id	sid	tid	token	lemma	pos
ejpam-77	1	1	3_rahmat.dvi	3_rahmat.dvi	NUM
ejpam-77	1	2	european	european	ADJ
ejpam-77	1	3	journal	journal	NOUN
ejpam-77	1	4	of	of	ADP
ejpam-77	1	5	pure	pure	ADJ
ejpam-77	1	6	and	and	CCONJ
ejpam-77	1	7	applied	apply	VERB
ejpam-77	1	8	mathematics	mathematic	NOUN
ejpam-77	1	9	vol	vol	NOUN
ejpam-77	1	10	.	.	PROPN
ejpam-77	2	1	2	2	NUM
ejpam-77	2	2	,	,	PUNCT
ejpam-77	2	3	no	no	INTJ
ejpam-77	2	4	.	.	NOUN
ejpam-77	2	5	2	2	NUM
ejpam-77	2	6	,	,	PUNCT
ejpam-77	2	7	2009	2009	NUM
ejpam-77	2	8	,	,	PUNCT
ejpam-77	2	9	(	(	PUNCT
ejpam-77	2	10	195	195	NUM
ejpam-77	2	11	-	-	PUNCT
ejpam-77	2	12	212	212	NUM
ejpam-77	2	13	)	)	PUNCT
ejpam-77	2	14	issn	issn	PROPN
ejpam-77	2	15	1307	1307	NUM
ejpam-77	2	16	-	-	SYM
ejpam-77	2	17	5543	5543	NUM
ejpam-77	2	18	–	–	PUNCT
ejpam-77	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-77	2	20	on	on	ADP
ejpam-77	2	21	i	i	PROPN
ejpam-77	2	22	-convergence	-convergence	PROPN
ejpam-77	2	23	in	in	ADP
ejpam-77	2	24	the	the	DET
ejpam-77	2	25	topology	topology	NOUN
ejpam-77	2	26	induced	induce	VERB
ejpam-77	2	27	by	by	ADP
ejpam-77	2	28	probabilistic	probabilistic	ADJ
ejpam-77	2	29	norms	norm	NOUN
ejpam-77	2	30	m.	m.	PROPN
ejpam-77	2	31	r.	r.	PROPN
ejpam-77	2	32	s.	s.	PROPN
ejpam-77	2	33	rahmat∗	rahmat∗	PROPN
ejpam-77	2	34	and	and	CCONJ
ejpam-77	2	35	harikrishnan	harikrishnan	PROPN
ejpam-77	2	36	k.	k.	PROPN
ejpam-77	2	37	k.	k.	PROPN
ejpam-77	3	1	school	school	PROPN
ejpam-77	3	2	of	of	ADP
ejpam-77	3	3	applied	apply	VERB
ejpam-77	3	4	mathematics	mathematic	NOUN
ejpam-77	3	5	,	,	PUNCT
ejpam-77	3	6	the	the	DET
ejpam-77	3	7	university	university	PROPN
ejpam-77	3	8	of	of	ADP
ejpam-77	3	9	nottingham	nottingham	PROPN
ejpam-77	3	10	malaysia	malaysia	PROPN
ejpam-77	3	11	campus	campus	PROPN
ejpam-77	3	12	jalan	jalan	PROPN
ejpam-77	3	13	broga	broga	PROPN
ejpam-77	3	14	,	,	PUNCT
ejpam-77	3	15	43500	43500	NUM
ejpam-77	3	16	semenyih	semenyih	NOUN
ejpam-77	3	17	,	,	PUNCT
ejpam-77	3	18	selangor	selangor	PROPN
ejpam-77	3	19	darul	darul	PROPN
ejpam-77	3	20	ehsan	ehsan	PROPN
ejpam-77	3	21	,	,	PUNCT
ejpam-77	3	22	malaysia	malaysia	PROPN
ejpam-77	3	23	abstract	abstract	NOUN
ejpam-77	3	24	.	.	PUNCT
ejpam-77	4	1	the	the	DET
ejpam-77	4	2	concepts	concept	NOUN
ejpam-77	4	3	of	of	ADP
ejpam-77	4	4	i	i	PROPN
ejpam-77	4	5	-convergence	-convergence	PROPN
ejpam-77	4	6	is	be	AUX
ejpam-77	4	7	a	a	DET
ejpam-77	4	8	natural	natural	ADJ
ejpam-77	4	9	generalization	generalization	NOUN
ejpam-77	4	10	of	of	ADP
ejpam-77	4	11	statistical	statistical	ADJ
ejpam-77	4	12	convergence	convergence	NOUN
ejpam-77	4	13	and	and	CCONJ
ejpam-77	4	14	it	it	PRON
ejpam-77	4	15	is	be	AUX
ejpam-77	4	16	dependent	dependent	ADJ
ejpam-77	4	17	on	on	ADP
ejpam-77	4	18	the	the	DET
ejpam-77	4	19	notion	notion	NOUN
ejpam-77	4	20	of	of	ADP
ejpam-77	4	21	the	the	DET
ejpam-77	4	22	ideal	ideal	NOUN
ejpam-77	4	23	of	of	ADP
ejpam-77	4	24	subsets	subset	NOUN
ejpam-77	4	25	of	of	ADP
ejpam-77	4	26	n	n	PROPN
ejpam-77	4	27	of	of	ADP
ejpam-77	4	28	positive	positive	ADJ
ejpam-77	4	29	integer	integer	NOUN
ejpam-77	4	30	set	set	NOUN
ejpam-77	4	31	.	.	PUNCT
ejpam-77	5	1	in	in	ADP
ejpam-77	5	2	this	this	DET
ejpam-77	5	3	paper	paper	NOUN
ejpam-77	5	4	we	we	PRON
ejpam-77	5	5	study	study	VERB
ejpam-77	5	6	the	the	DET
ejpam-77	5	7	i	i	PROPN
ejpam-77	5	8	-convergence	-convergence	PROPN
ejpam-77	5	9	of	of	ADP
ejpam-77	5	10	sequences	sequence	NOUN
ejpam-77	5	11	,	,	PUNCT
ejpam-77	5	12	i	i	PRON
ejpam-77	5	13	-convergence	-convergence	NOUN
ejpam-77	5	14	of	of	ADP
ejpam-77	5	15	sequences	sequence	NOUN
ejpam-77	5	16	of	of	ADP
ejpam-77	5	17	functions	function	NOUN
ejpam-77	5	18	and	and	CCONJ
ejpam-77	5	19	i	i	PRON
ejpam-77	5	20	-cauchy	-cauchy	VERB
ejpam-77	5	21	sequences	sequence	NOUN
ejpam-77	5	22	in	in	ADP
ejpam-77	5	23	probabilistic	probabilistic	ADJ
ejpam-77	5	24	normed	normed	ADJ
ejpam-77	5	25	spaces	space	NOUN
ejpam-77	5	26	and	and	CCONJ
ejpam-77	5	27	prove	prove	VERB
ejpam-77	5	28	some	some	DET
ejpam-77	5	29	important	important	ADJ
ejpam-77	5	30	results	result	NOUN
ejpam-77	5	31	.	.	PUNCT
ejpam-77	6	1	ams	am	NOUN
ejpam-77	6	2	subject	subject	ADJ
ejpam-77	6	3	classifications	classification	NOUN
ejpam-77	6	4	:	:	PUNCT
ejpam-77	6	5	47h10	47h10	NUM
ejpam-77	6	6	,	,	PUNCT
ejpam-77	6	7	54e17	54e17	NUM
ejpam-77	6	8	,	,	PUNCT
ejpam-77	6	9	54e50	54e50	NUM
ejpam-77	6	10	,	,	PUNCT
ejpam-77	6	11	54e70	54e70	NUM
ejpam-77	6	12	key	key	ADJ
ejpam-77	6	13	words	word	NOUN
ejpam-77	6	14	:	:	PUNCT
ejpam-77	6	15	probabilistic	probabilistic	ADJ
ejpam-77	6	16	norms	norm	NOUN
ejpam-77	6	17	,	,	PUNCT
ejpam-77	6	18	ideal	ideal	ADJ
ejpam-77	6	19	convergence	convergence	NOUN
ejpam-77	6	20	,	,	PUNCT
ejpam-77	6	21	statistical	statistical	ADJ
ejpam-77	6	22	convergence	convergence	NOUN
ejpam-77	6	23	,	,	PUNCT
ejpam-77	6	24	ideal	ideal	ADJ
ejpam-77	6	25	cauchy	cauchy	ADJ
ejpam-77	6	26	sequences	sequence	NOUN
ejpam-77	6	27	,	,	PUNCT
ejpam-77	6	28	f	f	X
ejpam-77	6	29	-	-	PUNCT
ejpam-77	6	30	topology	topology	NOUN
ejpam-77	6	31	∗corresponding	∗corresponde	VERB
ejpam-77	6	32	author	author	NOUN
ejpam-77	6	33	.	.	PUNCT
ejpam-77	7	1	email	email	NOUN
ejpam-77	7	2	addresses	address	NOUN
ejpam-77	7	3	:	:	PUNCT
ejpam-77	7	4	mohd.rafi�nottingham.edu.my	mohd.rafi�nottingham.edu.my	NOUN
ejpam-77	7	5	(	(	PUNCT
ejpam-77	7	6	m.	m.	NOUN
ejpam-77	7	7	rahmat),harikrishnan.kk	rahmat),harikrishnan.kk	PROPN
ejpam-77	7	8	�	�	PROPN
ejpam-77	7	9	nottingham.edu.my	nottingham.edu.my	PUNCT
ejpam-77	7	10	(	(	PUNCT
ejpam-77	7	11	harikrishnan	harikrishnan	PROPN
ejpam-77	7	12	k.	k.	PROPN
ejpam-77	7	13	)	)	PUNCT
ejpam-77	7	14	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-77	8	1	195	195	NUM
ejpam-77	8	2	c	c	NOUN
ejpam-77	8	3	©	©	PROPN
ejpam-77	8	4	2009	2009	NUM
ejpam-77	8	5	ejpam	ejpam	NOUN
ejpam-77	8	6	all	all	DET
ejpam-77	8	7	rights	right	NOUN
ejpam-77	8	8	reserved	reserve	VERB
ejpam-77	8	9	.	.	PUNCT
ejpam-77	9	1	m.	m.	NOUN
ejpam-77	9	2	rahmat	rahmat	PROPN
ejpam-77	9	3	and	and	CCONJ
ejpam-77	9	4	harikrishnan	harikrishnan	PROPN
ejpam-77	9	5	k.	k.	PROPN
ejpam-77	9	6	/	/	PUNCT
ejpam-77	9	7	eur	eur	PROPN
ejpam-77	9	8	.	.	PUNCT
ejpam-77	10	1	j.	j.	PROPN
ejpam-77	10	2	pure	pure	PROPN
ejpam-77	10	3	appl	appl	PROPN
ejpam-77	10	4	.	.	PROPN
ejpam-77	10	5	math	math	PROPN
ejpam-77	10	6	,	,	PUNCT
ejpam-77	10	7	2	2	NUM
ejpam-77	10	8	(	(	PUNCT
ejpam-77	10	9	2009	2009	NUM
ejpam-77	10	10	)	)	PUNCT
ejpam-77	10	11	,	,	PUNCT
ejpam-77	10	12	(	(	PUNCT
ejpam-77	10	13	195	195	NUM
ejpam-77	10	14	-	-	PUNCT
ejpam-77	10	15	212	212	NUM
ejpam-77	10	16	)	)	PUNCT
ejpam-77	10	17	196	196	NUM
ejpam-77	10	18	1	1	NUM
ejpam-77	10	19	.	.	PUNCT
ejpam-77	11	1	introduction	introduction	NOUN
ejpam-77	11	2	the	the	DET
ejpam-77	11	3	concepts	concept	NOUN
ejpam-77	11	4	of	of	ADP
ejpam-77	11	5	statistical	statistical	ADJ
ejpam-77	11	6	convergence	convergence	NOUN
ejpam-77	11	7	was	be	AUX
ejpam-77	11	8	introduced	introduce	VERB
ejpam-77	11	9	(	(	PUNCT
ejpam-77	11	10	independently	independently	ADV
ejpam-77	11	11	)	)	PUNCT
ejpam-77	11	12	by	by	ADP
ejpam-77	11	13	fast	fast	ADJ
ejpam-77	11	14	[	[	X
ejpam-77	11	15	7	7	NUM
ejpam-77	11	16	]	]	PUNCT
ejpam-77	11	17	and	and	CCONJ
ejpam-77	11	18	steinhause	steinhause	NOUN
ejpam-77	11	19	[	[	X
ejpam-77	11	20	25	25	NUM
ejpam-77	11	21	]	]	PUNCT
ejpam-77	11	22	.	.	PUNCT
ejpam-77	12	1	in	in	ADP
ejpam-77	12	2	their	their	PRON
ejpam-77	12	3	studies	study	NOUN
ejpam-77	12	4	,	,	PUNCT
ejpam-77	12	5	the	the	DET
ejpam-77	12	6	concept	concept	NOUN
ejpam-77	12	7	of	of	ADP
ejpam-77	12	8	ordinary	ordinary	ADJ
ejpam-77	12	9	convergence	convergence	NOUN
ejpam-77	12	10	of	of	ADP
ejpam-77	12	11	sequence	sequence	NOUN
ejpam-77	12	12	of	of	ADP
ejpam-77	12	13	real	real	ADJ
ejpam-77	12	14	numbers	number	NOUN
ejpam-77	12	15	was	be	AUX
ejpam-77	12	16	extended	extend	VERB
ejpam-77	12	17	to	to	ADP
ejpam-77	12	18	statistical	statistical	ADJ
ejpam-77	12	19	convergence	convergence	NOUN
ejpam-77	12	20	in	in	ADP
ejpam-77	12	21	the	the	DET
ejpam-77	12	22	following	following	ADJ
ejpam-77	12	23	way	way	NOUN
ejpam-77	12	24	:	:	PUNCT
ejpam-77	12	25	a	a	DET
ejpam-77	12	26	sequence	sequence	NOUN
ejpam-77	12	27	{	{	PUNCT
ejpam-77	12	28	xn	xn	PROPN
ejpam-77	12	29	}	}	PUNCT
ejpam-77	12	30	⊂	⊂	X
ejpam-77	13	1	r	r	NOUN
ejpam-77	13	2	is	be	AUX
ejpam-77	13	3	said	say	VERB
ejpam-77	13	4	to	to	PART
ejpam-77	13	5	be	be	AUX
ejpam-77	13	6	statistically	statistically	ADV
ejpam-77	13	7	convergent	convergent	ADJ
ejpam-77	13	8	to	to	ADP
ejpam-77	13	9	the	the	DET
ejpam-77	13	10	real	real	ADJ
ejpam-77	13	11	number	number	NOUN
ejpam-77	13	12	x0	x0	PROPN
ejpam-77	13	13	∈	∈	PROPN
ejpam-77	13	14	r	r	NOUN
ejpam-77	13	15	provided	provide	VERB
ejpam-77	13	16	that	that	SCONJ
ejpam-77	13	17	each	each	DET
ejpam-77	13	18	ε	ε	PROPN
ejpam-77	13	19	neighborhood	neighborhood	NOUN
ejpam-77	13	20	nε(x0	nε(x0	NOUN
ejpam-77	13	21	)	)	PUNCT
ejpam-77	13	22	of	of	ADP
ejpam-77	13	23	x0	x0	PROPN
ejpam-77	13	24	,	,	PUNCT
ejpam-77	13	25	the	the	DET
ejpam-77	13	26	set	set	NOUN
ejpam-77	13	27	consisting	consist	VERB
ejpam-77	13	28	of	of	ADP
ejpam-77	13	29	all	all	DET
ejpam-77	13	30	elements	element	NOUN
ejpam-77	13	31	not	not	PART
ejpam-77	13	32	contained	contain	VERB
ejpam-77	13	33	by	by	ADP
ejpam-77	13	34	nε(x0	nε(x0	NUM
ejpam-77	13	35	)	)	PUNCT
ejpam-77	13	36	has	have	VERB
ejpam-77	13	37	natural	natural	ADJ
ejpam-77	13	38	density	density	NOUN
ejpam-77	13	39	zero	zero	NUM
ejpam-77	13	40	for	for	ADP
ejpam-77	13	41	any	any	DET
ejpam-77	13	42	ε	ε	PROPN
ejpam-77	13	43	>	>	X
ejpam-77	13	44	0	0	PROPN
ejpam-77	13	45	.	.	PUNCT
ejpam-77	14	1	the	the	DET
ejpam-77	14	2	notion	notion	NOUN
ejpam-77	14	3	of	of	ADP
ejpam-77	14	4	natural	natural	ADJ
ejpam-77	14	5	density	density	NOUN
ejpam-77	14	6	here	here	ADV
ejpam-77	14	7	can	can	AUX
ejpam-77	14	8	be	be	AUX
ejpam-77	14	9	described	describe	VERB
ejpam-77	14	10	as	as	ADP
ejpam-77	14	11	a	a	DET
ejpam-77	14	12	function	function	NOUN
ejpam-77	14	13	δ	δ	NOUN
ejpam-77	14	14	:	:	PUNCT
ejpam-77	14	15	2n	2n	NUM
ejpam-77	14	16	→	→	PUNCT
ejpam-77	14	17	[	[	X
ejpam-77	14	18	0	0	NUM
ejpam-77	14	19	,	,	PUNCT
ejpam-77	14	20	1	1	NUM
ejpam-77	14	21	]	]	PUNCT
ejpam-77	14	22	and	and	CCONJ
ejpam-77	14	23	given	give	VERB
ejpam-77	14	24	by	by	ADP
ejpam-77	14	25	δ(k	δ(k	NOUN
ejpam-77	14	26	)	)	PUNCT
ejpam-77	14	27	:	:	PUNCT
ejpam-77	15	1	=	=	SYM
ejpam-77	15	2	limn→∞	limn→∞	PROPN
ejpam-77	15	3	n−1|{k	n−1|{k	PROPN
ejpam-77	15	4	∈	∈	PROPN
ejpam-77	15	5	k	k	NOUN
ejpam-77	15	6	:	:	PUNCT
ejpam-77	15	7	k	k	X
ejpam-77	15	8	≤	≤	PROPN
ejpam-77	15	9	n}|	n}|	VERB
ejpam-77	15	10	where	where	SCONJ
ejpam-77	15	11	k	k	PROPN
ejpam-77	15	12	⊂	⊂	PROPN
ejpam-77	15	13	n	n	CCONJ
ejpam-77	15	14	,	,	PUNCT
ejpam-77	15	15	and	and	CCONJ
ejpam-77	15	16	|a|	|a|	NOUN
ejpam-77	15	17	denotes	denote	VERB
ejpam-77	15	18	the	the	DET
ejpam-77	15	19	cardinality	cardinality	NOUN
ejpam-77	15	20	of	of	ADP
ejpam-77	15	21	the	the	DET
ejpam-77	15	22	set	set	NOUN
ejpam-77	15	23	a.	a.	NOUN
ejpam-77	15	24	the	the	DET
ejpam-77	15	25	concept	concept	NOUN
ejpam-77	15	26	of	of	ADP
ejpam-77	15	27	statistical	statistical	ADJ
ejpam-77	15	28	convergence	convergence	NOUN
ejpam-77	15	29	was	be	AUX
ejpam-77	15	30	further	far	ADV
ejpam-77	15	31	discussed	discuss	VERB
ejpam-77	15	32	and	and	CCONJ
ejpam-77	15	33	developed	develop	VERB
ejpam-77	15	34	by	by	ADP
ejpam-77	15	35	many	many	ADJ
ejpam-77	15	36	authors	author	NOUN
ejpam-77	15	37	including	include	VERB
ejpam-77	15	38	[	[	X
ejpam-77	15	39	1,4,8–11,19,21	1,4,8–11,19,21	NUM
ejpam-77	15	40	]	]	PUNCT
ejpam-77	15	41	.	.	PUNCT
ejpam-77	16	1	statistical	statistical	ADJ
ejpam-77	16	2	convergence	convergence	NOUN
ejpam-77	16	3	has	have	AUX
ejpam-77	16	4	also	also	ADV
ejpam-77	16	5	been	be	AUX
ejpam-77	16	6	discussed	discuss	VERB
ejpam-77	16	7	in	in	ADP
ejpam-77	16	8	more	more	ADJ
ejpam-77	16	9	general	general	ADJ
ejpam-77	16	10	abstract	abstract	ADJ
ejpam-77	16	11	spaces	space	NOUN
ejpam-77	16	12	such	such	ADJ
ejpam-77	16	13	as	as	ADP
ejpam-77	16	14	the	the	DET
ejpam-77	16	15	fuzzy	fuzzy	ADJ
ejpam-77	16	16	number	number	NOUN
ejpam-77	16	17	spaces	space	VERB
ejpam-77	16	18	[	[	X
ejpam-77	16	19	22	22	NUM
ejpam-77	16	20	]	]	PUNCT
ejpam-77	16	21	,	,	PUNCT
ejpam-77	16	22	locally	locally	ADV
ejpam-77	16	23	convex	convex	NOUN
ejpam-77	16	24	spaces	space	NOUN
ejpam-77	16	25	[	[	X
ejpam-77	16	26	18	18	NUM
ejpam-77	16	27	]	]	PUNCT
ejpam-77	16	28	,	,	PUNCT
ejpam-77	16	29	banach	banach	NOUN
ejpam-77	16	30	spaces	space	VERB
ejpam-77	16	31	[	[	X
ejpam-77	16	32	15	15	NUM
ejpam-77	16	33	]	]	PUNCT
ejpam-77	16	34	and	and	CCONJ
ejpam-77	16	35	characterization	characterization	NOUN
ejpam-77	16	36	of	of	ADP
ejpam-77	16	37	banach	banach	NOUN
ejpam-77	16	38	spaces	space	NOUN
ejpam-77	16	39	[	[	X
ejpam-77	16	40	5	5	NUM
ejpam-77	16	41	]	]	PUNCT
ejpam-77	16	42	.	.	PUNCT
ejpam-77	17	1	recently	recently	ADV
ejpam-77	17	2	,	,	PUNCT
ejpam-77	17	3	karakus	karaku	VERB
ejpam-77	17	4	[	[	PUNCT
ejpam-77	17	5	13	13	NUM
ejpam-77	17	6	]	]	PUNCT
ejpam-77	17	7	has	have	AUX
ejpam-77	17	8	extended	extend	VERB
ejpam-77	17	9	the	the	DET
ejpam-77	17	10	concept	concept	NOUN
ejpam-77	17	11	of	of	ADP
ejpam-77	17	12	statistical	statistical	ADJ
ejpam-77	17	13	convergence	convergence	NOUN
ejpam-77	17	14	for	for	ADP
ejpam-77	17	15	sequences	sequence	NOUN
ejpam-77	17	16	in	in	ADP
ejpam-77	17	17	probabilistic	probabilistic	ADJ
ejpam-77	17	18	normed	norme	VERB
ejpam-77	17	19	spaces	space	NOUN
ejpam-77	17	20	(	(	PUNCT
ejpam-77	17	21	pn	pn	NOUN
ejpam-77	17	22	space	space	NOUN
ejpam-77	17	23	)	)	PUNCT
ejpam-77	17	24	and	and	CCONJ
ejpam-77	17	25	proved	prove	VERB
ejpam-77	17	26	several	several	ADJ
ejpam-77	17	27	interesting	interesting	ADJ
ejpam-77	17	28	results	result	NOUN
ejpam-77	17	29	.	.	PUNCT
ejpam-77	18	1	in	in	ADP
ejpam-77	18	2	another	another	DET
ejpam-77	18	3	paper	paper	NOUN
ejpam-77	18	4	,	,	PUNCT
ejpam-77	18	5	karakus	karaku	NOUN
ejpam-77	18	6	and	and	CCONJ
ejpam-77	18	7	demirci	demirci	VERB
ejpam-77	18	8	[	[	X
ejpam-77	18	9	14	14	NUM
ejpam-77	18	10	]	]	PUNCT
ejpam-77	18	11	studied	study	VERB
ejpam-77	18	12	the	the	DET
ejpam-77	18	13	concept	concept	NOUN
ejpam-77	18	14	of	of	ADP
ejpam-77	18	15	statistical	statistical	ADJ
ejpam-77	18	16	convergence	convergence	NOUN
ejpam-77	18	17	of	of	ADP
ejpam-77	18	18	double	double	ADJ
ejpam-77	18	19	sequences	sequence	NOUN
ejpam-77	18	20	on	on	ADP
ejpam-77	18	21	pn	pn	PROPN
ejpam-77	18	22	spaces	space	NOUN
ejpam-77	18	23	.	.	PUNCT
ejpam-77	19	1	the	the	DET
ejpam-77	19	2	idea	idea	NOUN
ejpam-77	19	3	of	of	ADP
ejpam-77	19	4	i	i	PRON
ejpam-77	19	5	-convergence	-convergence	PROPN
ejpam-77	19	6	for	for	ADP
ejpam-77	19	7	sequences	sequence	NOUN
ejpam-77	19	8	,	,	PUNCT
ejpam-77	19	9	was	be	AUX
ejpam-77	19	10	inspired	inspire	VERB
ejpam-77	19	11	by	by	ADP
ejpam-77	19	12	the	the	DET
ejpam-77	19	13	concept	concept	NOUN
ejpam-77	19	14	of	of	ADP
ejpam-77	19	15	statistical	statistical	ADJ
ejpam-77	19	16	convergence	convergence	NOUN
ejpam-77	19	17	introduced	introduce	VERB
ejpam-77	19	18	in	in	ADP
ejpam-77	19	19	[	[	X
ejpam-77	19	20	7	7	NUM
ejpam-77	19	21	]	]	PUNCT
ejpam-77	19	22	,	,	PUNCT
ejpam-77	19	23	see	see	VERB
ejpam-77	19	24	kostyrko	kostyrko	PROPN
ejpam-77	19	25	et	et	PROPN
ejpam-77	19	26	al	al	PROPN
ejpam-77	19	27	.	.	PUNCT
ejpam-77	20	1	[	[	X
ejpam-77	20	2	16	16	NUM
ejpam-77	20	3	]	]	PUNCT
ejpam-77	20	4	for	for	ADP
ejpam-77	20	5	a	a	DET
ejpam-77	20	6	comprehensive	comprehensive	ADJ
ejpam-77	20	7	bibliography	bibliography	NOUN
ejpam-77	20	8	.	.	PUNCT
ejpam-77	21	1	it	it	PRON
ejpam-77	21	2	is	be	AUX
ejpam-77	21	3	a	a	DET
ejpam-77	21	4	natural	natural	ADJ
ejpam-77	21	5	generalization	generalization	NOUN
ejpam-77	21	6	of	of	ADP
ejpam-77	21	7	the	the	DET
ejpam-77	21	8	concept	concept	NOUN
ejpam-77	21	9	of	of	ADP
ejpam-77	21	10	statistical	statistical	ADJ
ejpam-77	21	11	convergence	convergence	NOUN
ejpam-77	21	12	.	.	PUNCT
ejpam-77	22	1	the	the	DET
ejpam-77	22	2	i	i	PROPN
ejpam-77	22	3	-convergence	-convergence	PROPN
ejpam-77	22	4	is	be	AUX
ejpam-77	22	5	based	base	VERB
ejpam-77	22	6	on	on	ADP
ejpam-77	22	7	the	the	DET
ejpam-77	22	8	notion	notion	NOUN
ejpam-77	22	9	of	of	ADP
ejpam-77	22	10	the	the	DET
ejpam-77	22	11	ideal	ideal	NOUN
ejpam-77	22	12	i	i	PRON
ejpam-77	22	13	of	of	ADP
ejpam-77	22	14	subsets	subset	NOUN
ejpam-77	22	15	of	of	ADP
ejpam-77	22	16	n	n	CCONJ
ejpam-77	22	17	,	,	PUNCT
ejpam-77	22	18	the	the	DET
ejpam-77	22	19	set	set	NOUN
ejpam-77	22	20	of	of	ADP
ejpam-77	22	21	positive	positive	ADJ
ejpam-77	22	22	integers	integer	NOUN
ejpam-77	22	23	.	.	PUNCT
ejpam-77	23	1	here	here	ADV
ejpam-77	23	2	,	,	PUNCT
ejpam-77	23	3	a	a	DET
ejpam-77	23	4	sequence	sequence	NOUN
ejpam-77	23	5	{	{	PUNCT
ejpam-77	23	6	xn	xn	PROPN
ejpam-77	23	7	}	}	PUNCT
ejpam-77	23	8	⊂	⊂	X
ejpam-77	24	1	r	r	NOUN
ejpam-77	24	2	is	be	AUX
ejpam-77	24	3	said	say	VERB
ejpam-77	24	4	to	to	PART
ejpam-77	24	5	be	be	AUX
ejpam-77	24	6	i	i	PRON
ejpam-77	24	7	-convergent	-convergent	ADJ
ejpam-77	24	8	to	to	ADP
ejpam-77	24	9	the	the	DET
ejpam-77	24	10	real	real	ADJ
ejpam-77	24	11	number	number	NOUN
ejpam-77	24	12	x0	x0	PROPN
ejpam-77	24	13	∈	∈	PROPN
ejpam-77	24	14	r	r	NOUN
ejpam-77	24	15	provided	provide	VERB
ejpam-77	24	16	that	that	SCONJ
ejpam-77	24	17	each	each	DET
ejpam-77	24	18	ε	ε	PROPN
ejpam-77	24	19	neighborhood	neighborhood	NOUN
ejpam-77	24	20	nε(x0	nε(x0	NOUN
ejpam-77	24	21	)	)	PUNCT
ejpam-77	24	22	of	of	ADP
ejpam-77	24	23	x0	x0	PROPN
ejpam-77	24	24	,	,	PUNCT
ejpam-77	24	25	the	the	DET
ejpam-77	24	26	set	set	NOUN
ejpam-77	24	27	consisting	consist	VERB
ejpam-77	24	28	of	of	ADP
ejpam-77	24	29	all	all	DET
ejpam-77	24	30	elements	element	NOUN
ejpam-77	24	31	not	not	PART
ejpam-77	24	32	contained	contain	VERB
ejpam-77	24	33	by	by	ADP
ejpam-77	24	34	nε(x0	nε(x0	NUM
ejpam-77	24	35	)	)	PUNCT
ejpam-77	24	36	belongs	belong	VERB
ejpam-77	24	37	to	to	ADP
ejpam-77	24	38	i	i	PRON
ejpam-77	24	39	for	for	ADP
ejpam-77	24	40	any	any	DET
ejpam-77	24	41	ε	ε	PROPN
ejpam-77	24	42	>	>	X
ejpam-77	24	43	0	0	X
ejpam-77	24	44	.	.	PUNCT
ejpam-77	25	1	further	further	PROPN
ejpam-77	25	2	works	work	VERB
ejpam-77	25	3	on	on	ADP
ejpam-77	25	4	ideal	ideal	ADJ
ejpam-77	25	5	convergence	convergence	NOUN
ejpam-77	25	6	can	can	AUX
ejpam-77	25	7	be	be	AUX
ejpam-77	25	8	found	find	VERB
ejpam-77	25	9	in	in	ADP
ejpam-77	25	10	[	[	X
ejpam-77	25	11	2,3,6,12,17,20	2,3,6,12,17,20	NUM
ejpam-77	25	12	]	]	X
ejpam-77	25	13	the	the	DET
ejpam-77	25	14	work	work	NOUN
ejpam-77	25	15	of	of	ADP
ejpam-77	25	16	karakus	karakus	NOUN
ejpam-77	26	1	[	[	X
ejpam-77	26	2	13	13	NUM
ejpam-77	26	3	]	]	PUNCT
ejpam-77	26	4	inspired	inspire	VERB
ejpam-77	26	5	us	we	PRON
ejpam-77	26	6	to	to	PART
ejpam-77	26	7	study	study	VERB
ejpam-77	26	8	the	the	DET
ejpam-77	26	9	i	i	PROPN
ejpam-77	26	10	-convergence	-convergence	PROPN
ejpam-77	26	11	and	and	CCONJ
ejpam-77	26	12	other	other	ADJ
ejpam-77	26	13	related	related	ADJ
ejpam-77	26	14	properties	property	NOUN
ejpam-77	26	15	in	in	ADP
ejpam-77	26	16	pn	pn	PROPN
ejpam-77	26	17	spaces	space	NOUN
ejpam-77	26	18	.	.	PUNCT
ejpam-77	27	1	in	in	ADP
ejpam-77	27	2	this	this	DET
ejpam-77	27	3	context	context	NOUN
ejpam-77	27	4	,	,	PUNCT
ejpam-77	27	5	we	we	PRON
ejpam-77	27	6	obtain	obtain	VERB
ejpam-77	27	7	m.	m.	NOUN
ejpam-77	27	8	rahmat	rahmat	NOUN
ejpam-77	27	9	and	and	CCONJ
ejpam-77	27	10	harikrishnan	harikrishnan	PROPN
ejpam-77	27	11	k.	k.	PROPN
ejpam-77	27	12	/	/	PUNCT
ejpam-77	27	13	eur	eur	PROPN
ejpam-77	27	14	.	.	PUNCT
ejpam-77	28	1	j.	j.	PROPN
ejpam-77	28	2	pure	pure	PROPN
ejpam-77	28	3	appl	appl	PROPN
ejpam-77	28	4	.	.	PROPN
ejpam-77	28	5	math	math	PROPN
ejpam-77	28	6	,	,	PUNCT
ejpam-77	28	7	2	2	NUM
ejpam-77	28	8	(	(	PUNCT
ejpam-77	28	9	2009	2009	NUM
ejpam-77	28	10	)	)	PUNCT
ejpam-77	28	11	,	,	PUNCT
ejpam-77	28	12	(	(	PUNCT
ejpam-77	28	13	195	195	NUM
ejpam-77	28	14	-	-	PUNCT
ejpam-77	28	15	212	212	NUM
ejpam-77	28	16	)	)	PUNCT
ejpam-77	28	17	197	197	NUM
ejpam-77	28	18	some	some	DET
ejpam-77	28	19	results	result	NOUN
ejpam-77	28	20	that	that	PRON
ejpam-77	28	21	parallel	parallel	VERB
ejpam-77	28	22	to	to	ADP
ejpam-77	28	23	the	the	DET
ejpam-77	28	24	one	one	NOUN
ejpam-77	28	25	given	give	VERB
ejpam-77	28	26	in	in	ADP
ejpam-77	28	27	[	[	X
ejpam-77	28	28	3,12,20,24	3,12,20,24	NUM
ejpam-77	28	29	]	]	PUNCT
ejpam-77	28	30	.	.	PUNCT
ejpam-77	29	1	now	now	ADV
ejpam-77	29	2	we	we	PRON
ejpam-77	29	3	recall	recall	VERB
ejpam-77	29	4	some	some	DET
ejpam-77	29	5	notation	notation	NOUN
ejpam-77	29	6	and	and	CCONJ
ejpam-77	29	7	definitions	definition	NOUN
ejpam-77	29	8	used	use	VERB
ejpam-77	29	9	in	in	ADP
ejpam-77	29	10	this	this	DET
ejpam-77	29	11	paper	paper	NOUN
ejpam-77	29	12	(	(	PUNCT
ejpam-77	29	13	see	see	VERB
ejpam-77	29	14	[	[	X
ejpam-77	29	15	26	26	NUM
ejpam-77	29	16	]	]	NUM
ejpam-77	29	17	)	)	PUNCT
ejpam-77	29	18	.	.	PUNCT
ejpam-77	30	1	definition	definition	NOUN
ejpam-77	30	2	1.1	1.1	NUM
ejpam-77	30	3	.	.	PUNCT
ejpam-77	31	1	a	a	DET
ejpam-77	31	2	function	function	NOUN
ejpam-77	31	3	f	f	NOUN
ejpam-77	31	4	:	:	PUNCT
ejpam-77	31	5	r	r	NOUN
ejpam-77	31	6	→	→	SYM
ejpam-77	31	7	r+0	r+0	PROPN
ejpam-77	31	8	is	be	AUX
ejpam-77	31	9	called	call	VERB
ejpam-77	31	10	a	a	DET
ejpam-77	31	11	distribution	distribution	NOUN
ejpam-77	31	12	function	function	NOUN
ejpam-77	31	13	if	if	SCONJ
ejpam-77	31	14	it	it	PRON
ejpam-77	31	15	is	be	AUX
ejpam-77	31	16	nondecreasing	nondecrease	VERB
ejpam-77	31	17	and	and	CCONJ
ejpam-77	31	18	left	left	ADJ
ejpam-77	31	19	-	-	PUNCT
ejpam-77	31	20	continuous	continuous	ADJ
ejpam-77	31	21	with	with	ADP
ejpam-77	32	1	inft∈r	inft∈r	PROPN
ejpam-77	32	2	f	f	PROPN
ejpam-77	32	3	(	(	PUNCT
ejpam-77	32	4	t	t	PROPN
ejpam-77	32	5	)	)	PUNCT
ejpam-77	32	6	=	=	SYM
ejpam-77	32	7	0	0	NUM
ejpam-77	32	8	and	and	CCONJ
ejpam-77	32	9	supt∈r	supt∈r	PROPN
ejpam-77	32	10	f	f	PROPN
ejpam-77	32	11	(	(	PUNCT
ejpam-77	32	12	t	t	PROPN
ejpam-77	32	13	)	)	PUNCT
ejpam-77	32	14	=	=	NOUN
ejpam-77	33	1	1	1	X
ejpam-77	33	2	.	.	X
ejpam-77	34	1	we	we	PRON
ejpam-77	34	2	denote	denote	VERB
ejpam-77	34	3	the	the	DET
ejpam-77	34	4	set	set	NOUN
ejpam-77	34	5	of	of	ADP
ejpam-77	34	6	all	all	DET
ejpam-77	34	7	distribution	distribution	NOUN
ejpam-77	34	8	function	function	NOUN
ejpam-77	34	9	by	by	ADP
ejpam-77	34	10	∆+	∆+	NOUN
ejpam-77	34	11	.	.	PUNCT
ejpam-77	35	1	definition	definition	NOUN
ejpam-77	35	2	1.2	1.2	NUM
ejpam-77	35	3	.	.	PUNCT
ejpam-77	36	1	a	a	DET
ejpam-77	36	2	t	t	NOUN
ejpam-77	36	3	-	-	PUNCT
ejpam-77	36	4	norm	norm	NOUN
ejpam-77	36	5	t	t	PROPN
ejpam-77	36	6	is	be	AUX
ejpam-77	36	7	a	a	DET
ejpam-77	36	8	continuous	continuous	ADJ
ejpam-77	36	9	mapping	mapping	NOUN
ejpam-77	36	10	t	t	NOUN
ejpam-77	36	11	:	:	PUNCT
ejpam-77	37	1	[	[	X
ejpam-77	37	2	0	0	NUM
ejpam-77	37	3	,	,	PUNCT
ejpam-77	37	4	1]×	1]×	NUM
ejpam-77	37	5	[	[	X
ejpam-77	37	6	0	0	NUM
ejpam-77	37	7	,	,	PUNCT
ejpam-77	37	8	1	1	NUM
ejpam-77	37	9	]	]	PUNCT
ejpam-77	37	10	→	→	PUNCT
ejpam-77	37	11	[	[	X
ejpam-77	37	12	0	0	NUM
ejpam-77	37	13	,	,	PUNCT
ejpam-77	37	14	1	1	NUM
ejpam-77	37	15	]	]	PUNCT
ejpam-77	37	16	such	such	ADJ
ejpam-77	37	17	that	that	SCONJ
ejpam-77	37	18	for	for	ADP
ejpam-77	37	19	all	all	DET
ejpam-77	37	20	a	a	DET
ejpam-77	37	21	,	,	PUNCT
ejpam-77	37	22	b	b	NOUN
ejpam-77	37	23	,	,	PUNCT
ejpam-77	37	24	c	c	NOUN
ejpam-77	37	25	,	,	PUNCT
ejpam-77	37	26	d	d	PROPN
ejpam-77	37	27	∈	∈	PROPN
ejpam-77	37	28	[	[	X
ejpam-77	37	29	0	0	NUM
ejpam-77	37	30	,	,	PUNCT
ejpam-77	37	31	1	1	NUM
ejpam-77	37	32	]	]	PUNCT
ejpam-77	37	33	(	(	PUNCT
ejpam-77	37	34	i	i	NOUN
ejpam-77	37	35	)	)	PUNCT
ejpam-77	37	36	t	t	PROPN
ejpam-77	37	37	(	(	PUNCT
ejpam-77	37	38	a	a	DET
ejpam-77	37	39	,	,	PUNCT
ejpam-77	37	40	b	b	NOUN
ejpam-77	37	41	)	)	PUNCT
ejpam-77	37	42	=	=	SYM
ejpam-77	37	43	t	t	PROPN
ejpam-77	37	44	(	(	PUNCT
ejpam-77	37	45	b	b	NOUN
ejpam-77	37	46	,	,	PUNCT
ejpam-77	37	47	a	a	PRON
ejpam-77	37	48	)	)	PUNCT
ejpam-77	37	49	;	;	PUNCT
ejpam-77	37	50	(	(	PUNCT
ejpam-77	37	51	ii)t(a	ii)t(a	NOUN
ejpam-77	37	52	,	,	PUNCT
ejpam-77	37	53	t(b	t(b	NOUN
ejpam-77	37	54	,	,	PUNCT
ejpam-77	37	55	c))=t(t(a	c))=t(t(a	VERB
ejpam-77	37	56	,	,	PUNCT
ejpam-77	37	57	b),c	b),c	NOUN
ejpam-77	37	58	)	)	PUNCT
ejpam-77	37	59	;	;	PUNCT
ejpam-77	37	60	(	(	PUNCT
ejpam-77	37	61	iv	iv	X
ejpam-77	37	62	)	)	PUNCT
ejpam-77	37	63	t	t	PROPN
ejpam-77	37	64	(	(	PUNCT
ejpam-77	37	65	a	a	PRON
ejpam-77	37	66	,	,	PUNCT
ejpam-77	37	67	b	b	NOUN
ejpam-77	37	68	)	)	PUNCT
ejpam-77	37	69	≤	≤	NOUN
ejpam-77	37	70	t	t	NOUN
ejpam-77	37	71	(	(	PUNCT
ejpam-77	37	72	c	c	X
ejpam-77	37	73	,	,	PUNCT
ejpam-77	37	74	d	d	NOUN
ejpam-77	37	75	)	)	PUNCT
ejpam-77	37	76	whenever	whenever	SCONJ
ejpam-77	37	77	a	a	DET
ejpam-77	37	78	≤	≤	NUM
ejpam-77	37	79	c	c	NOUN
ejpam-77	37	80	and	and	CCONJ
ejpam-77	37	81	b	b	NOUN
ejpam-77	37	82	≤	≤	NUM
ejpam-77	37	83	d	d	NOUN
ejpam-77	37	84	;	;	PUNCT
ejpam-77	37	85	(	(	PUNCT
ejpam-77	37	86	v	v	NOUN
ejpam-77	37	87	)	)	PUNCT
ejpam-77	37	88	t	t	NOUN
ejpam-77	37	89	(	(	PUNCT
ejpam-77	37	90	a	a	DET
ejpam-77	37	91	,	,	PUNCT
ejpam-77	37	92	1	1	NUM
ejpam-77	37	93	)	)	PUNCT
ejpam-77	37	94	=	=	PUNCT
ejpam-77	37	95	a.	a.	NOUN
ejpam-77	37	96	example	example	NOUN
ejpam-77	37	97	1.1	1.1	NUM
ejpam-77	37	98	.	.	PUNCT
ejpam-77	38	1	the	the	DET
ejpam-77	38	2	operation	operation	NOUN
ejpam-77	38	3	t	t	PROPN
ejpam-77	38	4	(	(	PUNCT
ejpam-77	38	5	a	a	DET
ejpam-77	38	6	,	,	PUNCT
ejpam-77	38	7	b	b	NOUN
ejpam-77	38	8	)	)	PUNCT
ejpam-77	38	9	=	=	SYM
ejpam-77	38	10	ab	ab	PROPN
ejpam-77	38	11	,	,	PUNCT
ejpam-77	38	12	t	t	PROPN
ejpam-77	38	13	(	(	PUNCT
ejpam-77	38	14	a	a	DET
ejpam-77	38	15	,	,	PUNCT
ejpam-77	38	16	b	b	NOUN
ejpam-77	38	17	)	)	PUNCT
ejpam-77	38	18	=	=	SYM
ejpam-77	38	19	max(a+	max(a+	PROPN
ejpam-77	38	20	b−1	b−1	PROPN
ejpam-77	38	21	,	,	PUNCT
ejpam-77	38	22	0	0	NUM
ejpam-77	38	23	)	)	PUNCT
ejpam-77	38	24	and	and	CCONJ
ejpam-77	38	25	t	t	PROPN
ejpam-77	38	26	(	(	PUNCT
ejpam-77	38	27	a	a	DET
ejpam-77	38	28	,	,	PUNCT
ejpam-77	38	29	b	b	NOUN
ejpam-77	38	30	)	)	PUNCT
ejpam-77	38	31	=	=	SYM
ejpam-77	38	32	min(a	min(a	PROPN
ejpam-77	38	33	,	,	PUNCT
ejpam-77	38	34	b	b	NOUN
ejpam-77	38	35	)	)	PUNCT
ejpam-77	38	36	on	on	ADP
ejpam-77	38	37	[	[	X
ejpam-77	38	38	0	0	NUM
ejpam-77	38	39	,	,	PUNCT
ejpam-77	38	40	1	1	NUM
ejpam-77	38	41	]	]	PUNCT
ejpam-77	38	42	are	be	AUX
ejpam-77	38	43	t	t	NOUN
ejpam-77	38	44	-	-	PUNCT
