id	sid	tid	token	lemma	pos
ejpam-232	1	1	5_232_alimohammedy.dvi	5_232_alimohammedy.dvi	NUM
ejpam-232	1	2	european	european	ADJ
ejpam-232	1	3	journal	journal	NOUN
ejpam-232	1	4	of	of	ADP
ejpam-232	1	5	pure	pure	ADJ
ejpam-232	1	6	and	and	CCONJ
ejpam-232	1	7	applied	apply	VERB
ejpam-232	1	8	mathematics	mathematic	NOUN
ejpam-232	1	9	vol	vol	NOUN
ejpam-232	1	10	.	.	PUNCT
ejpam-232	2	1	3	3	NUM
ejpam-232	2	2	,	,	PUNCT
ejpam-232	2	3	no	no	INTJ
ejpam-232	2	4	.	.	NOUN
ejpam-232	2	5	2	2	NUM
ejpam-232	2	6	,	,	PUNCT
ejpam-232	2	7	2010	2010	NUM
ejpam-232	2	8	,	,	PUNCT
ejpam-232	2	9	187	187	NUM
ejpam-232	2	10	-	-	SYM
ejpam-232	2	11	193	193	NUM
ejpam-232	2	12	issn	issn	PROPN
ejpam-232	2	13	1307	1307	NUM
ejpam-232	2	14	-	-	SYM
ejpam-232	2	15	5543	5543	NUM
ejpam-232	2	16	–	–	PUNCT
ejpam-232	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-232	2	18	extended	extend	VERB
ejpam-232	2	19	concavifications	concavification	NOUN
ejpam-232	2	20	and	and	CCONJ
ejpam-232	2	21	exact	exact	ADJ
ejpam-232	2	22	games	game	NOUN
ejpam-232	2	23	m.	m.	PROPN
ejpam-232	2	24	alimohammady1∗	alimohammady1∗	PROPN
ejpam-232	2	25	and	and	CCONJ
ejpam-232	2	26	v.	v.	ADP
ejpam-232	2	27	dadashi	dadashi	VERB
ejpam-232	2	28	2	2	NUM
ejpam-232	2	29	1	1	NUM
ejpam-232	2	30	department	department	NOUN
ejpam-232	2	31	of	of	ADP
ejpam-232	2	32	mathematics	mathematic	NOUN
ejpam-232	2	33	,	,	PUNCT
ejpam-232	2	34	faculty	faculty	NOUN
ejpam-232	2	35	of	of	ADP
ejpam-232	2	36	basic	basic	ADJ
ejpam-232	2	37	sciences	science	NOUN
ejpam-232	2	38	,	,	PUNCT
ejpam-232	2	39	university	university	NOUN
ejpam-232	2	40	of	of	ADP
ejpam-232	2	41	mazandaran	mazandaran	PROPN
ejpam-232	2	42	,	,	PUNCT
ejpam-232	2	43	babolsar	babolsar	PROPN
ejpam-232	2	44	,	,	PUNCT
ejpam-232	2	45	iran	iran	PROPN
ejpam-232	2	46	,	,	PUNCT
ejpam-232	2	47	2	2	NUM
ejpam-232	2	48	islamiz	islamiz	VERB
ejpam-232	2	49	azad	azad	PROPN
ejpam-232	2	50	university	university	PROPN
ejpam-232	2	51	–	–	PUNCT
ejpam-232	2	52	sari	sari	ADJ
ejpam-232	2	53	branch	branch	NOUN
ejpam-232	2	54	,	,	PUNCT
ejpam-232	2	55	sari	sari	NOUN
ejpam-232	2	56	,	,	PUNCT
ejpam-232	2	57	iran	iran	PROPN
ejpam-232	2	58	abstract	abstract	NOUN
ejpam-232	2	59	.	.	PUNCT
ejpam-232	3	1	in	in	ADP
ejpam-232	3	2	this	this	DET
ejpam-232	3	3	paper	paper	NOUN
ejpam-232	3	4	we	we	PRON
ejpam-232	3	5	propose	propose	VERB
ejpam-232	3	6	new	new	ADJ
ejpam-232	3	7	version	version	NOUN
ejpam-232	3	8	of	of	ADP
ejpam-232	3	9	cooperative	cooperative	ADJ
ejpam-232	3	10	games	game	NOUN
ejpam-232	3	11	.	.	PUNCT
ejpam-232	4	1	in	in	ADP
ejpam-232	4	2	fact	fact	NOUN
ejpam-232	4	3	the	the	DET
ejpam-232	4	4	notion	notion	NOUN
ejpam-232	4	5	of	of	ADP
ejpam-232	4	6	cooperative	cooperative	ADJ
ejpam-232	4	7	games	game	NOUN
ejpam-232	4	8	and	and	CCONJ
ejpam-232	4	9	their	their	PRON
ejpam-232	4	10	concavifications	concavification	NOUN
ejpam-232	4	11	are	be	AUX
ejpam-232	4	12	extended	extend	VERB
ejpam-232	4	13	.	.	PUNCT
ejpam-232	5	1	as	as	ADP
ejpam-232	5	2	a	a	DET
ejpam-232	5	3	consequence	consequence	NOUN
ejpam-232	5	4	,	,	PUNCT
ejpam-232	5	5	in	in	ADP
ejpam-232	5	6	this	this	DET
ejpam-232	5	7	new	new	ADJ
ejpam-232	5	8	setting	setting	NOUN
ejpam-232	5	9	it	it	PRON
ejpam-232	5	10	turn	turn	VERB
ejpam-232	5	11	out	out	ADP
ejpam-232	5	12	that	that	SCONJ
ejpam-232	5	13	corev	corev	VERB
ejpam-232	5	14	6=	6=	ADP
ejpam-232	5	15	;	;	PUNCT
ejpam-232	5	16	if	if	SCONJ
ejpam-232	5	17	and	and	CCONJ
ejpam-232	5	18	only	only	ADV
ejpam-232	5	19	if	if	SCONJ
ejpam-232	5	20	cav(u)(cω	cav(u)(cω	PROPN
ejpam-232	5	21	)	)	PUNCT
ejpam-232	5	22	=	=	SYM
ejpam-232	5	23	u(cω	u(cω	NOUN
ejpam-232	5	24	)	)	PUNCT
ejpam-232	5	25	.	.	PUNCT
ejpam-232	6	1	2000	2000	NUM
ejpam-232	6	2	mathematics	mathematic	NOUN
ejpam-232	6	3	subject	subject	NOUN
ejpam-232	6	4	classifications	classification	NOUN
ejpam-232	6	5	:	:	PUNCT
ejpam-232	6	6	46m35	46m35	NUM
ejpam-232	6	7	,	,	PUNCT
ejpam-232	6	8	54h25	54h25	NUM
ejpam-232	6	9	,	,	PUNCT
ejpam-232	6	10	47h10	47h10	NUM
ejpam-232	6	11	.	.	PUNCT
ejpam-232	7	1	key	key	ADJ
ejpam-232	7	2	words	word	NOUN
ejpam-232	7	3	and	and	CCONJ
ejpam-232	7	4	phrases	phrase	NOUN
ejpam-232	7	5	:	:	PUNCT
ejpam-232	7	6	concavification	concavification	NOUN
ejpam-232	7	7	,	,	PUNCT
ejpam-232	7	8	game	game	NOUN
ejpam-232	7	9	,	,	PUNCT
ejpam-232	7	10	exact	exact	ADJ
ejpam-232	7	11	game	game	NOUN
ejpam-232	7	12	,	,	PUNCT
ejpam-232	7	13	balanced	balanced	ADJ
ejpam-232	7	14	game	game	NOUN
ejpam-232	7	15	.	.	PUNCT
ejpam-232	8	1	1	1	X
ejpam-232	8	2	.	.	X
ejpam-232	8	3	introduction	introduction	NOUN
ejpam-232	8	4	usually	usually	ADV
ejpam-232	8	5	,	,	PUNCT
ejpam-232	8	6	a	a	DET
ejpam-232	8	7	game	game	NOUN
ejpam-232	8	8	v	v	NOUN
ejpam-232	8	9	with	with	ADP
ejpam-232	8	10	a	a	DET
ejpam-232	8	11	continum	continum	NOUN
ejpam-232	8	12	players	player	NOUN
ejpam-232	8	13	is	be	AUX
ejpam-232	8	14	a	a	DET
ejpam-232	8	15	bounded	bounded	ADJ
ejpam-232	8	16	real	real	ADV
ejpam-232	8	17	valued	value	VERB
ejpam-232	8	18	function	function	NOUN
ejpam-232	8	19	defined	define	VERB
ejpam-232	8	20	on	on	ADP
ejpam-232	8	21	∑	∑	DET
ejpam-232	8	22	the	the	DET
ejpam-232	8	23	borel	borel	NOUN
ejpam-232	8	24	subsets	subset	NOUN
ejpam-232	8	25	of	of	ADP
ejpam-232	8	26	i	i	PRON
ejpam-232	8	27	=	=	PUNCT
ejpam-232	9	1	[	[	X
ejpam-232	9	2	0,1	0,1	NUM
ejpam-232	9	3	]	]	PUNCT
ejpam-232	9	4	such	such	ADJ
ejpam-232	9	5	that	that	DET
ejpam-232	9	6	v	v	NOUN
ejpam-232	9	7	(	(	PUNCT
ejpam-232	9	8	;)	;)	SYM
ejpam-232	9	9	=	=	PUNCT
ejpam-232	9	10	0	0	X
ejpam-232	9	11	.	.	PUNCT
ejpam-232	10	1	any	any	DET
ejpam-232	10	2	member	member	NOUN
ejpam-232	10	3	of	of	ADP
ejpam-232	10	4	∑	∑	PROPN
ejpam-232	10	5	is	be	AUX
ejpam-232	10	6	interpreted	interpret	VERB
ejpam-232	10	7	as	as	ADP
ejpam-232	10	8	coalition	coalition	NOUN
ejpam-232	10	9	of	of	ADP
ejpam-232	10	10	player	player	NOUN
ejpam-232	10	11	,	,	PUNCT
ejpam-232	10	12	v	v	NOUN
ejpam-232	10	13	(	(	PUNCT
ejpam-232	10	14	r	r	NOUN
ejpam-232	10	15	)	)	PUNCT
ejpam-232	10	16	gives	give	VERB
ejpam-232	10	17	the	the	DET
ejpam-232	10	18	maximum	maximum	ADJ
ejpam-232	10	19	payoff	payoff	NOUN
ejpam-232	10	20	achieved	achieve	VERB
ejpam-232	10	21	by	by	ADP
ejpam-232	10	22	efforts	effort	NOUN
ejpam-232	10	23	of	of	ADP
ejpam-232	10	24	all	all	DET
ejpam-232	10	25	members	member	NOUN
ejpam-232	10	26	in	in	ADP
ejpam-232	10	27	the	the	DET
ejpam-232	10	28	coalition	coalition	NOUN
ejpam-232	10	29	r.	r.	NOUN
ejpam-232	10	30	of	of	ADP
ejpam-232	10	31	course	course	NOUN
ejpam-232	10	32	with	with	ADP
ejpam-232	10	33	this	this	DET
ejpam-232	10	34	interpretation	interpretation	NOUN
ejpam-232	10	35	usually	usually	ADV
ejpam-232	10	36	it	it	PRON
ejpam-232	10	37	is	be	AUX
ejpam-232	10	38	assumed	assume	VERB
ejpam-232	10	39	that	that	SCONJ
ejpam-232	10	40	v	v	NOUN
ejpam-232	10	41	is	be	AUX
ejpam-232	10	42	non	non	ADJ
ejpam-232	10	43	-	-	ADJ
ejpam-232	10	44	negative	negative	ADJ
ejpam-232	10	45	and	and	CCONJ
ejpam-232	10	46	not	not	PART
ejpam-232	10	47	identically	identically	ADV
ejpam-232	10	48	zero	zero	NUM
ejpam-232	10	49	.	.	PUNCT
ejpam-232	11	1	in	in	ADP
ejpam-232	11	2	[	[	X
ejpam-232	11	3	1	1	X
ejpam-232	11	4	]	]	PUNCT
ejpam-232	11	5	a	a	DET
ejpam-232	11	6	cooperative	cooperative	ADJ
ejpam-232	11	7	game	game	NOUN
ejpam-232	11	8	is	be	AUX
ejpam-232	11	9	viewed	view	VERB
ejpam-232	11	10	as	as	ADP
ejpam-232	11	11	a	a	DET
ejpam-232	11	12	real	real	ADV
ejpam-232	11	13	valued	value	VERB
ejpam-232	11	14	function	function	NOUN
ejpam-232	11	15	u	u	NOUN
ejpam-232	11	16	defined	define	VERB
ejpam-232	11	17	on	on	ADP
ejpam-232	11	18	a	a	DET
ejpam-232	11	19	finite	finite	ADJ
ejpam-232	11	20	set	set	NOUN
ejpam-232	11	21	of	of	ADP
ejpam-232	11	22	points	point	NOUN
ejpam-232	11	23	in	in	ADP
ejpam-232	11	24	the	the	DET
ejpam-232	11	25	unit	unit	NOUN
ejpam-232	11	26	simplex	simplex	NOUN
ejpam-232	11	27	,	,	PUNCT
ejpam-232	11	28	also	also	ADV
ejpam-232	11	29	a	a	DET
ejpam-232	11	30	concavification	concavification	NOUN
ejpam-232	11	31	of	of	ADP
ejpam-232	11	32	u	u	PRON
ejpam-232	11	33	used	use	VERB
ejpam-232	11	34	to	to	PART
ejpam-232	11	35	characterize	characterize	VERB
ejpam-232	11	36	well	well	ADV
ejpam-232	11	37	-	-	PUNCT
ejpam-232	11	38	known	know	VERB
ejpam-232	11	39	classes	class	NOUN
ejpam-232	11	40	of	of	ADP
ejpam-232	11	41	games	game	NOUN
ejpam-232	11	42	.	.	PUNCT
ejpam-232	12	1	2	2	X
ejpam-232	12	2	.	.	X
ejpam-232	12	3	preliminaries	preliminary	NOUN
ejpam-232	12	4	let	let	VERB
ejpam-232	12	5	x	x	PRON
ejpam-232	12	6	be	be	AUX
ejpam-232	12	7	a	a	DET
ejpam-232	12	8	normed	normed	ADJ
ejpam-232	12	9	space	space	NOUN
ejpam-232	12	10	.	.	PUNCT
ejpam-232	13	1	the	the	DET
ejpam-232	13	2	space	space	NOUN
ejpam-232	13	3	of	of	ADP
ejpam-232	13	4	all	all	DET
ejpam-232	13	5	continuous	continuous	ADJ
ejpam-232	13	6	linear	linear	ADJ
ejpam-232	13	7	functionals	functional	NOUN
ejpam-232	13	8	defined	define	VERB
ejpam-232	13	9	on	on	ADP
ejpam-232	13	10	x	x	SYM
ejpam-232	13	11	is	be	AUX
ejpam-232	13	12	called	call	VERB
ejpam-232	13	13	the	the	DET
ejpam-232	13	14	dual	dual	ADJ
ejpam-232	13	15	space	space	NOUN
ejpam-232	13	16	of	of	ADP
ejpam-232	13	17	x	x	PUNCT
ejpam-232	13	18	and	and	CCONJ
ejpam-232	13	19	denoted	denote	VERB
ejpam-232	13	20	by	by	ADP
ejpam-232	13	21	x	x	X
ejpam-232	13	22	∗.	∗.	PROPN
ejpam-232	13	23	let	let	VERB
ejpam-232	13	24	〈	〈	PROPN
ejpam-232	13	25	.	.	PROPN
ejpam-232	13	26	,	,	PUNCT
ejpam-232	13	27	.	.	PUNCT
ejpam-232	14	1	〉	〉	NOUN
ejpam-232	14	2	:	:	PUNCT
ejpam-232	14	3	x	x	SYM
ejpam-232	14	4	×	×	NOUN
ejpam-232	14	5	x	x	X
ejpam-232	14	6	∗→	∗→	ADJ
ejpam-232	14	7	r	r	NOUN
ejpam-232	14	8	be	be	VERB
ejpam-232	14	9	the	the	DET
ejpam-232	14	10	duality	duality	NOUN
ejpam-232	14	11	pairing	pair	VERB
ejpam-232	14	12	in	in	ADP
ejpam-232	14	13	x	x	X
ejpam-232	14	14	×x	×x	X
ejpam-232	14	15	∗.	∗.	PROPN
ejpam-232	14	16	the	the	DET
ejpam-232	14	17	weakest	weak	ADJ
ejpam-232	14	18	topology	topology	NOUN
ejpam-232	14	19	on	on	ADP
ejpam-232	14	20	x	x	PUNCT
ejpam-232	14	21	that	that	PRON
ejpam-232	14	22	make	make	VERB
ejpam-232	14	23	continuous	continuous	ADJ
ejpam-232	14	24	all	all	DET
ejpam-232	14	25	elements	element	NOUN
ejpam-232	14	26	of	of	ADP
ejpam-232	14	27	x∗	x∗	PROPN
ejpam-232	14	28	∈	∈	PROPN
ejpam-232	14	29	x	x	PUNCT
ejpam-232	14	30	∗	∗	NOUN
ejpam-232	14	31	is	be	AUX
ejpam-232	14	32	called	call	VERB
ejpam-232	14	33	the	the	DET
ejpam-232	14	34	weak	weak	ADJ
ejpam-232	14	35	topology	topology	NOUN
ejpam-232	14	36	on	on	ADP
ejpam-232	14	37	x	x	X
ejpam-232	14	38	.	.	PUNCT
ejpam-232	15	1	let	let	VERB
ejpam-232	16	1	φ	φ	NOUN
ejpam-232	16	2	:	:	PUNCT
ejpam-232	16	3	x	x	SYM
ejpam-232	16	4	→	→	SYM
ejpam-232	16	5	x	x	SYM
ejpam-232	16	6	∗∗	∗∗	NOUN
ejpam-232	16	7	defined	define	VERB
ejpam-232	16	8	by	by	ADP
ejpam-232	16	9	φ(x	φ(x	NOUN
ejpam-232	16	10	)	)	PUNCT
ejpam-232	16	11	=	=	SYM
ejpam-232	16	12	gx	gx	PROPN
ejpam-232	16	13	where	where	SCONJ
ejpam-232	16	14	gx(x	gx(x	VERB
ejpam-232	16	15	∗	∗	NOUN
ejpam-232	16	16	)	)	PUNCT
ejpam-232	16	17	=	=	SYM
ejpam-232	17	1	〈	〈	PRON
ejpam-232	17	2	x∗	x∗	NOUN
ejpam-232	17	3	,	,	PUNCT
ejpam-232	17	4	x	x	SYM
ejpam-232	17	5	〉	〉	NOUN
ejpam-232	17	6	,	,	PUNCT
ejpam-232	17	7	x∗	x∗	PROPN
ejpam-232	17	8	∈	∈	PROPN
ejpam-232	17	9	x	x	X
ejpam-232	17	10	∗	∗	NOUN
ejpam-232	17	11	and	and	CCONJ
ejpam-232	17	12	‖gx‖	‖gx‖	PROPN
ejpam-232	17	13	=	=	PUNCT
ejpam-232	17	14	‖x‖.	‖x‖.	PROPN
ejpam-232	17	15	the	the	DET
ejpam-232	17	16	weakest	weak	ADJ
ejpam-232	17	17	topology	topology	NOUN
ejpam-232	17	18	on	on	ADP
ejpam-232	17	19	x	x	PROPN
ejpam-232	17	20	∗	∗	NOUN
ejpam-232	17	21	that	that	PRON
ejpam-232	17	22	make	make	VERB
ejpam-232	17	23	continuous	continuous	ADJ
ejpam-232	17	24	all	all	DET
ejpam-232	17	25	φ(x	φ(x	NOUN
ejpam-232	17	26	)	)	PUNCT
ejpam-232	17	27	is	be	AUX
ejpam-232	17	28	called	call	VERB
ejpam-232	17	29	the	the	DET
ejpam-232	17	30	weak∗	weak∗	NOUN
ejpam-232	17	31	topology	topology	NOUN
ejpam-232	17	32	on	on	ADP
ejpam-232	17	33	x	x	PROPN
ejpam-232	17	34	∗.	∗.	PROPN
ejpam-232	17	35	the	the	DET
ejpam-232	17	36	weak	weak	ADJ
ejpam-232	17	37	topology	topology	NOUN
ejpam-232	17	38	on	on	ADP
ejpam-232	17	39	x	x	PUNCT
ejpam-232	17	40	and	and	CCONJ
ejpam-232	17	41	the	the	DET
ejpam-232	17	42	weak∗	weak∗	NOUN
ejpam-232	17	43	topology	topology	NOUN
ejpam-232	17	44	on	on	ADP
ejpam-232	17	45	x	x	PROPN
ejpam-232	17	46	∗	∗	NOUN
ejpam-232	17	47	are	be	AUX
