id	sid	tid	token	lemma	pos
ejpam-2881	1	1	european	european	PROPN
ejpam-2881	1	2	journal	journal	PROPN
ejpam-2881	1	3	of	of	ADP
ejpam-2881	1	4	pure	pure	ADJ
ejpam-2881	1	5	and	and	CCONJ
ejpam-2881	1	6	applied	apply	VERB
ejpam-2881	1	7	mathematics	mathematic	NOUN
ejpam-2881	1	8	vol	vol	NOUN
ejpam-2881	1	9	.	.	PROPN
ejpam-2881	2	1	10	10	NUM
ejpam-2881	2	2	,	,	PUNCT
ejpam-2881	2	3	no	no	INTJ
ejpam-2881	2	4	.	.	NOUN
ejpam-2881	2	5	2	2	NUM
ejpam-2881	2	6	,	,	PUNCT
ejpam-2881	2	7	2017	2017	NUM
ejpam-2881	2	8	,	,	PUNCT
ejpam-2881	2	9	238	238	NUM
ejpam-2881	2	10	-	-	SYM
ejpam-2881	2	11	254	254	NUM
ejpam-2881	2	12	issn	issn	PROPN
ejpam-2881	2	13	1307	1307	NUM
ejpam-2881	2	14	-	-	SYM
ejpam-2881	2	15	5543	5543	NUM
ejpam-2881	2	16	–	–	PUNCT
ejpam-2881	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2881	2	18	published	publish	VERB
ejpam-2881	2	19	by	by	ADP
ejpam-2881	2	20	new	new	PROPN
ejpam-2881	2	21	york	york	PROPN
ejpam-2881	2	22	business	business	PROPN
ejpam-2881	3	1	global	global	PROPN
ejpam-2881	3	2	the	the	DET
ejpam-2881	3	3	(	(	PUNCT
ejpam-2881	3	4	clrg)-property	clrg)-property	NOUN
ejpam-2881	3	5	for	for	ADP
ejpam-2881	3	6	coincidence	coincidence	NOUN
ejpam-2881	3	7	point	point	NOUN
ejpam-2881	3	8	theorems	theorem	NOUN
ejpam-2881	3	9	and	and	CCONJ
ejpam-2881	3	10	fredholm	fredholm	VERB
ejpam-2881	3	11	integral	integral	ADJ
ejpam-2881	3	12	equations	equation	NOUN
ejpam-2881	3	13	in	in	ADP
ejpam-2881	3	14	modular	modular	ADJ
ejpam-2881	3	15	metric	metric	ADJ
ejpam-2881	3	16	spaces	space	NOUN
ejpam-2881	3	17	phumin	phumin	VERB
ejpam-2881	3	18	sumalai1	sumalai1	ADJ
ejpam-2881	3	19	,	,	PUNCT
ejpam-2881	3	20	poom	poom	NOUN
ejpam-2881	3	21	kumam	kumam	NOUN
ejpam-2881	3	22	1,2,5,∗	1,2,5,∗	NUM
ejpam-2881	3	23	,	,	PUNCT
ejpam-2881	3	24	y.	y.	PROPN
ejpam-2881	3	25	j.	j.	PROPN
ejpam-2881	3	26	cho3,4	cho3,4	PROPN
ejpam-2881	3	27	,	,	PUNCT
ejpam-2881	3	28	anantachai	anantachai	PROPN
ejpam-2881	3	29	padcharoen1,2	padcharoen1,2	PROPN
ejpam-2881	3	30	1	1	NUM
ejpam-2881	3	31	kmutt	kmutt	NOUN
ejpam-2881	3	32	-	-	PUNCT
ejpam-2881	3	33	fixed	fix	VERB
ejpam-2881	3	34	point	point	NOUN
ejpam-2881	3	35	research	research	NOUN
ejpam-2881	3	36	laboratory	laboratory	NOUN
ejpam-2881	3	37	,	,	PUNCT
ejpam-2881	3	38	department	department	NOUN
ejpam-2881	3	39	of	of	ADP
ejpam-2881	3	40	mathematics	mathematic	NOUN
ejpam-2881	3	41	,	,	PUNCT
ejpam-2881	3	42	fixed	fix	VERB
ejpam-2881	3	43	point	point	NOUN
ejpam-2881	3	44	laboratory	laboratory	NOUN
ejpam-2881	3	45	,	,	PUNCT
ejpam-2881	3	46	faculty	faculty	NOUN
ejpam-2881	3	47	of	of	ADP
ejpam-2881	3	48	science	science	NOUN
ejpam-2881	3	49	,	,	PUNCT
ejpam-2881	3	50	king	king	PROPN
ejpam-2881	3	51	mongkut	mongkut	PROPN
ejpam-2881	3	52	’s	’s	PROPN
ejpam-2881	3	53	university	university	PROPN
ejpam-2881	3	54	of	of	ADP
ejpam-2881	3	55	technology	technology	PROPN
ejpam-2881	3	56	thonburi	thonburi	NOUN
ejpam-2881	3	57	(	(	PUNCT
ejpam-2881	3	58	kmutt	kmutt	PROPN
ejpam-2881	3	59	)	)	PUNCT
ejpam-2881	3	60	,	,	PUNCT
ejpam-2881	3	61	thrung	thrung	PROPN
ejpam-2881	3	62	khru	khru	NOUN
ejpam-2881	3	63	,	,	PUNCT
ejpam-2881	3	64	bangkok	bangkok	PROPN
ejpam-2881	3	65	,	,	PUNCT
ejpam-2881	3	66	thailand	thailand	PROPN
ejpam-2881	3	67	2	2	NUM
ejpam-2881	3	68	kmutt	kmutt	NOUN
ejpam-2881	3	69	-	-	PUNCT
ejpam-2881	3	70	fixed	fix	VERB
ejpam-2881	3	71	point	point	NOUN
ejpam-2881	3	72	theory	theory	NOUN
ejpam-2881	3	73	and	and	CCONJ
ejpam-2881	3	74	applications	application	NOUN
ejpam-2881	3	75	research	research	NOUN
ejpam-2881	3	76	group	group	NOUN
ejpam-2881	3	77	(	(	PUNCT
ejpam-2881	3	78	kmutt	kmutt	NOUN
ejpam-2881	3	79	-	-	PUNCT
ejpam-2881	3	80	fpta	fpta	NOUN
ejpam-2881	3	81	)	)	PUNCT
ejpam-2881	3	82	,	,	PUNCT
ejpam-2881	3	83	theoretical	theoretical	ADJ
ejpam-2881	3	84	and	and	CCONJ
ejpam-2881	3	85	computational	computational	ADJ
ejpam-2881	3	86	science	science	NOUN
ejpam-2881	3	87	center	center	NOUN
ejpam-2881	3	88	(	(	PUNCT
ejpam-2881	3	89	tacs	tacs	PROPN
ejpam-2881	3	90	)	)	PUNCT
ejpam-2881	3	91	,	,	PUNCT
ejpam-2881	3	92	faculty	faculty	NOUN
ejpam-2881	3	93	of	of	ADP
ejpam-2881	3	94	science	science	NOUN
ejpam-2881	3	95	,	,	PUNCT
ejpam-2881	3	96	king	king	PROPN
ejpam-2881	3	97	mongkut	mongkut	PROPN
ejpam-2881	3	98	’s	’s	PROPN
ejpam-2881	3	99	university	university	PROPN
ejpam-2881	3	100	of	of	ADP
ejpam-2881	3	101	technology	technology	PROPN
ejpam-2881	3	102	thonburi	thonburi	NOUN
ejpam-2881	3	103	(	(	PUNCT
ejpam-2881	3	104	kmutt	kmutt	PROPN
ejpam-2881	3	105	)	)	PUNCT
ejpam-2881	3	106	,	,	PUNCT
ejpam-2881	3	107	bangkok	bangkok	PROPN
ejpam-2881	3	108	,	,	PUNCT
ejpam-2881	3	109	thailand	thailand	PROPN
ejpam-2881	3	110	3	3	NUM
ejpam-2881	3	111	department	department	PROPN
ejpam-2881	3	112	of	of	ADP
ejpam-2881	3	113	mathematics	mathematics	PROPN
ejpam-2881	3	114	education	education	NOUN
ejpam-2881	3	115	and	and	CCONJ
ejpam-2881	3	116	the	the	DET
ejpam-2881	3	117	rins	rin	NOUN
ejpam-2881	3	118	,	,	PUNCT
ejpam-2881	3	119	gyeongsang	gyeongsang	PROPN
ejpam-2881	3	120	national	national	PROPN
ejpam-2881	3	121	university	university	PROPN
ejpam-2881	3	122	,	,	PUNCT
ejpam-2881	3	123	chinju	chinju	PROPN
ejpam-2881	3	124	,	,	PUNCT
ejpam-2881	3	125	korea	korea	PROPN
ejpam-2881	3	126	4	4	NUM
ejpam-2881	3	127	center	center	NOUN
ejpam-2881	3	128	for	for	ADP
ejpam-2881	3	129	general	general	ADJ
ejpam-2881	3	130	education	education	NOUN
ejpam-2881	3	131	,	,	PUNCT
ejpam-2881	3	132	china	china	PROPN
ejpam-2881	3	133	medical	medical	PROPN
ejpam-2881	3	134	university	university	PROPN
ejpam-2881	3	135	,	,	PUNCT
ejpam-2881	3	136	taichung	taichung	PROPN
ejpam-2881	3	137	,	,	PUNCT
ejpam-2881	3	138	taiwan	taiwan	PROPN
ejpam-2881	3	139	5	5	NUM
ejpam-2881	3	140	department	department	PROPN
ejpam-2881	3	141	of	of	ADP
ejpam-2881	3	142	medical	medical	ADJ
ejpam-2881	3	143	research	research	NOUN
ejpam-2881	3	144	,	,	PUNCT
ejpam-2881	3	145	china	china	PROPN
ejpam-2881	3	146	medical	medical	PROPN
ejpam-2881	3	147	university	university	PROPN
ejpam-2881	3	148	hospital	hospital	NOUN
ejpam-2881	3	149	,	,	PUNCT
ejpam-2881	3	150	china	china	PROPN
ejpam-2881	3	151	medical	medical	PROPN
ejpam-2881	3	152	university	university	PROPN
ejpam-2881	3	153	,	,	PUNCT
ejpam-2881	3	154	taichung	taichung	PROPN
ejpam-2881	3	155	,	,	PUNCT
ejpam-2881	3	156	taiwan	taiwan	PROPN
ejpam-2881	3	157	abstract	abstract	NOUN
ejpam-2881	3	158	.	.	PUNCT
ejpam-2881	4	1	in	in	ADP
ejpam-2881	4	2	paper	paper	NOUN
ejpam-2881	4	3	,	,	PUNCT
ejpam-2881	4	4	we	we	PRON
ejpam-2881	4	5	prove	prove	VERB
ejpam-2881	4	6	some	some	DET
ejpam-2881	4	7	common	common	ADJ
ejpam-2881	4	8	fixed	fix	VERB
ejpam-2881	4	9	point	point	NOUN
ejpam-2881	4	10	theorems	theorem	NOUN
ejpam-2881	4	11	for	for	ADP
ejpam-2881	4	12	the	the	DET
ejpam-2881	4	13	pair	pair	NOUN
ejpam-2881	4	14	of	of	ADP
ejpam-2881	4	15	self	self	NOUN
ejpam-2881	4	16	-	-	PUNCT
ejpam-2881	4	17	mappings	mapping	NOUN
ejpam-2881	4	18	with	with	ADP
ejpam-2881	4	19	the	the	DET
ejpam-2881	4	20	g	g	NOUN
ejpam-2881	4	21	-	-	PUNCT
ejpam-2881	4	22	quasi	quasi	NOUN
ejpam-2881	4	23	-	-	NOUN
ejpam-2881	4	24	condition	condition	NOUN
ejpam-2881	4	25	in	in	ADP
ejpam-2881	4	26	modular	modular	ADJ
ejpam-2881	4	27	metric	metric	ADJ
ejpam-2881	4	28	spaces	space	NOUN
ejpam-2881	4	29	.	.	PUNCT
ejpam-2881	5	1	also	also	ADV
ejpam-2881	5	2	,	,	PUNCT
ejpam-2881	5	3	we	we	PRON
ejpam-2881	5	4	modify	modify	VERB
ejpam-2881	5	5	and	and	CCONJ
ejpam-2881	5	6	prove	prove	VERB
ejpam-2881	5	7	some	some	DET
ejpam-2881	5	8	common	common	ADJ
ejpam-2881	5	9	fixed	fix	VERB
ejpam-2881	5	10	point	point	NOUN
ejpam-2881	5	11	theorems	theorem	NOUN
ejpam-2881	5	12	by	by	ADP
ejpam-2881	5	13	using	use	VERB
ejpam-2881	5	14	the	the	DET
ejpam-2881	5	15	(	(	PUNCT
ejpam-2881	5	16	clrg)-property	clrg)-property	PROPN
ejpam-2881	5	17	along	along	ADP
ejpam-2881	5	18	with	with	ADP
ejpam-2881	5	19	the	the	DET
ejpam-2881	5	20	weakly	weakly	ADJ
ejpam-2881	5	21	compatible	compatible	ADJ
ejpam-2881	5	22	mapping	mapping	NOUN
ejpam-2881	5	23	.	.	PUNCT
ejpam-2881	6	1	finally	finally	ADV
ejpam-2881	6	2	,	,	PUNCT
ejpam-2881	6	3	we	we	PRON
ejpam-2881	6	4	give	give	VERB
ejpam-2881	6	5	some	some	DET
ejpam-2881	6	6	applications	application	NOUN
ejpam-2881	6	7	on	on	ADP
ejpam-2881	6	8	integral	integral	ADJ
ejpam-2881	6	9	equations	equation	NOUN
ejpam-2881	6	10	to	to	PART
ejpam-2881	6	11	illustrate	illustrate	VERB
ejpam-2881	6	12	our	our	PRON
ejpam-2881	6	13	main	main	ADJ
ejpam-2881	6	14	results	result	NOUN
ejpam-2881	6	15	.	.	PUNCT
ejpam-2881	7	1	2010	2010	NUM
ejpam-2881	7	2	mathematics	mathematic	NOUN
ejpam-2881	7	3	subject	subject	NOUN
ejpam-2881	7	4	classifications	classification	NOUN
ejpam-2881	7	5	:	:	PUNCT
ejpam-2881	7	6	47h09	47h09	NUM
ejpam-2881	7	7	,	,	PUNCT
ejpam-2881	7	8	47h10	47h10	NUM
ejpam-2881	7	9	,	,	PUNCT
ejpam-2881	7	10	54h25	54h25	NUM
ejpam-2881	7	11	,	,	PUNCT
ejpam-2881	7	12	37c25	37c25	NUM
ejpam-2881	7	13	.	.	PUNCT
ejpam-2881	8	1	key	key	ADJ
ejpam-2881	8	2	words	word	NOUN
ejpam-2881	8	3	and	and	CCONJ
ejpam-2881	8	4	phrases	phrase	NOUN
ejpam-2881	8	5	:	:	PUNCT
ejpam-2881	8	6	coincidence	coincidence	NOUN
ejpam-2881	8	7	point	point	NOUN
ejpam-2881	8	8	,	,	PUNCT
ejpam-2881	8	9	fixed	fixed	ADJ
ejpam-2881	8	10	point	point	NOUN
ejpam-2881	8	11	,	,	PUNCT
ejpam-2881	8	12	g	g	NOUN
ejpam-2881	8	13	-	-	PUNCT
ejpam-2881	8	14	quasi	quasi	NOUN
ejpam-2881	8	15	-	-	NOUN
ejpam-2881	8	16	condition	condition	NOUN
ejpam-2881	8	17	,	,	PUNCT
ejpam-2881	8	18	(	(	PUNCT
ejpam-2881	8	19	clrg)-property	clrg)-property	PROPN
ejpam-2881	8	20	,	,	PUNCT
ejpam-2881	8	21	modular	modular	ADJ
ejpam-2881	8	22	metric	metric	ADJ
ejpam-2881	8	23	space	space	NOUN
ejpam-2881	8	24	.	.	PUNCT
ejpam-2881	9	1	1	1	X
ejpam-2881	9	2	.	.	X
ejpam-2881	9	3	introduction	introduction	NOUN
ejpam-2881	9	4	in	in	ADP
ejpam-2881	9	5	1998	1998	NUM
ejpam-2881	9	6	,	,	PUNCT
ejpam-2881	9	7	jungck	jungck	NOUN
ejpam-2881	9	8	and	and	CCONJ
ejpam-2881	9	9	rhoades	rhoade	NOUN
ejpam-2881	10	1	[	[	X
ejpam-2881	10	2	1	1	X
ejpam-2881	10	3	]	]	PUNCT
ejpam-2881	10	4	introduced	introduce	VERB
ejpam-2881	10	5	the	the	DET
ejpam-2881	10	6	notion	notion	NOUN
ejpam-2881	10	7	of	of	ADP
ejpam-2881	10	8	weakly	weakly	ADJ
ejpam-2881	10	9	compatible	compatible	ADJ
ejpam-2881	10	10	mappings	mapping	NOUN
ejpam-2881	10	11	as	as	SCONJ
ejpam-2881	10	12	follows	follow	VERB
ejpam-2881	10	13	:	:	PUNCT
ejpam-2881	10	14	let	let	VERB
ejpam-2881	10	15	x	x	PRON
ejpam-2881	10	16	be	be	AUX
ejpam-2881	10	17	a	a	DET
ejpam-2881	10	18	nonempty	nonempty	ADV
ejpam-2881	10	19	set	set	VERB
ejpam-2881	10	20	.	.	PUNCT
ejpam-2881	11	1	two	two	NUM
ejpam-2881	11	2	mappings	mapping	NOUN
ejpam-2881	11	3	f	f	X
ejpam-2881	11	4	,	,	PUNCT
ejpam-2881	11	5	g	g	NOUN
ejpam-2881	11	6	:	:	PUNCT
ejpam-2881	11	7	x	x	SYM
ejpam-2881	11	8	→	→	PUNCT
ejpam-2881	11	9	x	x	X
ejpam-2881	11	10	are	be	AUX
ejpam-2881	11	11	said	say	VERB
ejpam-2881	11	12	to	to	PART
ejpam-2881	11	13	be	be	AUX
ejpam-2881	11	14	weakly	weakly	ADV
ejpam-2881	11	15	compatible	compatible	ADJ
ejpam-2881	11	16	if	if	SCONJ
ejpam-2881	11	17	fx	fx	PROPN
ejpam-2881	11	18	=	=	SYM
ejpam-2881	11	19	gx	gx	PROPN
ejpam-2881	11	20	implies	imply	VERB
ejpam-2881	11	21	fgx	fgx	VERB
ejpam-2881	11	22	=	=	SYM
ejpam-2881	11	23	gfx	gfx	NOUN
ejpam-2881	11	24	for	for	ADP
ejpam-2881	11	25	any	any	DET
ejpam-2881	11	26	x	x	SYM
ejpam-2881	11	27	∈	∈	PROPN
ejpam-2881	11	28	x.	x.	NOUN
ejpam-2881	11	29	in	in	ADP
ejpam-2881	11	30	2011	2011	NUM
ejpam-2881	11	31	,	,	PUNCT
ejpam-2881	11	32	sintunavarat	sintunavarat	NOUN
ejpam-2881	11	33	and	and	CCONJ
ejpam-2881	11	34	kumam	kumam	VERB
ejpam-2881	12	1	[	[	X
ejpam-2881	12	2	4	4	X
ejpam-2881	12	3	]	]	PUNCT
ejpam-2881	12	4	introduced	introduce	VERB
ejpam-2881	12	5	a	a	DET
ejpam-2881	12	6	new	new	ADJ
ejpam-2881	12	7	relax	relax	NOUN
ejpam-2881	12	8	condition	condition	NOUN
ejpam-2881	12	9	is	be	AUX
ejpam-2881	12	10	called	call	VERB
ejpam-2881	12	11	the	the	DET
ejpam-2881	12	12	(	(	PUNCT
ejpam-2881	12	13	clrg)-property	clrg)-property	PROPN
ejpam-2881	12	14	as	as	SCONJ
ejpam-2881	12	15	follows	follow	VERB
ejpam-2881	12	16	:	:	PUNCT
ejpam-2881	12	17	∗corresponding	∗corresponde	VERB
ejpam-2881	12	18	author	author	NOUN
ejpam-2881	12	19	.	.	PUNCT
ejpam-2881	13	1	email	email	NOUN
ejpam-2881	13	2	addresses	address	NOUN
ejpam-2881	13	3	:	:	PUNCT
ejpam-2881	13	4	phumin.su28@mail.kmutt.ac.th	phumin.su28@mail.kmutt.ac.th	NOUN
ejpam-2881	13	5	(	(	PUNCT
ejpam-2881	13	6	p.	p.	NOUN
ejpam-2881	13	7	sumalai	sumalai	PROPN
ejpam-2881	13	8	)	)	PUNCT
ejpam-2881	13	9	,	,	PUNCT
ejpam-2881	14	1	poom.kum@kmutt.ac.th	poom.kum@kmutt.ac.th	NOUN
ejpam-2881	14	2	(	(	PUNCT
ejpam-2881	14	3	p.	p.	NOUN
ejpam-2881	14	4	kumam	kumam	PROPN
ejpam-2881	14	5	)	)	PUNCT
ejpam-2881	14	6	,	,	PUNCT
ejpam-2881	14	7	yjcho@gnu.ac.kr	yjcho@gnu.ac.kr	X
ejpam-2881	14	8	(	(	PUNCT
ejpam-2881	14	9	y.	y.	PROPN
ejpam-2881	14	10	j.	j.	PROPN
ejpam-2881	14	11	cho	cho	PROPN
ejpam-2881	14	12	)	)	PUNCT
ejpam-2881	14	13	,	,	PUNCT
ejpam-2881	14	14	apadcharoen@yahoo.com	apadcharoen@yahoo.com	X
ejpam-2881	15	1	(	(	PUNCT
ejpam-2881	15	2	a.	a.	NOUN
ejpam-2881	15	3	padcharoen	padcharoen	PROPN
ejpam-2881	15	4	)	)	PUNCT
ejpam-2881	15	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2881	16	1	238	238	NUM
ejpam-2881	16	2	c	c	X
ejpam-2881	16	3	©	©	PROPN
ejpam-2881	16	4	2017	2017	NUM
ejpam-2881	16	5	ejpam	ejpam	VERB
ejpam-2881	16	6	all	all	DET
ejpam-2881	16	7	rights	right	NOUN
ejpam-2881	16	8	reserved	reserve	VERB
ejpam-2881	16	9	.	.	PUNCT
ejpam-2881	17	1	p.	p.	NOUN
ejpam-2881	17	2	sumalai	sumalai	PROPN
ejpam-2881	17	3	,	,	PUNCT
ejpam-2881	17	4	p.	p.	PROPN
ejpam-2881	17	5	kumam	kumam	PROPN
ejpam-2881	17	6	,	,	PUNCT
ejpam-2881	17	7	y.	y.	PROPN
ejpam-2881	17	8	j.	j.	PROPN
ejpam-2881	17	9	cho	cho	PROPN
ejpam-2881	17	10	,	,	PUNCT
ejpam-2881	17	11	a.	a.	NOUN
ejpam-2881	17	12	padcharoen	padcharoen	PROPN
ejpam-2881	17	13	/	/	SYM
ejpam-2881	17	14	eur	eur	PROPN
ejpam-2881	17	15	.	.	PUNCT
ejpam-2881	18	1	j.	j.	PROPN
ejpam-2881	18	2	pure	pure	PROPN
ejpam-2881	18	3	appl	appl	PROPN
ejpam-2881	18	4	.	.	PROPN
ejpam-2881	18	5	math	math	PROPN
ejpam-2881	18	6	,	,	PUNCT
ejpam-2881	18	7	10	10	NUM
ejpam-2881	18	8	(	(	PUNCT
ejpam-2881	18	9	2	2	NUM
ejpam-2881	18	10	)	)	PUNCT
ejpam-2881	18	11	(	(	PUNCT
ejpam-2881	18	12	2017	2017	NUM
ejpam-2881	18	13	)	)	PUNCT
ejpam-2881	18	14	,	,	PUNCT
ejpam-2881	18	15	238	238	NUM
ejpam-2881	18	16	-	-	SYM
ejpam-2881	18	17	254	254	NUM
ejpam-2881	18	18	239	239	NUM
ejpam-2881	18	19	suppose	suppose	VERB
ejpam-2881	18	20	that	that	SCONJ
ejpam-2881	18	21	(	(	PUNCT
ejpam-2881	18	22	x	x	X
ejpam-2881	18	23	,	,	PUNCT
ejpam-2881	18	24	d	d	NOUN
ejpam-2881	18	25	)	)	PUNCT
ejpam-2881	18	26	is	be	AUX
ejpam-2881	18	27	a	a	DET
ejpam-2881	18	28	metric	metric	ADJ
ejpam-2881	18	29	space	space	NOUN
ejpam-2881	18	30	and	and	CCONJ
ejpam-2881	18	31	f	f	NOUN
ejpam-2881	18	32	,	,	PUNCT
ejpam-2881	18	33	g	g	NOUN
ejpam-2881	18	34	:	:	PUNCT
ejpam-2881	18	35	x	x	SYM
ejpam-2881	18	36	→	→	PUNCT
ejpam-2881	18	37	x	x	PUNCT
ejpam-2881	18	38	be	be	AUX
ejpam-2881	18	39	two	two	NUM
ejpam-2881	18	40	mappings	mapping	NOUN
ejpam-2881	18	41	.	.	PUNCT
ejpam-2881	19	1	the	the	DET
ejpam-2881	19	2	mappings	mapping	NOUN
ejpam-2881	19	3	f	f	PROPN
ejpam-2881	19	4	and	and	CCONJ
ejpam-2881	19	5	g	g	PROPN
ejpam-2881	19	6	are	be	AUX
ejpam-2881	19	7	said	say	VERB
ejpam-2881	19	8	to	to	PART
ejpam-2881	19	9	satisfy	satisfy	VERB
ejpam-2881	19	10	the	the	DET
ejpam-2881	19	11	common	common	ADJ
ejpam-2881	19	12	limit	limit	NOUN
ejpam-2881	19	13	in	in	ADP
ejpam-2881	19	14	the	the	DET
ejpam-2881	19	15	range	range	NOUN
ejpam-2881	19	16	of	of	ADP
ejpam-2881	19	17	g	g	PROPN
ejpam-2881	19	18	(	(	PUNCT
ejpam-2881	19	19	shortly	shortly	ADV
ejpam-2881	19	20	,	,	PUNCT
ejpam-2881	19	21	(	(	PUNCT
ejpam-2881	19	22	clrg)property	clrg)property	X
ejpam-2881	19	23	)	)	PUNCT
ejpam-2881	19	24	if	if	SCONJ
ejpam-2881	19	25	there	there	PRON
ejpam-2881	19	26	exists	exist	VERB
ejpam-2881	19	27	a	a	DET
ejpam-2881	19	28	sequence	sequence	NOUN
ejpam-2881	19	29	{	{	PUNCT
ejpam-2881	19	30	xn	xn	NOUN
ejpam-2881	19	31	}	}	PUNCT
ejpam-2881	19	32	in	in	ADP
ejpam-2881	19	33	x	x	SYM
ejpam-2881	19	34	such	such	ADJ
ejpam-2881	19	35	that	that	SCONJ
ejpam-2881	19	36	lim	lim	PROPN
ejpam-2881	19	37	n→∞	n→∞	PRON
ejpam-2881	19	38	fxn	fxn	PROPN
ejpam-2881	19	39	=	=	PUNCT
ejpam-2881	19	40	lim	lim	PROPN
ejpam-2881	19	41	n→∞	n→∞	NUM
ejpam-2881	19	42	gxn	gxn	PROPN
ejpam-2881	19	43	=	=	SYM
ejpam-2881	19	44	gx	gx	PROPN
ejpam-2881	19	45	for	for	ADP
ejpam-2881	19	46	some	some	DET
ejpam-2881	19	47	x	x	SYM
ejpam-2881	19	48	∈	∈	PROPN
ejpam-2881	19	49	x.	x.	NOUN
ejpam-2881	20	1	the	the	DET
ejpam-2881	20	2	importance	importance	NOUN
ejpam-2881	20	3	of	of	ADP
ejpam-2881	20	4	(	(	PUNCT
ejpam-2881	20	5	clrg)-property	clrg)-property	PROPN
ejpam-2881	20	6	ensures	ensure	VERB
ejpam-2881	20	7	that	that	SCONJ
ejpam-2881	20	8	one	one	PRON
ejpam-2881	20	9	does	do	AUX
ejpam-2881	20	10	not	not	PART
ejpam-2881	20	11	require	require	VERB
ejpam-2881	20	12	the	the	DET
ejpam-2881	20	13	closeness	closeness	NOUN
ejpam-2881	20	14	of	of	ADP
ejpam-2881	20	15	range	range	NOUN
ejpam-2881	20	16	subspaces	subspace	NOUN
ejpam-2881	20	17	on	on	ADP
ejpam-2881	20	18	the	the	DET
ejpam-2881	20	19	other	other	ADJ
ejpam-2881	20	20	hand	hand	NOUN
ejpam-2881	20	21	,	,	PUNCT
ejpam-2881	20	22	in	in	ADP
ejpam-2881	20	23	2010	2010	NUM
ejpam-2881	20	24	,	,	PUNCT
ejpam-2881	20	25	chistyakov	chistyakov	NOUN
ejpam-2881	20	26	[	[	X
ejpam-2881	20	27	2	2	NUM
ejpam-2881	20	28	]	]	PUNCT
ejpam-2881	20	29	introduced	introduce	VERB
ejpam-2881	20	30	the	the	DET
ejpam-2881	20	31	notion	notion	NOUN
ejpam-2881	20	32	of	of	ADP
ejpam-2881	20	33	a	a	DET
ejpam-2881	20	34	modular	modular	ADJ
ejpam-2881	20	35	metric	metric	ADJ
ejpam-2881	20	36	space	space	NOUN
ejpam-2881	20	37	which	which	PRON
ejpam-2881	20	38	is	be	AUX
ejpam-2881	20	39	a	a	DET
ejpam-2881	20	40	new	new	ADJ
ejpam-2881	20	41	generalization	generalization	NOUN
ejpam-2881	20	42	of	of	ADP
ejpam-2881	20	43	a	a	DET
ejpam-2881	20	44	metric	metric	ADJ
ejpam-2881	20	45	space	space	NOUN
ejpam-2881	20	46	.	.	PUNCT
ejpam-2881	21	1	in	in	ADP
ejpam-2881	21	2	the	the	DET
ejpam-2881	21	3	same	same	ADJ
ejpam-2881	21	4	way	way	NOUN
ejpam-2881	21	5	,	,	PUNCT
ejpam-2881	21	6	mongkolkeha	mongkolkeha	PROPN
ejpam-2881	21	7	et	et	PROPN
ejpam-2881	21	8	al	al	PROPN
ejpam-2881	21	9	.	.	PUNCT
ejpam-2881	22	1	[	[	X
ejpam-2881	22	2	3	3	X
ejpam-2881	22	3	]	]	PUNCT
ejpam-2881	22	4	proved	prove	VERB
ejpam-2881	22	5	the	the	DET
ejpam-2881	22	6	existence	existence	NOUN
ejpam-2881	22	7	of	of	ADP
ejpam-2881	22	8	fixed	fix	VERB
ejpam-2881	22	9	point	point	NOUN
ejpam-2881	22	10	theorems	theorem	NOUN
ejpam-2881	22	11	for	for	ADP
ejpam-2881	22	12	contraction	contraction	NOUN
ejpam-2881	22	13	mappings	mapping	NOUN
ejpam-2881	22	14	as	as	ADP
ejpam-2881	22	15	following	follow	VERB
ejpam-2881	22	16	:	:	PUNCT
ejpam-2881	22	17	let	let	VERB
ejpam-2881	22	18	ω	ω	PRON
ejpam-2881	22	19	be	be	AUX
ejpam-2881	22	20	a	a	DET
ejpam-2881	22	21	metric	metric	ADJ
ejpam-2881	22	22	modular	modular	NOUN
ejpam-2881	22	23	on	on	ADP
ejpam-2881	22	24	x	x	PUNCT
ejpam-2881	22	25	and	and	CCONJ
ejpam-2881	22	26	xω	xω	PRON
ejpam-2881	22	27	be	be	AUX
ejpam-2881	22	28	a	a	DET
ejpam-2881	22	29	modular	modular	ADJ
ejpam-2881	22	30	metric	metric	ADJ
ejpam-2881	22	31	space	space	NOUN
ejpam-2881	22	32	induced	induce	VERB
ejpam-2881	22	33	by	by	ADP
ejpam-2881	22	34	ω	ω	PROPN
ejpam-2881	22	35	.	.	PUNCT
ejpam-2881	23	1	if	if	SCONJ
ejpam-2881	23	2	xω	xω	PRON
ejpam-2881	23	3	is	be	AUX
ejpam-2881	23	4	a	a	DET
ejpam-2881	23	5	complete	complete	ADJ
ejpam-2881	23	6	modular	modular	ADJ
ejpam-2881	23	7	metric	metric	ADJ
ejpam-2881	23	8	space	space	NOUN
ejpam-2881	23	9	and	and	CCONJ
ejpam-2881	23	10	t	t	NOUN
ejpam-2881	23	11	:	:	PUNCT
ejpam-2881	23	12	xω	xω	X
ejpam-2881	23	13	→	→	PUNCT
ejpam-2881	23	14	xω	xω	NOUN
ejpam-2881	23	15	be	be	AUX
ejpam-2881	23	16	a	a	DET
ejpam-2881	23	17	mapping	mapping	NOUN
ejpam-2881	23	18	such	such	ADJ
ejpam-2881	23	19	there	there	PRON
ejpam-2881	23	20	exists	exist	VERB
ejpam-2881	23	21	k	k	PROPN
ejpam-2881	23	22	∈	∈	PROPN
ejpam-2881	24	1	[	[	X
ejpam-2881	24	2	0	0	NUM
ejpam-2881	24	3	,	,	PUNCT
ejpam-2881	24	4	1	1	NUM
ejpam-2881	24	5	)	)	PUNCT
ejpam-2881	24	6	with	with	ADP
ejpam-2881	24	7	ωλ(tx	ωλ(tx	PROPN
ejpam-2881	24	8	,	,	PUNCT
ejpam-2881	24	9	ty	ty	NOUN
ejpam-2881	24	10	)	)	PUNCT
ejpam-2881	24	11	≤	≤	PUNCT
ejpam-2881	24	12	kωλ(x	kωλ(x	PROPN
ejpam-2881	24	13	,	,	PUNCT
ejpam-2881	24	14	y	y	NOUN
ejpam-2881	24	15	)	)	PUNCT
ejpam-2881	24	16	for	for	ADP
ejpam-2881	24	17	all	all	DET
ejpam-2881	24	18	x	x	NOUN
ejpam-2881	24	19	,	,	PUNCT
ejpam-2881	24	20	y	y	PROPN
ejpam-2881	24	21	∈	∈	PROPN
ejpam-2881	24	22	xω	xω	X
ejpam-2881	24	23	and	and	CCONJ
ejpam-2881	24	24	λ	λ	X
ejpam-2881	24	25	>	>	X
ejpam-2881	24	26	0	0	PROPN
ejpam-2881	24	27	,	,	PUNCT
ejpam-2881	24	28	then	then	ADV
ejpam-2881	24	29	t	t	PROPN
ejpam-2881	24	30	has	have	VERB
ejpam-2881	24	31	a	a	DET
ejpam-2881	24	32	unique	unique	ADJ
ejpam-2881	24	33	fixed	fix	VERB
ejpam-2881	24	34	point	point	NOUN
ejpam-2881	24	35	in	in	ADP
ejpam-2881	24	36	xω	xω	PRON
ejpam-2881	24	37	.	.	PUNCT
ejpam-2881	25	1	currently	currently	ADV
ejpam-2881	25	2	aydi	aydi	VERB
ejpam-2881	25	3	et	et	PROPN
ejpam-2881	25	4	al	al	PROPN
ejpam-2881	25	5	.	.	PUNCT
ejpam-2881	26	1	[	[	X
ejpam-2881	26	2	5	5	NUM
ejpam-2881	26	3	]	]	PUNCT
ejpam-2881	26	4	established	establish	VERB
ejpam-2881	26	5	some	some	DET
ejpam-2881	26	6	coincidence	coincidence	NOUN
ejpam-2881	26	7	and	and	CCONJ
ejpam-2881	26	8	common	common	ADJ
ejpam-2881	26	9	fixed	fix	VERB
ejpam-2881	26	10	point	point	NOUN
ejpam-2881	26	11	results	result	NOUN
ejpam-2881	26	12	for	for	ADP
ejpam-2881	26	13	three	three	NUM
ejpam-2881	26	14	self	self	NOUN
ejpam-2881	26	15	-	-	PUNCT
ejpam-2881	26	16	mappings	mapping	NOUN
ejpam-2881	26	17	on	on	ADP
ejpam-2881	26	18	a	a	DET
ejpam-2881	26	19	partially	partially	ADV
ejpam-2881	26	20	ordered	order	VERB
ejpam-2881	26	21	cone	cone	NOUN
ejpam-2881	26	22	metric	metric	ADJ
ejpam-2881	26	23	space	space	NOUN
ejpam-2881	26	24	satisfying	satisfy	VERB
ejpam-2881	26	25	a	a	DET
ejpam-2881	26	26	contractive	contractive	ADJ
ejpam-2881	26	27	condition	condition	NOUN
ejpam-2881	26	28	and	and	CCONJ
ejpam-2881	26	29	proved	prove	VERB
ejpam-2881	26	30	an	an	DET
ejpam-2881	26	31	existence	existence	NOUN
ejpam-2881	26	32	theorem	theorem	NOUN
ejpam-2881	26	33	of	of	ADP
ejpam-2881	26	34	a	a	DET
ejpam-2881	26	35	common	common	ADJ
ejpam-2881	26	36	solution	solution	NOUN
ejpam-2881	26	37	of	of	ADP
ejpam-2881	26	38	integral	integral	ADJ
ejpam-2881	26	39	equations	equation	NOUN
ejpam-2881	26	40	.	.	PUNCT
ejpam-2881	27	1	in	in	ADP
ejpam-2881	27	2	the	the	DET
ejpam-2881	27	3	same	same	ADJ
ejpam-2881	27	4	way	way	NOUN
ejpam-2881	27	5	,	,	PUNCT
ejpam-2881	27	6	shatanawi	shatanawi	ADJ
ejpam-2881	27	7	et	et	NOUN
ejpam-2881	27	8	al.[6	al.[6	PROPN
ejpam-2881	27	9	]	]	PUNCT
ejpam-2881	27	10	studied	study	VERB
ejpam-2881	27	11	some	some	DET
ejpam-2881	27	12	new	new	ADJ
ejpam-2881	27	13	real	real	ADJ
ejpam-2881	27	14	generalizations	generalization	NOUN
ejpam-2881	27	15	on	on	ADP
ejpam-2881	27	16	coincidence	coincidence	NOUN
ejpam-2881	27	17	points	point	NOUN
ejpam-2881	27	18	for	for	ADP
ejpam-2881	27	19	weakly	weakly	ADJ
ejpam-2881	27	20	decreasing	decrease	VERB
ejpam-2881	27	21	mappings	mapping	NOUN
ejpam-2881	27	22	satisfying	satisfy	VERB
ejpam-2881	27	23	a	a	DET
ejpam-2881	27	24	weakly	weakly	ADV
ejpam-2881	27	25	contractive	contractive	ADJ
ejpam-2881	27	26	condition	condition	NOUN
ejpam-2881	27	27	in	in	ADP
ejpam-2881	27	28	an	an	DET
ejpam-2881	27	29	ordered	order	VERB
ejpam-2881	27	30	metric	metric	ADJ
ejpam-2881	27	31	space	space	NOUN
ejpam-2881	27	32	.	.	PUNCT
ejpam-2881	28	1	many	many	ADJ
ejpam-2881	28	2	author	author	NOUN
ejpam-2881	28	3	studies	study	NOUN
ejpam-2881	28	4	in	in	ADP
ejpam-2881	28	5	modular	modular	ADJ
ejpam-2881	28	6	metric	metric	ADJ
ejpam-2881	28	7	spaces	space	NOUN
ejpam-2881	28	8	[	[	X
ejpam-2881	28	9	11	11	NUM
ejpam-2881	28	10	,	,	PUNCT
ejpam-2881	28	11	12	12	NUM
ejpam-2881	28	12	,	,	PUNCT
ejpam-2881	28	13	13	13	NUM
ejpam-2881	28	14	,	,	PUNCT
ejpam-2881	28	15	14	14	NUM
ejpam-2881	28	16	,	,	PUNCT
ejpam-2881	28	17	15	15	NUM
ejpam-2881	28	18	,	,	PUNCT
ejpam-2881	28	19	16	16	NUM
ejpam-2881	28	20	,	,	PUNCT
ejpam-2881	28	21	17	17	NUM
ejpam-2881	28	22	]	]	PUNCT
ejpam-2881	28	23	.	.	PUNCT
ejpam-2881	29	1	in	in	ADP
ejpam-2881	29	2	this	this	DET
ejpam-2881	29	3	paper	paper	NOUN
ejpam-2881	29	4	,	,	PUNCT
ejpam-2881	29	5	we	we	PRON
ejpam-2881	29	6	study	study	VERB
ejpam-2881	29	7	and	and	CCONJ
ejpam-2881	29	8	prove	prove	VERB
ejpam-2881	29	9	the	the	DET
ejpam-2881	29	10	existence	existence	NOUN
ejpam-2881	29	11	of	of	ADP
ejpam-2881	29	12	some	some	DET
ejpam-2881	29	13	coincidence	coincidence	NOUN
ejpam-2881	29	14	point	point	NOUN
ejpam-2881	29	15	theorems	theorem	NOUN
ejpam-2881	29	16	for	for	ADP
ejpam-2881	29	17	generalized	generalized	ADJ
ejpam-2881	29	18	contraction	contraction	NOUN
ejpam-2881	29	19	mappings	mapping	NOUN
ejpam-2881	29	20	in	in	ADP
ejpam-2881	29	21	modular	modular	ADJ
ejpam-2881	29	22	metric	metric	ADJ
ejpam-2881	29	23	spaces	space	NOUN
ejpam-2881	29	24	and	and	CCONJ
ejpam-2881	29	25	give	give	VERB
ejpam-2881	29	26	some	some	DET
ejpam-2881	29	27	applications	application	NOUN
ejpam-2881	29	28	on	on	ADP
ejpam-2881	29	29	integral	integral	ADJ
ejpam-2881	29	30	equations	equation	NOUN
ejpam-2881	29	31	for	for	ADP
ejpam-2881	29	32	our	our	PRON
ejpam-2881	29	33	main	main	ADJ
ejpam-2881	29	34	results	result	NOUN
ejpam-2881	29	35	.	.	PUNCT
ejpam-2881	30	1	2	2	X
ejpam-2881	30	2	.	.	X
ejpam-2881	30	3	preliminaries	preliminary	NOUN
ejpam-2881	30	4	in	in	ADP
ejpam-2881	30	5	this	this	DET
ejpam-2881	30	6	section	section	NOUN
ejpam-2881	30	7	,	,	PUNCT
ejpam-2881	30	8	we	we	PRON
ejpam-2881	30	9	give	give	VERB
ejpam-2881	30	10	some	some	DET
ejpam-2881	30	11	definitions	definition	NOUN
ejpam-2881	30	12	and	and	CCONJ
ejpam-2881	30	13	their	their	PRON
ejpam-2881	30	14	properties	property	NOUN
ejpam-2881	30	15	for	for	ADP
ejpam-2881	30	16	our	our	PRON
ejpam-2881	30	17	main	main	ADJ
ejpam-2881	30	18	results	result	NOUN
ejpam-2881	30	19	.	.	PUNCT
ejpam-2881	31	1	definition	definition	NOUN
ejpam-2881	31	2	1	1	NUM
ejpam-2881	31	3	.	.	PUNCT
ejpam-2881	32	1	[	[	X
ejpam-2881	32	2	7	7	X
ejpam-2881	32	3	]	]	X
ejpam-2881	32	4	let	let	VERB
ejpam-2881	32	5	(	(	PUNCT
ejpam-2881	32	6	x	x	NOUN
ejpam-2881	32	7	,	,	PUNCT
ejpam-2881	32	8	d	d	NOUN
ejpam-2881	32	9	)	)	PUNCT
ejpam-2881	32	10	be	be	AUX
ejpam-2881	32	11	a	a	DET
ejpam-2881	32	12	metric	metric	ADJ
ejpam-2881	32	13	space	space	NOUN
ejpam-2881	32	14	.	.	PUNCT
ejpam-2881	33	1	two	two	NUM
ejpam-2881	33	2	mappings	mapping	NOUN
ejpam-2881	33	3	f	f	X
ejpam-2881	33	4	:	:	PUNCT
ejpam-2881	34	1	x	x	X
ejpam-2881	35	1	→	→	SYM
ejpam-2881	36	1	x	x	X
ejpam-2881	36	2	and	and	CCONJ
ejpam-2881	36	3	g	g	NOUN
ejpam-2881	36	4	:	:	PUNCT
ejpam-2881	36	5	x	x	SYM
ejpam-2881	36	6	→	→	PUNCT
ejpam-2881	36	7	x	x	X
ejpam-2881	36	8	are	be	AUX
ejpam-2881	36	9	said	say	VERB
ejpam-2881	36	10	to	to	PART
ejpam-2881	36	11	satisfy	satisfy	VERB
ejpam-2881	36	12	the	the	DET
ejpam-2881	36	13	(	(	PUNCT
ejpam-2881	36	14	e.a)-property	e.a)-property	NOUN
ejpam-2881	36	15	if	if	SCONJ
ejpam-2881	36	16	there	there	PRON
ejpam-2881	36	17	exist	exist	VERB
ejpam-2881	36	18	a	a	DET
ejpam-2881	36	19	sequences	sequence	NOUN
ejpam-2881	36	20	{	{	PUNCT
ejpam-2881	36	21	xn	xn	NUM
ejpam-2881	36	22	}	}	PUNCT
ejpam-2881	36	23	in	in	ADP
ejpam-2881	36	24	x	x	SYM
ejpam-2881	36	25	such	such	ADJ
ejpam-2881	36	26	that	that	SCONJ
ejpam-2881	36	27	lim	lim	PROPN
ejpam-2881	36	28	n→∞	n→∞	PRON
ejpam-2881	36	29	fxn	fxn	PROPN
ejpam-2881	36	30	=	=	PUNCT
ejpam-2881	36	31	lim	lim	PROPN
ejpam-2881	36	32	n→∞	n→∞	NUM
ejpam-2881	36	33	gxn	gxn	PROPN
ejpam-2881	36	34	=	=	SYM
ejpam-2881	36	35	t	t	PROPN
ejpam-2881	36	36	for	for	ADP
ejpam-2881	36	37	some	some	DET
ejpam-2881	36	38	t	t	NOUN
ejpam-2881	36	39	∈	∈	NOUN
ejpam-2881	36	40	x.	x.	NOUN
ejpam-2881	37	1	next	next	ADV
ejpam-2881	37	2	,	,	PUNCT
ejpam-2881	37	3	we	we	PRON
ejpam-2881	37	4	introduce	introduce	VERB
ejpam-2881	37	5	the	the	DET
ejpam-2881	37	6	notion	notion	NOUN
ejpam-2881	37	7	of	of	ADP
ejpam-2881	37	8	a	a	DET
ejpam-2881	37	9	modular	modular	ADJ
ejpam-2881	37	10	metric	metric	ADJ
ejpam-2881	37	11	space	space	NOUN
ejpam-2881	37	12	as	as	SCONJ
ejpam-2881	37	13	follows	follow	VERB
ejpam-2881	37	14	:	:	PUNCT
ejpam-2881	37	15	definition	definition	NOUN
ejpam-2881	37	16	2	2	NUM
ejpam-2881	37	17	.	.	PUNCT
ejpam-2881	38	1	let	let	VERB
ejpam-2881	38	2	x	x	PRON
ejpam-2881	38	3	be	be	AUX
ejpam-2881	38	4	a	a	DET
ejpam-2881	38	5	linear	linear	ADJ
ejpam-2881	38	6	space	space	NOUN
ejpam-2881	38	7	over	over	ADP
ejpam-2881	38	8	r	r	NOUN
ejpam-2881	38	9	with	with	ADP
ejpam-2881	38	10	θ	θ	PROPN
ejpam-2881	38	11	∈	∈	PROPN
ejpam-2881	38	12	x	x	PUNCT
ejpam-2881	38	13	as	as	ADP
ejpam-2881	38	14	its	its	PRON
ejpam-2881	38	15	zero	zero	NUM
ejpam-2881	38	16	element	element	NOUN
ejpam-2881	38	17	.	.	PUNCT
ejpam-2881	39	1	a	a	DET
ejpam-2881	39	2	functional	functional	ADJ
ejpam-2881	39	3	ρ	ρ	NOUN
ejpam-2881	39	4	:	:	PUNCT
ejpam-2881	39	5	x	x	X
ejpam-2881	39	6	→	→	PUNCT
ejpam-2881	39	7	[	[	X
ejpam-2881	39	8	0,+∞	0,+∞	NUM
ejpam-2881	39	9	]	]	X
ejpam-2881	39	10	is	be	AUX
ejpam-2881	39	11	called	call	VERB
ejpam-2881	39	12	a	a	DET
ejpam-2881	39	13	modular	modular	NOUN
ejpam-2881	39	14	on	on	ADP
ejpam-2881	39	15	x	x	PUNCT
ejpam-2881	39	16	if	if	SCONJ
ejpam-2881	39	17	,	,	PUNCT
ejpam-2881	39	18	for	for	ADP
ejpam-2881	39	19	all	all	DET
ejpam-2881	39	20	x	x	NOUN
ejpam-2881	39	21	,	,	PUNCT
ejpam-2881	39	22	y	y	PROPN
ejpam-2881	39	23	,	,	PUNCT
ejpam-2881	39	24	z	z	PROPN
ejpam-2881	39	25	∈	∈	PROPN
ejpam-2881	39	26	x	x	SYM
ejpam-2881	39	27	,	,	PUNCT
ejpam-2881	39	28	the	the	DET
ejpam-2881	39	29	following	follow	VERB
ejpam-2881	39	30	conditions	condition	NOUN
ejpam-2881	39	31	hold	hold	VERB
ejpam-2881	39	32	:	:	PUNCT
ejpam-2881	39	33	(	(	PUNCT
ejpam-2881	39	34	m1	m1	NOUN
ejpam-2881	39	35	)	)	PUNCT
ejpam-2881	39	36	ρ(x	ρ(x	NOUN
ejpam-2881	39	37	)	)	PUNCT
ejpam-2881	39	38	=	=	SYM
ejpam-2881	39	39	0	0	PUNCT
ejpam-2881	40	1	if	if	SCONJ
ejpam-2881	40	2	and	and	CCONJ
ejpam-2881	40	3	only	only	ADV
ejpam-2881	40	4	if	if	SCONJ
ejpam-2881	40	5	x	x	X
ejpam-2881	40	6	=	=	SYM
ejpam-2881	40	7	θ	θ	PROPN
ejpam-2881	40	8	;	;	PUNCT
ejpam-2881	40	9	p.	p.	NOUN
ejpam-2881	40	10	sumalai	sumalai	PROPN
ejpam-2881	40	11	,	,	PUNCT
ejpam-2881	40	12	p.	p.	PROPN
ejpam-2881	40	13	kumam	kumam	PROPN
ejpam-2881	40	14	,	,	PUNCT
ejpam-2881	40	15	y.	y.	PROPN
ejpam-2881	40	16	j.	j.	PROPN
ejpam-2881	40	17	cho	cho	PROPN
ejpam-2881	40	18	,	,	PUNCT
ejpam-2881	40	19	a.	a.	NOUN
ejpam-2881	40	20	padcharoen	padcharoen	PROPN
ejpam-2881	40	21	/	/	SYM
ejpam-2881	40	22	eur	eur	PROPN
ejpam-2881	40	23	.	.	PUNCT
ejpam-2881	41	1	j.	j.	PROPN
ejpam-2881	41	2	pure	pure	PROPN
ejpam-2881	41	3	appl	appl	PROPN
ejpam-2881	41	4	.	.	PROPN
ejpam-2881	41	5	math	math	PROPN
ejpam-2881	41	6	,	,	PUNCT
ejpam-2881	41	7	10	10	NUM
ejpam-2881	41	8	(	(	PUNCT
ejpam-2881	41	9	2	2	NUM
ejpam-2881	41	10	)	)	PUNCT
ejpam-2881	41	11	(	(	PUNCT
ejpam-2881	41	12	2017	2017	NUM
ejpam-2881	41	13	)	)	PUNCT
ejpam-2881	41	14	,	,	PUNCT
ejpam-2881	41	15	238	238	NUM
ejpam-2881	41	16	-	-	SYM
ejpam-2881	41	17	254	254	NUM
ejpam-2881	41	18	240	240	NUM
ejpam-2881	41	19	(	(	PUNCT
ejpam-2881	41	20	m2	m2	PROPN
ejpam-2881	41	21	)	)	PUNCT
ejpam-2881	41	22	ρ(x	ρ(x	PROPN
ejpam-2881	41	23	)	)	PUNCT
ejpam-2881	41	24	=	=	SYM
ejpam-2881	41	25	ρ(−x	ρ(−x	NOUN
ejpam-2881	41	26	)	)	PUNCT
ejpam-2881	41	27	;	;	PUNCT
ejpam-2881	41	28	(	(	PUNCT
ejpam-2881	41	29	m3	m3	PROPN
ejpam-2881	41	30	)	)	PUNCT
ejpam-2881	41	31	ρ(αx+	ρ(αx+	VERB
ejpam-2881	41	32	βy	βy	ADJ
ejpam-2881	41	33	)	)	PUNCT
ejpam-2881	41	34	≤	≤	NOUN
ejpam-2881	41	35	ρ(x	ρ(x	NOUN
ejpam-2881	41	36	)	)	PUNCT
ejpam-2881	42	1	+	+	CCONJ
ejpam-2881	42	2	ρ(y	ρ(y	NOUN
ejpam-2881	42	3	)	)	PUNCT
ejpam-2881	42	4	whenever	whenever	SCONJ
ejpam-2881	42	5	α	α	X
ejpam-2881	42	6	,	,	PUNCT
ejpam-2881	42	7	β	β	X
ejpam-2881	42	8	≥	≥	NOUN
ejpam-2881	42	9	0	0	NUM
ejpam-2881	42	10	and	and	CCONJ
ejpam-2881	42	11	α+	α+	PUNCT
ejpam-2881	42	12	β	β	X
ejpam-2881	42	13	=	=	SYM
ejpam-2881	42	14	1	1	X
ejpam-2881	42	15	.	.	PUNCT
ejpam-2881	43	1	the	the	DET
ejpam-2881	43	2	linear	linear	PROPN
ejpam-2881	43	3	subspace	subspace	NOUN
ejpam-2881	43	4	xρ	xρ	PROPN
ejpam-2881	43	5	:	:	PUNCT
ejpam-2881	43	6	=	=	SYM
ejpam-2881	43	7	{	{	PUNCT
ejpam-2881	43	8	x	x	PUNCT
ejpam-2881	43	9	∈	∈	NOUN
ejpam-2881	43	10	x	x	X
ejpam-2881	43	11	:	:	PUNCT
ejpam-2881	43	12	lim	lim	PROPN
ejpam-2881	43	13	λ→∞	λ→∞	NUM
ejpam-2881	43	14	ρ(λx	ρ(λx	PROPN
ejpam-2881	43	15	)	)	PUNCT
ejpam-2881	43	16	=	=	SYM
ejpam-2881	43	17	0	0	X
ejpam-2881	43	18	}	}	PUNCT
ejpam-2881	43	19	is	be	AUX
ejpam-2881	43	20	called	call	VERB
ejpam-2881	43	21	a	a	DET
ejpam-2881	43	22	modular	modular	ADJ
ejpam-2881	43	23	space	space	NOUN
ejpam-2881	43	24	.	.	PUNCT