ejpam-77	38	45	norms	norm	NOUN
ejpam-77	38	46	.	.	PUNCT
ejpam-77	39	1	the	the	DET
ejpam-77	39	2	following	follow	VERB
ejpam-77	39	3	definition	definition	NOUN
ejpam-77	39	4	is	be	AUX
ejpam-77	39	5	due	due	ADJ
ejpam-77	39	6	to	to	ADP
ejpam-77	39	7	a.	a.	PROPN
ejpam-77	39	8	n.	n.	PROPN
ejpam-77	39	9	šerstnev	šerstnev	PROPN
ejpam-77	40	1	[	[	X
ejpam-77	40	2	23	23	NUM
ejpam-77	40	3	]	]	PUNCT
ejpam-77	40	4	.	.	PUNCT
ejpam-77	41	1	definition	definition	NOUN
ejpam-77	41	2	1.3	1.3	NUM
ejpam-77	41	3	.	.	PUNCT
ejpam-77	42	1	a	a	DET
ejpam-77	42	2	probabilistic	probabilistic	ADJ
ejpam-77	42	3	normed	normed	ADJ
ejpam-77	42	4	space	space	NOUN
ejpam-77	42	5	(	(	PUNCT
ejpam-77	42	6	briefly	briefly	ADV
ejpam-77	42	7	,	,	PUNCT
ejpam-77	42	8	a	a	DET
ejpam-77	42	9	pn	pn	PROPN
ejpam-77	42	10	space	space	NOUN
ejpam-77	42	11	)	)	PUNCT
ejpam-77	42	12	is	be	AUX
ejpam-77	42	13	a	a	DET
ejpam-77	42	14	triplet	triplet	NOUN
ejpam-77	42	15	(	(	PUNCT
ejpam-77	42	16	x	x	NOUN
ejpam-77	42	17	,	,	PUNCT
ejpam-77	42	18	f	f	PROPN
ejpam-77	42	19	,	,	PUNCT
ejpam-77	42	20	t	t	PROPN
ejpam-77	42	21	)	)	PUNCT
ejpam-77	42	22	,	,	PUNCT
ejpam-77	42	23	where	where	SCONJ
ejpam-77	42	24	x	x	PRON
ejpam-77	42	25	is	be	AUX
ejpam-77	42	26	a	a	DET
ejpam-77	42	27	real	real	ADJ
ejpam-77	42	28	linear	linear	ADJ
ejpam-77	42	29	space	space	NOUN
ejpam-77	42	30	,	,	PUNCT
ejpam-77	42	31	t	t	PROPN
ejpam-77	42	32	is	be	AUX
ejpam-77	42	33	a	a	DET
ejpam-77	42	34	continuous	continuous	ADJ
ejpam-77	42	35	t	t	NOUN
ejpam-77	42	36	-	-	PUNCT
ejpam-77	42	37	norm	norm	NOUN
ejpam-77	42	38	,	,	PUNCT
ejpam-77	42	39	and	and	CCONJ
ejpam-77	42	40	f	f	PROPN
ejpam-77	42	41	(	(	PUNCT
ejpam-77	42	42	called	call	VERB
ejpam-77	42	43	probabilistic	probabilistic	ADJ
ejpam-77	42	44	norm	norm	NOUN
ejpam-77	42	45	)	)	PUNCT
ejpam-77	42	46	is	be	AUX
ejpam-77	42	47	a	a	DET
ejpam-77	42	48	mapping	mapping	NOUN
ejpam-77	42	49	from	from	ADP
ejpam-77	42	50	x	x	X
ejpam-77	42	51	into	into	ADP
ejpam-77	42	52	∆+	∆+	NUM
ejpam-77	42	53	(	(	PUNCT
ejpam-77	42	54	writing	write	VERB
ejpam-77	42	55	f(x	f(x	PROPN
ejpam-77	42	56	)	)	PUNCT
ejpam-77	42	57	as	as	ADP
ejpam-77	42	58	fx	fx	PROPN
ejpam-77	42	59	)	)	PUNCT
ejpam-77	42	60	,	,	PUNCT
ejpam-77	42	61	the	the	DET
ejpam-77	42	62	following	follow	VERB
ejpam-77	42	63	conditions	condition	NOUN
ejpam-77	42	64	hold	hold	VERB
ejpam-77	42	65	for	for	ADP
ejpam-77	42	66	every	every	PRON
ejpam-77	42	67	x	x	X
ejpam-77	42	68	,	,	PUNCT
ejpam-77	42	69	y	y	PROPN
ejpam-77	42	70	∈	∈	PROPN
ejpam-77	42	71	x	x	X
ejpam-77	42	72	and	and	CCONJ
ejpam-77	42	73	every	every	DET
ejpam-77	42	74	s	s	PROPN
ejpam-77	42	75	,	,	PUNCT
ejpam-77	42	76	t	t	X
ejpam-77	42	77	>	>	X
ejpam-77	42	78	0	0	NUM
ejpam-77	42	79	:	:	PUNCT
ejpam-77	42	80	(	(	PUNCT
ejpam-77	42	81	n1	n1	NOUN
ejpam-77	42	82	)	)	PUNCT
ejpam-77	42	83	fx(t	fx(t	PUNCT
ejpam-77	42	84	)	)	PUNCT
ejpam-77	42	85	=	=	SYM
ejpam-77	42	86	1	1	NUM
ejpam-77	42	87	if	if	SCONJ
ejpam-77	42	88	and	and	CCONJ
ejpam-77	42	89	only	only	ADV
ejpam-77	42	90	if	if	SCONJ
ejpam-77	42	91	x	x	X
ejpam-77	42	92	=	=	PUNCT
ejpam-77	42	93	θ(the	θ(the	DET
ejpam-77	42	94	null	null	ADJ
ejpam-77	42	95	vector	vector	NOUN
ejpam-77	42	96	of	of	ADP
ejpam-77	42	97	x	x	PROPN
ejpam-77	42	98	)	)	PUNCT
ejpam-77	42	99	;	;	PUNCT
ejpam-77	42	100	(	(	PUNCT
ejpam-77	42	101	n2	n2	ADJ
ejpam-77	42	102	)	)	PUNCT
ejpam-77	42	103	fαx(t	fαx(t	PROPN
ejpam-77	42	104	)	)	PUNCT
ejpam-77	42	105	=	=	SYM
ejpam-77	42	106	fx	fx	PROPN
ejpam-77	42	107	(	(	PUNCT
ejpam-77	42	108	t	t	PROPN
ejpam-77	42	109	|α|	|α|	PROPN
ejpam-77	42	110	)	)	PUNCT
ejpam-77	42	111	for	for	ADP
ejpam-77	42	112	α	α	PRON
ejpam-77	42	113	6=	6=	ADP
ejpam-77	42	114	0	0	NUM
ejpam-77	42	115	;	;	PUNCT
ejpam-77	42	116	(	(	PUNCT
ejpam-77	42	117	n3	n3	ADJ
ejpam-77	42	118	)	)	PUNCT
ejpam-77	42	119	fx+y(s+	fx+y(s+	NOUN
ejpam-77	42	120	t)≥	t)≥	PROPN
ejpam-77	42	121	t	t	PROPN
ejpam-77	42	122	(	(	PUNCT
ejpam-77	42	123	fx(s	fx(s	PROPN
ejpam-77	42	124	)	)	PUNCT
ejpam-77	42	125	,	,	PUNCT
ejpam-77	42	126	fy(t	fy(t	PROPN
ejpam-77	42	127	)	)	PUNCT
ejpam-77	42	128	)	)	PUNCT
ejpam-77	42	129	;	;	PUNCT
ejpam-77	42	130	example	example	NOUN
ejpam-77	42	131	1.2	1.2	NUM
ejpam-77	42	132	.	.	PUNCT
ejpam-77	43	1	let	let	AUX
ejpam-77	43	2	(	(	PUNCT
ejpam-77	43	3	x	x	NOUN
ejpam-77	43	4	,	,	PUNCT
ejpam-77	43	5	‖	‖	PROPN
ejpam-77	43	6	·	·	PUNCT
ejpam-77	43	7	‖	‖	NUM
ejpam-77	43	8	)	)	PUNCT
ejpam-77	43	9	is	be	AUX
ejpam-77	43	10	a	a	DET
ejpam-77	43	11	normed	normed	ADJ
ejpam-77	43	12	space	space	NOUN
ejpam-77	43	13	and	and	CCONJ
ejpam-77	43	14	t	t	PROPN
ejpam-77	43	15	(	(	PUNCT
ejpam-77	43	16	a	a	DET
ejpam-77	43	17	,	,	PUNCT
ejpam-77	43	18	b	b	NOUN
ejpam-77	43	19	)	)	PUNCT
ejpam-77	43	20	=	=	SYM
ejpam-77	43	21	ab	ab	PROPN
ejpam-77	43	22	(	(	PUNCT
ejpam-77	43	23	or	or	CCONJ
ejpam-77	43	24	t(a	t(a	NOUN
ejpam-77	43	25	,	,	PUNCT
ejpam-77	43	26	b)=min(a	b)=min(a	PROPN
ejpam-77	43	27	,	,	PUNCT
ejpam-77	43	28	b	b	NOUN
ejpam-77	43	29	)	)	PUNCT
ejpam-77	43	30	)	)	PUNCT
ejpam-77	43	31	.	.	PUNCT
ejpam-77	44	1	define	define	VERB
ejpam-77	44	2	fx(t	fx(t	PUNCT
ejpam-77	44	3	)	)	PUNCT
ejpam-77	45	1	=	=	SYM
ejpam-77	45	2	t	t	PROPN
ejpam-77	45	3	t	t	NOUN
ejpam-77	45	4	+	+	CCONJ
ejpam-77	45	5	‖x‖	‖x‖	PROPN
ejpam-77	45	6	m.	m.	NOUN
ejpam-77	45	7	rahmat	rahmat	NOUN
ejpam-77	45	8	and	and	CCONJ
ejpam-77	45	9	harikrishnan	harikrishnan	PROPN
ejpam-77	45	10	k.	k.	PROPN
ejpam-77	45	11	/	/	PUNCT
ejpam-77	45	12	eur	eur	PROPN
ejpam-77	45	13	.	.	PUNCT
ejpam-77	46	1	j.	j.	PROPN
ejpam-77	46	2	pure	pure	PROPN
ejpam-77	46	3	appl	appl	PROPN
ejpam-77	46	4	.	.	PROPN
ejpam-77	46	5	math	math	PROPN
ejpam-77	46	6	,	,	PUNCT
ejpam-77	46	7	2	2	NUM
ejpam-77	46	8	(	(	PUNCT
ejpam-77	46	9	2009	2009	NUM
ejpam-77	46	10	)	)	PUNCT
ejpam-77	46	11	,	,	PUNCT
ejpam-77	46	12	(	(	PUNCT
ejpam-77	46	13	195	195	NUM
ejpam-77	46	14	-	-	PUNCT
ejpam-77	46	15	212	212	NUM
ejpam-77	46	16	)	)	PUNCT
ejpam-77	46	17	198	198	NUM
ejpam-77	47	1	where	where	SCONJ
ejpam-77	47	2	x	x	PUNCT
ejpam-77	47	3	∈	∈	PROPN
ejpam-77	47	4	x	x	X
ejpam-77	47	5	and	and	CCONJ
ejpam-77	47	6	t	t	X
ejpam-77	47	7	>	>	X
ejpam-77	47	8	0	0	PROPN
ejpam-77	47	9	.	.	PUNCT
ejpam-77	48	1	then	then	ADV
ejpam-77	48	2	(	(	PUNCT
ejpam-77	48	3	x	x	X
ejpam-77	48	4	,	,	PUNCT
ejpam-77	48	5	f	f	PROPN
ejpam-77	48	6	,	,	PUNCT
ejpam-77	48	7	t	t	PROPN
ejpam-77	48	8	)	)	PUNCT
ejpam-77	48	9	is	be	AUX
ejpam-77	48	10	a	a	DET
ejpam-77	48	11	pn	pn	NOUN
ejpam-77	48	12	space	space	NOUN
ejpam-77	48	13	.	.	PUNCT
ejpam-77	49	1	let	let	VERB
ejpam-77	49	2	(	(	PUNCT
ejpam-77	49	3	x	x	SYM
ejpam-77	49	4	,	,	PUNCT
ejpam-77	49	5	f	f	PROPN
ejpam-77	49	6	,	,	PUNCT
ejpam-77	49	7	t	t	PROPN
ejpam-77	49	8	)	)	PUNCT
ejpam-77	49	9	be	be	AUX
ejpam-77	49	10	a	a	DET
ejpam-77	49	11	pn	pn	NOUN
ejpam-77	49	12	space	space	NOUN
ejpam-77	49	13	.	.	PUNCT
ejpam-77	50	1	since	since	SCONJ
ejpam-77	50	2	t	t	PROPN
ejpam-77	50	3	is	be	AUX
ejpam-77	50	4	a	a	DET
ejpam-77	50	5	continuous	continuous	ADJ
ejpam-77	50	6	t	t	NOUN
ejpam-77	50	7	-	-	PUNCT
ejpam-77	50	8	norm	norm	NOUN
ejpam-77	50	9	,	,	PUNCT
ejpam-77	50	10	the	the	DET
ejpam-77	50	11	system	system	NOUN
ejpam-77	50	12	of	of	ADP
ejpam-77	50	13	(	(	PUNCT
ejpam-77	50	14	ε	ε	PROPN
ejpam-77	50	15	,	,	PUNCT
ejpam-77	50	16	λ)neighborhoods	λ)neighborhoods	PROPN
ejpam-77	50	17	of	of	ADP
ejpam-77	50	18	θ	θ	PROPN
ejpam-77	50	19	(	(	PUNCT
ejpam-77	50	20	the	the	DET
ejpam-77	50	21	null	null	ADJ
ejpam-77	50	22	vector	vector	NOUN
ejpam-77	50	23	in	in	ADP
ejpam-77	50	24	x	x	X
ejpam-77	50	25	)	)	PUNCT
ejpam-77	50	26	{	{	PUNCT
ejpam-77	50	27	nθ	nθ	NOUN
ejpam-77	50	28	(	(	PUNCT
ejpam-77	50	29	ε	ε	PROPN
ejpam-77	50	30	,	,	PUNCT
ejpam-77	50	31	λ	λ	PROPN
ejpam-77	50	32	):	):	PUNCT
ejpam-77	50	33	ε	ε	PROPN
ejpam-77	50	34	>	>	PUNCT
ejpam-77	50	35	0,λ	0,λ	PROPN
ejpam-77	50	36	∈	∈	PROPN
ejpam-77	50	37	(	(	PUNCT
ejpam-77	50	38	0	0	NUM
ejpam-77	50	39	,	,	PUNCT
ejpam-77	50	40	1	1	NUM
ejpam-77	50	41	)	)	PUNCT
ejpam-77	50	42	}	}	PUNCT
ejpam-77	50	43	,	,	PUNCT
ejpam-77	50	44	(	(	PUNCT
ejpam-77	50	45	1.1	1.1	NUM
ejpam-77	50	46	)	)	PUNCT
ejpam-77	51	1	where	where	SCONJ
ejpam-77	51	2	nθ(ε	nθ(ε	NOUN
ejpam-77	51	3	,	,	PUNCT
ejpam-77	51	4	λ	λ	NOUN
ejpam-77	51	5	)	)	PUNCT
ejpam-77	51	6	=	=	AUX
ejpam-77	51	7	{	{	PUNCT
ejpam-77	51	8	x	x	PUNCT
ejpam-77	51	9	∈	∈	PROPN
ejpam-77	51	10	x	x	X
ejpam-77	51	11	:	:	PUNCT
ejpam-77	51	12	fx(ε	fx(ε	NUM
ejpam-77	51	13	)	)	PUNCT
ejpam-77	51	14	>	>	X
ejpam-77	51	15	1−λ	1−λ	NUM
ejpam-77	51	16	}	}	PUNCT
ejpam-77	51	17	(	(	PUNCT
ejpam-77	51	18	1.2	1.2	NUM
ejpam-77	51	19	)	)	PUNCT
ejpam-77	51	20	determines	determine	VERB
ejpam-77	51	21	a	a	DET
ejpam-77	51	22	first	first	ADJ
ejpam-77	51	23	countable	countable	ADJ
ejpam-77	51	24	hausdorff	hausdorff	NOUN
ejpam-77	51	25	topology	topology	NOUN
ejpam-77	51	26	on	on	ADP
ejpam-77	51	27	x	x	SYM
ejpam-77	51	28	,	,	PUNCT
ejpam-77	51	29	called	call	VERB
ejpam-77	51	30	the	the	DET
ejpam-77	51	31	f	f	NOUN
ejpam-77	51	32	-	-	PUNCT
ejpam-77	51	33	topology	topology	NOUN
ejpam-77	51	34	.	.	PUNCT
ejpam-77	52	1	thus	thus	ADV
ejpam-77	52	2	,	,	PUNCT
ejpam-77	52	3	the	the	DET
ejpam-77	52	4	f	f	PROPN
ejpam-77	52	5	-topology	-topology	NOUN
ejpam-77	52	6	can	can	AUX
ejpam-77	52	7	be	be	AUX
ejpam-77	52	8	completely	completely	ADV
ejpam-77	52	9	specified	specify	VERB
ejpam-77	52	10	by	by	ADP
ejpam-77	52	11	means	mean	NOUN
ejpam-77	52	12	of	of	ADP
ejpam-77	52	13	f	f	PROPN
ejpam-77	52	14	-convergence	-convergence	PROPN
ejpam-77	52	15	of	of	ADP
ejpam-77	52	16	sequences	sequence	NOUN
ejpam-77	52	17	.	.	PUNCT
ejpam-77	53	1	it	it	PRON
ejpam-77	53	2	is	be	AUX
ejpam-77	53	3	clear	clear	ADJ
ejpam-77	53	4	that	that	SCONJ
ejpam-77	53	5	x	x	X
ejpam-77	53	6	−	−	NOUN
ejpam-77	53	7	y	y	PROPN
ejpam-77	53	8	∈	∈	PROPN
ejpam-77	53	9	nθ	nθ	NOUN
ejpam-77	53	10	means	mean	VERB
ejpam-77	53	11	y	y	PROPN
ejpam-77	53	12	∈	∈	PROPN
ejpam-77	53	13	nx	nx	NOUN
ejpam-77	53	14	and	and	CCONJ
ejpam-77	53	15	vice	vice	NOUN
ejpam-77	53	16	-	-	NOUN
ejpam-77	53	17	versa	versa	NOUN
ejpam-77	53	18	.	.	PUNCT
ejpam-77	54	1	a	a	DET
ejpam-77	54	2	sequence	sequence	NOUN
ejpam-77	54	3	(	(	PUNCT
ejpam-77	54	4	xn	xn	X
ejpam-77	54	5	)	)	PUNCT
ejpam-77	54	6	is	be	AUX
ejpam-77	54	7	said	say	VERB
ejpam-77	54	8	to	to	PART
ejpam-77	54	9	be	be	AUX
ejpam-77	54	10	f	f	NOUN
ejpam-77	54	11	-convergent	-convergent	ADJ
ejpam-77	54	12	to	to	ADP
ejpam-77	54	13	ξ	ξ	PROPN
ejpam-77	54	14	∈	∈	PROPN
ejpam-77	54	15	x	x	SYM
ejpam-77	54	16	if	if	SCONJ
ejpam-77	54	17	for	for	ADP
ejpam-77	54	18	every	every	DET
ejpam-77	54	19	ε	ε	PROPN
ejpam-77	54	20	>	>	X
ejpam-77	54	21	0	0	PROPN
ejpam-77	54	22	,	,	PUNCT
ejpam-77	54	23	and	and	CCONJ
ejpam-77	54	24	for	for	ADP
ejpam-77	54	25	every	every	DET
ejpam-77	54	26	λ	λ	PROPN
ejpam-77	54	27	∈	∈	PROPN
ejpam-77	54	28	(	(	PUNCT
ejpam-77	54	29	0	0	NUM
ejpam-77	54	30	,	,	PUNCT
ejpam-77	54	31	1	1	NUM
ejpam-77	54	32	)	)	PUNCT
ejpam-77	54	33	there	there	PRON
ejpam-77	54	34	exists	exist	VERB
ejpam-77	54	35	a	a	DET
ejpam-77	54	36	number	number	NOUN
ejpam-77	54	37	n	n	NOUN
ejpam-77	54	38	∈	∈	NOUN
ejpam-77	54	39	n	n	PRON
ejpam-77	54	40	such	such	ADJ
ejpam-77	54	41	that	that	SCONJ
ejpam-77	54	42	xn−	xn−	PUNCT
ejpam-77	54	43	ξ	ξ	PROPN
ejpam-77	54	44	∈	∈	PROPN
ejpam-77	54	45	nθ	nθ	NOUN
ejpam-77	54	46	(	(	PUNCT
ejpam-77	54	47	ε	ε	PROPN
ejpam-77	54	48	,	,	PUNCT
ejpam-77	54	49	λ	λ	NOUN
ejpam-77	54	50	)	)	PUNCT
ejpam-77	54	51	for	for	ADP
ejpam-77	54	52	all	all	DET
ejpam-77	54	53	n	n	DET
ejpam-77	54	54	≥	≥	NOUN
ejpam-77	54	55	n	n	NOUN
ejpam-77	54	56	.	.	PUNCT
ejpam-77	54	57	or	or	CCONJ
ejpam-77	54	58	equivalently	equivalently	ADV
ejpam-77	54	59	,	,	PUNCT
ejpam-77	54	60	xn	xn	PROPN
ejpam-77	54	61	∈	∈	PROPN
ejpam-77	54	62	nξ(ε	nξ(ε	VERB
ejpam-77	54	63	,	,	PUNCT
ejpam-77	54	64	λ	λ	NOUN
ejpam-77	54	65	)	)	PUNCT
ejpam-77	54	66	for	for	ADP
ejpam-77	54	67	all	all	DET
ejpam-77	54	68	n	n	DET
ejpam-77	54	69	≥	≥	NOUN
ejpam-77	54	70	n	n	ADV
ejpam-77	54	71	.	.	PUNCT
ejpam-77	55	1	in	in	ADP
ejpam-77	55	2	this	this	DET
ejpam-77	55	3	case	case	NOUN
ejpam-77	55	4	we	we	PRON
ejpam-77	55	5	write	write	VERB
ejpam-77	55	6	f	f	PROPN
ejpam-77	55	7	−	−	PROPN
ejpam-77	55	8	lim	lim	PROPN
ejpam-77	55	9	xn	xn	PUNCT
ejpam-77	56	1	=	=	SYM
ejpam-77	56	2	ξ	ξ	X
ejpam-77	56	3	.	.	PUNCT
ejpam-77	56	4	lemma	lemma	PROPN
ejpam-77	56	5	1.1	1.1	NUM
ejpam-77	56	6	.	.	PUNCT
ejpam-77	57	1	let	let	AUX
ejpam-77	57	2	(	(	PUNCT
ejpam-77	57	3	x	x	X
ejpam-77	57	4	,	,	PUNCT
ejpam-77	57	5	‖	‖	PROPN
ejpam-77	57	6	·	·	SYM
ejpam-77	57	7	‖	‖	NUM
ejpam-77	57	8	)	)	PUNCT
ejpam-77	57	9	be	be	AUX
ejpam-77	57	10	a	a	DET
ejpam-77	57	11	real	real	ADV
ejpam-77	57	12	normed	normed	ADJ
ejpam-77	57	13	space	space	NOUN
ejpam-77	57	14	and	and	CCONJ
ejpam-77	57	15	(	(	PUNCT
ejpam-77	57	16	x	x	INTJ
ejpam-77	57	17	,	,	PUNCT
ejpam-77	57	18	f	f	PROPN
ejpam-77	57	19	,	,	PUNCT
ejpam-77	57	20	t	t	PROPN
ejpam-77	57	21	)	)	PUNCT
ejpam-77	57	22	be	be	AUX
ejpam-77	57	23	a	a	DET
ejpam-77	57	24	pn	pn	NOUN
ejpam-77	57	25	space	space	NOUN
ejpam-77	57	26	induced	induce	VERB
ejpam-77	57	27	by	by	ADP
ejpam-77	57	28	the	the	DET
ejpam-77	57	29	probabilistic	probabilistic	ADJ
ejpam-77	57	30	norm	norm	NOUN
ejpam-77	57	31	fx(t	fx(t	PUNCT
ejpam-77	57	32	)	)	PUNCT
ejpam-77	57	33	=	=	SYM
ejpam-77	57	34	t	t	PROPN
ejpam-77	57	35	t+‖x‖	t+‖x‖	PUNCT
ejpam-77	57	36	,	,	PUNCT
ejpam-77	57	37	where	where	SCONJ
ejpam-77	57	38	x	x	SYM
ejpam-77	57	39	∈	∈	PROPN
ejpam-77	57	40	x	x	X
ejpam-77	57	41	and	and	CCONJ
ejpam-77	57	42	t	t	X
ejpam-77	57	43	>	>	X
ejpam-77	57	44	0	0	PROPN
ejpam-77	57	45	.	.	PUNCT
ejpam-77	58	1	then	then	ADV
ejpam-77	58	2	for	for	ADP
ejpam-77	58	3	every	every	PRON
ejpam-77	58	4	{	{	PUNCT
ejpam-77	58	5	xn	xn	NOUN
ejpam-77	58	6	}	}	PUNCT
ejpam-77	58	7	in	in	ADP
ejpam-77	58	8	x	x	PROPN
ejpam-77	58	9	lim	lim	PROPN
ejpam-77	58	10	xn	xn	PROPN
ejpam-77	59	1	=	=	PROPN
ejpam-77	59	2	ξ⇒ℑ−	ξ⇒ℑ−	PROPN
ejpam-77	59	3	lim	lim	NOUN
ejpam-77	59	4	xn	xn	PUNCT
ejpam-77	60	1	=	=	SYM
ejpam-77	60	2	ξ	ξ	X
ejpam-77	60	3	.	.	PUNCT
ejpam-77	60	4	proof	proof	NOUN
ejpam-77	60	5	.	.	PUNCT
ejpam-77	61	1	let	let	AUX
ejpam-77	61	2	suppose	suppose	VERB
ejpam-77	61	3	that	that	SCONJ
ejpam-77	61	4	lim	lim	PROPN
ejpam-77	61	5	xn	xn	PROPN
ejpam-77	62	1	=	=	SYM
ejpam-77	62	2	ξ	ξ	PROPN
ejpam-77	62	3	.	.	PUNCT
ejpam-77	62	4	then	then	ADV
ejpam-77	62	5	for	for	ADP
ejpam-77	62	6	every	every	DET
ejpam-77	62	7	t	t	NOUN
ejpam-77	62	8	>	>	X
ejpam-77	62	9	0	0	PUNCT
ejpam-77	63	1	there	there	PRON
ejpam-77	63	2	exists	exist	VERB
ejpam-77	63	3	a	a	DET
ejpam-77	63	4	positive	positive	ADJ
ejpam-77	63	5	integer	integer	NOUN
ejpam-77	63	6	n	n	PROPN
ejpam-77	63	7	=	=	SYM
ejpam-77	63	8	n(t	n(t	PROPN
ejpam-77	63	9	)	)	PUNCT
ejpam-77	63	10	such	such	ADJ
ejpam-77	63	11	that	that	SCONJ
ejpam-77	63	12	‖xn−	‖xn−	NUM
ejpam-77	63	13	ξ‖	ξ‖	NOUN
ejpam-77	63	14	<	<	X
ejpam-77	63	15	t	t	NOUN
ejpam-77	63	16	for	for	ADP
ejpam-77	63	17	all	all	DET
ejpam-77	63	18	n	n	DET
ejpam-77	63	19	≥	≥	NOUN
ejpam-77	63	20	n	n	NOUN
ejpam-77	63	21	.	.	PUNCT
ejpam-77	64	1	we	we	PRON
ejpam-77	64	2	observe	observe	VERB
ejpam-77	64	3	that	that	SCONJ
ejpam-77	64	4	for	for	ADP
ejpam-77	64	5	any	any	DET
ejpam-77	64	6	given	give	VERB
ejpam-77	64	7	ε	ε	PROPN
ejpam-77	64	8	>	>	X
ejpam-77	64	9	0	0	PROPN
ejpam-77	64	10	,	,	PUNCT
ejpam-77	64	11	m.	m.	NOUN
ejpam-77	64	12	rahmat	rahmat	NOUN
ejpam-77	64	13	and	and	CCONJ
ejpam-77	64	14	harikrishnan	harikrishnan	PROPN
ejpam-77	64	15	k.	k.	PROPN
ejpam-77	64	16	/	/	PUNCT
ejpam-77	64	17	eur	eur	PROPN
ejpam-77	64	18	.	.	PUNCT
ejpam-77	65	1	j.	j.	PROPN
ejpam-77	65	2	pure	pure	PROPN
ejpam-77	65	3	appl	appl	PROPN
ejpam-77	65	4	.	.	PROPN
ejpam-77	65	5	math	math	PROPN
ejpam-77	65	6	,	,	PUNCT
ejpam-77	65	7	2	2	NUM
ejpam-77	65	8	(	(	PUNCT
ejpam-77	65	9	2009	2009	NUM
ejpam-77	65	10	)	)	PUNCT
ejpam-77	65	11	,	,	PUNCT
ejpam-77	65	12	(	(	PUNCT
ejpam-77	65	13	195	195	NUM
ejpam-77	65	14	-	-	PUNCT
ejpam-77	65	15	212	212	NUM
ejpam-77	65	16	)	)	PUNCT
ejpam-77	65	17	199	199	NUM
ejpam-77	65	18	ε+	ε+	NOUN
ejpam-77	65	19	‖xn−	‖xn−	PROPN
ejpam-77	65	20	ξ‖	ξ‖	ADJ
ejpam-77	65	21	ε	ε	PROPN
ejpam-77	65	22	<	<	X
ejpam-77	65	23	ε+	ε+	X
ejpam-77	65	24	t	t	X
ejpam-77	65	25	ε	ε	PROPN
ejpam-77	65	26	which	which	PRON
ejpam-77	65	27	is	be	AUX
ejpam-77	65	28	equivalent	equivalent	ADJ
ejpam-77	65	29	to	to	PART
ejpam-77	65	30	ε	ε	PROPN
ejpam-77	65	31	ε+	ε+	X
ejpam-77	65	32	‖xn−	‖xn−	PROPN
ejpam-77	65	33	ξ‖	ξ‖	PROPN
ejpam-77	65	34	>	>	X
ejpam-77	65	35	ε	ε	PROPN
ejpam-77	65	36	ε+	ε+	X
ejpam-77	65	37	t	t	PROPN
ejpam-77	65	38	=	=	SYM
ejpam-77	65	39	1−	1−	NUM
ejpam-77	65	40	t	t	PROPN
ejpam-77	65	41	ε+	ε+	X
ejpam-77	65	42	t	t	PROPN
ejpam-77	65	43	.	.	PUNCT
ejpam-77	66	1	therefore	therefore	ADV
ejpam-77	66	2	,	,	PUNCT
ejpam-77	66	3	by	by	ADP
ejpam-77	66	4	letting	let	VERB
ejpam-77	66	5	λ	λ	X
ejpam-77	66	6	=	=	SYM
ejpam-77	66	7	t	t	PROPN
ejpam-77	66	8	ε+t	ε+t	NUM
ejpam-77	66	9	∈	∈	PROPN
ejpam-77	66	10	(	(	PUNCT
ejpam-77	66	11	0	0	NUM
ejpam-77	66	12	,	,	PUNCT
ejpam-77	66	13	1	1	X
ejpam-77	66	14	)	)	PUNCT
ejpam-77	66	15	we	we	PRON
ejpam-77	66	16	have	have	VERB
ejpam-77	66	17	fxn−ξ(ε	fxn−ξ(ε	PROPN
ejpam-77	66	18	)	)	PUNCT
ejpam-77	66	19	>	>	X
ejpam-77	67	1	1−λ	1−λ	NUM
ejpam-77	67	2	for	for	ADP
ejpam-77	67	3	all	all	DET
ejpam-77	67	4	n	n	DET
ejpam-77	67	5	≥	≥	NOUN
ejpam-77	67	6	n	n	ADV
ejpam-77	67	7	.	.	PUNCT
ejpam-77	68	1	this	this	PRON
ejpam-77	68	2	implies	imply	VERB
ejpam-77	68	3	that	that	SCONJ
ejpam-77	68	4	xn	xn	PROPN
ejpam-77	68	5	∈nξ(ε	∈nξ(ε	PROPN
ejpam-77	68	6	,	,	PUNCT
ejpam-77	68	7	λ	λ	PROPN
ejpam-77	68	8	)	)	PUNCT
ejpam-77	68	9	for	for	ADP
ejpam-77	68	10	all	all	DET
ejpam-77	68	11	n	n	DET
ejpam-77	68	12	≥	≥	NOUN
ejpam-77	68	13	n	n	ADV
ejpam-77	68	14	as	as	SCONJ
ejpam-77	68	15	required	require	VERB
ejpam-77	68	16	.	.	PUNCT
ejpam-77	69	1	we	we	PRON
ejpam-77	69	2	recall	recall	VERB
ejpam-77	69	3	the	the	DET
ejpam-77	69	4	definition	definition	NOUN
ejpam-77	69	5	and	and	CCONJ
ejpam-77	69	6	notations	notation	NOUN
ejpam-77	69	7	of	of	ADP
ejpam-77	69	8	ideal	ideal	NOUN
ejpam-77	69	9	.	.	PUNCT
ejpam-77	70	1	definition	definition	NOUN
ejpam-77	70	2	1.4	1.4	NUM
ejpam-77	70	3	.	.	PUNCT
ejpam-77	71	1	a	a	DET
ejpam-77	71	2	non	non	ADJ
ejpam-77	71	3	-	-	ADJ
ejpam-77	71	4	empty	empty	ADJ
ejpam-77	71	5	subset	subset	NOUN
ejpam-77	71	6	i	i	PRON
ejpam-77	71	7	of	of	ADP
ejpam-77	71	8	2n	2n	NUM
ejpam-77	71	9	is	be	AUX
ejpam-77	71	10	called	call	VERB
ejpam-77	71	11	an	an	DET
ejpam-77	71	12	ideal	ideal	NOUN
ejpam-77	71	13	on	on	ADP
ejpam-77	71	14	n	n	NOUN
ejpam-77	71	15	if	if	SCONJ
ejpam-77	71	16	(	(	PUNCT
ejpam-77	71	17	i	i	NOUN
ejpam-77	71	18	)	)	PUNCT
ejpam-77	71	19	b	b	PROPN
ejpam-77	72	1	∈	∈	PROPN
ejpam-77	73	1	i	i	PRON
ejpam-77	73	2	whenever	whenever	SCONJ
ejpam-77	73	3	b	b	X
ejpam-77	73	4	⊆	⊆	SYM
ejpam-77	73	5	a	a	PRON
ejpam-77	73	6	for	for	ADP
ejpam-77	73	7	some	some	DET
ejpam-77	73	8	a∈	a∈	PROPN
ejpam-77	73	9	i	i	PRON
ejpam-77	73	10	(	(	PUNCT
ejpam-77	73	11	closed	close	VERB
ejpam-77	73	12	under	under	ADP
ejpam-77	73	13	subsets	subset	NOUN
ejpam-77	73	14	)	)	PUNCT
ejpam-77	73	15	,	,	PUNCT
ejpam-77	73	16	(	(	PUNCT
ejpam-77	73	17	ii)a∪	ii)a∪	PROPN
ejpam-77	73	18	b	b	X
ejpam-77	73	19	∈	∈	ADV
ejpam-77	73	20	i	i	PRON
ejpam-77	73	21	whenever	whenever	SCONJ
ejpam-77	73	22	a	a	DET
ejpam-77	73	23	,	,	PUNCT
ejpam-77	73	24	b	b	X
ejpam-77	73	25	∈	∈	PROPN
ejpam-77	73	26	i	i	PRON
ejpam-77	73	27	(	(	PUNCT
ejpam-77	73	28	closed	close	VERB
ejpam-77	73	29	under	under	ADP
ejpam-77	73	30	unions	union	NOUN
ejpam-77	73	31	)	)	PUNCT
ejpam-77	73	32	.	.	PUNCT
ejpam-77	74	1	an	an	DET
ejpam-77	74	2	ideal	ideal	NOUN
ejpam-77	74	3	called	call	VERB
ejpam-77	74	4	proper	proper	ADJ
ejpam-77	74	5	ifn	ifn	NOUN
ejpam-77	74	6	/∈	/∈	INTJ
ejpam-77	75	1	i	i	INTJ
ejpam-77	75	2	.	.	PUNCT
ejpam-77	76	1	an	an	DET
ejpam-77	76	2	ideal	ideal	NOUN
ejpam-77	76	3	called	call	VERB
ejpam-77	76	4	admissible	admissible	ADJ
ejpam-77	76	5	if	if	SCONJ
ejpam-77	76	6	its	its	PRON
ejpam-77	76	7	proper	proper	ADJ
ejpam-77	76	8	and	and	CCONJ
ejpam-77	76	9	contains	contain	VERB
ejpam-77	76	10	all	all	DET
ejpam-77	76	11	finite	finite	ADJ
ejpam-77	76	12	subsets	subset	NOUN
ejpam-77	76	13	.	.	PUNCT
ejpam-77	77	1	filter	filter	NOUN
ejpam-77	77	2	f	f	PROPN
ejpam-77	77	3	is	be	AUX
ejpam-77	77	4	a	a	DET
ejpam-77	77	5	dual	dual	ADJ
ejpam-77	77	6	notion	notion	NOUN
ejpam-77	77	7	to	to	PART
ejpam-77	77	8	ideal	ideal	VERB
ejpam-77	77	9	i	i	PRON
ejpam-77	77	10	-it	-it	VERB
ejpam-77	77	11	is	be	AUX
ejpam-77	77	12	closed	close	VERB
ejpam-77	77	13	under	under	ADP
ejpam-77	77	14	supersets	superset	NOUN
ejpam-77	77	15	and	and	CCONJ
ejpam-77	77	16	intersections	intersection	NOUN
ejpam-77	77	17	.	.	PUNCT
ejpam-77	78	1	it	it	PRON
ejpam-77	78	2	holds	hold	VERB
ejpam-77	78	3	that	that	SCONJ
ejpam-77	78	4	{	{	PUNCT
ejpam-77	78	5	n\a	n\a	PROPN
ejpam-77	78	6	:	:	PUNCT
ejpam-77	78	7	a∈	a∈	PROPN
ejpam-77	78	8	i	i	PRON
ejpam-77	78	9	}	}	PUNCT
ejpam-77	78	10	is	be	AUX
ejpam-77	78	11	a	a	DET
ejpam-77	78	12	filter	filter	NOUN
ejpam-77	78	13	if	if	SCONJ
ejpam-77	78	14	and	and	CCONJ
ejpam-77	78	15	only	only	ADV
ejpam-77	78	16	if	if	SCONJ
ejpam-77	78	17	i	i	PRON
ejpam-77	78	18	is	be	AUX
ejpam-77	78	19	ideal	ideal	ADJ
ejpam-77	78	20	.	.	PUNCT
ejpam-77	79	1	the	the	DET
ejpam-77	79	2	filter	filter	NOUN
ejpam-77	79	3	f	f	PROPN
ejpam-77	79	4	(	(	PUNCT
ejpam-77	79	5	i	i	NOUN
ejpam-77	79	6	)	)	PUNCT
ejpam-77	79	7	is	be	AUX
ejpam-77	79	8	called	call	VERB
ejpam-77	79	9	the	the	DET
ejpam-77	79	10	filter	filter	NOUN
ejpam-77	79	11	associated	associate	VERB
ejpam-77	79	12	with	with	ADP
ejpam-77	79	13	the	the	DET
ejpam-77	79	14	ideal	ideal	NOUN
ejpam-77	79	15	i	i	PRON
ejpam-77	79	16	.	.	PUNCT
ejpam-77	80	1	thus	thus	ADV
ejpam-77	80	2	,	,	PUNCT
ejpam-77	80	3	one	one	PRON
ejpam-77	80	4	can	can	AUX
ejpam-77	80	5	write	write	VERB
ejpam-77	80	6	a∈	a∈	PROPN
ejpam-77	80	7	i	i	PRON
ejpam-77	81	1	⇔	⇔	PROPN
ejpam-77	81	2	ac	ac	PROPN
ejpam-77	81	3	∈	∈	PROPN
ejpam-77	81	4	f	f	X
ejpam-77	81	5	(	(	PUNCT
ejpam-77	81	6	i	i	NOUN
ejpam-77	81	7	)	)	PUNCT
ejpam-77	81	8	.	.	PUNCT
ejpam-77	82	1	where	where	SCONJ
ejpam-77	82	2	ac	ac	PROPN
ejpam-77	82	3	denotes	denote	VERB
ejpam-77	82	4	the	the	DET
ejpam-77	82	5	complement	complement	NOUN
ejpam-77	82	6	of	of	ADP
ejpam-77	82	7	a.	a.	NOUN
ejpam-77	82	8	ideal	ideal	NOUN
ejpam-77	82	9	can	can	AUX
ejpam-77	82	10	be	be	AUX
ejpam-77	82	11	viewed	view	VERB
ejpam-77	82	12	as	as	ADP
ejpam-77	82	13	a	a	DET
ejpam-77	82	14	way	way	NOUN
ejpam-77	82	15	to	to	PART
ejpam-77	82	16	describe	describe	VERB
ejpam-77	82	17	which	which	DET
ejpam-77	82	18	sets	set	NOUN
ejpam-77	82	19	will	will	AUX
ejpam-77	82	20	be	be	AUX
ejpam-77	82	21	considered	consider	VERB
ejpam-77	82	22	"	"	PUNCT
ejpam-77	82	23	small	small	ADJ
ejpam-77	82	24	"	"	PUNCT
ejpam-77	82	25	,	,	PUNCT
ejpam-77	82	26	i.e.	i.e.	X
ejpam-77	82	27	,	,	PUNCT
ejpam-77	82	28	finite	finite	PROPN
ejpam-77	82	29	.	.	PUNCT
ejpam-77	83	1	filter	filter	NOUN
ejpam-77	83	2	is	be	AUX
ejpam-77	83	3	collection	collection	NOUN
ejpam-77	83	4	of	of	ADP
ejpam-77	83	5	all	all	DET
ejpam-77	83	6	"	"	PUNCT
ejpam-77	83	7	large	large	ADJ
ejpam-77	83	8	"	"	PUNCT
ejpam-77	83	9	sets	set	NOUN
ejpam-77	83	10	.	.	PUNCT
ejpam-77	84	1	m.	m.	NOUN
ejpam-77	84	2	rahmat	rahmat	PROPN
ejpam-77	84	3	and	and	CCONJ
ejpam-77	84	4	harikrishnan	harikrishnan	PROPN
ejpam-77	84	5	k.	k.	PROPN
ejpam-77	84	6	/	/	PUNCT
ejpam-77	84	7	eur	eur	PROPN
ejpam-77	84	8	.	.	PUNCT
ejpam-77	85	1	j.	j.	PROPN
ejpam-77	85	2	pure	pure	PROPN
ejpam-77	85	3	appl	appl	PROPN
ejpam-77	85	4	.	.	PROPN
ejpam-77	85	5	math	math	PROPN
ejpam-77	85	6	,	,	PUNCT
ejpam-77	85	7	2	2	NUM
ejpam-77	85	8	(	(	PUNCT
ejpam-77	85	9	2009	2009	NUM
ejpam-77	85	10	)	)	PUNCT
ejpam-77	85	11	,	,	PUNCT
ejpam-77	85	12	(	(	PUNCT
ejpam-77	85	13	195	195	NUM
ejpam-77	85	14	-	-	PUNCT
ejpam-77	85	15	212	212	NUM
ejpam-77	85	16	)	)	PUNCT
ejpam-77	85	17	200	200	NUM
ejpam-77	85	18	2	2	NUM
ejpam-77	85	19	.	.	PUNCT
ejpam-77	86	1	i	i	PRON
ejpam-77	86	2	-convergence	-convergence	VERB
ejpam-77	86	3	for	for	ADP
ejpam-77	86	4	sequences	sequence	NOUN
ejpam-77	86	5	in	in	ADP
ejpam-77	86	6	pn	pn	PROPN
ejpam-77	86	7	spaces	space	NOUN
ejpam-77	86	8	in	in	ADP
ejpam-77	86	9	this	this	DET
ejpam-77	86	10	section	section	NOUN
ejpam-77	86	11	we	we	PRON
ejpam-77	86	12	define	define	VERB
ejpam-77	86	13	the	the	DET
ejpam-77	86	14	ideal	ideal	ADJ
ejpam-77	86	15	convergence	convergence	NOUN
ejpam-77	86	16	of	of	ADP
ejpam-77	86	17	a	a	DET
ejpam-77	86	18	sequence	sequence	NOUN
ejpam-77	86	19	in	in	ADP
ejpam-77	86	20	(	(	PUNCT
ejpam-77	86	21	x	x	INTJ
ejpam-77	86	22	,	,	PUNCT
ejpam-77	86	23	f	f	PROPN
ejpam-77	86	24	,	,	PUNCT
ejpam-77	86	25	t	t	PROPN
ejpam-77	86	26	)	)	PUNCT
ejpam-77	86	27	and	and	CCONJ
ejpam-77	86	28	prove	prove	VERB
ejpam-77	86	29	some	some	DET
ejpam-77	86	30	important	important	ADJ
ejpam-77	86	31	results	result	NOUN
ejpam-77	86	32	.	.	PUNCT
ejpam-77	87	1	definition	definition	NOUN
ejpam-77	87	2	2.1	2.1	NUM
ejpam-77	87	3	.	.	PUNCT
ejpam-77	88	1	let	let	VERB
ejpam-77	88	2	i	i	PRON
ejpam-77	88	3	⊆	⊆	NUM
ejpam-77	88	4	2n	2n	NUM
ejpam-77	88	5	be	be	AUX
ejpam-77	88	6	a	a	DET
ejpam-77	88	7	proper	proper	ADJ
ejpam-77	88	8	ideal	ideal	NOUN
ejpam-77	88	9	in	in	ADP
ejpam-77	88	10	n	n	PROPN
ejpam-77	88	11	and	and	CCONJ
ejpam-77	88	12	(	(	PUNCT
ejpam-77	88	13	x	x	X
ejpam-77	88	14	,	,	PUNCT
ejpam-77	88	15	f	f	PROPN
ejpam-77	88	16	,	,	PUNCT
ejpam-77	88	17	t	t	PROPN
ejpam-77	88	18	)	)	PUNCT
ejpam-77	88	19	be	be	AUX
ejpam-77	88	20	a	a	DET
ejpam-77	88	21	pn	pn	NOUN
ejpam-77	88	22	space	space	NOUN
ejpam-77	88	23	.	.	PUNCT
ejpam-77	89	1	the	the	DET
ejpam-77	89	2	sequence	sequence	NOUN
ejpam-77	89	3	(	(	PUNCT
ejpam-77	89	4	xn	xn	X
ejpam-77	89	5	)	)	PUNCT
ejpam-77	89	6	in	in	ADP
ejpam-77	89	7	x	x	PROPN
ejpam-77	89	8	is	be	AUX
ejpam-77	89	9	said	say	VERB
ejpam-77	89	10	to	to	PART
ejpam-77	89	11	be	be	AUX
ejpam-77	89	12	i	i	PRON
ejpam-77	89	13	f	f	PROPN
ejpam-77	89	14	−	−	PROPN
ejpam-77	89	15	conver	conver	PROPN
ejpam-77	89	16	gent	gent	NOUN
ejpam-77	89	17	to	to	ADP
ejpam-77	89	18	x	x	PROPN
ejpam-77	89	19	∈	∈	PROPN
ejpam-77	89	20	x	x	X
ejpam-77	89	21	(	(	PUNCT
ejpam-77	89	22	i	i	PRON
ejpam-77	89	23	−	−	PROPN
ejpam-77	89	24	conver	conver	PROPN
ejpam-77	89	25	gent	gent	NOUN
ejpam-77	89	26	to	to	ADP
ejpam-77	89	27	x	x	PROPN
ejpam-77	89	28	∈	∈	PROPN
ejpam-77	89	29	x	x	PUNCT
ejpam-77	89	30	with	with	ADP