ejpam-232	17	48	usually	usually	ADV
ejpam-232	17	49	denoted	denote	VERB
ejpam-232	17	50	by	by	ADP
ejpam-232	17	51	σ(x	σ(x	PROPN
ejpam-232	17	52	,	,	PUNCT
ejpam-232	17	53	x	x	NOUN
ejpam-232	17	54	∗	∗	NOUN
ejpam-232	17	55	)	)	PUNCT
ejpam-232	17	56	and	and	CCONJ
ejpam-232	17	57	σ(x	σ(x	PROPN
ejpam-232	17	58	∗	∗	NOUN
ejpam-232	17	59	,	,	PUNCT
ejpam-232	17	60	x	x	X
ejpam-232	17	61	)	)	PUNCT
ejpam-232	17	62	respectively	respectively	ADV
ejpam-232	17	63	.	.	PUNCT
ejpam-232	18	1	∗corresponding	∗corresponde	VERB
ejpam-232	18	2	author	author	NOUN
ejpam-232	18	3	.	.	PUNCT
ejpam-232	19	1	email	email	NOUN
ejpam-232	19	2	addresses	address	NOUN
ejpam-232	19	3	:	:	PUNCT
ejpam-232	19	4	amohsen	amohsen	PROPN
ejpam-232	19	5	�	�	PROPN
ejpam-232	19	6	umz.a	umz.a	PROPN
ejpam-232	19	7	.ir	.ir	PUNCT
ejpam-232	20	1	(	(	PUNCT
ejpam-232	20	2	m.	m.	NOUN
ejpam-232	20	3	alimohammady	alimohammady	NOUN
ejpam-232	20	4	)	)	PUNCT
ejpam-232	20	5	,	,	PUNCT
ejpam-232	20	6	v.dadashi	v.dadashi	X
ejpam-232	20	7	�	�	PROPN
ejpam-232	20	8	iausari.a	iausari.a	PROPN
ejpam-232	20	9	.ir	.ir	PUNCT
ejpam-232	21	1	(	(	PUNCT
ejpam-232	21	2	v.	v.	ADP
ejpam-232	21	3	dadashi	dadashi	PROPN
ejpam-232	21	4	)	)	PUNCT
ejpam-232	21	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-232	22	1	187	187	NUM
ejpam-232	22	2	c	c	X
ejpam-232	22	3	©	©	PROPN
ejpam-232	22	4	2010	2010	NUM
ejpam-232	22	5	ejpam	ejpam	NOUN
ejpam-232	22	6	all	all	DET
ejpam-232	22	7	rights	right	NOUN
ejpam-232	22	8	reserved	reserve	VERB
ejpam-232	22	9	.	.	PUNCT
ejpam-232	23	1	m.	m.	NOUN
ejpam-232	23	2	alimohammady	alimohammady	PROPN
ejpam-232	23	3	,	,	PUNCT
ejpam-232	23	4	v.	v.	CCONJ
ejpam-232	23	5	dadashi	dadashi	PROPN
ejpam-232	23	6	/	/	SYM
ejpam-232	23	7	eur	eur	PROPN
ejpam-232	23	8	.	.	PUNCT
ejpam-232	24	1	j.	j.	PROPN
ejpam-232	24	2	pure	pure	PROPN
ejpam-232	24	3	appl	appl	PROPN
ejpam-232	24	4	.	.	PROPN
ejpam-232	24	5	math	math	PROPN
ejpam-232	24	6	,	,	PUNCT
ejpam-232	24	7	3	3	NUM
ejpam-232	24	8	(	(	PUNCT
ejpam-232	24	9	2010	2010	NUM
ejpam-232	24	10	)	)	PUNCT
ejpam-232	24	11	,	,	PUNCT
ejpam-232	24	12	187	187	NUM
ejpam-232	24	13	-	-	SYM
ejpam-232	24	14	193	193	NUM
ejpam-232	24	15	188	188	NUM
ejpam-232	24	16	definition	definition	NOUN
ejpam-232	24	17	1	1	NUM
ejpam-232	24	18	.	.	PUNCT
ejpam-232	25	1	let	let	VERB
ejpam-232	25	2	x	x	PRON
ejpam-232	25	3	be	be	AUX
ejpam-232	25	4	a	a	DET
ejpam-232	25	5	normed	normed	ADJ
ejpam-232	25	6	space	space	NOUN
ejpam-232	25	7	,	,	PUNCT
ejpam-232	25	8	(	(	PUNCT
ejpam-232	25	9	a	a	X
ejpam-232	25	10	)	)	PUNCT
ejpam-232	25	11	a	a	DET
ejpam-232	25	12	net	net	NOUN
ejpam-232	25	13	{	{	PUNCT
ejpam-232	25	14	xn	xn	NOUN
ejpam-232	25	15	}	}	PUNCT
ejpam-232	25	16	in	in	ADP
ejpam-232	25	17	x	x	PROPN
ejpam-232	25	18	is	be	AUX
ejpam-232	25	19	called	call	VERB
ejpam-232	25	20	weak∗	weak∗	NOUN
ejpam-232	25	21	convergent	convergent	NOUN
ejpam-232	25	22	in	in	ADP
ejpam-232	25	23	x	x	X
ejpam-232	25	24	,	,	PUNCT
ejpam-232	25	25	if	if	SCONJ
ejpam-232	25	26	there	there	PRON
ejpam-232	25	27	exists	exist	VERB
ejpam-232	25	28	an	an	DET
ejpam-232	25	29	element	element	NOUN
ejpam-232	25	30	x	x	SYM
ejpam-232	25	31	∈	∈	PROPN
ejpam-232	25	32	x	x	X
ejpam-232	25	33	such	such	ADJ
ejpam-232	25	34	that	that	SCONJ
ejpam-232	25	35	lim	lim	PROPN
ejpam-232	25	36	n→∞	n→∞	PRON
ejpam-232	26	1	|x∗(xn)−	|x∗(xn)−	PROPN
ejpam-232	26	2	x∗(x)|=	x∗(x)|=	PROPN
ejpam-232	26	3	0	0	NUM
ejpam-232	26	4	,	,	PUNCT
ejpam-232	26	5	∀x∗	∀x∗	NOUN
ejpam-232	26	6	∈	∈	NOUN
ejpam-232	26	7	x	x	PUNCT
ejpam-232	26	8	∗	∗	NOUN
ejpam-232	26	9	;	;	PUNCT
ejpam-232	26	10	(	(	PUNCT
ejpam-232	26	11	b	b	X
ejpam-232	26	12	)	)	PUNCT
ejpam-232	26	13	a	a	DET
ejpam-232	26	14	subset	subset	NOUN
ejpam-232	26	15	a	a	PRON
ejpam-232	26	16	of	of	ADP
ejpam-232	26	17	x	x	SYM
ejpam-232	26	18	is	be	AUX
ejpam-232	26	19	called	call	VERB
ejpam-232	26	20	compact	compact	ADJ
ejpam-232	26	21	in	in	ADP
ejpam-232	26	22	weak∗	weak∗	NOUN
ejpam-232	26	23	topology	topology	NOUN
ejpam-232	26	24	or	or	CCONJ
ejpam-232	26	25	weak∗	weak∗	NOUN
ejpam-232	26	26	compact	compact	NOUN
ejpam-232	26	27	set	set	VERB
ejpam-232	26	28	if	if	SCONJ
ejpam-232	26	29	every	every	DET
ejpam-232	26	30	net	net	NOUN
ejpam-232	26	31	in	in	ADP
ejpam-232	26	32	a	a	DET
ejpam-232	26	33	contains	contain	VERB
ejpam-232	26	34	a	a	DET
ejpam-232	26	35	subnet	subnet	NOUN
ejpam-232	26	36	which	which	PRON
ejpam-232	26	37	is	be	AUX
ejpam-232	26	38	weak∗	weak∗	NOUN
ejpam-232	26	39	convergent	convergent	NOUN
ejpam-232	26	40	in	in	ADP
ejpam-232	26	41	a.	a.	NOUN
ejpam-232	26	42	definition	definition	NOUN
ejpam-232	26	43	2	2	NUM
ejpam-232	26	44	.	.	PUNCT
ejpam-232	27	1	a	a	DET
ejpam-232	27	2	game	game	NOUN
ejpam-232	27	3	v	v	NOUN
ejpam-232	27	4	is	be	AUX
ejpam-232	27	5	called	call	VERB
ejpam-232	27	6	a	a	DET
ejpam-232	27	7	balanced	balanced	ADJ
ejpam-232	27	8	game	game	NOUN
ejpam-232	27	9	if	if	SCONJ
ejpam-232	27	10	sup	sup	NOUN
ejpam-232	27	11	∑	∑	PROPN
ejpam-232	27	12	(	(	PUNCT
ejpam-232	27	13	r	r	NOUN
ejpam-232	27	14	)	)	PUNCT
ejpam-232	27	15	αrµ(r)u(cr)≤	αrµ(r)u(cr)≤	PROPN
ejpam-232	27	16	u(cω	u(cω	NOUN
ejpam-232	27	17	)	)	PUNCT
ejpam-232	27	18	,	,	PUNCT
ejpam-232	27	19	where	where	SCONJ
ejpam-232	27	20	sup	sup	NOUN
ejpam-232	27	21	is	be	AUX
ejpam-232	27	22	taken	take	VERB
ejpam-232	27	23	over	over	ADP
ejpam-232	27	24	all	all	DET
ejpam-232	27	25	finite	finite	NOUN
ejpam-232	27	26	sums	sum	NOUN
ejpam-232	27	27	∑	∑	PUNCT
ejpam-232	27	28	(	(	PUNCT
ejpam-232	27	29	r)αrµ(r)u(cr	r)αrµ(r)u(cr	PROPN
ejpam-232	27	30	)	)	PUNCT
ejpam-232	27	31	,	,	PUNCT
ejpam-232	27	32	αr	αr	NUM
ejpam-232	27	33	≥	≥	NOUN
ejpam-232	27	34	0	0	NUM
ejpam-232	27	35	and	and	CCONJ
ejpam-232	27	36	∑	∑	PROPN
ejpam-232	27	37	(	(	PUNCT
ejpam-232	27	38	r)αrµ(r	r)αrµ(r	NOUN
ejpam-232	27	39	)	)	PUNCT
ejpam-232	27	40	=	=	SYM
ejpam-232	28	1	1	1	X
ejpam-232	28	2	.	.	X
ejpam-232	28	3	definition	definition	NOUN
ejpam-232	28	4	3	3	NUM
ejpam-232	28	5	.	.	PUNCT
ejpam-232	29	1	given	give	VERB
ejpam-232	29	2	such	such	DET
ejpam-232	29	3	a	a	DET
ejpam-232	29	4	function	function	NOUN
ejpam-232	29	5	u	u	NOUN
ejpam-232	29	6	,	,	PUNCT
ejpam-232	29	7	we	we	PRON
ejpam-232	29	8	consider	consider	VERB
ejpam-232	29	9	the	the	DET
ejpam-232	29	10	concavification	concavification	NOUN
ejpam-232	29	11	of	of	ADP
ejpam-232	29	12	u	u	NOUN
ejpam-232	29	13	,	,	PUNCT
ejpam-232	29	14	denoted	denote	VERB
ejpam-232	29	15	by	by	ADP
ejpam-232	29	16	cav(u	cav(u	PROPN
ejpam-232	29	17	)	)	PUNCT
ejpam-232	29	18	,	,	PUNCT
ejpam-232	29	19	which	which	PRON
ejpam-232	29	20	is	be	AUX
ejpam-232	29	21	a	a	DET
ejpam-232	29	22	function	function	NOUN
ejpam-232	29	23	defined	define	VERB
ejpam-232	29	24	on	on	ADP
ejpam-232	29	25	∆=	∆=	ADJ
ejpam-232	29	26	{	{	PUNCT
ejpam-232	29	27	g	g	NOUN
ejpam-232	29	28	:	:	PUNCT
ejpam-232	29	29	g	g	NOUN
ejpam-232	29	30	≥	≥	NUM
ejpam-232	29	31	0	0	NUM
ejpam-232	29	32	,	,	PUNCT
ejpam-232	29	33	g	g	PROPN
ejpam-232	29	34	is	be	AUX
ejpam-232	29	35	simple	simple	ADJ
ejpam-232	29	36	measurable	measurable	ADJ
ejpam-232	29	37	f	f	PROPN
ejpam-232	29	38	unction	unction	NOUN
ejpam-232	29	39	and	and	CCONJ
ejpam-232	29	40	∫	∫	PROPN
ejpam-232	29	41	ω	ω	PROPN
ejpam-232	29	42	gdµ=	gdµ=	PROPN
ejpam-232	29	43	1	1	NUM
ejpam-232	29	44	}	}	PUNCT
ejpam-232	29	45	,	,	PUNCT
ejpam-232	29	46	as	as	ADP
ejpam-232	29	47	the	the	DET
ejpam-232	29	48	infimum	infimum	NOUN
ejpam-232	29	49	of	of	ADP
ejpam-232	29	50	all	all	DET
ejpam-232	29	51	concave	concave	NOUN
ejpam-232	29	52	functions	function	NOUN
ejpam-232	29	53	that	that	PRON
ejpam-232	29	54	are	be	AUX
ejpam-232	29	55	greater	great	ADJ
ejpam-232	29	56	than	than	ADP
ejpam-232	29	57	or	or	CCONJ
ejpam-232	29	58	equal	equal	ADJ
ejpam-232	29	59	to	to	PART
ejpam-232	29	60	u.	u.	VERB
ejpam-232	29	61	since	since	SCONJ
ejpam-232	29	62	the	the	DET
ejpam-232	29	63	infimum	infimum	NOUN
ejpam-232	29	64	of	of	ADP
ejpam-232	29	65	a	a	DET
ejpam-232	29	66	family	family	NOUN
ejpam-232	29	67	of	of	ADP
ejpam-232	29	68	concave	concave	NOUN
ejpam-232	29	69	functions	function	NOUN
ejpam-232	29	70	is	be	AUX
ejpam-232	29	71	concave	concave	VERB
ejpam-232	29	72	,	,	PUNCT
ejpam-232	29	73	so	so	ADV
ejpam-232	29	74	cav(u	cav(u	NOUN
ejpam-232	29	75	)	)	PUNCT
ejpam-232	29	76	is	be	AUX
ejpam-232	29	77	concave	concave	VERB
ejpam-232	29	78	and	and	CCONJ
ejpam-232	29	79	is	be	AUX
ejpam-232	29	80	greater	great	ADJ
ejpam-232	29	81	than	than	ADP
ejpam-232	29	82	or	or	CCONJ
ejpam-232	29	83	equal	equal	ADJ
ejpam-232	29	84	to	to	ADP
ejpam-232	29	85	u	u	PRON
ejpam-232	29	86	as	as	SCONJ
ejpam-232	29	87	it	it	PRON
ejpam-232	29	88	is	be	AUX
ejpam-232	29	89	shown	show	VERB
ejpam-232	29	90	in	in	ADP
ejpam-232	29	91	lemma	lemma	PROPN
ejpam-232	29	92	2	2	NUM
ejpam-232	29	93	.	.	PUNCT
ejpam-232	29	94	definition	definition	NOUN
ejpam-232	29	95	4	4	NUM
ejpam-232	29	96	.	.	PUNCT
ejpam-232	30	1	in	in	ADP
ejpam-232	30	2	the	the	DET
ejpam-232	30	3	extended	extended	ADJ
ejpam-232	30	4	version	version	NOUN
ejpam-232	30	5	of	of	ADP
ejpam-232	30	6	cooperative	cooperative	ADJ
ejpam-232	30	7	game	game	NOUN
ejpam-232	30	8	,	,	PUNCT
ejpam-232	30	9	we	we	PRON
ejpam-232	30	10	consider	consider	VERB
ejpam-232	30	11	a	a	DET
ejpam-232	30	12	non	non	ADJ
ejpam-232	30	13	-	-	ADJ
ejpam-232	30	14	empty	empty	ADJ
ejpam-232	30	15	set	set	ADJ
ejpam-232	30	16	ω	ω	NOUN
ejpam-232	30	17	and	and	CCONJ
ejpam-232	30	18	a	a	DET
ejpam-232	30	19	finite	finite	ADJ
ejpam-232	30	20	measure	measure	NOUN
ejpam-232	30	21	space	space	NOUN
ejpam-232	30	22	(	(	PUNCT
ejpam-232	30	23	ω	ω	NOUN
ejpam-232	30	24	,	,	PUNCT
ejpam-232	30	25	∑	∑	ADV
ejpam-232	30	26	,	,	PUNCT
ejpam-232	30	27	µ	µ	NOUN
ejpam-232	30	28	)	)	PUNCT
ejpam-232	30	29	,	,	PUNCT
ejpam-232	30	30	a	a	DET
ejpam-232	30	31	game	game	NOUN
ejpam-232	30	32	v	v	NOUN
ejpam-232	30	33	is	be	AUX
ejpam-232	30	34	a	a	DET
ejpam-232	30	35	bounded	bounded	ADJ
ejpam-232	30	36	real	real	ADV
ejpam-232	30	37	valued	value	VERB
ejpam-232	30	38	function	function	NOUN
ejpam-232	30	39	on	on	ADP
ejpam-232	30	40	∑	∑	PUNCT
ejpam-232	30	41	such	such	ADJ
ejpam-232	30	42	that	that	DET
ejpam-232	30	43	v	v	NOUN
ejpam-232	30	44	(	(	PUNCT
ejpam-232	30	45	;)	;)	NOUN
ejpam-232	30	46	=	=	PUNCT
ejpam-232	30	47	0	0	X
ejpam-232	30	48	.	.	PUNCT
ejpam-232	31	1	for	for	ADP
ejpam-232	31	2	r	r	PROPN
ejpam-232	31	3	∈	∈	PROPN
ejpam-232	31	4	∑	∑	PUNCT
ejpam-232	31	5	,	,	PUNCT
ejpam-232	31	6	we	we	PRON
ejpam-232	31	7	denote	denote	VERB
ejpam-232	31	8	by	by	ADP
ejpam-232	31	9	χr	χr	NOUN
ejpam-232	31	10	the	the	DET
ejpam-232	31	11	characteristic	characteristic	ADJ
ejpam-232	31	12	function	function	NOUN
ejpam-232	31	13	of	of	ADP
ejpam-232	31	14	r.	r.	PROPN
ejpam-232	31	15	let	let	VERB
ejpam-232	31	16	b	b	X
ejpam-232	31	17	be	be	AUX
ejpam-232	31	18	the	the	DET
ejpam-232	31	19	banach	banach	NOUN
ejpam-232	31	20	space	space	NOUN
ejpam-232	31	21	spanned	span	VERB
ejpam-232	31	22	by	by	ADP
ejpam-232	31	23	the	the	DET
ejpam-232	31	24	set	set	NOUN
ejpam-232	31	25	{	{	PUNCT
ejpam-232	31	26	χr	χr	NOUN
ejpam-232	31	27	:	:	PUNCT
ejpam-232	31	28	r	r	NOUN
ejpam-232	31	29	∈	∈	PROPN
ejpam-232	31	30	∑	∑	PUNCT
ejpam-232	31	31	}	}	PUNCT
ejpam-232	31	32	with	with	ADP
ejpam-232	31	33	the	the	DET
ejpam-232	31	34	sup	sup	NOUN
ejpam-232	31	35	norm	norm	NOUN
ejpam-232	31	36	,	,	PUNCT
ejpam-232	31	37	where	where	SCONJ
ejpam-232	31	38	χr	χr	NOUN
ejpam-232	31	39	is	be	AUX
ejpam-232	31	40	the	the	DET
ejpam-232	31	41	characteristic	characteristic	ADJ
ejpam-232	31	42	function	function	NOUN
ejpam-232	31	43	of	of	ADP
ejpam-232	31	44	r.	r.	PROPN
ejpam-232	31	45	then	then	ADV
ejpam-232	31	46	the	the	DET
ejpam-232	31	47	space	space	NOUN
ejpam-232	31	48	of	of	ADP
ejpam-232	31	49	all	all	DET
ejpam-232	31	50	bounded	bounded	ADJ
ejpam-232	31	51	additive	additive	ADJ
ejpam-232	31	52	functions	function	NOUN
ejpam-232	31	53	on	on	ADP
ejpam-232	31	54	∑	∑	PROPN
ejpam-232	31	55	is	be	AUX
ejpam-232	31	56	denoted	denote	VERB
ejpam-232	31	57	by	by	ADP
ejpam-232	31	58	ba	ba	PROPN
ejpam-232	31	59	would	would	AUX
ejpam-232	31	60	be	be	AUX
ejpam-232	31	61	isometrically	isometrically	NOUN
ejpam-232	31	62	isomorphic	isomorphic	ADJ
ejpam-232	31	63	to	to	ADP
ejpam-232	31	64	the	the	DET
ejpam-232	31	65	norm	norm	NOUN
ejpam-232	31	66	-	-	PUNCT
ejpam-232	31	67	dual	dual	ADJ
ejpam-232	31	68	of	of	ADP
ejpam-232	31	69	b.	b.	PROPN
ejpam-232	31	70	a	a	DET
ejpam-232	31	71	payoff	payoff	PROPN
ejpam-232	31	72	µ	µ	PROPN
