id	sid	tid	token	lemma	pos
ejpam-1518	1	1	7_kucukaslan.dvi	7_kucukaslan.dvi	NUM
ejpam-1518	1	2	european	european	ADJ
ejpam-1518	1	3	journal	journal	NOUN
ejpam-1518	1	4	of	of	ADP
ejpam-1518	1	5	pure	pure	ADJ
ejpam-1518	1	6	and	and	CCONJ
ejpam-1518	1	7	applied	apply	VERB
ejpam-1518	1	8	mathematics	mathematic	NOUN
ejpam-1518	1	9	vol	vol	NOUN
ejpam-1518	1	10	.	.	PROPN
ejpam-1518	1	11	5	5	NUM
ejpam-1518	1	12	,	,	PUNCT
ejpam-1518	1	13	no	no	INTJ
ejpam-1518	1	14	.	.	NOUN
ejpam-1518	1	15	2	2	NUM
ejpam-1518	1	16	,	,	PUNCT
ejpam-1518	1	17	2012	2012	NUM
ejpam-1518	1	18	,	,	PUNCT
ejpam-1518	1	19	174	174	NUM
ejpam-1518	1	20	-	-	SYM
ejpam-1518	1	21	186	186	NUM
ejpam-1518	1	22	issn	issn	PROPN
ejpam-1518	1	23	1307	1307	NUM
ejpam-1518	1	24	-	-	SYM
ejpam-1518	1	25	5543	5543	NUM
ejpam-1518	1	26	–	–	PUNCT
ejpam-1518	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1518	1	28	on	on	ADP
ejpam-1518	1	29	statistical	statistical	ADJ
ejpam-1518	1	30	boundedness	boundedness	NOUN
ejpam-1518	1	31	of	of	ADP
ejpam-1518	1	32	metric	metric	ADJ
ejpam-1518	1	33	valued	value	VERB
ejpam-1518	1	34	sequences	sequence	NOUN
ejpam-1518	1	35	mehmet	mehmet	PROPN
ejpam-1518	1	36	küçükaslan∗	küçükaslan∗	PROPN
ejpam-1518	1	37	,	,	PUNCT
ejpam-1518	1	38	uğur	uğur	NUM
ejpam-1518	1	39	değer	değer	PROPN
ejpam-1518	1	40	department	department	PROPN
ejpam-1518	1	41	of	of	ADP
ejpam-1518	1	42	mathematics	mathematic	NOUN
ejpam-1518	1	43	,	,	PUNCT
ejpam-1518	1	44	faculty	faculty	NOUN
ejpam-1518	1	45	of	of	ADP
ejpam-1518	1	46	science	science	NOUN
ejpam-1518	1	47	and	and	CCONJ
ejpam-1518	1	48	literature	literature	PROPN
ejpam-1518	1	49	,	,	PUNCT
ejpam-1518	1	50	mersin	mersin	PROPN
ejpam-1518	1	51	university	university	PROPN
ejpam-1518	1	52	,	,	PUNCT
ejpam-1518	1	53	mersin	mersin	PROPN
ejpam-1518	1	54	,	,	PUNCT
ejpam-1518	1	55	turkey	turkey	NOUN
ejpam-1518	1	56	abstract	abstract	NOUN
ejpam-1518	1	57	.	.	PUNCT
ejpam-1518	2	1	in	in	ADP
ejpam-1518	2	2	this	this	DET
ejpam-1518	2	3	work	work	NOUN
ejpam-1518	2	4	,	,	PUNCT
ejpam-1518	2	5	statistical	statistical	ADJ
ejpam-1518	2	6	boundedness	boundedness	NOUN
ejpam-1518	2	7	is	be	AUX
ejpam-1518	2	8	defined	define	VERB
ejpam-1518	2	9	in	in	ADP
ejpam-1518	2	10	a	a	DET
ejpam-1518	2	11	metric	metric	ADJ
ejpam-1518	2	12	space	space	NOUN
ejpam-1518	2	13	and	and	CCONJ
ejpam-1518	2	14	,	,	PUNCT
ejpam-1518	2	15	statistical	statistical	ADJ
ejpam-1518	2	16	boundedness	boundedness	NOUN
ejpam-1518	2	17	of	of	ADP
ejpam-1518	2	18	metric	metric	ADJ
ejpam-1518	2	19	valued	value	VERB
ejpam-1518	2	20	sequences	sequence	NOUN
ejpam-1518	2	21	and	and	CCONJ
ejpam-1518	2	22	their	their	PRON
ejpam-1518	2	23	subsequences	subsequence	NOUN
ejpam-1518	2	24	are	be	AUX
ejpam-1518	2	25	studied	study	VERB
ejpam-1518	2	26	.	.	PUNCT
ejpam-1518	3	1	the	the	DET
ejpam-1518	3	2	interplay	interplay	NOUN
ejpam-1518	3	3	between	between	ADP
ejpam-1518	3	4	the	the	DET
ejpam-1518	3	5	statistical	statistical	ADJ
ejpam-1518	3	6	boundedness	boundedness	NOUN
ejpam-1518	3	7	and	and	CCONJ
ejpam-1518	3	8	boundedness	boundedness	NOUN
ejpam-1518	3	9	in	in	ADP
ejpam-1518	3	10	a	a	DET
ejpam-1518	3	11	metric	metric	ADJ
ejpam-1518	3	12	spaces	space	NOUN
ejpam-1518	3	13	are	be	AUX
ejpam-1518	3	14	also	also	ADV
ejpam-1518	3	15	studied	study	VERB
ejpam-1518	3	16	,	,	PUNCT
ejpam-1518	3	17	and	and	CCONJ
ejpam-1518	3	18	it	it	PRON
ejpam-1518	3	19	is	be	AUX
ejpam-1518	3	20	shown	show	VERB
ejpam-1518	3	21	that	that	SCONJ
ejpam-1518	3	22	boundedness	boundedness	NOUN
ejpam-1518	3	23	imply	imply	VERB
ejpam-1518	3	24	statistical	statistical	ADJ
ejpam-1518	3	25	boundedness	boundedness	NOUN
ejpam-1518	4	1	and	and	CCONJ
ejpam-1518	4	2	if	if	SCONJ
ejpam-1518	4	3	the	the	DET
ejpam-1518	4	4	number	number	NOUN
ejpam-1518	4	5	of	of	ADP
ejpam-1518	4	6	elements	element	NOUN
ejpam-1518	4	7	of	of	ADP
ejpam-1518	4	8	the	the	DET
ejpam-1518	4	9	metric	metric	ADJ
ejpam-1518	4	10	space	space	NOUN
ejpam-1518	4	11	is	be	AUX
ejpam-1518	4	12	finite	finite	ADJ
ejpam-1518	4	13	then	then	ADV
ejpam-1518	4	14	these	these	DET
ejpam-1518	4	15	two	two	NUM
ejpam-1518	4	16	concepts	concept	NOUN
ejpam-1518	4	17	coincide	coincide	NOUN
ejpam-1518	4	18	.	.	PUNCT
ejpam-1518	5	1	moreover	moreover	ADV
ejpam-1518	5	2	,	,	PUNCT
ejpam-1518	5	3	here	here	ADV
ejpam-1518	5	4	is	be	AUX
ejpam-1518	5	5	given	give	VERB
ejpam-1518	5	6	analogy	analogy	NOUN
ejpam-1518	5	7	of	of	ADP
ejpam-1518	5	8	balzano	balzano	ADJ
ejpam-1518	5	9	-	-	PUNCT
ejpam-1518	5	10	weierstrass	weierstrass	NOUN
ejpam-1518	5	11	theorem	theorem	NOUN
ejpam-1518	5	12	.	.	PROPN
ejpam-1518	5	13	2010	2010	NUM
ejpam-1518	5	14	mathematics	mathematic	NOUN
ejpam-1518	5	15	subject	subject	NOUN
ejpam-1518	5	16	classifications	classification	NOUN
ejpam-1518	5	17	:	:	PUNCT
ejpam-1518	5	18	40a35	40a35	NUM
ejpam-1518	5	19	,	,	PUNCT
ejpam-1518	5	20	30lxx	30lxx	NUM
ejpam-1518	5	21	,	,	PUNCT
ejpam-1518	5	22	40g15	40g15	NUM
ejpam-1518	5	23	,	,	PUNCT
ejpam-1518	5	24	46a19	46a19	NUM
ejpam-1518	5	25	,	,	PUNCT
ejpam-1518	5	26	28axx	28axx	NOUN
ejpam-1518	5	27	,	,	PUNCT
ejpam-1518	5	28	43a85	43a85	NUM
ejpam-1518	5	29	key	key	ADJ
ejpam-1518	5	30	words	word	NOUN
ejpam-1518	5	31	and	and	CCONJ
ejpam-1518	5	32	phrases	phrase	NOUN
ejpam-1518	5	33	:	:	PUNCT
ejpam-1518	5	34	statistical	statistical	ADJ
ejpam-1518	5	35	convergence	convergence	NOUN
ejpam-1518	5	36	,	,	PUNCT
ejpam-1518	5	37	metric	metric	ADJ
ejpam-1518	5	38	spaces	space	NOUN
ejpam-1518	5	39	,	,	PUNCT
ejpam-1518	5	40	statistical	statistical	ADJ
ejpam-1518	5	41	boundedness	boundedness	NOUN
ejpam-1518	5	42	,	,	PUNCT
ejpam-1518	5	43	asymptotic	asymptotic	ADJ
ejpam-1518	5	44	density	density	NOUN
ejpam-1518	5	45	1	1	NUM
ejpam-1518	5	46	.	.	PUNCT
ejpam-1518	6	1	introduction	introduction	NOUN
ejpam-1518	6	2	and	and	CCONJ
ejpam-1518	6	3	definitions	definition	NOUN
ejpam-1518	6	4	the	the	DET
ejpam-1518	6	5	statistical	statistical	ADJ
ejpam-1518	6	6	convergence	convergence	NOUN
ejpam-1518	6	7	of	of	ADP
ejpam-1518	6	8	real	real	ADJ
ejpam-1518	6	9	or	or	CCONJ
ejpam-1518	6	10	complex	complex	ADJ
ejpam-1518	6	11	valued	value	VERB
ejpam-1518	6	12	sequences	sequence	NOUN
ejpam-1518	6	13	was	be	AUX
ejpam-1518	6	14	first	first	ADV
ejpam-1518	6	15	introduced	introduce	VERB
ejpam-1518	6	16	by	by	ADP
ejpam-1518	6	17	fast	fast	ADJ
ejpam-1518	6	18	[	[	X
ejpam-1518	6	19	7	7	NUM
ejpam-1518	6	20	]	]	PUNCT
ejpam-1518	6	21	,	,	PUNCT
ejpam-1518	6	22	but	but	CCONJ
ejpam-1518	6	23	the	the	DET
ejpam-1518	6	24	idea	idea	NOUN
ejpam-1518	6	25	of	of	ADP
ejpam-1518	6	26	statistical	statistical	ADJ
ejpam-1518	6	27	convergence	convergence	NOUN
ejpam-1518	6	28	goes	go	VERB
ejpam-1518	6	29	back	back	ADV
ejpam-1518	6	30	to	to	ADP
ejpam-1518	6	31	zygmund	zygmund	NOUN
ejpam-1518	6	32	[	[	X
ejpam-1518	6	33	16	16	NUM
ejpam-1518	6	34	]	]	PUNCT
ejpam-1518	6	35	.	.	PUNCT
ejpam-1518	7	1	in	in	ADP
ejpam-1518	7	2	recent	recent	ADJ
ejpam-1518	7	3	years	year	NOUN
ejpam-1518	7	4	,	,	PUNCT
ejpam-1518	7	5	statistical	statistical	ADJ
ejpam-1518	7	6	convergence	convergence	NOUN
ejpam-1518	7	7	has	have	AUX
ejpam-1518	7	8	become	become	VERB
ejpam-1518	7	9	popular	popular	ADJ
ejpam-1518	7	10	research	research	NOUN
ejpam-1518	7	11	area	area	NOUN
ejpam-1518	7	12	for	for	ADP
ejpam-1518	7	13	many	many	ADJ
ejpam-1518	7	14	mathematicians	mathematician	NOUN
ejpam-1518	7	15	[	[	X
ejpam-1518	7	16	2	2	NUM
ejpam-1518	7	17	,	,	PUNCT
ejpam-1518	7	18	3	3	NUM
ejpam-1518	7	19	,	,	PUNCT
ejpam-1518	7	20	8	8	NUM
ejpam-1518	7	21	,	,	PUNCT
ejpam-1518	7	22	9	9	NUM
ejpam-1518	7	23	,	,	PUNCT
ejpam-1518	7	24	10	10	NUM
ejpam-1518	7	25	,	,	PUNCT
ejpam-1518	7	26	12	12	NUM
ejpam-1518	7	27	,	,	PUNCT
ejpam-1518	7	28	13	13	NUM
ejpam-1518	7	29	,	,	PUNCT
ejpam-1518	7	30	14	14	NUM
ejpam-1518	7	31	,	,	PUNCT
ejpam-1518	7	32	15	15	NUM
ejpam-1518	7	33	]	]	PUNCT
ejpam-1518	7	34	etc	etc	X
ejpam-1518	7	35	.	.	X
ejpam-1518	8	1	on	on	ADP
ejpam-1518	8	2	the	the	DET
ejpam-1518	8	3	other	other	ADJ
ejpam-1518	8	4	hand	hand	NOUN
ejpam-1518	8	5	,	,	PUNCT
ejpam-1518	8	6	analysis	analysis	NOUN
ejpam-1518	8	7	on	on	ADP
ejpam-1518	8	8	metric	metric	ADJ
ejpam-1518	8	9	spaces	space	NOUN
ejpam-1518	8	10	has	have	AUX
ejpam-1518	8	11	rapidly	rapidly	ADV
ejpam-1518	8	12	developed	develop	VERB
ejpam-1518	8	13	in	in	ADP
ejpam-1518	8	14	present	present	ADJ
ejpam-1518	8	15	time	time	NOUN
ejpam-1518	8	16	[	[	X
ejpam-1518	8	17	see	see	VERB
ejpam-1518	8	18	11	11	NUM
ejpam-1518	8	19	]	]	PUNCT
ejpam-1518	8	20	.	.	PUNCT
ejpam-1518	9	1	this	this	DET
ejpam-1518	9	2	development	development	NOUN
ejpam-1518	9	3	is	be	AUX
ejpam-1518	9	4	usually	usually	ADV
ejpam-1518	9	5	based	base	VERB
ejpam-1518	9	6	on	on	ADP
ejpam-1518	9	7	some	some	DET
ejpam-1518	9	8	generalizations	generalization	NOUN
ejpam-1518	9	9	of	of	ADP
ejpam-1518	9	10	the	the	DET
ejpam-1518	9	11	differentiability	differentiability	NOUN
ejpam-1518	9	12	.	.	PUNCT
ejpam-1518	10	1	some	some	DET
ejpam-1518	10	2	approaches	approach	NOUN
ejpam-1518	10	3	which	which	PRON
ejpam-1518	10	4	based	base	VERB
ejpam-1518	10	5	on	on	ADP
ejpam-1518	10	6	the	the	DET
ejpam-1518	10	7	convergence	convergence	NOUN
ejpam-1518	10	8	of	of	ADP
ejpam-1518	10	9	the	the	DET
ejpam-1518	10	10	metric	metric	ADJ
ejpam-1518	10	11	valued	value	VERB
ejpam-1518	10	12	sequences	sequence	NOUN
ejpam-1518	10	13	have	have	AUX
ejpam-1518	10	14	been	be	AUX
ejpam-1518	10	15	studied	study	VERB
ejpam-1518	10	16	in	in	ADP
ejpam-1518	10	17	[	[	X
ejpam-1518	10	18	6	6	NUM
ejpam-1518	10	19	]	]	PUNCT
ejpam-1518	11	1	[	[	X
ejpam-1518	11	2	see	see	VERB
ejpam-1518	11	3	also	also	ADV
ejpam-1518	11	4	1	1	NUM
ejpam-1518	11	5	,	,	PUNCT
ejpam-1518	11	6	4	4	NUM
ejpam-1518	11	7	,	,	PUNCT
ejpam-1518	11	8	5	5	NUM
ejpam-1518	11	9	]	]	PUNCT
ejpam-1518	11	10	.	.	PUNCT
ejpam-1518	12	1	but	but	CCONJ
ejpam-1518	12	2	in	in	ADP
ejpam-1518	12	3	these	these	DET
ejpam-1518	12	4	studies	study	NOUN
ejpam-1518	12	5	it	it	PRON
ejpam-1518	12	6	is	be	AUX
ejpam-1518	12	7	not	not	PART
ejpam-1518	12	8	deductive	deductive	ADJ
ejpam-1518	12	9	clear	clear	ADJ
ejpam-1518	12	10	that	that	SCONJ
ejpam-1518	12	11	the	the	DET
ejpam-1518	12	12	usual	usual	ADJ
ejpam-1518	12	13	convergence	convergence	NOUN
ejpam-1518	12	14	is	be	AUX
ejpam-1518	12	15	the	the	DET
ejpam-1518	12	16	best	good	ADJ
ejpam-1518	12	17	possible	possible	ADJ
ejpam-1518	12	18	way	way	NOUN
ejpam-1518	12	19	to	to	PART
ejpam-1518	12	20	obtain	obtain	VERB
ejpam-1518	12	21	the	the	DET
ejpam-1518	12	22	smooth	smooth	ADJ
ejpam-1518	12	23	structure	structure	NOUN
ejpam-1518	12	24	for	for	ADP
ejpam-1518	12	25	arbitrary	arbitrary	ADJ
ejpam-1518	12	26	metric	metric	ADJ
ejpam-1518	12	27	space	space	NOUN
ejpam-1518	12	28	.	.	PUNCT
ejpam-1518	13	1	a	a	DET
ejpam-1518	13	2	lot	lot	NOUN
ejpam-1518	13	3	of	of	ADP
ejpam-1518	13	4	different	different	ADJ
ejpam-1518	13	5	convergence	convergence	NOUN
ejpam-1518	13	6	methods	method	NOUN
ejpam-1518	13	7	were	be	AUX
ejpam-1518	13	8	defined	define	VERB
ejpam-1518	13	9	(	(	PUNCT
ejpam-1518	13	10	cesaro	cesaro	NOUN
ejpam-1518	13	11	,	,	PUNCT
ejpam-1518	13	12	nörlund	nörlund	NOUN
ejpam-1518	13	13	,	,	PUNCT
ejpam-1518	13	14	weighted	weight	VERB
ejpam-1518	13	15	mean	mean	NOUN
ejpam-1518	13	16	,	,	PUNCT
ejpam-1518	13	17	abel	abel	PROPN
ejpam-1518	13	18	etc	etc	X
ejpam-1518	13	19	.	.	PUNCT
ejpam-1518	13	20	)	)	PUNCT
ejpam-1518	13	21	and	and	CCONJ
ejpam-1518	13	22	applied	apply	VERB
ejpam-1518	13	23	to	to	ADP
ejpam-1518	13	24	many	many	ADJ
ejpam-1518	13	25	branches	branch	NOUN
ejpam-1518	13	26	of	of	ADP
ejpam-1518	13	27	mathematics	mathematic	NOUN
ejpam-1518	13	28	.	.	PUNCT
ejpam-1518	14	1	almost	almost	ADV
ejpam-1518	14	2	all	all	DET
ejpam-1518	14	3	convergence	convergence	NOUN
ejpam-1518	14	4	methods	method	NOUN
ejpam-1518	14	5	depend	depend	VERB
ejpam-1518	14	6	on	on	ADP
ejpam-1518	14	7	the	the	DET
ejpam-1518	14	8	algebraic	algebraic	ADJ
ejpam-1518	14	9	structure	structure	NOUN
ejpam-1518	14	10	of	of	ADP
ejpam-1518	14	11	the	the	DET
ejpam-1518	14	12	space	space	NOUN
ejpam-1518	14	13	.	.	PUNCT
ejpam-1518	15	1	it	it	PRON
ejpam-1518	15	2	is	be	AUX
ejpam-1518	15	3	clear	clear	ADJ
ejpam-1518	15	4	that	that	SCONJ
ejpam-1518	15	5	metric	metric	ADJ
ejpam-1518	15	6	space	space	NOUN
ejpam-1518	15	7	does	do	AUX
ejpam-1518	15	8	not	not	PART
ejpam-1518	15	9	have	have	VERB
ejpam-1518	15	10	the	the	DET
ejpam-1518	15	11	algebraic	algebraic	ADJ
ejpam-1518	15	12	structure	structure	NOUN
ejpam-1518	15	13	in	in	ADP
ejpam-1518	15	14	general	general	ADJ
ejpam-1518	15	15	.	.	PUNCT
ejpam-1518	16	1	so	so	ADV
ejpam-1518	16	2	,	,	PUNCT
ejpam-1518	16	3	the	the	DET
ejpam-1518	16	4	generalization	generalization	NOUN
ejpam-1518	16	5	of	of	ADP
ejpam-1518	16	6	boundedness	boundedness	NOUN
ejpam-1518	16	7	by	by	ADP
ejpam-1518	16	8	using	use	VERB
ejpam-1518	16	9	these	these	DET
ejpam-1518	16	10	methods	method	NOUN
ejpam-1518	16	11	for	for	ADP
ejpam-1518	16	12	metric	metric	ADJ
ejpam-1518	16	13	valued	value	VERB
ejpam-1518	16	14	sequences	sequence	NOUN
ejpam-1518	16	15	is	be	AUX
ejpam-1518	16	16	impossible	impossible	ADJ
ejpam-1518	16	17	.	.	PUNCT
ejpam-1518	17	1	however	however	ADV
ejpam-1518	17	2	,	,	PUNCT
ejpam-1518	17	3	the	the	DET
ejpam-1518	17	4	notion	notion	NOUN
ejpam-1518	17	5	of	of	ADP
ejpam-1518	17	6	statistical	statistical	ADJ
ejpam-1518	17	7	convergence	convergence	NOUN
ejpam-1518	17	8	is	be	AUX
ejpam-1518	17	9	easy	easy	ADJ
ejpam-1518	17	10	to	to	PART
ejpam-1518	17	11	extend	extend	VERB
ejpam-1518	17	12	for	for	ADP
ejpam-1518	17	13	arbitrary	arbitrary	ADJ
ejpam-1518	17	14	metric	metric	ADJ
ejpam-1518	17	15	spaces	space	NOUN
ejpam-1518	17	16	.	.	PUNCT
ejpam-1518	18	1	∗corresponding	∗corresponde	VERB
ejpam-1518	18	2	author	author	NOUN
ejpam-1518	18	3	.	.	PUNCT
ejpam-1518	19	1	email	email	NOUN
ejpam-1518	19	2	addresses	address	NOUN
ejpam-1518	19	3	:	:	PUNCT
ejpam-1518	19	4	mku	mku	NOUN
ejpam-1518	19	5	ukaslan	ukaslan	PROPN
ejpam-1518	19	6	�	�	PROPN
ejpam-1518	19	7	mersin.edu.tr(mkkaslan	mersin.edu.tr(mkkaslan	NOUN
ejpam-1518	19	8	�	�	PROPN
ejpam-1518	19	9	gmail	gmail	NOUN
ejpam-1518	19	10	.	.	PUNCT
ejpam-1518	20	1	om	om	PROPN
ejpam-1518	20	2	)	)	PUNCT
ejpam-1518	20	3	(	(	PUNCT
ejpam-1518	20	4	m.	m.	NOUN
ejpam-1518	20	5	küçükaslan),udeger	küçükaslan),udeger	SYM
ejpam-1518	20	6	�	�	PROPN
ejpam-1518	20	7	mersin.edu.tr(degpar	mersin.edu.tr(degpar	NOUN
ejpam-1518	20	8	�	�	NOUN
ejpam-1518	20	9	hotmail	hotmail	NOUN
ejpam-1518	20	10	.	.	PUNCT
ejpam-1518	21	1	om	om	NOUN
ejpam-1518	21	2	)	)	PUNCT
ejpam-1518	21	3	(	(	PUNCT
ejpam-1518	21	4	u.	u.	NOUN
ejpam-1518	21	5	değer	değer	NOUN
ejpam-1518	21	6	)	)	PUNCT
ejpam-1518	21	7	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1518	22	1	174	174	NUM
ejpam-1518	22	2	c	c	NOUN
ejpam-1518	22	3	©	©	PROPN
ejpam-1518	22	4	2012	2012	NUM
ejpam-1518	22	5	ejpam	ejpam	VERB
ejpam-1518	22	6	all	all	DET
ejpam-1518	22	7	rights	right	NOUN
ejpam-1518	22	8	reserved	reserve	VERB
ejpam-1518	22	9	.	.	PUNCT
ejpam-1518	23	1	m.	m.	NOUN
ejpam-1518	23	2	küçükaslan	küçükaslan	PROPN
ejpam-1518	23	3	,	,	PUNCT
ejpam-1518	23	4	u.	u.	PROPN
ejpam-1518	23	5	değer	değer	PROPN
ejpam-1518	23	6	/	/	SYM
ejpam-1518	23	7	eur	eur	PROPN
ejpam-1518	23	8	.	.	PUNCT
ejpam-1518	24	1	j.	j.	PROPN
ejpam-1518	24	2	pure	pure	PROPN
ejpam-1518	24	3	appl	appl	PROPN
ejpam-1518	24	4	.	.	PROPN
ejpam-1518	24	5	math	math	PROPN
ejpam-1518	24	6	,	,	PUNCT
ejpam-1518	24	7	5	5	NUM
ejpam-1518	24	8	(	(	PUNCT
ejpam-1518	24	9	2012	2012	NUM
ejpam-1518	24	10	)	)	PUNCT
ejpam-1518	24	11	,	,	PUNCT
ejpam-1518	24	12	174	174	NUM
ejpam-1518	24	13	-	-	SYM
ejpam-1518	24	14	186	186	NUM
ejpam-1518	24	15	175	175	NUM
ejpam-1518	24	16	the	the	DET
ejpam-1518	24	17	concept	concept	NOUN
ejpam-1518	24	18	d	d	ADJ
ejpam-1518	24	19	-	-	ADJ
ejpam-1518	24	20	statistical	statistical	ADJ
ejpam-1518	24	21	convergence	convergence	NOUN
ejpam-1518	24	22	for	for	ADP
ejpam-1518	24	23	metric	metric	ADJ
ejpam-1518	24	24	valued	value	VERB
ejpam-1518	24	25	sequences	sequence	NOUN
ejpam-1518	24	26	was	be	AUX
ejpam-1518	24	27	given	give	VERB
ejpam-1518	24	28	first	first	ADJ
ejpam-1518	24	29	time	time	NOUN
ejpam-1518	24	30	in	in	ADP
ejpam-1518	24	31	[	[	X
ejpam-1518	24	32	12	12	NUM
ejpam-1518	24	33	]	]	PUNCT
ejpam-1518	24	34	.	.	PUNCT
ejpam-1518	25	1	in	in	ADP
ejpam-1518	25	2	this	this	DET
ejpam-1518	25	3	work	work	NOUN
ejpam-1518	25	4	,	,	PUNCT
ejpam-1518	25	5	dstatistical	dstatistical	ADJ
ejpam-1518	25	6	boundedness	boundedness	NOUN
ejpam-1518	25	7	of	of	ADP
ejpam-1518	25	8	metric	metric	ADJ
ejpam-1518	25	9	valued	value	VERB
ejpam-1518	25	10	sequences	sequence	NOUN
ejpam-1518	25	11	is	be	AUX
ejpam-1518	25	12	defined	define	VERB
ejpam-1518	25	13	,	,	PUNCT
ejpam-1518	25	14	and	and	CCONJ
ejpam-1518	25	15	the	the	DET
ejpam-1518	25	16	relations	relation	NOUN
ejpam-1518	25	17	between	between	ADP
ejpam-1518	25	18	usual	usual	ADJ
ejpam-1518	25	19	boundedness	boundedness	NOUN
ejpam-1518	25	20	,	,	PUNCT
ejpam-1518	25	21	convergence	convergence	NOUN
ejpam-1518	25	22	,	,	PUNCT
ejpam-1518	25	23	dstatistical	dstatistical	ADJ
ejpam-1518	25	24	convergence	convergence	NOUN
ejpam-1518	25	25	and	and	CCONJ
ejpam-1518	25	26	d	d	ADJ
ejpam-1518	25	27	-	-	ADJ
ejpam-1518	25	28	statistical	statistical	ADJ
ejpam-1518	25	29	boundedness	boundedness	NOUN
ejpam-1518	25	30	are	be	AUX
ejpam-1518	25	31	investigated	investigate	VERB
ejpam-1518	25	32	.	.	PUNCT
ejpam-1518	26	1	let	let	VERB
ejpam-1518	26	2	(	(	PUNCT
ejpam-1518	26	3	x	x	X
ejpam-1518	26	4	,	,	PUNCT
ejpam-1518	26	5	d	d	X
ejpam-1518	26	6	)	)	PUNCT
ejpam-1518	26	7	be	be	AUX
ejpam-1518	26	8	a	a	DET
ejpam-1518	26	9	metric	metric	ADJ
ejpam-1518	26	10	space	space	NOUN
ejpam-1518	26	11	.	.	PUNCT
ejpam-1518	27	1	for	for	ADP
ejpam-1518	27	2	convenience	convenience	NOUN
ejpam-1518	27	3	denote	denote	NOUN
ejpam-1518	27	4	by	by	ADP
ejpam-1518	27	5	x̃	x̃	PROPN
ejpam-1518	27	6	the	the	DET
ejpam-1518	27	7	set	set	NOUN
ejpam-1518	27	8	of	of	ADP
ejpam-1518	27	9	all	all	DET
ejpam-1518	27	10	sequences	sequence	NOUN
ejpam-1518	27	11	of	of	ADP
ejpam-1518	27	12	points	point	NOUN
ejpam-1518	27	13	from	from	ADP
ejpam-1518	27	14	x	x	X
ejpam-1518	27	15	.	.	PUNCT
ejpam-1518	28	1	that	that	PRON
ejpam-1518	28	2	is	be	AUX
ejpam-1518	28	3	,	,	PUNCT
ejpam-1518	28	4	x̃	x̃	PROPN
ejpam-1518	28	5	=	=	PUNCT
ejpam-1518	28	6	{	{	PUNCT
ejpam-1518	29	1	x̃	x̃	PROPN
ejpam-1518	29	2	=	=	SYM
ejpam-1518	29	3	(	(	PUNCT
ejpam-1518	29	4	xn	xn	PROPN
ejpam-1518	29	5	)	)	PUNCT
ejpam-1518	29	6	:	:	PUNCT
ejpam-1518	30	1	xn	xn	PUNCT
ejpam-1518	30	2	∈	∈	PROPN
ejpam-1518	30	3	x	x	PUNCT
ejpam-1518	30	4	}	}	PUNCT
ejpam-1518	30	5	.	.	PUNCT
ejpam-1518	31	1	let	let	VERB
ejpam-1518	31	2	us	we	PRON
ejpam-1518	31	3	remember	remember	VERB
ejpam-1518	31	4	the	the	DET
ejpam-1518	31	5	usual	usual	ADJ
ejpam-1518	31	6	definition	definition	NOUN
ejpam-1518	31	7	of	of	ADP
ejpam-1518	31	8	convergence	convergence	NOUN
ejpam-1518	31	9	and	and	CCONJ
ejpam-1518	31	10	boundedness	boundedness	NOUN
ejpam-1518	31	11	in	in	ADP
ejpam-1518	31	12	any	any	DET
ejpam-1518	31	13	arbitrary	arbitrary	ADJ
ejpam-1518	31	14	metric	metric	ADJ
ejpam-1518	31	15	space	space	NOUN
ejpam-1518	31	16	:	:	PUNCT
ejpam-1518	31	17	definition	definition	NOUN
ejpam-1518	31	18	1	1	NUM
ejpam-1518	31	19	(	(	PUNCT
ejpam-1518	31	20	in	in	ADP
ejpam-1518	31	21	usual	usual	ADJ
ejpam-1518	31	22	case	case	NOUN
ejpam-1518	31	23	)	)	PUNCT
ejpam-1518	31	24	.	.	PUNCT
ejpam-1518	32	1	let	let	VERB
ejpam-1518	33	1	x̃	x̃	PROPN
ejpam-1518	33	2	=	=	SYM
ejpam-1518	33	3	(	(	PUNCT
ejpam-1518	33	4	xn	xn	X
ejpam-1518	33	5	)	)	PUNCT
ejpam-1518	33	6	∈	∈	PROPN
ejpam-1518	33	7	x̃	x̃	PROPN
ejpam-1518	33	8	be	be	AUX
ejpam-1518	33	9	a	a	DET
ejpam-1518	33	10	sequence	sequence	NOUN
ejpam-1518	33	11	.	.	PUNCT
ejpam-1518	34	1	(	(	PUNCT
ejpam-1518	34	2	i	i	NOUN
ejpam-1518	34	3	)	)	PUNCT
ejpam-1518	34	4	x̃	x̃	PROPN
ejpam-1518	34	5	is	be	AUX
ejpam-1518	34	6	called	call	VERB
ejpam-1518	34	7	convergent	convergent	NOUN
ejpam-1518	34	8	to	to	ADP
ejpam-1518	34	9	a	a	DET
ejpam-1518	34	10	point	point	NOUN
ejpam-1518	34	11	a	a	DET
ejpam-1518	34	12	∈	∈	NOUN
ejpam-1518	34	13	x	x	PUNCT
ejpam-1518	34	14	if	if	SCONJ
ejpam-1518	34	15	for	for	ADP
ejpam-1518	34	16	every	every	DET
ejpam-1518	34	17	ε	ε	PROPN
ejpam-1518	34	18	>	>	X
ejpam-1518	34	19	0	0	PUNCT
ejpam-1518	35	1	there	there	PRON
ejpam-1518	35	2	exist	exist	VERB
ejpam-1518	35	3	an	an	DET
ejpam-1518	35	4	n0	n0	X
ejpam-1518	35	5	=	=	SYM
ejpam-1518	35	6	n0(ε	n0(ε	X
ejpam-1518	35	7	)	)	PUNCT
ejpam-1518	35	8	∈	∈	PROPN
ejpam-1518	35	9	n	n	PRON
ejpam-1518	35	10	such	such	ADJ
ejpam-1518	35	11	that	that	SCONJ
ejpam-1518	35	12	d(xn	d(xn	PROPN
ejpam-1518	35	13	,	,	PUNCT
ejpam-1518	35	14	a	a	X
ejpam-1518	35	15	)	)	PUNCT
ejpam-1518	35	16	<	<	X
ejpam-1518	35	17	ε	ε	PROPN
ejpam-1518	35	18	(	(	PUNCT
ejpam-1518	35	19	1	1	NUM
ejpam-1518	35	20	)	)	PUNCT
ejpam-1518	35	21	for	for	ADP
ejpam-1518	35	22	every	every	DET
ejpam-1518	35	23	n≥	n≥	PROPN
ejpam-1518	35	24	n0	n0	PROPN
ejpam-1518	35	25	.	.	PUNCT
ejpam-1518	35	26	(	(	PUNCT
ejpam-1518	35	27	ii	ii	NOUN
ejpam-1518	35	28	)	)	PUNCT
ejpam-1518	35	29	x̃	x̃	PROPN
ejpam-1518	35	30	is	be	AUX
ejpam-1518	35	31	called	call	VERB
ejpam-1518	35	32	bounded	bounded	ADJ
ejpam-1518	35	33	if	if	SCONJ
ejpam-1518	35	34	for	for	ADP
ejpam-1518	35	35	every	every	DET
ejpam-1518	35	36	x	x	SYM
ejpam-1518	35	37	∈	∈	PROPN
ejpam-1518	35	38	x	x	PUNCT
ejpam-1518	35	39	there	there	PRON
ejpam-1518	35	40	is	be	VERB
ejpam-1518	35	41	a	a	DET
ejpam-1518	35	42	m	m	NOUN
ejpam-1518	35	43	>	>	X
ejpam-1518	35	44	0	0	NUM
ejpam-1518	35	45	such	such	ADJ
ejpam-1518	35	46	that	that	SCONJ
ejpam-1518	35	47	d(xn	d(xn	PROPN
ejpam-1518	35	48	,	,	PUNCT
ejpam-1518	35	49	x	x	X
ejpam-1518	35	50	)	)	PUNCT
ejpam-1518	35	51	<	<	X
ejpam-1518	35	52	m	m	PROPN
ejpam-1518	35	53	(	(	PUNCT
ejpam-1518	35	54	2	2	NUM
ejpam-1518	35	55	)	)	PUNCT
ejpam-1518	35	56	for	for	ADP
ejpam-1518	35	57	all	all	DET
ejpam-1518	35	58	n	n	DET
ejpam-1518	35	59	∈	∈	PROPN
ejpam-1518	35	60	n.	n.	NOUN
ejpam-1518	35	61	the	the	DET
ejpam-1518	35	62	set	set	NOUN
ejpam-1518	35	63	of	of	ADP
ejpam-1518	35	64	convergent	convergent	NOUN