ejpam-77	89	31	respect	respect	NOUN
ejpam-77	89	32	to	to	ADP
ejpam-77	89	33	f	f	NOUN
ejpam-77	89	34	-	-	PUNCT
ejpam-77	89	35	topology	topology	NOUN
ejpam-77	89	36	)	)	PUNCT
ejpam-77	89	37	if	if	SCONJ
ejpam-77	89	38	for	for	ADP
ejpam-77	89	39	each	each	DET
ejpam-77	89	40	ε	ε	PROPN
ejpam-77	89	41	>	>	X
ejpam-77	89	42	0	0	PROPN
ejpam-77	89	43	,	,	PUNCT
ejpam-77	89	44	and	and	CCONJ
ejpam-77	89	45	λ	λ	X
ejpam-77	89	46	∈	∈	PROPN
ejpam-77	89	47	(	(	PUNCT
ejpam-77	89	48	0	0	NUM
ejpam-77	89	49	,	,	PUNCT
ejpam-77	89	50	1	1	NUM
ejpam-77	89	51	)	)	PUNCT
ejpam-77	89	52	{	{	PUNCT
ejpam-77	89	53	n	n	NOUN
ejpam-77	89	54	∈	∈	PROPN
ejpam-77	89	55	n	n	NOUN
ejpam-77	89	56	:	:	PUNCT
ejpam-77	89	57	xn	xn	PROPN
ejpam-77	89	58	/∈	/∈	PUNCT
ejpam-77	89	59	nx(ε	nx(ε	NOUN
ejpam-77	89	60	,	,	PUNCT
ejpam-77	89	61	λ	λ	NOUN
ejpam-77	89	62	)	)	PUNCT
ejpam-77	89	63	}	}	PUNCT
ejpam-77	89	64	∈	∈	PROPN
ejpam-77	90	1	i	i	PRON
ejpam-77	90	2	.	.	PUNCT
ejpam-77	91	1	the	the	DET
ejpam-77	91	2	vector	vector	NOUN
ejpam-77	91	3	x	x	PUNCT
ejpam-77	91	4	is	be	AUX
ejpam-77	91	5	called	call	VERB
ejpam-77	91	6	the	the	DET
ejpam-77	91	7	i	i	PRON
ejpam-77	91	8	f−	f−	PROPN
ejpam-77	91	9	l	l	NOUN
ejpam-77	91	10	imit	imit	NOUN
ejpam-77	91	11	of	of	ADP
ejpam-77	91	12	the	the	DET
ejpam-77	91	13	sequence	sequence	NOUN
ejpam-77	91	14	{	{	PUNCT
ejpam-77	91	15	xn	xn	PUNCT
ejpam-77	91	16	}	}	PUNCT
ejpam-77	91	17	and	and	CCONJ
ejpam-77	91	18	we	we	PRON
ejpam-77	91	19	write	write	VERB
ejpam-77	91	20	i	i	PRON
ejpam-77	91	21	f−	f−	PROPN
ejpam-77	91	22	lim	lim	PROPN
ejpam-77	91	23	xn	xn	PUNCT
ejpam-77	92	1	=	=	PUNCT
ejpam-77	92	2	x.	x.	NOUN
ejpam-77	92	3	definition	definition	NOUN
ejpam-77	92	4	2.2	2.2	NUM
ejpam-77	92	5	.	.	PUNCT
ejpam-77	93	1	let	let	VERB
ejpam-77	93	2	(	(	PUNCT
ejpam-77	93	3	x	x	SYM
ejpam-77	93	4	,	,	PUNCT
ejpam-77	93	5	f	f	PROPN
ejpam-77	93	6	,	,	PUNCT
ejpam-77	93	7	t	t	PROPN
ejpam-77	93	8	)	)	PUNCT
ejpam-77	93	9	be	be	AUX
ejpam-77	93	10	a	a	DET
ejpam-77	93	11	pn	pn	NOUN
ejpam-77	93	12	space	space	NOUN
ejpam-77	94	1	and	and	CCONJ
ejpam-77	94	2	i	i	PRON
ejpam-77	94	3	be	be	VERB
ejpam-77	94	4	an	an	DET
ejpam-77	94	5	admissible	admissible	ADJ
ejpam-77	94	6	ideal	ideal	NOUN
ejpam-77	94	7	in	in	ADP
ejpam-77	94	8	n.	n.	PROPN
ejpam-77	94	9	the	the	DET
ejpam-77	94	10	sequence	sequence	NOUN
ejpam-77	94	11	{	{	PUNCT
ejpam-77	94	12	xn	xn	NOUN
ejpam-77	94	13	}	}	PUNCT
ejpam-77	94	14	in	in	ADP
ejpam-77	94	15	x	x	VERB
ejpam-77	94	16	is	be	AUX
ejpam-77	94	17	said	say	VERB
ejpam-77	94	18	to	to	PART
ejpam-77	94	19	be	be	AUX
ejpam-77	94	20	i	i	PRON
ejpam-77	94	21	f∗	f∗	NOUN
ejpam-77	94	22	-convergent	-convergent	ADJ
ejpam-77	94	23	to	to	ADP
ejpam-77	94	24	ξ	ξ	PROPN
ejpam-77	94	25	∈	∈	PROPN
ejpam-77	94	26	x	x	X
ejpam-77	94	27	(	(	PUNCT
ejpam-77	94	28	i.e.	i.e.	X
ejpam-77	94	29	,	,	PUNCT
ejpam-77	94	30	i	i	PRON
ejpam-77	94	31	f∗−	f∗−	VERB
ejpam-77	94	32	lim	lim	PROPN
ejpam-77	94	33	xn	xn	PUNCT
ejpam-77	95	1	=	=	SYM
ejpam-77	95	2	ξ	ξ	X
ejpam-77	95	3	)	)	PUNCT
ejpam-77	95	4	if	if	SCONJ
ejpam-77	95	5	and	and	CCONJ
ejpam-77	95	6	only	only	ADV
ejpam-77	95	7	if	if	SCONJ
ejpam-77	95	8	there	there	PRON
ejpam-77	95	9	exists	exist	VERB
ejpam-77	95	10	a	a	DET
ejpam-77	95	11	set	set	NOUN
ejpam-77	95	12	m	m	NOUN
ejpam-77	95	13	=	=	PUNCT
ejpam-77	95	14	{	{	PUNCT
ejpam-77	95	15	m1	m1	PROPN
ejpam-77	95	16	<	<	X
ejpam-77	95	17	m2	m2	PROPN
ejpam-77	95	18	<	<	X
ejpam-77	95	19	·	·	PUNCT
ejpam-77	95	20	·	·	PUNCT
ejpam-77	95	21	·	·	PUNCT
ejpam-77	95	22	}	}	PUNCT
ejpam-77	95	23	∈	∈	PROPN
ejpam-77	96	1	f	f	X
ejpam-77	96	2	(	(	PUNCT
ejpam-77	96	3	i	i	NOUN
ejpam-77	96	4	)	)	PUNCT
ejpam-77	96	5	such	such	ADJ
ejpam-77	96	6	that	that	SCONJ
ejpam-77	96	7	ℑ−	ℑ−	NUM
ejpam-77	96	8	lim	lim	PROPN
ejpam-77	96	9	xmk	xmk	PROPN
ejpam-77	96	10	=	=	SYM
ejpam-77	97	1	ξ	ξ	X
ejpam-77	97	2	.	.	PUNCT
ejpam-77	97	3	lemma	lemma	PROPN
ejpam-77	97	4	2.1	2.1	NUM
ejpam-77	97	5	.	.	PUNCT
ejpam-77	98	1	let	let	VERB
ejpam-77	98	2	(	(	PUNCT
ejpam-77	98	3	x	x	SYM
ejpam-77	98	4	,	,	PUNCT
ejpam-77	98	5	f	f	PROPN
ejpam-77	98	6	,	,	PUNCT
ejpam-77	98	7	t	t	PROPN
ejpam-77	98	8	)	)	PUNCT
ejpam-77	98	9	be	be	AUX
ejpam-77	98	10	a	a	DET
ejpam-77	98	11	pn	pn	NOUN
ejpam-77	98	12	space	space	NOUN
ejpam-77	98	13	.	.	PUNCT
ejpam-77	99	1	i	i	PRON
ejpam-77	99	2	f	f	X
ejpam-77	100	1	−	−	NOUN
ejpam-77	100	2	l	l	NOUN
ejpam-77	100	3	imit	imit	NOUN
ejpam-77	100	4	of	of	ADP
ejpam-77	100	5	any	any	DET
ejpam-77	100	6	sequence	sequence	NOUN
ejpam-77	100	7	if	if	SCONJ
ejpam-77	100	8	exists	exist	VERB
ejpam-77	100	9	is	be	AUX
ejpam-77	100	10	unique	unique	ADJ
ejpam-77	100	11	.	.	PUNCT
ejpam-77	101	1	proof	proof	NOUN
ejpam-77	101	2	.	.	PUNCT
ejpam-77	102	1	let	let	VERB
ejpam-77	102	2	{	{	PUNCT
ejpam-77	102	3	xn	xn	VERB
ejpam-77	102	4	}	}	PUNCT
ejpam-77	102	5	be	be	AUX
ejpam-77	102	6	any	any	DET
ejpam-77	102	7	sequence	sequence	NOUN
ejpam-77	102	8	and	and	CCONJ
ejpam-77	102	9	suppose	suppose	VERB
ejpam-77	102	10	that	that	SCONJ
ejpam-77	102	11	i	i	PRON
ejpam-77	102	12	f−lim	f−lim	VERB
ejpam-77	102	13	xn	xn	PROPN
ejpam-77	103	1	=	=	SYM
ejpam-77	103	2	ξ	ξ	PROPN
ejpam-77	103	3	,	,	PUNCT
ejpam-77	103	4	i	i	PRON
ejpam-77	103	5	f−lim	f−lim	VERB
ejpam-77	103	6	xn	xn	PROPN
ejpam-77	104	1	=	=	PROPN
ejpam-77	104	2	η	η	PROPN
ejpam-77	104	3	where	where	SCONJ
ejpam-77	104	4	ξ	ξ	PROPN
ejpam-77	104	5	6=	6=	PROPN
ejpam-77	104	6	η	η	PROPN
ejpam-77	104	7	.	.	PROPN
ejpam-77	104	8	since	since	SCONJ
ejpam-77	104	9	ξ	ξ	PROPN
ejpam-77	104	10	6=	6=	PROPN
ejpam-77	104	11	η	η	PROPN
ejpam-77	104	12	,	,	PUNCT
ejpam-77	104	13	select	select	ADJ
ejpam-77	104	14	ε	ε	PROPN
ejpam-77	104	15	>	>	X
ejpam-77	104	16	0	0	PUNCT
ejpam-77	104	17	and	and	CCONJ
ejpam-77	104	18	λ	λ	PROPN
ejpam-77	104	19	∈	∈	PROPN
ejpam-77	104	20	(	(	PUNCT
ejpam-77	104	21	0	0	NUM
ejpam-77	104	22	,	,	PUNCT
ejpam-77	104	23	1	1	NUM
ejpam-77	104	24	)	)	PUNCT
ejpam-77	104	25	such	such	ADJ
ejpam-77	104	26	thatnξ(ε	thatnξ(ε	NOUN
ejpam-77	104	27	,	,	PUNCT
ejpam-77	104	28	λ	λ	NOUN
ejpam-77	104	29	)	)	PUNCT
ejpam-77	104	30	andnη(ε	andnη(ε	PROPN
ejpam-77	104	31	,	,	PUNCT
ejpam-77	104	32	λ	λ	NOUN
ejpam-77	104	33	)	)	PUNCT
ejpam-77	104	34	are	be	AUX
ejpam-77	104	35	disjoint	disjoint	NOUN
ejpam-77	104	36	neighborhoods	neighborhood	NOUN
ejpam-77	104	37	of	of	ADP
ejpam-77	104	38	ξ	ξ	PROPN
ejpam-77	104	39	and	and	CCONJ
ejpam-77	104	40	η	η	PROPN
ejpam-77	104	41	.	.	PROPN
ejpam-77	104	42	since	since	SCONJ
ejpam-77	104	43	ξ	ξ	PROPN
ejpam-77	104	44	and	and	CCONJ
ejpam-77	104	45	η	η	PROPN
ejpam-77	104	46	both	both	PRON
ejpam-77	104	47	are	be	AUX
ejpam-77	104	48	i	i	PRON
ejpam-77	104	49	f	f	NOUN
ejpam-77	104	50	−	−	PROPN
ejpam-77	104	51	l	l	NOUN
ejpam-77	104	52	imit	imit	NOUN
ejpam-77	104	53	of	of	ADP
ejpam-77	104	54	the	the	DET
ejpam-77	104	55	sequence	sequence	NOUN
ejpam-77	104	56	{	{	PUNCT
ejpam-77	104	57	xn	xn	NUM
ejpam-77	104	58	}	}	PUNCT
ejpam-77	104	59	,	,	PUNCT
ejpam-77	104	60	we	we	PRON
ejpam-77	104	61	have	have	AUX
ejpam-77	104	62	a=	a=	VERB
ejpam-77	104	63	{	{	PUNCT
ejpam-77	104	64	n	n	NOUN
ejpam-77	104	65	∈	∈	PROPN
ejpam-77	104	66	n	n	NOUN
ejpam-77	104	67	:	:	PUNCT
ejpam-77	104	68	xn	xn	PROPN
ejpam-77	104	69	/∈	/∈	PUNCT
ejpam-77	104	70	nξ(ε	nξ(ε	PROPN
ejpam-77	104	71	,	,	PUNCT
ejpam-77	104	72	λ	λ	NOUN
ejpam-77	104	73	)	)	PUNCT
ejpam-77	104	74	}	}	PUNCT
ejpam-77	104	75	and	and	CCONJ
ejpam-77	104	76	b	b	X
ejpam-77	104	77	=	=	SYM
ejpam-77	104	78	{	{	PUNCT
ejpam-77	104	79	n	n	NOUN
ejpam-77	104	80	∈	∈	PROPN
ejpam-77	104	81	n	n	NOUN
ejpam-77	104	82	:	:	PUNCT
ejpam-77	104	83	xn	xn	PROPN
ejpam-77	104	84	/∈	/∈	PUNCT
ejpam-77	104	85	nη(ε	nη(ε	NOUN
ejpam-77	104	86	,	,	PUNCT
ejpam-77	104	87	λ	λ	NOUN
ejpam-77	104	88	)	)	PUNCT
ejpam-77	104	89	}	}	PUNCT
ejpam-77	104	90	are	be	AUX
ejpam-77	104	91	both	both	PRON
ejpam-77	104	92	belongs	belong	VERB
ejpam-77	104	93	to	to	ADP
ejpam-77	104	94	i	i	PRON
ejpam-77	104	95	.	.	PUNCT
ejpam-77	105	1	this	this	PRON
ejpam-77	105	2	implies	imply	VERB
ejpam-77	105	3	that	that	SCONJ
ejpam-77	105	4	the	the	DET
ejpam-77	105	5	sets	set	NOUN
ejpam-77	105	6	ac	ac	VERB
ejpam-77	105	7	=	=	PUNCT
ejpam-77	105	8	{	{	PUNCT
ejpam-77	105	9	n	n	NOUN
ejpam-77	105	10	∈	∈	PROPN
ejpam-77	105	11	n	n	NOUN
ejpam-77	105	12	:	:	PUNCT
ejpam-77	105	13	xn	xn	PROPN
ejpam-77	105	14	∈	∈	PROPN
ejpam-77	105	15	nξ(ε	nξ(ε	PRON
ejpam-77	105	16	,	,	PUNCT
ejpam-77	105	17	λ	λ	NOUN
ejpam-77	105	18	)	)	PUNCT
ejpam-77	105	19	}	}	PUNCT
ejpam-77	105	20	and	and	CCONJ
ejpam-77	105	21	bc	bc	PROPN
ejpam-77	105	22	=	=	SYM
ejpam-77	105	23	{	{	PUNCT
ejpam-77	105	24	n	n	NOUN
ejpam-77	105	25	∈	∈	PROPN
ejpam-77	105	26	n	n	NOUN
ejpam-77	105	27	:	:	PUNCT
ejpam-77	105	28	xn	xn	PROPN
ejpam-77	105	29	∈	∈	PROPN
ejpam-77	105	30	nη(ε	nη(ε	NOUN
ejpam-77	105	31	,	,	PUNCT
ejpam-77	105	32	λ	λ	NOUN
ejpam-77	105	33	)	)	PUNCT
ejpam-77	105	34	}	}	PUNCT
ejpam-77	105	35	belongs	belong	VERB
ejpam-77	105	36	to	to	ADP
ejpam-77	105	37	f	f	PROPN
ejpam-77	105	38	(	(	PUNCT
ejpam-77	105	39	i	i	NOUN
ejpam-77	105	40	)	)	PUNCT
ejpam-77	105	41	.	.	PUNCT
ejpam-77	106	1	since	since	SCONJ
ejpam-77	106	2	f	f	PROPN
ejpam-77	106	3	(	(	PUNCT
ejpam-77	106	4	i	i	NOUN
ejpam-77	106	5	)	)	PUNCT
ejpam-77	106	6	is	be	AUX
ejpam-77	106	7	a	a	DET
ejpam-77	106	8	filter	filter	NOUN
ejpam-77	106	9	in	in	ADP
ejpam-77	106	10	n	n	CCONJ
ejpam-77	106	11	,	,	PUNCT
ejpam-77	106	12	we	we	PRON
ejpam-77	106	13	have	have	VERB
ejpam-77	106	14	ac	ac	PROPN
ejpam-77	106	15	∩	∩	PROPN
ejpam-77	106	16	bc	bc	PROPN
ejpam-77	106	17	is	be	AUX
ejpam-77	106	18	a	a	DET
ejpam-77	106	19	nonempty	nonempty	NOUN
ejpam-77	106	20	in	in	ADP
ejpam-77	106	21	f	f	PROPN
ejpam-77	106	22	(	(	PUNCT
ejpam-77	106	23	i	i	NOUN
ejpam-77	106	24	)	)	PUNCT
ejpam-77	106	25	.	.	PUNCT
ejpam-77	107	1	in	in	ADP
ejpam-77	107	2	this	this	DET
ejpam-77	107	3	way	way	NOUN
ejpam-77	107	4	we	we	PRON
ejpam-77	107	5	obtain	obtain	VERB
ejpam-77	107	6	a	a	DET
ejpam-77	107	7	contradiction	contradiction	NOUN
ejpam-77	107	8	to	to	ADP
ejpam-77	107	9	the	the	DET
ejpam-77	107	10	fact	fact	NOUN
ejpam-77	107	11	that	that	SCONJ
ejpam-77	107	12	the	the	DET
ejpam-77	107	13	neighborhoods	neighborhood	NOUN
ejpam-77	107	14	nξ(ε	nξ(ε	VERB
ejpam-77	107	15	,	,	PUNCT
ejpam-77	107	16	λ	λ	NOUN
ejpam-77	107	17	)	)	PUNCT
ejpam-77	107	18	and	and	CCONJ
ejpam-77	107	19	nη(ε	nη(ε	NOUN
ejpam-77	107	20	,	,	PUNCT
ejpam-77	107	21	λ	λ	NOUN
ejpam-77	107	22	)	)	PUNCT
ejpam-77	107	23	of	of	ADP
ejpam-77	107	24	ξ	ξ	PROPN
ejpam-77	107	25	and	and	CCONJ
ejpam-77	107	26	η	η	PROPN
ejpam-77	107	27	are	be	AUX
ejpam-77	107	28	disjoints	disjoint	NOUN
ejpam-77	107	29	.	.	PUNCT
ejpam-77	108	1	hence	hence	ADV
ejpam-77	108	2	we	we	PRON
ejpam-77	108	3	have	have	VERB
ejpam-77	108	4	ξ	ξ	PROPN
ejpam-77	108	5	=	=	SYM
ejpam-77	108	6	η	η	PROPN
ejpam-77	108	7	.	.	PROPN
ejpam-77	109	1	this	this	PRON
ejpam-77	109	2	completes	complete	VERB
ejpam-77	109	3	the	the	DET
ejpam-77	109	4	proof	proof	NOUN
ejpam-77	109	5	.	.	PUNCT
ejpam-77	110	1	m.	m.	NOUN
ejpam-77	110	2	rahmat	rahmat	PROPN
ejpam-77	110	3	and	and	CCONJ
ejpam-77	110	4	harikrishnan	harikrishnan	PROPN
ejpam-77	110	5	k.	k.	PROPN
ejpam-77	110	6	/	/	PUNCT
ejpam-77	110	7	eur	eur	PROPN
ejpam-77	110	8	.	.	PUNCT
ejpam-77	111	1	j.	j.	PROPN
ejpam-77	111	2	pure	pure	PROPN
ejpam-77	111	3	appl	appl	PROPN
ejpam-77	111	4	.	.	PROPN
ejpam-77	111	5	math	math	PROPN
ejpam-77	111	6	,	,	PUNCT
ejpam-77	111	7	2	2	NUM
ejpam-77	111	8	(	(	PUNCT
ejpam-77	111	9	2009	2009	NUM
ejpam-77	111	10	)	)	PUNCT
ejpam-77	111	11	,	,	PUNCT
ejpam-77	111	12	(	(	PUNCT
ejpam-77	111	13	195	195	NUM
ejpam-77	111	14	-	-	PUNCT
ejpam-77	111	15	212	212	NUM
ejpam-77	111	16	)	)	PUNCT
ejpam-77	111	17	201	201	NUM
ejpam-77	111	18	lemma	lemma	PROPN
ejpam-77	111	19	2.2	2.2	NUM
ejpam-77	111	20	.	.	PUNCT
ejpam-77	112	1	let	let	VERB
ejpam-77	112	2	(	(	PUNCT
ejpam-77	112	3	x	x	SYM
ejpam-77	112	4	,	,	PUNCT
ejpam-77	112	5	f	f	PROPN
ejpam-77	112	6	,	,	PUNCT
ejpam-77	112	7	t	t	PROPN
ejpam-77	112	8	)	)	PUNCT
ejpam-77	112	9	be	be	AUX
ejpam-77	112	10	a	a	DET
ejpam-77	112	11	pn	pn	NOUN
ejpam-77	112	12	space	space	NOUN
ejpam-77	112	13	and	and	CCONJ
ejpam-77	112	14	ifin	ifin	NOUN
ejpam-77	112	15	be	be	AUX
ejpam-77	112	16	fréchet	fréchet	VERB
ejpam-77	112	17	ideal	ideal	ADJ
ejpam-77	112	18	(	(	PUNCT
ejpam-77	112	19	finite	finite	VERB
ejpam-77	112	20	subsets	subset	NOUN
ejpam-77	112	21	on	on	ADP
ejpam-77	112	22	n	n	CCONJ
ejpam-77	112	23	)	)	PUNCT
ejpam-77	112	24	.	.	PUNCT
ejpam-77	113	1	then	then	ADV
ejpam-77	113	2	f	f	PROPN
ejpam-77	113	3	−	−	PROPN
ejpam-77	113	4	conver	conver	NOUN
ejpam-77	113	5	gence	gence	NOUN
ejpam-77	113	6	implies	imply	VERB
ejpam-77	113	7	i	i	PRON
ejpam-77	113	8	f	f	PROPN
ejpam-77	113	9	fin	fin	NOUN
ejpam-77	113	10	−	−	PROPN
ejpam-77	113	11	conver	conver	NOUN
ejpam-77	113	12	gence	gence	NOUN
ejpam-77	113	13	.	.	PUNCT
ejpam-77	114	1	proof	proof	NOUN
ejpam-77	114	2	.	.	PUNCT
ejpam-77	115	1	let	let	VERB
ejpam-77	115	2	ε	ε	PROPN
ejpam-77	115	3	>	>	X
ejpam-77	115	4	0	0	PUNCT
ejpam-77	116	1	and	and	CCONJ
ejpam-77	116	2	λ	λ	PROPN
ejpam-77	116	3	∈	∈	PROPN
ejpam-77	116	4	(	(	PUNCT
ejpam-77	116	5	0	0	NUM
ejpam-77	116	6	,	,	PUNCT
ejpam-77	116	7	1	1	NUM
ejpam-77	116	8	)	)	PUNCT
ejpam-77	116	9	.	.	PUNCT
ejpam-77	116	10	suppose	suppose	VERB
ejpam-77	116	11	that	that	SCONJ
ejpam-77	116	12	{	{	PUNCT
ejpam-77	116	13	xn	xn	X
ejpam-77	116	14	}	}	PUNCT
ejpam-77	116	15	is	be	AUX
ejpam-77	116	16	f	f	PROPN
ejpam-77	116	17	−	−	PROPN
ejpam-77	116	18	conver	conver	PROPN
ejpam-77	116	19	gent	gent	NOUN
ejpam-77	116	20	to	to	ADP
ejpam-77	116	21	ξ	ξ	PROPN
ejpam-77	116	22	.	.	PUNCT
ejpam-77	117	1	then	then	ADV
ejpam-77	117	2	,	,	PUNCT
ejpam-77	117	3	there	there	PRON
ejpam-77	117	4	exists	exist	VERB
ejpam-77	117	5	a	a	DET
ejpam-77	117	6	number	number	NOUN
ejpam-77	117	7	n	n	NOUN
ejpam-77	117	8	∈	∈	NOUN
ejpam-77	117	9	n	n	PRON
ejpam-77	117	10	such	such	ADJ
ejpam-77	117	11	that	that	SCONJ
ejpam-77	117	12	xn	xn	PROPN
ejpam-77	117	13	∈	∈	PROPN
ejpam-77	117	14	nξ(ε	nξ(ε	VERB
ejpam-77	117	15	,	,	PUNCT
ejpam-77	117	16	λ	λ	NOUN
ejpam-77	117	17	)	)	PUNCT
ejpam-77	117	18	for	for	ADP
ejpam-77	117	19	every	every	DET
ejpam-77	117	20	n	n	PRON
ejpam-77	117	21	≥	≥	NOUN
ejpam-77	117	22	n	n	NOUN
ejpam-77	117	23	.	.	PUNCT
ejpam-77	118	1	this	this	PRON
ejpam-77	118	2	implies	imply	VERB
ejpam-77	118	3	that	that	SCONJ
ejpam-77	118	4	the	the	DET
ejpam-77	118	5	set	set	NOUN
ejpam-77	118	6	a=	a=	NOUN
ejpam-77	118	7	{	{	PUNCT
ejpam-77	118	8	n	n	NOUN
ejpam-77	118	9	∈	∈	PROPN
ejpam-77	118	10	n	n	NOUN
ejpam-77	118	11	:	:	PUNCT
ejpam-77	118	12	xn	xn	PROPN
ejpam-77	118	13	/∈	/∈	PUNCT
ejpam-77	118	14	nξ(ε	nξ(ε	PROPN
ejpam-77	118	15	,	,	PUNCT
ejpam-77	118	16	λ	λ	NOUN
ejpam-77	118	17	)	)	PUNCT
ejpam-77	118	18	}	}	PUNCT
ejpam-77	118	19	⊆	⊆	NUM
ejpam-77	118	20	{	{	PUNCT
ejpam-77	118	21	1	1	NUM
ejpam-77	118	22	,	,	PUNCT
ejpam-77	118	23	2	2	NUM
ejpam-77	118	24	,	,	PUNCT
ejpam-77	118	25	·	·	PUNCT
ejpam-77	118	26	·	·	PUNCT
ejpam-77	118	27	·	·	PUNCT
ejpam-77	118	28	,	,	PUNCT
ejpam-77	118	29	n	n	CCONJ
ejpam-77	118	30	−	−	PROPN
ejpam-77	118	31	1	1	NUM
ejpam-77	118	32	}	}	PUNCT
ejpam-77	118	33	.	.	PUNCT
ejpam-77	119	1	since	since	SCONJ
ejpam-77	119	2	the	the	DET
ejpam-77	119	3	right	right	ADJ
ejpam-77	119	4	hand	hand	NOUN
ejpam-77	119	5	side	side	NOUN
ejpam-77	119	6	belongs	belong	VERB
ejpam-77	119	7	to	to	ADP
ejpam-77	119	8	i	i	PRON
ejpam-77	119	9	f	f	PROPN
ejpam-77	119	10	,	,	PUNCT
ejpam-77	119	11	we	we	PRON
ejpam-77	119	12	have	have	VERB
ejpam-77	119	13	a∈	a∈	PROPN
ejpam-77	119	14	ifin	ifin	NOUN
ejpam-77	119	15	.	.	PUNCT
ejpam-77	120	1	this	this	PRON
ejpam-77	120	2	shows	show	VERB
ejpam-77	120	3	that	that	SCONJ
ejpam-77	120	4	{	{	PUNCT
ejpam-77	120	5	xn	xn	X
ejpam-77	120	6	}	}	PUNCT
ejpam-77	120	7	is	be	AUX
ejpam-77	120	8	i	i	PRON
ejpam-77	120	9	f	f	PROPN
ejpam-77	120	10	fin−	fin−	PROPN
ejpam-77	120	11	conver	conver	PROPN
ejpam-77	120	12	gent	gent	NOUN
ejpam-77	120	13	to	to	ADP
ejpam-77	120	14	ξ	ξ	PROPN
ejpam-77	120	15	.	.	PUNCT
ejpam-77	121	1	the	the	DET
ejpam-77	121	2	following	follow	VERB
ejpam-77	121	3	example	example	NOUN
ejpam-77	121	4	shows	show	VERB
ejpam-77	121	5	that	that	SCONJ
ejpam-77	121	6	the	the	DET
ejpam-77	121	7	converse	converse	NOUN
ejpam-77	121	8	of	of	ADP
ejpam-77	121	9	above	above	ADJ
ejpam-77	121	10	theorem	theorem	NOUN
ejpam-77	121	11	is	be	AUX
ejpam-77	121	12	not	not	PART
ejpam-77	121	13	valid	valid	ADJ
ejpam-77	121	14	.	.	PUNCT
ejpam-77	122	1	example	example	NOUN
ejpam-77	122	2	2.1	2.1	NUM
ejpam-77	122	3	.	.	PUNCT
ejpam-77	123	1	by	by	ADP
ejpam-77	123	2	letting	let	VERB
ejpam-77	123	3	x	x	PUNCT
ejpam-77	123	4	=	=	PUNCT
ejpam-77	123	5	r	r	NOUN
ejpam-77	123	6	in	in	ADP
ejpam-77	123	7	example	example	NOUN
ejpam-77	123	8	1	1	NUM
ejpam-77	123	9	,	,	PUNCT
ejpam-77	123	10	we	we	PRON
ejpam-77	123	11	have	have	VERB
ejpam-77	123	12	(	(	PUNCT
ejpam-77	123	13	r	r	NOUN
ejpam-77	123	14	,	,	PUNCT
ejpam-77	123	15	f	f	PROPN
ejpam-77	123	16	,	,	PUNCT
ejpam-77	123	17	t	t	PROPN
ejpam-77	123	18	)	)	PUNCT
ejpam-77	123	19	is	be	AUX
ejpam-77	123	20	a	a	DET
ejpam-77	123	21	pn	pn	PROPN
ejpam-77	123	22	space	space	NOUN
ejpam-77	123	23	induced	induce	VERB
ejpam-77	123	24	by	by	ADP
ejpam-77	123	25	the	the	DET
ejpam-77	123	26	probabilistic	probabilistic	ADJ
ejpam-77	123	27	norm	norm	NOUN
ejpam-77	123	28	fx(ε	fx(ε	PUNCT
ejpam-77	123	29	)	)	PUNCT
ejpam-77	123	30	=	=	SYM
ejpam-77	123	31	ε	ε	PROPN
ejpam-77	123	32	ε+‖x‖	ε+‖x‖	PUNCT
ejpam-77	123	33	.	.	PUNCT
ejpam-77	124	1	let	let	VERB
ejpam-77	124	2	us	we	PRON
ejpam-77	124	3	suppose	suppose	VERB
ejpam-77	124	4	that	that	SCONJ
ejpam-77	124	5	a∈	a∈	PROPN
ejpam-77	124	6	ifin	ifin	PROPN
ejpam-77	124	7	.	.	PUNCT
ejpam-77	125	1	define	define	VERB
ejpam-77	125	2	a	a	DET
ejpam-77	125	3	sequence	sequence	NOUN
ejpam-77	125	4	{	{	PUNCT
ejpam-77	125	5	xn	xn	NOUN
ejpam-77	125	6	}	}	PUNCT
ejpam-77	125	7	in	in	ADP
ejpam-77	125	8	r	r	NOUN
ejpam-77	125	9	via	via	ADP
ejpam-77	125	10	xn	xn	NOUN
ejpam-77	126	1	=	=	PUNCT
ejpam-77	126	2			PROPN
ejpam-77	126	3			X
ejpam-77	126	4			NOUN
ejpam-77	126	5	1	1	NUM
ejpam-77	126	6	,	,	PUNCT
ejpam-77	126	7	if	if	SCONJ
ejpam-77	126	8	n	n	PRON
ejpam-77	126	9	∈	∈	VERB
ejpam-77	126	10	a	a	DET
ejpam-77	126	11	0	0	NUM
ejpam-77	126	12	,	,	PUNCT
ejpam-77	126	13	otherwise	otherwise	ADV
ejpam-77	126	14	.	.	PUNCT
ejpam-77	127	1	then	then	ADV
ejpam-77	127	2	,	,	PUNCT
ejpam-77	127	3	for	for	ADP
ejpam-77	127	4	every	every	DET
ejpam-77	127	5	ε	ε	PROPN
ejpam-77	127	6	>	>	X
ejpam-77	127	7	0	0	PUNCT
ejpam-77	127	8	and	and	CCONJ
ejpam-77	127	9	λ	λ	PROPN
ejpam-77	127	10	∈	∈	PROPN
ejpam-77	127	11	(	(	PUNCT
ejpam-77	127	12	0	0	NUM
ejpam-77	127	13	,	,	PUNCT
ejpam-77	127	14	1	1	NUM
ejpam-77	127	15	)	)	PUNCT
ejpam-77	127	16	,	,	PUNCT
ejpam-77	127	17	let	let	VERB
ejpam-77	127	18	k	k	PROPN
ejpam-77	127	19	=	=	PRON
ejpam-77	127	20	{	{	PUNCT
ejpam-77	127	21	n	n	NOUN
ejpam-77	127	22	∈	∈	PROPN
ejpam-77	127	23	n	n	NOUN
ejpam-77	127	24	:	:	PUNCT
ejpam-77	127	25	xn	xn	PROPN
ejpam-77	127	26	/∈	/∈	PUNCT
ejpam-77	128	1	nθ	nθ	CCONJ
ejpam-77	128	2	(	(	PUNCT
ejpam-77	128	3	ε	ε	PROPN
ejpam-77	128	4	,	,	PUNCT
ejpam-77	128	5	λ	λ	NOUN
ejpam-77	128	6	)	)	PUNCT
ejpam-77	128	7	}	}	PUNCT
ejpam-77	128	8	.	.	PUNCT
ejpam-77	129	1	we	we	PRON
ejpam-77	129	2	observe	observe	VERB
ejpam-77	129	3	that	that	SCONJ
ejpam-77	129	4	xn	xn	PROPN
ejpam-77	129	5	/∈nθ	/∈nθ	PUNCT
ejpam-77	129	6	(	(	PUNCT
ejpam-77	129	7	ε	ε	PROPN
ejpam-77	129	8	,	,	PUNCT
ejpam-77	129	9	λ	λ	NOUN
ejpam-77	129	10	)	)	PUNCT
ejpam-77	129	11	⇒	⇒	PROPN
ejpam-77	129	12	fxn	fxn	NOUN
ejpam-77	129	13	(	(	PUNCT
ejpam-77	129	14	ε)≤	ε)≤	NOUN
ejpam-77	129	15	1−λ	1−λ	NUM
ejpam-77	129	16	⇒	⇒	NOUN
ejpam-77	129	17	ε	ε	PROPN
ejpam-77	129	18	ε+	ε+	X
ejpam-77	129	19	‖xn‖	‖xn‖	ADJ
ejpam-77	129	20	≤	≤	NUM
ejpam-77	129	21	1−λ	1−λ	NUM
ejpam-77	129	22	⇒	⇒	NOUN
ejpam-77	129	23	‖xn‖	‖xn‖	PROPN
ejpam-77	129	24	≥	≥	PROPN
ejpam-77	129	25	ελ	ελ	NUM
ejpam-77	129	26	1−λ	1−λ	NUM
ejpam-77	129	27	>	>	PUNCT
ejpam-77	129	28	0	0	X
ejpam-77	129	29	.	.	PUNCT
ejpam-77	130	1	hence	hence	ADV
ejpam-77	130	2	,	,	PUNCT
ejpam-77	130	3	we	we	PRON
ejpam-77	130	4	have	have	VERB
ejpam-77	130	5	k	k	NOUN
ejpam-77	130	6	=	=	X
ejpam-77	130	7	{	{	PUNCT
ejpam-77	130	8	n	n	NOUN
ejpam-77	130	9	∈	∈	PROPN
ejpam-77	130	10	n	n	CCONJ
ejpam-77	130	11	:	:	PUNCT
ejpam-77	130	12	‖xn‖	‖xn‖	ADJ
ejpam-77	130	13	>	>	X
ejpam-77	130	14	0	0	NUM
ejpam-77	130	15	}	}	PUNCT
ejpam-77	130	16	=	=	SYM
ejpam-77	130	17	{	{	PUNCT
ejpam-77	130	18	n	n	NOUN
ejpam-77	130	19	∈	∈	PROPN
ejpam-77	130	20	n	n	NOUN
ejpam-77	130	21	:	:	PUNCT
ejpam-77	130	22	xn	xn	PUNCT
ejpam-77	131	1	=	=	SYM
ejpam-77	131	2	1	1	X
ejpam-77	131	3	}	}	PUNCT
ejpam-77	131	4	=	=	SYM
ejpam-77	131	5	a∈	a∈	PROPN
ejpam-77	132	1	i	i	PRON
ejpam-77	132	2	f	f	PROPN
ejpam-77	132	3	.	.	PUNCT
ejpam-77	133	1	therefore	therefore	ADV
ejpam-77	133	2	i	i	PRON
ejpam-77	133	3	f	f	PROPN
ejpam-77	133	4	fin	fin	NOUN
ejpam-77	133	5	−	−	PROPN
ejpam-77	133	6	lim	lim	PROPN
ejpam-77	133	7	xn	xn	PUNCT
ejpam-77	134	1	=	=	SYM
ejpam-77	134	2	θ	θ	PROPN
ejpam-77	134	3	.	.	PUNCT
ejpam-77	135	1	but	but	CCONJ
ejpam-77	135	2	the	the	DET
ejpam-77	135	3	sequence	sequence	NOUN
ejpam-77	135	4	{	{	PUNCT
ejpam-77	135	5	xn	xn	NOUN
ejpam-77	135	6	}	}	PUNCT
ejpam-77	135	7	is	be	AUX
ejpam-77	135	8	not	not	PART
ejpam-77	135	9	convergent	convergent	ADJ
ejpam-77	135	10	to	to	ADP
ejpam-77	135	11	θ	θ	PROPN
ejpam-77	135	12	in	in	ADP
ejpam-77	135	13	(	(	PUNCT
ejpam-77	135	14	r,‖	r,‖	PROPN
ejpam-77	135	15	·	·	PUNCT
ejpam-77	135	16	‖	‖	NUM
ejpam-77	135	17	)	)	PUNCT
ejpam-77	135	18	.	.	PUNCT
ejpam-77	136	1	by	by	ADP
ejpam-77	136	2	lemma	lemma	PROPN
ejpam-77	136	3	1	1	NUM
ejpam-77	136	4	,	,	PUNCT
ejpam-77	136	5	this	this	PRON
ejpam-77	136	6	implies	imply	VERB
ejpam-77	136	7	that	that	SCONJ
ejpam-77	136	8	f	f	PROPN
ejpam-77	136	9	−	−	PROPN
ejpam-77	136	10	lim	lim	PROPN
ejpam-77	136	11	xn	xn	PROPN
ejpam-77	137	1	6=	6=	PROPN
ejpam-77	137	2	θ	θ	PROPN
ejpam-77	137	3	.	.	PUNCT
ejpam-77	138	1	m.	m.	NOUN
ejpam-77	138	2	rahmat	rahmat	PROPN
ejpam-77	138	3	and	and	CCONJ
ejpam-77	138	4	harikrishnan	harikrishnan	PROPN
ejpam-77	138	5	k.	k.	PROPN
ejpam-77	138	6	/	/	PUNCT
ejpam-77	138	7	eur	eur	PROPN
ejpam-77	138	8	.	.	PUNCT
ejpam-77	139	1	j.	j.	PROPN
ejpam-77	139	2	pure	pure	PROPN
ejpam-77	139	3	appl	appl	PROPN
ejpam-77	139	4	.	.	PROPN
ejpam-77	139	5	math	math	PROPN
ejpam-77	139	6	,	,	PUNCT
ejpam-77	139	7	2	2	NUM
ejpam-77	139	8	(	(	PUNCT
ejpam-77	139	9	2009	2009	NUM
ejpam-77	139	10	)	)	PUNCT
ejpam-77	139	11	,	,	PUNCT
ejpam-77	139	12	(	(	PUNCT
ejpam-77	139	13	195	195	NUM
ejpam-77	139	14	-	-	PUNCT
ejpam-77	139	15	212	212	NUM
ejpam-77	139	16	)	)	PUNCT
ejpam-77	139	17	202	202	NUM
ejpam-77	140	1	lemma	lemma	PROPN
ejpam-77	140	2	2.3	2.3	NUM
ejpam-77	140	3	.	.	PUNCT
ejpam-77	141	1	let	let	VERB
ejpam-77	141	2	(	(	PUNCT
ejpam-77	141	3	x	x	SYM
ejpam-77	141	4	,	,	PUNCT
ejpam-77	141	5	f	f	PROPN
ejpam-77	141	6	,	,	PUNCT
ejpam-77	141	7	t	t	PROPN
ejpam-77	141	8	)	)	PUNCT
ejpam-77	141	9	be	be	AUX
ejpam-77	141	10	a	a	DET
ejpam-77	141	11	pn	pn	NOUN
ejpam-77	141	12	space	space	NOUN
ejpam-77	142	1	and	and	CCONJ
ejpam-77	142	2	i	i	PRON
ejpam-77	142	3	is	be	AUX
ejpam-77	142	4	an	an	DET
ejpam-77	142	5	admissible	admissible	ADJ
ejpam-77	142	6	ideal	ideal	NOUN
ejpam-77	142	7	on	on	ADP
ejpam-77	142	8	x	x	X
ejpam-77	142	9	.	.	PUNCT
ejpam-77	143	1	then	then	ADV
ejpam-77	143	2	i	i	PRON
ejpam-77	143	3	f	f	PROPN
ejpam-77	143	4	fin	fin	NOUN
ejpam-77	143	5	-convergence	-convergence	PROPN
ejpam-77	143	6	implies	imply	VERB
ejpam-77	143	7	i	i	PRON
ejpam-77	143	8	f	f	PROPN
ejpam-77	143	9	-convergence	-convergence	PROPN
ejpam-77	143	10	.	.	PUNCT
ejpam-77	144	1	proof	proof	NOUN
ejpam-77	144	2	.	.	PUNCT
ejpam-77	145	1	for	for	SCONJ
ejpam-77	145	2	i	i	PRON
ejpam-77	145	3	be	be	VERB
ejpam-77	145	4	an	an	DET
ejpam-77	145	5	admissible	admissible	ADJ
ejpam-77	145	6	ideal	ideal	NOUN
ejpam-77	145	7	,	,	PUNCT
ejpam-77	145	8	we	we	PRON
ejpam-77	145	9	have	have	VERB
ejpam-77	145	10	⋃	⋃	VERB
ejpam-77	146	1	i	i	PRON
ejpam-77	146	2	=	=	PUNCT
ejpam-77	146	3	n.	n.	NOUN
ejpam-77	146	4	this	this	PRON
ejpam-77	146	5	implies	imply	VERB
ejpam-77	146	6	that	that	SCONJ
ejpam-77	146	7	ifin	ifin	PROPN
ejpam-77	147	1	⊂	⊂	PROPN
ejpam-77	148	1	i	i	PRON
ejpam-77	148	2	.	.	PUNCT
ejpam-77	149	1	so	so	ADV
ejpam-77	149	2	,	,	PUNCT
ejpam-77	149	3	i	i	PRON
ejpam-77	149	4	f	f	PROPN
ejpam-77	149	5	fin	fin	NOUN
ejpam-77	149	6	-convergence	-convergence	PROPN
ejpam-77	149	7	implies	imply	VERB
ejpam-77	149	8	i	i	PRON
ejpam-77	149	9	f	f	PROPN
ejpam-77	149	10	-convergence	-convergence	PROPN
ejpam-77	149	11	.	.	PUNCT
ejpam-77	150	1	the	the	DET
ejpam-77	150	2	following	follow	VERB
ejpam-77	150	3	lemma	lemma	PROPN
ejpam-77	150	4	is	be	AUX
ejpam-77	150	5	an	an	DET
ejpam-77	150	6	immediate	immediate	ADJ
ejpam-77	150	7	consequence	consequence	NOUN
ejpam-77	150	8	of	of	ADP
ejpam-77	150	9	definition	definition	NOUN
ejpam-77	150	10	of	of	ADP
ejpam-77	150	11	statistical	statistical	ADJ
ejpam-77	150	12	convergence	convergence	NOUN
ejpam-77	150	13	sequence	sequence	NOUN
ejpam-77	150	14	.	.	PUNCT
ejpam-77	151	1	lemma	lemma	PROPN
ejpam-77	151	2	2.4	2.4	NUM
ejpam-77	151	3	.	.	PUNCT
ejpam-77	152	1	let	let	AUX
ejpam-77	152	2	(	(	PUNCT
ejpam-77	152	3	x	x	SYM
ejpam-77	152	4	,	,	PUNCT
ejpam-77	152	5	f	f	PROPN
ejpam-77	152	6	,	,	PUNCT
ejpam-77	152	7	t	t	PROPN
ejpam-77	152	8	)	)	PUNCT
ejpam-77	152	9	be	be	AUX
ejpam-77	152	10	a	a	DET
ejpam-77	152	11	pn	pn	NOUN
ejpam-77	152	12	space	space	NOUN
ejpam-77	152	13	.	.	PUNCT
ejpam-77	153	1	if	if	SCONJ
ejpam-77	153	2	iδ	iδ	VERB
ejpam-77	153	3	=	=	PUNCT
ejpam-77	153	4	{	{	PUNCT
ejpam-77	153	5	a⊆	a⊆	PROPN
ejpam-77	153	6	n	n	X
ejpam-77	153	7	:	:	PUNCT
ejpam-77	153	8	δ(a	δ(a	X
ejpam-77	153	9	)	)	PUNCT
ejpam-77	154	1	=	=	PUNCT
ejpam-77	154	2	0	0	X
ejpam-77	154	3	}	}	PUNCT
ejpam-77	154	4	where	where	SCONJ
ejpam-77	154	5	δ(a	δ(a	PROPN
ejpam-77	154	6	)	)	PUNCT
ejpam-77	154	7	be	be	VERB
ejpam-77	154	8	the	the	DET
ejpam-77	154	9	density	density	NOUN
ejpam-77	154	10	of	of	ADP
ejpam-77	154	11	a	a	PRON
ejpam-77	154	12	,	,	PUNCT
ejpam-77	154	13	then	then	ADV
ejpam-77	154	14	i	i	PRON
ejpam-77	154	15	f	f	PROPN
ejpam-77	154	16	δ	δ	PROPN
ejpam-77	154	17	-convergence	-convergence	PROPN
ejpam-77	154	18	coincide	coincide	NOUN
ejpam-77	154	19	with	with	ADP
ejpam-77	154	20	statistical	statistical	ADJ