ejpam-232	31	73	of	of	ADP
ejpam-232	31	74	v	v	NOUN
ejpam-232	31	75	is	be	AUX
ejpam-232	31	76	an	an	DET
ejpam-232	31	77	element	element	NOUN
ejpam-232	31	78	of	of	ADP
ejpam-232	31	79	ba	ba	PROPN
ejpam-232	31	80	with	with	ADP
ejpam-232	31	81	µ(ω	µ(ω	NOUN
ejpam-232	31	82	)	)	PUNCT
ejpam-232	32	1	=	=	SYM
ejpam-232	32	2	v	v	X
ejpam-232	32	3	(	(	PUNCT
ejpam-232	32	4	ω	ω	NOUN
ejpam-232	32	5	)	)	PUNCT
ejpam-232	32	6	.	.	PUNCT
ejpam-232	33	1	the	the	DET
ejpam-232	33	2	core	core	NOUN
ejpam-232	33	3	of	of	ADP
ejpam-232	33	4	v	v	NOUN
ejpam-232	33	5	consists	consist	VERB
ejpam-232	33	6	of	of	ADP
ejpam-232	33	7	all	all	DET
ejpam-232	33	8	payoffs	payoff	NOUN
ejpam-232	33	9	µ	µ	PRON
ejpam-232	33	10	such	such	ADJ
ejpam-232	33	11	that	that	PRON
ejpam-232	33	12	µ(r	µ(r	NOUN
ejpam-232	33	13	)	)	PUNCT
ejpam-232	33	14	≥	≥	NUM
ejpam-232	33	15	v	v	NOUN
ejpam-232	33	16	(	(	PUNCT
ejpam-232	33	17	r	r	NOUN
ejpam-232	33	18	)	)	PUNCT
ejpam-232	33	19	for	for	ADP
ejpam-232	33	20	each	each	DET
ejpam-232	33	21	r	r	NOUN
ejpam-232	33	22	∈	∈	PROPN
ejpam-232	33	23	∑	∑	PUNCT
ejpam-232	33	24	.	.	PUNCT
ejpam-232	34	1	we	we	PRON
ejpam-232	34	2	can	can	AUX
ejpam-232	34	3	also	also	ADV
ejpam-232	34	4	identify	identify	VERB
ejpam-232	34	5	the	the	DET
ejpam-232	34	6	coalition	coalition	NOUN
ejpam-232	34	7	r	r	NOUN
ejpam-232	34	8	cr	cr	NOUN
ejpam-232	34	9	=	=	SYM
ejpam-232	34	10	χr	χr	PROPN
ejpam-232	34	11	µ(r	µ(r	NUM
ejpam-232	34	12	)	)	PUNCT
ejpam-232	34	13	.	.	PUNCT
ejpam-232	35	1	thus	thus	ADV
ejpam-232	35	2	,	,	PUNCT
ejpam-232	35	3	the	the	DET
ejpam-232	35	4	coalition	coalition	NOUN
ejpam-232	35	5	will	will	AUX
ejpam-232	35	6	be	be	AUX
ejpam-232	35	7	identified	identify	VERB
ejpam-232	35	8	with	with	ADP
ejpam-232	35	9	the	the	DET
ejpam-232	35	10	uniform	uniform	ADJ
ejpam-232	35	11	distribution	distribution	NOUN
ejpam-232	35	12	over	over	ADP
ejpam-232	35	13	the	the	DET
ejpam-232	35	14	members	member	NOUN
ejpam-232	35	15	of	of	ADP
ejpam-232	35	16	r.	r.	PROPN
ejpam-232	35	17	a	a	DET
ejpam-232	35	18	game	game	NOUN
ejpam-232	35	19	v	v	NOUN
ejpam-232	35	20	is	be	AUX
ejpam-232	35	21	converted	convert	VERB
ejpam-232	35	22	a	a	DET
ejpam-232	35	23	function	function	NOUN
ejpam-232	35	24	u	u	NOUN
ejpam-232	35	25	defined	define	VERB
ejpam-232	35	26	over	over	ADP
ejpam-232	35	27	the	the	DET
ejpam-232	35	28	points	point	NOUN
ejpam-232	35	29	cr	cr	NOUN
ejpam-232	35	30	for	for	ADP
ejpam-232	35	31	r	r	PROPN
ejpam-232	35	32	∈	∈	PROPN
ejpam-232	35	33	∑′	∑′	PROPN
ejpam-232	35	34	,	,	PUNCT
ejpam-232	35	35	where	where	SCONJ
ejpam-232	35	36	∑′	∑′	PROPN
ejpam-232	35	37	=	=	PUNCT
ejpam-232	35	38	{	{	PUNCT
ejpam-232	35	39	r	r	NOUN
ejpam-232	35	40	∈	∈	PROPN
ejpam-232	35	41	∑	∑	NOUN
ejpam-232	35	42	:	:	PUNCT
ejpam-232	35	43	µ(r	µ(r	NUM
ejpam-232	35	44	)	)	PUNCT
ejpam-232	35	45	6=	6=	ADP
ejpam-232	35	46	0	0	NUM
ejpam-232	35	47	}	}	PUNCT
ejpam-232	35	48	.	.	PUNCT
ejpam-232	36	1	the	the	DET
ejpam-232	36	2	value	value	NOUN
ejpam-232	36	3	of	of	ADP
ejpam-232	36	4	u	u	NOUN
ejpam-232	36	5	at	at	ADP
ejpam-232	36	6	cr	cr	PROPN
ejpam-232	36	7	is	be	AUX
ejpam-232	36	8	the	the	DET
ejpam-232	36	9	average	average	NOUN
ejpam-232	36	10	of	of	ADP
ejpam-232	36	11	the	the	DET
ejpam-232	36	12	worth	worth	NOUN
ejpam-232	36	13	of	of	ADP
ejpam-232	36	14	r	r	NOUN
ejpam-232	36	15	,	,	PUNCT
ejpam-232	36	16	that	that	ADV
ejpam-232	36	17	is	is	ADV
ejpam-232	36	18	,	,	PUNCT
ejpam-232	36	19	u(cr	u(cr	ADJ
ejpam-232	36	20	)	)	PUNCT
ejpam-232	36	21	=	=	SYM
ejpam-232	36	22	v	v	NOUN
ejpam-232	36	23	(	(	PUNCT
ejpam-232	36	24	r	r	NOUN
ejpam-232	36	25	)	)	PUNCT
ejpam-232	36	26	µ(r	µ(r	NOUN
ejpam-232	36	27	)	)	PUNCT
ejpam-232	36	28	.	.	PUNCT
ejpam-232	37	1	we	we	PRON
ejpam-232	37	2	set	set	VERB
ejpam-232	37	3	h	h	NOUN
ejpam-232	37	4	=	=	PRON
ejpam-232	37	5	{	{	PUNCT
ejpam-232	37	6	f	f	X
ejpam-232	37	7	:	:	PUNCT
ejpam-232	37	8	△	△	X
ejpam-232	37	9	→	→	SYM
ejpam-232	37	10	r	r	NOUN
ejpam-232	38	1	|	|	NOUN
ejpam-232	38	2	f	f	PROPN
ejpam-232	38	3	is	be	AUX
ejpam-232	38	4	concave	concave	ADJ
ejpam-232	38	5	and	and	CCONJ
ejpam-232	38	6	f	f	PROPN
ejpam-232	38	7	≥	≥	PROPN
ejpam-232	38	8	u	u	PROPN
ejpam-232	38	9	on	on	ADP
ejpam-232	38	10	∆′	∆′	PROPN
ejpam-232	38	11	}	}	PUNCT
ejpam-232	38	12	where	where	SCONJ
ejpam-232	38	13	,	,	PUNCT
ejpam-232	38	14	∆′	∆′	PROPN
ejpam-232	38	15	=	=	PROPN
ejpam-232	38	16	{	{	PUNCT
ejpam-232	38	17	cr	cr	NOUN
ejpam-232	38	18	:	:	PUNCT
ejpam-232	38	19	r	r	NOUN
ejpam-232	38	20	∈	∈	PROPN
ejpam-232	38	21	∑′	∑′	PROPN
ejpam-232	38	22	}	}	PUNCT
ejpam-232	38	23	.	.	PUNCT
ejpam-232	39	1	for	for	ADP
ejpam-232	39	2	any	any	DET
ejpam-232	39	3	g	g	NOUN
ejpam-232	39	4	∈∆	∈∆	ADV
ejpam-232	39	5	we	we	PRON
ejpam-232	39	6	set	set	VERB
ejpam-232	39	7	lg	lg	NOUN
ejpam-232	39	8	=	=	X
ejpam-232	39	9	{	{	PUNCT
ejpam-232	39	10	∑	∑	PROPN
ejpam-232	39	11	(	(	PUNCT
ejpam-232	39	12	r)αrµ(r)u(cr	r)αrµ(r)u(cr	PROPN
ejpam-232	39	13	)	)	PUNCT
ejpam-232	39	14	:	:	PUNCT
ejpam-232	40	1	g	g	X
ejpam-232	40	2	=	=	SYM
ejpam-232	40	3	∑	∑	PUNCT
ejpam-232	40	4	(	(	PUNCT
ejpam-232	40	5	r	r	NOUN
ejpam-232	40	6	)	)	PUNCT
ejpam-232	40	7	αrχr	αrχr	NOUN
ejpam-232	40	8	and	and	CCONJ
ejpam-232	40	9	αr	αr	ADP
ejpam-232	40	10	>	>	NUM
ejpam-232	40	11	0	0	NUM
ejpam-232	40	12	,	,	PUNCT
ejpam-232	40	13	∑	∑	ADV
ejpam-232	40	14	(	(	PUNCT
ejpam-232	40	15	r)αrµ(r	r)αrµ(r	NOUN
ejpam-232	40	16	)	)	PUNCT
ejpam-232	40	17	=	=	SYM
ejpam-232	40	18	1	1	NUM
ejpam-232	40	19	}	}	PUNCT
ejpam-232	40	20	.	.	PUNCT
ejpam-232	41	1	we	we	PRON
ejpam-232	41	2	can	can	AUX
ejpam-232	41	3	define	define	VERB
ejpam-232	41	4	two	two	NUM
ejpam-232	41	5	functions	function	NOUN
ejpam-232	41	6	w	w	NOUN
ejpam-232	41	7	:	:	PUNCT
ejpam-232	41	8	∆→	∆→	PROPN
ejpam-232	41	9	r	r	NOUN
ejpam-232	41	10	and	and	CCONJ
ejpam-232	41	11	cavu	cavu	PROPN
ejpam-232	41	12	:	:	PUNCT
ejpam-232	41	13	∆→	∆→	PROPN
ejpam-232	41	14	r	r	NOUN
ejpam-232	41	15	by	by	ADP
ejpam-232	41	16	w(g	w(g	PROPN
ejpam-232	41	17	)	)	PUNCT
ejpam-232	42	1	=	=	SYM
ejpam-232	42	2	sup	sup	NOUN
ejpam-232	42	3	lg	lg	NOUN
ejpam-232	42	4	and	and	CCONJ
ejpam-232	42	5	cavu(g	cavu(g	ADJ
ejpam-232	42	6	)	)	PUNCT
ejpam-232	42	7	=	=	SYM
ejpam-232	42	8	inf	inf	NOUN
ejpam-232	42	9	h(g	h(g	NOUN
ejpam-232	42	10	)	)	PUNCT
ejpam-232	42	11	.	.	PUNCT
ejpam-232	43	1	m.	m.	NOUN
ejpam-232	43	2	alimohammady	alimohammady	PROPN
ejpam-232	43	3	,	,	PUNCT
ejpam-232	43	4	v.	v.	CCONJ
ejpam-232	43	5	dadashi	dadashi	PROPN
ejpam-232	43	6	/	/	SYM
ejpam-232	43	7	eur	eur	PROPN
ejpam-232	43	8	.	.	PUNCT
ejpam-232	44	1	j.	j.	PROPN
ejpam-232	44	2	pure	pure	PROPN
ejpam-232	44	3	appl	appl	PROPN
ejpam-232	44	4	.	.	PROPN
ejpam-232	44	5	math	math	PROPN
ejpam-232	44	6	,	,	PUNCT
ejpam-232	44	7	3	3	NUM
ejpam-232	44	8	(	(	PUNCT
ejpam-232	44	9	2010	2010	NUM
ejpam-232	44	10	)	)	PUNCT
ejpam-232	44	11	,	,	PUNCT
ejpam-232	44	12	187	187	NUM
ejpam-232	44	13	-	-	SYM
ejpam-232	44	14	193	193	NUM
ejpam-232	44	15	189	189	NUM
ejpam-232	44	16	3	3	NUM
ejpam-232	44	17	.	.	PUNCT
ejpam-232	44	18	main	main	ADJ
ejpam-232	44	19	results	result	NOUN
ejpam-232	44	20	theorem	theorem	VERB
ejpam-232	44	21	1	1	NUM
ejpam-232	44	22	.	.	X
ejpam-232	45	1	for	for	ADP
ejpam-232	45	2	any	any	DET
ejpam-232	45	3	game	game	NOUN
ejpam-232	45	4	v	v	NOUN
ejpam-232	45	5	,	,	PUNCT
ejpam-232	45	6	core(v	core(v	PROPN
ejpam-232	45	7	)	)	PUNCT
ejpam-232	45	8	is	be	AUX
ejpam-232	45	9	bounded	bound	VERB
ejpam-232	45	10	and	and	CCONJ
ejpam-232	45	11	weak∗	weak∗	NOUN
ejpam-232	45	12	compact	compact	ADJ
ejpam-232	45	13	.	.	PUNCT
ejpam-232	46	1	proof	proof	NOUN
ejpam-232	46	2	.	.	PUNCT
ejpam-232	47	1	for	for	ADP
ejpam-232	47	2	each	each	DET
ejpam-232	47	3	λ	λ	PROPN
ejpam-232	47	4	∈	∈	PROPN
ejpam-232	47	5	core(v	core(v	PROPN
ejpam-232	47	6	)	)	PUNCT
ejpam-232	47	7	,	,	PUNCT
ejpam-232	47	8	0	0	NUM
ejpam-232	47	9	≤	≤	NUM
ejpam-232	47	10	λ(r	λ(r	NOUN
ejpam-232	47	11	)	)	PUNCT
ejpam-232	47	12	≤	≤	PUNCT
ejpam-232	47	13	λ(ω	λ(ω	PROPN
ejpam-232	47	14	)	)	PUNCT
ejpam-232	47	15	=	=	SYM
ejpam-232	47	16	v	v	X
ejpam-232	47	17	(	(	PUNCT
ejpam-232	47	18	ω	ω	NOUN
ejpam-232	47	19	)	)	PUNCT
ejpam-232	47	20	,	,	PUNCT
ejpam-232	47	21	(	(	PUNCT
ejpam-232	47	22	∀r	∀r	X
ejpam-232	47	23	∈	∈	PROPN
ejpam-232	47	24	∑	∑	PUNCT
ejpam-232	47	25	)	)	PUNCT
ejpam-232	47	26	.	.	PUNCT
ejpam-232	48	1	therefore	therefore	ADV
ejpam-232	48	2	,	,	PUNCT
ejpam-232	48	3	core(v	core(v	NOUN
ejpam-232	48	4	)	)	PUNCT
ejpam-232	48	5	is	be	AUX
ejpam-232	48	6	bounded	bound	VERB
ejpam-232	48	7	.	.	PUNCT
ejpam-232	49	1	for	for	ADP
ejpam-232	49	2	each	each	DET
ejpam-232	49	3	net	net	NOUN
ejpam-232	49	4	(	(	PUNCT
ejpam-232	49	5	λα)⊆	λα)⊆	PROPN
ejpam-232	49	6	core(v	core(v	PROPN
ejpam-232	49	7	)	)	PUNCT
ejpam-232	49	8	,	,	PUNCT
ejpam-232	49	9	since	since	SCONJ
ejpam-232	49	10	bounded	bounded	ADJ
ejpam-232	49	11	sets	set	NOUN
ejpam-232	49	12	in	in	ADP
ejpam-232	49	13	b	b	NOUN
ejpam-232	49	14	are	be	AUX
ejpam-232	49	15	relatively	relatively	ADV
ejpam-232	49	16	weak∗	weak∗	NOUN
ejpam-232	49	17	compact	compact	NOUN
ejpam-232	49	18	,	,	PUNCT
ejpam-232	49	19	so	so	CCONJ
ejpam-232	49	20	(	(	PUNCT
ejpam-232	49	21	λα	λα	NOUN
ejpam-232	49	22	)	)	PUNCT
ejpam-232	49	23	has	have	VERB
ejpam-232	49	24	a	a	DET
ejpam-232	49	25	subnet	subnet	NOUN
ejpam-232	49	26	(	(	PUNCT
ejpam-232	49	27	λαβ	λαβ	NOUN
ejpam-232	49	28	)	)	PUNCT
ejpam-232	49	29	β∈i	β∈i	NOUN
ejpam-232	49	30	which	which	PRON
ejpam-232	49	31	converges	converge	VERB
ejpam-232	49	32	in	in	ADP
ejpam-232	49	33	weak∗	weak∗	NOUN
ejpam-232	49	34	topology	topology	NOUN
ejpam-232	49	35	to	to	AUX
ejpam-232	49	36	λ0	λ0	NOUN
ejpam-232	49	37	∈	∈	PROPN
ejpam-232	49	38	b.	b.	NOUN
ejpam-232	49	39	but	but	CCONJ
ejpam-232	49	40	λ0(ω	λ0(ω	PROPN
ejpam-232	50	1	)	)	PUNCT
ejpam-232	50	2	=	=	SYM
ejpam-232	50	3	limλαβ	limλαβ	NOUN
ejpam-232	50	4	(	(	PUNCT
ejpam-232	50	5	ω	ω	NOUN
ejpam-232	50	6	)	)	PUNCT
ejpam-232	50	7	=	=	SYM
ejpam-232	50	8	v	v	X
ejpam-232	50	9	(	(	PUNCT
ejpam-232	50	10	ω	ω	NOUN
ejpam-232	50	11	)	)	PUNCT
ejpam-232	50	12	and	and	CCONJ
ejpam-232	50	13	λαβ	λαβ	NOUN
ejpam-232	50	14	(	(	PUNCT
ejpam-232	50	15	r	r	NOUN
ejpam-232	50	16	)	)	PUNCT
ejpam-232	50	17	≥	≥	NOUN
ejpam-232	50	18	v	v	NOUN
ejpam-232	50	19	(	(	PUNCT
ejpam-232	50	20	r	r	NOUN
ejpam-232	50	21	)	)	PUNCT
ejpam-232	50	22	(	(	PUNCT
ejpam-232	50	23	∀r	∀r	X
ejpam-232	50	24	∈	∈	PROPN
ejpam-232	50	25	∑	∑	PUNCT
ejpam-232	50	26	)	)	PUNCT
ejpam-232	51	1	,	,	PUNCT
ejpam-232	51	2	it	it	PRON
ejpam-232	51	3	shows	show	VERB
ejpam-232	51	4	that	that	SCONJ
ejpam-232	51	5	λ0(r	λ0(r	NOUN
ejpam-232	51	6	)	)	PUNCT
ejpam-232	51	7	≥	≥	NOUN
ejpam-232	51	8	v	v	NOUN
ejpam-232	51	9	(	(	PUNCT
ejpam-232	51	10	r	r	NOUN
ejpam-232	51	11	)	)	PUNCT
ejpam-232	51	12	.	.	PUNCT
ejpam-232	52	1	both	both	PRON
ejpam-232	52	2	implies	imply	VERB
ejpam-232	52	3	that	that	SCONJ
ejpam-232	52	4	λ0	λ0	NOUN
ejpam-232	52	5	∈	∈	NOUN
ejpam-232	52	6	core(v	core(v	NOUN
ejpam-232	52	7	)	)	PUNCT
ejpam-232	52	8	.	.	PUNCT
ejpam-232	53	1	these	these	DET
ejpam-232	53	2	facts	fact	NOUN
ejpam-232	53	3	imply	imply	VERB
ejpam-232	53	4	that	that	SCONJ
ejpam-232	53	5	core(v	core(v	NOUN
ejpam-232	53	6	)	)	PUNCT
ejpam-232	53	7	is	be	AUX
ejpam-232	53	8	weak∗	weak∗	NOUN
ejpam-232	53	9	compact	compact	NOUN
ejpam-232	53	10	.	.	PUNCT
ejpam-232	54	1	lemma	lemma	PROPN
ejpam-232	54	2	1	1	NUM
ejpam-232	54	3	.	.	PUNCT
ejpam-232	55	1	w	w	PROPN
ejpam-232	55	2	is	be	AUX
ejpam-232	55	3	a	a	DET
ejpam-232	55	4	concave	concave	NOUN
ejpam-232	55	5	map	map	NOUN
ejpam-232	55	6	.	.	PUNCT
ejpam-232	56	1	proof	proof	NOUN
ejpam-232	56	2	.	.	PUNCT
ejpam-232	57	1	for	for	ADP
ejpam-232	57	2	ε	ε	PROPN
ejpam-232	57	3	>	>	X
ejpam-232	57	4	0	0	PUNCT
ejpam-232	57	5	there	there	PRON
ejpam-232	57	6	are	be	VERB
ejpam-232	57	7	two	two	NUM
ejpam-232	57	8	elements	element	NOUN
ejpam-232	57	9	∑	∑	PUNCT
ejpam-232	57	10	(	(	PUNCT
ejpam-232	57	11	r	r	NOUN
ejpam-232	57	12	)	)	PUNCT
ejpam-232	57	13	αrµ(r)u(cr	αrµ(r)u(cr	NUM
ejpam-232	57	14	)	)	PUNCT
ejpam-232	57	15	and	and	CCONJ
ejpam-232	57	16	∑	∑	PROPN
ejpam-232	57	17	(	(	PUNCT
ejpam-232	57	18	r′	r′	NUM
ejpam-232	57	19	)	)	PUNCT
ejpam-232	57	20	βr′µ(r	βr′µ(r	ADP
ejpam-232	57	21	′)u(cr′	′)u(cr′	NOUN
ejpam-232	57	22	)	)	PUNCT
ejpam-232	57	23	such	such	ADJ
ejpam-232	57	24	that	that	PRON
ejpam-232	57	25	tw(g	tw(g	PUNCT
ejpam-232	57	26	)	)	PUNCT
ejpam-232	57	27	+	+	CCONJ
ejpam-232	57	28	(	(	PUNCT
ejpam-232	57	29	1−	1−	NUM
ejpam-232	57	30	t)w(h)−	t)w(h)−	NUM
ejpam-232	57	31	ε	ε	NOUN