ejpam-2881	44	1	definition	definition	NOUN
ejpam-2881	44	2	3	3	NUM
ejpam-2881	44	3	.	.	PUNCT
ejpam-2881	45	1	[	[	X
ejpam-2881	45	2	2	2	X
ejpam-2881	45	3	]	]	PUNCT
ejpam-2881	45	4	let	let	VERB
ejpam-2881	45	5	x	x	PRON
ejpam-2881	45	6	be	be	AUX
ejpam-2881	45	7	a	a	DET
ejpam-2881	45	8	nonempty	nonempty	ADJ
ejpam-2881	45	9	set	set	VERB
ejpam-2881	45	10	.	.	PUNCT
ejpam-2881	46	1	(	(	PUNCT
ejpam-2881	46	2	1	1	X
ejpam-2881	46	3	)	)	PUNCT
ejpam-2881	46	4	a	a	DET
ejpam-2881	46	5	function	function	NOUN
ejpam-2881	46	6	ω	ω	NOUN
ejpam-2881	46	7	:	:	PUNCT
ejpam-2881	46	8	(	(	PUNCT
ejpam-2881	46	9	0,∞	0,∞	NUM
ejpam-2881	46	10	)	)	PUNCT
ejpam-2881	46	11	×x	×x	VERB
ejpam-2881	46	12	×x	×x	NOUN
ejpam-2881	46	13	→	→	PUNCT
ejpam-2881	46	14	[	[	X
ejpam-2881	46	15	0,∞	0,∞	X
ejpam-2881	46	16	]	]	PUNCT
ejpam-2881	46	17	is	be	AUX
ejpam-2881	46	18	called	call	VERB
ejpam-2881	46	19	a	a	DET
ejpam-2881	46	20	metric	metric	ADJ
ejpam-2881	46	21	modular	modular	NOUN
ejpam-2881	46	22	on	on	ADP
ejpam-2881	46	23	x	x	SYM
ejpam-2881	46	24	if	if	SCONJ
ejpam-2881	46	25	,	,	PUNCT
ejpam-2881	46	26	for	for	ADP
ejpam-2881	46	27	all	all	DET
ejpam-2881	46	28	x	x	NOUN
ejpam-2881	46	29	,	,	PUNCT
ejpam-2881	46	30	y	y	PROPN
ejpam-2881	46	31	,	,	PUNCT
ejpam-2881	46	32	z	z	PROPN
ejpam-2881	46	33	∈	∈	PROPN
ejpam-2881	47	1	x	x	SYM
ejpam-2881	47	2	,	,	PUNCT
ejpam-2881	47	3	the	the	DET
ejpam-2881	47	4	following	follow	VERB
ejpam-2881	47	5	conditions	condition	NOUN
ejpam-2881	47	6	hold	hold	VERB
ejpam-2881	47	7	:	:	PUNCT
ejpam-2881	47	8	(	(	PUNCT
ejpam-2881	47	9	mm1	mm1	PROPN
ejpam-2881	47	10	)	)	PUNCT
ejpam-2881	47	11	ωλ(x	ωλ(x	PUNCT
ejpam-2881	47	12	,	,	PUNCT
ejpam-2881	47	13	y	y	X
ejpam-2881	47	14	)	)	PUNCT
ejpam-2881	47	15	=	=	SYM
ejpam-2881	47	16	0	0	NUM
ejpam-2881	47	17	for	for	ADP
ejpam-2881	47	18	all	all	DET
ejpam-2881	47	19	λ	λ	PROPN
ejpam-2881	47	20	>	>	X
ejpam-2881	47	21	0	0	PUNCT
ejpam-2881	48	1	if	if	SCONJ
ejpam-2881	48	2	and	and	CCONJ
ejpam-2881	48	3	only	only	ADV
ejpam-2881	48	4	if	if	SCONJ
ejpam-2881	48	5	x	x	X
ejpam-2881	48	6	=	=	SYM
ejpam-2881	48	7	y	y	PROPN
ejpam-2881	48	8	;	;	PUNCT
ejpam-2881	48	9	(	(	PUNCT
ejpam-2881	48	10	mm2	mm2	NOUN
ejpam-2881	48	11	)	)	PUNCT
ejpam-2881	48	12	ωλ(x	ωλ(x	NUM
ejpam-2881	48	13	,	,	PUNCT
ejpam-2881	48	14	y	y	NOUN
ejpam-2881	48	15	)	)	PUNCT
ejpam-2881	48	16	=	=	SYM
ejpam-2881	48	17	ωλ(y	ωλ(y	NUM
ejpam-2881	48	18	,	,	PUNCT
ejpam-2881	48	19	x	x	NOUN
ejpam-2881	48	20	)	)	PUNCT
ejpam-2881	48	21	for	for	ADP
ejpam-2881	48	22	all	all	DET
ejpam-2881	48	23	λ	λ	PROPN
ejpam-2881	48	24	>	>	X
ejpam-2881	48	25	0	0	NUM
ejpam-2881	48	26	;	;	PUNCT
ejpam-2881	48	27	(	(	PUNCT
ejpam-2881	48	28	mm3	mm3	NOUN
ejpam-2881	48	29	)	)	PUNCT
ejpam-2881	48	30	ωλ+µ(x	ωλ+µ(x	PROPN
ejpam-2881	48	31	,	,	PUNCT
ejpam-2881	48	32	y	y	NOUN
ejpam-2881	48	33	)	)	PUNCT
ejpam-2881	48	34	≤	≤	NOUN
ejpam-2881	48	35	ωλ(x	ωλ(x	NUM
ejpam-2881	48	36	,	,	PUNCT
ejpam-2881	48	37	z	z	NOUN
ejpam-2881	48	38	)	)	PUNCT
ejpam-2881	48	39	+	+	CCONJ
ejpam-2881	48	40	ωµ(z	ωµ(z	NOUN
ejpam-2881	48	41	,	,	PUNCT
ejpam-2881	48	42	y	y	NOUN
ejpam-2881	48	43	)	)	PUNCT
ejpam-2881	48	44	for	for	ADP
ejpam-2881	48	45	all	all	DET
ejpam-2881	48	46	λ	λ	PROPN
ejpam-2881	48	47	,	,	PUNCT
ejpam-2881	48	48	µ	µ	X
ejpam-2881	48	49	>	>	X
ejpam-2881	48	50	0	0	NUM
ejpam-2881	48	51	.	.	PUNCT
ejpam-2881	49	1	(	(	PUNCT
ejpam-2881	49	2	2	2	X
ejpam-2881	49	3	)	)	PUNCT
ejpam-2881	49	4	if	if	SCONJ
ejpam-2881	49	5	,	,	PUNCT
ejpam-2881	49	6	instead	instead	ADV
ejpam-2881	49	7	of	of	ADP
ejpam-2881	49	8	the	the	DET
ejpam-2881	49	9	condition	condition	NOUN
ejpam-2881	49	10	(	(	PUNCT
ejpam-2881	49	11	mm1	mm1	PROPN
ejpam-2881	49	12	)	)	PUNCT
ejpam-2881	49	13	,	,	PUNCT
ejpam-2881	49	14	we	we	PRON
ejpam-2881	49	15	have	have	VERB
ejpam-2881	49	16	the	the	DET
ejpam-2881	49	17	following	follow	VERB
ejpam-2881	49	18	condition	condition	NOUN
ejpam-2881	49	19	:	:	PUNCT
ejpam-2881	49	20	(	(	PUNCT
ejpam-2881	49	21	mm1′	mm1′	NOUN
ejpam-2881	49	22	)	)	PUNCT
ejpam-2881	49	23	ωλ(x	ωλ(x	X
ejpam-2881	49	24	,	,	PUNCT
ejpam-2881	49	25	x	x	X
ejpam-2881	49	26	)	)	PUNCT
ejpam-2881	49	27	=	=	SYM
ejpam-2881	49	28	0	0	NUM
ejpam-2881	49	29	for	for	ADP
ejpam-2881	49	30	all	all	DET
ejpam-2881	49	31	λ	λ	PROPN
ejpam-2881	49	32	>	>	X
ejpam-2881	49	33	0	0	PROPN
ejpam-2881	49	34	,	,	PUNCT
ejpam-2881	49	35	then	then	ADV
ejpam-2881	49	36	ω	ω	PROPN
ejpam-2881	49	37	is	be	AUX
ejpam-2881	49	38	called	call	VERB
ejpam-2881	49	39	a	a	DET
ejpam-2881	49	40	(	(	PUNCT
ejpam-2881	49	41	metric	metric	ADJ
ejpam-2881	49	42	)	)	PUNCT
ejpam-2881	49	43	pseudo	pseudo	NOUN
ejpam-2881	49	44	-	-	NOUN
ejpam-2881	49	45	modular	modular	NOUN
ejpam-2881	49	46	on	on	ADP
ejpam-2881	49	47	x.	x.	NOUN
ejpam-2881	49	48	remark	remark	PROPN
ejpam-2881	49	49	1	1	NUM
ejpam-2881	49	50	.	.	PUNCT
ejpam-2881	50	1	a	a	DET
ejpam-2881	50	2	modular	modular	ADJ
ejpam-2881	50	3	ω	ω	NOUN
ejpam-2881	50	4	on	on	ADP
ejpam-2881	50	5	a	a	DET
ejpam-2881	50	6	set	set	NOUN
ejpam-2881	50	7	x	x	NOUN
ejpam-2881	50	8	,	,	PUNCT
ejpam-2881	50	9	the	the	DET
ejpam-2881	50	10	function	function	NOUN
ejpam-2881	50	11	0	0	PUNCT
ejpam-2881	50	12	<	<	X
ejpam-2881	50	13	λ	λ	X
ejpam-2881	50	14	7→	7→	NUM
ejpam-2881	50	15	ωλ(x	ωλ(x	NUM
ejpam-2881	50	16	,	,	PUNCT
ejpam-2881	50	17	y	y	NOUN
ejpam-2881	50	18	)	)	PUNCT
ejpam-2881	50	19	∈	∈	PROPN
ejpam-2881	51	1	[	[	X
ejpam-2881	51	2	0,∞	0,∞	X
ejpam-2881	51	3	]	]	PUNCT
ejpam-2881	51	4	for	for	ADP
ejpam-2881	51	5	all	all	DET
ejpam-2881	51	6	x	x	NOUN
ejpam-2881	51	7	,	,	PUNCT
ejpam-2881	51	8	y	y	PROPN
ejpam-2881	51	9	∈	∈	PROPN
ejpam-2881	51	10	x	x	X
ejpam-2881	51	11	,	,	PUNCT
ejpam-2881	51	12	is	be	AUX
ejpam-2881	51	13	a	a	DET
ejpam-2881	51	14	non	non	ADJ
ejpam-2881	51	15	-	-	ADJ
ejpam-2881	51	16	increasing	increase	VERB
ejpam-2881	51	17	on	on	ADP
ejpam-2881	51	18	(	(	PUNCT
ejpam-2881	51	19	0,∞	0,∞	NOUN
ejpam-2881	51	20	)	)	PUNCT
ejpam-2881	51	21	.	.	PUNCT
ejpam-2881	52	1	in	in	ADP
ejpam-2881	52	2	fact	fact	NOUN
ejpam-2881	52	3	,	,	PUNCT
ejpam-2881	52	4	if	if	SCONJ
ejpam-2881	52	5	0	0	NUM
ejpam-2881	52	6	<	<	X
ejpam-2881	52	7	µ	µ	X
ejpam-2881	52	8	<	<	X
ejpam-2881	52	9	λ	λ	PROPN
ejpam-2881	52	10	,	,	PUNCT
ejpam-2881	52	11	then	then	ADV
ejpam-2881	52	12	the	the	DET
ejpam-2881	52	13	conditions	condition	NOUN
ejpam-2881	52	14	(	(	PUNCT
ejpam-2881	52	15	mm3	mm3	NOUN
ejpam-2881	52	16	)	)	PUNCT
ejpam-2881	52	17	,	,	PUNCT
ejpam-2881	52	18	(	(	PUNCT
ejpam-2881	52	19	mm1′	mm1′	NOUN
ejpam-2881	52	20	)	)	PUNCT
ejpam-2881	52	21	and	and	CCONJ
ejpam-2881	52	22	(	(	PUNCT
ejpam-2881	52	23	mm2	mm2	NOUN
ejpam-2881	52	24	)	)	PUNCT
ejpam-2881	52	25	imply	imply	VERB
ejpam-2881	52	26	ωλ(x	ωλ(x	ADJ
ejpam-2881	52	27	,	,	PUNCT
ejpam-2881	52	28	y	y	NOUN
ejpam-2881	52	29	)	)	PUNCT
ejpam-2881	52	30	≤	≤	NOUN
ejpam-2881	52	31	ωλ−µ(x	ωλ−µ(x	PROPN
ejpam-2881	52	32	,	,	PUNCT
ejpam-2881	52	33	x	x	X
ejpam-2881	52	34	)	)	PUNCT
ejpam-2881	52	35	+	+	CCONJ
ejpam-2881	52	36	ωµ(x	ωµ(x	NOUN
ejpam-2881	52	37	,	,	PUNCT
ejpam-2881	52	38	y	y	NOUN
ejpam-2881	52	39	)	)	PUNCT
ejpam-2881	52	40	=	=	SYM
ejpam-2881	52	41	ωµ(x	ωµ(x	X
ejpam-2881	52	42	,	,	PUNCT
ejpam-2881	52	43	y	y	NOUN
ejpam-2881	52	44	)	)	PUNCT
ejpam-2881	52	45	.	.	PUNCT
ejpam-2881	53	1	(	(	PUNCT
ejpam-2881	53	2	1	1	X
ejpam-2881	53	3	)	)	PUNCT
ejpam-2881	53	4	it	it	PRON
ejpam-2881	53	5	follows	follow	VERB
ejpam-2881	53	6	that	that	SCONJ
ejpam-2881	53	7	,	,	PUNCT
ejpam-2881	53	8	at	at	ADP
ejpam-2881	53	9	each	each	DET
ejpam-2881	53	10	point	point	NOUN
ejpam-2881	53	11	λ	λ	X
ejpam-2881	53	12	>	>	X
ejpam-2881	53	13	0	0	PROPN
ejpam-2881	53	14	,	,	PUNCT
ejpam-2881	53	15	the	the	DET
ejpam-2881	53	16	right	right	ADJ
ejpam-2881	53	17	limit	limit	NOUN
ejpam-2881	53	18	ωλ+0(x	ωλ+0(x	PROPN
ejpam-2881	53	19	,	,	PUNCT
ejpam-2881	53	20	y	y	PROPN
ejpam-2881	53	21	)	)	PUNCT
ejpam-2881	53	22	:	:	PUNCT
ejpam-2881	53	23	=	=	SYM
ejpam-2881	53	24	lim	lim	PROPN
ejpam-2881	53	25	ε→+0	ε→+0	PROPN
ejpam-2881	53	26	ωλ+ε(x	ωλ+ε(x	PROPN
ejpam-2881	53	27	,	,	PUNCT
ejpam-2881	53	28	y	y	NOUN
ejpam-2881	53	29	)	)	PUNCT
ejpam-2881	53	30	and	and	CCONJ
ejpam-2881	53	31	the	the	DET
ejpam-2881	53	32	left	left	ADJ
ejpam-2881	53	33	limit	limit	NOUN
ejpam-2881	53	34	ωλ−0(x	ωλ−0(x	NOUN
ejpam-2881	53	35	,	,	PUNCT
ejpam-2881	53	36	y	y	PROPN
ejpam-2881	53	37	)	)	PUNCT
ejpam-2881	53	38	:	:	PUNCT
ejpam-2881	53	39	=	=	SYM
ejpam-2881	53	40	lim	lim	PROPN
ejpam-2881	53	41	ε→+0	ε→+0	PROPN
ejpam-2881	53	42	ωλ−ε(x	ωλ−ε(x	PROPN
ejpam-2881	53	43	,	,	PUNCT
ejpam-2881	53	44	y	y	NOUN
ejpam-2881	53	45	)	)	PUNCT
ejpam-2881	53	46	exist	exist	VERB
ejpam-2881	53	47	in	in	ADP
ejpam-2881	53	48	[	[	X
ejpam-2881	53	49	0,∞	0,∞	NOUN
ejpam-2881	53	50	]	]	PUNCT
ejpam-2881	53	51	and	and	CCONJ
ejpam-2881	53	52	the	the	DET
ejpam-2881	53	53	following	follow	VERB
ejpam-2881	53	54	two	two	NUM
ejpam-2881	53	55	inequalities	inequality	NOUN
ejpam-2881	53	56	hold	hold	VERB
ejpam-2881	53	57	:	:	PUNCT
ejpam-2881	53	58	ωλ+0(x	ωλ+0(x	NUM
ejpam-2881	53	59	,	,	PUNCT
ejpam-2881	53	60	y	y	PROPN
ejpam-2881	53	61	)	)	PUNCT
ejpam-2881	53	62	≤	≤	NOUN
ejpam-2881	53	63	ωλ(x	ωλ(x	NUM
ejpam-2881	53	64	,	,	PUNCT
ejpam-2881	53	65	y	y	NOUN
ejpam-2881	53	66	)	)	PUNCT
ejpam-2881	53	67	≤	≤	NOUN
ejpam-2881	53	68	ωλ−0(x	ωλ−0(x	NOUN
ejpam-2881	53	69	,	,	PUNCT
ejpam-2881	53	70	y	y	PROPN
ejpam-2881	53	71	)	)	PUNCT
ejpam-2881	53	72	.	.	PUNCT
ejpam-2881	54	1	(	(	PUNCT
ejpam-2881	54	2	2	2	X
ejpam-2881	54	3	)	)	PUNCT
ejpam-2881	54	4	for	for	ADP
ejpam-2881	54	5	all	all	DET
ejpam-2881	54	6	x	x	NOUN
ejpam-2881	54	7	,	,	PUNCT
ejpam-2881	54	8	y	y	PROPN
ejpam-2881	54	9	∈	∈	PROPN
ejpam-2881	54	10	x.	x.	NOUN
ejpam-2881	54	11	we	we	PRON
ejpam-2881	54	12	know	know	VERB
ejpam-2881	54	13	that	that	SCONJ
ejpam-2881	54	14	,	,	PUNCT
ejpam-2881	55	1	if	if	SCONJ
ejpam-2881	55	2	x0	x0	PROPN
ejpam-2881	55	3	∈	∈	PROPN
ejpam-2881	55	4	x	x	PRON
ejpam-2881	55	5	,	,	PUNCT
ejpam-2881	55	6	the	the	DET
ejpam-2881	55	7	set	set	NOUN
ejpam-2881	55	8	xω	xω	X
ejpam-2881	55	9	=	=	SYM
ejpam-2881	55	10	{	{	PUNCT
ejpam-2881	55	11	x	x	PUNCT
ejpam-2881	55	12	∈	∈	PROPN
ejpam-2881	55	13	x	x	X
ejpam-2881	55	14	:	:	PUNCT
ejpam-2881	55	15	lim	lim	PROPN
ejpam-2881	55	16	λ→∞	λ→∞	NUM
ejpam-2881	55	17	ωλ(x	ωλ(x	X
ejpam-2881	55	18	,	,	PUNCT
ejpam-2881	55	19	x0	x0	NUM
ejpam-2881	55	20	)	)	PUNCT
ejpam-2881	56	1	=	=	SYM
ejpam-2881	56	2	0	0	X
ejpam-2881	56	3	}	}	PUNCT
ejpam-2881	56	4	is	be	AUX
ejpam-2881	56	5	a	a	DET
ejpam-2881	56	6	metric	metric	ADJ
ejpam-2881	56	7	space	space	NOUN
ejpam-2881	56	8	,	,	PUNCT
ejpam-2881	56	9	which	which	PRON
ejpam-2881	56	10	is	be	AUX
ejpam-2881	56	11	called	call	VERB
ejpam-2881	56	12	a	a	DET
ejpam-2881	56	13	modular	modular	ADJ
ejpam-2881	56	14	space	space	NOUN
ejpam-2881	56	15	,	,	PUNCT
ejpam-2881	56	16	whose	whose	DET
ejpam-2881	56	17	metric	metric	NOUN
ejpam-2881	56	18	is	be	AUX
ejpam-2881	56	19	given	give	VERB
ejpam-2881	56	20	by	by	ADP
ejpam-2881	56	21	d0ω(x	d0ω(x	PROPN
ejpam-2881	56	22	,	,	PUNCT
ejpam-2881	56	23	y	y	NOUN
ejpam-2881	56	24	)	)	PUNCT
ejpam-2881	57	1	=	=	SYM
ejpam-2881	57	2	inf{λ	inf{λ	X
ejpam-2881	57	3	>	>	X
ejpam-2881	57	4	0	0	NUM
ejpam-2881	58	1	:	:	PUNCT
ejpam-2881	58	2	ωλλ(x	ωλλ(x	PROPN
ejpam-2881	58	3	,	,	PUNCT
ejpam-2881	58	4	y	y	NOUN
ejpam-2881	58	5	)	)	PUNCT
ejpam-2881	58	6	≤	≤	PUNCT
ejpam-2881	58	7	λ	λ	PROPN
ejpam-2881	58	8	}	}	PUNCT
ejpam-2881	58	9	for	for	ADP
ejpam-2881	58	10	all	all	DET
ejpam-2881	58	11	x	x	NOUN
ejpam-2881	58	12	,	,	PUNCT
ejpam-2881	58	13	y	y	PROPN
ejpam-2881	58	14	∈	∈	PROPN
ejpam-2881	58	15	xω	xω	VERB
ejpam-2881	58	16	.	.	PUNCT
ejpam-2881	59	1	also	also	ADV
ejpam-2881	59	2	,	,	PUNCT
ejpam-2881	59	3	it	it	PRON
ejpam-2881	59	4	follows	follow	VERB
ejpam-2881	59	5	that	that	SCONJ
ejpam-2881	59	6	,	,	PUNCT
ejpam-2881	59	7	if	if	SCONJ
ejpam-2881	59	8	x	x	PRON
ejpam-2881	59	9	is	be	AUX
ejpam-2881	59	10	a	a	DET
ejpam-2881	59	11	real	real	ADJ
ejpam-2881	59	12	linear	linear	ADJ
ejpam-2881	59	13	space	space	NOUN
ejpam-2881	59	14	,	,	PUNCT
ejpam-2881	59	15	ρ	ρ	NOUN
ejpam-2881	59	16	:	:	PUNCT
ejpam-2881	59	17	x	x	SYM
ejpam-2881	59	18	→	→	PUNCT
ejpam-2881	59	19	[	[	X
ejpam-2881	59	20	0,∞	0,∞	X
ejpam-2881	59	21	]	]	PUNCT
ejpam-2881	59	22	and	and	CCONJ
ejpam-2881	59	23	ωλ(x	ωλ(x	X
ejpam-2881	59	24	,	,	PUNCT
ejpam-2881	59	25	y	y	NOUN
ejpam-2881	59	26	)	)	PUNCT
ejpam-2881	59	27	=	=	SYM
ejpam-2881	59	28	ρ	ρ	PROPN
ejpam-2881	59	29	(	(	PUNCT
ejpam-2881	59	30	x−	x−	PROPN
ejpam-2881	59	31	y	y	PROPN
ejpam-2881	59	32	λ	λ	PROPN
ejpam-2881	59	33	)	)	PUNCT
ejpam-2881	59	34	for	for	ADP
ejpam-2881	59	35	all	all	DET
ejpam-2881	59	36	λ	λ	PROPN
ejpam-2881	59	37	>	>	X
ejpam-2881	59	38	0	0	PUNCT
ejpam-2881	60	1	and	and	CCONJ
ejpam-2881	60	2	x	x	NOUN
ejpam-2881	60	3	,	,	PUNCT
ejpam-2881	60	4	y	y	PROPN
ejpam-2881	60	5	∈	∈	PROPN
ejpam-2881	60	6	x	x	X
ejpam-2881	60	7	,	,	PUNCT
ejpam-2881	60	8	then	then	ADV
ejpam-2881	60	9	ρ	ρ	PROPN
ejpam-2881	60	10	is	be	AUX
ejpam-2881	60	11	a	a	DET
ejpam-2881	60	12	modular	modular	NOUN
ejpam-2881	60	13	on	on	ADP
ejpam-2881	60	14	x	x	SYM
ejpam-2881	60	15	if	if	SCONJ
ejpam-2881	61	1	and	and	CCONJ
ejpam-2881	61	2	only	only	ADV
ejpam-2881	61	3	if	if	SCONJ
ejpam-2881	61	4	ω	ω	PROPN
ejpam-2881	61	5	is	be	AUX
ejpam-2881	61	6	a	a	DET
ejpam-2881	61	7	metric	metric	ADJ
ejpam-2881	61	8	modular	modular	NOUN
ejpam-2881	61	9	on	on	ADP
ejpam-2881	61	10	x	x	PART
ejpam-2881	61	11	(	(	PUNCT
ejpam-2881	61	12	see	see	VERB
ejpam-2881	61	13	[	[	X
ejpam-2881	61	14	2	2	NUM
ejpam-2881	61	15	]	]	PUNCT
ejpam-2881	61	16	)	)	PUNCT
ejpam-2881	61	17	.	.	PUNCT
ejpam-2881	62	1	example	example	NOUN
ejpam-2881	63	1	1	1	NUM
ejpam-2881	63	2	.	.	PUNCT
ejpam-2881	64	1	[	[	X
ejpam-2881	64	2	8	8	X
ejpam-2881	64	3	]	]	X
ejpam-2881	64	4	the	the	DET
ejpam-2881	64	5	following	follow	VERB
ejpam-2881	64	6	indexed	index	VERB
ejpam-2881	64	7	objects	object	NOUN
ejpam-2881	64	8	ω	ω	NOUN
ejpam-2881	64	9	are	be	AUX
ejpam-2881	64	10	simple	simple	ADJ
ejpam-2881	64	11	examples	example	NOUN
ejpam-2881	64	12	of	of	ADP
ejpam-2881	64	13	a	a	DET
ejpam-2881	64	14	modular	modular	NOUN
ejpam-2881	64	15	on	on	ADP
ejpam-2881	64	16	a	a	DET
ejpam-2881	64	17	set	set	NOUN
ejpam-2881	64	18	x.	x.	NOUN
ejpam-2881	64	19	let	let	VERB
ejpam-2881	64	20	λ	λ	X
ejpam-2881	64	21	>	>	X
ejpam-2881	64	22	0	0	PUNCT
ejpam-2881	65	1	and	and	CCONJ
ejpam-2881	65	2	x	x	NOUN
ejpam-2881	65	3	,	,	PUNCT
ejpam-2881	65	4	y	y	PROPN
ejpam-2881	65	5	∈	∈	PROPN
ejpam-2881	65	6	x.	x.	NOUN
ejpam-2881	66	1	then	then	ADV
ejpam-2881	66	2	we	we	PRON
ejpam-2881	66	3	have	have	VERB
ejpam-2881	66	4	(	(	PUNCT
ejpam-2881	66	5	1	1	NUM
ejpam-2881	66	6	)	)	PUNCT
ejpam-2881	66	7	ωλ(x	ωλ(x	NUM
ejpam-2881	66	8	,	,	PUNCT
ejpam-2881	66	9	y	y	NOUN
ejpam-2881	66	10	)	)	PUNCT
ejpam-2881	67	1	=	=	NOUN
ejpam-2881	67	2	∞	∞	NOUN
ejpam-2881	67	3	if	if	SCONJ
ejpam-2881	67	4	λ	λ	PROPN
ejpam-2881	67	5	≤	≤	NOUN
ejpam-2881	67	6	d(x	d(x	PROPN
ejpam-2881	67	7	,	,	PUNCT
ejpam-2881	67	8	y	y	NOUN
ejpam-2881	67	9	)	)	PUNCT
ejpam-2881	67	10	,	,	PUNCT
ejpam-2881	67	11	and	and	CCONJ
ejpam-2881	67	12	ωλ(x	ωλ(x	X
ejpam-2881	67	13	,	,	PUNCT
ejpam-2881	67	14	y	y	NOUN
ejpam-2881	67	15	)	)	PUNCT
ejpam-2881	68	1	=	=	SYM
ejpam-2881	68	2	0	0	PUNCT
ejpam-2881	69	1	if	if	SCONJ
ejpam-2881	69	2	λ	λ	X
ejpam-2881	69	3	>	>	X
ejpam-2881	69	4	d(x	d(x	PROPN
ejpam-2881	69	5	,	,	PUNCT
ejpam-2881	69	6	y	y	PROPN
ejpam-2881	69	7	)	)	PUNCT
ejpam-2881	69	8	;	;	PUNCT
ejpam-2881	69	9	(	(	PUNCT
ejpam-2881	69	10	2	2	X
ejpam-2881	69	11	)	)	PUNCT
ejpam-2881	69	12	ωλ(x	ωλ(x	NUM
ejpam-2881	69	13	,	,	PUNCT
ejpam-2881	69	14	y	y	NOUN
ejpam-2881	69	15	)	)	PUNCT
ejpam-2881	70	1	=	=	NOUN
ejpam-2881	70	2	∞	∞	NOUN
ejpam-2881	70	3	if	if	SCONJ
ejpam-2881	70	4	λ	λ	X
ejpam-2881	70	5	<	<	X
ejpam-2881	70	6	d(x	d(x	PROPN
ejpam-2881	70	7	,	,	PUNCT
ejpam-2881	70	8	y	y	NOUN
ejpam-2881	70	9	)	)	PUNCT
ejpam-2881	70	10	,	,	PUNCT
ejpam-2881	70	11	and	and	CCONJ
ejpam-2881	70	12	ωλ(x	ωλ(x	X
ejpam-2881	70	13	,	,	PUNCT
ejpam-2881	70	14	y	y	NOUN
ejpam-2881	70	15	)	)	PUNCT
ejpam-2881	71	1	=	=	SYM
ejpam-2881	71	2	0	0	PUNCT
ejpam-2881	72	1	if	if	SCONJ
ejpam-2881	72	2	λ	λ	PROPN
ejpam-2881	72	3	≥	≥	NOUN
ejpam-2881	72	4	d(x	d(x	PROPN
ejpam-2881	72	5	,	,	PUNCT
ejpam-2881	72	6	y	y	NOUN
ejpam-2881	72	7	)	)	PUNCT
ejpam-2881	73	1	.	.	PUNCT
ejpam-2881	74	1	p.	p.	NOUN
ejpam-2881	74	2	sumalai	sumalai	PROPN
ejpam-2881	74	3	,	,	PUNCT
ejpam-2881	74	4	p.	p.	PROPN
ejpam-2881	74	5	kumam	kumam	PROPN
ejpam-2881	74	6	,	,	PUNCT
ejpam-2881	74	7	y.	y.	PROPN
ejpam-2881	74	8	j.	j.	PROPN
ejpam-2881	74	9	cho	cho	PROPN
ejpam-2881	74	10	,	,	PUNCT
ejpam-2881	74	11	a.	a.	NOUN
ejpam-2881	74	12	padcharoen	padcharoen	PROPN
ejpam-2881	74	13	/	/	SYM
ejpam-2881	74	14	eur	eur	PROPN
ejpam-2881	74	15	.	.	PUNCT
ejpam-2881	75	1	j.	j.	PROPN
ejpam-2881	75	2	pure	pure	PROPN
ejpam-2881	75	3	appl	appl	PROPN
ejpam-2881	75	4	.	.	PROPN
ejpam-2881	75	5	math	math	PROPN
ejpam-2881	75	6	,	,	PUNCT
ejpam-2881	75	7	10	10	NUM
ejpam-2881	75	8	(	(	PUNCT
ejpam-2881	75	9	2	2	NUM
ejpam-2881	75	10	)	)	PUNCT
ejpam-2881	75	11	(	(	PUNCT
ejpam-2881	75	12	2017	2017	NUM
ejpam-2881	75	13	)	)	PUNCT
ejpam-2881	75	14	,	,	PUNCT
ejpam-2881	75	15	238	238	NUM
ejpam-2881	75	16	-	-	SYM
ejpam-2881	75	17	254	254	NUM
ejpam-2881	75	18	241	241	NUM
ejpam-2881	75	19	definition	definition	NOUN
ejpam-2881	75	20	4	4	NUM
ejpam-2881	75	21	.	.	PUNCT
ejpam-2881	76	1	[	[	X
ejpam-2881	76	2	3	3	X
ejpam-2881	76	3	]	]	PUNCT
ejpam-2881	76	4	let	let	VERB
ejpam-2881	76	5	xω	xω	PRON
ejpam-2881	76	6	be	be	AUX
ejpam-2881	76	7	a	a	DET
ejpam-2881	76	8	modular	modular	ADJ
ejpam-2881	76	9	metric	metric	ADJ
ejpam-2881	76	10	space	space	NOUN
ejpam-2881	76	11	.	.	PUNCT
ejpam-2881	77	1	(	(	PUNCT
ejpam-2881	77	2	1	1	X
ejpam-2881	77	3	)	)	PUNCT
ejpam-2881	77	4	the	the	DET
ejpam-2881	77	5	sequence	sequence	NOUN
ejpam-2881	77	6	{	{	PUNCT
ejpam-2881	77	7	xn	xn	NOUN
ejpam-2881	77	8	}	}	PUNCT
ejpam-2881	77	9	in	in	ADP
ejpam-2881	77	10	xω	xω	PROPN
ejpam-2881	77	11	is	be	AUX
ejpam-2881	77	12	said	say	VERB
ejpam-2881	77	13	to	to	PART
ejpam-2881	77	14	be	be	AUX
ejpam-2881	77	15	ω	ω	NOUN
ejpam-2881	77	16	-	-	NOUN
ejpam-2881	77	17	convergent	convergent	NOUN
ejpam-2881	77	18	to	to	ADP
ejpam-2881	77	19	a	a	DET
ejpam-2881	77	20	point	point	NOUN
ejpam-2881	77	21	x	x	X
ejpam-2881	77	22	∈	∈	NOUN
ejpam-2881	77	23	xω	xω	INTJ
ejpam-2881	77	24	if	if	SCONJ
ejpam-2881	77	25	ωλ(xn	ωλ(xn	NOUN
ejpam-2881	77	26	,	,	PUNCT
ejpam-2881	77	27	x)→	x)→	PROPN
ejpam-2881	77	28	0	0	PUNCT
ejpam-2881	78	1	as	as	ADP
ejpam-2881	78	2	n→∞	n→∞	NUM
ejpam-2881	78	3	for	for	ADP
ejpam-2881	78	4	all	all	DET
ejpam-2881	78	5	λ	λ	PROPN
ejpam-2881	78	6	>	>	X
ejpam-2881	78	7	0	0	NUM
ejpam-2881	78	8	;	;	PUNCT
ejpam-2881	78	9	(	(	PUNCT
ejpam-2881	78	10	2	2	X
ejpam-2881	78	11	)	)	PUNCT
ejpam-2881	78	12	the	the	DET
ejpam-2881	78	13	sequence	sequence	NOUN
ejpam-2881	78	14	{	{	PUNCT
ejpam-2881	78	15	xn	xn	NOUN
ejpam-2881	78	16	}	}	PUNCT
ejpam-2881	78	17	in	in	ADP
ejpam-2881	78	18	xω	xω	PROPN
ejpam-2881	78	19	is	be	AUX
ejpam-2881	78	20	called	call	VERB
ejpam-2881	78	21	an	an	DET
ejpam-2881	78	22	ω	ω	ADJ
ejpam-2881	78	23	-	-	ADJ
ejpam-2881	78	24	cauchy	cauchy	ADJ
ejpam-2881	78	25	sequence	sequence	NOUN
ejpam-2881	78	26	if	if	SCONJ
ejpam-2881	78	27	ωλ(xm	ωλ(xm	PROPN
ejpam-2881	78	28	,	,	PUNCT
ejpam-2881	78	29	xn	xn	PROPN
ejpam-2881	78	30	)	)	PUNCT
ejpam-2881	78	31	→	→	SYM
ejpam-2881	78	32	0	0	NUM
ejpam-2881	78	33	as	as	ADP
ejpam-2881	78	34	m	m	PROPN
ejpam-2881	78	35	,	,	PUNCT
ejpam-2881	78	36	n→∞	n→∞	X
ejpam-2881	78	37	for	for	ADP
ejpam-2881	78	38	all	all	DET
ejpam-2881	78	39	λ	λ	PROPN
ejpam-2881	78	40	>	>	X
ejpam-2881	78	41	0	0	NUM
ejpam-2881	78	42	;	;	PUNCT
ejpam-2881	78	43	(	(	PUNCT
ejpam-2881	78	44	3	3	X
ejpam-2881	78	45	)	)	PUNCT
ejpam-2881	78	46	a	a	DET
ejpam-2881	78	47	subset	subset	NOUN
ejpam-2881	78	48	c	c	NOUN
ejpam-2881	78	49	of	of	ADP
ejpam-2881	78	50	xω	xω	PROPN
ejpam-2881	78	51	is	be	AUX
ejpam-2881	78	52	said	say	VERB
ejpam-2881	78	53	to	to	PART
ejpam-2881	78	54	be	be	AUX
ejpam-2881	78	55	ω	ω	NOUN
ejpam-2881	78	56	-	-	ADJ
ejpam-2881	78	57	closed	closed	ADJ
ejpam-2881	78	58	if	if	SCONJ
ejpam-2881	78	59	the	the	DET
ejpam-2881	78	60	limit	limit	NOUN
ejpam-2881	78	61	of	of	ADP
ejpam-2881	78	62	a	a	DET
ejpam-2881	78	63	convergent	convergent	NOUN
ejpam-2881	78	64	sequence	sequence	NOUN
ejpam-2881	78	65	{	{	PUNCT
ejpam-2881	78	66	xn	xn	NOUN
ejpam-2881	78	67	}	}	PUNCT
ejpam-2881	78	68	of	of	ADP
ejpam-2881	78	69	c	c	NOUN
ejpam-2881	78	70	always	always	ADV
ejpam-2881	78	71	belongs	belong	VERB
ejpam-2881	78	72	to	to	ADP
ejpam-2881	78	73	c	c	NOUN
ejpam-2881	78	74	;	;	PUNCT
ejpam-2881	78	75	(	(	PUNCT
ejpam-2881	78	76	4	4	X
ejpam-2881	78	77	)	)	PUNCT
ejpam-2881	78	78	a	a	DET
ejpam-2881	78	79	subset	subset	NOUN
ejpam-2881	78	80	c	c	NOUN
ejpam-2881	78	81	of	of	ADP
ejpam-2881	78	82	xω	xω	PROPN
ejpam-2881	78	83	is	be	AUX
ejpam-2881	78	84	said	say	VERB
ejpam-2881	78	85	to	to	PART
ejpam-2881	78	86	be	be	AUX
ejpam-2881	78	87	ω	ω	NOUN
ejpam-2881	78	88	-	-	NOUN
ejpam-2881	78	89	complete	complete	ADJ
ejpam-2881	78	90	if	if	SCONJ
ejpam-2881	78	91	any	any	DET
ejpam-2881	78	92	ω	ω	ADJ
ejpam-2881	78	93	-	-	PUNCT
ejpam-2881	78	94	cauchy	cauchy	ADJ
ejpam-2881	78	95	sequence	sequence	NOUN
ejpam-2881	78	96	{	{	PUNCT
ejpam-2881	78	97	xn	xn	NOUN
ejpam-2881	78	98	}	}	PUNCT
ejpam-2881	78	99	in	in	ADP
ejpam-2881	78	100	c	c	PROPN
ejpam-2881	78	101	is	be	AUX
ejpam-2881	78	102	ω	ω	NOUN
ejpam-2881	78	103	-	-	NOUN
ejpam-2881	78	104	convergent	convergent	NOUN
ejpam-2881	78	105	to	to	ADP
ejpam-2881	78	106	a	a	DET
ejpam-2881	78	107	point	point	NOUN
ejpam-2881	78	108	is	be	AUX
ejpam-2881	78	109	in	in	ADP
ejpam-2881	78	110	c	c	NOUN
ejpam-2881	78	111	;	;	PUNCT
ejpam-2881	78	112	(	(	PUNCT
ejpam-2881	78	113	5	5	X
ejpam-2881	78	114	)	)	PUNCT
ejpam-2881	78	115	a	a	DET
ejpam-2881	78	116	subset	subset	NOUN
ejpam-2881	78	117	c	c	NOUN
ejpam-2881	78	118	of	of	ADP
ejpam-2881	78	119	xω	xω	PROPN
ejpam-2881	78	120	is	be	AUX
ejpam-2881	78	121	said	say	VERB
ejpam-2881	78	122	to	to	PART
ejpam-2881	78	123	be	be	AUX
ejpam-2881	78	124	ω	ω	NOUN
ejpam-2881	78	125	-	-	PUNCT
ejpam-2881	78	126	bounded	bounded	ADJ
ejpam-2881	78	127	if	if	SCONJ
ejpam-2881	78	128	,	,	PUNCT
ejpam-2881	78	129	for	for	ADP
ejpam-2881	78	130	all	all	DET
ejpam-2881	78	131	λ	λ	PROPN
ejpam-2881	78	132	>	>	X
ejpam-2881	78	133	0	0	NUM
ejpam-2881	78	134	,	,	PUNCT
ejpam-2881	78	135	δω(c	δω(c	X
ejpam-2881	78	136	)	)	PUNCT
ejpam-2881	78	137	=	=	SYM
ejpam-2881	78	138	sup{ωλ(x	sup{ωλ(x	X
ejpam-2881	78	139	,	,	PUNCT
ejpam-2881	78	140	y	y	PROPN
ejpam-2881	78	141	)	)	PUNCT
ejpam-2881	78	142	:	:	PUNCT
ejpam-2881	78	143	x	x	X
ejpam-2881	78	144	,	,	PUNCT
ejpam-2881	78	145	y	y	PROPN
ejpam-2881	78	146	∈	∈	PROPN
ejpam-2881	78	147	c	c	AUX
ejpam-2881	78	148	}	}	PUNCT
ejpam-2881	78	149	<	<	X
ejpam-2881	78	150	∞.	∞.	PROPN
ejpam-2881	78	151	definition	definition	NOUN
ejpam-2881	78	152	5	5	NUM
ejpam-2881	78	153	.	.	PUNCT
ejpam-2881	79	1	let	let	VERB
ejpam-2881	79	2	xω	xω	PRON
ejpam-2881	79	3	be	be	AUX
ejpam-2881	79	4	a	a	DET
ejpam-2881	79	5	modular	modular	ADJ
ejpam-2881	79	6	metric	metric	ADJ
ejpam-2881	79	7	space	space	NOUN
ejpam-2881	79	8	and	and	CCONJ
ejpam-2881	79	9	f	f	NOUN
ejpam-2881	79	10	,	,	PUNCT
ejpam-2881	79	11	g	g	NOUN
ejpam-2881	79	12	:	:	PUNCT
ejpam-2881	79	13	x	x	SYM
ejpam-2881	79	14	→	→	PUNCT
ejpam-2881	79	15	x	x	PUNCT
ejpam-2881	79	16	be	be	AUX
ejpam-2881	79	17	two	two	NUM
ejpam-2881	79	18	mappings	mapping	NOUN
ejpam-2881	79	19	.	.	PUNCT
ejpam-2881	80	1	the	the	DET
ejpam-2881	80	2	mappings	mapping	NOUN
ejpam-2881	80	3	f	f	PROPN
ejpam-2881	80	4	and	and	CCONJ
ejpam-2881	80	5	g	g	PROPN
ejpam-2881	80	6	are	be	AUX
ejpam-2881	80	7	said	say	VERB
ejpam-2881	80	8	to	to	PART
ejpam-2881	80	9	satisfy	satisfy	VERB
ejpam-2881	80	10	the	the	DET
ejpam-2881	80	11	common	common	ADJ
ejpam-2881	80	12	limit	limit	NOUN
ejpam-2881	80	13	in	in	ADP
ejpam-2881	80	14	the	the	DET
ejpam-2881	80	15	range	range	NOUN
ejpam-2881	80	16	of	of	ADP
ejpam-2881	80	17	g	g	PROPN
ejpam-2881	80	18	(	(	PUNCT
ejpam-2881	80	19	shortly	shortly	ADV
ejpam-2881	80	20	,	,	PUNCT
ejpam-2881	80	21	(	(	PUNCT
ejpam-2881	80	22	clrg)-property	clrg)-property	NOUN
ejpam-2881	80	23	)	)	PUNCT
ejpam-2881	80	24	if	if	SCONJ
ejpam-2881	80	25	lim	lim	PROPN
ejpam-2881	80	26	n→∞	n→∞	PRON
ejpam-2881	80	27	fxn	fxn	PROPN
ejpam-2881	80	28	=	=	PUNCT
ejpam-2881	80	29	lim	lim	PROPN
ejpam-2881	80	30	n→∞	n→∞	NUM
ejpam-2881	80	31	gxn	gxn	PROPN
ejpam-2881	80	32	=	=	SYM
ejpam-2881	80	33	gx	gx	PROPN
ejpam-2881	80	34	for	for	ADP
ejpam-2881	80	35	some	some	DET
ejpam-2881	80	36	x	x	SYM
ejpam-2881	80	37	∈	∈	PROPN
ejpam-2881	80	38	xω	xω	NOUN
ejpam-2881	80	39	.	.	PUNCT
ejpam-2881	81	1	definition	definition	NOUN
ejpam-2881	81	2	6	6	NUM
ejpam-2881	81	3	.	.	PUNCT
ejpam-2881	82	1	[	[	X
ejpam-2881	82	2	9	9	NUM
ejpam-2881	82	3	]	]	PUNCT
ejpam-2881	82	4	let	let	VERB
ejpam-2881	82	5	xω	xω	PRON
ejpam-2881	82	6	be	be	AUX
ejpam-2881	82	7	a	a	DET
ejpam-2881	82	8	modular	modular	ADJ
ejpam-2881	82	9	metric	metric	ADJ
ejpam-2881	82	10	space	space	NOUN
ejpam-2881	82	11	.	.	PUNCT
ejpam-2881	83	1	we	we	PRON
ejpam-2881	83	2	say	say	VERB
ejpam-2881	83	3	that	that	SCONJ
ejpam-2881	83	4	ω	ω	PROPN
ejpam-2881	83	5	satisfies	satisfy	VERB
ejpam-2881	83	6	the	the	DET
ejpam-2881	83	7	∆2condition	∆2condition	NOUN
ejpam-2881	83	8	if	if	SCONJ
ejpam-2881	83	9	,	,	PUNCT
ejpam-2881	83	10	for	for	ADP
ejpam-2881	83	11	any	any	DET
ejpam-2881	83	12	sequence	sequence	NOUN
ejpam-2881	83	13	{	{	PUNCT
ejpam-2881	83	14	xn	xn	NOUN
ejpam-2881	83	15	}	}	PUNCT
ejpam-2881	83	16	⊂	⊂	PRON
ejpam-2881	83	17	xω	xω	X
ejpam-2881	83	18	and	and	CCONJ
ejpam-2881	83	19	x	x	PROPN
ejpam-2881	83	20	∈	∈	PROPN
ejpam-2881	83	21	xw	xw	PROPN
ejpam-2881	83	22	,	,	PUNCT
ejpam-2881	83	23	there	there	PRON
ejpam-2881	83	24	exists	exist	VERB
ejpam-2881	83	25	a	a	DET
ejpam-2881	83	26	number	number	NOUN
ejpam-2881	83	27	λ	λ	X
ejpam-2881	83	28	>	>	X
ejpam-2881	83	29	0	0	NUM
ejpam-2881	83	30	,	,	PUNCT
ejpam-2881	83	31	possibly	possibly	ADV
ejpam-2881	83	32	depending	depend	VERB
ejpam-2881	83	33	on	on	ADP
ejpam-2881	83	34	{	{	PUNCT
ejpam-2881	83	35	xn	xn	NOUN
ejpam-2881	83	36	}	}	PUNCT
ejpam-2881	83	37	and	and	CCONJ
ejpam-2881	83	38	x	x	ADP
ejpam-2881	83	39	,	,	PUNCT
ejpam-2881	83	40	such	such	ADJ
ejpam-2881	83	41	that	that	SCONJ
ejpam-2881	83	42	lim	lim	PROPN
ejpam-2881	83	43	n→∞	n→∞	NUM
ejpam-2881	83	44	ωλ(xn	ωλ(xn	PROPN
ejpam-2881	83	45	,	,	PUNCT
ejpam-2881	83	46	x	x	X
ejpam-2881	83	47	)	)	PUNCT
ejpam-2881	83	48	=	=	SYM
ejpam-2881	83	49	0	0	NUM
ejpam-2881	83	50	for	for	ADP
ejpam-2881	83	51	some	some	DET
ejpam-2881	83	52	λ	λ	PROPN
ejpam-2881	83	53	>	>	X
ejpam-2881	83	54	0	0	NUM
ejpam-2881	83	55	implies	imply	VERB
ejpam-2881	83	56	lim	lim	PROPN
ejpam-2881	83	57	n→∞	n→∞	NUM
ejpam-2881	83	58	ωλ(xn	ωλ(xn	PROPN
ejpam-2881	83	59	,	,	PUNCT
ejpam-2881	83	60	x	x	X
ejpam-2881	83	61	)	)	PUNCT
ejpam-2881	83	62	=	=	SYM
ejpam-2881	83	63	0	0	NUM
ejpam-2881	83	64	for	for	ADP
ejpam-2881	83	65	all	all	DET
ejpam-2881	83	66	λ	λ	PROPN
ejpam-2881	83	67	>	>	X
ejpam-2881	83	68	0	0	X
ejpam-2881	83	69	.	.	PUNCT
ejpam-2881	84	1	note	note	VERB
ejpam-2881	84	2	that	that	SCONJ
ejpam-2881	84	3	,	,	PUNCT
ejpam-2881	84	4	in	in	ADP
ejpam-2881	84	5	this	this	DET
ejpam-2881	84	6	paper	paper	NOUN
ejpam-2881	84	7	,	,	PUNCT
ejpam-2881	84	8	we	we	PRON
ejpam-2881	84	9	suppose	suppose	VERB
ejpam-2881	84	10	that	that	SCONJ
ejpam-2881	84	11	ω	ω	PROPN
ejpam-2881	84	12	is	be	AUX
ejpam-2881	84	13	a	a	DET
ejpam-2881	84	14	modular	modular	NOUN
ejpam-2881	84	15	on	on	ADP
ejpam-2881	84	16	x	x	PUNCT
ejpam-2881	84	17	and	and	CCONJ
ejpam-2881	84	18	satisfies	satisfy	VERB
ejpam-2881	84	19	the	the	DET
ejpam-2881	84	20	∆2	∆2	NOUN
ejpam-2881	84	21	-	-	PUNCT
ejpam-2881	84	22	condition	condition	NOUN
ejpam-2881	84	23	on	on	ADP
ejpam-2881	84	24	x.	x.	NOUN
ejpam-2881	84	25	3	3	X
ejpam-2881	84	26	.	.	PUNCT
ejpam-2881	84	27	fixed	fix	VERB
ejpam-2881	84	28	point	point	NOUN
ejpam-2881	84	29	results	result	NOUN
ejpam-2881	84	30	for	for	ADP
ejpam-2881	84	31	the	the	DET
ejpam-2881	84	32	contractive	contractive	ADJ
ejpam-2881	84	33	condition	condition	NOUN
ejpam-2881	84	34	lemma	lemma	PROPN
ejpam-2881	84	35	1	1	X
ejpam-2881	84	36	.	.	PUNCT
ejpam-2881	85	1	let	let	VERB
ejpam-2881	85	2	f	f	PROPN
ejpam-2881	85	3	and	and	CCONJ
ejpam-2881	85	4	g	g	PROPN
ejpam-2881	85	5	be	be	VERB
ejpam-2881	85	6	weakly	weakly	ADV
ejpam-2881	85	7	compatible	compatible	ADJ
ejpam-2881	85	8	self	self	NOUN
ejpam-2881	85	9	-	-	PUNCT
ejpam-2881	85	10	mappings	mapping	NOUN
ejpam-2881	85	11	of	of	ADP
ejpam-2881	85	12	a	a	DET
ejpam-2881	85	13	set	set	NOUN
ejpam-2881	85	14	xω	xω	PRON
ejpam-2881	85	15	.	.	PUNCT
ejpam-2881	86	1	if	if	SCONJ
ejpam-2881	86	2	f	f	PROPN
ejpam-2881	86	3	and	and	CCONJ
ejpam-2881	86	4	g	g	PROPN
ejpam-2881	86	5	have	have	VERB
ejpam-2881	86	6	a	a	DET
ejpam-2881	86	7	unique	unique	ADJ
ejpam-2881	86	8	coincidence	coincidence	NOUN
ejpam-2881	86	9	point	point	NOUN
ejpam-2881	86	10	,	,	PUNCT
ejpam-2881	86	11	that	that	ADV
ejpam-2881	86	12	is	is	ADV
ejpam-2881	86	13	,	,	PUNCT
ejpam-2881	86	14	t	t	NOUN
ejpam-2881	86	15	=	=	SYM
ejpam-2881	86	16	fx	fx	PROPN
ejpam-2881	86	17	=	=	SYM
ejpam-2881	86	18	gx	gx	PROPN
ejpam-2881	86	19	,	,	PUNCT
ejpam-2881	86	20	then	then	ADV
ejpam-2881	86	21	t	t	PROPN
ejpam-2881	86	22	is	be	AUX
ejpam-2881	86	23	the	the	DET
ejpam-2881	86	24	common	common	ADJ
ejpam-2881	86	25	fixed	fix	VERB
ejpam-2881	86	26	point	point	NOUN
ejpam-2881	86	27	of	of	ADP
ejpam-2881	86	28	f	f	PROPN
ejpam-2881	86	29	and	and	CCONJ
ejpam-2881	86	30	g.	g.	PROPN
ejpam-2881	86	31	theorem	theorem	VERB
ejpam-2881	86	32	1	1	X
ejpam-2881	86	33	.	.	PUNCT
ejpam-2881	87	1	let	let	VERB
ejpam-2881	87	2	xω	xω	PRON
ejpam-2881	87	3	be	be	AUX
ejpam-2881	87	4	a	a	DET
ejpam-2881	87	5	modular	modular	ADJ
ejpam-2881	87	6	metric	metric	ADJ
ejpam-2881	87	7	space	space	NOUN
ejpam-2881	87	8	and	and	CCONJ
ejpam-2881	87	9	f	f	NOUN
ejpam-2881	87	10	,	,	PUNCT
ejpam-2881	87	11	g	g	NOUN
ejpam-2881	87	12	:	:	PUNCT
ejpam-2881	87	13	xω	xω	PROPN
ejpam-2881	87	14	→	→	PUNCT
ejpam-2881	87	15	xω	xω	NOUN
ejpam-2881	87	16	be	be	AUX
ejpam-2881	87	17	weakly	weakly	ADV
ejpam-2881	87	18	compatible	compatible	ADJ
ejpam-2881	87	19	mappings	mapping	NOUN
ejpam-2881	87	20	such	such	ADJ
ejpam-2881	87	21	that	that	DET
ejpam-2881	87	22	f(xω	f(xω	NOUN
ejpam-2881	87	23	)	)	PUNCT
ejpam-2881	88	1	⊂	⊂	PROPN
ejpam-2881	88	2	g(xω	g(xω	NOUN
ejpam-2881	88	3	)	)	PUNCT
ejpam-2881	88	4	and	and	CCONJ
ejpam-2881	88	5	g(xω	g(xω	NOUN
ejpam-2881	88	6	)	)	PUNCT
ejpam-2881	88	7	is	be	AUX
ejpam-2881	88	8	a	a	DET
ejpam-2881	88	9	ω	ω	ADJ
ejpam-2881	88	10	-	-	ADJ
ejpam-2881	88	11	complete	complete	ADJ
ejpam-2881	88	12	subspace	subspace	NOUN
ejpam-2881	88	13	of	of	ADP
ejpam-2881	88	14	xω	xω	PROPN
ejpam-2881	88	15	.	.	PUNCT
ejpam-2881	89	1	suppose	suppose	VERB
ejpam-2881	89	2	there	there	PRON
ejpam-2881	89	3	exists	exist	VERB
ejpam-2881	89	4	number	number	NOUN
ejpam-2881	89	5	a	a	DET
ejpam-2881	89	6	∈	∈	NOUN
ejpam-2881	90	1	[	[	X
ejpam-2881	90	2	0	0	NUM
ejpam-2881	90	3	,	,	PUNCT
ejpam-2881	90	4	1	1	NUM
ejpam-2881	90	5	4	4	NUM
ejpam-2881	90	6	)	)	PUNCT
ejpam-2881	90	7	for	for	ADP
ejpam-2881	90	8	all	all	DET
ejpam-2881	90	9	x	x	NOUN
ejpam-2881	90	10	,	,	PUNCT
ejpam-2881	90	11	y	y	PROPN
ejpam-2881	90	12	∈	∈	PROPN
ejpam-2881	90	13	xω	xω	X
ejpam-2881	91	1	and	and	CCONJ
ejpam-2881	91	2	λ	λ	X
ejpam-2881	91	3	>	>	X
ejpam-2881	91	4	0	0	NUM
ejpam-2881	92	1	such	such	ADJ
ejpam-2881	92	2	that	that	SCONJ
ejpam-2881	92	3	(	(	PUNCT
ejpam-2881	92	4	a	a	X
ejpam-2881	92	5	)	)	PUNCT
ejpam-2881	92	6	there	there	PRON
ejpam-2881	92	7	exists	exist	VERB
ejpam-2881	92	8	x0	x0	PROPN
ejpam-2881	92	9	,	,	PUNCT
ejpam-2881	92	10	x1	x1	PROPN
ejpam-2881	92	11	∈	∈	PROPN
ejpam-2881	92	12	xω	xω	PRON
ejpam-2881	92	13	such	such	ADJ
ejpam-2881	92	14	that	that	SCONJ
ejpam-2881	92	15	ωλ(fx0	ωλ(fx0	NUM
ejpam-2881	92	16	,	,	PUNCT
ejpam-2881	92	17	gx1	gx1	PROPN
ejpam-2881	92	18	)	)	PUNCT
ejpam-2881	92	19	<	<	X
ejpam-2881	92	20	∞	∞	PROPN
ejpam-2881	92	21	;	;	PUNCT
ejpam-2881	92	22	(	(	PUNCT
ejpam-2881	92	23	b	b	X
ejpam-2881	92	24	)	)	PUNCT
ejpam-2881	92	25	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	92	26	,	,	PUNCT
ejpam-2881	92	27	fy	fy	PROPN
ejpam-2881	92	28	)	)	PUNCT
ejpam-2881	92	29	≤	≤	NOUN
ejpam-2881	92	30	a[ωλ(fx	a[ωλ(fx	NOUN
ejpam-2881	92	31	,	,	PUNCT
ejpam-2881	92	32	gy	gy	NOUN
ejpam-2881	92	33	)	)	PUNCT
ejpam-2881	92	34	+	+	CCONJ
ejpam-2881	92	35	ω2λ(fy	ω2λ(fy	ADJ
ejpam-2881	92	36	,	,	PUNCT
ejpam-2881	92	37	gx	gx	PROPN
ejpam-2881	92	38	)	)	PUNCT
ejpam-2881	92	39	+	+	CCONJ
ejpam-2881	92	40	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	92	41	,	,	PUNCT
ejpam-2881	92	42	gx	gx	PROPN
ejpam-2881	92	43	)	)	PUNCT
ejpam-2881	93	1	+	+	CCONJ
ejpam-2881	93	2	ωλ(fy	ωλ(fy	PROPN
ejpam-2881	93	3	,	,	PUNCT
ejpam-2881	93	4	gy	gy	NOUN
ejpam-2881	93	5	)	)	PUNCT
ejpam-2881	93	6	]	]	PUNCT
ejpam-2881	93	7	.	.	PUNCT
ejpam-2881	94	1	then	then	ADV
ejpam-2881	94	2	f	f	PROPN
ejpam-2881	94	3	and	and	CCONJ
ejpam-2881	94	4	g	g	PROPN
ejpam-2881	94	5	have	have	VERB
ejpam-2881	94	6	a	a	DET
ejpam-2881	94	7	coincidence	coincidence	NOUN
ejpam-2881	94	8	point	point	NOUN