ejpam-77	154	21	convergence	convergence	NOUN
ejpam-77	154	22	.	.	PUNCT
ejpam-77	155	1	lemma	lemma	PROPN
ejpam-77	155	2	2.5	2.5	NUM
ejpam-77	155	3	.	.	PUNCT
ejpam-77	156	1	if	if	SCONJ
ejpam-77	156	2	{	{	PUNCT
ejpam-77	156	3	xn	xn	X
ejpam-77	156	4	}	}	PUNCT
ejpam-77	156	5	and	and	CCONJ
ejpam-77	156	6	{	{	PUNCT
ejpam-77	156	7	yn	yn	NOUN
ejpam-77	156	8	}	}	PUNCT
ejpam-77	156	9	are	be	AUX
ejpam-77	156	10	two	two	NUM
ejpam-77	156	11	sequences	sequence	NOUN
ejpam-77	156	12	in	in	ADP
ejpam-77	156	13	(	(	PUNCT
ejpam-77	156	14	x	x	INTJ
ejpam-77	156	15	,	,	PUNCT
ejpam-77	156	16	f	f	PROPN
ejpam-77	156	17	,	,	PUNCT
ejpam-77	156	18	t	t	PROPN
ejpam-77	156	19	)	)	PUNCT
ejpam-77	156	20	with	with	ADP
ejpam-77	156	21	t	t	PROPN
ejpam-77	156	22	(	(	PUNCT
ejpam-77	156	23	a	a	DET
ejpam-77	156	24	,	,	PUNCT
ejpam-77	156	25	a	a	NOUN
ejpam-77	156	26	)	)	PUNCT
ejpam-77	156	27	>	>	PUNCT
ejpam-77	156	28	a	a	PRON
ejpam-77	156	29	for	for	ADP
ejpam-77	156	30	every	every	DET
ejpam-77	156	31	a	a	DET
ejpam-77	156	32	∈	∈	PROPN
ejpam-77	156	33	(	(	PUNCT
ejpam-77	156	34	0	0	NUM
ejpam-77	156	35	,	,	PUNCT
ejpam-77	156	36	1	1	NUM
ejpam-77	156	37	)	)	PUNCT
ejpam-77	156	38	,	,	PUNCT
ejpam-77	156	39	then	then	ADV
ejpam-77	156	40	(	(	PUNCT
ejpam-77	156	41	i	i	NOUN
ejpam-77	156	42	)	)	PUNCT
ejpam-77	156	43	if	if	SCONJ
ejpam-77	156	44	i	i	PRON
ejpam-77	156	45	f	f	PROPN
ejpam-77	157	1	−	−	PROPN
ejpam-77	157	2	lim	lim	PROPN
ejpam-77	157	3	xn	xn	PUNCT
ejpam-77	158	1	=	=	SYM
ejpam-77	158	2	ξ	ξ	PROPN
ejpam-77	158	3	and	and	CCONJ
ejpam-77	158	4	i	i	PRON
ejpam-77	158	5	f	f	PROPN
ejpam-77	159	1	−	−	PROPN
ejpam-77	159	2	lim	lim	PROPN
ejpam-77	159	3	yn	yn	PROPN
ejpam-77	159	4	=	=	PROPN
ejpam-77	159	5	η	η	PROPN
ejpam-77	159	6	,	,	PUNCT
ejpam-77	159	7	then	then	ADV
ejpam-77	159	8	i	i	PRON
ejpam-77	159	9	f	f	PROPN
ejpam-77	160	1	−	−	PROPN
ejpam-77	160	2	lim(xn+	lim(xn+	PROPN
ejpam-77	160	3	yn	yn	PROPN
ejpam-77	160	4	)	)	PUNCT
ejpam-77	160	5	=	=	PUNCT
ejpam-77	160	6	ξ+η	ξ+η	NUM
ejpam-77	160	7	.	.	PUNCT
ejpam-77	161	1	(	(	PUNCT
ejpam-77	161	2	ii)if	ii)if	PUNCT
ejpam-77	161	3	i	i	INTJ
ejpam-77	161	4	f	f	PROPN
ejpam-77	162	1	−	−	PROPN
ejpam-77	162	2	lim	lim	PROPN
ejpam-77	162	3	xn	xn	PUNCT
ejpam-77	162	4	=	=	SYM
ejpam-77	162	5	ξ	ξ	PROPN
ejpam-77	162	6	and	and	CCONJ
ejpam-77	162	7	α	α	NOUN
ejpam-77	162	8	∈	∈	PROPN
ejpam-77	162	9	r	r	NOUN
ejpam-77	162	10	,	,	PUNCT
ejpam-77	162	11	then	then	ADV
ejpam-77	162	12	i	i	PRON
ejpam-77	162	13	f	f	NOUN
ejpam-77	162	14	−	−	PROPN
ejpam-77	162	15	limαxn	limαxn	PROPN
ejpam-77	162	16	=	=	SYM
ejpam-77	162	17	αξ	αξ	PROPN
ejpam-77	162	18	.	.	PUNCT
ejpam-77	163	1	(	(	PUNCT
ejpam-77	163	2	iii	iii	X
ejpam-77	163	3	)	)	PUNCT
ejpam-77	163	4	if	if	SCONJ
ejpam-77	163	5	i	i	PRON
ejpam-77	163	6	f	f	PROPN
ejpam-77	164	1	−	−	PROPN
ejpam-77	164	2	lim	lim	PROPN
ejpam-77	164	3	xn	xn	PUNCT
ejpam-77	165	1	=	=	SYM
ejpam-77	165	2	ξ	ξ	PROPN
ejpam-77	165	3	and	and	CCONJ
ejpam-77	165	4	i	i	PRON
ejpam-77	165	5	f	f	PROPN
ejpam-77	166	1	−	−	PROPN
ejpam-77	166	2	lim	lim	PROPN
ejpam-77	166	3	yn	yn	PROPN
ejpam-77	166	4	=	=	PROPN
ejpam-77	166	5	η	η	PROPN
ejpam-77	166	6	,	,	PUNCT
ejpam-77	166	7	then	then	ADV
ejpam-77	166	8	i	i	PRON
ejpam-77	166	9	f	f	PROPN
ejpam-77	167	1	−	−	PROPN
ejpam-77	167	2	lim(xn−	lim(xn−	PROPN
ejpam-77	167	3	yn	yn	PROPN
ejpam-77	167	4	)	)	PUNCT
ejpam-77	167	5	=	=	SYM
ejpam-77	167	6	ξ−η	ξ−η	NOUN
ejpam-77	167	7	.	.	PUNCT
ejpam-77	168	1	proof	proof	NOUN
ejpam-77	168	2	.	.	PUNCT
ejpam-77	169	1	(	(	PUNCT
ejpam-77	169	2	i	i	NOUN
ejpam-77	169	3	)	)	PUNCT
ejpam-77	169	4	let	let	VERB
ejpam-77	169	5	ε	ε	PROPN
ejpam-77	169	6	>	>	X
ejpam-77	169	7	0	0	PUNCT
ejpam-77	170	1	and	and	CCONJ
ejpam-77	170	2	λ	λ	PROPN
ejpam-77	170	3	∈	∈	PROPN
ejpam-77	170	4	(	(	PUNCT
ejpam-77	170	5	0	0	NUM
ejpam-77	170	6	,	,	PUNCT
ejpam-77	170	7	1	1	NUM
ejpam-77	170	8	)	)	PUNCT
ejpam-77	170	9	.	.	PUNCT
ejpam-77	171	1	since	since	SCONJ
ejpam-77	171	2	i	i	PRON
ejpam-77	171	3	f	f	PROPN
ejpam-77	171	4	−	−	PROPN
ejpam-77	171	5	lim	lim	PROPN
ejpam-77	171	6	xn	xn	PUNCT
ejpam-77	172	1	=	=	SYM
ejpam-77	172	2	ξ	ξ	PROPN
ejpam-77	172	3	and	and	CCONJ
ejpam-77	172	4	i	i	PRON
ejpam-77	172	5	f	f	PROPN
ejpam-77	173	1	−	−	PROPN
ejpam-77	173	2	lim	lim	PROPN
ejpam-77	173	3	yn	yn	PROPN
ejpam-77	173	4	=	=	PROPN
ejpam-77	173	5	η	η	PROPN
ejpam-77	173	6	,	,	PUNCT
ejpam-77	173	7	the	the	DET
ejpam-77	173	8	sets	set	VERB
ejpam-77	173	9	a	a	DET
ejpam-77	173	10	=	=	SYM
ejpam-77	173	11	{	{	PUNCT
ejpam-77	173	12	n	n	NOUN
ejpam-77	173	13	∈	∈	PROPN
ejpam-77	174	1	n	n	NOUN
ejpam-77	174	2	:	:	PUNCT
ejpam-77	174	3	xn	xn	PROPN
ejpam-77	174	4	/∈	/∈	PROPN
ejpam-77	175	1	nξ	nξ	PROPN
ejpam-77	175	2	(	(	PUNCT
ejpam-77	175	3	ε	ε	PROPN
ejpam-77	175	4	2	2	NUM
ejpam-77	175	5	,	,	PUNCT
ejpam-77	175	6	λ	λ	NOUN
ejpam-77	175	7	)	)	PUNCT
ejpam-77	175	8	}	}	PUNCT
ejpam-77	175	9	and	and	CCONJ
ejpam-77	175	10	b	b	X
ejpam-77	175	11	=	=	SYM
ejpam-77	175	12	{	{	PUNCT
ejpam-77	175	13	n	n	NOUN
ejpam-77	175	14	∈	∈	PROPN
ejpam-77	175	15	n	n	NOUN
ejpam-77	175	16	:	:	PUNCT
ejpam-77	175	17	xn	xn	PROPN
ejpam-77	175	18	/∈	/∈	PUNCT
ejpam-77	176	1	nη	nη	CCONJ
ejpam-77	176	2	(	(	PUNCT
ejpam-77	176	3	ε	ε	PROPN
ejpam-77	176	4	2	2	NUM
ejpam-77	176	5	,	,	PUNCT
ejpam-77	176	6	λ	λ	NOUN
ejpam-77	176	7	)	)	PUNCT
ejpam-77	176	8	}	}	PUNCT
ejpam-77	176	9	are	be	AUX
ejpam-77	176	10	belongs	belong	VERB
ejpam-77	176	11	to	to	ADP
ejpam-77	176	12	i	i	PRON
ejpam-77	176	13	.	.	PUNCT
ejpam-77	177	1	let	let	VERB
ejpam-77	177	2	c	c	NOUN
ejpam-77	177	3	=	=	PRON
ejpam-77	177	4	{	{	PUNCT
ejpam-77	177	5	n	n	NOUN
ejpam-77	177	6	∈	∈	PROPN
ejpam-77	178	1	n	n	CCONJ
ejpam-77	178	2	:	:	PUNCT
ejpam-77	178	3	xn+	xn+	PROPN
ejpam-77	179	1	yn	yn	X
ejpam-77	179	2	/∈	/∈	PUNCT
ejpam-77	179	3	nξ+η(ε	nξ+η(ε	PRON
ejpam-77	179	4	,	,	PUNCT
ejpam-77	179	5	λ	λ	NOUN
ejpam-77	179	6	)	)	PUNCT
ejpam-77	179	7	}	}	PUNCT
ejpam-77	179	8	.	.	PUNCT
ejpam-77	180	1	since	since	SCONJ
ejpam-77	180	2	i	i	PRON
ejpam-77	180	3	is	be	AUX
ejpam-77	180	4	an	an	DET
ejpam-77	180	5	ideal	ideal	NOUN
ejpam-77	180	6	it	it	PRON
ejpam-77	180	7	is	be	AUX
ejpam-77	180	8	sufficient	sufficient	ADJ
ejpam-77	180	9	to	to	PART
ejpam-77	180	10	show	show	VERB
ejpam-77	180	11	that	that	SCONJ
ejpam-77	180	12	c	c	PROPN
ejpam-77	180	13	⊂	⊂	PROPN
ejpam-77	180	14	a∪	a∪	PROPN
ejpam-77	181	1	b.	b.	PROPN
ejpam-77	182	1	this	this	PRON
ejpam-77	182	2	is	be	AUX
ejpam-77	182	3	equivalent	equivalent	ADJ
ejpam-77	182	4	to	to	PART
ejpam-77	182	5	show	show	VERB
ejpam-77	182	6	that	that	SCONJ
ejpam-77	182	7	c	c	PROPN
ejpam-77	182	8	c	c	PROPN
ejpam-77	182	9	⊃	⊃	PROPN
ejpam-77	182	10	ac	ac	PROPN
ejpam-77	182	11	∩	∩	PROPN
ejpam-77	182	12	bc	bc	PROPN
ejpam-77	182	13	where	where	SCONJ
ejpam-77	182	14	ac	ac	PROPN
ejpam-77	182	15	and	and	CCONJ
ejpam-77	182	16	bc	bc	PROPN
ejpam-77	182	17	are	be	AUX
ejpam-77	182	18	belongs	belong	VERB
ejpam-77	182	19	to	to	ADP
ejpam-77	182	20	f	f	PROPN
ejpam-77	182	21	(	(	PUNCT
ejpam-77	182	22	i	i	NOUN
ejpam-77	182	23	)	)	PUNCT
ejpam-77	182	24	.	.	PUNCT
ejpam-77	183	1	let	let	VERB
ejpam-77	183	2	n	n	PRON
ejpam-77	183	3	∈	∈	PROPN
ejpam-77	183	4	ac	ac	PROPN
ejpam-77	183	5	∩	∩	PROPN
ejpam-77	183	6	bc	bc	PROPN
ejpam-77	183	7	,	,	PUNCT
ejpam-77	183	8	i.e.	i.e.	X
ejpam-77	183	9	,	,	PUNCT
ejpam-77	183	10	n	n	PROPN
ejpam-77	183	11	∈	∈	NOUN
ejpam-77	183	12	ac	ac	PROPN
ejpam-77	183	13	and	and	CCONJ
ejpam-77	183	14	n	n	DET
ejpam-77	183	15	∈	∈	PROPN
ejpam-77	183	16	bc	bc	PROPN
ejpam-77	183	17	then	then	ADV
ejpam-77	183	18	by	by	ADP
ejpam-77	183	19	(	(	PUNCT
ejpam-77	183	20	n4	n4	PROPN
ejpam-77	183	21	)	)	PUNCT
ejpam-77	183	22	we	we	PRON
ejpam-77	183	23	have	have	VERB
ejpam-77	183	24	f(xn+yn)−(ξ+η)(ε	f(xn+yn)−(ξ+η)(ε	NOUN
ejpam-77	183	25	)	)	PUNCT
ejpam-77	183	26	≥	≥	NOUN
ejpam-77	184	1	τt	τt	X
ejpam-77	184	2	(	(	PUNCT
ejpam-77	184	3	fxn−ξ	fxn−ξ	NOUN
ejpam-77	184	4	,	,	PUNCT
ejpam-77	184	5	fyn−η)(ε	fyn−η)(ε	NOUN
ejpam-77	184	6	)	)	PUNCT
ejpam-77	184	7	≥	≥	PROPN
ejpam-77	184	8	t	t	PROPN
ejpam-77	184	9	�	�	PROPN
ejpam-77	184	10	fxn−ξ	fxn−ξ	PROPN
ejpam-77	184	11	(	(	PUNCT
ejpam-77	184	12	ε	ε	PROPN
ejpam-77	184	13	2	2	NUM
ejpam-77	184	14	)	)	PUNCT
ejpam-77	184	15	,	,	PUNCT
ejpam-77	184	16	fyn−η	fyn−η	PROPN
ejpam-77	184	17	(	(	PUNCT
ejpam-77	184	18	ε	ε	PROPN
ejpam-77	184	19	2	2	NUM
ejpam-77	184	20	)	)	PUNCT
ejpam-77	184	21	�	�	PROPN
ejpam-77	184	22	>	>	X
ejpam-77	184	23	t	t	PROPN
ejpam-77	184	24	(	(	PUNCT
ejpam-77	184	25	1−λ	1−λ	NUM
ejpam-77	184	26	,	,	PUNCT
ejpam-77	184	27	1−λ	1−λ	NUM
ejpam-77	184	28	)	)	PUNCT
ejpam-77	184	29	>	>	X
ejpam-77	184	30	1−λ	1−λ	NUM
ejpam-77	184	31	.	.	PUNCT
ejpam-77	185	1	hence	hence	ADV
ejpam-77	185	2	,	,	PUNCT
ejpam-77	185	3	n	n	PROPN
ejpam-77	185	4	∈	∈	NOUN
ejpam-77	185	5	c	c	NOUN
ejpam-77	185	6	c	c	X
ejpam-77	185	7	⊃	⊃	PROPN
ejpam-77	185	8	ac	ac	PROPN
ejpam-77	185	9	∩	∩	PROPN
ejpam-77	185	10	bc	bc	PROPN
ejpam-77	185	11	∈	∈	PROPN
ejpam-77	185	12	f	f	PROPN
ejpam-77	185	13	(	(	PUNCT
ejpam-77	185	14	i	i	PROPN
ejpam-77	185	15	)	)	PUNCT
ejpam-77	185	16	which	which	PRON
ejpam-77	185	17	implies	imply	VERB
ejpam-77	185	18	c	c	PROPN
ejpam-77	185	19	⊂	⊂	PROPN
ejpam-77	185	20	a∪	a∪	X
ejpam-77	186	1	b	b	X
ejpam-77	186	2	∈	∈	PROPN
ejpam-77	187	1	i	i	PRON
ejpam-77	187	2	and	and	CCONJ
ejpam-77	187	3	the	the	DET
ejpam-77	187	4	result	result	NOUN
ejpam-77	187	5	follows	follow	VERB
ejpam-77	187	6	.	.	PUNCT
ejpam-77	188	1	m.	m.	NOUN
ejpam-77	188	2	rahmat	rahmat	PROPN
ejpam-77	188	3	and	and	CCONJ
ejpam-77	188	4	harikrishnan	harikrishnan	PROPN
ejpam-77	188	5	k.	k.	PROPN
ejpam-77	188	6	/	/	PUNCT
ejpam-77	188	7	eur	eur	PROPN
ejpam-77	188	8	.	.	PUNCT
ejpam-77	189	1	j.	j.	PROPN
ejpam-77	189	2	pure	pure	PROPN
ejpam-77	189	3	appl	appl	PROPN
ejpam-77	189	4	.	.	PROPN
ejpam-77	189	5	math	math	PROPN
ejpam-77	189	6	,	,	PUNCT
ejpam-77	189	7	2	2	NUM
ejpam-77	189	8	(	(	PUNCT
ejpam-77	189	9	2009	2009	NUM
ejpam-77	189	10	)	)	PUNCT
ejpam-77	189	11	,	,	PUNCT
ejpam-77	189	12	(	(	PUNCT
ejpam-77	189	13	195	195	NUM
ejpam-77	189	14	-	-	PUNCT
ejpam-77	189	15	212	212	NUM
ejpam-77	189	16	)	)	PUNCT
ejpam-77	189	17	203	203	NUM
ejpam-77	189	18	(	(	PUNCT
ejpam-77	189	19	ii)let	ii)let	PROPN
ejpam-77	189	20	ε	ε	PROPN
ejpam-77	189	21	>	>	X
ejpam-77	189	22	0	0	PUNCT
ejpam-77	190	1	and	and	CCONJ
ejpam-77	190	2	λ	λ	PROPN
ejpam-77	190	3	∈	∈	PROPN
ejpam-77	190	4	(	(	PUNCT
ejpam-77	190	5	0	0	NUM
ejpam-77	190	6	,	,	PUNCT
ejpam-77	190	7	1	1	NUM
ejpam-77	190	8	)	)	PUNCT
ejpam-77	190	9	.	.	PUNCT
ejpam-77	191	1	since	since	SCONJ
ejpam-77	191	2	i	i	PRON
ejpam-77	191	3	f	f	PROPN
ejpam-77	191	4	−	−	PROPN
ejpam-77	191	5	lim	lim	PROPN
ejpam-77	191	6	xn	xn	PUNCT
ejpam-77	192	1	=	=	SYM
ejpam-77	192	2	ξ	ξ	PROPN
ejpam-77	192	3	,	,	PUNCT
ejpam-77	192	4	we	we	PRON
ejpam-77	192	5	have	have	VERB
ejpam-77	192	6	a	a	DET
ejpam-77	192	7	=	=	X
ejpam-77	192	8	{	{	PUNCT
ejpam-77	192	9	n	n	NOUN
ejpam-77	192	10	∈	∈	PROPN
ejpam-77	192	11	n	n	NOUN
ejpam-77	192	12	:	:	PUNCT
ejpam-77	192	13	xn	xn	PROPN
ejpam-77	192	14	/∈	/∈	PUNCT
ejpam-77	192	15	nξ(ε	nξ(ε	PROPN
ejpam-77	192	16	,	,	PUNCT
ejpam-77	192	17	λ	λ	NOUN
ejpam-77	192	18	)	)	PUNCT
ejpam-77	192	19	}	}	PUNCT
ejpam-77	192	20	∈	∈	PROPN
ejpam-77	193	1	i	i	PRON
ejpam-77	193	2	.	.	PUNCT
ejpam-77	194	1	this	this	PRON
ejpam-77	194	2	implies	imply	VERB
ejpam-77	194	3	that	that	SCONJ
ejpam-77	194	4	ac	ac	PROPN
ejpam-77	194	5	=	=	PUNCT
ejpam-77	194	6	{	{	PUNCT
ejpam-77	194	7	n	n	NOUN
ejpam-77	194	8	∈	∈	PROPN
ejpam-77	194	9	n	n	NOUN
ejpam-77	194	10	:	:	PUNCT
ejpam-77	194	11	xn	xn	PROPN
ejpam-77	194	12	∈	∈	PROPN
ejpam-77	194	13	nξ(ε	nξ(ε	PRON
ejpam-77	194	14	,	,	PUNCT
ejpam-77	194	15	λ	λ	NOUN
ejpam-77	194	16	)	)	PUNCT
ejpam-77	194	17	}	}	PUNCT
ejpam-77	194	18	∈	∈	PROPN
ejpam-77	194	19	f	f	X
ejpam-77	194	20	(	(	PUNCT
ejpam-77	194	21	i	i	NOUN
ejpam-77	194	22	)	)	PUNCT
ejpam-77	194	23	.	.	PUNCT
ejpam-77	195	1	let	let	VERB
ejpam-77	195	2	n	n	PRON
ejpam-77	195	3	∈	∈	PROPN
ejpam-77	195	4	ac	ac	PROPN
ejpam-77	195	5	.	.	PUNCT
ejpam-77	196	1	for	for	ADP
ejpam-77	196	2	the	the	DET
ejpam-77	196	3	case	case	NOUN
ejpam-77	196	4	α	α	X
ejpam-77	196	5	=	=	SYM
ejpam-77	196	6	0	0	NUM
ejpam-77	196	7	,	,	PUNCT
ejpam-77	196	8	we	we	PRON
ejpam-77	196	9	have	have	VERB
ejpam-77	196	10	f0xn−0ξ(ε	f0xn−0ξ(ε	NUM
ejpam-77	196	11	)	)	PUNCT
ejpam-77	197	1	=	=	SYM
ejpam-77	197	2	f0ε=	f0ε=	PROPN
ejpam-77	197	3	1	1	NUM
ejpam-77	197	4	>	>	SYM
ejpam-77	197	5	1−λ	1−λ	NUM
ejpam-77	197	6	and	and	CCONJ
ejpam-77	197	7	for	for	ADP
ejpam-77	197	8	the	the	DET
ejpam-77	197	9	case	case	NOUN
ejpam-77	197	10	α	α	NOUN
ejpam-77	197	11	6=	6=	NOUN
ejpam-77	197	12	0	0	NUM
ejpam-77	197	13	,	,	PUNCT
ejpam-77	197	14	we	we	PRON
ejpam-77	197	15	have	have	VERB
ejpam-77	197	16	fαxn−αξ(ε	fαxn−αξ(ε	NOUN
ejpam-77	197	17	)	)	PUNCT
ejpam-77	198	1	=	=	SYM
ejpam-77	198	2	fxn−ξ	fxn−ξ	NOUN
ejpam-77	198	3	(	(	PUNCT
ejpam-77	198	4	ε	ε	PROPN
ejpam-77	198	5	|α|	|α|	PROPN
ejpam-77	198	6	)	)	PUNCT
ejpam-77	198	7	≥	≥	PROPN
ejpam-77	198	8	t	t	PROPN
ejpam-77	198	9	�	�	PROPN
ejpam-77	198	10	fxn−ξ(ε	fxn−ξ(ε	PROPN
ejpam-77	198	11	)	)	PUNCT
ejpam-77	198	12	,	,	PUNCT
ejpam-77	198	13	f0	f0	PROPN
ejpam-77	198	14	(	(	PUNCT
ejpam-77	198	15	ε	ε	PROPN
ejpam-77	198	16	|α|	|α|	PROPN
ejpam-77	198	17	−	−	PROPN
ejpam-77	198	18	ε	ε	PROPN
ejpam-77	198	19	)	)	PUNCT
ejpam-77	198	20	�	�	PROPN
ejpam-77	198	21	>	>	X
ejpam-77	198	22	t	t	PROPN
ejpam-77	198	23	(	(	PUNCT
ejpam-77	198	24	1−λ	1−λ	NUM
ejpam-77	198	25	,	,	PUNCT
ejpam-77	198	26	,	,	PUNCT
ejpam-77	198	27	1	1	X
ejpam-77	198	28	)	)	PUNCT
ejpam-77	198	29	=	=	SYM
ejpam-77	198	30	1−λ	1−λ	NUM
ejpam-77	198	31	.	.	PUNCT
ejpam-77	199	1	this	this	PRON
ejpam-77	199	2	shows	show	VERB
ejpam-77	199	3	that	that	SCONJ
ejpam-77	199	4	{	{	PUNCT
ejpam-77	199	5	n	n	X
ejpam-77	199	6	∈	∈	NOUN
ejpam-77	199	7	n	n	CCONJ
ejpam-77	199	8	:	:	PUNCT
ejpam-77	199	9	αxn	αxn	PROPN
ejpam-77	199	10	/∈	/∈	PUNCT
ejpam-77	200	1	nαξ(ε	nαξ(ε	NOUN
ejpam-77	200	2	,	,	PUNCT
ejpam-77	200	3	λ	λ	NOUN
ejpam-77	200	4	)	)	PUNCT
ejpam-77	200	5	}	}	PUNCT
ejpam-77	200	6	∈	∈	PROPN
ejpam-77	201	1	i	i	PRON
ejpam-77	201	2	and	and	CCONJ
ejpam-77	201	3	consequently	consequently	ADV
ejpam-77	201	4	we	we	PRON
ejpam-77	201	5	have	have	VERB
ejpam-77	201	6	i	i	PRON
ejpam-77	201	7	ℑ	ℑ	PROPN
ejpam-77	201	8	−	−	PROPN
ejpam-77	201	9	limαxn	limαxn	NOUN
ejpam-77	201	10	=	=	SYM
ejpam-77	201	11	αξ	αξ	PROPN
ejpam-77	201	12	.	.	PUNCT
ejpam-77	202	1	(	(	PUNCT
ejpam-77	202	2	iii	iii	X
ejpam-77	202	3	)	)	PUNCT
ejpam-77	202	4	the	the	DET
ejpam-77	202	5	proof	proof	NOUN
ejpam-77	202	6	is	be	AUX
ejpam-77	202	7	obvious	obvious	ADJ
ejpam-77	202	8	from	from	ADP
ejpam-77	202	9	(	(	PUNCT
ejpam-77	202	10	i	i	NOUN
ejpam-77	202	11	)	)	PUNCT
ejpam-77	202	12	and	and	CCONJ
ejpam-77	202	13	(	(	PUNCT
ejpam-77	202	14	ii	ii	NOUN
ejpam-77	202	15	)	)	PUNCT
ejpam-77	202	16	.	.	PUNCT
ejpam-77	203	1	definition	definition	NOUN
ejpam-77	203	2	2.3	2.3	NUM
ejpam-77	203	3	.	.	PUNCT
ejpam-77	204	1	let	let	VERB
ejpam-77	204	2	(	(	PUNCT
ejpam-77	204	3	x	x	SYM
ejpam-77	204	4	,	,	PUNCT
ejpam-77	204	5	f	f	PROPN
ejpam-77	204	6	,	,	PUNCT
ejpam-77	204	7	t	t	PROPN
ejpam-77	204	8	)	)	PUNCT
ejpam-77	204	9	be	be	AUX
ejpam-77	204	10	a	a	DET
ejpam-77	204	11	pn	pn	NOUN
ejpam-77	204	12	space	space	NOUN
ejpam-77	204	13	.	.	PUNCT
ejpam-77	205	1	a	a	DET
ejpam-77	205	2	subset	subset	NOUN
ejpam-77	205	3	a	a	DET
ejpam-77	205	4	=	=	X
ejpam-77	205	5	{	{	PUNCT
ejpam-77	205	6	xn	xn	NOUN
ejpam-77	205	7	}	}	PUNCT
ejpam-77	205	8	of	of	ADP
ejpam-77	205	9	x	x	SYM
ejpam-77	205	10	is	be	AUX
ejpam-77	205	11	said	say	VERB
ejpam-77	205	12	to	to	PART
ejpam-77	205	13	be	be	AUX
ejpam-77	205	14	i	i	PRON
ejpam-77	205	15	f	f	PROPN
ejpam-77	205	16	bounded	bound	VERB
ejpam-77	205	17	on	on	ADP
ejpam-77	205	18	pn	pn	PROPN
ejpam-77	205	19	spaces	space	NOUN
ejpam-77	205	20	if	if	SCONJ
ejpam-77	205	21	for	for	ADP
ejpam-77	205	22	every	every	DET
ejpam-77	205	23	λ	λ	PROPN
ejpam-77	205	24	∈	∈	PROPN
ejpam-77	205	25	(	(	PUNCT
ejpam-77	205	26	0	0	NUM
ejpam-77	205	27	,	,	PUNCT
ejpam-77	205	28	1	1	NUM
ejpam-77	205	29	)	)	PUNCT
ejpam-77	205	30	,	,	PUNCT
ejpam-77	205	31	there	there	PRON
ejpam-77	205	32	exists	exist	VERB
ejpam-77	205	33	ε	ε	PROPN
ejpam-77	205	34	>	>	X
ejpam-77	205	35	0	0	NUM
ejpam-77	206	1	such	such	ADJ
ejpam-77	206	2	that	that	SCONJ
ejpam-77	206	3	{	{	PUNCT
ejpam-77	206	4	n	n	NOUN
ejpam-77	206	5	∈	∈	NOUN
ejpam-77	206	6	n	n	NOUN
ejpam-77	206	7	:	:	PUNCT
ejpam-77	206	8	xn	xn	PROPN
ejpam-77	206	9	/∈	/∈	PROPN
ejpam-77	206	10	nθ(ε	nθ(ε	NOUN
ejpam-77	206	11	,	,	PUNCT
ejpam-77	206	12	λ	λ	NOUN
ejpam-77	206	13	)	)	PUNCT
ejpam-77	206	14	}	}	PUNCT
ejpam-77	206	15	∈	∈	PROPN
ejpam-77	207	1	i	i	PRON
ejpam-77	207	2	.	.	PUNCT
ejpam-77	208	1	let	let	VERB
ejpam-77	208	2	(	(	PUNCT
ejpam-77	208	3	x	x	SYM
ejpam-77	208	4	,	,	PUNCT
ejpam-77	208	5	f	f	PROPN
ejpam-77	208	6	,	,	PUNCT
ejpam-77	208	7	t	t	PROPN
ejpam-77	208	8	)	)	PUNCT
ejpam-77	208	9	.	.	PUNCT
ejpam-77	209	1	we	we	PRON
ejpam-77	209	2	denote	denote	VERB
ejpam-77	209	3	i	i	PRON
ejpam-77	209	4	f	f	PROPN
ejpam-77	209	5	b	b	PROPN
ejpam-77	209	6	(	(	PUNCT
ejpam-77	209	7	x	x	X
ejpam-77	209	8	)	)	PUNCT
ejpam-77	209	9	the	the	DET
ejpam-77	209	10	set	set	NOUN
ejpam-77	209	11	of	of	ADP
ejpam-77	209	12	all	all	PRON
ejpam-77	210	1	i	i	PRON
ejpam-77	210	2	f	f	NOUN
ejpam-77	210	3	-bounded	-bounded	PROPN
ejpam-77	211	1	i	i	PRON
ejpam-77	211	2	f	f	NOUN
ejpam-77	211	3	−	−	PROPN
ejpam-77	211	4	conver	conver	PROPN
ejpam-77	211	5	gent	gent	NOUN
ejpam-77	211	6	sequences	sequence	VERB
ejpam-77	211	7	on	on	ADP
ejpam-77	211	8	x	x	PUNCT
ejpam-77	211	9	and	and	CCONJ
ejpam-77	211	10	lf	lf	ADP
ejpam-77	211	11	∞(x	∞(x	PROPN
ejpam-77	211	12	)	)	PUNCT
ejpam-77	211	13	the	the	DET
ejpam-77	211	14	set	set	NOUN
ejpam-77	211	15	of	of	ADP
ejpam-77	211	16	all	all	PRON
ejpam-77	212	1	i	i	PRON
ejpam-77	212	2	f	f	NOUN
ejpam-77	212	3	-bounded	-bounde	VERB
ejpam-77	212	4	sequences	sequence	NOUN
ejpam-77	212	5	on	on	ADP
ejpam-77	212	6	x	x	X
ejpam-77	212	7	.	.	PUNCT
ejpam-77	213	1	theorem	theorem	VERB
ejpam-77	213	2	2.1	2.1	NUM
ejpam-77	213	3	.	.	PUNCT
ejpam-77	214	1	let	let	VERB
ejpam-77	214	2	(	(	PUNCT
ejpam-77	214	3	x	x	SYM
ejpam-77	214	4	,	,	PUNCT
ejpam-77	214	5	f	f	PROPN
ejpam-77	214	6	,	,	PUNCT
ejpam-77	214	7	t	t	PROPN
ejpam-77	214	8	)	)	PUNCT
ejpam-77	214	9	be	be	AUX
ejpam-77	214	10	a	a	DET
ejpam-77	214	11	pn	pn	NOUN
ejpam-77	214	12	space	space	NOUN
ejpam-77	215	1	such	such	ADJ
ejpam-77	215	2	that	that	SCONJ
ejpam-77	215	3	t	t	PROPN
ejpam-77	215	4	(	(	PUNCT
ejpam-77	215	5	a	a	PRON
ejpam-77	215	6	,	,	PUNCT
ejpam-77	215	7	a	a	NOUN
ejpam-77	215	8	)	)	PUNCT
ejpam-77	215	9	>	>	PUNCT
ejpam-77	215	10	a	a	PRON
ejpam-77	215	11	for	for	ADP
ejpam-77	215	12	every	every	DET
ejpam-77	215	13	a	a	DET
ejpam-77	215	14	∈	∈	PROPN
ejpam-77	215	15	(	(	PUNCT
ejpam-77	215	16	0	0	NUM
ejpam-77	215	17	,	,	PUNCT
ejpam-77	215	18	1	1	NUM
ejpam-77	215	19	)	)	PUNCT
ejpam-77	215	20	.	.	PUNCT
ejpam-77	216	1	let	let	VERB
ejpam-77	216	2	i	i	PRON
ejpam-77	216	3	⊂	⊂	PROPN
ejpam-77	216	4	2n	2n	NUM
ejpam-77	216	5	be	be	VERB
ejpam-77	216	6	an	an	DET
ejpam-77	216	7	admissible	admissible	ADJ
ejpam-77	216	8	ideal	ideal	NOUN
ejpam-77	216	9	in	in	ADP
ejpam-77	216	10	n.	n.	NOUN
ejpam-77	217	1	then	then	ADV
ejpam-77	217	2	i	i	PRON
ejpam-77	217	3	f	f	PROPN
ejpam-77	217	4	b	b	PROPN
ejpam-77	217	5	(	(	PUNCT
ejpam-77	217	6	x	x	X
ejpam-77	217	7	)	)	PUNCT
ejpam-77	217	8	is	be	AUX
ejpam-77	217	9	a	a	DET
ejpam-77	217	10	closed	closed	ADJ
ejpam-77	217	11	linear	linear	ADJ
ejpam-77	217	12	subspace	subspace	NOUN
ejpam-77	217	13	of	of	ADP
ejpam-77	217	14	the	the	DET
ejpam-77	217	15	set	set	NOUN
ejpam-77	217	16	lf	lf	ADP
ejpam-77	217	17	∞(x	∞(x	PROPN
ejpam-77	217	18	)	)	PUNCT
ejpam-77	217	19	.	.	PUNCT
ejpam-77	218	1	proof	proof	NOUN
ejpam-77	218	2	.	.	PUNCT
ejpam-77	219	1	in	in	ADP
ejpam-77	219	2	view	view	NOUN
ejpam-77	219	3	of	of	ADP
ejpam-77	219	4	lemma	lemma	PROPN
ejpam-77	219	5	(	(	PUNCT
ejpam-77	219	6	)	)	PUNCT
ejpam-77	219	7	,	,	PUNCT
ejpam-77	219	8	it	it	PRON
ejpam-77	219	9	is	be	AUX
ejpam-77	219	10	clear	clear	ADJ
ejpam-77	219	11	that	that	SCONJ
ejpam-77	219	12	the	the	DET
ejpam-77	219	13	set	set	NOUN
ejpam-77	219	14	i	i	PRON
ejpam-77	219	15	f	f	PROPN
ejpam-77	219	16	b	b	PROPN
ejpam-77	219	17	(	(	PUNCT
ejpam-77	219	18	x	x	X
ejpam-77	219	19	)	)	PUNCT
ejpam-77	219	20	is	be	AUX
ejpam-77	219	21	a	a	DET
ejpam-77	219	22	linear	linear	ADJ
ejpam-77	219	23	subspace	subspace	NOUN
ejpam-77	219	24	of	of	ADP
ejpam-77	219	25	the	the	DET
ejpam-77	219	26	set	set	NOUN
ejpam-77	219	27	lf	lf	ADP
ejpam-77	219	28	∞(x	∞(x	PROPN
ejpam-77	219	29	)	)	PUNCT
ejpam-77	219	30	.	.	PUNCT
ejpam-77	220	1	so	so	ADV
ejpam-77	220	2	to	to	PART
ejpam-77	220	3	prove	prove	VERB
ejpam-77	220	4	the	the	DET
ejpam-77	220	5	result	result	NOUN
ejpam-77	220	6	it	it	PRON
ejpam-77	220	7	is	be	AUX
ejpam-77	220	8	sufficient	sufficient	ADJ
ejpam-77	220	9	to	to	PART
ejpam-77	220	10	prove	prove	VERB
ejpam-77	220	11	that	that	SCONJ
ejpam-77	221	1	i	i	PRON
ejpam-77	221	2	f	f	PROPN
ejpam-77	221	3	b	b	PROPN
ejpam-77	221	4	(	(	PUNCT
ejpam-77	221	5	x	x	PROPN
ejpam-77	221	6	)	)	PUNCT
ejpam-77	222	1	=	=	PUNCT
ejpam-77	223	1	i	i	PRON
ejpam-77	223	2	f	f	PROPN
ejpam-77	223	3	b	b	PROPN
ejpam-77	223	4	(	(	PUNCT
ejpam-77	223	5	x	x	PROPN
ejpam-77	223	6	)	)	PUNCT
ejpam-77	223	7	.	.	PUNCT
ejpam-77	224	1	it	it	PRON
ejpam-77	224	2	m.	m.	VERB
ejpam-77	224	3	rahmat	rahmat	NOUN
ejpam-77	224	4	and	and	CCONJ
ejpam-77	224	5	harikrishnan	harikrishnan	PROPN
ejpam-77	224	6	k.	k.	PROPN
ejpam-77	224	7	/	/	PUNCT
ejpam-77	224	8	eur	eur	PROPN
ejpam-77	224	9	.	.	PUNCT
ejpam-77	225	1	j.	j.	PROPN
ejpam-77	225	2	pure	pure	PROPN
ejpam-77	225	3	appl	appl	PROPN
ejpam-77	225	4	.	.	PROPN
ejpam-77	225	5	math	math	PROPN
ejpam-77	225	6	,	,	PUNCT
ejpam-77	225	7	2	2	NUM
ejpam-77	225	8	(	(	PUNCT
ejpam-77	225	9	2009	2009	NUM
ejpam-77	225	10	)	)	PUNCT
ejpam-77	225	11	,	,	PUNCT
ejpam-77	225	12	(	(	PUNCT
ejpam-77	225	13	195	195	NUM
ejpam-77	225	14	-	-	PUNCT
ejpam-77	225	15	212	212	NUM
ejpam-77	225	16	)	)	PUNCT
ejpam-77	225	17	204	204	NUM
ejpam-77	225	18	is	be	AUX
ejpam-77	225	19	clear	clear	ADJ
ejpam-77	225	20	that	that	SCONJ
ejpam-77	226	1	i	i	PRON
ejpam-77	226	2	f	f	PROPN
ejpam-77	226	3	b	b	PROPN
ejpam-77	226	4	(	(	PUNCT
ejpam-77	226	5	x	x	SYM
ejpam-77	226	6	)	)	PUNCT
ejpam-77	227	1	⊂	⊂	PROPN
ejpam-77	228	1	i	i	PRON
ejpam-77	228	2	f	f	PROPN
ejpam-77	228	3	b	b	PROPN
ejpam-77	228	4	(	(	PUNCT
ejpam-77	228	5	x	x	PROPN
ejpam-77	228	6	)	)	PUNCT
ejpam-77	228	7	.	.	PUNCT
ejpam-77	229	1	now	now	ADV
ejpam-77	229	2	we	we	PRON
ejpam-77	229	3	show	show	VERB
ejpam-77	229	4	that	that	SCONJ
ejpam-77	230	1	i	i	PRON
ejpam-77	230	2	fm	fm	PROPN
ejpam-77	230	3	b	b	X
ejpam-77	230	4	(	(	PUNCT
ejpam-77	230	5	x	x	SYM
ejpam-77	230	6	)	)	PUNCT
ejpam-77	231	1	⊂	⊂	PROPN
ejpam-77	232	1	i	i	PRON
ejpam-77	232	2	f	f	PROPN
ejpam-77	232	3	b	b	PROPN
ejpam-77	232	4	(	(	PUNCT
ejpam-77	232	5	x	x	PROPN
ejpam-77	232	6	)	)	PUNCT
ejpam-77	232	7	.	.	PUNCT
ejpam-77	233	1	let	let	VERB
ejpam-77	233	2	y	y	PROPN
ejpam-77	233	3	∈	∈	PROPN
ejpam-77	234	1	i	i	PRON
ejpam-77	234	2	f	f	PROPN
ejpam-77	234	3	b	b	PROPN
ejpam-77	234	4	(	(	PUNCT
ejpam-77	234	5	x	x	PROPN
ejpam-77	234	6	)	)	PUNCT
ejpam-77	234	7	.	.	PUNCT
ejpam-77	235	1	we	we	PRON
ejpam-77	235	2	notice	notice	VERB
ejpam-77	235	3	that	that	SCONJ
ejpam-77	235	4	since	since	SCONJ
ejpam-77	235	5	ny(ε	ny(ε	NOUN
ejpam-77	235	6	,	,	PUNCT
ejpam-77	235	7	λ)∩i	λ)∩i	PROPN
ejpam-77	235	8	f	f	PROPN
ejpam-77	235	9	b	b	PROPN
ejpam-77	235	10	(	(	PUNCT
ejpam-77	235	11	x	x	PROPN
ejpam-77	235	12	)	)	PUNCT
ejpam-77	235	13	6=	6=	NUM
ejpam-77	235	14	;	;	PUNCT
ejpam-77	235	15	for	for	ADP
ejpam-77	235	16	every	every	DET
ejpam-77	235	17	ε	ε	PROPN
ejpam-77	235	18	>	>	X
ejpam-77	235	19	0	0	PUNCT
ejpam-77	235	20	and	and	CCONJ
ejpam-77	235	21	λ	λ	PROPN
ejpam-77	235	22	∈	∈	PROPN
ejpam-77	235	23	(	(	PUNCT
ejpam-77	235	24	0	0	NUM
ejpam-77	235	25	,	,	PUNCT
ejpam-77	235	26	1	1	NUM
ejpam-77	235	27	)	)	PUNCT
ejpam-77	235	28	,	,	PUNCT
ejpam-77	235	29	there	there	PRON
ejpam-77	235	30	exists	exist	VERB
ejpam-77	235	31	an	an	DET
ejpam-77	235	32	x	x	SYM
ejpam-77	235	33	∈	∈	NOUN
ejpam-77	235	34	ny(ε	ny(ε	NOUN
ejpam-77	235	35	,	,	PUNCT
ejpam-77	236	1	λ)∩	λ)∩	PROPN
ejpam-77	236	2	i	i	PRON
ejpam-77	236	3	f	f	PROPN
ejpam-77	236	4	b	b	PROPN
ejpam-77	236	5	(	(	PUNCT
ejpam-77	236	6	x	x	PROPN
ejpam-77	236	7	)	)	PUNCT
ejpam-77	236	8	such	such	ADJ
ejpam-77	236	9	that	that	SCONJ
ejpam-77	236	10	the	the	DET
ejpam-77	236	11	set	set	NOUN
ejpam-77	236	12	k	k	PROPN
ejpam-77	236	13	=	=	PUNCT
ejpam-77	236	14	{	{	PUNCT
ejpam-77	236	15	n	n	NOUN
ejpam-77	236	16	∈	∈	NOUN
ejpam-77	236	17	n	n	NOUN
ejpam-77	236	18	:	:	PUNCT
ejpam-77	236	19	x	x	X
ejpam-77	236	20	/∈	/∈	PUNCT
ejpam-77	236	21	ny	ny	PROPN
ejpam-77	236	22	(	(	PUNCT
ejpam-77	236	23	ε	ε	PROPN
ejpam-77	236	24	2	2	NUM
ejpam-77	236	25	,	,	PUNCT
ejpam-77	236	26	λ	λ	NOUN
ejpam-77	236	27	)	)	PUNCT
ejpam-77	236	28	}	}	PUNCT
ejpam-77	236	29	belongs	belong	VERB
ejpam-77	236	30	to	to	ADP
ejpam-77	236	31	i	i	PRON
ejpam-77	236	32	.	.	PUNCT
ejpam-77	237	1	this	this	PRON
ejpam-77	237	2	implies	imply	VERB
ejpam-77	237	3	that	that	SCONJ
ejpam-77	237	4	k	k	PROPN
ejpam-77	237	5	c	c	PROPN
ejpam-77	237	6	=	=	PRON
ejpam-77	237	7	{	{	PUNCT
ejpam-77	237	8	n	n	NOUN
ejpam-77	237	9	∈	∈	NOUN
ejpam-77	237	10	n	n	NOUN
ejpam-77	237	11	:	:	PUNCT
ejpam-77	237	12	x	x	SYM
ejpam-77	237	13	∈	∈	PROPN
ejpam-77	237	14	ny	ny	PROPN
ejpam-77	237	15	(	(	PUNCT
ejpam-77	237	16	ε	ε	PROPN
ejpam-77	237	17	2	2	NUM
ejpam-77	237	18	,	,	PUNCT
ejpam-77	237	19	λ	λ	NOUN
ejpam-77	237	20	)	)	PUNCT
ejpam-77	237	21	}	}	PUNCT
ejpam-77	237	22	∈	∈	PROPN
ejpam-77	237	23	f	f	X
ejpam-77	237	24	(	(	PUNCT
ejpam-77	237	25	i	i	NOUN
ejpam-77	237	26	)	)	PUNCT
ejpam-77	237	27	.	.	PUNCT
ejpam-77	238	1	now	now	ADV
ejpam-77	238	2	let	let	VERB
ejpam-77	238	3	n	n	PRON
ejpam-77	238	4	∈	∈	PROPN
ejpam-77	238	5	k	k	PROPN
ejpam-77	238	6	c	c	NOUN
ejpam-77	238	7	,	,	PUNCT
ejpam-77	238	8	then	then	ADV
ejpam-77	238	9	by	by	ADP
ejpam-77	238	10	(	(	PUNCT
ejpam-77	238	11	n4	n4	PROPN
ejpam-77	238	12	)	)	PUNCT
ejpam-77	238	13	,	,	PUNCT
ejpam-77	238	14	we	we	PRON
ejpam-77	238	15	have	have	VERB
ejpam-77	238	16	fyn	fyn	PROPN
ejpam-77	238	17	(	(	PUNCT
ejpam-77	238	18	ε	ε	PROPN
ejpam-77	238	19	)	)	PUNCT
ejpam-77	239	1	=	=	SYM
ejpam-77	239	2	fyn−xn+xn	fyn−xn+xn	PROPN
ejpam-77	239	3	(	(	PUNCT
ejpam-77	239	4	ε	ε	PROPN
ejpam-77	239	5	)	)	PUNCT