ejpam-232	57	32	=	=	PUNCT
ejpam-232	57	33	t[w(g)−	t[w(g)−	NOUN
ejpam-232	57	34	ε	ε	VERB
ejpam-232	57	35	]	]	X
ejpam-232	57	36	+	+	CCONJ
ejpam-232	57	37	(	(	PUNCT
ejpam-232	57	38	1−	1−	NUM
ejpam-232	57	39	t)[w(h)−	t)[w(h)−	NOUN
ejpam-232	57	40	ε	ε	X
ejpam-232	57	41	]	]	X
ejpam-232	57	42	<	<	X
ejpam-232	57	43	t	t	PROPN
ejpam-232	57	44	∑	∑	PUNCT
ejpam-232	57	45	(	(	PUNCT
ejpam-232	57	46	r	r	NOUN
ejpam-232	57	47	)	)	PUNCT
ejpam-232	57	48	αrµ(r)u(cr	αrµ(r)u(cr	NUM
ejpam-232	57	49	)	)	PUNCT
ejpam-232	58	1	+	+	CCONJ
ejpam-232	58	2	(	(	PUNCT
ejpam-232	58	3	1−	1−	NUM
ejpam-232	58	4	t	t	NUM
ejpam-232	58	5	)	)	PUNCT
ejpam-232	58	6	∑	∑	PUNCT
ejpam-232	58	7	(	(	PUNCT
ejpam-232	58	8	r′	r′	NUM
ejpam-232	58	9	)	)	PUNCT
ejpam-232	58	10	βr′µ(r	βr′µ(r	ADP
ejpam-232	58	11	′)u(cr′	′)u(cr′	NOUN
ejpam-232	58	12	)	)	PUNCT
ejpam-232	58	13	≤	≤	NOUN
ejpam-232	58	14	w(t	w(t	VERB
ejpam-232	58	15	g	g	NOUN
ejpam-232	58	16	+	+	CCONJ
ejpam-232	58	17	(	(	PUNCT
ejpam-232	58	18	1−	1−	NUM
ejpam-232	58	19	t)h	t)h	NOUN
ejpam-232	58	20	)	)	PUNCT
ejpam-232	58	21	.	.	PUNCT
ejpam-232	59	1	lemma	lemma	PROPN
ejpam-232	60	1	2	2	NUM
ejpam-232	60	2	.	.	NUM
ejpam-232	60	3	cav(u)(cr)≥	cav(u)(cr)≥	PROPN
ejpam-232	60	4	u(cr	u(cr	PROPN
ejpam-232	60	5	)	)	PUNCT
ejpam-232	60	6	.	.	PUNCT
ejpam-232	61	1	proof	proof	NOUN
ejpam-232	61	2	.	.	PUNCT
ejpam-232	62	1	by	by	ADP
ejpam-232	62	2	concavity	concavity	NOUN
ejpam-232	62	3	of	of	ADP
ejpam-232	62	4	cav(u	cav(u	PROPN
ejpam-232	62	5	)	)	PUNCT
ejpam-232	62	6	and	and	CCONJ
ejpam-232	62	7	f	f	PROPN
ejpam-232	62	8	∈	∈	PROPN
ejpam-232	62	9	h	h	NOUN
ejpam-232	63	1	it	it	PRON
ejpam-232	63	2	follows	follow	VERB
ejpam-232	63	3	that	that	SCONJ
ejpam-232	63	4	f	f	PROPN
ejpam-232	63	5	≥	≥	PRON
ejpam-232	63	6	u.	u.	VERB
ejpam-232	63	7	hence	hence	ADV
ejpam-232	63	8	cav(u	cav(u	NUM
ejpam-232	63	9	)	)	PUNCT
ejpam-232	63	10	∈	∈	PROPN
ejpam-232	63	11	h	h	NOUN
ejpam-232	63	12	and	and	CCONJ
ejpam-232	63	13	cav(u)(cr)≥	cav(u)(cr)≥	PROPN
ejpam-232	63	14	u(cr	u(cr	PROPN
ejpam-232	63	15	)	)	PUNCT
ejpam-232	63	16	,	,	PUNCT
ejpam-232	63	17	for	for	ADP
ejpam-232	63	18	any	any	DET
ejpam-232	63	19	r	r	NOUN
ejpam-232	63	20	∈	∈	NOUN
ejpam-232	63	21	∑	∑	PUNCT
ejpam-232	63	22	.	.	PUNCT
ejpam-232	64	1	proposition	proposition	NOUN
ejpam-232	64	2	1	1	NUM
ejpam-232	64	3	.	.	PUNCT
ejpam-232	64	4	w(g	w(g	PROPN
ejpam-232	64	5	)	)	PUNCT
ejpam-232	65	1	=	=	SYM
ejpam-232	65	2	cav(u)(g	cav(u)(g	NOUN
ejpam-232	65	3	)	)	PUNCT
ejpam-232	65	4	for	for	ADP
ejpam-232	65	5	any	any	DET
ejpam-232	65	6	g	g	PROPN
ejpam-232	65	7	∈	∈	PROPN
ejpam-232	65	8	△	△	PROPN
ejpam-232	65	9	.	.	PUNCT
ejpam-232	65	10	proof	proof	NOUN
ejpam-232	65	11	.	.	PUNCT
ejpam-232	66	1	suppose	suppose	VERB
ejpam-232	66	2	∑	∑	INTJ
ejpam-232	66	3	(	(	PUNCT
ejpam-232	66	4	r	r	NOUN
ejpam-232	66	5	)	)	PUNCT
ejpam-232	66	6	αrµ(r)u(cr	αrµ(r)u(cr	NUM
ejpam-232	66	7	)	)	PUNCT
ejpam-232	66	8	∈	∈	PROPN
ejpam-232	66	9	lg	lg	NOUN
ejpam-232	66	10	.	.	PUNCT
ejpam-232	67	1	choosing	choose	VERB
ejpam-232	67	2	g	g	PROPN
ejpam-232	67	3	=	=	PUNCT
ejpam-232	67	4	∑	∑	PUNCT
ejpam-232	67	5	(	(	PUNCT
ejpam-232	67	6	r	r	NOUN
ejpam-232	67	7	)	)	PUNCT
ejpam-232	67	8	αrχr	αrχr	ADV
ejpam-232	67	9	such	such	ADJ
ejpam-232	67	10	that	that	SCONJ
ejpam-232	67	11	αr	αr	NUM
ejpam-232	67	12	≥	≥	NOUN
ejpam-232	67	13	0	0	NUM
ejpam-232	67	14	and	and	CCONJ
ejpam-232	67	15	∑	∑	ADP
ejpam-232	67	16	(	(	PUNCT
ejpam-232	67	17	r	r	NOUN
ejpam-232	67	18	)	)	PUNCT
ejpam-232	67	19	αrµ(r	αrµ(r	NOUN
ejpam-232	67	20	)	)	PUNCT
ejpam-232	67	21	=	=	SYM
ejpam-232	68	1	1	1	X
ejpam-232	68	2	.	.	PUNCT
ejpam-232	68	3	then	then	ADV
ejpam-232	68	4	cav(u)(g	cav(u)(g	NUM
ejpam-232	68	5	)	)	PUNCT
ejpam-232	69	1	=	=	PUNCT
ejpam-232	69	2	cav(u	cav(u	NOUN
ejpam-232	69	3	)	)	PUNCT
ejpam-232	69	4	(	(	PUNCT
ejpam-232	69	5	∑	∑	PUNCT
ejpam-232	69	6	(	(	PUNCT
ejpam-232	69	7	r	r	NOUN
ejpam-232	69	8	)	)	PUNCT
ejpam-232	69	9	αrχr	αrχr	ADJ
ejpam-232	69	10	)	)	PUNCT
ejpam-232	70	1	=	=	SYM
ejpam-232	70	2	cav(u	cav(u	NOUN
ejpam-232	70	3	)	)	PUNCT
ejpam-232	70	4	(	(	PUNCT
ejpam-232	70	5	∑	∑	PUNCT
ejpam-232	70	6	(	(	PUNCT
ejpam-232	70	7	r	r	NOUN
ejpam-232	70	8	)	)	PUNCT
ejpam-232	70	9	αrµ(r	αrµ(r	NOUN
ejpam-232	70	10	)	)	PUNCT
ejpam-232	70	11	χr	χr	NOUN
ejpam-232	70	12	µ(r	µ(r	NOUN
ejpam-232	70	13	)	)	PUNCT
ejpam-232	70	14	)	)	PUNCT
ejpam-232	70	15	≥	≥	X
ejpam-232	70	16	∑	∑	PUNCT
ejpam-232	70	17	(	(	PUNCT
ejpam-232	70	18	r	r	NOUN
ejpam-232	70	19	)	)	PUNCT
ejpam-232	70	20	αrµ(r)cav(u	αrµ(r)cav(u	NOUN
ejpam-232	70	21	)	)	PUNCT
ejpam-232	70	22	(	(	PUNCT
ejpam-232	70	23	χr	χr	PROPN
ejpam-232	70	24	µ(r	µ(r	NOUN
ejpam-232	70	25	)	)	PUNCT
ejpam-232	70	26	)	)	PUNCT
ejpam-232	70	27	≥	≥	X
ejpam-232	70	28	∑	∑	PUNCT
ejpam-232	70	29	(	(	PUNCT
ejpam-232	70	30	r	r	NOUN
ejpam-232	70	31	)	)	PUNCT
ejpam-232	70	32	αrµ(r)u(cr	αrµ(r)u(cr	NUM
ejpam-232	70	33	)	)	PUNCT
ejpam-232	70	34	.	.	PUNCT
ejpam-232	71	1	this	this	PRON
ejpam-232	71	2	shows	show	VERB
ejpam-232	71	3	that	that	SCONJ
ejpam-232	71	4	w(g	w(g	PROPN
ejpam-232	71	5	)	)	PUNCT
ejpam-232	71	6	≤	≤	NUM
ejpam-232	71	7	cav(u)(g	cav(u)(g	NOUN
ejpam-232	71	8	)	)	PUNCT
ejpam-232	71	9	.	.	PUNCT
ejpam-232	72	1	for	for	ADP
ejpam-232	72	2	the	the	DET
ejpam-232	72	3	converse	converse	NOUN
ejpam-232	72	4	,	,	PUNCT
ejpam-232	72	5	we	we	PRON
ejpam-232	72	6	note	note	VERB
ejpam-232	72	7	that	that	SCONJ
ejpam-232	72	8	w	w	NOUN
ejpam-232	72	9	is	be	AUX
ejpam-232	72	10	concave	concave	VERB
ejpam-232	72	11	from	from	ADP
ejpam-232	72	12	lemma	lemma	PROPN
ejpam-232	72	13	1	1	NUM
ejpam-232	72	14	,	,	PUNCT
ejpam-232	72	15	w(cr)≥	w(cr)≥	VERB
ejpam-232	72	16	u(cr	u(cr	NOUN
ejpam-232	72	17	)	)	PUNCT
ejpam-232	72	18	.	.	PUNCT
ejpam-232	73	1	therefore	therefore	ADV
ejpam-232	73	2	,	,	PUNCT
ejpam-232	73	3	cav(u)≤	cav(u)≤	PROPN
ejpam-232	73	4	w.	w.	PROPN
ejpam-232	73	5	m.	m.	PROPN
ejpam-232	73	6	alimohammady	alimohammady	PROPN
ejpam-232	73	7	,	,	PUNCT
ejpam-232	73	8	v.	v.	CCONJ
ejpam-232	73	9	dadashi	dadashi	PROPN
ejpam-232	73	10	/	/	SYM
ejpam-232	73	11	eur	eur	PROPN
ejpam-232	73	12	.	.	PUNCT
ejpam-232	74	1	j.	j.	PROPN
ejpam-232	74	2	pure	pure	PROPN
ejpam-232	74	3	appl	appl	PROPN
ejpam-232	74	4	.	.	PROPN
ejpam-232	74	5	math	math	PROPN
ejpam-232	74	6	,	,	PUNCT
ejpam-232	74	7	3	3	NUM
ejpam-232	74	8	(	(	PUNCT
ejpam-232	74	9	2010	2010	NUM
ejpam-232	74	10	)	)	PUNCT
ejpam-232	74	11	,	,	PUNCT
ejpam-232	74	12	187	187	NUM
ejpam-232	74	13	-	-	SYM
ejpam-232	74	14	193	193	NUM
ejpam-232	74	15	190	190	NUM
ejpam-232	74	16	definition	definition	NOUN
ejpam-232	74	17	5	5	NUM
ejpam-232	74	18	.	.	PUNCT
ejpam-232	75	1	λ	λ	NOUN
ejpam-232	75	2	∈	∈	PROPN
ejpam-232	75	3	ba	ba	PROPN
ejpam-232	75	4	is	be	AUX
ejpam-232	75	5	called	call	VERB
ejpam-232	75	6	linear	linear	ADJ
ejpam-232	75	7	support	support	NOUN
ejpam-232	75	8	of	of	ADP
ejpam-232	75	9	f	f	PROPN
ejpam-232	75	10	:	:	PUNCT
ejpam-232	75	11	△	△	NOUN
ejpam-232	75	12	→	→	SYM
ejpam-232	75	13	r	r	NOUN
ejpam-232	75	14	at	at	ADP
ejpam-232	75	15	g	g	PROPN
ejpam-232	75	16	∈	∈	PROPN
ejpam-232	75	17	△	△	PROPN
ejpam-232	75	18	if	if	SCONJ
ejpam-232	75	19	f	f	PROPN
ejpam-232	75	20	(	(	PUNCT
ejpam-232	75	21	g	g	NOUN
ejpam-232	75	22	)	)	PUNCT
ejpam-232	75	23	=	=	SYM
ejpam-232	75	24	∫	∫	PROPN
ejpam-232	75	25	ω	ω	NUM
ejpam-232	75	26	gdλ	gdλ	PROPN
ejpam-232	75	27	and	and	CCONJ
ejpam-232	75	28	f	f	PROPN
ejpam-232	75	29	(	(	PUNCT
ejpam-232	75	30	g′)≤	g′)≤	PROPN
ejpam-232	75	31	∫	∫	PROPN
ejpam-232	75	32	ω	ω	NUM
ejpam-232	75	33	g′dλ	g′dλ	NOUN
ejpam-232	75	34	(	(	PUNCT
ejpam-232	75	35	∀g′	∀g′	X
ejpam-232	75	36	∈	∈	PROPN
ejpam-232	75	37	△	△	NOUN
ejpam-232	75	38	)	)	PUNCT
ejpam-232	75	39	.	.	PUNCT
ejpam-232	76	1	proposition	proposition	NOUN
ejpam-232	76	2	2	2	NUM
ejpam-232	76	3	.	.	PUNCT
ejpam-232	77	1	cav(u)(cω	cav(u)(cω	NOUN
ejpam-232	77	2	)	)	PUNCT
ejpam-232	77	3	=	=	SYM
ejpam-232	77	4	u(cω	u(cω	NOUN
ejpam-232	77	5	)	)	PUNCT
ejpam-232	77	6	if	if	SCONJ
ejpam-232	77	7	corev	corev	PROPN
ejpam-232	77	8	6=	6=	NUM
ejpam-232	77	9	;	;	PUNCT
ejpam-232	77	10	.	.	PUNCT
ejpam-232	78	1	proof	proof	NOUN
ejpam-232	78	2	.	.	PUNCT
ejpam-232	79	1	corev	corev	PROPN
ejpam-232	79	2	6=	6=	NUM
ejpam-232	79	3	;	;	PUNCT
ejpam-232	79	4	implies	imply	VERB
ejpam-232	79	5	that	that	SCONJ
ejpam-232	79	6	there	there	PRON
ejpam-232	79	7	is	be	VERB
ejpam-232	79	8	λ	λ	PROPN
ejpam-232	79	9	∈	∈	PROPN
ejpam-232	79	10	ba	ba	NOUN
ejpam-232	79	11	which	which	PRON
ejpam-232	79	12	satisfies	satisfy	VERB
ejpam-232	79	13	λ(ω	λ(ω	PRON
ejpam-232	79	14	)	)	PUNCT
ejpam-232	79	15	=	=	SYM
ejpam-232	79	16	v	v	X
ejpam-232	79	17	(	(	PUNCT
ejpam-232	79	18	ω	ω	NOUN
ejpam-232	79	19	)	)	PUNCT
ejpam-232	79	20	and	and	CCONJ
ejpam-232	79	21	λ(r	λ(r	PROPN
ejpam-232	79	22	)	)	PUNCT
ejpam-232	79	23	≥	≥	NOUN
ejpam-232	79	24	v	v	NOUN
ejpam-232	79	25	(	(	PUNCT
ejpam-232	79	26	r	r	NOUN
ejpam-232	79	27	)	)	PUNCT
ejpam-232	79	28	(	(	PUNCT
ejpam-232	79	29	∀r	∀r	NOUN
ejpam-232	79	30	∈	∈	PROPN
ejpam-232	79	31	∑′	∑′	PROPN
ejpam-232	79	32	)	)	PUNCT
ejpam-232	79	33	.	.	PUNCT
ejpam-232	80	1	set	set	VERB
ejpam-232	80	2	f	f	PROPN
ejpam-232	80	3	:	:	PUNCT
ejpam-232	80	4	△	△	X
ejpam-232	80	5	→	→	SYM
ejpam-232	80	6	r	r	NOUN
ejpam-232	80	7	by	by	ADP
ejpam-232	80	8	f	f	PROPN
ejpam-232	80	9	(	(	PUNCT
ejpam-232	80	10	g	g	NOUN
ejpam-232	80	11	)	)	PUNCT
ejpam-232	80	12	=	=	SYM
ejpam-232	80	13	∫	∫	PROPN
ejpam-232	80	14	ω	ω	PROPN
ejpam-232	80	15	gdλ	gdλ	PROPN
ejpam-232	80	16	.	.	PUNCT
ejpam-232	81	1	it	it	PRON
ejpam-232	81	2	is	be	AUX
ejpam-232	81	3	clear	clear	ADJ
ejpam-232	81	4	that	that	SCONJ
ejpam-232	81	5	f	f	PROPN
ejpam-232	81	6	would	would	AUX
ejpam-232	81	7	be	be	AUX
ejpam-232	81	8	a	a	DET
ejpam-232	81	9	concave	concave	NOUN
ejpam-232	81	10	map	map	NOUN
ejpam-232	81	11	.	.	PUNCT
ejpam-232	82	1	on	on	ADP
ejpam-232	82	2	the	the	DET
ejpam-232	82	3	other	other	ADJ
ejpam-232	82	4	hand	hand	NOUN
ejpam-232	82	5	,	,	PUNCT
ejpam-232	82	6	f	f	PROPN
ejpam-232	82	7	(	(	PUNCT
ejpam-232	82	8	cr	cr	PROPN
ejpam-232	82	9	)	)	PUNCT
ejpam-232	82	10	≥	≥	NOUN
ejpam-232	82	11	u(cr	u(cr	PROPN
ejpam-232	82	12	)	)	PUNCT
ejpam-232	82	13	.	.	PUNCT
ejpam-232	83	1	therefore	therefore	ADV
ejpam-232	83	2	,	,	PUNCT
ejpam-232	83	3	f	f	PROPN
ejpam-232	83	4	∈	∈	PROPN
ejpam-232	83	5	h	h	NOUN
ejpam-232	83	6	,	,	PUNCT
ejpam-232	83	7	so	so	ADV
ejpam-232	83	8	cav(u)(cr	cav(u)(cr	NOUN
ejpam-232	83	9	)	)	PUNCT
ejpam-232	83	10	≤	≤	NUM
ejpam-232	83	11	f	f	PROPN
ejpam-232	83	12	(	(	PUNCT
ejpam-232	83	13	cr	cr	NOUN
ejpam-232	83	14	)	)	PUNCT
ejpam-232	83	15	for	for	ADP
ejpam-232	83	16	any	any	DET
ejpam-232	83	17	r	r	NOUN
ejpam-232	83	18	∈	∈	PROPN
ejpam-232	83	19	∑′	∑′	PROPN
ejpam-232	83	20	.	.	PUNCT
ejpam-232	84	1	but	but	CCONJ
ejpam-232	84	2	f	f	PROPN
ejpam-232	84	3	(	(	PUNCT
ejpam-232	84	4	cω	cω	NOUN
ejpam-232	84	5	)	)	PUNCT
ejpam-232	84	6	=	=	SYM
ejpam-232	84	7	u(cω	u(cω	NOUN
ejpam-232	84	8	)	)	PUNCT
ejpam-232	84	9	which	which	PRON
ejpam-232	84	10	implies	imply	VERB
ejpam-232	84	11	that	that	SCONJ
ejpam-232	84	12	,	,	PUNCT
ejpam-232	84	13	cav(u)(cω	cav(u)(cω	NOUN
ejpam-232	84	14	)	)	PUNCT
ejpam-232	84	15	≤	≤	NOUN
ejpam-232	84	16	u(cω	u(cω	NOUN
ejpam-232	84	17	)	)	PUNCT
ejpam-232	84	18	.	.	PUNCT
ejpam-232	85	1	so	so	ADV
ejpam-232	85	2	from	from	ADP
ejpam-232	85	3	lemma	lemma	PROPN
ejpam-232	85	4	2	2	NUM
ejpam-232	85	5	cav(u)(cω	cav(u)(cω	NOUN
ejpam-232	85	6	)	)	PUNCT
ejpam-232	85	7	=	=	SYM
ejpam-232	85	8	u(cω	u(cω	NOUN
ejpam-232	85	9	)	)	PUNCT
ejpam-232	85	10	.	.	PUNCT
ejpam-232	86	1	corollary	corollary	ADJ
ejpam-232	86	2	1	1	NUM
ejpam-232	86	3	.	.	PUNCT
ejpam-232	87	1	λ	λ	NOUN
ejpam-232	87	2	is	be	AUX
ejpam-232	87	3	a	a	DET
ejpam-232	87	4	linear	linear	ADJ
ejpam-232	87	5	support	support	NOUN
ejpam-232	87	6	for	for	ADP
ejpam-232	87	7	cav(u	cav(u	NOUN
ejpam-232	87	8	)	)	PUNCT
ejpam-232	87	9	at	at	ADP
ejpam-232	87	10	cω	cω	NOUN
ejpam-232	87	11	if	if	SCONJ
ejpam-232	87	12	λ	λ	PROPN
ejpam-232	87	13	∈	∈	NOUN
ejpam-232	87	14	core(v	core(v	PROPN
ejpam-232	87	15	)	)	PUNCT
ejpam-232	87	16	.	.	PUNCT
ejpam-232	88	1	proposition	proposition	NOUN
ejpam-232	88	2	3	3	NUM
ejpam-232	88	3	.	.	X
ejpam-232	88	4	v	v	NOUN
ejpam-232	88	5	is	be	AUX
ejpam-232	88	6	balanced	balanced	ADJ
ejpam-232	88	7	game	game	NOUN
ejpam-232	88	8	if	if	SCONJ
ejpam-232	88	9	core(v	core(v	NOUN
ejpam-232	88	10	)	)	PUNCT
ejpam-232	88	11	6=	6=	NUM
ejpam-232	88	12	;	;	PUNCT
ejpam-232	88	13	.	.	PUNCT
ejpam-232	89	1	proof	proof	NOUN
ejpam-232	89	2	.	.	PUNCT