ejpam-2881	94	9	.	.	PUNCT
ejpam-2881	95	1	p.	p.	NOUN
ejpam-2881	95	2	sumalai	sumalai	PROPN
ejpam-2881	95	3	,	,	PUNCT
ejpam-2881	95	4	p.	p.	PROPN
ejpam-2881	95	5	kumam	kumam	PROPN
ejpam-2881	95	6	,	,	PUNCT
ejpam-2881	95	7	y.	y.	PROPN
ejpam-2881	95	8	j.	j.	PROPN
ejpam-2881	95	9	cho	cho	PROPN
ejpam-2881	95	10	,	,	PUNCT
ejpam-2881	95	11	a.	a.	NOUN
ejpam-2881	95	12	padcharoen	padcharoen	PROPN
ejpam-2881	95	13	/	/	SYM
ejpam-2881	95	14	eur	eur	PROPN
ejpam-2881	95	15	.	.	PUNCT
ejpam-2881	96	1	j.	j.	PROPN
ejpam-2881	96	2	pure	pure	PROPN
ejpam-2881	96	3	appl	appl	PROPN
ejpam-2881	96	4	.	.	PROPN
ejpam-2881	96	5	math	math	PROPN
ejpam-2881	96	6	,	,	PUNCT
ejpam-2881	96	7	10	10	NUM
ejpam-2881	96	8	(	(	PUNCT
ejpam-2881	96	9	2	2	NUM
ejpam-2881	96	10	)	)	PUNCT
ejpam-2881	96	11	(	(	PUNCT
ejpam-2881	96	12	2017	2017	NUM
ejpam-2881	96	13	)	)	PUNCT
ejpam-2881	96	14	,	,	PUNCT
ejpam-2881	96	15	238	238	NUM
ejpam-2881	96	16	-	-	SYM
ejpam-2881	96	17	254	254	NUM
ejpam-2881	96	18	242	242	NUM
ejpam-2881	96	19	proof	proof	NOUN
ejpam-2881	96	20	.	.	PUNCT
ejpam-2881	97	1	let	let	VERB
ejpam-2881	97	2	x0	x0	PROPN
ejpam-2881	97	3	be	be	AUX
ejpam-2881	97	4	an	an	DET
ejpam-2881	97	5	arbitrary	arbitrary	ADJ
ejpam-2881	97	6	point	point	NOUN
ejpam-2881	97	7	in	in	ADP
ejpam-2881	97	8	xω	xω	PRON
ejpam-2881	97	9	.	.	PUNCT
ejpam-2881	98	1	since	since	SCONJ
ejpam-2881	98	2	f(xω	f(xω	PROPN
ejpam-2881	98	3	)	)	PUNCT
ejpam-2881	98	4	⊂	⊂	PROPN
ejpam-2881	98	5	g(xω	g(xω	NOUN
ejpam-2881	98	6	)	)	PUNCT
ejpam-2881	98	7	,	,	PUNCT
ejpam-2881	98	8	there	there	PRON
ejpam-2881	98	9	exists	exist	VERB
ejpam-2881	98	10	a	a	DET
ejpam-2881	98	11	sequence	sequence	NOUN
ejpam-2881	98	12	{	{	PUNCT
ejpam-2881	98	13	xn	xn	NUM
ejpam-2881	98	14	}	}	PUNCT
ejpam-2881	98	15	in	in	ADP
ejpam-2881	98	16	xω	xω	PRON
ejpam-2881	98	17	such	such	ADJ
ejpam-2881	98	18	that	that	DET
ejpam-2881	98	19	gxn	gxn	NOUN
ejpam-2881	98	20	=	=	SYM
ejpam-2881	98	21	fxn−1	fxn−1	PROPN
ejpam-2881	98	22	for	for	ADP
ejpam-2881	98	23	all	all	DET
ejpam-2881	98	24	n	n	PRON
ejpam-2881	98	25	≥	≥	NOUN
ejpam-2881	98	26	1	1	NUM
ejpam-2881	98	27	.	.	PUNCT
ejpam-2881	99	1	now	now	ADV
ejpam-2881	99	2	,	,	PUNCT
ejpam-2881	99	3	setting	set	VERB
ejpam-2881	99	4	x	x	PUNCT
ejpam-2881	99	5	=	=	PUNCT
ejpam-2881	99	6	xn	xn	PROPN
ejpam-2881	99	7	and	and	CCONJ
ejpam-2881	99	8	y	y	PROPN
ejpam-2881	99	9	=	=	SYM
ejpam-2881	99	10	xn+1	xn+1	PROPN
ejpam-2881	99	11	in	in	ADP
ejpam-2881	99	12	(	(	PUNCT
ejpam-2881	99	13	b	b	NOUN
ejpam-2881	99	14	)	)	PUNCT
ejpam-2881	99	15	,	,	PUNCT
ejpam-2881	99	16	we	we	PRON
ejpam-2881	99	17	have	have	VERB
ejpam-2881	99	18	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	99	19	,	,	PUNCT
ejpam-2881	99	20	fxn+1	fxn+1	PROPN
ejpam-2881	99	21	)	)	PUNCT
ejpam-2881	99	22	≤	≤	PROPN
ejpam-2881	100	1	a[ωλ(fxn	a[ωλ(fxn	PROPN
ejpam-2881	100	2	,	,	PUNCT
ejpam-2881	100	3	fxn	fxn	NOUN
ejpam-2881	100	4	)	)	PUNCT
ejpam-2881	100	5	+	+	CCONJ
ejpam-2881	100	6	ω2λ(fxn+1	ω2λ(fxn+1	ADJ
ejpam-2881	100	7	,	,	PUNCT
ejpam-2881	100	8	fxn−1	fxn−1	PROPN
ejpam-2881	100	9	)	)	PUNCT
ejpam-2881	100	10	+	+	NUM
ejpam-2881	100	11	ωλ(gxn+1	ωλ(gxn+1	ADJ
ejpam-2881	100	12	,	,	PUNCT
ejpam-2881	100	13	gxn	gxn	ADJ
ejpam-2881	100	14	)	)	PUNCT
ejpam-2881	100	15	+	+	CCONJ
ejpam-2881	100	16	ωλ(fxn+1	ωλ(fxn+1	ADJ
ejpam-2881	100	17	,	,	PUNCT
ejpam-2881	100	18	fxn	fxn	NOUN
ejpam-2881	100	19	)	)	PUNCT
ejpam-2881	100	20	]	]	PUNCT
ejpam-2881	101	1	=	=	PUNCT
ejpam-2881	101	2	a[ω2λ(fxn+1	a[ω2λ(fxn+1	PROPN
ejpam-2881	101	3	,	,	PUNCT
ejpam-2881	101	4	fxn−1	fxn−1	PROPN
ejpam-2881	101	5	)	)	PUNCT
ejpam-2881	101	6	+	+	NUM
ejpam-2881	101	7	ωλ(gxn+1	ωλ(gxn+1	ADJ
ejpam-2881	101	8	,	,	PUNCT
ejpam-2881	101	9	gxn	gxn	ADJ
ejpam-2881	101	10	)	)	PUNCT
ejpam-2881	101	11	+	+	CCONJ
ejpam-2881	101	12	ωλ(fxn+1	ωλ(fxn+1	ADJ
ejpam-2881	101	13	,	,	PUNCT
ejpam-2881	101	14	fxn	fxn	NOUN
ejpam-2881	101	15	)	)	PUNCT
ejpam-2881	101	16	]	]	PUNCT
ejpam-2881	101	17	for	for	ADP
ejpam-2881	101	18	all	all	DET
ejpam-2881	101	19	λ	λ	PROPN
ejpam-2881	101	20	>	>	X
ejpam-2881	101	21	0	0	X
ejpam-2881	101	22	.	.	PUNCT
ejpam-2881	102	1	on	on	ADP
ejpam-2881	102	2	the	the	DET
ejpam-2881	102	3	other	other	ADJ
ejpam-2881	102	4	hand	hand	NOUN
ejpam-2881	102	5	,	,	PUNCT
ejpam-2881	102	6	we	we	PRON
ejpam-2881	102	7	have	have	VERB
ejpam-2881	102	8	ω2λ(fxn+1	ω2λ(fxn+1	ADJ
ejpam-2881	102	9	,	,	PUNCT
ejpam-2881	102	10	fxn−1	fxn−1	PROPN
ejpam-2881	102	11	)	)	PUNCT
ejpam-2881	102	12	≤	≤	NOUN
ejpam-2881	102	13	ωλ(fxn+1	ωλ(fxn+1	NOUN
ejpam-2881	102	14	,	,	PUNCT
ejpam-2881	102	15	fxn	fxn	NOUN
ejpam-2881	102	16	)	)	PUNCT
ejpam-2881	103	1	+	+	CCONJ
ejpam-2881	103	2	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	103	3	,	,	PUNCT
ejpam-2881	103	4	fxn−1	fxn−1	PROPN
ejpam-2881	103	5	)	)	PUNCT
ejpam-2881	103	6	=	=	PUNCT
ejpam-2881	103	7	ωλ(fxn+1	ωλ(fxn+1	ADJ
ejpam-2881	103	8	,	,	PUNCT
ejpam-2881	103	9	fxn	fxn	NOUN
ejpam-2881	103	10	)	)	PUNCT
ejpam-2881	104	1	+	+	CCONJ
ejpam-2881	104	2	ωλ(gxn+1	ωλ(gxn+1	ADJ
ejpam-2881	104	3	,	,	PUNCT
ejpam-2881	104	4	gxn	gxn	ADJ
ejpam-2881	104	5	)	)	PUNCT
ejpam-2881	104	6	and	and	CCONJ
ejpam-2881	105	1	so	so	ADV
ejpam-2881	105	2	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	105	3	,	,	PUNCT
ejpam-2881	105	4	fxn+1	fxn+1	PROPN
ejpam-2881	105	5	)	)	PUNCT
ejpam-2881	105	6	≤	≤	ADV
ejpam-2881	105	7	a[ωλ(fxn+1	a[ωλ(fxn+1	ADJ
ejpam-2881	105	8	,	,	PUNCT
ejpam-2881	105	9	fxn)+ωλ(gxn+1	fxn)+ωλ(gxn+1	X
ejpam-2881	105	10	,	,	PUNCT
ejpam-2881	105	11	gxn)+ωλ(gxn+1	gxn)+ωλ(gxn+1	PROPN
ejpam-2881	105	12	,	,	PUNCT
ejpam-2881	105	13	gxn)+ωλ(fxn+1	gxn)+ωλ(fxn+1	NOUN
ejpam-2881	105	14	,	,	PUNCT
ejpam-2881	105	15	fxn	fxn	NOUN
ejpam-2881	105	16	)	)	PUNCT
ejpam-2881	105	17	]	]	PUNCT
ejpam-2881	105	18	.	.	PUNCT
ejpam-2881	106	1	this	this	PRON
ejpam-2881	106	2	implies	imply	VERB
ejpam-2881	106	3	that	that	SCONJ
ejpam-2881	106	4	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	106	5	,	,	PUNCT
ejpam-2881	106	6	fxn+1	fxn+1	PROPN
ejpam-2881	106	7	)	)	PUNCT
ejpam-2881	106	8	≤	≤	NOUN
ejpam-2881	106	9	2a	2a	NUM
ejpam-2881	106	10	1−	1−	NUM
ejpam-2881	106	11	2a	2a	NUM
ejpam-2881	106	12	ωλ(gxn	ωλ(gxn	NUM
ejpam-2881	106	13	,	,	PUNCT
ejpam-2881	106	14	gxn+1	gxn+1	PROPN
ejpam-2881	106	15	)	)	PUNCT
ejpam-2881	106	16	for	for	ADP
ejpam-2881	106	17	all	all	PRON
ejpam-2881	106	18	n	n	PRON
ejpam-2881	106	19	∈	∈	PROPN
ejpam-2881	106	20	n	n	CCONJ
ejpam-2881	106	21	,	,	PUNCT
ejpam-2881	106	22	where	where	SCONJ
ejpam-2881	106	23	α	α	NOUN
ejpam-2881	106	24	=	=	SYM
ejpam-2881	106	25	2a	2a	NUM
ejpam-2881	106	26	1−	1−	NUM
ejpam-2881	106	27	2a	2a	NUM
ejpam-2881	106	28	<	<	X
ejpam-2881	106	29	1	1	X
ejpam-2881	106	30	.	.	PUNCT
ejpam-2881	106	31	by	by	ADP
ejpam-2881	106	32	induction	induction	NOUN
ejpam-2881	106	33	,	,	PUNCT
ejpam-2881	106	34	we	we	PRON
ejpam-2881	106	35	have	have	VERB
ejpam-2881	106	36	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	106	37	,	,	PUNCT
ejpam-2881	106	38	fxn+1	fxn+1	PROPN
ejpam-2881	106	39	)	)	PUNCT
ejpam-2881	106	40	≤	≤	NOUN
ejpam-2881	106	41	αnωλ(gx0	αnωλ(gx0	PROPN
ejpam-2881	106	42	,	,	PUNCT
ejpam-2881	106	43	gx1	gx1	PROPN
ejpam-2881	106	44	)	)	PUNCT
ejpam-2881	106	45	(	(	PUNCT
ejpam-2881	106	46	3	3	X
ejpam-2881	106	47	)	)	PUNCT
ejpam-2881	106	48	for	for	ADP
ejpam-2881	106	49	all	all	PRON
ejpam-2881	106	50	n	n	DET
ejpam-2881	106	51	∈	∈	NOUN
ejpam-2881	106	52	n.	n.	NOUN
ejpam-2881	106	53	by	by	ADP
ejpam-2881	106	54	(	(	PUNCT
ejpam-2881	106	55	a	a	X
ejpam-2881	106	56	)	)	PUNCT
ejpam-2881	106	57	,	,	PUNCT
ejpam-2881	106	58	it	it	PRON
ejpam-2881	106	59	follows	follow	VERB
ejpam-2881	106	60	that	that	SCONJ
ejpam-2881	106	61	{	{	PUNCT
ejpam-2881	106	62	fxn	fxn	NOUN
ejpam-2881	106	63	}	}	PUNCT
ejpam-2881	106	64	is	be	AUX
ejpam-2881	106	65	a	a	DET
ejpam-2881	106	66	ω	ω	ADJ
ejpam-2881	106	67	-	-	ADJ
ejpam-2881	106	68	cauchy	cauchy	ADJ
ejpam-2881	106	69	sequence	sequence	NOUN
ejpam-2881	106	70	.	.	PUNCT
ejpam-2881	107	1	since	since	SCONJ
ejpam-2881	107	2	g(xω	g(xω	NOUN
ejpam-2881	107	3	)	)	PUNCT
ejpam-2881	107	4	is	be	AUX
ejpam-2881	107	5	ω	ω	NOUN
ejpam-2881	107	6	-	-	NOUN
ejpam-2881	107	7	complete	complete	ADJ
ejpam-2881	107	8	,	,	PUNCT
ejpam-2881	107	9	there	there	PRON
ejpam-2881	107	10	exists	exist	VERB
ejpam-2881	107	11	u	u	NOUN
ejpam-2881	107	12	,	,	PUNCT
ejpam-2881	107	13	v	v	ADP
ejpam-2881	107	14	∈	∈	NOUN
ejpam-2881	107	15	xω	xω	NOUN
ejpam-2881	107	16	such	such	ADJ
ejpam-2881	107	17	that	that	DET
ejpam-2881	107	18	u	u	NOUN
ejpam-2881	107	19	=	=	SYM
ejpam-2881	107	20	g(v	g(v	X
ejpam-2881	107	21	)	)	PUNCT
ejpam-2881	107	22	and	and	CCONJ
ejpam-2881	107	23	fxn	fxn	ADJ
ejpam-2881	107	24	→	→	SYM
ejpam-2881	107	25	u	u	NOUN
ejpam-2881	107	26	as	as	ADP
ejpam-2881	107	27	n	n	PROPN
ejpam-2881	107	28	→	→	SYM
ejpam-2881	107	29	∞.	∞.	PROPN
ejpam-2881	107	30	since	since	SCONJ
ejpam-2881	107	31	ω	ω	PROPN
ejpam-2881	107	32	satisfy	satisfy	VERB
ejpam-2881	107	33	the	the	DET
ejpam-2881	107	34	∆2	∆2	NOUN
ejpam-2881	107	35	-	-	PUNCT
ejpam-2881	107	36	condition	condition	NOUN
ejpam-2881	107	37	on	on	ADP
ejpam-2881	107	38	x	x	NOUN
ejpam-2881	107	39	,	,	PUNCT
ejpam-2881	107	40	we	we	PRON
ejpam-2881	107	41	have	have	VERB
ejpam-2881	107	42	lim	lim	PROPN
ejpam-2881	107	43	n→∞	n→∞	PROPN
ejpam-2881	107	44	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	107	45	,	,	PUNCT
ejpam-2881	107	46	u	u	NOUN
ejpam-2881	107	47	)	)	PUNCT
ejpam-2881	107	48	=	=	SYM
ejpam-2881	107	49	0	0	NUM
ejpam-2881	107	50	for	for	ADP
ejpam-2881	107	51	all	all	DET
ejpam-2881	107	52	λ	λ	PROPN
ejpam-2881	107	53	>	>	X
ejpam-2881	107	54	0	0	PUNCT
ejpam-2881	108	1	and	and	CCONJ
ejpam-2881	108	2	hence	hence	ADV
ejpam-2881	108	3	lim	lim	PROPN
ejpam-2881	108	4	n→∞	n→∞	PROPN
ejpam-2881	108	5	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	108	6	,	,	PUNCT
ejpam-2881	108	7	u	u	NOUN
ejpam-2881	108	8	)	)	PUNCT
ejpam-2881	108	9	=	=	SYM
ejpam-2881	108	10	lim	lim	PROPN
ejpam-2881	108	11	n→∞	n→∞	NUM
ejpam-2881	108	12	ωλ(gxn	ωλ(gxn	PROPN
ejpam-2881	108	13	,	,	PUNCT
ejpam-2881	108	14	u	u	NOUN
ejpam-2881	108	15	)	)	PUNCT
ejpam-2881	108	16	=	=	SYM
ejpam-2881	108	17	0	0	NUM
ejpam-2881	108	18	(	(	PUNCT
ejpam-2881	108	19	4	4	NUM
ejpam-2881	108	20	)	)	PUNCT
ejpam-2881	108	21	for	for	ADP
ejpam-2881	108	22	all	all	DET
ejpam-2881	108	23	λ	λ	PROPN
ejpam-2881	108	24	>	>	X
ejpam-2881	108	25	0	0	X
ejpam-2881	108	26	.	.	PUNCT
ejpam-2881	109	1	letting	let	VERB
ejpam-2881	109	2	x	x	PUNCT
ejpam-2881	109	3	=	=	PUNCT
ejpam-2881	109	4	xn	xn	PROPN
ejpam-2881	109	5	and	and	CCONJ
ejpam-2881	109	6	y	y	PROPN
ejpam-2881	109	7	=	=	NOUN
ejpam-2881	109	8	v	v	PROPN
ejpam-2881	109	9	in	in	ADP
ejpam-2881	109	10	(	(	PUNCT
ejpam-2881	109	11	b	b	NOUN
ejpam-2881	109	12	)	)	PUNCT
ejpam-2881	109	13	,	,	PUNCT
ejpam-2881	109	14	we	we	PRON
ejpam-2881	109	15	have	have	VERB
ejpam-2881	109	16	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	109	17	,	,	PUNCT
ejpam-2881	109	18	fv	fv	PROPN
ejpam-2881	109	19	)	)	PUNCT
ejpam-2881	109	20	≤	≤	NOUN
ejpam-2881	110	1	a[ωλ(fxn	a[ωλ(fxn	ADP
ejpam-2881	110	2	,	,	PUNCT
ejpam-2881	110	3	gv	gv	ADP
ejpam-2881	110	4	)	)	PUNCT
ejpam-2881	110	5	+	+	CCONJ
ejpam-2881	110	6	ω2λ(fv	ω2λ(fv	PROPN
ejpam-2881	110	7	,	,	PUNCT
ejpam-2881	110	8	gxn	gxn	ADJ
ejpam-2881	110	9	)	)	PUNCT
ejpam-2881	110	10	+	+	SYM
ejpam-2881	111	1	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	111	2	,	,	PUNCT
ejpam-2881	111	3	gxn	gxn	PROPN
ejpam-2881	111	4	)	)	PUNCT
ejpam-2881	111	5	+	+	NUM
ejpam-2881	111	6	ωλ(fv	ωλ(fv	NOUN
ejpam-2881	111	7	,	,	PUNCT
ejpam-2881	111	8	gv	gv	NOUN
ejpam-2881	111	9	)	)	PUNCT
ejpam-2881	111	10	]	]	PUNCT
ejpam-2881	111	11	≤	≤	PROPN
ejpam-2881	112	1	a[ωλ(fxn	a[ωλ(fxn	ADV
ejpam-2881	112	2	,	,	PUNCT
ejpam-2881	112	3	gv	gv	ADP
ejpam-2881	112	4	)	)	PUNCT
ejpam-2881	112	5	+	+	CCONJ
ejpam-2881	112	6	ω2λ(fv	ω2λ(fv	PROPN
ejpam-2881	112	7	,	,	PUNCT
ejpam-2881	112	8	fxn	fxn	NOUN
ejpam-2881	112	9	)	)	PUNCT
ejpam-2881	112	10	+	+	CCONJ
ejpam-2881	113	1	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	113	2	,	,	PUNCT
ejpam-2881	113	3	gxn	gxn	PROPN
ejpam-2881	113	4	)	)	PUNCT
ejpam-2881	113	5	+	+	NUM
ejpam-2881	113	6	ωλ(fv	ωλ(fv	NOUN
ejpam-2881	113	7	,	,	PUNCT
ejpam-2881	113	8	gv	gv	NOUN
ejpam-2881	113	9	)	)	PUNCT
ejpam-2881	113	10	]	]	PUNCT
ejpam-2881	113	11	and	and	CCONJ
ejpam-2881	113	12	,	,	PUNCT
ejpam-2881	113	13	by	by	ADP
ejpam-2881	113	14	remark	remark	NOUN
ejpam-2881	113	15	1	1	NUM
ejpam-2881	113	16	,	,	PUNCT
ejpam-2881	113	17	since	since	SCONJ
ejpam-2881	113	18	the	the	DET
ejpam-2881	113	19	function	function	NOUN
ejpam-2881	113	20	λ	λ	PROPN
ejpam-2881	113	21	7→	7→	NUM
ejpam-2881	113	22	ωλ(x	ωλ(x	NUM
ejpam-2881	113	23	,	,	PUNCT
ejpam-2881	113	24	y	y	NOUN
ejpam-2881	113	25	)	)	PUNCT
ejpam-2881	113	26	is	be	AUX
ejpam-2881	113	27	non	non	ADJ
ejpam-2881	113	28	-	-	ADJ
ejpam-2881	113	29	increasing	increase	VERB
ejpam-2881	113	30	,	,	PUNCT
ejpam-2881	113	31	we	we	PRON
ejpam-2881	113	32	have	have	VERB
ejpam-2881	113	33	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	113	34	,	,	PUNCT
ejpam-2881	113	35	fv	fv	PROPN
ejpam-2881	113	36	)	)	PUNCT
ejpam-2881	113	37	≤	≤	NOUN
ejpam-2881	114	1	a[ωλ(fxn	a[ωλ(fxn	ADP
ejpam-2881	114	2	,	,	PUNCT
ejpam-2881	114	3	gv	gv	ADP
ejpam-2881	114	4	)	)	PUNCT
ejpam-2881	114	5	+	+	CCONJ
ejpam-2881	114	6	ωλ(fv	ωλ(fv	NOUN
ejpam-2881	114	7	,	,	PUNCT
ejpam-2881	114	8	fxn	fxn	NOUN
ejpam-2881	114	9	)	)	PUNCT
ejpam-2881	115	1	+	+	CCONJ
ejpam-2881	115	2	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	115	3	,	,	PUNCT
ejpam-2881	115	4	gxn	gxn	PROPN
ejpam-2881	115	5	)	)	PUNCT
ejpam-2881	115	6	+	+	NUM
ejpam-2881	115	7	ωλ(fv	ωλ(fv	NOUN
ejpam-2881	115	8	,	,	PUNCT
ejpam-2881	115	9	gv	gv	NOUN
ejpam-2881	115	10	)	)	PUNCT
ejpam-2881	115	11	]	]	PUNCT
ejpam-2881	115	12	.	.	PUNCT
ejpam-2881	116	1	by	by	ADP
ejpam-2881	116	2	(	(	PUNCT
ejpam-2881	116	3	b	b	NOUN
ejpam-2881	116	4	)	)	PUNCT
ejpam-2881	116	5	,	,	PUNCT
ejpam-2881	116	6	letting	let	VERB
ejpam-2881	116	7	n→∞	n→∞	PRON
ejpam-2881	116	8	in	in	ADP
ejpam-2881	116	9	the	the	DET
ejpam-2881	116	10	above	above	ADJ
ejpam-2881	116	11	inequality	inequality	NOUN
ejpam-2881	116	12	,	,	PUNCT
ejpam-2881	116	13	we	we	PRON
ejpam-2881	116	14	have	have	VERB
ejpam-2881	116	15	ωλ(fv	ωλ(fv	NOUN
ejpam-2881	116	16	,	,	PUNCT
ejpam-2881	116	17	gv	gv	ADP
ejpam-2881	116	18	)	)	PUNCT
ejpam-2881	116	19	≤	≤	NOUN
ejpam-2881	117	1	[	[	X
ejpam-2881	117	2	ωλ(fv	ωλ(fv	NOUN
ejpam-2881	117	3	,	,	PUNCT
ejpam-2881	117	4	gv	gv	ADP
ejpam-2881	117	5	)	)	PUNCT
ejpam-2881	117	6	+	+	CCONJ
ejpam-2881	117	7	ωλ(fv	ωλ(fv	NOUN
ejpam-2881	117	8	,	,	PUNCT
ejpam-2881	117	9	fv	fv	NOUN
ejpam-2881	117	10	)	)	PUNCT
ejpam-2881	117	11	+	+	NUM
ejpam-2881	117	12	ωλ(fv	ωλ(fv	NOUN
ejpam-2881	117	13	,	,	PUNCT
ejpam-2881	117	14	gv	gv	ADP
ejpam-2881	117	15	)	)	PUNCT
ejpam-2881	118	1	+	+	CCONJ
ejpam-2881	118	2	ωλ(fv	ωλ(fv	NOUN
ejpam-2881	118	3	,	,	PUNCT
ejpam-2881	118	4	gv	gv	NOUN
ejpam-2881	118	5	)	)	PUNCT
ejpam-2881	118	6	]	]	PUNCT
ejpam-2881	118	7	.	.	PUNCT
ejpam-2881	119	1	thus	thus	ADV
ejpam-2881	119	2	(	(	PUNCT
ejpam-2881	119	3	1−	1−	NUM
ejpam-2881	119	4	4k)ωλ(fv	4k)ωλ(fv	NOUN
ejpam-2881	119	5	,	,	PUNCT
ejpam-2881	119	6	gv	gv	NOUN
ejpam-2881	119	7	)	)	PUNCT
ejpam-2881	119	8	≤	≤	NOUN
ejpam-2881	119	9	0	0	NUM
ejpam-2881	119	10	for	for	ADP
ejpam-2881	119	11	all	all	DET
ejpam-2881	119	12	λ	λ	PROPN
ejpam-2881	119	13	>	>	X
ejpam-2881	119	14	0	0	PUNCT
ejpam-2881	120	1	and	and	CCONJ
ejpam-2881	120	2	so	so	ADV
ejpam-2881	120	3	gv	gv	ADV
ejpam-2881	120	4	=	=	SYM
ejpam-2881	120	5	fv	fv	PROPN
ejpam-2881	120	6	=	=	SYM
ejpam-2881	120	7	u	u	PROPN
ejpam-2881	120	8	,	,	PUNCT
ejpam-2881	120	9	which	which	PRON
ejpam-2881	120	10	proves	prove	VERB
ejpam-2881	120	11	that	that	SCONJ
ejpam-2881	120	12	g	g	PROPN
ejpam-2881	120	13	and	and	CCONJ
ejpam-2881	120	14	f	f	PROPN
ejpam-2881	120	15	have	have	VERB
ejpam-2881	120	16	a	a	DET
ejpam-2881	120	17	coincidence	coincidence	NOUN
ejpam-2881	120	18	point	point	NOUN
ejpam-2881	120	19	.	.	PUNCT
ejpam-2881	121	1	now	now	ADV
ejpam-2881	121	2	,	,	PUNCT
ejpam-2881	121	3	we	we	PRON
ejpam-2881	121	4	generalize	generalize	VERB
ejpam-2881	121	5	theorem	theorem	VERB
ejpam-2881	121	6	1	1	NUM
ejpam-2881	121	7	by	by	ADP
ejpam-2881	121	8	using	use	VERB
ejpam-2881	121	9	(	(	PUNCT
ejpam-2881	121	10	clrg)-property	clrg)-property	NOUN
ejpam-2881	121	11	for	for	ADP
ejpam-2881	121	12	weakly	weakly	ADJ
ejpam-2881	121	13	compatible	compatible	ADJ
ejpam-2881	121	14	mappings	mapping	NOUN
ejpam-2881	121	15	as	as	SCONJ
ejpam-2881	121	16	follows	follow	VERB
ejpam-2881	121	17	:	:	PUNCT
ejpam-2881	121	18	p.	p.	NOUN
ejpam-2881	121	19	sumalai	sumalai	PROPN
ejpam-2881	121	20	,	,	PUNCT
ejpam-2881	121	21	p.	p.	PROPN
ejpam-2881	121	22	kumam	kumam	PROPN
ejpam-2881	121	23	,	,	PUNCT
ejpam-2881	121	24	y.	y.	PROPN
ejpam-2881	121	25	j.	j.	PROPN
ejpam-2881	121	26	cho	cho	PROPN
ejpam-2881	121	27	,	,	PUNCT
ejpam-2881	121	28	a.	a.	NOUN
ejpam-2881	121	29	padcharoen	padcharoen	PROPN
ejpam-2881	121	30	/	/	SYM
ejpam-2881	121	31	eur	eur	PROPN
ejpam-2881	121	32	.	.	PUNCT
ejpam-2881	122	1	j.	j.	PROPN
ejpam-2881	122	2	pure	pure	PROPN
ejpam-2881	122	3	appl	appl	PROPN
ejpam-2881	122	4	.	.	PROPN
ejpam-2881	122	5	math	math	PROPN
ejpam-2881	122	6	,	,	PUNCT
ejpam-2881	122	7	10	10	NUM
ejpam-2881	122	8	(	(	PUNCT
ejpam-2881	122	9	2	2	NUM
ejpam-2881	122	10	)	)	PUNCT
ejpam-2881	122	11	(	(	PUNCT
ejpam-2881	122	12	2017	2017	NUM
ejpam-2881	122	13	)	)	PUNCT
ejpam-2881	122	14	,	,	PUNCT
ejpam-2881	122	15	238	238	NUM
ejpam-2881	122	16	-	-	SYM
ejpam-2881	122	17	254	254	NUM
ejpam-2881	122	18	243	243	NUM
ejpam-2881	122	19	theorem	theorem	NOUN
ejpam-2881	122	20	2	2	NUM
ejpam-2881	122	21	.	.	PUNCT
ejpam-2881	123	1	let	let	VERB
ejpam-2881	123	2	xω	xω	PRON
ejpam-2881	123	3	be	be	AUX
ejpam-2881	123	4	a	a	DET
ejpam-2881	123	5	modular	modular	ADJ
ejpam-2881	123	6	metric	metric	ADJ
ejpam-2881	123	7	space	space	NOUN
ejpam-2881	123	8	and	and	CCONJ
ejpam-2881	123	9	f	f	NOUN
ejpam-2881	123	10	,	,	PUNCT
ejpam-2881	123	11	g	g	NOUN
ejpam-2881	123	12	:	:	PUNCT
ejpam-2881	123	13	xω	xω	PROPN
ejpam-2881	123	14	→	→	PUNCT
ejpam-2881	123	15	xω	xω	NOUN
ejpam-2881	123	16	be	be	AUX
ejpam-2881	123	17	weakly	weakly	ADV
ejpam-2881	123	18	compatible	compatible	ADJ
ejpam-2881	123	19	mappings	mapping	NOUN
ejpam-2881	123	20	such	such	ADJ
ejpam-2881	123	21	that	that	PRON
ejpam-2881	123	22	f(xω	f(xω	NOUN
ejpam-2881	123	23	)	)	PUNCT
ejpam-2881	123	24	⊂	⊂	PROPN
ejpam-2881	123	25	g(xω	g(xω	NOUN
ejpam-2881	123	26	)	)	PUNCT
ejpam-2881	123	27	.	.	PUNCT
ejpam-2881	124	1	suppose	suppose	VERB
ejpam-2881	124	2	there	there	PRON
ejpam-2881	124	3	exists	exist	VERB
ejpam-2881	124	4	a	a	DET
ejpam-2881	124	5	number	number	NOUN
ejpam-2881	124	6	a	a	DET
ejpam-2881	124	7	∈	∈	NOUN
ejpam-2881	125	1	[	[	X
ejpam-2881	125	2	0	0	NUM
ejpam-2881	125	3	,	,	PUNCT
ejpam-2881	125	4	14	14	NUM
ejpam-2881	125	5	)	)	PUNCT
ejpam-2881	125	6	for	for	ADP
ejpam-2881	125	7	all	all	DET
ejpam-2881	125	8	x	x	NOUN
ejpam-2881	125	9	,	,	PUNCT
ejpam-2881	125	10	y	y	PROPN
ejpam-2881	125	11	∈	∈	PROPN
ejpam-2881	125	12	xω	xω	X
ejpam-2881	125	13	and	and	CCONJ
ejpam-2881	125	14	λ	λ	X
ejpam-2881	125	15	>	>	X
ejpam-2881	125	16	0	0	NUM
ejpam-2881	126	1	such	such	ADJ
ejpam-2881	126	2	that	that	SCONJ
ejpam-2881	126	3	(	(	PUNCT
ejpam-2881	126	4	a	a	X
ejpam-2881	126	5	)	)	PUNCT
ejpam-2881	126	6	there	there	PRON
ejpam-2881	126	7	exists	exist	VERB
ejpam-2881	126	8	x0	x0	PROPN
ejpam-2881	126	9	,	,	PUNCT
ejpam-2881	126	10	x1	x1	PROPN
ejpam-2881	126	11	∈	∈	PROPN
ejpam-2881	126	12	xω	xω	PRON
ejpam-2881	126	13	such	such	ADJ
ejpam-2881	126	14	that	that	SCONJ
ejpam-2881	126	15	ωλ(fx0	ωλ(fx0	NUM
ejpam-2881	126	16	,	,	PUNCT
ejpam-2881	126	17	gx1	gx1	PROPN
ejpam-2881	126	18	)	)	PUNCT
ejpam-2881	126	19	<	<	X
ejpam-2881	126	20	∞	∞	PROPN
ejpam-2881	126	21	;	;	PUNCT
ejpam-2881	126	22	(	(	PUNCT
ejpam-2881	126	23	b	b	X
ejpam-2881	126	24	)	)	PUNCT
ejpam-2881	126	25	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	126	26	,	,	PUNCT
ejpam-2881	126	27	fy	fy	PROPN
ejpam-2881	126	28	)	)	PUNCT
ejpam-2881	126	29	≤	≤	NOUN
ejpam-2881	126	30	a[ωλ(fx	a[ωλ(fx	NOUN
ejpam-2881	126	31	,	,	PUNCT
ejpam-2881	126	32	gy	gy	NOUN
ejpam-2881	126	33	)	)	PUNCT
ejpam-2881	126	34	+	+	CCONJ
ejpam-2881	126	35	ω2λ(fy	ω2λ(fy	ADJ
ejpam-2881	126	36	,	,	PUNCT
ejpam-2881	126	37	gx	gx	PROPN
ejpam-2881	126	38	)	)	PUNCT
ejpam-2881	126	39	+	+	CCONJ
ejpam-2881	126	40	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	126	41	,	,	PUNCT
ejpam-2881	126	42	gx	gx	PROPN
ejpam-2881	126	43	)	)	PUNCT
ejpam-2881	127	1	+	+	CCONJ
ejpam-2881	127	2	ωλ(fy	ωλ(fy	PROPN
ejpam-2881	127	3	,	,	PUNCT
ejpam-2881	127	4	gy	gy	NOUN
ejpam-2881	127	5	)	)	PUNCT
ejpam-2881	127	6	]	]	PUNCT
ejpam-2881	127	7	.	.	PUNCT
ejpam-2881	128	1	if	if	SCONJ
ejpam-2881	128	2	f	f	PROPN
ejpam-2881	128	3	and	and	CCONJ
ejpam-2881	128	4	g	g	PROPN
ejpam-2881	128	5	satisfy	satisfy	VERB
ejpam-2881	128	6	the	the	DET
ejpam-2881	128	7	(	(	PUNCT
ejpam-2881	128	8	clrg)-property	clrg)-property	PROPN
ejpam-2881	128	9	,	,	PUNCT
ejpam-2881	128	10	then	then	ADV
ejpam-2881	128	11	f	f	PROPN
ejpam-2881	128	12	and	and	CCONJ
ejpam-2881	128	13	g	g	PROPN
ejpam-2881	128	14	have	have	VERB
ejpam-2881	128	15	a	a	DET
ejpam-2881	128	16	unique	unique	ADJ
ejpam-2881	128	17	common	common	ADJ
ejpam-2881	128	18	fixed	fix	VERB
ejpam-2881	128	19	point	point	NOUN
ejpam-2881	128	20	.	.	PUNCT
ejpam-2881	129	1	proof	proof	NOUN
ejpam-2881	129	2	.	.	PUNCT
ejpam-2881	130	1	since	since	SCONJ
ejpam-2881	130	2	f	f	PROPN
ejpam-2881	130	3	and	and	CCONJ
ejpam-2881	130	4	g	g	PROPN
ejpam-2881	130	5	satisfy	satisfy	VERB
ejpam-2881	130	6	the	the	DET
ejpam-2881	130	7	(	(	PUNCT
ejpam-2881	130	8	clrg)-property	clrg)-property	PROPN
ejpam-2881	130	9	,	,	PUNCT
ejpam-2881	130	10	there	there	PRON
ejpam-2881	130	11	exists	exist	VERB
ejpam-2881	130	12	a	a	DET
ejpam-2881	130	13	sequence	sequence	NOUN
ejpam-2881	130	14	{	{	PUNCT
ejpam-2881	130	15	xn	xn	NUM
ejpam-2881	130	16	}	}	PUNCT
ejpam-2881	130	17	in	in	ADP
ejpam-2881	130	18	xω	xω	PRON
ejpam-2881	130	19	such	such	ADJ
ejpam-2881	130	20	that	that	SCONJ
ejpam-2881	130	21	lim	lim	PROPN
ejpam-2881	130	22	n→∞	n→∞	PRON
ejpam-2881	130	23	fxn	fxn	PROPN
ejpam-2881	130	24	=	=	PUNCT
ejpam-2881	130	25	lim	lim	PROPN
ejpam-2881	130	26	n−→∞	n−→∞	PROPN
ejpam-2881	130	27	gxn	gxn	PROPN
ejpam-2881	130	28	=	=	SYM
ejpam-2881	130	29	gx	gx	PROPN
ejpam-2881	130	30	for	for	ADP
ejpam-2881	130	31	some	some	DET
ejpam-2881	130	32	x	x	SYM
ejpam-2881	130	33	∈	∈	PROPN
ejpam-2881	130	34	xω	xω	PROPN
ejpam-2881	130	35	.	.	PUNCT
ejpam-2881	131	1	from	from	ADP
ejpam-2881	131	2	(	(	PUNCT
ejpam-2881	131	3	b	b	NOUN
ejpam-2881	131	4	)	)	PUNCT
ejpam-2881	131	5	,	,	PUNCT
ejpam-2881	131	6	we	we	PRON
ejpam-2881	131	7	have	have	VERB
ejpam-2881	131	8	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	131	9	,	,	PUNCT
ejpam-2881	131	10	fx	fx	PROPN
ejpam-2881	131	11	)	)	PUNCT
ejpam-2881	131	12	≤	≤	PROPN
ejpam-2881	132	1	a[ωλ(fxn	a[ωλ(fxn	PROPN
ejpam-2881	132	2	,	,	PUNCT
ejpam-2881	132	3	gx	gx	PROPN
ejpam-2881	132	4	)	)	PUNCT
ejpam-2881	132	5	+	+	CCONJ
ejpam-2881	132	6	ω2λ(fx	ω2λ(fx	NOUN
ejpam-2881	132	7	,	,	PUNCT
ejpam-2881	132	8	gxn	gxn	ADJ
ejpam-2881	132	9	)	)	PUNCT
ejpam-2881	133	1	+	+	CCONJ
ejpam-2881	133	2	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	133	3	,	,	PUNCT
ejpam-2881	133	4	gxn	gxn	ADJ
ejpam-2881	133	5	)	)	PUNCT
ejpam-2881	133	6	+	+	SYM
ejpam-2881	133	7	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	133	8	,	,	PUNCT
ejpam-2881	133	9	gx	gx	PROPN
ejpam-2881	133	10	)	)	PUNCT
ejpam-2881	133	11	]	]	PUNCT
ejpam-2881	134	1	for	for	ADP
ejpam-2881	134	2	all	all	DET
ejpam-2881	134	3	n	n	PRON
ejpam-2881	134	4	≥	≥	NUM
ejpam-2881	134	5	1	1	NUM
ejpam-2881	134	6	.	.	PUNCT
ejpam-2881	135	1	letting	let	VERB
ejpam-2881	135	2	n	n	X
ejpam-2881	135	3	→	→	SYM
ejpam-2881	135	4	∞	∞	PROPN
ejpam-2881	135	5	,	,	PUNCT
ejpam-2881	135	6	we	we	PRON
ejpam-2881	135	7	have	have	VERB
ejpam-2881	135	8	gx	gx	PROPN
ejpam-2881	135	9	=	=	SYM
ejpam-2881	135	10	fx	fx	PROPN
ejpam-2881	135	11	.	.	PUNCT
ejpam-2881	136	1	let	let	VERB
ejpam-2881	136	2	t	t	NOUN
ejpam-2881	136	3	=	=	PUNCT
ejpam-2881	136	4	fx	fx	PROPN
ejpam-2881	136	5	=	=	SYM
ejpam-2881	136	6	gx	gx	PROPN
ejpam-2881	136	7	.	.	PUNCT
ejpam-2881	137	1	since	since	SCONJ
ejpam-2881	137	2	f	f	PROPN
ejpam-2881	137	3	and	and	CCONJ
ejpam-2881	137	4	g	g	PROPN
ejpam-2881	137	5	are	be	AUX
ejpam-2881	137	6	weakly	weakly	ADV
ejpam-2881	137	7	compatible	compatible	ADJ
ejpam-2881	137	8	mappings	mapping	NOUN
ejpam-2881	137	9	,	,	PUNCT
ejpam-2881	137	10	fgx	fgx	VERB
ejpam-2881	137	11	=	=	PUNCT
ejpam-2881	137	12	gfx	gfx	PROPN
ejpam-2881	137	13	implies	imply	VERB
ejpam-2881	137	14	that	that	SCONJ
ejpam-2881	137	15	ft	ft	X
ejpam-2881	137	16	=	=	PUNCT
ejpam-2881	137	17	fgx	fgx	VERB
ejpam-2881	137	18	=	=	SYM
ejpam-2881	137	19	gfx	gfx	PROPN
ejpam-2881	137	20	=	=	PROPN
ejpam-2881	137	21	gt	gt	PROPN
ejpam-2881	137	22	.	.	PUNCT
ejpam-2881	138	1	now	now	ADV
ejpam-2881	138	2	,	,	PUNCT
ejpam-2881	138	3	we	we	PRON
ejpam-2881	138	4	claim	claim	VERB
ejpam-2881	138	5	that	that	SCONJ
ejpam-2881	138	6	ft	ft	NOUN
ejpam-2881	138	7	=	=	PUNCT
ejpam-2881	138	8	t.	t.	NOUN
ejpam-2881	138	9	from	from	ADP
ejpam-2881	138	10	(	(	PUNCT
ejpam-2881	138	11	b	b	NOUN
ejpam-2881	138	12	)	)	PUNCT
ejpam-2881	138	13	,	,	PUNCT
ejpam-2881	138	14	we	we	PRON
ejpam-2881	138	15	have	have	VERB
ejpam-2881	138	16	ωλ(ft	ωλ(ft	NUM
ejpam-2881	138	17	,	,	PUNCT
ejpam-2881	138	18	t	t	PROPN
ejpam-2881	138	19	)	)	PUNCT
ejpam-2881	139	1	=	=	SYM
ejpam-2881	139	2	ωλ(ft	ωλ(ft	PROPN
ejpam-2881	139	3	,	,	PUNCT
ejpam-2881	139	4	fx	fx	NOUN
ejpam-2881	139	5	)	)	PUNCT
ejpam-2881	139	6	≤	≤	NOUN
ejpam-2881	139	7	a[ωλ(ft	a[ωλ(ft	NOUN
ejpam-2881	139	8	,	,	PUNCT
ejpam-2881	139	9	gx	gx	PROPN
ejpam-2881	139	10	)	)	PUNCT
ejpam-2881	139	11	+	+	CCONJ
ejpam-2881	139	12	ω2λ(fx	ω2λ(fx	NOUN
ejpam-2881	139	13	,	,	PUNCT
ejpam-2881	139	14	gt	gt	PROPN
ejpam-2881	139	15	)	)	PUNCT
ejpam-2881	139	16	+	+	SYM
ejpam-2881	139	17	ωλ(ft	ωλ(ft	PROPN
ejpam-2881	139	18	,	,	PUNCT
ejpam-2881	139	19	gt	gt	PROPN
ejpam-2881	139	20	)	)	PUNCT
ejpam-2881	139	21	+	+	CCONJ
ejpam-2881	139	22	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	139	23	,	,	PUNCT
ejpam-2881	139	24	gx	gx	PROPN
ejpam-2881	139	25	)	)	PUNCT
ejpam-2881	139	26	]	]	PUNCT
ejpam-2881	140	1	=	=	SYM
ejpam-2881	140	2	a[ωλ(ft	a[ωλ(ft	X
ejpam-2881	140	3	,	,	PUNCT
ejpam-2881	140	4	gx	gx	PROPN
ejpam-2881	140	5	)	)	PUNCT
ejpam-2881	140	6	+	+	CCONJ
ejpam-2881	140	7	ω2λ(fx	ω2λ(fx	PROPN
ejpam-2881	140	8	,	,	PUNCT
ejpam-2881	140	9	gt	gt	PROPN
ejpam-2881	140	10	)	)	PUNCT
ejpam-2881	140	11	]	]	PUNCT
ejpam-2881	141	1	=	=	SYM
ejpam-2881	141	2	a[ωλ(ft	a[ωλ(ft	X
ejpam-2881	141	3	,	,	PUNCT
ejpam-2881	141	4	t	t	PROPN
ejpam-2881	141	5	)	)	PUNCT
ejpam-2881	141	6	+	+	CCONJ
ejpam-2881	141	7	ω2λ(t	ω2λ(t	NUM
ejpam-2881	141	8	,	,	PUNCT
ejpam-2881	141	9	ft	ft	NOUN
ejpam-2881	141	10	)	)	PUNCT
ejpam-2881	141	11	]	]	PUNCT
ejpam-2881	141	12	and	and	CCONJ
ejpam-2881	141	13	,	,	PUNCT
ejpam-2881	141	14	by	by	ADP
ejpam-2881	141	15	remark	remark	NOUN
ejpam-2881	141	16	1	1	NUM
ejpam-2881	141	17	,	,	PUNCT
ejpam-2881	141	18	since	since	SCONJ
ejpam-2881	141	19	the	the	DET
ejpam-2881	141	20	function	function	NOUN
ejpam-2881	141	21	λ	λ	PROPN
ejpam-2881	141	22	7→	7→	NUM
ejpam-2881	141	23	ωλ(x	ωλ(x	NUM
ejpam-2881	141	24	,	,	PUNCT
ejpam-2881	141	25	y	y	NOUN
ejpam-2881	141	26	)	)	PUNCT
ejpam-2881	141	27	is	be	AUX
ejpam-2881	141	28	non	non	ADJ
ejpam-2881	141	29	-	-	ADJ
ejpam-2881	141	30	increasing	increase	VERB
ejpam-2881	141	31	,	,	PUNCT
ejpam-2881	141	32	we	we	PRON
ejpam-2881	141	33	have	have	VERB
ejpam-2881	141	34	ωλ(ft	ωλ(ft	NUM
ejpam-2881	141	35	,	,	PUNCT
ejpam-2881	141	36	t	t	PROPN
ejpam-2881	141	37	)	)	PUNCT
ejpam-2881	141	38	≤	≤	NOUN
ejpam-2881	141	39	a[ωλ(ft	a[ωλ(ft	ADJ
ejpam-2881	141	40	,	,	PUNCT
ejpam-2881	141	41	t	t	PROPN
ejpam-2881	141	42	)	)	PUNCT
ejpam-2881	141	43	+	+	NUM
ejpam-2881	141	44	ωλ(t	ωλ(t	NOUN
ejpam-2881	141	45	,	,	PUNCT
ejpam-2881	141	46	ft	ft	NOUN
ejpam-2881	141	47	)	)	PUNCT
ejpam-2881	141	48	]	]	PUNCT
ejpam-2881	141	49	.	.	PUNCT
ejpam-2881	142	1	this	this	PRON
ejpam-2881	142	2	implies	imply	VERB
ejpam-2881	142	3	that	that	SCONJ
ejpam-2881	142	4	(	(	PUNCT
ejpam-2881	142	5	1	1	NUM
ejpam-2881	142	6	−	−	NOUN
ejpam-2881	142	7	2a)ωλ(ft	2a)ωλ(ft	NOUN
ejpam-2881	142	8	,	,	PUNCT
ejpam-2881	142	9	t	t	PROPN
ejpam-2881	142	10	)	)	PUNCT
ejpam-2881	142	11	≤	≤	NOUN
ejpam-2881	142	12	0	0	NUM
ejpam-2881	142	13	for	for	ADP
ejpam-2881	142	14	all	all	DET
ejpam-2881	142	15	λ	λ	PROPN
ejpam-2881	142	16	>	>	X
ejpam-2881	142	17	0	0	NUM
ejpam-2881	142	18	,	,	PUNCT
ejpam-2881	142	19	that	that	ADV
ejpam-2881	142	20	is	is	ADV
ejpam-2881	142	21	,	,	PUNCT
ejpam-2881	142	22	ωλ(ft	ωλ(ft	PROPN
ejpam-2881	142	23	,	,	PUNCT
ejpam-2881	142	24	t	t	PROPN
ejpam-2881	142	25	)	)	PUNCT
ejpam-2881	142	26	=	=	SYM
ejpam-2881	142	27	0	0	PUNCT
ejpam-2881	143	1	and	and	CCONJ
ejpam-2881	143	2	so	so	ADV
ejpam-2881	143	3	ft	ft	NOUN
ejpam-2881	143	4	=	=	SYM
ejpam-2881	143	5	t	t	PROPN
ejpam-2881	143	6	=	=	SYM
ejpam-2881	143	7	gt	gt	PROPN
ejpam-2881	143	8	.	.	PUNCT
ejpam-2881	144	1	thus	thus	ADV
ejpam-2881	144	2	t	t	PROPN
ejpam-2881	144	3	is	be	AUX
ejpam-2881	144	4	a	a	DET
ejpam-2881	144	5	common	common	ADJ
ejpam-2881	144	6	fixed	fix	VERB
ejpam-2881	144	7	point	point	NOUN
ejpam-2881	144	8	of	of	ADP
ejpam-2881	144	9	f	f	PROPN
ejpam-2881	144	10	and	and	CCONJ
ejpam-2881	144	11	g.	g.	PROPN
ejpam-2881	144	12	for	for	ADP
ejpam-2881	144	13	the	the	DET
ejpam-2881	144	14	uniqueness	uniqueness	NOUN
ejpam-2881	144	15	of	of	ADP
ejpam-2881	144	16	the	the	DET
ejpam-2881	144	17	common	common	ADJ
ejpam-2881	144	18	fixed	fix	VERB
ejpam-2881	144	19	point	point	NOUN
ejpam-2881	144	20	,	,	PUNCT
ejpam-2881	144	21	we	we	PRON
ejpam-2881	144	22	suppose	suppose	VERB
ejpam-2881	144	23	that	that	SCONJ
ejpam-2881	144	24	u	u	PROPN
ejpam-2881	144	25	is	be	AUX
ejpam-2881	144	26	another	another	DET
ejpam-2881	144	27	common	common	ADJ
ejpam-2881	144	28	fixed	fix	VERB
ejpam-2881	144	29	point	point	NOUN
ejpam-2881	144	30	in	in	ADP
ejpam-2881	144	31	xω	xω	PRON
ejpam-2881	144	32	such	such	ADJ
ejpam-2881	144	33	that	that	DET
ejpam-2881	144	34	fu	fu	NOUN
ejpam-2881	144	35	=	=	PUNCT
ejpam-2881	144	36	gu	gu	PROPN
ejpam-2881	144	37	.	.	PROPN
ejpam-2881	145	1	from	from	ADP
ejpam-2881	145	2	(	(	PUNCT
ejpam-2881	145	3	b	b	NOUN
ejpam-2881	145	4	)	)	PUNCT
ejpam-2881	145	5	,	,	PUNCT
ejpam-2881	145	6	we	we	PRON
ejpam-2881	145	7	have	have	VERB
ejpam-2881	145	8	ωλ(gu	ωλ(gu	NOUN
ejpam-2881	145	9	,	,	PUNCT
ejpam-2881	145	10	gt	gt	PROPN
ejpam-2881	145	11	)	)	PUNCT
ejpam-2881	145	12	=	=	PUNCT
ejpam-2881	146	1	ωλ(fu	ωλ(fu	PROPN
ejpam-2881	146	2	,	,	PUNCT
ejpam-2881	146	3	ft	ft	NOUN
ejpam-2881	146	4	)	)	PUNCT
ejpam-2881	146	5	≤	≤	NOUN
ejpam-2881	146	6	a[ωλ(fu	a[ωλ(fu	NOUN
ejpam-2881	146	7	,	,	PUNCT
ejpam-2881	146	8	gt	gt	PROPN
ejpam-2881	146	9	)	)	PUNCT
ejpam-2881	146	10	+	+	X
ejpam-2881	146	11	ω2λ(ft	ω2λ(ft	NUM
ejpam-2881	146	12	,	,	PUNCT
ejpam-2881	146	13	gu	gu	NOUN
ejpam-2881	146	14	)	)	PUNCT
ejpam-2881	146	15	+	+	CCONJ
ejpam-2881	146	16	ωλ(fu	ωλ(fu	PROPN
ejpam-2881	146	17	,	,	PUNCT
ejpam-2881	146	18	gu	gu	NOUN
ejpam-2881	146	19	)	)	PUNCT
ejpam-2881	146	20	+	+	CCONJ
ejpam-2881	146	21	ωλ(ft	ωλ(ft	PROPN
ejpam-2881	146	22	,	,	PUNCT
ejpam-2881	146	23	gt	gt	PROPN
ejpam-2881	146	24	)	)	PUNCT
ejpam-2881	146	25	]	]	PUNCT
ejpam-2881	147	1	=	=	SYM
ejpam-2881	147	2	a[ωλ(fu	a[ωλ(fu	X
ejpam-2881	147	3	,	,	PUNCT
ejpam-2881	147	4	gt	gt	PROPN
ejpam-2881	147	5	)	)	PUNCT
ejpam-2881	147	6	+	+	SYM
ejpam-2881	147	7	ω2λ(ft	ω2λ(ft	NUM
ejpam-2881	147	8	,	,	PUNCT
ejpam-2881	147	9	gu	gu	NOUN
ejpam-2881	147	10	)	)	PUNCT
ejpam-2881	147	11	]	]	PUNCT
ejpam-2881	148	1	=	=	PUNCT
ejpam-2881	148	2	a[ωλ(gu	a[ωλ(gu	ADJ
ejpam-2881	148	3	,	,	PUNCT
ejpam-2881	148	4	gt	gt	PROPN
ejpam-2881	148	5	)	)	PUNCT
ejpam-2881	148	6	+	+	CCONJ
ejpam-2881	148	7	ω2λ(gt	ω2λ(gt	PROPN
ejpam-2881	148	8	,	,	PUNCT
ejpam-2881	148	9	gu	gu	NOUN
ejpam-2881	148	10	)	)	PUNCT
ejpam-2881	148	11	]	]	PUNCT
ejpam-2881	148	12	and	and	CCONJ
ejpam-2881	148	13	,	,	PUNCT
ejpam-2881	148	14	by	by	ADP
ejpam-2881	148	15	remark	remark	NOUN
ejpam-2881	148	16	1	1	NUM
ejpam-2881	148	17	,	,	PUNCT
ejpam-2881	148	18	since	since	SCONJ
ejpam-2881	148	19	the	the	DET
ejpam-2881	148	20	function	function	NOUN
ejpam-2881	148	21	λ	λ	PROPN
ejpam-2881	148	22	7→	7→	NUM
ejpam-2881	148	23	ωλ(x	ωλ(x	NUM
ejpam-2881	148	24	,	,	PUNCT
ejpam-2881	148	25	y	y	NOUN
ejpam-2881	148	26	)	)	PUNCT
ejpam-2881	148	27	is	be	AUX
ejpam-2881	148	28	non	non	ADJ
ejpam-2881	148	29	-	-	ADJ
ejpam-2881	148	30	increasing	increase	VERB
ejpam-2881	148	31	,	,	PUNCT
ejpam-2881	148	32	we	we	PRON
ejpam-2881	148	33	have	have	VERB
ejpam-2881	148	34	ωλ(gu	ωλ(gu	NOUN
ejpam-2881	148	35	,	,	PUNCT
ejpam-2881	148	36	gt	gt	PROPN
ejpam-2881	148	37	)	)	PUNCT
ejpam-2881	148	38	≤	≤	ADV
ejpam-2881	148	39	a[ωλ(gu	a[ωλ(gu	ADJ
ejpam-2881	148	40	,	,	PUNCT
ejpam-2881	148	41	gt	gt	PROPN
ejpam-2881	148	42	)	)	PUNCT
ejpam-2881	149	1	+	+	CCONJ
ejpam-2881	149	2	ωλ(gt	ωλ(gt	PROPN
ejpam-2881	149	3	,	,	PUNCT
ejpam-2881	149	4	gu	gu	NOUN