ejpam-77	239	6	≥	≥	PROPN
ejpam-77	239	7	t	t	PROPN
ejpam-77	239	8	�	�	PROPN
ejpam-77	239	9	fyn−xn	fyn−xn	PROPN
ejpam-77	239	10	(	(	PUNCT
ejpam-77	239	11	ε	ε	PROPN
ejpam-77	239	12	2	2	NUM
ejpam-77	239	13	)	)	PUNCT
ejpam-77	239	14	,	,	PUNCT
ejpam-77	239	15	fxn	fxn	NOUN
ejpam-77	239	16	(	(	PUNCT
ejpam-77	239	17	ε	ε	PROPN
ejpam-77	239	18	2	2	NUM
ejpam-77	239	19	)	)	PUNCT
ejpam-77	239	20	�	�	PROPN
ejpam-77	239	21	>	>	X
ejpam-77	239	22	t	t	PROPN
ejpam-77	239	23	(	(	PUNCT
ejpam-77	239	24	1−λ	1−λ	NUM
ejpam-77	239	25	,	,	PUNCT
ejpam-77	239	26	1−λ	1−λ	NUM
ejpam-77	239	27	)	)	PUNCT
ejpam-77	239	28	>	>	X
ejpam-77	240	1	1−λ	1−λ	NUM
ejpam-77	240	2	.	.	PUNCT
ejpam-77	241	1	thus	thus	ADV
ejpam-77	241	2	,	,	PUNCT
ejpam-77	241	3	we	we	PRON
ejpam-77	241	4	have	have	VERB
ejpam-77	241	5	{	{	PUNCT
ejpam-77	241	6	n	n	NOUN
ejpam-77	241	7	∈	∈	PROPN
ejpam-77	241	8	k	k	NOUN
ejpam-77	241	9	c	c	NOUN
ejpam-77	241	10	:	:	PUNCT
ejpam-77	241	11	yn	yn	PROPN
ejpam-77	241	12	∈	∈	PROPN
ejpam-77	241	13	nθ(ε	nθ(ε	NOUN
ejpam-77	241	14	)	)	PUNCT
ejpam-77	241	15	>	>	X
ejpam-77	241	16	1−λ	1−λ	NUM
ejpam-77	241	17	}	}	PUNCT
ejpam-77	241	18	∈	∈	PROPN
ejpam-77	241	19	f	f	X
ejpam-77	241	20	(	(	PUNCT
ejpam-77	241	21	i	i	PROPN
ejpam-77	241	22	)	)	PUNCT
ejpam-77	241	23	which	which	PRON
ejpam-77	241	24	implies	imply	VERB
ejpam-77	241	25	that	that	SCONJ
ejpam-77	241	26	{	{	PUNCT
ejpam-77	241	27	n	n	X
ejpam-77	241	28	∈	∈	NOUN
ejpam-77	241	29	n	n	NOUN
ejpam-77	241	30	:	:	PUNCT
ejpam-77	241	31	yn	yn	PROPN
ejpam-77	241	32	/∈	/∈	PUNCT
ejpam-77	241	33	nθ(ε	nθ(ε	NOUN
ejpam-77	241	34	)	)	PUNCT
ejpam-77	241	35	>	>	X
ejpam-77	241	36	1−λ	1−λ	NUM
ejpam-77	241	37	}	}	PUNCT
ejpam-77	241	38	∈	∈	PROPN
ejpam-77	241	39	i	i	PRON
ejpam-77	241	40	.	.	PUNCT
ejpam-77	242	1	thus	thus	ADV
ejpam-77	242	2	y	y	PROPN
ejpam-77	242	3	∈	∈	PROPN
ejpam-77	243	1	i	i	PRON
ejpam-77	243	2	f	f	PROPN
ejpam-77	243	3	b	b	PROPN
ejpam-77	243	4	(	(	PUNCT
ejpam-77	243	5	x	x	PROPN
ejpam-77	243	6	)	)	PUNCT
ejpam-77	243	7	and	and	CCONJ
ejpam-77	243	8	this	this	PRON
ejpam-77	243	9	completes	complete	VERB
ejpam-77	243	10	the	the	DET
ejpam-77	243	11	proof	proof	NOUN
ejpam-77	243	12	.	.	PUNCT
ejpam-77	244	1	lemma	lemma	PROPN
ejpam-77	244	2	2.6	2.6	NUM
ejpam-77	244	3	.	.	PUNCT
ejpam-77	245	1	if	if	SCONJ
ejpam-77	245	2	a	a	DET
ejpam-77	245	3	sequence	sequence	NOUN
ejpam-77	245	4	in	in	ADP
ejpam-77	245	5	a	a	DET
ejpam-77	245	6	pn	pn	NOUN
ejpam-77	245	7	space	space	NOUN
ejpam-77	245	8	(	(	PUNCT
ejpam-77	245	9	x	x	SYM
ejpam-77	245	10	,	,	PUNCT
ejpam-77	245	11	f	f	PROPN
ejpam-77	245	12	,	,	PUNCT
ejpam-77	245	13	t	t	PROPN
ejpam-77	245	14	)	)	PUNCT
ejpam-77	245	15	is	be	AUX
ejpam-77	245	16	i	i	PRON
ejpam-77	245	17	f∗	f∗	NOUN
ejpam-77	245	18	-convergent	-convergent	NOUN
ejpam-77	245	19	,	,	PUNCT
ejpam-77	245	20	then	then	ADV
ejpam-77	245	21	it	it	PRON
ejpam-77	245	22	is	be	AUX
ejpam-77	245	23	i	i	INTJ
ejpam-77	245	24	f	f	PROPN
ejpam-77	245	25	f	f	PROPN
ejpam-77	245	26	-convergent	-convergent	ADJ
ejpam-77	245	27	to	to	ADP
ejpam-77	245	28	the	the	DET
ejpam-77	245	29	same	same	ADJ
ejpam-77	245	30	limit	limit	NOUN
ejpam-77	245	31	.	.	PUNCT
ejpam-77	246	1	proof	proof	NOUN
ejpam-77	246	2	.	.	PUNCT
ejpam-77	247	1	let	let	VERB
ejpam-77	247	2	i	i	PRON
ejpam-77	247	3	f∗	f∗	VERB
ejpam-77	247	4	−	−	PROPN
ejpam-77	247	5	lim	lim	PROPN
ejpam-77	247	6	xn	xn	PUNCT
ejpam-77	248	1	=	=	SYM
ejpam-77	248	2	ξ	ξ	PROPN
ejpam-77	248	3	,	,	PUNCT
ejpam-77	248	4	then	then	ADV
ejpam-77	248	5	by	by	ADP
ejpam-77	248	6	definition	definition	NOUN
ejpam-77	248	7	,	,	PUNCT
ejpam-77	248	8	there	there	PRON
ejpam-77	248	9	exists	exist	VERB
ejpam-77	248	10	m	m	NOUN
ejpam-77	248	11	=	=	SYM
ejpam-77	248	12	{	{	PUNCT
ejpam-77	248	13	m1	m1	PROPN
ejpam-77	248	14	<	<	X
ejpam-77	248	15	m2	m2	PROPN
ejpam-77	248	16	<	<	X
ejpam-77	248	17	·	·	PUNCT
ejpam-77	248	18	·	·	PUNCT
ejpam-77	248	19	·	·	PUNCT
ejpam-77	248	20	}	}	PUNCT
ejpam-77	248	21	∈	∈	PROPN
ejpam-77	248	22	f	f	X
ejpam-77	248	23	(	(	PUNCT
ejpam-77	248	24	i	i	NOUN
ejpam-77	248	25	)	)	PUNCT
ejpam-77	248	26	such	such	ADJ
ejpam-77	248	27	that	that	SCONJ
ejpam-77	248	28	f	f	PROPN
ejpam-77	249	1	−	−	PROPN
ejpam-77	249	2	lim	lim	PROPN
ejpam-77	249	3	xmk	xmk	PROPN
ejpam-77	250	1	=	=	SYM
ejpam-77	250	2	ξ	ξ	X
ejpam-77	250	3	.	.	PUNCT
ejpam-77	250	4	let	let	VERB
ejpam-77	250	5	ε	ε	PROPN
ejpam-77	250	6	>	>	X
ejpam-77	250	7	0	0	PUNCT
ejpam-77	251	1	and	and	CCONJ
ejpam-77	251	2	λ	λ	PROPN
ejpam-77	251	3	∈	∈	PROPN
ejpam-77	251	4	(	(	PUNCT
ejpam-77	251	5	0	0	NUM
ejpam-77	251	6	,	,	PUNCT
ejpam-77	251	7	1	1	NUM
ejpam-77	251	8	)	)	PUNCT
ejpam-77	251	9	be	be	AUX
ejpam-77	251	10	given	give	VERB
ejpam-77	251	11	.	.	PUNCT
ejpam-77	252	1	since	since	SCONJ
ejpam-77	252	2	f	f	PROPN
ejpam-77	252	3	−	−	PROPN
ejpam-77	252	4	lim	lim	PROPN
ejpam-77	252	5	xmk	xmk	PROPN
ejpam-77	252	6	=	=	SYM
ejpam-77	252	7	ξ	ξ	PROPN
ejpam-77	252	8	,	,	PUNCT
ejpam-77	252	9	there	there	PRON
ejpam-77	252	10	exists	exist	VERB
ejpam-77	252	11	n	n	PRON
ejpam-77	252	12	∈	∈	PROPN
ejpam-77	252	13	n	n	PRON
ejpam-77	252	14	such	such	ADJ
ejpam-77	252	15	that	that	SCONJ
ejpam-77	252	16	xmk	xmk	PROPN
ejpam-77	252	17	∈	∈	PROPN
ejpam-77	252	18	nξ(ε	nξ(ε	VERB
ejpam-77	252	19	,	,	PUNCT
ejpam-77	252	20	λ	λ	NOUN
ejpam-77	252	21	)	)	PUNCT
ejpam-77	252	22	for	for	ADP
ejpam-77	252	23	every	every	DET
ejpam-77	252	24	k	k	PROPN
ejpam-77	252	25	≥	≥	PROPN
ejpam-77	252	26	n	n	ADV
ejpam-77	252	27	.	.	PUNCT
ejpam-77	253	1	let	let	VERB
ejpam-77	253	2	a	a	DET
ejpam-77	253	3	=	=	SYM
ejpam-77	253	4	{	{	PUNCT
ejpam-77	253	5	k	k	PROPN
ejpam-77	253	6	∈	∈	PROPN
ejpam-77	253	7	n	n	CCONJ
ejpam-77	253	8	:	:	PUNCT
ejpam-77	253	9	xmk	xmk	PROPN
ejpam-77	253	10	/∈	/∈	PUNCT
ejpam-77	253	11	nξ(ε	nξ(ε	NUM
ejpam-77	253	12	,	,	PUNCT
ejpam-77	253	13	λ	λ	NOUN
ejpam-77	253	14	)	)	PUNCT
ejpam-77	253	15	}	}	PUNCT
ejpam-77	253	16	.	.	PUNCT
ejpam-77	254	1	then	then	ADV
ejpam-77	254	2	it	it	PRON
ejpam-77	254	3	is	be	AUX
ejpam-77	254	4	clear	clear	ADJ
ejpam-77	254	5	that	that	SCONJ
ejpam-77	254	6	a	a	DET
ejpam-77	254	7	⊂	⊂	X
ejpam-77	254	8	{	{	PUNCT
ejpam-77	254	9	1	1	NUM
ejpam-77	254	10	,	,	PUNCT
ejpam-77	254	11	2	2	NUM
ejpam-77	254	12	,	,	PUNCT
ejpam-77	254	13	·	·	PUNCT
ejpam-77	254	14	·	·	PUNCT
ejpam-77	254	15	·	·	PUNCT
ejpam-77	254	16	,	,	PUNCT
ejpam-77	254	17	n	n	CCONJ
ejpam-77	254	18	−	−	PROPN
ejpam-77	254	19	1	1	NUM
ejpam-77	254	20	}	}	PUNCT
ejpam-77	254	21	∈	∈	PROPN
ejpam-77	255	1	i	i	PRON
ejpam-77	255	2	f	f	PROPN
ejpam-77	255	3	.	.	PUNCT
ejpam-77	256	1	therefore	therefore	ADV
ejpam-77	256	2	,	,	PUNCT
ejpam-77	256	3	the	the	DET
ejpam-77	256	4	sequence	sequence	NOUN
ejpam-77	256	5	{	{	PUNCT
ejpam-77	256	6	xn	xn	PROPN
ejpam-77	256	7	}	}	PUNCT
ejpam-77	256	8	is	be	AUX
ejpam-77	256	9	i	i	INTJ
ejpam-77	256	10	f	f	PROPN
ejpam-77	257	1	−	−	PROPN
ejpam-77	258	1	lim	lim	PROPN
ejpam-77	258	2	xn	xn	PUNCT
ejpam-77	259	1	=	=	SYM
ejpam-77	259	2	ξ	ξ	PROPN
ejpam-77	259	3	.	.	NOUN
ejpam-77	260	1	3	3	X
ejpam-77	260	2	.	.	X
ejpam-77	261	1	i	i	PRON
ejpam-77	261	2	-convergence	-convergence	VERB
ejpam-77	261	3	for	for	ADP
ejpam-77	261	4	continuous	continuous	ADJ
ejpam-77	261	5	functions	function	NOUN
ejpam-77	261	6	in	in	ADP
ejpam-77	261	7	pn	pn	PROPN
ejpam-77	261	8	spaces	space	NOUN
ejpam-77	261	9	in	in	ADP
ejpam-77	261	10	this	this	DET
ejpam-77	261	11	short	short	ADJ
ejpam-77	261	12	section	section	NOUN
ejpam-77	261	13	,	,	PUNCT
ejpam-77	261	14	we	we	PRON
ejpam-77	261	15	extend	extend	VERB
ejpam-77	261	16	the	the	DET
ejpam-77	261	17	study	study	NOUN
ejpam-77	261	18	of	of	ADP
ejpam-77	261	19	ideal	ideal	ADJ
ejpam-77	261	20	convergence	convergence	NOUN
ejpam-77	261	21	to	to	ADP
ejpam-77	261	22	a	a	DET
ejpam-77	261	23	sequence	sequence	NOUN
ejpam-77	261	24	of	of	ADP
ejpam-77	261	25	function	function	NOUN
ejpam-77	261	26	fn	fn	INTJ
ejpam-77	261	27	in	in	ADP
ejpam-77	261	28	(	(	PUNCT
ejpam-77	261	29	x	x	INTJ
ejpam-77	261	30	,	,	PUNCT
ejpam-77	261	31	f	f	PROPN
ejpam-77	261	32	,	,	PUNCT
ejpam-77	261	33	t	t	PROPN
ejpam-77	261	34	)	)	PUNCT
ejpam-77	261	35	and	and	CCONJ
ejpam-77	261	36	prove	prove	VERB
ejpam-77	261	37	a	a	DET
ejpam-77	261	38	theorem	theorem	NOUN
ejpam-77	261	39	about	about	ADP
ejpam-77	261	40	ideal	ideal	ADJ
ejpam-77	261	41	convergence	convergence	NOUN
ejpam-77	261	42	.	.	PUNCT
ejpam-77	262	1	we	we	PRON
ejpam-77	262	2	begin	begin	VERB
ejpam-77	262	3	with	with	ADP
ejpam-77	262	4	the	the	DET
ejpam-77	262	5	following	follow	VERB
ejpam-77	262	6	definition	definition	NOUN
ejpam-77	262	7	.	.	PUNCT
ejpam-77	263	1	m.	m.	NOUN
ejpam-77	263	2	rahmat	rahmat	PROPN
ejpam-77	263	3	and	and	CCONJ
ejpam-77	263	4	harikrishnan	harikrishnan	PROPN
ejpam-77	263	5	k.	k.	PROPN
ejpam-77	263	6	/	/	PUNCT
ejpam-77	263	7	eur	eur	PROPN
ejpam-77	263	8	.	.	PUNCT
ejpam-77	264	1	j.	j.	PROPN
ejpam-77	264	2	pure	pure	PROPN
ejpam-77	264	3	appl	appl	PROPN
ejpam-77	264	4	.	.	PROPN
ejpam-77	264	5	math	math	PROPN
ejpam-77	264	6	,	,	PUNCT
ejpam-77	264	7	2	2	NUM
ejpam-77	264	8	(	(	PUNCT
ejpam-77	264	9	2009	2009	NUM
ejpam-77	264	10	)	)	PUNCT
ejpam-77	264	11	,	,	PUNCT
ejpam-77	264	12	(	(	PUNCT
ejpam-77	264	13	195	195	NUM
ejpam-77	264	14	-	-	PUNCT
ejpam-77	264	15	212	212	NUM
ejpam-77	264	16	)	)	PUNCT
ejpam-77	264	17	205	205	NUM
ejpam-77	264	18	definition	definition	NOUN
ejpam-77	264	19	3.1	3.1	NUM
ejpam-77	264	20	.	.	PUNCT
ejpam-77	265	1	let	let	AUX
ejpam-77	265	2	(	(	PUNCT
ejpam-77	265	3	x	x	SYM
ejpam-77	265	4	,	,	PUNCT
ejpam-77	265	5	f	f	PROPN
ejpam-77	265	6	,	,	PUNCT
ejpam-77	265	7	t	t	PROPN
ejpam-77	265	8	)	)	PUNCT
ejpam-77	265	9	be	be	AUX
ejpam-77	265	10	a	a	DET
ejpam-77	265	11	pn	pn	NOUN
ejpam-77	265	12	spaces	space	NOUN
ejpam-77	265	13	and	and	CCONJ
ejpam-77	265	14	i	i	PRON
ejpam-77	265	15	be	be	VERB
ejpam-77	265	16	an	an	DET
ejpam-77	265	17	arbitrary	arbitrary	ADJ
ejpam-77	265	18	admissible	admissible	ADJ
ejpam-77	265	19	ideal	ideal	NOUN
ejpam-77	265	20	in	in	ADP
ejpam-77	265	21	n.	n.	NOUN
ejpam-77	265	22	we	we	PRON
ejpam-77	265	23	say	say	VERB
ejpam-77	265	24	that	that	SCONJ
ejpam-77	265	25	a	a	DET
ejpam-77	265	26	sequence	sequence	NOUN
ejpam-77	265	27	of	of	ADP
ejpam-77	265	28	functions	function	NOUN
ejpam-77	265	29	fn	fn	NOUN
ejpam-77	265	30	:	:	PUNCT
ejpam-77	265	31	x	x	X
ejpam-77	265	32	→	→	PUNCT
ejpam-77	265	33	x	x	X
ejpam-77	265	34	is	be	AUX
ejpam-77	265	35	i	i	PRON
ejpam-77	265	36	f	f	PROPN
ejpam-77	265	37	-convergent	-convergent	ADJ
ejpam-77	265	38	to	to	ADP
ejpam-77	265	39	a	a	DET
ejpam-77	265	40	function	function	NOUN
ejpam-77	265	41	f	f	NOUN
ejpam-77	265	42	:	:	PUNCT
ejpam-77	265	43	x	x	X
ejpam-77	265	44	→	→	SYM
ejpam-77	265	45	x	x	X
ejpam-77	265	46	)	)	PUNCT
ejpam-77	265	47	denoted	denote	VERB
ejpam-77	265	48	i	i	PRON
ejpam-77	265	49	f	f	PROPN
ejpam-77	265	50	−	−	PROPN
ejpam-77	266	1	lim	lim	PROPN
ejpam-77	266	2	fn	fn	PROPN
ejpam-77	266	3	=	=	SYM
ejpam-77	266	4	f	f	PROPN
ejpam-77	266	5	,	,	PUNCT
ejpam-77	266	6	if	if	SCONJ
ejpam-77	266	7	for	for	ADP
ejpam-77	266	8	every	every	DET
ejpam-77	266	9	x	x	SYM
ejpam-77	266	10	∈	∈	PROPN
ejpam-77	266	11	x	x	X
ejpam-77	266	12	,	,	PUNCT
ejpam-77	266	13	ε	ε	PROPN
ejpam-77	266	14	>	>	PUNCT
ejpam-77	266	15	0	0	PUNCT
ejpam-77	267	1	and	and	CCONJ
ejpam-77	267	2	λ	λ	PROPN
ejpam-77	267	3	∈	∈	PROPN
ejpam-77	267	4	(	(	PUNCT
ejpam-77	267	5	0	0	NUM
ejpam-77	267	6	,	,	PUNCT
ejpam-77	267	7	1	1	NUM
ejpam-77	267	8	)	)	PUNCT
ejpam-77	267	9	the	the	DET
ejpam-77	267	10	set	set	NOUN
ejpam-77	267	11	{	{	PUNCT
ejpam-77	267	12	n	n	NOUN
ejpam-77	267	13	∈	∈	NOUN
ejpam-77	267	14	n	n	NOUN
ejpam-77	267	15	:	:	PUNCT
ejpam-77	267	16	fn(x)−	fn(x)−	PROPN
ejpam-77	267	17	f	f	PROPN
ejpam-77	267	18	(	(	PUNCT
ejpam-77	267	19	x	x	X
ejpam-77	267	20	)	)	PUNCT
ejpam-77	267	21	/∈	/∈	PUNCT
ejpam-77	268	1	nθ	nθ	CCONJ
ejpam-77	268	2	(	(	PUNCT
ejpam-77	268	3	ε	ε	PROPN
ejpam-77	268	4	,	,	PUNCT
ejpam-77	268	5	λ	λ	NOUN
ejpam-77	268	6	)	)	PUNCT
ejpam-77	268	7	}	}	PUNCT
ejpam-77	268	8	belongs	belong	VERB
ejpam-77	268	9	to	to	ADP
ejpam-77	268	10	i	i	PRON
ejpam-77	268	11	.	.	PUNCT
ejpam-77	269	1	theorem	theorem	VERB
ejpam-77	269	2	3.1	3.1	NUM
ejpam-77	269	3	.	.	PUNCT
ejpam-77	270	1	let	let	AUX
ejpam-77	270	2	(	(	PUNCT
ejpam-77	270	3	x	x	SYM
ejpam-77	270	4	,	,	PUNCT
ejpam-77	270	5	f	f	PROPN
ejpam-77	270	6	,	,	PUNCT
ejpam-77	270	7	t	t	PROPN
ejpam-77	270	8	)	)	PUNCT
ejpam-77	270	9	be	be	AUX
ejpam-77	270	10	a	a	DET
ejpam-77	270	11	pn	pn	NOUN
ejpam-77	270	12	spaces	space	NOUN
ejpam-77	270	13	such	such	ADJ
ejpam-77	270	14	that	that	DET
ejpam-77	270	15	supa<1	supa<1	ADJ
ejpam-77	270	16	t	t	NOUN
ejpam-77	270	17	(	(	PUNCT
ejpam-77	270	18	a	a	DET
ejpam-77	270	19	,	,	PUNCT
ejpam-77	270	20	a	a	NOUN
ejpam-77	270	21	)	)	PUNCT
ejpam-77	270	22	=	=	SYM
ejpam-77	270	23	1	1	NUM
ejpam-77	270	24	and	and	CCONJ
ejpam-77	270	25	let	let	VERB
ejpam-77	270	26	i	i	PRON
ejpam-77	270	27	be	be	AUX
ejpam-77	270	28	an	an	DET
ejpam-77	270	29	arbitrary	arbitrary	ADJ
ejpam-77	270	30	admissible	admissible	ADJ
ejpam-77	270	31	ideal	ideal	NOUN
ejpam-77	270	32	in	in	ADP
ejpam-77	270	33	n.	n.	NOUN
ejpam-77	270	34	let	let	VERB
ejpam-77	270	35	i	i	PRON
ejpam-77	270	36	f	f	PROPN
ejpam-77	271	1	−	−	PROPN
ejpam-77	272	1	lim	lim	PROPN
ejpam-77	272	2	fn	fn	PROPN
ejpam-77	273	1	=	=	SYM
ejpam-77	273	2	f	f	PROPN
ejpam-77	273	3	(	(	PUNCT
ejpam-77	273	4	on	on	ADP
ejpam-77	273	5	x	x	NOUN
ejpam-77	273	6	)	)	PUNCT
ejpam-77	273	7	where	where	SCONJ
ejpam-77	273	8	fn	fn	NOUN
ejpam-77	273	9	:	:	PUNCT
ejpam-77	273	10	x	x	X
ejpam-77	273	11	→	→	SYM
ejpam-77	273	12	x	x	SYM
ejpam-77	273	13	,	,	PUNCT
ejpam-77	273	14	n	n	PROPN
ejpam-77	273	15	∈	∈	PROPN
ejpam-77	273	16	n	n	CCONJ
ejpam-77	273	17	,	,	PUNCT
ejpam-77	273	18	are	be	AUX
ejpam-77	273	19	equi	equi	NOUN
ejpam-77	273	20	-	-	PUNCT
ejpam-77	273	21	continuous	continuous	ADJ
ejpam-77	273	22	(	(	PUNCT
ejpam-77	273	23	on	on	ADP
ejpam-77	273	24	x	x	NOUN
ejpam-77	273	25	)	)	PUNCT
ejpam-77	273	26	and	and	CCONJ
ejpam-77	273	27	f	f	X
ejpam-77	273	28	:	:	PUNCT
ejpam-77	273	29	x	x	X
ejpam-77	274	1	→	→	SYM
ejpam-77	274	2	x	x	X
ejpam-77	274	3	.	.	PUNCT
ejpam-77	275	1	then	then	ADV
ejpam-77	275	2	f	f	PROPN
ejpam-77	275	3	is	be	AUX
ejpam-77	275	4	f	f	PROPN
ejpam-77	275	5	-continuous	-continuous	ADJ
ejpam-77	275	6	(	(	PUNCT
ejpam-77	275	7	on	on	ADP
ejpam-77	275	8	x	x	NOUN
ejpam-77	275	9	)	)	PUNCT
ejpam-77	275	10	.	.	PUNCT
ejpam-77	276	1	proof	proof	NOUN
ejpam-77	276	2	.	.	PUNCT
ejpam-77	277	1	let	let	VERB
ejpam-77	277	2	x0	x0	PROPN
ejpam-77	277	3	∈	∈	PROPN
ejpam-77	277	4	x	x	X
ejpam-77	277	5	and	and	CCONJ
ejpam-77	277	6	x	x	SYM
ejpam-77	277	7	−	−	NOUN
ejpam-77	277	8	x0	x0	PROPN
ejpam-77	277	9	∈	∈	PROPN
ejpam-77	277	10	nθ(ε	nθ(ε	NOUN
ejpam-77	277	11	,	,	PUNCT
ejpam-77	277	12	λ	λ	X
ejpam-77	277	13	)	)	PUNCT
ejpam-77	277	14	be	be	AUX
ejpam-77	277	15	fixed	fix	VERB
ejpam-77	277	16	.	.	PUNCT
ejpam-77	278	1	by	by	ADP
ejpam-77	278	2	equi	equi	NOUN
ejpam-77	278	3	-	-	PUNCT
ejpam-77	278	4	continuity	continuity	NOUN
ejpam-77	278	5	of	of	ADP
ejpam-77	278	6	fn	fn	NOUN
ejpam-77	278	7	’s	’s	X
ejpam-77	278	8	,	,	PUNCT
ejpam-77	278	9	for	for	ADP
ejpam-77	278	10	every	every	DET
ejpam-77	278	11	ε	ε	PROPN
ejpam-77	278	12	>	>	X
ejpam-77	278	13	0	0	PROPN
ejpam-77	278	14	,	,	PUNCT
ejpam-77	278	15	there	there	PRON
ejpam-77	278	16	exists	exist	VERB
ejpam-77	278	17	a	a	DET
ejpam-77	278	18	γ	γ	X
ejpam-77	278	19	∈	∈	PROPN
ejpam-77	278	20	(	(	PUNCT
ejpam-77	278	21	0	0	NUM
ejpam-77	278	22	,	,	PUNCT
ejpam-77	278	23	1	1	NUM
ejpam-77	278	24	)	)	PUNCT
ejpam-77	278	25	with	with	ADP
ejpam-77	278	26	γ	γ	X
ejpam-77	278	27	<	<	X
ejpam-77	278	28	λ	λ	PROPN
ejpam-77	278	29	such	such	ADJ
ejpam-77	278	30	that	that	DET
ejpam-77	278	31	fn(x)−	fn(x)−	PROPN
ejpam-77	278	32	fn(x0	fn(x0	PROPN
ejpam-77	278	33	)	)	PUNCT
ejpam-77	278	34	∈	∈	PROPN
ejpam-77	278	35	nθ	nθ	PROPN
ejpam-77	278	36	(	(	PUNCT
ejpam-77	278	37	ε	ε	PROPN
ejpam-77	278	38	3	3	NUM
ejpam-77	278	39	,	,	PUNCT
ejpam-77	278	40	γ	γ	NOUN
ejpam-77	278	41	)	)	PUNCT
ejpam-77	278	42	for	for	ADP
ejpam-77	278	43	every	every	DET
ejpam-77	278	44	n	n	PRON
ejpam-77	278	45	∈	∈	PROPN
ejpam-77	278	46	n.	n.	NOUN
ejpam-77	278	47	since	since	SCONJ
ejpam-77	278	48	i	i	PRON
ejpam-77	278	49	f	f	PROPN
ejpam-77	278	50	−	−	PROPN
ejpam-77	279	1	lim	lim	PROPN
ejpam-77	279	2	fn	fn	PROPN
ejpam-77	280	1	=	=	SYM
ejpam-77	280	2	f	f	PROPN
ejpam-77	280	3	,	,	PUNCT
ejpam-77	280	4	the	the	DET
ejpam-77	280	5	set	set	NOUN
ejpam-77	280	6	k	k	PROPN
ejpam-77	280	7	=	=	PUNCT
ejpam-77	280	8	{	{	PUNCT
ejpam-77	280	9	n	n	NOUN
ejpam-77	280	10	∈	∈	PROPN
ejpam-77	280	11	n	n	NOUN
ejpam-77	280	12	:	:	PUNCT
ejpam-77	280	13	fn(x0)−	fn(x0)−	PROPN
ejpam-77	280	14	f	f	PROPN
ejpam-77	280	15	(	(	PUNCT
ejpam-77	280	16	x0	x0	PROPN
ejpam-77	280	17	)	)	PUNCT
ejpam-77	280	18	/∈	/∈	PUNCT
ejpam-77	281	1	nθ	nθ	ADJ
ejpam-77	281	2	(	(	PUNCT
ejpam-77	281	3	ε	ε	PROPN
ejpam-77	281	4	3	3	NUM
ejpam-77	281	5	,	,	PUNCT
ejpam-77	281	6	γ	γ	NOUN
ejpam-77	281	7	)	)	PUNCT
ejpam-77	281	8	}	}	PUNCT
ejpam-77	281	9	⋃	⋃	NOUN
ejpam-77	281	10	{	{	PUNCT
ejpam-77	281	11	n	n	NOUN
ejpam-77	281	12	∈	∈	NOUN
ejpam-77	282	1	n	n	NOUN
ejpam-77	282	2	:	:	PUNCT
ejpam-77	282	3	fn(x)−	fn(x)−	PROPN
ejpam-77	282	4	f	f	PROPN
ejpam-77	282	5	(	(	PUNCT
ejpam-77	282	6	x	x	NOUN
ejpam-77	282	7	)	)	PUNCT
ejpam-77	282	8	)	)	PUNCT
ejpam-77	282	9	/∈	/∈	PUNCT
ejpam-77	283	1	nθ	nθ	CCONJ
ejpam-77	283	2	(	(	PUNCT
ejpam-77	283	3	ε	ε	PROPN
ejpam-77	283	4	3	3	NUM
ejpam-77	283	5	,	,	PUNCT
ejpam-77	283	6	γ	γ	NOUN
ejpam-77	283	7	)	)	PUNCT
ejpam-77	283	8	}	}	PUNCT
ejpam-77	283	9	is	be	AUX
ejpam-77	283	10	in	in	ADP
ejpam-77	283	11	i	i	PRON
ejpam-77	283	12	and	and	CCONJ
ejpam-77	283	13	different	different	ADJ
ejpam-77	283	14	from	from	ADP
ejpam-77	283	15	n.	n.	NOUN
ejpam-77	283	16	hence	hence	ADV
ejpam-77	283	17	,	,	PUNCT
ejpam-77	283	18	there	there	PRON
ejpam-77	283	19	exists	exist	VERB
ejpam-77	283	20	n	n	PRON
ejpam-77	283	21	∈	∈	PROPN
ejpam-77	283	22	f	f	X
ejpam-77	283	23	(	(	PUNCT
ejpam-77	283	24	k	k	NOUN
ejpam-77	283	25	)	)	PUNCT
ejpam-77	284	1	such	such	ADJ
ejpam-77	284	2	that	that	SCONJ
ejpam-77	284	3	fn(x0)−	fn(x0)−	PROPN
ejpam-77	285	1	f	f	X
ejpam-77	286	1	(	(	PUNCT
ejpam-77	286	2	x0	x0	PROPN
ejpam-77	286	3	)	)	PUNCT
ejpam-77	286	4	∈nθ	∈nθ	PROPN
ejpam-77	286	5	(	(	PUNCT
ejpam-77	286	6	ε	ε	PROPN
ejpam-77	286	7	3	3	NUM
ejpam-77	286	8	,	,	PUNCT
ejpam-77	286	9	γ	γ	NOUN
ejpam-77	286	10	)	)	PUNCT
ejpam-77	286	11	)	)	PUNCT
ejpam-77	286	12	and	and	CCONJ
ejpam-77	286	13	fn(x)−	fn(x)−	PROPN
ejpam-77	286	14	f	f	PROPN
ejpam-77	286	15	(	(	PUNCT
ejpam-77	286	16	x	x	NOUN
ejpam-77	286	17	)	)	PUNCT
ejpam-77	286	18	∈nθ	∈nθ	PROPN
ejpam-77	286	19	(	(	PUNCT
ejpam-77	286	20	ε	ε	PROPN
ejpam-77	286	21	3	3	NUM
ejpam-77	286	22	,	,	PUNCT
ejpam-77	286	23	γ	γ	NOUN
ejpam-77	286	24	)	)	PUNCT
ejpam-77	286	25	.	.	PUNCT
ejpam-77	287	1	it	it	PRON
ejpam-77	287	2	follows	follow	VERB
ejpam-77	287	3	that	that	SCONJ
ejpam-77	287	4	f	f	PROPN
ejpam-77	287	5	f	f	X
ejpam-77	287	6	(	(	PUNCT
ejpam-77	287	7	x0)−	x0)−	PROPN
ejpam-77	287	8	f	f	X
ejpam-77	287	9	(	(	PUNCT
ejpam-77	287	10	x)(ε	x)(ε	PROPN
ejpam-77	287	11	)	)	PUNCT
ejpam-77	287	12	≥	≥	PROPN
ejpam-77	287	13	t	t	PROPN
ejpam-77	287	14	�	�	PROPN
ejpam-77	287	15	f	f	PROPN
ejpam-77	287	16	f	f	PROPN
ejpam-77	287	17	(	(	PUNCT
ejpam-77	287	18	x0)−	x0)−	X
ejpam-77	287	19	fn(x0	fn(x0	NOUN
ejpam-77	287	20	)	)	PUNCT
ejpam-77	287	21	(	(	PUNCT
ejpam-77	287	22	ε	ε	PROPN
ejpam-77	287	23	3	3	NUM
ejpam-77	287	24	)	)	PUNCT
ejpam-77	287	25	,	,	PUNCT
ejpam-77	287	26	t	t	PROPN
ejpam-77	287	27	(	(	PUNCT
ejpam-77	287	28	f	f	PROPN
ejpam-77	287	29	fn(x0)−	fn(x0)−	PROPN
ejpam-77	287	30	fn(x	fn(x	PROPN
ejpam-77	287	31	)	)	PUNCT
ejpam-77	287	32	(	(	PUNCT
ejpam-77	287	33	ε	ε	PROPN
ejpam-77	287	34	3	3	NUM
ejpam-77	287	35	)	)	PUNCT
ejpam-77	287	36	,	,	PUNCT
ejpam-77	287	37	f	f	PROPN
ejpam-77	287	38	fn(x)−	fn(x)−	PROPN
ejpam-77	287	39	f	f	PROPN
ejpam-77	287	40	(	(	PUNCT
ejpam-77	287	41	x	x	X
ejpam-77	287	42	)	)	PUNCT
ejpam-77	287	43	(	(	PUNCT
ejpam-77	287	44	ε	ε	PROPN
ejpam-77	287	45	3	3	NUM
ejpam-77	287	46	)	)	PUNCT
ejpam-77	287	47	�	�	PROPN
ejpam-77	287	48	>	>	X
ejpam-77	287	49	t	t	PROPN
ejpam-77	287	50	(	(	PUNCT
ejpam-77	287	51	1−	1−	NUM
ejpam-77	287	52	γ	γ	X
ejpam-77	287	53	,	,	PUNCT
ejpam-77	287	54	t	t	PROPN
ejpam-77	287	55	(	(	PUNCT
ejpam-77	287	56	1−	1−	NUM
ejpam-77	287	57	γ	γ	X
ejpam-77	287	58	,	,	PUNCT
ejpam-77	287	59	1−	1−	NUM
ejpam-77	287	60	γ	γ	NOUN
ejpam-77	287	61	)	)	PUNCT
ejpam-77	287	62	)	)	PUNCT
ejpam-77	287	63	>	>	X
ejpam-77	288	1	t	t	PROPN
ejpam-77	288	2	(	(	PUNCT
ejpam-77	288	3	1−	1−	NUM
ejpam-77	288	4	γ	γ	X
ejpam-77	288	5	,	,	PUNCT
ejpam-77	288	6	1−	1−	NUM
ejpam-77	288	7	γ	γ	X
ejpam-77	288	8	)	)	PUNCT
ejpam-77	288	9	>	>	X
ejpam-77	288	10	1−	1−	NUM
ejpam-77	288	11	γ	γ	X
ejpam-77	288	12	>	>	X
ejpam-77	288	13	1−λ	1−λ	NUM
ejpam-77	288	14	.	.	PUNCT
ejpam-77	289	1	this	this	PRON
ejpam-77	289	2	implies	imply	VERB
ejpam-77	289	3	that	that	SCONJ
ejpam-77	289	4	f	f	PROPN
ejpam-77	289	5	is	be	AUX
ejpam-77	289	6	f	f	PROPN
ejpam-77	289	7	-continuous	-continuous	ADJ
ejpam-77	289	8	(	(	PUNCT
ejpam-77	289	9	on	on	ADP
ejpam-77	289	10	x	x	X
ejpam-77	289	11	)	)	PUNCT
ejpam-77	289	12	.	.	PUNCT
ejpam-77	290	1	m.	m.	NOUN
ejpam-77	290	2	rahmat	rahmat	PROPN
ejpam-77	290	3	and	and	CCONJ
ejpam-77	290	4	harikrishnan	harikrishnan	PROPN
ejpam-77	290	5	k.	k.	PROPN
ejpam-77	290	6	/	/	PUNCT
ejpam-77	290	7	eur	eur	PROPN
ejpam-77	290	8	.	.	PUNCT
ejpam-77	291	1	j.	j.	PROPN
ejpam-77	291	2	pure	pure	PROPN
ejpam-77	291	3	appl	appl	PROPN
ejpam-77	291	4	.	.	PROPN
ejpam-77	291	5	math	math	PROPN
ejpam-77	291	6	,	,	PUNCT
ejpam-77	291	7	2	2	NUM
ejpam-77	291	8	(	(	PUNCT
ejpam-77	291	9	2009	2009	NUM
ejpam-77	291	10	)	)	PUNCT
ejpam-77	291	11	,	,	PUNCT
ejpam-77	291	12	(	(	PUNCT
ejpam-77	291	13	195	195	NUM
ejpam-77	291	14	-	-	PUNCT
ejpam-77	291	15	212	212	NUM
ejpam-77	291	16	)	)	PUNCT
ejpam-77	291	17	206	206	NUM
ejpam-77	291	18	4	4	NUM
ejpam-77	291	19	.	.	PUNCT
ejpam-77	292	1	i	i	PRON
ejpam-77	292	2	-continuity	-continuity	PROPN
ejpam-77	292	3	of	of	ADP
ejpam-77	292	4	a	a	DET
ejpam-77	292	5	function	function	NOUN
ejpam-77	292	6	in	in	ADP
ejpam-77	292	7	pn	pn	PROPN
ejpam-77	292	8	spaces	space	NOUN
ejpam-77	292	9	we	we	PRON
ejpam-77	292	10	begin	begin	VERB
ejpam-77	292	11	with	with	ADP
ejpam-77	292	12	the	the	DET
ejpam-77	292	13	definition	definition	NOUN
ejpam-77	292	14	of	of	ADP
ejpam-77	292	15	continuity	continuity	NOUN
ejpam-77	292	16	an	an	DET
ejpam-77	292	17	important	important	ADJ
ejpam-77	292	18	type	type	NOUN
ejpam-77	292	19	of	of	ADP
ejpam-77	292	20	sequential	sequential	ADJ
ejpam-77	292	21	continuity	continuity	NOUN
ejpam-77	292	22	in	in	ADP
ejpam-77	292	23	pn	pn	PROPN
ejpam-77	292	24	space	space	NOUN
ejpam-77	292	25	.	.	PUNCT
ejpam-77	293	1	definition	definition	NOUN
ejpam-77	293	2	4.1	4.1	NUM
ejpam-77	293	3	.	.	PUNCT
ejpam-77	294	1	let	let	AUX
ejpam-77	294	2	i	i	PRON
ejpam-77	294	3	be	be	AUX
ejpam-77	294	4	an	an	DET
ejpam-77	294	5	ideal	ideal	NOUN
ejpam-77	294	6	and	and	CCONJ
ejpam-77	294	7	(	(	PUNCT
ejpam-77	294	8	x	x	INTJ
ejpam-77	294	9	,	,	PUNCT
ejpam-77	294	10	f	f	PROPN
ejpam-77	294	11	,	,	PUNCT
ejpam-77	294	12	t	t	PROPN
ejpam-77	294	13	)	)	PUNCT
ejpam-77	294	14	be	be	AUX
ejpam-77	294	15	a	a	DET
ejpam-77	294	16	pn	pn	NOUN
ejpam-77	294	17	space	space	NOUN
ejpam-77	294	18	.	.	PUNCT
ejpam-77	295	1	a	a	DET
ejpam-77	295	2	map	map	NOUN
ejpam-77	295	3	f	f	X
ejpam-77	295	4	:	:	PUNCT
ejpam-77	295	5	x	x	X
ejpam-77	295	6	→	→	PUNCT
ejpam-77	295	7	x	x	X
ejpam-77	295	8	is	be	AUX
ejpam-77	295	9	called	call	VERB
ejpam-77	295	10	f	f	PROPN
ejpam-77	295	11	−	−	PROPN
ejpam-77	295	12	cont	cont	NOUN
ejpam-77	295	13	inuous	inuous	ADJ
ejpam-77	295	14	at	at	ADP
ejpam-77	295	15	a	a	DET
ejpam-77	295	16	point	point	NOUN
ejpam-77	295	17	ξ	ξ	X
ejpam-77	295	18	∈	∈	NOUN
ejpam-77	295	19	x	x	X
ejpam-77	295	20	,	,	PUNCT
ejpam-77	295	21	if	if	SCONJ
ejpam-77	295	22	f	f	PROPN
ejpam-77	295	23	−	−	PROPN
ejpam-77	295	24	lim	lim	PROPN
ejpam-77	295	25	xn	xn	PUNCT
ejpam-77	296	1	=	=	SYM
ejpam-77	296	2	ξ	ξ	X
ejpam-77	296	3	=	=	NOUN
ejpam-77	296	4	⇒	⇒	X
ejpam-77	296	5	f	f	PROPN
ejpam-77	297	1	−	−	PROPN
ejpam-77	297	2	lim	lim	PROPN
ejpam-77	297	3	f	f	PROPN
ejpam-77	297	4	(	(	PUNCT
ejpam-77	297	5	xn	xn	PROPN
ejpam-77	297	6	)	)	PUNCT
ejpam-77	298	1	=	=	SYM
ejpam-77	298	2	f	f	X
ejpam-77	298	3	(	(	PUNCT
ejpam-77	298	4	ξ	ξ	NOUN
ejpam-77	298	5	)	)	PUNCT
ejpam-77	298	6	.	.	PUNCT
ejpam-77	299	1	this	this	PRON
ejpam-77	299	2	means	mean	VERB
ejpam-77	299	3	for	for	ADP
ejpam-77	299	4	every	every	DET
ejpam-77	299	5	ε	ε	PROPN
ejpam-77	299	6	>	>	X
ejpam-77	299	7	0	0	PUNCT
ejpam-77	300	1	and	and	CCONJ
ejpam-77	300	2	λ	λ	PROPN
ejpam-77	300	3	∈	∈	PROPN
ejpam-77	300	4	(	(	PUNCT
ejpam-77	300	5	0	0	NUM
ejpam-77	300	6	,	,	PUNCT
ejpam-77	300	7	1	1	NUM
ejpam-77	300	8	)	)	PUNCT
ejpam-77	300	9	,	,	PUNCT
ejpam-77	300	10	there	there	PRON
ejpam-77	300	11	exists	exist	VERB
ejpam-77	300	12	a	a	DET
ejpam-77	300	13	number	number	NOUN
ejpam-77	300	14	n	n	NOUN
ejpam-77	300	15	∈	∈	NOUN
ejpam-77	300	16	n	n	PRON
ejpam-77	300	17	such	such	ADJ
ejpam-77	300	18	that	that	PRON
ejpam-77	300	19	for	for	ADP
ejpam-77	300	20	n	n	PRON
ejpam-77	300	21	≥	≥	NOUN
ejpam-77	300	22	n	n	CCONJ
ejpam-77	300	23	,	,	PUNCT
ejpam-77	300	24	we	we	PRON
ejpam-77	300	25	have	have	VERB
ejpam-77	300	26	xn−	xn−	PUNCT
ejpam-77	300	27	ξ	ξ	PROPN
ejpam-77	300	28	∈	∈	PROPN
ejpam-77	300	29	nθ(ε	nθ(ε	NOUN
ejpam-77	300	30	,	,	PUNCT
ejpam-77	300	31	λ	λ	NOUN
ejpam-77	300	32	)	)	PUNCT
ejpam-77	300	33	implies	imply	VERB
ejpam-77	300	34	f	f	PROPN
ejpam-77	300	35	(	(	PUNCT
ejpam-77	300	36	xn)−	xn)−	NOUN
ejpam-77	300	37	f	f	X
ejpam-77	300	38	(	(	PUNCT
ejpam-77	300	39	ξ	ξ	NOUN
ejpam-77	300	40	)	)	PUNCT
ejpam-77	300	41	∈nθ	∈nθ	PROPN
ejpam-77	300	42	(	(	PUNCT
ejpam-77	300	43	ε	ε	PROPN
ejpam-77	300	44	,	,	PUNCT
ejpam-77	300	45	λ	λ	NOUN
ejpam-77	300	46	)	)	PUNCT
ejpam-77	300	47	.	.	PUNCT
ejpam-77	301	1	definition	definition	NOUN
ejpam-77	301	2	4.2	4.2	NUM
ejpam-77	301	3	.	.	PUNCT
ejpam-77	302	1	let	let	VERB
ejpam-77	302	2	i	i	PRON
ejpam-77	302	3	be	be	AUX
ejpam-77	302	4	an	an	DET
ejpam-77	302	5	ideal	ideal	NOUN
ejpam-77	302	6	and	and	CCONJ
ejpam-77	302	7	(	(	PUNCT
ejpam-77	302	8	x	x	INTJ
ejpam-77	302	9	,	,	PUNCT
ejpam-77	302	10	f	f	PROPN
ejpam-77	302	11	,	,	PUNCT
ejpam-77	302	12	t	t	PROPN
ejpam-77	302	13	)	)	PUNCT
ejpam-77	302	14	be	be	AUX
ejpam-77	302	15	a	a	DET