ejpam-232	90	1	assuming	assume	VERB
ejpam-232	90	2	corev	corev	PROPN
ejpam-232	90	3	6=	6=	NUM
ejpam-232	90	4	;	;	PUNCT
ejpam-232	90	5	by	by	ADP
ejpam-232	90	6	proposition	proposition	NOUN
ejpam-232	90	7	2	2	NUM
ejpam-232	90	8	yields	yield	NOUN
ejpam-232	90	9	cav(u)(cω	cav(u)(cω	NOUN
ejpam-232	90	10	)	)	PUNCT
ejpam-232	90	11	=	=	SYM
ejpam-232	90	12	u(cω	u(cω	NOUN
ejpam-232	90	13	)	)	PUNCT
ejpam-232	90	14	.	.	PUNCT
ejpam-232	91	1	since	since	SCONJ
ejpam-232	91	2	cav(u)(cω	cav(u)(cω	PROPN
ejpam-232	91	3	)	)	PUNCT
ejpam-232	91	4	=	=	SYM
ejpam-232	91	5	w(cω	w(cω	NOUN
ejpam-232	91	6	)	)	PUNCT
ejpam-232	91	7	=	=	SYM
ejpam-232	91	8	sup	sup	NOUN
ejpam-232	91	9	{	{	PUNCT
ejpam-232	91	10	∑	∑	PROPN
ejpam-232	91	11	(	(	PUNCT
ejpam-232	91	12	r	r	NOUN
ejpam-232	91	13	)	)	PUNCT
ejpam-232	91	14	αrµ(r)u(cr	αrµ(r)u(cr	NUM
ejpam-232	91	15	)	)	PUNCT
ejpam-232	91	16	:	:	PUNCT
ejpam-232	91	17	σαrµ(r	σαrµ(r	X
ejpam-232	91	18	)	)	PUNCT
ejpam-232	91	19	=	=	SYM
ejpam-232	91	20	1,αr	1,αr	NUM
ejpam-232	91	21	≥	≥	NOUN
ejpam-232	91	22	0	0	NUM
ejpam-232	91	23	,	,	PUNCT
ejpam-232	91	24	∑	∑	ADP
ejpam-232	91	25	(	(	PUNCT
ejpam-232	91	26	r	r	NOUN
ejpam-232	91	27	)	)	PUNCT
ejpam-232	91	28	αrχr	αrχr	NOUN
ejpam-232	91	29	=	=	PUNCT
ejpam-232	91	30	cω	cω	NOUN
ejpam-232	91	31	}	}	PUNCT
ejpam-232	91	32	,	,	PUNCT
ejpam-232	91	33	so	so	ADV
ejpam-232	91	34	∑	∑	ADV
ejpam-232	91	35	(	(	PUNCT
ejpam-232	91	36	r	r	NOUN
ejpam-232	91	37	)	)	PUNCT
ejpam-232	91	38	αrµ(r)u(cr)≤	αrµ(r)u(cr)≤	PROPN
ejpam-232	91	39	cav(u)(cω	cav(u)(cω	NOUN
ejpam-232	91	40	)	)	PUNCT
ejpam-232	91	41	=	=	SYM
ejpam-232	91	42	u(cω	u(cω	NOUN
ejpam-232	91	43	)	)	PUNCT
ejpam-232	91	44	.	.	PUNCT
ejpam-232	92	1	hence	hence	ADV
ejpam-232	92	2	,	,	PUNCT
ejpam-232	92	3	sup	sup	INTJ
ejpam-232	92	4	∑	∑	PROPN
ejpam-232	92	5	(	(	PUNCT
ejpam-232	92	6	r	r	NOUN
ejpam-232	92	7	)	)	PUNCT
ejpam-232	92	8	αrµ(r)u(cr)≤	αrµ(r)u(cr)≤	PROPN
ejpam-232	92	9	u(cω	u(cω	NUM
ejpam-232	92	10	)	)	PUNCT
ejpam-232	92	11	.	.	PUNCT
ejpam-232	93	1	lemma	lemma	PROPN
ejpam-232	93	2	3	3	X
ejpam-232	93	3	.	.	PUNCT
ejpam-232	93	4	suppose	suppose	VERB
ejpam-232	93	5	that	that	SCONJ
ejpam-232	93	6	s	s	VERB
ejpam-232	93	7	is	be	AUX
ejpam-232	93	8	the	the	DET
ejpam-232	93	9	set	set	NOUN
ejpam-232	93	10	of	of	ADP
ejpam-232	93	11	all	all	DET
ejpam-232	93	12	simple	simple	ADJ
ejpam-232	93	13	functions	function	NOUN
ejpam-232	93	14	on	on	ADP
ejpam-232	93	15	(	(	PUNCT
ejpam-232	93	16	ω	ω	NOUN
ejpam-232	93	17	,	,	PUNCT
ejpam-232	93	18	∑	∑	ADV
ejpam-232	93	19	,	,	PUNCT
ejpam-232	93	20	µ	µ	X
ejpam-232	93	21	)	)	PUNCT
ejpam-232	93	22	and	and	CCONJ
ejpam-232	93	23	f	f	X
ejpam-232	93	24	:	:	PUNCT
ejpam-232	93	25	△	△	PUNCT
ejpam-232	93	26	→	→	SYM
ejpam-232	93	27	r	r	NOUN
ejpam-232	93	28	is	be	AUX
ejpam-232	93	29	the	the	DET
ejpam-232	93	30	concave	concave	NOUN
ejpam-232	93	31	map	map	NOUN
ejpam-232	93	32	.	.	PUNCT
ejpam-232	94	1	then	then	ADV
ejpam-232	94	2	for	for	ADP
ejpam-232	94	3	any	any	DET
ejpam-232	94	4	g	g	PROPN
ejpam-232	94	5	∈	∈	PROPN
ejpam-232	94	6	s	s	NOUN
ejpam-232	94	7	,	,	PUNCT
ejpam-232	94	8	there	there	PRON
ejpam-232	94	9	is	be	VERB
ejpam-232	94	10	a	a	DET
ejpam-232	94	11	linear	linear	ADJ
ejpam-232	94	12	map	map	NOUN
ejpam-232	94	13	g	g	ADP
ejpam-232	94	14	such	such	ADJ
ejpam-232	94	15	that	that	DET
ejpam-232	94	16	g(g	g(g	NOUN
ejpam-232	94	17	)	)	PUNCT
ejpam-232	94	18	=	=	SYM
ejpam-232	94	19	f	f	X
ejpam-232	94	20	(	(	PUNCT
ejpam-232	94	21	g	g	NOUN
ejpam-232	94	22	)	)	PUNCT
ejpam-232	94	23	and	and	CCONJ
ejpam-232	94	24	f	f	PROPN
ejpam-232	94	25	(	(	PUNCT
ejpam-232	94	26	h)≤	h)≤	PROPN
ejpam-232	94	27	g(h	g(h	PROPN
ejpam-232	94	28	)	)	PUNCT
ejpam-232	94	29	,	,	PUNCT
ejpam-232	94	30	(	(	PUNCT
ejpam-232	94	31	∀h	∀h	PROPN
ejpam-232	94	32	∈	∈	PROPN
ejpam-232	94	33	s	s	PART
ejpam-232	94	34	)	)	PUNCT
ejpam-232	94	35	proof	proof	NOUN
ejpam-232	94	36	.	.	PUNCT
ejpam-232	95	1	the	the	DET
ejpam-232	95	2	function	function	NOUN
ejpam-232	95	3	−	−	PROPN
ejpam-232	95	4	f	f	PROPN
ejpam-232	95	5	is	be	AUX
ejpam-232	95	6	a	a	DET
ejpam-232	95	7	convex	convex	ADJ
ejpam-232	95	8	function	function	NOUN
ejpam-232	95	9	.	.	PUNCT
ejpam-232	96	1	now	now	ADV
ejpam-232	96	2	applying	apply	VERB
ejpam-232	96	3	hahn	hahn	NOUN
ejpam-232	96	4	banach	banach	NOUN
ejpam-232	96	5	theorem	theorem	VERB
ejpam-232	96	6	for	for	ADP
ejpam-232	96	7	l	l	NOUN
ejpam-232	97	1	=	=	X
ejpam-232	97	2	<	<	X
ejpam-232	97	3	{	{	PUNCT
ejpam-232	97	4	g	g	NOUN
ejpam-232	97	5	}	}	PUNCT
ejpam-232	97	6	>	>	X
ejpam-232	97	7	and	and	CCONJ
ejpam-232	97	8	−	−	PROPN
ejpam-232	97	9	f	f	NOUN
ejpam-232	97	10	,	,	PUNCT
ejpam-232	97	11	there	there	PRON
ejpam-232	97	12	is	be	VERB
ejpam-232	97	13	a	a	DET
ejpam-232	97	14	linear	linear	ADJ
ejpam-232	97	15	function	function	NOUN
ejpam-232	97	16	f	f	NOUN
ejpam-232	97	17	:	:	PUNCT
ejpam-232	98	1	s→	s→	X
ejpam-232	98	2	r	r	NOUN
ejpam-232	98	3	such	such	ADJ
ejpam-232	98	4	that	that	DET
ejpam-232	98	5	f(g	f(g	NOUN
ejpam-232	98	6	)	)	PUNCT
ejpam-232	98	7	=	=	PUNCT
ejpam-232	99	1	−	−	PROPN
ejpam-232	99	2	f	f	X
ejpam-232	99	3	(	(	PUNCT
ejpam-232	99	4	g	g	NOUN
ejpam-232	99	5	)	)	PUNCT
ejpam-232	99	6	and	and	CCONJ
ejpam-232	99	7	f(h	f(h	PROPN
ejpam-232	99	8	)	)	PUNCT
ejpam-232	99	9	≤	≤	NOUN
ejpam-232	100	1	−	−	PROPN
ejpam-232	100	2	f	f	NOUN
ejpam-232	100	3	(	(	PUNCT
ejpam-232	100	4	h	h	NOUN
ejpam-232	100	5	)	)	PUNCT
ejpam-232	100	6	,	,	PUNCT
ejpam-232	100	7	(	(	PUNCT
ejpam-232	100	8	∀h∈	∀h∈	NOUN
ejpam-232	100	9	s	s	PROPN
ejpam-232	100	10	)	)	PUNCT
ejpam-232	100	11	.	.	PUNCT
ejpam-232	101	1	set	set	VERB
ejpam-232	101	2	g	g	PROPN
ejpam-232	101	3	=	=	SYM
ejpam-232	101	4	−f	−f	PROPN
ejpam-232	101	5	,	,	PUNCT
ejpam-232	101	6	then	then	ADV
ejpam-232	101	7	g(g	g(g	PROPN
ejpam-232	101	8	)	)	PUNCT
ejpam-232	102	1	=	=	SYM
ejpam-232	102	2	f	f	X
ejpam-232	102	3	(	(	PUNCT
ejpam-232	102	4	g	g	NOUN
ejpam-232	102	5	)	)	PUNCT
ejpam-232	102	6	and	and	CCONJ
ejpam-232	102	7	f	f	PROPN
ejpam-232	102	8	(	(	PUNCT
ejpam-232	102	9	h)≤	h)≤	PROPN
ejpam-232	102	10	g(h	g(h	PROPN
ejpam-232	102	11	)	)	PUNCT
ejpam-232	102	12	,	,	PUNCT
ejpam-232	102	13	(	(	PUNCT
ejpam-232	102	14	∀h	∀h	PROPN
ejpam-232	102	15	∈	∈	PROPN
ejpam-232	102	16	s	s	PART
ejpam-232	102	17	)	)	PUNCT
ejpam-232	102	18	.	.	PUNCT
ejpam-232	103	1	theorem	theorem	ADJ
ejpam-232	103	2	2	2	NUM
ejpam-232	103	3	.	.	NOUN
ejpam-232	103	4	corev	corev	PROPN
ejpam-232	103	5	6=	6=	NUM
ejpam-232	103	6	;	;	PUNCT
ejpam-232	103	7	if	if	SCONJ
ejpam-232	103	8	cav(u)(cω	cav(u)(cω	PROPN
ejpam-232	103	9	)	)	PUNCT
ejpam-232	103	10	=	=	VERB
ejpam-232	104	1	u(cω)(here	u(cω)(here	ADV
ejpam-232	104	2	,	,	PUNCT
ejpam-232	104	3	we	we	PRON
ejpam-232	104	4	have	have	AUX
ejpam-232	104	5	not	not	PART
ejpam-232	104	6	assumed	assume	VERB
ejpam-232	104	7	that	that	SCONJ
ejpam-232	104	8	the	the	DET
ejpam-232	104	9	elements	element	NOUN
ejpam-232	104	10	of	of	ADP
ejpam-232	104	11	core(v	core(v	NOUN
ejpam-232	104	12	)	)	PUNCT
ejpam-232	104	13	are	be	AUX
ejpam-232	104	14	bounded	bound	VERB
ejpam-232	104	15	)	)	PUNCT
ejpam-232	104	16	.	.	PUNCT
ejpam-232	105	1	proof	proof	NOUN
ejpam-232	105	2	.	.	PUNCT
ejpam-232	106	1	since	since	SCONJ
ejpam-232	106	2	cav(u	cav(u	PROPN
ejpam-232	106	3	)	)	PUNCT
ejpam-232	106	4	is	be	AUX
ejpam-232	106	5	a	a	DET
ejpam-232	106	6	concave	concave	NOUN
ejpam-232	106	7	map	map	NOUN
ejpam-232	106	8	,	,	PUNCT
ejpam-232	106	9	so	so	ADV
ejpam-232	106	10	from	from	ADP
ejpam-232	106	11	lemma	lemma	PROPN
ejpam-232	106	12	1	1	NUM
ejpam-232	106	13	,	,	PUNCT
ejpam-232	106	14	there	there	PRON
ejpam-232	106	15	is	be	VERB
ejpam-232	106	16	a	a	DET
ejpam-232	106	17	linear	linear	ADJ
ejpam-232	106	18	map	map	NOUN
ejpam-232	106	19	g	g	NOUN
ejpam-232	106	20	:	:	PUNCT
ejpam-232	106	21	s	s	X
ejpam-232	106	22	→	→	SYM
ejpam-232	106	23	r	r	NOUN
ejpam-232	106	24	such	such	ADJ
ejpam-232	106	25	that	that	DET
ejpam-232	106	26	cav(u)(cω	cav(u)(cω	NOUN
ejpam-232	106	27	)	)	PUNCT
ejpam-232	106	28	=	=	SYM
ejpam-232	106	29	g(cω	g(cω	PROPN
ejpam-232	106	30	)	)	PUNCT
ejpam-232	106	31	and	and	CCONJ
ejpam-232	106	32	cav(u)(cr	cav(u)(cr	NOUN
ejpam-232	106	33	)	)	PUNCT
ejpam-232	106	34	≤	≤	NOUN
ejpam-232	106	35	g(cr	g(cr	NOUN
ejpam-232	106	36	)	)	PUNCT
ejpam-232	106	37	.	.	PUNCT
ejpam-232	107	1	then	then	ADV
ejpam-232	107	2	g(cω	g(cω	PROPN
ejpam-232	107	3	)	)	PUNCT
ejpam-232	107	4	=	=	SYM
ejpam-232	107	5	u(cω	u(cω	ADJ
ejpam-232	107	6	)	)	PUNCT
ejpam-232	107	7	=	=	SYM
ejpam-232	107	8	v	v	X
ejpam-232	107	9	(	(	PUNCT
ejpam-232	107	10	ω	ω	NOUN
ejpam-232	107	11	)	)	PUNCT
ejpam-232	107	12	µ(ω	µ(ω	NOUN
ejpam-232	107	13	)	)	PUNCT
ejpam-232	107	14	and	and	CCONJ
ejpam-232	107	15	u(cr	u(cr	NOUN
ejpam-232	107	16	)	)	PUNCT
ejpam-232	107	17	≤	≤	NUM
ejpam-232	107	18	cav(u)(cr	cav(u)(cr	PART
ejpam-232	107	19	)	)	PUNCT
ejpam-232	107	20	≤	≤	NOUN
ejpam-232	107	21	g(cr	g(cr	NOUN
ejpam-232	107	22	)	)	PUNCT
ejpam-232	107	23	.	.	PUNCT
ejpam-232	108	1	define	define	VERB
ejpam-232	108	2	λ	λ	X
ejpam-232	108	3	:	:	PUNCT
ejpam-232	108	4	∑	∑	PUNCT
ejpam-232	108	5	→	→	SYM
ejpam-232	108	6	r	r	NOUN
ejpam-232	108	7	by	by	ADP
ejpam-232	108	8	λ(r	λ(r	NOUN
ejpam-232	108	9	)	)	PUNCT
ejpam-232	108	10	=	=	SYM
ejpam-232	108	11	g(χr	g(χr	PROPN
ejpam-232	108	12	)	)	PUNCT
ejpam-232	108	13	.	.	PUNCT
ejpam-232	109	1	it	it	PRON
ejpam-232	109	2	easy	easy	ADJ
ejpam-232	109	3	to	to	PART
ejpam-232	109	4	see	see	VERB
ejpam-232	109	5	that	that	SCONJ
ejpam-232	109	6	λ	λ	PROPN
ejpam-232	109	7	is	be	AUX
ejpam-232	109	8	a	a	DET
ejpam-232	109	9	finitely	finitely	ADV
ejpam-232	109	10	additive	additive	ADJ
ejpam-232	109	11	measure	measure	NOUN
ejpam-232	109	12	.	.	PUNCT
ejpam-232	110	1	moreover	moreover	ADV
ejpam-232	110	2	,	,	PUNCT
ejpam-232	110	3	λ(ω	λ(ω	PRON
ejpam-232	110	4	)	)	PUNCT
ejpam-232	110	5	=	=	SYM
ejpam-232	111	1	g(χω	g(χω	NOUN
ejpam-232	111	2	)	)	PUNCT
ejpam-232	111	3	=	=	SYM
ejpam-232	111	4	µ(ω)g	µ(ω)g	PROPN
ejpam-232	111	5	(	(	PUNCT
ejpam-232	111	6	χω	χω	ADV
ejpam-232	111	7	µ(ω	µ(ω	NOUN
ejpam-232	111	8	)	)	PUNCT
ejpam-232	111	9	)	)	PUNCT
ejpam-232	111	10	m.	m.	NOUN
ejpam-232	111	11	alimohammady	alimohammady	NOUN
ejpam-232	111	12	,	,	PUNCT
ejpam-232	111	13	v.	v.	CCONJ
ejpam-232	111	14	dadashi	dadashi	PROPN
ejpam-232	111	15	/	/	SYM
ejpam-232	111	16	eur	eur	PROPN
ejpam-232	111	17	.	.	PUNCT
ejpam-232	112	1	j.	j.	PROPN
ejpam-232	112	2	pure	pure	PROPN
ejpam-232	112	3	appl	appl	PROPN
ejpam-232	112	4	.	.	PROPN
ejpam-232	112	5	math	math	PROPN
ejpam-232	112	6	,	,	PUNCT
ejpam-232	112	7	3	3	NUM
ejpam-232	112	8	(	(	PUNCT
ejpam-232	112	9	2010	2010	NUM
ejpam-232	112	10	)	)	PUNCT
ejpam-232	112	11	,	,	PUNCT
ejpam-232	112	12	187	187	NUM
ejpam-232	112	13	-	-	SYM
ejpam-232	112	14	193	193	NUM
ejpam-232	112	15	191	191	NUM
ejpam-232	112	16	=	=	SYM
ejpam-232	112	17	µ(ω)g(cω	µ(ω)g(cω	ADJ
ejpam-232	112	18	)	)	PUNCT
ejpam-232	112	19	=	=	SYM
ejpam-232	112	20	µ(ω	µ(ω	X
ejpam-232	112	21	)	)	PUNCT
ejpam-232	112	22	v	v	ADP
ejpam-232	112	23	(	(	PUNCT
ejpam-232	112	24	ω	ω	NOUN
ejpam-232	112	25	)	)	PUNCT
ejpam-232	112	26	µ(ω	µ(ω	NOUN
ejpam-232	112	27	)	)	PUNCT
ejpam-232	112	28	=	=	SYM
ejpam-232	112	29	v	v	X
ejpam-232	112	30	(	(	PUNCT
ejpam-232	112	31	ω	ω	NOUN
ejpam-232	112	32	)	)	PUNCT
ejpam-232	112	33	.	.	PUNCT
ejpam-232	113	1	also	also	ADV
ejpam-232	113	2	λ(r	λ(r	X
ejpam-232	113	3	)	)	PUNCT
ejpam-232	113	4	=	=	SYM
ejpam-232	113	5	g(χr	g(χr	X
ejpam-232	113	6	)	)	PUNCT
ejpam-232	113	7	=	=	SYM
ejpam-232	114	1	µ(r)g	µ(r)g	PROPN
ejpam-232	114	2	(	(	PUNCT
ejpam-232	114	3	χr	χr	PROPN
ejpam-232	114	4	µ(r	µ(r	NOUN
ejpam-232	114	5	)	)	PUNCT
ejpam-232	114	6	)	)	PUNCT
ejpam-232	115	1	=	=	PUNCT
ejpam-232	115	2	µ(r)g(cr)≥	µ(r)g(cr)≥	NUM
ejpam-232	115	3	µ(r)u(cr	µ(r)u(cr	NOUN
ejpam-232	115	4	)	)	PUNCT
ejpam-232	115	5	=	=	PUNCT
ejpam-232	115	6	µ(r	µ(r	NOUN
ejpam-232	115	7	)	)	PUNCT
ejpam-232	115	8	v	v	NOUN
ejpam-232	115	9	(	(	PUNCT
ejpam-232	115	10	r	r	NOUN
ejpam-232	115	11	)	)	PUNCT
ejpam-232	115	12	µ(r	µ(r	NOUN
ejpam-232	115	13	)	)	PUNCT
ejpam-232	115	14	=	=	SYM
ejpam-232	115	15	v	v	X
ejpam-232	115	16	(	(	PUNCT
ejpam-232	115	17	r	r	NOUN
ejpam-232	115	18	)	)	PUNCT
ejpam-232	115	19	.	.	PUNCT
ejpam-232	116	1	therefore	therefore	ADV
ejpam-232	116	2	,	,	PUNCT
ejpam-232	116	3	λ	λ	PROPN
ejpam-232	116	4	∈	∈	NOUN
ejpam-232	116	5	core(v	core(v	PROPN
ejpam-232	116	6	)	)	PUNCT
ejpam-232	116	7	which	which	PRON
ejpam-232	116	8	it	it	PRON
ejpam-232	116	9	completes	complete	VERB
ejpam-232	116	10	the	the	DET