ejpam-2881	149	5	)	)	PUNCT
ejpam-2881	149	6	]	]	PUNCT
ejpam-2881	149	7	.	.	PUNCT
ejpam-2881	150	1	this	this	PRON
ejpam-2881	150	2	implies	imply	VERB
ejpam-2881	150	3	gu	gu	X
ejpam-2881	150	4	=	=	SYM
ejpam-2881	150	5	gt	gt	PROPN
ejpam-2881	150	6	.	.	PUNCT
ejpam-2881	151	1	thus	thus	ADV
ejpam-2881	151	2	,	,	PUNCT
ejpam-2881	151	3	by	by	ADP
ejpam-2881	151	4	lemma	lemma	PROPN
ejpam-2881	151	5	1	1	NUM
ejpam-2881	151	6	,	,	PUNCT
ejpam-2881	151	7	we	we	PRON
ejpam-2881	151	8	have	have	VERB
ejpam-2881	151	9	f	f	PROPN
ejpam-2881	151	10	and	and	CCONJ
ejpam-2881	151	11	g	g	PROPN
ejpam-2881	151	12	have	have	VERB
ejpam-2881	151	13	a	a	DET
ejpam-2881	151	14	unique	unique	ADJ
ejpam-2881	151	15	common	common	ADJ
ejpam-2881	151	16	fixed	fix	VERB
ejpam-2881	151	17	point	point	NOUN
ejpam-2881	151	18	.	.	PUNCT
ejpam-2881	152	1	p.	p.	NOUN
ejpam-2881	152	2	sumalai	sumalai	PROPN
ejpam-2881	152	3	,	,	PUNCT
ejpam-2881	152	4	p.	p.	PROPN
ejpam-2881	152	5	kumam	kumam	PROPN
ejpam-2881	152	6	,	,	PUNCT
ejpam-2881	152	7	y.	y.	PROPN
ejpam-2881	152	8	j.	j.	PROPN
ejpam-2881	152	9	cho	cho	PROPN
ejpam-2881	152	10	,	,	PUNCT
ejpam-2881	152	11	a.	a.	NOUN
ejpam-2881	152	12	padcharoen	padcharoen	PROPN
ejpam-2881	152	13	/	/	SYM
ejpam-2881	152	14	eur	eur	PROPN
ejpam-2881	152	15	.	.	PUNCT
ejpam-2881	153	1	j.	j.	PROPN
ejpam-2881	153	2	pure	pure	PROPN
ejpam-2881	153	3	appl	appl	PROPN
ejpam-2881	153	4	.	.	PROPN
ejpam-2881	153	5	math	math	PROPN
ejpam-2881	153	6	,	,	PUNCT
ejpam-2881	153	7	10	10	NUM
ejpam-2881	153	8	(	(	PUNCT
ejpam-2881	153	9	2	2	NUM
ejpam-2881	153	10	)	)	PUNCT
ejpam-2881	153	11	(	(	PUNCT
ejpam-2881	153	12	2017	2017	NUM
ejpam-2881	153	13	)	)	PUNCT
ejpam-2881	153	14	,	,	PUNCT
ejpam-2881	153	15	238	238	NUM
ejpam-2881	153	16	-	-	SYM
ejpam-2881	153	17	254	254	NUM
ejpam-2881	153	18	244	244	NUM
ejpam-2881	153	19	theorem	theorem	NOUN
ejpam-2881	153	20	3	3	X
ejpam-2881	153	21	.	.	PUNCT
ejpam-2881	154	1	let	let	VERB
ejpam-2881	154	2	xω	xω	PRON
ejpam-2881	154	3	be	be	AUX
ejpam-2881	154	4	a	a	DET
ejpam-2881	154	5	modular	modular	ADJ
ejpam-2881	154	6	metric	metric	ADJ
ejpam-2881	154	7	space	space	NOUN
ejpam-2881	154	8	and	and	CCONJ
ejpam-2881	154	9	f	f	NOUN
ejpam-2881	154	10	,	,	PUNCT
ejpam-2881	154	11	g	g	NOUN
ejpam-2881	154	12	:	:	PUNCT
ejpam-2881	154	13	xω	xω	PROPN
ejpam-2881	154	14	→	→	PUNCT
ejpam-2881	154	15	xω	xω	NOUN
ejpam-2881	154	16	be	be	AUX
ejpam-2881	154	17	weakly	weakly	ADV
ejpam-2881	154	18	compatible	compatible	ADJ
ejpam-2881	154	19	mappings	mapping	NOUN
ejpam-2881	154	20	such	such	ADJ
ejpam-2881	154	21	that	that	PRON
ejpam-2881	154	22	f(xω	f(xω	NOUN
ejpam-2881	154	23	)	)	PUNCT
ejpam-2881	154	24	⊂	⊂	PROPN
ejpam-2881	154	25	g(xω	g(xω	NOUN
ejpam-2881	154	26	)	)	PUNCT
ejpam-2881	154	27	.	.	PUNCT
ejpam-2881	155	1	suppose	suppose	VERB
ejpam-2881	155	2	that	that	SCONJ
ejpam-2881	155	3	there	there	PRON
ejpam-2881	155	4	exist	exist	VERB
ejpam-2881	155	5	a1	a1	NOUN
ejpam-2881	155	6	,	,	PUNCT
ejpam-2881	155	7	a2	a2	PROPN
ejpam-2881	155	8	,	,	PUNCT
ejpam-2881	155	9	a3	a3	NOUN
ejpam-2881	155	10	,	,	PUNCT
ejpam-2881	155	11	a4	a4	PROPN
ejpam-2881	155	12	,	,	PUNCT
ejpam-2881	155	13	a5	a5	PROPN
ejpam-2881	155	14	∈	∈	PROPN
ejpam-2881	156	1	[	[	X
ejpam-2881	156	2	0	0	NUM
ejpam-2881	156	3	,	,	PUNCT
ejpam-2881	156	4	14	14	NUM
ejpam-2881	156	5	)	)	PUNCT
ejpam-2881	156	6	and	and	CCONJ
ejpam-2881	156	7	5∑	5∑	NUM
ejpam-2881	156	8	i=1	i=1	X
ejpam-2881	156	9	ai	ai	VERB
ejpam-2881	156	10	<	<	X
ejpam-2881	156	11	1	1	NUM
ejpam-2881	156	12	such	such	ADJ
ejpam-2881	156	13	that	that	SCONJ
ejpam-2881	156	14	,	,	PUNCT
ejpam-2881	156	15	for	for	ADP
ejpam-2881	156	16	all	all	DET
ejpam-2881	156	17	x	x	NOUN
ejpam-2881	156	18	,	,	PUNCT
ejpam-2881	156	19	y	y	PROPN
ejpam-2881	156	20	∈	∈	PROPN
ejpam-2881	157	1	xω	xω	X
ejpam-2881	157	2	and	and	CCONJ
ejpam-2881	157	3	λ	λ	X
ejpam-2881	157	4	>	>	X
ejpam-2881	157	5	0	0	NUM
ejpam-2881	157	6	,	,	PUNCT
ejpam-2881	157	7	(	(	PUNCT
ejpam-2881	157	8	a	a	X
ejpam-2881	157	9	)	)	PUNCT
ejpam-2881	157	10	there	there	PRON
ejpam-2881	157	11	exists	exist	VERB
ejpam-2881	157	12	x0	x0	PROPN
ejpam-2881	157	13	,	,	PUNCT
ejpam-2881	157	14	x1	x1	PROPN
ejpam-2881	157	15	∈	∈	PROPN
ejpam-2881	157	16	xω	xω	PRON
ejpam-2881	157	17	such	such	ADJ
ejpam-2881	157	18	that	that	SCONJ
ejpam-2881	157	19	ωλ(fx0	ωλ(fx0	NUM
ejpam-2881	157	20	,	,	PUNCT
ejpam-2881	157	21	gx1	gx1	PROPN
ejpam-2881	157	22	)	)	PUNCT
ejpam-2881	157	23	<	<	X
ejpam-2881	157	24	∞	∞	PROPN
ejpam-2881	157	25	;	;	PUNCT
ejpam-2881	157	26	(	(	PUNCT
ejpam-2881	157	27	b	b	X
ejpam-2881	157	28	)	)	PUNCT
ejpam-2881	157	29	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	157	30	,	,	PUNCT
ejpam-2881	157	31	fy	fy	PROPN
ejpam-2881	157	32	)	)	PUNCT
ejpam-2881	157	33	≤	≤	NOUN
ejpam-2881	157	34	a1ωλ(fx	a1ωλ(fx	PROPN
ejpam-2881	157	35	,	,	PUNCT
ejpam-2881	157	36	gx)+a2ωλ(fy	gx)+a2ωλ(fy	PROPN
ejpam-2881	157	37	,	,	PUNCT
ejpam-2881	157	38	gy)+a3ωλ(fy	gy)+a3ωλ(fy	PROPN
ejpam-2881	157	39	,	,	PUNCT
ejpam-2881	157	40	gx)+a4ωλ(fx	gx)+a4ωλ(fx	PROPN
ejpam-2881	157	41	,	,	PUNCT
ejpam-2881	157	42	gy)+a5ωλ(gy	gy)+a5ωλ(gy	PROPN
ejpam-2881	157	43	,	,	PUNCT
ejpam-2881	157	44	gx	gx	PROPN
ejpam-2881	157	45	)	)	PUNCT
ejpam-2881	157	46	.	.	PUNCT
ejpam-2881	158	1	if	if	SCONJ
ejpam-2881	158	2	f	f	PROPN
ejpam-2881	158	3	and	and	CCONJ
ejpam-2881	158	4	g	g	PROPN
ejpam-2881	158	5	satisfy	satisfy	NOUN
ejpam-2881	158	6	(	(	PUNCT
ejpam-2881	158	7	clrg)-property	clrg)-property	PROPN
ejpam-2881	158	8	,	,	PUNCT
ejpam-2881	158	9	then	then	ADV
ejpam-2881	158	10	f	f	PROPN
ejpam-2881	158	11	and	and	CCONJ
ejpam-2881	158	12	g	g	PROPN
ejpam-2881	158	13	have	have	VERB
ejpam-2881	158	14	a	a	DET
ejpam-2881	158	15	unique	unique	ADJ
ejpam-2881	158	16	common	common	ADJ
ejpam-2881	158	17	fixed	fix	VERB
ejpam-2881	158	18	point	point	NOUN
ejpam-2881	158	19	.	.	PUNCT
ejpam-2881	159	1	proof	proof	NOUN
ejpam-2881	159	2	.	.	PUNCT
ejpam-2881	160	1	since	since	SCONJ
ejpam-2881	160	2	f	f	PROPN
ejpam-2881	160	3	and	and	CCONJ
ejpam-2881	160	4	g	g	PROPN
ejpam-2881	160	5	satisfy	satisfy	VERB
ejpam-2881	160	6	the	the	DET
ejpam-2881	160	7	(	(	PUNCT
ejpam-2881	160	8	clrg)-property	clrg)-property	PROPN
ejpam-2881	160	9	,	,	PUNCT
ejpam-2881	160	10	there	there	PRON
ejpam-2881	160	11	exists	exist	VERB
ejpam-2881	160	12	a	a	DET
ejpam-2881	160	13	sequence	sequence	NOUN
ejpam-2881	160	14	{	{	PUNCT
ejpam-2881	160	15	xn	xn	NUM
ejpam-2881	160	16	}	}	PUNCT
ejpam-2881	160	17	in	in	ADP
ejpam-2881	160	18	xω	xω	PRON
ejpam-2881	160	19	such	such	ADJ
ejpam-2881	160	20	that	that	SCONJ
ejpam-2881	160	21	lim	lim	PROPN
ejpam-2881	160	22	n→∞	n→∞	PRON
ejpam-2881	160	23	fxn	fxn	PROPN
ejpam-2881	160	24	=	=	PUNCT
ejpam-2881	160	25	lim	lim	PROPN
ejpam-2881	160	26	n−→∞	n−→∞	PROPN
ejpam-2881	160	27	gxn	gxn	PROPN
ejpam-2881	160	28	=	=	SYM
ejpam-2881	160	29	gx	gx	PROPN
ejpam-2881	160	30	for	for	ADP
ejpam-2881	160	31	some	some	DET
ejpam-2881	160	32	x	x	SYM
ejpam-2881	160	33	∈	∈	PROPN
ejpam-2881	160	34	xω	xω	PROPN
ejpam-2881	160	35	.	.	PUNCT
ejpam-2881	161	1	from	from	ADP
ejpam-2881	161	2	(	(	PUNCT
ejpam-2881	161	3	b	b	NOUN
ejpam-2881	161	4	)	)	PUNCT
ejpam-2881	161	5	,	,	PUNCT
ejpam-2881	161	6	we	we	PRON
ejpam-2881	161	7	have	have	VERB
ejpam-2881	161	8	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	161	9	,	,	PUNCT
ejpam-2881	161	10	fx	fx	PROPN
ejpam-2881	161	11	)	)	PUNCT
ejpam-2881	161	12	≤	≤	NOUN
ejpam-2881	161	13	a1ωλ(fxn	a1ωλ(fxn	PROPN
ejpam-2881	161	14	,	,	PUNCT
ejpam-2881	161	15	gxn	gxn	ADJ
ejpam-2881	161	16	)	)	PUNCT
ejpam-2881	161	17	+	+	NUM
ejpam-2881	161	18	a2ωλ(fx	a2ωλ(fx	NOUN
ejpam-2881	161	19	,	,	PUNCT
ejpam-2881	161	20	gx	gx	PROPN
ejpam-2881	161	21	)	)	PUNCT
ejpam-2881	162	1	+	+	PROPN
ejpam-2881	162	2	a3ωλ(fx	a3ωλ(fx	PROPN
ejpam-2881	162	3	,	,	PUNCT
ejpam-2881	162	4	gxn	gxn	PROPN
ejpam-2881	162	5	)	)	PUNCT
ejpam-2881	162	6	+	+	SYM
ejpam-2881	162	7	a4ωλ(fxn	a4ωλ(fxn	PROPN
ejpam-2881	162	8	,	,	PUNCT
ejpam-2881	162	9	gx	gx	PROPN
ejpam-2881	162	10	)	)	PUNCT
ejpam-2881	162	11	+	+	CCONJ
ejpam-2881	163	1	a5ωλ(gx	a5ωλ(gx	ADJ
ejpam-2881	163	2	,	,	PUNCT
ejpam-2881	163	3	gxn	gxn	PROPN
ejpam-2881	163	4	)	)	PUNCT
ejpam-2881	163	5	for	for	ADP
ejpam-2881	163	6	all	all	DET
ejpam-2881	163	7	n	n	PRON
ejpam-2881	163	8	≥	≥	NOUN
ejpam-2881	163	9	1	1	NUM
ejpam-2881	163	10	.	.	PUNCT
ejpam-2881	164	1	by	by	ADP
ejpam-2881	164	2	taking	take	VERB
ejpam-2881	164	3	the	the	DET
ejpam-2881	164	4	limit	limit	NOUN
ejpam-2881	164	5	n→∞	n→∞	NUM
ejpam-2881	164	6	,	,	PUNCT
ejpam-2881	164	7	we	we	PRON
ejpam-2881	164	8	have	have	VERB
ejpam-2881	164	9	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	164	10	,	,	PUNCT
ejpam-2881	164	11	fx	fx	PROPN
ejpam-2881	164	12	)	)	PUNCT
ejpam-2881	164	13	≤	≤	NOUN
ejpam-2881	164	14	a1ωλ(gx	a1ωλ(gx	PROPN
ejpam-2881	164	15	,	,	PUNCT
ejpam-2881	164	16	gx	gx	PROPN
ejpam-2881	164	17	)	)	PUNCT
ejpam-2881	165	1	+	+	NUM
ejpam-2881	165	2	a2ωλ(fx	a2ωλ(fx	PROPN
ejpam-2881	165	3	,	,	PUNCT
ejpam-2881	165	4	gx	gx	PROPN
ejpam-2881	165	5	)	)	PUNCT
ejpam-2881	165	6	+	+	PROPN
ejpam-2881	165	7	a3ωλ(fx	a3ωλ(fx	PROPN
ejpam-2881	165	8	,	,	PUNCT
ejpam-2881	165	9	gx	gx	PROPN
ejpam-2881	165	10	)	)	PUNCT
ejpam-2881	166	1	+	+	CCONJ
ejpam-2881	166	2	a4ωλ(gx	a4ωλ(gx	ADJ
ejpam-2881	166	3	,	,	PUNCT
ejpam-2881	166	4	gx	gx	PROPN
ejpam-2881	166	5	)	)	PUNCT
ejpam-2881	167	1	+	+	CCONJ
ejpam-2881	167	2	a5ωλ(gx	a5ωλ(gx	PROPN
ejpam-2881	167	3	,	,	PUNCT
ejpam-2881	167	4	gx	gx	PROPN
ejpam-2881	167	5	)	)	PUNCT
ejpam-2881	167	6	=	=	SYM
ejpam-2881	167	7	(	(	PUNCT
ejpam-2881	167	8	a2	a2	PROPN
ejpam-2881	167	9	+	+	CCONJ
ejpam-2881	167	10	a3)ωλ(fx	a3)ωλ(fx	PROPN
ejpam-2881	167	11	,	,	PUNCT
ejpam-2881	167	12	gx	gx	PROPN
ejpam-2881	167	13	)	)	PUNCT
ejpam-2881	167	14	.	.	PUNCT
ejpam-2881	168	1	this	this	PRON
ejpam-2881	168	2	implies	imply	VERB
ejpam-2881	168	3	that	that	SCONJ
ejpam-2881	168	4	(	(	PUNCT
ejpam-2881	168	5	1−a2−a3)ωλ(fx	1−a2−a3)ωλ(fx	PROPN
ejpam-2881	168	6	,	,	PUNCT
ejpam-2881	168	7	gx	gx	PROPN
ejpam-2881	168	8	)	)	PUNCT
ejpam-2881	168	9	≤	≤	NOUN
ejpam-2881	168	10	0	0	NUM
ejpam-2881	168	11	for	for	ADP
ejpam-2881	168	12	all	all	DET
ejpam-2881	168	13	λ	λ	PROPN
ejpam-2881	168	14	>	>	X
ejpam-2881	168	15	0	0	PROPN
ejpam-2881	168	16	,	,	PUNCT
ejpam-2881	168	17	which	which	PRON
ejpam-2881	168	18	is	be	AUX
ejpam-2881	168	19	a	a	DET
ejpam-2881	168	20	contradiction	contradiction	NOUN
ejpam-2881	168	21	.	.	PUNCT
ejpam-2881	169	1	thus	thus	ADV
ejpam-2881	169	2	fx	fx	PROPN
ejpam-2881	169	3	=	=	SYM
ejpam-2881	169	4	gx	gx	PROPN
ejpam-2881	169	5	.	.	PUNCT
ejpam-2881	170	1	now	now	ADV
ejpam-2881	170	2	,	,	PUNCT
ejpam-2881	170	3	let	let	VERB
ejpam-2881	170	4	t	t	NOUN
ejpam-2881	170	5	=	=	PUNCT
ejpam-2881	170	6	fx	fx	PROPN
ejpam-2881	170	7	=	=	SYM
ejpam-2881	170	8	gx	gx	PROPN
ejpam-2881	170	9	.	.	PUNCT
ejpam-2881	171	1	since	since	SCONJ
ejpam-2881	171	2	f	f	PROPN
ejpam-2881	171	3	and	and	CCONJ
ejpam-2881	171	4	g	g	PROPN
ejpam-2881	171	5	are	be	AUX
ejpam-2881	171	6	weakly	weakly	ADV
ejpam-2881	171	7	compatible	compatible	ADJ
ejpam-2881	171	8	mappings	mapping	NOUN
ejpam-2881	171	9	,	,	PUNCT
ejpam-2881	171	10	we	we	PRON
ejpam-2881	171	11	have	have	AUX
ejpam-2881	171	12	fgx	fgx	VERB
ejpam-2881	171	13	=	=	SYM
ejpam-2881	171	14	gfx	gfx	PROPN
ejpam-2881	171	15	,	,	PUNCT
ejpam-2881	171	16	which	which	PRON
ejpam-2881	171	17	implies	imply	VERB
ejpam-2881	171	18	that	that	SCONJ
ejpam-2881	171	19	ft	ft	PROPN
ejpam-2881	171	20	=	=	PUNCT
ejpam-2881	171	21	fgx	fgx	VERB
ejpam-2881	171	22	=	=	SYM
ejpam-2881	171	23	gfx	gfx	PROPN
ejpam-2881	171	24	=	=	PROPN
ejpam-2881	171	25	gt	gt	PROPN
ejpam-2881	171	26	.	.	PUNCT
ejpam-2881	172	1	now	now	ADV
ejpam-2881	172	2	,	,	PUNCT
ejpam-2881	172	3	we	we	PRON
ejpam-2881	172	4	show	show	VERB
ejpam-2881	172	5	that	that	SCONJ
ejpam-2881	172	6	gt	gt	PROPN
ejpam-2881	172	7	=	=	PUNCT
ejpam-2881	172	8	t.	t.	PROPN
ejpam-2881	172	9	suppose	suppose	VERB
ejpam-2881	172	10	ωλ(gt	ωλ(gt	PROPN
ejpam-2881	172	11	,	,	PUNCT
ejpam-2881	172	12	t	t	PROPN
ejpam-2881	172	13	)	)	PUNCT
ejpam-2881	172	14	>	>	X
ejpam-2881	173	1	0	0	X
ejpam-2881	173	2	.	.	PUNCT
ejpam-2881	174	1	then	then	ADV
ejpam-2881	174	2	,	,	PUNCT
ejpam-2881	174	3	from	from	ADP
ejpam-2881	174	4	(	(	PUNCT
ejpam-2881	174	5	b	b	NOUN
ejpam-2881	174	6	)	)	PUNCT
ejpam-2881	174	7	,	,	PUNCT
ejpam-2881	174	8	we	we	PRON
ejpam-2881	174	9	have	have	VERB
ejpam-2881	174	10	ωλ(gt	ωλ(gt	PROPN
ejpam-2881	174	11	,	,	PUNCT
ejpam-2881	174	12	t	t	PROPN
ejpam-2881	174	13	)	)	PUNCT
ejpam-2881	174	14	=	=	SYM
ejpam-2881	174	15	ωλ(ft	ωλ(ft	PROPN
ejpam-2881	174	16	,	,	PUNCT
ejpam-2881	174	17	fx	fx	NOUN
ejpam-2881	174	18	)	)	PUNCT
ejpam-2881	174	19	≤	≤	NOUN
ejpam-2881	175	1	a1ωλ(ft	a1ωλ(ft	PROPN
ejpam-2881	175	2	,	,	PUNCT
ejpam-2881	175	3	gt	gt	PROPN
ejpam-2881	175	4	)	)	PUNCT
ejpam-2881	175	5	+	+	NUM
ejpam-2881	175	6	a2ωλ(fx	a2ωλ(fx	NOUN
ejpam-2881	175	7	,	,	PUNCT
ejpam-2881	175	8	gx	gx	PROPN
ejpam-2881	175	9	)	)	PUNCT
ejpam-2881	175	10	+	+	PROPN
ejpam-2881	175	11	a3ωλ(fx	a3ωλ(fx	PROPN
ejpam-2881	175	12	,	,	PUNCT
ejpam-2881	175	13	gt	gt	PROPN
ejpam-2881	175	14	)	)	PUNCT
ejpam-2881	175	15	+	+	CCONJ
ejpam-2881	175	16	a4ωλ(ft	a4ωλ(ft	PROPN
ejpam-2881	175	17	,	,	PUNCT
ejpam-2881	175	18	gx	gx	PROPN
ejpam-2881	175	19	)	)	PUNCT
ejpam-2881	175	20	+	+	CCONJ
ejpam-2881	175	21	a5ωλ(gx	a5ωλ(gx	PROPN
ejpam-2881	175	22	,	,	PUNCT
ejpam-2881	175	23	gt	gt	PROPN
ejpam-2881	175	24	)	)	PUNCT
ejpam-2881	175	25	≤	≤	NOUN
ejpam-2881	175	26	a3ωλ(t	a3ωλ(t	PROPN
ejpam-2881	175	27	,	,	PUNCT
ejpam-2881	175	28	gt	gt	PROPN
ejpam-2881	175	29	)	)	PUNCT
ejpam-2881	175	30	+	+	NUM
ejpam-2881	175	31	a4ωλ(gt	a4ωλ(gt	PROPN
ejpam-2881	175	32	,	,	PUNCT
ejpam-2881	175	33	t	t	PROPN
ejpam-2881	175	34	)	)	PUNCT
ejpam-2881	175	35	+	+	CCONJ
ejpam-2881	175	36	a5ωλ(t	a5ωλ(t	PROPN
ejpam-2881	175	37	,	,	PUNCT
ejpam-2881	175	38	gt	gt	PROPN
ejpam-2881	175	39	)	)	PUNCT
ejpam-2881	175	40	=	=	SYM
ejpam-2881	175	41	(	(	PUNCT
ejpam-2881	175	42	a3	a3	NOUN
ejpam-2881	175	43	+	+	CCONJ
ejpam-2881	175	44	a4	a4	NOUN
ejpam-2881	175	45	+	+	CCONJ
ejpam-2881	175	46	a5)ωλ(gt	a5)ωλ(gt	PROPN
ejpam-2881	175	47	,	,	PUNCT
ejpam-2881	175	48	t	t	PROPN
ejpam-2881	175	49	)	)	PUNCT
ejpam-2881	175	50	.	.	PUNCT
ejpam-2881	176	1	this	this	PRON
ejpam-2881	176	2	implies	imply	VERB
ejpam-2881	176	3	that	that	SCONJ
ejpam-2881	176	4	(	(	PUNCT
ejpam-2881	176	5	1	1	NUM
ejpam-2881	176	6	−	−	NOUN
ejpam-2881	176	7	a3	a3	NOUN
ejpam-2881	176	8	−	−	PROPN
ejpam-2881	176	9	a4	a4	NOUN
ejpam-2881	176	10	−	−	PROPN
ejpam-2881	176	11	a5)ωλ(gt	a5)ωλ(gt	PROPN
ejpam-2881	176	12	,	,	PUNCT
ejpam-2881	176	13	t	t	PROPN
ejpam-2881	176	14	)	)	PUNCT
ejpam-2881	176	15	≤	≤	NOUN
ejpam-2881	176	16	0	0	NUM
ejpam-2881	176	17	for	for	ADP
ejpam-2881	176	18	all	all	DET
ejpam-2881	176	19	λ	λ	PROPN
ejpam-2881	176	20	>	>	X
ejpam-2881	176	21	0	0	PROPN
ejpam-2881	176	22	,	,	PUNCT
ejpam-2881	176	23	which	which	PRON
ejpam-2881	176	24	is	be	AUX
ejpam-2881	176	25	a	a	DET
ejpam-2881	176	26	contradiction	contradiction	NOUN
ejpam-2881	176	27	.	.	PUNCT
ejpam-2881	177	1	thus	thus	ADV
ejpam-2881	177	2	t	t	PROPN
ejpam-2881	177	3	is	be	AUX
ejpam-2881	177	4	a	a	DET
ejpam-2881	177	5	common	common	ADJ
ejpam-2881	177	6	fixed	fix	VERB
ejpam-2881	177	7	point	point	NOUN
ejpam-2881	177	8	of	of	ADP
ejpam-2881	177	9	f	f	PROPN
ejpam-2881	177	10	and	and	CCONJ
ejpam-2881	177	11	g.	g.	PROPN
ejpam-2881	177	12	for	for	ADP
ejpam-2881	177	13	the	the	DET
ejpam-2881	177	14	uniqueness	uniqueness	NOUN
ejpam-2881	177	15	of	of	ADP
ejpam-2881	177	16	the	the	DET
ejpam-2881	177	17	common	common	ADJ
ejpam-2881	177	18	fixed	fix	VERB
ejpam-2881	177	19	point	point	NOUN
ejpam-2881	177	20	,	,	PUNCT
ejpam-2881	177	21	we	we	PRON
ejpam-2881	177	22	suppose	suppose	VERB
ejpam-2881	177	23	that	that	SCONJ
ejpam-2881	177	24	u	u	PROPN
ejpam-2881	177	25	is	be	AUX
ejpam-2881	177	26	another	another	DET
ejpam-2881	177	27	common	common	ADJ
ejpam-2881	177	28	fixed	fix	VERB
ejpam-2881	177	29	point	point	NOUN
ejpam-2881	177	30	in	in	ADP
ejpam-2881	177	31	xω	xω	PRON
ejpam-2881	177	32	such	such	ADJ
ejpam-2881	177	33	that	that	DET
ejpam-2881	177	34	fu	fu	NOUN
ejpam-2881	177	35	=	=	PUNCT
ejpam-2881	177	36	gu	gu	PROPN
ejpam-2881	177	37	.	.	PROPN
ejpam-2881	178	1	from	from	ADP
ejpam-2881	178	2	(	(	PUNCT
ejpam-2881	178	3	b	b	NOUN
ejpam-2881	178	4	)	)	PUNCT
ejpam-2881	178	5	,	,	PUNCT
ejpam-2881	178	6	we	we	PRON
ejpam-2881	178	7	have	have	VERB
ejpam-2881	178	8	ωλ(u	ωλ(u	NUM
ejpam-2881	178	9	,	,	PUNCT
ejpam-2881	178	10	t	t	PROPN
ejpam-2881	178	11	)	)	PUNCT
ejpam-2881	178	12	=	=	SYM
ejpam-2881	179	1	ωλ(gu	ωλ(gu	NOUN
ejpam-2881	179	2	,	,	PUNCT
ejpam-2881	179	3	gt	gt	PROPN
ejpam-2881	179	4	)	)	PUNCT
ejpam-2881	179	5	=	=	PUNCT
ejpam-2881	180	1	ωλ(fu	ωλ(fu	PROPN
ejpam-2881	180	2	,	,	PUNCT
ejpam-2881	180	3	ft	ft	NOUN
ejpam-2881	180	4	)	)	PUNCT
ejpam-2881	180	5	≤	≤	NOUN
ejpam-2881	180	6	a1ωλ(fu	a1ωλ(fu	PROPN
ejpam-2881	180	7	,	,	PUNCT
ejpam-2881	180	8	gu	gu	NOUN
ejpam-2881	180	9	)	)	PUNCT
ejpam-2881	180	10	+	+	CCONJ
ejpam-2881	180	11	a2ωλ(ft	a2ωλ(ft	PROPN
ejpam-2881	180	12	,	,	PUNCT
ejpam-2881	180	13	gt	gt	PROPN
ejpam-2881	180	14	)	)	PUNCT
ejpam-2881	180	15	+	+	CCONJ
ejpam-2881	180	16	a3ωλ(ft	a3ωλ(ft	ADV
ejpam-2881	180	17	,	,	PUNCT
ejpam-2881	180	18	gu	gu	NOUN
ejpam-2881	180	19	)	)	PUNCT
ejpam-2881	180	20	+	+	CCONJ
ejpam-2881	180	21	a4ωλ(fu	a4ωλ(fu	PROPN
ejpam-2881	180	22	,	,	PUNCT
ejpam-2881	180	23	gt	gt	PROPN
ejpam-2881	180	24	)	)	PUNCT
ejpam-2881	180	25	+	+	CCONJ
ejpam-2881	180	26	a5ωλ(gt	a5ωλ(gt	PROPN
ejpam-2881	180	27	,	,	PUNCT
ejpam-2881	180	28	gu	gu	NOUN
ejpam-2881	180	29	)	)	PUNCT
ejpam-2881	180	30	≤	≤	NOUN
ejpam-2881	180	31	a3ωλ(ft	a3ωλ(ft	ADV
ejpam-2881	180	32	,	,	PUNCT
ejpam-2881	180	33	gu	gu	NOUN
ejpam-2881	180	34	)	)	PUNCT
ejpam-2881	180	35	+	+	X
ejpam-2881	180	36	a4ωλ(gu	a4ωλ(gu	ADJ
ejpam-2881	180	37	,	,	PUNCT
ejpam-2881	180	38	ft	ft	NOUN
ejpam-2881	180	39	)	)	PUNCT
ejpam-2881	180	40	+	+	CCONJ
ejpam-2881	180	41	a5ωλ(ft	a5ωλ(ft	ADV
ejpam-2881	180	42	,	,	PUNCT
ejpam-2881	180	43	gu	gu	NOUN
ejpam-2881	180	44	)	)	PUNCT
ejpam-2881	180	45	=	=	PRON
ejpam-2881	180	46	(	(	PUNCT
ejpam-2881	180	47	a3	a3	NOUN
ejpam-2881	180	48	+	+	CCONJ
ejpam-2881	180	49	a4	a4	NOUN
ejpam-2881	180	50	+	+	CCONJ
ejpam-2881	180	51	a5)ωλ(u	a5)ωλ(u	NUM
ejpam-2881	180	52	,	,	PUNCT
ejpam-2881	180	53	t	t	PROPN
ejpam-2881	180	54	)	)	PUNCT
ejpam-2881	180	55	.	.	PUNCT
ejpam-2881	181	1	p.	p.	NOUN
ejpam-2881	181	2	sumalai	sumalai	PROPN
ejpam-2881	181	3	,	,	PUNCT
ejpam-2881	181	4	p.	p.	PROPN
ejpam-2881	181	5	kumam	kumam	PROPN
ejpam-2881	181	6	,	,	PUNCT
ejpam-2881	181	7	y.	y.	PROPN
ejpam-2881	181	8	j.	j.	PROPN
ejpam-2881	181	9	cho	cho	PROPN
ejpam-2881	181	10	,	,	PUNCT
ejpam-2881	181	11	a.	a.	NOUN
ejpam-2881	181	12	padcharoen	padcharoen	PROPN
ejpam-2881	181	13	/	/	SYM
ejpam-2881	181	14	eur	eur	PROPN
ejpam-2881	181	15	.	.	PUNCT
ejpam-2881	182	1	j.	j.	PROPN
ejpam-2881	182	2	pure	pure	PROPN
ejpam-2881	182	3	appl	appl	PROPN
ejpam-2881	182	4	.	.	PROPN
ejpam-2881	182	5	math	math	PROPN
ejpam-2881	182	6	,	,	PUNCT
ejpam-2881	182	7	10	10	NUM
ejpam-2881	182	8	(	(	PUNCT
ejpam-2881	182	9	2	2	NUM
ejpam-2881	182	10	)	)	PUNCT
ejpam-2881	182	11	(	(	PUNCT
ejpam-2881	182	12	2017	2017	NUM
ejpam-2881	182	13	)	)	PUNCT
ejpam-2881	182	14	,	,	PUNCT
ejpam-2881	182	15	238	238	NUM
ejpam-2881	182	16	-	-	SYM
ejpam-2881	182	17	254	254	NUM
ejpam-2881	182	18	245	245	NUM
ejpam-2881	182	19	this	this	PRON
ejpam-2881	182	20	implies	imply	VERB
ejpam-2881	182	21	that	that	SCONJ
ejpam-2881	182	22	(	(	PUNCT
ejpam-2881	182	23	1	1	NUM
ejpam-2881	182	24	−	−	NOUN
ejpam-2881	182	25	a3	a3	NOUN
ejpam-2881	182	26	−	−	PROPN
ejpam-2881	182	27	a4	a4	NOUN
ejpam-2881	182	28	−	−	PROPN
ejpam-2881	182	29	a5)ωλ(u	a5)ωλ(u	NUM
ejpam-2881	182	30	,	,	PUNCT
ejpam-2881	182	31	t	t	NOUN
ejpam-2881	182	32	)	)	PUNCT
ejpam-2881	182	33	≤	≤	NOUN
ejpam-2881	182	34	0	0	NUM
ejpam-2881	182	35	for	for	ADP
ejpam-2881	182	36	all	all	DET
ejpam-2881	182	37	λ	λ	PROPN
ejpam-2881	182	38	>	>	X
ejpam-2881	182	39	0	0	PROPN
ejpam-2881	182	40	,	,	PUNCT
ejpam-2881	182	41	which	which	PRON
ejpam-2881	182	42	is	be	AUX
ejpam-2881	182	43	a	a	DET
ejpam-2881	182	44	contradiction	contradiction	NOUN
ejpam-2881	182	45	.	.	PUNCT
ejpam-2881	183	1	thus	thus	ADV
ejpam-2881	183	2	ωλ(u	ωλ(u	NUM
ejpam-2881	183	3	,	,	PUNCT
ejpam-2881	183	4	t	t	PROPN
ejpam-2881	183	5	)	)	PUNCT
ejpam-2881	183	6	=	=	SYM
ejpam-2881	183	7	0	0	NUM
ejpam-2881	184	1	and	and	CCONJ
ejpam-2881	184	2	so	so	ADV
ejpam-2881	184	3	u	u	NOUN
ejpam-2881	184	4	=	=	NOUN
ejpam-2881	184	5	t.	t.	NOUN
ejpam-2881	184	6	hence	hence	ADV
ejpam-2881	184	7	f	f	PROPN
ejpam-2881	184	8	and	and	CCONJ
ejpam-2881	184	9	g	g	PROPN
ejpam-2881	184	10	have	have	VERB
ejpam-2881	184	11	a	a	DET
ejpam-2881	184	12	unique	unique	ADJ
ejpam-2881	184	13	common	common	ADJ
ejpam-2881	184	14	fixed	fix	VERB
ejpam-2881	184	15	point	point	NOUN
ejpam-2881	184	16	.	.	PUNCT
ejpam-2881	185	1	by	by	ADP
ejpam-2881	185	2	setting	set	VERB
ejpam-2881	185	3	g	g	NOUN
ejpam-2881	185	4	=	=	PUNCT
ejpam-2881	185	5	ixω	ixω	ADJ
ejpam-2881	185	6	,	,	PUNCT
ejpam-2881	185	7	we	we	PRON
ejpam-2881	185	8	deduce	deduce	VERB
ejpam-2881	185	9	the	the	DET
ejpam-2881	185	10	following	following	ADJ
ejpam-2881	185	11	result	result	NOUN
ejpam-2881	185	12	of	of	ADP
ejpam-2881	185	13	fixed	fix	VERB
ejpam-2881	185	14	point	point	NOUN
ejpam-2881	185	15	for	for	ADP
ejpam-2881	185	16	one	one	NUM
ejpam-2881	185	17	self	self	NOUN
ejpam-2881	185	18	-	-	PUNCT
ejpam-2881	185	19	mapping	mapping	NOUN
ejpam-2881	185	20	from	from	ADP
ejpam-2881	185	21	theorem	theorem	ADJ
ejpam-2881	185	22	3	3	NUM
ejpam-2881	185	23	.	.	PUNCT
ejpam-2881	185	24	corollary	corollary	ADJ
ejpam-2881	185	25	1	1	NUM
ejpam-2881	185	26	.	.	PUNCT
ejpam-2881	186	1	let	let	VERB
ejpam-2881	186	2	xω	xω	PRON
ejpam-2881	186	3	be	be	AUX
ejpam-2881	186	4	an	an	DET
ejpam-2881	186	5	ω	ω	ADJ
ejpam-2881	186	6	-	-	ADJ
ejpam-2881	186	7	complete	complete	ADJ
ejpam-2881	186	8	modular	modular	ADJ
ejpam-2881	186	9	metric	metric	ADJ
ejpam-2881	186	10	space	space	NOUN
ejpam-2881	186	11	and	and	CCONJ
ejpam-2881	186	12	f	f	NOUN
ejpam-2881	186	13	:	:	PUNCT
ejpam-2881	186	14	xω	xω	PROPN
ejpam-2881	187	1	→	→	PUNCT
ejpam-2881	187	2	xω	xω	X
ejpam-2881	187	3	such	such	ADJ
ejpam-2881	187	4	that	that	SCONJ
ejpam-2881	187	5	,	,	PUNCT
ejpam-2881	187	6	for	for	ADP
ejpam-2881	187	7	all	all	DET
ejpam-2881	187	8	λ	λ	PROPN
ejpam-2881	187	9	>	>	X
ejpam-2881	187	10	0	0	PUNCT
ejpam-2881	187	11	and	and	CCONJ
ejpam-2881	187	12	x	x	NOUN
ejpam-2881	187	13	,	,	PUNCT
ejpam-2881	187	14	y	y	PROPN
ejpam-2881	187	15	∈	∈	PROPN
ejpam-2881	187	16	xω	xω	PROPN
ejpam-2881	187	17	,	,	PUNCT
ejpam-2881	187	18	ωλ(x0	ωλ(x0	NOUN
ejpam-2881	187	19	,	,	PUNCT
ejpam-2881	187	20	fx0	fx0	PROPN
ejpam-2881	187	21	)	)	PUNCT
ejpam-2881	187	22	<	<	X
ejpam-2881	187	23	∞	∞	NUM
ejpam-2881	187	24	and	and	CCONJ
ejpam-2881	187	25	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	187	26	,	,	PUNCT
ejpam-2881	187	27	fy	fy	PROPN
ejpam-2881	187	28	)	)	PUNCT
ejpam-2881	187	29	≤	≤	NOUN
ejpam-2881	187	30	a1ωλ(fx	a1ωλ(fx	NOUN
ejpam-2881	187	31	,	,	PUNCT
ejpam-2881	187	32	x	x	PRON
ejpam-2881	187	33	)	)	PUNCT
ejpam-2881	187	34	+	+	CCONJ
ejpam-2881	187	35	a2ωλ(fy	a2ωλ(fy	ADJ
ejpam-2881	187	36	,	,	PUNCT
ejpam-2881	187	37	y	y	NOUN
ejpam-2881	187	38	)	)	PUNCT
ejpam-2881	188	1	+	+	CCONJ
ejpam-2881	188	2	a3ωλ(fy	a3ωλ(fy	NOUN
ejpam-2881	188	3	,	,	PUNCT
ejpam-2881	188	4	x	x	PRON
ejpam-2881	188	5	)	)	PUNCT
ejpam-2881	188	6	+	+	CCONJ
ejpam-2881	188	7	a4ωλ(fx	a4ωλ(fx	PROPN
ejpam-2881	188	8	,	,	PUNCT
ejpam-2881	188	9	y	y	NOUN
ejpam-2881	188	10	)	)	PUNCT
ejpam-2881	188	11	+	+	CCONJ
ejpam-2881	188	12	a5ωλ(x	a5ωλ(x	PROPN
ejpam-2881	188	13	,	,	PUNCT
ejpam-2881	188	14	y	y	NOUN
ejpam-2881	188	15	)	)	PUNCT
ejpam-2881	188	16	where	where	SCONJ
ejpam-2881	188	17	a1	a1	NOUN
ejpam-2881	188	18	,	,	PUNCT
ejpam-2881	188	19	a2	a2	PROPN
ejpam-2881	188	20	,	,	PUNCT
ejpam-2881	188	21	a3	a3	NOUN
ejpam-2881	188	22	,	,	PUNCT
ejpam-2881	188	23	a4	a4	PROPN
ejpam-2881	188	24	,	,	PUNCT
ejpam-2881	188	25	a5	a5	PROPN
ejpam-2881	188	26	∈	∈	PROPN
ejpam-2881	188	27	[	[	X
ejpam-2881	188	28	0	0	NUM
ejpam-2881	188	29	,	,	PUNCT
ejpam-2881	188	30	14	14	NUM
ejpam-2881	188	31	)	)	PUNCT
ejpam-2881	188	32	with	with	ADP
ejpam-2881	188	33	5∑	5∑	PROPN
ejpam-2881	188	34	i=1	i=1	PROPN
ejpam-2881	188	35	ai	ai	VERB
ejpam-2881	188	36	<	<	X
ejpam-2881	188	37	1	1	NUM
ejpam-2881	188	38	.	.	PUNCT
ejpam-2881	189	1	then	then	ADV
ejpam-2881	189	2	f	f	PROPN
ejpam-2881	189	3	has	have	VERB
ejpam-2881	189	4	a	a	DET
ejpam-2881	189	5	unique	unique	ADJ
ejpam-2881	189	6	fixed	fix	VERB
ejpam-2881	189	7	point	point	NOUN
ejpam-2881	189	8	z.	z.	PROPN
ejpam-2881	189	9	further	far	ADV
ejpam-2881	189	10	,	,	PUNCT
ejpam-2881	189	11	for	for	ADP
ejpam-2881	189	12	any	any	DET
ejpam-2881	189	13	x0	x0	PROPN
ejpam-2881	189	14	∈	∈	PROPN
ejpam-2881	189	15	xω	xω	PROPN
ejpam-2881	189	16	,	,	PUNCT
ejpam-2881	189	17	the	the	DET
ejpam-2881	189	18	picard	picard	NOUN
ejpam-2881	189	19	sequence	sequence	NOUN
ejpam-2881	189	20	{	{	PUNCT
ejpam-2881	189	21	fxn	fxn	NOUN
ejpam-2881	189	22	}	}	PUNCT
ejpam-2881	189	23	with	with	ADP
ejpam-2881	189	24	an	an	DET
ejpam-2881	189	25	initial	initial	ADJ
ejpam-2881	189	26	point	point	NOUN
ejpam-2881	189	27	x0	x0	PROPN
ejpam-2881	189	28	is	be	AUX
ejpam-2881	189	29	ω	ω	NOUN
ejpam-2881	189	30	-	-	NOUN
ejpam-2881	189	31	convergent	convergent	NOUN
ejpam-2881	189	32	to	to	ADP
ejpam-2881	189	33	the	the	DET
ejpam-2881	189	34	fixed	fixed	ADJ
ejpam-2881	189	35	point	point	NOUN
ejpam-2881	189	36	z.	z.	PROPN
ejpam-2881	189	37	corollary	corollary	NOUN
ejpam-2881	189	38	2	2	PROPN
ejpam-2881	189	39	.	.	PUNCT
ejpam-2881	190	1	let	let	VERB
ejpam-2881	190	2	xω	xω	PRON
ejpam-2881	190	3	be	be	AUX
ejpam-2881	190	4	an	an	DET
ejpam-2881	190	5	ω	ω	ADJ
ejpam-2881	190	6	-	-	ADJ
ejpam-2881	190	7	complete	complete	ADJ
ejpam-2881	190	8	modular	modular	ADJ
ejpam-2881	190	9	metric	metric	ADJ
ejpam-2881	190	10	space	space	NOUN
ejpam-2881	190	11	and	and	CCONJ
ejpam-2881	190	12	f	f	NOUN
ejpam-2881	190	13	:	:	PUNCT
ejpam-2881	190	14	xω	xω	PROPN
ejpam-2881	191	1	→	→	PUNCT
ejpam-2881	191	2	xω	xω	X
ejpam-2881	191	3	such	such	ADJ
ejpam-2881	191	4	that	that	SCONJ
ejpam-2881	191	5	,	,	PUNCT
ejpam-2881	191	6	for	for	ADP
ejpam-2881	191	7	all	all	DET
ejpam-2881	191	8	λ	λ	PROPN
ejpam-2881	191	9	>	>	X
ejpam-2881	191	10	0	0	PUNCT
ejpam-2881	191	11	and	and	CCONJ
ejpam-2881	191	12	x	x	NOUN
ejpam-2881	191	13	,	,	PUNCT
ejpam-2881	191	14	y	y	PROPN
ejpam-2881	191	15	∈	∈	PROPN
ejpam-2881	191	16	xω	xω	PROPN
ejpam-2881	191	17	,	,	PUNCT
ejpam-2881	191	18	ωλ(x0	ωλ(x0	NOUN
ejpam-2881	191	19	,	,	PUNCT
ejpam-2881	191	20	fx0	fx0	PROPN
ejpam-2881	191	21	)	)	PUNCT
ejpam-2881	191	22	<	<	X
ejpam-2881	191	23	∞	∞	NUM
ejpam-2881	191	24	and	and	CCONJ
ejpam-2881	191	25	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	191	26	,	,	PUNCT
ejpam-2881	191	27	fy	fy	PROPN
ejpam-2881	191	28	)	)	PUNCT
ejpam-2881	191	29	≤	≤	NOUN
ejpam-2881	191	30	a1ωλ(fx	a1ωλ(fx	NOUN
ejpam-2881	191	31	,	,	PUNCT
ejpam-2881	191	32	x	x	PRON
ejpam-2881	191	33	)	)	PUNCT
ejpam-2881	191	34	+	+	CCONJ
ejpam-2881	191	35	a2ωλ(fy	a2ωλ(fy	ADJ
ejpam-2881	191	36	,	,	PUNCT
ejpam-2881	191	37	y	y	NOUN
ejpam-2881	191	38	)	)	PUNCT
ejpam-2881	191	39	+	+	CCONJ
ejpam-2881	191	40	a3ωλ(x	a3ωλ(x	PROPN
ejpam-2881	191	41	,	,	PUNCT
ejpam-2881	191	42	y	y	NOUN
ejpam-2881	191	43	)	)	PUNCT
ejpam-2881	191	44	where	where	SCONJ
ejpam-2881	191	45	a1	a1	NOUN
ejpam-2881	191	46	,	,	PUNCT
ejpam-2881	191	47	a2	a2	PROPN
ejpam-2881	191	48	,	,	PUNCT
ejpam-2881	191	49	a3	a3	NOUN
ejpam-2881	191	50	∈	∈	PROPN
ejpam-2881	192	1	[	[	X
ejpam-2881	192	2	0	0	NUM
ejpam-2881	192	3	,	,	PUNCT
ejpam-2881	192	4	14	14	NUM
ejpam-2881	192	5	)	)	PUNCT
ejpam-2881	192	6	with	with	ADP
ejpam-2881	192	7	0	0	NUM
ejpam-2881	192	8	≤	≤	NOUN
ejpam-2881	192	9	a1	a1	NOUN
ejpam-2881	192	10	+	+	CCONJ
ejpam-2881	192	11	a2	a2	PROPN
ejpam-2881	192	12	+	+	CCONJ
ejpam-2881	192	13	a3	a3	NOUN
ejpam-2881	192	14	<	<	X
ejpam-2881	192	15	1	1	X
ejpam-2881	192	16	.	.	PUNCT
ejpam-2881	192	17	then	then	ADV
ejpam-2881	192	18	f	f	PROPN
ejpam-2881	192	19	has	have	VERB
ejpam-2881	192	20	a	a	DET
ejpam-2881	192	21	unique	unique	ADJ
ejpam-2881	192	22	fixed	fix	VERB
ejpam-2881	192	23	point	point	NOUN
ejpam-2881	192	24	.	.	PUNCT
ejpam-2881	193	1	corollary	corollary	ADJ
ejpam-2881	193	2	3	3	X
ejpam-2881	193	3	.	.	PUNCT
ejpam-2881	194	1	let	let	VERB
ejpam-2881	194	2	xω	xω	PRON
ejpam-2881	194	3	be	be	AUX
ejpam-2881	194	4	an	an	DET
ejpam-2881	194	5	ω	ω	ADJ
ejpam-2881	194	6	-	-	ADJ
ejpam-2881	194	7	complete	complete	ADJ
ejpam-2881	194	8	modular	modular	ADJ
ejpam-2881	194	9	metric	metric	ADJ
ejpam-2881	194	10	space	space	NOUN
ejpam-2881	194	11	and	and	CCONJ
ejpam-2881	194	12	f	f	NOUN
ejpam-2881	194	13	:	:	PUNCT
ejpam-2881	194	14	xω	xω	PROPN
ejpam-2881	195	1	→	→	PUNCT
ejpam-2881	195	2	xω	xω	X
ejpam-2881	195	3	such	such	ADJ
ejpam-2881	195	4	that	that	SCONJ
ejpam-2881	195	5	,	,	PUNCT
ejpam-2881	195	6	for	for	ADP
ejpam-2881	195	7	all	all	DET
ejpam-2881	195	8	λ	λ	PROPN
ejpam-2881	195	9	>	>	X
ejpam-2881	195	10	0	0	PUNCT
ejpam-2881	195	11	and	and	CCONJ
ejpam-2881	195	12	x	x	NOUN
ejpam-2881	195	13	,	,	PUNCT
ejpam-2881	195	14	y	y	PROPN
ejpam-2881	195	15	∈	∈	PROPN
ejpam-2881	195	16	xω	xω	PROPN
ejpam-2881	195	17	,	,	PUNCT
ejpam-2881	195	18	ωλ(x0	ωλ(x0	NOUN
ejpam-2881	195	19	,	,	PUNCT
ejpam-2881	195	20	fx0	fx0	PROPN
ejpam-2881	195	21	)	)	PUNCT
ejpam-2881	195	22	<	<	X
ejpam-2881	195	23	∞	∞	NUM
ejpam-2881	195	24	and	and	CCONJ
ejpam-2881	195	25	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	195	26	,	,	PUNCT
ejpam-2881	195	27	fy	fy	PROPN
ejpam-2881	195	28	)	)	PUNCT
ejpam-2881	195	29	≤	≤	PUNCT
ejpam-2881	195	30	aωλ(x	aωλ(x	PROPN
ejpam-2881	195	31	,	,	PUNCT
ejpam-2881	195	32	y	y	NOUN
ejpam-2881	195	33	)	)	PUNCT
ejpam-2881	195	34	where	where	SCONJ
ejpam-2881	195	35	0	0	NUM
ejpam-2881	195	36	≤	≤	NOUN
ejpam-2881	195	37	a	a	DET
ejpam-2881	195	38	<	<	X
ejpam-2881	195	39	1	1	NUM
ejpam-2881	195	40	.	.	PUNCT
ejpam-2881	196	1	then	then	ADV
ejpam-2881	196	2	f	f	PROPN
ejpam-2881	196	3	has	have	VERB
ejpam-2881	196	4	a	a	DET
ejpam-2881	196	5	unique	unique	ADJ
ejpam-2881	196	6	fixed	fix	VERB
ejpam-2881	196	7	point	point	NOUN
ejpam-2881	196	8	.	.	PUNCT
ejpam-2881	197	1	now	now	ADV
ejpam-2881	197	2	,	,	PUNCT
ejpam-2881	197	3	we	we	PRON
ejpam-2881	197	4	give	give	VERB
ejpam-2881	197	5	some	some	DET
ejpam-2881	197	6	examples	example	NOUN
ejpam-2881	197	7	of	of	ADP
ejpam-2881	197	8	the	the	DET
ejpam-2881	197	9	(	(	PUNCT
ejpam-2881	197	10	clrg)-property	clrg)-property	PROPN
ejpam-2881	197	11	as	as	SCONJ
ejpam-2881	197	12	follows	follow	VERB
ejpam-2881	197	13	:	:	PUNCT
ejpam-2881	197	14	example	example	NOUN
ejpam-2881	197	15	2	2	X
ejpam-2881	197	16	.	.	PUNCT
ejpam-2881	198	1	let	let	VERB
ejpam-2881	198	2	xω	xω	PUNCT
ejpam-2881	199	1	=	=	PUNCT
ejpam-2881	200	1	[	[	X
ejpam-2881	200	2	0,∞	0,∞	X
ejpam-2881	200	3	)	)	PUNCT
ejpam-2881	200	4	be	be	VERB
ejpam-2881	200	5	a	a	DET
ejpam-2881	200	6	modular	modular	ADJ
ejpam-2881	200	7	metric	metric	ADJ
ejpam-2881	200	8	space	space	NOUN
ejpam-2881	200	9	.	.	PUNCT
ejpam-2881	201	1	define	define	VERB
ejpam-2881	201	2	two	two	NUM
ejpam-2881	201	3	mappings	mapping	NOUN
ejpam-2881	201	4	f	f	NOUN
ejpam-2881	201	5	,	,	PUNCT
ejpam-2881	201	6	g	g	NOUN
ejpam-2881	201	7	:	:	PUNCT
ejpam-2881	201	8	xω	xω	PROPN
ejpam-2881	201	9	→	→	SYM
ejpam-2881	201	10	xω	xω	X
ejpam-2881	201	11	by	by	ADP
ejpam-2881	201	12	fx	fx	NOUN
ejpam-2881	201	13	=	=	PUNCT
ejpam-2881	201	14	x+	x+	PROPN
ejpam-2881	201	15	4	4	NUM
ejpam-2881	201	16	and	and	CCONJ
ejpam-2881	201	17	gx	gx	PROPN
ejpam-2881	201	18	=	=	PUNCT
ejpam-2881	201	19	5x	5x	NOUN
ejpam-2881	201	20	for	for	ADP
ejpam-2881	201	21	all	all	DET
ejpam-2881	201	22	x	x	SYM
ejpam-2881	201	23	∈	∈	PROPN
ejpam-2881	201	24	xω	xω	NOUN
ejpam-2881	201	25	,	,	PUNCT
ejpam-2881	201	26	respectively	respectively	ADV
ejpam-2881	201	27	.	.	PUNCT
ejpam-2881	202	1	now	now	ADV
ejpam-2881	202	2	,	,	PUNCT
ejpam-2881	202	3	we	we	PRON
ejpam-2881	202	4	consider	consider	VERB
ejpam-2881	202	5	the	the	DET
ejpam-2881	202	6	sequence	sequence	NOUN
ejpam-2881	202	7	{	{	PUNCT
ejpam-2881	202	8	xn	xn	NOUN
ejpam-2881	202	9	}	}	PUNCT
ejpam-2881	202	10	defined	define	VERB
ejpam-2881	202	11	by	by	ADP
ejpam-2881	202	12	xn	xn	PROPN
ejpam-2881	202	13	=	=	SYM
ejpam-2881	202	14	{	{	PUNCT
ejpam-2881	202	15	1	1	NUM
ejpam-2881	202	16	+	+	SYM
ejpam-2881	202	17	1	1	NUM
ejpam-2881	202	18	n	n	CCONJ
ejpam-2881	202	19	}	}	PUNCT
ejpam-2881	202	20	for	for	ADP
ejpam-2881	202	21	each	each	DET
ejpam-2881	202	22	n	n	PRON
ejpam-2881	202	23	≥	≥	NOUN
ejpam-2881	202	24	1	1	NUM
ejpam-2881	202	25	.	.	PUNCT
ejpam-2881	203	1	since	since	SCONJ
ejpam-2881	203	2	lim	lim	PROPN
ejpam-2881	203	3	n→∞	n→∞	PRON
ejpam-2881	203	4	fxn	fxn	PROPN
ejpam-2881	203	5	=	=	PUNCT
ejpam-2881	203	6	lim	lim	PROPN
ejpam-2881	203	7	n→∞	n→∞	NUM
ejpam-2881	203	8	gxn	gxn	NOUN
ejpam-2881	203	9	=	=	SYM
ejpam-2881	203	10	5	5	NUM
ejpam-2881	203	11	=	=	SYM
ejpam-2881	203	12	g(1	g(1	PROPN
ejpam-2881	203	13	)	)	PUNCT
ejpam-2881	203	14	∈	∈	PROPN
ejpam-2881	203	15	xω	xω	PROPN
ejpam-2881	203	16	,	,	PUNCT