ejpam-77	302	16	pn	pn	NOUN
ejpam-77	302	17	space	space	NOUN
ejpam-77	302	18	.	.	PUNCT
ejpam-77	303	1	a	a	DET
ejpam-77	303	2	map	map	NOUN
ejpam-77	303	3	f	f	X
ejpam-77	303	4	:	:	PUNCT
ejpam-77	303	5	x	x	X
ejpam-77	303	6	→	→	PUNCT
ejpam-77	303	7	x	x	X
ejpam-77	303	8	is	be	AUX
ejpam-77	303	9	called	call	VERB
ejpam-77	304	1	i	i	PRON
ejpam-77	304	2	f	f	NOUN
ejpam-77	305	1	−	−	PROPN
ejpam-77	305	2	cont	cont	NOUN
ejpam-77	305	3	inuous	inuous	ADJ
ejpam-77	305	4	at	at	ADP
ejpam-77	305	5	a	a	DET
ejpam-77	305	6	point	point	NOUN
ejpam-77	305	7	ξ	ξ	X
ejpam-77	305	8	∈	∈	NOUN
ejpam-77	305	9	x	x	X
ejpam-77	305	10	,	,	PUNCT
ejpam-77	305	11	if	if	SCONJ
ejpam-77	305	12	i	i	PRON
ejpam-77	305	13	f	f	PROPN
ejpam-77	306	1	−	−	PROPN
ejpam-77	306	2	lim	lim	PROPN
ejpam-77	306	3	xn	xn	PUNCT
ejpam-77	307	1	=	=	SYM
ejpam-77	307	2	ξ	ξ	X
ejpam-77	307	3	=	=	NOUN
ejpam-77	307	4	⇒	⇒	VERB
ejpam-77	307	5	i	i	NOUN
ejpam-77	307	6	f	f	NOUN
ejpam-77	308	1	−	−	PROPN
ejpam-77	308	2	lim	lim	PROPN
ejpam-77	308	3	f	f	PROPN
ejpam-77	308	4	(	(	PUNCT
ejpam-77	308	5	xn	xn	PROPN
ejpam-77	308	6	)	)	PUNCT
ejpam-77	309	1	=	=	SYM
ejpam-77	309	2	f	f	X
ejpam-77	309	3	(	(	PUNCT
ejpam-77	309	4	ξ	ξ	NOUN
ejpam-77	309	5	)	)	PUNCT
ejpam-77	309	6	.	.	PUNCT
ejpam-77	310	1	theorem	theorem	VERB
ejpam-77	310	2	4.1	4.1	NUM
ejpam-77	310	3	.	.	PUNCT
ejpam-77	311	1	let	let	VERB
ejpam-77	311	2	(	(	PUNCT
ejpam-77	311	3	x	x	SYM
ejpam-77	311	4	,	,	PUNCT
ejpam-77	311	5	f	f	PROPN
ejpam-77	311	6	,	,	PUNCT
ejpam-77	311	7	t	t	PROPN
ejpam-77	311	8	)	)	PUNCT
ejpam-77	311	9	be	be	AUX
ejpam-77	311	10	a	a	DET
ejpam-77	311	11	pn	pn	NOUN
ejpam-77	311	12	space	space	NOUN
ejpam-77	312	1	and	and	CCONJ
ejpam-77	312	2	i	i	PRON
ejpam-77	312	3	be	be	VERB
ejpam-77	312	4	an	an	DET
ejpam-77	312	5	arbitrary	arbitrary	ADJ
ejpam-77	312	6	ideal	ideal	NOUN
ejpam-77	312	7	in	in	ADP
ejpam-77	312	8	n.	n.	PROPN
ejpam-77	312	9	if	if	SCONJ
ejpam-77	312	10	f	f	PROPN
ejpam-77	312	11	:	:	PUNCT
ejpam-77	312	12	x	x	X
ejpam-77	312	13	→	→	PUNCT
ejpam-77	312	14	x	x	X
ejpam-77	312	15	is	be	AUX
ejpam-77	312	16	f	f	PROPN
ejpam-77	312	17	-continuous	-continuous	ADJ
ejpam-77	312	18	then	then	ADV
ejpam-77	312	19	it	it	PRON
ejpam-77	312	20	is	be	AUX
ejpam-77	312	21	i	i	PRON
ejpam-77	312	22	f	f	PROPN
ejpam-77	312	23	-continuous	-continuous	ADJ
ejpam-77	312	24	.	.	PUNCT
ejpam-77	313	1	proof	proof	NOUN
ejpam-77	313	2	.	.	PUNCT
ejpam-77	314	1	let	let	VERB
ejpam-77	314	2	{	{	PUNCT
ejpam-77	314	3	xn	xn	NOUN
ejpam-77	314	4	}	}	PUNCT
ejpam-77	314	5	∈	∈	NOUN
ejpam-77	314	6	x	x	X
ejpam-77	315	1	and	and	CCONJ
ejpam-77	315	2	i	i	PRON
ejpam-77	315	3	f	f	PROPN
ejpam-77	316	1	−	−	PROPN
ejpam-77	316	2	lim	lim	PROPN
ejpam-77	316	3	xn	xn	PUNCT
ejpam-77	317	1	=	=	SYM
ejpam-77	317	2	ξ	ξ	PROPN
ejpam-77	317	3	.	.	PUNCT
ejpam-77	317	4	then	then	ADV
ejpam-77	317	5	by	by	ADP
ejpam-77	317	6	f	f	PROPN
ejpam-77	317	7	-continuity	-continuity	PROPN
ejpam-77	317	8	of	of	ADP
ejpam-77	317	9	f	f	PROPN
ejpam-77	317	10	at	at	ADP
ejpam-77	317	11	ξ	ξ	PROPN
ejpam-77	317	12	∈	∈	PROPN
ejpam-77	317	13	x	x	PUNCT
ejpam-77	317	14	we	we	PRON
ejpam-77	317	15	means	mean	VERB
ejpam-77	317	16	for	for	ADP
ejpam-77	317	17	every	every	DET
ejpam-77	317	18	ε	ε	PROPN
ejpam-77	317	19	>	>	X
ejpam-77	317	20	0	0	PUNCT
ejpam-77	318	1	and	and	CCONJ
ejpam-77	318	2	λ	λ	PROPN
ejpam-77	318	3	∈	∈	PROPN
ejpam-77	318	4	(	(	PUNCT
ejpam-77	318	5	0	0	NUM
ejpam-77	318	6	,	,	PUNCT
ejpam-77	318	7	1	1	NUM
ejpam-77	318	8	)	)	PUNCT
ejpam-77	318	9	,	,	PUNCT
ejpam-77	318	10	we	we	PRON
ejpam-77	318	11	have	have	VERB
ejpam-77	318	12	xn−ξ	xn−ξ	PROPN
ejpam-77	318	13	∈	∈	PROPN
ejpam-77	318	14	nθ	nθ	PROPN
ejpam-77	318	15	(	(	PUNCT
ejpam-77	318	16	ε	ε	PROPN
ejpam-77	318	17	,	,	PUNCT
ejpam-77	318	18	λ	λ	NOUN
ejpam-77	318	19	)	)	PUNCT
ejpam-77	318	20	implies	imply	VERB
ejpam-77	318	21	f	f	PROPN
ejpam-77	318	22	(	(	PUNCT
ejpam-77	318	23	xn)−	xn)−	NOUN
ejpam-77	318	24	f	f	X
ejpam-77	318	25	(	(	PUNCT
ejpam-77	318	26	ξ	ξ	PROPN
ejpam-77	318	27	)	)	PUNCT
ejpam-77	318	28	∈	∈	PROPN
ejpam-77	318	29	nθ(ε	nθ(ε	NOUN
ejpam-77	318	30	,	,	PUNCT
ejpam-77	318	31	λ	λ	NOUN
ejpam-77	318	32	)	)	PUNCT
ejpam-77	318	33	.	.	PUNCT
ejpam-77	319	1	thus	thus	ADV
ejpam-77	319	2	{	{	PUNCT
ejpam-77	319	3	n	n	NOUN
ejpam-77	319	4	∈	∈	NOUN
ejpam-77	319	5	n	n	NOUN
ejpam-77	319	6	:	:	PUNCT
ejpam-77	319	7	f	f	PROPN
ejpam-77	319	8	(	(	PUNCT
ejpam-77	319	9	xn	xn	PROPN
ejpam-77	319	10	)	)	PUNCT
ejpam-77	320	1	−	−	PROPN
ejpam-77	320	2	f	f	PROPN
ejpam-77	320	3	(	(	PUNCT
ejpam-77	320	4	ξ	ξ	PROPN
ejpam-77	320	5	)	)	PUNCT
ejpam-77	320	6	/∈	/∈	PUNCT
ejpam-77	321	1	nθ	nθ	CCONJ
ejpam-77	321	2	(	(	PUNCT
ejpam-77	321	3	ε	ε	PROPN
ejpam-77	321	4	,	,	PUNCT
ejpam-77	321	5	λ	λ	NOUN
ejpam-77	321	6	)	)	PUNCT
ejpam-77	321	7	}	}	PUNCT
ejpam-77	321	8	⊂	⊂	PRON
ejpam-77	321	9	{	{	PUNCT
ejpam-77	321	10	n	n	CCONJ
ejpam-77	321	11	∈	∈	PROPN
ejpam-77	321	12	n	n	NOUN
ejpam-77	321	13	:	:	PUNCT
ejpam-77	321	14	xn	xn	PROPN
ejpam-77	322	1	−	−	PROPN
ejpam-77	322	2	ξ	ξ	X
ejpam-77	322	3	/∈	/∈	PUNCT
ejpam-77	322	4	nθ	nθ	CCONJ
ejpam-77	322	5	(	(	PUNCT
ejpam-77	322	6	ε	ε	PROPN
ejpam-77	322	7	,	,	PUNCT
ejpam-77	322	8	λ	λ	NOUN
ejpam-77	322	9	)	)	PUNCT
ejpam-77	322	10	}	}	PUNCT
ejpam-77	322	11	.	.	PUNCT
ejpam-77	323	1	since	since	SCONJ
ejpam-77	323	2	i	i	PRON
ejpam-77	323	3	f	f	PROPN
ejpam-77	323	4	−	−	PROPN
ejpam-77	323	5	lim	lim	PROPN
ejpam-77	323	6	xn	xn	PUNCT
ejpam-77	324	1	=	=	SYM
ejpam-77	324	2	ξ	ξ	PROPN
ejpam-77	324	3	,	,	PUNCT
ejpam-77	324	4	we	we	PRON
ejpam-77	324	5	have	have	VERB
ejpam-77	324	6	{	{	PUNCT
ejpam-77	324	7	n	n	SYM
ejpam-77	324	8	∈	∈	NOUN
ejpam-77	324	9	n	n	NOUN
ejpam-77	324	10	:	:	PUNCT
ejpam-77	324	11	xn	xn	PROPN
ejpam-77	325	1	−	−	PROPN
ejpam-77	325	2	ξ	ξ	X
ejpam-77	325	3	/∈	/∈	PUNCT
ejpam-77	325	4	nθ(ε	nθ(ε	NOUN
ejpam-77	325	5	,	,	PUNCT
ejpam-77	325	6	λ	λ	NOUN
ejpam-77	325	7	)	)	PUNCT
ejpam-77	325	8	}	}	PUNCT
ejpam-77	325	9	∈	∈	PROPN
ejpam-77	326	1	i	i	PRON
ejpam-77	326	2	.	.	PUNCT
ejpam-77	327	1	this	this	PRON
ejpam-77	327	2	implies	imply	VERB
ejpam-77	327	3	that	that	SCONJ
ejpam-77	327	4	{	{	PUNCT
ejpam-77	327	5	n	n	X
ejpam-77	327	6	∈	∈	NOUN
ejpam-77	327	7	n	n	NOUN
ejpam-77	327	8	:	:	PUNCT
ejpam-77	327	9	f	f	X
ejpam-77	327	10	(	(	PUNCT
ejpam-77	327	11	xn)−	xn)−	NOUN
ejpam-77	327	12	f	f	X
ejpam-77	327	13	(	(	PUNCT
ejpam-77	327	14	ξ	ξ	PROPN
ejpam-77	327	15	)	)	PUNCT
ejpam-77	327	16	/∈	/∈	PUNCT
ejpam-77	327	17	nθ(ε	nθ(ε	NOUN
ejpam-77	327	18	,	,	PUNCT
ejpam-77	327	19	λ	λ	NOUN
ejpam-77	327	20	)	)	PUNCT
ejpam-77	327	21	}	}	PUNCT
ejpam-77	327	22	∈	∈	PROPN
ejpam-77	327	23	i	i	PRON
ejpam-77	327	24	which	which	PRON
ejpam-77	327	25	means	mean	VERB
ejpam-77	327	26	i	i	PRON
ejpam-77	327	27	f	f	PROPN
ejpam-77	328	1	−	−	PROPN
ejpam-77	328	2	lim	lim	PROPN
ejpam-77	328	3	f	f	PROPN
ejpam-77	328	4	(	(	PUNCT
ejpam-77	328	5	xn	xn	PROPN
ejpam-77	328	6	)	)	PUNCT
ejpam-77	329	1	=	=	SYM
ejpam-77	329	2	f	f	X
ejpam-77	329	3	(	(	PUNCT
ejpam-77	329	4	ξ	ξ	NOUN
ejpam-77	329	5	)	)	PUNCT
ejpam-77	329	6	.	.	PUNCT
ejpam-77	330	1	hence	hence	ADV
ejpam-77	330	2	,	,	PUNCT
ejpam-77	330	3	f	f	PROPN
ejpam-77	330	4	is	be	AUX
ejpam-77	330	5	an	an	DET
ejpam-77	330	6	i	i	NOUN
ejpam-77	330	7	f	f	PROPN
ejpam-77	330	8	-continuous	-continuous	PROPN
ejpam-77	330	9	.	.	PUNCT
ejpam-77	331	1	theorem	theorem	VERB
ejpam-77	331	2	4.2	4.2	NUM
ejpam-77	331	3	.	.	PUNCT
ejpam-77	332	1	let	let	VERB
ejpam-77	332	2	(	(	PUNCT
ejpam-77	332	3	x	x	SYM
ejpam-77	332	4	,	,	PUNCT
ejpam-77	332	5	f	f	PROPN
ejpam-77	332	6	,	,	PUNCT
ejpam-77	332	7	t	t	PROPN
ejpam-77	332	8	)	)	PUNCT
ejpam-77	332	9	be	be	AUX
ejpam-77	332	10	a	a	DET
ejpam-77	332	11	pn	pn	NOUN
ejpam-77	332	12	space	space	NOUN
ejpam-77	333	1	and	and	CCONJ
ejpam-77	333	2	i	i	PRON
ejpam-77	333	3	be	be	VERB
ejpam-77	333	4	an	an	DET
ejpam-77	333	5	arbitrary	arbitrary	ADJ
ejpam-77	333	6	admissible	admissible	ADJ
ejpam-77	333	7	ideal	ideal	NOUN
ejpam-77	333	8	in	in	ADP
ejpam-77	333	9	n.	n.	PROPN
ejpam-77	333	10	if	if	SCONJ
ejpam-77	333	11	f	f	PROPN
ejpam-77	333	12	:	:	PUNCT
ejpam-77	333	13	x	x	X
ejpam-77	333	14	→	→	PUNCT
ejpam-77	333	15	x	x	X
ejpam-77	333	16	is	be	AUX
ejpam-77	333	17	i	i	PRON
ejpam-77	333	18	f	f	PROPN
ejpam-77	333	19	-continuous	-continuous	ADJ
ejpam-77	333	20	then	then	ADV
ejpam-77	333	21	f	f	PROPN
ejpam-77	333	22	is	be	AUX
ejpam-77	333	23	i	i	PRON
ejpam-77	333	24	f	f	PROPN
ejpam-77	333	25	fin	fin	NOUN
ejpam-77	333	26	-continuous	-continuous	ADJ
ejpam-77	333	27	.	.	PUNCT
ejpam-77	334	1	m.	m.	NOUN
ejpam-77	334	2	rahmat	rahmat	PROPN
ejpam-77	334	3	and	and	CCONJ
ejpam-77	334	4	harikrishnan	harikrishnan	PROPN
ejpam-77	334	5	k.	k.	PROPN
ejpam-77	334	6	/	/	PUNCT
ejpam-77	334	7	eur	eur	PROPN
ejpam-77	334	8	.	.	PUNCT
ejpam-77	335	1	j.	j.	PROPN
ejpam-77	335	2	pure	pure	PROPN
ejpam-77	335	3	appl	appl	PROPN
ejpam-77	335	4	.	.	PROPN
ejpam-77	335	5	math	math	PROPN
ejpam-77	335	6	,	,	PUNCT
ejpam-77	335	7	2	2	NUM
ejpam-77	335	8	(	(	PUNCT
ejpam-77	335	9	2009	2009	NUM
ejpam-77	335	10	)	)	PUNCT
ejpam-77	335	11	,	,	PUNCT
ejpam-77	335	12	(	(	PUNCT
ejpam-77	335	13	195	195	NUM
ejpam-77	335	14	-	-	PUNCT
ejpam-77	335	15	212	212	NUM
ejpam-77	335	16	)	)	PUNCT
ejpam-77	335	17	207	207	NUM
ejpam-77	335	18	proof	proof	NOUN
ejpam-77	335	19	.	.	PUNCT
ejpam-77	336	1	let	let	VERB
ejpam-77	336	2	f	f	PROPN
ejpam-77	336	3	is	be	AUX
ejpam-77	336	4	i	i	PRON
ejpam-77	336	5	f	f	PROPN
ejpam-77	336	6	-continuous	-continuous	ADJ
ejpam-77	336	7	at	at	ADP
ejpam-77	336	8	ξ	ξ	PROPN
ejpam-77	336	9	∈	∈	PROPN
ejpam-77	336	10	x	x	INTJ
ejpam-77	336	11	.	.	PUNCT
ejpam-77	336	12	suppose	suppose	VERB
ejpam-77	336	13	that	that	SCONJ
ejpam-77	336	14	f	f	PROPN
ejpam-77	336	15	is	be	AUX
ejpam-77	336	16	not	not	PART
ejpam-77	336	17	i	i	PRON
ejpam-77	336	18	f	f	NOUN
ejpam-77	336	19	f	f	PROPN
ejpam-77	336	20	-continuous	-continuous	PROPN
ejpam-77	336	21	,	,	PUNCT
ejpam-77	336	22	then	then	ADV
ejpam-77	336	23	the	the	DET
ejpam-77	336	24	set	set	NOUN
ejpam-77	336	25	a=	a=	NOUN
ejpam-77	336	26	{	{	PUNCT
ejpam-77	336	27	n	n	NOUN
ejpam-77	336	28	∈	∈	NOUN
ejpam-77	336	29	n	n	NOUN
ejpam-77	336	30	:	:	PUNCT
ejpam-77	336	31	f	f	X
ejpam-77	336	32	(	(	PUNCT
ejpam-77	336	33	xn)−	xn)−	NOUN
ejpam-77	336	34	f	f	X
ejpam-77	336	35	(	(	PUNCT
ejpam-77	336	36	ξ	ξ	PROPN
ejpam-77	336	37	)	)	PUNCT
ejpam-77	336	38	/∈	/∈	PUNCT
ejpam-77	337	1	nθ(ε	nθ(ε	NOUN
ejpam-77	337	2	,	,	PUNCT
ejpam-77	337	3	λ	λ	NOUN
ejpam-77	337	4	)	)	PUNCT
ejpam-77	337	5	}	}	PUNCT
ejpam-77	337	6	6∈	6∈	NOUN
ejpam-77	338	1	i	i	PRON
ejpam-77	338	2	f	f	PROPN
ejpam-77	338	3	,	,	PUNCT
ejpam-77	338	4	i.e.	i.e.	X
ejpam-77	338	5	,	,	PUNCT
ejpam-77	338	6	a	a	PRON
ejpam-77	338	7	is	be	AUX
ejpam-77	338	8	infinite	infinite	ADJ
ejpam-77	338	9	set	set	VERB
ejpam-77	338	10	whenever	whenever	SCONJ
ejpam-77	338	11	{	{	PUNCT
ejpam-77	338	12	n	n	NOUN
ejpam-77	338	13	∈	∈	NOUN
ejpam-77	338	14	n	n	NOUN
ejpam-77	338	15	:	:	PUNCT
ejpam-77	338	16	xn	xn	PROPN
ejpam-77	339	1	−	−	PROPN
ejpam-77	339	2	ξ	ξ	X
ejpam-77	339	3	/∈	/∈	PUNCT
ejpam-77	339	4	nθ(ε	nθ(ε	NOUN
ejpam-77	339	5	,	,	PUNCT
ejpam-77	339	6	λ	λ	NOUN
ejpam-77	339	7	)	)	PUNCT
ejpam-77	339	8	}	}	PUNCT
ejpam-77	339	9	∈	∈	PROPN
ejpam-77	340	1	i	i	PRON
ejpam-77	340	2	f	f	X
ejpam-77	340	3	.	.	PUNCT
ejpam-77	341	1	let	let	VERB
ejpam-77	341	2	{	{	PUNCT
ejpam-77	341	3	yn	yn	NOUN
ejpam-77	341	4	}	}	PUNCT
ejpam-77	341	5	be	be	VERB
ejpam-77	341	6	the	the	DET
ejpam-77	341	7	subsequence	subsequence	NOUN
ejpam-77	341	8	of	of	ADP
ejpam-77	341	9	{	{	PUNCT
ejpam-77	341	10	xn	xn	NOUN
ejpam-77	341	11	}	}	PUNCT
ejpam-77	341	12	given	give	VERB
ejpam-77	341	13	by	by	ADP
ejpam-77	341	14	the	the	DET
ejpam-77	341	15	subset	subset	NOUN
ejpam-77	341	16	a	a	PRON
ejpam-77	341	17	of	of	ADP
ejpam-77	341	18	n.	n.	NOUN
ejpam-77	341	19	then	then	ADV
ejpam-77	341	20	{	{	PUNCT
ejpam-77	341	21	n	n	NOUN
ejpam-77	341	22	∈	∈	PROPN
ejpam-77	342	1	n	n	NOUN
ejpam-77	342	2	:	:	PUNCT
ejpam-77	342	3	f	f	X
ejpam-77	342	4	(	(	PUNCT
ejpam-77	342	5	yn)−	yn)−	PROPN
ejpam-77	342	6	f	f	PROPN
ejpam-77	342	7	(	(	PUNCT
ejpam-77	342	8	ξ	ξ	PROPN
ejpam-77	342	9	)	)	PUNCT
ejpam-77	342	10	/∈	/∈	PUNCT
ejpam-77	343	1	nθ	nθ	CCONJ
ejpam-77	343	2	(	(	PUNCT
ejpam-77	343	3	ε	ε	PROPN
ejpam-77	343	4	,	,	PUNCT
ejpam-77	343	5	λ	λ	NOUN
ejpam-77	343	6	)	)	PUNCT
ejpam-77	343	7	}	}	PUNCT
ejpam-77	343	8	=	=	VERB
ejpam-77	343	9	n.	n.	NOUN
ejpam-77	343	10	also	also	ADV
ejpam-77	343	11	,	,	PUNCT
ejpam-77	343	12	the	the	DET
ejpam-77	343	13	subsequence	subsequence	NOUN
ejpam-77	343	14	{	{	PUNCT
ejpam-77	343	15	yn	yn	NOUN
ejpam-77	343	16	}	}	PUNCT
ejpam-77	343	17	holds	hold	VERB
ejpam-77	343	18	i	i	PRON
ejpam-77	343	19	f	f	PROPN
ejpam-77	343	20	f	f	PROPN
ejpam-77	344	1	−	−	PROPN
ejpam-77	344	2	lim	lim	PROPN
ejpam-77	344	3	yn	yn	PROPN
ejpam-77	344	4	=	=	SYM
ejpam-77	344	5	ξ	ξ	PROPN
ejpam-77	344	6	.	.	PUNCT
ejpam-77	344	7	by	by	ADP
ejpam-77	344	8	lemma	lemma	PROPN
ejpam-77	344	9	4	4	NUM
ejpam-77	344	10	,	,	PUNCT
ejpam-77	344	11	this	this	PRON
ejpam-77	344	12	implies	imply	VERB
ejpam-77	344	13	i	i	PRON
ejpam-77	344	14	f	f	PROPN
ejpam-77	345	1	−	−	PROPN
ejpam-77	345	2	lim	lim	PROPN
ejpam-77	345	3	yn	yn	PROPN
ejpam-77	345	4	=	=	SYM
ejpam-77	345	5	ξ	ξ	PROPN
ejpam-77	345	6	.	.	PUNCT
ejpam-77	345	7	thus	thus	ADV
ejpam-77	345	8	,	,	PUNCT
ejpam-77	345	9	by	by	ADP
ejpam-77	345	10	i	i	PRON
ejpam-77	345	11	f	f	PROPN
ejpam-77	345	12	continuity	continuity	NOUN
ejpam-77	345	13	of	of	ADP
ejpam-77	345	14	f	f	PROPN
ejpam-77	345	15	,	,	PUNCT
ejpam-77	345	16	we	we	PRON
ejpam-77	345	17	have	have	VERB
ejpam-77	345	18	i	i	PRON
ejpam-77	345	19	f	f	X
ejpam-77	346	1	−	−	PROPN
ejpam-77	347	1	lim	lim	PROPN
ejpam-77	347	2	f	f	PROPN
ejpam-77	347	3	(	(	PUNCT
ejpam-77	347	4	yn	yn	PROPN
ejpam-77	347	5	)	)	PUNCT
ejpam-77	347	6	=	=	SYM
ejpam-77	347	7	f	f	PROPN
ejpam-77	347	8	(	(	PUNCT
ejpam-77	347	9	ξ	ξ	NOUN
ejpam-77	347	10	)	)	PUNCT
ejpam-77	347	11	.	.	PUNCT
ejpam-77	348	1	hence	hence	ADV
ejpam-77	348	2	{	{	PUNCT
ejpam-77	348	3	n	n	CCONJ
ejpam-77	348	4	∈	∈	NOUN
ejpam-77	348	5	n	n	NOUN
ejpam-77	348	6	:	:	PUNCT
ejpam-77	348	7	f	f	X
ejpam-77	348	8	(	(	PUNCT
ejpam-77	348	9	yn)−	yn)−	PROPN
ejpam-77	348	10	f	f	PROPN
ejpam-77	348	11	(	(	PUNCT
ejpam-77	348	12	ξ	ξ	PROPN
ejpam-77	348	13	)	)	PUNCT
ejpam-77	348	14	/∈	/∈	PUNCT
ejpam-77	348	15	nθ(ε	nθ(ε	NOUN
ejpam-77	348	16	,	,	PUNCT
ejpam-77	348	17	λ	λ	NOUN
ejpam-77	348	18	)	)	PUNCT
ejpam-77	348	19	}	}	PUNCT
ejpam-77	348	20	=	=	SYM
ejpam-77	348	21	n	n	X
ejpam-77	348	22	∈	∈	NOUN
ejpam-77	349	1	i	i	PRON
ejpam-77	349	2	,	,	PUNCT
ejpam-77	349	3	a	a	DET
ejpam-77	349	4	contradiction	contradiction	NOUN
ejpam-77	349	5	.	.	PUNCT
ejpam-77	350	1	therefore	therefore	ADV
ejpam-77	350	2	f	f	PROPN
ejpam-77	350	3	is	be	AUX
ejpam-77	350	4	i	i	PRON
ejpam-77	350	5	f	f	PROPN
ejpam-77	350	6	f	f	PROPN
ejpam-77	350	7	-continuous	-continuous	PROPN
ejpam-77	350	8	.	.	PUNCT
ejpam-77	351	1	from	from	ADP
ejpam-77	351	2	theorem	theorem	ADJ
ejpam-77	351	3	4.3	4.3	NUM
ejpam-77	351	4	and	and	CCONJ
ejpam-77	351	5	4.4	4.4	NUM
ejpam-77	351	6	,	,	PUNCT
ejpam-77	351	7	we	we	PRON
ejpam-77	351	8	can	can	AUX
ejpam-77	351	9	easily	easily	ADV
ejpam-77	351	10	prove	prove	VERB
ejpam-77	351	11	the	the	DET
ejpam-77	351	12	following	follow	VERB
ejpam-77	351	13	lemma	lemma	PROPN
ejpam-77	351	14	.	.	PUNCT
ejpam-77	352	1	lemma	lemma	PROPN
ejpam-77	352	2	4.1	4.1	NUM
ejpam-77	352	3	.	.	PUNCT
ejpam-77	353	1	let	let	VERB
ejpam-77	353	2	(	(	PUNCT
ejpam-77	353	3	x	x	SYM
ejpam-77	353	4	,	,	PUNCT
ejpam-77	353	5	f	f	PROPN
ejpam-77	353	6	,	,	PUNCT
ejpam-77	353	7	t	t	PROPN
ejpam-77	353	8	)	)	PUNCT
ejpam-77	353	9	be	be	AUX
ejpam-77	353	10	a	a	DET
ejpam-77	353	11	pn	pn	NOUN
ejpam-77	353	12	space	space	NOUN
ejpam-77	354	1	and	and	CCONJ
ejpam-77	354	2	i	i	PRON
ejpam-77	354	3	be	be	VERB
ejpam-77	354	4	an	an	DET
ejpam-77	354	5	arbitrary	arbitrary	ADJ
ejpam-77	354	6	admissible	admissible	ADJ
ejpam-77	354	7	ideal	ideal	NOUN
ejpam-77	354	8	in	in	ADP
ejpam-77	354	9	n.	n.	PROPN
ejpam-77	354	10	if	if	SCONJ
ejpam-77	354	11	f	f	PROPN
ejpam-77	354	12	:	:	PUNCT
ejpam-77	354	13	x	x	X
ejpam-77	354	14	→	→	PUNCT
ejpam-77	354	15	x	x	X
ejpam-77	354	16	is	be	AUX
ejpam-77	354	17	a	a	DET
ejpam-77	354	18	map	map	NOUN
ejpam-77	354	19	,	,	PUNCT
ejpam-77	354	20	then	then	ADV
ejpam-77	354	21	the	the	DET
ejpam-77	354	22	following	follow	VERB
ejpam-77	354	23	implication	implication	NOUN
ejpam-77	354	24	hold	hold	VERB
ejpam-77	354	25	:	:	PUNCT
ejpam-77	354	26	f	f	PROPN
ejpam-77	354	27	−	−	PROPN
ejpam-77	354	28	cont	cont	NOUN
ejpam-77	354	29	inuous⇒i	inuous⇒i	ADP
ejpam-77	354	30	f	f	NOUN
ejpam-77	354	31	−	−	PROPN
ejpam-77	354	32	cont	cont	NOUN
ejpam-77	354	33	inuous⇒ifin−	inuous⇒ifin−	NOUN
ejpam-77	354	34	cont	cont	VERB
ejpam-77	354	35	inuous	inuous	ADJ
ejpam-77	354	36	5	5	NUM
ejpam-77	354	37	.	.	PUNCT
ejpam-77	355	1	i	i	PRON
ejpam-77	355	2	-cauchy	-cauchy	VERB
ejpam-77	355	3	sequences	sequence	NOUN
ejpam-77	355	4	in	in	ADP
ejpam-77	355	5	pn	pn	PROPN
ejpam-77	355	6	spaces	space	NOUN
ejpam-77	355	7	definition	definition	NOUN
ejpam-77	355	8	5.1	5.1	NUM
ejpam-77	355	9	.	.	PUNCT
ejpam-77	356	1	let	let	AUX
ejpam-77	356	2	(	(	PUNCT
ejpam-77	356	3	x	x	SYM
ejpam-77	356	4	,	,	PUNCT
ejpam-77	356	5	f	f	PROPN
ejpam-77	356	6	,	,	PUNCT
ejpam-77	356	7	t	t	PROPN
ejpam-77	356	8	)	)	PUNCT
ejpam-77	356	9	be	be	AUX
ejpam-77	356	10	a	a	DET
ejpam-77	356	11	pn	pn	NOUN
ejpam-77	356	12	space	space	NOUN
ejpam-77	356	13	.	.	PUNCT
ejpam-77	357	1	a	a	DET
ejpam-77	357	2	sequence	sequence	NOUN
ejpam-77	357	3	{	{	PUNCT
ejpam-77	357	4	xn	xn	NOUN
ejpam-77	357	5	}	}	PUNCT
ejpam-77	357	6	in	in	ADP
ejpam-77	357	7	x	x	VERB
ejpam-77	357	8	is	be	AUX
ejpam-77	357	9	said	say	VERB
ejpam-77	357	10	to	to	PART
ejpam-77	357	11	be	be	AUX
ejpam-77	357	12	f	f	PROPN
ejpam-77	357	13	-cauchy	-cauchy	ADJ
ejpam-77	357	14	,	,	PUNCT
ejpam-77	357	15	if	if	SCONJ
ejpam-77	357	16	for	for	ADP
ejpam-77	357	17	every	every	DET
ejpam-77	357	18	ε	ε	PROPN
ejpam-77	357	19	>	>	X
ejpam-77	357	20	0	0	PUNCT
ejpam-77	357	21	and	and	CCONJ
ejpam-77	357	22	λ	λ	PROPN
ejpam-77	357	23	∈	∈	PROPN
ejpam-77	357	24	(	(	PUNCT
ejpam-77	357	25	0	0	NUM
ejpam-77	357	26	,	,	PUNCT
ejpam-77	357	27	1	1	NUM
ejpam-77	357	28	)	)	PUNCT
ejpam-77	357	29	,	,	PUNCT
ejpam-77	357	30	there	there	PRON
ejpam-77	357	31	exists	exist	VERB
ejpam-77	357	32	a	a	DET
ejpam-77	357	33	number	number	NOUN
ejpam-77	357	34	n	n	NOUN
ejpam-77	357	35	=	=	SYM
ejpam-77	357	36	n(ε	n(ε	PROPN
ejpam-77	357	37	,	,	PUNCT
ejpam-77	357	38	λ	λ	NOUN
ejpam-77	357	39	)	)	PUNCT
ejpam-77	357	40	∈	∈	PROPN
ejpam-77	357	41	n	n	PRON
ejpam-77	357	42	such	such	ADJ
ejpam-77	357	43	that	that	SCONJ
ejpam-77	357	44	xn−	xn−	PROPN
ejpam-77	357	45	xm	xm	PROPN
ejpam-77	357	46	∈	∈	PROPN
ejpam-77	357	47	nθ	nθ	PROPN
ejpam-77	357	48	(	(	PUNCT
ejpam-77	357	49	ε	ε	PROPN
ejpam-77	357	50	,	,	PUNCT
ejpam-77	357	51	λ	λ	PROPN
ejpam-77	357	52	)	)	PUNCT
ejpam-77	357	53	for	for	ADP
ejpam-77	357	54	every	every	DET
ejpam-77	357	55	n	n	CCONJ
ejpam-77	357	56	,	,	PUNCT
ejpam-77	357	57	m	m	VERB
ejpam-77	357	58	≥	≥	NOUN
ejpam-77	357	59	n	n	NOUN
ejpam-77	357	60	.	.	PUNCT
ejpam-77	358	1	definition	definition	NOUN
ejpam-77	358	2	5.2	5.2	NUM
ejpam-77	358	3	.	.	PUNCT
ejpam-77	359	1	let	let	AUX
ejpam-77	359	2	(	(	PUNCT
ejpam-77	359	3	x	x	SYM
ejpam-77	359	4	,	,	PUNCT
ejpam-77	359	5	f	f	PROPN
ejpam-77	359	6	,	,	PUNCT
ejpam-77	359	7	t	t	PROPN
ejpam-77	359	8	)	)	PUNCT
ejpam-77	359	9	be	be	AUX
ejpam-77	359	10	a	a	DET
ejpam-77	359	11	pn	pn	NOUN
ejpam-77	359	12	space	space	NOUN
ejpam-77	360	1	and	and	CCONJ
ejpam-77	360	2	i	i	PRON
ejpam-77	360	3	be	be	VERB
ejpam-77	360	4	an	an	DET
ejpam-77	360	5	admissible	admissible	ADJ
ejpam-77	360	6	ideal	ideal	NOUN
ejpam-77	360	7	.	.	PUNCT
ejpam-77	361	1	then	then	ADV
ejpam-77	361	2	a	a	DET
ejpam-77	361	3	sequence	sequence	NOUN
ejpam-77	361	4	(	(	PUNCT
ejpam-77	361	5	xn	xn	X
ejpam-77	361	6	)	)	PUNCT
ejpam-77	361	7	in	in	ADP
ejpam-77	361	8	x	x	PROPN
ejpam-77	361	9	is	be	AUX
ejpam-77	361	10	called	call	VERB
ejpam-77	361	11	i	i	PRON
ejpam-77	361	12	f−cauchy	f−cauchy	NOUN
ejpam-77	361	13	sequence	sequence	NOUN
ejpam-77	361	14	in	in	ADP
ejpam-77	361	15	x	x	PUNCT
ejpam-77	361	16	if	if	SCONJ
ejpam-77	361	17	for	for	ADP
ejpam-77	361	18	every	every	DET
ejpam-77	361	19	ε	ε	PROPN
ejpam-77	361	20	>	>	X
ejpam-77	361	21	0	0	PUNCT
ejpam-77	362	1	and	and	CCONJ
ejpam-77	362	2	λ	λ	PROPN
ejpam-77	362	3	∈	∈	PROPN
ejpam-77	362	4	(	(	PUNCT
ejpam-77	362	5	0	0	NUM
ejpam-77	362	6	,	,	PUNCT
ejpam-77	362	7	1	1	NUM
ejpam-77	362	8	)	)	PUNCT
ejpam-77	362	9	,	,	PUNCT
ejpam-77	362	10	there	there	PRON
ejpam-77	362	11	exists	exist	VERB
ejpam-77	362	12	m	m	PROPN
ejpam-77	362	13	=	=	SYM
ejpam-77	362	14	m(ε	m(ε	NUM
ejpam-77	362	15	,	,	PUNCT
ejpam-77	362	16	λ	λ	NOUN
ejpam-77	362	17	)	)	PUNCT
ejpam-77	362	18	∈	∈	PROPN
ejpam-77	362	19	n	n	PRON
ejpam-77	362	20	such	such	ADJ
ejpam-77	362	21	that	that	SCONJ
ejpam-77	362	22	{	{	PUNCT
ejpam-77	362	23	n	n	NOUN
ejpam-77	362	24	∈	∈	NOUN
ejpam-77	362	25	n	n	NOUN
ejpam-77	362	26	:	:	PUNCT
ejpam-77	362	27	xn−	xn−	PROPN
ejpam-77	362	28	xm	xm	PROPN
ejpam-77	362	29	/∈	/∈	PUNCT
ejpam-77	362	30	nθ(ε	nθ(ε	NOUN
ejpam-77	362	31	,	,	PUNCT
ejpam-77	362	32	λ	λ	NOUN
ejpam-77	362	33	)	)	PUNCT
ejpam-77	362	34	}	}	PUNCT
ejpam-77	362	35	∈	∈	PROPN
ejpam-77	362	36	i	i	PRON
ejpam-77	362	37	.	.	PUNCT
ejpam-77	363	1	definition	definition	NOUN
ejpam-77	363	2	5.3	5.3	NUM
ejpam-77	363	3	.	.	PUNCT
ejpam-77	364	1	let	let	VERB
ejpam-77	364	2	(	(	PUNCT
ejpam-77	364	3	x	x	SYM
ejpam-77	364	4	,	,	PUNCT
ejpam-77	364	5	f	f	PROPN
ejpam-77	364	6	,	,	PUNCT
ejpam-77	364	7	t	t	PROPN
ejpam-77	364	8	)	)	PUNCT
ejpam-77	364	9	be	be	AUX
ejpam-77	364	10	a	a	DET
ejpam-77	364	11	pn	pn	NOUN
ejpam-77	364	12	space	space	NOUN
ejpam-77	365	1	and	and	CCONJ
ejpam-77	365	2	i	i	PRON
ejpam-77	365	3	be	be	VERB
ejpam-77	365	4	an	an	DET
ejpam-77	365	5	admissible	admissible	ADJ
ejpam-77	365	6	ideal	ideal	NOUN
ejpam-77	365	7	.	.	PUNCT
ejpam-77	366	1	then	then	ADV
ejpam-77	366	2	a	a	DET
ejpam-77	366	3	sequence	sequence	NOUN
ejpam-77	366	4	(	(	PUNCT
ejpam-77	366	5	xn	xn	X
ejpam-77	366	6	)	)	PUNCT
ejpam-77	366	7	in	in	ADP
ejpam-77	366	8	x	x	PROPN
ejpam-77	366	9	is	be	AUX
ejpam-77	366	10	called	call	VERB
ejpam-77	366	11	i	i	PRON
ejpam-77	366	12	f∗−cauchy	f∗−cauchy	ADJ
ejpam-77	366	13	sequence	sequence	NOUN
ejpam-77	366	14	in	in	ADP
ejpam-77	366	15	x	x	PUNCT
ejpam-77	366	16	if	if	SCONJ
ejpam-77	366	17	for	for	ADP
ejpam-77	366	18	every	every	DET
ejpam-77	366	19	ε	ε	PROPN
ejpam-77	366	20	>	>	X
ejpam-77	366	21	0	0	PUNCT
ejpam-77	367	1	and	and	CCONJ
ejpam-77	367	2	λ	λ	PROPN
ejpam-77	367	3	∈	∈	PROPN
ejpam-77	367	4	(	(	PUNCT
ejpam-77	367	5	0	0	NUM
ejpam-77	367	6	,	,	PUNCT
ejpam-77	367	7	1	1	NUM
ejpam-77	367	8	)	)	PUNCT
ejpam-77	367	9	,	,	PUNCT
ejpam-77	367	10	m.	m.	NOUN
ejpam-77	367	11	rahmat	rahmat	PROPN
ejpam-77	367	12	and	and	CCONJ
ejpam-77	367	13	harikrishnan	harikrishnan	PROPN
ejpam-77	367	14	k.	k.	PROPN
ejpam-77	367	15	/	/	PUNCT
ejpam-77	367	16	eur	eur	PROPN
ejpam-77	367	17	.	.	PUNCT
ejpam-77	368	1	j.	j.	PROPN
ejpam-77	368	2	pure	pure	PROPN
ejpam-77	368	3	appl	appl	PROPN
ejpam-77	368	4	.	.	PROPN
ejpam-77	368	5	math	math	PROPN
ejpam-77	368	6	,	,	PUNCT
ejpam-77	368	7	2	2	NUM
ejpam-77	368	8	(	(	PUNCT
ejpam-77	368	9	2009	2009	NUM
ejpam-77	368	10	)	)	PUNCT
ejpam-77	368	11	,	,	PUNCT
ejpam-77	368	12	(	(	PUNCT
ejpam-77	368	13	195	195	NUM
ejpam-77	368	14	-	-	PUNCT
ejpam-77	368	15	212	212	NUM
ejpam-77	368	16	)	)	PUNCT
ejpam-77	368	17	208	208	NUM
ejpam-77	368	18	there	there	ADV
ejpam-77	368	19	exists	exist	VERB
ejpam-77	368	20	a	a	DET
ejpam-77	368	21	set	set	NOUN
ejpam-77	368	22	m	m	NOUN
ejpam-77	368	23	=	=	PUNCT
ejpam-77	368	24	{	{	PUNCT
ejpam-77	368	25	m1	m1	PROPN
ejpam-77	368	26	<	<	X
ejpam-77	368	27	m2	m2	PROPN
ejpam-77	368	28	<	<	X
ejpam-77	368	29	·	·	PUNCT
ejpam-77	368	30	·	·	PUNCT
ejpam-77	368	31	·	·	PUNCT
ejpam-77	369	1	<	<	X
ejpam-77	369	2	mk	mk	PROPN
ejpam-77	369	3	,	,	PUNCT
ejpam-77	369	4	·	·	PUNCT
ejpam-77	369	5	·	·	PUNCT
ejpam-77	369	6	·	·	PUNCT
ejpam-77	369	7	}	}	PUNCT
ejpam-77	369	8	∈	∈	PROPN
ejpam-77	370	1	f	f	X
ejpam-77	370	2	(	(	PUNCT
ejpam-77	370	3	i	i	NOUN
ejpam-77	370	4	)	)	PUNCT
ejpam-77	370	5	such	such	ADJ
ejpam-77	370	6	that	that	SCONJ
ejpam-77	370	7	the	the	DET
ejpam-77	370	8	subsequence	subsequence	NOUN
ejpam-77	370	9	xm	xm	PROPN
ejpam-77	370	10	=	=	SYM
ejpam-77	370	11	(	(	PUNCT
ejpam-77	370	12	xmk	xmk	PROPN
ejpam-77	370	13	)	)	PUNCT
ejpam-77	370	14	is	be	AUX
ejpam-77	370	15	f	f	PROPN
ejpam-77	370	16	−	−	PROPN
ejpam-77	370	17	cauchy	cauchy	NOUN
ejpam-77	370	18	in	in	ADP
ejpam-77	370	19	x	x	SYM
ejpam-77	370	20	,	,	PUNCT
ejpam-77	370	21	i.e.	i.e.	X
ejpam-77	370	22	there	there	PRON
ejpam-77	370	23	exists	exist	VERB
ejpam-77	370	24	a	a	DET
ejpam-77	370	25	number	number	NOUN
ejpam-77	370	26	k0	k0	PROPN
ejpam-77	370	27	∈	∈	PROPN
ejpam-77	370	28	n	n	CCONJ
ejpam-77	371	1	such	such	ADJ
ejpam-77	371	2	that	that	SCONJ
ejpam-77	371	3	xmk	xmk	PROPN
ejpam-77	371	4	−	−	PROPN
ejpam-77	372	1	xmp	xmp	PROPN
ejpam-77	372	2	∈	∈	PROPN
ejpam-77	372	3	nθ(ε	nθ(ε	NOUN
ejpam-77	372	4	,	,	PUNCT
ejpam-77	372	5	λ	λ	NOUN
ejpam-77	372	6	)	)	PUNCT
ejpam-77	372	7	for	for	ADP
ejpam-77	372	8	every	every	DET
ejpam-77	372	9	k	k	PROPN
ejpam-77	372	10	,	,	PUNCT
ejpam-77	372	11	p	p	PROPN
ejpam-77	372	12	≥	≥	PROPN
ejpam-77	372	13	k0	k0	PROPN
ejpam-77	372	14	.	.	PUNCT
ejpam-77	372	15	theorem	theorem	VERB
ejpam-77	372	16	5.1	5.1	NUM
ejpam-77	372	17	.	.	PUNCT
ejpam-77	373	1	let	let	AUX
ejpam-77	373	2	(	(	PUNCT
ejpam-77	373	3	x	x	SYM
ejpam-77	373	4	,	,	PUNCT
ejpam-77	373	5	f	f	PROPN
ejpam-77	373	6	,	,	PUNCT
ejpam-77	373	7	t	t	PROPN
ejpam-77	373	8	)	)	PUNCT
ejpam-77	373	9	be	be	AUX
ejpam-77	373	10	a	a	DET
ejpam-77	373	11	pn	pn	NOUN
ejpam-77	373	12	space	space	NOUN
ejpam-77	373	13	and	and	CCONJ
ejpam-77	373	14	i	i	PRON
ejpam-77	373	15	in	in	ADP
ejpam-77	373	16	n	n	PROPN
ejpam-77	373	17	is	be	AUX
ejpam-77	373	18	an	an	DET
ejpam-77	373	19	admissible	admissible	ADJ
ejpam-77	373	20	ideal	ideal	NOUN
ejpam-77	373	21	.	.	PUNCT
ejpam-77	374	1	if	if	SCONJ
ejpam-77	374	2	{	{	PUNCT
ejpam-77	374	3	xn	xn	X
ejpam-77	374	4	}	}	PUNCT
ejpam-77	374	5	in	in	ADP
ejpam-77	374	6	x	x	SYM
ejpam-77	374	7	is	be	AUX
ejpam-77	374	8	i	i	PRON
ejpam-77	374	9	f∗	f∗	NOUN
ejpam-77	374	10	−	−	PROPN
ejpam-77	374	11	cauchy	cauchy	NOUN
ejpam-77	374	12	then	then	ADV
ejpam-77	374	13	it	it	PRON
ejpam-77	374	14	is	be	AUX