ejpam-232	116	11	proof	proof	NOUN
ejpam-232	116	12	.	.	PUNCT
ejpam-232	117	1	definition	definition	NOUN
ejpam-232	117	2	6	6	NUM
ejpam-232	117	3	.	.	PUNCT
ejpam-232	118	1	[	[	X
ejpam-232	118	2	4	4	X
ejpam-232	118	3	]	]	X
ejpam-232	118	4	a	a	DET
ejpam-232	118	5	game	game	NOUN
ejpam-232	118	6	v	v	NOUN
ejpam-232	118	7	is	be	AUX
ejpam-232	118	8	called	call	VERB
ejpam-232	118	9	an	an	DET
ejpam-232	118	10	exact	exact	ADJ
ejpam-232	118	11	game	game	NOUN
ejpam-232	118	12	if	if	SCONJ
ejpam-232	118	13	for	for	ADP
ejpam-232	118	14	each	each	DET
ejpam-232	118	15	coalition	coalition	NOUN
ejpam-232	118	16	r	r	NOUN
ejpam-232	118	17	there	there	PRON
ejpam-232	118	18	is	be	VERB
ejpam-232	118	19	λ	λ	PROPN
ejpam-232	118	20	∈	∈	NOUN
ejpam-232	118	21	core(v	core(v	PROPN
ejpam-232	118	22	)	)	PUNCT
ejpam-232	118	23	such	such	ADJ
ejpam-232	118	24	that	that	SCONJ
ejpam-232	118	25	λ(r	λ(r	NOUN
ejpam-232	118	26	)	)	PUNCT
ejpam-232	118	27	=	=	SYM
ejpam-232	118	28	v	v	NOUN
ejpam-232	118	29	(	(	PUNCT
ejpam-232	118	30	r	r	NOUN
ejpam-232	118	31	)	)	PUNCT
ejpam-232	118	32	.	.	PUNCT
ejpam-232	119	1	theorem	theorem	NOUN
ejpam-232	119	2	3	3	X
ejpam-232	119	3	.	.	PUNCT
ejpam-232	119	4	suppose	suppose	VERB
ejpam-232	119	5	v	v	NOUN
ejpam-232	119	6	is	be	AUX
ejpam-232	119	7	an	an	DET
ejpam-232	119	8	exact	exact	ADJ
ejpam-232	119	9	game	game	NOUN
ejpam-232	119	10	.	.	PUNCT
ejpam-232	120	1	then	then	ADV
ejpam-232	120	2	u	u	PRON
ejpam-232	120	3	is	be	AUX
ejpam-232	120	4	continuous	continuous	ADJ
ejpam-232	120	5	at	at	ADP
ejpam-232	120	6	cω	cω	NOUN
ejpam-232	120	7	if	if	SCONJ
ejpam-232	121	1	and	and	CCONJ
ejpam-232	121	2	only	only	ADV
ejpam-232	121	3	if	if	SCONJ
ejpam-232	121	4	each	each	DET
ejpam-232	121	5	λ	λ	PROPN
ejpam-232	121	6	∈	∈	NOUN
ejpam-232	121	7	core(v	core(v	PROPN
ejpam-232	121	8	)	)	PUNCT
ejpam-232	121	9	is	be	AUX
ejpam-232	121	10	countably	countably	ADV
ejpam-232	121	11	additive	additive	ADJ
ejpam-232	121	12	.	.	PUNCT
ejpam-232	122	1	proof	proof	NOUN
ejpam-232	122	2	.	.	PUNCT
ejpam-232	123	1	it	it	PRON
ejpam-232	123	2	is	be	AUX
ejpam-232	123	3	well	well	ADV
ejpam-232	123	4	known	know	VERB
ejpam-232	123	5	that	that	SCONJ
ejpam-232	123	6	λ	λ	PROPN
ejpam-232	123	7	∈	∈	PROPN
ejpam-232	123	8	ba	ba	PROPN
ejpam-232	123	9	is	be	AUX
ejpam-232	123	10	countably	countably	ADV
ejpam-232	123	11	additive	additive	ADJ
ejpam-232	123	12	if	if	SCONJ
ejpam-232	123	13	and	and	CCONJ
ejpam-232	123	14	only	only	ADV
ejpam-232	123	15	if	if	SCONJ
ejpam-232	123	16	it	it	PRON
ejpam-232	123	17	is	be	AUX
ejpam-232	123	18	continuous	continuous	ADJ
ejpam-232	123	19	at	at	ADP
ejpam-232	123	20	ω	ω	PROPN
ejpam-232	123	21	.	.	PUNCT
ejpam-232	124	1	assume	assume	VERB
ejpam-232	124	2	λ	λ	X
ejpam-232	124	3	∈	∈	PROPN
ejpam-232	124	4	core(v	core(v	PROPN
ejpam-232	124	5	)	)	PUNCT
ejpam-232	124	6	,	,	PUNCT
ejpam-232	124	7	u	u	NOUN
ejpam-232	124	8	is	be	AUX
ejpam-232	124	9	continuous	continuous	ADJ
ejpam-232	124	10	at	at	ADP
ejpam-232	124	11	cω	cω	NOUN
ejpam-232	124	12	and	and	CCONJ
ejpam-232	124	13	(	(	PUNCT
ejpam-232	124	14	rn)n	rn)n	PROPN
ejpam-232	124	15	is	be	AUX
ejpam-232	124	16	a	a	DET
ejpam-232	124	17	monotone	monotone	ADJ
ejpam-232	124	18	sequence	sequence	NOUN
ejpam-232	124	19	in	in	ADP
ejpam-232	124	20	ω	ω	NUM
ejpam-232	125	1	such	such	ADJ
ejpam-232	125	2	that	that	SCONJ
ejpam-232	125	3	⋃	⋃	PROPN
ejpam-232	125	4	rn	rn	PROPN
ejpam-232	125	5	=	=	PROPN
ejpam-232	125	6	ω	ω	PROPN
ejpam-232	125	7	.	.	PUNCT
ejpam-232	126	1	we	we	PRON
ejpam-232	126	2	must	must	AUX
ejpam-232	126	3	show	show	VERB
ejpam-232	126	4	that	that	SCONJ
ejpam-232	126	5	λ(rn	λ(rn	NOUN
ejpam-232	126	6	)	)	PUNCT
ejpam-232	126	7	→	→	SYM
ejpam-232	126	8	λ(ω	λ(ω	PROPN
ejpam-232	126	9	)	)	PUNCT
ejpam-232	126	10	.	.	PUNCT
ejpam-232	127	1	from	from	ADP
ejpam-232	127	2	the	the	DET
ejpam-232	127	3	assumption	assumption	NOUN
ejpam-232	127	4	u(crn	u(crn	PROPN
ejpam-232	127	5	)	)	PUNCT
ejpam-232	128	1	→	→	PUNCT
ejpam-232	128	2	u(cω	u(cω	NUM
ejpam-232	128	3	)	)	PUNCT
ejpam-232	128	4	.	.	PUNCT
ejpam-232	129	1	but	but	CCONJ
ejpam-232	129	2	u(crn	u(crn	ADJ
ejpam-232	129	3	)	)	PUNCT
ejpam-232	130	1	=	=	SYM
ejpam-232	130	2	v	v	X
ejpam-232	130	3	(	(	PUNCT
ejpam-232	130	4	rn	rn	NOUN
ejpam-232	130	5	)	)	PUNCT
ejpam-232	130	6	µ(rn	µ(rn	NOUN
ejpam-232	130	7	)	)	PUNCT
ejpam-232	130	8	≤	≤	NUM
ejpam-232	130	9	λ(rn	λ(rn	NOUN
ejpam-232	130	10	)	)	PUNCT
ejpam-232	130	11	µ(rn	µ(rn	NOUN
ejpam-232	130	12	)	)	PUNCT
ejpam-232	130	13	≤	≤	NUM
ejpam-232	130	14	λ(ω	λ(ω	PROPN
ejpam-232	130	15	)	)	PUNCT
ejpam-232	130	16	µ(rn	µ(rn	NOUN
ejpam-232	130	17	)	)	PUNCT
ejpam-232	130	18	=	=	SYM
ejpam-232	130	19	v	v	X
ejpam-232	130	20	(	(	PUNCT
ejpam-232	130	21	ω	ω	NOUN
ejpam-232	130	22	)	)	PUNCT
ejpam-232	130	23	µ(rn	µ(rn	NOUN
ejpam-232	130	24	)	)	PUNCT
ejpam-232	130	25	.	.	PUNCT
ejpam-232	131	1	tending	tend	VERB
ejpam-232	131	2	n	n	NOUN
ejpam-232	131	3	→	→	SYM
ejpam-232	131	4	∞	∞	PROPN
ejpam-232	131	5	and	and	CCONJ
ejpam-232	131	6	since	since	SCONJ
ejpam-232	131	7	u(crn	u(crn	PROPN
ejpam-232	131	8	)	)	PUNCT
ejpam-232	131	9	and	and	CCONJ
ejpam-232	131	10	v	v	X
ejpam-232	131	11	(	(	PUNCT
ejpam-232	131	12	ω	ω	NOUN
ejpam-232	131	13	)	)	PUNCT
ejpam-232	131	14	µ(rn	µ(rn	NOUN
ejpam-232	131	15	)	)	PUNCT
ejpam-232	131	16	→	→	SYM
ejpam-232	131	17	u(cω	u(cω	NUM
ejpam-232	131	18	)	)	PUNCT
ejpam-232	131	19	,	,	PUNCT
ejpam-232	131	20	so	so	ADV
ejpam-232	131	21	λ(rn	λ(rn	NOUN
ejpam-232	131	22	)	)	PUNCT
ejpam-232	131	23	µ(rn	µ(rn	NOUN
ejpam-232	131	24	)	)	PUNCT
ejpam-232	131	25	→	→	SYM
ejpam-232	131	26	u(cω	u(cω	ADJ
ejpam-232	131	27	)	)	PUNCT
ejpam-232	131	28	=	=	SYM
ejpam-232	131	29	v	v	X
ejpam-232	131	30	(	(	PUNCT
ejpam-232	131	31	ω	ω	NOUN
ejpam-232	131	32	)	)	PUNCT
ejpam-232	131	33	µ(ω	µ(ω	NOUN
ejpam-232	131	34	)	)	PUNCT
ejpam-232	131	35	.	.	PUNCT
ejpam-232	132	1	but	but	CCONJ
ejpam-232	132	2	µ	µ	X
ejpam-232	132	3	is	be	AUX
ejpam-232	132	4	a	a	DET
ejpam-232	132	5	measure	measure	NOUN
ejpam-232	132	6	so	so	SCONJ
ejpam-232	132	7	µ(rn	µ(rn	NOUN
ejpam-232	132	8	)	)	PUNCT
ejpam-232	132	9	→	→	SYM
ejpam-232	132	10	µ(ω	µ(ω	NOUN
ejpam-232	132	11	)	)	PUNCT
ejpam-232	132	12	.	.	PUNCT
ejpam-232	133	1	this	this	PRON
ejpam-232	133	2	shows	show	VERB
ejpam-232	133	3	that	that	SCONJ
ejpam-232	133	4	λ(rn	λ(rn	NOUN
ejpam-232	133	5	)	)	PUNCT
ejpam-232	133	6	→	→	SYM
ejpam-232	133	7	v	v	X
ejpam-232	133	8	(	(	PUNCT
ejpam-232	133	9	ω	ω	NOUN
ejpam-232	133	10	)	)	PUNCT
ejpam-232	133	11	=	=	SYM
ejpam-232	133	12	λ(ω	λ(ω	PROPN
ejpam-232	133	13	)	)	PUNCT
ejpam-232	133	14	.	.	PUNCT
ejpam-232	134	1	for	for	ADP
ejpam-232	134	2	the	the	DET
ejpam-232	134	3	converse	converse	NOUN
ejpam-232	134	4	,	,	PUNCT
ejpam-232	134	5	we	we	PRON
ejpam-232	134	6	assume	assume	VERB
ejpam-232	134	7	that	that	SCONJ
ejpam-232	134	8	λ	λ	PROPN
ejpam-232	134	9	∈	∈	PROPN
ejpam-232	134	10	corev	corev	NOUN
ejpam-232	134	11	is	be	AUX
ejpam-232	134	12	countably	countably	ADV
ejpam-232	134	13	additive	additive	ADJ
ejpam-232	134	14	,	,	PUNCT
ejpam-232	134	15	(	(	PUNCT
ejpam-232	134	16	rn	rn	NOUN
ejpam-232	134	17	)	)	PUNCT
ejpam-232	134	18	⊆	⊆	PROPN
ejpam-232	134	19	∑′	∑′	PROPN
ejpam-232	134	20	,	,	PUNCT
ejpam-232	134	21	⋃	⋃	PROPN
ejpam-232	134	22	rn	rn	PROPN
ejpam-232	134	23	=	=	PROPN
ejpam-232	134	24	ω	ω	PROPN
ejpam-232	134	25	and	and	CCONJ
ejpam-232	134	26	a	a	PRON
ejpam-232	134	27	is	be	AUX
ejpam-232	134	28	a	a	DET
ejpam-232	134	29	limit	limit	NOUN
ejpam-232	134	30	point	point	NOUN
ejpam-232	134	31	for	for	ADP
ejpam-232	134	32	(	(	PUNCT
ejpam-232	134	33	u(crn	u(crn	ADJ
ejpam-232	134	34	)	)	PUNCT
ejpam-232	134	35	)	)	PUNCT
ejpam-232	135	1	n.	n.	NOUN
ejpam-232	135	2	without	without	ADP
ejpam-232	135	3	loss	loss	NOUN
ejpam-232	135	4	of	of	ADP
ejpam-232	135	5	generality	generality	NOUN
ejpam-232	135	6	one	one	PRON
ejpam-232	135	7	can	can	AUX
ejpam-232	135	8	assume	assume	VERB
ejpam-232	135	9	that	that	SCONJ
ejpam-232	135	10	u(crn	u(crn	PROPN
ejpam-232	135	11	)	)	PUNCT
ejpam-232	135	12	→	→	SYM
ejpam-232	135	13	a	a	PRON
ejpam-232	135	14	(	(	PUNCT
ejpam-232	135	15	otherwise	otherwise	ADV
ejpam-232	135	16	we	we	PRON
ejpam-232	135	17	can	can	AUX
ejpam-232	135	18	pass	pass	VERB
ejpam-232	135	19	to	to	ADP
ejpam-232	135	20	a	a	DET
ejpam-232	135	21	subsequence	subsequence	NOUN
ejpam-232	135	22	)	)	PUNCT
ejpam-232	135	23	.	.	PUNCT
ejpam-232	136	1	from	from	ADP
ejpam-232	136	2	exactness	exactness	NOUN
ejpam-232	136	3	of	of	ADP
ejpam-232	136	4	v	v	NOUN
ejpam-232	136	5	for	for	ADP
ejpam-232	136	6	each	each	DET
ejpam-232	136	7	rn	rn	PROPN
ejpam-232	136	8	there	there	PRON
ejpam-232	136	9	is	be	VERB
ejpam-232	136	10	λn	λn	PROPN
ejpam-232	136	11	∈	∈	PROPN
ejpam-232	136	12	corev	corev	NOUN
ejpam-232	136	13	such	such	ADJ
ejpam-232	136	14	that	that	DET
ejpam-232	136	15	λn(rn	λn(rn	PROPN
ejpam-232	136	16	)	)	PUNCT
ejpam-232	137	1	=	=	SYM
ejpam-232	137	2	v	v	X
ejpam-232	137	3	(	(	PUNCT
ejpam-232	137	4	rn	rn	NOUN
ejpam-232	137	5	)	)	PUNCT
ejpam-232	137	6	.	.	PUNCT
ejpam-232	138	1	from	from	ADP
ejpam-232	138	2	the	the	DET
ejpam-232	138	3	compactness	compactness	NOUN
ejpam-232	138	4	of	of	ADP
ejpam-232	138	5	core(v	core(v	NOUN
ejpam-232	138	6	)	)	PUNCT
ejpam-232	138	7	,	,	PUNCT
ejpam-232	138	8	one	one	PRON
ejpam-232	138	9	can	can	AUX
ejpam-232	138	10	assume	assume	VERB
ejpam-232	138	11	λn	λn	PROPN
ejpam-232	138	12	→	→	SYM
ejpam-232	138	13	λ	λ	PROPN
ejpam-232	138	14	,	,	PUNCT
ejpam-232	138	15	where	where	SCONJ
ejpam-232	138	16	λ	λ	PROPN
ejpam-232	138	17	∈	∈	PROPN
ejpam-232	138	18	corev	corev	NOUN
ejpam-232	138	19	.	.	PUNCT
ejpam-232	139	1	assume	assume	VERB
ejpam-232	139	2	ε	ε	PROPN
ejpam-232	139	3	>	>	X
ejpam-232	139	4	0	0	PROPN
ejpam-232	139	5	,	,	PUNCT
ejpam-232	139	6	there	there	PRON
ejpam-232	139	7	is	be	VERB
ejpam-232	139	8	k	k	PROPN
ejpam-232	139	9	∈	∈	PROPN
ejpam-232	139	10	n	n	X
ejpam-232	139	11	satisfying	satisfy	VERB
ejpam-232	139	12	in	in	ADP
ejpam-232	139	13	λ(rn	λ(rn	NOUN
ejpam-232	139	14	)	)	PUNCT
ejpam-232	139	15	>	>	X
ejpam-232	140	1	λ(ω)−	λ(ω)−	NOUN
ejpam-232	140	2	εµ(ω	εµ(ω	NUM
ejpam-232	140	3	)	)	PUNCT
ejpam-232	140	4	for	for	ADP
ejpam-232	140	5	any	any	DET
ejpam-232	140	6	n	n	DET
ejpam-232	140	7	≥	≥	NOUN
ejpam-232	140	8	k.	k.	X
ejpam-232	141	1	there	there	PRON
ejpam-232	141	2	is	be	VERB
ejpam-232	141	3	m′	m′	NUM
ejpam-232	141	4	∈	∈	NOUN
ejpam-232	141	5	n	n	PRON
ejpam-232	141	6	such	such	ADJ
ejpam-232	141	7	that	that	SCONJ
ejpam-232	141	8	|λm(rn)−	|λm(rn)−	X
ejpam-232	141	9	λ(rn)|	λ(rn)|	X
ejpam-232	141	10	<	<	X
ejpam-232	141	11	ε	ε	PROPN
ejpam-232	141	12	and	and	CCONJ
ejpam-232	141	13	so	so	ADV
ejpam-232	141	14	λ(rn	λ(rn	NOUN
ejpam-232	141	15	)	)	PUNCT
ejpam-232	141	16	<	<	X
ejpam-232	141	17	λm(rn	λm(rn	PROPN
ejpam-232	141	18	)	)	PUNCT
ejpam-232	142	1	+	+	CCONJ
ejpam-232	143	1	ε	ε	PROPN
ejpam-232	143	2	for	for	ADP
ejpam-232	143	3	each	each	DET
ejpam-232	143	4	m	m	PROPN
ejpam-232	143	5	≥	≥	NOUN
ejpam-232	143	6	m′.	m′.	PROPN
ejpam-232	143	7	consider	consider	VERB
ejpam-232	143	8	n	n	DET
ejpam-232	143	9	≥	≥	NOUN
ejpam-232	143	10	k	k	NOUN
ejpam-232	143	11	and	and	CCONJ
ejpam-232	143	12	l′	l′	VERB
ejpam-232	143	13	≥	≥	NOUN
ejpam-232	143	14	max{n	max{n	ADJ
ejpam-232	143	15	,	,	PUNCT
ejpam-232	143	16	m′	m′	NUM
ejpam-232	143	17	}	}	PUNCT
ejpam-232	143	18	,	,	PUNCT
ejpam-232	143	19	now	now	ADV
ejpam-232	143	20	for	for	ADP
ejpam-232	143	21	each	each	DET
ejpam-232	143	22	l	l	NOUN
ejpam-232	143	23	≥	≥	NOUN
ejpam-232	143	24	l′	l′	NOUN
ejpam-232	143	25	,	,	PUNCT
ejpam-232	143	26	u(cω	u(cω	NOUN
ejpam-232	143	27	)	)	PUNCT
ejpam-232	143	28	=	=	SYM
ejpam-232	143	29	v	v	X
ejpam-232	143	30	(	(	PUNCT
ejpam-232	143	31	ω	ω	NOUN
ejpam-232	143	32	)	)	PUNCT
ejpam-232	143	33	µ(ω	µ(ω	NOUN
ejpam-232	143	34	)	)	PUNCT
ejpam-232	143	35	=	=	PUNCT
ejpam-232	143	36	λ(ω	λ(ω	PROPN
ejpam-232	143	37	)	)	PUNCT
ejpam-232	143	38	µ(ω	µ(ω	NOUN
ejpam-232	143	39	)	)	PUNCT
ejpam-232	143	40	<	<	X
ejpam-232	143	41	λ(rn	λ(rn	PROPN
ejpam-232	143	42	)	)	PUNCT
ejpam-232	143	43	+	+	NUM
ejpam-232	143	44	εµ(ω	εµ(ω	NUM
ejpam-232	143	45	)	)	PUNCT
ejpam-232	143	46	µ(ω	µ(ω	NOUN
ejpam-232	143	47	)	)	PUNCT
ejpam-232	143	48	=	=	SYM
ejpam-232	143	49	λ(rn	λ(rn	PROPN
ejpam-232	143	50	)	)	PUNCT
ejpam-232	143	51	µ(ω	µ(ω	NOUN
ejpam-232	143	52	)	)	PUNCT
ejpam-232	144	1	+	+	CCONJ
ejpam-232	144	2	ε	ε	PROPN
ejpam-232	144	3	<	<	X
ejpam-232	144	4	λl(rn	λl(rn	PROPN
ejpam-232	144	5	)	)	PUNCT
ejpam-232	144	6	µ(ω	µ(ω	NOUN
ejpam-232	144	7	)	)	PUNCT