ejpam-2881	203	17	f	f	PROPN
ejpam-2881	203	18	and	and	CCONJ
ejpam-2881	203	19	g	g	PROPN
ejpam-2881	203	20	satisfy	satisfy	VERB
ejpam-2881	203	21	the	the	DET
ejpam-2881	203	22	(	(	PUNCT
ejpam-2881	203	23	clrg)-property	clrg)-property	PROPN
ejpam-2881	203	24	.	.	PROPN
ejpam-2881	203	25	example	example	NOUN
ejpam-2881	204	1	3	3	NUM
ejpam-2881	204	2	.	.	PUNCT
ejpam-2881	205	1	the	the	DET
ejpam-2881	205	2	conclusion	conclusion	NOUN
ejpam-2881	205	3	of	of	ADP
ejpam-2881	205	4	example	example	NOUN
ejpam-2881	205	5	2	2	NUM
ejpam-2881	205	6	remains	remain	VERB
ejpam-2881	205	7	true	true	ADJ
ejpam-2881	205	8	if	if	SCONJ
ejpam-2881	205	9	the	the	DET
ejpam-2881	205	10	self	self	NOUN
ejpam-2881	205	11	-	-	PUNCT
ejpam-2881	205	12	mappings	mapping	NOUN
ejpam-2881	205	13	f	f	NOUN
ejpam-2881	205	14	and	and	CCONJ
ejpam-2881	205	15	g	g	PROPN
ejpam-2881	205	16	is	be	AUX
ejpam-2881	205	17	defined	define	VERB
ejpam-2881	205	18	on	on	ADP
ejpam-2881	205	19	xω	xω	X
ejpam-2881	205	20	by	by	ADP
ejpam-2881	205	21	f(x	f(x	PROPN
ejpam-2881	205	22	)	)	PUNCT
ejpam-2881	206	1	=	=	PUNCT
ejpam-2881	206	2	x	x	SYM
ejpam-2881	206	3	4	4	NUM
ejpam-2881	206	4	and	and	CCONJ
ejpam-2881	206	5	g(x	g(x	NOUN
ejpam-2881	206	6	)	)	PUNCT
ejpam-2881	207	1	=	=	PUNCT
ejpam-2881	207	2	x	x	SYM
ejpam-2881	207	3	2	2	NUM
ejpam-2881	207	4	for	for	ADP
ejpam-2881	207	5	all	all	DET
ejpam-2881	207	6	x	x	SYM
ejpam-2881	207	7	∈	∈	PROPN
ejpam-2881	207	8	xω	xω	NOUN
ejpam-2881	207	9	,	,	PUNCT
ejpam-2881	207	10	respectively	respectively	ADV
ejpam-2881	207	11	.	.	PUNCT
ejpam-2881	208	1	let	let	VERB
ejpam-2881	208	2	a	a	DET
ejpam-2881	208	3	sequence	sequence	NOUN
ejpam-2881	208	4	{	{	PUNCT
ejpam-2881	208	5	xn	xn	NOUN
ejpam-2881	208	6	}	}	PUNCT
ejpam-2881	208	7	be	be	AUX
ejpam-2881	208	8	defined	define	VERB
ejpam-2881	208	9	by	by	ADP
ejpam-2881	208	10	xn	xn	PROPN
ejpam-2881	208	11	=	=	NOUN
ejpam-2881	208	12	{	{	PUNCT
ejpam-2881	208	13	1n	1n	NUM
ejpam-2881	208	14	}	}	PUNCT
ejpam-2881	208	15	in	in	ADP
ejpam-2881	208	16	xω	xω	PRON
ejpam-2881	208	17	.	.	PUNCT
ejpam-2881	209	1	since	since	SCONJ
ejpam-2881	209	2	lim	lim	PROPN
ejpam-2881	209	3	n→∞	n→∞	PRON
ejpam-2881	209	4	fxn	fxn	PROPN
ejpam-2881	209	5	=	=	PUNCT
ejpam-2881	209	6	lim	lim	PROPN
ejpam-2881	209	7	n→∞	n→∞	NUM
ejpam-2881	209	8	gxn	gxn	NOUN
ejpam-2881	209	9	=	=	SYM
ejpam-2881	209	10	0	0	PUNCT
ejpam-2881	209	11	=	=	SYM
ejpam-2881	209	12	g(0	g(0	PROPN
ejpam-2881	209	13	)	)	PUNCT
ejpam-2881	209	14	∈	∈	PROPN
ejpam-2881	209	15	xω	xω	PROPN
ejpam-2881	209	16	,	,	PUNCT
ejpam-2881	209	17	f	f	PROPN
ejpam-2881	209	18	and	and	CCONJ
ejpam-2881	209	19	g	g	PROPN
ejpam-2881	209	20	satisfy	satisfy	VERB
ejpam-2881	209	21	the	the	DET
ejpam-2881	209	22	(	(	PUNCT
ejpam-2881	209	23	clrg)-property	clrg)-property	PROPN
ejpam-2881	209	24	.	.	PUNCT
ejpam-2881	210	1	p.	p.	NOUN
ejpam-2881	210	2	sumalai	sumalai	PROPN
ejpam-2881	210	3	,	,	PUNCT
ejpam-2881	210	4	p.	p.	PROPN
ejpam-2881	210	5	kumam	kumam	PROPN
ejpam-2881	210	6	,	,	PUNCT
ejpam-2881	210	7	y.	y.	PROPN
ejpam-2881	210	8	j.	j.	PROPN
ejpam-2881	210	9	cho	cho	PROPN
ejpam-2881	210	10	,	,	PUNCT
ejpam-2881	210	11	a.	a.	NOUN
ejpam-2881	210	12	padcharoen	padcharoen	PROPN
ejpam-2881	210	13	/	/	SYM
ejpam-2881	210	14	eur	eur	PROPN
ejpam-2881	210	15	.	.	PUNCT
ejpam-2881	211	1	j.	j.	PROPN
ejpam-2881	211	2	pure	pure	PROPN
ejpam-2881	211	3	appl	appl	PROPN
ejpam-2881	211	4	.	.	PROPN
ejpam-2881	211	5	math	math	PROPN
ejpam-2881	211	6	,	,	PUNCT
ejpam-2881	211	7	10	10	NUM
ejpam-2881	211	8	(	(	PUNCT
ejpam-2881	211	9	2	2	NUM
ejpam-2881	211	10	)	)	PUNCT
ejpam-2881	211	11	(	(	PUNCT
ejpam-2881	211	12	2017	2017	NUM
ejpam-2881	211	13	)	)	PUNCT
ejpam-2881	211	14	,	,	PUNCT
ejpam-2881	211	15	238	238	NUM
ejpam-2881	211	16	-	-	SYM
ejpam-2881	211	17	254	254	NUM
ejpam-2881	211	18	246	246	NUM
ejpam-2881	211	19	4	4	NUM
ejpam-2881	211	20	.	.	PUNCT
ejpam-2881	211	21	fixed	fix	VERB
ejpam-2881	211	22	point	point	NOUN
ejpam-2881	211	23	results	result	NOUN
ejpam-2881	211	24	for	for	ADP
ejpam-2881	211	25	the	the	DET
ejpam-2881	211	26	strict	strict	ADJ
ejpam-2881	211	27	contractive	contractive	ADJ
ejpam-2881	211	28	condition	condition	NOUN
ejpam-2881	211	29	definition	definition	NOUN
ejpam-2881	211	30	7	7	NUM
ejpam-2881	211	31	.	.	PUNCT
ejpam-2881	212	1	let	let	AUX
ejpam-2881	212	2	(	(	PUNCT
ejpam-2881	212	3	x	x	NOUN
ejpam-2881	212	4	,	,	PUNCT
ejpam-2881	212	5	ω	ω	NUM
ejpam-2881	212	6	)	)	PUNCT
ejpam-2881	212	7	be	be	AUX
ejpam-2881	212	8	a	a	DET
ejpam-2881	212	9	modular	modular	ADJ
ejpam-2881	212	10	metric	metric	ADJ
ejpam-2881	212	11	space	space	NOUN
ejpam-2881	212	12	and	and	CCONJ
ejpam-2881	212	13	(	(	PUNCT
ejpam-2881	212	14	f	f	X
ejpam-2881	212	15	,	,	PUNCT
ejpam-2881	212	16	g	g	NOUN
ejpam-2881	212	17	)	)	PUNCT
ejpam-2881	212	18	be	be	AUX
ejpam-2881	212	19	a	a	DET
ejpam-2881	212	20	pair	pair	NOUN
ejpam-2881	212	21	of	of	ADP
ejpam-2881	212	22	self	self	NOUN
ejpam-2881	212	23	-	-	PUNCT
ejpam-2881	212	24	mappings	mapping	NOUN
ejpam-2881	212	25	on	on	ADP
ejpam-2881	212	26	xω	xω	PRON
ejpam-2881	212	27	.	.	PUNCT
ejpam-2881	213	1	for	for	ADP
ejpam-2881	213	2	any	any	DET
ejpam-2881	213	3	x	x	NOUN
ejpam-2881	213	4	,	,	PUNCT
ejpam-2881	213	5	y	y	PROPN
ejpam-2881	213	6	∈	∈	PROPN
ejpam-2881	213	7	xω	xω	X
ejpam-2881	213	8	,	,	PUNCT
ejpam-2881	213	9	consider	consider	VERB
ejpam-2881	213	10	the	the	DET
ejpam-2881	213	11	following	follow	VERB
ejpam-2881	213	12	sets	set	NOUN
ejpam-2881	213	13	:	:	PUNCT
ejpam-2881	213	14	mf	mf	X
ejpam-2881	213	15	,	,	PUNCT
ejpam-2881	213	16	g	g	PROPN
ejpam-2881	213	17	0	0	NUM
ejpam-2881	213	18	(	(	PUNCT
ejpam-2881	213	19	x	x	NOUN
ejpam-2881	213	20	,	,	PUNCT
ejpam-2881	213	21	y	y	PROPN
ejpam-2881	213	22	)	)	PUNCT
ejpam-2881	214	1	=	=	PRON
ejpam-2881	214	2	{	{	PUNCT
ejpam-2881	214	3	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	214	4	,	,	PUNCT
ejpam-2881	214	5	gy	gy	NOUN
ejpam-2881	214	6	)	)	PUNCT
ejpam-2881	214	7	,	,	PUNCT
ejpam-2881	214	8	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	214	9	,	,	PUNCT
ejpam-2881	214	10	fx	fx	PROPN
ejpam-2881	214	11	)	)	PUNCT
ejpam-2881	214	12	,	,	PUNCT
ejpam-2881	214	13	ωλ(gy	ωλ(gy	PROPN
ejpam-2881	214	14	,	,	PUNCT
ejpam-2881	214	15	fy	fy	PROPN
ejpam-2881	214	16	)	)	PUNCT
ejpam-2881	214	17	,	,	PUNCT
ejpam-2881	214	18	ωλ(gx	ωλ(gx	PROPN
ejpam-2881	214	19	,	,	PUNCT
ejpam-2881	214	20	fy	fy	PROPN
ejpam-2881	214	21	)	)	PUNCT
ejpam-2881	214	22	,	,	PUNCT
ejpam-2881	214	23	ωλ(gy	ωλ(gy	PROPN
ejpam-2881	214	24	,	,	PUNCT
ejpam-2881	214	25	fx	fx	PROPN
ejpam-2881	214	26	)	)	PUNCT
ejpam-2881	214	27	}	}	PUNCT
ejpam-2881	214	28	,	,	PUNCT
ejpam-2881	214	29	mf	mf	X
ejpam-2881	214	30	,	,	PUNCT
ejpam-2881	214	31	g	g	PROPN
ejpam-2881	214	32	1	1	NUM
ejpam-2881	214	33	(	(	PUNCT
ejpam-2881	214	34	x	x	NOUN
ejpam-2881	214	35	,	,	PUNCT
ejpam-2881	214	36	y	y	NOUN
ejpam-2881	214	37	)	)	PUNCT
ejpam-2881	214	38	=	=	PRON
ejpam-2881	214	39	{	{	PUNCT
ejpam-2881	214	40	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	214	41	,	,	PUNCT
ejpam-2881	214	42	gy	gy	NOUN
ejpam-2881	214	43	)	)	PUNCT
ejpam-2881	214	44	,	,	PUNCT
ejpam-2881	214	45	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	214	46	,	,	PUNCT
ejpam-2881	214	47	fx	fx	PROPN
ejpam-2881	214	48	)	)	PUNCT
ejpam-2881	214	49	,	,	PUNCT
ejpam-2881	214	50	ωλ(gy	ωλ(gy	PROPN
ejpam-2881	214	51	,	,	PUNCT
ejpam-2881	214	52	fy	fy	PROPN
ejpam-2881	214	53	)	)	PUNCT
ejpam-2881	214	54	,	,	PUNCT
ejpam-2881	214	55	ωλ(gx	ωλ(gx	PROPN
ejpam-2881	214	56	,	,	PUNCT
ejpam-2881	214	57	fy	fy	PROPN
ejpam-2881	214	58	)	)	PUNCT
ejpam-2881	215	1	+	+	CCONJ
ejpam-2881	215	2	ωλ(gy	ωλ(gy	PROPN
ejpam-2881	215	3	,	,	PUNCT
ejpam-2881	215	4	fx	fx	NOUN
ejpam-2881	215	5	)	)	PUNCT
ejpam-2881	215	6	2	2	NUM
ejpam-2881	215	7	}	}	PUNCT
ejpam-2881	215	8	,	,	PUNCT
ejpam-2881	215	9	mf	mf	NOUN
ejpam-2881	215	10	,	,	PUNCT
ejpam-2881	215	11	g	g	PROPN
ejpam-2881	215	12	2	2	NUM
ejpam-2881	215	13	(	(	PUNCT
ejpam-2881	215	14	x	x	NOUN
ejpam-2881	215	15	,	,	PUNCT
ejpam-2881	215	16	y	y	PROPN
ejpam-2881	215	17	)	)	PUNCT
ejpam-2881	215	18	=	=	PRON
ejpam-2881	215	19	{	{	PUNCT
ejpam-2881	215	20	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	215	21	,	,	PUNCT
ejpam-2881	215	22	gy	gy	NOUN
ejpam-2881	215	23	)	)	PUNCT
ejpam-2881	215	24	,	,	PUNCT
ejpam-2881	215	25	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	215	26	,	,	PUNCT
ejpam-2881	215	27	fx	fx	PROPN
ejpam-2881	215	28	)	)	PUNCT
ejpam-2881	215	29	+	+	CCONJ
ejpam-2881	215	30	ωλ(gy	ωλ(gy	PROPN
ejpam-2881	215	31	,	,	PUNCT
ejpam-2881	215	32	fy	fy	PROPN
ejpam-2881	215	33	)	)	PUNCT
ejpam-2881	215	34	2	2	NUM
ejpam-2881	215	35	,	,	PUNCT
ejpam-2881	215	36	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	215	37	,	,	PUNCT
ejpam-2881	215	38	fy	fy	PROPN
ejpam-2881	215	39	)	)	PUNCT
ejpam-2881	215	40	+	+	CCONJ
ejpam-2881	215	41	ωλ(gy	ωλ(gy	PROPN
ejpam-2881	215	42	,	,	PUNCT
ejpam-2881	215	43	fx	fx	NOUN
ejpam-2881	215	44	)	)	PUNCT
ejpam-2881	215	45	2	2	NUM
ejpam-2881	215	46	}	}	PUNCT
ejpam-2881	215	47	.	.	PUNCT
ejpam-2881	216	1	and	and	CCONJ
ejpam-2881	216	2	define	define	VERB
ejpam-2881	216	3	the	the	DET
ejpam-2881	216	4	following	following	ADJ
ejpam-2881	216	5	conditions	condition	NOUN
ejpam-2881	216	6	:	:	PUNCT
ejpam-2881	216	7	(	(	PUNCT
ejpam-2881	216	8	c1	c1	NOUN
ejpam-2881	216	9	)	)	PUNCT
ejpam-2881	216	10	for	for	ADP
ejpam-2881	216	11	any	any	DET
ejpam-2881	216	12	x	x	NOUN
ejpam-2881	216	13	,	,	PUNCT
ejpam-2881	216	14	y	y	PROPN
ejpam-2881	216	15	∈	∈	PROPN
ejpam-2881	216	16	xω	xω	PRON
ejpam-2881	216	17	,	,	PUNCT
ejpam-2881	216	18	there	there	PRON
ejpam-2881	216	19	exists	exist	VERB
ejpam-2881	216	20	α0(x	α0(x	NOUN
ejpam-2881	216	21	,	,	PUNCT
ejpam-2881	216	22	y	y	NOUN
ejpam-2881	216	23	)	)	PUNCT
ejpam-2881	216	24	∈mf	∈mf	NOUN
ejpam-2881	216	25	,	,	PUNCT
ejpam-2881	216	26	g	g	PROPN
ejpam-2881	216	27	0	0	NUM
ejpam-2881	216	28	(	(	PUNCT
ejpam-2881	216	29	x	x	NOUN
ejpam-2881	216	30	,	,	PUNCT
ejpam-2881	216	31	y	y	NOUN
ejpam-2881	216	32	)	)	PUNCT
ejpam-2881	216	33	such	such	ADJ
ejpam-2881	216	34	that	that	DET
ejpam-2881	216	35	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	216	36	,	,	PUNCT
ejpam-2881	216	37	fy	fy	PROPN
ejpam-2881	216	38	)	)	PUNCT
ejpam-2881	216	39	<	<	X
ejpam-2881	216	40	α0(x	α0(x	PROPN
ejpam-2881	216	41	,	,	PUNCT
ejpam-2881	216	42	y	y	PROPN
ejpam-2881	216	43	)	)	PUNCT
ejpam-2881	216	44	,	,	PUNCT
ejpam-2881	216	45	(	(	PUNCT
ejpam-2881	216	46	c2	c2	PROPN
ejpam-2881	216	47	)	)	PUNCT
ejpam-2881	216	48	for	for	ADP
ejpam-2881	216	49	any	any	DET
ejpam-2881	216	50	x	x	NOUN
ejpam-2881	216	51	,	,	PUNCT
ejpam-2881	216	52	y	y	PROPN
ejpam-2881	216	53	∈	∈	PROPN
ejpam-2881	216	54	xω	xω	PRON
ejpam-2881	216	55	,	,	PUNCT
ejpam-2881	216	56	there	there	PRON
ejpam-2881	216	57	exists	exist	VERB
ejpam-2881	216	58	α1(x	α1(x	PROPN
ejpam-2881	216	59	,	,	PUNCT
ejpam-2881	216	60	y	y	NOUN
ejpam-2881	216	61	)	)	PUNCT
ejpam-2881	216	62	∈mf	∈mf	NUM
ejpam-2881	216	63	,	,	PUNCT
ejpam-2881	216	64	g	g	PROPN
ejpam-2881	216	65	1	1	NUM
ejpam-2881	216	66	(	(	PUNCT
ejpam-2881	216	67	x	x	NOUN
ejpam-2881	216	68	,	,	PUNCT
ejpam-2881	216	69	y	y	NOUN
ejpam-2881	216	70	)	)	PUNCT
ejpam-2881	216	71	such	such	ADJ
ejpam-2881	216	72	that	that	DET
ejpam-2881	216	73	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	216	74	,	,	PUNCT
ejpam-2881	216	75	fy	fy	PROPN
ejpam-2881	216	76	)	)	PUNCT
ejpam-2881	216	77	<	<	X
ejpam-2881	216	78	α1(x	α1(x	PROPN
ejpam-2881	216	79	,	,	PUNCT
ejpam-2881	216	80	y	y	PROPN
ejpam-2881	216	81	)	)	PUNCT
ejpam-2881	216	82	,	,	PUNCT
ejpam-2881	216	83	(	(	PUNCT
ejpam-2881	216	84	c3	c3	PROPN
ejpam-2881	216	85	)	)	PUNCT
ejpam-2881	216	86	for	for	ADP
ejpam-2881	216	87	any	any	DET
ejpam-2881	216	88	x	x	NOUN
ejpam-2881	216	89	,	,	PUNCT
ejpam-2881	216	90	y	y	PROPN
ejpam-2881	216	91	∈	∈	PROPN
ejpam-2881	216	92	xω	xω	PRON
ejpam-2881	216	93	,	,	PUNCT
ejpam-2881	216	94	there	there	PRON
ejpam-2881	216	95	exists	exist	VERB
ejpam-2881	216	96	α2(x	α2(x	PROPN
ejpam-2881	216	97	,	,	PUNCT
ejpam-2881	216	98	y	y	NOUN
ejpam-2881	216	99	)	)	PUNCT
ejpam-2881	216	100	∈mf	∈mf	NOUN
ejpam-2881	216	101	,	,	PUNCT
ejpam-2881	216	102	g	g	NOUN
ejpam-2881	216	103	2	2	NUM
ejpam-2881	216	104	(	(	PUNCT
ejpam-2881	216	105	x	x	NOUN
ejpam-2881	216	106	,	,	PUNCT
ejpam-2881	216	107	y	y	NOUN
ejpam-2881	216	108	)	)	PUNCT
ejpam-2881	216	109	such	such	ADJ
ejpam-2881	216	110	that	that	DET
ejpam-2881	216	111	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	216	112	,	,	PUNCT
ejpam-2881	216	113	fy	fy	PROPN
ejpam-2881	216	114	)	)	PUNCT
ejpam-2881	216	115	<	<	X
ejpam-2881	217	1	α2(x	α2(x	PROPN
ejpam-2881	217	2	,	,	PUNCT
ejpam-2881	217	3	y	y	PROPN
ejpam-2881	217	4	)	)	PUNCT
ejpam-2881	217	5	.	.	PUNCT
ejpam-2881	218	1	these	these	DET
ejpam-2881	218	2	conditions	condition	NOUN
ejpam-2881	218	3	are	be	AUX
ejpam-2881	218	4	called	call	VERB
ejpam-2881	218	5	the	the	DET
ejpam-2881	218	6	strict	strict	ADJ
ejpam-2881	218	7	contractive	contractive	ADJ
ejpam-2881	218	8	conditions	condition	NOUN
ejpam-2881	218	9	.	.	PUNCT
ejpam-2881	219	1	definition	definition	NOUN
ejpam-2881	219	2	8	8	NUM
ejpam-2881	219	3	.	.	PUNCT
ejpam-2881	220	1	let	let	AUX
ejpam-2881	220	2	(	(	PUNCT
ejpam-2881	220	3	x	x	NOUN
ejpam-2881	220	4	,	,	PUNCT
ejpam-2881	220	5	ω	ω	NUM
ejpam-2881	220	6	)	)	PUNCT
ejpam-2881	220	7	be	be	AUX
ejpam-2881	220	8	a	a	DET
ejpam-2881	220	9	modular	modular	ADJ
ejpam-2881	220	10	metric	metric	ADJ
ejpam-2881	220	11	space	space	NOUN
ejpam-2881	220	12	.	.	PUNCT
ejpam-2881	221	1	let	let	VERB
ejpam-2881	221	2	f	f	X
ejpam-2881	221	3	,	,	PUNCT
ejpam-2881	221	4	g	g	PROPN
ejpam-2881	221	5	be	be	VERB
ejpam-2881	221	6	self	self	NOUN
ejpam-2881	221	7	-	-	PUNCT
ejpam-2881	221	8	mappings	mapping	NOUN
ejpam-2881	221	9	on	on	ADP
ejpam-2881	221	10	xω	xω	PROPN
ejpam-2881	221	11	.	.	PUNCT
ejpam-2881	222	1	then	then	ADV
ejpam-2881	222	2	f	f	PROPN
ejpam-2881	222	3	is	be	AUX
ejpam-2881	222	4	called	call	VERB
ejpam-2881	222	5	a	a	DET
ejpam-2881	222	6	g	g	NOUN
ejpam-2881	222	7	-	-	PUNCT
ejpam-2881	222	8	quasi	quasi	NOUN
ejpam-2881	222	9	-	-	NOUN
ejpam-2881	222	10	contraction	contraction	NOUN
ejpam-2881	222	11	if	if	SCONJ
ejpam-2881	222	12	,	,	PUNCT
ejpam-2881	222	13	for	for	ADP
ejpam-2881	222	14	some	some	PRON
ejpam-2881	222	15	constant	constant	ADJ
ejpam-2881	222	16	a	a	DET
ejpam-2881	222	17	∈	∈	PROPN
ejpam-2881	222	18	(	(	PUNCT
ejpam-2881	222	19	0	0	NUM
ejpam-2881	222	20	,	,	PUNCT
ejpam-2881	222	21	1	1	NUM
ejpam-2881	222	22	)	)	PUNCT
ejpam-2881	222	23	,	,	PUNCT
ejpam-2881	222	24	there	there	PRON
ejpam-2881	222	25	exists	exist	VERB
ejpam-2881	222	26	α(x	α(x	PROPN
ejpam-2881	222	27	,	,	PUNCT
ejpam-2881	222	28	y	y	PROPN
ejpam-2881	222	29	)	)	PUNCT
ejpam-2881	222	30	∈	∈	PROPN
ejpam-2881	222	31	mf	mf	VERB
ejpam-2881	222	32	,	,	PUNCT
ejpam-2881	222	33	g	g	PROPN
ejpam-2881	222	34	0	0	NUM
ejpam-2881	222	35	(	(	PUNCT
ejpam-2881	222	36	x	x	NOUN
ejpam-2881	222	37	,	,	PUNCT
ejpam-2881	222	38	y	y	NOUN
ejpam-2881	222	39	)	)	PUNCT
ejpam-2881	222	40	such	such	ADJ
ejpam-2881	222	41	that	that	DET
ejpam-2881	222	42	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	222	43	,	,	PUNCT
ejpam-2881	222	44	fy	fy	PROPN
ejpam-2881	222	45	)	)	PUNCT
ejpam-2881	222	46	≤	≤	NOUN
ejpam-2881	222	47	aα(x	aα(x	PUNCT
ejpam-2881	222	48	,	,	PUNCT
ejpam-2881	222	49	y	y	NOUN
ejpam-2881	222	50	)	)	PUNCT
ejpam-2881	222	51	for	for	ADP
ejpam-2881	222	52	all	all	DET
ejpam-2881	222	53	x	x	NOUN
ejpam-2881	222	54	,	,	PUNCT
ejpam-2881	222	55	y	y	PROPN
ejpam-2881	222	56	∈	∈	PROPN
ejpam-2881	222	57	xω	xω	PROPN
ejpam-2881	222	58	.	.	PUNCT
ejpam-2881	223	1	theorem	theorem	VERB
ejpam-2881	223	2	4	4	NUM
ejpam-2881	223	3	.	.	PUNCT
ejpam-2881	224	1	let	let	VERB
ejpam-2881	224	2	xω	xω	PRON
ejpam-2881	224	3	be	be	AUX
ejpam-2881	224	4	a	a	DET
ejpam-2881	224	5	modular	modular	ADJ
ejpam-2881	224	6	metric	metric	ADJ
ejpam-2881	224	7	space	space	NOUN
ejpam-2881	224	8	and	and	CCONJ
ejpam-2881	224	9	f	f	NOUN
ejpam-2881	224	10	,	,	PUNCT
ejpam-2881	224	11	g	g	NOUN
ejpam-2881	224	12	:	:	PUNCT
ejpam-2881	224	13	xω	xω	PROPN
ejpam-2881	224	14	→	→	SYM
ejpam-2881	224	15	xω	xω	NOUN
ejpam-2881	224	16	are	be	AUX
ejpam-2881	224	17	weakly	weakly	ADV
ejpam-2881	224	18	compatible	compatible	ADJ
ejpam-2881	224	19	mappings	mapping	NOUN
ejpam-2881	224	20	such	such	ADJ
ejpam-2881	224	21	that	that	PRON
ejpam-2881	224	22	f(xω	f(xω	NOUN
ejpam-2881	224	23	)	)	PUNCT
ejpam-2881	224	24	⊂	⊂	PROPN
ejpam-2881	224	25	g(xω	g(xω	NOUN
ejpam-2881	224	26	)	)	PUNCT
ejpam-2881	224	27	satisfies	satisfy	VERB
ejpam-2881	224	28	the	the	DET
ejpam-2881	224	29	condition	condition	NOUN
ejpam-2881	224	30	(	(	PUNCT
ejpam-2881	224	31	c3	c3	PROPN
ejpam-2881	224	32	)	)	PUNCT
ejpam-2881	224	33	for	for	ADP
ejpam-2881	224	34	all	all	DET
ejpam-2881	224	35	x	x	NOUN
ejpam-2881	224	36	,	,	PUNCT
ejpam-2881	224	37	y	y	PROPN
ejpam-2881	224	38	∈	∈	PROPN
ejpam-2881	225	1	xω	xω	X
ejpam-2881	225	2	and	and	CCONJ
ejpam-2881	225	3	λ	λ	X
ejpam-2881	225	4	>	>	X
ejpam-2881	225	5	0	0	X
ejpam-2881	225	6	.	.	PUNCT
ejpam-2881	226	1	if	if	SCONJ
ejpam-2881	226	2	f	f	PROPN
ejpam-2881	226	3	and	and	CCONJ
ejpam-2881	226	4	g	g	PROPN
ejpam-2881	226	5	satisfy	satisfy	VERB
ejpam-2881	226	6	the	the	DET
ejpam-2881	226	7	(	(	PUNCT
ejpam-2881	226	8	clrg)-property	clrg)-property	PROPN
ejpam-2881	226	9	,	,	PUNCT
ejpam-2881	226	10	then	then	ADV
ejpam-2881	226	11	f	f	PROPN
ejpam-2881	226	12	and	and	CCONJ
ejpam-2881	226	13	g	g	PROPN
ejpam-2881	226	14	have	have	VERB
ejpam-2881	226	15	a	a	DET
ejpam-2881	226	16	unique	unique	ADJ
ejpam-2881	226	17	common	common	ADJ
ejpam-2881	226	18	fixed	fix	VERB
ejpam-2881	226	19	point	point	NOUN
ejpam-2881	226	20	.	.	PUNCT
ejpam-2881	227	1	proof	proof	NOUN
ejpam-2881	227	2	.	.	PUNCT
ejpam-2881	228	1	since	since	SCONJ
ejpam-2881	228	2	f	f	PROPN
ejpam-2881	228	3	and	and	CCONJ
ejpam-2881	228	4	g	g	PROPN
ejpam-2881	228	5	satisfy	satisfy	VERB
ejpam-2881	228	6	the	the	DET
ejpam-2881	228	7	(	(	PUNCT
ejpam-2881	228	8	clrg)-property	clrg)-property	PROPN
ejpam-2881	228	9	,	,	PUNCT
ejpam-2881	228	10	there	there	PRON
ejpam-2881	228	11	exists	exist	VERB
ejpam-2881	228	12	a	a	DET
ejpam-2881	228	13	sequence	sequence	NOUN
ejpam-2881	228	14	{	{	PUNCT
ejpam-2881	228	15	xn	xn	NUM
ejpam-2881	228	16	}	}	PUNCT
ejpam-2881	228	17	in	in	ADP
ejpam-2881	228	18	xω	xω	PRON
ejpam-2881	228	19	such	such	ADJ
ejpam-2881	228	20	that	that	SCONJ
ejpam-2881	228	21	lim	lim	PROPN
ejpam-2881	228	22	n→∞	n→∞	PRON
ejpam-2881	228	23	fxn	fxn	PROPN
ejpam-2881	228	24	=	=	PUNCT
ejpam-2881	228	25	lim	lim	PROPN
ejpam-2881	228	26	n−→∞	n−→∞	PROPN
ejpam-2881	228	27	gxn	gxn	PROPN
ejpam-2881	228	28	=	=	SYM
ejpam-2881	228	29	gx	gx	PROPN
ejpam-2881	228	30	for	for	ADP
ejpam-2881	228	31	some	some	DET
ejpam-2881	228	32	x	x	SYM
ejpam-2881	228	33	∈	∈	PROPN
ejpam-2881	228	34	xω	xω	PROPN
ejpam-2881	228	35	.	.	PUNCT
ejpam-2881	229	1	from	from	ADP
ejpam-2881	229	2	(	(	PUNCT
ejpam-2881	229	3	c3	c3	PROPN
ejpam-2881	229	4	)	)	PUNCT
ejpam-2881	229	5	,	,	PUNCT
ejpam-2881	229	6	we	we	PRON
ejpam-2881	229	7	have	have	VERB
ejpam-2881	229	8	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	229	9	,	,	PUNCT
ejpam-2881	229	10	fx	fx	PROPN
ejpam-2881	229	11	)	)	PUNCT
ejpam-2881	229	12	<	<	X
ejpam-2881	229	13	α2(xn	α2(xn	NUM
ejpam-2881	229	14	,	,	PUNCT
ejpam-2881	229	15	x	x	NOUN
ejpam-2881	229	16	)	)	PUNCT
ejpam-2881	229	17	,	,	PUNCT
ejpam-2881	229	18	where	where	SCONJ
ejpam-2881	229	19	α2(xn	α2(xn	NUM
ejpam-2881	229	20	,	,	PUNCT
ejpam-2881	229	21	x	x	NOUN
ejpam-2881	229	22	)	)	PUNCT
ejpam-2881	229	23	∈mf	∈mf	NUM
ejpam-2881	229	24	,	,	PUNCT
ejpam-2881	229	25	g	g	PROPN
ejpam-2881	229	26	2	2	NUM
ejpam-2881	229	27	(	(	PUNCT
ejpam-2881	229	28	xn	xn	PROPN
ejpam-2881	229	29	,	,	PUNCT
ejpam-2881	229	30	x	x	NOUN
ejpam-2881	229	31	)	)	PUNCT
ejpam-2881	229	32	.	.	PUNCT
ejpam-2881	230	1	therefore	therefore	ADV
ejpam-2881	230	2	,	,	PUNCT
ejpam-2881	230	3	we	we	PRON
ejpam-2881	230	4	have	have	VERB
ejpam-2881	230	5	mf	mf	NOUN
ejpam-2881	230	6	,	,	PUNCT
ejpam-2881	230	7	g	g	PROPN
ejpam-2881	230	8	2	2	NUM
ejpam-2881	230	9	(	(	PUNCT
ejpam-2881	230	10	xn	xn	PROPN
ejpam-2881	230	11	,	,	PUNCT
ejpam-2881	230	12	x	x	NOUN
ejpam-2881	230	13	)	)	PUNCT
ejpam-2881	230	14	=	=	PRON
ejpam-2881	230	15	{	{	PUNCT
ejpam-2881	230	16	ωλ(gxn	ωλ(gxn	PROPN
ejpam-2881	230	17	,	,	PUNCT
ejpam-2881	230	18	gx	gx	PROPN
ejpam-2881	230	19	)	)	PUNCT
ejpam-2881	230	20	,	,	PUNCT
ejpam-2881	230	21	ωλ(gxn	ωλ(gxn	NUM
ejpam-2881	230	22	,	,	PUNCT
ejpam-2881	230	23	fxn	fxn	NOUN
ejpam-2881	230	24	)	)	PUNCT
ejpam-2881	231	1	+	+	CCONJ
ejpam-2881	231	2	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	231	3	,	,	PUNCT
ejpam-2881	231	4	fx	fx	NOUN
ejpam-2881	231	5	)	)	PUNCT
ejpam-2881	231	6	2	2	NUM
ejpam-2881	231	7	,	,	PUNCT
ejpam-2881	231	8	ωλ(gxn	ωλ(gxn	NUM
ejpam-2881	231	9	,	,	PUNCT
ejpam-2881	231	10	fx	fx	NOUN
ejpam-2881	231	11	)	)	PUNCT
ejpam-2881	232	1	+	+	CCONJ
ejpam-2881	232	2	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	232	3	,	,	PUNCT
ejpam-2881	232	4	fxn	fxn	NOUN
ejpam-2881	232	5	)	)	PUNCT
ejpam-2881	232	6	2	2	NUM
ejpam-2881	232	7	}	}	PUNCT
ejpam-2881	232	8	.	.	PUNCT
ejpam-2881	233	1	p.	p.	NOUN
ejpam-2881	233	2	sumalai	sumalai	PROPN
ejpam-2881	233	3	,	,	PUNCT
ejpam-2881	233	4	p.	p.	PROPN
ejpam-2881	233	5	kumam	kumam	PROPN
ejpam-2881	233	6	,	,	PUNCT
ejpam-2881	233	7	y.	y.	PROPN
ejpam-2881	233	8	j.	j.	PROPN
ejpam-2881	233	9	cho	cho	PROPN
ejpam-2881	233	10	,	,	PUNCT
ejpam-2881	233	11	a.	a.	NOUN
ejpam-2881	233	12	padcharoen	padcharoen	PROPN
ejpam-2881	233	13	/	/	SYM
ejpam-2881	233	14	eur	eur	PROPN
ejpam-2881	233	15	.	.	PUNCT
ejpam-2881	234	1	j.	j.	PROPN
ejpam-2881	234	2	pure	pure	PROPN
ejpam-2881	234	3	appl	appl	PROPN
ejpam-2881	234	4	.	.	PROPN
ejpam-2881	234	5	math	math	PROPN
ejpam-2881	234	6	,	,	PUNCT
ejpam-2881	234	7	10	10	NUM
ejpam-2881	234	8	(	(	PUNCT
ejpam-2881	234	9	2	2	NUM
ejpam-2881	234	10	)	)	PUNCT
ejpam-2881	234	11	(	(	PUNCT
ejpam-2881	234	12	2017	2017	NUM
ejpam-2881	234	13	)	)	PUNCT
ejpam-2881	234	14	,	,	PUNCT
ejpam-2881	234	15	238	238	NUM
ejpam-2881	234	16	-	-	SYM
ejpam-2881	234	17	254	254	NUM
ejpam-2881	234	18	247	247	NUM
ejpam-2881	234	19	now	now	ADV
ejpam-2881	235	1	,	,	PUNCT
ejpam-2881	235	2	we	we	PRON
ejpam-2881	235	3	show	show	VERB
ejpam-2881	235	4	that	that	SCONJ
ejpam-2881	235	5	fx	fx	PROPN
ejpam-2881	235	6	=	=	SYM
ejpam-2881	235	7	gx	gx	PROPN
ejpam-2881	235	8	.	.	PROPN
ejpam-2881	235	9	suppose	suppose	VERB
ejpam-2881	235	10	that	that	SCONJ
ejpam-2881	235	11	fx	fx	PROPN
ejpam-2881	235	12	6=	6=	PROPN
ejpam-2881	235	13	gx	gx	PROPN
ejpam-2881	235	14	.	.	PROPN
ejpam-2881	235	15	from	from	ADP
ejpam-2881	235	16	(	(	PUNCT
ejpam-2881	235	17	c3	c3	PROPN
ejpam-2881	235	18	)	)	PUNCT
ejpam-2881	235	19	,	,	PUNCT
ejpam-2881	235	20	we	we	PRON
ejpam-2881	235	21	have	have	VERB
ejpam-2881	235	22	the	the	DET
ejpam-2881	235	23	following	follow	VERB
ejpam-2881	235	24	three	three	NUM
ejpam-2881	235	25	cases	case	NOUN
ejpam-2881	235	26	:	:	PUNCT
ejpam-2881	235	27	case	case	NOUN
ejpam-2881	235	28	1	1	NUM
ejpam-2881	235	29	.	.	X
ejpam-2881	236	1	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	236	2	,	,	PUNCT
ejpam-2881	236	3	fx	fx	PROPN
ejpam-2881	236	4	)	)	PUNCT
ejpam-2881	236	5	<	<	X
ejpam-2881	236	6	α2(xn	α2(xn	NUM
ejpam-2881	236	7	,	,	PUNCT
ejpam-2881	236	8	x	x	NOUN
ejpam-2881	236	9	)	)	PUNCT
ejpam-2881	236	10	.	.	PUNCT
ejpam-2881	237	1	taking	take	VERB
ejpam-2881	237	2	limit	limit	NOUN
ejpam-2881	237	3	as	as	ADP
ejpam-2881	237	4	n	n	PROPN
ejpam-2881	237	5	→	→	SYM
ejpam-2881	237	6	∞	∞	PROPN
ejpam-2881	237	7	,	,	PUNCT
ejpam-2881	237	8	we	we	PRON
ejpam-2881	237	9	have	have	VERB
ejpam-2881	237	10	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	237	11	,	,	PUNCT
ejpam-2881	237	12	fx	fx	PROPN
ejpam-2881	237	13	)	)	PUNCT
ejpam-2881	237	14	<	<	X
ejpam-2881	238	1	ωλ(gx	ωλ(gx	PROPN
ejpam-2881	238	2	,	,	PUNCT
ejpam-2881	238	3	gx	gx	PROPN
ejpam-2881	238	4	)	)	PUNCT
ejpam-2881	238	5	=	=	SYM
ejpam-2881	238	6	0	0	NUM
ejpam-2881	238	7	,	,	PUNCT
ejpam-2881	238	8	which	which	PRON
ejpam-2881	238	9	is	be	AUX
ejpam-2881	238	10	a	a	DET
ejpam-2881	238	11	contradiction	contradiction	NOUN
ejpam-2881	238	12	.	.	PUNCT
ejpam-2881	239	1	case	case	NOUN
ejpam-2881	239	2	2	2	NUM
ejpam-2881	239	3	.	.	X
ejpam-2881	239	4	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	239	5	,	,	PUNCT
ejpam-2881	239	6	fx	fx	PROPN
ejpam-2881	239	7	)	)	PUNCT
ejpam-2881	239	8	<	<	X
ejpam-2881	239	9	ωλ(gxn	ωλ(gxn	PROPN
ejpam-2881	239	10	,	,	PUNCT
ejpam-2881	239	11	fxn	fxn	NOUN
ejpam-2881	239	12	)	)	PUNCT
ejpam-2881	239	13	+	+	CCONJ
ejpam-2881	239	14	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	239	15	,	,	PUNCT
ejpam-2881	239	16	fx	fx	NOUN
ejpam-2881	239	17	)	)	PUNCT
ejpam-2881	239	18	2	2	NUM
ejpam-2881	239	19	.	.	PUNCT
ejpam-2881	240	1	taking	take	VERB
ejpam-2881	240	2	limit	limit	NOUN
ejpam-2881	240	3	as	as	ADP
ejpam-2881	240	4	n→∞	n→∞	NUM
ejpam-2881	240	5	,	,	PUNCT
ejpam-2881	240	6	we	we	PRON
ejpam-2881	240	7	have	have	VERB
ejpam-2881	240	8	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	240	9	,	,	PUNCT
ejpam-2881	240	10	fx	fx	PROPN
ejpam-2881	240	11	)	)	PUNCT
ejpam-2881	240	12	<	<	X
ejpam-2881	241	1	ωλ(gx	ωλ(gx	PROPN
ejpam-2881	241	2	,	,	PUNCT
ejpam-2881	241	3	gx	gx	PROPN
ejpam-2881	241	4	)	)	PUNCT
ejpam-2881	242	1	+	+	CCONJ
ejpam-2881	242	2	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	242	3	,	,	PUNCT
ejpam-2881	242	4	fx	fx	NOUN
ejpam-2881	242	5	)	)	PUNCT
ejpam-2881	242	6	2	2	NUM
ejpam-2881	242	7	=	=	SYM
ejpam-2881	242	8	1	1	NUM
ejpam-2881	242	9	2	2	NUM
ejpam-2881	242	10	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	242	11	,	,	PUNCT
ejpam-2881	242	12	fx	fx	PROPN
ejpam-2881	242	13	)	)	PUNCT
ejpam-2881	242	14	,	,	PUNCT
ejpam-2881	242	15	which	which	PRON
ejpam-2881	242	16	is	be	AUX
ejpam-2881	242	17	a	a	DET
ejpam-2881	242	18	contradiction	contradiction	NOUN
ejpam-2881	242	19	.	.	PUNCT
ejpam-2881	243	1	case	case	NOUN
ejpam-2881	243	2	3	3	X
ejpam-2881	243	3	.	.	X
ejpam-2881	244	1	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	244	2	,	,	PUNCT
ejpam-2881	244	3	fx	fx	PROPN
ejpam-2881	244	4	)	)	PUNCT
ejpam-2881	244	5	<	<	X
ejpam-2881	244	6	ωλ(gxn	ωλ(gxn	PROPN
ejpam-2881	244	7	,	,	PUNCT
ejpam-2881	244	8	fx	fx	NOUN
ejpam-2881	244	9	)	)	PUNCT
ejpam-2881	245	1	+	+	CCONJ
ejpam-2881	245	2	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	245	3	,	,	PUNCT
ejpam-2881	245	4	fxn	fxn	NOUN
ejpam-2881	245	5	)	)	PUNCT
ejpam-2881	245	6	2	2	NUM
ejpam-2881	245	7	.	.	PUNCT
ejpam-2881	246	1	taking	take	VERB
ejpam-2881	246	2	limit	limit	NOUN
ejpam-2881	246	3	as	as	ADP
ejpam-2881	246	4	n→∞	n→∞	NUM
ejpam-2881	246	5	,	,	PUNCT
ejpam-2881	246	6	we	we	PRON
ejpam-2881	246	7	have	have	VERB
ejpam-2881	246	8	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	246	9	,	,	PUNCT
ejpam-2881	246	10	fx	fx	PROPN
ejpam-2881	246	11	)	)	PUNCT
ejpam-2881	246	12	<	<	X
ejpam-2881	246	13	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	246	14	,	,	PUNCT
ejpam-2881	246	15	fx	fx	PROPN
ejpam-2881	246	16	)	)	PUNCT
ejpam-2881	247	1	+	+	CCONJ
ejpam-2881	247	2	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	247	3	,	,	PUNCT
ejpam-2881	247	4	gx	gx	PROPN
ejpam-2881	247	5	)	)	PUNCT
ejpam-2881	247	6	2	2	NUM
ejpam-2881	247	7	=	=	SYM
ejpam-2881	247	8	1	1	NUM
ejpam-2881	247	9	2	2	NUM
ejpam-2881	247	10	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	247	11	,	,	PUNCT
ejpam-2881	247	12	fx	fx	PROPN
ejpam-2881	247	13	)	)	PUNCT
ejpam-2881	247	14	,	,	PUNCT
ejpam-2881	247	15	which	which	PRON
ejpam-2881	247	16	is	be	AUX
ejpam-2881	247	17	a	a	DET
ejpam-2881	247	18	contradiction	contradiction	NOUN
ejpam-2881	247	19	.	.	PUNCT
ejpam-2881	248	1	hence	hence	ADV
ejpam-2881	248	2	gx	gx	PROPN
ejpam-2881	248	3	=	=	PUNCT
ejpam-2881	248	4	fx	fx	PROPN
ejpam-2881	248	5	in	in	ADP
ejpam-2881	248	6	all	all	DET
ejpam-2881	248	7	the	the	DET
ejpam-2881	248	8	cases	case	NOUN
ejpam-2881	248	9	.	.	PUNCT
ejpam-2881	249	1	let	let	VERB
ejpam-2881	249	2	t	t	NOUN
ejpam-2881	249	3	=	=	PUNCT
ejpam-2881	249	4	fx	fx	PROPN
ejpam-2881	249	5	=	=	SYM
ejpam-2881	249	6	gx	gx	PROPN
ejpam-2881	249	7	.	.	PUNCT
ejpam-2881	250	1	since	since	SCONJ
ejpam-2881	250	2	f	f	PROPN
ejpam-2881	250	3	and	and	CCONJ
ejpam-2881	250	4	g	g	PROPN
ejpam-2881	250	5	are	be	AUX
ejpam-2881	250	6	weakly	weakly	ADV
ejpam-2881	250	7	compatible	compatible	ADJ
ejpam-2881	250	8	mappings	mapping	NOUN
ejpam-2881	250	9	,	,	PUNCT
ejpam-2881	250	10	fgx	fgx	VERB
ejpam-2881	250	11	=	=	SYM
ejpam-2881	250	12	gfx	gfx	PROPN
ejpam-2881	250	13	,	,	PUNCT
ejpam-2881	250	14	which	which	PRON
ejpam-2881	250	15	implies	imply	VERB
ejpam-2881	250	16	that	that	SCONJ
ejpam-2881	250	17	ft	ft	PROPN
ejpam-2881	250	18	=	=	PUNCT
ejpam-2881	250	19	fgx	fgx	VERB
ejpam-2881	250	20	=	=	SYM
ejpam-2881	250	21	gfx	gfx	PROPN
ejpam-2881	250	22	=	=	PROPN
ejpam-2881	250	23	gt	gt	PROPN
ejpam-2881	250	24	.	.	PUNCT
ejpam-2881	251	1	now	now	ADV
ejpam-2881	251	2	,	,	PUNCT
ejpam-2881	251	3	we	we	PRON
ejpam-2881	251	4	show	show	VERB
ejpam-2881	251	5	that	that	SCONJ
ejpam-2881	251	6	ft	ft	NOUN
ejpam-2881	251	7	=	=	PUNCT
ejpam-2881	251	8	t.	t.	PROPN
ejpam-2881	251	9	suppose	suppose	VERB
ejpam-2881	251	10	that	that	SCONJ
ejpam-2881	251	11	ft	ft	PROPN
ejpam-2881	251	12	6=	6=	PROPN
ejpam-2881	251	13	t.	t.	NOUN
ejpam-2881	251	14	from	from	ADP
ejpam-2881	251	15	(	(	PUNCT
ejpam-2881	251	16	c3	c3	PROPN
ejpam-2881	251	17	)	)	PUNCT
ejpam-2881	251	18	,	,	PUNCT
ejpam-2881	251	19	we	we	PRON
ejpam-2881	251	20	have	have	VERB
ejpam-2881	251	21	ωλ(ft	ωλ(ft	NUM
ejpam-2881	251	22	,	,	PUNCT
ejpam-2881	251	23	t	t	PROPN
ejpam-2881	251	24	)	)	PUNCT
ejpam-2881	251	25	=	=	SYM
ejpam-2881	251	26	ωλ(ft	ωλ(ft	PROPN
ejpam-2881	251	27	,	,	PUNCT
ejpam-2881	251	28	fx	fx	PROPN
ejpam-2881	251	29	)	)	PUNCT
ejpam-2881	251	30	<	<	X
ejpam-2881	252	1	α2(t	α2(t	PROPN
ejpam-2881	252	2	,	,	PUNCT
ejpam-2881	252	3	x	x	NOUN
ejpam-2881	252	4	)	)	PUNCT
ejpam-2881	252	5	,	,	PUNCT
ejpam-2881	252	6	where	where	SCONJ
ejpam-2881	252	7	α2(t	α2(t	NOUN
ejpam-2881	252	8	,	,	PUNCT
ejpam-2881	252	9	x	x	NOUN
ejpam-2881	252	10	)	)	PUNCT
ejpam-2881	252	11	∈mf	∈mf	NUM
ejpam-2881	252	12	,	,	PUNCT
ejpam-2881	252	13	g	g	PROPN
ejpam-2881	252	14	2	2	NUM
ejpam-2881	252	15	(	(	PUNCT
ejpam-2881	252	16	t	t	PROPN
ejpam-2881	252	17	,	,	PUNCT
ejpam-2881	252	18	x	x	NOUN
ejpam-2881	252	19	)	)	PUNCT
ejpam-2881	252	20	.	.	PUNCT
ejpam-2881	253	1	therefore	therefore	ADV
ejpam-2881	253	2	,	,	PUNCT
ejpam-2881	253	3	we	we	PRON
ejpam-2881	253	4	have	have	VERB
ejpam-2881	253	5	mf	mf	NOUN
ejpam-2881	253	6	,	,	PUNCT
ejpam-2881	253	7	g	g	PROPN
ejpam-2881	253	8	2	2	NUM
ejpam-2881	253	9	(	(	PUNCT
ejpam-2881	253	10	t	t	PROPN
ejpam-2881	253	11	,	,	PUNCT
ejpam-2881	253	12	x	x	NOUN
ejpam-2881	253	13	)	)	PUNCT
ejpam-2881	253	14	=	=	PRON
ejpam-2881	253	15	{	{	PUNCT
ejpam-2881	253	16	ωλ(gt	ωλ(gt	PROPN
ejpam-2881	253	17	,	,	PUNCT
ejpam-2881	253	18	gx	gx	PROPN
ejpam-2881	253	19	)	)	PUNCT
ejpam-2881	253	20	,	,	PUNCT
ejpam-2881	253	21	ωλ(gt	ωλ(gt	PROPN
ejpam-2881	253	22	,	,	PUNCT
ejpam-2881	253	23	ft	ft	NOUN
ejpam-2881	253	24	)	)	PUNCT
ejpam-2881	254	1	+	+	CCONJ
ejpam-2881	254	2	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	254	3	,	,	PUNCT
ejpam-2881	254	4	fx	fx	NOUN
ejpam-2881	254	5	)	)	PUNCT
ejpam-2881	254	6	2	2	NUM
ejpam-2881	254	7	,	,	PUNCT
ejpam-2881	254	8	ωλ(gt	ωλ(gt	PROPN
ejpam-2881	254	9	,	,	PUNCT
ejpam-2881	254	10	fx	fx	PROPN
ejpam-2881	254	11	)	)	PUNCT
ejpam-2881	255	1	+	+	CCONJ
ejpam-2881	255	2	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	255	3	,	,	PUNCT
ejpam-2881	255	4	ft	ft	NOUN
ejpam-2881	255	5	)	)	PUNCT
ejpam-2881	255	6	2	2	NUM
ejpam-2881	255	7	}	}	PUNCT
ejpam-2881	255	8	=	=	SYM
ejpam-2881	255	9	{	{	PUNCT
ejpam-2881	255	10	ωλ(ft	ωλ(ft	PROPN
ejpam-2881	255	11	,	,	PUNCT
ejpam-2881	255	12	t	t	PROPN
ejpam-2881	255	13	)	)	PUNCT
ejpam-2881	255	14	,	,	PUNCT
ejpam-2881	255	15	0	0	NUM
ejpam-2881	255	16	,	,	PUNCT
ejpam-2881	255	17	ωλ(ft	ωλ(ft	PROPN
ejpam-2881	255	18	,	,	PUNCT
ejpam-2881	255	19	t	t	PROPN
ejpam-2881	255	20	)	)	PUNCT
ejpam-2881	255	21	}	}	PUNCT
ejpam-2881	255	22	.	.	PUNCT
ejpam-2881	256	1	so	so	ADV
ejpam-2881	256	2	,	,	PUNCT
ejpam-2881	256	3	we	we	PRON
ejpam-2881	256	4	have	have	VERB
ejpam-2881	256	5	only	only	ADV
ejpam-2881	256	6	two	two	NUM
ejpam-2881	256	7	possible	possible	ADJ
ejpam-2881	256	8	cases	case	NOUN
ejpam-2881	256	9	:	:	PUNCT
ejpam-2881	256	10	case	case	NOUN
ejpam-2881	256	11	4	4	NUM
ejpam-2881	256	12	.	.	X
ejpam-2881	256	13	ωλ(ft	ωλ(ft	PROPN
ejpam-2881	256	14	,	,	PUNCT
ejpam-2881	256	15	t	t	PROPN
ejpam-2881	256	16	)	)	PUNCT
ejpam-2881	256	17	<	<	X
ejpam-2881	256	18	ωλ(ft	ωλ(ft	PROPN
ejpam-2881	256	19	,	,	PUNCT
ejpam-2881	256	20	t	t	PROPN
ejpam-2881	256	21	)	)	PUNCT
ejpam-2881	256	22	,	,	PUNCT
ejpam-2881	256	23	which	which	PRON
ejpam-2881	256	24	is	be	AUX
ejpam-2881	256	25	a	a	DET
ejpam-2881	256	26	contradiction	contradiction	NOUN
ejpam-2881	256	27	.	.	PUNCT
ejpam-2881	257	1	case	case	NOUN
ejpam-2881	257	2	5	5	NUM
ejpam-2881	257	3	.	.	X
ejpam-2881	257	4	ωλ(ft	ωλ(ft	PROPN
ejpam-2881	257	5	,	,	PUNCT
ejpam-2881	257	6	t	t	PROPN
ejpam-2881	257	7	)	)	PUNCT
ejpam-2881	257	8	<	<	X
ejpam-2881	257	9	0	0	NUM