ejpam-77	374	15	i	i	PROPN
ejpam-77	374	16	f	f	NOUN
ejpam-77	375	1	−	−	PROPN
ejpam-77	376	1	cauchy	cauchy	PROPN
ejpam-77	376	2	.	.	PUNCT
ejpam-77	377	1	proof	proof	NOUN
ejpam-77	377	2	.	.	PUNCT
ejpam-77	378	1	let	let	VERB
ejpam-77	378	2	{	{	PUNCT
ejpam-77	378	3	xn	xn	VERB
ejpam-77	378	4	}	}	PUNCT
ejpam-77	378	5	be	be	AUX
ejpam-77	378	6	a	a	DET
ejpam-77	378	7	i	i	PROPN
ejpam-77	378	8	f∗	f∗	VERB
ejpam-77	379	1	−	−	PROPN
ejpam-77	379	2	cauchy	cauchy	ADJ
ejpam-77	379	3	sequence	sequence	NOUN
ejpam-77	379	4	.	.	PUNCT
ejpam-77	380	1	then	then	ADV
ejpam-77	380	2	for	for	ADP
ejpam-77	380	3	every	every	DET
ejpam-77	380	4	ε	ε	PROPN
ejpam-77	380	5	>	>	X
ejpam-77	380	6	0	0	PUNCT
ejpam-77	380	7	and	and	CCONJ
ejpam-77	380	8	λ	λ	PROPN
ejpam-77	380	9	∈	∈	PROPN
ejpam-77	380	10	(	(	PUNCT
ejpam-77	380	11	0	0	NUM
ejpam-77	380	12	,	,	PUNCT
ejpam-77	380	13	1	1	NUM
ejpam-77	380	14	)	)	PUNCT
ejpam-77	380	15	there	there	PRON
ejpam-77	380	16	exists	exist	VERB
ejpam-77	380	17	a	a	DET
ejpam-77	380	18	set	set	NOUN
ejpam-77	380	19	m	m	NOUN
ejpam-77	380	20	=	=	PUNCT
ejpam-77	380	21	{	{	PUNCT
ejpam-77	380	22	m1	m1	PROPN
ejpam-77	380	23	<	<	X
ejpam-77	380	24	m2	m2	PROPN
ejpam-77	380	25	<	<	X
ejpam-77	380	26	·	·	PUNCT
ejpam-77	380	27	·	·	PUNCT
ejpam-77	380	28	·	·	PUNCT
ejpam-77	381	1	<	<	X
ejpam-77	381	2	mk	mk	PROPN
ejpam-77	381	3	,	,	PUNCT
ejpam-77	381	4	·	·	PUNCT
ejpam-77	381	5	·	·	PUNCT
ejpam-77	381	6	·	·	PUNCT
ejpam-77	381	7	}	}	PUNCT
ejpam-77	381	8	∈	∈	PROPN
ejpam-77	382	1	f	f	X
ejpam-77	382	2	(	(	PUNCT
ejpam-77	382	3	i	i	NOUN
ejpam-77	382	4	)	)	PUNCT
ejpam-77	382	5	and	and	CCONJ
ejpam-77	382	6	a	a	DET
ejpam-77	382	7	number	number	NOUN
ejpam-77	382	8	k0	k0	PROPN
ejpam-77	382	9	∈	∈	PROPN
ejpam-77	382	10	n	n	CCONJ
ejpam-77	382	11	such	such	ADJ
ejpam-77	382	12	that	that	SCONJ
ejpam-77	382	13	xmk	xmk	PROPN
ejpam-77	382	14	−	−	PROPN
ejpam-77	383	1	xmp	xmp	PROPN
ejpam-77	383	2	∈	∈	PROPN
ejpam-77	383	3	nθ(ε	nθ(ε	NOUN
ejpam-77	383	4	,	,	PUNCT
ejpam-77	383	5	λ	λ	NOUN
ejpam-77	383	6	)	)	PUNCT
ejpam-77	383	7	for	for	ADP
ejpam-77	383	8	every	every	DET
ejpam-77	383	9	k	k	PROPN
ejpam-77	383	10	,	,	PUNCT
ejpam-77	383	11	p	p	PROPN
ejpam-77	383	12	≥	≥	PROPN
ejpam-77	383	13	k0	k0	PROPN
ejpam-77	383	14	.	.	PUNCT
ejpam-77	384	1	now	now	ADV
ejpam-77	384	2	,	,	PUNCT
ejpam-77	384	3	fix	fix	VERB
ejpam-77	384	4	n	n	NOUN
ejpam-77	384	5	=	=	PUNCT
ejpam-77	384	6	mk0	mk0	NOUN
ejpam-77	384	7	+	+	PROPN
ejpam-77	384	8	1	1	NUM
ejpam-77	384	9	.	.	PUNCT
ejpam-77	385	1	then	then	ADV
ejpam-77	385	2	for	for	ADP
ejpam-77	385	3	every	every	DET
ejpam-77	385	4	ε	ε	PROPN
ejpam-77	385	5	>	>	X
ejpam-77	385	6	0	0	PUNCT
ejpam-77	386	1	and	and	CCONJ
ejpam-77	386	2	λ	λ	PROPN
ejpam-77	386	3	∈	∈	PROPN
ejpam-77	386	4	(	(	PUNCT
ejpam-77	386	5	0	0	NUM
ejpam-77	386	6	,	,	PUNCT
ejpam-77	386	7	1	1	NUM
ejpam-77	386	8	)	)	PUNCT
ejpam-77	386	9	,	,	PUNCT
ejpam-77	386	10	we	we	PRON
ejpam-77	386	11	have	have	VERB
ejpam-77	386	12	xmk	xmk	PROPN
ejpam-77	387	1	−	−	NOUN
ejpam-77	387	2	xn	xn	SYM
ejpam-77	387	3	∈	∈	PROPN
ejpam-77	387	4	nθ	nθ	PROPN
ejpam-77	387	5	(	(	PUNCT
ejpam-77	387	6	ε	ε	PROPN
ejpam-77	387	7	,	,	PUNCT
ejpam-77	387	8	λ	λ	PROPN
ejpam-77	387	9	)	)	PUNCT
ejpam-77	387	10	for	for	ADP
ejpam-77	387	11	every	every	DET
ejpam-77	387	12	k	k	PROPN
ejpam-77	387	13	≥	≥	PROPN
ejpam-77	387	14	k0	k0	PROPN
ejpam-77	387	15	.	.	PUNCT
ejpam-77	388	1	let	let	VERB
ejpam-77	388	2	h	h	NOUN
ejpam-77	388	3	=	=	PUNCT
ejpam-77	388	4	n\m	n\m	ADV
ejpam-77	388	5	.	.	PUNCT
ejpam-77	389	1	it	it	PRON
ejpam-77	389	2	is	be	AUX
ejpam-77	389	3	obvious	obvious	ADJ
ejpam-77	389	4	that	that	SCONJ
ejpam-77	389	5	h	h	NOUN
ejpam-77	389	6	∈	∈	PROPN
ejpam-77	389	7	i	i	PROPN
ejpam-77	389	8	and	and	CCONJ
ejpam-77	389	9	a(ε	a(ε	PROPN
ejpam-77	389	10	,	,	PUNCT
ejpam-77	389	11	λ	λ	PROPN
ejpam-77	389	12	)	)	PUNCT
ejpam-77	389	13	=	=	SYM
ejpam-77	389	14	{	{	PUNCT
ejpam-77	389	15	n	n	NOUN
ejpam-77	389	16	∈	∈	PROPN
ejpam-77	389	17	n	n	NOUN
ejpam-77	389	18	:	:	PUNCT
ejpam-77	389	19	xn	xn	PROPN
ejpam-77	390	1	−	−	PROPN
ejpam-77	390	2	xn	xn	PROPN
ejpam-77	390	3	/∈	/∈	PUNCT
ejpam-77	391	1	nθ	nθ	CCONJ
ejpam-77	391	2	(	(	PUNCT
ejpam-77	391	3	ε	ε	PROPN
ejpam-77	391	4	,	,	PUNCT
ejpam-77	391	5	λ	λ	NOUN
ejpam-77	391	6	)	)	PUNCT
ejpam-77	391	7	}	}	PUNCT
ejpam-77	392	1	⊂	⊂	PROPN
ejpam-77	392	2	h	h	PROPN
ejpam-77	392	3	∪	∪	X
ejpam-77	392	4	{	{	PUNCT
ejpam-77	392	5	m1	m1	PROPN
ejpam-77	392	6	<	<	X
ejpam-77	392	7	m2	m2	PROPN
ejpam-77	392	8	<	<	X
ejpam-77	392	9	·	·	PUNCT
ejpam-77	392	10	·	·	PUNCT
ejpam-77	392	11	·	·	PUNCT
ejpam-77	392	12	<	<	X
ejpam-77	392	13	mk0	mk0	X
ejpam-77	392	14	}	}	PUNCT
ejpam-77	392	15	.	.	PUNCT
ejpam-77	393	1	clearly	clearly	ADV
ejpam-77	393	2	,	,	PUNCT
ejpam-77	393	3	the	the	DET
ejpam-77	393	4	right	right	ADJ
ejpam-77	393	5	hand	hand	NOUN
ejpam-77	393	6	side	side	NOUN
ejpam-77	393	7	of	of	ADP
ejpam-77	393	8	the	the	DET
ejpam-77	393	9	last	last	ADJ
ejpam-77	393	10	argument	argument	NOUN
ejpam-77	393	11	is	be	AUX
ejpam-77	393	12	belongs	belong	VERB
ejpam-77	393	13	to	to	ADP
ejpam-77	393	14	i	i	PRON
ejpam-77	393	15	.	.	PUNCT
ejpam-77	394	1	therefore	therefore	ADV
ejpam-77	394	2	,	,	PUNCT
ejpam-77	394	3	for	for	ADP
ejpam-77	394	4	every	every	DET
ejpam-77	394	5	ε	ε	PROPN
ejpam-77	394	6	>	>	X
ejpam-77	394	7	0	0	PUNCT
ejpam-77	394	8	and	and	CCONJ
ejpam-77	394	9	λ	λ	PROPN
ejpam-77	394	10	∈	∈	PROPN
ejpam-77	394	11	(	(	PUNCT
ejpam-77	394	12	0	0	NUM
ejpam-77	394	13	,	,	PUNCT
ejpam-77	394	14	1	1	X
ejpam-77	394	15	)	)	PUNCT
ejpam-77	394	16	we	we	PRON
ejpam-77	394	17	can	can	AUX
ejpam-77	394	18	find	find	VERB
ejpam-77	394	19	n	n	NOUN
ejpam-77	394	20	=	=	SYM
ejpam-77	394	21	n(ε	n(ε	PROPN
ejpam-77	394	22	,	,	PUNCT
ejpam-77	394	23	λ	λ	NOUN
ejpam-77	394	24	)	)	PUNCT
ejpam-77	394	25	∈	∈	PROPN
ejpam-77	394	26	n	n	PRON
ejpam-77	394	27	such	such	ADJ
ejpam-77	394	28	that	that	SCONJ
ejpam-77	394	29	a(ε	a(ε	PROPN
ejpam-77	394	30	,	,	PUNCT
ejpam-77	394	31	λ	λ	PROPN
ejpam-77	394	32	)	)	PUNCT
ejpam-77	394	33	∈	∈	PROPN
ejpam-77	394	34	i	i	PRON
ejpam-77	394	35	,	,	PUNCT
ejpam-77	394	36	i.e.	i.e.	X
ejpam-77	394	37	,	,	PUNCT
ejpam-77	394	38	{	{	PUNCT
ejpam-77	394	39	xn	xn	X
ejpam-77	394	40	}	}	PUNCT
ejpam-77	394	41	is	be	AUX
ejpam-77	394	42	i	i	PRON
ejpam-77	394	43	f	f	X
ejpam-77	395	1	−	−	X
ejpam-77	395	2	cauchy	cauchy	ADJ
ejpam-77	395	3	sequence	sequence	NOUN
ejpam-77	395	4	in	in	ADP
ejpam-77	395	5	x	x	PROPN
ejpam-77	395	6	.	.	PUNCT
ejpam-77	396	1	theorem	theorem	VERB
ejpam-77	396	2	5.2	5.2	NUM
ejpam-77	396	3	.	.	PUNCT
ejpam-77	397	1	let	let	AUX
ejpam-77	397	2	(	(	PUNCT
ejpam-77	397	3	x	x	SYM
ejpam-77	397	4	,	,	PUNCT
ejpam-77	397	5	f	f	PROPN
ejpam-77	397	6	,	,	PUNCT
ejpam-77	397	7	t	t	PROPN
ejpam-77	397	8	)	)	PUNCT
ejpam-77	397	9	be	be	AUX
ejpam-77	397	10	a	a	DET
ejpam-77	397	11	pn	pn	NOUN
ejpam-77	397	12	space	space	NOUN
ejpam-77	397	13	such	such	ADJ
ejpam-77	397	14	that	that	SCONJ
ejpam-77	397	15	t	t	PROPN
ejpam-77	397	16	(	(	PUNCT
ejpam-77	397	17	a	a	PRON
ejpam-77	397	18	,	,	PUNCT
ejpam-77	397	19	a	a	NOUN
ejpam-77	397	20	)	)	PUNCT
ejpam-77	397	21	>	>	PUNCT
ejpam-77	397	22	a	a	PRON
ejpam-77	397	23	for	for	ADP
ejpam-77	397	24	every	every	DET
ejpam-77	397	25	a	a	DET
ejpam-77	397	26	∈	∈	PROPN
ejpam-77	397	27	(	(	PUNCT
ejpam-77	397	28	0	0	NUM
ejpam-77	397	29	,	,	PUNCT
ejpam-77	397	30	1	1	NUM
ejpam-77	397	31	)	)	PUNCT
ejpam-77	397	32	and	and	CCONJ
ejpam-77	397	33	i	i	PRON
ejpam-77	397	34	be	be	VERB
ejpam-77	397	35	an	an	DET
ejpam-77	397	36	admissible	admissible	ADJ
ejpam-77	397	37	ideal	ideal	NOUN
ejpam-77	397	38	.	.	PUNCT
ejpam-77	398	1	a	a	DET
ejpam-77	398	2	sequence	sequence	NOUN
ejpam-77	398	3	{	{	PUNCT
ejpam-77	398	4	xn	xn	NOUN
ejpam-77	398	5	}	}	PUNCT
ejpam-77	398	6	in	in	ADP
ejpam-77	398	7	x	x	SYM
ejpam-77	398	8	is	be	AUX
ejpam-77	398	9	i	i	PRON
ejpam-77	398	10	f	f	NOUN
ejpam-77	398	11	-convergent	-convergent	ADJ
ejpam-77	398	12	if	if	SCONJ
ejpam-77	398	13	and	and	CCONJ
ejpam-77	398	14	only	only	ADV
ejpam-77	398	15	if	if	SCONJ
ejpam-77	398	16	it	it	PRON
ejpam-77	398	17	is	be	AUX
ejpam-77	398	18	i	i	PRON
ejpam-77	398	19	f	f	PROPN
ejpam-77	398	20	-cauchy	-cauchy	ADJ
ejpam-77	398	21	.	.	PUNCT
ejpam-77	399	1	proof	proof	NOUN
ejpam-77	399	2	:	:	PUNCT
ejpam-77	399	3	necessity	necessity	NOUN
ejpam-77	399	4	:	:	PUNCT
ejpam-77	399	5	suppose	suppose	VERB
ejpam-77	399	6	that	that	SCONJ
ejpam-77	399	7	{	{	PUNCT
ejpam-77	399	8	xn	xn	X
ejpam-77	399	9	}	}	PUNCT
ejpam-77	399	10	is	be	AUX
ejpam-77	399	11	i	i	PRON
ejpam-77	399	12	f	f	PROPN
ejpam-77	399	13	-convergent	-convergent	ADJ
ejpam-77	399	14	to	to	ADP
ejpam-77	399	15	ξ	ξ	PROPN
ejpam-77	399	16	∈	∈	PROPN
ejpam-77	399	17	x	x	X
ejpam-77	399	18	.	.	PUNCT
ejpam-77	400	1	let	let	VERB
ejpam-77	400	2	ε	ε	PROPN
ejpam-77	400	3	>	>	X
ejpam-77	400	4	0	0	PUNCT
ejpam-77	401	1	and	and	CCONJ
ejpam-77	401	2	λ	λ	PROPN
ejpam-77	401	3	∈	∈	PROPN
ejpam-77	401	4	(	(	PUNCT
ejpam-77	401	5	0	0	NUM
ejpam-77	401	6	,	,	PUNCT
ejpam-77	401	7	1	1	NUM
ejpam-77	401	8	)	)	PUNCT
ejpam-77	401	9	be	be	AUX
ejpam-77	401	10	given	give	VERB
ejpam-77	401	11	.	.	PUNCT
ejpam-77	402	1	since	since	SCONJ
ejpam-77	402	2	i	i	PRON
ejpam-77	402	3	f	f	PROPN
ejpam-77	402	4	−	−	PROPN
ejpam-77	402	5	lim	lim	PROPN
ejpam-77	402	6	xn	xn	PUNCT
ejpam-77	403	1	=	=	SYM
ejpam-77	403	2	ξ	ξ	PROPN
ejpam-77	403	3	,	,	PUNCT
ejpam-77	403	4	we	we	PRON
ejpam-77	403	5	have	have	AUX
ejpam-77	403	6	a=	a=	VERB
ejpam-77	403	7	{	{	PUNCT
ejpam-77	403	8	n	n	NOUN
ejpam-77	403	9	∈	∈	PROPN
ejpam-77	403	10	n	n	NOUN
ejpam-77	403	11	:	:	PUNCT
ejpam-77	403	12	xn	xn	PROPN
ejpam-77	403	13	/∈	/∈	PROPN
ejpam-77	404	1	nξ	nξ	PROPN
ejpam-77	404	2	(	(	PUNCT
ejpam-77	404	3	ε	ε	PROPN
ejpam-77	404	4	2	2	NUM
ejpam-77	404	5	,	,	PUNCT
ejpam-77	404	6	λ	λ	NOUN
ejpam-77	404	7	)	)	PUNCT
ejpam-77	404	8	}	}	PUNCT
ejpam-77	404	9	∈	∈	PROPN
ejpam-77	405	1	i	i	PRON
ejpam-77	405	2	.	.	PUNCT
ejpam-77	406	1	this	this	PRON
ejpam-77	406	2	implies	imply	VERB
ejpam-77	406	3	that	that	SCONJ
ejpam-77	406	4	ac	ac	PROPN
ejpam-77	406	5	=	=	PUNCT
ejpam-77	406	6	{	{	PUNCT
ejpam-77	406	7	n	n	NOUN
ejpam-77	406	8	∈	∈	PROPN
ejpam-77	406	9	n	n	NOUN
ejpam-77	407	1	:	:	PUNCT
ejpam-77	407	2	xn	xn	PROPN
ejpam-77	407	3	∈	∈	PROPN
ejpam-77	407	4	nξ	nξ	PROPN
ejpam-77	407	5	(	(	PUNCT
ejpam-77	407	6	ε	ε	PROPN
ejpam-77	407	7	2	2	NUM
ejpam-77	407	8	,	,	PUNCT
ejpam-77	407	9	λ	λ	NOUN
ejpam-77	407	10	)	)	PUNCT
ejpam-77	407	11	}	}	PUNCT
ejpam-77	407	12	∈	∈	PROPN
ejpam-77	407	13	f	f	X
ejpam-77	407	14	(	(	PUNCT
ejpam-77	407	15	i	i	NOUN
ejpam-77	407	16	)	)	PUNCT
ejpam-77	407	17	.	.	PUNCT
ejpam-77	408	1	now	now	ADV
ejpam-77	408	2	,	,	PUNCT
ejpam-77	408	3	by	by	ADP
ejpam-77	408	4	(	(	PUNCT
ejpam-77	408	5	n4	n4	PROPN
ejpam-77	408	6	)	)	PUNCT
ejpam-77	408	7	,	,	PUNCT
ejpam-77	408	8	for	for	ADP
ejpam-77	408	9	every	every	DET
ejpam-77	408	10	n	n	NOUN
ejpam-77	408	11	,	,	PUNCT
ejpam-77	408	12	m	m	PROPN
ejpam-77	408	13	∈	∈	PROPN
ejpam-77	408	14	ac	ac	PROPN
ejpam-77	408	15	,	,	PUNCT
ejpam-77	408	16	νxn−xm	νxn−xm	NOUN
ejpam-77	408	17	(	(	PUNCT
ejpam-77	408	18	ε	ε	PROPN
ejpam-77	408	19	)	)	PUNCT
ejpam-77	408	20	≥	≥	PROPN
ejpam-77	408	21	t	t	PROPN
ejpam-77	408	22	�	�	PROPN
ejpam-77	408	23	νxn−ξ	νxn−ξ	PROPN
ejpam-77	408	24	(	(	PUNCT
ejpam-77	408	25	ε	ε	PROPN
ejpam-77	408	26	2	2	NUM
ejpam-77	408	27	)	)	PUNCT
ejpam-77	408	28	,	,	PUNCT
ejpam-77	408	29	νxm−ξ	νxm−ξ	PROPN
ejpam-77	408	30	(	(	PUNCT
ejpam-77	408	31	ε	ε	PROPN
ejpam-77	408	32	2	2	NUM
ejpam-77	408	33	)	)	PUNCT
ejpam-77	408	34	�	�	PROPN
ejpam-77	408	35	>	>	X
ejpam-77	408	36	t	t	PROPN
ejpam-77	408	37	(	(	PUNCT
ejpam-77	408	38	1−λ	1−λ	NUM
ejpam-77	408	39	,	,	PUNCT
ejpam-77	408	40	1−λ	1−λ	NUM
ejpam-77	408	41	)	)	PUNCT
ejpam-77	408	42	>	>	X
ejpam-77	408	43	1−λ	1−λ	NUM
ejpam-77	408	44	.	.	PUNCT
ejpam-77	409	1	hence	hence	ADV
ejpam-77	409	2	,	,	PUNCT
ejpam-77	409	3	{	{	PUNCT
ejpam-77	409	4	n	n	CCONJ
ejpam-77	409	5	∈	∈	NOUN
ejpam-77	409	6	n	n	NOUN
ejpam-77	409	7	:	:	PUNCT
ejpam-77	409	8	xn−	xn−	PROPN
ejpam-77	409	9	xm	xm	PROPN
ejpam-77	409	10	∈	∈	PROPN
ejpam-77	409	11	nθ	nθ	PROPN
ejpam-77	409	12	(	(	PUNCT
ejpam-77	409	13	ε	ε	PROPN
ejpam-77	409	14	,	,	PUNCT
ejpam-77	409	15	λ	λ	NOUN
ejpam-77	409	16	)	)	PUNCT
ejpam-77	409	17	}	}	PUNCT
ejpam-77	409	18	∈	∈	PROPN
ejpam-77	409	19	f	f	X
ejpam-77	409	20	(	(	PUNCT
ejpam-77	409	21	i	i	NOUN
ejpam-77	409	22	)	)	PUNCT
ejpam-77	409	23	.	.	PUNCT
ejpam-77	410	1	this	this	PRON
ejpam-77	410	2	implies	imply	VERB
ejpam-77	410	3	that	that	SCONJ
ejpam-77	410	4	{	{	PUNCT
ejpam-77	410	5	n	n	X
ejpam-77	410	6	∈	∈	NOUN
ejpam-77	410	7	n	n	NOUN
ejpam-77	410	8	:	:	PUNCT
ejpam-77	410	9	xn−	xn−	PROPN
ejpam-77	410	10	xm	xm	PROPN
ejpam-77	410	11	/∈	/∈	PUNCT
ejpam-77	410	12	nθ(ε	nθ(ε	NOUN
ejpam-77	410	13	,	,	PUNCT
ejpam-77	410	14	λ	λ	NOUN
ejpam-77	410	15	)	)	PUNCT
ejpam-77	410	16	}	}	PUNCT
ejpam-77	410	17	∈	∈	PROPN
ejpam-77	410	18	i	i	PRON
ejpam-77	410	19	,	,	PUNCT
ejpam-77	410	20	i.e.	i.e.	X
ejpam-77	410	21	,	,	PUNCT
ejpam-77	410	22	{	{	PUNCT
ejpam-77	410	23	xn	xn	X
ejpam-77	410	24	}	}	PUNCT
ejpam-77	410	25	is	be	AUX
ejpam-77	410	26	a	a	DET
ejpam-77	410	27	i	i	NOUN
ejpam-77	410	28	f	f	PROPN
ejpam-77	410	29	-cauchy	-cauchy	ADJ
ejpam-77	410	30	sequence	sequence	NOUN
ejpam-77	410	31	.	.	PUNCT
ejpam-77	411	1	m.	m.	NOUN
ejpam-77	411	2	rahmat	rahmat	PROPN
ejpam-77	411	3	and	and	CCONJ
ejpam-77	411	4	harikrishnan	harikrishnan	PROPN
ejpam-77	411	5	k.	k.	PROPN
ejpam-77	411	6	/	/	PUNCT
ejpam-77	411	7	eur	eur	PROPN
ejpam-77	411	8	.	.	PUNCT
ejpam-77	412	1	j.	j.	PROPN
ejpam-77	412	2	pure	pure	PROPN
ejpam-77	412	3	appl	appl	PROPN
ejpam-77	412	4	.	.	PROPN
ejpam-77	412	5	math	math	PROPN
ejpam-77	412	6	,	,	PUNCT
ejpam-77	412	7	2	2	NUM
ejpam-77	412	8	(	(	PUNCT
ejpam-77	412	9	2009	2009	NUM
ejpam-77	412	10	)	)	PUNCT
ejpam-77	412	11	,	,	PUNCT
ejpam-77	412	12	(	(	PUNCT
ejpam-77	412	13	195	195	NUM
ejpam-77	412	14	-	-	PUNCT
ejpam-77	412	15	212	212	NUM
ejpam-77	412	16	)	)	PUNCT
ejpam-77	412	17	209	209	NUM
ejpam-77	412	18	proof	proof	NOUN
ejpam-77	412	19	.	.	PUNCT
ejpam-77	413	1	sufficiency	sufficiency	NOUN
ejpam-77	413	2	:	:	PUNCT
ejpam-77	413	3	assume	assume	VERB
ejpam-77	413	4	that	that	SCONJ
ejpam-77	413	5	{	{	PUNCT
ejpam-77	413	6	xn	xn	X
ejpam-77	413	7	}	}	PUNCT
ejpam-77	413	8	is	be	AUX
ejpam-77	413	9	a	a	DET
ejpam-77	413	10	i	i	NOUN
ejpam-77	413	11	f	f	PROPN
ejpam-77	413	12	-cauchy	-cauchy	ADJ
ejpam-77	413	13	sequence	sequence	NOUN
ejpam-77	413	14	.	.	PUNCT
ejpam-77	414	1	we	we	PRON
ejpam-77	414	2	shall	shall	AUX
ejpam-77	414	3	prove	prove	VERB
ejpam-77	414	4	that	that	SCONJ
ejpam-77	414	5	{	{	PUNCT
ejpam-77	414	6	xn	xn	X
ejpam-77	414	7	}	}	PUNCT
ejpam-77	414	8	is	be	AUX
ejpam-77	414	9	i	i	PRON
ejpam-77	414	10	f	f	NOUN
ejpam-77	414	11	-convergent	-convergent	ADJ
ejpam-77	414	12	sequence	sequence	NOUN
ejpam-77	414	13	.	.	PUNCT
ejpam-77	415	1	for	for	ADP
ejpam-77	415	2	this	this	PRON
ejpam-77	415	3	,	,	PUNCT
ejpam-77	415	4	let	let	VERB
ejpam-77	415	5	{	{	PUNCT
ejpam-77	415	6	εp	εp	PART
ejpam-77	415	7	}	}	PUNCT
ejpam-77	415	8	be	be	AUX
ejpam-77	415	9	a	a	DET
ejpam-77	415	10	strictly	strictly	ADV
ejpam-77	415	11	decreasing	decrease	VERB
ejpam-77	415	12	sequence	sequence	NOUN
ejpam-77	415	13	of	of	ADP
ejpam-77	415	14	positive	positive	ADJ
ejpam-77	415	15	real	real	ADJ
ejpam-77	415	16	numbers	number	NOUN
ejpam-77	415	17	such	such	ADJ
ejpam-77	415	18	that	that	PRON
ejpam-77	415	19	εp	εp	ADP
ejpam-77	415	20	→	→	SYM
ejpam-77	415	21	0	0	PROPN
ejpam-77	415	22	as	as	ADP
ejpam-77	415	23	p	p	PROPN
ejpam-77	415	24	→	→	SYM
ejpam-77	415	25	∞.	∞.	PROPN
ejpam-77	415	26	since	since	SCONJ
ejpam-77	415	27	{	{	PUNCT
ejpam-77	415	28	xn	xn	X
ejpam-77	415	29	}	}	PUNCT
ejpam-77	415	30	is	be	AUX
ejpam-77	415	31	a	a	DET
ejpam-77	415	32	i	i	NOUN
ejpam-77	415	33	f	f	PROPN
ejpam-77	415	34	-cauchy	-cauchy	PROPN
ejpam-77	415	35	sequence	sequence	NOUN
ejpam-77	415	36	,	,	PUNCT
ejpam-77	415	37	there	there	PRON
ejpam-77	415	38	exists	exist	VERB
ejpam-77	415	39	a	a	DET
ejpam-77	415	40	strictly	strictly	ADV
ejpam-77	415	41	increasing	increase	VERB
ejpam-77	415	42	sequence	sequence	NOUN
ejpam-77	415	43	{	{	PUNCT
ejpam-77	415	44	mp	mp	NOUN
ejpam-77	415	45	}	}	PUNCT
ejpam-77	415	46	of	of	ADP
ejpam-77	415	47	positive	positive	ADJ
ejpam-77	415	48	integers	integer	NOUN
ejpam-77	415	49	such	such	ADJ
ejpam-77	415	50	that	that	PRON
ejpam-77	415	51	ap	ap	PROPN
ejpam-77	415	52	=	=	PUNCT
ejpam-77	415	53	{	{	PUNCT
ejpam-77	415	54	n	n	NOUN
ejpam-77	415	55	∈	∈	NOUN
ejpam-77	415	56	n	n	NOUN
ejpam-77	415	57	:	:	PUNCT
ejpam-77	415	58	xn−	xn−	PUNCT
ejpam-77	415	59	xmp	xmp	PROPN
ejpam-77	415	60	/∈nθ	/∈nθ	PUNCT
ejpam-77	415	61	(	(	PUNCT
ejpam-77	415	62	εp	εp	PROPN
ejpam-77	415	63	,	,	PUNCT
ejpam-77	415	64	λ	λ	NOUN
ejpam-77	415	65	)	)	PUNCT
ejpam-77	415	66	}	}	PUNCT
ejpam-77	415	67	∈	∈	PROPN
ejpam-77	416	1	i	i	PRON
ejpam-77	416	2	p	p	NOUN
ejpam-77	416	3	=	=	ADJ
ejpam-77	416	4	1	1	NUM
ejpam-77	416	5	,	,	PUNCT
ejpam-77	416	6	2	2	NUM
ejpam-77	416	7	,	,	PUNCT
ejpam-77	416	8	3	3	NUM
ejpam-77	416	9	,	,	PUNCT
ejpam-77	416	10	·	·	PUNCT
ejpam-77	416	11	·	·	PUNCT
ejpam-77	416	12	·	·	PUNCT
ejpam-77	416	13	.	.	PUNCT
ejpam-77	417	1	this	this	PRON
ejpam-77	417	2	implies	imply	VERB
ejpam-77	417	3	that	that	PRON
ejpam-77	417	4	;	;	PUNCT
ejpam-77	417	5	6=	6=	NUM
ejpam-77	417	6	{	{	PUNCT
ejpam-77	417	7	n	n	PRON
ejpam-77	417	8	∈	∈	NOUN
ejpam-77	417	9	n	n	NOUN
ejpam-77	417	10	:	:	PUNCT
ejpam-77	417	11	xn−	xn−	PROPN
ejpam-77	417	12	xmp	xmp	PROPN
ejpam-77	417	13	∈nθ	∈nθ	PROPN
ejpam-77	417	14	(	(	PUNCT
ejpam-77	417	15	εp	εp	PROPN
ejpam-77	417	16	,	,	PUNCT
ejpam-77	417	17	λ	λ	NOUN
ejpam-77	417	18	)	)	PUNCT
ejpam-77	417	19	}	}	PUNCT
ejpam-77	417	20	∈	∈	PROPN
ejpam-77	417	21	f	f	X
ejpam-77	417	22	(	(	PUNCT
ejpam-77	417	23	i	i	NOUN
ejpam-77	417	24	)	)	PUNCT
ejpam-77	417	25	p	p	X
ejpam-77	418	1	=	=	NOUN
ejpam-77	418	2	1	1	NUM
ejpam-77	418	3	,	,	PUNCT
ejpam-77	418	4	2	2	NUM
ejpam-77	418	5	,	,	PUNCT
ejpam-77	418	6	3	3	NUM
ejpam-77	418	7	,	,	PUNCT
ejpam-77	418	8	·	·	PUNCT
ejpam-77	418	9	·	·	PUNCT
ejpam-77	418	10	·	·	PUNCT
ejpam-77	418	11	.	.	PUNCT
ejpam-77	419	1	(	(	PUNCT
ejpam-77	419	2	5.1	5.1	NUM
ejpam-77	419	3	)	)	PUNCT
ejpam-77	419	4	let	let	VERB
ejpam-77	419	5	p	p	NOUN
ejpam-77	419	6	and	and	CCONJ
ejpam-77	419	7	q	q	AUX
ejpam-77	419	8	be	be	AUX
ejpam-77	419	9	two	two	NUM
ejpam-77	419	10	positive	positive	ADJ
ejpam-77	419	11	integers	integer	NOUN
ejpam-77	420	1	such	such	ADJ
ejpam-77	420	2	that	that	SCONJ
ejpam-77	420	3	p	p	PROPN
ejpam-77	420	4	6=	6=	ADP
ejpam-77	420	5	q.	q.	PROPN
ejpam-77	420	6	then	then	ADV
ejpam-77	420	7	by	by	ADP
ejpam-77	420	8	(	(	PUNCT
ejpam-77	420	9	3	3	NUM
ejpam-77	420	10	)	)	PUNCT
ejpam-77	420	11	,	,	PUNCT
ejpam-77	420	12	both	both	CCONJ
ejpam-77	420	13	the	the	DET
ejpam-77	420	14	sets	set	NOUN
ejpam-77	420	15	{	{	PUNCT
ejpam-77	420	16	n	n	CCONJ
ejpam-77	420	17	∈	∈	NOUN
ejpam-77	420	18	n	n	NOUN
ejpam-77	420	19	:	:	PUNCT
ejpam-77	420	20	xn	xn	PROPN
ejpam-77	420	21	−	−	PROPN
ejpam-77	420	22	xmp	xmp	PROPN
ejpam-77	420	23	∈	∈	PROPN
ejpam-77	420	24	nθ(εp	nθ(εp	NOUN
ejpam-77	420	25	,	,	PUNCT
ejpam-77	420	26	λ	λ	NOUN
ejpam-77	420	27	)	)	PUNCT
ejpam-77	420	28	}	}	PUNCT
ejpam-77	420	29	and	and	CCONJ
ejpam-77	420	30	{	{	PUNCT
ejpam-77	420	31	n	n	X
ejpam-77	420	32	∈	∈	NOUN
ejpam-77	420	33	n	n	NOUN
ejpam-77	420	34	:	:	PUNCT
ejpam-77	420	35	xn	xn	PROPN
ejpam-77	420	36	−	−	NUM
ejpam-77	420	37	xmq	xmq	PROPN
ejpam-77	420	38	∈	∈	PROPN
ejpam-77	420	39	nθ	nθ	NOUN
ejpam-77	420	40	(	(	PUNCT
ejpam-77	420	41	εq	εq	ADJ
ejpam-77	420	42	,	,	PUNCT
ejpam-77	420	43	λ	λ	NOUN
ejpam-77	420	44	)	)	PUNCT
ejpam-77	420	45	}	}	PUNCT
ejpam-77	420	46	are	be	AUX
ejpam-77	420	47	nonempty	nonempty	ADJ
ejpam-77	420	48	elements	element	NOUN
ejpam-77	420	49	of	of	ADP
ejpam-77	420	50	f	f	PROPN
ejpam-77	420	51	(	(	PUNCT
ejpam-77	420	52	i	i	NOUN
ejpam-77	420	53	)	)	PUNCT
ejpam-77	420	54	.	.	PUNCT
ejpam-77	421	1	since	since	SCONJ
ejpam-77	421	2	f	f	PROPN
ejpam-77	421	3	(	(	PUNCT
ejpam-77	421	4	i	i	NOUN
ejpam-77	421	5	)	)	PUNCT
ejpam-77	421	6	is	be	AUX
ejpam-77	421	7	a	a	DET
ejpam-77	421	8	filter	filter	NOUN
ejpam-77	421	9	on	on	ADP
ejpam-77	421	10	n	n	CCONJ
ejpam-77	421	11	,	,	PUNCT
ejpam-77	421	12	therefore	therefore	ADV
ejpam-77	421	13	;	;	PUNCT
ejpam-77	421	14	6=	6=	NUM
ejpam-77	421	15	{	{	PUNCT
ejpam-77	421	16	n	n	PRON
ejpam-77	421	17	∈	∈	NOUN
ejpam-77	421	18	n	n	NOUN
ejpam-77	421	19	:	:	PUNCT
ejpam-77	421	20	xn−	xn−	PROPN
ejpam-77	421	21	xmp	xmp	PROPN
ejpam-77	421	22	∈nθ	∈nθ	PROPN
ejpam-77	421	23	(	(	PUNCT
ejpam-77	421	24	εp	εp	PROPN
ejpam-77	421	25	,	,	PUNCT
ejpam-77	421	26	λ	λ	NOUN
ejpam-77	421	27	)	)	PUNCT
ejpam-77	421	28	}	}	PUNCT
ejpam-77	421	29	∩	∩	NOUN
ejpam-77	421	30	{	{	PUNCT
ejpam-77	421	31	n	n	SYM
ejpam-77	421	32	∈	∈	NOUN
ejpam-77	421	33	n	n	NOUN
ejpam-77	421	34	:	:	PUNCT
ejpam-77	421	35	xn−	xn−	PUNCT
ejpam-77	421	36	xmq	xmq	NUM
ejpam-77	422	1	∈	∈	PROPN
ejpam-77	422	2	nθ	nθ	NOUN
ejpam-77	422	3	(	(	PUNCT
ejpam-77	422	4	εq	εq	ADJ
ejpam-77	422	5	,	,	PUNCT
ejpam-77	422	6	λ	λ	NOUN
ejpam-77	422	7	)	)	PUNCT
ejpam-77	422	8	}	}	PUNCT
ejpam-77	422	9	∈	∈	PROPN
ejpam-77	422	10	f	f	X
ejpam-77	422	11	(	(	PUNCT
ejpam-77	422	12	i	i	NOUN
ejpam-77	422	13	)	)	PUNCT
ejpam-77	422	14	.	.	PUNCT
ejpam-77	423	1	thus	thus	ADV
ejpam-77	423	2	,	,	PUNCT
ejpam-77	423	3	for	for	ADP
ejpam-77	423	4	each	each	DET
ejpam-77	423	5	p	p	NOUN
ejpam-77	423	6	and	and	CCONJ
ejpam-77	423	7	q	q	NOUN
ejpam-77	423	8	with	with	ADP
ejpam-77	423	9	p	p	PROPN
ejpam-77	423	10	6=	6=	PROPN
ejpam-77	423	11	q	q	PROPN
ejpam-77	423	12	,	,	PUNCT
ejpam-77	423	13	we	we	PRON
ejpam-77	423	14	can	can	AUX
ejpam-77	423	15	select	select	VERB
ejpam-77	423	16	np	np	ADP
ejpam-77	423	17	,	,	PUNCT
ejpam-77	423	18	nq	nq	PROPN
ejpam-77	423	19	∈	∈	PROPN
ejpam-77	423	20	n	n	PRON
ejpam-77	423	21	such	such	ADJ
ejpam-77	423	22	that	that	DET
ejpam-77	423	23	xnp	xnp	PROPN
ejpam-77	423	24	−	−	PROPN
ejpam-77	423	25	xmp	xmp	PROPN
ejpam-77	423	26	∈	∈	PROPN
ejpam-77	423	27	nθ(εp	nθ(εp	NOUN
ejpam-77	423	28	,	,	PUNCT
ejpam-77	423	29	λ	λ	NOUN
ejpam-77	423	30	)	)	PUNCT
ejpam-77	423	31	and	and	CCONJ
ejpam-77	423	32	xnq	xnq	PROPN
ejpam-77	424	1	−	−	PROPN
ejpam-77	424	2	xmq	xmq	PROPN
ejpam-77	424	3	∈	∈	PROPN
ejpam-77	424	4	nθ	nθ	NOUN
ejpam-77	424	5	(	(	PUNCT
ejpam-77	424	6	εq	εq	ADJ
ejpam-77	424	7	,	,	PUNCT
ejpam-77	424	8	λ	λ	NOUN
ejpam-77	424	9	)	)	PUNCT
ejpam-77	424	10	.	.	PUNCT
ejpam-77	425	1	let	let	VERB
ejpam-77	425	2	ε	ε	PROPN
ejpam-77	425	3	=	=	SYM
ejpam-77	425	4	εp	εp	PROPN
ejpam-77	425	5	+	+	CCONJ
ejpam-77	425	6	εq	εq	X
ejpam-77	425	7	.	.	PUNCT
ejpam-77	426	1	then	then	ADV
ejpam-77	426	2	by	by	ADP
ejpam-77	426	3	(	(	PUNCT
ejpam-77	426	4	n4	n4	PROPN
ejpam-77	426	5	)	)	PUNCT
ejpam-77	426	6	,	,	PUNCT
ejpam-77	426	7	we	we	PRON
ejpam-77	426	8	have	have	VERB
ejpam-77	426	9	νxmp	νxmp	VERB
ejpam-77	426	10	−xmq	−xmq	NOUN
ejpam-77	426	11	(	(	PUNCT
ejpam-77	426	12	ε	ε	PROPN
ejpam-77	426	13	)	)	PUNCT
ejpam-77	426	14	≥	≥	PROPN
ejpam-77	426	15	t	t	PROPN
ejpam-77	426	16	(	(	PUNCT
ejpam-77	426	17	νxnp	νxnp	NOUN
ejpam-77	426	18	−xmp	−xmp	ADV
ejpam-77	426	19	(	(	PUNCT
ejpam-77	426	20	εp),νxnp	εp),νxnp	NOUN
ejpam-77	426	21	−xmq	−xmq	X
ejpam-77	426	22	(	(	PUNCT
ejpam-77	426	23	εq	εq	NUM
ejpam-77	426	24	)	)	PUNCT
ejpam-77	426	25	)	)	PUNCT
ejpam-77	426	26	>	>	X
ejpam-77	427	1	t	t	PROPN
ejpam-77	427	2	(	(	PUNCT
ejpam-77	427	3	1−λ	1−λ	NUM
ejpam-77	427	4	,	,	PUNCT
ejpam-77	427	5	1−λ	1−λ	NUM
ejpam-77	427	6	)	)	PUNCT
ejpam-77	427	7	>	>	X
ejpam-77	427	8	1−λ	1−λ	NUM
ejpam-77	427	9	.	.	PUNCT
ejpam-77	428	1	this	this	PRON
ejpam-77	428	2	implies	imply	VERB
ejpam-77	428	3	that	that	SCONJ
ejpam-77	428	4	{	{	PUNCT
ejpam-77	428	5	xmp	xmp	PROPN
ejpam-77	428	6	}	}	PUNCT
ejpam-77	428	7	is	be	AUX
ejpam-77	428	8	a	a	DET
ejpam-77	428	9	f−cauchy	f−cauchy	NOUN
ejpam-77	428	10	sequence	sequence	NOUN
ejpam-77	428	11	and	and	CCONJ
ejpam-77	428	12	satisfies	satisfy	VERB
ejpam-77	428	13	the	the	DET
ejpam-77	428	14	cauchy	cauchy	ADJ
ejpam-77	428	15	criterion	criterion	NOUN
ejpam-77	428	16	.	.	PUNCT
ejpam-77	429	1	say	say	VERB
ejpam-77	430	1	lim	lim	PROPN
ejpam-77	430	2	xmp	xmp	PROPN
ejpam-77	430	3	=	=	SYM
ejpam-77	430	4	ξ	ξ	PROPN
ejpam-77	430	5	.	.	PUNCT
ejpam-77	431	1	also	also	ADV
ejpam-77	431	2	we	we	PRON
ejpam-77	431	3	have	have	VERB
ejpam-77	431	4	ε	ε	PROPN
ejpam-77	431	5	→	→	SYM
ejpam-77	431	6	0	0	PUNCT
ejpam-77	431	7	as	as	ADP
ejpam-77	431	8	p	p	X
ejpam-77	431	9	→	→	SYM
ejpam-77	431	10	∞	∞	PROPN
ejpam-77	431	11	,	,	PUNCT
ejpam-77	431	12	so	so	ADV
ejpam-77	431	13	for	for	ADP
ejpam-77	431	14	each	each	DET
ejpam-77	431	15	ε	ε	PROPN
ejpam-77	431	16	>	>	X
ejpam-77	431	17	0	0	NUM
ejpam-77	432	1	we	we	PRON
ejpam-77	432	2	can	can	AUX
ejpam-77	432	3	choose	choose	VERB
ejpam-77	432	4	p0	p0	NOUN
ejpam-77	432	5	∈	∈	PROPN
ejpam-77	432	6	n	n	PRON
ejpam-77	432	7	such	such	ADJ
ejpam-77	432	8	that	that	PRON
ejpam-77	432	9	εp0	εp0	VERB
ejpam-77	432	10	<	<	X
ejpam-77	432	11	ε	ε	PROPN
ejpam-77	432	12	2	2	NUM
ejpam-77	432	13	and	and	CCONJ
ejpam-77	432	14	xmp	xmp	PROPN
ejpam-77	432	15	∈	∈	PROPN
ejpam-77	432	16	nξ	nξ	PROPN
ejpam-77	432	17	(	(	PUNCT
ejpam-77	432	18	ε	ε	PROPN
ejpam-77	432	19	2	2	NUM
ejpam-77	432	20	,	,	PUNCT
ejpam-77	432	21	λ	λ	NOUN
ejpam-77	432	22	)	)	PUNCT
ejpam-77	432	23	for	for	ADP
ejpam-77	432	24	p	p	DET
ejpam-77	432	25	≥	≥	NOUN
ejpam-77	432	26	p0	p0	NOUN
ejpam-77	432	27	.	.	PUNCT
ejpam-77	433	1	next	next	ADV
ejpam-77	433	2	we	we	PRON
ejpam-77	433	3	prove	prove	VERB
ejpam-77	433	4	that	that	SCONJ
ejpam-77	433	5	a	a	DET
ejpam-77	433	6	=	=	X
ejpam-77	433	7	{	{	PUNCT
ejpam-77	433	8	n	n	NOUN
ejpam-77	433	9	∈	∈	PROPN
ejpam-77	433	10	n	n	NOUN
ejpam-77	433	11	:	:	PUNCT
ejpam-77	433	12	xn	xn	PROPN
ejpam-77	433	13	/∈	/∈	PUNCT
ejpam-77	433	14	nξ(ε	nξ(ε	PROPN
ejpam-77	433	15	,	,	PUNCT
ejpam-77	433	16	λ	λ	NOUN
ejpam-77	433	17	)	)	PUNCT
ejpam-77	433	18	}	}	PUNCT
ejpam-77	433	19	⊂	⊂	PROPN
ejpam-77	433	20	ap0	ap0	VERB
ejpam-77	433	21	=	=	PUNCT
ejpam-77	433	22	{	{	PUNCT
ejpam-77	433	23	n	n	NOUN
ejpam-77	433	24	∈	∈	PROPN
ejpam-77	433	25	n	n	NOUN
ejpam-77	433	26	:	:	PUNCT
ejpam-77	433	27	xn	xn	PROPN
ejpam-77	434	1	−	−	PROPN
ejpam-77	434	2	xmp0	xmp0	PROPN
ejpam-77	434	3	/∈	/∈	PUNCT
ejpam-77	435	1	nθ(εp0	nθ(εp0	NUM
ejpam-77	435	2	,	,	PUNCT
ejpam-77	435	3	λ	λ	NOUN
ejpam-77	435	4	)	)	PUNCT
ejpam-77	435	5	}	}	PUNCT
ejpam-77	435	6	.	.	PUNCT
ejpam-77	436	1	since	since	SCONJ