ejpam-1518	35	65	and	and	CCONJ
ejpam-1518	35	66	bounded	bound	VERB
ejpam-1518	35	67	sequences	sequence	NOUN
ejpam-1518	35	68	in	in	ADP
ejpam-1518	35	69	x̃	x̃	PROPN
ejpam-1518	35	70	will	will	AUX
ejpam-1518	35	71	be	be	AUX
ejpam-1518	35	72	denoted	denote	VERB
ejpam-1518	35	73	by	by	ADP
ejpam-1518	35	74	c(x̃	c(x̃	NOUN
ejpam-1518	35	75	)	)	PUNCT
ejpam-1518	35	76	and	and	CCONJ
ejpam-1518	35	77	b(x̃	b(x̃	PROPN
ejpam-1518	35	78	)	)	PUNCT
ejpam-1518	35	79	,	,	PUNCT
ejpam-1518	35	80	respectively	respectively	ADV
ejpam-1518	35	81	.	.	PUNCT
ejpam-1518	36	1	it	it	PRON
ejpam-1518	36	2	is	be	AUX
ejpam-1518	36	3	clear	clear	ADJ
ejpam-1518	36	4	that	that	SCONJ
ejpam-1518	36	5	c(x̃	c(x̃	NOUN
ejpam-1518	36	6	)	)	PUNCT
ejpam-1518	37	1	⊂	⊂	PROPN
ejpam-1518	37	2	b(x̃	b(x̃	PROPN
ejpam-1518	37	3	)	)	PUNCT
ejpam-1518	37	4	.	.	PUNCT
ejpam-1518	38	1	but	but	CCONJ
ejpam-1518	38	2	,	,	PUNCT
ejpam-1518	38	3	in	in	ADP
ejpam-1518	38	4	general	general	ADJ
ejpam-1518	38	5	the	the	DET
ejpam-1518	38	6	inverse	inverse	NOUN
ejpam-1518	38	7	is	be	AUX
ejpam-1518	38	8	not	not	PART
ejpam-1518	38	9	true	true	ADJ
ejpam-1518	38	10	:	:	PUNCT
ejpam-1518	38	11	to	to	PART
ejpam-1518	38	12	see	see	VERB
ejpam-1518	38	13	this	this	PRON
ejpam-1518	38	14	,	,	PUNCT
ejpam-1518	38	15	take	take	VERB
ejpam-1518	38	16	into	into	PART
ejpam-1518	38	17	consider	consider	VERB
ejpam-1518	38	18	the	the	DET
ejpam-1518	38	19	sequence	sequence	NOUN
ejpam-1518	38	20	x̃	x̃	PROPN
ejpam-1518	39	1	=	=	PUNCT
ejpam-1518	40	1	(	(	PUNCT
ejpam-1518	40	2	xn	xn	PROPN
ejpam-1518	40	3	)	)	PUNCT
ejpam-1518	41	1	with	with	ADP
ejpam-1518	41	2	xn	xn	PROPN
ejpam-1518	41	3	=	=	SYM
ejpam-1518	41	4	(	(	PUNCT
ejpam-1518	41	5	x	x	X
ejpam-1518	41	6	,	,	PUNCT
ejpam-1518	41	7	n	n	CCONJ
ejpam-1518	41	8	even	even	ADV
ejpam-1518	41	9	y	y	PROPN
ejpam-1518	41	10	,	,	PUNCT
ejpam-1518	41	11	n	n	PRON
ejpam-1518	41	12	odd	odd	ADJ
ejpam-1518	41	13	for	for	ADP
ejpam-1518	41	14	an	an	DET
ejpam-1518	41	15	arbitrary	arbitrary	ADJ
ejpam-1518	41	16	x	x	NOUN
ejpam-1518	41	17	,	,	PUNCT
ejpam-1518	41	18	y	y	PROPN
ejpam-1518	41	19	∈	∈	PROPN
ejpam-1518	42	1	x	x	X
ejpam-1518	42	2	.	.	PUNCT
ejpam-1518	43	1	it	it	PRON
ejpam-1518	43	2	is	be	AUX
ejpam-1518	43	3	clear	clear	ADJ
ejpam-1518	43	4	that	that	SCONJ
ejpam-1518	43	5	x̃	x̃	PROPN
ejpam-1518	43	6	is	be	AUX
ejpam-1518	43	7	bounded	bound	VERB
ejpam-1518	43	8	,	,	PUNCT
ejpam-1518	43	9	but	but	CCONJ
ejpam-1518	43	10	it	it	PRON
ejpam-1518	43	11	is	be	AUX
ejpam-1518	43	12	not	not	PART
ejpam-1518	43	13	convergent	convergent	ADJ
ejpam-1518	43	14	.	.	PUNCT
ejpam-1518	44	1	definition	definition	NOUN
ejpam-1518	44	2	2	2	NUM
ejpam-1518	44	3	(	(	PUNCT
ejpam-1518	44	4	statistical	statistical	ADJ
ejpam-1518	44	5	case	case	NOUN
ejpam-1518	44	6	)	)	PUNCT
ejpam-1518	44	7	.	.	PUNCT
ejpam-1518	45	1	let	let	VERB
ejpam-1518	46	1	x̃	x̃	PROPN
ejpam-1518	46	2	=	=	SYM
ejpam-1518	46	3	(	(	PUNCT
ejpam-1518	46	4	xn	xn	X
ejpam-1518	46	5	)	)	PUNCT
ejpam-1518	46	6	∈	∈	PROPN
ejpam-1518	46	7	x̃	x̃	PROPN
ejpam-1518	46	8	be	be	AUX
ejpam-1518	46	9	a	a	DET
ejpam-1518	46	10	sequence	sequence	NOUN
ejpam-1518	46	11	.	.	PUNCT
ejpam-1518	47	1	(	(	PUNCT
ejpam-1518	47	2	i	i	NOUN
ejpam-1518	47	3	)	)	PUNCT
ejpam-1518	47	4	x̃	x̃	PROPN
ejpam-1518	47	5	is	be	AUX
ejpam-1518	47	6	called	call	VERB
ejpam-1518	47	7	d−statistical	d−statistical	SCONJ
ejpam-1518	48	1	convergent	convergent	NOUN
ejpam-1518	48	2	to	to	ADP
ejpam-1518	48	3	a	a	DET
ejpam-1518	48	4	point	point	NOUN
ejpam-1518	48	5	a	a	DET
ejpam-1518	48	6	∈	∈	NOUN
ejpam-1518	48	7	x	x	PUNCT
ejpam-1518	48	8	if	if	SCONJ
ejpam-1518	48	9	,	,	PUNCT
ejpam-1518	48	10	for	for	ADP
ejpam-1518	48	11	every	every	DET
ejpam-1518	48	12	ε	ε	PROPN
ejpam-1518	48	13	>	>	X
ejpam-1518	48	14	0	0	PROPN
ejpam-1518	48	15	,	,	PUNCT
ejpam-1518	49	1	lim	lim	PROPN
ejpam-1518	49	2	n→∞	n→∞	NUM
ejpam-1518	49	3	1	1	NUM
ejpam-1518	49	4	n	n	PRON
ejpam-1518	49	5	�	�	PROPN
ejpam-1518	49	6	�	�	PROPN
ejpam-1518	49	7	�	�	PROPN
ejpam-1518	49	8	k	k	NOUN
ejpam-1518	49	9	:	:	PUNCT
ejpam-1518	49	10	k	k	PROPN
ejpam-1518	49	11	≤	≤	PROPN
ejpam-1518	49	12	n	n	CCONJ
ejpam-1518	49	13	and	and	CCONJ
ejpam-1518	49	14	d(xk	d(xk	PROPN
ejpam-1518	49	15	,	,	PUNCT
ejpam-1518	49	16	a)≥	a)≥	PROPN
ejpam-1518	49	17	ε	ε	PROPN
ejpam-1518	49	18	�	�	PROPN
ejpam-1518	49	19	�	�	PROPN
ejpam-1518	49	20	=	=	SYM
ejpam-1518	49	21	0	0	NUM
ejpam-1518	49	22	(	(	PUNCT
ejpam-1518	49	23	3	3	X
ejpam-1518	49	24	)	)	PUNCT
ejpam-1518	49	25	is	be	AUX
ejpam-1518	49	26	satisfied	satisfied	ADJ
ejpam-1518	49	27	.	.	PUNCT
ejpam-1518	50	1	(	(	PUNCT
ejpam-1518	50	2	ii	ii	NOUN
ejpam-1518	50	3	)	)	PUNCT
ejpam-1518	51	1	x̃	x̃	PROPN
ejpam-1518	51	2	is	be	AUX
ejpam-1518	51	3	called	call	VERB
ejpam-1518	51	4	d	d	ADJ
ejpam-1518	51	5	-	-	ADJ
ejpam-1518	51	6	statistical	statistical	ADJ
ejpam-1518	51	7	bounded	bound	VERB
ejpam-1518	51	8	if	if	SCONJ
ejpam-1518	51	9	,	,	PUNCT
ejpam-1518	51	10	for	for	ADP
ejpam-1518	51	11	an	an	DET
ejpam-1518	51	12	arbitrary	arbitrary	ADJ
ejpam-1518	51	13	x	x	SYM
ejpam-1518	51	14	∈	∈	PROPN
ejpam-1518	51	15	x	x	PUNCT
ejpam-1518	51	16	there	there	PRON
ejpam-1518	51	17	is	be	VERB
ejpam-1518	51	18	a	a	DET
ejpam-1518	51	19	m	m	NOUN
ejpam-1518	51	20	>	>	X
ejpam-1518	51	21	0	0	NUM
ejpam-1518	51	22	such	such	ADJ
ejpam-1518	51	23	that	that	SCONJ
ejpam-1518	51	24	lim	lim	PROPN
ejpam-1518	51	25	n→∞	n→∞	NUM
ejpam-1518	51	26	1	1	NUM
ejpam-1518	51	27	n	n	PRON
ejpam-1518	51	28	�	�	PROPN
ejpam-1518	51	29	�	�	PROPN
ejpam-1518	51	30	�	�	PROPN
ejpam-1518	51	31	k	k	NOUN
ejpam-1518	51	32	:	:	PUNCT
ejpam-1518	51	33	k	k	PROPN
ejpam-1518	51	34	≤	≤	PROPN
ejpam-1518	51	35	n	n	CCONJ
ejpam-1518	51	36	and	and	CCONJ
ejpam-1518	51	37	d(xk	d(xk	PROPN
ejpam-1518	51	38	,	,	PUNCT
ejpam-1518	51	39	x)≥	x)≥	PROPN
ejpam-1518	51	40	m	m	PROPN
ejpam-1518	51	41	�	�	PROPN
ejpam-1518	51	42	�	�	NOUN
ejpam-1518	51	43	=	=	SYM
ejpam-1518	51	44	0	0	NUM
ejpam-1518	51	45	(	(	PUNCT
ejpam-1518	51	46	4	4	NUM
ejpam-1518	51	47	)	)	PUNCT
ejpam-1518	51	48	is	be	AUX
ejpam-1518	51	49	satisfied	satisfied	ADJ
ejpam-1518	51	50	.	.	PUNCT
ejpam-1518	52	1	m.	m.	NOUN
ejpam-1518	52	2	küçükaslan	küçükaslan	PROPN
ejpam-1518	52	3	,	,	PUNCT
ejpam-1518	52	4	u.	u.	PROPN
ejpam-1518	52	5	değer	değer	PROPN
ejpam-1518	52	6	/	/	SYM
ejpam-1518	52	7	eur	eur	PROPN
ejpam-1518	52	8	.	.	PUNCT
ejpam-1518	53	1	j.	j.	PROPN
ejpam-1518	53	2	pure	pure	PROPN
ejpam-1518	53	3	appl	appl	PROPN
ejpam-1518	53	4	.	.	PROPN
ejpam-1518	53	5	math	math	PROPN
ejpam-1518	53	6	,	,	PUNCT
ejpam-1518	53	7	5	5	NUM
ejpam-1518	53	8	(	(	PUNCT
ejpam-1518	53	9	2012	2012	NUM
ejpam-1518	53	10	)	)	PUNCT
ejpam-1518	53	11	,	,	PUNCT
ejpam-1518	53	12	174	174	NUM
ejpam-1518	53	13	-	-	SYM
ejpam-1518	53	14	186	186	NUM
ejpam-1518	53	15	176	176	NUM
ejpam-1518	53	16	in	in	ADP
ejpam-1518	53	17	(	(	PUNCT
ejpam-1518	53	18	3	3	NUM
ejpam-1518	53	19	)	)	PUNCT
ejpam-1518	53	20	and	and	CCONJ
ejpam-1518	53	21	later	later	ADV
ejpam-1518	53	22	|b|	|b|	PROPN
ejpam-1518	53	23	denotes	denote	VERB
ejpam-1518	53	24	the	the	DET
ejpam-1518	53	25	number	number	NOUN
ejpam-1518	53	26	of	of	ADP
ejpam-1518	53	27	elements	element	NOUN
ejpam-1518	53	28	of	of	ADP
ejpam-1518	53	29	the	the	DET
ejpam-1518	53	30	set	set	PROPN
ejpam-1518	53	31	b.	b.	PROPN
ejpam-1518	53	32	the	the	DET
ejpam-1518	53	33	set	set	NOUN
ejpam-1518	53	34	of	of	ADP
ejpam-1518	53	35	d	d	ADJ
ejpam-1518	53	36	-	-	ADJ
ejpam-1518	53	37	statistical	statistical	ADJ
ejpam-1518	53	38	convergent	convergent	NOUN
ejpam-1518	53	39	sequences	sequence	NOUN
ejpam-1518	53	40	and	and	CCONJ
ejpam-1518	53	41	d	d	ADJ
ejpam-1518	53	42	-	-	ADJ
ejpam-1518	53	43	statistical	statistical	ADJ
ejpam-1518	53	44	bounded	bounded	ADJ
ejpam-1518	53	45	sequences	sequence	NOUN
ejpam-1518	53	46	in	in	ADP
ejpam-1518	53	47	x̃	x̃	PROPN
ejpam-1518	53	48	will	will	AUX
ejpam-1518	53	49	be	be	AUX
ejpam-1518	53	50	denoted	denote	VERB
ejpam-1518	53	51	by	by	ADP
ejpam-1518	53	52	c	c	PROPN
ejpam-1518	53	53	d	d	NOUN
ejpam-1518	53	54	st(x̃	st(x̃	PROPN
ejpam-1518	53	55	)	)	PUNCT
ejpam-1518	53	56	and	and	CCONJ
ejpam-1518	53	57	bd	bd	PROPN
ejpam-1518	53	58	st(x̃	st(x̃	NOUN
ejpam-1518	53	59	)	)	PUNCT
ejpam-1518	53	60	,	,	PUNCT
ejpam-1518	53	61	respectively	respectively	ADV
ejpam-1518	53	62	.	.	PUNCT
ejpam-1518	54	1	definition	definition	NOUN
ejpam-1518	54	2	3	3	NUM
ejpam-1518	54	3	(	(	PUNCT
ejpam-1518	54	4	asymptotic	asymptotic	ADJ
ejpam-1518	54	5	density	density	NOUN
ejpam-1518	54	6	)	)	PUNCT
ejpam-1518	54	7	.	.	PUNCT
ejpam-1518	55	1	(	(	PUNCT
ejpam-1518	55	2	i	i	NOUN
ejpam-1518	55	3	)	)	PUNCT
ejpam-1518	55	4	let	let	VERB
ejpam-1518	55	5	k	k	PROPN
ejpam-1518	55	6	⊆	⊆	NUM
ejpam-1518	55	7	n	n	NOUN
ejpam-1518	55	8	and	and	CCONJ
ejpam-1518	55	9	δ(k	δ(k	NOUN
ejpam-1518	55	10	)	)	PUNCT
ejpam-1518	55	11	:	:	PUNCT
ejpam-1518	56	1	=	=	PUNCT
ejpam-1518	56	2	lim	lim	PROPN
ejpam-1518	56	3	n→∞	n→∞	NUM
ejpam-1518	56	4	1	1	NUM
ejpam-1518	56	5	n	n	PROPN
ejpam-1518	56	6	|k(n)|	|k(n)|	PROPN
ejpam-1518	56	7	,	,	PUNCT
ejpam-1518	56	8	where	where	SCONJ
ejpam-1518	56	9	k(n	k(n	X
ejpam-1518	56	10	)	)	PUNCT
ejpam-1518	56	11	:	:	PUNCT
ejpam-1518	56	12	=	=	SYM
ejpam-1518	56	13	{	{	PUNCT
ejpam-1518	56	14	k	k	PROPN
ejpam-1518	56	15	∈	∈	PROPN
ejpam-1518	56	16	k	k	X
ejpam-1518	56	17	:	:	PUNCT
ejpam-1518	56	18	k	k	PROPN
ejpam-1518	56	19	≤	≤	PROPN
ejpam-1518	56	20	n	n	CCONJ
ejpam-1518	56	21	}	}	PUNCT
ejpam-1518	56	22	.	.	PUNCT
ejpam-1518	57	1	if	if	SCONJ
ejpam-1518	57	2	the	the	DET
ejpam-1518	57	3	limit	limit	NOUN
ejpam-1518	57	4	exists	exist	VERB
ejpam-1518	57	5	and	and	CCONJ
ejpam-1518	57	6	finite	finite	NOUN
ejpam-1518	57	7	,	,	PUNCT
ejpam-1518	57	8	then	then	ADV
ejpam-1518	57	9	the	the	DET
ejpam-1518	57	10	number	number	NOUN
ejpam-1518	57	11	δ(k	δ(k	NOUN
ejpam-1518	57	12	)	)	PUNCT
ejpam-1518	57	13	is	be	AUX
ejpam-1518	57	14	called	call	VERB
ejpam-1518	57	15	asymptotic	asymptotic	ADJ
ejpam-1518	57	16	density	density	NOUN
ejpam-1518	57	17	of	of	ADP
ejpam-1518	57	18	the	the	DET
ejpam-1518	57	19	set	set	NOUN
ejpam-1518	57	20	k	k	PROPN
ejpam-1518	58	1	[	[	X
ejpam-1518	58	2	13	13	NUM
ejpam-1518	58	3	]	]	PUNCT
ejpam-1518	58	4	.	.	PUNCT
ejpam-1518	59	1	(	(	PUNCT
ejpam-1518	59	2	ii	ii	NOUN
ejpam-1518	59	3	)	)	PUNCT
ejpam-1518	59	4	if	if	SCONJ
ejpam-1518	59	5	δ(k	δ(k	NOUN
ejpam-1518	59	6	)	)	PUNCT
ejpam-1518	59	7	=	=	SYM
ejpam-1518	60	1	1	1	NUM
ejpam-1518	60	2	then	then	ADV
ejpam-1518	60	3	the	the	DET
ejpam-1518	60	4	set	set	NOUN
ejpam-1518	60	5	k	k	PROPN
ejpam-1518	60	6	⊆	⊆	NUM
ejpam-1518	60	7	n	n	NUM
ejpam-1518	60	8	is	be	AUX
ejpam-1518	60	9	called	call	VERB
ejpam-1518	60	10	a	a	DET
ejpam-1518	60	11	statistical	statistical	ADJ
ejpam-1518	60	12	dense	dense	ADJ
ejpam-1518	60	13	subset	subset	NOUN
ejpam-1518	60	14	of	of	ADP
ejpam-1518	60	15	n	n	PROPN
ejpam-1518	60	16	[	[	X
ejpam-1518	60	17	7	7	NUM
ejpam-1518	60	18	]	]	PUNCT
ejpam-1518	60	19	.	.	PUNCT
ejpam-1518	61	1	2	2	X
ejpam-1518	61	2	.	.	X
ejpam-1518	61	3	main	main	ADJ
ejpam-1518	61	4	theorems	theorem	NOUN
ejpam-1518	61	5	and	and	CCONJ
ejpam-1518	61	6	their	their	PRON
ejpam-1518	61	7	proofs	proof	NOUN
ejpam-1518	61	8	the	the	DET
ejpam-1518	61	9	relation	relation	NOUN
ejpam-1518	61	10	between	between	ADP
ejpam-1518	61	11	bounded	bounded	ADJ
ejpam-1518	61	12	sequences	sequence	NOUN
ejpam-1518	61	13	and	and	CCONJ
ejpam-1518	61	14	convergent	convergent	ADJ
ejpam-1518	61	15	sequences	sequence	NOUN
ejpam-1518	61	16	in	in	ADP
ejpam-1518	61	17	an	an	DET
ejpam-1518	61	18	arbitrary	arbitrary	ADJ
ejpam-1518	61	19	metric	metric	ADJ
ejpam-1518	61	20	space	space	NOUN
ejpam-1518	61	21	is	be	AUX
ejpam-1518	61	22	known	know	VERB
ejpam-1518	61	23	.	.	PUNCT
ejpam-1518	62	1	how	how	SCONJ
ejpam-1518	62	2	will	will	AUX
ejpam-1518	62	3	be	be	AUX
ejpam-1518	62	4	it	it	PRON
ejpam-1518	62	5	for	for	ADP
ejpam-1518	62	6	d−	d−	PROPN
ejpam-1518	62	7	statistical	statistical	ADJ
ejpam-1518	62	8	boundedness	boundedness	NOUN
ejpam-1518	62	9	and	and	CCONJ
ejpam-1518	62	10	d−	d−	ADJ
ejpam-1518	62	11	statistical	statistical	ADJ
ejpam-1518	62	12	convergence	convergence	NOUN
ejpam-1518	62	13	?	?	PUNCT
ejpam-1518	63	1	in	in	ADP
ejpam-1518	63	2	this	this	DET
ejpam-1518	63	3	section	section	NOUN
ejpam-1518	63	4	,	,	PUNCT
ejpam-1518	63	5	we	we	PRON
ejpam-1518	63	6	will	will	AUX
ejpam-1518	63	7	answer	answer	VERB
ejpam-1518	63	8	this	this	DET
ejpam-1518	63	9	question	question	NOUN
ejpam-1518	63	10	and	and	CCONJ
ejpam-1518	63	11	give	give	VERB
ejpam-1518	63	12	some	some	DET
ejpam-1518	63	13	relations	relation	NOUN
ejpam-1518	63	14	between	between	ADP
ejpam-1518	63	15	d−	d−	PROPN
ejpam-1518	63	16	statistical	statistical	ADJ
ejpam-1518	63	17	boundedness	boundedness	NOUN
ejpam-1518	63	18	and	and	CCONJ
ejpam-1518	63	19	d−	d−	PROPN
ejpam-1518	63	20	statistical	statistical	ADJ
ejpam-1518	63	21	convergence	convergence	NOUN
ejpam-1518	63	22	and	and	CCONJ
ejpam-1518	63	23	with	with	ADP
ejpam-1518	63	24	usual	usual	ADJ
ejpam-1518	63	25	boundedness	boundedness	NOUN
ejpam-1518	63	26	and	and	CCONJ
ejpam-1518	63	27	convergence	convergence	NOUN
ejpam-1518	63	28	.	.	PUNCT
ejpam-1518	64	1	theorem	theorem	NOUN
ejpam-1518	64	2	1	1	NUM
ejpam-1518	64	3	.	.	PUNCT
ejpam-1518	65	1	let	let	AUX
ejpam-1518	65	2	(	(	PUNCT
ejpam-1518	65	3	x	x	X
ejpam-1518	65	4	,	,	PUNCT
ejpam-1518	65	5	d	d	X
ejpam-1518	65	6	)	)	PUNCT
ejpam-1518	65	7	be	be	AUX
ejpam-1518	65	8	a	a	DET
ejpam-1518	65	9	metric	metric	ADJ
ejpam-1518	65	10	space	space	NOUN
ejpam-1518	65	11	and	and	CCONJ
ejpam-1518	66	1	x̃	x̃	PROPN
ejpam-1518	66	2	=	=	SYM
ejpam-1518	66	3	(	(	PUNCT
ejpam-1518	66	4	xn	xn	X
ejpam-1518	66	5	)	)	PUNCT
ejpam-1518	66	6	∈	∈	PROPN
ejpam-1518	66	7	x̃	x̃	PROPN
ejpam-1518	66	8	.	.	PUNCT
ejpam-1518	67	1	the	the	DET
ejpam-1518	67	2	following	follow	VERB
ejpam-1518	67	3	statements	statement	NOUN
ejpam-1518	67	4	hold	hold	VERB
ejpam-1518	67	5	:	:	PUNCT
ejpam-1518	67	6	(	(	PUNCT
ejpam-1518	67	7	i	i	NOUN
ejpam-1518	67	8	)	)	PUNCT
ejpam-1518	67	9	if	if	SCONJ
ejpam-1518	67	10	x̃	x̃	PROPN
ejpam-1518	67	11	is	be	AUX
ejpam-1518	67	12	bounded	bound	VERB
ejpam-1518	67	13	,	,	PUNCT
ejpam-1518	67	14	then	then	ADV
ejpam-1518	67	15	x̃	x̃	PROPN
ejpam-1518	67	16	is	be	AUX
ejpam-1518	67	17	dstatistical	dstatistical	ADJ
ejpam-1518	67	18	bounded	bound	VERB
ejpam-1518	67	19	.	.	PUNCT
ejpam-1518	68	1	(	(	PUNCT
ejpam-1518	68	2	ii	ii	NOUN
ejpam-1518	68	3	)	)	PUNCT
ejpam-1518	68	4	if	if	SCONJ
ejpam-1518	68	5	x̃	x̃	PROPN
ejpam-1518	68	6	is	be	AUX
ejpam-1518	68	7	dstatistical	dstatistical	ADJ
ejpam-1518	68	8	convergent	convergent	NOUN
ejpam-1518	68	9	to	to	ADP
ejpam-1518	68	10	a	a	DET
ejpam-1518	68	11	∈	∈	NOUN
ejpam-1518	68	12	x	x	X
ejpam-1518	68	13	,	,	PUNCT
ejpam-1518	68	14	then	then	ADV
ejpam-1518	68	15	x̃	x̃	PROPN
ejpam-1518	68	16	is	be	AUX
ejpam-1518	68	17	dstatistical	dstatistical	ADJ
ejpam-1518	68	18	bounded	bound	VERB
ejpam-1518	68	19	.	.	PUNCT
ejpam-1518	69	1	proof	proof	NOUN
ejpam-1518	69	2	.	.	PUNCT
ejpam-1518	70	1	(	(	PUNCT
ejpam-1518	70	2	i	i	NOUN
ejpam-1518	70	3	)	)	PUNCT
ejpam-1518	70	4	if	if	SCONJ
ejpam-1518	70	5	x̃	x̃	PROPN
ejpam-1518	70	6	is	be	AUX
ejpam-1518	70	7	bounded	bound	VERB
ejpam-1518	70	8	,	,	PUNCT
ejpam-1518	70	9	then	then	ADV
ejpam-1518	70	10	for	for	ADP
ejpam-1518	70	11	an	an	DET
ejpam-1518	70	12	arbitrary	arbitrary	ADJ
ejpam-1518	70	13	x	x	SYM
ejpam-1518	70	14	∈	∈	PROPN
ejpam-1518	70	15	x	x	PUNCT
ejpam-1518	70	16	there	there	PRON
ejpam-1518	70	17	is	be	VERB
ejpam-1518	70	18	m	m	PROPN
ejpam-1518	70	19	>	>	X
ejpam-1518	70	20	0	0	NUM
ejpam-1518	70	21	such	such	ADJ
ejpam-1518	70	22	that	that	PRON
ejpam-1518	70	23	for	for	ADP
ejpam-1518	70	24	all	all	DET
ejpam-1518	70	25	n	n	PRON
ejpam-1518	70	26	∈	∈	PROPN
ejpam-1518	70	27	n	n	CCONJ
ejpam-1518	70	28	d(xn	d(xn	PROPN
ejpam-1518	70	29	,	,	PUNCT
ejpam-1518	70	30	x	x	X
ejpam-1518	70	31	)	)	PUNCT
ejpam-1518	70	32	<	<	X
ejpam-1518	70	33	m	m	NOUN
ejpam-1518	70	34	.	.	PUNCT
ejpam-1518	71	1	that	that	PRON
ejpam-1518	71	2	is	is	ADV
ejpam-1518	71	3	,	,	PUNCT
ejpam-1518	71	4	{	{	PUNCT
ejpam-1518	71	5	k	k	NOUN
ejpam-1518	71	6	:	:	PUNCT
ejpam-1518	71	7	k	k	PROPN
ejpam-1518	71	8	≤	≤	PROPN
ejpam-1518	71	9	n	n	CCONJ
ejpam-1518	71	10	,	,	PUNCT
ejpam-1518	71	11	d(xk	d(xk	PROPN
ejpam-1518	71	12	,	,	PUNCT
ejpam-1518	71	13	x)≥	x)≥	PROPN
ejpam-1518	71	14	m	m	PROPN
ejpam-1518	71	15	}	}	PUNCT
ejpam-1518	71	16	=	=	SYM
ejpam-1518	71	17	;	;	PUNCT
ejpam-1518	71	18	.	.	PUNCT
ejpam-1518	72	1	hence	hence	ADV
ejpam-1518	72	2	,	,	PUNCT
ejpam-1518	72	3	we	we	PRON
ejpam-1518	72	4	have	have	VERB
ejpam-1518	72	5	lim	lim	PROPN
ejpam-1518	72	6	n→∞	n→∞	NUM
ejpam-1518	72	7	1	1	NUM
ejpam-1518	72	8	n	n	PRON
ejpam-1518	72	9	�	�	PROPN
ejpam-1518	72	10	�	�	PROPN
ejpam-1518	72	11	�	�	PROPN
ejpam-1518	72	12	k	k	NOUN
ejpam-1518	72	13	:	:	PUNCT
ejpam-1518	72	14	k	k	PROPN
ejpam-1518	72	15	≤	≤	PROPN
ejpam-1518	72	16	n	n	CCONJ
ejpam-1518	72	17	and	and	CCONJ
ejpam-1518	72	18	d(xk	d(xk	PROPN
ejpam-1518	72	19	,	,	PUNCT
ejpam-1518	72	20	x)≥	x)≥	PROPN
ejpam-1518	72	21	m	m	PROPN
ejpam-1518	72	22	�	�	PROPN
ejpam-1518	72	23	�	�	PROPN
ejpam-1518	72	24	=	=	SYM
ejpam-1518	72	25	0	0	PROPN
ejpam-1518	72	26	.	.	PUNCT
ejpam-1518	72	27	(	(	PUNCT
ejpam-1518	72	28	ii	ii	NOUN
ejpam-1518	72	29	)	)	PUNCT
ejpam-1518	72	30	for	for	ADP
ejpam-1518	72	31	any	any	DET
ejpam-1518	72	32	arbitrary	arbitrary	ADJ
ejpam-1518	72	33	ε	ε	PROPN
ejpam-1518	72	34	>	>	X
ejpam-1518	72	35	0	0	PUNCT
ejpam-1518	73	1	and	and	CCONJ
ejpam-1518	73	2	large	large	ADJ
ejpam-1518	73	3	m	m	PROPN
ejpam-1518	73	4	>	>	X
ejpam-1518	73	5	0	0	NUM
ejpam-1518	74	1	we	we	PRON
ejpam-1518	74	2	have	have	VERB
ejpam-1518	74	3	�	�	PROPN
ejpam-1518	74	4	k	k	NOUN
ejpam-1518	74	5	:	:	PUNCT
ejpam-1518	75	1	k	k	PROPN
ejpam-1518	75	2	≤	≤	PROPN
ejpam-1518	75	3	n	n	CCONJ
ejpam-1518	75	4	and	and	CCONJ
ejpam-1518	75	5	d(xk	d(xk	PROPN
ejpam-1518	75	6	,	,	PUNCT
ejpam-1518	75	7	a	a	PRON
ejpam-1518	75	8	)	)	PUNCT
ejpam-1518	75	9	≥	≥	NOUN
ejpam-1518	75	10	m	m	PROPN
ejpam-1518	75	11	⊂	⊂	PROPN
ejpam-1518	75	12	�	�	PROPN
ejpam-1518	75	13	k	k	PROPN
ejpam-1518	75	14	:	:	PUNCT
ejpam-1518	75	15	k	k	PROPN
ejpam-1518	75	16	≤	≤	PROPN
ejpam-1518	75	17	n	n	CCONJ
ejpam-1518	75	18	and	and	CCONJ
ejpam-1518	75	19	d(xk	d(xk	PROPN
ejpam-1518	75	20	,	,	PUNCT
ejpam-1518	75	21	a	a	PRON
ejpam-1518	75	22	)	)	PUNCT
ejpam-1518	75	23	≥	≥	NOUN
ejpam-1518	75	24	ε	ε	PROPN
ejpam-1518	75	25	.	.	PUNCT
ejpam-1518	76	1	this	this	DET
ejpam-1518	76	2	inclusion	inclusion	NOUN
ejpam-1518	76	3	gives	give	VERB
ejpam-1518	76	4	|	|	PRON
ejpam-1518	76	5	�	�	PROPN
ejpam-1518	76	6	k	k	NOUN
ejpam-1518	76	7	:	:	PUNCT
ejpam-1518	76	8	k	k	PROPN
ejpam-1518	76	9	≤	≤	PROPN
ejpam-1518	76	10	n	n	CCONJ
ejpam-1518	76	11	and	and	CCONJ
ejpam-1518	76	12	d(xk	d(xk	PROPN
ejpam-1518	76	13	,	,	PUNCT
ejpam-1518	76	14	a)≥	a)≥	PROPN
ejpam-1518	76	15	m	m	PROPN
ejpam-1518	76	16	|	|	ADV
ejpam-1518	76	17	≤	≤	PUNCT
ejpam-1518	76	18	|	|	NOUN
ejpam-1518	76	19	�	�	SYM
ejpam-1518	76	20	k	k	NOUN
ejpam-1518	76	21	:	:	PUNCT
ejpam-1518	76	22	k	k	PROPN
ejpam-1518	76	23	≤	≤	PROPN
ejpam-1518	76	24	n	n	CCONJ
ejpam-1518	76	25	and	and	CCONJ
ejpam-1518	76	26	d(xk	d(xk	PROPN
ejpam-1518	76	27	,	,	PUNCT
ejpam-1518	76	28	a	a	PRON
ejpam-1518	76	29	)	)	PUNCT
ejpam-1518	76	30	≥	≥	NOUN
ejpam-1518	76	31	ε	ε	PROPN
ejpam-1518	76	32	|	|	NOUN
ejpam-1518	76	33	.	.	PUNCT
ejpam-1518	77	1	m.	m.	NOUN
ejpam-1518	77	2	küçükaslan	küçükaslan	PROPN
ejpam-1518	77	3	,	,	PUNCT
ejpam-1518	77	4	u.	u.	PROPN
ejpam-1518	77	5	değer	değer	PROPN
ejpam-1518	77	6	/	/	SYM
ejpam-1518	77	7	eur	eur	PROPN
ejpam-1518	77	8	.	.	PUNCT
ejpam-1518	78	1	j.	j.	PROPN
ejpam-1518	78	2	pure	pure	PROPN
ejpam-1518	78	3	appl	appl	PROPN
ejpam-1518	78	4	.	.	PROPN
ejpam-1518	78	5	math	math	PROPN
ejpam-1518	78	6	,	,	PUNCT
ejpam-1518	78	7	5	5	NUM
ejpam-1518	78	8	(	(	PUNCT
ejpam-1518	78	9	2012	2012	NUM
ejpam-1518	78	10	)	)	PUNCT
ejpam-1518	78	11	,	,	PUNCT
ejpam-1518	78	12	174	174	NUM
ejpam-1518	78	13	-	-	SYM
ejpam-1518	78	14	186	186	NUM
ejpam-1518	78	15	177	177	NUM
ejpam-1518	78	16	from	from	ADP
ejpam-1518	78	17	this	this	DET
ejpam-1518	78	18	inequality	inequality	NOUN
ejpam-1518	78	19	,	,	PUNCT
ejpam-1518	78	20	we	we	PRON
ejpam-1518	78	21	have	have	VERB
ejpam-1518	78	22	lim	lim	PROPN
ejpam-1518	78	23	n→∞	n→∞	NUM
ejpam-1518	78	24	1	1	NUM
ejpam-1518	78	25	n	n	PRON
ejpam-1518	78	26	�	�	PROPN
ejpam-1518	78	27	�	�	PROPN
ejpam-1518	78	28	�	�	PROPN
ejpam-1518	78	29	k	k	NOUN
ejpam-1518	78	30	:	:	PUNCT
ejpam-1518	78	31	k	k	PROPN
ejpam-1518	78	32	≤	≤	PROPN
ejpam-1518	78	33	n	n	CCONJ
ejpam-1518	78	34	and	and	CCONJ
ejpam-1518	78	35	d(xk	d(xk	PROPN
ejpam-1518	78	36	,	,	PUNCT
ejpam-1518	78	37	a	a	PRON
ejpam-1518	78	38	)	)	PUNCT
ejpam-1518	78	39	≥	≥	NOUN
ejpam-1518	78	40	m	m	PROPN
ejpam-1518	78	41	�	�	PROPN
ejpam-1518	78	42	�	�	PROPN
ejpam-1518	78	43	=	=	SYM
ejpam-1518	78	44	0	0	NUM
ejpam-1518	78	45	for	for	ADP
ejpam-1518	78	46	every	every	DET
ejpam-1518	78	47	ε	ε	PROPN
ejpam-1518	78	48	>	>	X
ejpam-1518	78	49	0	0	PROPN
ejpam-1518	78	50	.	.	PUNCT
ejpam-1518	79	1	this	this	PRON
ejpam-1518	79	2	gives	give	VERB
ejpam-1518	79	3	the	the	DET
ejpam-1518	79	4	proof	proof	NOUN
ejpam-1518	79	5	.	.	PUNCT
ejpam-1518	80	1	remark	remark	NOUN
ejpam-1518	80	2	1	1	NUM
ejpam-1518	80	3	.	.	PUNCT
ejpam-1518	81	1	the	the	DET
ejpam-1518	81	2	inverse	inverse	NOUN
ejpam-1518	81	3	of	of	ADP
ejpam-1518	81	4	(	(	PUNCT
ejpam-1518	81	5	i	i	NOUN
ejpam-1518	81	6	)	)	PUNCT
ejpam-1518	81	7	in	in	ADP
ejpam-1518	81	8	theorem	theorem	NOUN
ejpam-1518	81	9	1	1	NUM
ejpam-1518	81	10	is	be	AUX
ejpam-1518	81	11	not	not	PART
ejpam-1518	81	12	true	true	ADJ
ejpam-1518	81	13	in	in	ADP
ejpam-1518	81	14	general	general	ADJ
ejpam-1518	81	15	.	.	PUNCT
ejpam-1518	81	16	example	example	NOUN
ejpam-1518	82	1	1	1	NUM
ejpam-1518	82	2	.	.	PUNCT
ejpam-1518	82	3	let	let	VERB
ejpam-1518	82	4	us	we	PRON
ejpam-1518	82	5	take	take	VERB
ejpam-1518	82	6	x	x	PUNCT
ejpam-1518	82	7	=	=	PUNCT
ejpam-1518	82	8	r	r	NOUN
ejpam-1518	82	9	with	with	ADP
ejpam-1518	82	10	usual	usual	ADJ
ejpam-1518	82	11	metric	metric	ADJ
ejpam-1518	82	12	d(x	d(x	NOUN
ejpam-1518	82	13	,	,	PUNCT
ejpam-1518	82	14	y	y	PROPN
ejpam-1518	82	15	)	)	PUNCT