ejpam-2881	257	10	,	,	PUNCT
ejpam-2881	257	11	which	which	PRON
ejpam-2881	257	12	is	be	AUX
ejpam-2881	257	13	a	a	DET
ejpam-2881	257	14	contradiction	contradiction	NOUN
ejpam-2881	257	15	.	.	PUNCT
ejpam-2881	258	1	hence	hence	ADV
ejpam-2881	258	2	ft	ft	PROPN
ejpam-2881	258	3	=	=	SYM
ejpam-2881	258	4	t	t	PROPN
ejpam-2881	258	5	=	=	SYM
ejpam-2881	258	6	gt	gt	PROPN
ejpam-2881	258	7	.	.	PUNCT
ejpam-2881	258	8	therefor	therefor	PROPN
ejpam-2881	258	9	,	,	PUNCT
ejpam-2881	258	10	t	t	PROPN
ejpam-2881	258	11	is	be	AUX
ejpam-2881	258	12	a	a	DET
ejpam-2881	258	13	common	common	ADJ
ejpam-2881	258	14	fixed	fix	VERB
ejpam-2881	258	15	point	point	NOUN
ejpam-2881	258	16	of	of	ADP
ejpam-2881	258	17	f	f	PROPN
ejpam-2881	258	18	and	and	CCONJ
ejpam-2881	258	19	g.	g.	PROPN
ejpam-2881	258	20	for	for	ADP
ejpam-2881	258	21	the	the	DET
ejpam-2881	258	22	uniqueness	uniqueness	NOUN
ejpam-2881	258	23	of	of	ADP
ejpam-2881	258	24	the	the	DET
ejpam-2881	258	25	common	common	ADJ
ejpam-2881	258	26	fixed	fix	VERB
ejpam-2881	258	27	point	point	NOUN
ejpam-2881	258	28	,	,	PUNCT
ejpam-2881	258	29	we	we	PRON
ejpam-2881	258	30	suppose	suppose	VERB
ejpam-2881	258	31	that	that	SCONJ
ejpam-2881	258	32	u	u	PROPN
ejpam-2881	258	33	is	be	AUX
ejpam-2881	258	34	another	another	DET
ejpam-2881	258	35	common	common	ADJ
ejpam-2881	258	36	fixed	fix	VERB
ejpam-2881	258	37	point	point	NOUN
ejpam-2881	258	38	in	in	ADP
ejpam-2881	258	39	xω	xω	PRON
ejpam-2881	258	40	such	such	ADJ
ejpam-2881	258	41	that	that	DET
ejpam-2881	258	42	fu	fu	NOUN
ejpam-2881	258	43	=	=	PUNCT
ejpam-2881	258	44	gu	gu	PROPN
ejpam-2881	258	45	.	.	PROPN
ejpam-2881	259	1	from	from	ADP
ejpam-2881	259	2	(	(	PUNCT
ejpam-2881	259	3	c3	c3	PROPN
ejpam-2881	259	4	)	)	PUNCT
ejpam-2881	259	5	,	,	PUNCT
ejpam-2881	259	6	we	we	PRON
ejpam-2881	259	7	have	have	VERB
ejpam-2881	259	8	ωλ(t	ωλ(t	NOUN
ejpam-2881	259	9	,	,	PUNCT
ejpam-2881	259	10	u	u	NOUN
ejpam-2881	259	11	)	)	PUNCT
ejpam-2881	259	12	=	=	SYM
ejpam-2881	259	13	ωλ(gt	ωλ(gt	PROPN
ejpam-2881	259	14	,	,	PUNCT
ejpam-2881	259	15	gu	gu	NOUN
ejpam-2881	259	16	)	)	PUNCT
ejpam-2881	259	17	=	=	SYM
ejpam-2881	259	18	ωλ(ft	ωλ(ft	PROPN
ejpam-2881	259	19	,	,	PUNCT
ejpam-2881	259	20	fu	fu	NOUN
ejpam-2881	259	21	)	)	PUNCT
ejpam-2881	259	22	<	<	X
ejpam-2881	260	1	α2(t	α2(t	PROPN
ejpam-2881	260	2	,	,	PUNCT
ejpam-2881	260	3	u	u	NOUN
ejpam-2881	260	4	)	)	PUNCT
ejpam-2881	260	5	,	,	PUNCT
ejpam-2881	260	6	where	where	SCONJ
ejpam-2881	260	7	α2(t	α2(t	NOUN
ejpam-2881	260	8	,	,	PUNCT
ejpam-2881	260	9	u	u	NOUN
ejpam-2881	260	10	)	)	PUNCT
ejpam-2881	260	11	∈mf	∈mf	NUM
ejpam-2881	260	12	,	,	PUNCT
ejpam-2881	260	13	g	g	PROPN
ejpam-2881	260	14	2	2	NUM
ejpam-2881	260	15	(	(	PUNCT
ejpam-2881	260	16	t	t	PROPN
ejpam-2881	260	17	,	,	PUNCT
ejpam-2881	260	18	u	u	NOUN
ejpam-2881	260	19	)	)	PUNCT
ejpam-2881	260	20	.	.	PUNCT
ejpam-2881	261	1	therefore	therefore	ADV
ejpam-2881	261	2	,	,	PUNCT
ejpam-2881	261	3	we	we	PRON
ejpam-2881	261	4	have	have	VERB
ejpam-2881	261	5	mf	mf	NOUN
ejpam-2881	261	6	,	,	PUNCT
ejpam-2881	261	7	g	g	PROPN
ejpam-2881	261	8	2	2	NUM
ejpam-2881	261	9	(	(	PUNCT
ejpam-2881	261	10	t	t	PROPN
ejpam-2881	261	11	,	,	PUNCT
ejpam-2881	261	12	u	u	NOUN
ejpam-2881	261	13	)	)	PUNCT
ejpam-2881	261	14	=	=	SYM
ejpam-2881	261	15	{	{	PUNCT
ejpam-2881	261	16	ωλ(gt	ωλ(gt	PROPN
ejpam-2881	261	17	,	,	PUNCT
ejpam-2881	261	18	gu	gu	NOUN
ejpam-2881	261	19	)	)	PUNCT
ejpam-2881	261	20	,	,	PUNCT
ejpam-2881	261	21	ωλ(gt	ωλ(gt	PROPN
ejpam-2881	261	22	,	,	PUNCT
ejpam-2881	261	23	ft	ft	NOUN
ejpam-2881	261	24	)	)	PUNCT
ejpam-2881	261	25	+	+	NOUN
ejpam-2881	261	26	ωλ(gu	ωλ(gu	NOUN
ejpam-2881	261	27	,	,	PUNCT
ejpam-2881	261	28	fu	fu	ADJ
ejpam-2881	261	29	)	)	PUNCT
ejpam-2881	261	30	2	2	NUM
ejpam-2881	261	31	,	,	PUNCT
ejpam-2881	261	32	ωλ(gt	ωλ(gt	PROPN
ejpam-2881	261	33	,	,	PUNCT
ejpam-2881	261	34	fu	fu	NOUN
ejpam-2881	261	35	)	)	PUNCT
ejpam-2881	262	1	+	+	PUNCT
ejpam-2881	262	2	ωλ(gu	ωλ(gu	NOUN
ejpam-2881	262	3	,	,	PUNCT
ejpam-2881	262	4	ft	ft	NOUN
ejpam-2881	262	5	)	)	PUNCT
ejpam-2881	262	6	2	2	NUM
ejpam-2881	262	7	}	}	PUNCT
ejpam-2881	262	8	=	=	SYM
ejpam-2881	262	9	{	{	PUNCT
ejpam-2881	262	10	ωλ(gt	ωλ(gt	PROPN
ejpam-2881	262	11	,	,	PUNCT
ejpam-2881	262	12	gu	gu	NOUN
ejpam-2881	262	13	)	)	PUNCT
ejpam-2881	262	14	,	,	PUNCT
ejpam-2881	262	15	0	0	NUM
ejpam-2881	262	16	,	,	PUNCT
ejpam-2881	262	17	ωλ(gt	ωλ(gt	PROPN
ejpam-2881	262	18	,	,	PUNCT
ejpam-2881	262	19	gu	gu	NOUN
ejpam-2881	262	20	)	)	PUNCT
ejpam-2881	262	21	}	}	PUNCT
ejpam-2881	262	22	.	.	PUNCT
ejpam-2881	263	1	so	so	ADV
ejpam-2881	263	2	,	,	PUNCT
ejpam-2881	263	3	we	we	PRON
ejpam-2881	263	4	have	have	VERB
ejpam-2881	263	5	only	only	ADV
ejpam-2881	263	6	two	two	NUM
ejpam-2881	263	7	possible	possible	ADJ
ejpam-2881	263	8	cases	case	NOUN
ejpam-2881	263	9	.	.	PUNCT
ejpam-2881	264	1	case	case	NOUN
ejpam-2881	264	2	6	6	NUM
ejpam-2881	264	3	.	.	PUNCT
ejpam-2881	265	1	ωλ(gu	ωλ(gu	NOUN
ejpam-2881	265	2	,	,	PUNCT
ejpam-2881	265	3	gt	gt	PROPN
ejpam-2881	265	4	)	)	PUNCT
ejpam-2881	265	5	<	<	X
ejpam-2881	266	1	ωλ(gu	ωλ(gu	PROPN
ejpam-2881	266	2	,	,	PUNCT
ejpam-2881	266	3	gt	gt	PROPN
ejpam-2881	266	4	)	)	PUNCT
ejpam-2881	266	5	,	,	PUNCT
ejpam-2881	266	6	which	which	PRON
ejpam-2881	266	7	is	be	AUX
ejpam-2881	266	8	a	a	DET
ejpam-2881	266	9	contradiction	contradiction	NOUN
ejpam-2881	266	10	.	.	PUNCT
ejpam-2881	267	1	case	case	NOUN
ejpam-2881	267	2	7	7	NUM
ejpam-2881	267	3	.	.	X
ejpam-2881	268	1	ωλ(gu	ωλ(gu	NOUN
ejpam-2881	268	2	,	,	PUNCT
ejpam-2881	268	3	gt	gt	PROPN
ejpam-2881	268	4	)	)	PUNCT
ejpam-2881	268	5	<	<	X
ejpam-2881	268	6	0	0	NUM
ejpam-2881	268	7	,	,	PUNCT
ejpam-2881	268	8	which	which	PRON
ejpam-2881	268	9	is	be	AUX
ejpam-2881	268	10	a	a	DET
ejpam-2881	268	11	contradiction	contradiction	NOUN
ejpam-2881	268	12	.	.	PUNCT
ejpam-2881	269	1	hence	hence	ADV
ejpam-2881	269	2	gu	gu	PROPN
ejpam-2881	269	3	=	=	SYM
ejpam-2881	269	4	gt	gt	PROPN
ejpam-2881	269	5	.	.	PROPN
ejpam-2881	269	6	implies	imply	VERB
ejpam-2881	269	7	u	u	PROPN
ejpam-2881	269	8	=	=	PROPN
ejpam-2881	269	9	t	t	PROPN
ejpam-2881	270	1	and	and	CCONJ
ejpam-2881	270	2	so	so	ADV
ejpam-2881	270	3	f	f	PROPN
ejpam-2881	270	4	and	and	CCONJ
ejpam-2881	270	5	g	g	PROPN
ejpam-2881	270	6	have	have	VERB
ejpam-2881	270	7	a	a	DET
ejpam-2881	270	8	unique	unique	ADJ
ejpam-2881	270	9	common	common	ADJ
ejpam-2881	270	10	fixed	fix	VERB
ejpam-2881	270	11	point	point	NOUN
ejpam-2881	270	12	.	.	PUNCT
ejpam-2881	271	1	p.	p.	NOUN
ejpam-2881	271	2	sumalai	sumalai	PROPN
ejpam-2881	271	3	,	,	PUNCT
ejpam-2881	271	4	p.	p.	PROPN
ejpam-2881	271	5	kumam	kumam	PROPN
ejpam-2881	271	6	,	,	PUNCT
ejpam-2881	271	7	y.	y.	PROPN
ejpam-2881	271	8	j.	j.	PROPN
ejpam-2881	271	9	cho	cho	PROPN
ejpam-2881	271	10	,	,	PUNCT
ejpam-2881	271	11	a.	a.	NOUN
ejpam-2881	271	12	padcharoen	padcharoen	PROPN
ejpam-2881	271	13	/	/	SYM
ejpam-2881	271	14	eur	eur	PROPN
ejpam-2881	271	15	.	.	PUNCT
ejpam-2881	272	1	j.	j.	PROPN
ejpam-2881	272	2	pure	pure	PROPN
ejpam-2881	272	3	appl	appl	PROPN
ejpam-2881	272	4	.	.	PROPN
ejpam-2881	272	5	math	math	PROPN
ejpam-2881	272	6	,	,	PUNCT
ejpam-2881	272	7	10	10	NUM
ejpam-2881	272	8	(	(	PUNCT
ejpam-2881	272	9	2	2	NUM
ejpam-2881	272	10	)	)	PUNCT
ejpam-2881	272	11	(	(	PUNCT
ejpam-2881	272	12	2017	2017	NUM
ejpam-2881	272	13	)	)	PUNCT
ejpam-2881	272	14	,	,	PUNCT
ejpam-2881	272	15	238	238	NUM
ejpam-2881	272	16	-	-	SYM
ejpam-2881	272	17	254	254	NUM
ejpam-2881	272	18	248	248	NUM
ejpam-2881	272	19	theorem	theorem	NOUN
ejpam-2881	272	20	5	5	NUM
ejpam-2881	272	21	.	.	PUNCT
ejpam-2881	273	1	let	let	VERB
ejpam-2881	273	2	xω	xω	PRON
ejpam-2881	273	3	be	be	AUX
ejpam-2881	273	4	a	a	DET
ejpam-2881	273	5	modular	modular	ADJ
ejpam-2881	273	6	metric	metric	ADJ
ejpam-2881	273	7	space	space	NOUN
ejpam-2881	273	8	and	and	CCONJ
ejpam-2881	273	9	f	f	NOUN
ejpam-2881	273	10	,	,	PUNCT
ejpam-2881	273	11	g	g	NOUN
ejpam-2881	273	12	:	:	PUNCT
ejpam-2881	273	13	xω	xω	PROPN
ejpam-2881	273	14	→	→	PUNCT
ejpam-2881	273	15	xω	xω	NOUN
ejpam-2881	273	16	be	be	AUX
ejpam-2881	273	17	weakly	weakly	ADV
ejpam-2881	273	18	compatible	compatible	ADJ
ejpam-2881	273	19	mappings	mapping	NOUN
ejpam-2881	273	20	such	such	ADJ
ejpam-2881	273	21	that	that	SCONJ
ejpam-2881	273	22	f	f	PROPN
ejpam-2881	273	23	is	be	AUX
ejpam-2881	273	24	the	the	DET
ejpam-2881	273	25	g	g	NOUN
ejpam-2881	273	26	-	-	PUNCT
ejpam-2881	273	27	quasi	quasi	NOUN
ejpam-2881	273	28	-	-	NOUN
ejpam-2881	273	29	contraction	contraction	NOUN
ejpam-2881	273	30	for	for	ADP
ejpam-2881	273	31	all	all	DET
ejpam-2881	273	32	x	x	NOUN
ejpam-2881	273	33	,	,	PUNCT
ejpam-2881	273	34	y	y	PROPN
ejpam-2881	273	35	∈	∈	PROPN
ejpam-2881	274	1	xω	xω	X
ejpam-2881	274	2	and	and	CCONJ
ejpam-2881	274	3	λ	λ	X
ejpam-2881	274	4	>	>	X
ejpam-2881	274	5	0	0	X
ejpam-2881	274	6	.	.	PUNCT
ejpam-2881	275	1	if	if	SCONJ
ejpam-2881	275	2	f	f	PROPN
ejpam-2881	275	3	and	and	CCONJ
ejpam-2881	275	4	g	g	PROPN
ejpam-2881	275	5	satisfy	satisfy	NOUN
ejpam-2881	275	6	(	(	PUNCT
ejpam-2881	275	7	clrg)-property	clrg)-property	PROPN
ejpam-2881	275	8	,	,	PUNCT
ejpam-2881	275	9	then	then	ADV
ejpam-2881	275	10	f	f	PROPN
ejpam-2881	275	11	and	and	CCONJ
ejpam-2881	275	12	g	g	PROPN
ejpam-2881	275	13	have	have	VERB
ejpam-2881	275	14	a	a	DET
ejpam-2881	275	15	unique	unique	ADJ
ejpam-2881	275	16	common	common	ADJ
ejpam-2881	275	17	fixed	fix	VERB
ejpam-2881	275	18	point	point	NOUN
ejpam-2881	275	19	.	.	PUNCT
ejpam-2881	276	1	proof	proof	NOUN
ejpam-2881	276	2	.	.	PUNCT
ejpam-2881	277	1	since	since	SCONJ
ejpam-2881	277	2	f	f	PROPN
ejpam-2881	277	3	and	and	CCONJ
ejpam-2881	277	4	g	g	PROPN
ejpam-2881	277	5	satisfy	satisfy	VERB
ejpam-2881	277	6	the	the	DET
ejpam-2881	277	7	(	(	PUNCT
ejpam-2881	277	8	clrg)-property	clrg)-property	PROPN
ejpam-2881	277	9	,	,	PUNCT
ejpam-2881	277	10	there	there	PRON
ejpam-2881	277	11	exists	exist	VERB
ejpam-2881	277	12	a	a	DET
ejpam-2881	277	13	sequence	sequence	NOUN
ejpam-2881	277	14	{	{	PUNCT
ejpam-2881	277	15	xn	xn	NUM
ejpam-2881	277	16	}	}	PUNCT
ejpam-2881	277	17	in	in	ADP
ejpam-2881	277	18	xω	xω	PRON
ejpam-2881	277	19	such	such	ADJ
ejpam-2881	277	20	that	that	SCONJ
ejpam-2881	277	21	lim	lim	PROPN
ejpam-2881	277	22	n→∞	n→∞	PRON
ejpam-2881	277	23	fxn	fxn	PROPN
ejpam-2881	277	24	=	=	PUNCT
ejpam-2881	277	25	lim	lim	PROPN
ejpam-2881	277	26	n−→∞	n−→∞	PROPN
ejpam-2881	277	27	gxn	gxn	PROPN
ejpam-2881	277	28	=	=	SYM
ejpam-2881	277	29	gx	gx	PROPN
ejpam-2881	277	30	for	for	ADP
ejpam-2881	277	31	some	some	DET
ejpam-2881	277	32	x	x	SYM
ejpam-2881	277	33	∈	∈	PROPN
ejpam-2881	277	34	xω	xω	PROPN
ejpam-2881	277	35	.	.	PUNCT
ejpam-2881	278	1	since	since	SCONJ
ejpam-2881	278	2	f	f	PROPN
ejpam-2881	278	3	is	be	AUX
ejpam-2881	278	4	the	the	DET
ejpam-2881	278	5	g	g	NOUN
ejpam-2881	278	6	-	-	PUNCT
ejpam-2881	278	7	quasi	quasi	NOUN
ejpam-2881	278	8	-	-	NOUN
ejpam-2881	278	9	contraction	contraction	NOUN
ejpam-2881	278	10	,	,	PUNCT
ejpam-2881	278	11	we	we	PRON
ejpam-2881	278	12	have	have	VERB
ejpam-2881	278	13	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	278	14	,	,	PUNCT
ejpam-2881	278	15	fx	fx	PROPN
ejpam-2881	278	16	)	)	PUNCT
ejpam-2881	278	17	≤	≤	NUM
ejpam-2881	278	18	aα0(xn	aα0(xn	PUNCT
ejpam-2881	278	19	,	,	PUNCT
ejpam-2881	278	20	x	x	NOUN
ejpam-2881	278	21	)	)	PUNCT
ejpam-2881	278	22	,	,	PUNCT
ejpam-2881	278	23	where	where	SCONJ
ejpam-2881	278	24	α0(xn	α0(xn	NOUN
ejpam-2881	278	25	,	,	PUNCT
ejpam-2881	278	26	x	x	NOUN
ejpam-2881	278	27	)	)	PUNCT
ejpam-2881	278	28	∈mf	∈mf	NUM
ejpam-2881	278	29	,	,	PUNCT
ejpam-2881	278	30	g	g	PROPN
ejpam-2881	278	31	0	0	NUM
ejpam-2881	278	32	(	(	PUNCT
ejpam-2881	278	33	xn	xn	PROPN
ejpam-2881	278	34	,	,	PUNCT
ejpam-2881	278	35	x	x	NOUN
ejpam-2881	278	36	)	)	PUNCT
ejpam-2881	278	37	.	.	PUNCT
ejpam-2881	279	1	therefore	therefore	ADV
ejpam-2881	279	2	,	,	PUNCT
ejpam-2881	279	3	we	we	PRON
ejpam-2881	279	4	have	have	VERB
ejpam-2881	279	5	mf	mf	NOUN
ejpam-2881	279	6	,	,	PUNCT
ejpam-2881	279	7	g	g	PROPN
ejpam-2881	279	8	0	0	NUM
ejpam-2881	279	9	(	(	PUNCT
ejpam-2881	279	10	xn	xn	PROPN
ejpam-2881	279	11	,	,	PUNCT
ejpam-2881	279	12	x	x	NOUN
ejpam-2881	279	13	)	)	PUNCT
ejpam-2881	279	14	=	=	PRON
ejpam-2881	279	15	{	{	PUNCT
ejpam-2881	279	16	ωλ(gxn	ωλ(gxn	PROPN
ejpam-2881	279	17	,	,	PUNCT
ejpam-2881	279	18	gx	gx	PROPN
ejpam-2881	279	19	)	)	PUNCT
ejpam-2881	279	20	,	,	PUNCT
ejpam-2881	279	21	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	279	22	,	,	PUNCT
ejpam-2881	279	23	fx	fx	PROPN
ejpam-2881	279	24	)	)	PUNCT
ejpam-2881	279	25	,	,	PUNCT
ejpam-2881	279	26	ωλ(gxn	ωλ(gxn	NUM
ejpam-2881	279	27	,	,	PUNCT
ejpam-2881	279	28	fxn	fxn	NOUN
ejpam-2881	279	29	)	)	PUNCT
ejpam-2881	279	30	,	,	PUNCT
ejpam-2881	279	31	ωλ(gxn	ωλ(gxn	NUM
ejpam-2881	279	32	,	,	PUNCT
ejpam-2881	279	33	fx	fx	NOUN
ejpam-2881	279	34	)	)	PUNCT
ejpam-2881	279	35	,	,	PUNCT
ejpam-2881	279	36	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	279	37	,	,	PUNCT
ejpam-2881	279	38	fxn	fxn	NOUN
ejpam-2881	279	39	)	)	PUNCT
ejpam-2881	279	40	}	}	PUNCT
ejpam-2881	279	41	.	.	PUNCT
ejpam-2881	280	1	now	now	ADV
ejpam-2881	280	2	,	,	PUNCT
ejpam-2881	280	3	we	we	PRON
ejpam-2881	280	4	have	have	VERB
ejpam-2881	280	5	the	the	DET
ejpam-2881	280	6	following	follow	VERB
ejpam-2881	280	7	five	five	NUM
ejpam-2881	280	8	cases	case	NOUN
ejpam-2881	280	9	:	:	PUNCT
ejpam-2881	280	10	case	case	NOUN
ejpam-2881	280	11	1	1	NUM
ejpam-2881	280	12	.	.	X
ejpam-2881	281	1	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	281	2	,	,	PUNCT
ejpam-2881	281	3	fx	fx	PROPN
ejpam-2881	281	4	)	)	PUNCT
ejpam-2881	281	5	≤	≤	NUM
ejpam-2881	281	6	aωλ(gxn	aωλ(gxn	NOUN
ejpam-2881	281	7	,	,	PUNCT
ejpam-2881	281	8	gx	gx	PROPN
ejpam-2881	281	9	)	)	PUNCT
ejpam-2881	281	10	.	.	PUNCT
ejpam-2881	282	1	taking	take	VERB
ejpam-2881	282	2	the	the	DET
ejpam-2881	282	3	limit	limit	NOUN
ejpam-2881	282	4	as	as	ADP
ejpam-2881	282	5	n→∞	n→∞	NUM
ejpam-2881	282	6	,	,	PUNCT
ejpam-2881	282	7	we	we	PRON
ejpam-2881	282	8	have	have	VERB
ejpam-2881	282	9	gx	gx	PROPN
ejpam-2881	282	10	=	=	SYM
ejpam-2881	282	11	fx	fx	PROPN
ejpam-2881	282	12	.	.	PUNCT
ejpam-2881	282	13	case	case	NOUN
ejpam-2881	282	14	2	2	NUM
ejpam-2881	282	15	.	.	X
ejpam-2881	283	1	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	283	2	,	,	PUNCT
ejpam-2881	283	3	fx	fx	PROPN
ejpam-2881	283	4	)	)	PUNCT
ejpam-2881	283	5	≤	≤	NUM
ejpam-2881	283	6	aωλ(gxn	aωλ(gxn	NOUN
ejpam-2881	283	7	,	,	PUNCT
ejpam-2881	283	8	fxn	fxn	NOUN
ejpam-2881	283	9	)	)	PUNCT
ejpam-2881	283	10	.	.	PUNCT
ejpam-2881	284	1	taking	take	VERB
ejpam-2881	284	2	the	the	DET
ejpam-2881	284	3	limit	limit	NOUN
ejpam-2881	284	4	as	as	ADP
ejpam-2881	284	5	n→∞	n→∞	NUM
ejpam-2881	284	6	,	,	PUNCT
ejpam-2881	284	7	we	we	PRON
ejpam-2881	284	8	have	have	VERB
ejpam-2881	284	9	gx	gx	PROPN
ejpam-2881	284	10	=	=	SYM
ejpam-2881	284	11	fx	fx	PROPN
ejpam-2881	284	12	.	.	PUNCT
ejpam-2881	284	13	case	case	NOUN
ejpam-2881	285	1	3	3	X
ejpam-2881	285	2	.	.	X
ejpam-2881	285	3	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	285	4	,	,	PUNCT
ejpam-2881	285	5	fx	fx	PROPN
ejpam-2881	285	6	)	)	PUNCT
ejpam-2881	285	7	≤	≤	NOUN
ejpam-2881	285	8	aωλ(gx	aωλ(gx	NOUN
ejpam-2881	285	9	,	,	PUNCT
ejpam-2881	285	10	fx	fx	NOUN
ejpam-2881	285	11	)	)	PUNCT
ejpam-2881	285	12	.	.	PUNCT
ejpam-2881	286	1	taking	take	VERB
ejpam-2881	286	2	the	the	DET
ejpam-2881	286	3	limit	limit	NOUN
ejpam-2881	286	4	as	as	ADP
ejpam-2881	286	5	n→∞	n→∞	NUM
ejpam-2881	286	6	,	,	PUNCT
ejpam-2881	286	7	we	we	PRON
ejpam-2881	286	8	have	have	VERB
ejpam-2881	286	9	gx	gx	PROPN
ejpam-2881	286	10	=	=	SYM
ejpam-2881	286	11	fx	fx	PROPN
ejpam-2881	286	12	.	.	PUNCT
ejpam-2881	286	13	case	case	NOUN
ejpam-2881	286	14	4	4	NUM
ejpam-2881	286	15	.	.	X
ejpam-2881	287	1	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	287	2	,	,	PUNCT
ejpam-2881	287	3	fx	fx	PROPN
ejpam-2881	287	4	)	)	PUNCT
ejpam-2881	287	5	≤	≤	NOUN
ejpam-2881	287	6	aωλ(gx	aωλ(gx	ADJ
ejpam-2881	287	7	,	,	PUNCT
ejpam-2881	287	8	fxn	fxn	NOUN
ejpam-2881	287	9	)	)	PUNCT
ejpam-2881	287	10	.	.	PUNCT
ejpam-2881	288	1	taking	take	VERB
ejpam-2881	288	2	the	the	DET
ejpam-2881	288	3	limit	limit	NOUN
ejpam-2881	288	4	as	as	ADP
ejpam-2881	288	5	n→∞	n→∞	NUM
ejpam-2881	288	6	,	,	PUNCT
ejpam-2881	288	7	we	we	PRON
ejpam-2881	288	8	have	have	VERB
ejpam-2881	288	9	gx	gx	PROPN
ejpam-2881	288	10	=	=	SYM
ejpam-2881	288	11	fx	fx	PROPN
ejpam-2881	288	12	.	.	PUNCT
ejpam-2881	288	13	case	case	NOUN
ejpam-2881	288	14	5	5	NUM
ejpam-2881	288	15	.	.	X
ejpam-2881	289	1	ωλ(fxn	ωλ(fxn	PROPN
ejpam-2881	289	2	,	,	PUNCT
ejpam-2881	289	3	fx	fx	PROPN
ejpam-2881	289	4	)	)	PUNCT
ejpam-2881	289	5	≤	≤	NOUN
ejpam-2881	289	6	aωλ(gx	aωλ(gx	ADJ
ejpam-2881	289	7	,	,	PUNCT
ejpam-2881	289	8	fxn	fxn	NOUN
ejpam-2881	289	9	)	)	PUNCT
ejpam-2881	289	10	.	.	PUNCT
ejpam-2881	290	1	taking	take	VERB
ejpam-2881	290	2	the	the	DET
ejpam-2881	290	3	limit	limit	NOUN
ejpam-2881	290	4	as	as	ADP
ejpam-2881	290	5	n→∞	n→∞	NUM
ejpam-2881	290	6	,	,	PUNCT
ejpam-2881	290	7	we	we	PRON
ejpam-2881	290	8	have	have	VERB
ejpam-2881	290	9	gx	gx	PROPN
ejpam-2881	290	10	=	=	SYM
ejpam-2881	290	11	fx	fx	PROPN
ejpam-2881	290	12	.	.	PUNCT
ejpam-2881	291	1	hence	hence	ADV
ejpam-2881	291	2	,	,	PUNCT
ejpam-2881	291	3	in	in	ADP
ejpam-2881	291	4	all	all	DET
ejpam-2881	291	5	the	the	DET
ejpam-2881	291	6	possible	possible	ADJ
ejpam-2881	291	7	cases	case	NOUN
ejpam-2881	291	8	,	,	PUNCT
ejpam-2881	291	9	gx	gx	PROPN
ejpam-2881	291	10	=	=	SYM
ejpam-2881	291	11	fx	fx	PROPN
ejpam-2881	291	12	.	.	PUNCT
ejpam-2881	292	1	now	now	ADV
ejpam-2881	292	2	,	,	PUNCT
ejpam-2881	292	3	let	let	VERB
ejpam-2881	292	4	t	t	NOUN
ejpam-2881	292	5	=	=	PUNCT
ejpam-2881	292	6	fx	fx	PROPN
ejpam-2881	292	7	=	=	SYM
ejpam-2881	292	8	gx	gx	PROPN
ejpam-2881	292	9	.	.	PUNCT
ejpam-2881	293	1	since	since	SCONJ
ejpam-2881	293	2	f	f	PROPN
ejpam-2881	293	3	and	and	CCONJ
ejpam-2881	293	4	g	g	PROPN
ejpam-2881	293	5	are	be	AUX
ejpam-2881	293	6	weakly	weakly	ADV
ejpam-2881	293	7	compatible	compatible	ADJ
ejpam-2881	293	8	mappings	mapping	NOUN
ejpam-2881	293	9	,	,	PUNCT
ejpam-2881	293	10	it	it	PRON
ejpam-2881	293	11	follows	follow	VERB
ejpam-2881	293	12	that	that	DET
ejpam-2881	293	13	fgx	fgx	VERB
ejpam-2881	293	14	=	=	SYM
ejpam-2881	293	15	gfx	gfx	PROPN
ejpam-2881	293	16	,	,	PUNCT
ejpam-2881	293	17	which	which	PRON
ejpam-2881	293	18	implies	imply	VERB
ejpam-2881	293	19	that	that	SCONJ
ejpam-2881	293	20	ft	ft	PROPN
ejpam-2881	293	21	=	=	PUNCT
ejpam-2881	293	22	fgx	fgx	VERB
ejpam-2881	293	23	=	=	SYM
ejpam-2881	293	24	gfx	gfx	PROPN
ejpam-2881	293	25	=	=	PROPN
ejpam-2881	293	26	gt	gt	PROPN
ejpam-2881	293	27	.	.	PUNCT
ejpam-2881	294	1	now	now	ADV
ejpam-2881	294	2	,	,	PUNCT
ejpam-2881	294	3	we	we	PRON
ejpam-2881	294	4	claim	claim	VERB
ejpam-2881	294	5	that	that	SCONJ
ejpam-2881	294	6	ft	ft	NOUN
ejpam-2881	294	7	=	=	PUNCT
ejpam-2881	294	8	t.	t.	NOUN
ejpam-2881	294	9	since	since	SCONJ
ejpam-2881	294	10	f	f	PROPN
ejpam-2881	294	11	is	be	AUX
ejpam-2881	294	12	the	the	DET
ejpam-2881	294	13	g	g	NOUN
ejpam-2881	294	14	-	-	PUNCT
ejpam-2881	294	15	quasi	quasi	NOUN
ejpam-2881	294	16	-	-	NOUN
ejpam-2881	294	17	contraction	contraction	NOUN
ejpam-2881	294	18	,	,	PUNCT
ejpam-2881	294	19	we	we	PRON
ejpam-2881	294	20	have	have	VERB
ejpam-2881	294	21	ωλ(ft	ωλ(ft	NUM
ejpam-2881	294	22	,	,	PUNCT
ejpam-2881	294	23	t	t	PROPN
ejpam-2881	294	24	)	)	PUNCT
ejpam-2881	295	1	=	=	SYM
ejpam-2881	295	2	ωλ(ft	ωλ(ft	PROPN
ejpam-2881	295	3	,	,	PUNCT
ejpam-2881	295	4	fx	fx	PROPN
ejpam-2881	295	5	)	)	PUNCT
ejpam-2881	295	6	≤	≤	NOUN
ejpam-2881	295	7	aα0(t	aα0(t	PROPN
ejpam-2881	295	8	,	,	PUNCT
ejpam-2881	295	9	x	x	NOUN
ejpam-2881	295	10	)	)	PUNCT
ejpam-2881	295	11	,	,	PUNCT
ejpam-2881	295	12	where	where	SCONJ
ejpam-2881	295	13	α0(t	α0(t	NUM
ejpam-2881	295	14	,	,	PUNCT
ejpam-2881	295	15	x	x	NOUN
ejpam-2881	295	16	)	)	PUNCT
ejpam-2881	295	17	∈mf	∈mf	NUM
ejpam-2881	295	18	,	,	PUNCT
ejpam-2881	295	19	g	g	PROPN
ejpam-2881	295	20	0	0	NUM
ejpam-2881	295	21	(	(	PUNCT
ejpam-2881	295	22	t	t	PROPN
ejpam-2881	295	23	,	,	PUNCT
ejpam-2881	295	24	x	x	NOUN
ejpam-2881	295	25	)	)	PUNCT
ejpam-2881	295	26	.	.	PUNCT
ejpam-2881	296	1	therefore	therefore	ADV
ejpam-2881	296	2	,	,	PUNCT
ejpam-2881	296	3	we	we	PRON
ejpam-2881	296	4	have	have	VERB
ejpam-2881	296	5	mf	mf	NOUN
ejpam-2881	296	6	,	,	PUNCT
ejpam-2881	296	7	g	g	PROPN
ejpam-2881	296	8	0	0	NUM
ejpam-2881	296	9	(	(	PUNCT
ejpam-2881	296	10	t	t	PROPN
ejpam-2881	296	11	,	,	PUNCT
ejpam-2881	296	12	x	x	NOUN
ejpam-2881	296	13	)	)	PUNCT
ejpam-2881	296	14	=	=	SYM
ejpam-2881	296	15	{	{	PUNCT
ejpam-2881	296	16	ωλ(gt	ωλ(gt	PROPN
ejpam-2881	296	17	,	,	PUNCT
ejpam-2881	296	18	gx	gx	PROPN
ejpam-2881	296	19	)	)	PUNCT
ejpam-2881	296	20	,	,	PUNCT
ejpam-2881	296	21	ωλ(gt	ωλ(gt	PROPN
ejpam-2881	296	22	,	,	PUNCT
ejpam-2881	296	23	ft	ft	NOUN
ejpam-2881	296	24	)	)	PUNCT
ejpam-2881	296	25	,	,	PUNCT
ejpam-2881	296	26	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	296	27	,	,	PUNCT
ejpam-2881	296	28	fx	fx	PROPN
ejpam-2881	296	29	)	)	PUNCT
ejpam-2881	296	30	,	,	PUNCT
ejpam-2881	296	31	ωλ(gt	ωλ(gt	PROPN
ejpam-2881	296	32	,	,	PUNCT
ejpam-2881	296	33	fx	fx	PROPN
ejpam-2881	296	34	)	)	PUNCT
ejpam-2881	296	35	,	,	PUNCT
ejpam-2881	296	36	ωλ(gx	ωλ(gx	PROPN
ejpam-2881	296	37	,	,	PUNCT
ejpam-2881	296	38	ft	ft	NOUN
ejpam-2881	296	39	)	)	PUNCT
ejpam-2881	296	40	}	}	PUNCT
ejpam-2881	296	41	=	=	SYM
ejpam-2881	296	42	{	{	PUNCT
ejpam-2881	296	43	ωλ(ft	ωλ(ft	PROPN
ejpam-2881	296	44	,	,	PUNCT
ejpam-2881	296	45	t	t	PROPN
ejpam-2881	296	46	)	)	PUNCT
ejpam-2881	296	47	,	,	PUNCT
ejpam-2881	296	48	0	0	NUM
ejpam-2881	296	49	,	,	PUNCT
ejpam-2881	296	50	0	0	NUM
ejpam-2881	296	51	,	,	PUNCT
ejpam-2881	296	52	ωλ(ft	ωλ(ft	PROPN
ejpam-2881	296	53	,	,	PUNCT
ejpam-2881	296	54	t	t	PROPN
ejpam-2881	296	55	)	)	PUNCT
ejpam-2881	296	56	,	,	PUNCT
ejpam-2881	296	57	ωλ(t	ωλ(t	NOUN
ejpam-2881	296	58	,	,	PUNCT
ejpam-2881	296	59	ft	ft	NOUN
ejpam-2881	296	60	)	)	PUNCT
ejpam-2881	296	61	}	}	PUNCT
ejpam-2881	296	62	.	.	PUNCT
ejpam-2881	297	1	now	now	ADV
ejpam-2881	297	2	,	,	PUNCT
ejpam-2881	297	3	we	we	PRON
ejpam-2881	297	4	have	have	VERB
ejpam-2881	297	5	two	two	NUM
ejpam-2881	297	6	cases	case	NOUN
ejpam-2881	297	7	.	.	PUNCT
ejpam-2881	298	1	case	case	NOUN
ejpam-2881	298	2	6	6	NUM
ejpam-2881	298	3	.	.	PUNCT
ejpam-2881	298	4	ωλ(ft	ωλ(ft	PROPN
ejpam-2881	298	5	,	,	PUNCT
ejpam-2881	298	6	t	t	PROPN
ejpam-2881	298	7	)	)	PUNCT
ejpam-2881	298	8	≤	≤	NOUN
ejpam-2881	298	9	aωλ(ft	aωλ(ft	NOUN
ejpam-2881	298	10	,	,	PUNCT
ejpam-2881	298	11	t	t	PROPN
ejpam-2881	298	12	)	)	PUNCT
ejpam-2881	298	13	.	.	PUNCT
ejpam-2881	299	1	this	this	PRON
ejpam-2881	299	2	implies	imply	VERB
ejpam-2881	299	3	ft	ft	NOUN
ejpam-2881	299	4	=	=	PUNCT
ejpam-2881	299	5	t.	t.	NOUN
ejpam-2881	299	6	case	case	NOUN
ejpam-2881	299	7	7	7	NUM
ejpam-2881	299	8	.	.	X
ejpam-2881	299	9	ωλ(ft	ωλ(ft	PROPN
ejpam-2881	299	10	,	,	PUNCT
ejpam-2881	299	11	t	t	PROPN
ejpam-2881	299	12	)	)	PUNCT
ejpam-2881	299	13	≤	≤	NOUN
ejpam-2881	299	14	0	0	NUM
ejpam-2881	299	15	.	.	PUNCT
ejpam-2881	300	1	this	this	PRON
ejpam-2881	300	2	implies	imply	VERB
ejpam-2881	300	3	ft	ft	NOUN
ejpam-2881	300	4	=	=	PUNCT
ejpam-2881	300	5	t.	t.	NOUN
ejpam-2881	300	6	hence	hence	ADV
ejpam-2881	300	7	ft	ft	PROPN
ejpam-2881	300	8	=	=	SYM
ejpam-2881	300	9	t	t	PROPN
ejpam-2881	300	10	=	=	PUNCT
ejpam-2881	300	11	gt	gt	PROPN
ejpam-2881	301	1	and	and	CCONJ
ejpam-2881	301	2	so	so	ADV
ejpam-2881	301	3	t	t	PROPN
ejpam-2881	301	4	is	be	AUX
ejpam-2881	301	5	a	a	DET
ejpam-2881	301	6	common	common	ADJ
ejpam-2881	301	7	fixed	fix	VERB
ejpam-2881	301	8	point	point	NOUN
ejpam-2881	301	9	of	of	ADP
ejpam-2881	301	10	f	f	PROPN
ejpam-2881	301	11	and	and	CCONJ
ejpam-2881	301	12	g.	g.	PROPN
ejpam-2881	301	13	for	for	ADP
ejpam-2881	301	14	the	the	DET
ejpam-2881	301	15	uniqueness	uniqueness	NOUN
ejpam-2881	301	16	of	of	ADP
ejpam-2881	301	17	the	the	DET
ejpam-2881	301	18	common	common	ADJ
ejpam-2881	301	19	fixed	fix	VERB
ejpam-2881	301	20	point	point	NOUN
ejpam-2881	301	21	t	t	PROPN
ejpam-2881	301	22	,	,	PUNCT
ejpam-2881	301	23	we	we	PRON
ejpam-2881	301	24	suppose	suppose	VERB
ejpam-2881	301	25	that	that	SCONJ
ejpam-2881	301	26	u	u	PROPN
ejpam-2881	301	27	is	be	AUX
ejpam-2881	301	28	another	another	DET
ejpam-2881	301	29	common	common	ADJ
ejpam-2881	301	30	fixed	fix	VERB
ejpam-2881	301	31	point	point	NOUN
ejpam-2881	301	32	in	in	ADP
ejpam-2881	301	33	xω	xω	PRON
ejpam-2881	301	34	such	such	ADJ
ejpam-2881	301	35	that	that	DET
ejpam-2881	301	36	fu	fu	NOUN
ejpam-2881	301	37	=	=	PUNCT
ejpam-2881	301	38	gu	gu	PROPN
ejpam-2881	301	39	.	.	PUNCT
ejpam-2881	302	1	since	since	SCONJ
ejpam-2881	302	2	f	f	PROPN
ejpam-2881	302	3	is	be	AUX
ejpam-2881	302	4	the	the	DET
ejpam-2881	302	5	g	g	NOUN
ejpam-2881	302	6	-	-	PUNCT
ejpam-2881	302	7	quasi	quasi	NOUN
ejpam-2881	302	8	-	-	NOUN
ejpam-2881	302	9	contraction	contraction	NOUN
ejpam-2881	302	10	,	,	PUNCT
ejpam-2881	302	11	we	we	PRON
ejpam-2881	302	12	have	have	VERB
ejpam-2881	302	13	ωλ(gt	ωλ(gt	PROPN
ejpam-2881	302	14	,	,	PUNCT
ejpam-2881	302	15	gu	gu	NOUN
ejpam-2881	302	16	)	)	PUNCT
ejpam-2881	302	17	=	=	SYM
ejpam-2881	302	18	ωλ(ft	ωλ(ft	ADJ
ejpam-2881	302	19	,	,	PUNCT
ejpam-2881	302	20	fu	fu	NOUN
ejpam-2881	302	21	)	)	PUNCT
ejpam-2881	302	22	≤	≤	NOUN
ejpam-2881	302	23	aα0(t	aα0(t	PROPN
ejpam-2881	302	24	,	,	PUNCT
ejpam-2881	302	25	u	u	NOUN
ejpam-2881	302	26	)	)	PUNCT
ejpam-2881	302	27	,	,	PUNCT
ejpam-2881	302	28	where	where	SCONJ
ejpam-2881	302	29	α0(t	α0(t	NUM
ejpam-2881	302	30	,	,	PUNCT
ejpam-2881	302	31	u	u	NOUN
ejpam-2881	302	32	)	)	PUNCT
ejpam-2881	302	33	∈mf	∈mf	PUNCT
ejpam-2881	302	34	,	,	PUNCT
ejpam-2881	302	35	g	g	PROPN
ejpam-2881	302	36	0	0	NUM
ejpam-2881	302	37	(	(	PUNCT
ejpam-2881	302	38	t	t	PROPN
ejpam-2881	302	39	,	,	PUNCT
ejpam-2881	302	40	u	u	NOUN
ejpam-2881	302	41	)	)	PUNCT
ejpam-2881	302	42	.	.	PUNCT
ejpam-2881	303	1	therefore	therefore	ADV
ejpam-2881	303	2	,	,	PUNCT
ejpam-2881	303	3	we	we	PRON
ejpam-2881	303	4	have	have	VERB
ejpam-2881	303	5	mf	mf	NOUN
ejpam-2881	303	6	,	,	PUNCT
ejpam-2881	303	7	g	g	PROPN
ejpam-2881	303	8	0	0	NUM
ejpam-2881	303	9	(	(	PUNCT
ejpam-2881	303	10	t	t	PROPN
ejpam-2881	303	11	,	,	PUNCT
ejpam-2881	303	12	u	u	NOUN
ejpam-2881	303	13	)	)	PUNCT
ejpam-2881	303	14	=	=	SYM
ejpam-2881	303	15	{	{	PUNCT
ejpam-2881	303	16	ωλ(gt	ωλ(gt	PROPN
ejpam-2881	303	17	,	,	PUNCT
ejpam-2881	303	18	gu	gu	NOUN
ejpam-2881	303	19	)	)	PUNCT
ejpam-2881	303	20	,	,	PUNCT
ejpam-2881	303	21	ωλ(gt	ωλ(gt	PROPN
ejpam-2881	303	22	,	,	PUNCT
ejpam-2881	303	23	ft	ft	NOUN
ejpam-2881	303	24	)	)	PUNCT
ejpam-2881	303	25	,	,	PUNCT
ejpam-2881	303	26	ωλ(gu	ωλ(gu	NOUN
ejpam-2881	303	27	,	,	PUNCT
ejpam-2881	303	28	fu	fu	PROPN
ejpam-2881	303	29	)	)	PUNCT
ejpam-2881	303	30	,	,	PUNCT
ejpam-2881	303	31	ωλ(gt	ωλ(gt	PROPN
ejpam-2881	303	32	,	,	PUNCT
ejpam-2881	303	33	fu	fu	NOUN
ejpam-2881	303	34	)	)	PUNCT
ejpam-2881	303	35	,	,	PUNCT
ejpam-2881	303	36	ωλ(gu	ωλ(gu	NOUN
ejpam-2881	303	37	,	,	PUNCT
ejpam-2881	303	38	ft	ft	NOUN
ejpam-2881	303	39	)	)	PUNCT
ejpam-2881	303	40	}	}	PUNCT
ejpam-2881	303	41	=	=	SYM
ejpam-2881	303	42	{	{	PUNCT
ejpam-2881	303	43	ωλ(ft	ωλ(ft	ADJ
ejpam-2881	303	44	,	,	PUNCT
ejpam-2881	303	45	fu	fu	NOUN
ejpam-2881	303	46	)	)	PUNCT
ejpam-2881	303	47	,	,	PUNCT
ejpam-2881	303	48	0	0	NUM
ejpam-2881	303	49	,	,	PUNCT
ejpam-2881	303	50	0	0	NUM
ejpam-2881	303	51	,	,	PUNCT
ejpam-2881	303	52	ωλ(ft	ωλ(ft	NUM
ejpam-2881	303	53	,	,	PUNCT
ejpam-2881	303	54	fu	fu	NOUN
ejpam-2881	303	55	)	)	PUNCT
ejpam-2881	303	56	,	,	PUNCT
ejpam-2881	303	57	ωλ(fu	ωλ(fu	PROPN
ejpam-2881	303	58	,	,	PUNCT
ejpam-2881	303	59	ft	ft	NOUN
ejpam-2881	303	60	)	)	PUNCT
ejpam-2881	303	61	}	}	PUNCT
ejpam-2881	303	62	p.	p.	NOUN
ejpam-2881	303	63	sumalai	sumalai	NOUN
ejpam-2881	303	64	,	,	PUNCT
ejpam-2881	303	65	p.	p.	PROPN
ejpam-2881	303	66	kumam	kumam	PROPN
ejpam-2881	303	67	,	,	PUNCT
ejpam-2881	303	68	y.	y.	PROPN
ejpam-2881	303	69	j.	j.	PROPN
ejpam-2881	303	70	cho	cho	PROPN
ejpam-2881	303	71	,	,	PUNCT
ejpam-2881	303	72	a.	a.	NOUN
ejpam-2881	303	73	padcharoen	padcharoen	PROPN
ejpam-2881	303	74	/	/	SYM
ejpam-2881	303	75	eur	eur	PROPN
ejpam-2881	303	76	.	.	PUNCT
ejpam-2881	304	1	j.	j.	PROPN
ejpam-2881	304	2	pure	pure	PROPN
ejpam-2881	304	3	appl	appl	PROPN
ejpam-2881	304	4	.	.	PROPN
ejpam-2881	304	5	math	math	PROPN
ejpam-2881	304	6	,	,	PUNCT
ejpam-2881	304	7	10	10	NUM
ejpam-2881	304	8	(	(	PUNCT
ejpam-2881	304	9	2	2	NUM
ejpam-2881	304	10	)	)	PUNCT
ejpam-2881	304	11	(	(	PUNCT
ejpam-2881	304	12	2017	2017	NUM
ejpam-2881	304	13	)	)	PUNCT
ejpam-2881	304	14	,	,	PUNCT
ejpam-2881	304	15	238	238	NUM
ejpam-2881	304	16	-	-	SYM
ejpam-2881	304	17	254	254	NUM
ejpam-2881	304	18	249	249	NUM
ejpam-2881	305	1	so	so	ADV
ejpam-2881	305	2	,	,	PUNCT
ejpam-2881	305	3	we	we	PRON
ejpam-2881	305	4	have	have	VERB
ejpam-2881	305	5	only	only	ADV
ejpam-2881	305	6	two	two	NUM
ejpam-2881	305	7	possible	possible	ADJ
ejpam-2881	305	8	cases	case	NOUN
ejpam-2881	305	9	.	.	PUNCT
ejpam-2881	306	1	case	case	NOUN
ejpam-2881	306	2	8	8	NUM
ejpam-2881	306	3	.	.	PUNCT
ejpam-2881	307	1	ωλ(ft	ωλ(ft	ADJ
ejpam-2881	307	2	,	,	PUNCT
ejpam-2881	307	3	fu	fu	NOUN
ejpam-2881	307	4	)	)	PUNCT
ejpam-2881	307	5	≤	≤	NOUN
ejpam-2881	307	6	aωλ(ft	aωλ(ft	NOUN
ejpam-2881	307	7	,	,	PUNCT
ejpam-2881	307	8	fu	fu	NOUN
ejpam-2881	307	9	)	)	PUNCT
ejpam-2881	307	10	.	.	PUNCT
ejpam-2881	308	1	this	this	PRON
ejpam-2881	308	2	implies	imply	VERB
ejpam-2881	308	3	ft	ft	NOUN
ejpam-2881	308	4	=	=	SYM
ejpam-2881	308	5	fu	fu	NOUN
ejpam-2881	308	6	.	.	PUNCT
ejpam-2881	308	7	case	case	NOUN
ejpam-2881	308	8	9	9	NUM
ejpam-2881	308	9	.	.	PUNCT
ejpam-2881	308	10	ωλ(ft	ωλ(ft	PROPN
ejpam-2881	308	11	,	,	PUNCT
ejpam-2881	308	12	fu	fu	NOUN
ejpam-2881	308	13	)	)	PUNCT
ejpam-2881	308	14	≤	≤	NOUN
ejpam-2881	308	15	0	0	NUM
ejpam-2881	308	16	.	.	PUNCT
ejpam-2881	309	1	this	this	PRON
ejpam-2881	309	2	implies	imply	VERB
ejpam-2881	309	3	ft	ft	NOUN
ejpam-2881	309	4	=	=	SYM
ejpam-2881	309	5	fu	fu	PROPN
ejpam-2881	309	6	.	.	PUNCT
ejpam-2881	310	1	therefore	therefore	ADV
ejpam-2881	310	2	,	,	PUNCT
ejpam-2881	310	3	f	f	PROPN
ejpam-2881	310	4	and	and	CCONJ
ejpam-2881	310	5	g	g	PROPN
ejpam-2881	310	6	have	have	VERB
ejpam-2881	310	7	a	a	DET
ejpam-2881	310	8	unique	unique	ADJ
ejpam-2881	310	9	common	common	ADJ
ejpam-2881	310	10	fixed	fix	VERB
ejpam-2881	310	11	point	point	NOUN
ejpam-2881	310	12	.	.	PUNCT
ejpam-2881	310	13	example	example	NOUN
ejpam-2881	311	1	4	4	NUM
ejpam-2881	311	2	.	.	PUNCT
ejpam-2881	311	3	let	let	VERB
ejpam-2881	311	4	xω	xω	PUNCT
ejpam-2881	311	5	=	=	SYM
ejpam-2881	311	6	(	(	PUNCT
ejpam-2881	311	7	0	0	NUM
ejpam-2881	311	8	,	,	PUNCT
ejpam-2881	311	9	1	1	NUM
ejpam-2881	311	10	]	]	PUNCT
ejpam-2881	311	11	with	with	ADP
ejpam-2881	311	12	ωλ(x	ωλ(x	NUM
ejpam-2881	311	13	,	,	PUNCT
ejpam-2881	311	14	y	y	NOUN
ejpam-2881	311	15	)	)	PUNCT
ejpam-2881	311	16	=	=	SYM
ejpam-2881	311	17	1	1	NUM
ejpam-2881	311	18	λ	λ	NOUN
ejpam-2881	311	19	|x−y|	|x−y|	NOUN
ejpam-2881	311	20	for	for	ADP
ejpam-2881	311	21	all	all	DET
ejpam-2881	311	22	λ	λ	PROPN
ejpam-2881	311	23	>	>	X
ejpam-2881	311	24	0	0	X
ejpam-2881	311	25	.	.	PUNCT
ejpam-2881	311	26	consider	consider	VERB
ejpam-2881	311	27	the	the	DET
ejpam-2881	311	28	functions	function	NOUN
ejpam-2881	311	29	f	f	PROPN
ejpam-2881	311	30	and	and	CCONJ
ejpam-2881	311	31	g	g	PROPN
ejpam-2881	311	32	defined	define	VERB
ejpam-2881	311	33	by	by	ADP
ejpam-2881	311	34	fx	fx	NOUN
ejpam-2881	311	35	=	=	PUNCT
ejpam-2881	312	1			PROPN
ejpam-2881	312	2	4	4	NUM
ejpam-2881	312	3	5	5	NUM
ejpam-2881	312	4	,	,	PUNCT
ejpam-2881	312	5	if	if	SCONJ
ejpam-2881	312	6	x	x	SYM
ejpam-2881	312	7	∈	∈	PROPN
ejpam-2881	312	8	(	(	PUNCT
ejpam-2881	312	9	0	0	NUM
ejpam-2881	312	10	,	,	PUNCT
ejpam-2881	312	11	4	4	NUM
ejpam-2881	312	12	5	5	NUM
ejpam-2881	312	13	]	]	PUNCT
ejpam-2881	312	14	,	,	PUNCT
ejpam-2881	312	15	1	1	NUM
ejpam-2881	312	16	5	5	NUM
ejpam-2881	312	17	,	,	PUNCT
ejpam-2881	312	18	if	if	SCONJ
ejpam-2881	312	19	x	x	SYM
ejpam-2881	312	20	∈	∈	PROPN
ejpam-2881	312	21	(	(	PUNCT
ejpam-2881	312	22	4	4	NUM
ejpam-2881	312	23	5	5	NUM
ejpam-2881	312	24	,	,	PUNCT
ejpam-2881	312	25	1	1	NUM
ejpam-2881	312	26	]	]	PUNCT
ejpam-2881	312	27	.	.	PUNCT
ejpam-2881	313	1	gx	gx	PROPN
ejpam-2881	313	2	=	=	PUNCT
ejpam-2881	314	1			PROPN
ejpam-2881	314	2	1−	1−	NUM
ejpam-2881	314	3	x	x	SYM
ejpam-2881	314	4	4	4	NUM
ejpam-2881	314	5	,	,	PUNCT
ejpam-2881	314	6	if	if	SCONJ
ejpam-2881	314	7	x	x	SYM
ejpam-2881	314	8	∈	∈	PROPN
ejpam-2881	314	9	(	(	PUNCT
ejpam-2881	314	10	0	0	NUM
ejpam-2881	314	11	,	,	PUNCT
ejpam-2881	314	12	4	4	NUM
ejpam-2881	314	13	5	5	NUM
ejpam-2881	314	14	]	]	PUNCT
ejpam-2881	314	15	,	,	PUNCT
ejpam-2881	314	16	9	9	NUM
ejpam-2881	314	17	10	10	NUM
ejpam-2881	314	18	,	,	PUNCT
ejpam-2881	314	19	if	if	SCONJ
ejpam-2881	314	20	x	x	SYM
ejpam-2881	314	21	∈	∈	PROPN
ejpam-2881	314	22	(	(	PUNCT
ejpam-2881	314	23	4	4	NUM
ejpam-2881	314	24	5	5	NUM
ejpam-2881	314	25	,	,	PUNCT
ejpam-2881	314	26	1	1	NUM
ejpam-2881	314	27	]	]	PUNCT
ejpam-2881	314	28	.	.	PUNCT
ejpam-2881	315	1	choosing	choose	VERB
ejpam-2881	315	2	a	a	DET
ejpam-2881	315	3	sequences	sequence	NOUN
ejpam-2881	315	4	{	{	PUNCT
ejpam-2881	315	5	xn	xn	NOUN
ejpam-2881	315	6	}	}	PUNCT