ejpam-77	436	2	a	a	PRON
ejpam-77	436	3	and	and	CCONJ
ejpam-77	436	4	ap0	ap0	VERB
ejpam-77	436	5	are	be	AUX
ejpam-77	436	6	both	both	PRON
ejpam-77	436	7	in	in	ADP
ejpam-77	436	8	i	i	PRON
ejpam-77	436	9	,	,	PUNCT
ejpam-77	436	10	it	it	PRON
ejpam-77	436	11	is	be	AUX
ejpam-77	436	12	sufficient	sufficient	ADJ
ejpam-77	436	13	to	to	PART
ejpam-77	436	14	show	show	VERB
ejpam-77	436	15	that	that	SCONJ
ejpam-77	436	16	ac	ac	PROPN
ejpam-77	436	17	⊃	⊃	PROPN
ejpam-77	436	18	ac	ac	PROPN
ejpam-77	436	19	p0	p0	PROPN
ejpam-77	436	20	.	.	PUNCT
ejpam-77	437	1	references	reference	NOUN
ejpam-77	437	2	210	210	NUM
ejpam-77	437	3	let	let	VERB
ejpam-77	437	4	n	n	PRON
ejpam-77	437	5	∈	∈	PROPN
ejpam-77	437	6	ac	ac	PROPN
ejpam-77	437	7	p0	p0	NOUN
ejpam-77	437	8	,	,	PUNCT
ejpam-77	437	9	then	then	ADV
ejpam-77	437	10	we	we	PRON
ejpam-77	437	11	have	have	VERB
ejpam-77	437	12	νxn−ξ(ε	νxn−ξ(ε	PROPN
ejpam-77	437	13	)	)	PUNCT
ejpam-77	437	14	≥	≥	PROPN
ejpam-77	437	15	t	t	PROPN
ejpam-77	437	16	�	�	PROPN
ejpam-77	437	17	νxn−xmp0	νxn−xmp0	PROPN
ejpam-77	437	18	(	(	PUNCT
ejpam-77	437	19	ε	ε	PROPN
ejpam-77	437	20	2	2	NUM
ejpam-77	437	21	)	)	PUNCT
ejpam-77	437	22	,	,	PUNCT
ejpam-77	437	23	νxmp0	νxmp0	NOUN
ejpam-77	437	24	−ξ	−ξ	NOUN
ejpam-77	437	25	(	(	PUNCT
ejpam-77	437	26	ε	ε	PROPN
ejpam-77	437	27	2	2	NUM
ejpam-77	437	28	)	)	PUNCT
ejpam-77	437	29	�	�	PROPN
ejpam-77	437	30	>	>	X
ejpam-77	437	31	t	t	PROPN
ejpam-77	437	32	(	(	PUNCT
ejpam-77	437	33	1−λ	1−λ	NUM
ejpam-77	437	34	,	,	PUNCT
ejpam-77	437	35	1−λ	1−λ	NUM
ejpam-77	437	36	)	)	PUNCT
ejpam-77	437	37	>	>	X
ejpam-77	437	38	1−λ	1−λ	NUM
ejpam-77	437	39	.	.	PUNCT
ejpam-77	438	1	this	this	PRON
ejpam-77	438	2	implies	imply	VERB
ejpam-77	438	3	that	that	SCONJ
ejpam-77	438	4	n	n	PROPN
ejpam-77	438	5	∈	∈	PROPN
ejpam-77	438	6	ac	ac	PROPN
ejpam-77	438	7	.	.	PUNCT
ejpam-77	438	8	therefore	therefore	ADV
ejpam-77	438	9	a⊂	a⊂	VERB
ejpam-77	438	10	ap0	ap0	VERB
ejpam-77	438	11	.	.	PUNCT
ejpam-77	439	1	since	since	SCONJ
ejpam-77	439	2	ap0	ap0	PROPN
ejpam-77	439	3	⊂	⊂	PROPN
ejpam-77	439	4	i	i	PRON
ejpam-77	439	5	,	,	PUNCT
ejpam-77	439	6	we	we	PRON
ejpam-77	439	7	conclude	conclude	VERB
ejpam-77	439	8	that	that	PRON
ejpam-77	439	9	a⊂	a⊂	VERB
ejpam-77	439	10	i	i	PRON
ejpam-77	439	11	.	.	PUNCT
ejpam-77	440	1	this	this	PRON
ejpam-77	440	2	proves	prove	VERB
ejpam-77	440	3	that	that	SCONJ
ejpam-77	440	4	the	the	DET
ejpam-77	440	5	sequence	sequence	NOUN
ejpam-77	440	6	(	(	PUNCT
ejpam-77	440	7	xn	xn	X
ejpam-77	440	8	)	)	PUNCT
ejpam-77	440	9	is	be	AUX
ejpam-77	440	10	i	i	PRON
ejpam-77	440	11	f	f	PROPN
ejpam-77	440	12	-convergent	-convergent	ADJ
ejpam-77	440	13	to	to	ADP
ejpam-77	440	14	ξ	ξ	PROPN
ejpam-77	440	15	.	.	PUNCT
ejpam-77	440	16	acknowledgements	acknowledgement	NOUN
ejpam-77	440	17	.	.	PUNCT
ejpam-77	441	1	the	the	DET
ejpam-77	441	2	authors	author	NOUN
ejpam-77	441	3	would	would	AUX
ejpam-77	441	4	like	like	VERB
ejpam-77	441	5	to	to	PART
ejpam-77	441	6	thank	thank	VERB
ejpam-77	441	7	the	the	DET
ejpam-77	441	8	referee	referee	NOUN
ejpam-77	441	9	for	for	ADP
ejpam-77	441	10	giving	give	VERB
ejpam-77	441	11	useful	useful	ADJ
ejpam-77	441	12	comments	comment	NOUN
ejpam-77	441	13	and	and	CCONJ
ejpam-77	441	14	suggestions	suggestion	NOUN
ejpam-77	441	15	for	for	ADP
ejpam-77	441	16	the	the	DET
ejpam-77	441	17	improvement	improvement	NOUN
ejpam-77	441	18	of	of	ADP
ejpam-77	441	19	this	this	DET
ejpam-77	441	20	paper	paper	NOUN
ejpam-77	441	21	.	.	PUNCT
ejpam-77	442	1	references	reference	NOUN
ejpam-77	442	2	[	[	X
ejpam-77	442	3	1	1	X
ejpam-77	442	4	]	]	PUNCT
ejpam-77	442	5	s.	s.	PROPN
ejpam-77	442	6	aytar	aytar	PROPN
ejpam-77	442	7	and	and	CCONJ
ejpam-77	442	8	s.	s.	PROPN
ejpam-77	442	9	pehlivan	pehlivan	PROPN
ejpam-77	442	10	,	,	PUNCT
ejpam-77	442	11	statistically	statistically	ADV
ejpam-77	442	12	monotonic	monotonic	ADJ
ejpam-77	442	13	and	and	CCONJ
ejpam-77	442	14	statistically	statistically	ADV
ejpam-77	442	15	bounded	bound	VERB
ejpam-77	442	16	sequences	sequence	NOUN
ejpam-77	442	17	of	of	ADP
ejpam-77	442	18	fuzzy	fuzzy	ADJ
ejpam-77	442	19	numbers	number	NOUN
ejpam-77	442	20	.	.	PUNCT
ejpam-77	443	1	information	information	NOUN
ejpam-77	443	2	sciences	sciences	PROPN
ejpam-77	443	3	,	,	PUNCT
ejpam-77	443	4	176	176	NUM
ejpam-77	443	5	:	:	PUNCT
ejpam-77	443	6	734	734	NUM
ejpam-77	443	7	-	-	SYM
ejpam-77	443	8	744	744	NUM
ejpam-77	443	9	(	(	PUNCT
ejpam-77	443	10	2006	2006	NUM
ejpam-77	443	11	)	)	PUNCT
ejpam-77	443	12	.	.	PUNCT
ejpam-77	444	1	[	[	X
ejpam-77	444	2	2	2	X
ejpam-77	444	3	]	]	PUNCT
ejpam-77	444	4	v.	v.	ADP
ejpam-77	444	5	balaz	balaz	PROPN
ejpam-77	444	6	,	,	PUNCT
ejpam-77	444	7	j.	j.	PROPN
ejpam-77	444	8	cervennansky	cervennansky	PROPN
ejpam-77	444	9	,	,	PUNCT
ejpam-77	444	10	t.	t.	PROPN
ejpam-77	444	11	kostyrko	kostyrko	PROPN
ejpam-77	444	12	,	,	PUNCT
ejpam-77	444	13	t.	t.	NOUN
ejpam-77	444	14	salat	salat	NOUN
ejpam-77	444	15	,	,	PUNCT
ejpam-77	444	16	i	i	PRON
ejpam-77	444	17	-convergence	-convergence	PROPN
ejpam-77	445	1	and	and	CCONJ
ejpam-77	445	2	i	i	PRON
ejpam-77	445	3	-continuity	-continuity	ADJ
ejpam-77	445	4	of	of	ADP
ejpam-77	445	5	real	real	ADJ
ejpam-77	445	6	functions	function	NOUN
ejpam-77	445	7	.	.	PUNCT
ejpam-77	446	1	acta	acta	PROPN
ejpam-77	446	2	mathematica	mathematica	PROPN
ejpam-77	446	3	,	,	PUNCT
ejpam-77	446	4	faculty	faculty	NOUN
ejpam-77	446	5	of	of	ADP
ejpam-77	446	6	natural	natural	ADJ
ejpam-77	446	7	sciences	science	NOUN
ejpam-77	446	8	,	,	PUNCT
ejpam-77	446	9	constantine	constantine	VERB
ejpam-77	446	10	the	the	DET
ejpam-77	446	11	philosopher	philosopher	NOUN
ejpam-77	446	12	university	university	PROPN
ejpam-77	446	13	nitra	nitra	PROPN
ejpam-77	446	14	5	5	NUM
ejpam-77	446	15	:	:	SYM
ejpam-77	446	16	43	43	NUM
ejpam-77	446	17	-	-	SYM
ejpam-77	446	18	50	50	NUM
ejpam-77	446	19	(	(	PUNCT
ejpam-77	446	20	2002	2002	NUM
ejpam-77	446	21	)	)	PUNCT
ejpam-77	446	22	.	.	PUNCT
ejpam-77	447	1	[	[	X
ejpam-77	447	2	3	3	X
ejpam-77	447	3	]	]	PUNCT
ejpam-77	447	4	m.	m.	NOUN
ejpam-77	447	5	balcerzak	balcerzak	NOUN
ejpam-77	447	6	,	,	PUNCT
ejpam-77	447	7	k.	k.	PROPN
ejpam-77	447	8	dems	dems	PROPN
ejpam-77	447	9	,	,	PUNCT
ejpam-77	447	10	a.	a.	NOUN
ejpam-77	447	11	komisarski	komisarski	PROPN
ejpam-77	447	12	,	,	PUNCT
ejpam-77	447	13	statistical	statistical	ADJ
ejpam-77	447	14	convergence	convergence	NOUN
ejpam-77	447	15	and	and	CCONJ
ejpam-77	447	16	ideal	ideal	ADJ
ejpam-77	447	17	convergence	convergence	NOUN
ejpam-77	447	18	for	for	ADP
ejpam-77	447	19	sequences	sequence	NOUN
ejpam-77	447	20	of	of	ADP
ejpam-77	447	21	functions	function	NOUN
ejpam-77	447	22	.	.	PUNCT
ejpam-77	448	1	j.	j.	PROPN
ejpam-77	448	2	math	math	PROPN
ejpam-77	448	3	.	.	PUNCT
ejpam-77	449	1	anal	anal	PROPN
ejpam-77	449	2	.	.	PUNCT
ejpam-77	449	3	appl	appl	PROPN
ejpam-77	449	4	.	.	PUNCT
ejpam-77	450	1	328	328	NUM
ejpam-77	450	2	:	:	PUNCT
ejpam-77	450	3	715	715	NUM
ejpam-77	450	4	-	-	SYM
ejpam-77	450	5	729	729	NUM
ejpam-77	450	6	(	(	PUNCT
ejpam-77	450	7	2007	2007	NUM
ejpam-77	450	8	)	)	PUNCT
ejpam-77	450	9	.	.	PUNCT
ejpam-77	451	1	[	[	X
ejpam-77	451	2	4	4	X
ejpam-77	451	3	]	]	PUNCT
ejpam-77	451	4	j.	j.	PROPN
ejpam-77	451	5	connor	connor	PROPN
ejpam-77	451	6	,	,	PUNCT
ejpam-77	451	7	the	the	DET
ejpam-77	451	8	statistical	statistical	ADJ
ejpam-77	451	9	and	and	CCONJ
ejpam-77	451	10	strong	strong	ADJ
ejpam-77	451	11	p	p	NOUN
ejpam-77	451	12	-	-	PUNCT
ejpam-77	451	13	cesaro	cesaro	ADJ
ejpam-77	451	14	convergence	convergence	NOUN
ejpam-77	451	15	of	of	ADP
ejpam-77	451	16	sequences	sequence	NOUN
ejpam-77	451	17	.	.	PUNCT
ejpam-77	452	1	analysis	analysis	NOUN
ejpam-77	452	2	8	8	NUM
ejpam-77	452	3	:	:	SYM
ejpam-77	452	4	4763	4763	NUM
ejpam-77	452	5	(	(	PUNCT
ejpam-77	452	6	1988	1988	NUM
ejpam-77	452	7	)	)	PUNCT
ejpam-77	452	8	.	.	PUNCT
ejpam-77	453	1	[	[	X
ejpam-77	453	2	5	5	X
ejpam-77	453	3	]	]	PUNCT
ejpam-77	453	4	j.	j.	PROPN
ejpam-77	453	5	connor	connor	PROPN
ejpam-77	453	6	,	,	PUNCT
ejpam-77	453	7	m.	m.	NOUN
ejpam-77	453	8	ganichev	ganichev	PROPN
ejpam-77	453	9	,	,	PUNCT
ejpam-77	453	10	v.	v.	ADP
ejpam-77	453	11	kadets	kadet	NOUN
ejpam-77	453	12	,	,	PUNCT
ejpam-77	453	13	a	a	DET
ejpam-77	453	14	characterization	characterization	NOUN
ejpam-77	453	15	of	of	ADP
ejpam-77	453	16	banach	banach	NOUN
ejpam-77	453	17	spaces	space	NOUN
ejpam-77	453	18	with	with	ADP
ejpam-77	453	19	separable	separable	ADJ
ejpam-77	453	20	duals	dual	NOUN
ejpam-77	453	21	via	via	ADP
ejpam-77	453	22	weak	weak	ADJ
ejpam-77	453	23	statistical	statistical	ADJ
ejpam-77	453	24	convergence	convergence	NOUN
ejpam-77	453	25	.	.	PUNCT
ejpam-77	454	1	j.	j.	PROPN
ejpam-77	454	2	math	math	PROPN
ejpam-77	454	3	.	.	PUNCT
ejpam-77	455	1	anal	anal	PROPN
ejpam-77	455	2	.	.	PUNCT
ejpam-77	455	3	appl	appl	PROPN
ejpam-77	455	4	.	.	PUNCT
ejpam-77	456	1	244	244	NUM
ejpam-77	456	2	:	:	PUNCT
ejpam-77	456	3	251	251	NUM
ejpam-77	456	4	-	-	SYM
ejpam-77	456	5	261	261	NUM
ejpam-77	456	6	(	(	PUNCT
ejpam-77	456	7	2000	2000	NUM
ejpam-77	456	8	)	)	PUNCT
ejpam-77	456	9	.	.	PUNCT
ejpam-77	457	1	[	[	X
ejpam-77	457	2	6	6	NUM
ejpam-77	457	3	]	]	PUNCT
ejpam-77	457	4	k.	k.	PROPN
ejpam-77	457	5	dems	dems	PROPN
ejpam-77	457	6	,	,	PUNCT
ejpam-77	457	7	on	on	ADP
ejpam-77	457	8	i	i	PRON
ejpam-77	457	9	-cauchy	-cauchy	ADJ
ejpam-77	457	10	sequences	sequence	NOUN
ejpam-77	457	11	.	.	PUNCT
ejpam-77	458	1	real	real	ADJ
ejpam-77	458	2	anal	anal	PROPN
ejpam-77	458	3	.	.	PUNCT
ejpam-77	459	1	exch	exch	PROPN
ejpam-77	459	2	.	.	PUNCT
ejpam-77	460	1	30	30	NUM
ejpam-77	460	2	:	:	PUNCT
ejpam-77	460	3	123	123	NUM
ejpam-77	460	4	-	-	SYM
ejpam-77	460	5	128	128	NUM
ejpam-77	460	6	(	(	PUNCT
ejpam-77	460	7	2004/2005	2004/2005	NUM
ejpam-77	460	8	)	)	PUNCT
ejpam-77	460	9	.	.	PUNCT
ejpam-77	461	1	[	[	X
ejpam-77	461	2	7	7	X
ejpam-77	461	3	]	]	X
ejpam-77	461	4	h.	h.	PROPN
ejpam-77	461	5	fast	fast	PROPN
ejpam-77	461	6	,	,	PUNCT
ejpam-77	461	7	sur	sur	PROPN
ejpam-77	461	8	la	la	PRON
ejpam-77	461	9	convergence	convergence	NOUN
ejpam-77	461	10	statistique	statistique	NOUN
ejpam-77	461	11	.	.	PUNCT
ejpam-77	462	1	colloq	colloq	PROPN
ejpam-77	462	2	.	.	PUNCT
ejpam-77	463	1	math	math	NOUN
ejpam-77	463	2	.	.	PUNCT
ejpam-77	464	1	2	2	NUM
ejpam-77	464	2	:	:	PUNCT
ejpam-77	464	3	241	241	NUM
ejpam-77	464	4	-	-	SYM
ejpam-77	464	5	244	244	NUM
ejpam-77	464	6	(	(	PUNCT
ejpam-77	464	7	1951	1951	NUM
ejpam-77	464	8	)	)	PUNCT
ejpam-77	464	9	.	.	PUNCT
ejpam-77	465	1	[	[	X
ejpam-77	465	2	8	8	NUM
ejpam-77	465	3	]	]	PUNCT
ejpam-77	465	4	a.	a.	PROPN
ejpam-77	465	5	r.	r.	PROPN
ejpam-77	465	6	freedman	freedman	PROPN
ejpam-77	465	7	and	and	CCONJ
ejpam-77	465	8	j.	j.	PROPN
ejpam-77	465	9	j.	j.	PROPN
ejpam-77	465	10	sember	sember	PROPN
ejpam-77	465	11	,	,	PUNCT
ejpam-77	465	12	densities	density	NOUN
ejpam-77	465	13	and	and	CCONJ
ejpam-77	465	14	summability	summability	NOUN
ejpam-77	465	15	.	.	PUNCT
ejpam-77	466	1	pasific	pasific	PROPN
ejpam-77	466	2	j.	j.	PROPN
ejpam-77	466	3	math	math	PROPN
ejpam-77	466	4	.	.	PUNCT
ejpam-77	467	1	95	95	NUM
ejpam-77	467	2	:	:	PUNCT
ejpam-77	467	3	293	293	NUM
ejpam-77	467	4	-	-	SYM
ejpam-77	467	5	305	305	NUM
ejpam-77	467	6	(	(	PUNCT
ejpam-77	467	7	1981	1981	NUM
ejpam-77	467	8	)	)	PUNCT
ejpam-77	467	9	.	.	PUNCT
ejpam-77	468	1	references	reference	NOUN
ejpam-77	468	2	211	211	NUM
ejpam-77	469	1	[	[	X
ejpam-77	469	2	9	9	NUM
ejpam-77	469	3	]	]	PUNCT
ejpam-77	469	4	j.	j.	PROPN
ejpam-77	469	5	a.	a.	PROPN
ejpam-77	469	6	fridy	fridy	PROPN
ejpam-77	469	7	,	,	PUNCT
ejpam-77	469	8	on	on	ADP
ejpam-77	469	9	statistical	statistical	ADJ
ejpam-77	469	10	convergence	convergence	NOUN
ejpam-77	469	11	.	.	PUNCT
ejpam-77	470	1	analysis	analysis	NOUN
ejpam-77	470	2	5	5	NUM
ejpam-77	470	3	:	:	SYM
ejpam-77	470	4	301	301	NUM
ejpam-77	470	5	-	-	SYM
ejpam-77	470	6	313	313	NUM
ejpam-77	470	7	(	(	PUNCT
ejpam-77	470	8	1985	1985	NUM
ejpam-77	470	9	)	)	PUNCT
ejpam-77	470	10	.	.	PUNCT
ejpam-77	471	1	[	[	X
ejpam-77	471	2	10	10	NUM
ejpam-77	471	3	]	]	PUNCT
ejpam-77	471	4	j.	j.	PROPN
ejpam-77	471	5	a.	a.	PROPN
ejpam-77	471	6	fridy	fridy	PROPN
ejpam-77	471	7	,	,	PUNCT
ejpam-77	471	8	statistical	statistical	ADJ
ejpam-77	471	9	limit	limit	NOUN
ejpam-77	471	10	points	point	NOUN
ejpam-77	471	11	.	.	PUNCT
ejpam-77	472	1	proc	proc	NOUN
ejpam-77	472	2	.	.	PUNCT
ejpam-77	473	1	amer	amer	PROPN
ejpam-77	473	2	.	.	PUNCT
ejpam-77	473	3	math	math	PROPN
ejpam-77	473	4	.	.	PUNCT
ejpam-77	474	1	soc	soc	PROPN
ejpam-77	474	2	.	.	PUNCT
ejpam-77	475	1	118	118	NUM
ejpam-77	475	2	:	:	PUNCT
ejpam-77	475	3	1187	1187	NUM
ejpam-77	475	4	-	-	SYM
ejpam-77	475	5	1192	1192	NUM
ejpam-77	475	6	(	(	PUNCT
ejpam-77	475	7	1993	1993	NUM
ejpam-77	475	8	)	)	PUNCT
ejpam-77	475	9	.	.	PUNCT
ejpam-77	476	1	[	[	X
ejpam-77	476	2	11	11	NUM
ejpam-77	476	3	]	]	PUNCT
ejpam-77	476	4	j.	j.	PROPN
ejpam-77	476	5	a.	a.	PROPN
ejpam-77	476	6	fridy	fridy	PROPN
ejpam-77	476	7	and	and	CCONJ
ejpam-77	476	8	c.	c.	PROPN
ejpam-77	476	9	orhan	orhan	PROPN
ejpam-77	476	10	,	,	PUNCT
ejpam-77	476	11	statistical	statistical	ADJ
ejpam-77	476	12	limit	limit	NOUN
ejpam-77	476	13	superior	superior	ADJ
ejpam-77	476	14	and	and	CCONJ
ejpam-77	476	15	limit	limit	VERB
ejpam-77	476	16	inferior	inferior	ADJ
ejpam-77	476	17	.	.	PUNCT
ejpam-77	477	1	proc	proc	PROPN
ejpam-77	477	2	.	.	PUNCT
ejpam-77	478	1	amer	amer	PROPN
ejpam-77	478	2	.	.	PUNCT
ejpam-77	478	3	math	math	PROPN
ejpam-77	478	4	.	.	PUNCT
ejpam-77	479	1	soc	soc	PROPN
ejpam-77	479	2	.	.	PUNCT
ejpam-77	480	1	125	125	NUM
ejpam-77	480	2	:	:	PUNCT
ejpam-77	480	3	3625	3625	NUM
ejpam-77	480	4	-	-	SYM
ejpam-77	480	5	3631	3631	NUM
ejpam-77	480	6	(	(	PUNCT
ejpam-77	480	7	1997	1997	NUM
ejpam-77	480	8	)	)	PUNCT
ejpam-77	480	9	.	.	PUNCT
ejpam-77	481	1	[	[	X
ejpam-77	481	2	12	12	NUM
ejpam-77	481	3	]	]	PUNCT
ejpam-77	481	4	j.	j.	PROPN
ejpam-77	481	5	jasinski	jasinski	PROPN
ejpam-77	481	6	,	,	PUNCT
ejpam-77	481	7	i.	i.	PROPN
ejpam-77	481	8	reclaw	reclaw	PROPN
ejpam-77	481	9	,	,	PUNCT
ejpam-77	481	10	ideal	ideal	ADJ
ejpam-77	481	11	convergence	convergence	NOUN
ejpam-77	481	12	of	of	ADP
ejpam-77	481	13	continuous	continuous	ADJ
ejpam-77	481	14	functions	function	NOUN
ejpam-77	481	15	.	.	PUNCT
ejpam-77	482	1	topology	topology	NOUN
ejpam-77	482	2	and	and	CCONJ
ejpam-77	482	3	its	its	PRON
ejpam-77	482	4	applications	application	NOUN
ejpam-77	482	5	,	,	PUNCT
ejpam-77	482	6	153	153	NUM
ejpam-77	482	7	:	:	PUNCT
ejpam-77	482	8	3511	3511	NUM
ejpam-77	482	9	-	-	SYM
ejpam-77	482	10	3518	3518	NUM
ejpam-77	482	11	(	(	PUNCT
ejpam-77	482	12	2006	2006	NUM
ejpam-77	482	13	)	)	PUNCT
ejpam-77	482	14	.	.	PUNCT
ejpam-77	483	1	[	[	X
ejpam-77	483	2	13	13	NUM
ejpam-77	483	3	]	]	PUNCT
ejpam-77	483	4	s.	s.	PROPN
ejpam-77	483	5	karakus	karakus	PROPN
ejpam-77	483	6	,	,	PUNCT
ejpam-77	483	7	statistical	statistical	ADJ
ejpam-77	483	8	convergence	convergence	NOUN
ejpam-77	483	9	on	on	ADP
ejpam-77	483	10	probabilistic	probabilistic	ADJ
ejpam-77	483	11	normed	normed	ADJ
ejpam-77	483	12	spaces	space	NOUN
ejpam-77	483	13	.	.	PUNCT
ejpam-77	483	14	math	math	NOUN
ejpam-77	483	15	.	.	PUNCT
ejpam-77	484	1	comm	comm	NOUN
ejpam-77	484	2	.	.	PUNCT
ejpam-77	485	1	12	12	NUM
ejpam-77	485	2	:	:	PUNCT
ejpam-77	485	3	11	11	NUM
ejpam-77	485	4	-	-	SYM
ejpam-77	485	5	23	23	NUM
ejpam-77	485	6	(	(	PUNCT
ejpam-77	485	7	2007	2007	NUM
ejpam-77	485	8	)	)	PUNCT
ejpam-77	485	9	.	.	PUNCT
ejpam-77	486	1	[	[	X
ejpam-77	486	2	14	14	NUM
ejpam-77	486	3	]	]	X
ejpam-77	486	4	s.	s.	PROPN
ejpam-77	486	5	karakus	karakus	PROPN
ejpam-77	486	6	,	,	PUNCT
ejpam-77	486	7	k.	k.	PROPN
ejpam-77	486	8	demirci	demirci	PROPN
ejpam-77	486	9	,	,	PUNCT
ejpam-77	486	10	statisitcval	statisitcval	NOUN
ejpam-77	486	11	convergence	convergence	NOUN
ejpam-77	486	12	of	of	ADP
ejpam-77	486	13	double	double	ADJ
ejpam-77	486	14	sequences	sequence	NOUN
ejpam-77	486	15	on	on	ADP
ejpam-77	486	16	probabilistic	probabilistic	ADJ
ejpam-77	486	17	normed	normed	ADJ
ejpam-77	486	18	spaces	space	NOUN
ejpam-77	486	19	.	.	PUNCT
ejpam-77	487	1	int	int	NOUN
ejpam-77	487	2	.	.	PUNCT
ejpam-77	488	1	j.	j.	PROPN
ejpam-77	488	2	math	math	PROPN
ejpam-77	488	3	.	.	PUNCT
ejpam-77	489	1	math	math	NOUN
ejpam-77	489	2	.	.	PUNCT
ejpam-77	490	1	sci	sci	PROPN
ejpam-77	490	2	.	.	PROPN
ejpam-77	491	1	2007	2007	NUM
ejpam-77	491	2	:	:	PUNCT
ejpam-77	492	1	11	11	NUM
ejpam-77	492	2	pages	page	NOUN
ejpam-77	492	3	(	(	PUNCT
ejpam-77	492	4	2007	2007	NUM
ejpam-77	492	5	)	)	PUNCT
ejpam-77	493	1	[	[	X
ejpam-77	493	2	15	15	NUM
ejpam-77	493	3	]	]	X
ejpam-77	493	4	e.	e.	PROPN
ejpam-77	493	5	kolk	kolk	PROPN
ejpam-77	493	6	,	,	PUNCT
ejpam-77	493	7	the	the	DET
ejpam-77	493	8	statistical	statistical	ADJ
ejpam-77	493	9	convergence	convergence	NOUN
ejpam-77	493	10	in	in	ADP
ejpam-77	493	11	banach	banach	NOUN
ejpam-77	493	12	spaces	space	NOUN
ejpam-77	493	13	.	.	PUNCT
ejpam-77	494	1	acta	acta	PROPN
ejpam-77	494	2	comment	comment	PROPN
ejpam-77	494	3	.	.	PUNCT
ejpam-77	495	1	univ	univ	PROPN
ejpam-77	495	2	.	.	PROPN
ejpam-77	495	3	tartu	tartu	PROPN
ejpam-77	495	4	.	.	PUNCT
ejpam-77	496	1	928	928	NUM
ejpam-77	496	2	:	:	PUNCT
ejpam-77	496	3	41	41	NUM
ejpam-77	496	4	-	-	SYM
ejpam-77	496	5	52	52	NUM
ejpam-77	496	6	(	(	PUNCT
ejpam-77	496	7	1991	1991	NUM
ejpam-77	496	8	)	)	PUNCT
ejpam-77	496	9	.	.	PUNCT
ejpam-77	497	1	[	[	X
ejpam-77	497	2	16	16	NUM
ejpam-77	497	3	]	]	PUNCT
ejpam-77	497	4	p.	p.	PROPN
ejpam-77	497	5	kostyrko	kostyrko	PROPN
ejpam-77	497	6	,	,	PUNCT
ejpam-77	497	7	t.	t.	NOUN
ejpam-77	497	8	salat	salat	NOUN
ejpam-77	497	9	,	,	PUNCT
ejpam-77	497	10	w.	w.	PROPN
ejpam-77	497	11	wilczynski	wilczynski	PROPN
ejpam-77	497	12	,	,	PUNCT
ejpam-77	497	13	i	i	PRON
ejpam-77	497	14	-convergence	-convergence	PROPN
ejpam-77	497	15	.	.	PUNCT
ejpam-77	498	1	real	real	ADJ
ejpam-77	498	2	anal	anal	PROPN
ejpam-77	498	3	.	.	PUNCT
ejpam-77	499	1	exch	exch	PROPN
ejpam-77	499	2	.	.	PROPN
ejpam-77	500	1	26	26	NUM
ejpam-77	500	2	,	,	PUNCT
ejpam-77	500	3	2	2	NUM
ejpam-77	500	4	:	:	SYM
ejpam-77	500	5	669	669	NUM
ejpam-77	500	6	-	-	SYM
ejpam-77	500	7	686	686	NUM
ejpam-77	500	8	(	(	PUNCT
ejpam-77	500	9	2000/2001	2000/2001	NUM
ejpam-77	500	10	)	)	PUNCT
ejpam-77	500	11	.	.	PUNCT
ejpam-77	501	1	[	[	X
ejpam-77	501	2	17	17	NUM
ejpam-77	501	3	]	]	PUNCT
ejpam-77	501	4	p.	p.	PROPN
ejpam-77	501	5	kostyrko	kostyrko	PROPN
ejpam-77	501	6	,	,	PUNCT
ejpam-77	501	7	m.	m.	NOUN
ejpam-77	501	8	macaj	macaj	NOUN
ejpam-77	501	9	,	,	PUNCT
ejpam-77	501	10	t.	t.	NOUN
ejpam-77	501	11	salat	salat	NOUN
ejpam-77	501	12	,	,	PUNCT
ejpam-77	501	13	m.	m.	NOUN
ejpam-77	501	14	sleziak	sleziak	PROPN
ejpam-77	501	15	.	.	PUNCT
ejpam-77	502	1	i	i	PRON
ejpam-77	502	2	-convergence	-convergence	VERB
ejpam-77	502	3	and	and	CCONJ
ejpam-77	502	4	extremal	extremal	ADJ
ejpam-77	502	5	i	i	PRON
ejpam-77	502	6	-limit	-limit	VERB
ejpam-77	502	7	point	point	NOUN
ejpam-77	502	8	.	.	PUNCT
ejpam-77	503	1	math	math	NOUN
ejpam-77	503	2	.	.	PUNCT
ejpam-77	504	1	slovaca	slovaca	NOUN
ejpam-77	504	2	55	55	NUM
ejpam-77	504	3	:	:	PUNCT
ejpam-77	504	4	443	443	NUM
ejpam-77	504	5	-	-	SYM
ejpam-77	504	6	464	464	NUM
ejpam-77	504	7	(	(	PUNCT
ejpam-77	504	8	2005	2005	NUM
ejpam-77	504	9	)	)	PUNCT
ejpam-77	504	10	.	.	PUNCT
ejpam-77	505	1	[	[	X
ejpam-77	505	2	18	18	NUM
ejpam-77	505	3	]	]	X
ejpam-77	505	4	i.	i.	PROPN
ejpam-77	505	5	j.	j.	PROPN
ejpam-77	505	6	maddox	maddox	PROPN
ejpam-77	505	7	,	,	PUNCT
ejpam-77	505	8	statistical	statistical	ADJ
ejpam-77	505	9	convergence	convergence	NOUN
ejpam-77	505	10	in	in	ADP
ejpam-77	505	11	a	a	DET
ejpam-77	505	12	locally	locally	ADV
ejpam-77	505	13	convex	convex	ADJ
ejpam-77	505	14	space	space	NOUN
ejpam-77	505	15	.	.	PUNCT
ejpam-77	506	1	math	math	NOUN
ejpam-77	506	2	.	.	PUNCT
ejpam-77	507	1	proc	proc	PROPN
ejpam-77	507	2	.	.	PUNCT
ejpam-77	508	1	cambridge	cambridge	PROPN
ejpam-77	508	2	phil	phil	PROPN
ejpam-77	508	3	.	.	PUNCT
ejpam-77	509	1	soc	soc	PROPN
ejpam-77	509	2	.	.	PUNCT
ejpam-77	510	1	104	104	NUM
ejpam-77	510	2	:	:	SYM
ejpam-77	510	3	141	141	NUM
ejpam-77	510	4	-	-	SYM
ejpam-77	510	5	145	145	NUM
ejpam-77	510	6	(	(	PUNCT
ejpam-77	510	7	1988	1988	NUM
ejpam-77	510	8	)	)	PUNCT
ejpam-77	510	9	.	.	PUNCT
ejpam-77	511	1	[	[	X
ejpam-77	511	2	19	19	NUM
ejpam-77	511	3	]	]	X
ejpam-77	511	4	mursaleen	mursaleen	PROPN
ejpam-77	511	5	and	and	CCONJ
ejpam-77	511	6	o.	o.	PROPN
ejpam-77	511	7	h.	h.	PROPN
ejpam-77	511	8	h.	h.	PROPN
ejpam-77	511	9	edely	edely	ADV
ejpam-77	511	10	,	,	PUNCT
ejpam-77	511	11	statistical	statistical	ADJ
ejpam-77	511	12	convergence	convergence	NOUN
ejpam-77	511	13	of	of	ADP
ejpam-77	511	14	double	double	ADJ
ejpam-77	511	15	sequences	sequence	NOUN
ejpam-77	511	16	.	.	PUNCT
ejpam-77	512	1	j.	j.	PROPN
ejpam-77	512	2	math	math	PROPN
ejpam-77	512	3	.	.	PUNCT
ejpam-77	513	1	anal	anal	PROPN
ejpam-77	513	2	.	.	PUNCT
ejpam-77	513	3	appl	appl	PROPN
ejpam-77	513	4	.	.	PUNCT
ejpam-77	514	1	288	288	NUM
ejpam-77	514	2	:	:	PUNCT
ejpam-77	514	3	223	223	NUM
ejpam-77	514	4	-	-	SYM
ejpam-77	514	5	231	231	NUM
ejpam-77	514	6	(	(	PUNCT
ejpam-77	514	7	2003	2003	NUM
ejpam-77	514	8	)	)	PUNCT
ejpam-77	514	9	.	.	PUNCT
ejpam-77	515	1	[	[	X
ejpam-77	515	2	20	20	NUM
ejpam-77	515	3	]	]	PUNCT
ejpam-77	515	4	a.	a.	NOUN
ejpam-77	515	5	nabiev	nabiev	PROPN
ejpam-77	515	6	,	,	PUNCT
ejpam-77	515	7	s.	s.	PROPN
ejpam-77	515	8	pehlivan	pehlivan	PROPN
ejpam-77	515	9	,	,	PUNCT
ejpam-77	515	10	m.	m.	NOUN
ejpam-77	515	11	gurdal	gurdal	NOUN
ejpam-77	515	12	,	,	PUNCT
ejpam-77	515	13	on	on	ADP
ejpam-77	515	14	i	i	PRON
ejpam-77	515	15	-cauchy	-cauchy	ADJ
ejpam-77	515	16	sequence	sequence	NOUN
ejpam-77	515	17	.	.	PUNCT
ejpam-77	516	1	taiwanese	taiwanese	ADJ
ejpam-77	516	2	j.	j.	PROPN
ejpam-77	516	3	math	math	PROPN
ejpam-77	516	4	.	.	PUNCT
ejpam-77	517	1	11	11	NUM
ejpam-77	517	2	,	,	PUNCT
ejpam-77	517	3	2	2	NUM
ejpam-77	517	4	:	:	PUNCT
ejpam-77	517	5	569	569	NUM
ejpam-77	517	6	-	-	SYM
ejpam-77	517	7	576	576	NUM
ejpam-77	517	8	(	(	PUNCT
ejpam-77	517	9	2007	2007	NUM
ejpam-77	517	10	)	)	PUNCT
ejpam-77	517	11	.	.	PUNCT
ejpam-77	518	1	[	[	X
ejpam-77	518	2	21	21	NUM
ejpam-77	518	3	]	]	X
ejpam-77	518	4	t.	t.	NOUN
ejpam-77	518	5	šalát	šalát	NOUN
ejpam-77	518	6	,	,	PUNCT
ejpam-77	518	7	on	on	ADP
ejpam-77	518	8	statistical	statistical	ADJ
ejpam-77	518	9	convergent	convergent	NOUN
ejpam-77	518	10	sequences	sequence	NOUN
ejpam-77	518	11	of	of	ADP
ejpam-77	518	12	real	real	ADJ
ejpam-77	518	13	numbers	number	NOUN
ejpam-77	518	14	.	.	PUNCT
ejpam-77	519	1	math	math	NOUN
ejpam-77	519	2	.	.	PUNCT
ejpam-77	520	1	slovaca	slovaca	PROPN
ejpam-77	520	2	30	30	NUM
ejpam-77	520	3	:	:	SYM
ejpam-77	520	4	139150	139150	NUM
ejpam-77	520	5	(	(	PUNCT
ejpam-77	520	6	1980	1980	NUM
ejpam-77	520	7	)	)	PUNCT
ejpam-77	520	8	.	.	PUNCT
ejpam-77	521	1	[	[	X
ejpam-77	521	2	22	22	NUM
ejpam-77	521	3	]	]	PUNCT
ejpam-77	521	4	e.	e.	PROPN
ejpam-77	521	5	savaş	savaş	PROPN
ejpam-77	521	6	,	,	PUNCT
ejpam-77	521	7	on	on	ADP
ejpam-77	521	8	statistically	statistically	ADV
ejpam-77	521	9	convergent	convergent	ADJ
ejpam-77	521	10	sequences	sequence	NOUN
ejpam-77	521	11	of	of	ADP
ejpam-77	521	12	fuzzy	fuzzy	ADJ
ejpam-77	521	13	numbers	number	NOUN
ejpam-77	521	14	.	.	PUNCT
ejpam-77	522	1	information	information	NOUN
ejpam-77	522	2	sciences	science	NOUN
ejpam-77	522	3	,	,	PUNCT
ejpam-77	522	4	137	137	NUM
ejpam-77	522	5	:	:	PUNCT
ejpam-77	522	6	277	277	NUM
ejpam-77	522	7	-	-	SYM
ejpam-77	522	8	282	282	NUM
ejpam-77	522	9	(	(	PUNCT
ejpam-77	522	10	2001	2001	NUM
ejpam-77	522	11	)	)	PUNCT
ejpam-77	522	12	.	.	PUNCT
ejpam-77	523	1	[	[	X
ejpam-77	523	2	23	23	NUM
ejpam-77	523	3	]	]	PUNCT
ejpam-77	523	4	a.	a.	NOUN
ejpam-77	523	5	n.	n.	PROPN
ejpam-77	523	6	šerstnev	šerstnev	PROPN
ejpam-77	523	7	,	,	PUNCT
ejpam-77	523	8	on	on	ADP
ejpam-77	523	9	the	the	DET
ejpam-77	523	10	notion	notion	NOUN
ejpam-77	523	11	of	of	ADP
ejpam-77	523	12	a	a	DET
ejpam-77	523	13	random	random	ADJ
ejpam-77	523	14	normed	normed	ADJ
ejpam-77	523	15	spaces	space	NOUN
ejpam-77	523	16	.	.	PUNCT
ejpam-77	524	1	dokl	dokl	NOUN
ejpam-77	524	2	.	.	PUNCT
ejpam-77	525	1	akad	akad	PROPN
ejpam-77	525	2	.	.	PUNCT
ejpam-77	526	1	nauk	nauk	PROPN
ejpam-77	526	2	sssr	sssr	NOUN
ejpam-77	526	3	149	149	NUM
ejpam-77	526	4	:	:	PUNCT
ejpam-77	526	5	280	280	NUM
ejpam-77	526	6	-	-	SYM
ejpam-77	526	7	283	283	NUM
ejpam-77	526	8	(	(	PUNCT
ejpam-77	526	9	1963	1963	NUM
ejpam-77	526	10	)	)	PUNCT
ejpam-77	526	11	.	.	PUNCT
ejpam-77	527	1	[	[	X
ejpam-77	527	2	24	24	NUM
ejpam-77	527	3	]	]	PUNCT
ejpam-77	527	4	m.	m.	NOUN
ejpam-77	527	5	sleziak	sleziak	PROPN
ejpam-77	527	6	,	,	PUNCT
ejpam-77	527	7	i	i	PRON
ejpam-77	527	8	-continuity	-continuity	ADJ
ejpam-77	527	9	in	in	ADP
ejpam-77	527	10	topological	topological	ADJ
ejpam-77	527	11	spaces	space	NOUN
ejpam-77	527	12	.	.	PUNCT
ejpam-77	528	1	preprint	preprint	NOUN
ejpam-77	528	2	.	.	PUNCT
ejpam-77	529	1	references	reference	NOUN
ejpam-77	529	2	212	212	NUM
ejpam-77	529	3	[	[	X
ejpam-77	529	4	25	25	NUM
ejpam-77	529	5	]	]	X
ejpam-77	529	6	h.	h.	PROPN
ejpam-77	529	7	steinhaus	steinhaus	PROPN
ejpam-77	529	8	,	,	PUNCT
ejpam-77	529	9	sur	sur	PROPN
ejpam-77	529	10	la	la	PROPN
ejpam-77	529	11	convergence	convergence	NOUN
ejpam-77	529	12	ordinaire	ordinaire	NOUN
ejpam-77	529	13	et	et	NOUN
ejpam-77	529	14	la	la	PROPN
ejpam-77	529	15	convergence	convergence	NOUN
ejpam-77	529	16	asymptotique	asymptotique	NOUN
ejpam-77	529	17	.	.	PUNCT
ejpam-77	530	1	collog	collog	PROPN
ejpam-77	530	2	.	.	PUNCT
ejpam-77	531	1	math	math	NOUN
ejpam-77	531	2	.	.	PUNCT
ejpam-77	532	1	2	2	NUM
ejpam-77	532	2	:	:	PUNCT
ejpam-77	532	3	73	73	NUM
ejpam-77	532	4	-	-	SYM
ejpam-77	532	5	74	74	NUM
ejpam-77	532	6	(	(	PUNCT
ejpam-77	532	7	1951	1951	NUM
ejpam-77	532	8	)	)	PUNCT
ejpam-77	532	9	.	.	PUNCT
ejpam-77	533	1	[	[	X
ejpam-77	533	2	26	26	NUM
ejpam-77	533	3	]	]	X
ejpam-77	533	4	b.	b.	PROPN
ejpam-77	533	5	schweizer	schweizer	PROPN
ejpam-77	533	6	,	,	PUNCT
ejpam-77	533	7	a.	a.	NOUN
ejpam-77	533	8	sklar	sklar	PROPN
ejpam-77	533	9	,	,	PUNCT
ejpam-77	533	10	probabilistic	probabilistic	ADJ
ejpam-77	533	11	metric	metric	ADJ
ejpam-77	533	12	spaces	space	NOUN
ejpam-77	533	13	,	,	PUNCT
ejpam-77	533	14	elsevier	elsevier	NOUN
ejpam-77	533	15	/	/	SYM
ejpam-77	533	16	north	north	PROPN
ejpam-77	533	17	-	-	PUNCT
ejpam-77	533	18	holand	holand	PROPN
ejpam-77	533	19	.	.	PUNCT
ejpam-77	534	1	new	new	PROPN
ejpam-77	534	2	york	york	PROPN
ejpam-77	534	3	,	,	PUNCT
ejpam-77	534	4	1983	1983	NUM
ejpam-77	534	5	.	.	PUNCT