ejpam-232	145	1	+	+	NUM
ejpam-232	145	2	2ε	2ε	NOUN
ejpam-232	145	3	≤	≤	PUNCT
ejpam-232	145	4	λl(rl	λl(rl	PROPN
ejpam-232	145	5	)	)	PUNCT
ejpam-232	145	6	µ(ω	µ(ω	NOUN
ejpam-232	145	7	)	)	PUNCT
ejpam-232	146	1	+	+	CCONJ
ejpam-232	146	2	2ε=	2ε=	NUM
ejpam-232	146	3	v	v	NOUN
ejpam-232	146	4	(	(	PUNCT
ejpam-232	146	5	rl	rl	NOUN
ejpam-232	146	6	)	)	PUNCT
ejpam-232	146	7	µ(ω	µ(ω	NOUN
ejpam-232	146	8	)	)	PUNCT
ejpam-232	147	1	+	+	NUM
ejpam-232	147	2	2ε	2ε	NOUN
ejpam-232	147	3	≤	≤	NOUN
ejpam-232	147	4	v	v	NOUN
ejpam-232	147	5	(	(	PUNCT
ejpam-232	147	6	rl	rl	NOUN
ejpam-232	147	7	)	)	PUNCT
ejpam-232	147	8	µ(rl	µ(rl	NOUN
ejpam-232	147	9	)	)	PUNCT
ejpam-232	147	10	+	+	CCONJ
ejpam-232	148	1	2ε=	2ε=	NUM
ejpam-232	148	2	u(cl)+	u(cl)+	PROPN
ejpam-232	148	3	2ε	2ε	NOUN
ejpam-232	148	4	=	=	SYM
ejpam-232	148	5	a+	a+	PUNCT
ejpam-232	148	6	2ε	2ε	NUM
ejpam-232	148	7	.	.	PUNCT
ejpam-232	149	1	m.	m.	NOUN
ejpam-232	149	2	alimohammady	alimohammady	PROPN
ejpam-232	149	3	,	,	PUNCT
ejpam-232	149	4	v.	v.	CCONJ
ejpam-232	149	5	dadashi	dadashi	PROPN
ejpam-232	149	6	/	/	SYM
ejpam-232	149	7	eur	eur	PROPN
ejpam-232	149	8	.	.	PUNCT
ejpam-232	150	1	j.	j.	PROPN
ejpam-232	150	2	pure	pure	PROPN
ejpam-232	150	3	appl	appl	PROPN
ejpam-232	150	4	.	.	PROPN
ejpam-232	150	5	math	math	PROPN
ejpam-232	150	6	,	,	PUNCT
ejpam-232	150	7	3	3	NUM
ejpam-232	150	8	(	(	PUNCT
ejpam-232	150	9	2010	2010	NUM
ejpam-232	150	10	)	)	PUNCT
ejpam-232	150	11	,	,	PUNCT
ejpam-232	150	12	187	187	NUM
ejpam-232	150	13	-	-	SYM
ejpam-232	150	14	193	193	NUM
ejpam-232	150	15	192	192	NUM
ejpam-232	150	16	therefore	therefore	ADV
ejpam-232	150	17	,	,	PUNCT
ejpam-232	150	18	u(cω	u(cω	NOUN
ejpam-232	150	19	)	)	PUNCT
ejpam-232	150	20	≤	≤	NUM
ejpam-232	150	21	a.	a.	NOUN
ejpam-232	150	22	on	on	ADP
ejpam-232	150	23	the	the	DET
ejpam-232	150	24	other	other	ADJ
ejpam-232	150	25	hand	hand	NOUN
ejpam-232	150	26	,	,	PUNCT
ejpam-232	150	27	u(crn	u(crn	ADJ
ejpam-232	150	28	)	)	PUNCT
ejpam-232	151	1	=	=	SYM
ejpam-232	151	2	v	v	X
ejpam-232	151	3	(	(	PUNCT
ejpam-232	151	4	rn	rn	NOUN
ejpam-232	151	5	)	)	PUNCT
ejpam-232	151	6	µ(rn	µ(rn	NOUN
ejpam-232	151	7	)	)	PUNCT
ejpam-232	151	8	≤	≤	NUM
ejpam-232	151	9	λ(rn	λ(rn	NOUN
ejpam-232	151	10	)	)	PUNCT
ejpam-232	151	11	µ(rn	µ(rn	NOUN
ejpam-232	151	12	)	)	PUNCT
ejpam-232	151	13	≤	≤	NUM
ejpam-232	151	14	λ(ω	λ(ω	PROPN
ejpam-232	151	15	)	)	PUNCT
ejpam-232	151	16	µ(rn	µ(rn	NOUN
ejpam-232	151	17	)	)	PUNCT
ejpam-232	151	18	.	.	PUNCT
ejpam-232	152	1	let	let	VERB
ejpam-232	152	2	n	n	PRON
ejpam-232	152	3	→∞	→∞	NOUN
ejpam-232	152	4	,	,	PUNCT
ejpam-232	152	5	then	then	ADV
ejpam-232	152	6	a	a	DET
ejpam-232	152	7	≤	≤	NUM
ejpam-232	152	8	λ(ω	λ(ω	PROPN
ejpam-232	152	9	)	)	PUNCT
ejpam-232	152	10	µ(ω	µ(ω	NOUN
ejpam-232	152	11	)	)	PUNCT
ejpam-232	152	12	=	=	SYM
ejpam-232	152	13	v	v	X
ejpam-232	152	14	(	(	PUNCT
ejpam-232	152	15	ω	ω	NOUN
ejpam-232	152	16	)	)	PUNCT
ejpam-232	152	17	µ(ω	µ(ω	NOUN
ejpam-232	152	18	)	)	PUNCT
ejpam-232	152	19	=	=	SYM
ejpam-232	152	20	u(cω	u(cω	NOUN
ejpam-232	152	21	)	)	PUNCT
ejpam-232	152	22	.	.	PUNCT
ejpam-232	153	1	hence	hence	ADV
ejpam-232	153	2	,	,	PUNCT
ejpam-232	153	3	a	a	DET
ejpam-232	153	4	=	=	X
ejpam-232	153	5	u(cω	u(cω	NOUN
ejpam-232	153	6	)	)	PUNCT
ejpam-232	153	7	.	.	PUNCT
ejpam-232	154	1	set	set	VERB
ejpam-232	154	2	bar	bar	NOUN
ejpam-232	154	3	=	=	SYM
ejpam-232	154	4	{	{	PUNCT
ejpam-232	154	5	λ	λ	X
ejpam-232	154	6	∈	∈	PROPN
ejpam-232	154	7	ba	ba	PROPN
ejpam-232	154	8	,	,	PUNCT
ejpam-232	154	9	λ(r	λ(r	X
ejpam-232	154	10	)	)	PUNCT
ejpam-232	154	11	=	=	SYM
ejpam-232	154	12	v	v	NOUN
ejpam-232	154	13	(	(	PUNCT
ejpam-232	154	14	r	r	NOUN
ejpam-232	154	15	)	)	PUNCT
ejpam-232	154	16	}	}	PUNCT
ejpam-232	154	17	.	.	PUNCT
ejpam-232	155	1	then	then	ADV
ejpam-232	155	2	if	if	SCONJ
ejpam-232	155	3	λ	λ	PROPN
ejpam-232	155	4	∈	∈	PROPN
ejpam-232	155	5	bar	bar	NOUN
ejpam-232	155	6	we	we	PRON
ejpam-232	155	7	can	can	AUX
ejpam-232	155	8	define	define	VERB
ejpam-232	155	9	fλ(g	fλ(g	PUNCT
ejpam-232	155	10	)	)	PUNCT
ejpam-232	155	11	=	=	SYM
ejpam-232	155	12	∫	∫	PROPN
ejpam-232	155	13	ω	ω	NUM
ejpam-232	155	14	gdλ	gdλ	PROPN
ejpam-232	155	15	.	.	PUNCT
ejpam-232	156	1	so	so	ADV
ejpam-232	156	2	we	we	PRON
ejpam-232	156	3	define	define	VERB
ejpam-232	156	4	corerv	corerv	NOUN
ejpam-232	156	5	=	=	PUNCT
ejpam-232	156	6	{	{	PUNCT
ejpam-232	156	7	λ	λ	X
ejpam-232	156	8	∈	∈	NOUN
ejpam-232	156	9	core(v	core(v	PROPN
ejpam-232	156	10	)	)	PUNCT
ejpam-232	156	11	;	;	PUNCT
ejpam-232	156	12	λ(r	λ(r	X
ejpam-232	156	13	)	)	PUNCT
ejpam-232	156	14	=	=	SYM
ejpam-232	156	15	v	v	NOUN
ejpam-232	156	16	(	(	PUNCT
ejpam-232	156	17	r	r	NOUN
ejpam-232	156	18	)	)	PUNCT
ejpam-232	156	19	}	}	PUNCT
ejpam-232	156	20	.	.	PUNCT
ejpam-232	157	1	lemma	lemma	PROPN
ejpam-232	157	2	4	4	X
ejpam-232	157	3	.	.	PUNCT
ejpam-232	157	4	bar	bar	PROPN
ejpam-232	157	5	6=	6=	NUM
ejpam-232	157	6	;	;	PUNCT
ejpam-232	157	7	if	if	SCONJ
ejpam-232	157	8	r	r	NOUN
ejpam-232	157	9	∈	∈	PROPN
ejpam-232	157	10	∑	∑	PUNCT
ejpam-232	157	11	and	and	CCONJ
ejpam-232	157	12	r	r	PROPN
ejpam-232	157	13	6=	6=	NUM
ejpam-232	157	14	;	;	PUNCT
ejpam-232	157	15	.	.	PUNCT
ejpam-232	158	1	proof	proof	NOUN
ejpam-232	158	2	.	.	PUNCT
ejpam-232	159	1	it	it	PRON
ejpam-232	159	2	is	be	AUX
ejpam-232	159	3	easy	easy	ADJ
ejpam-232	159	4	to	to	PART
ejpam-232	159	5	see	see	VERB
ejpam-232	159	6	that	that	SCONJ
ejpam-232	159	7	,	,	PUNCT
ejpam-232	159	8	there	there	PRON
ejpam-232	159	9	is	be	VERB
ejpam-232	159	10	λ0	λ0	NOUN
ejpam-232	159	11	∈	∈	PROPN
ejpam-232	159	12	ba	ba	NOUN
ejpam-232	159	13	,	,	PUNCT
ejpam-232	159	14	such	such	ADJ
ejpam-232	159	15	that	that	PRON
ejpam-232	159	16	λ0(s	λ0(s	PROPN
ejpam-232	159	17	)	)	PUNCT
ejpam-232	159	18	6=	6=	ADP
ejpam-232	159	19	0	0	X
ejpam-232	159	20	.	.	PUNCT
ejpam-232	160	1	set	set	VERB
ejpam-232	160	2	λ	λ	PROPN
ejpam-232	160	3	=	=	SYM
ejpam-232	160	4	v	v	X
ejpam-232	160	5	(	(	PUNCT
ejpam-232	160	6	s	s	NOUN
ejpam-232	160	7	)	)	PUNCT
ejpam-232	160	8	λ0(s	λ0(s	NOUN
ejpam-232	160	9	)	)	PUNCT
ejpam-232	160	10	λ0	λ0	NOUN
ejpam-232	160	11	.	.	PUNCT
ejpam-232	161	1	then	then	ADV
ejpam-232	161	2	λ	λ	PROPN
ejpam-232	161	3	∈	∈	PROPN
ejpam-232	161	4	bar	bar	NOUN
ejpam-232	161	5	.	.	PUNCT
ejpam-232	162	1	lemma	lemma	PROPN
ejpam-232	162	2	5	5	NUM
ejpam-232	162	3	.	.	PUNCT
ejpam-232	163	1	(	(	PUNCT
ejpam-232	163	2	a	a	X
ejpam-232	163	3	)	)	PUNCT
ejpam-232	163	4	let	let	VERB
ejpam-232	163	5	λ	λ	X
ejpam-232	163	6	∈	∈	PROPN
ejpam-232	163	7	bar	bar	NOUN
ejpam-232	163	8	and	and	CCONJ
ejpam-232	163	9	fλ	fλ	ADJ
ejpam-232	163	10	:	:	PUNCT
ejpam-232	163	11	△	△	NOUN
ejpam-232	163	12	→	→	SYM
ejpam-232	163	13	r	r	NOUN
ejpam-232	163	14	by	by	X
ejpam-232	163	15	fλ(g	fλ(g	NOUN
ejpam-232	163	16	)	)	PUNCT
ejpam-232	164	1	=	=	SYM
ejpam-232	164	2	∫	∫	PROPN
ejpam-232	164	3	ω	ω	NUM
ejpam-232	164	4	gdλ	gdλ	PROPN
ejpam-232	164	5	.	.	PUNCT
ejpam-232	165	1	then	then	ADV
ejpam-232	165	2	fλ(cr	fλ(cr	VERB
ejpam-232	165	3	)	)	PUNCT
ejpam-232	166	1	=	=	SYM
ejpam-232	166	2	u(cr	u(cr	PROPN
ejpam-232	166	3	)	)	PUNCT
ejpam-232	166	4	.	.	PUNCT
ejpam-232	167	1	(	(	PUNCT
ejpam-232	167	2	b	b	X
ejpam-232	167	3	)	)	PUNCT
ejpam-232	167	4	let	let	VERB
ejpam-232	167	5	λ	λ	X
ejpam-232	167	6	∈	∈	PROPN
ejpam-232	167	7	corer(v	corer(v	PROPN
ejpam-232	167	8	)	)	PUNCT
ejpam-232	167	9	,	,	PUNCT
ejpam-232	167	10	then	then	ADV
ejpam-232	167	11	fλ(cr	fλ(cr	PUNCT
ejpam-232	167	12	)	)	PUNCT
ejpam-232	168	1	=	=	SYM
ejpam-232	168	2	u(cr	u(cr	PROPN
ejpam-232	168	3	)	)	PUNCT
ejpam-232	168	4	and	and	CCONJ
ejpam-232	168	5	fλ(cs)≥	fλ(cs)≥	ADJ
ejpam-232	168	6	u(cs	u(cs	NOUN
ejpam-232	168	7	)	)	PUNCT
ejpam-232	168	8	,	,	PUNCT
ejpam-232	168	9	(	(	PUNCT
ejpam-232	168	10	∀s	∀s	PROPN
ejpam-232	168	11	∈	∈	PROPN
ejpam-232	168	12	∑	∑	PUNCT
ejpam-232	168	13	)	)	PUNCT
ejpam-232	168	14	.	.	PUNCT
ejpam-232	169	1	proof	proof	NOUN
ejpam-232	169	2	.	.	PUNCT
ejpam-232	170	1	(	(	PUNCT
ejpam-232	170	2	a	a	X
ejpam-232	170	3	)	)	PUNCT
ejpam-232	170	4	fλ(cr	fλ(cr	NOUN
ejpam-232	170	5	)	)	PUNCT
ejpam-232	171	1	=	=	SYM
ejpam-232	171	2	∫	∫	PROPN
ejpam-232	172	1	ω	ω	NUM
ejpam-232	172	2	crdλ=	crdλ=	PUNCT
ejpam-232	172	3	λ(r	λ(r	NOUN
ejpam-232	172	4	)	)	PUNCT
ejpam-232	172	5	µ(r	µ(r	NOUN
ejpam-232	172	6	)	)	PUNCT
ejpam-232	172	7	=	=	SYM
ejpam-232	172	8	v	v	X
ejpam-232	172	9	(	(	PUNCT
ejpam-232	172	10	r	r	NOUN
ejpam-232	172	11	)	)	PUNCT
ejpam-232	172	12	µ(r	µ(r	NOUN
ejpam-232	172	13	)	)	PUNCT
ejpam-232	172	14	=	=	SYM
ejpam-232	172	15	u(cr	u(cr	PROPN
ejpam-232	172	16	)	)	PUNCT
ejpam-232	172	17	.	.	PUNCT
ejpam-232	173	1	(	(	PUNCT
ejpam-232	173	2	b	b	X
ejpam-232	173	3	)	)	PUNCT
ejpam-232	173	4	it	it	PRON
ejpam-232	173	5	is	be	AUX
ejpam-232	173	6	similar	similar	ADJ
ejpam-232	173	7	to	to	ADP
ejpam-232	173	8	(	(	PUNCT
ejpam-232	173	9	a	a	PRON
ejpam-232	173	10	)	)	PUNCT
ejpam-232	173	11	fλ(cr	fλ(cr	NOUN
ejpam-232	173	12	)	)	PUNCT
ejpam-232	174	1	=	=	SYM
ejpam-232	174	2	u(cr	u(cr	PROPN
ejpam-232	174	3	)	)	PUNCT
ejpam-232	174	4	.	.	PUNCT
ejpam-232	175	1	for	for	ADP
ejpam-232	175	2	an	an	DET
ejpam-232	175	3	arbitrary	arbitrary	ADJ
ejpam-232	175	4	element	element	NOUN
ejpam-232	175	5	s	s	PART
ejpam-232	175	6	∈	∈	PROPN
ejpam-232	175	7	∑	∑	PUNCT
ejpam-232	175	8	,	,	PUNCT
ejpam-232	175	9	fλ(cs	fλ(cs	PROPN
ejpam-232	175	10	)	)	PUNCT
ejpam-232	175	11	=	=	SYM
ejpam-232	175	12	∫	∫	PROPN
ejpam-232	175	13	ω	ω	PROPN
ejpam-232	175	14	csdλ=	csdλ=	NUM
ejpam-232	175	15	λ(s	λ(s	PROPN
ejpam-232	175	16	)	)	PUNCT
ejpam-232	175	17	µ(s	µ(s	X
ejpam-232	175	18	)	)	PUNCT
ejpam-232	175	19	≥	≥	NUM
ejpam-232	175	20	v	v	NOUN
ejpam-232	175	21	(	(	PUNCT
ejpam-232	175	22	s	s	NOUN
ejpam-232	175	23	)	)	PUNCT
ejpam-232	175	24	µ(s	µ(	NOUN
ejpam-232	175	25	)	)	PUNCT
ejpam-232	175	26	=	=	PUNCT
ejpam-232	175	27	u(cs	u(cs	NOUN
ejpam-232	175	28	)	)	PUNCT
ejpam-232	175	29	.	.	PUNCT
ejpam-232	175	30	theorem	theorem	ADJ
ejpam-232	175	31	4	4	NUM
ejpam-232	175	32	.	.	PUNCT
ejpam-232	175	33	suppose	suppose	VERB
ejpam-232	175	34	that	that	SCONJ
ejpam-232	175	35	v	v	NOUN
ejpam-232	175	36	is	be	AUX
ejpam-232	175	37	an	an	DET
ejpam-232	175	38	exact	exact	ADJ
ejpam-232	175	39	game	game	NOUN
ejpam-232	175	40	.	.	PUNCT
ejpam-232	176	1	then	then	ADV
ejpam-232	176	2	u	u	PROPN
ejpam-232	176	3	=	=	PROPN
ejpam-232	176	4	inf	inf	PROPN
ejpam-232	176	5	{	{	PUNCT
ejpam-232	176	6	fλ	fλ	NOUN
ejpam-232	176	7	:	:	PUNCT
ejpam-232	176	8	λ	λ	PROPN
ejpam-232	176	9	∈	∈	NOUN
ejpam-232	176	10	corerv	corerv	NOUN
ejpam-232	176	11	,	,	PUNCT
ejpam-232	176	12	r	r	NOUN
ejpam-232	176	13	∈	∈	PROPN
ejpam-232	176	14	∑	∑	PUNCT
ejpam-232	176	15	}	}	PUNCT
ejpam-232	176	16	.	.	PUNCT
ejpam-232	177	1	proof	proof	NOUN
ejpam-232	177	2	.	.	PUNCT
ejpam-232	178	1	for	for	ADP
ejpam-232	178	2	each	each	DET
ejpam-232	178	3	λ	λ	PROPN
ejpam-232	178	4	∈	∈	PROPN
ejpam-232	178	5	corerv	corerv	NOUN
ejpam-232	178	6	,	,	PUNCT
ejpam-232	178	7	then	then	ADV
ejpam-232	178	8	fλ(cr	fλ(cr	PROPN
ejpam-232	178	9	)	)	PUNCT
ejpam-232	178	10	≥	≥	NOUN
ejpam-232	178	11	u(cr	u(cr	PROPN
ejpam-232	178	12	)	)	PUNCT
ejpam-232	178	13	.	.	PUNCT
ejpam-232	179	1	therefore	therefore	ADV
ejpam-232	179	2	,	,	PUNCT
ejpam-232	179	3	inf	inf	PROPN
ejpam-232	179	4	{	{	PUNCT
ejpam-232	179	5	fλ	fλ	INTJ
ejpam-232	179	6	:	:	PUNCT
ejpam-232	179	7	λ	λ	X
ejpam-232	179	8	∈	∈	PROPN
ejpam-232	179	9	corer(v	corer(v	PROPN
ejpam-232	179	10	)	)	PUNCT
ejpam-232	179	11	,	,	PUNCT
ejpam-232	179	12	r	r	NOUN
ejpam-232	179	13	∈	∈	PROPN
ejpam-232	179	14	∑	∑	PUNCT
ejpam-232	179	15	}	}	PUNCT
ejpam-232	179	16	≥	≥	X
ejpam-232	179	17	u.	u.	NOUN
ejpam-232	179	18	since	since	SCONJ
ejpam-232	179	19	v	v	NUM
ejpam-232	179	20	is	be	AUX
ejpam-232	179	21	an	an	DET
ejpam-232	179	22	exact	exact	ADJ
ejpam-232	179	23	game	game	NOUN
ejpam-232	179	24	so	so	ADV
ejpam-232	179	25	for	for	ADP
ejpam-232	179	26	each	each	DET
ejpam-232	179	27	r	r	NOUN
ejpam-232	179	28	∈	∈	PROPN
ejpam-232	179	29	∑	∑	PUNCT
ejpam-232	179	30	,	,	PUNCT
ejpam-232	179	31	there	there	PRON
ejpam-232	179	32	is	be	VERB
ejpam-232	179	33	a	a	DET
ejpam-232	179	34	λ	λ	PROPN
ejpam-232	179	35	∈	∈	PROPN
ejpam-232	179	36	corer(v	corer(v	PROPN
ejpam-232	179	37	)	)	PUNCT
ejpam-232	179	38	.	.	PUNCT
ejpam-232	180	1	it	it	PRON
ejpam-232	180	2	follows	follow	VERB
ejpam-232	180	3	by	by	ADP
ejpam-232	180	4	lemma	lemma	PROPN
ejpam-232	180	5	3	3	NUM
ejpam-232	180	6	fλ(cr	fλ(cr	PROPN
ejpam-232	180	7	)	)	PUNCT
ejpam-232	181	1	=	=	SYM
ejpam-232	181	2	u(cr	u(cr	PROPN
ejpam-232	181	3	)	)	PUNCT