ejpam-2881	315	7	=	=	SYM
ejpam-2881	315	8	{	{	PUNCT
ejpam-2881	315	9	4	4	NUM
ejpam-2881	315	10	5	5	NUM
ejpam-2881	315	11	−	−	NUM
ejpam-2881	315	12	1	1	NUM
ejpam-2881	315	13	n	n	NOUN
ejpam-2881	315	14	}	}	PUNCT
ejpam-2881	315	15	,	,	PUNCT
ejpam-2881	315	16	we	we	PRON
ejpam-2881	315	17	can	can	AUX
ejpam-2881	315	18	see	see	VERB
ejpam-2881	315	19	that	that	SCONJ
ejpam-2881	315	20	f	f	PROPN
ejpam-2881	315	21	and	and	CCONJ
ejpam-2881	315	22	g	g	PROPN
ejpam-2881	315	23	enjoy	enjoy	VERB
ejpam-2881	315	24	the	the	DET
ejpam-2881	315	25	(	(	PUNCT
ejpam-2881	315	26	clrg)-property	clrg)-property	PROPN
ejpam-2881	315	27	lim	lim	PROPN
ejpam-2881	315	28	n→∞	n→∞	PRON
ejpam-2881	315	29	fxn	fxn	PROPN
ejpam-2881	315	30	=	=	PUNCT
ejpam-2881	315	31	lim	lim	PROPN
ejpam-2881	315	32	n→∞	n→∞	NUM
ejpam-2881	315	33	gxn	gxn	NOUN
ejpam-2881	315	34	=	=	NOUN
ejpam-2881	315	35	4	4	NUM
ejpam-2881	315	36	5	5	NUM
ejpam-2881	315	37	=	=	SYM
ejpam-2881	315	38	g	g	NOUN
ejpam-2881	315	39	(	(	PUNCT
ejpam-2881	315	40	4	4	NUM
ejpam-2881	315	41	5	5	NUM
ejpam-2881	315	42	)	)	PUNCT
ejpam-2881	315	43	.	.	PUNCT
ejpam-2881	316	1	also	also	ADV
ejpam-2881	316	2	,	,	PUNCT
ejpam-2881	316	3	f	f	X
ejpam-2881	316	4	(	(	PUNCT
ejpam-2881	316	5	4	4	NUM
ejpam-2881	316	6	5	5	NUM
ejpam-2881	316	7	)	)	PUNCT
ejpam-2881	316	8	=	=	SYM
ejpam-2881	316	9	g	g	NOUN
ejpam-2881	316	10	(	(	PUNCT
ejpam-2881	316	11	4	4	NUM
ejpam-2881	316	12	5	5	NUM
ejpam-2881	316	13	)	)	PUNCT
ejpam-2881	316	14	implies	imply	VERB
ejpam-2881	316	15	fg	fg	PROPN
ejpam-2881	316	16	(	(	PUNCT
ejpam-2881	316	17	4	4	NUM
ejpam-2881	316	18	5	5	NUM
ejpam-2881	316	19	)	)	PUNCT
ejpam-2881	316	20	=	=	SYM
ejpam-2881	317	1	gf	gf	X
ejpam-2881	317	2	(	(	PUNCT
ejpam-2881	317	3	4	4	NUM
ejpam-2881	317	4	5	5	NUM
ejpam-2881	317	5	)	)	PUNCT
ejpam-2881	317	6	,	,	PUNCT
ejpam-2881	317	7	which	which	PRON
ejpam-2881	317	8	shows	show	VERB
ejpam-2881	317	9	that	that	SCONJ
ejpam-2881	317	10	f	f	PROPN
ejpam-2881	317	11	and	and	CCONJ
ejpam-2881	317	12	g	g	PROPN
ejpam-2881	317	13	are	be	AUX
ejpam-2881	317	14	weakly	weakly	ADV
ejpam-2881	317	15	compatible	compatible	ADJ
ejpam-2881	317	16	.	.	PUNCT
ejpam-2881	318	1	case	case	NOUN
ejpam-2881	318	2	1	1	NUM
ejpam-2881	318	3	.	.	X
ejpam-2881	319	1	for	for	ADP
ejpam-2881	319	2	each	each	DET
ejpam-2881	319	3	x	x	NOUN
ejpam-2881	319	4	,	,	PUNCT
ejpam-2881	319	5	y	y	PROPN
ejpam-2881	319	6	∈	∈	PROPN
ejpam-2881	319	7	(	(	PUNCT
ejpam-2881	319	8	0	0	NUM
ejpam-2881	319	9	,	,	PUNCT
ejpam-2881	319	10	4	4	NUM
ejpam-2881	319	11	5	5	NUM
ejpam-2881	319	12	]	]	PUNCT
ejpam-2881	319	13	,	,	PUNCT
ejpam-2881	319	14	we	we	PRON
ejpam-2881	319	15	have	have	VERB
ejpam-2881	319	16	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	319	17	,	,	PUNCT
ejpam-2881	319	18	fy	fy	PROPN
ejpam-2881	319	19	)	)	PUNCT
ejpam-2881	319	20	=	=	SYM
ejpam-2881	319	21	1	1	NUM
ejpam-2881	319	22	λ	λ	NOUN
ejpam-2881	319	23	|fx−	|fx−	NUM
ejpam-2881	319	24	fy|	fy|	NOUN
ejpam-2881	319	25	=	=	SYM
ejpam-2881	319	26	1	1	NUM
ejpam-2881	319	27	λ	λ	NOUN
ejpam-2881	319	28	|4	|4	NUM
ejpam-2881	319	29	5	5	NUM
ejpam-2881	319	30	−	−	NOUN
ejpam-2881	319	31	4	4	NUM
ejpam-2881	319	32	5	5	NUM
ejpam-2881	319	33	|	|	ADV
ejpam-2881	319	34	and	and	CCONJ
ejpam-2881	319	35	mf	mf	VERB
ejpam-2881	319	36	,	,	PUNCT
ejpam-2881	319	37	g	g	PROPN
ejpam-2881	319	38	0	0	NUM
ejpam-2881	319	39	(	(	PUNCT
ejpam-2881	319	40	x	x	NOUN
ejpam-2881	319	41	,	,	PUNCT
ejpam-2881	319	42	y	y	PROPN
ejpam-2881	319	43	)	)	PUNCT
ejpam-2881	319	44	=	=	PRON
ejpam-2881	320	1	{	{	PUNCT
ejpam-2881	320	2	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	320	3	,	,	PUNCT
ejpam-2881	320	4	gy	gy	NOUN
ejpam-2881	320	5	)	)	PUNCT
ejpam-2881	320	6	,	,	PUNCT
ejpam-2881	320	7	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	320	8	,	,	PUNCT
ejpam-2881	320	9	fx	fx	PROPN
ejpam-2881	320	10	)	)	PUNCT
ejpam-2881	320	11	,	,	PUNCT
ejpam-2881	320	12	ωλ(gy	ωλ(gy	PROPN
ejpam-2881	320	13	,	,	PUNCT
ejpam-2881	320	14	fy	fy	PROPN
ejpam-2881	320	15	)	)	PUNCT
ejpam-2881	320	16	,	,	PUNCT
ejpam-2881	320	17	ωλ(gx	ωλ(gx	PROPN
ejpam-2881	320	18	,	,	PUNCT
ejpam-2881	320	19	fy	fy	PROPN
ejpam-2881	320	20	)	)	PUNCT
ejpam-2881	320	21	,	,	PUNCT
ejpam-2881	320	22	ωλ(gy	ωλ(gy	PROPN
ejpam-2881	320	23	,	,	PUNCT
ejpam-2881	320	24	fx	fx	PROPN
ejpam-2881	320	25	)	)	PUNCT
ejpam-2881	320	26	}	}	PUNCT
ejpam-2881	320	27	=	=	SYM
ejpam-2881	320	28	{	{	PUNCT
ejpam-2881	320	29	1	1	NUM
ejpam-2881	320	30	λ	λ	PROPN
ejpam-2881	320	31	|gx−	|gx−	PROPN
ejpam-2881	320	32	gy|	gy|	PROPN
ejpam-2881	320	33	,	,	PUNCT
ejpam-2881	320	34	1	1	NUM
ejpam-2881	320	35	λ	λ	PROPN
ejpam-2881	320	36	|gx−	|gx−	NUM
ejpam-2881	320	37	fx|	fx|	NOUN
ejpam-2881	320	38	,	,	PUNCT
ejpam-2881	320	39	1	1	NUM
ejpam-2881	320	40	λ	λ	SYM
ejpam-2881	320	41	|gy	|gy	NUM
ejpam-2881	320	42	−	−	PROPN
ejpam-2881	320	43	fy|	fy|	PROPN
ejpam-2881	320	44	,	,	PUNCT
ejpam-2881	320	45	1	1	NUM
ejpam-2881	320	46	λ	λ	PROPN
ejpam-2881	320	47	|gx−	|gx−	PROPN
ejpam-2881	320	48	fy|	fy|	PROPN
ejpam-2881	320	49	,	,	PUNCT
ejpam-2881	320	50	1	1	NUM
ejpam-2881	320	51	λ	λ	SYM
ejpam-2881	320	52	|gy	|gy	NUM
ejpam-2881	320	53	−	−	DET
ejpam-2881	320	54	fx|	fx|	NOUN
ejpam-2881	320	55	}	}	PUNCT
ejpam-2881	320	56	=	=	SYM
ejpam-2881	320	57	{	{	PUNCT
ejpam-2881	320	58	1	1	NUM
ejpam-2881	320	59	λ	λ	X
ejpam-2881	320	60	|1−	|1−	VERB
ejpam-2881	320	61	x	x	SYM
ejpam-2881	320	62	4	4	NUM
ejpam-2881	320	63	−	−	NOUN
ejpam-2881	320	64	(	(	PUNCT
ejpam-2881	320	65	1−	1−	NUM
ejpam-2881	320	66	y	y	PROPN
ejpam-2881	320	67	4	4	NUM
ejpam-2881	320	68	)	)	PUNCT
ejpam-2881	321	1	|	|	ADV
ejpam-2881	321	2	,	,	PUNCT
ejpam-2881	321	3	1	1	NUM
ejpam-2881	321	4	λ	λ	NOUN
ejpam-2881	321	5	|1−	|1−	VERB
ejpam-2881	321	6	x	x	SYM
ejpam-2881	321	7	4	4	NUM
ejpam-2881	321	8	−	−	NOUN
ejpam-2881	321	9	4	4	NUM
ejpam-2881	321	10	5	5	NUM
ejpam-2881	321	11	|	|	ADV
ejpam-2881	321	12	,	,	PUNCT
ejpam-2881	321	13	1	1	NUM
ejpam-2881	321	14	λ	λ	X
ejpam-2881	321	15	|1−	|1−	VERB
ejpam-2881	321	16	y	y	PRON
ejpam-2881	321	17	4	4	NUM
ejpam-2881	321	18	−	−	NOUN
ejpam-2881	321	19	4	4	NUM
ejpam-2881	321	20	5	5	NUM
ejpam-2881	321	21	|	|	ADV
ejpam-2881	321	22	,	,	PUNCT
ejpam-2881	321	23	1	1	NUM
ejpam-2881	321	24	λ	λ	NOUN
ejpam-2881	321	25	|1−	|1−	VERB
ejpam-2881	321	26	x	x	SYM
ejpam-2881	321	27	4	4	NUM
ejpam-2881	321	28	−	−	NOUN
ejpam-2881	321	29	4	4	NUM
ejpam-2881	321	30	5	5	NUM
ejpam-2881	321	31	|	|	ADV
ejpam-2881	321	32	,	,	PUNCT
ejpam-2881	321	33	1	1	NUM
ejpam-2881	321	34	λ	λ	X
ejpam-2881	321	35	|1−	|1−	VERB
ejpam-2881	321	36	y	y	PRON
ejpam-2881	321	37	4	4	NUM
ejpam-2881	321	38	−	−	NOUN
ejpam-2881	321	39	4	4	NUM
ejpam-2881	321	40	5	5	NUM
ejpam-2881	321	41	|	|	NOUN
ejpam-2881	321	42	}	}	PUNCT
ejpam-2881	321	43	.	.	PUNCT
ejpam-2881	322	1	thus	thus	ADV
ejpam-2881	322	2	,	,	PUNCT
ejpam-2881	322	3	we	we	PRON
ejpam-2881	322	4	obtain	obtain	VERB
ejpam-2881	322	5	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	322	6	,	,	PUNCT
ejpam-2881	322	7	fy	fy	NOUN
ejpam-2881	322	8	)	)	PUNCT
ejpam-2881	322	9	≤	≤	NOUN
ejpam-2881	323	1	aα0(x	aα0(x	PROPN
ejpam-2881	323	2	,	,	PUNCT
ejpam-2881	323	3	y	y	PROPN
ejpam-2881	323	4	)	)	PUNCT
ejpam-2881	323	5	,	,	PUNCT
ejpam-2881	323	6	where	where	SCONJ
ejpam-2881	323	7	a	a	DET
ejpam-2881	323	8	∈	∈	NOUN
ejpam-2881	323	9	(	(	PUNCT
ejpam-2881	323	10	0	0	NUM
ejpam-2881	323	11	,	,	PUNCT
ejpam-2881	323	12	1	1	NUM
ejpam-2881	323	13	)	)	PUNCT
ejpam-2881	323	14	.	.	PUNCT
ejpam-2881	324	1	p.	p.	NOUN
ejpam-2881	324	2	sumalai	sumalai	PROPN
ejpam-2881	324	3	,	,	PUNCT
ejpam-2881	324	4	p.	p.	PROPN
ejpam-2881	324	5	kumam	kumam	PROPN
ejpam-2881	324	6	,	,	PUNCT
ejpam-2881	324	7	y.	y.	PROPN
ejpam-2881	324	8	j.	j.	PROPN
ejpam-2881	324	9	cho	cho	PROPN
ejpam-2881	324	10	,	,	PUNCT
ejpam-2881	324	11	a.	a.	NOUN
ejpam-2881	324	12	padcharoen	padcharoen	PROPN
ejpam-2881	324	13	/	/	SYM
ejpam-2881	324	14	eur	eur	PROPN
ejpam-2881	324	15	.	.	PUNCT
ejpam-2881	325	1	j.	j.	PROPN
ejpam-2881	325	2	pure	pure	PROPN
ejpam-2881	325	3	appl	appl	PROPN
ejpam-2881	325	4	.	.	PROPN
ejpam-2881	325	5	math	math	PROPN
ejpam-2881	325	6	,	,	PUNCT
ejpam-2881	325	7	10	10	NUM
ejpam-2881	325	8	(	(	PUNCT
ejpam-2881	325	9	2	2	NUM
ejpam-2881	325	10	)	)	PUNCT
ejpam-2881	325	11	(	(	PUNCT
ejpam-2881	325	12	2017	2017	NUM
ejpam-2881	325	13	)	)	PUNCT
ejpam-2881	325	14	,	,	PUNCT
ejpam-2881	325	15	238	238	NUM
ejpam-2881	325	16	-	-	SYM
ejpam-2881	325	17	254	254	NUM
ejpam-2881	325	18	250	250	NUM
ejpam-2881	325	19	case	case	NOUN
ejpam-2881	325	20	2	2	NUM
ejpam-2881	325	21	.	.	X
ejpam-2881	326	1	for	for	ADP
ejpam-2881	326	2	x	x	PROPN
ejpam-2881	326	3	∈	∈	PROPN
ejpam-2881	326	4	(	(	PUNCT
ejpam-2881	326	5	0	0	NUM
ejpam-2881	326	6	,	,	PUNCT
ejpam-2881	326	7	4	4	NUM
ejpam-2881	326	8	5	5	NUM
ejpam-2881	326	9	]	]	PUNCT
ejpam-2881	326	10	and	and	CCONJ
ejpam-2881	326	11	y	y	PROPN
ejpam-2881	326	12	∈	∈	PROPN
ejpam-2881	326	13	(	(	PUNCT
ejpam-2881	326	14	4	4	NUM
ejpam-2881	326	15	5	5	NUM
ejpam-2881	326	16	,	,	PUNCT
ejpam-2881	326	17	1	1	X
ejpam-2881	326	18	]	]	PUNCT
ejpam-2881	326	19	we	we	PRON
ejpam-2881	326	20	have	have	VERB
ejpam-2881	326	21	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	326	22	,	,	PUNCT
ejpam-2881	326	23	fy	fy	PROPN
ejpam-2881	326	24	)	)	PUNCT
ejpam-2881	326	25	=	=	SYM
ejpam-2881	326	26	1	1	NUM
ejpam-2881	326	27	λ	λ	NOUN
ejpam-2881	326	28	|fx−	|fx−	NUM
ejpam-2881	326	29	fy|	fy|	NOUN
ejpam-2881	326	30	=	=	SYM
ejpam-2881	326	31	1	1	NUM
ejpam-2881	326	32	λ	λ	NOUN
ejpam-2881	326	33	|4	|4	NUM
ejpam-2881	326	34	5	5	NUM
ejpam-2881	326	35	−	−	NOUN
ejpam-2881	326	36	1	1	NUM
ejpam-2881	326	37	5	5	NUM
ejpam-2881	326	38	|	|	ADV
ejpam-2881	326	39	and	and	CCONJ
ejpam-2881	326	40	mf	mf	VERB
ejpam-2881	326	41	,	,	PUNCT
ejpam-2881	326	42	g	g	PROPN
ejpam-2881	326	43	0	0	NUM
ejpam-2881	326	44	(	(	PUNCT
ejpam-2881	326	45	x	x	NOUN
ejpam-2881	326	46	,	,	PUNCT
ejpam-2881	326	47	y	y	PROPN
ejpam-2881	326	48	)	)	PUNCT
ejpam-2881	326	49	=	=	PRON
ejpam-2881	327	1	{	{	PUNCT
ejpam-2881	327	2	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	327	3	,	,	PUNCT
ejpam-2881	327	4	gy	gy	NOUN
ejpam-2881	327	5	)	)	PUNCT
ejpam-2881	327	6	,	,	PUNCT
ejpam-2881	327	7	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	327	8	,	,	PUNCT
ejpam-2881	327	9	fx	fx	PROPN
ejpam-2881	327	10	)	)	PUNCT
ejpam-2881	327	11	,	,	PUNCT
ejpam-2881	327	12	ωλ(gy	ωλ(gy	PROPN
ejpam-2881	327	13	,	,	PUNCT
ejpam-2881	327	14	fy	fy	PROPN
ejpam-2881	327	15	)	)	PUNCT
ejpam-2881	327	16	,	,	PUNCT
ejpam-2881	327	17	ωλ(gx	ωλ(gx	PROPN
ejpam-2881	327	18	,	,	PUNCT
ejpam-2881	327	19	fy	fy	PROPN
ejpam-2881	327	20	)	)	PUNCT
ejpam-2881	327	21	,	,	PUNCT
ejpam-2881	327	22	ωλ(gy	ωλ(gy	PROPN
ejpam-2881	327	23	,	,	PUNCT
ejpam-2881	327	24	fx	fx	PROPN
ejpam-2881	327	25	)	)	PUNCT
ejpam-2881	327	26	}	}	PUNCT
ejpam-2881	327	27	=	=	SYM
ejpam-2881	327	28	{	{	PUNCT
ejpam-2881	327	29	1	1	NUM
ejpam-2881	327	30	λ	λ	PROPN
ejpam-2881	327	31	|gx−	|gx−	PROPN
ejpam-2881	327	32	gy|	gy|	PROPN
ejpam-2881	327	33	,	,	PUNCT
ejpam-2881	327	34	1	1	NUM
ejpam-2881	327	35	λ	λ	PROPN
ejpam-2881	327	36	|gx−	|gx−	NUM
ejpam-2881	327	37	fx|	fx|	NOUN
ejpam-2881	327	38	,	,	PUNCT
ejpam-2881	327	39	1	1	NUM
ejpam-2881	327	40	λ	λ	SYM
ejpam-2881	327	41	|gy	|gy	NUM
ejpam-2881	327	42	−	−	PROPN
ejpam-2881	327	43	fy|	fy|	PROPN
ejpam-2881	327	44	,	,	PUNCT
ejpam-2881	327	45	1	1	NUM
ejpam-2881	327	46	λ	λ	PROPN
ejpam-2881	327	47	|gx−	|gx−	PROPN
ejpam-2881	327	48	fy|	fy|	PROPN
ejpam-2881	327	49	,	,	PUNCT
ejpam-2881	327	50	1	1	NUM
ejpam-2881	327	51	λ	λ	SYM
ejpam-2881	327	52	|gy	|gy	NUM
ejpam-2881	327	53	−	−	DET
ejpam-2881	327	54	fx|	fx|	NOUN
ejpam-2881	327	55	}	}	PUNCT
ejpam-2881	327	56	=	=	SYM
ejpam-2881	327	57	{	{	PUNCT
ejpam-2881	327	58	1	1	NUM
ejpam-2881	327	59	λ	λ	X
ejpam-2881	327	60	|1−	|1−	NOUN
ejpam-2881	327	61	x	x	SYM
ejpam-2881	327	62	4	4	NUM
ejpam-2881	327	63	−	−	NOUN
ejpam-2881	327	64	9	9	NUM
ejpam-2881	327	65	10	10	NUM
ejpam-2881	327	66	|	|	ADV
ejpam-2881	327	67	,	,	PUNCT
ejpam-2881	327	68	1	1	NUM
ejpam-2881	327	69	λ	λ	NOUN
ejpam-2881	327	70	|1−	|1−	VERB
ejpam-2881	327	71	x	x	SYM
ejpam-2881	327	72	4	4	NUM
ejpam-2881	327	73	−	−	NOUN
ejpam-2881	327	74	4	4	NUM
ejpam-2881	327	75	5	5	NUM
ejpam-2881	327	76	|	|	ADV
ejpam-2881	327	77	,	,	PUNCT
ejpam-2881	327	78	1	1	NUM
ejpam-2881	327	79	λ	λ	NOUN
ejpam-2881	327	80	|	|	NOUN
ejpam-2881	327	81	9	9	NUM
ejpam-2881	327	82	10	10	NUM
ejpam-2881	327	83	−	−	NOUN
ejpam-2881	327	84	1	1	NUM
ejpam-2881	327	85	5	5	NUM
ejpam-2881	327	86	|	|	ADV
ejpam-2881	327	87	,	,	PUNCT
ejpam-2881	327	88	1	1	NUM
ejpam-2881	327	89	λ	λ	NOUN
ejpam-2881	327	90	|1−	|1−	VERB
ejpam-2881	327	91	x	x	SYM
ejpam-2881	327	92	4	4	NUM
ejpam-2881	327	93	−	−	NOUN
ejpam-2881	327	94	1	1	NUM
ejpam-2881	327	95	5	5	NUM
ejpam-2881	327	96	|	|	ADV
ejpam-2881	327	97	,	,	PUNCT
ejpam-2881	327	98	1	1	NUM
ejpam-2881	327	99	λ	λ	NOUN
ejpam-2881	327	100	|	|	NOUN
ejpam-2881	327	101	9	9	NUM
ejpam-2881	327	102	10	10	NUM
ejpam-2881	327	103	−	−	NOUN
ejpam-2881	327	104	4	4	NUM
ejpam-2881	327	105	5	5	NUM
ejpam-2881	327	106	|	|	NOUN
ejpam-2881	327	107	}	}	PUNCT
ejpam-2881	327	108	.	.	PUNCT
ejpam-2881	328	1	thus	thus	ADV
ejpam-2881	328	2	,	,	PUNCT
ejpam-2881	328	3	we	we	PRON
ejpam-2881	328	4	obtain	obtain	VERB
ejpam-2881	328	5	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	328	6	,	,	PUNCT
ejpam-2881	328	7	fy	fy	NOUN
ejpam-2881	328	8	)	)	PUNCT
ejpam-2881	328	9	≤	≤	NOUN
ejpam-2881	329	1	aα0(x	aα0(x	PROPN
ejpam-2881	329	2	,	,	PUNCT
ejpam-2881	329	3	y	y	PROPN
ejpam-2881	329	4	)	)	PUNCT
ejpam-2881	329	5	,	,	PUNCT
ejpam-2881	329	6	where	where	SCONJ
ejpam-2881	329	7	a	a	DET
ejpam-2881	329	8	∈	∈	NOUN
ejpam-2881	329	9	(	(	PUNCT
ejpam-2881	329	10	0	0	NUM
ejpam-2881	329	11	,	,	PUNCT
ejpam-2881	329	12	1	1	NUM
ejpam-2881	329	13	)	)	PUNCT
ejpam-2881	329	14	.	.	PUNCT
ejpam-2881	330	1	case	case	NOUN
ejpam-2881	330	2	3	3	NUM
ejpam-2881	330	3	.	.	X
ejpam-2881	331	1	for	for	ADP
ejpam-2881	331	2	x	x	PROPN
ejpam-2881	331	3	∈	∈	PROPN
ejpam-2881	331	4	(	(	PUNCT
ejpam-2881	331	5	4	4	NUM
ejpam-2881	331	6	5	5	NUM
ejpam-2881	331	7	,	,	PUNCT
ejpam-2881	331	8	1	1	NUM
ejpam-2881	331	9	]	]	PUNCT
ejpam-2881	331	10	and	and	CCONJ
ejpam-2881	331	11	y	y	PROPN
ejpam-2881	331	12	∈	∈	PROPN
ejpam-2881	331	13	(	(	PUNCT
ejpam-2881	331	14	0	0	NUM
ejpam-2881	331	15	,	,	PUNCT
ejpam-2881	331	16	4	4	NUM
ejpam-2881	331	17	5	5	NUM
ejpam-2881	331	18	]	]	PUNCT
ejpam-2881	331	19	,	,	PUNCT
ejpam-2881	331	20	we	we	PRON
ejpam-2881	331	21	have	have	VERB
ejpam-2881	331	22	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	331	23	,	,	PUNCT
ejpam-2881	331	24	fy	fy	PROPN
ejpam-2881	331	25	)	)	PUNCT
ejpam-2881	331	26	=	=	SYM
ejpam-2881	331	27	1	1	NUM
ejpam-2881	331	28	λ	λ	NOUN
ejpam-2881	331	29	|fx−	|fx−	NUM
ejpam-2881	331	30	fy|	fy|	NOUN
ejpam-2881	331	31	=	=	SYM
ejpam-2881	331	32	1	1	NUM
ejpam-2881	331	33	λ	λ	SYM
ejpam-2881	331	34	|1	|1	NUM
ejpam-2881	331	35	5	5	NUM
ejpam-2881	331	36	−	−	NOUN
ejpam-2881	331	37	4	4	NUM
ejpam-2881	331	38	5	5	NUM
ejpam-2881	331	39	|	|	ADV
ejpam-2881	331	40	and	and	CCONJ
ejpam-2881	331	41	mf	mf	VERB
ejpam-2881	331	42	,	,	PUNCT
ejpam-2881	331	43	g	g	PROPN
ejpam-2881	331	44	0	0	NUM
ejpam-2881	331	45	(	(	PUNCT
ejpam-2881	331	46	x	x	NOUN
ejpam-2881	331	47	,	,	PUNCT
ejpam-2881	331	48	y	y	PROPN
ejpam-2881	331	49	)	)	PUNCT
ejpam-2881	331	50	=	=	PRON
ejpam-2881	332	1	{	{	PUNCT
ejpam-2881	332	2	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	332	3	,	,	PUNCT
ejpam-2881	332	4	gy	gy	NOUN
ejpam-2881	332	5	)	)	PUNCT
ejpam-2881	332	6	,	,	PUNCT
ejpam-2881	332	7	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	332	8	,	,	PUNCT
ejpam-2881	332	9	fx	fx	PROPN
ejpam-2881	332	10	)	)	PUNCT
ejpam-2881	332	11	,	,	PUNCT
ejpam-2881	332	12	ωλ(gy	ωλ(gy	PROPN
ejpam-2881	332	13	,	,	PUNCT
ejpam-2881	332	14	fy	fy	PROPN
ejpam-2881	332	15	)	)	PUNCT
ejpam-2881	332	16	,	,	PUNCT
ejpam-2881	332	17	ωλ(gx	ωλ(gx	PROPN
ejpam-2881	332	18	,	,	PUNCT
ejpam-2881	332	19	fy	fy	PROPN
ejpam-2881	332	20	)	)	PUNCT
ejpam-2881	332	21	,	,	PUNCT
ejpam-2881	332	22	ωλ(gy	ωλ(gy	PROPN
ejpam-2881	332	23	,	,	PUNCT
ejpam-2881	332	24	fx	fx	PROPN
ejpam-2881	332	25	)	)	PUNCT
ejpam-2881	332	26	}	}	PUNCT
ejpam-2881	332	27	=	=	SYM
ejpam-2881	332	28	{	{	PUNCT
ejpam-2881	332	29	1	1	NUM
ejpam-2881	332	30	λ	λ	PROPN
ejpam-2881	332	31	|gx−	|gx−	PROPN
ejpam-2881	332	32	gy|	gy|	PROPN
ejpam-2881	332	33	,	,	PUNCT
ejpam-2881	332	34	1	1	NUM
ejpam-2881	332	35	λ	λ	PROPN
ejpam-2881	332	36	|gx−	|gx−	NUM
ejpam-2881	332	37	fx|	fx|	NOUN
ejpam-2881	332	38	,	,	PUNCT
ejpam-2881	332	39	1	1	NUM
ejpam-2881	332	40	λ	λ	SYM
ejpam-2881	332	41	|gy	|gy	NUM
ejpam-2881	332	42	−	−	PROPN
ejpam-2881	332	43	fy|	fy|	PROPN
ejpam-2881	332	44	,	,	PUNCT
ejpam-2881	332	45	1	1	NUM
ejpam-2881	332	46	λ	λ	PROPN
ejpam-2881	332	47	|gx−	|gx−	PROPN
ejpam-2881	332	48	fy|	fy|	PROPN
ejpam-2881	332	49	,	,	PUNCT
ejpam-2881	332	50	1	1	NUM
ejpam-2881	332	51	λ	λ	SYM
ejpam-2881	332	52	|gy	|gy	NUM
ejpam-2881	332	53	−	−	PRON
ejpam-2881	332	54	fx|	fx|	NOUN
ejpam-2881	332	55	}	}	PUNCT
ejpam-2881	332	56	=	=	SYM
ejpam-2881	332	57	{	{	PUNCT
ejpam-2881	332	58	1	1	NUM
ejpam-2881	332	59	λ	λ	NOUN
ejpam-2881	332	60	|	|	NOUN
ejpam-2881	332	61	9	9	NUM
ejpam-2881	332	62	10	10	NUM
ejpam-2881	332	63	−	−	PROPN
ejpam-2881	332	64	(	(	PUNCT
ejpam-2881	332	65	1−	1−	NUM
ejpam-2881	332	66	y	y	PROPN
ejpam-2881	332	67	4	4	NUM
ejpam-2881	332	68	)	)	PUNCT
ejpam-2881	333	1	|	|	ADV
ejpam-2881	333	2	,	,	PUNCT
ejpam-2881	333	3	1	1	NUM
ejpam-2881	333	4	λ	λ	NOUN
ejpam-2881	333	5	|	|	NOUN
ejpam-2881	333	6	9	9	NUM
ejpam-2881	333	7	10	10	NUM
ejpam-2881	333	8	−	−	NOUN
ejpam-2881	333	9	1	1	NUM
ejpam-2881	333	10	5	5	NUM
ejpam-2881	333	11	|	|	ADV
ejpam-2881	333	12	,	,	PUNCT
ejpam-2881	333	13	1	1	NUM
ejpam-2881	333	14	λ	λ	X
ejpam-2881	333	15	|1−	|1−	VERB
ejpam-2881	333	16	y	y	PRON
ejpam-2881	333	17	4	4	NUM
ejpam-2881	333	18	−	−	NOUN
ejpam-2881	333	19	4	4	NUM
ejpam-2881	333	20	5	5	NUM
ejpam-2881	333	21	|	|	ADV
ejpam-2881	333	22	,	,	PUNCT
ejpam-2881	333	23	1	1	NUM
ejpam-2881	333	24	λ	λ	NOUN
ejpam-2881	333	25	|	|	NOUN
ejpam-2881	333	26	9	9	NUM
ejpam-2881	333	27	10	10	NUM
ejpam-2881	333	28	−	−	NOUN
ejpam-2881	333	29	4	4	NUM
ejpam-2881	333	30	5	5	NUM
ejpam-2881	333	31	|	|	ADV
ejpam-2881	333	32	,	,	PUNCT
ejpam-2881	333	33	1	1	NUM
ejpam-2881	333	34	λ	λ	X
ejpam-2881	333	35	|1−	|1−	VERB
ejpam-2881	333	36	y	y	PRON
ejpam-2881	333	37	4	4	NUM
ejpam-2881	333	38	−	−	NOUN
ejpam-2881	333	39	1	1	NUM
ejpam-2881	333	40	5	5	NUM
ejpam-2881	333	41	|	|	ADV
ejpam-2881	333	42	}	}	PUNCT
ejpam-2881	333	43	.	.	PUNCT
ejpam-2881	334	1	thus	thus	ADV
ejpam-2881	334	2	,	,	PUNCT
ejpam-2881	334	3	we	we	PRON
ejpam-2881	334	4	obtain	obtain	VERB
ejpam-2881	334	5	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	334	6	,	,	PUNCT
ejpam-2881	334	7	fy	fy	NOUN
ejpam-2881	334	8	)	)	PUNCT
ejpam-2881	334	9	≤	≤	NOUN
ejpam-2881	335	1	aα0(x	aα0(x	PROPN
ejpam-2881	335	2	,	,	PUNCT
ejpam-2881	335	3	y	y	PROPN
ejpam-2881	335	4	)	)	PUNCT
ejpam-2881	335	5	,	,	PUNCT
ejpam-2881	335	6	where	where	SCONJ
ejpam-2881	335	7	a	a	DET
ejpam-2881	335	8	∈	∈	NOUN
ejpam-2881	335	9	(	(	PUNCT
ejpam-2881	335	10	0	0	NUM
ejpam-2881	335	11	,	,	PUNCT
ejpam-2881	335	12	1	1	NUM
ejpam-2881	335	13	)	)	PUNCT
ejpam-2881	335	14	.	.	PUNCT
ejpam-2881	336	1	case	case	NOUN
ejpam-2881	336	2	4	4	NUM
ejpam-2881	336	3	.	.	X
ejpam-2881	337	1	for	for	ADP
ejpam-2881	337	2	each	each	DET
ejpam-2881	337	3	x	x	NOUN
ejpam-2881	337	4	,	,	PUNCT
ejpam-2881	337	5	y	y	PROPN
ejpam-2881	337	6	∈	∈	PROPN
ejpam-2881	337	7	(	(	PUNCT
ejpam-2881	337	8	4	4	NUM
ejpam-2881	337	9	5	5	NUM
ejpam-2881	337	10	,	,	PUNCT
ejpam-2881	337	11	1	1	NUM
ejpam-2881	337	12	]	]	PUNCT
ejpam-2881	337	13	,	,	PUNCT
ejpam-2881	337	14	we	we	PRON
ejpam-2881	337	15	have	have	VERB
ejpam-2881	337	16	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	337	17	,	,	PUNCT
ejpam-2881	337	18	fy	fy	PROPN
ejpam-2881	337	19	)	)	PUNCT
ejpam-2881	337	20	=	=	SYM
ejpam-2881	337	21	1	1	NUM
ejpam-2881	337	22	λ	λ	NOUN
ejpam-2881	337	23	|fx−	|fx−	NUM
ejpam-2881	337	24	fy|	fy|	NOUN
ejpam-2881	337	25	=	=	SYM
ejpam-2881	337	26	1	1	NUM
ejpam-2881	337	27	λ	λ	SYM
ejpam-2881	337	28	|1	|1	NUM
ejpam-2881	337	29	5	5	NUM
ejpam-2881	337	30	−	−	NOUN
ejpam-2881	337	31	1	1	NUM
ejpam-2881	337	32	5	5	NUM
ejpam-2881	337	33	|	|	ADV
ejpam-2881	337	34	p.	p.	NOUN
ejpam-2881	337	35	sumalai	sumalai	NOUN
ejpam-2881	337	36	,	,	PUNCT
ejpam-2881	337	37	p.	p.	PROPN
ejpam-2881	337	38	kumam	kumam	PROPN
ejpam-2881	337	39	,	,	PUNCT
ejpam-2881	337	40	y.	y.	PROPN
ejpam-2881	337	41	j.	j.	PROPN
ejpam-2881	337	42	cho	cho	PROPN
ejpam-2881	337	43	,	,	PUNCT
ejpam-2881	337	44	a.	a.	NOUN
ejpam-2881	337	45	padcharoen	padcharoen	PROPN
ejpam-2881	337	46	/	/	SYM
ejpam-2881	337	47	eur	eur	PROPN
ejpam-2881	337	48	.	.	PUNCT
ejpam-2881	338	1	j.	j.	PROPN
ejpam-2881	338	2	pure	pure	PROPN
ejpam-2881	338	3	appl	appl	PROPN
ejpam-2881	338	4	.	.	PROPN
ejpam-2881	338	5	math	math	PROPN
ejpam-2881	338	6	,	,	PUNCT
ejpam-2881	338	7	10	10	NUM
ejpam-2881	338	8	(	(	PUNCT
ejpam-2881	338	9	2	2	NUM
ejpam-2881	338	10	)	)	PUNCT
ejpam-2881	338	11	(	(	PUNCT
ejpam-2881	338	12	2017	2017	NUM
ejpam-2881	338	13	)	)	PUNCT
ejpam-2881	338	14	,	,	PUNCT
ejpam-2881	338	15	238	238	NUM
ejpam-2881	338	16	-	-	SYM
ejpam-2881	338	17	254	254	NUM
ejpam-2881	338	18	251	251	NUM
ejpam-2881	338	19	and	and	CCONJ
ejpam-2881	338	20	mf	mf	VERB
ejpam-2881	338	21	,	,	PUNCT
ejpam-2881	338	22	g	g	PROPN
ejpam-2881	338	23	0	0	NUM
ejpam-2881	338	24	(	(	PUNCT
ejpam-2881	338	25	x	x	NOUN
ejpam-2881	338	26	,	,	PUNCT
ejpam-2881	338	27	y	y	PROPN
ejpam-2881	338	28	)	)	PUNCT
ejpam-2881	338	29	=	=	PRON
ejpam-2881	338	30	{	{	PUNCT
ejpam-2881	338	31	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	338	32	,	,	PUNCT
ejpam-2881	338	33	gy	gy	NOUN
ejpam-2881	338	34	)	)	PUNCT
ejpam-2881	338	35	,	,	PUNCT
ejpam-2881	338	36	ωλ(gx	ωλ(gx	ADJ
ejpam-2881	338	37	,	,	PUNCT
ejpam-2881	338	38	fx	fx	PROPN
ejpam-2881	338	39	)	)	PUNCT
ejpam-2881	338	40	,	,	PUNCT
ejpam-2881	338	41	ωλ(gy	ωλ(gy	PROPN
ejpam-2881	338	42	,	,	PUNCT
ejpam-2881	338	43	fy	fy	PROPN
ejpam-2881	338	44	)	)	PUNCT
ejpam-2881	338	45	,	,	PUNCT
ejpam-2881	338	46	ωλ(gx	ωλ(gx	PROPN
ejpam-2881	338	47	,	,	PUNCT
ejpam-2881	338	48	fy	fy	PROPN
ejpam-2881	338	49	)	)	PUNCT
ejpam-2881	338	50	,	,	PUNCT
ejpam-2881	338	51	ωλ(gy	ωλ(gy	PROPN
ejpam-2881	338	52	,	,	PUNCT
ejpam-2881	338	53	fx	fx	PROPN
ejpam-2881	338	54	)	)	PUNCT
ejpam-2881	338	55	}	}	PUNCT
ejpam-2881	338	56	=	=	SYM
ejpam-2881	338	57	{	{	PUNCT
ejpam-2881	338	58	1	1	NUM
ejpam-2881	338	59	λ	λ	PROPN
ejpam-2881	338	60	|gx−	|gx−	PROPN
ejpam-2881	338	61	gy|	gy|	PROPN
ejpam-2881	338	62	,	,	PUNCT
ejpam-2881	338	63	1	1	NUM
ejpam-2881	338	64	λ	λ	PROPN
ejpam-2881	338	65	|gx−	|gx−	NUM
ejpam-2881	338	66	fx|	fx|	NOUN
ejpam-2881	338	67	,	,	PUNCT
ejpam-2881	338	68	1	1	NUM
ejpam-2881	338	69	λ	λ	SYM
ejpam-2881	338	70	|gy	|gy	NUM
ejpam-2881	338	71	−	−	PROPN
ejpam-2881	338	72	fy|	fy|	PROPN
ejpam-2881	338	73	,	,	PUNCT
ejpam-2881	338	74	1	1	NUM
ejpam-2881	338	75	λ	λ	PROPN
ejpam-2881	338	76	|gx−	|gx−	PROPN
ejpam-2881	338	77	fy|	fy|	PROPN
ejpam-2881	338	78	,	,	PUNCT
ejpam-2881	338	79	1	1	NUM
ejpam-2881	338	80	λ	λ	SYM
ejpam-2881	338	81	|gy	|gy	NUM
ejpam-2881	338	82	−	−	PRON
ejpam-2881	338	83	fx|	fx|	NOUN
ejpam-2881	338	84	}	}	PUNCT
ejpam-2881	338	85	=	=	SYM
ejpam-2881	338	86	{	{	PUNCT
ejpam-2881	338	87	1	1	NUM
ejpam-2881	338	88	λ	λ	NOUN
ejpam-2881	338	89	|	|	NOUN
ejpam-2881	338	90	9	9	NUM
ejpam-2881	338	91	10	10	NUM
ejpam-2881	338	92	−	−	NOUN
ejpam-2881	338	93	1	1	NUM
ejpam-2881	338	94	5	5	NUM
ejpam-2881	338	95	|	|	ADV
ejpam-2881	338	96	,	,	PUNCT
ejpam-2881	338	97	1	1	NUM
ejpam-2881	338	98	λ	λ	NOUN
ejpam-2881	338	99	|	|	NOUN
ejpam-2881	338	100	9	9	NUM
ejpam-2881	338	101	10	10	NUM
ejpam-2881	338	102	−	−	NOUN
ejpam-2881	338	103	1	1	NUM
ejpam-2881	338	104	5	5	NUM
ejpam-2881	338	105	|	|	ADV
ejpam-2881	338	106	,	,	PUNCT
ejpam-2881	338	107	1	1	NUM
ejpam-2881	338	108	λ	λ	NOUN
ejpam-2881	338	109	|	|	NOUN
ejpam-2881	338	110	9	9	NUM
ejpam-2881	338	111	10	10	NUM
ejpam-2881	338	112	−	−	NOUN
ejpam-2881	338	113	1	1	NUM
ejpam-2881	338	114	5	5	NUM
ejpam-2881	338	115	|	|	ADV
ejpam-2881	338	116	,	,	PUNCT
ejpam-2881	338	117	1	1	NUM
ejpam-2881	338	118	λ	λ	NOUN
ejpam-2881	338	119	|	|	NOUN
ejpam-2881	338	120	9	9	NUM
ejpam-2881	338	121	10	10	NUM
ejpam-2881	338	122	−	−	NOUN
ejpam-2881	338	123	1	1	NUM
ejpam-2881	338	124	5	5	NUM
ejpam-2881	338	125	|	|	ADV
ejpam-2881	338	126	,	,	PUNCT
ejpam-2881	338	127	1	1	NUM
ejpam-2881	338	128	λ	λ	X
ejpam-2881	338	129	|1−	|1−	VERB
ejpam-2881	338	130	9	9	NUM
ejpam-2881	338	131	10	10	NUM
ejpam-2881	338	132	−	−	NOUN
ejpam-2881	338	133	1	1	NUM
ejpam-2881	338	134	5	5	NUM
ejpam-2881	338	135	|	|	NOUN
ejpam-2881	338	136	}	}	PUNCT
ejpam-2881	338	137	.	.	PUNCT
ejpam-2881	339	1	thus	thus	ADV
ejpam-2881	339	2	,	,	PUNCT
ejpam-2881	339	3	we	we	PRON
ejpam-2881	339	4	obtain	obtain	VERB
ejpam-2881	339	5	ωλ(fx	ωλ(fx	NOUN
ejpam-2881	339	6	,	,	PUNCT
ejpam-2881	339	7	fy	fy	NOUN
ejpam-2881	339	8	)	)	PUNCT
ejpam-2881	339	9	≤	≤	NOUN
ejpam-2881	340	1	aα0(x	aα0(x	PROPN
ejpam-2881	340	2	,	,	PUNCT
ejpam-2881	340	3	y	y	PROPN
ejpam-2881	340	4	)	)	PUNCT
ejpam-2881	340	5	,	,	PUNCT
ejpam-2881	340	6	where	where	SCONJ
ejpam-2881	340	7	a	a	DET
ejpam-2881	340	8	∈	∈	NOUN
ejpam-2881	340	9	(	(	PUNCT
ejpam-2881	340	10	0	0	NUM
ejpam-2881	340	11	,	,	PUNCT
ejpam-2881	340	12	1	1	NUM
ejpam-2881	340	13	)	)	PUNCT
ejpam-2881	340	14	.	.	PUNCT
ejpam-2881	341	1	therefore	therefore	ADV
ejpam-2881	341	2	,	,	PUNCT
ejpam-2881	341	3	f	f	PROPN
ejpam-2881	341	4	and	and	CCONJ
ejpam-2881	341	5	g	g	PROPN
ejpam-2881	341	6	satisfy	satisfy	VERB
ejpam-2881	341	7	all	all	DET
ejpam-2881	341	8	conditions	condition	NOUN
ejpam-2881	341	9	of	of	ADP
ejpam-2881	341	10	theorem	theorem	NOUN
ejpam-2881	341	11	5	5	NUM
ejpam-2881	341	12	are	be	AUX
ejpam-2881	341	13	satisfied	satisfied	ADJ
ejpam-2881	341	14	and	and	CCONJ
ejpam-2881	341	15	x	x	SYM
ejpam-2881	341	16	=	=	SYM
ejpam-2881	341	17	4	4	NUM
ejpam-2881	341	18	5	5	NUM
ejpam-2881	341	19	is	be	AUX
ejpam-2881	341	20	the	the	DET
ejpam-2881	341	21	unique	unique	ADJ
ejpam-2881	341	22	common	common	ADJ
ejpam-2881	341	23	fixed	fix	VERB
ejpam-2881	341	24	point	point	NOUN
ejpam-2881	341	25	of	of	ADP
ejpam-2881	341	26	f	f	PROPN
ejpam-2881	341	27	and	and	CCONJ
ejpam-2881	341	28	g.	g.	PROPN
ejpam-2881	341	29	5	5	NUM
ejpam-2881	341	30	.	.	PUNCT
ejpam-2881	342	1	some	some	DET
ejpam-2881	342	2	applications	application	NOUN
ejpam-2881	342	3	to	to	PART
ejpam-2881	342	4	fredholm	fredholm	VERB
ejpam-2881	342	5	integral	integral	ADJ
ejpam-2881	342	6	equations	equation	NOUN
ejpam-2881	342	7	the	the	DET
ejpam-2881	342	8	purpose	purpose	NOUN
ejpam-2881	342	9	of	of	ADP
ejpam-2881	342	10	this	this	DET
ejpam-2881	342	11	section	section	NOUN
ejpam-2881	342	12	is	be	AUX
ejpam-2881	342	13	to	to	PART
ejpam-2881	342	14	show	show	VERB
ejpam-2881	342	15	the	the	DET
ejpam-2881	342	16	existence	existence	NOUN
ejpam-2881	342	17	and	and	CCONJ
ejpam-2881	342	18	uniqueness	uniqueness	NOUN
ejpam-2881	342	19	of	of	ADP
ejpam-2881	342	20	a	a	DET
ejpam-2881	342	21	solution	solution	NOUN
ejpam-2881	342	22	of	of	ADP
ejpam-2881	342	23	fredholm	fredholm	ADJ
ejpam-2881	342	24	integral	integral	ADJ
ejpam-2881	342	25	equations	equation	NOUN
ejpam-2881	342	26	in	in	ADP
ejpam-2881	342	27	modular	modular	ADJ
ejpam-2881	342	28	metric	metric	ADJ
ejpam-2881	342	29	spaces	space	NOUN
ejpam-2881	342	30	with	with	ADP
ejpam-2881	342	31	a	a	DET
ejpam-2881	342	32	function	function	NOUN
ejpam-2881	342	33	space	space	NOUN
ejpam-2881	342	34	(	(	PUNCT
ejpam-2881	342	35	c(i	c(i	NOUN
ejpam-2881	342	36	,	,	PUNCT
ejpam-2881	342	37	r	r	NOUN
ejpam-2881	342	38	)	)	PUNCT
ejpam-2881	342	39	,	,	PUNCT
ejpam-2881	342	40	ωλ	ωλ	VERB
ejpam-2881	342	41	)	)	PUNCT
ejpam-2881	342	42	and	and	CCONJ
ejpam-2881	342	43	a	a	DET
ejpam-2881	342	44	contraction	contraction	NOUN
ejpam-2881	342	45	by	by	ADP
ejpam-2881	342	46	using	use	VERB
ejpam-2881	342	47	our	our	PRON
ejpam-2881	342	48	main	main	ADJ
ejpam-2881	342	49	results	result	NOUN
ejpam-2881	342	50	.	.	PUNCT
ejpam-2881	343	1	consider	consider	VERB
ejpam-2881	343	2	the	the	DET
ejpam-2881	343	3	integral	integral	ADJ
ejpam-2881	343	4	equation	equation	NOUN
ejpam-2881	343	5	:	:	PUNCT
ejpam-2881	343	6	fx(t)−	fx(t)−	PROPN
ejpam-2881	343	7	µ	µ	X
ejpam-2881	343	8	∫	∫	PROPN
ejpam-2881	343	9	r	r	NOUN
ejpam-2881	343	10	0	0	PUNCT
ejpam-2881	343	11	k(t	k(t	PROPN
ejpam-2881	343	12	,	,	PUNCT
ejpam-2881	343	13	s)hx(s)ds	s)hx(s)ds	PROPN
ejpam-2881	343	14	=	=	SYM
ejpam-2881	343	15	g(t	g(t	PROPN
ejpam-2881	343	16	)	)	PUNCT
ejpam-2881	343	17	,	,	PUNCT
ejpam-2881	343	18	(	(	PUNCT
ejpam-2881	343	19	5	5	X
ejpam-2881	343	20	)	)	PUNCT
ejpam-2881	343	21	where	where	SCONJ
ejpam-2881	343	22	x	x	X
ejpam-2881	343	23	:	:	PUNCT
ejpam-2881	343	24	i	i	PRON
ejpam-2881	343	25	→	→	PUNCT
ejpam-2881	343	26	r	r	NOUN
ejpam-2881	343	27	is	be	AUX
ejpam-2881	343	28	an	an	DET
ejpam-2881	343	29	unknown	unknown	ADJ
ejpam-2881	343	30	function	function	NOUN
ejpam-2881	343	31	,	,	PUNCT
ejpam-2881	343	32	g	g	NOUN
ejpam-2881	343	33	:	:	PUNCT
ejpam-2881	344	1	i	i	PROPN
ejpam-2881	344	2	→	→	SYM
ejpam-2881	344	3	r	r	NOUN
ejpam-2881	344	4	and	and	CCONJ
ejpam-2881	344	5	h	h	NOUN
ejpam-2881	344	6	,	,	PUNCT
ejpam-2881	344	7	f	f	X
ejpam-2881	344	8	:	:	PUNCT
ejpam-2881	344	9	r	r	NOUN
ejpam-2881	344	10	→	→	SYM
ejpam-2881	344	11	r	r	NOUN
ejpam-2881	344	12	are	be	AUX
ejpam-2881	344	13	two	two	NUM
ejpam-2881	344	14	functions	function	NOUN
ejpam-2881	344	15	,	,	PUNCT
ejpam-2881	344	16	µ	µ	X
ejpam-2881	344	17	is	be	AUX
ejpam-2881	344	18	a	a	DET
ejpam-2881	344	19	parameter	parameter	NOUN
ejpam-2881	344	20	.	.	PUNCT
ejpam-2881	345	1	the	the	DET
ejpam-2881	345	2	kernel	kernel	PROPN
ejpam-2881	345	3	k	k	PROPN
ejpam-2881	345	4	of	of	ADP
ejpam-2881	345	5	the	the	DET
ejpam-2881	345	6	integral	integral	ADJ
ejpam-2881	345	7	equation	equation	NOUN
ejpam-2881	345	8	is	be	AUX
ejpam-2881	345	9	defined	define	VERB
ejpam-2881	345	10	by	by	ADP
ejpam-2881	345	11	i	i	PRON
ejpam-2881	345	12	×	×	NOUN
ejpam-2881	345	13	r	r	NOUN
ejpam-2881	345	14	→	→	SYM
ejpam-2881	345	15	r	r	NOUN
ejpam-2881	345	16	,	,	PUNCT
ejpam-2881	345	17	where	where	SCONJ
ejpam-2881	345	18	i	i	PRON
ejpam-2881	345	19	=	=	PUNCT
ejpam-2881	346	1	[	[	X
ejpam-2881	346	2	0	0	NUM
ejpam-2881	346	3	,	,	PUNCT
ejpam-2881	346	4	r	r	NOUN
ejpam-2881	346	5	]	]	PUNCT
ejpam-2881	346	6	.	.	PUNCT
ejpam-2881	347	1	theorem	theorem	ADJ
ejpam-2881	347	2	6	6	NUM
ejpam-2881	347	3	.	.	PUNCT
ejpam-2881	348	1	let	let	VERB
ejpam-2881	348	2	k	k	NOUN
ejpam-2881	348	3	,	,	PUNCT
ejpam-2881	348	4	f	f	PROPN
ejpam-2881	348	5	,	,	PUNCT
ejpam-2881	348	6	g	g	PROPN
ejpam-2881	348	7	,	,	PUNCT
ejpam-2881	348	8	h	h	NOUN
ejpam-2881	348	9	be	be	AUX
ejpam-2881	348	10	continuous	continuous	ADJ
ejpam-2881	348	11	.	.	PUNCT
ejpam-2881	349	1	suppose	suppose	VERB
ejpam-2881	349	2	that	that	SCONJ
ejpam-2881	349	3	c	c	PROPN
ejpam-2881	349	4	∈	∈	PROPN
ejpam-2881	349	5	r	r	NOUN
ejpam-2881	349	6	is	be	AUX
ejpam-2881	349	7	such	such	ADJ
ejpam-2881	349	8	that	that	SCONJ
ejpam-2881	349	9	,	,	PUNCT
ejpam-2881	349	10	for	for	ADP
ejpam-2881	349	11	all	all	DET
ejpam-2881	349	12	t	t	PROPN
ejpam-2881	349	13	,	,	PUNCT
ejpam-2881	349	14	s	s	VERB
ejpam-2881	349	15	∈	∈	PROPN
ejpam-2881	349	16	i	i	PROPN
ejpam-2881	349	17	,	,	PUNCT
ejpam-2881	349	18	|k(t	|k(t	PROPN
ejpam-2881	349	19	,	,	PUNCT
ejpam-2881	349	20	s)|	s)|	NOUN
ejpam-2881	349	21	≤	≤	PUNCT
ejpam-2881	349	22	c	c	PROPN
ejpam-2881	349	23	and	and	CCONJ
ejpam-2881	349	24	,	,	PUNCT
ejpam-2881	349	25	for	for	SCONJ
ejpam-2881	349	26	each	each	DET
ejpam-2881	349	27	x	x	SYM
ejpam-2881	349	28	∈	∈	PROPN
ejpam-2881	349	29	(	(	PUNCT
ejpam-2881	349	30	c(i	c(i	NOUN
ejpam-2881	349	31	,	,	PUNCT
ejpam-2881	349	32	r	r	NOUN
ejpam-2881	349	33	)	)	PUNCT
ejpam-2881	349	34	,	,	PUNCT
ejpam-2881	349	35	ωλ	ωλ	ADJ
ejpam-2881	349	36	)	)	PUNCT
ejpam-2881	349	37	,	,	PUNCT
ejpam-2881	349	38	there	there	PRON
ejpam-2881	349	39	exists	exist	VERB
ejpam-2881	349	40	y	y	PROPN
ejpam-2881	349	41	∈	∈	PROPN
ejpam-2881	349	42	(	(	PUNCT
ejpam-2881	349	43	c(i	c(i	NOUN
ejpam-2881	349	44	,	,	PUNCT
ejpam-2881	349	45	r	r	NOUN
ejpam-2881	349	46	)	)	PUNCT
ejpam-2881	349	47	,	,	PUNCT
ejpam-2881	349	48	ωλ	ωλ	VERB
ejpam-2881	349	49	)	)	PUNCT
ejpam-2881	349	50	such	such	ADJ
ejpam-2881	349	51	that	that	SCONJ
ejpam-2881	349	52	(	(	PUNCT
ejpam-2881	349	53	fy)(t	fy)(t	ADJ
ejpam-2881	349	54	)	)	PUNCT
ejpam-2881	349	55	=	=	SYM
ejpam-2881	349	56	g(t	g(t	PROPN
ejpam-2881	349	57	)	)	PUNCT
ejpam-2881	350	1	+	+	CCONJ
ejpam-2881	350	2	µ	µ	PRON
ejpam-2881	350	3	∫	∫	PROPN
ejpam-2881	350	4	r	r	NOUN
ejpam-2881	350	5	0	0	PUNCT
ejpam-2881	350	6	k(t	k(t	PROPN
ejpam-2881	350	7	,	,	PUNCT
ejpam-2881	350	8	s)hx(s)ds	s)hx(s)d	VERB
ejpam-2881	350	9	for	for	ADP
ejpam-2881	350	10	all	all	DET
ejpam-2881	350	11	r	r	NOUN
ejpam-2881	350	12	∈	∈	PROPN
ejpam-2881	350	13	c(i	c(i	NOUN
ejpam-2881	350	14	,	,	PUNCT
ejpam-2881	350	15	r	r	NOUN
ejpam-2881	350	16	)	)	PUNCT
ejpam-2881	350	17	.	.	PUNCT
ejpam-2881	351	1	if	if	SCONJ
ejpam-2881	351	2	f	f	PROPN
ejpam-2881	351	3	is	be	AUX
ejpam-2881	351	4	injective	injective	ADJ
ejpam-2881	351	5	,	,	PUNCT
ejpam-2881	351	6	there	there	PRON