ejpam-1518	82	16	:	:	PUNCT
ejpam-1518	82	17	=	=	X
ejpam-1518	82	18	|x	|x	X
ejpam-1518	82	19	−	−	VERB
ejpam-1518	82	20	y|	y|	NOUN
ejpam-1518	82	21	and	and	CCONJ
ejpam-1518	82	22	consider	consider	VERB
ejpam-1518	82	23	the	the	DET
ejpam-1518	82	24	sequence	sequence	NOUN
ejpam-1518	82	25	x̃	x̃	PROPN
ejpam-1518	83	1	=	=	PUNCT
ejpam-1518	84	1	(	(	PUNCT
ejpam-1518	84	2	xn	xn	X
ejpam-1518	84	3	)	)	PUNCT
ejpam-1518	85	1	=	=	SYM
ejpam-1518	85	2	(	(	PUNCT
ejpam-1518	85	3	1,1,−1,2,−1,1,−1,1,3	1,1,−1,2,−1,1,−1,1,3	PROPN
ejpam-1518	85	4	,	,	PUNCT
ejpam-1518	85	5	.	.	PUNCT
ejpam-1518	85	6	.	.	PUNCT
ejpam-1518	85	7	.	.	PUNCT
ejpam-1518	85	8	)	)	PUNCT
ejpam-1518	86	1	with	with	ADP
ejpam-1518	86	2	xn	xn	PROPN
ejpam-1518	86	3	:	:	PUNCT
ejpam-1518	86	4	=	=	SYM
ejpam-1518	86	5	(	(	PUNCT
ejpam-1518	86	6	k	k	X
ejpam-1518	86	7	,	,	PUNCT
ejpam-1518	86	8	n=	n=	ADJ
ejpam-1518	86	9	k2	k2	PROPN
ejpam-1518	86	10	,	,	PUNCT
ejpam-1518	86	11	(	(	PUNCT
ejpam-1518	86	12	−1)n	−1)n	NOUN
ejpam-1518	86	13	,	,	PUNCT
ejpam-1518	86	14	n	n	CCONJ
ejpam-1518	86	15	6=	6=	X
ejpam-1518	86	16	k2	k2	ADJ
ejpam-1518	86	17	.	.	PUNCT
ejpam-1518	87	1	it	it	PRON
ejpam-1518	87	2	is	be	AUX
ejpam-1518	87	3	clear	clear	ADJ
ejpam-1518	87	4	that	that	SCONJ
ejpam-1518	87	5	x̃	x̃	PROPN
ejpam-1518	87	6	is	be	AUX
ejpam-1518	87	7	not	not	PART
ejpam-1518	87	8	bounded	bound	VERB
ejpam-1518	87	9	in	in	ADP
ejpam-1518	87	10	usual	usual	ADJ
ejpam-1518	87	11	case	case	NOUN
ejpam-1518	87	12	.	.	PUNCT
ejpam-1518	88	1	let	let	VERB
ejpam-1518	88	2	’s	’s	NOUN
ejpam-1518	88	3	show	show	VERB
ejpam-1518	88	4	that	that	SCONJ
ejpam-1518	88	5	x̃	x̃	PROPN
ejpam-1518	88	6	is	be	AUX
ejpam-1518	88	7	d	d	ADJ
ejpam-1518	88	8	-	-	ADJ
ejpam-1518	88	9	statistical	statistical	ADJ
ejpam-1518	88	10	bounded	bound	VERB
ejpam-1518	88	11	.	.	PUNCT
ejpam-1518	89	1	for	for	ADP
ejpam-1518	89	2	this	this	DET
ejpam-1518	89	3	aim	aim	NOUN
ejpam-1518	89	4	,	,	PUNCT
ejpam-1518	89	5	choose	choose	VERB
ejpam-1518	89	6	x	x	X
ejpam-1518	89	7	=	=	SYM
ejpam-1518	89	8	0	0	NUM
ejpam-1518	89	9	and	and	CCONJ
ejpam-1518	89	10	a	a	DET
ejpam-1518	89	11	sufficiently	sufficiently	ADV
ejpam-1518	89	12	large	large	ADJ
ejpam-1518	89	13	m	m	VERB
ejpam-1518	89	14	>	>	X
ejpam-1518	89	15	0	0	NUM
ejpam-1518	89	16	.	.	PUNCT
ejpam-1518	90	1	then	then	ADV
ejpam-1518	90	2	,	,	PUNCT
ejpam-1518	90	3	1	1	NUM
ejpam-1518	90	4	n	n	NOUN
ejpam-1518	90	5	|{k	|{k	NUM
ejpam-1518	90	6	:	:	PUNCT
ejpam-1518	90	7	k	k	PROPN
ejpam-1518	90	8	≤	≤	PROPN
ejpam-1518	90	9	n	n	CCONJ
ejpam-1518	90	10	,	,	PUNCT
ejpam-1518	90	11	|xk|	|xk|	ADJ
ejpam-1518	90	12	≥	≥	NUM
ejpam-1518	90	13	m}|	m}|	NOUN
ejpam-1518	90	14	=	=	SYM
ejpam-1518	90	15	1	1	NUM
ejpam-1518	90	16	n	n	NOUN
ejpam-1518	90	17	|{k	|{k	PRON
ejpam-1518	90	18	:	:	PUNCT
ejpam-1518	90	19	k	k	PROPN
ejpam-1518	90	20	=	=	SYM
ejpam-1518	90	21	m2	m2	PROPN
ejpam-1518	90	22	≤	≤	PROPN
ejpam-1518	90	23	n	n	CCONJ
ejpam-1518	90	24	,	,	PUNCT
ejpam-1518	90	25	|m|	|m|	VERB
ejpam-1518	90	26	≥	≥	NOUN
ejpam-1518	90	27	m}|	m}|	NOUN
ejpam-1518	90	28	≤	≤	NOUN
ejpam-1518	91	1	[	[	X
ejpam-1518	91	2	|	|	ADV
ejpam-1518	91	3	p	p	NOUN
ejpam-1518	91	4	n|]−	n|]−	NOUN
ejpam-1518	92	1	[	[	X
ejpam-1518	92	2	|m	|m	NOUN
ejpam-1518	92	3	|	|	NOUN
ejpam-1518	92	4	]	]	X
ejpam-1518	92	5	+	+	CCONJ
ejpam-1518	92	6	2	2	NUM
ejpam-1518	92	7	n	n	NOUN
ejpam-1518	92	8	this	this	DET
ejpam-1518	92	9	calculation	calculation	NOUN
ejpam-1518	92	10	shows	show	VERB
ejpam-1518	92	11	x̃	x̃	PROPN
ejpam-1518	92	12	=	=	SYM
ejpam-1518	92	13	(	(	PUNCT
ejpam-1518	92	14	xn	xn	X
ejpam-1518	92	15	)	)	PUNCT
ejpam-1518	92	16	is	be	AUX
ejpam-1518	92	17	d	d	ADJ
ejpam-1518	92	18	-	-	ADJ
ejpam-1518	92	19	statistical	statistical	ADJ
ejpam-1518	92	20	bounded	bound	VERB
ejpam-1518	92	21	.	.	PUNCT
ejpam-1518	93	1	remark	remark	PROPN
ejpam-1518	93	2	2	2	NUM
ejpam-1518	93	3	.	.	PUNCT
ejpam-1518	94	1	the	the	DET
ejpam-1518	94	2	inverse	inverse	NOUN
ejpam-1518	94	3	of	of	ADP
ejpam-1518	94	4	(	(	PUNCT
ejpam-1518	94	5	ii	ii	NOUN
ejpam-1518	94	6	)	)	PUNCT
ejpam-1518	94	7	in	in	ADP
ejpam-1518	94	8	theorem	theorem	NOUN
ejpam-1518	94	9	1	1	NUM
ejpam-1518	94	10	is	be	AUX
ejpam-1518	94	11	not	not	PART
ejpam-1518	94	12	true	true	ADJ
ejpam-1518	94	13	in	in	ADP
ejpam-1518	94	14	general	general	ADJ
ejpam-1518	94	15	.	.	PUNCT
ejpam-1518	94	16	example	example	NOUN
ejpam-1518	95	1	2	2	NUM
ejpam-1518	95	2	.	.	X
ejpam-1518	95	3	assume	assume	VERB
ejpam-1518	95	4	that	that	SCONJ
ejpam-1518	95	5	x	x	SYM
ejpam-1518	95	6	,	,	PUNCT
ejpam-1518	95	7	y	y	PROPN
ejpam-1518	95	8	∈	∈	PROPN
ejpam-1518	95	9	x	x	AUX
ejpam-1518	95	10	are	be	AUX
ejpam-1518	95	11	distinct	distinct	ADJ
ejpam-1518	95	12	points	point	NOUN
ejpam-1518	95	13	and	and	CCONJ
ejpam-1518	95	14	let	let	VERB
ejpam-1518	95	15	us	we	PRON
ejpam-1518	95	16	define	define	VERB
ejpam-1518	95	17	the	the	DET
ejpam-1518	95	18	sequence	sequence	NOUN
ejpam-1518	95	19	x̃	x̃	PROPN
ejpam-1518	95	20	=	=	PUNCT
ejpam-1518	95	21	(	(	PUNCT
ejpam-1518	95	22	xn	xn	PROPN
ejpam-1518	95	23	)	)	PUNCT
ejpam-1518	95	24	with	with	ADP
ejpam-1518	95	25	xn	xn	PROPN
ejpam-1518	95	26	:	:	PUNCT
ejpam-1518	95	27	=	=	SYM
ejpam-1518	95	28	(	(	PUNCT
ejpam-1518	95	29	x	x	X
ejpam-1518	95	30	,	,	PUNCT
ejpam-1518	95	31	if	if	SCONJ
ejpam-1518	95	32	n=	n=	ADJ
ejpam-1518	95	33	2k+	2k+	NUM
ejpam-1518	95	34	1	1	NUM
ejpam-1518	95	35	,	,	PUNCT
ejpam-1518	95	36	k	k	PROPN
ejpam-1518	95	37	∈	∈	PROPN
ejpam-1518	95	38	n	n	CCONJ
ejpam-1518	95	39	y	y	NOUN
ejpam-1518	95	40	,	,	PUNCT
ejpam-1518	95	41	if	if	SCONJ
ejpam-1518	95	42	n=	n=	ADJ
ejpam-1518	95	43	2k	2k	NOUN
ejpam-1518	95	44	that	that	PRON
ejpam-1518	95	45	is	be	AUX
ejpam-1518	95	46	,	,	PUNCT
ejpam-1518	95	47	x̃	x̃	PROPN
ejpam-1518	95	48	=	=	PUNCT
ejpam-1518	95	49	(	(	PUNCT
ejpam-1518	95	50	1	1	NUM
ejpam-1518	95	51	bx	bx	PROPN
ejpam-1518	95	52	,	,	PUNCT
ejpam-1518	95	53	y	y	PROPN
ejpam-1518	95	54	,	,	PUNCT
ejpam-1518	95	55	3	3	NUM
ejpam-1518	95	56	bx	bx	NOUN
ejpam-1518	95	57	,	,	PUNCT
ejpam-1518	95	58	y	y	PROPN
ejpam-1518	95	59	,	,	PUNCT
ejpam-1518	95	60	5	5	NUM
ejpam-1518	95	61	bx	bx	X
ejpam-1518	95	62	,	,	PUNCT
ejpam-1518	95	63	y	y	PROPN
ejpam-1518	95	64	,	,	PUNCT
ejpam-1518	95	65	7	7	NUM
ejpam-1518	95	66	bx	bx	NOUN
ejpam-1518	95	67	,	,	PUNCT
ejpam-1518	95	68	.	.	PUNCT
ejpam-1518	95	69	.	.	PUNCT
ejpam-1518	95	70	.	.	PUNCT
ejpam-1518	95	71	)	)	PUNCT
ejpam-1518	95	72	.	.	PUNCT
ejpam-1518	96	1	let	let	VERB
ejpam-1518	96	2	us	we	PRON
ejpam-1518	96	3	choose	choose	VERB
ejpam-1518	96	4	m	m	PROPN
ejpam-1518	96	5	>	>	X
ejpam-1518	96	6	0	0	PUNCT
ejpam-1518	97	1	satisfying	satisfy	VERB
ejpam-1518	97	2	m	m	VERB
ejpam-1518	97	3	>	>	X
ejpam-1518	97	4	2	2	NUM
ejpam-1518	97	5	max{d(x	max{d(x	NOUN
ejpam-1518	97	6	,	,	PUNCT
ejpam-1518	97	7	z	z	NOUN
ejpam-1518	97	8	)	)	PUNCT
ejpam-1518	97	9	,	,	PUNCT
ejpam-1518	97	10	d(y	d(y	PROPN
ejpam-1518	97	11	,	,	PUNCT
ejpam-1518	97	12	z	z	NOUN
ejpam-1518	97	13	)	)	PUNCT
ejpam-1518	97	14	}	}	PUNCT
ejpam-1518	97	15	for	for	ADP
ejpam-1518	97	16	an	an	DET
ejpam-1518	97	17	arbitrary	arbitrary	ADJ
ejpam-1518	97	18	fixed	fix	VERB
ejpam-1518	97	19	z	z	NOUN
ejpam-1518	97	20	∈	∈	PROPN
ejpam-1518	97	21	x	x	X
ejpam-1518	97	22	.	.	PUNCT
ejpam-1518	98	1	then	then	ADV
ejpam-1518	98	2	we	we	PRON
ejpam-1518	98	3	have	have	VERB
ejpam-1518	98	4	{	{	PUNCT
ejpam-1518	98	5	k	k	NOUN
ejpam-1518	98	6	:	:	PUNCT
ejpam-1518	98	7	k	k	PROPN
ejpam-1518	98	8	≤	≤	PROPN
ejpam-1518	98	9	n	n	CCONJ
ejpam-1518	98	10	,	,	PUNCT
ejpam-1518	98	11	d(xk	d(xk	PROPN
ejpam-1518	98	12	,	,	PUNCT
ejpam-1518	98	13	z	z	NOUN
ejpam-1518	98	14	)	)	PUNCT
ejpam-1518	98	15	≥	≥	NOUN
ejpam-1518	98	16	m	m	NOUN
ejpam-1518	98	17	}	}	PUNCT
ejpam-1518	98	18	=	=	SYM
ejpam-1518	98	19	;	;	PUNCT
ejpam-1518	98	20	.	.	PUNCT
ejpam-1518	99	1	so	so	ADV
ejpam-1518	99	2	,	,	PUNCT
ejpam-1518	99	3	we	we	PRON
ejpam-1518	99	4	obtain	obtain	VERB
ejpam-1518	99	5	lim	lim	PROPN
ejpam-1518	99	6	n→∞	n→∞	NUM
ejpam-1518	99	7	1	1	NUM
ejpam-1518	99	8	n	n	DET
ejpam-1518	99	9	�	�	PROPN
ejpam-1518	99	10	�	�	PROPN
ejpam-1518	99	11	�	�	PROPN
ejpam-1518	99	12	k	k	NOUN
ejpam-1518	99	13	:	:	PUNCT
ejpam-1518	99	14	k	k	PROPN
ejpam-1518	99	15	≤	≤	PROPN
ejpam-1518	99	16	n	n	CCONJ
ejpam-1518	99	17	and	and	CCONJ
ejpam-1518	99	18	d(xk	d(xk	PROPN
ejpam-1518	99	19	,	,	PUNCT
ejpam-1518	99	20	z	z	NOUN
ejpam-1518	99	21	)	)	PUNCT
ejpam-1518	99	22	≥	≥	PROPN
ejpam-1518	99	23	m	m	PROPN
ejpam-1518	99	24	�	�	PROPN
ejpam-1518	99	25	�	�	NOUN
ejpam-1518	99	26	=	=	SYM
ejpam-1518	99	27	0	0	PROPN
ejpam-1518	99	28	.	.	PUNCT
ejpam-1518	100	1	this	this	PRON
ejpam-1518	100	2	shows	show	VERB
ejpam-1518	100	3	that	that	SCONJ
ejpam-1518	100	4	x̃	x̃	PROPN
ejpam-1518	100	5	is	be	AUX
ejpam-1518	100	6	d	d	ADJ
ejpam-1518	100	7	–	–	PUNCT
ejpam-1518	100	8	statistical	statistical	ADJ
ejpam-1518	100	9	bounded	bound	VERB
ejpam-1518	100	10	.	.	PUNCT
ejpam-1518	101	1	now	now	ADV
ejpam-1518	101	2	let	let	VERB
ejpam-1518	101	3	us	we	PRON
ejpam-1518	101	4	show	show	VERB
ejpam-1518	101	5	that	that	SCONJ
ejpam-1518	101	6	x̃	x̃	PROPN
ejpam-1518	101	7	is	be	AUX
ejpam-1518	101	8	not	not	PART
ejpam-1518	101	9	d	d	ADJ
ejpam-1518	101	10	–	–	PUNCT
ejpam-1518	101	11	statistical	statistical	ADJ
ejpam-1518	101	12	convergent	convergent	NOUN
ejpam-1518	101	13	to	to	ADP
ejpam-1518	101	14	x(or	x(or	PROPN
ejpam-1518	101	15	y	y	PROPN
ejpam-1518	101	16	)	)	PUNCT
ejpam-1518	101	17	.	.	PUNCT
ejpam-1518	102	1	for	for	ADP
ejpam-1518	102	2	this	this	DET
ejpam-1518	102	3	aim	aim	NOUN
ejpam-1518	102	4	,	,	PUNCT
ejpam-1518	102	5	set	set	VERB
ejpam-1518	102	6	ε	ε	PROPN
ejpam-1518	102	7	<	<	X
ejpam-1518	102	8	d(x	d(x	PROPN
ejpam-1518	102	9	,	,	PUNCT
ejpam-1518	102	10	y	y	PROPN
ejpam-1518	102	11	)	)	PUNCT
ejpam-1518	102	12	.	.	PUNCT
ejpam-1518	103	1	then	then	ADV
ejpam-1518	103	2	we	we	PRON
ejpam-1518	103	3	have	have	VERB
ejpam-1518	103	4	|{k	|{k	NUM
ejpam-1518	103	5	:	:	PUNCT
ejpam-1518	103	6	k	k	PROPN
ejpam-1518	103	7	≤	≤	PROPN
ejpam-1518	103	8	n	n	CCONJ
ejpam-1518	103	9	,	,	PUNCT
ejpam-1518	103	10	d(xk	d(xk	PROPN
ejpam-1518	103	11	,	,	PUNCT
ejpam-1518	103	12	x(or	x(or	PROPN
ejpam-1518	103	13	y))≥	y))≥	PROPN
ejpam-1518	103	14	ε}|	ε}|	NOUN
ejpam-1518	103	15	=	=	PUNCT
ejpam-1518	103	16	(	(	PUNCT
ejpam-1518	103	17	=	=	SYM
ejpam-1518	103	18	n	n	PRON
ejpam-1518	103	19	2	2	NUM
ejpam-1518	103	20	,	,	PUNCT
ejpam-1518	103	21	n	n	CCONJ
ejpam-1518	103	22	even	even	ADV
ejpam-1518	103	23	;	;	PUNCT
ejpam-1518	103	24	<	<	X
ejpam-1518	103	25	n	n	PRON
ejpam-1518	103	26	2	2	NUM
ejpam-1518	103	27	,	,	PUNCT
ejpam-1518	103	28	n	n	PRON
ejpam-1518	103	29	odd	odd	ADJ
ejpam-1518	103	30	.	.	PUNCT
ejpam-1518	103	31	m.	m.	NOUN
ejpam-1518	103	32	küçükaslan	küçükaslan	PROPN
ejpam-1518	103	33	,	,	PUNCT
ejpam-1518	103	34	u.	u.	PROPN
ejpam-1518	103	35	değer	değer	PROPN
ejpam-1518	103	36	/	/	SYM
ejpam-1518	103	37	eur	eur	PROPN
ejpam-1518	103	38	.	.	PUNCT
ejpam-1518	104	1	j.	j.	PROPN
ejpam-1518	104	2	pure	pure	PROPN
ejpam-1518	104	3	appl	appl	PROPN
ejpam-1518	104	4	.	.	PROPN
ejpam-1518	104	5	math	math	PROPN
ejpam-1518	104	6	,	,	PUNCT
ejpam-1518	104	7	5	5	NUM
ejpam-1518	104	8	(	(	PUNCT
ejpam-1518	104	9	2012	2012	NUM
ejpam-1518	104	10	)	)	PUNCT
ejpam-1518	104	11	,	,	PUNCT
ejpam-1518	104	12	174	174	NUM
ejpam-1518	104	13	-	-	SYM
ejpam-1518	104	14	186	186	NUM
ejpam-1518	104	15	178	178	NUM
ejpam-1518	104	16	according	accord	VERB
ejpam-1518	104	17	to	to	ADP
ejpam-1518	104	18	this	this	PRON
ejpam-1518	104	19	,	,	PUNCT
ejpam-1518	104	20	lim	lim	PROPN
ejpam-1518	104	21	n→∞	n→∞	NUM
ejpam-1518	104	22	1	1	NUM
ejpam-1518	104	23	n	n	PRON
ejpam-1518	104	24	�	�	PROPN
ejpam-1518	104	25	�	�	PROPN
ejpam-1518	104	26	�	�	PROPN
ejpam-1518	104	27	k	k	NOUN
ejpam-1518	104	28	:	:	PUNCT
ejpam-1518	104	29	k	k	PROPN
ejpam-1518	104	30	≤	≤	PROPN
ejpam-1518	104	31	n	n	CCONJ
ejpam-1518	104	32	and	and	CCONJ
ejpam-1518	104	33	d(xk	d(xk	PROPN
ejpam-1518	104	34	,	,	PUNCT
ejpam-1518	104	35	x(or	x(or	PROPN
ejpam-1518	104	36	y))≥	y))≥	PROPN
ejpam-1518	104	37	ε	ε	PROPN
ejpam-1518	104	38	�	�	PROPN
ejpam-1518	104	39	�	�	PROPN
ejpam-1518	104	40	=	=	SYM
ejpam-1518	104	41	1	1	NUM
ejpam-1518	104	42	2	2	NUM
ejpam-1518	104	43	6=	6=	ADP
ejpam-1518	104	44	0	0	NUM
ejpam-1518	104	45	.	.	PUNCT
ejpam-1518	105	1	so	so	ADV
ejpam-1518	105	2	,	,	PUNCT
ejpam-1518	105	3	x̃	x̃	PROPN
ejpam-1518	105	4	is	be	AUX
ejpam-1518	105	5	not	not	PART
ejpam-1518	105	6	d	d	ADJ
ejpam-1518	105	7	–	–	PUNCT
ejpam-1518	105	8	statistical	statistical	ADJ
ejpam-1518	105	9	convergent	convergent	NOUN
ejpam-1518	105	10	to	to	ADP
ejpam-1518	105	11	x(or	x(or	PROPN
ejpam-1518	105	12	y	y	PROPN
ejpam-1518	105	13	)	)	PUNCT
ejpam-1518	105	14	.	.	PUNCT
ejpam-1518	106	1	examples	example	NOUN
ejpam-1518	106	2	1	1	NUM
ejpam-1518	106	3	and	and	CCONJ
ejpam-1518	106	4	2	2	NUM
ejpam-1518	106	5	show	show	VERB
ejpam-1518	106	6	that	that	SCONJ
ejpam-1518	106	7	the	the	DET
ejpam-1518	106	8	inclusions	inclusion	NOUN
ejpam-1518	106	9	b(x̃	b(x̃	PROPN
ejpam-1518	106	10	)	)	PUNCT
ejpam-1518	107	1	⊂	⊂	PROPN
ejpam-1518	107	2	bd	bd	PROPN
ejpam-1518	107	3	st(x̃	st(x̃	PROPN
ejpam-1518	107	4	)	)	PUNCT
ejpam-1518	107	5	and	and	CCONJ
ejpam-1518	107	6	c	c	X
ejpam-1518	107	7	d	d	PRON
ejpam-1518	107	8	st(x̃	st(x̃	NOUN
ejpam-1518	107	9	)	)	PUNCT
ejpam-1518	107	10	⊂	⊂	PROPN
ejpam-1518	107	11	bd	bd	PROPN
ejpam-1518	107	12	st(x̃	st(x̃	NOUN
ejpam-1518	107	13	)	)	PUNCT
ejpam-1518	107	14	are	be	AUX
ejpam-1518	107	15	sharp	sharp	ADJ
ejpam-1518	107	16	.	.	PUNCT
ejpam-1518	108	1	corollary	corollary	ADJ
ejpam-1518	108	2	1	1	NUM
ejpam-1518	108	3	.	.	PUNCT
ejpam-1518	109	1	if	if	SCONJ
ejpam-1518	109	2	x̃	x̃	PROPN
ejpam-1518	109	3	=	=	SYM
ejpam-1518	109	4	(	(	PUNCT
ejpam-1518	109	5	xn	xn	X
ejpam-1518	109	6	)	)	PUNCT
ejpam-1518	109	7	is	be	AUX
ejpam-1518	109	8	convergent	convergent	ADJ
ejpam-1518	109	9	to	to	ADP
ejpam-1518	109	10	a	a	DET
ejpam-1518	109	11	point	point	NOUN
ejpam-1518	109	12	a	a	DET
ejpam-1518	109	13	∈	∈	NOUN
ejpam-1518	109	14	x	x	X
ejpam-1518	109	15	,	,	PUNCT
ejpam-1518	109	16	then	then	ADV
ejpam-1518	109	17	x̃	x̃	PROPN
ejpam-1518	109	18	is	be	AUX
ejpam-1518	109	19	dstatistical	dstatistical	ADJ
ejpam-1518	109	20	bounded	bound	VERB
ejpam-1518	109	21	.	.	PUNCT
ejpam-1518	110	1	proof	proof	NOUN
ejpam-1518	110	2	.	.	PUNCT
ejpam-1518	111	1	from	from	ADP
ejpam-1518	111	2	[	[	X
ejpam-1518	111	3	12	12	NUM
ejpam-1518	111	4	]	]	PUNCT
ejpam-1518	111	5	we	we	PRON
ejpam-1518	111	6	know	know	VERB
ejpam-1518	111	7	that	that	SCONJ
ejpam-1518	111	8	convergence	convergence	NOUN
ejpam-1518	111	9	implies	imply	VERB
ejpam-1518	111	10	dst	dst	NOUN
ejpam-1518	111	11	convergence	convergence	NOUN
ejpam-1518	111	12	in	in	ADP
ejpam-1518	111	13	an	an	DET
ejpam-1518	111	14	arbitrary	arbitrary	ADJ
ejpam-1518	111	15	metric	metric	ADJ
ejpam-1518	111	16	space	space	NOUN
ejpam-1518	111	17	.	.	PUNCT
ejpam-1518	112	1	therefore	therefore	ADV
ejpam-1518	112	2	,	,	PUNCT
ejpam-1518	112	3	taking	take	VERB
ejpam-1518	112	4	into	into	ADP
ejpam-1518	112	5	account	account	NOUN
ejpam-1518	112	6	(	(	PUNCT
ejpam-1518	112	7	ii	ii	NOUN
ejpam-1518	112	8	)	)	PUNCT
ejpam-1518	112	9	in	in	ADP
ejpam-1518	112	10	theorem	theorem	NOUN
ejpam-1518	112	11	1	1	NUM
ejpam-1518	112	12	,	,	PUNCT
ejpam-1518	112	13	we	we	PRON
ejpam-1518	112	14	get	get	VERB
ejpam-1518	112	15	the	the	DET
ejpam-1518	112	16	proof	proof	NOUN
ejpam-1518	112	17	.	.	PUNCT
ejpam-1518	113	1	another	another	DET
ejpam-1518	113	2	way	way	NOUN
ejpam-1518	113	3	,	,	PUNCT
ejpam-1518	113	4	if	if	SCONJ
ejpam-1518	113	5	x̃	x̃	PROPN
ejpam-1518	113	6	is	be	AUX
ejpam-1518	113	7	convergent	convergent	ADJ
ejpam-1518	113	8	to	to	ADP
ejpam-1518	113	9	a	a	DET
ejpam-1518	113	10	∈	∈	NOUN
ejpam-1518	113	11	x	x	X
ejpam-1518	113	12	,	,	PUNCT
ejpam-1518	113	13	x̃	x̃	PROPN
ejpam-1518	113	14	is	be	AUX
ejpam-1518	113	15	bounded	bound	VERB
ejpam-1518	113	16	.	.	PUNCT
ejpam-1518	114	1	by	by	ADP
ejpam-1518	114	2	using	use	VERB
ejpam-1518	114	3	(	(	PUNCT
ejpam-1518	114	4	i	i	NOUN
ejpam-1518	114	5	)	)	PUNCT
ejpam-1518	114	6	in	in	ADP
ejpam-1518	114	7	theorem	theorem	NOUN
ejpam-1518	114	8	1	1	NUM
ejpam-1518	114	9	,	,	PUNCT
ejpam-1518	114	10	we	we	PRON
ejpam-1518	114	11	have	have	VERB
ejpam-1518	114	12	the	the	DET
ejpam-1518	114	13	result	result	NOUN
ejpam-1518	114	14	.	.	PUNCT
ejpam-1518	115	1	corollary	corollary	ADJ
ejpam-1518	115	2	2	2	NUM
ejpam-1518	115	3	.	.	PUNCT
ejpam-1518	116	1	let	let	AUX
ejpam-1518	116	2	(	(	PUNCT
ejpam-1518	116	3	x	x	X
ejpam-1518	116	4	,	,	PUNCT
ejpam-1518	116	5	d	d	X
ejpam-1518	116	6	)	)	PUNCT
ejpam-1518	116	7	be	be	AUX
ejpam-1518	116	8	an	an	DET
ejpam-1518	116	9	arbitrary	arbitrary	ADJ
ejpam-1518	116	10	metric	metric	ADJ
ejpam-1518	116	11	space	space	NOUN
ejpam-1518	116	12	.	.	PUNCT
ejpam-1518	117	1	then	then	ADV
ejpam-1518	117	2	the	the	DET
ejpam-1518	117	3	following	follow	VERB
ejpam-1518	117	4	diagram	diagram	NOUN
ejpam-1518	117	5	holds	hold	VERB
ejpam-1518	117	6	:	:	PUNCT
ejpam-1518	117	7	b(x̃	b(x̃	PROPN
ejpam-1518	117	8	)	)	PUNCT
ejpam-1518	118	1	(	(	PUNCT
ejpam-1518	118	2	2	2	X
ejpam-1518	118	3	)	)	PUNCT
ejpam-1518	118	4	//	//	NOUN
ejpam-1518	118	5	bd	bd	PROPN
ejpam-1518	118	6	st(x̃	st(x̃	PROPN
ejpam-1518	118	7	)	)	PUNCT
ejpam-1518	118	8	c(x̃	c(x̃	NOUN
ejpam-1518	118	9	)	)	PUNCT
ejpam-1518	119	1	(	(	PUNCT
ejpam-1518	119	2	1	1	X
ejpam-1518	119	3	)	)	PUNCT
ejpam-1518	119	4	oo	oo	INTJ
ejpam-1518	119	5	(	(	PUNCT
ejpam-1518	119	6	5	5	NUM
ejpam-1518	119	7	)	)	PUNCT
ejpam-1518	119	8	;	;	PUNCT
ejpam-1518	119	9	;	;	PUNCT
ejpam-1518	119	10	x	x	PUNCT
ejpam-1518	119	11	x	x	PUNCT
ejpam-1518	119	12	x	x	PUNCT
ejpam-1518	119	13	x	x	PUNCT
ejpam-1518	119	14	x	x	PUNCT
ejpam-1518	119	15	x	x	PUNCT
ejpam-1518	119	16	x	x	PUNCT
ejpam-1518	119	17	x	x	SYM
ejpam-1518	119	18	x	x	X
ejpam-1518	119	19	(	(	PUNCT
ejpam-1518	119	20	3	3	NUM
ejpam-1518	119	21	)	)	PUNCT
ejpam-1518	119	22	//	//	NOUN
ejpam-1518	119	23	c	c	PROPN
ejpam-1518	119	24	d	d	X
ejpam-1518	119	25	st(x̃	st(x̃	NOUN
ejpam-1518	119	26	)	)	PUNCT
ejpam-1518	119	27	(	(	PUNCT
ejpam-1518	119	28	4	4	X
ejpam-1518	119	29	)	)	PUNCT
ejpam-1518	119	30	oo	oo	INTJ
ejpam-1518	119	31	where	where	SCONJ
ejpam-1518	119	32	a→	a→	X
ejpam-1518	119	33	b	b	NOUN
ejpam-1518	119	34	means	mean	VERB
ejpam-1518	119	35	that	that	SCONJ
ejpam-1518	119	36	a⊂	a⊂	ADP
ejpam-1518	119	37	b.	b.	NOUN
ejpam-1518	119	38	proof	proof	NOUN
ejpam-1518	119	39	.	.	PUNCT
ejpam-1518	120	1	the	the	DET
ejpam-1518	120	2	inclusion	inclusion	NOUN
ejpam-1518	120	3	(	(	PUNCT
ejpam-1518	120	4	5	5	NUM
ejpam-1518	120	5	)	)	PUNCT
ejpam-1518	120	6	is	be	AUX
ejpam-1518	120	7	obtained	obtain	VERB
ejpam-1518	120	8	directly	directly	ADV
ejpam-1518	120	9	from	from	ADP
ejpam-1518	120	10	corollary	corollary	ADJ
ejpam-1518	120	11	1	1	NUM
ejpam-1518	120	12	.	.	PUNCT
ejpam-1518	121	1	the	the	DET
ejpam-1518	121	2	inclusions	inclusion	NOUN
ejpam-1518	121	3	(	(	PUNCT
ejpam-1518	121	4	2	2	NUM
ejpam-1518	121	5	)	)	PUNCT
ejpam-1518	121	6	and	and	CCONJ
ejpam-1518	121	7	(	(	PUNCT
ejpam-1518	121	8	4	4	X
ejpam-1518	121	9	)	)	PUNCT
ejpam-1518	121	10	are	be	AUX
ejpam-1518	121	11	obtained	obtain	VERB
ejpam-1518	121	12	from	from	ADP
ejpam-1518	121	13	theorem	theorem	NOUN
ejpam-1518	121	14	1-(i	1-(i	NUM
ejpam-1518	121	15	)	)	PUNCT
ejpam-1518	121	16	and	and	CCONJ
ejpam-1518	121	17	(	(	PUNCT
ejpam-1518	121	18	ii	ii	NOUN
ejpam-1518	121	19	)	)	PUNCT
ejpam-1518	121	20	,	,	PUNCT
ejpam-1518	121	21	respectively	respectively	ADV
ejpam-1518	121	22	.	.	PUNCT
ejpam-1518	122	1	the	the	DET
ejpam-1518	122	2	inclusion	inclusion	NOUN
ejpam-1518	122	3	(	(	PUNCT
ejpam-1518	122	4	3	3	X
ejpam-1518	122	5	)	)	PUNCT
ejpam-1518	122	6	is	be	AUX
ejpam-1518	122	7	obtained	obtain	VERB
ejpam-1518	122	8	from	from	ADP
ejpam-1518	122	9	proposition	proposition	NOUN
ejpam-1518	122	10	2.1	2.1	NUM
ejpam-1518	122	11	in	in	ADP
ejpam-1518	122	12	[	[	X
ejpam-1518	122	13	12	12	NUM
ejpam-1518	122	14	]	]	PUNCT
ejpam-1518	122	15	.	.	PUNCT
ejpam-1518	123	1	the	the	DET
ejpam-1518	123	2	inverse	inverse	NOUN
ejpam-1518	123	3	of	of	ADP
ejpam-1518	123	4	all	all	DET
ejpam-1518	123	5	inclusions	inclusion	NOUN
ejpam-1518	123	6	in	in	ADP
ejpam-1518	123	7	the	the	DET
ejpam-1518	123	8	diagram	diagram	NOUN
ejpam-1518	123	9	are	be	AUX
ejpam-1518	123	10	not	not	PART
ejpam-1518	123	11	true	true	ADJ
ejpam-1518	123	12	.	.	PUNCT
ejpam-1518	124	1	take	take	VERB
ejpam-1518	124	2	into	into	AUX
ejpam-1518	124	3	consider	consider	VERB
ejpam-1518	124	4	example	example	NOUN
ejpam-1518	124	5	1	1	NUM
ejpam-1518	124	6	in	in	ADP
ejpam-1518	124	7	[	[	X
ejpam-1518	124	8	12	12	NUM
ejpam-1518	124	9	]	]	PUNCT
ejpam-1518	124	10	for	for	ADP
ejpam-1518	124	11	the	the	DET
ejpam-1518	124	12	inverse	inverse	NOUN
ejpam-1518	124	13	of	of	ADP
ejpam-1518	124	14	(	(	PUNCT
ejpam-1518	124	15	3	3	NUM
ejpam-1518	124	16	)	)	PUNCT
ejpam-1518	124	17	,	,	PUNCT
ejpam-1518	124	18	and	and	CCONJ
ejpam-1518	124	19	in	in	ADP
ejpam-1518	124	20	this	this	DET
ejpam-1518	124	21	work	work	NOUN
ejpam-1518	124	22	example	example	NOUN
ejpam-1518	124	23	1	1	NUM
ejpam-1518	124	24	and	and	CCONJ
ejpam-1518	124	25	example	example	NOUN
ejpam-1518	124	26	2	2	NUM
ejpam-1518	124	27	for	for	ADP
ejpam-1518	124	28	the	the	DET
ejpam-1518	124	29	inverse	inverse	NOUN
ejpam-1518	124	30	of	of	ADP
ejpam-1518	124	31	(	(	PUNCT
ejpam-1518	124	32	2	2	NUM
ejpam-1518	124	33	)	)	PUNCT
ejpam-1518	124	34	and	and	CCONJ
ejpam-1518	124	35	(	(	PUNCT
ejpam-1518	124	36	4	4	NUM
ejpam-1518	124	37	)	)	PUNCT
ejpam-1518	124	38	.	.	PUNCT
ejpam-1518	125	1	the	the	DET
ejpam-1518	125	2	following	follow	VERB
ejpam-1518	125	3	theorem	theorem	NOUN
ejpam-1518	125	4	gives	give	VERB
ejpam-1518	125	5	necessary	necessary	ADJ
ejpam-1518	125	6	and	and	CCONJ
ejpam-1518	125	7	sufficient	sufficient	ADJ
ejpam-1518	125	8	condition	condition	NOUN
ejpam-1518	125	9	on	on	ADP
ejpam-1518	125	10	x	x	PUNCT
ejpam-1518	125	11	for	for	ADP
ejpam-1518	125	12	which	which	PRON
ejpam-1518	125	13	the	the	DET
ejpam-1518	125	14	inverse	inverse	NOUN
ejpam-1518	125	15	of	of	ADP
ejpam-1518	125	16	the	the	DET
ejpam-1518	125	17	inclusion	inclusion	NOUN
ejpam-1518	125	18	(	(	PUNCT
ejpam-1518	125	19	2	2	NUM
ejpam-1518	125	20	)	)	PUNCT
