	PUNCT
ejpam-1563	268	11	a.	a.	PROPN
ejpam-1563	268	12	h.	h.	PROPN
ejpam-1563	268	13	siddiqi	siddiqi	PROPN
ejpam-1563	268	14	(	(	PUNCT
ejpam-1563	268	15	eds	ed	NOUN
ejpam-1563	268	16	.	.	PUNCT
ejpam-1563	268	17	)	)	PUNCT
ejpam-1563	268	18	,	,	PUNCT
ejpam-1563	268	19	functional	functional	ADJ
ejpam-1563	268	20	analysis	analysis	NOUN
ejpam-1563	268	21	with	with	ADP
ejpam-1563	268	22	current	current	ADJ
ejpam-1563	268	23	applications	application	NOUN
ejpam-1563	268	24	in	in	ADP
ejpam-1563	268	25	science	science	NOUN
ejpam-1563	268	26	,	,	PUNCT
ejpam-1563	268	27	technology	technology	NOUN
ejpam-1563	268	28	and	and	CCONJ
ejpam-1563	268	29	industry	industry	NOUN
ejpam-1563	268	30	,	,	PUNCT
ejpam-1563	268	31	pitman	pitman	NOUN
ejpam-1563	268	32	research	research	NOUN
ejpam-1563	268	33	notes	note	NOUN
ejpam-1563	268	34	in	in	ADP
ejpam-1563	268	35	mathematics	mathematics	NOUN
ejpam-1563	268	36	series	series	NOUN
ejpam-1563	268	37	,	,	PUNCT
ejpam-1563	268	38	vol	vol	NOUN
ejpam-1563	268	39	.	.	PROPN
ejpam-1563	268	40	377	377	NUM
ejpam-1563	268	41	,	,	PUNCT
ejpam-1563	268	42	longman	longman	NOUN
ejpam-1563	268	43	,	,	PUNCT
ejpam-1563	268	44	london	london	PROPN
ejpam-1563	268	45	,	,	PUNCT
ejpam-1563	268	46	145	145	NUM
ejpam-1563	268	47	-	-	SYM
ejpam-1563	268	48	154	154	NUM
ejpam-1563	268	49	,	,	PUNCT
ejpam-1563	268	50	1998	1998	NUM
ejpam-1563	268	51	.	.	PUNCT
ejpam-1563	269	1	[	[	X
ejpam-1563	269	2	12	12	NUM
ejpam-1563	269	3	]	]	X
ejpam-1563	269	4	w.	w.	PROPN
ejpam-1563	269	5	oettli	oettli	PROPN
ejpam-1563	269	6	and	and	CCONJ
ejpam-1563	269	7	d.	d.	PROPN
ejpam-1563	269	8	schläger	schläger	PROPN
ejpam-1563	269	9	.	.	PUNCT
ejpam-1563	270	1	existence	existence	NOUN
ejpam-1563	270	2	of	of	ADP
ejpam-1563	270	3	equilibria	equilibrium	NOUN
ejpam-1563	270	4	for	for	ADP
ejpam-1563	270	5	monotone	monotone	ADJ
ejpam-1563	270	6	multivalued	multivalue	VERB
ejpam-1563	270	7	mappings	mapping	NOUN
ejpam-1563	270	8	,	,	PUNCT
ejpam-1563	270	9	mathematical	mathematical	ADJ
ejpam-1563	270	10	methods	method	NOUN
ejpam-1563	270	11	of	of	ADP
ejpam-1563	270	12	operations	operation	NOUN
ejpam-1563	270	13	research	research	NOUN
ejpam-1563	270	14	,	,	PUNCT
ejpam-1563	270	15	48	48	NUM
ejpam-1563	270	16	,	,	PUNCT
ejpam-1563	270	17	219–228	219–228	NUM
ejpam-1563	270	18	,	,	PUNCT
ejpam-1563	270	19	1998	1998	NUM
ejpam-1563	270	20	.	.	PUNCT
ejpam-1563	271	1	[	[	X
ejpam-1563	271	2	13	13	NUM
ejpam-1563	271	3	]	]	X
ejpam-1563	271	4	i.	i.	NOUN
ejpam-1563	271	5	sadeqi	sadeqi	PROPN
ejpam-1563	271	6	and	and	CCONJ
ejpam-1563	271	7	c.	c.	PROPN
ejpam-1563	271	8	g.	g.	PROPN
ejpam-1563	271	9	alizadeh	alizadeh	PROPN
ejpam-1563	271	10	.	.	PUNCT
ejpam-1563	272	1	existence	existence	NOUN
ejpam-1563	272	2	of	of	ADP
ejpam-1563	272	3	solutions	solution	NOUN
ejpam-1563	272	4	of	of	ADP
ejpam-1563	272	5	generalized	generalized	ADJ
ejpam-1563	272	6	vector	vector	NOUN
ejpam-1563	272	7	equilibrium	equilibrium	NOUN
ejpam-1563	272	8	problems	problem	NOUN
ejpam-1563	272	9	in	in	ADP
ejpam-1563	272	10	reflexive	reflexive	ADJ
ejpam-1563	272	11	banach	banach	NOUN
ejpam-1563	272	12	space	space	NOUN
ejpam-1563	272	13	,	,	PUNCT
ejpam-1563	272	14	nonlinear	nonlinear	ADJ
ejpam-1563	272	15	analysis	analysis	NOUN
ejpam-1563	272	16	,	,	PUNCT
ejpam-1563	272	17	74	74	NUM
ejpam-1563	272	18	,	,	PUNCT
ejpam-1563	272	19	2226–2234	2226–2234	NUM
ejpam-1563	272	20	,	,	PUNCT
ejpam-1563	272	21	2011	2011	NUM
ejpam-1563	272	22	.	.	PUNCT
ejpam-1563	273	1	[	[	X
ejpam-1563	273	2	14	14	NUM
ejpam-1563	273	3	]	]	PUNCT
ejpam-1563	273	4	a.	a.	NOUN
ejpam-1563	273	5	g.	g.	PROPN
ejpam-1563	273	6	sukharev	sukharev	VERB
ejpam-1563	273	7	,	,	PUNCT
ejpam-1563	273	8	a.	a.	PROPN
ejpam-1563	273	9	v.	v.	ADP
ejpam-1563	273	10	timokhov	timokhov	NOUN
ejpam-1563	273	11	and	and	CCONJ
ejpam-1563	273	12	v.	v.	ADP
ejpam-1563	273	13	v.	v.	CCONJ
ejpam-1563	273	14	fedorov	fedorov	PROPN
ejpam-1563	273	15	.	.	PUNCT
ejpam-1563	274	1	a	a	DET
ejpam-1563	274	2	course	course	NOUN
ejpam-1563	274	3	in	in	ADP
ejpam-1563	274	4	optimization	optimization	NOUN
ejpam-1563	274	5	methods	method	NOUN
ejpam-1563	274	6	,	,	PUNCT
ejpam-1563	274	7	nauka	nauka	PROPN
ejpam-1563	274	8	,	,	PUNCT
ejpam-1563	274	9	moscow	moscow	PROPN
ejpam-1563	274	10	(	(	PUNCT
ejpam-1563	274	11	in	in	ADP
ejpam-1563	274	12	russian	russian	PROPN
ejpam-1563	274	13	)	)	PUNCT
ejpam-1563	274	14	,	,	PUNCT
ejpam-1563	274	15	1986	1986	NUM
ejpam-1563	274	16	.	.	PUNCT