ejpam-2881	351	7	exists	exist	VERB
ejpam-2881	351	8	l	l	NOUN
ejpam-2881	351	9	∈	∈	PROPN
ejpam-2881	351	10	r	r	NOUN
ejpam-2881	351	11	such	such	ADJ
ejpam-2881	351	12	that	that	PRON
ejpam-2881	351	13	,	,	PUNCT
ejpam-2881	351	14	for	for	ADP
ejpam-2881	351	15	all	all	DET
ejpam-2881	351	16	x	x	NOUN
ejpam-2881	351	17	,	,	PUNCT
ejpam-2881	351	18	y	y	PROPN
ejpam-2881	351	19	∈	∈	PROPN
ejpam-2881	351	20	r	r	PROPN
ejpam-2881	351	21	,	,	PUNCT
ejpam-2881	351	22	|hx−	|hx−	PROPN
ejpam-2881	351	23	hy|	hy|	NOUN
ejpam-2881	351	24	≤	≤	NOUN
ejpam-2881	351	25	l|fx−	l|fx−	NUM
ejpam-2881	351	26	fy|	fy|	PROPN
ejpam-2881	351	27	and	and	CCONJ
ejpam-2881	351	28	{	{	PUNCT
ejpam-2881	351	29	fx	fx	NOUN
ejpam-2881	351	30	:	:	PUNCT
ejpam-2881	351	31	x	x	SYM
ejpam-2881	351	32	∈	∈	NOUN
ejpam-2881	351	33	(	(	PUNCT
ejpam-2881	351	34	c(i	c(i	NOUN
ejpam-2881	351	35	,	,	PUNCT
ejpam-2881	351	36	r	r	NOUN
ejpam-2881	351	37	)	)	PUNCT
ejpam-2881	351	38	,	,	PUNCT
ejpam-2881	351	39	ωλ	ωλ	ADJ
ejpam-2881	351	40	)	)	PUNCT
ejpam-2881	351	41	}	}	PUNCT
ejpam-2881	351	42	is	be	AUX
ejpam-2881	351	43	complete	complete	ADJ
ejpam-2881	351	44	,	,	PUNCT
ejpam-2881	351	45	then	then	ADV
ejpam-2881	351	46	,	,	PUNCT
ejpam-2881	351	47	for	for	ADP
ejpam-2881	351	48	any	any	DET
ejpam-2881	351	49	µ	µ	PROPN
ejpam-2881	351	50	∈	∈	NOUN
ejpam-2881	351	51	(	(	PUNCT
ejpam-2881	351	52	−	−	PROPN
ejpam-2881	351	53	1	1	NUM
ejpam-2881	351	54	crl	crl	PROPN
ejpam-2881	351	55	,	,	PUNCT
ejpam-2881	351	56	1	1	NUM
ejpam-2881	351	57	crl	crl	PROPN
ejpam-2881	351	58	)	)	PUNCT
ejpam-2881	351	59	,	,	PUNCT
ejpam-2881	351	60	there	there	PRON
ejpam-2881	351	61	exists	exist	VERB
ejpam-2881	351	62	w	w	PROPN
ejpam-2881	351	63	∈	∈	PROPN
ejpam-2881	351	64	(	(	PUNCT
ejpam-2881	351	65	c(i	c(i	NOUN
ejpam-2881	351	66	,	,	PUNCT
ejpam-2881	351	67	r	r	NOUN
ejpam-2881	351	68	)	)	PUNCT
ejpam-2881	351	69	,	,	PUNCT
ejpam-2881	351	70	ωλ	ωλ	VERB
ejpam-2881	351	71	)	)	PUNCT
ejpam-2881	351	72	such	such	ADJ
ejpam-2881	351	73	that	that	SCONJ
ejpam-2881	351	74	,	,	PUNCT
ejpam-2881	351	75	for	for	ADP
ejpam-2881	351	76	any	any	DET
ejpam-2881	351	77	x0	x0	PROPN
ejpam-2881	351	78	∈	∈	PROPN
ejpam-2881	351	79	(	(	PUNCT
ejpam-2881	351	80	c(i	c(i	NOUN
ejpam-2881	351	81	,	,	PUNCT
ejpam-2881	351	82	r	r	NOUN
ejpam-2881	351	83	)	)	PUNCT
ejpam-2881	351	84	,	,	PUNCT
ejpam-2881	351	85	ωλ	ωλ	ADJ
ejpam-2881	351	86	)	)	PUNCT
ejpam-2881	351	87	,	,	PUNCT
ejpam-2881	351	88	fw(t	fw(t	PROPN
ejpam-2881	351	89	)	)	PUNCT
ejpam-2881	352	1	=	=	VERB
ejpam-2881	352	2	lim	lim	PROPN
ejpam-2881	352	3	x→∞	x→∞	NUM
ejpam-2881	352	4	fxn(t	fxn(t	NUM
ejpam-2881	352	5	)	)	PUNCT
ejpam-2881	353	1	=	=	VERB
ejpam-2881	353	2	lim	lim	PROPN
ejpam-2881	353	3	x→∞	x→∞	NUM
ejpam-2881	354	1	[	[	PUNCT
ejpam-2881	354	2	g(t	g(t	PROPN
ejpam-2881	354	3	)	)	PUNCT
ejpam-2881	355	1	+	+	CCONJ
ejpam-2881	355	2	µ	µ	PRON
ejpam-2881	355	3	∫	∫	PROPN
ejpam-2881	355	4	r	r	NOUN
ejpam-2881	355	5	0	0	PUNCT
ejpam-2881	355	6	k(t	k(t	NOUN
ejpam-2881	355	7	,	,	PUNCT
ejpam-2881	355	8	s)hxn−1(s)ds	s)hxn−1(s)ds	X
ejpam-2881	355	9	]	]	PUNCT
ejpam-2881	355	10	(	(	PUNCT
ejpam-2881	355	11	6	6	NUM
ejpam-2881	355	12	)	)	PUNCT
ejpam-2881	355	13	and	and	CCONJ
ejpam-2881	355	14	w	w	NOUN
ejpam-2881	355	15	is	be	AUX
ejpam-2881	355	16	the	the	DET
ejpam-2881	355	17	unique	unique	ADJ
ejpam-2881	355	18	solution	solution	NOUN
ejpam-2881	355	19	of	of	ADP
ejpam-2881	355	20	the	the	DET
ejpam-2881	355	21	equation	equation	NOUN
ejpam-2881	355	22	(	(	PUNCT
ejpam-2881	355	23	5	5	NUM
ejpam-2881	355	24	)	)	PUNCT
ejpam-2881	355	25	.	.	PUNCT
ejpam-2881	356	1	references	reference	NOUN
ejpam-2881	356	2	252	252	NUM
ejpam-2881	356	3	proof	proof	NOUN
ejpam-2881	356	4	.	.	PUNCT
ejpam-2881	357	1	let	let	VERB
ejpam-2881	357	2	xω	xω	PUNCT
ejpam-2881	358	1	=	=	PUNCT
ejpam-2881	358	2	yω	yω	NOUN
ejpam-2881	358	3	=	=	SYM
ejpam-2881	358	4	(	(	PUNCT
ejpam-2881	358	5	c(i	c(i	NOUN
ejpam-2881	358	6	,	,	PUNCT
ejpam-2881	358	7	r	r	NOUN
ejpam-2881	358	8	)	)	PUNCT
ejpam-2881	358	9	,	,	PUNCT
ejpam-2881	358	10	ωλ	ωλ	VERB
ejpam-2881	358	11	)	)	PUNCT
ejpam-2881	358	12	and	and	CCONJ
ejpam-2881	358	13	define	define	VERB
ejpam-2881	358	14	d(x	d(x	PROPN
ejpam-2881	358	15	,	,	PUNCT
ejpam-2881	358	16	y	y	NOUN
ejpam-2881	358	17	)	)	PUNCT
ejpam-2881	359	1	=	=	PUNCT
ejpam-2881	359	2	maxt∈i	maxt∈i	PROPN
ejpam-2881	359	3	|x(t	|x(t	PROPN
ejpam-2881	359	4	)	)	PUNCT
ejpam-2881	359	5	−	−	PROPN
ejpam-2881	359	6	y(t)|	y(t)|	PROPN
ejpam-2881	359	7	for	for	ADP
ejpam-2881	359	8	all	all	DET
ejpam-2881	359	9	x	x	NOUN
ejpam-2881	359	10	,	,	PUNCT
ejpam-2881	359	11	y	y	PROPN
ejpam-2881	359	12	∈	∈	PROPN
ejpam-2881	360	1	xω	xω	VERB
ejpam-2881	360	2	.	.	PUNCT
ejpam-2881	361	1	let	let	VERB
ejpam-2881	361	2	t	t	NOUN
ejpam-2881	361	3	,	,	PUNCT
ejpam-2881	361	4	s	s	PART
ejpam-2881	361	5	∈	∈	NOUN
ejpam-2881	362	1	xω	xω	PRON
ejpam-2881	362	2	→	→	PUNCT
ejpam-2881	362	3	xω	xω	NOUN
ejpam-2881	362	4	be	be	AUX
ejpam-2881	362	5	the	the	DET
ejpam-2881	362	6	mappings	mapping	NOUN
ejpam-2881	362	7	defined	define	VERB
ejpam-2881	362	8	as	as	ADP
ejpam-2881	362	9	follows	follow	VERB
ejpam-2881	362	10	:	:	PUNCT
ejpam-2881	362	11	(	(	PUNCT
ejpam-2881	362	12	tx)(t	tx)(t	PROPN
ejpam-2881	362	13	)	)	PUNCT
ejpam-2881	362	14	=	=	SYM
ejpam-2881	362	15	g(t	g(t	PROPN
ejpam-2881	362	16	)	)	PUNCT
ejpam-2881	363	1	+	+	CCONJ
ejpam-2881	363	2	µ	µ	PRON
ejpam-2881	363	3	∫	∫	PROPN
ejpam-2881	363	4	r	r	NOUN
ejpam-2881	363	5	0	0	PUNCT
ejpam-2881	363	6	k(t	k(t	NOUN
ejpam-2881	363	7	,	,	PUNCT
ejpam-2881	363	8	s)(hx)(s)ds	s)(hx)(s)ds	PROPN
ejpam-2881	363	9	,	,	PUNCT
ejpam-2881	363	10	sx	sx	PROPN
ejpam-2881	363	11	=	=	SYM
ejpam-2881	363	12	fx	fx	PROPN
ejpam-2881	363	13	.	.	PUNCT
ejpam-2881	364	1	then	then	ADV
ejpam-2881	364	2	,	,	PUNCT
ejpam-2881	364	3	by	by	ADP
ejpam-2881	364	4	the	the	DET
ejpam-2881	364	5	assumptions	assumption	NOUN
ejpam-2881	364	6	,	,	PUNCT
ejpam-2881	364	7	s(xω	s(xω	NOUN
ejpam-2881	364	8	)	)	PUNCT
ejpam-2881	364	9	=	=	SYM
ejpam-2881	364	10	{	{	PUNCT
ejpam-2881	364	11	sx	sx	INTJ
ejpam-2881	364	12	:	:	PUNCT
ejpam-2881	364	13	x	x	SYM
ejpam-2881	364	14	∈	∈	PROPN
ejpam-2881	364	15	xω	xω	NOUN
ejpam-2881	364	16	}	}	PUNCT
ejpam-2881	364	17	is	be	AUX
ejpam-2881	364	18	complete	complete	ADJ
ejpam-2881	364	19	.	.	PUNCT
ejpam-2881	365	1	let	let	VERB
ejpam-2881	365	2	x∗	x∗	PROPN
ejpam-2881	365	3	∈	∈	PROPN
ejpam-2881	365	4	t	t	PROPN
ejpam-2881	365	5	(	(	PUNCT
ejpam-2881	365	6	xω	xω	PROPN
ejpam-2881	365	7	)	)	PUNCT
ejpam-2881	365	8	for	for	ADP
ejpam-2881	365	9	any	any	DET
ejpam-2881	365	10	x	x	SYM
ejpam-2881	365	11	∈	∈	PROPN
ejpam-2881	365	12	xω	xω	NOUN
ejpam-2881	365	13	and	and	CCONJ
ejpam-2881	365	14	x∗(t	x∗(t	NOUN
ejpam-2881	365	15	)	)	PUNCT
ejpam-2881	365	16	=	=	SYM
ejpam-2881	365	17	tx(t	tx(t	NOUN
ejpam-2881	365	18	)	)	PUNCT
ejpam-2881	365	19	.	.	PUNCT
ejpam-2881	366	1	by	by	ADP
ejpam-2881	366	2	the	the	DET
ejpam-2881	366	3	assumptions	assumption	NOUN
ejpam-2881	366	4	,	,	PUNCT
ejpam-2881	366	5	there	there	PRON
ejpam-2881	366	6	exists	exist	VERB
ejpam-2881	366	7	y	y	PROPN
ejpam-2881	366	8	∈	∈	PROPN
ejpam-2881	366	9	xω	xω	PRON
ejpam-2881	366	10	such	such	ADJ
ejpam-2881	366	11	that	that	SCONJ
ejpam-2881	366	12	tx(t	tx(t	NOUN
ejpam-2881	366	13	)	)	PUNCT
ejpam-2881	366	14	=	=	SYM
ejpam-2881	366	15	fy(t	fy(t	X
ejpam-2881	366	16	)	)	PUNCT
ejpam-2881	366	17	and	and	CCONJ
ejpam-2881	366	18	hence	hence	ADV
ejpam-2881	366	19	t	t	PROPN
ejpam-2881	366	20	(	(	PUNCT
ejpam-2881	366	21	xω	xω	PROPN
ejpam-2881	366	22	)	)	PUNCT
ejpam-2881	366	23	⊆	⊆	NUM
ejpam-2881	366	24	s(xω	s(xω	NOUN
ejpam-2881	366	25	)	)	PUNCT
ejpam-2881	366	26	.	.	PUNCT
ejpam-2881	367	1	since	since	SCONJ
ejpam-2881	367	2	ωλ(tx	ωλ(tx	PROPN
ejpam-2881	367	3	,	,	PUNCT
ejpam-2881	367	4	ty	ty	INTJ
ejpam-2881	367	5	)	)	PUNCT
ejpam-2881	367	6	=	=	SYM
ejpam-2881	367	7	|µ|	|µ|	PROPN
ejpam-2881	367	8	∣∣∣	∣∣∣	ADJ
ejpam-2881	367	9	∫	∫	PROPN
ejpam-2881	367	10	r	r	NOUN
ejpam-2881	367	11	0	0	PUNCT
ejpam-2881	368	1	[	[	X
ejpam-2881	368	2	k(t	k(t	PROPN
ejpam-2881	368	3	,	,	PUNCT
ejpam-2881	368	4	s)(hx)(s)ds]−	s)(hx)(s)ds]−	ADJ
ejpam-2881	368	5	∫	∫	PROPN
ejpam-2881	369	1	r	r	NOUN
ejpam-2881	369	2	0	0	PUNCT
ejpam-2881	370	1	[	[	X
ejpam-2881	370	2	k(t	k(t	NOUN
ejpam-2881	370	3	,	,	PUNCT
ejpam-2881	370	4	s)(hy)(s)ds	s)(hy)(s)d	NOUN
ejpam-2881	370	5	]	]	PUNCT
ejpam-2881	370	6	∣∣∣	∣∣∣	NOUN
ejpam-2881	370	7	≤	≤	NUM
ejpam-2881	370	8	|µ|	|µ|	PROPN
ejpam-2881	370	9	∫	∫	PROPN
ejpam-2881	370	10	r	r	NOUN
ejpam-2881	370	11	0	0	NUM
ejpam-2881	370	12	c|(hx)(s)−	c|(hx)(s)−	PROPN
ejpam-2881	370	13	(	(	PUNCT
ejpam-2881	370	14	hy)(s)|ds	hy)(s)|ds	PROPN
ejpam-2881	370	15	≤	≤	NUM
ejpam-2881	370	16	l|µ|c	l|µ|c	NOUN
ejpam-2881	370	17	∫	∫	PROPN
ejpam-2881	371	1	r	r	NOUN
ejpam-2881	371	2	0	0	X
ejpam-2881	371	3	|(fx)(s)−	|(fx)(s)−	PROPN
ejpam-2881	371	4	(	(	PUNCT
ejpam-2881	371	5	fy)(s)|ds	fy)(s)|ds	PROPN
ejpam-2881	371	6	≤	≤	PROPN
ejpam-2881	371	7	l|µ|c	l|µ|c	NOUN
ejpam-2881	371	8	∫	∫	PROPN
ejpam-2881	371	9	r	r	NOUN
ejpam-2881	371	10	0	0	NUM
ejpam-2881	371	11	|(sx)(s)−	|(sx)(s)−	PROPN
ejpam-2881	371	12	(	(	PUNCT
ejpam-2881	371	13	sy)(s)|ds	sy)(s)|ds	PROPN
ejpam-2881	371	14	≤	≤	NUM
ejpam-2881	371	15	(	(	PUNCT
ejpam-2881	371	16	sup	sup	NOUN
ejpam-2881	371	17	t∈i	t∈i	NOUN
ejpam-2881	371	18	|(sx)(t)−	|(sx)(t)−	PROPN
ejpam-2881	371	19	(	(	PUNCT
ejpam-2881	371	20	sy)(t)|	sy)(t)|	PROPN
ejpam-2881	371	21	)	)	PUNCT
ejpam-2881	371	22	l|µ|c	l|µ|c	NOUN
ejpam-2881	371	23	∫	∫	PROPN
ejpam-2881	371	24	r	r	NOUN
ejpam-2881	371	25	0	0	NUM
ejpam-2881	371	26	ds	ds	PROPN
ejpam-2881	371	27	≤	≤	PROPN
ejpam-2881	371	28	l|µ|crd(sx	l|µ|crd(sx	PROPN
ejpam-2881	371	29	,	,	PUNCT
ejpam-2881	371	30	sy	sy	NOUN
ejpam-2881	371	31	)	)	PUNCT
ejpam-2881	371	32	.	.	PUNCT
ejpam-2881	372	1	therefore	therefore	ADV
ejpam-2881	372	2	,	,	PUNCT
ejpam-2881	372	3	for	for	ADP
ejpam-2881	372	4	any	any	DET
ejpam-2881	372	5	µ	µ	PROPN
ejpam-2881	372	6	∈	∈	NOUN
ejpam-2881	372	7	(	(	PUNCT
ejpam-2881	372	8	−	−	PROPN
ejpam-2881	372	9	1	1	NUM
ejpam-2881	372	10	crl	crl	PROPN
ejpam-2881	372	11	,	,	PUNCT
ejpam-2881	372	12	1	1	NUM
ejpam-2881	372	13	crl	crl	PROPN
ejpam-2881	372	14	)	)	PUNCT
ejpam-2881	372	15	,	,	PUNCT
ejpam-2881	372	16	there	there	PRON
ejpam-2881	372	17	exists	exist	VERB
ejpam-2881	372	18	a	a	DET
ejpam-2881	372	19	unique	unique	ADJ
ejpam-2881	372	20	w	w	ADP
ejpam-2881	372	21	∈	∈	NOUN
ejpam-2881	372	22	xω	xω	NOUN
ejpam-2881	372	23	such	such	ADJ
ejpam-2881	372	24	that	that	DET
ejpam-2881	372	25	fw(t	fw(t	NOUN
ejpam-2881	372	26	)	)	PUNCT
ejpam-2881	373	1	=	=	VERB
ejpam-2881	373	2	lim	lim	PROPN
ejpam-2881	373	3	x→∞	x→∞	NUM
ejpam-2881	374	1	sxn(t	sxn(t	PROPN
ejpam-2881	374	2	)	)	PUNCT
ejpam-2881	374	3	=	=	PROPN
ejpam-2881	374	4	lim	lim	PROPN
ejpam-2881	374	5	x→∞	x→∞	NUM
ejpam-2881	374	6	txn−1(t	txn−1(t	PRON
ejpam-2881	374	7	)	)	PUNCT
ejpam-2881	375	1	=	=	SYM
ejpam-2881	375	2	t	t	PROPN
ejpam-2881	375	3	(	(	PUNCT
ejpam-2881	375	4	w)(t	w)(t	PROPN
ejpam-2881	375	5	)	)	PUNCT
ejpam-2881	375	6	,	,	PUNCT
ejpam-2881	375	7	x0	x0	PROPN
ejpam-2881	375	8	∈	∈	PROPN
ejpam-2881	375	9	xω	xω	X
ejpam-2881	376	1	for	for	ADP
ejpam-2881	376	2	all	all	DET
ejpam-2881	376	3	t	t	NOUN
ejpam-2881	376	4	∈	∈	PROPN
ejpam-2881	376	5	i	i	PRON
ejpam-2881	376	6	,	,	PUNCT
ejpam-2881	376	7	which	which	PRON
ejpam-2881	376	8	is	be	AUX
ejpam-2881	376	9	the	the	DET
ejpam-2881	376	10	unique	unique	ADJ
ejpam-2881	376	11	solution	solution	NOUN
ejpam-2881	376	12	of	of	ADP
ejpam-2881	376	13	the	the	DET
ejpam-2881	376	14	equation	equation	NOUN
ejpam-2881	376	15	(	(	PUNCT
ejpam-2881	376	16	5	5	NUM
ejpam-2881	376	17	)	)	PUNCT
ejpam-2881	376	18	.	.	PUNCT
ejpam-2881	377	1	so	so	ADV
ejpam-2881	377	2	,	,	PUNCT
ejpam-2881	377	3	s	s	X
ejpam-2881	377	4	and	and	CCONJ
ejpam-2881	377	5	t	t	PROPN
ejpam-2881	377	6	have	have	VERB
ejpam-2881	377	7	a	a	DET
ejpam-2881	377	8	coincidence	coincidence	NOUN
ejpam-2881	377	9	point	point	NOUN
ejpam-2881	377	10	in	in	ADP
ejpam-2881	377	11	xω	xω	PRON
ejpam-2881	377	12	.	.	PUNCT
ejpam-2881	378	1	moreover	moreover	ADV
ejpam-2881	378	2	,	,	PUNCT
ejpam-2881	378	3	if	if	SCONJ
ejpam-2881	378	4	either	either	PRON
ejpam-2881	378	5	t	t	NOUN
ejpam-2881	378	6	or	or	CCONJ
ejpam-2881	378	7	s	s	NOUN
ejpam-2881	378	8	is	be	AUX
ejpam-2881	378	9	injective	injective	ADJ
ejpam-2881	378	10	,	,	PUNCT
ejpam-2881	378	11	then	then	ADV
ejpam-2881	378	12	s	s	PROPN
ejpam-2881	378	13	and	and	CCONJ
ejpam-2881	378	14	t	t	PROPN
ejpam-2881	378	15	have	have	VERB
ejpam-2881	378	16	a	a	DET
ejpam-2881	378	17	unique	unique	ADJ
ejpam-2881	378	18	coincidence	coincidence	NOUN
ejpam-2881	378	19	point	point	NOUN
ejpam-2881	378	20	in	in	ADP
ejpam-2881	378	21	xω	xω	PRON
ejpam-2881	378	22	.	.	PUNCT
ejpam-2881	379	1	acknowledgements	acknowledgement	NOUN
ejpam-2881	379	2	this	this	DET
ejpam-2881	379	3	project	project	NOUN
ejpam-2881	379	4	was	be	AUX
ejpam-2881	379	5	supported	support	VERB
ejpam-2881	379	6	by	by	ADP
ejpam-2881	379	7	the	the	DET
ejpam-2881	379	8	theoretical	theoretical	ADJ
ejpam-2881	379	9	and	and	CCONJ
ejpam-2881	379	10	computational	computational	ADJ
ejpam-2881	379	11	science	science	NOUN
ejpam-2881	379	12	(	(	PUNCT
ejpam-2881	379	13	tacs	tacs	PROPN
ejpam-2881	379	14	)	)	PUNCT
ejpam-2881	379	15	center	center	NOUN
ejpam-2881	379	16	under	under	ADP
ejpam-2881	379	17	computational	computational	ADJ
ejpam-2881	379	18	and	and	CCONJ
ejpam-2881	379	19	applied	apply	VERB
ejpam-2881	379	20	science	science	NOUN
ejpam-2881	379	21	for	for	ADP
ejpam-2881	379	22	smart	smart	ADJ
ejpam-2881	379	23	innovation	innovation	NOUN
ejpam-2881	379	24	research	research	NOUN
ejpam-2881	379	25	cluster	cluster	NOUN
ejpam-2881	379	26	(	(	PUNCT
ejpam-2881	379	27	classic	classic	ADJ
ejpam-2881	379	28	)	)	PUNCT
ejpam-2881	379	29	,	,	PUNCT
ejpam-2881	379	30	faculty	faculty	NOUN
ejpam-2881	379	31	of	of	ADP
ejpam-2881	379	32	science	science	NOUN
ejpam-2881	379	33	,	,	PUNCT
ejpam-2881	379	34	kmutt	kmutt	PROPN
ejpam-2881	379	35	.	.	PUNCT
ejpam-2881	380	1	references	reference	NOUN
ejpam-2881	380	2	[	[	X
ejpam-2881	380	3	1	1	NUM
ejpam-2881	380	4	]	]	X
ejpam-2881	380	5	b.e	b.e	PROPN
ejpam-2881	380	6	.	.	PROPN
ejpam-2881	380	7	rhoades	rhoade	NOUN
ejpam-2881	380	8	,	,	PUNCT
ejpam-2881	380	9	some	some	DET
ejpam-2881	380	10	theorems	theorem	NOUN
ejpam-2881	380	11	on	on	ADP
ejpam-2881	380	12	weakly	weakly	ADJ
ejpam-2881	380	13	contractive	contractive	ADJ
ejpam-2881	380	14	maps	map	NOUN
ejpam-2881	380	15	,	,	PUNCT
ejpam-2881	380	16	nonlinear	nonlinear	ADJ
ejpam-2881	380	17	anal	anal	NOUN
ejpam-2881	380	18	.	.	PUNCT
ejpam-2881	381	1	47	47	NUM
ejpam-2881	381	2	(	(	PUNCT
ejpam-2881	381	3	2001	2001	NUM
ejpam-2881	381	4	)	)	PUNCT
ejpam-2881	381	5	2683	2683	NUM
ejpam-2881	381	6	-	-	SYM
ejpam-2881	381	7	2693	2693	NUM
ejpam-2881	381	8	.	.	PUNCT
ejpam-2881	382	1	[	[	X
ejpam-2881	382	2	2	2	NUM
ejpam-2881	382	3	]	]	X
ejpam-2881	382	4	v.v	v.v	PROPN
ejpam-2881	382	5	.	.	PROPN
ejpam-2881	382	6	chistyakov	chistyakov	PROPN
ejpam-2881	382	7	,	,	PUNCT
ejpam-2881	382	8	modular	modular	ADJ
ejpam-2881	382	9	metric	metric	ADJ
ejpam-2881	382	10	spaces	space	NOUN
ejpam-2881	382	11	i	i	PRON
ejpam-2881	382	12	:	:	PUNCT
ejpam-2881	382	13	basic	basic	ADJ
ejpam-2881	382	14	concepts	concept	NOUN
ejpam-2881	382	15	,	,	PUNCT
ejpam-2881	382	16	nonlinear	nonlinear	ADJ
ejpam-2881	382	17	anal	anal	NOUN
ejpam-2881	382	18	.	.	PUNCT
ejpam-2881	383	1	72(2010	72(2010	NUM
ejpam-2881	383	2	)	)	PUNCT
ejpam-2881	383	3	,	,	PUNCT
ejpam-2881	383	4	1	1	NUM
ejpam-2881	383	5	-	-	SYM
ejpam-2881	383	6	14	14	NUM
ejpam-2881	383	7	.	.	PUNCT
ejpam-2881	384	1	references	reference	NOUN
ejpam-2881	384	2	253	253	NUM
ejpam-2881	384	3	[	[	X
ejpam-2881	384	4	3	3	NUM
ejpam-2881	384	5	]	]	X
ejpam-2881	384	6	c.	c.	PROPN
ejpam-2881	384	7	mongkolkeha	mongkolkeha	PROPN
ejpam-2881	384	8	,	,	PUNCT
ejpam-2881	384	9	w.	w.	PROPN
ejpam-2881	384	10	sintunavarat	sintunavarat	PROPN
ejpam-2881	384	11	,	,	PUNCT
ejpam-2881	384	12	p.	p.	PROPN
ejpam-2881	384	13	kumam	kumam	PROPN
ejpam-2881	384	14	,	,	PUNCT
ejpam-2881	384	15	fixed	fix	VERB
ejpam-2881	384	16	point	point	NOUN
ejpam-2881	384	17	theorems	theorem	NOUN
ejpam-2881	384	18	for	for	ADP
ejpam-2881	384	19	contraction	contraction	NOUN
ejpam-2881	384	20	mappings	mapping	NOUN
ejpam-2881	384	21	in	in	ADP
ejpam-2881	384	22	modular	modular	ADJ
ejpam-2881	384	23	metric	metric	ADJ
ejpam-2881	384	24	spaces	space	NOUN
ejpam-2881	384	25	,	,	PUNCT
ejpam-2881	384	26	j.	j.	PROPN
ejpam-2881	384	27	appl	appl	PROPN
ejpam-2881	384	28	.	.	PROPN
ejpam-2881	384	29	math	math	PROPN
ejpam-2881	384	30	.	.	PUNCT
ejpam-2881	385	1	2012	2012	NUM
ejpam-2881	385	2	,	,	PUNCT
ejpam-2881	385	3	art	art	NOUN
ejpam-2881	385	4	.	.	PUNCT
ejpam-2881	386	1	i	i	PRON
ejpam-2881	386	2	d	d	PROPN
ejpam-2881	386	3	907951	907951	NUM
ejpam-2881	386	4	,	,	PUNCT
ejpam-2881	386	5	5	5	NUM
ejpam-2881	386	6	pp	pp	NOUN
ejpam-2881	386	7	.	.	PUNCT
ejpam-2881	387	1	[	[	X
ejpam-2881	387	2	4	4	X
ejpam-2881	387	3	]	]	PUNCT
ejpam-2881	387	4	w.	w.	PROPN
ejpam-2881	387	5	sintunavarat	sintunavarat	PROPN
ejpam-2881	387	6	,	,	PUNCT
ejpam-2881	387	7	p.	p.	PROPN
ejpam-2881	387	8	kumam	kumam	PROPN
ejpam-2881	387	9	,	,	PUNCT
ejpam-2881	387	10	common	common	ADJ
ejpam-2881	387	11	fixed	fix	VERB
ejpam-2881	387	12	point	point	NOUN
ejpam-2881	387	13	theorems	theorem	NOUN
ejpam-2881	387	14	for	for	ADP
ejpam-2881	387	15	a	a	DET
ejpam-2881	387	16	pair	pair	NOUN
ejpam-2881	387	17	of	of	ADP
ejpam-2881	387	18	weakly	weakly	ADJ
ejpam-2881	387	19	compatible	compatible	ADJ
ejpam-2881	387	20	mappings	mapping	NOUN
ejpam-2881	387	21	in	in	ADP
ejpam-2881	387	22	fuzzy	fuzzy	ADJ
ejpam-2881	387	23	metric	metric	ADJ
ejpam-2881	387	24	spaces	space	NOUN
ejpam-2881	387	25	,	,	PUNCT
ejpam-2881	387	26	j.	j.	PROPN
ejpam-2881	387	27	appl	appl	PROPN
ejpam-2881	387	28	.	.	PROPN
ejpam-2881	387	29	math	math	PROPN
ejpam-2881	387	30	.	.	PUNCT
ejpam-2881	388	1	2011	2011	NUM
ejpam-2881	388	2	,	,	PUNCT
ejpam-2881	388	3	art	art	NOUN
ejpam-2881	388	4	.	.	PUNCT
ejpam-2881	389	1	i	i	PRON
ejpam-2881	389	2	d	d	PROPN
ejpam-2881	389	3	637958	637958	NUM
ejpam-2881	389	4	,	,	PUNCT
ejpam-2881	389	5	14	14	NUM
ejpam-2881	389	6	pp	pp	NOUN
ejpam-2881	389	7	.	.	PUNCT
ejpam-2881	390	1	[	[	X
ejpam-2881	390	2	5	5	X
ejpam-2881	390	3	]	]	X
ejpam-2881	390	4	h.	h.	PROPN
ejpam-2881	390	5	aydi	aydi	PROPN
ejpam-2881	390	6	,	,	PUNCT
ejpam-2881	390	7	h.k	h.k	PROPN
ejpam-2881	390	8	.	.	PROPN
ejpam-2881	390	9	nashine	nashine	PROPN
ejpam-2881	390	10	,	,	PUNCT
ejpam-2881	390	11	b.	b.	PROPN
ejpam-2881	390	12	samet	samet	PROPN
ejpam-2881	390	13	,	,	PUNCT
ejpam-2881	390	14	h.	h.	PROPN
ejpam-2881	390	15	yazidi	yazidi	PROPN
ejpam-2881	390	16	,	,	PUNCT
ejpam-2881	390	17	coincidence	coincidence	NOUN
ejpam-2881	390	18	and	and	CCONJ
ejpam-2881	390	19	common	common	ADJ
ejpam-2881	390	20	fixed	fix	VERB
ejpam-2881	390	21	point	point	NOUN
ejpam-2881	390	22	results	result	NOUN
ejpam-2881	390	23	in	in	ADP
ejpam-2881	390	24	partially	partially	ADV
ejpam-2881	390	25	ordered	order	VERB
ejpam-2881	390	26	cone	cone	NOUN
ejpam-2881	390	27	metric	metric	ADJ
ejpam-2881	390	28	spaces	space	NOUN
ejpam-2881	390	29	and	and	CCONJ
ejpam-2881	390	30	applications	application	NOUN
ejpam-2881	390	31	to	to	ADP
ejpam-2881	390	32	integral	integral	ADJ
ejpam-2881	390	33	equations	equation	NOUN
ejpam-2881	390	34	.	.	PUNCT
ejpam-2881	391	1	nonlinear	nonlinear	ADJ
ejpam-2881	391	2	anal	anal	NOUN
ejpam-2881	391	3	.	.	PUNCT
ejpam-2881	392	1	74	74	NUM
ejpam-2881	392	2	,	,	PUNCT
ejpam-2881	392	3	6814	6814	NUM
ejpam-2881	392	4	-	-	SYM
ejpam-2881	392	5	6825	6825	NUM
ejpam-2881	392	6	(	(	PUNCT
ejpam-2881	392	7	2011	2011	NUM
ejpam-2881	392	8	)	)	PUNCT
ejpam-2881	392	9	.	.	PUNCT
ejpam-2881	393	1	[	[	X
ejpam-2881	393	2	6	6	NUM
ejpam-2881	393	3	]	]	X
ejpam-2881	393	4	w.	w.	PROPN
ejpam-2881	393	5	shatanawi	shatanawi	PROPN
ejpam-2881	393	6	,	,	PUNCT
ejpam-2881	393	7	z.	z.	PROPN
ejpam-2881	393	8	mustafa	mustafa	PROPN
ejpam-2881	393	9	,	,	PUNCT
ejpam-2881	393	10	n.	n.	PROPN
ejpam-2881	393	11	tahat	tahat	PROPN
ejpam-2881	393	12	,	,	PUNCT
ejpam-2881	393	13	some	some	DET
ejpam-2881	393	14	coincidence	coincidence	NOUN
ejpam-2881	393	15	point	point	NOUN
ejpam-2881	393	16	theorems	theorem	NOUN
ejpam-2881	393	17	for	for	ADP
ejpam-2881	393	18	nonlinear	nonlinear	ADJ
ejpam-2881	393	19	,	,	PUNCT
ejpam-2881	393	20	contraction	contraction	NOUN
ejpam-2881	393	21	in	in	ADP
ejpam-2881	393	22	ordered	order	VERB
ejpam-2881	393	23	metric	metric	ADJ
ejpam-2881	393	24	spaces	space	NOUN
ejpam-2881	393	25	.	.	PUNCT
ejpam-2881	394	1	fixed	fix	VERB
ejpam-2881	394	2	point	point	NOUN
ejpam-2881	394	3	theory	theory	NOUN
ejpam-2881	394	4	and	and	CCONJ
ejpam-2881	394	5	applications	application	NOUN
ejpam-2881	394	6	2011	2011	NUM
ejpam-2881	394	7	,	,	PUNCT
ejpam-2881	394	8	68	68	NUM
ejpam-2881	394	9	(	(	PUNCT
ejpam-2881	394	10	2011	2011	NUM
ejpam-2881	394	11	)	)	PUNCT
ejpam-2881	394	12	.	.	PUNCT
ejpam-2881	395	1	[	[	X
ejpam-2881	395	2	7	7	X
ejpam-2881	395	3	]	]	X
ejpam-2881	395	4	m.	m.	NOUN
ejpam-2881	395	5	aamri	aamri	PROPN
ejpam-2881	395	6	,	,	PUNCT
ejpam-2881	395	7	d.	d.	PROPN
ejpam-2881	395	8	el	el	PROPN
ejpam-2881	395	9	moutawakil	moutawakil	PROPN
ejpam-2881	395	10	,	,	PUNCT
ejpam-2881	395	11	some	some	DET
ejpam-2881	395	12	new	new	ADJ
ejpam-2881	395	13	common	common	ADJ
ejpam-2881	395	14	fixed	fix	VERB
ejpam-2881	395	15	point	point	NOUN
ejpam-2881	395	16	theorems	theorem	NOUN
ejpam-2881	395	17	under	under	ADP
ejpam-2881	395	18	strict	strict	ADJ
ejpam-2881	395	19	contractive	contractive	ADJ
ejpam-2881	395	20	conditions	condition	NOUN
ejpam-2881	395	21	,	,	PUNCT
ejpam-2881	395	22	j.	j.	PROPN
ejpam-2881	395	23	math	math	PROPN
ejpam-2881	395	24	.	.	PUNCT
ejpam-2881	396	1	anal	anal	PROPN
ejpam-2881	396	2	.	.	PUNCT
ejpam-2881	397	1	appl	appl	PROPN
ejpam-2881	397	2	.	.	PUNCT
ejpam-2881	398	1	270(2002	270(2002	NUM
ejpam-2881	398	2	)	)	PUNCT
ejpam-2881	398	3	,	,	PUNCT
ejpam-2881	398	4	181	181	NUM
ejpam-2881	398	5	-	-	SYM
ejpam-2881	398	6	188	188	NUM
ejpam-2881	398	7	.	.	PUNCT
ejpam-2881	399	1	[	[	X
ejpam-2881	399	2	8	8	NUM
ejpam-2881	399	3	]	]	PUNCT
ejpam-2881	399	4	b.	b.	PROPN
ejpam-2881	399	5	azadifar	azadifar	PROPN
ejpam-2881	399	6	,	,	PUNCT
ejpam-2881	399	7	g.	g.	PROPN
ejpam-2881	399	8	sadeghi	sadeghi	PROPN
ejpam-2881	399	9	,	,	PUNCT
ejpam-2881	399	10	r.	r.	PROPN
ejpam-2881	399	11	saadati	saadati	PROPN
ejpam-2881	399	12	,	,	PUNCT
ejpam-2881	399	13	c.	c.	PROPN
ejpam-2881	399	14	park	park	PROPN
ejpam-2881	399	15	,	,	PUNCT
ejpam-2881	399	16	integral	integral	ADJ
ejpam-2881	399	17	type	type	NOUN
ejpam-2881	399	18	contractions	contraction	NOUN
ejpam-2881	399	19	in	in	ADP
ejpam-2881	399	20	modular	modular	ADJ
ejpam-2881	399	21	metric	metric	ADJ
ejpam-2881	399	22	spaces	space	NOUN
ejpam-2881	399	23	,	,	PUNCT
ejpam-2881	399	24	j.	j.	PROPN
ejpam-2881	399	25	inequal	inequal	PROPN
ejpam-2881	399	26	.	.	PUNCT
ejpam-2881	400	1	appl	appl	PROPN
ejpam-2881	400	2	.	.	PROPN
ejpam-2881	401	1	2013	2013	NUM
ejpam-2881	401	2	,	,	PUNCT
ejpam-2881	401	3	2013:483	2013:483	NOUN
ejpam-2881	401	4	.	.	PUNCT
ejpam-2881	402	1	[	[	X
ejpam-2881	402	2	9	9	NUM
ejpam-2881	402	3	]	]	X
ejpam-2881	402	4	v.	v.	PROPN
ejpam-2881	402	5	v.	v.	ADP
ejpam-2881	402	6	chistyakov	chistyakov	PROPN
ejpam-2881	402	7	,	,	PUNCT
ejpam-2881	402	8	a	a	DET
ejpam-2881	402	9	fixed	fix	VERB
ejpam-2881	402	10	point	point	NOUN
ejpam-2881	402	11	theorem	theorem	NOUN
ejpam-2881	402	12	for	for	ADP
ejpam-2881	402	13	contractions	contraction	NOUN
ejpam-2881	402	14	in	in	ADP
ejpam-2881	402	15	modular	modular	ADJ
ejpam-2881	402	16	metric	metric	ADJ
ejpam-2881	402	17	spaces	space	NOUN
ejpam-2881	402	18	,	,	PUNCT
ejpam-2881	402	19	perprint	perprint	NOUN
ejpam-2881	402	20	submited	submit	VERB
ejpam-2881	402	21	to	to	ADP
ejpam-2881	402	22	arxiv	arxiv	PROPN
ejpam-2881	402	23	(	(	PUNCT
ejpam-2881	402	24	2011	2011	NUM
ejpam-2881	402	25	)	)	PUNCT
ejpam-2881	402	26	.	.	PUNCT
ejpam-2881	403	1	[	[	X
ejpam-2881	403	2	10	10	NUM
ejpam-2881	403	3	]	]	X
ejpam-2881	403	4	p.	p.	NOUN
ejpam-2881	403	5	kumam	kumam	PROPN
ejpam-2881	403	6	,	,	PUNCT
ejpam-2881	403	7	fixed	fix	VERB
ejpam-2881	403	8	point	point	NOUN
ejpam-2881	403	9	theorems	theorem	NOUN
ejpam-2881	403	10	for	for	ADP
ejpam-2881	403	11	nonexpansive	nonexpansive	ADJ
ejpam-2881	403	12	mapping	mapping	NOUN
ejpam-2881	403	13	in	in	ADP
ejpam-2881	403	14	modular	modular	ADJ
ejpam-2881	403	15	spaces	space	NOUN
ejpam-2881	403	16	,	,	PUNCT
ejpam-2881	403	17	arch	arch	NOUN
ejpam-2881	403	18	.	.	PUNCT
ejpam-2881	404	1	math	math	NOUN
ejpam-2881	404	2	.	.	PUNCT
ejpam-2881	405	1	40(2004	40(2004	PROPN
ejpam-2881	405	2	)	)	PUNCT
ejpam-2881	405	3	,	,	PUNCT
ejpam-2881	405	4	345	345	NUM
ejpam-2881	405	5	-	-	SYM
ejpam-2881	405	6	353	353	NUM
ejpam-2881	405	7	.	.	PUNCT
ejpam-2881	406	1	[	[	X
ejpam-2881	406	2	11	11	NUM
ejpam-2881	406	3	]	]	PUNCT
ejpam-2881	406	4	a.	a.	NOUN
ejpam-2881	406	5	razani	razani	PROPN
ejpam-2881	406	6	,	,	PUNCT
ejpam-2881	406	7	e.	e.	PROPN
ejpam-2881	406	8	nabizadeh	nabizadeh	PROPN
ejpam-2881	406	9	,	,	PUNCT
ejpam-2881	406	10	m.	m.	NOUN
ejpam-2881	406	11	beyg	beyg	NOUN
ejpam-2881	406	12	mohamadi	mohamadi	NOUN
ejpam-2881	406	13	,	,	PUNCT
ejpam-2881	406	14	s.	s.	PROPN
ejpam-2881	406	15	homaeipour	homaeipour	PROPN
ejpam-2881	406	16	,	,	PUNCT
ejpam-2881	406	17	fixed	fix	VERB
ejpam-2881	406	18	point	point	NOUN
ejpam-2881	406	19	of	of	ADP
ejpam-2881	406	20	nonlinear	nonlinear	ADJ
ejpam-2881	406	21	and	and	CCONJ
ejpam-2881	406	22	asymptotic	asymptotic	ADJ
ejpam-2881	406	23	contractions	contraction	NOUN
ejpam-2881	406	24	in	in	ADP
ejpam-2881	406	25	the	the	DET
ejpam-2881	406	26	modular	modular	ADJ
ejpam-2881	406	27	space	space	NOUN
ejpam-2881	406	28	,	,	PUNCT
ejpam-2881	406	29	proc	proc	NOUN
ejpam-2881	406	30	.	.	PUNCT
ejpam-2881	407	1	amer	amer	PROPN
ejpam-2881	407	2	.	.	PUNCT
ejpam-2881	407	3	math	math	PROPN
ejpam-2881	407	4	.	.	PUNCT
ejpam-2881	408	1	soc	soc	PROPN
ejpam-2881	408	2	.	.	PUNCT
ejpam-2881	409	1	22(2009	22(2009	NUM
ejpam-2881	409	2	)	)	PUNCT
ejpam-2881	409	3	,	,	PUNCT
ejpam-2881	409	4	1877	1877	NUM
ejpam-2881	409	5	-	-	SYM
ejpam-2881	409	6	1881	1881	NUM
ejpam-2881	409	7	.	.	PUNCT
ejpam-2881	410	1	[	[	X
ejpam-2881	410	2	12	12	NUM
ejpam-2881	410	3	]	]	X
ejpam-2881	410	4	j.	j.	PROPN
ejpam-2881	410	5	mosielak	mosielak	PROPN
ejpam-2881	410	6	,	,	PUNCT
ejpam-2881	410	7	w.	w.	PROPN
ejpam-2881	410	8	orlicz	orlicz	PROPN
ejpam-2881	410	9	,	,	PUNCT
ejpam-2881	410	10	on	on	ADP
ejpam-2881	410	11	modular	modular	ADJ
ejpam-2881	410	12	spaces	space	NOUN
ejpam-2881	410	13	,	,	PUNCT
ejpam-2881	410	14	studia	studia	PROPN
ejpam-2881	410	15	math	math	NOUN
ejpam-2881	410	16	.	.	PUNCT
ejpam-2881	411	1	18(1959	18(1959	NUM
ejpam-2881	411	2	)	)	PUNCT
ejpam-2881	411	3	,	,	PUNCT
ejpam-2881	411	4	49	49	NUM
ejpam-2881	411	5	-	-	SYM
ejpam-2881	411	6	65	65	NUM
ejpam-2881	411	7	.	.	PUNCT
ejpam-2881	412	1	[	[	X
ejpam-2881	412	2	13	13	NUM
ejpam-2881	412	3	]	]	SYM
ejpam-2881	412	4	ph	ph	PROPN
ejpam-2881	412	5	.	.	PROPN
ejpam-2881	412	6	turpin	turpin	PROPN
ejpam-2881	412	7	,	,	PUNCT
ejpam-2881	412	8	fubini	fubini	ADJ
ejpam-2881	412	9	inequalities	inequality	NOUN
ejpam-2881	412	10	and	and	CCONJ
ejpam-2881	412	11	bounded	bound	VERB
ejpam-2881	412	12	multiplier	multipli	ADJ
ejpam-2881	412	13	property	property	NOUN
ejpam-2881	412	14	in	in	ADP
ejpam-2881	412	15	generalized	generalized	ADJ
ejpam-2881	412	16	modular	modular	ADJ
ejpam-2881	412	17	spaces	space	NOUN
ejpam-2881	412	18	,	,	PUNCT
ejpam-2881	412	19	comment	comment	NOUN
ejpam-2881	412	20	.	.	PUNCT
ejpam-2881	413	1	math	math	NOUN
ejpam-2881	413	2	.	.	PUNCT
ejpam-2881	414	1	tomus	tomus	PROPN
ejpam-2881	414	2	specialis	specialis	PROPN
ejpam-2881	414	3	in	in	ADP
ejpam-2881	414	4	honorem	honorem	ADJ
ejpam-2881	414	5	ladislai	ladislai	NOUN
ejpam-2881	414	6	orlicz	orlicz	NOUN
ejpam-2881	414	7	i	i	PRON
ejpam-2881	414	8	,	,	PUNCT
ejpam-2881	414	9	331	331	PROPN
ejpam-2881	414	10	-	-	SYM
ejpam-2881	414	11	353	353	NUM
ejpam-2881	414	12	(	(	PUNCT
ejpam-2881	414	13	1978	1978	NUM
ejpam-2881	414	14	)	)	PUNCT
ejpam-2881	414	15	.	.	PUNCT
ejpam-2881	415	1	[	[	X
ejpam-2881	415	2	14	14	NUM
ejpam-2881	415	3	]	]	X
ejpam-2881	415	4	d.	d.	PROPN
ejpam-2881	415	5	jain	jain	PROPN
ejpam-2881	415	6	,	,	PUNCT
ejpam-2881	415	7	a.	a.	NOUN
ejpam-2881	415	8	padcharoen	padcharoen	PROPN
ejpam-2881	415	9	,	,	PUNCT
ejpam-2881	415	10	p.	p.	PROPN
ejpam-2881	415	11	kumam	kumam	PROPN
ejpam-2881	415	12	,	,	PUNCT
ejpam-2881	415	13	d.	d.	PROPN
ejpam-2881	415	14	gopal	gopal	PROPN
ejpam-2881	415	15	,	,	PUNCT
ejpam-2881	415	16	a	a	DET
ejpam-2881	415	17	new	new	ADJ
ejpam-2881	415	18	approach	approach	NOUN
ejpam-2881	415	19	to	to	PART
ejpam-2881	415	20	study	study	VERB
ejpam-2881	415	21	fixed	fix	VERB
ejpam-2881	415	22	point	point	NOUN
ejpam-2881	415	23	of	of	ADP
ejpam-2881	415	24	multivalued	multivalue	VERB
ejpam-2881	415	25	mappings	mapping	NOUN
ejpam-2881	415	26	in	in	ADP
ejpam-2881	415	27	modular	modular	ADJ
ejpam-2881	415	28	metric	metric	ADJ
ejpam-2881	415	29	spaces	space	NOUN
ejpam-2881	415	30	and	and	CCONJ
ejpam-2881	415	31	applications	application	NOUN
ejpam-2881	415	32	,	,	PUNCT
ejpam-2881	415	33	mathematics	mathematics	NOUN
ejpam-2881	415	34	2016	2016	NUM
ejpam-2881	415	35	,	,	PUNCT
ejpam-2881	415	36	4(3	4(3	NUM
ejpam-2881	415	37	)	)	PUNCT
ejpam-2881	415	38	,	,	PUNCT
ejpam-2881	415	39	51	51	NUM
ejpam-2881	415	40	.	.	PUNCT
ejpam-2881	416	1	[	[	X
ejpam-2881	416	2	15	15	NUM
ejpam-2881	416	3	]	]	X
ejpam-2881	416	4	m.	m.	NOUN
ejpam-2881	416	5	beygmohammadi	beygmohammadi	NOUN
ejpam-2881	416	6	,	,	PUNCT
ejpam-2881	416	7	a.	a.	NOUN
ejpam-2881	416	8	razani	razani	PROPN
ejpam-2881	416	9	,	,	PUNCT
ejpam-2881	416	10	two	two	NUM
ejpam-2881	416	11	fixed	fix	VERB
ejpam-2881	416	12	point	point	NOUN
ejpam-2881	416	13	theorems	theorem	NOUN
ejpam-2881	416	14	for	for	ADP
ejpam-2881	416	15	mappings	mapping	NOUN
ejpam-2881	416	16	satisfying	satisfy	VERB
ejpam-2881	416	17	a	a	DET
ejpam-2881	416	18	general	general	ADJ
ejpam-2881	416	19	contractive	contractive	ADJ
ejpam-2881	416	20	condition	condition	NOUN
ejpam-2881	416	21	of	of	ADP
ejpam-2881	416	22	integral	integral	ADJ
ejpam-2881	416	23	type	type	NOUN
ejpam-2881	416	24	in	in	ADP
ejpam-2881	416	25	the	the	DET
ejpam-2881	416	26	modular	modular	ADJ
ejpam-2881	416	27	spaces	space	NOUN
ejpam-2881	416	28	,	,	PUNCT
ejpam-2881	416	29	internat	internat	PROPN
ejpam-2881	416	30	.	.	PUNCT
ejpam-2881	417	1	j.math	j.math	PROPN
ejpam-2881	417	2	.	.	PUNCT
ejpam-2881	418	1	sci	sci	PROPN
ejpam-2881	418	2	.	.	PROPN
ejpam-2881	418	3	2010	2010	NUM
ejpam-2881	418	4	,	,	PUNCT
ejpam-2881	418	5	art	art	NOUN
ejpam-2881	418	6	.	.	PUNCT
ejpam-2881	419	1	i	i	PRON
ejpam-2881	419	2	d	d	PROPN
ejpam-2881	419	3	317107	317107	NUM
ejpam-2881	419	4	,	,	PUNCT
ejpam-2881	419	5	10	10	NUM
ejpam-2881	419	6	pp	pp	NOUN
ejpam-2881	419	7	.	.	PUNCT
ejpam-2881	420	1	[	[	X
ejpam-2881	420	2	16	16	NUM
ejpam-2881	420	3	]	]	PUNCT
ejpam-2881	420	4	t.	t.	PROPN
ejpam-2881	420	5	dominguez	dominguez	PROPN
ejpam-2881	420	6	-	-	PUNCT
ejpam-2881	420	7	benavides	benavides	PROPN
ejpam-2881	420	8	,	,	PUNCT
ejpam-2881	420	9	m.a	m.a	PROPN
ejpam-2881	420	10	.	.	PROPN
ejpam-2881	420	11	khamsi	khamsi	PROPN
ejpam-2881	420	12	,	,	PUNCT
ejpam-2881	420	13	s.	s.	PROPN
ejpam-2881	420	14	samadi	samadi	PROPN
ejpam-2881	420	15	,	,	PUNCT
ejpam-2881	420	16	uniformly	uniformly	ADV
ejpam-2881	420	17	lipschitzian	lipschitzian	ADJ
ejpam-2881	420	18	mappings	mapping	NOUN
ejpam-2881	420	19	in	in	ADP
ejpam-2881	420	20	modular	modular	ADJ
ejpam-2881	420	21	function	function	NOUN
ejpam-2881	420	22	spaces	space	NOUN
ejpam-2881	420	23	,	,	PUNCT
ejpam-2881	420	24	nonlinear	nonlinear	ADJ
ejpam-2881	420	25	anal	anal	NOUN
ejpam-2881	420	26	.	.	PUNCT
ejpam-2881	421	1	46(2001	46(2001	PROPN
ejpam-2881	421	2	)	)	PUNCT
ejpam-2881	421	3	,	,	PUNCT
ejpam-2881	421	4	267	267	NUM
ejpam-2881	421	5	-	-	SYM
ejpam-2881	421	6	278	278	NUM
ejpam-2881	421	7	.	.	PUNCT
ejpam-2881	422	1	references	reference	NOUN
ejpam-2881	422	2	254	254	NUM
ejpam-2881	422	3	[	[	SYM
ejpam-2881	422	4	17	17	NUM
ejpam-2881	422	5	]	]	X
ejpam-2881	422	6	y.j.cho	y.j.cho	PROPN
ejpam-2881	422	7	,	,	PUNCT
ejpam-2881	422	8	r.	r.	PROPN
ejpam-2881	422	9	saadati	saadati	PROPN
ejpam-2881	422	10	,	,	PUNCT
ejpam-2881	422	11	g.	g.	PROPN
ejpam-2881	422	12	sadeghi	sadeghi	PROPN
ejpam-2881	422	13	,	,	PUNCT
ejpam-2881	422	14	quasi	quasi	ADJ
ejpam-2881	422	15	contraction	contraction	NOUN
ejpam-2881	422	16	mappings	mapping	NOUN
ejpam-2881	422	17	in	in	ADP
ejpam-2881	422	18	modular	modular	ADJ
ejpam-2881	422	19	metric	metric	ADJ
ejpam-2881	422	20	spaces	space	NOUN
ejpam-2881	422	21	.	.	PUNCT
ejpam-2881	423	1	journal	journal	NOUN
ejpam-2881	423	2	of	of	ADP
ejpam-2881	423	3	applied	apply	VERB
ejpam-2881	423	4	mathematics	mathematic	NOUN
ejpam-2881	423	5	volume	volume	NOUN
ejpam-2881	423	6	2012	2012	NUM
ejpam-2881	423	7	,	,	PUNCT
ejpam-2881	423	8	article	article	NOUN
ejpam-2881	423	9	i	i	PROPN
ejpam-2881	423	10	d	d	PROPN
ejpam-2881	423	11	907951	907951	NUM
ejpam-2881	423	12	,	,	PUNCT
ejpam-2881	423	13	5	5	NUM
ejpam-2881	423	14	pages	page	NOUN
ejpam-2881	423	15	.	.	PUNCT