ejpam-1518	125	21	in	in	ADP
ejpam-1518	125	22	the	the	DET
ejpam-1518	125	23	corollary	corollary	ADJ
ejpam-1518	125	24	2	2	NUM
ejpam-1518	125	25	is	be	AUX
ejpam-1518	125	26	true	true	ADJ
ejpam-1518	125	27	:	:	PUNCT
ejpam-1518	125	28	theorem	theorem	NOUN
ejpam-1518	125	29	2	2	NUM
ejpam-1518	125	30	.	.	PUNCT
ejpam-1518	126	1	let	let	AUX
ejpam-1518	126	2	(	(	PUNCT
ejpam-1518	126	3	x	x	X
ejpam-1518	126	4	,	,	PUNCT
ejpam-1518	126	5	d	d	X
ejpam-1518	126	6	)	)	PUNCT
ejpam-1518	126	7	be	be	AUX
ejpam-1518	126	8	a	a	DET
ejpam-1518	126	9	metric	metric	ADJ
ejpam-1518	126	10	space	space	NOUN
ejpam-1518	126	11	with	with	ADP
ejpam-1518	126	12	x	x	PRON
ejpam-1518	126	13	6=	6=	NUM
ejpam-1518	126	14	;	;	PUNCT
ejpam-1518	126	15	.	.	PUNCT
ejpam-1518	127	1	the	the	DET
ejpam-1518	127	2	following	follow	VERB
ejpam-1518	127	3	two	two	NUM
ejpam-1518	127	4	statements	statement	NOUN
ejpam-1518	127	5	are	be	AUX
ejpam-1518	127	6	equivalent	equivalent	ADJ
ejpam-1518	127	7	:	:	PUNCT
ejpam-1518	127	8	(	(	PUNCT
ejpam-1518	127	9	i	i	NOUN
ejpam-1518	127	10	)	)	PUNCT
ejpam-1518	127	11	the	the	DET
ejpam-1518	127	12	set	set	NOUN
ejpam-1518	127	13	of	of	ADP
ejpam-1518	127	14	all	all	DET
ejpam-1518	127	15	bounded	bound	VERB
ejpam-1518	127	16	sequences	sequence	NOUN
ejpam-1518	127	17	x̃	x̃	PROPN
ejpam-1518	127	18	=	=	SYM
ejpam-1518	127	19	(	(	PUNCT
ejpam-1518	127	20	xk	xk	ADJ
ejpam-1518	127	21	)	)	PUNCT
ejpam-1518	127	22	∈	∈	PROPN
ejpam-1518	127	23	x̃	x̃	PROPN
ejpam-1518	127	24	is	be	AUX
ejpam-1518	127	25	the	the	DET
ejpam-1518	127	26	same	same	ADJ
ejpam-1518	127	27	as	as	ADP
ejpam-1518	127	28	the	the	DET
ejpam-1518	127	29	set	set	NOUN
ejpam-1518	127	30	of	of	ADP
ejpam-1518	127	31	all	all	DET
ejpam-1518	127	32	d	d	PROPN
ejpam-1518	127	33	–	–	PUNCT
ejpam-1518	127	34	statistical	statistical	ADJ
ejpam-1518	127	35	bounded	bound	VERB
ejpam-1518	127	36	sequences	sequence	NOUN
ejpam-1518	127	37	x̃	x̃	PROPN
ejpam-1518	127	38	∈	∈	PROPN
ejpam-1518	128	1	x̃	x̃	PROPN
ejpam-1518	128	2	.	.	PUNCT
ejpam-1518	129	1	(	(	PUNCT
ejpam-1518	129	2	ii	ii	X
ejpam-1518	129	3	)	)	PUNCT
ejpam-1518	129	4	the	the	DET
ejpam-1518	129	5	cardinality	cardinality	NOUN
ejpam-1518	129	6	of	of	ADP
ejpam-1518	129	7	x	x	PROPN
ejpam-1518	129	8	is	be	AUX
ejpam-1518	129	9	finite	finite	PROPN
ejpam-1518	129	10	.	.	PUNCT
ejpam-1518	129	11	m.	m.	PROPN
ejpam-1518	129	12	küçükaslan	küçükaslan	PROPN
ejpam-1518	129	13	,	,	PUNCT
ejpam-1518	129	14	u.	u.	PROPN
ejpam-1518	129	15	değer	değer	PROPN
ejpam-1518	129	16	/	/	SYM
ejpam-1518	129	17	eur	eur	PROPN
ejpam-1518	129	18	.	.	PUNCT
ejpam-1518	130	1	j.	j.	PROPN
ejpam-1518	130	2	pure	pure	PROPN
ejpam-1518	130	3	appl	appl	PROPN
ejpam-1518	130	4	.	.	PROPN
ejpam-1518	130	5	math	math	PROPN
ejpam-1518	130	6	,	,	PUNCT
ejpam-1518	130	7	5	5	NUM
ejpam-1518	130	8	(	(	PUNCT
ejpam-1518	130	9	2012	2012	NUM
ejpam-1518	130	10	)	)	PUNCT
ejpam-1518	130	11	,	,	PUNCT
ejpam-1518	130	12	174	174	NUM
ejpam-1518	130	13	-	-	SYM
ejpam-1518	130	14	186	186	NUM
ejpam-1518	130	15	179	179	NUM
ejpam-1518	130	16	proof	proof	NOUN
ejpam-1518	130	17	.	.	PUNCT
ejpam-1518	131	1	(	(	PUNCT
ejpam-1518	131	2	ii	ii	NOUN
ejpam-1518	131	3	)	)	PUNCT
ejpam-1518	131	4	⇒	⇒	NOUN
ejpam-1518	131	5	(	(	PUNCT
ejpam-1518	131	6	i	i	NOUN
ejpam-1518	131	7	)	)	PUNCT
ejpam-1518	131	8	the	the	DET
ejpam-1518	131	9	cardinality	cardinality	NOUN
ejpam-1518	131	10	of	of	ADP
ejpam-1518	131	11	x	x	PROPN
ejpam-1518	131	12	is	be	AUX
ejpam-1518	131	13	finite	finite	ADJ
ejpam-1518	131	14	.	.	PUNCT
ejpam-1518	132	1	that	that	PRON
ejpam-1518	132	2	is	be	AUX
ejpam-1518	132	3	,	,	PUNCT
ejpam-1518	132	4	there	there	PRON
ejpam-1518	132	5	exist	exist	VERB
ejpam-1518	132	6	a	a	DET
ejpam-1518	132	7	number	number	NOUN
ejpam-1518	132	8	n0	n0	NUM
ejpam-1518	132	9	∈	∈	PROPN
ejpam-1518	132	10	n	n	PRON
ejpam-1518	132	11	such	such	ADJ
ejpam-1518	132	12	that	that	SCONJ
ejpam-1518	132	13	x	x	SYM
ejpam-1518	132	14	=	=	PRON
ejpam-1518	132	15	{	{	PUNCT
ejpam-1518	132	16	x0	x0	PROPN
ejpam-1518	132	17	,	,	PUNCT
ejpam-1518	132	18	x1	x1	PROPN
ejpam-1518	132	19	,	,	PUNCT
ejpam-1518	132	20	.	.	PUNCT
ejpam-1518	132	21	.	.	PUNCT
ejpam-1518	133	1	.	.	PUNCT
ejpam-1518	134	1	,	,	PUNCT
ejpam-1518	134	2	xn0	xn0	PROPN
ejpam-1518	134	3	}	}	PUNCT
ejpam-1518	134	4	,	,	PUNCT
ejpam-1518	134	5	since	since	SCONJ
ejpam-1518	134	6	the	the	DET
ejpam-1518	134	7	cardinality	cardinality	NOUN
ejpam-1518	134	8	of	of	ADP
ejpam-1518	134	9	x	x	PROPN
ejpam-1518	134	10	is	be	AUX
ejpam-1518	134	11	finite	finite	ADJ
ejpam-1518	134	12	.	.	PUNCT
ejpam-1518	135	1	from	from	ADP
ejpam-1518	135	2	the	the	DET
ejpam-1518	135	3	hypothesis	hypothesis	NOUN
ejpam-1518	135	4	,	,	PUNCT
ejpam-1518	135	5	the	the	DET
ejpam-1518	135	6	diameter	diameter	NOUN
ejpam-1518	135	7	of	of	ADP
ejpam-1518	135	8	x	x	PROPN
ejpam-1518	135	9	,	,	PUNCT
ejpam-1518	135	10	d(x	d(x	PROPN
ejpam-1518	135	11	)	)	PUNCT
ejpam-1518	135	12	:	:	PUNCT
ejpam-1518	135	13	=	=	SYM
ejpam-1518	135	14	sup{d(xk	sup{d(xk	NOUN
ejpam-1518	135	15	,	,	PUNCT
ejpam-1518	135	16	x	x	X
ejpam-1518	135	17	l	l	NOUN
ejpam-1518	135	18	)	)	PUNCT
ejpam-1518	135	19	:	:	PUNCT
ejpam-1518	135	20	xk	xk	PROPN
ejpam-1518	135	21	,	,	PUNCT
ejpam-1518	135	22	x	x	X
ejpam-1518	135	23	l	l	NOUN
ejpam-1518	135	24	∈	∈	PROPN
ejpam-1518	135	25	x	x	X
ejpam-1518	135	26	;	;	PUNCT
ejpam-1518	135	27	k	k	X
ejpam-1518	135	28	,	,	PUNCT
ejpam-1518	135	29	l	l	NOUN
ejpam-1518	135	30	=	=	SYM
ejpam-1518	135	31	0	0	NUM
ejpam-1518	135	32	,	,	PUNCT
ejpam-1518	135	33	n0	n0	NUM
ejpam-1518	135	34	}	}	PUNCT
ejpam-1518	135	35	is	be	AUX
ejpam-1518	135	36	finite	finite	ADJ
ejpam-1518	135	37	.	.	PUNCT
ejpam-1518	136	1	if	if	SCONJ
ejpam-1518	136	2	x̃	x̃	PROPN
ejpam-1518	136	3	is	be	AUX
ejpam-1518	136	4	bounded	bound	VERB
ejpam-1518	136	5	,	,	PUNCT
ejpam-1518	136	6	then	then	ADV
ejpam-1518	136	7	from	from	ADP
ejpam-1518	136	8	theorem	theorem	NOUN
ejpam-1518	136	9	1-(i	1-(i	NUM
ejpam-1518	136	10	)	)	PUNCT
ejpam-1518	136	11	,	,	PUNCT
ejpam-1518	136	12	x̃	x̃	PROPN
ejpam-1518	136	13	is	be	AUX
ejpam-1518	136	14	also	also	ADV
ejpam-1518	136	15	d	d	ADJ
ejpam-1518	136	16	–	–	PUNCT
ejpam-1518	136	17	statistical	statistical	ADJ
ejpam-1518	136	18	bounded	bound	VERB
ejpam-1518	136	19	.	.	PUNCT
ejpam-1518	137	1	so	so	ADV
ejpam-1518	137	2	,	,	PUNCT
ejpam-1518	137	3	we	we	PRON
ejpam-1518	137	4	must	must	AUX
ejpam-1518	137	5	only	only	ADV
ejpam-1518	137	6	show	show	VERB
ejpam-1518	137	7	the	the	DET
ejpam-1518	137	8	inverse	inverse	NOUN
ejpam-1518	137	9	is	be	AUX
ejpam-1518	137	10	true	true	ADJ
ejpam-1518	137	11	under	under	ADP
ejpam-1518	137	12	the	the	DET
ejpam-1518	137	13	hypothesis	hypothesis	NOUN
ejpam-1518	137	14	.	.	PUNCT
ejpam-1518	138	1	let	let	VERB
ejpam-1518	138	2	’s	’s	PRON
ejpam-1518	138	3	take	take	VERB
ejpam-1518	138	4	d	d	NOUN
ejpam-1518	138	5	–	–	PUNCT
ejpam-1518	138	6	statistical	statistical	ADJ
ejpam-1518	138	7	bounded	bounded	ADJ
ejpam-1518	138	8	sequence	sequence	NOUN
ejpam-1518	138	9	x̃	x̃	PROPN
ejpam-1518	138	10	=	=	SYM
ejpam-1518	138	11	(	(	PUNCT
ejpam-1518	138	12	xk	xk	ADJ
ejpam-1518	138	13	)	)	PUNCT
ejpam-1518	138	14	∈	∈	PROPN
ejpam-1518	138	15	x̃	x̃	PROPN
ejpam-1518	138	16	,	,	PUNCT
ejpam-1518	138	17	i.e.	i.e.	X
ejpam-1518	138	18	,	,	PUNCT
ejpam-1518	138	19	∃m	∃m	PROPN
ejpam-1518	138	20	>	>	X
ejpam-1518	138	21	0	0	PUNCT
ejpam-1518	139	1	and	and	CCONJ
ejpam-1518	139	2	x	x	SYM
ejpam-1518	139	3	∈	∈	PROPN
ejpam-1518	139	4	x	x	X
ejpam-1518	139	5	such	such	ADJ
ejpam-1518	139	6	that	that	SCONJ
ejpam-1518	139	7	lim	lim	PROPN
ejpam-1518	139	8	n→∞	n→∞	NUM
ejpam-1518	139	9	1	1	NUM
ejpam-1518	139	10	n	n	PROPN
ejpam-1518	139	11	|{k	|{k	PUNCT
ejpam-1518	139	12	:	:	PUNCT
ejpam-1518	139	13	k	k	PROPN
ejpam-1518	139	14	≤	≤	PROPN
ejpam-1518	139	15	n	n	CCONJ
ejpam-1518	139	16	,	,	PUNCT
ejpam-1518	139	17	d(xk	d(xk	PROPN
ejpam-1518	139	18	,	,	PUNCT
ejpam-1518	139	19	x)≥	x)≥	PROPN
ejpam-1518	139	20	m}|	m}|	NOUN
ejpam-1518	139	21	=	=	SYM
ejpam-1518	139	22	0	0	NUM
ejpam-1518	139	23	.	.	PUNCT
ejpam-1518	140	1	(	(	PUNCT
ejpam-1518	140	2	5	5	NUM
ejpam-1518	140	3	)	)	PUNCT
ejpam-1518	140	4	especially	especially	ADV
ejpam-1518	140	5	,	,	PUNCT
ejpam-1518	140	6	if	if	SCONJ
ejpam-1518	140	7	we	we	PRON
ejpam-1518	140	8	take	take	VERB
ejpam-1518	140	9	m	m	VERB
ejpam-1518	140	10	:	:	PUNCT
ejpam-1518	140	11	=	=	SYM
ejpam-1518	140	12	2d(x	2d(x	NUM
ejpam-1518	140	13	)	)	PUNCT
ejpam-1518	140	14	,	,	PUNCT
ejpam-1518	140	15	we	we	PRON
ejpam-1518	140	16	have	have	VERB
ejpam-1518	140	17	,	,	PUNCT
ejpam-1518	140	18	from	from	ADP
ejpam-1518	140	19	(	(	PUNCT
ejpam-1518	140	20	5	5	NUM
ejpam-1518	140	21	)	)	PUNCT
ejpam-1518	140	22	,	,	PUNCT
ejpam-1518	140	23	{	{	PUNCT
ejpam-1518	140	24	k	k	NOUN
ejpam-1518	140	25	:	:	PUNCT
ejpam-1518	140	26	k	k	PROPN
ejpam-1518	140	27	≤	≤	PROPN
ejpam-1518	140	28	n	n	CCONJ
ejpam-1518	140	29	,	,	PUNCT
ejpam-1518	140	30	d(xk	d(xk	PROPN
ejpam-1518	140	31	,	,	PUNCT
ejpam-1518	140	32	x)≥	x)≥	PROPN
ejpam-1518	140	33	2d(x	2d(x	NUM
ejpam-1518	140	34	)	)	PUNCT
ejpam-1518	140	35	}	}	PUNCT
ejpam-1518	140	36	=	=	SYM
ejpam-1518	140	37	;	;	PUNCT
ejpam-1518	140	38	.	.	PUNCT
ejpam-1518	141	1	in	in	ADP
ejpam-1518	141	2	other	other	ADJ
ejpam-1518	141	3	words	word	NOUN
ejpam-1518	141	4	,	,	PUNCT
ejpam-1518	141	5	{	{	PUNCT
ejpam-1518	141	6	k	k	NOUN
ejpam-1518	141	7	:	:	PUNCT
ejpam-1518	141	8	k	k	PROPN
ejpam-1518	141	9	≤	≤	PROPN
ejpam-1518	141	10	n	n	CCONJ
ejpam-1518	141	11	,	,	PUNCT
ejpam-1518	141	12	d(xk	d(xk	PROPN
ejpam-1518	141	13	,	,	PUNCT
ejpam-1518	141	14	x	x	NOUN
ejpam-1518	141	15	)	)	PUNCT
ejpam-1518	141	16	<	<	X
ejpam-1518	141	17	2d(x	2d(x	NUM
ejpam-1518	141	18	)	)	PUNCT
ejpam-1518	141	19	}	}	PUNCT
ejpam-1518	141	20	=	=	SYM
ejpam-1518	141	21	n.	n.	PROPN
ejpam-1518	141	22	therefore	therefore	ADV
ejpam-1518	141	23	,	,	PUNCT
ejpam-1518	141	24	lim	lim	PROPN
ejpam-1518	141	25	n→∞	n→∞	NUM
ejpam-1518	141	26	1	1	NUM
ejpam-1518	141	27	n	n	PROPN
ejpam-1518	141	28	|{k	|{k	PUNCT
ejpam-1518	141	29	:	:	PUNCT
ejpam-1518	141	30	k	k	PROPN
ejpam-1518	141	31	≤	≤	PROPN
ejpam-1518	141	32	n	n	CCONJ
ejpam-1518	141	33	,	,	PUNCT
ejpam-1518	141	34	d(xk	d(xk	PROPN
ejpam-1518	141	35	,	,	PUNCT
ejpam-1518	141	36	x	x	NOUN
ejpam-1518	141	37	)	)	PUNCT
ejpam-1518	141	38	<	<	X
ejpam-1518	141	39	2d(x	2d(x	NUM
ejpam-1518	141	40	)	)	PUNCT
ejpam-1518	141	41	}	}	PUNCT
ejpam-1518	141	42	|=	|=	X
ejpam-1518	141	43	1	1	X
ejpam-1518	141	44	.	.	PUNCT
ejpam-1518	142	1	this	this	PRON
ejpam-1518	142	2	shows	show	VERB
ejpam-1518	142	3	that	that	SCONJ
ejpam-1518	142	4	x̃	x̃	PROPN
ejpam-1518	142	5	is	be	AUX
ejpam-1518	142	6	a	a	DET
ejpam-1518	142	7	bounded	bounded	ADJ
ejpam-1518	142	8	sequence	sequence	NOUN
ejpam-1518	142	9	.	.	PUNCT
ejpam-1518	143	1	(	(	PUNCT
ejpam-1518	143	2	i)⇒	i)⇒	PROPN
ejpam-1518	143	3	(	(	PUNCT
ejpam-1518	143	4	ii	ii	NOUN
ejpam-1518	143	5	)	)	PUNCT
ejpam-1518	143	6	suppose	suppose	VERB
ejpam-1518	143	7	that	that	SCONJ
ejpam-1518	143	8	|x	|x	PROPN
ejpam-1518	143	9	|=∞.	|=∞.	VERB
ejpam-1518	143	10	then	then	ADV
ejpam-1518	143	11	,	,	PUNCT
ejpam-1518	143	12	there	there	PRON
ejpam-1518	143	13	exist	exist	VERB
ejpam-1518	143	14	at	at	ADV
ejpam-1518	143	15	least	least	ADV
ejpam-1518	143	16	one	one	NUM
ejpam-1518	143	17	sequence	sequence	NOUN
ejpam-1518	143	18	that	that	PRON
ejpam-1518	143	19	d	d	X
ejpam-1518	143	20	–	–	PUNCT
ejpam-1518	143	21	statistical	statistical	ADJ
ejpam-1518	143	22	bounded	bounded	ADJ
ejpam-1518	143	23	but	but	CCONJ
ejpam-1518	143	24	not	not	PART
ejpam-1518	143	25	bounded	bound	VERB
ejpam-1518	143	26	(	(	PUNCT
ejpam-1518	143	27	see	see	VERB
ejpam-1518	143	28	example	example	NOUN
ejpam-1518	143	29	1	1	NUM
ejpam-1518	143	30	)	)	PUNCT
ejpam-1518	143	31	.	.	PUNCT
ejpam-1518	144	1	that	that	PRON
ejpam-1518	144	2	’s	’	VERB
ejpam-1518	144	3	why	why	SCONJ
ejpam-1518	144	4	,	,	PUNCT
ejpam-1518	144	5	our	our	PRON
ejpam-1518	144	6	assumption	assumption	NOUN
ejpam-1518	144	7	is	be	AUX
ejpam-1518	144	8	not	not	PART
ejpam-1518	144	9	true	true	ADJ
ejpam-1518	144	10	.	.	PUNCT
ejpam-1518	145	1	corollary	corollary	ADJ
ejpam-1518	145	2	3	3	X
ejpam-1518	145	3	.	.	PUNCT
ejpam-1518	146	1	let	let	AUX
ejpam-1518	146	2	(	(	PUNCT
ejpam-1518	146	3	x	x	X
ejpam-1518	146	4	,	,	PUNCT
ejpam-1518	146	5	d	d	X
ejpam-1518	146	6	)	)	PUNCT
ejpam-1518	146	7	be	be	AUX
ejpam-1518	146	8	a	a	DET
ejpam-1518	146	9	metric	metric	ADJ
ejpam-1518	146	10	space	space	NOUN
ejpam-1518	146	11	with	with	ADP
ejpam-1518	146	12	finite	finite	ADJ
ejpam-1518	146	13	number	number	NOUN
ejpam-1518	146	14	elements	element	NOUN
ejpam-1518	146	15	.	.	PUNCT
ejpam-1518	147	1	then	then	ADV
ejpam-1518	147	2	,	,	PUNCT
ejpam-1518	147	3	the	the	DET
ejpam-1518	147	4	following	follow	VERB
ejpam-1518	147	5	diagram	diagram	NOUN
ejpam-1518	147	6	holds	hold	VERB
ejpam-1518	147	7	:	:	PUNCT
ejpam-1518	147	8	b(x̃	b(x̃	PROPN
ejpam-1518	147	9	)	)	PUNCT
ejpam-1518	148	1	(	(	PUNCT
ejpam-1518	148	2	2	2	X
ejpam-1518	148	3	)	)	PUNCT
ejpam-1518	148	4	//	//	NOUN
ejpam-1518	148	5	bd	bd	PROPN
ejpam-1518	148	6	st(x̃	st(x̃	NOUN
ejpam-1518	148	7	)	)	PUNCT
ejpam-1518	148	8	oo	oo	ADP
ejpam-1518	148	9	c(x̃	c(x̃	NOUN
ejpam-1518	148	10	)	)	PUNCT
ejpam-1518	148	11	(	(	PUNCT
ejpam-1518	148	12	1	1	X
ejpam-1518	148	13	)	)	PUNCT
ejpam-1518	148	14	oo	oo	INTJ
ejpam-1518	148	15	(	(	PUNCT
ejpam-1518	148	16	5	5	NUM
ejpam-1518	148	17	)	)	PUNCT
ejpam-1518	148	18	;	;	PUNCT
ejpam-1518	148	19	;	;	PUNCT
ejpam-1518	148	20	x	x	PUNCT
ejpam-1518	148	21	x	x	PUNCT
ejpam-1518	148	22	x	x	PUNCT
ejpam-1518	148	23	x	x	PUNCT
ejpam-1518	148	24	x	x	PUNCT
ejpam-1518	148	25	x	x	PUNCT
ejpam-1518	148	26	x	x	PUNCT
ejpam-1518	148	27	x	x	SYM
ejpam-1518	148	28	x	x	X
ejpam-1518	148	29	(	(	PUNCT
ejpam-1518	148	30	3	3	NUM
ejpam-1518	148	31	)	)	PUNCT
ejpam-1518	148	32	//	//	NOUN
ejpam-1518	148	33	c	c	PROPN
ejpam-1518	149	1	d	d	X
ejpam-1518	149	2	st(x̃	st(x̃	NOUN
ejpam-1518	149	3	)	)	PUNCT
ejpam-1518	149	4	(	(	PUNCT
ejpam-1518	149	5	4	4	X
ejpam-1518	149	6	)	)	PUNCT
ejpam-1518	149	7	oo	oo	INTJ
ejpam-1518	149	8	corollary	corollary	ADJ
ejpam-1518	149	9	4	4	NUM
ejpam-1518	149	10	.	.	PUNCT
ejpam-1518	150	1	let	let	AUX
ejpam-1518	150	2	(	(	PUNCT
ejpam-1518	150	3	x	x	X
ejpam-1518	150	4	,	,	PUNCT
ejpam-1518	150	5	d	d	X
ejpam-1518	150	6	)	)	PUNCT
ejpam-1518	150	7	be	be	AUX
ejpam-1518	150	8	a	a	DET
ejpam-1518	150	9	metric	metric	ADJ
ejpam-1518	150	10	space	space	NOUN
ejpam-1518	150	11	with	with	ADP
ejpam-1518	150	12	x	x	PRON
ejpam-1518	150	13	6=	6=	NUM
ejpam-1518	150	14	;	;	PUNCT
ejpam-1518	150	15	.	.	PUNCT
ejpam-1518	151	1	then	then	ADV
ejpam-1518	151	2	,	,	PUNCT
ejpam-1518	151	3	the	the	DET
ejpam-1518	151	4	following	follow	VERB
ejpam-1518	151	5	two	two	NUM
ejpam-1518	151	6	statements	statement	NOUN
ejpam-1518	151	7	are	be	AUX
ejpam-1518	151	8	equivalent	equivalent	ADJ
ejpam-1518	151	9	:	:	PUNCT
ejpam-1518	151	10	(	(	PUNCT
ejpam-1518	151	11	i	i	NOUN
ejpam-1518	151	12	)	)	PUNCT
ejpam-1518	151	13	b(x̃	b(x̃	PROPN
ejpam-1518	151	14	)	)	PUNCT
ejpam-1518	152	1	=	=	PUNCT
ejpam-1518	152	2	c(x̃	c(x̃	NOUN
ejpam-1518	152	3	)	)	PUNCT
ejpam-1518	153	1	=	=	PUNCT
ejpam-1518	153	2	bd	bd	PROPN
ejpam-1518	153	3	st(x̃	st(x̃	NOUN
ejpam-1518	153	4	)	)	PUNCT
ejpam-1518	153	5	=	=	PUNCT
ejpam-1518	154	1	c	c	X
ejpam-1518	154	2	d	d	X
ejpam-1518	154	3	st(x̃	st(x̃	NOUN
ejpam-1518	154	4	)	)	PUNCT
ejpam-1518	154	5	(	(	PUNCT
ejpam-1518	154	6	ii	ii	NOUN
ejpam-1518	154	7	)	)	PUNCT
ejpam-1518	154	8	the	the	DET
ejpam-1518	154	9	set	set	NOUN
ejpam-1518	154	10	x	x	PUNCT
ejpam-1518	154	11	is	be	AUX
ejpam-1518	154	12	a	a	DET
ejpam-1518	154	13	singleton	singleton	NOUN
ejpam-1518	154	14	.	.	PUNCT
ejpam-1518	155	1	proof	proof	NOUN
ejpam-1518	155	2	.	.	PUNCT
ejpam-1518	156	1	the	the	DET
ejpam-1518	156	2	proof	proof	NOUN
ejpam-1518	156	3	is	be	AUX
ejpam-1518	156	4	open	open	ADJ
ejpam-1518	156	5	from	from	ADP
ejpam-1518	156	6	above	above	ADP
ejpam-1518	156	7	the	the	DET
ejpam-1518	156	8	theorem	theorem	ADJ
ejpam-1518	156	9	2	2	NUM
ejpam-1518	156	10	and	and	CCONJ
ejpam-1518	156	11	theorem	theorem	VERB
ejpam-1518	156	12	2.2	2.2	NUM
ejpam-1518	156	13	in	in	ADP
ejpam-1518	156	14	[	[	X
ejpam-1518	156	15	12	12	NUM
ejpam-1518	156	16	]	]	PUNCT
ejpam-1518	156	17	.	.	PUNCT
ejpam-1518	157	1	theorem	theorem	NOUN
ejpam-1518	157	2	3	3	X
ejpam-1518	157	3	.	.	PUNCT
ejpam-1518	158	1	let	let	VERB
ejpam-1518	158	2	x	x	PRON
ejpam-1518	158	3	be	be	AUX
ejpam-1518	158	4	a	a	DET
ejpam-1518	158	5	set	set	NOUN
ejpam-1518	158	6	which	which	PRON
ejpam-1518	158	7	has	have	VERB
ejpam-1518	158	8	at	at	ADV
ejpam-1518	158	9	least	least	ADV
ejpam-1518	158	10	two	two	NUM
ejpam-1518	158	11	elements	element	NOUN
ejpam-1518	158	12	and	and	CCONJ
ejpam-1518	158	13	endowed	endow	VERB
ejpam-1518	158	14	ρ	ρ	NUM
ejpam-1518	158	15	discrete	discrete	NOUN
ejpam-1518	158	16	metric	metric	ADJ
ejpam-1518	158	17	.	.	PUNCT
ejpam-1518	159	1	then	then	ADV
ejpam-1518	159	2	,	,	PUNCT
ejpam-1518	159	3	we	we	PRON
ejpam-1518	159	4	have	have	VERB
ejpam-1518	159	5	x̃	x̃	PROPN
ejpam-1518	159	6	=	=	SYM
ejpam-1518	159	7	b(x̃	b(x̃	PROPN
ejpam-1518	159	8	)	)	PUNCT
ejpam-1518	160	1	=	=	PUNCT
ejpam-1518	160	2	b	b	PROPN
ejpam-1518	160	3	ρ	ρ	NOUN
ejpam-1518	160	4	st(x̃	st(x̃	NOUN
ejpam-1518	160	5	)	)	PUNCT
ejpam-1518	160	6	(	(	PUNCT
ejpam-1518	160	7	6	6	NUM
ejpam-1518	160	8	)	)	PUNCT
ejpam-1518	160	9	and	and	CCONJ
ejpam-1518	160	10	c(x̃	c(x̃	NOUN
ejpam-1518	160	11	)	)	PUNCT
ejpam-1518	161	1	⊂	⊂	PROPN
ejpam-1518	161	2	c	c	PROPN
ejpam-1518	161	3	ρ	ρ	NOUN
ejpam-1518	161	4	st(x̃	st(x̃	PROPN
ejpam-1518	161	5	)	)	PUNCT
ejpam-1518	161	6	.	.	PUNCT
ejpam-1518	162	1	(	(	PUNCT
ejpam-1518	162	2	7	7	X
ejpam-1518	162	3	)	)	PUNCT
ejpam-1518	162	4	m.	m.	NOUN
ejpam-1518	162	5	küçükaslan	küçükaslan	NOUN
ejpam-1518	162	6	,	,	PUNCT
ejpam-1518	162	7	u.	u.	PROPN
ejpam-1518	162	8	değer	değer	PROPN
ejpam-1518	162	9	/	/	SYM
ejpam-1518	162	10	eur	eur	PROPN
ejpam-1518	162	11	.	.	PUNCT
ejpam-1518	163	1	j.	j.	PROPN
ejpam-1518	163	2	pure	pure	PROPN
ejpam-1518	163	3	appl	appl	PROPN
ejpam-1518	163	4	.	.	PROPN
ejpam-1518	163	5	math	math	PROPN
ejpam-1518	163	6	,	,	PUNCT
ejpam-1518	163	7	5	5	NUM
ejpam-1518	163	8	(	(	PUNCT
ejpam-1518	163	9	2012	2012	NUM
ejpam-1518	163	10	)	)	PUNCT
ejpam-1518	163	11	,	,	PUNCT
ejpam-1518	163	12	174	174	NUM
ejpam-1518	163	13	-	-	SYM
ejpam-1518	163	14	186	186	NUM
ejpam-1518	163	15	180	180	NUM
ejpam-1518	163	16	proof	proof	NOUN
ejpam-1518	163	17	.	.	PUNCT
ejpam-1518	164	1	we	we	PRON
ejpam-1518	164	2	know	know	VERB
ejpam-1518	164	3	that	that	SCONJ
ejpam-1518	164	4	any	any	DET
ejpam-1518	164	5	space	space	NOUN
ejpam-1518	164	6	with	with	ADP
ejpam-1518	164	7	discrete	discrete	ADJ
ejpam-1518	164	8	metric	metric	NOUN
ejpam-1518	164	9	has	have	VERB
ejpam-1518	164	10	finite	finite	ADJ
ejpam-1518	164	11	diameter	diameter	NOUN
ejpam-1518	164	12	.	.	PUNCT
ejpam-1518	165	1	therefore	therefore	ADV
ejpam-1518	165	2	,	,	PUNCT
ejpam-1518	165	3	any	any	DET
ejpam-1518	165	4	sequence	sequence	NOUN
ejpam-1518	165	5	in	in	ADP
ejpam-1518	165	6	this	this	DET
ejpam-1518	165	7	space	space	NOUN
ejpam-1518	165	8	is	be	AUX
ejpam-1518	165	9	bounded	bound	VERB
ejpam-1518	165	10	.	.	PUNCT
ejpam-1518	166	1	that	that	PRON
ejpam-1518	166	2	is	be	AUX
ejpam-1518	166	3	,	,	PUNCT
ejpam-1518	166	4	there	there	PRON
ejpam-1518	166	5	is	be	VERB
ejpam-1518	166	6	a	a	DET
ejpam-1518	166	7	m	m	NOUN
ejpam-1518	166	8	>	>	X
ejpam-1518	166	9	0	0	PUNCT
ejpam-1518	167	1	and	and	CCONJ
ejpam-1518	167	2	arbitrary	arbitrary	ADJ
ejpam-1518	167	3	x	x	SYM
ejpam-1518	167	4	∈	∈	PROPN
ejpam-1518	167	5	x	x	X
ejpam-1518	167	6	such	such	ADJ
ejpam-1518	167	7	that	that	SCONJ
ejpam-1518	167	8	ρ(xn	ρ(xn	NUM
ejpam-1518	167	9	,	,	PUNCT
ejpam-1518	167	10	x	x	NOUN
ejpam-1518	167	11	)	)	PUNCT
ejpam-1518	167	12	<	<	X
ejpam-1518	167	13	m	m	VERB
ejpam-1518	167	14	for	for	ADP
ejpam-1518	167	15	every	every	PRON
ejpam-1518	167	16	x̃	x̃	PROPN
ejpam-1518	167	17	=	=	SYM
ejpam-1518	167	18	(	(	PUNCT
ejpam-1518	167	19	xn	xn	X
ejpam-1518	167	20	)	)	PUNCT
ejpam-1518	167	21	∈	∈	PROPN
ejpam-1518	168	1	x̃	x̃	PROPN
ejpam-1518	168	2	.	.	PUNCT
ejpam-1518	169	1	so	so	ADV
ejpam-1518	169	2	,	,	PUNCT
ejpam-1518	169	3	we	we	PRON
ejpam-1518	169	4	have	have	VERB
ejpam-1518	169	5	{	{	PUNCT
ejpam-1518	169	6	k	k	NOUN
ejpam-1518	169	7	:	:	PUNCT
ejpam-1518	169	8	k	k	PROPN
ejpam-1518	169	9	≤	≤	PROPN
ejpam-1518	169	10	n	n	CCONJ
ejpam-1518	169	11	,	,	PUNCT
ejpam-1518	169	12	ρ(xk	ρ(xk	NUM
ejpam-1518	169	13	,	,	PUNCT
ejpam-1518	169	14	x)≥	x)≥	PROPN
ejpam-1518	169	15	m	m	PROPN
ejpam-1518	169	16	}	}	PUNCT
ejpam-1518	169	17	=	=	SYM
ejpam-1518	169	18	;	;	PUNCT
ejpam-1518	169	19	.	.	PUNCT
ejpam-1518	170	1	hence	hence	ADV
ejpam-1518	170	2	,	,	PUNCT
ejpam-1518	170	3	lim	lim	PROPN
ejpam-1518	170	4	n→∞	n→∞	NUM
ejpam-1518	170	5	1	1	NUM
ejpam-1518	170	6	n	n	PROPN
ejpam-1518	170	7	|{k	|{k	PUNCT
ejpam-1518	170	8	:	:	PUNCT
ejpam-1518	170	9	k	k	PROPN
ejpam-1518	170	10	≤	≤	PROPN
ejpam-1518	170	11	n	n	CCONJ
ejpam-1518	170	12	,	,	PUNCT
ejpam-1518	170	13	ρ(xk	ρ(xk	NUM
ejpam-1518	170	14	,	,	PUNCT
ejpam-1518	170	15	x)≥	x)≥	NOUN
ejpam-1518	170	16	m}|	m}|	NOUN
ejpam-1518	170	17	=	=	SYM
ejpam-1518	170	18	0	0	NUM
ejpam-1518	170	19	.	.	PUNCT
ejpam-1518	171	1	this	this	PRON
ejpam-1518	171	2	shows	show	VERB
ejpam-1518	171	3	that	that	SCONJ
ejpam-1518	171	4	x̃	x̃	PROPN
ejpam-1518	171	5	∈	∈	PROPN
ejpam-1518	171	6	b	b	PROPN
ejpam-1518	171	7	ρ	ρ	PROPN
ejpam-1518	171	8	st(x̃	st(x̃	NOUN
ejpam-1518	171	9	)	)	PUNCT
ejpam-1518	171	10	for	for	ADP
ejpam-1518	171	11	all	all	DET
ejpam-1518	171	12	x̃	x̃	PROPN
ejpam-1518	171	13	∈	∈	PROPN
ejpam-1518	171	14	x̃	x̃	PROPN
ejpam-1518	171	15	.	.	PUNCT
ejpam-1518	172	1	let	let	VERB
ejpam-1518	172	2	us	we	PRON
ejpam-1518	172	3	take	take	VERB
ejpam-1518	172	4	an	an	DET
ejpam-1518	172	5	arbitrary	arbitrary	ADJ
ejpam-1518	172	6	sequence	sequence	NOUN
ejpam-1518	172	7	x̃	x̃	PROPN
ejpam-1518	172	8	∈	∈	PROPN
ejpam-1518	172	9	b	b	PROPN
ejpam-1518	172	10	ρ	ρ	PROPN
ejpam-1518	172	11	st	st	PROPN
ejpam-1518	172	12	.	.	PUNCT
ejpam-1518	173	1	if	if	SCONJ
ejpam-1518	173	2	we	we	PRON
ejpam-1518	173	3	choose	choose	VERB
ejpam-1518	173	4	m	m	PRON
ejpam-1518	173	5	>	>	X
ejpam-1518	173	6	1	1	NUM