ejpam-232	181	4	.	.	PUNCT
ejpam-232	182	1	hence	hence	ADV
ejpam-232	182	2	,	,	PUNCT
ejpam-232	182	3	u	u	PROPN
ejpam-232	182	4	=	=	PROPN
ejpam-232	182	5	inf	inf	PROPN
ejpam-232	182	6	{	{	PUNCT
ejpam-232	182	7	fλ	fλ	INTJ
ejpam-232	182	8	:	:	PUNCT
ejpam-232	182	9	λ	λ	X
ejpam-232	182	10	∈	∈	PROPN
ejpam-232	182	11	corer(v	corer(v	PROPN
ejpam-232	182	12	)	)	PUNCT
ejpam-232	182	13	,	,	PUNCT
ejpam-232	182	14	r	r	NOUN
ejpam-232	182	15	∈	∈	PROPN
ejpam-232	182	16	∑	∑	PUNCT
ejpam-232	182	17	}	}	PUNCT
ejpam-232	182	18	.	.	PUNCT
ejpam-232	183	1	theorem	theorem	NOUN
ejpam-232	183	2	5	5	NUM
ejpam-232	183	3	.	.	PUNCT
ejpam-232	184	1	let	let	VERB
ejpam-232	184	2	u	u	PRON
ejpam-232	184	3	=	=	PROPN
ejpam-232	184	4	inf	inf	PROPN
ejpam-232	184	5	{	{	PUNCT
ejpam-232	184	6	fλ	fλ	X
ejpam-232	184	7	:	:	PUNCT
ejpam-232	184	8	s	s	X
ejpam-232	184	9	∈	∈	PROPN
ejpam-232	184	10	∑	∑	PUNCT
ejpam-232	184	11	,	,	PUNCT
ejpam-232	184	12	λ	λ	PROPN
ejpam-232	184	13	∈	∈	PROPN
ejpam-232	184	14	bas	bas	X
ejpam-232	184	15	,	,	PUNCT
ejpam-232	184	16	λ(ω	λ(ω	PRON
ejpam-232	184	17	)	)	PUNCT
ejpam-232	185	1	=	=	SYM
ejpam-232	185	2	v	v	X
ejpam-232	185	3	(	(	PUNCT
ejpam-232	185	4	ω	ω	NOUN
ejpam-232	185	5	)	)	PUNCT
ejpam-232	185	6	}	}	PUNCT
ejpam-232	185	7	.	.	PUNCT
ejpam-232	186	1	then	then	ADV
ejpam-232	186	2	the	the	DET
ejpam-232	186	3	equation	equation	NOUN
ejpam-232	186	4	∑	∑	ADV
ejpam-232	186	5	αrcr	αrcr	ADV
ejpam-232	186	6	=	=	SYM
ejpam-232	186	7	βct	βct	X
ejpam-232	186	8	+	+	CCONJ
ejpam-232	186	9	(	(	PUNCT
ejpam-232	186	10	1−	1−	NUM
ejpam-232	186	11	β)cω	β)cω	PROPN
ejpam-232	186	12	implies	imply	VERB
ejpam-232	186	13	∑	∑	NOUN
ejpam-232	186	14	αru(cr	αru(cr	NOUN
ejpam-232	186	15	)	)	PUNCT
ejpam-232	186	16	≤	≤	NOUN
ejpam-232	186	17	βu(ct	βu(ct	PUNCT
ejpam-232	186	18	)	)	PUNCT
ejpam-232	187	1	+	+	CCONJ
ejpam-232	187	2	(	(	PUNCT
ejpam-232	187	3	1−	1−	NUM
ejpam-232	187	4	β)u(cω	β)u(cω	NOUN
ejpam-232	187	5	)	)	PUNCT
ejpam-232	187	6	,	,	PUNCT
ejpam-232	187	7	where	where	SCONJ
ejpam-232	187	8	αr	αr	ADP
ejpam-232	187	9	>	>	SYM
ejpam-232	187	10	0	0	NUM
ejpam-232	187	11	,	,	PUNCT
ejpam-232	187	12	∑	∑	ADV
ejpam-232	187	13	αr	αr	NUM
ejpam-232	187	14	=	=	SYM
ejpam-232	187	15	1,β	1,β	NUM
ejpam-232	187	16	∈	∈	PROPN
ejpam-232	188	1	[	[	X
ejpam-232	188	2	0,1	0,1	NUM
ejpam-232	188	3	]	]	PUNCT
ejpam-232	188	4	and	and	CCONJ
ejpam-232	188	5	t	t	PROPN
ejpam-232	188	6	is	be	AUX
ejpam-232	188	7	a	a	DET
ejpam-232	188	8	coalition	coalition	NOUN
ejpam-232	188	9	.	.	PUNCT
ejpam-232	189	1	proof	proof	NOUN
ejpam-232	189	2	.	.	PUNCT
ejpam-232	190	1	consider	consider	VERB
ejpam-232	190	2	r	r	NOUN
ejpam-232	190	3	∈	∈	PROPN
ejpam-232	190	4	∑	∑	PUNCT
ejpam-232	190	5	.	.	PUNCT
ejpam-232	191	1	then	then	ADV
ejpam-232	191	2	u(cr	u(cr	NOUN
ejpam-232	191	3	)	)	PUNCT
ejpam-232	191	4	=	=	SYM
ejpam-232	191	5	fλ(cr	fλ(cr	PROPN
ejpam-232	191	6	)	)	PUNCT
ejpam-232	191	7	where	where	SCONJ
ejpam-232	191	8	,	,	PUNCT
ejpam-232	191	9	λ	λ	PROPN
ejpam-232	191	10	∈	∈	PROPN
ejpam-232	191	11	bar	bar	NOUN
ejpam-232	191	12	is	be	AUX
ejpam-232	191	13	suitable	suitable	ADJ
ejpam-232	191	14	element	element	NOUN
ejpam-232	191	15	with	with	ADP
ejpam-232	191	16	λ(ω	λ(ω	PRON
ejpam-232	191	17	)	)	PUNCT
ejpam-232	191	18	=	=	SYM
ejpam-232	191	19	v	v	X
ejpam-232	191	20	(	(	PUNCT
ejpam-232	191	21	ω	ω	NOUN
ejpam-232	191	22	)	)	PUNCT
ejpam-232	191	23	.	.	PUNCT
ejpam-232	192	1	it	it	PRON
ejpam-232	192	2	is	be	AUX
ejpam-232	192	3	easy	easy	ADJ
ejpam-232	192	4	to	to	PART
ejpam-232	192	5	see	see	VERB
ejpam-232	192	6	that	that	DET
ejpam-232	192	7	fλ(cω	fλ(cω	NOUN
ejpam-232	192	8	)	)	PUNCT
ejpam-232	193	1	=	=	SYM
ejpam-232	193	2	u(cω	u(cω	NOUN
ejpam-232	193	3	)	)	PUNCT
ejpam-232	193	4	.	.	PUNCT
ejpam-232	194	1	suppose	suppose	VERB
ejpam-232	194	2	that	that	SCONJ
ejpam-232	194	3	l	l	PROPN
ejpam-232	194	4	denotes	denote	VERB
ejpam-232	194	5	the	the	DET
ejpam-232	194	6	segment	segment	NOUN
ejpam-232	194	7	connecting	connect	VERB
ejpam-232	194	8	(	(	PUNCT
ejpam-232	194	9	cr	cr	X
ejpam-232	194	10	,	,	PUNCT
ejpam-232	194	11	u(cr	u(cr	PROPN
ejpam-232	194	12	)	)	PUNCT
ejpam-232	194	13	)	)	PUNCT
ejpam-232	194	14	to	to	ADP
ejpam-232	194	15	(	(	PUNCT
ejpam-232	194	16	cω	cω	NOUN
ejpam-232	194	17	,	,	PUNCT
ejpam-232	194	18	u(cω	u(cω	NOUN
ejpam-232	194	19	)	)	PUNCT
ejpam-232	194	20	)	)	PUNCT
ejpam-232	194	21	.	.	PUNCT
ejpam-232	195	1	then	then	ADV
ejpam-232	195	2	l	l	PROPN
ejpam-232	195	3	lies	lie	VERB
ejpam-232	195	4	on	on	ADP
ejpam-232	195	5	the	the	DET
ejpam-232	195	6	graph	graph	NOUN
ejpam-232	195	7	of	of	ADP
ejpam-232	195	8	fλ	fλ	PROPN
ejpam-232	195	9	.	.	NOUN
ejpam-232	195	10	since	since	SCONJ
ejpam-232	195	11	cav(u	cav(u	PROPN
ejpam-232	195	12	)	)	PUNCT
ejpam-232	195	13	is	be	AUX
ejpam-232	195	14	concave	concave	VERB
ejpam-232	195	15	,	,	PUNCT
ejpam-232	195	16	l	l	NOUN
ejpam-232	195	17	is	be	AUX
ejpam-232	195	18	below	below	ADP
ejpam-232	195	19	the	the	DET
ejpam-232	195	20	graph	graph	NOUN
ejpam-232	195	21	of	of	ADP
ejpam-232	195	22	cav(u	cav(u	NOUN
ejpam-232	195	23	)	)	PUNCT
ejpam-232	195	24	.	.	PUNCT
ejpam-232	196	1	as	as	ADP
ejpam-232	196	2	cav(u	cav(u	PROPN
ejpam-232	196	3	)	)	PUNCT
ejpam-232	196	4	≤	≤	NUM
ejpam-232	196	5	fλ	fλ	NOUN
ejpam-232	196	6	,	,	PUNCT
ejpam-232	196	7	l	l	NOUN
ejpam-232	196	8	is	be	AUX
ejpam-232	196	9	above	above	ADP
ejpam-232	196	10	the	the	DET
ejpam-232	196	11	graph	graph	NOUN
ejpam-232	196	12	of	of	ADP
ejpam-232	196	13	cav(u	cav(u	NOUN
ejpam-232	196	14	)	)	PUNCT
ejpam-232	196	15	.	.	PUNCT
ejpam-232	197	1	thus	thus	ADV
ejpam-232	197	2	,	,	PUNCT
ejpam-232	197	3	l	l	NOUN
ejpam-232	197	4	is	be	AUX
ejpam-232	197	5	on	on	ADP
ejpam-232	197	6	the	the	DET
ejpam-232	197	7	graph	graph	NOUN
ejpam-232	197	8	cav(u	cav(u	NOUN
ejpam-232	197	9	)	)	PUNCT
ejpam-232	197	10	.	.	PUNCT
ejpam-232	198	1	now	now	ADV
ejpam-232	198	2	by	by	ADP
ejpam-232	198	3	concavity	concavity	NOUN
ejpam-232	198	4	of	of	ADP
ejpam-232	198	5	cav(u	cav(u	PROPN
ejpam-232	198	6	)	)	PUNCT
ejpam-232	198	7	,	,	PUNCT
ejpam-232	198	8	∑	∑	PUNCT
ejpam-232	198	9	r	r	NOUN
ejpam-232	198	10	αrcav(u)(cr	αrcav(u)(cr	PROPN
ejpam-232	198	11	)	)	PUNCT
ejpam-232	198	12	≤	≤	NUM
ejpam-232	198	13	cav(u	cav(u	NOUN
ejpam-232	198	14	)	)	PUNCT
ejpam-232	198	15	(	(	PUNCT
ejpam-232	198	16	∑	∑	INTJ
ejpam-232	198	17	r	r	NOUN
ejpam-232	198	18	αrcr	αrcr	ADV
ejpam-232	198	19	)	)	PUNCT
ejpam-232	199	1	=	=	SYM
ejpam-232	199	2	cav(u)(βct	cav(u)(βct	PROPN
ejpam-232	199	3	+	+	CCONJ
ejpam-232	199	4	(	(	PUNCT
ejpam-232	199	5	1−	1−	NUM
ejpam-232	199	6	β)cω	β)cω	PROPN
ejpam-232	199	7	)	)	PUNCT
ejpam-232	199	8	=	=	SYM
ejpam-232	199	9	βu(ct	βu(ct	PROPN
ejpam-232	199	10	)	)	PUNCT
ejpam-232	200	1	+	+	CCONJ
ejpam-232	200	2	(	(	PUNCT
ejpam-232	200	3	1−	1−	NUM
ejpam-232	200	4	β)u(cω	β)u(cω	NOUN
ejpam-232	200	5	)	)	PUNCT
ejpam-232	200	6	.	.	PUNCT
ejpam-232	201	1	that	that	PRON
ejpam-232	201	2	is	be	AUX
ejpam-232	201	3	∑	∑	PUNCT
ejpam-232	201	4	r	r	NOUN
ejpam-232	201	5	αru(cr)≤	αru(cr)≤	PROPN
ejpam-232	201	6	βu(ct	βu(ct	PROPN
ejpam-232	201	7	)	)	PUNCT
ejpam-232	202	1	+	+	CCONJ
ejpam-232	202	2	(	(	PUNCT
ejpam-232	202	3	1−	1−	NUM
ejpam-232	202	4	β)u(cω	β)u(cω	NOUN
ejpam-232	202	5	)	)	PUNCT
ejpam-232	202	6	.	.	PUNCT
ejpam-232	203	1	references	reference	NOUN
ejpam-232	203	2	193	193	NUM
ejpam-232	203	3	references	reference	NOUN
ejpam-232	203	4	[	[	X
ejpam-232	203	5	1	1	NUM
ejpam-232	203	6	]	]	X
ejpam-232	203	7	y	y	PROPN
ejpam-232	203	8	azrieli	azrieli	ADV
ejpam-232	203	9	and	and	CCONJ
ejpam-232	203	10	e	e	NOUN
ejpam-232	203	11	lehrer	lehrer	PROPN
ejpam-232	203	12	.	.	PUNCT
ejpam-232	204	1	on	on	ADP
ejpam-232	204	2	concavification	concavification	NOUN
ejpam-232	204	3	and	and	CCONJ
ejpam-232	204	4	convex	convex	PROPN
ejpam-232	204	5	games	game	NOUN
ejpam-232	204	6	.	.	PUNCT
ejpam-232	205	1	game	game	NOUN
ejpam-232	205	2	theory	theory	NOUN
ejpam-232	205	3	and	and	CCONJ
ejpam-232	205	4	information	information	NOUN
ejpam-232	205	5	0408002	0408002	NUM
ejpam-232	205	6	,	,	PUNCT
ejpam-232	205	7	economics	economics	NOUN
ejpam-232	205	8	working	work	VERB
ejpam-232	205	9	paper	paper	NOUN
ejpam-232	205	10	archive	archive	NOUN
ejpam-232	205	11	at	at	ADP
ejpam-232	205	12	wustl	wustl	PROPN
ejpam-232	205	13	.	.	PUNCT
ejpam-232	206	1	[	[	X
ejpam-232	206	2	2	2	X
ejpam-232	206	3	]	]	X
ejpam-232	206	4	g	g	PROPN
ejpam-232	206	5	b	b	PROPN
ejpam-232	206	6	foland	foland	NOUN
ejpam-232	206	7	.	.	PUNCT
ejpam-232	207	1	real	real	ADJ
ejpam-232	207	2	analysis	analysis	NOUN
ejpam-232	207	3	:	:	PUNCT
ejpam-232	207	4	modern	modern	ADJ
ejpam-232	207	5	techniques	technique	NOUN
ejpam-232	207	6	and	and	CCONJ
ejpam-232	207	7	their	their	PRON
ejpam-232	207	8	applications	application	NOUN
ejpam-232	207	9	(	(	PUNCT
ejpam-232	207	10	2nd	2nd	NOUN
ejpam-232	207	11	edition	edition	NOUN
ejpam-232	207	12	)	)	PUNCT
ejpam-232	207	13	.	.	PUNCT
ejpam-232	208	1	wiley	wiley	PROPN
ejpam-232	208	2	-	-	PUNCT
ejpam-232	208	3	interscience	interscience	PROPN
ejpam-232	208	4	/	/	SYM
ejpam-232	208	5	john	john	PROPN
ejpam-232	208	6	wiley	wiley	PROPN
ejpam-232	208	7	sons	sons	PROPN
ejpam-232	208	8	,	,	PUNCT
ejpam-232	208	9	inc	inc	PROPN
ejpam-232	208	10	,	,	PUNCT
ejpam-232	208	11	1999	1999	NUM
ejpam-232	208	12	.	.	PUNCT
ejpam-232	209	1	[	[	X
ejpam-232	209	2	3	3	X
ejpam-232	209	3	]	]	PUNCT
ejpam-232	209	4	w	w	X
ejpam-232	209	5	rudin	rudin	PROPN
ejpam-232	209	6	.	.	PUNCT
ejpam-232	210	1	functional	functional	ADJ
ejpam-232	210	2	analysis	analysis	NOUN
ejpam-232	210	3	.	.	PUNCT
ejpam-232	211	1	mcgraw	mcgraw	PROPN
ejpam-232	211	2	-	-	PUNCT
ejpam-232	211	3	hill	hill	PROPN
ejpam-232	211	4	inc	inc	PROPN
ejpam-232	211	5	.	.	PROPN
ejpam-232	211	6	book	book	NOUN
ejpam-232	211	7	company	company	NOUN
ejpam-232	211	8	,	,	PUNCT
ejpam-232	211	9	new	new	PROPN
ejpam-232	211	10	york	york	PROPN
ejpam-232	211	11	,	,	PUNCT
ejpam-232	211	12	1991	1991	NUM
ejpam-232	211	13	.	.	PUNCT
ejpam-232	212	1	[	[	X
ejpam-232	212	2	4	4	NUM
ejpam-232	212	3	]	]	X
ejpam-232	212	4	d	d	X
ejpam-232	212	5	schmeidler	schmeidler	NOUN
ejpam-232	212	6	.	.	PUNCT
ejpam-232	213	1	cores	core	NOUN
ejpam-232	213	2	of	of	ADP
ejpam-232	213	3	exact	exact	ADJ
ejpam-232	213	4	games	game	NOUN
ejpam-232	213	5	.	.	PUNCT
ejpam-232	214	1	j.	j.	PROPN
ejpam-232	214	2	math	math	PROPN
ejpam-232	214	3	.	.	PUNCT
ejpam-232	215	1	anal	anal	PROPN
ejpam-232	215	2	.	.	PUNCT
ejpam-232	216	1	appl	appl	PROPN
ejpam-232	216	2	40	40	NUM
ejpam-232	216	3	:	:	SYM
ejpam-232	216	4	214–225	214–225	NUM
ejpam-232	216	5	1972	1972	NUM
ejpam-232	216	6	.	.	PUNCT
ejpam-232	217	1	[	[	X
ejpam-232	217	2	5	5	NUM
ejpam-232	217	3	]	]	X
ejpam-232	217	4	d	d	X
ejpam-232	217	5	schmeidler	schmeidler	NOUN
ejpam-232	217	6	.	.	PUNCT
ejpam-232	218	1	subjective	subjective	ADJ
ejpam-232	218	2	probabilities	probability	NOUN
ejpam-232	218	3	without	without	ADP
ejpam-232	218	4	additivity	additivity	NOUN
ejpam-232	218	5	.	.	PUNCT
ejpam-232	219	1	econometrica	econometrica	PROPN
ejpam-232	219	2	57	57	NUM
ejpam-232	219	3	:	:	PUNCT
ejpam-232	219	4	571–587	571–587	NUM
ejpam-232	219	5	1989	1989	NUM
ejpam-232	219	6	.	.	PUNCT
ejpam-232	220	1	[	[	X
ejpam-232	220	2	6	6	NUM
ejpam-232	220	3	]	]	SYM
ejpam-232	220	4	l	l	NOUN
ejpam-232	220	5	s	s	PART
ejpam-232	220	6	shapley	shapley	NOUN
ejpam-232	220	7	.	.	PUNCT
ejpam-232	221	1	cores	core	NOUN
ejpam-232	221	2	of	of	ADP
ejpam-232	221	3	convex	convex	PROPN
ejpam-232	221	4	games	game	NOUN
ejpam-232	221	5	.	.	PUNCT
ejpam-232	222	1	int	int	NOUN
ejpam-232	222	2	.	.	PUNCT
ejpam-232	223	1	j.	j.	PROPN
ejpam-232	223	2	game	game	PROPN
ejpam-232	223	3	theory	theory	NOUN
ejpam-232	223	4	1	1	NUM
ejpam-232	223	5	:	:	PUNCT
ejpam-232	223	6	11–26	11–26	NUM
ejpam-232	223	7	1971	1971	NUM
ejpam-232	223	8	.	.	PUNCT
ejpam-232	224	1	[	[	X
ejpam-232	224	2	7	7	X
ejpam-232	224	3	]	]	X
ejpam-232	224	4	a	a	DET
ejpam-232	224	5	w	w	PROPN
ejpam-232	224	6	tuker.contributions	tuker.contribution	NOUN
ejpam-232	224	7	to	to	ADP
ejpam-232	224	8	the	the	DET
ejpam-232	224	9	theory	theory	NOUN
ejpam-232	224	10	of	of	ADP
ejpam-232	224	11	games	games	PROPN
ejpam-232	224	12	.	.	PUNCT
ejpam-232	225	1	princeton	princeton	PROPN
ejpam-232	225	2	university	university	PROPN
ejpam-232	225	3	press	press	NOUN
ejpam-232	225	4	.	.	PUNCT
ejpam-232	226	1	princeton	princeton	PROPN
ejpam-232	226	2	,	,	PUNCT
ejpam-232	226	3	nj	nj	PROPN
ejpam-232	226	4	,	,	PUNCT
ejpam-232	226	5	307317	307317	NUM
ejpam-232	226	6	.	.	PUNCT