ejpam-1518	173	7	,	,	PUNCT
ejpam-1518	173	8	then	then	ADV
ejpam-1518	173	9	{	{	PUNCT
ejpam-1518	173	10	k	k	NOUN
ejpam-1518	173	11	:	:	PUNCT
ejpam-1518	173	12	k	k	PROPN
ejpam-1518	173	13	≤	≤	PROPN
ejpam-1518	173	14	n	n	CCONJ
ejpam-1518	173	15	,	,	PUNCT
ejpam-1518	173	16	ρ(xk	ρ(xk	NUM
ejpam-1518	173	17	,	,	PUNCT
ejpam-1518	173	18	x	x	X
ejpam-1518	173	19	)	)	PUNCT
ejpam-1518	173	20	≥	≥	NUM
ejpam-1518	173	21	m	m	NOUN
ejpam-1518	173	22	}	}	PUNCT
ejpam-1518	173	23	=	=	SYM
ejpam-1518	173	24	;	;	PUNCT
ejpam-1518	173	25	.	.	PUNCT
ejpam-1518	174	1	it	it	PRON
ejpam-1518	174	2	means	mean	VERB
ejpam-1518	174	3	that	that	SCONJ
ejpam-1518	174	4	ρ(xk	ρ(xk	ADJ
ejpam-1518	174	5	,	,	PUNCT
ejpam-1518	174	6	x	x	X
ejpam-1518	174	7	)	)	PUNCT
ejpam-1518	174	8	<	<	X
ejpam-1518	174	9	m	m	VERB
ejpam-1518	174	10	for	for	ADP
ejpam-1518	174	11	all	all	DET
ejpam-1518	174	12	k	k	PROPN
ejpam-1518	174	13	∈	∈	PROPN
ejpam-1518	174	14	n.	n.	PROPN
ejpam-1518	174	15	thus	thus	ADV
ejpam-1518	174	16	,	,	PUNCT
ejpam-1518	174	17	we	we	PRON
ejpam-1518	174	18	see	see	VERB
ejpam-1518	174	19	that	that	SCONJ
ejpam-1518	174	20	x̃	x̃	PROPN
ejpam-1518	174	21	∈	∈	PROPN
ejpam-1518	174	22	b(x̃	b(x̃	PROPN
ejpam-1518	174	23	)	)	PUNCT
ejpam-1518	174	24	.	.	PUNCT
ejpam-1518	175	1	now	now	ADV
ejpam-1518	175	2	let	let	VERB
ejpam-1518	175	3	us	we	PRON
ejpam-1518	175	4	see	see	VERB
ejpam-1518	175	5	that	that	SCONJ
ejpam-1518	175	6	c(x̃	c(x̃	NOUN
ejpam-1518	175	7	)	)	PUNCT
ejpam-1518	176	1	⊂	⊂	PROPN
ejpam-1518	176	2	c	c	PROPN
ejpam-1518	176	3	ρ	ρ	NOUN
ejpam-1518	176	4	st(x̃	st(x̃	PROPN
ejpam-1518	176	5	)	)	PUNCT
ejpam-1518	176	6	.	.	PUNCT
ejpam-1518	177	1	let	let	VERB
ejpam-1518	177	2	x̃	x̃	PROPN
ejpam-1518	177	3	∈	∈	PROPN
ejpam-1518	177	4	c(x̃	c(x̃	PROPN
ejpam-1518	177	5	)	)	PUNCT
ejpam-1518	177	6	.	.	PUNCT
ejpam-1518	178	1	then	then	ADV
ejpam-1518	178	2	for	for	ADP
ejpam-1518	178	3	an	an	DET
ejpam-1518	178	4	arbitrary	arbitrary	ADJ
ejpam-1518	178	5	ǫ	ǫ	NOUN
ejpam-1518	178	6	>	>	X
ejpam-1518	178	7	0	0	PUNCT
ejpam-1518	178	8	there	there	PRON
ejpam-1518	178	9	exist	exist	VERB
ejpam-1518	178	10	n0	n0	X
ejpam-1518	178	11	=	=	SYM
ejpam-1518	178	12	n0(ǫ	n0(ǫ	PROPN
ejpam-1518	178	13	)	)	PUNCT
ejpam-1518	178	14	∈	∈	PROPN
ejpam-1518	178	15	n	n	PRON
ejpam-1518	178	16	such	such	ADJ
ejpam-1518	178	17	that	that	PRON
ejpam-1518	178	18	xn	xn	PROPN
ejpam-1518	179	1	=	=	PUNCT
ejpam-1518	179	2	xn0	xn0	PROPN
ejpam-1518	179	3	for	for	ADP
ejpam-1518	179	4	all	all	DET
ejpam-1518	179	5	n≥	n≥	PROPN
ejpam-1518	179	6	n0	n0	NUM
ejpam-1518	179	7	.	.	PUNCT
ejpam-1518	180	1	therefore	therefore	ADV
ejpam-1518	180	2	,	,	PUNCT
ejpam-1518	180	3	we	we	PRON
ejpam-1518	180	4	have	have	VERB
ejpam-1518	180	5	lim	lim	PROPN
ejpam-1518	180	6	n→∞	n→∞	NUM
ejpam-1518	180	7	1	1	NUM
ejpam-1518	180	8	n	n	NOUN
ejpam-1518	180	9	|{k	|{k	PUNCT
ejpam-1518	180	10	:	:	PUNCT
ejpam-1518	180	11	k	k	PROPN
ejpam-1518	180	12	≤	≤	PROPN
ejpam-1518	180	13	n	n	CCONJ
ejpam-1518	180	14	,	,	PUNCT
ejpam-1518	180	15	ρ(xk	ρ(xk	NUM
ejpam-1518	180	16	,	,	PUNCT
ejpam-1518	180	17	xn0	xn0	PROPN
ejpam-1518	180	18	)	)	PUNCT
ejpam-1518	180	19	≥	≥	X
ejpam-1518	180	20	ǫ}|	ǫ}|	NOUN
ejpam-1518	180	21	≤	≤	NUM
ejpam-1518	181	1	lim	lim	PROPN
ejpam-1518	181	2	n→∞	n→∞	NUM
ejpam-1518	181	3	n0	n0	PROPN
ejpam-1518	181	4	n	n	PROPN
ejpam-1518	181	5	=	=	SYM
ejpam-1518	181	6	0	0	PROPN
ejpam-1518	181	7	.	.	PUNCT
ejpam-1518	182	1	this	this	PRON
ejpam-1518	182	2	shows	show	VERB
ejpam-1518	182	3	that	that	SCONJ
ejpam-1518	182	4	x̃	x̃	PROPN
ejpam-1518	182	5	∈	∈	PROPN
ejpam-1518	182	6	c	c	PROPN
ejpam-1518	182	7	ρ	ρ	NOUN
ejpam-1518	182	8	st(x̃	st(x̃	PROPN
ejpam-1518	182	9	)	)	PUNCT
ejpam-1518	182	10	.	.	PUNCT
ejpam-1518	183	1	if	if	SCONJ
ejpam-1518	183	2	we	we	PRON
ejpam-1518	183	3	consider	consider	VERB
ejpam-1518	183	4	the	the	DET
ejpam-1518	183	5	sequence	sequence	NOUN
ejpam-1518	183	6	x̃	x̃	PROPN
ejpam-1518	183	7	=	=	PUNCT
ejpam-1518	183	8	(	(	PUNCT
ejpam-1518	183	9	xn	xn	PROPN
ejpam-1518	183	10	)	)	PUNCT
ejpam-1518	183	11	with	with	ADP
ejpam-1518	183	12	xn	xn	PROPN
ejpam-1518	183	13	:	:	PUNCT
ejpam-1518	183	14	=	=	SYM
ejpam-1518	183	15	(	(	PUNCT
ejpam-1518	183	16	x	x	X
ejpam-1518	183	17	if	if	SCONJ
ejpam-1518	183	18	n=	n=	ADJ
ejpam-1518	183	19	k2	k2	NOUN
ejpam-1518	183	20	,	,	PUNCT
ejpam-1518	183	21	k	k	PROPN
ejpam-1518	183	22	∈	∈	PROPN
ejpam-1518	183	23	n	n	CCONJ
ejpam-1518	183	24	y	y	PROPN
ejpam-1518	183	25	if	if	SCONJ
ejpam-1518	183	26	n	n	PROPN
ejpam-1518	183	27	6=	6=	PROPN
ejpam-1518	183	28	k2	k2	PROPN
ejpam-1518	183	29	then	then	ADV
ejpam-1518	183	30	x̃	x̃	PROPN
ejpam-1518	183	31	is	be	AUX
ejpam-1518	183	32	ρstatistical	ρstatistical	ADJ
ejpam-1518	183	33	convergent	convergent	NOUN
ejpam-1518	183	34	to	to	ADP
ejpam-1518	183	35	x	x	PUNCT
ejpam-1518	183	36	but	but	CCONJ
ejpam-1518	183	37	not	not	PART
ejpam-1518	183	38	convergent	convergent	NOUN
ejpam-1518	183	39	.	.	PUNCT
ejpam-1518	184	1	so	so	ADV
ejpam-1518	184	2	,	,	PUNCT
ejpam-1518	184	3	the	the	DET
ejpam-1518	184	4	inclusion	inclusion	NOUN
ejpam-1518	184	5	in	in	ADP
ejpam-1518	184	6	(	(	PUNCT
ejpam-1518	184	7	7	7	X
ejpam-1518	184	8	)	)	PUNCT
ejpam-1518	184	9	is	be	AUX
ejpam-1518	184	10	sharp	sharp	ADJ
ejpam-1518	184	11	.	.	PUNCT
ejpam-1518	185	1	corollary	corollary	ADJ
ejpam-1518	185	2	5	5	NUM
ejpam-1518	185	3	.	.	PUNCT
ejpam-1518	186	1	let	let	VERB
ejpam-1518	186	2	x	x	PRON
ejpam-1518	186	3	be	be	AUX
ejpam-1518	186	4	a	a	DET
ejpam-1518	186	5	set	set	NOUN
ejpam-1518	186	6	which	which	PRON
ejpam-1518	186	7	has	have	VERB
ejpam-1518	186	8	at	at	ADV
ejpam-1518	186	9	least	least	ADV
ejpam-1518	186	10	two	two	NUM
ejpam-1518	186	11	elements	element	NOUN
ejpam-1518	186	12	and	and	CCONJ
ejpam-1518	186	13	endowed	endow	VERB
ejpam-1518	186	14	bounded	bounded	ADJ
ejpam-1518	186	15	metric	metric	PROPN
ejpam-1518	186	16	.	.	PUNCT
ejpam-1518	187	1	then	then	ADV
ejpam-1518	187	2	,	,	PUNCT
ejpam-1518	187	3	(	(	PUNCT
ejpam-1518	187	4	6	6	NUM
ejpam-1518	187	5	)	)	PUNCT
ejpam-1518	187	6	and	and	CCONJ
ejpam-1518	187	7	(	(	PUNCT
ejpam-1518	187	8	7	7	X
ejpam-1518	187	9	)	)	PUNCT
ejpam-1518	187	10	hold	hold	NOUN
ejpam-1518	187	11	.	.	PUNCT
ejpam-1518	188	1	theorem	theorem	ADJ
ejpam-1518	188	2	4	4	NUM
ejpam-1518	188	3	.	.	PUNCT
ejpam-1518	189	1	let	let	AUX
ejpam-1518	189	2	(	(	PUNCT
ejpam-1518	189	3	x	x	X
ejpam-1518	189	4	,	,	PUNCT
ejpam-1518	189	5	d	d	X
ejpam-1518	189	6	)	)	PUNCT
ejpam-1518	189	7	be	be	AUX
ejpam-1518	189	8	a	a	DET
ejpam-1518	189	9	metric	metric	ADJ
ejpam-1518	189	10	space	space	NOUN
ejpam-1518	189	11	,	,	PUNCT
ejpam-1518	190	1	x̃	x̃	PROPN
ejpam-1518	190	2	=	=	SYM
ejpam-1518	190	3	(	(	PUNCT
ejpam-1518	190	4	xn	xn	X
ejpam-1518	190	5	)	)	PUNCT
ejpam-1518	190	6	∈	∈	PROPN
ejpam-1518	190	7	x̃	x̃	PROPN
ejpam-1518	191	1	and	and	CCONJ
ejpam-1518	191	2	let	let	VERB
ejpam-1518	191	3	x̃	x̃	PROPN
ejpam-1518	191	4	′	′	NUM
ejpam-1518	192	1	=	=	PUNCT
ejpam-1518	192	2	(	(	PUNCT
ejpam-1518	192	3	xnk	xnk	PROPN
ejpam-1518	192	4	)	)	PUNCT
ejpam-1518	192	5	be	be	AUX
ejpam-1518	192	6	a	a	DET
ejpam-1518	192	7	subsequence	subsequence	NOUN
ejpam-1518	192	8	of	of	ADP
ejpam-1518	192	9	x̃.	x̃.	ADJ
ejpam-1518	192	10	if	if	SCONJ
ejpam-1518	192	11	x̃	x̃	PROPN
ejpam-1518	192	12	is	be	AUX
ejpam-1518	192	13	d	d	ADJ
ejpam-1518	192	14	-	-	ADJ
ejpam-1518	192	15	statistical	statistical	ADJ
ejpam-1518	192	16	bounded	bounded	NOUN
ejpam-1518	192	17	then	then	ADV
ejpam-1518	192	18	x̃	x̃	PROPN
ejpam-1518	192	19	′	′	PROPN
ejpam-1518	192	20	is	be	AUX
ejpam-1518	192	21	also	also	ADV
ejpam-1518	192	22	d	d	ADJ
ejpam-1518	192	23	-	-	ADJ
ejpam-1518	192	24	statistical	statistical	ADJ
ejpam-1518	192	25	bounded	bound	VERB
ejpam-1518	192	26	.	.	PUNCT
ejpam-1518	193	1	proof	proof	NOUN
ejpam-1518	193	2	.	.	PUNCT
ejpam-1518	194	1	suppose	suppose	VERB
ejpam-1518	194	2	that	that	SCONJ
ejpam-1518	194	3	x̃	x̃	PROPN
ejpam-1518	194	4	is	be	AUX
ejpam-1518	194	5	d	d	NOUN
ejpam-1518	194	6	–	–	PUNCT
ejpam-1518	194	7	statistical	statistical	ADJ
ejpam-1518	194	8	bounded	bound	VERB
ejpam-1518	194	9	.	.	PUNCT
ejpam-1518	195	1	it	it	PRON
ejpam-1518	195	2	is	be	AUX
ejpam-1518	195	3	clear	clear	ADJ
ejpam-1518	195	4	that	that	SCONJ
ejpam-1518	195	5	there	there	PRON
ejpam-1518	195	6	is	be	VERB
ejpam-1518	195	7	a	a	DET
ejpam-1518	195	8	number	number	NOUN
ejpam-1518	195	9	m	m	NOUN
ejpam-1518	195	10	>	>	X
ejpam-1518	195	11	0	0	PUNCT
ejpam-1518	196	1	and	and	CCONJ
ejpam-1518	196	2	x	x	SYM
ejpam-1518	196	3	∈	∈	PROPN
ejpam-1518	196	4	x	x	PUNCT
ejpam-1518	196	5	such	such	ADJ
ejpam-1518	196	6	that	that	SCONJ
ejpam-1518	196	7	{	{	PUNCT
ejpam-1518	196	8	nk	nk	INTJ
ejpam-1518	196	9	:	:	PUNCT
ejpam-1518	196	10	nk	nk	PROPN
ejpam-1518	196	11	≤	≤	PROPN
ejpam-1518	196	12	n	n	CCONJ
ejpam-1518	196	13	,	,	PUNCT
ejpam-1518	196	14	d(xnk	d(xnk	PROPN
ejpam-1518	196	15	,	,	PUNCT
ejpam-1518	196	16	x)≥	x)≥	PROPN
ejpam-1518	196	17	m	m	NOUN
ejpam-1518	196	18	}	}	PUNCT
ejpam-1518	196	19	⊂	⊂	PRON
ejpam-1518	196	20	{	{	PUNCT
ejpam-1518	196	21	k	k	X
ejpam-1518	196	22	:	:	PUNCT
ejpam-1518	196	23	k	k	PROPN
ejpam-1518	196	24	≤	≤	PROPN
ejpam-1518	196	25	n	n	CCONJ
ejpam-1518	196	26	,	,	PUNCT
ejpam-1518	196	27	d(xk	d(xk	PROPN
ejpam-1518	196	28	,	,	PUNCT
ejpam-1518	196	29	x)≥	x)≥	PROPN
ejpam-1518	196	30	m	m	PROPN
ejpam-1518	196	31	}	}	PUNCT
ejpam-1518	196	32	.	.	PUNCT
ejpam-1518	197	1	then	then	ADV
ejpam-1518	197	2	,	,	PUNCT
ejpam-1518	197	3	since	since	SCONJ
ejpam-1518	197	4	|{nk	|{nk	PROPN
ejpam-1518	197	5	:	:	PUNCT
ejpam-1518	197	6	nk	nk	PROPN
ejpam-1518	197	7	≤	≤	PROPN
ejpam-1518	197	8	n	n	CCONJ
ejpam-1518	197	9	,	,	PUNCT
ejpam-1518	197	10	d(xnk	d(xnk	PROPN
ejpam-1518	197	11	,	,	PUNCT
ejpam-1518	197	12	x)≥	x)≥	PROPN
ejpam-1518	197	13	m}|	m}|	NOUN
ejpam-1518	197	14	≤	≤	NUM
ejpam-1518	197	15	|{k	|{k	PUNCT
ejpam-1518	197	16	:	:	PUNCT
ejpam-1518	198	1	k	k	PROPN
ejpam-1518	198	2	≤	≤	PROPN
ejpam-1518	198	3	n	n	CCONJ
ejpam-1518	198	4	,	,	PUNCT
ejpam-1518	198	5	d(xk	d(xk	PROPN
ejpam-1518	198	6	,	,	PUNCT
ejpam-1518	198	7	x)≥	x)≥	PROPN
ejpam-1518	198	8	m}|	m}|	NOUN
ejpam-1518	198	9	,	,	PUNCT
ejpam-1518	198	10	we	we	PRON
ejpam-1518	198	11	have	have	VERB
ejpam-1518	198	12	0≤	0≤	ADJ
ejpam-1518	198	13	lim	lim	NOUN
ejpam-1518	198	14	n→∞	n→∞	NUM
ejpam-1518	199	1	1	1	NUM
ejpam-1518	199	2	n	n	PRON
ejpam-1518	199	3	�	�	PROPN
ejpam-1518	199	4	�	�	PROPN
ejpam-1518	199	5	�	�	PROPN
ejpam-1518	199	6	¦	¦	PROPN
ejpam-1518	199	7	nk	nk	PROPN
ejpam-1518	199	8	:	:	PUNCT
ejpam-1518	199	9	nk	nk	PROPN
ejpam-1518	199	10	≤	≤	PROPN
ejpam-1518	199	11	n	n	CCONJ
ejpam-1518	199	12	and	and	CCONJ
ejpam-1518	199	13	d(xnk	d(xnk	PROPN
ejpam-1518	199	14	,	,	PUNCT
ejpam-1518	199	15	x)≥	x)≥	PROPN
ejpam-1518	199	16	m	m	PROPN
ejpam-1518	199	17	©	©	PROPN
ejpam-1518	199	18	�	�	PROPN
ejpam-1518	199	19	�	�	PROPN
ejpam-1518	199	20	�	�	NOUN
ejpam-1518	199	21	≤	≤	NOUN
ejpam-1518	199	22	0	0	NUM
ejpam-1518	199	23	.	.	PUNCT
ejpam-1518	200	1	the	the	DET
ejpam-1518	200	2	last	last	ADJ
ejpam-1518	200	3	inequality	inequality	NOUN
ejpam-1518	200	4	shows	show	VERB
ejpam-1518	200	5	that	that	SCONJ
ejpam-1518	200	6	x̃	x̃	PROPN
ejpam-1518	200	7	′	′	NUM
ejpam-1518	200	8	is	be	AUX
ejpam-1518	200	9	d	d	NOUN
ejpam-1518	200	10	–	–	PUNCT
ejpam-1518	200	11	statistical	statistical	ADJ
ejpam-1518	200	12	bounded	bound	VERB
ejpam-1518	200	13	.	.	PUNCT
ejpam-1518	201	1	m.	m.	PROPN
ejpam-1518	201	2	küçükaslan	küçükaslan	PROPN
ejpam-1518	201	3	,	,	PUNCT
ejpam-1518	201	4	u.	u.	PROPN
ejpam-1518	201	5	değer	değer	PROPN
ejpam-1518	201	6	/	/	SYM
ejpam-1518	201	7	eur	eur	PROPN
ejpam-1518	201	8	.	.	PUNCT
ejpam-1518	202	1	j.	j.	PROPN
ejpam-1518	202	2	pure	pure	PROPN
ejpam-1518	202	3	appl	appl	PROPN
ejpam-1518	202	4	.	.	PROPN
ejpam-1518	202	5	math	math	PROPN
ejpam-1518	202	6	,	,	PUNCT
ejpam-1518	202	7	5	5	NUM
ejpam-1518	202	8	(	(	PUNCT
ejpam-1518	202	9	2012	2012	NUM
ejpam-1518	202	10	)	)	PUNCT
ejpam-1518	202	11	,	,	PUNCT
ejpam-1518	202	12	174	174	NUM
ejpam-1518	202	13	-	-	SYM
ejpam-1518	202	14	186	186	NUM
ejpam-1518	202	15	181	181	NUM
ejpam-1518	202	16	lemma	lemma	PROPN
ejpam-1518	202	17	1	1	NUM
ejpam-1518	202	18	.	.	PUNCT
ejpam-1518	203	1	let	let	AUX
ejpam-1518	203	2	(	(	PUNCT
ejpam-1518	203	3	x	x	X
ejpam-1518	203	4	,	,	PUNCT
ejpam-1518	203	5	d	d	X
ejpam-1518	203	6	)	)	PUNCT
ejpam-1518	203	7	be	be	AUX
ejpam-1518	203	8	a	a	DET
ejpam-1518	203	9	metric	metric	ADJ
ejpam-1518	203	10	space	space	NOUN
ejpam-1518	203	11	and	and	CCONJ
ejpam-1518	203	12	ex	ex	NOUN
ejpam-1518	203	13	=	=	SYM
ejpam-1518	203	14	(	(	PUNCT
ejpam-1518	203	15	xn	xn	X
ejpam-1518	203	16	)	)	PUNCT
ejpam-1518	203	17	∈	∈	PROPN
ejpam-1518	204	1	ex	ex	X
ejpam-1518	204	2	.	.	PUNCT
ejpam-1518	205	1	then	then	ADV
ejpam-1518	205	2	,	,	PUNCT
ejpam-1518	205	3	the	the	DET
ejpam-1518	205	4	sequence	sequence	NOUN
ejpam-1518	205	5	x̃	x̃	PROPN
ejpam-1518	205	6	is	be	AUX
ejpam-1518	205	7	d−st	d−st	NOUN
ejpam-1518	205	8	bounded	bound	VERB
ejpam-1518	205	9	if	if	SCONJ
ejpam-1518	205	10	and	and	CCONJ
ejpam-1518	205	11	only	only	ADV
ejpam-1518	205	12	if	if	SCONJ
ejpam-1518	205	13	the	the	DET
ejpam-1518	205	14	real	real	ADJ
ejpam-1518	205	15	sequence	sequence	NOUN
ejpam-1518	205	16	�	�	PROPN
ejpam-1518	205	17	d(xn	d(xn	PROPN
ejpam-1518	205	18	,	,	PUNCT
ejpam-1518	205	19	x	x	X
ejpam-1518	205	20	)	)	PUNCT
ejpam-1518	205	21	�	�	PROPN
ejpam-1518	205	22	is	be	AUX
ejpam-1518	205	23	statistical	statistical	ADJ
ejpam-1518	205	24	bounded	bounded	ADJ
ejpam-1518	205	25	for	for	ADP
ejpam-1518	205	26	an	an	DET
ejpam-1518	205	27	arbitrary	arbitrary	ADJ
ejpam-1518	205	28	x	x	SYM
ejpam-1518	205	29	∈	∈	PROPN
ejpam-1518	205	30	x	x	X
ejpam-1518	205	31	.	.	PUNCT
ejpam-1518	206	1	it	it	PRON
ejpam-1518	206	2	can	can	AUX
ejpam-1518	206	3	be	be	AUX
ejpam-1518	206	4	obtained	obtain	VERB
ejpam-1518	206	5	directly	directly	ADV
ejpam-1518	206	6	from	from	ADP
ejpam-1518	206	7	the	the	DET
ejpam-1518	206	8	definition	definition	NOUN
ejpam-1518	206	9	1.2-(ii	1.2-(ii	NUM
ejpam-1518	206	10	)	)	PUNCT
ejpam-1518	206	11	.	.	PUNCT
ejpam-1518	207	1	so	so	ADV
ejpam-1518	207	2	,	,	PUNCT
ejpam-1518	207	3	the	the	DET
ejpam-1518	207	4	proof	proof	NOUN
ejpam-1518	207	5	is	be	AUX
ejpam-1518	207	6	omitted	omit	VERB
ejpam-1518	207	7	here	here	ADV
ejpam-1518	207	8	.	.	PUNCT
ejpam-1518	208	1	lemma	lemma	PROPN
ejpam-1518	208	2	2	2	X
ejpam-1518	208	3	.	.	PUNCT
ejpam-1518	209	1	let	let	AUX
ejpam-1518	209	2	(	(	PUNCT
ejpam-1518	209	3	x	x	X
ejpam-1518	209	4	,	,	PUNCT
ejpam-1518	209	5	d	d	X
ejpam-1518	209	6	)	)	PUNCT
ejpam-1518	209	7	be	be	AUX
ejpam-1518	209	8	a	a	DET
ejpam-1518	209	9	metric	metric	ADJ
ejpam-1518	209	10	space	space	NOUN
ejpam-1518	209	11	and	and	CCONJ
ejpam-1518	209	12	ex	ex	NOUN
ejpam-1518	209	13	=	=	SYM
ejpam-1518	209	14	(	(	PUNCT
ejpam-1518	209	15	xn	xn	X
ejpam-1518	209	16	)	)	PUNCT
ejpam-1518	209	17	∈	∈	PROPN
ejpam-1518	209	18	ex	ex	X
ejpam-1518	209	19	be	be	AUX
ejpam-1518	209	20	a	a	DET
ejpam-1518	209	21	d−statistical	d−statistical	PROPN
ejpam-1518	209	22	bounded	bounded	ADJ
ejpam-1518	209	23	sequence	sequence	NOUN
ejpam-1518	209	24	.	.	PUNCT
ejpam-1518	210	1	then	then	ADV
ejpam-1518	210	2	,	,	PUNCT
ejpam-1518	210	3	the	the	DET
ejpam-1518	210	4	sequence	sequence	NOUN
ejpam-1518	210	5	ex	ex	NOUN
ejpam-1518	210	6	has	have	VERB
ejpam-1518	210	7	at	at	ADV
ejpam-1518	210	8	least	least	ADJ
ejpam-1518	210	9	one	one	NUM
ejpam-1518	210	10	bounded	bounded	ADJ
ejpam-1518	210	11	subsequence	subsequence	NOUN
ejpam-1518	210	12	.	.	PUNCT
ejpam-1518	211	1	proof	proof	NOUN
ejpam-1518	211	2	.	.	PUNCT
ejpam-1518	212	1	from	from	ADP
ejpam-1518	212	2	the	the	DET
ejpam-1518	212	3	lemma	lemma	PROPN
ejpam-1518	212	4	1	1	NUM
ejpam-1518	212	5	the	the	DET
ejpam-1518	212	6	real	real	ADJ
ejpam-1518	212	7	sequence	sequence	NOUN
ejpam-1518	212	8	�	�	PROPN
ejpam-1518	212	9	d(xn	d(xn	PROPN
ejpam-1518	212	10	,	,	PUNCT
ejpam-1518	212	11	x	x	X
ejpam-1518	212	12	)	)	PUNCT
ejpam-1518	212	13	�	�	PROPN
ejpam-1518	212	14	is	be	AUX
ejpam-1518	212	15	statistical	statistical	ADJ
ejpam-1518	212	16	bounded	bounded	ADJ
ejpam-1518	212	17	in	in	ADP
ejpam-1518	212	18	real	real	ADJ
ejpam-1518	212	19	numbers	number	NOUN
ejpam-1518	212	20	.	.	PUNCT
ejpam-1518	213	1	that	that	PRON
ejpam-1518	213	2	is	be	AUX
ejpam-1518	213	3	,	,	PUNCT
ejpam-1518	213	4	there	there	PRON
ejpam-1518	213	5	is	be	VERB
ejpam-1518	213	6	a	a	DET
ejpam-1518	213	7	positive	positive	ADJ
ejpam-1518	213	8	number	number	NOUN
ejpam-1518	213	9	m	m	VERB
ejpam-1518	213	10	such	such	ADJ
ejpam-1518	213	11	that	that	SCONJ
ejpam-1518	213	12	δ(a	δ(a	PROPN
ejpam-1518	213	13	)	)	PUNCT
ejpam-1518	214	1	=	=	SYM
ejpam-1518	214	2	1,δ(b	1,δ(b	X
ejpam-1518	214	3	)	)	PUNCT
ejpam-1518	214	4	=	=	SYM
ejpam-1518	214	5	0	0	NUM
ejpam-1518	215	1	where	where	SCONJ
ejpam-1518	215	2	a	a	DET
ejpam-1518	215	3	:	:	PUNCT
ejpam-1518	215	4	=	=	SYM
ejpam-1518	215	5	�	�	PROPN
ejpam-1518	215	6	k	k	PROPN
ejpam-1518	215	7	:	:	PUNCT
ejpam-1518	215	8	d(xk	d(xk	PROPN
ejpam-1518	215	9	,	,	PUNCT
ejpam-1518	215	10	x	x	NOUN
ejpam-1518	215	11	)	)	PUNCT
ejpam-1518	215	12	<	<	X
ejpam-1518	215	13	m	m	PROPN
ejpam-1518	215	14	,	,	PUNCT
ejpam-1518	215	15	b	b	X
ejpam-1518	215	16	:	:	PUNCT
ejpam-1518	215	17	=	=	PUNCT
ejpam-1518	215	18	�	�	PROPN
ejpam-1518	215	19	k	k	PROPN
ejpam-1518	215	20	:	:	PUNCT
ejpam-1518	215	21	d(xk	d(xk	PROPN
ejpam-1518	215	22	,	,	PUNCT
ejpam-1518	215	23	x)≥	x)≥	PROPN
ejpam-1518	215	24	m	m	PROPN
ejpam-1518	215	25	.	.	PUNCT
ejpam-1518	216	1	let	let	VERB
ejpam-1518	216	2	k1	k1	PROPN
ejpam-1518	216	3	∈	∈	PROPN
ejpam-1518	216	4	n	n	PRON
ejpam-1518	216	5	be	be	AUX
ejpam-1518	216	6	the	the	DET
ejpam-1518	216	7	minimal	minimal	ADJ
ejpam-1518	216	8	element	element	NOUN
ejpam-1518	216	9	of	of	ADP
ejpam-1518	216	10	a	a	PRON
ejpam-1518	216	11	and	and	CCONJ
ejpam-1518	216	12	d(xk1	d(xk1	PROPN
ejpam-1518	216	13	,	,	PUNCT
ejpam-1518	216	14	x	x	X
ejpam-1518	216	15	)	)	PUNCT
ejpam-1518	216	16	<	<	X
ejpam-1518	216	17	m	m	PROPN
ejpam-1518	216	18	.	.	PUNCT
ejpam-1518	217	1	since	since	SCONJ
ejpam-1518	217	2	δ(a	δ(a	PROPN
ejpam-1518	217	3	)	)	PUNCT
ejpam-1518	217	4	=	=	PUNCT
ejpam-1518	217	5	1	1	NUM
ejpam-1518	217	6	,	,	PUNCT
ejpam-1518	217	7	it	it	PRON
ejpam-1518	217	8	can	can	AUX
ejpam-1518	217	9	be	be	AUX
ejpam-1518	217	10	choosen	choosen	VERB
ejpam-1518	217	11	k2	k2	PROPN
ejpam-1518	217	12	≥	≥	PROPN
ejpam-1518	217	13	k1	k1	PROPN
ejpam-1518	217	14	such	such	ADJ
ejpam-1518	217	15	that	that	SCONJ
ejpam-1518	217	16	the	the	DET
ejpam-1518	217	17	minimal	minimal	ADJ
ejpam-1518	217	18	element	element	NOUN
ejpam-1518	217	19	of	of	ADP
ejpam-1518	217	20	the	the	DET
ejpam-1518	217	21	set	set	NOUN
ejpam-1518	217	22	�	�	PROPN
ejpam-1518	217	23	k	k	NOUN
ejpam-1518	217	24	:	:	PUNCT
ejpam-1518	217	25	k	k	PROPN
ejpam-1518	217	26	>	>	X
ejpam-1518	217	27	k1	k1	PROPN
ejpam-1518	217	28	,	,	PUNCT
ejpam-1518	217	29	k	k	PROPN
ejpam-1518	217	30	∈	∈	PROPN
ejpam-1518	217	31	a	a	DET
ejpam-1518	217	32	satisfying	satisfying	ADJ
ejpam-1518	217	33	d(xk2	d(xk2	NOUN
ejpam-1518	217	34	,	,	PUNCT
ejpam-1518	217	35	x	x	X
ejpam-1518	217	36	)	)	PUNCT
ejpam-1518	217	37	<	<	X
ejpam-1518	217	38	m	m	NOUN
ejpam-1518	217	39	.	.	PUNCT
ejpam-1518	218	1	in	in	ADP
ejpam-1518	218	2	the	the	DET
ejpam-1518	218	3	n	n	ADV
ejpam-1518	218	4	-	-	PUNCT
ejpam-1518	218	5	th	th	VERB
ejpam-1518	218	6	step	step	NOUN
ejpam-1518	218	7	we	we	PRON
ejpam-1518	218	8	can	can	AUX
ejpam-1518	218	9	choose	choose	VERB
ejpam-1518	218	10	kn	kn	PROPN
ejpam-1518	218	11	≥	≥	PROPN
ejpam-1518	218	12	kn−1	kn−1	PROPN
ejpam-1518	218	13	which	which	PRON
ejpam-1518	218	14	is	be	AUX
ejpam-1518	218	15	the	the	DET
ejpam-1518	218	16	minimal	minimal	ADJ
ejpam-1518	218	17	element	element	NOUN
ejpam-1518	218	18	of	of	ADP
ejpam-1518	218	19	the	the	DET
ejpam-1518	218	20	set	set	NOUN
ejpam-1518	218	21	�	�	PROPN
ejpam-1518	218	22	k	k	PROPN
ejpam-1518	218	23	:	:	PUNCT
ejpam-1518	219	1	k	k	PROPN
ejpam-1518	219	2	≥	≥	NUM
ejpam-1518	219	3	kn−1	kn−1	PROPN
ejpam-1518	219	4	,	,	PUNCT
ejpam-1518	219	5	k	k	PROPN
ejpam-1518	219	6	∈	∈	PROPN
ejpam-1518	219	7	a	a	DET
ejpam-1518	219	8	such	such	ADJ
ejpam-1518	219	9	that	that	SCONJ
ejpam-1518	219	10	d(xkn	d(xkn	NOUN
ejpam-1518	219	11	,	,	PUNCT
ejpam-1518	219	12	x	x	X
ejpam-1518	219	13	)	)	PUNCT
ejpam-1518	219	14	<	<	X
ejpam-1518	219	15	m	m	NOUN
ejpam-1518	219	16	.	.	PUNCT
ejpam-1518	220	1	so	so	ADV
ejpam-1518	220	2	,	,	PUNCT
ejpam-1518	220	3	we	we	PRON
ejpam-1518	220	4	obtain	obtain	VERB
ejpam-1518	220	5	non	non	ADJ
ejpam-1518	220	6	-	-	ADJ
ejpam-1518	220	7	decreasing	decrease	VERB
ejpam-1518	220	8	sequence	sequence	NOUN
ejpam-1518	220	9	�	�	PROPN
ejpam-1518	220	10	kn	kn	PROPN
ejpam-1518	220	11	�	�	PROPN
ejpam-1518	220	12	n∈n	n∈n	NOUN
ejpam-1518	220	13	such	such	ADJ
ejpam-1518	220	14	that	that	SCONJ
ejpam-1518	220	15	ex	ex	X
ejpam-1518	220	16	′	′	NOUN
ejpam-1518	220	17	=	=	SYM
ejpam-1518	220	18	(	(	PUNCT
ejpam-1518	220	19	xkn	xkn	X
ejpam-1518	220	20	)	)	PUNCT
ejpam-1518	220	21	is	be	AUX
ejpam-1518	220	22	the	the	DET
ejpam-1518	220	23	subsequence	subsequence	NOUN
ejpam-1518	220	24	of	of	ADP
ejpam-1518	220	25	x̃	x̃	PROPN
ejpam-1518	220	26	satisfying	satisfy	VERB
ejpam-1518	220	27	d(xkn	d(xkn	NOUN
ejpam-1518	220	28	,	,	PUNCT
ejpam-1518	220	29	x	x	X
ejpam-1518	220	30	)	)	PUNCT
ejpam-1518	220	31	<	<	X
ejpam-1518	220	32	m	m	VERB
ejpam-1518	220	33	for	for	ADP
ejpam-1518	220	34	all	all	DET
ejpam-1518	220	35	kn	kn	PROPN
ejpam-1518	220	36	∈	∈	PROPN
ejpam-1518	220	37	n.	n.	NOUN
ejpam-1518	220	38	this	this	PRON
ejpam-1518	220	39	shows	show	VERB
ejpam-1518	220	40	that	that	SCONJ
ejpam-1518	220	41	the	the	DET
ejpam-1518	220	42	subsequence	subsequence	NOUN
ejpam-1518	220	43	ex	ex	PRON
ejpam-1518	220	44	′	′	NOUN
ejpam-1518	220	45	is	be	AUX
ejpam-1518	220	46	bounded	bound	VERB
ejpam-1518	220	47	.	.	PUNCT
ejpam-1518	221	1	the	the	DET
ejpam-1518	221	2	following	follow	VERB
ejpam-1518	221	3	theorem	theorem	NOUN
ejpam-1518	221	4	gives	give	VERB
ejpam-1518	221	5	the	the	DET
ejpam-1518	221	6	analogy	analogy	NOUN
ejpam-1518	221	7	of	of	ADP
ejpam-1518	221	8	balzano	balzano	ADJ
ejpam-1518	221	9	-	-	PUNCT
ejpam-1518	221	10	weierstrass	weierstrass	NOUN
ejpam-1518	221	11	theorem	theorem	NOUN
ejpam-1518	221	12	:	:	PUNCT
ejpam-1518	221	13	theorem	theorem	NOUN
ejpam-1518	221	14	5	5	NUM
ejpam-1518	221	15	.	.	PUNCT
ejpam-1518	222	1	let	let	AUX
ejpam-1518	222	2	(	(	PUNCT
ejpam-1518	222	3	x	x	X
ejpam-1518	222	4	,	,	PUNCT
ejpam-1518	222	5	d	d	X
ejpam-1518	222	6	)	)	PUNCT
ejpam-1518	222	7	be	be	AUX
ejpam-1518	222	8	an	an	DET
ejpam-1518	222	9	arbitrary	arbitrary	ADJ
ejpam-1518	222	10	metric	metric	ADJ
ejpam-1518	222	11	space	space	NOUN
ejpam-1518	222	12	.	.	PUNCT
ejpam-1518	223	1	every	every	DET
ejpam-1518	223	2	d−statistical	d−statistical	PROPN
ejpam-1518	223	3	bounded	bound	VERB
ejpam-1518	223	4	sequence	sequence	NOUN
ejpam-1518	223	5	has	have	VERB
ejpam-1518	223	6	at	at	ADV
ejpam-1518	223	7	least	least	ADJ
ejpam-1518	223	8	d−statistical	d−statistical	ADJ
ejpam-1518	223	9	convergent	convergent	NOUN
ejpam-1518	223	10	subsequence	subsequence	NOUN
ejpam-1518	223	11	.	.	PUNCT
ejpam-1518	224	1	proof	proof	NOUN
ejpam-1518	224	2	.	.	PUNCT
ejpam-1518	225	1	let	let	VERB
ejpam-1518	225	2	us	we	PRON
ejpam-1518	225	3	take	take	VERB
ejpam-1518	225	4	d−statistical	d−statistical	PROPN
ejpam-1518	226	1	bounded	bounded	ADJ
ejpam-1518	226	2	sequence	sequence	NOUN
ejpam-1518	226	3	ex	ex	X
ejpam-1518	226	4	=	=	SYM
ejpam-1518	226	5	(	(	PUNCT
ejpam-1518	226	6	xn	xn	X
ejpam-1518	226	7	)	)	PUNCT
ejpam-1518	226	8	∈	∈	PROPN
ejpam-1518	226	9	ex	ex	X
ejpam-1518	226	10	and	and	CCONJ
ejpam-1518	226	11	denote	denote	VERB
ejpam-1518	226	12	the	the	DET
ejpam-1518	226	13	real	real	ADJ
ejpam-1518	226	14	sequence	sequence	NOUN
ejpam-1518	226	15	(	(	PUNCT
ejpam-1518	226	16	d(xn	d(xn	PROPN
ejpam-1518	226	17	,	,	PUNCT
ejpam-1518	226	18	x	x	NOUN
ejpam-1518	226	19	)	)	PUNCT
ejpam-1518	226	20	)	)	PUNCT
ejpam-1518	226	21	for	for	ADP
ejpam-1518	226	22	arbitrary	arbitrary	ADJ
ejpam-1518	226	23	x	x	SYM
ejpam-1518	226	24	∈	∈	PROPN
ejpam-1518	226	25	x	x	PUNCT
ejpam-1518	226	26	by	by	ADP
ejpam-1518	226	27	(	(	PUNCT
ejpam-1518	226	28	yn	yn	PROPN
ejpam-1518	226	29	)	)	PUNCT
ejpam-1518	226	30	.	.	PUNCT
ejpam-1518	227	1	from	from	ADP
ejpam-1518	227	2	lemma	lemma	PROPN
ejpam-1518	227	3	1	1	NUM
ejpam-1518	227	4	,	,	PUNCT
ejpam-1518	227	5	the	the	DET
ejpam-1518	227	6	real	real	ADJ
ejpam-1518	227	7	sequence	sequence	NOUN
ejpam-1518	227	8	(	(	PUNCT
ejpam-1518	227	9	yn	yn	NOUN
ejpam-1518	227	10	)	)	PUNCT
ejpam-1518	227	11	is	be	AUX
ejpam-1518	227	12	statistical	statistical	ADJ
ejpam-1518	227	13	bounded	bound	VERB
ejpam-1518	227	14	with	with	ADP
ejpam-1518	227	15	usual	usual	ADJ
ejpam-1518	227	16	metric	metric	NOUN
ejpam-1518	227	17	on	on	ADP
ejpam-1518	227	18	r.	r.	PROPN
ejpam-1518	227	19	take	take	VERB
ejpam-1518	227	20	into	into	ADP
ejpam-1518	227	21	account	account	NOUN
ejpam-1518	227	22	the	the	DET
ejpam-1518	227	23	following	follow	VERB
ejpam-1518	227	24	sets	set	NOUN
ejpam-1518	227	25	for	for	ADP
ejpam-1518	227	26	sufficiently	sufficiently	ADV
ejpam-1518	227	27	large	large	ADJ
ejpam-1518	227	28	m	m	PROPN
ejpam-1518	227	29	>	>	X
ejpam-1518	227	30	0	0	NUM
ejpam-1518	227	31	,	,	PUNCT
ejpam-1518	227	32	a([0	a([0	NOUN
ejpam-1518	227	33	,	,	PUNCT
ejpam-1518	227	34	m	m	X
ejpam-1518	227	35	]	]	X
ejpam-1518	227	36	,	,	PUNCT
ejpam-1518	227	37	n	n	CCONJ
ejpam-1518	227	38	)	)	PUNCT
ejpam-1518	227	39	:	:	PUNCT
ejpam-1518	228	1	=	=	PUNCT
ejpam-1518	228	2	�	�	PROPN
ejpam-1518	228	3	k	k	NOUN
ejpam-1518	228	4	:	:	PUNCT
ejpam-1518	228	5	k	k	PROPN
ejpam-1518	228	6	≤	≤	PROPN
ejpam-1518	228	7	n	n	CCONJ
ejpam-1518	228	8	,	,	PUNCT
ejpam-1518	228	9	yk	yk	PROPN
ejpam-1518	228	10	∈	∈	PROPN
ejpam-1518	229	1	[	[	X
ejpam-1518	229	2	0	0	NUM
ejpam-1518	229	3	,	,	PUNCT
ejpam-1518	229	4	m	m	NOUN
ejpam-1518	229	5	)	)	PUNCT
ejpam-1518	229	6	,	,	PUNCT
ejpam-1518	229	7	b	b	X
ejpam-1518	229	8	(	(	PUNCT
ejpam-1518	229	9	[	[	X
ejpam-1518	229	10	0	0	NUM
ejpam-1518	229	11	,	,	PUNCT
ejpam-1518	229	12	m	m	NOUN
ejpam-1518	229	13	]	]	X
ejpam-1518	229	14	,	,	PUNCT
ejpam-1518	229	15	n	n	CCONJ
ejpam-1518	229	16	)	)	PUNCT
ejpam-1518	229	17	:	:	PUNCT
ejpam-1518	229	18	=	=	PUNCT
ejpam-1518	229	19	�	�	PROPN
ejpam-1518	230	1	k	k	NOUN
ejpam-1518	230	2	:	:	PUNCT
ejpam-1518	230	3	k	k	PROPN
ejpam-1518	230	4	≤	≤	PROPN
ejpam-1518	230	5	n	n	CCONJ
ejpam-1518	230	6	,	,	PUNCT
ejpam-1518	230	7	yk	yk	PROPN
ejpam-1518	230	8	∈	∈	PROPN
ejpam-1518	231	1	[	[	X
ejpam-1518	231	2	m	m	X
ejpam-1518	231	3	,	,	PUNCT
ejpam-1518	231	4	∞	∞	PROPN
ejpam-1518	231	5	)	)	PUNCT
ejpam-1518	231	6	such	such	ADJ
ejpam-1518	231	7	that	that	SCONJ
ejpam-1518	231	8	a∪	a∪	PROPN
ejpam-1518	231	9	b	b	NOUN
ejpam-1518	231	10	=	=	PUNCT
ejpam-1518	231	11	{	{	PUNCT
ejpam-1518	231	12	1,2,3	1,2,3	NUM
ejpam-1518	231	13	,	,	PUNCT
ejpam-1518	231	14	.	.	PUNCT
ejpam-1518	231	15	.	.	PUNCT
ejpam-1518	232	1	.	.	PUNCT
ejpam-1518	233	1	,	,	PUNCT
ejpam-1518	233	2	n	n	CCONJ
ejpam-1518	233	3	}	}	PUNCT
ejpam-1518	233	4	and	and	CCONJ
ejpam-1518	233	5	δ(a	δ(a	PROPN
ejpam-1518	233	6	)	)	PUNCT
ejpam-1518	233	7	=	=	SYM
ejpam-1518	233	8	1	1	NUM
ejpam-1518	233	9	,	,	PUNCT
ejpam-1518	233	10	δ(b	δ(b	VERB
ejpam-1518	233	11	)	)	PUNCT
ejpam-1518	233	12	=	=	SYM
ejpam-1518	234	1	0	0	X
ejpam-1518	234	2	.	.	PUNCT
ejpam-1518	234	3	also	also	ADV
ejpam-1518	234	4	,	,	PUNCT
ejpam-1518	234	5	denote	denote	VERB
ejpam-1518	234	6	i0	i0	PROPN
ejpam-1518	234	7	:	:	PUNCT
ejpam-1518	234	8	=	=	SYM
ejpam-1518	235	1	[	[	X
ejpam-1518	235	2	0	0	NUM
ejpam-1518	235	3	,	,	PUNCT
ejpam-1518	235	4	m	m	VERB
ejpam-1518	235	5	]	]	PUNCT
ejpam-1518	235	6	with	with	ADP
ejpam-1518	235	7	the	the	DET
ejpam-1518	235	8	length	length	NOUN
ejpam-1518	235	9	l(i0	l(i0	NOUN
ejpam-1518	235	10	)	)	PUNCT
ejpam-1518	235	11	=	=	SYM
ejpam-1518	235	12	m	m	NOUN
ejpam-1518	235	13	and	and	CCONJ
ejpam-1518	235	14	divide	divide	VERB
ejpam-1518	235	15	it	it	PRON
ejpam-1518	235	16	into	into	ADP
ejpam-1518	235	17	two	two	NUM
ejpam-1518	235	18	parts	part	NOUN
ejpam-1518	235	19	as	as	ADP
ejpam-1518	235	20	i1	i1	PROPN
ejpam-1518	235	21	0	0	NUM
ejpam-1518	236	1	:	:	PUNCT
ejpam-1518	236	2	=	=	PUNCT
ejpam-1518	236	3	�	�	PROPN
ejpam-1518	236	4	0	0	NUM
ejpam-1518	236	5	,	,	PUNCT
ejpam-1518	236	6	m	m	PROPN
ejpam-1518	236	7	2	2	NUM
ejpam-1518	236	8	�	�	NOUN
ejpam-1518	236	9	and	and	CCONJ
ejpam-1518	236	10	i2	i2	PROPN
ejpam-1518	236	11	0	0	NUM
ejpam-1518	237	1	:	:	PUNCT
ejpam-1518	237	2	=	=	SYM
ejpam-1518	237	3	�	�	PROPN
ejpam-1518	237	4	m	m	VERB
ejpam-1518	237	5	2	2	NUM
ejpam-1518	237	6	,	,	PUNCT
ejpam-1518	237	7	m	m	VERB
ejpam-1518	237	8	�	�	PROPN
ejpam-1518	237	9	.	.	PUNCT
ejpam-1518	238	1	it	it	PRON
ejpam-1518	238	2	is	be	AUX
ejpam-1518	238	3	clear	clear	ADJ
ejpam-1518	238	4	that	that	SCONJ
ejpam-1518	238	5	asymptotic	asymptotic	ADJ
ejpam-1518	238	6	density	density	NOUN
ejpam-1518	238	7	of	of	ADP
ejpam-1518	238	8	these	these	DET
ejpam-1518	238	9	sets	set	NOUN
ejpam-1518	238	10	satisfy	satisfy	VERB
ejpam-1518	238	11	0≤	0≤	PUNCT
ejpam-1518	238	12	δ(i1	δ(i1	NOUN
ejpam-1518	238	13	0	0	NUM
ejpam-1518	238	14	)	)	PUNCT
ejpam-1518	238	15	≤	≤	NOUN
ejpam-1518	238	16	1	1	NUM
ejpam-1518	238	17	,	,	PUNCT
ejpam-1518	238	18	0≤	0≤	NUM
ejpam-1518	238	19	δ(i2	δ(i2	NOUN
ejpam-1518	238	20	0	0	NUM
ejpam-1518	238	21	)	)	PUNCT
ejpam-1518	238	22	≤	≤	NUM
ejpam-1518	238	23	1	1	NUM
ejpam-1518	238	24	.	.	PUNCT
ejpam-1518	238	25	m.	m.	NOUN
ejpam-1518	238	26	küçükaslan	küçükaslan	PROPN
ejpam-1518	238	27	,	,	PUNCT
ejpam-1518	238	28	u.	u.	PROPN
ejpam-1518	238	29	değer	değer	PROPN
ejpam-1518	238	30	/	/	SYM
ejpam-1518	238	31	eur	eur	PROPN
ejpam-1518	238	32	.	.	PUNCT
ejpam-1518	239	1	j.	j.	PROPN
ejpam-1518	239	2	pure	pure	PROPN
ejpam-1518	239	3	appl	appl	PROPN
ejpam-1518	239	4	.	.	PROPN
ejpam-1518	239	5	math	math	PROPN
ejpam-1518	239	6	,	,	PUNCT
ejpam-1518	239	7	5	5	NUM
ejpam-1518	239	8	(	(	PUNCT
ejpam-1518	239	9	2012	2012	NUM
ejpam-1518	239	10	)	)	PUNCT
ejpam-1518	239	11	,	,	PUNCT
ejpam-1518	239	12	174	174	NUM
ejpam-1518	239	13	-	-	SYM
ejpam-1518	239	14	186	186	NUM
ejpam-1518	239	15	182	182	NUM
ejpam-1518	239	16	if	if	SCONJ
ejpam-1518	239	17	δ(i1	δ(i1	NOUN
ejpam-1518	239	18	0	0	NUM
ejpam-1518	239	19	)	)	PUNCT
ejpam-1518	240	1	=	=	SYM
ejpam-1518	240	2	0	0	PUNCT
ejpam-1518	240	3	(	(	PUNCT
ejpam-1518	240	4	or	or	CCONJ
ejpam-1518	240	5	δ(i2	δ(i2	NOUN
ejpam-1518	240	6	0	0	NUM
ejpam-1518	240	7	)	)	PUNCT
ejpam-1518	241	1	=	=	SYM
ejpam-1518	241	2	0	0	NUM
ejpam-1518	241	3	)	)	PUNCT
ejpam-1518	241	4	,	,	PUNCT
ejpam-1518	241	5	consider	consider	VERB
ejpam-1518	241	6	i2	i2	PROPN
ejpam-1518	241	7	0	0	PUNCT
ejpam-1518	241	8	(	(	PUNCT
ejpam-1518	241	9	or	or	CCONJ
ejpam-1518	241	10	consider	consider	VERB
ejpam-1518	241	11	i1	i1	PROPN
ejpam-1518	241	12	0	0	NUM
ejpam-1518	241	13	)	)	PUNCT
ejpam-1518	241	14	otherwise	otherwise	ADV
ejpam-1518	241	15	consider	consider	VERB
ejpam-1518	241	16	the	the	DET
ejpam-1518	241	17	interval	interval	NOUN
ejpam-1518	241	18	having	have	VERB
ejpam-1518	241	19	big	big	ADJ
ejpam-1518	241	20	asymptotic	asymptotic	ADJ
ejpam-1518	241	21	density	density	NOUN
ejpam-1518	241	22	and	and	CCONJ
ejpam-1518	241	23	denote	denote	VERB
ejpam-1518	241	24	it	it	PRON
ejpam-1518	241	25	by	by	ADP
ejpam-1518	241	26	i1	i1	PROPN
ejpam-1518	241	27	.	.	PUNCT
ejpam-1518	242	1	note	note	VERB
ejpam-1518	242	2	that	that	SCONJ
ejpam-1518	242	3	the	the	DET
ejpam-1518	242	4	length	length	NOUN
ejpam-1518	242	5	of	of	ADP
ejpam-1518	242	6	i1	i1	PROPN
ejpam-1518	242	7	is	be	AUX
ejpam-1518	242	8	l(i1	l(i1	NOUN
ejpam-1518	242	9	)	)	PUNCT
ejpam-1518	243	1	=	=	PUNCT
ejpam-1518	243	2	m	m	VERB
ejpam-1518	243	3	2	2	NUM
ejpam-1518	243	4	and	and	CCONJ
ejpam-1518	243	5	i1	i1	PROPN
ejpam-1518	243	6	⊂	⊂	PROPN
ejpam-1518	243	7	i0	i0	PROPN
ejpam-1518	243	8	.	.	PUNCT
ejpam-1518	244	1	if	if	SCONJ
ejpam-1518	244	2	we	we	PRON
ejpam-1518	244	3	divide	divide	VERB
ejpam-1518	244	4	the	the	DET
ejpam-1518	244	5	new	new	ADJ
ejpam-1518	244	6	closed	closed	ADJ
ejpam-1518	244	7	interval	interval	NOUN
ejpam-1518	244	8	into	into	ADP
ejpam-1518	244	9	two	two	NUM
ejpam-1518	244	10	parts	part	NOUN
ejpam-1518	244	11	as	as	ADP
ejpam-1518	244	12	i1	i1	PROPN
ejpam-1518	244	13	1	1	NUM
ejpam-1518	244	14	and	and	CCONJ
ejpam-1518	244	15	i1	i1	PROPN
ejpam-1518	244	16	2	2	NUM
ejpam-1518	244	17	,	,	PUNCT
ejpam-1518	244	18	we	we	PRON
ejpam-1518	244	19	can	can	AUX
ejpam-1518	244	20	choose	choose	VERB
ejpam-1518	244	21	a	a	DET
ejpam-1518	244	22	new	new	ADJ
ejpam-1518	244	23	one	one	NOUN
ejpam-1518	244	24	and	and	CCONJ
ejpam-1518	244	25	denote	denote	VERB
ejpam-1518	244	26	this	this	DET
ejpam-1518	244	27	interval	interval	NOUN
ejpam-1518	244	28	by	by	ADP
ejpam-1518	244	29	i2	i2	PROPN
ejpam-1518	244	30	from	from	ADP
ejpam-1518	244	31	the	the	DET
ejpam-1518	244	32	above	above	ADJ
ejpam-1518	244	33	explanation	explanation	NOUN
ejpam-1518	244	34	such	such	ADJ
ejpam-1518	244	35	that	that	SCONJ
ejpam-1518	244	36	the	the	DET
ejpam-1518	244	37	length	length	NOUN
ejpam-1518	244	38	of	of	ADP
ejpam-1518	244	39	this	this	DET
ejpam-1518	244	40	interval	interval	NOUN
ejpam-1518	244	41	l(i2	l(i2	NOUN
ejpam-1518	244	42	)	)	PUNCT
ejpam-1518	244	43	=	=	PUNCT
ejpam-1518	245	1	m	m	VERB
ejpam-1518	245	2	22	22	NUM
ejpam-1518	245	3	and	and	CCONJ
ejpam-1518	245	4	i2	i2	PROPN
ejpam-1518	245	5	⊂	⊂	PROPN
ejpam-1518	245	6	i1	i1	PROPN
ejpam-1518	245	7	.	.	PUNCT
ejpam-1518	246	1	after	after	ADP
ejpam-1518	246	2	continuing	continue	VERB
ejpam-1518	246	3	this	this	DET
ejpam-1518	246	4	procedure	procedure	NOUN
ejpam-1518	246	5	we	we	PRON
ejpam-1518	246	6	obtain	obtain	VERB
ejpam-1518	246	7	closed	closed	ADJ
ejpam-1518	246	8	nested	nest	VERB
ejpam-1518	246	9	intervals	interval	NOUN
ejpam-1518	246	10	which	which	DET
ejpam-1518	246	11	length	length	NOUN
ejpam-1518	246	12	tends	tend	VERB
ejpam-1518	246	13	to	to	ADP
ejpam-1518	246	14	zero	zero	NUM
ejpam-1518	246	15	.	.	PUNCT
ejpam-1518	247	1	from	from	ADP
ejpam-1518	247	2	the	the	DET
ejpam-1518	247	3	nested	nested	ADJ
ejpam-1518	247	4	theorem	theorem	NOUN
ejpam-1518	247	5	,	,	PUNCT
ejpam-1518	247	6	we	we	PRON
ejpam-1518	247	7	get	get	VERB
ejpam-1518	247	8	∞⋂	∞⋂	PROPN
ejpam-1518	247	9	n=1	n=1	PROPN
ejpam-1518	247	10	in	in	ADP
ejpam-1518	247	11	=	=	PROPN
ejpam-1518	247	12	�	�	PROPN
ejpam-1518	247	13	y∗	y∗	ADV
ejpam-1518	247	14	.	.	PUNCT
ejpam-1518	248	1	(	(	PUNCT
ejpam-1518	248	2	8)	8)	NUM
ejpam-1518	248	3	now	now	ADV
ejpam-1518	248	4	our	our	PRON
ejpam-1518	248	5	aim	aim	NOUN
ejpam-1518	248	6	to	to	PART
ejpam-1518	248	7	construct	construct	VERB
ejpam-1518	248	8	a	a	DET
ejpam-1518	248	9	subsequence	subsequence	NOUN
ejpam-1518	248	10	of	of	ADP
ejpam-1518	248	11	(	(	PUNCT
ejpam-1518	248	12	yn	yn	PROPN
ejpam-1518	248	13	)	)	PUNCT
ejpam-1518	248	14	such	such	ADJ
ejpam-1518	248	15	that	that	SCONJ
ejpam-1518	248	16	it	it	PRON
ejpam-1518	248	17	is	be	AUX
ejpam-1518	248	18	convergent	convergent	ADJ
ejpam-1518	248	19	to	to	ADP
ejpam-1518	248	20	y∗.	y∗.	NUM
ejpam-1518	248	21	for	for	ADP
ejpam-1518	248	22	this	this	DET
ejpam-1518	248	23	turn	turn	NOUN
ejpam-1518	248	24	to	to	PART
ejpam-1518	248	25	begin	begin	VERB
ejpam-1518	248	26	of	of	ADP
ejpam-1518	248	27	the	the	DET
ejpam-1518	248	28	proof	proof	NOUN
ejpam-1518	248	29	and	and	CCONJ
ejpam-1518	248	30	choose	choose	VERB
ejpam-1518	248	31	k1	k1	NOUN
ejpam-1518	248	32	which	which	PRON
ejpam-1518	248	33	is	be	AUX
ejpam-1518	248	34	the	the	DET
ejpam-1518	248	35	minimal	minimal	ADJ
ejpam-1518	248	36	element	element	NOUN
ejpam-1518	248	37	of	of	ADP
ejpam-1518	248	38	i0	i0	PROPN
ejpam-1518	248	39	,	,	PUNCT
ejpam-1518	248	40	choose	choose	VERB
ejpam-1518	248	41	k2	k2	PROPN
ejpam-1518	248	42	≥	≥	PROPN
ejpam-1518	248	43	k1	k1	NOUN
ejpam-1518	248	44	which	which	PRON
ejpam-1518	248	45	is	be	AUX
ejpam-1518	248	46	the	the	DET
ejpam-1518	248	47	minimal	minimal	ADJ
ejpam-1518	248	48	element	element	NOUN
ejpam-1518	248	49	of	of	ADP
ejpam-1518	248	50	i1	i1	PROPN
ejpam-1518	248	51	and	and	CCONJ
ejpam-1518	248	52	so	so	ADV
ejpam-1518	248	53	on	on	ADV
ejpam-1518	248	54	.	.	PUNCT
ejpam-1518	249	1	if	if	SCONJ
ejpam-1518	249	2	continue	continue	VERB
ejpam-1518	249	3	this	this	DET
ejpam-1518	249	4	process	process	NOUN
ejpam-1518	249	5	we	we	PRON
ejpam-1518	249	6	obtain	obtain	VERB
ejpam-1518	249	7	kn	kn	PROPN
ejpam-1518	249	8	≥	≥	PROPN
ejpam-1518	249	9	kn−1	kn−1	PROPN
ejpam-1518	249	10	which	which	PRON
ejpam-1518	249	11	is	be	AUX
ejpam-1518	249	12	the	the	DET
ejpam-1518	249	13	minimal	minimal	ADJ
ejpam-1518	249	14	element	element	NOUN
ejpam-1518	249	15	of	of	ADP
ejpam-1518	249	16	in	in	ADP
ejpam-1518	249	17	.	.	PUNCT
ejpam-1518	250	1	also	also	ADV
ejpam-1518	250	2	,	,	PUNCT
ejpam-1518	250	3	we	we	PRON
ejpam-1518	250	4	can	can	AUX
ejpam-1518	250	5	choose	choose	VERB
ejpam-1518	250	6	kn+1	kn+1	PROPN
ejpam-1518	250	7	≥	≥	PROPN
ejpam-1518	250	8	kn	kn	PROPN
ejpam-1518	250	9	that	that	PRON
ejpam-1518	250	10	is	be	AUX
ejpam-1518	250	11	minimal	minimal	ADJ
ejpam-1518	250	12	element	element	NOUN
ejpam-1518	250	13	of	of	ADP
ejpam-1518	250	14	in+1	in+1	PROPN
ejpam-1518	250	15	.	.	PUNCT
ejpam-1518	251	1	otherwise	otherwise	ADV
ejpam-1518	251	2	the	the	DET
ejpam-1518	251	3	number	number	NOUN
ejpam-1518	251	4	of	of	ADP
ejpam-1518	251	5	elements	element	NOUN
ejpam-1518	251	6	of	of	ADP
ejpam-1518	251	7	i1	i1	PROPN
ejpam-1518	251	8	n	n	CCONJ
ejpam-1518	251	9	(	(	PUNCT
ejpam-1518	251	10	or	or	CCONJ
ejpam-1518	251	11	i2	i2	PROPN
ejpam-1518	251	12	n	n	CCONJ
ejpam-1518	251	13	)	)	PUNCT
ejpam-1518	251	14	is	be	AUX
ejpam-1518	251	15	at	at	ADP
ejpam-1518	251	16	most	most	ADJ
ejpam-1518	251	17	kn	kn	PROPN
ejpam-1518	251	18	.	.	PUNCT
ejpam-1518	252	1	this	this	PRON
ejpam-1518	252	2	is	be	AUX
ejpam-1518	252	3	contradiction	contradiction	NOUN
ejpam-1518	252	4	to	to	ADP
ejpam-1518	252	5	assumption	assumption	NOUN
ejpam-1518	252	6	on	on	ADP
ejpam-1518	252	7	i1	i1	PROPN
ejpam-1518	252	8	n	n	PROPN
ejpam-1518	252	9	(	(	PUNCT
ejpam-1518	252	10	or	or	CCONJ
ejpam-1518	252	11	i2	i2	PROPN
ejpam-1518	252	12	n	n	CCONJ
ejpam-1518	252	13	)	)	PUNCT
ejpam-1518	252	14	.	.	PUNCT
ejpam-1518	253	1	so	so	ADV
ejpam-1518	253	2	,	,	PUNCT
ejpam-1518	253	3	non	non	ADJ
ejpam-1518	253	4	-	-	ADJ
ejpam-1518	253	5	decreasing	decrease	VERB
ejpam-1518	253	6	sequence	sequence	NOUN
ejpam-1518	253	7	(	(	PUNCT
ejpam-1518	253	8	kn	kn	PROPN
ejpam-1518	253	9	)	)	PUNCT
ejpam-1518	253	10	gives	give	VERB
ejpam-1518	253	11	the	the	DET
ejpam-1518	253	12	subsequence	subsequence	NOUN
ejpam-1518	253	13	(	(	PUNCT
ejpam-1518	253	14	ykn	ykn	NOUN
ejpam-1518	253	15	)	)	PUNCT
ejpam-1518	253	16	of	of	ADP
ejpam-1518	253	17	the	the	DET
ejpam-1518	253	18	sequence	sequence	NOUN
ejpam-1518	253	19	(	(	PUNCT
ejpam-1518	253	20	yn	yn	NOUN
ejpam-1518	253	21	)	)	PUNCT
ejpam-1518	253	22	satisfying	satisfy	VERB
ejpam-1518	253	23	�	�	PROPN
ejpam-1518	253	24	�	�	PROPN
ejpam-1518	253	25	ykn	ykn	PRON
ejpam-1518	253	26	−	−	PROPN
ejpam-1518	253	27	y∗	y∗	PROPN
ejpam-1518	253	28	�	�	PROPN
ejpam-1518	253	29	�	�	PROPN
ejpam-1518	253	30	<	<	X
ejpam-1518	253	31	l(ik	l(ik	PROPN
ejpam-1518	253	32	)	)	PUNCT
ejpam-1518	253	33	=	=	PUNCT
ejpam-1518	253	34	m	m	VERB
ejpam-1518	253	35	2n	2n	NUM
ejpam-1518	253	36	.	.	PUNCT
ejpam-1518	254	1	(	(	PUNCT
ejpam-1518	254	2	9	9	NUM
ejpam-1518	254	3	)	)	PUNCT
ejpam-1518	254	4	for	for	ADP
ejpam-1518	254	5	every	every	DET
ejpam-1518	254	6	ǫ	ǫ	PROPN
ejpam-1518	254	7	>	>	X
ejpam-1518	254	8	0	0	NUM
ejpam-1518	254	9	,	,	PUNCT
ejpam-1518	254	10	there	there	PRON
ejpam-1518	254	11	is	be	VERB
ejpam-1518	254	12	a	a	DET
ejpam-1518	254	13	kn0	kn0	NOUN
ejpam-1518	254	14	=	=	SYM
ejpam-1518	254	15	kn0	kn0	PROPN
ejpam-1518	254	16	(	(	PUNCT
ejpam-1518	254	17	ǫ	ǫ	NOUN
ejpam-1518	254	18	)	)	PUNCT
ejpam-1518	254	19	∈	∈	NOUN
ejpam-1518	254	20	n	n	PRON
ejpam-1518	254	21	such	such	ADJ
ejpam-1518	254	22	that	that	SCONJ
ejpam-1518	254	23	1	1	NUM
ejpam-1518	254	24	2kn	2kn	ADJ
ejpam-1518	254	25	<	<	X
ejpam-1518	254	26	ǫ	ǫ	NOUN
ejpam-1518	254	27	for	for	ADP
ejpam-1518	254	28	every	every	DET
ejpam-1518	254	29	kn	kn	PROPN
ejpam-1518	254	30	≥	≥	NUM
ejpam-1518	254	31	kn0	kn0	NOUN
ejpam-1518	254	32	.	.	PUNCT
ejpam-1518	255	1	so	so	ADV
ejpam-1518	255	2	,	,	PUNCT
ejpam-1518	255	3	from	from	ADP
ejpam-1518	255	4	(	(	PUNCT
ejpam-1518	255	5	9	9	X
ejpam-1518	255	6	)	)	PUNCT
ejpam-1518	255	7	we	we	PRON
ejpam-1518	255	8	have	have	VERB
ejpam-1518	255	9	�	�	PROPN
ejpam-1518	255	10	�	�	PROPN
ejpam-1518	255	11	ykn	ykn	PRON
ejpam-1518	255	12	−	−	PROPN
ejpam-1518	255	13	y∗	y∗	PROPN
ejpam-1518	255	14	�	�	PROPN
ejpam-1518	255	15	�	�	PROPN
ejpam-1518	255	16	<	<	X
ejpam-1518	255	17	ǫ	ǫ	X
ejpam-1518	255	18	.	.	PUNCT
ejpam-1518	256	1	(	(	PUNCT
ejpam-1518	256	2	10	10	NUM
ejpam-1518	256	3	)	)	PUNCT
ejpam-1518	256	4	the	the	DET
ejpam-1518	256	5	equation	equation	NOUN
ejpam-1518	256	6	(	(	PUNCT
ejpam-1518	256	7	10	10	NUM
ejpam-1518	256	8	)	)	PUNCT
ejpam-1518	256	9	shows	show	NOUN
ejpam-1518	256	10	(	(	PUNCT
ejpam-1518	256	11	ykn	ykn	NOUN
ejpam-1518	256	12	)	)	PUNCT
ejpam-1518	256	13	is	be	AUX
ejpam-1518	256	14	convergent	convergent	ADJ
ejpam-1518	256	15	to	to	ADP
ejpam-1518	256	16	y∗	y∗	PROPN
ejpam-1518	256	17	in	in	ADP
ejpam-1518	256	18	usual	usual	ADJ
ejpam-1518	256	19	case	case	NOUN
ejpam-1518	256	20	.	.	PUNCT
ejpam-1518	257	1	it	it	PRON
ejpam-1518	257	2	means	mean	VERB
ejpam-1518	257	3	that	that	SCONJ
ejpam-1518	257	4	there	there	PRON
ejpam-1518	257	5	is	be	VERB
ejpam-1518	257	6	an	an	DET
ejpam-1518	257	7	element	element	NOUN
ejpam-1518	257	8	x∗	x∗	NOUN
ejpam-1518	257	9	∈	∈	PROPN
ejpam-1518	257	10	x	x	PUNCT
ejpam-1518	257	11	such	such	ADJ
ejpam-1518	257	12	that	that	SCONJ
ejpam-1518	257	13	the	the	DET
ejpam-1518	257	14	sequence	sequence	NOUN
ejpam-1518	257	15	yn	yn	X
ejpam-1518	257	16	:	:	PUNCT
ejpam-1518	257	17	=	=	X
ejpam-1518	257	18	d(xkn	d(xkn	NOUN
ejpam-1518	257	19	,	,	PUNCT
ejpam-1518	257	20	x	x	X
ejpam-1518	257	21	)	)	PUNCT
ejpam-1518	257	22	convergent	convergent	NOUN
ejpam-1518	257	23	to	to	ADP
ejpam-1518	257	24	y∗	y∗	PROPN
ejpam-1518	257	25	=	=	SYM
ejpam-1518	257	26	d(x∗	d(x∗	NOUN
ejpam-1518	257	27	,	,	PUNCT
ejpam-1518	257	28	x	x	NOUN
ejpam-1518	257	29	)	)	PUNCT
ejpam-1518	257	30	.	.	PUNCT
ejpam-1518	258	1	in	in	ADP
ejpam-1518	258	2	[	[	X
ejpam-1518	258	3	12	12	NUM
ejpam-1518	258	4	]	]	PUNCT
ejpam-1518	258	5	,	,	PUNCT
ejpam-1518	258	6	we	we	PRON
ejpam-1518	258	7	know	know	VERB
ejpam-1518	258	8	that	that	SCONJ
ejpam-1518	258	9	this	this	PRON
ejpam-1518	258	10	implies	imply	VERB
ejpam-1518	258	11	the	the	DET
ejpam-1518	258	12	sequence	sequence	NOUN
ejpam-1518	258	13	d(xkn	d(xkn	NOUN
ejpam-1518	258	14	,	,	PUNCT
ejpam-1518	258	15	x	x	X
ejpam-1518	258	16	)	)	PUNCT
ejpam-1518	258	17	is	be	AUX
ejpam-1518	258	18	d−statistical	d−statistical	X
ejpam-1518	258	19	convergent	convergent	NOUN
ejpam-1518	258	20	to	to	ADP
ejpam-1518	258	21	d(x∗	d(x∗	PROPN
ejpam-1518	258	22	,	,	PUNCT
ejpam-1518	258	23	x	x	NOUN
ejpam-1518	258	24	)	)	PUNCT
ejpam-1518	258	25	.	.	PUNCT
ejpam-1518	259	1	hence	hence	ADV
ejpam-1518	259	2	,	,	PUNCT
ejpam-1518	259	3	we	we	PRON
ejpam-1518	259	4	have	have	VERB
ejpam-1518	259	5	¦	¦	PROPN
ejpam-1518	259	6	kn	kn	PROPN
ejpam-1518	259	7	:	:	PUNCT
ejpam-1518	259	8	kn	kn	PROPN
ejpam-1518	259	9	≤	≤	PROPN
ejpam-1518	259	10	n	n	CCONJ
ejpam-1518	259	11	,	,	PUNCT
ejpam-1518	259	12	d(xkn	d(xkn	NOUN
ejpam-1518	259	13	,	,	PUNCT
ejpam-1518	259	14	x∗)≥	x∗)≥	PUNCT
ejpam-1518	260	1	ǫ	ǫ	X
ejpam-1518	260	2	©	©	PROPN
ejpam-1518	260	3	⊂	⊂	PROPN
ejpam-1518	260	4	¦	¦	PROPN
ejpam-1518	260	5	kn	kn	PROPN
ejpam-1518	260	6	:	:	PUNCT
ejpam-1518	260	7	kn	kn	PROPN
ejpam-1518	260	8	≤	≤	PROPN
ejpam-1518	260	9	n	n	CCONJ
ejpam-1518	260	10	,	,	PUNCT
ejpam-1518	260	11	�	�	PROPN
ejpam-1518	260	12	�	�	PROPN
ejpam-1518	260	13	d(xkn	d(xkn	NOUN
ejpam-1518	260	14	,	,	PUNCT
ejpam-1518	260	15	x)−	x)−	PROPN
ejpam-1518	260	16	d(x∗	d(x∗	NOUN
ejpam-1518	260	17	,	,	PUNCT
ejpam-1518	260	18	x	x	NOUN
ejpam-1518	260	19	)	)	PUNCT
ejpam-1518	260	20	�	�	PROPN
ejpam-1518	260	21	�	�	PROPN
ejpam-1518	260	22	≥	≥	NOUN
ejpam-1518	260	23	ǫ	ǫ	NUM
ejpam-1518	260	24	©	©	PROPN
ejpam-1518	260	25	.	.	PUNCT
ejpam-1518	261	1	from	from	ADP
ejpam-1518	261	2	this	this	DET
ejpam-1518	261	3	inclusion	inclusion	NOUN
ejpam-1518	261	4	and	and	CCONJ
ejpam-1518	261	5	the	the	DET
ejpam-1518	261	6	definition	definition	NOUN
ejpam-1518	261	7	2-(i	2-(i	NUM
ejpam-1518	261	8	)	)	PUNCT
ejpam-1518	261	9	we	we	PRON
ejpam-1518	261	10	have	have	VERB
ejpam-1518	261	11	0≤	0≤	ADJ
ejpam-1518	261	12	lim	lim	NOUN
ejpam-1518	261	13	n→∞	n→∞	NUM
ejpam-1518	261	14	1	1	NUM
ejpam-1518	261	15	n	n	PRON
ejpam-1518	261	16	�	�	PROPN
ejpam-1518	261	17	�	�	PROPN
ejpam-1518	261	18	�	�	PROPN
ejpam-1518	261	19	¦	¦	PROPN
ejpam-1518	261	20	kn	kn	PROPN
ejpam-1518	261	21	:	:	PUNCT
ejpam-1518	262	1	kn	kn	PROPN
ejpam-1518	262	2	≤	≤	PROPN
ejpam-1518	262	3	n	n	CCONJ
ejpam-1518	262	4	,	,	PUNCT
ejpam-1518	262	5	d(xkn	d(xkn	NOUN
ejpam-1518	262	6	,	,	PUNCT
ejpam-1518	262	7	x∗)≥	x∗)≥	PUNCT
ejpam-1518	263	1	ǫ	ǫ	PROPN
ejpam-1518	263	2	©	©	PROPN
ejpam-1518	263	3	�	�	PROPN
ejpam-1518	263	4	�	�	PROPN
ejpam-1518	263	5	�	�	PROPN
ejpam-1518	263	6	≤	≤	PROPN
ejpam-1518	263	7	lim	lim	PROPN
ejpam-1518	263	8	n→∞	n→∞	NUM
ejpam-1518	263	9	1	1	NUM
ejpam-1518	263	10	n	n	DET
ejpam-1518	263	11	�	�	PROPN
ejpam-1518	263	12	�	�	PROPN
ejpam-1518	263	13	�	�	PROPN
ejpam-1518	263	14	¦	¦	PROPN
ejpam-1518	263	15	kn	kn	PROPN
ejpam-1518	263	16	:	:	PUNCT
ejpam-1518	263	17	kn	kn	PROPN
ejpam-1518	263	18	≤	≤	PROPN
ejpam-1518	263	19	n	n	CCONJ
ejpam-1518	263	20	,	,	PUNCT
ejpam-1518	263	21	�	�	PROPN
ejpam-1518	263	22	�	�	PROPN
ejpam-1518	263	23	d(xkn	d(xkn	NOUN
ejpam-1518	263	24	,	,	PUNCT
ejpam-1518	263	25	x)−	x)−	PROPN
ejpam-1518	263	26	d(x∗	d(x∗	NOUN
ejpam-1518	263	27	,	,	PUNCT
ejpam-1518	263	28	x	x	NOUN
ejpam-1518	263	29	)	)	PUNCT
ejpam-1518	263	30	�	�	PROPN
ejpam-1518	263	31	�	�	PROPN
ejpam-1518	263	32	≥	≥	PROPN
ejpam-1518	263	33	ǫ	ǫ	PROPN
ejpam-1518	263	34	©	©	PROPN
ejpam-1518	263	35	�	�	PROPN
ejpam-1518	263	36	�	�	PROPN
ejpam-1518	263	37	�	�	PROPN
ejpam-1518	263	38	=	=	SYM
ejpam-1518	263	39	0	0	PROPN
ejpam-1518	263	40	.	.	PUNCT
ejpam-1518	264	1	the	the	DET
ejpam-1518	264	2	last	last	ADJ
ejpam-1518	264	3	inequality	inequality	NOUN
ejpam-1518	264	4	says	say	VERB
ejpam-1518	264	5	the	the	DET
ejpam-1518	264	6	sequence	sequence	NOUN
ejpam-1518	264	7	x̃	x̃	PROPN
ejpam-1518	264	8	has	have	VERB
ejpam-1518	264	9	a	a	DET
ejpam-1518	264	10	d	d	ADJ
ejpam-1518	264	11	-	-	ADJ
ejpam-1518	264	12	statistical	statistical	ADJ
ejpam-1518	264	13	convergent	convergent	NOUN
ejpam-1518	264	14	subsequence	subsequence	NOUN
ejpam-1518	264	15	.	.	PUNCT
ejpam-1518	265	1	the	the	DET
ejpam-1518	265	2	following	follow	VERB
ejpam-1518	265	3	theorem	theorem	NOUN
ejpam-1518	265	4	gives	give	VERB
ejpam-1518	265	5	the	the	DET
ejpam-1518	265	6	relation	relation	NOUN
ejpam-1518	265	7	between	between	ADP
ejpam-1518	265	8	statistical	statistical	ADJ
ejpam-1518	265	9	equivalence	equivalence	NOUN
ejpam-1518	265	10	and	and	CCONJ
ejpam-1518	265	11	statistical	statistical	ADJ
ejpam-1518	265	12	boundedness	boundedness	NOUN
ejpam-1518	265	13	for	for	ADP
ejpam-1518	265	14	sequences	sequence	NOUN
ejpam-1518	265	15	.	.	PUNCT
ejpam-1518	266	1	theorem	theorem	NOUN
ejpam-1518	266	2	6	6	NUM
ejpam-1518	266	3	.	.	PUNCT
ejpam-1518	267	1	let	let	AUX
ejpam-1518	267	2	(	(	PUNCT
ejpam-1518	267	3	x	x	X
ejpam-1518	267	4	,	,	PUNCT
ejpam-1518	267	5	d	d	X
ejpam-1518	267	6	)	)	PUNCT
ejpam-1518	267	7	be	be	AUX
ejpam-1518	267	8	a	a	DET
ejpam-1518	267	9	metric	metric	ADJ
ejpam-1518	267	10	space	space	NOUN
ejpam-1518	267	11	,	,	PUNCT
ejpam-1518	267	12	x̃	x̃	PROPN
ejpam-1518	267	13	and	and	CCONJ
ejpam-1518	267	14	ỹ	ỹ	PROPN
ejpam-1518	267	15	belong	belong	VERB
ejpam-1518	267	16	to	to	ADP
ejpam-1518	267	17	x̃	x̃	PROPN
ejpam-1518	267	18	and	and	CCONJ
ejpam-1518	267	19	assume	assume	VERB
ejpam-1518	267	20	that	that	SCONJ
ejpam-1518	267	21	x̃	x̃	PROPN
ejpam-1518	267	22	be	be	AUX
ejpam-1518	267	23	a	a	DET
ejpam-1518	267	24	d	d	NOUN
ejpam-1518	267	25	–	–	PUNCT
ejpam-1518	267	26	statistical	statistical	ADJ
ejpam-1518	267	27	bounded	bounded	ADJ
ejpam-1518	267	28	sequence	sequence	NOUN
ejpam-1518	267	29	.	.	PUNCT
ejpam-1518	268	1	if	if	SCONJ
ejpam-1518	268	2	x̃	x̃	PROPN
ejpam-1518	268	3	≍	≍	VERB
ejpam-1518	268	4	ỹ	ỹ	PROPN
ejpam-1518	268	5	,	,	PUNCT
ejpam-1518	268	6	then	then	ADV
ejpam-1518	268	7	ỹ	ỹ	PROPN
ejpam-1518	268	8	is	be	AUX
ejpam-1518	268	9	also	also	ADV
ejpam-1518	268	10	d	d	ADJ
ejpam-1518	268	11	–	–	PUNCT
ejpam-1518	268	12	statistical	statistical	ADJ
ejpam-1518	268	13	bounded	bound	VERB
ejpam-1518	268	14	.	.	PUNCT
ejpam-1518	269	1	proof	proof	NOUN
ejpam-1518	269	2	.	.	PUNCT
ejpam-1518	270	1	we	we	PRON
ejpam-1518	270	2	can	can	AUX
ejpam-1518	270	3	follow	follow	VERB
ejpam-1518	270	4	the	the	DET
ejpam-1518	270	5	method	method	NOUN
ejpam-1518	270	6	in	in	ADP
ejpam-1518	270	7	the	the	DET
ejpam-1518	270	8	proof	proof	NOUN
ejpam-1518	270	9	of	of	ADP
ejpam-1518	270	10	lemma	lemma	PROPN
ejpam-1518	270	11	3.2	3.2	NUM
ejpam-1518	270	12	given	give	VERB
ejpam-1518	270	13	in	in	ADP
ejpam-1518	270	14	[	[	X
ejpam-1518	270	15	12	12	NUM
ejpam-1518	270	16	]	]	PUNCT
ejpam-1518	270	17	.	.	PUNCT
ejpam-1518	271	1	let	let	VERB
ejpam-1518	271	2	us	we	PRON
ejpam-1518	271	3	define	define	VERB
ejpam-1518	271	4	a	a	DET
ejpam-1518	271	5	subset	subset	NOUN
ejpam-1518	271	6	a	a	DET
ejpam-1518	271	7	ofn	ofn	NOUN
ejpam-1518	271	8	as	as	ADP
ejpam-1518	271	9	"	"	PUNCT
ejpam-1518	271	10	n	n	PRON
ejpam-1518	271	11	∈	∈	NOUN
ejpam-1518	271	12	a⇔	a⇔	NOUN
ejpam-1518	271	13	xn	xn	PUNCT
ejpam-1518	272	1	6=	6=	NUM
ejpam-1518	272	2	yn	yn	PROPN
ejpam-1518	272	3	"	"	PUNCT
ejpam-1518	272	4	.	.	PUNCT
ejpam-1518	273	1	then	then	ADV
ejpam-1518	273	2	,	,	PUNCT
ejpam-1518	273	3	subsetn\a	subsetn\a	PROPN
ejpam-1518	273	4	is	be	AUX
ejpam-1518	273	5	statistical	statistical	ADJ
ejpam-1518	273	6	dense	dense	ADJ
ejpam-1518	273	7	from	from	ADP
ejpam-1518	273	8	the	the	DET
ejpam-1518	273	9	definition	definition	NOUN
ejpam-1518	273	10	2(ii	2(ii	NUM
ejpam-1518	273	11	)	)	PUNCT
ejpam-1518	273	12	.	.	PUNCT
ejpam-1518	274	1	this	this	PRON
ejpam-1518	274	2	implies	imply	VERB
ejpam-1518	274	3	that	that	SCONJ
ejpam-1518	274	4	lim	lim	PROPN
ejpam-1518	274	5	n→∞	n→∞	NUM
ejpam-1518	274	6	1	1	NUM
ejpam-1518	274	7	n	n	NOUN
ejpam-1518	274	8	|{m	|{m	NOUN
ejpam-1518	274	9	∈	∈	NOUN
ejpam-1518	274	10	a	a	PRON
ejpam-1518	274	11	:	:	PUNCT
ejpam-1518	274	12	m	m	VERB
ejpam-1518	274	13	≤	≤	ADJ
ejpam-1518	274	14	n}|	n}|	NOUN
ejpam-1518	274	15	=	=	SYM
ejpam-1518	274	16	0	0	NUM
ejpam-1518	274	17	.	.	PUNCT
ejpam-1518	275	1	(	(	PUNCT
ejpam-1518	275	2	11	11	NUM
ejpam-1518	275	3	)	)	PUNCT
ejpam-1518	275	4	m.	m.	NOUN
ejpam-1518	275	5	küçükaslan	küçükaslan	NOUN
ejpam-1518	275	6	,	,	PUNCT
ejpam-1518	275	7	u.	u.	PROPN
ejpam-1518	275	8	değer	değer	PROPN
ejpam-1518	275	9	/	/	SYM
ejpam-1518	275	10	eur	eur	PROPN
ejpam-1518	275	11	.	.	PUNCT
ejpam-1518	276	1	j.	j.	PROPN
ejpam-1518	276	2	pure	pure	PROPN
ejpam-1518	276	3	appl	appl	PROPN
ejpam-1518	276	4	.	.	PROPN
ejpam-1518	276	5	math	math	PROPN
ejpam-1518	276	6	,	,	PUNCT
ejpam-1518	276	7	5	5	NUM
ejpam-1518	276	8	(	(	PUNCT
ejpam-1518	276	9	2012	2012	NUM
ejpam-1518	276	10	)	)	PUNCT
ejpam-1518	276	11	,	,	PUNCT
ejpam-1518	276	12	174	174	NUM
ejpam-1518	276	13	-	-	SYM
ejpam-1518	276	14	186	186	NUM
ejpam-1518	276	15	183	183	NUM
ejpam-1518	276	16	let	let	VERB
ejpam-1518	276	17	m	m	PRON
ejpam-1518	276	18	>	>	X
ejpam-1518	276	19	0	0	PUNCT
ejpam-1518	276	20	be	be	AUX
ejpam-1518	276	21	a	a	DET
ejpam-1518	276	22	sufficiently	sufficiently	ADV
ejpam-1518	276	23	large	large	ADJ
ejpam-1518	276	24	number	number	NOUN
ejpam-1518	276	25	.	.	PUNCT
ejpam-1518	277	1	according	accord	VERB
ejpam-1518	277	2	to	to	ADP
ejpam-1518	277	3	the	the	DET
ejpam-1518	277	4	definition	definition	NOUN
ejpam-1518	277	5	of	of	ADP
ejpam-1518	277	6	a	a	PRON
ejpam-1518	277	7	we	we	PRON
ejpam-1518	277	8	have	have	VERB
ejpam-1518	277	9	{	{	PUNCT
ejpam-1518	277	10	m	m	NOUN
ejpam-1518	277	11	∈	∈	PROPN
ejpam-1518	277	12	a	a	DET
ejpam-1518	277	13	:	:	PUNCT
ejpam-1518	277	14	m≤	m≤	NOUN
ejpam-1518	277	15	n	n	NOUN
ejpam-1518	277	16	and	and	CCONJ
ejpam-1518	277	17	d(ym	d(ym	PROPN
ejpam-1518	277	18	,	,	PUNCT
ejpam-1518	277	19	a	a	PRON
ejpam-1518	277	20	)	)	PUNCT
ejpam-1518	277	21	≥	≥	NOUN
ejpam-1518	277	22	m	m	PROPN
ejpam-1518	277	23	}	}	PUNCT
ejpam-1518	277	24	⊆	⊆	NUM
ejpam-1518	277	25	{	{	PUNCT
ejpam-1518	277	26	m	m	NOUN
ejpam-1518	277	27	∈	∈	PROPN
ejpam-1518	277	28	a	a	DET
ejpam-1518	277	29	:	:	PUNCT
ejpam-1518	277	30	m	m	VERB
ejpam-1518	277	31	≤	≤	NUM
ejpam-1518	277	32	n	n	CCONJ
ejpam-1518	277	33	}	}	PUNCT
ejpam-1518	277	34	∪	∪	ADJ
ejpam-1518	277	35	{	{	PUNCT
ejpam-1518	277	36	m	m	PROPN
ejpam-1518	277	37	∈	∈	PROPN
ejpam-1518	277	38	a	a	DET
ejpam-1518	277	39	:	:	PUNCT
ejpam-1518	277	40	m	m	VERB
ejpam-1518	277	41	≤	≤	NOUN
ejpam-1518	277	42	n	n	PRON
ejpam-1518	277	43	and	and	CCONJ
ejpam-1518	277	44	d(xm	d(xm	PROPN
ejpam-1518	277	45	,	,	PUNCT
ejpam-1518	277	46	a)≥	a)≥	PROPN
ejpam-1518	277	47	m	m	PRON
ejpam-1518	277	48	}	}	PUNCT
ejpam-1518	277	49	,	,	PUNCT
ejpam-1518	277	50	for	for	ADP
ejpam-1518	277	51	all	all	DET
ejpam-1518	277	52	n	n	DET
ejpam-1518	277	53	∈	∈	PROPN
ejpam-1518	277	54	n	n	NOUN
ejpam-1518	277	55	and	and	CCONJ
ejpam-1518	277	56	arbitrary	arbitrary	ADJ
ejpam-1518	277	57	point	point	VERB
ejpam-1518	277	58	a	a	DET
ejpam-1518	277	59	∈	∈	NOUN
ejpam-1518	277	60	x	x	X
ejpam-1518	277	61	.	.	PUNCT
ejpam-1518	278	1	by	by	ADP
ejpam-1518	278	2	using	use	VERB
ejpam-1518	278	3	this	this	DET
ejpam-1518	278	4	inclusion	inclusion	NOUN
ejpam-1518	278	5	and	and	CCONJ
ejpam-1518	278	6	equality	equality	NOUN
ejpam-1518	278	7	(	(	PUNCT
ejpam-1518	278	8	11	11	NUM
ejpam-1518	278	9	)	)	PUNCT
ejpam-1518	278	10	,	,	PUNCT
ejpam-1518	278	11	we	we	PRON
ejpam-1518	278	12	get	get	VERB
ejpam-1518	278	13	lim	lim	PROPN
ejpam-1518	278	14	sup	sup	X
ejpam-1518	278	15	n→∞	n→∞	NUM
ejpam-1518	278	16	�	�	PROPN
ejpam-1518	278	17	�	�	PROPN
ejpam-1518	278	18	{	{	PUNCT
ejpam-1518	278	19	m	m	PROPN
ejpam-1518	278	20	∈	∈	NOUN
ejpam-1518	278	21	n	n	NOUN
ejpam-1518	278	22	:	:	PUNCT
ejpam-1518	278	23	m	m	VERB
ejpam-1518	278	24	≤	≤	ADJ
ejpam-1518	278	25	n	n	CCONJ
ejpam-1518	278	26	and	and	CCONJ
ejpam-1518	278	27	d(ym	d(ym	PROPN
ejpam-1518	278	28	,	,	PUNCT
ejpam-1518	278	29	a	a	PRON
ejpam-1518	278	30	)	)	PUNCT
ejpam-1518	278	31	≥	≥	NOUN
ejpam-1518	278	32	m	m	PROPN
ejpam-1518	278	33	}	}	PUNCT
ejpam-1518	278	34	�	�	PROPN
ejpam-1518	278	35	�	�	PROPN
ejpam-1518	278	36	n	n	CCONJ
ejpam-1518	278	37	≤	≤	NOUN
ejpam-1518	278	38	lim	lim	PROPN
ejpam-1518	278	39	sup	sup	VERB
ejpam-1518	278	40	n→∞	n→∞	NUM
ejpam-1518	278	41	|{m	|{m	NOUN
ejpam-1518	278	42	∈	∈	NOUN
ejpam-1518	278	43	a	a	DET
ejpam-1518	278	44	:	:	PUNCT
ejpam-1518	278	45	m	m	VERB
ejpam-1518	278	46	≤	≤	NOUN
ejpam-1518	278	47	n}|	n}|	VERB
ejpam-1518	278	48	n	n	NOUN
ejpam-1518	278	49	+	+	CCONJ
ejpam-1518	278	50	lim	lim	PROPN
ejpam-1518	278	51	sup	sup	PROPN
ejpam-1518	278	52	n→∞	n→∞	NUM
ejpam-1518	278	53	�	�	PROPN
ejpam-1518	278	54	�	�	PROPN
ejpam-1518	278	55	{	{	PUNCT
ejpam-1518	278	56	m	m	PROPN
ejpam-1518	278	57	∈	∈	NOUN
ejpam-1518	278	58	n	n	NOUN
ejpam-1518	278	59	:	:	PUNCT
ejpam-1518	278	60	m	m	VERB
ejpam-1518	278	61	≤	≤	NOUN
ejpam-1518	278	62	n	n	PRON
ejpam-1518	278	63	and	and	CCONJ
ejpam-1518	278	64	d(xm	d(xm	PROPN
ejpam-1518	278	65	,	,	PUNCT
ejpam-1518	278	66	a)≥	a)≥	PROPN
ejpam-1518	278	67	m	m	PRON
ejpam-1518	278	68	}	}	PUNCT
ejpam-1518	278	69	�	�	PROPN
ejpam-1518	278	70	�	�	PROPN
ejpam-1518	278	71	n	n	NOUN
ejpam-1518	278	72	=	=	SYM
ejpam-1518	278	73	lim	lim	PROPN
ejpam-1518	278	74	sup	sup	VERB
ejpam-1518	278	75	n→∞	n→∞	NUM
ejpam-1518	278	76	�	�	PROPN
ejpam-1518	278	77	�	�	PROPN
ejpam-1518	278	78	{	{	PUNCT
ejpam-1518	278	79	m	m	PROPN
ejpam-1518	278	80	∈	∈	NOUN
ejpam-1518	278	81	n	n	NOUN
ejpam-1518	278	82	:	:	PUNCT
ejpam-1518	278	83	m	m	VERB
ejpam-1518	278	84	≤	≤	NOUN
ejpam-1518	278	85	n	n	PRON
ejpam-1518	278	86	and	and	CCONJ
ejpam-1518	278	87	d(xm	d(xm	PROPN
ejpam-1518	278	88	,	,	PUNCT
ejpam-1518	278	89	a)≥	a)≥	PROPN
ejpam-1518	278	90	m	m	PRON
ejpam-1518	278	91	}	}	PUNCT
ejpam-1518	278	92	�	�	PROPN
ejpam-1518	278	93	�	�	PROPN
ejpam-1518	278	94	n	n	PROPN
ejpam-1518	278	95	.	.	PUNCT
ejpam-1518	279	1	since	since	SCONJ
ejpam-1518	279	2	x̃	x̃	PROPN
ejpam-1518	279	3	is	be	AUX
ejpam-1518	279	4	d	d	NOUN
ejpam-1518	279	5	–	–	PUNCT
ejpam-1518	279	6	statistical	statistical	ADJ
ejpam-1518	279	7	bounded	bound	VERB
ejpam-1518	279	8	,	,	PUNCT
ejpam-1518	279	9	we	we	PRON
ejpam-1518	279	10	have	have	VERB
ejpam-1518	279	11	lim	lim	PROPN
ejpam-1518	279	12	sup	sup	X
ejpam-1518	279	13	n→∞	n→∞	NUM
ejpam-1518	279	14	�	�	PROPN
ejpam-1518	279	15	�	�	PROPN
ejpam-1518	279	16	{	{	PUNCT
ejpam-1518	279	17	m	m	PROPN
ejpam-1518	279	18	∈	∈	NOUN
ejpam-1518	279	19	n	n	NOUN
ejpam-1518	279	20	:	:	PUNCT
ejpam-1518	279	21	m	m	VERB
ejpam-1518	279	22	≤	≤	NOUN
ejpam-1518	279	23	n	n	PRON
ejpam-1518	279	24	and	and	CCONJ
ejpam-1518	279	25	d(xm	d(xm	PROPN
ejpam-1518	279	26	,	,	PUNCT
ejpam-1518	279	27	a)≥	a)≥	PROPN
ejpam-1518	279	28	m	m	PRON
ejpam-1518	279	29	}	}	PUNCT
ejpam-1518	279	30	�	�	PROPN
ejpam-1518	279	31	�	�	PROPN
ejpam-1518	279	32	n	n	NOUN
ejpam-1518	279	33	=	=	SYM
ejpam-1518	279	34	0	0	PROPN
ejpam-1518	279	35	.	.	PUNCT
ejpam-1518	280	1	consequently	consequently	ADV
ejpam-1518	280	2	the	the	DET
ejpam-1518	280	3	inequality	inequality	NOUN
ejpam-1518	280	4	lim	lim	PROPN
ejpam-1518	280	5	sup	sup	VERB
ejpam-1518	280	6	n→∞	n→∞	NUM
ejpam-1518	280	7	�	�	PROPN
ejpam-1518	280	8	�	�	PROPN
ejpam-1518	280	9	{	{	PUNCT
ejpam-1518	280	10	m	m	PROPN
ejpam-1518	280	11	∈	∈	NOUN
ejpam-1518	280	12	n	n	NOUN
ejpam-1518	280	13	:	:	PUNCT
ejpam-1518	280	14	m	m	VERB
ejpam-1518	280	15	≤	≤	ADJ
ejpam-1518	280	16	n	n	CCONJ
ejpam-1518	280	17	and	and	CCONJ
ejpam-1518	280	18	d(ym	d(ym	PROPN
ejpam-1518	280	19	,	,	PUNCT
ejpam-1518	280	20	a)≥	a)≥	PROPN
ejpam-1518	280	21	m	m	PRON
ejpam-1518	280	22	}	}	PUNCT
ejpam-1518	280	23	�	�	PROPN
ejpam-1518	280	24	�	�	PROPN
ejpam-1518	280	25	n	n	CCONJ
ejpam-1518	280	26	≤	≤	NOUN
ejpam-1518	280	27	0	0	NUM
ejpam-1518	281	1	(	(	PUNCT
ejpam-1518	281	2	12	12	NUM
ejpam-1518	281	3	)	)	PUNCT
ejpam-1518	281	4	holds	hold	VERB
ejpam-1518	281	5	.	.	PUNCT
ejpam-1518	282	1	by	by	ADP
ejpam-1518	282	2	using	use	VERB
ejpam-1518	282	3	(	(	PUNCT
ejpam-1518	282	4	12	12	NUM
ejpam-1518	282	5	)	)	PUNCT
ejpam-1518	282	6	we	we	PRON
ejpam-1518	282	7	obtain	obtain	VERB
ejpam-1518	282	8	0≤	0≤	NUM
ejpam-1518	282	9	lim	lim	PROPN
ejpam-1518	282	10	inf	inf	PROPN
ejpam-1518	282	11	n→∞	n→∞	NUM
ejpam-1518	282	12	�	�	PROPN
ejpam-1518	282	13	�	�	PROPN
ejpam-1518	282	14	{	{	PUNCT
ejpam-1518	282	15	m	m	PROPN
ejpam-1518	282	16	∈	∈	NOUN
ejpam-1518	282	17	n	n	NOUN
ejpam-1518	282	18	:	:	PUNCT
ejpam-1518	282	19	m	m	VERB
ejpam-1518	282	20	≤	≤	ADJ
ejpam-1518	282	21	n	n	CCONJ
ejpam-1518	282	22	and	and	CCONJ
ejpam-1518	282	23	d(ym	d(ym	PROPN
ejpam-1518	282	24	,	,	PUNCT
ejpam-1518	282	25	a)≥	a)≥	PROPN
ejpam-1518	282	26	m	m	PRON
ejpam-1518	282	27	}	}	PUNCT
ejpam-1518	282	28	�	�	PROPN
ejpam-1518	282	29	�	�	PROPN
ejpam-1518	282	30	n	n	CCONJ
ejpam-1518	282	31	≤	≤	NOUN
ejpam-1518	282	32	lim	lim	PROPN
ejpam-1518	282	33	sup	sup	VERB
ejpam-1518	282	34	n→∞	n→∞	NUM
ejpam-1518	282	35	�	�	PROPN
ejpam-1518	282	36	�	�	PROPN
ejpam-1518	282	37	{	{	PUNCT
ejpam-1518	282	38	m	m	PROPN
ejpam-1518	282	39	∈	∈	NOUN
ejpam-1518	282	40	n	n	NOUN
ejpam-1518	282	41	:	:	PUNCT
ejpam-1518	282	42	m	m	VERB
ejpam-1518	282	43	≤	≤	ADJ
ejpam-1518	282	44	n	n	CCONJ
ejpam-1518	282	45	and	and	CCONJ
ejpam-1518	282	46	d(ym	d(ym	PROPN
ejpam-1518	282	47	,	,	PUNCT
ejpam-1518	282	48	a	a	PRON
ejpam-1518	282	49	)	)	PUNCT
ejpam-1518	282	50	≥	≥	NOUN
ejpam-1518	282	51	m	m	PROPN
ejpam-1518	282	52	}	}	PUNCT
ejpam-1518	282	53	�	�	PROPN
ejpam-1518	282	54	�	�	PROPN
ejpam-1518	282	55	n	n	CCONJ
ejpam-1518	282	56	≤	≤	NOUN
ejpam-1518	282	57	0	0	NUM
ejpam-1518	282	58	.	.	PUNCT
ejpam-1518	283	1	hence	hence	ADV
ejpam-1518	283	2	the	the	DET
ejpam-1518	283	3	limit	limit	NOUN
ejpam-1518	283	4	relation	relation	NOUN
ejpam-1518	283	5	lim	lim	PROPN
ejpam-1518	283	6	n→∞	n→∞	NUM
ejpam-1518	283	7	�	�	PROPN
ejpam-1518	283	8	�	�	PROPN
ejpam-1518	283	9	{	{	PUNCT
ejpam-1518	283	10	m	m	PROPN
ejpam-1518	283	11	∈	∈	NOUN
ejpam-1518	283	12	n	n	NOUN
ejpam-1518	283	13	:	:	PUNCT
ejpam-1518	283	14	m≤	m≤	VERB
ejpam-1518	283	15	n	n	NOUN
ejpam-1518	284	1	and	and	CCONJ
ejpam-1518	285	1	d(ym	d(ym	PROPN
ejpam-1518	285	2	,	,	PUNCT
ejpam-1518	285	3	a	a	PRON
ejpam-1518	285	4	)	)	PUNCT
ejpam-1518	285	5	≥	≥	NOUN
ejpam-1518	285	6	m	m	PROPN
ejpam-1518	285	7	}	}	PUNCT
ejpam-1518	285	8	�	�	PROPN
ejpam-1518	285	9	�	�	PROPN
ejpam-1518	285	10	n	n	NOUN
ejpam-1518	285	11	=	=	SYM
ejpam-1518	285	12	0	0	NUM
ejpam-1518	285	13	holds	hold	NOUN
ejpam-1518	285	14	.	.	PUNCT
ejpam-1518	286	1	therefore	therefore	ADV
ejpam-1518	286	2	,	,	PUNCT
ejpam-1518	286	3	this	this	PRON
ejpam-1518	286	4	gives	give	VERB
ejpam-1518	286	5	the	the	DET
ejpam-1518	286	6	desired	desire	VERB
ejpam-1518	286	7	result	result	NOUN
ejpam-1518	286	8	.	.	PUNCT
ejpam-1518	287	1	suppose	suppose	VERB
ejpam-1518	287	2	(	(	PUNCT
ejpam-1518	287	3	x	x	X
ejpam-1518	287	4	,	,	PUNCT
ejpam-1518	287	5	d	d	PROPN
ejpam-1518	287	6	)	)	PUNCT
ejpam-1518	287	7	and	and	CCONJ
ejpam-1518	287	8	(	(	PUNCT
ejpam-1518	287	9	y	y	PROPN
ejpam-1518	287	10	,	,	PUNCT
ejpam-1518	287	11	d	d	NOUN
ejpam-1518	287	12	′	′	NOUN
ejpam-1518	287	13	)	)	PUNCT
ejpam-1518	287	14	are	be	AUX
ejpam-1518	287	15	two	two	NUM
ejpam-1518	287	16	metric	metric	ADJ
ejpam-1518	287	17	spaces	space	NOUN
ejpam-1518	287	18	.	.	PUNCT
ejpam-1518	288	1	we	we	PRON
ejpam-1518	288	2	say	say	VERB
ejpam-1518	288	3	that	that	SCONJ
ejpam-1518	288	4	y	y	PROPN
ejpam-1518	288	5	is	be	AUX
ejpam-1518	288	6	a	a	DET
ejpam-1518	288	7	metric	metric	ADJ
ejpam-1518	288	8	subspace	subspace	NOUN
ejpam-1518	288	9	of	of	ADP
ejpam-1518	288	10	x	x	PUNCT
ejpam-1518	288	11	and	and	CCONJ
ejpam-1518	288	12	x	x	X
ejpam-1518	288	13	is	be	AUX
ejpam-1518	288	14	a	a	DET
ejpam-1518	288	15	metric	metric	ADJ
ejpam-1518	288	16	superspace	superspace	NOUN
ejpam-1518	288	17	of	of	ADP
ejpam-1518	288	18	y	y	PROPN
ejpam-1518	288	19	if	if	SCONJ
ejpam-1518	288	20	,	,	PUNCT
ejpam-1518	288	21	and	and	CCONJ
ejpam-1518	288	22	only	only	ADV
ejpam-1518	288	23	if	if	SCONJ
ejpam-1518	288	24	y	y	PROPN
ejpam-1518	288	25	is	be	AUX
ejpam-1518	288	26	a	a	DET
ejpam-1518	288	27	subset	subset	NOUN
ejpam-1518	288	28	of	of	ADP
ejpam-1518	288	29	x	x	PUNCT
ejpam-1518	288	30	and	and	CCONJ
ejpam-1518	288	31	d	d	NOUN
ejpam-1518	288	32	′	′	NOUN
ejpam-1518	288	33	is	be	AUX
ejpam-1518	288	34	a	a	DET
ejpam-1518	288	35	restriction	restriction	NOUN
ejpam-1518	288	36	of	of	ADP
ejpam-1518	288	37	d	d	PROPN
ejpam-1518	288	38	,	,	PUNCT
ejpam-1518	288	39	i.e.	i.e.	X
ejpam-1518	288	40	d	d	ADP
ejpam-1518	288	41	′(x	′(x	NOUN
ejpam-1518	288	42	,	,	PUNCT
ejpam-1518	288	43	y	y	PROPN
ejpam-1518	288	44	)	)	PUNCT
ejpam-1518	288	45	:	:	PUNCT
ejpam-1518	289	1	=	=	X
ejpam-1518	289	2	dy	dy	X
ejpam-1518	289	3	(	(	PUNCT
ejpam-1518	289	4	x	x	PROPN
ejpam-1518	289	5	,	,	PUNCT
ejpam-1518	289	6	y	y	PROPN
ejpam-1518	289	7	)	)	PUNCT
ejpam-1518	289	8	.	.	PUNCT
ejpam-1518	290	1	theorem	theorem	ADJ
ejpam-1518	290	2	7	7	NUM
ejpam-1518	290	3	.	.	PUNCT
ejpam-1518	291	1	let	let	AUX
ejpam-1518	291	2	(	(	PUNCT
ejpam-1518	291	3	x	x	X
ejpam-1518	291	4	,	,	PUNCT
ejpam-1518	291	5	d	d	X
ejpam-1518	291	6	)	)	PUNCT
ejpam-1518	291	7	be	be	AUX
ejpam-1518	291	8	a	a	DET
ejpam-1518	291	9	metric	metric	ADJ
ejpam-1518	291	10	space	space	NOUN
ejpam-1518	291	11	and	and	CCONJ
ejpam-1518	291	12	(	(	PUNCT
ejpam-1518	291	13	y	y	PROPN
ejpam-1518	291	14	,	,	PUNCT
ejpam-1518	291	15	d	d	NOUN
ejpam-1518	291	16	′	′	NOUN
ejpam-1518	291	17	)	)	PUNCT
ejpam-1518	291	18	be	be	AUX
ejpam-1518	291	19	a	a	DET
ejpam-1518	291	20	metric	metric	ADJ
ejpam-1518	291	21	subspace	subspace	NOUN
ejpam-1518	291	22	.	.	PUNCT
ejpam-1518	292	1	then	then	ADV
ejpam-1518	292	2	,	,	PUNCT
ejpam-1518	292	3	the	the	DET
ejpam-1518	292	4	following	follow	VERB
ejpam-1518	292	5	statements	statement	NOUN
ejpam-1518	292	6	hold	hold	VERB
ejpam-1518	292	7	:	:	PUNCT
ejpam-1518	292	8	(	(	PUNCT
ejpam-1518	292	9	i	i	NOUN
ejpam-1518	292	10	)	)	PUNCT
ejpam-1518	292	11	if	if	SCONJ
ejpam-1518	292	12	(	(	PUNCT
ejpam-1518	292	13	yn	yn	NOUN
ejpam-1518	292	14	)	)	PUNCT
ejpam-1518	292	15	∈	∈	PROPN
ejpam-1518	292	16	ey	ey	X
ejpam-1518	292	17	is	be	AUX
ejpam-1518	292	18	d	d	PROPN
ejpam-1518	292	19	′−statistical	′−statistical	PROPN
ejpam-1518	292	20	bounded	bound	VERB
ejpam-1518	292	21	then	then	ADV
ejpam-1518	292	22	(	(	PUNCT
ejpam-1518	292	23	yn	yn	NOUN
ejpam-1518	292	24	)	)	PUNCT
ejpam-1518	292	25	is	be	AUX
ejpam-1518	292	26	d−statistical	d−statistical	PROPN
ejpam-1518	293	1	bounded	bounded	PROPN
ejpam-1518	293	2	.	.	PUNCT
ejpam-1518	294	1	m.	m.	PROPN
ejpam-1518	294	2	küçükaslan	küçükaslan	PROPN
ejpam-1518	294	3	,	,	PUNCT
ejpam-1518	294	4	u.	u.	PROPN
ejpam-1518	294	5	değer	değer	PROPN
ejpam-1518	294	6	/	/	SYM
ejpam-1518	294	7	eur	eur	PROPN
ejpam-1518	294	8	.	.	PUNCT
ejpam-1518	295	1	j.	j.	PROPN
ejpam-1518	295	2	pure	pure	PROPN
ejpam-1518	295	3	appl	appl	PROPN
ejpam-1518	295	4	.	.	PROPN
ejpam-1518	295	5	math	math	PROPN
ejpam-1518	295	6	,	,	PUNCT
ejpam-1518	295	7	5	5	NUM
ejpam-1518	295	8	(	(	PUNCT
ejpam-1518	295	9	2012	2012	NUM
ejpam-1518	295	10	)	)	PUNCT
ejpam-1518	295	11	,	,	PUNCT
ejpam-1518	295	12	174	174	NUM
ejpam-1518	295	13	-	-	SYM
ejpam-1518	295	14	186	186	NUM
ejpam-1518	295	15	184	184	NUM
ejpam-1518	295	16	(	(	PUNCT
ejpam-1518	295	17	ii	ii	NOUN
ejpam-1518	295	18	)	)	PUNCT
ejpam-1518	295	19	if	if	SCONJ
ejpam-1518	295	20	(	(	PUNCT
ejpam-1518	295	21	xn	xn	X
ejpam-1518	295	22	)	)	PUNCT
ejpam-1518	295	23	∈	∈	PROPN
ejpam-1518	295	24	ex	ex	X
ejpam-1518	295	25	is	be	AUX
ejpam-1518	295	26	d−statistical	d−statistical	PROPN
ejpam-1518	295	27	bounded	bounded	PROPN
ejpam-1518	295	28	,	,	PUNCT
ejpam-1518	295	29	then	then	ADV
ejpam-1518	295	30	(	(	PUNCT
ejpam-1518	295	31	xn	xn	X
ejpam-1518	295	32	)	)	PUNCT
ejpam-1518	296	1	d	d	PROPN
ejpam-1518	296	2	′−statistical	′−statistical	PROPN
ejpam-1518	296	3	bounded	bound	VERB
ejpam-1518	296	4	in	in	ADP
ejpam-1518	296	5	subspace	subspace	NOUN
ejpam-1518	296	6	that	that	PRON
ejpam-1518	296	7	contains	contain	VERB
ejpam-1518	296	8	all	all	DET
ejpam-1518	296	9	terms	term	NOUN
ejpam-1518	296	10	of	of	ADP
ejpam-1518	296	11	(	(	PUNCT
ejpam-1518	296	12	xn	xn	PROPN
ejpam-1518	296	13	)	)	PUNCT
ejpam-1518	296	14	.	.	PUNCT
ejpam-1518	297	1	proof	proof	NOUN
ejpam-1518	297	2	.	.	PUNCT
ejpam-1518	298	1	(	(	PUNCT
ejpam-1518	298	2	i	i	NOUN
ejpam-1518	298	3	)	)	PUNCT
ejpam-1518	298	4	from	from	ADP
ejpam-1518	298	5	the	the	DET
ejpam-1518	298	6	definition	definition	NOUN
ejpam-1518	298	7	of	of	ADP
ejpam-1518	298	8	subspace	subspace	NOUN
ejpam-1518	298	9	metric	metric	ADJ
ejpam-1518	298	10	and	and	CCONJ
ejpam-1518	298	11	statistical	statistical	ADJ
ejpam-1518	298	12	boundednes	boundedne	NOUN
ejpam-1518	298	13	and	and	CCONJ
ejpam-1518	298	14	for	for	ADP
ejpam-1518	298	15	arbitrary	arbitrary	ADJ
ejpam-1518	298	16	y∗	y∗	PROPN
ejpam-1518	298	17	∈	∈	PROPN
ejpam-1518	298	18	y	y	PROPN
ejpam-1518	298	19	and	and	CCONJ
ejpam-1518	298	20	sufficiently	sufficiently	ADV
ejpam-1518	298	21	large	large	ADJ
ejpam-1518	298	22	positive	positive	ADJ
ejpam-1518	298	23	m	m	NOUN
ejpam-1518	298	24	>	>	X
ejpam-1518	298	25	0	0	NUM
ejpam-1518	299	1	we	we	PRON
ejpam-1518	299	2	have	have	VERB
ejpam-1518	299	3	�	�	PROPN
ejpam-1518	299	4	k	k	NOUN
ejpam-1518	299	5	:	:	PUNCT
ejpam-1518	299	6	k	k	PROPN
ejpam-1518	299	7	≤	≤	PROPN
ejpam-1518	299	8	n	n	CCONJ
ejpam-1518	299	9	,	,	PUNCT
ejpam-1518	299	10	d	d	PROPN
ejpam-1518	299	11	′(yk	′(yk	PROPN
ejpam-1518	299	12	,	,	PUNCT
ejpam-1518	299	13	y∗)≥	y∗)≥	NOUN
ejpam-1518	299	14	m	m	NOUN
ejpam-1518	299	15	=	=	PROPN
ejpam-1518	299	16	�	�	PROPN
ejpam-1518	299	17	k	k	NOUN
ejpam-1518	299	18	:	:	PUNCT
ejpam-1518	299	19	k	k	PROPN
ejpam-1518	299	20	≤	≤	PROPN
ejpam-1518	299	21	n	n	CCONJ
ejpam-1518	299	22	,	,	PUNCT
ejpam-1518	299	23	d(yk	d(yk	NOUN
ejpam-1518	299	24	,	,	PUNCT
ejpam-1518	299	25	y∗)≥	y∗)≥	NOUN
ejpam-1518	299	26	m	m	NOUN
ejpam-1518	299	27	.	.	PUNCT
ejpam-1518	300	1	therefore	therefore	ADV
ejpam-1518	300	2	,	,	PUNCT
ejpam-1518	300	3	0=	0=	NOUN
ejpam-1518	301	1	lim	lim	PROPN
ejpam-1518	301	2	n→∞	n→∞	NUM
ejpam-1518	301	3	1	1	NUM
ejpam-1518	301	4	n	n	PRON
ejpam-1518	301	5	�	�	PROPN
ejpam-1518	301	6	�	�	PROPN
ejpam-1518	301	7	�	�	PROPN
ejpam-1518	301	8	k	k	NOUN
ejpam-1518	301	9	:	:	PUNCT
ejpam-1518	301	10	k	k	PROPN
ejpam-1518	301	11	≤	≤	PROPN
ejpam-1518	301	12	n	n	CCONJ
ejpam-1518	301	13	,	,	PUNCT
ejpam-1518	301	14	d	d	PROPN
ejpam-1518	301	15	′(yk	′(yk	PROPN
ejpam-1518	301	16	,	,	PUNCT
ejpam-1518	301	17	y∗)≥	y∗)≥	NUM
ejpam-1518	301	18	m	m	PROPN
ejpam-1518	301	19	�	�	PROPN
ejpam-1518	301	20	�	�	PROPN
ejpam-1518	301	21	=	=	SYM
ejpam-1518	301	22	lim	lim	PROPN
ejpam-1518	301	23	n→∞	n→∞	NUM
ejpam-1518	301	24	1	1	NUM
ejpam-1518	301	25	n	n	PRON
ejpam-1518	301	26	�	�	PROPN
ejpam-1518	301	27	�	�	PROPN
ejpam-1518	301	28	�	�	PROPN
ejpam-1518	301	29	k	k	NOUN
ejpam-1518	301	30	:	:	PUNCT
ejpam-1518	301	31	k	k	PROPN
ejpam-1518	301	32	≤	≤	PROPN
ejpam-1518	301	33	n	n	CCONJ
ejpam-1518	301	34	,	,	PUNCT
ejpam-1518	301	35	d(yk	d(yk	NOUN
ejpam-1518	301	36	,	,	PUNCT
ejpam-1518	301	37	y∗)≥	y∗)≥	NUM
ejpam-1518	301	38	m	m	PROPN
ejpam-1518	301	39	�	�	PROPN
ejpam-1518	301	40	�	�	PROPN
ejpam-1518	301	41	.	.	PUNCT
ejpam-1518	302	1	(	(	PUNCT
ejpam-1518	302	2	ii	ii	X
ejpam-1518	302	3	)	)	PUNCT
ejpam-1518	302	4	it	it	PRON
ejpam-1518	302	5	can	can	AUX
ejpam-1518	302	6	be	be	AUX
ejpam-1518	302	7	prove	prove	VERB
ejpam-1518	302	8	by	by	ADP
ejpam-1518	302	9	using	use	VERB
ejpam-1518	302	10	the	the	DET
ejpam-1518	302	11	same	same	ADJ
ejpam-1518	302	12	arguments	argument	NOUN
ejpam-1518	302	13	in	in	ADP
ejpam-1518	302	14	(	(	PUNCT
ejpam-1518	302	15	i	i	NOUN
ejpam-1518	302	16	)	)	PUNCT
ejpam-1518	302	17	.	.	PUNCT
ejpam-1518	303	1	let	let	VERB
ejpam-1518	303	2	x	x	X
ejpam-1518	303	3	6=	6=	NUM
ejpam-1518	303	4	;	;	PUNCT
ejpam-1518	303	5	be	be	AUX
ejpam-1518	303	6	a	a	DET
ejpam-1518	303	7	metric	metric	ADJ
ejpam-1518	303	8	space	space	NOUN
ejpam-1518	303	9	with	with	ADP
ejpam-1518	303	10	equivalent	equivalent	ADJ
ejpam-1518	303	11	metrics	metric	NOUN
ejpam-1518	303	12	d1	d1	PROPN
ejpam-1518	303	13	and	and	CCONJ
ejpam-1518	303	14	d2	d2	PROPN
ejpam-1518	303	15	.	.	PUNCT
ejpam-1518	304	1	that	that	PRON
ejpam-1518	304	2	is	be	AUX
ejpam-1518	304	3	,	,	PUNCT
ejpam-1518	304	4	there	there	PRON
ejpam-1518	304	5	are	be	VERB
ejpam-1518	304	6	positive	positive	ADJ
ejpam-1518	304	7	constant	constant	ADJ
ejpam-1518	304	8	m1	m1	NOUN
ejpam-1518	304	9	and	and	CCONJ
ejpam-1518	304	10	m2	m2	PROPN
ejpam-1518	304	11	such	such	ADJ
ejpam-1518	304	12	that	that	DET
ejpam-1518	304	13	m1d1(x	m1d1(x	NOUN
ejpam-1518	304	14	,	,	PUNCT
ejpam-1518	304	15	y)≤	y)≤	PRON
ejpam-1518	304	16	d2(x	d2(x	PROPN
ejpam-1518	304	17	,	,	PUNCT
ejpam-1518	304	18	y	y	NOUN
ejpam-1518	304	19	)	)	PUNCT
ejpam-1518	304	20	≤	≤	NOUN
ejpam-1518	305	1	m2d1(x	m2d1(x	PROPN
ejpam-1518	305	2	,	,	PUNCT
ejpam-1518	305	3	y	y	PROPN
ejpam-1518	305	4	)	)	PUNCT
ejpam-1518	305	5	(	(	PUNCT
ejpam-1518	305	6	13	13	NUM
ejpam-1518	305	7	)	)	PUNCT
ejpam-1518	305	8	for	for	ADP
ejpam-1518	305	9	every	every	DET
ejpam-1518	305	10	x	x	X
ejpam-1518	305	11	,	,	PUNCT
ejpam-1518	305	12	y	y	PROPN
ejpam-1518	305	13	∈	∈	PROPN
ejpam-1518	305	14	x	x	X
ejpam-1518	305	15	.	.	PUNCT
ejpam-1518	306	1	theorem	theorem	ADJ
ejpam-1518	306	2	8	8	NUM
ejpam-1518	306	3	.	.	PUNCT
ejpam-1518	307	1	let	let	VERB
ejpam-1518	307	2	x	x	PRON
ejpam-1518	307	3	be	be	AUX
ejpam-1518	307	4	a	a	DET
ejpam-1518	307	5	metric	metric	ADJ
ejpam-1518	307	6	space	space	NOUN
ejpam-1518	307	7	with	with	ADP
ejpam-1518	307	8	equivalent	equivalent	ADJ
ejpam-1518	307	9	d1	d1	PROPN
ejpam-1518	307	10	and	and	CCONJ
ejpam-1518	307	11	d2	d2	NOUN
ejpam-1518	307	12	metrics	metric	NOUN
ejpam-1518	307	13	.	.	PUNCT
ejpam-1518	308	1	then	then	ADV
ejpam-1518	308	2	,	,	PUNCT
ejpam-1518	308	3	the	the	DET
ejpam-1518	308	4	following	follow	VERB
ejpam-1518	308	5	statements	statement	NOUN
ejpam-1518	308	6	hold	hold	VERB
ejpam-1518	308	7	:	:	PUNCT
ejpam-1518	308	8	(	(	PUNCT
ejpam-1518	308	9	i	i	NOUN
ejpam-1518	308	10	)	)	PUNCT
ejpam-1518	308	11	b	b	PROPN
ejpam-1518	308	12	d1	d1	PROPN
ejpam-1518	308	13	st	st	PROPN
ejpam-1518	309	1	(	(	PUNCT
ejpam-1518	309	2	ex	ex	X
ejpam-1518	309	3	)	)	PUNCT
ejpam-1518	309	4	=	=	SYM
ejpam-1518	309	5	b	b	PROPN
ejpam-1518	309	6	d2	d2	PROPN
ejpam-1518	309	7	st	st	PROPN
ejpam-1518	309	8	(	(	PUNCT
ejpam-1518	309	9	ex	ex	X
ejpam-1518	309	10	)	)	PUNCT
ejpam-1518	309	11	,	,	PUNCT
ejpam-1518	309	12	(	(	PUNCT
ejpam-1518	309	13	ii	ii	NOUN
ejpam-1518	309	14	)	)	PUNCT
ejpam-1518	309	15	c	c	PROPN
ejpam-1518	309	16	d1	d1	PROPN
ejpam-1518	309	17	st	st	PROPN
ejpam-1518	309	18	(	(	PUNCT
ejpam-1518	309	19	ex	ex	X
ejpam-1518	309	20	)	)	PUNCT
ejpam-1518	309	21	=	=	PUNCT
ejpam-1518	309	22	c	c	PROPN
ejpam-1518	309	23	d2	d2	PROPN
ejpam-1518	309	24	st	st	PROPN
ejpam-1518	309	25	(	(	PUNCT
ejpam-1518	309	26	ex	ex	NOUN
ejpam-1518	309	27	)	)	PUNCT
ejpam-1518	309	28	.	.	PUNCT
ejpam-1518	310	1	proof	proof	NOUN
ejpam-1518	310	2	.	.	PUNCT
ejpam-1518	311	1	(	(	PUNCT
ejpam-1518	311	2	i	i	NOUN
ejpam-1518	311	3	)	)	PUNCT
ejpam-1518	311	4	assume	assume	VERB
ejpam-1518	311	5	that	that	SCONJ
ejpam-1518	311	6	x̃	x̃	PROPN
ejpam-1518	311	7	=	=	SYM
ejpam-1518	311	8	(	(	PUNCT
ejpam-1518	311	9	xn	xn	X
ejpam-1518	311	10	)	)	PUNCT
ejpam-1518	311	11	∈	∈	PROPN
ejpam-1518	311	12	ex	ex	NOUN
ejpam-1518	311	13	is	be	AUX
ejpam-1518	311	14	an	an	DET
ejpam-1518	311	15	arbitrary	arbitrary	ADJ
ejpam-1518	311	16	d1statistical	d1statistical	PROPN
ejpam-1518	311	17	bounded	bounded	ADJ
ejpam-1518	311	18	sequence	sequence	NOUN
ejpam-1518	311	19	,	,	PUNCT
ejpam-1518	311	20	i.e.	i.e.	X
ejpam-1518	311	21	x̃	x̃	PROPN
ejpam-1518	311	22	∈	∈	PROPN
ejpam-1518	311	23	b	b	PROPN
ejpam-1518	311	24	d1	d1	PROPN
ejpam-1518	311	25	st	st	PROPN
ejpam-1518	311	26	(	(	PUNCT
ejpam-1518	311	27	ex	ex	NOUN
ejpam-1518	311	28	)	)	PUNCT
ejpam-1518	311	29	.	.	PUNCT
ejpam-1518	312	1	then	then	ADV
ejpam-1518	312	2	,	,	PUNCT
ejpam-1518	312	3	there	there	PRON
ejpam-1518	312	4	is	be	VERB
ejpam-1518	312	5	a	a	DET
ejpam-1518	312	6	positive	positive	ADJ
ejpam-1518	312	7	m	m	NOUN
ejpam-1518	312	8	>	>	X
ejpam-1518	312	9	0	0	PUNCT
ejpam-1518	312	10	and	and	CCONJ
ejpam-1518	312	11	arbitrary	arbitrary	ADJ
ejpam-1518	312	12	x∗	x∗	PROPN
ejpam-1518	312	13	∈	∈	PROPN
ejpam-1518	312	14	x	x	PUNCT
ejpam-1518	312	15	such	such	ADJ
ejpam-1518	312	16	that	that	SCONJ
ejpam-1518	312	17	lim	lim	PROPN
ejpam-1518	312	18	n→∞	n→∞	NUM
ejpam-1518	312	19	1	1	NUM
ejpam-1518	312	20	n	n	PRON
ejpam-1518	312	21	�	�	PROPN
ejpam-1518	312	22	�	�	PROPN
ejpam-1518	312	23	�	�	PROPN
ejpam-1518	312	24	k	k	NOUN
ejpam-1518	312	25	:	:	PUNCT
ejpam-1518	312	26	k	k	PROPN
ejpam-1518	312	27	≤	≤	PROPN
ejpam-1518	312	28	n	n	CCONJ
ejpam-1518	312	29	,	,	PUNCT
ejpam-1518	312	30	d1(xk	d1(xk	PROPN
ejpam-1518	312	31	,	,	PUNCT
ejpam-1518	312	32	x∗)≥	x∗)≥	PUNCT
ejpam-1518	313	1	m	m	PROPN
ejpam-1518	313	2	�	�	PROPN
ejpam-1518	313	3	�	�	PROPN
ejpam-1518	313	4	=	=	SYM
ejpam-1518	313	5	0	0	NUM
ejpam-1518	313	6	.	.	PUNCT
ejpam-1518	313	7	also	also	ADV
ejpam-1518	313	8	,	,	PUNCT
ejpam-1518	313	9	from	from	ADP
ejpam-1518	313	10	(	(	PUNCT
ejpam-1518	313	11	13	13	NUM
ejpam-1518	313	12	)	)	PUNCT
ejpam-1518	313	13	we	we	PRON
ejpam-1518	313	14	have	have	VERB
ejpam-1518	313	15	�	�	PROPN
ejpam-1518	313	16	k	k	NOUN
ejpam-1518	313	17	:	:	PUNCT
ejpam-1518	313	18	k	k	PROPN
ejpam-1518	313	19	≤	≤	PROPN
ejpam-1518	313	20	n	n	CCONJ
ejpam-1518	313	21	,	,	PUNCT
ejpam-1518	313	22	d1(xk	d1(xk	PROPN
ejpam-1518	313	23	,	,	PUNCT
ejpam-1518	313	24	x∗)≥	x∗)≥	PUNCT
ejpam-1518	314	1	m	m	PROPN
ejpam-1518	314	2	⊂	⊂	PROPN
ejpam-1518	314	3	�	�	PROPN
ejpam-1518	314	4	k	k	PROPN
ejpam-1518	314	5	:	:	PUNCT
ejpam-1518	314	6	k	k	PROPN
ejpam-1518	314	7	≤	≤	PROPN
ejpam-1518	314	8	n	n	CCONJ
ejpam-1518	314	9	,	,	PUNCT
ejpam-1518	314	10	d2(xk	d2(xk	PROPN
ejpam-1518	314	11	,	,	PUNCT
ejpam-1518	314	12	x∗)≥	x∗)≥	PUNCT
ejpam-1518	315	1	m1	m1	PROPN
ejpam-1518	315	2	m	m	PROPN
ejpam-1518	315	3	⊂	⊂	PROPN
ejpam-1518	315	4	�	�	PROPN
ejpam-1518	316	1	k	k	NOUN
ejpam-1518	316	2	:	:	PUNCT
ejpam-1518	316	3	k	k	PROPN
ejpam-1518	316	4	≤	≤	PROPN
ejpam-1518	316	5	n	n	CCONJ
ejpam-1518	316	6	,	,	PUNCT
ejpam-1518	316	7	d1(xk	d1(xk	PROPN
ejpam-1518	316	8	,	,	PUNCT
ejpam-1518	316	9	x∗)≥	x∗)≥	PUNCT
ejpam-1518	317	1	m1	m1	PROPN
ejpam-1518	317	2	m2	m2	PROPN
ejpam-1518	317	3	m	m	PROPN
ejpam-1518	317	4	�	�	PROPN
ejpam-1518	317	5	and	and	CCONJ
ejpam-1518	317	6	�	�	PROPN
ejpam-1518	317	7	�	�	PROPN
ejpam-1518	317	8	�	�	PROPN
ejpam-1518	317	9	k	k	NOUN
ejpam-1518	317	10	:	:	PUNCT
ejpam-1518	317	11	k	k	PROPN
ejpam-1518	317	12	≤	≤	PROPN
ejpam-1518	317	13	n	n	CCONJ
ejpam-1518	317	14	,	,	PUNCT
ejpam-1518	317	15	d1(xk	d1(xk	PROPN
ejpam-1518	317	16	,	,	PUNCT
ejpam-1518	317	17	x∗)≥	x∗)≥	PUNCT
ejpam-1518	317	18	m	m	PROPN
ejpam-1518	317	19	�	�	PROPN
ejpam-1518	317	20	�	�	PROPN
ejpam-1518	317	21	≤	≤	PROPN
ejpam-1518	317	22	�	�	PROPN
ejpam-1518	317	23	�	�	PROPN
ejpam-1518	317	24	�	�	PROPN
ejpam-1518	317	25	k	k	NOUN
ejpam-1518	317	26	:	:	PUNCT
ejpam-1518	317	27	k	k	PROPN
ejpam-1518	317	28	≤	≤	PROPN
ejpam-1518	317	29	n	n	CCONJ
ejpam-1518	317	30	,	,	PUNCT
ejpam-1518	317	31	d2(xk	d2(xk	PROPN
ejpam-1518	317	32	,	,	PUNCT
ejpam-1518	317	33	x∗)≥	x∗)≥	PUNCT
ejpam-1518	317	34	m1	m1	PROPN
ejpam-1518	317	35	m	m	PROPN
ejpam-1518	317	36	�	�	PROPN
ejpam-1518	317	37	�	�	PROPN
ejpam-1518	317	38	references	reference	NOUN
ejpam-1518	317	39	185	185	NUM
ejpam-1518	317	40	≤	≤	NUM
ejpam-1518	317	41	�	�	PROPN
ejpam-1518	317	42	�	�	PROPN
ejpam-1518	317	43	�	�	PROPN
ejpam-1518	317	44	�	�	PROPN
ejpam-1518	317	45	�	�	PROPN
ejpam-1518	317	46	k	k	PROPN
ejpam-1518	317	47	:	:	PUNCT
ejpam-1518	317	48	k	k	PROPN
ejpam-1518	317	49	≤	≤	PROPN
ejpam-1518	317	50	n	n	CCONJ
ejpam-1518	317	51	,	,	PUNCT
ejpam-1518	317	52	d1(xk	d1(xk	PROPN
ejpam-1518	317	53	,	,	PUNCT
ejpam-1518	317	54	x∗)≥	x∗)≥	PUNCT
ejpam-1518	318	1	m1	m1	PROPN
ejpam-1518	318	2	m2	m2	PROPN
ejpam-1518	318	3	m	m	PROPN
ejpam-1518	318	4	�	�	PROPN
ejpam-1518	318	5	�	�	PROPN
ejpam-1518	318	6	�	�	PROPN
ejpam-1518	318	7	�	�	PROPN
ejpam-1518	318	8	�	�	PROPN
ejpam-1518	318	9	.	.	PUNCT
ejpam-1518	319	1	by	by	ADP
ejpam-1518	319	2	using	use	VERB
ejpam-1518	319	3	this	this	DET
ejpam-1518	319	4	inequality	inequality	NOUN
ejpam-1518	319	5	,	,	PUNCT
ejpam-1518	319	6	we	we	PRON
ejpam-1518	319	7	obtain	obtain	VERB
ejpam-1518	319	8	lim	lim	PROPN
ejpam-1518	319	9	n→∞	n→∞	NUM
ejpam-1518	319	10	1	1	NUM
ejpam-1518	319	11	n	n	DET
ejpam-1518	319	12	�	�	PROPN
ejpam-1518	319	13	�	�	PROPN
ejpam-1518	319	14	�	�	PROPN
ejpam-1518	319	15	k	k	NOUN
ejpam-1518	319	16	:	:	PUNCT
ejpam-1518	320	1	k	k	PROPN
ejpam-1518	320	2	≤	≤	PROPN
ejpam-1518	320	3	n	n	CCONJ
ejpam-1518	320	4	,	,	PUNCT
ejpam-1518	320	5	d2(xk	d2(xk	PROPN
ejpam-1518	320	6	,	,	PUNCT
ejpam-1518	320	7	x∗)≥	x∗)≥	PUNCT
ejpam-1518	320	8	m1	m1	PROPN
ejpam-1518	320	9	m	m	PROPN
ejpam-1518	320	10	�	�	PROPN
ejpam-1518	320	11	�	�	NOUN
ejpam-1518	320	12	=	=	SYM
ejpam-1518	320	13	0	0	PROPN
ejpam-1518	320	14	.	.	PUNCT
ejpam-1518	321	1	this	this	PRON
ejpam-1518	321	2	shows	show	VERB
ejpam-1518	321	3	that	that	SCONJ
ejpam-1518	321	4	x̃	x̃	PROPN
ejpam-1518	321	5	=	=	SYM
ejpam-1518	321	6	(	(	PUNCT
ejpam-1518	321	7	xn	xn	X
ejpam-1518	321	8	)	)	PUNCT
ejpam-1518	321	9	∈	∈	PROPN
ejpam-1518	321	10	ex	ex	NOUN
ejpam-1518	321	11	is	be	AUX
ejpam-1518	321	12	d2statistical	d2statistical	ADJ
ejpam-1518	321	13	bounded	bounded	ADJ
ejpam-1518	321	14	sequence	sequence	NOUN
ejpam-1518	321	15	,	,	PUNCT
ejpam-1518	321	16	i.e.	i.e.	X
ejpam-1518	321	17	x̃	x̃	PROPN
ejpam-1518	321	18	∈	∈	PROPN
ejpam-1518	321	19	b	b	PROPN
ejpam-1518	321	20	d2	d2	PROPN
ejpam-1518	321	21	st	st	PROPN
ejpam-1518	321	22	(	(	PUNCT
ejpam-1518	321	23	ex	ex	NOUN
ejpam-1518	321	24	)	)	PUNCT
ejpam-1518	321	25	.	.	PUNCT
ejpam-1518	322	1	to	to	PART
ejpam-1518	322	2	obtain	obtain	VERB
ejpam-1518	322	3	inverse	inverse	NOUN
ejpam-1518	322	4	,	,	PUNCT
ejpam-1518	322	5	it	it	PRON
ejpam-1518	322	6	is	be	AUX
ejpam-1518	322	7	enough	enough	ADJ
ejpam-1518	322	8	to	to	PART
ejpam-1518	322	9	consider	consider	VERB
ejpam-1518	322	10	(	(	PUNCT
ejpam-1518	322	11	13	13	NUM
ejpam-1518	322	12	)	)	PUNCT
ejpam-1518	322	13	as	as	SCONJ
ejpam-1518	322	14	follows	follow	VERB
ejpam-1518	322	15	:	:	PUNCT
ejpam-1518	322	16	1	1	NUM
ejpam-1518	322	17	m2	m2	PROPN
ejpam-1518	322	18	d2(x	d2(x	PROPN
ejpam-1518	322	19	,	,	PUNCT
ejpam-1518	322	20	y)≤	y)≤	PROPN
ejpam-1518	322	21	d1(x	d1(x	PROPN
ejpam-1518	322	22	,	,	PUNCT
ejpam-1518	322	23	y)≤	y)≤	PROPN
ejpam-1518	322	24	1	1	NUM
ejpam-1518	322	25	m1	m1	PROPN
ejpam-1518	322	26	d2(x	d2(x	PROPN
ejpam-1518	322	27	,	,	PUNCT
ejpam-1518	322	28	y	y	PROPN
ejpam-1518	322	29	)	)	PUNCT
ejpam-1518	322	30	for	for	ADP
ejpam-1518	322	31	every	every	DET
ejpam-1518	322	32	x	x	X
ejpam-1518	322	33	,	,	PUNCT
ejpam-1518	322	34	y	y	PROPN
ejpam-1518	322	35	∈	∈	PROPN
ejpam-1518	322	36	x	x	X
ejpam-1518	322	37	.	.	PUNCT
ejpam-1518	323	1	(	(	PUNCT
ejpam-1518	323	2	ii	ii	X
ejpam-1518	323	3	)	)	PUNCT
ejpam-1518	323	4	the	the	DET
ejpam-1518	323	5	proof	proof	NOUN
ejpam-1518	323	6	is	be	AUX
ejpam-1518	323	7	clear	clear	ADJ
ejpam-1518	323	8	from	from	ADP
ejpam-1518	323	9	theorem	theorem	ADJ
ejpam-1518	323	10	2.3	2.3	NUM
ejpam-1518	323	11	in	in	ADP
ejpam-1518	323	12	[	[	X
ejpam-1518	323	13	12	12	NUM
ejpam-1518	323	14	]	]	PUNCT
ejpam-1518	323	15	.	.	PUNCT
ejpam-1518	324	1	references	reference	NOUN
ejpam-1518	324	2	[	[	X
ejpam-1518	324	3	1	1	NUM
ejpam-1518	324	4	]	]	X
ejpam-1518	324	5	f	f	PROPN
ejpam-1518	324	6	abdullayev	abdullayev	PROPN
ejpam-1518	324	7	,	,	PUNCT
ejpam-1518	324	8	o	o	PROPN
ejpam-1518	324	9	dovgoshey	dovgoshey	PROPN
ejpam-1518	324	10	and	and	CCONJ
ejpam-1518	324	11	m	m	PROPN
ejpam-1518	324	12	küçükaslan	küçükaslan	NOUN
ejpam-1518	324	13	.	.	PUNCT
ejpam-1518	325	1	metric	metric	ADJ
ejpam-1518	325	2	spaces	space	NOUN
ejpam-1518	325	3	with	with	ADP
ejpam-1518	325	4	unique	unique	ADJ
ejpam-1518	325	5	pretangent	pretangent	NOUN
ejpam-1518	325	6	spaces	space	NOUN
ejpam-1518	325	7	.	.	PUNCT
ejpam-1518	326	1	conditions	condition	NOUN
ejpam-1518	326	2	of	of	ADP
ejpam-1518	326	3	the	the	DET
ejpam-1518	326	4	uniqueness	uniqueness	NOUN
ejpam-1518	326	5	,	,	PUNCT
ejpam-1518	326	6	ann	ann	PROPN
ejpam-1518	326	7	.	.	PUNCT
ejpam-1518	326	8	acad	acad	PROPN
ejpam-1518	326	9	.	.	PUNCT
ejpam-1518	327	1	sci	sci	PROPN
ejpam-1518	327	2	.	.	PUNCT
ejpam-1518	327	3	fenn	fenn	PROPN
ejpam-1518	327	4	.	.	PUNCT
ejpam-1518	327	5	math	math	PROPN
ejpam-1518	327	6	.	.	PUNCT
ejpam-1518	327	7	,	,	PUNCT
ejpam-1518	328	1	36	36	NUM
ejpam-1518	328	2	:	:	PUNCT
ejpam-1518	328	3	353	353	NUM
ejpam-1518	328	4	-	-	SYM
ejpam-1518	328	5	392	392	NUM
ejpam-1518	328	6	,	,	PUNCT
ejpam-1518	328	7	2011	2011	NUM
ejpam-1518	328	8	.	.	PUNCT
ejpam-1518	329	1	[	[	X
ejpam-1518	329	2	2	2	NUM
ejpam-1518	329	3	]	]	X
ejpam-1518	329	4	j	j	PROPN
ejpam-1518	329	5	cervanansky	cervanansky	NOUN
ejpam-1518	329	6	.	.	PUNCT
ejpam-1518	330	1	statistical	statistical	ADJ
ejpam-1518	330	2	covergence	covergence	NOUN
ejpam-1518	330	3	and	and	CCONJ
ejpam-1518	330	4	statistical	statistical	ADJ
ejpam-1518	330	5	continuity	continuity	NOUN
ejpam-1518	330	6	.	.	PUNCT
ejpam-1518	331	1	zbornik	zbornik	PROPN
ejpam-1518	331	2	vedeckych	vedeckych	PROPN
ejpam-1518	331	3	prac	prac	PROPN
ejpam-1518	331	4	mtf	mtf	PROPN
ejpam-1518	331	5	stu	stu	PROPN
ejpam-1518	331	6	.	.	PROPN
ejpam-1518	332	1	6	6	NUM
ejpam-1518	332	2	:	:	PUNCT
ejpam-1518	332	3	924–931	924–931	NUM
ejpam-1518	332	4	,	,	PUNCT
ejpam-1518	332	5	1943	1943	NUM
ejpam-1518	332	6	.	.	PUNCT
ejpam-1518	333	1	[	[	X
ejpam-1518	333	2	3	3	X
ejpam-1518	333	3	]	]	X
ejpam-1518	333	4	j	j	PROPN
ejpam-1518	333	5	connor	connor	PROPN
ejpam-1518	333	6	.	.	PUNCT
ejpam-1518	334	1	the	the	DET
ejpam-1518	334	2	statistical	statistical	ADJ
ejpam-1518	334	3	and	and	CCONJ
ejpam-1518	334	4	strong	strong	ADJ
ejpam-1518	334	5	p	p	NOUN
ejpam-1518	334	6	-	-	PUNCT
ejpam-1518	334	7	cesaro	cesaro	ADJ
ejpam-1518	334	8	convergence	convergence	NOUN
ejpam-1518	334	9	of	of	ADP
ejpam-1518	334	10	sequences	sequence	NOUN
ejpam-1518	334	11	.	.	PUNCT
ejpam-1518	335	1	analysis	analysis	NOUN
ejpam-1518	335	2	,	,	PUNCT
ejpam-1518	335	3	8:207	8:207	NUM
ejpam-1518	335	4	–	–	PUNCT
ejpam-1518	335	5	212	212	NUM
ejpam-1518	335	6	,	,	PUNCT
ejpam-1518	335	7	1998	1998	NUM
ejpam-1518	335	8	.	.	PUNCT
ejpam-1518	336	1	[	[	X
ejpam-1518	336	2	4	4	NUM
ejpam-1518	336	3	]	]	X
ejpam-1518	336	4	o	o	X
ejpam-1518	336	5	dovgoshey	dovgoshey	PROPN
ejpam-1518	336	6	.	.	PUNCT
ejpam-1518	337	1	tangent	tangent	PROPN
ejpam-1518	337	2	spaces	space	VERB
ejpam-1518	337	3	to	to	ADP
ejpam-1518	337	4	metric	metric	ADJ
ejpam-1518	337	5	spaces	space	NOUN
ejpam-1518	337	6	and	and	CCONJ
ejpam-1518	337	7	to	to	ADP
ejpam-1518	337	8	their	their	PRON
ejpam-1518	337	9	subspaces	subspace	NOUN
ejpam-1518	337	10	.	.	PUNCT
ejpam-1518	338	1	ukr	ukr	PROPN
ejpam-1518	338	2	.	.	PROPN
ejpam-1518	338	3	mat	mat	PROPN
ejpam-1518	338	4	.	.	PUNCT
ejpam-1518	338	5	visn	visn	PROPN
ejpam-1518	338	6	.	.	PUNCT
ejpam-1518	338	7	,	,	PUNCT
ejpam-1518	338	8	5:468–485	5:468–485	NUM
ejpam-1518	338	9	,	,	PUNCT
ejpam-1518	338	10	2008	2008	NUM
ejpam-1518	338	11	.	.	PUNCT
ejpam-1518	339	1	[	[	X
ejpam-1518	339	2	5	5	NUM
ejpam-1518	339	3	]	]	X
ejpam-1518	339	4	o	o	X
ejpam-1518	339	5	dovgoshey	dovgoshey	PROPN
ejpam-1518	339	6	,	,	PUNCT
ejpam-1518	339	7	f	f	PROPN
ejpam-1518	339	8	abdullayev	abdullayev	PROPN
ejpam-1518	339	9	and	and	CCONJ
ejpam-1518	339	10	m	m	PROPN
ejpam-1518	339	11	küçükaslan	küçükaslan	NOUN
ejpam-1518	339	12	.	.	PUNCT
ejpam-1518	340	1	compactness	compactness	NOUN
ejpam-1518	340	2	and	and	CCONJ
ejpam-1518	340	3	boundedness	boundedness	NOUN
ejpam-1518	340	4	of	of	ADP
ejpam-1518	340	5	tangent	tangent	NOUN
ejpam-1518	340	6	spaces	space	NOUN
ejpam-1518	340	7	to	to	ADP
ejpam-1518	340	8	metric	metric	ADJ
ejpam-1518	340	9	spaces	space	NOUN
ejpam-1518	340	10	.	.	PUNCT
ejpam-1518	341	1	beiträge	beiträge	ADJ
ejpam-1518	341	2	algebra	algebra	PROPN
ejpam-1518	341	3	geom	geom	PROPN
ejpam-1518	341	4	.	.	PROPN
ejpam-1518	341	5	,	,	PUNCT
ejpam-1518	342	1	51:547–576	51:547–576	PROPN
ejpam-1518	342	2	,	,	PUNCT
ejpam-1518	342	3	2010	2010	NUM
ejpam-1518	342	4	.	.	PUNCT
ejpam-1518	343	1	[	[	X
ejpam-1518	343	2	6	6	NUM
ejpam-1518	343	3	]	]	PUNCT
ejpam-1518	343	4	o	o	X
ejpam-1518	343	5	dovgoshey	dovgoshey	NOUN
ejpam-1518	343	6	and	and	CCONJ
ejpam-1518	343	7	o	o	NOUN
ejpam-1518	343	8	martio	martio	NOUN
ejpam-1518	343	9	.	.	PUNCT
ejpam-1518	344	1	tangent	tangent	PROPN
ejpam-1518	344	2	spaces	space	VERB
ejpam-1518	344	3	to	to	ADP
ejpam-1518	344	4	metric	metric	ADJ
ejpam-1518	344	5	spaces	space	NOUN
ejpam-1518	344	6	.	.	PUNCT
ejpam-1518	345	1	reports	report	NOUN
ejpam-1518	345	2	in	in	ADP
ejpam-1518	345	3	math	math	NOUN
ejpam-1518	345	4	.	.	PUNCT
ejpam-1518	346	1	helsinki	helsinki	PROPN
ejpam-1518	346	2	univ	univ	PROPN
ejpam-1518	346	3	.	.	PROPN
ejpam-1518	346	4	,	,	PUNCT
ejpam-1518	346	5	480	480	NUM
ejpam-1518	346	6	:	:	PUNCT
ejpam-1518	346	7	2008	2008	NUM
ejpam-1518	346	8	.	.	PUNCT
ejpam-1518	347	1	[	[	X
ejpam-1518	347	2	7	7	X
ejpam-1518	347	3	]	]	X
ejpam-1518	347	4	h	h	NOUN
ejpam-1518	347	5	fast	fast	ADV
ejpam-1518	347	6	.	.	PUNCT
ejpam-1518	348	1	sur	sur	PROPN
ejpam-1518	348	2	la	la	PROPN
ejpam-1518	348	3	convergence	convergence	NOUN
ejpam-1518	348	4	statistique	statistique	NOUN
ejpam-1518	348	5	,	,	PUNCT
ejpam-1518	348	6	colloquium	colloquium	NOUN
ejpam-1518	348	7	mathematicum	mathematicum	NOUN
ejpam-1518	348	8	,	,	PUNCT
ejpam-1518	348	9	2:241–244	2:241–244	NUM
ejpam-1518	348	10	,	,	PUNCT
ejpam-1518	348	11	1951	1951	NUM
ejpam-1518	348	12	.	.	PUNCT
ejpam-1518	349	1	[	[	X
ejpam-1518	349	2	8	8	NUM
ejpam-1518	349	3	]	]	X
ejpam-1518	349	4	j	j	PROPN
ejpam-1518	349	5	fridy	fridy	PROPN
ejpam-1518	349	6	.	.	PUNCT
ejpam-1518	350	1	on	on	ADP
ejpam-1518	350	2	statistical	statistical	ADJ
ejpam-1518	350	3	convergence	convergence	NOUN
ejpam-1518	350	4	.	.	PUNCT
ejpam-1518	351	1	analysis	analysis	NOUN
ejpam-1518	351	2	,	,	PUNCT
ejpam-1518	351	3	5:301–313	5:301–313	NUM
ejpam-1518	351	4	,	,	PUNCT
ejpam-1518	351	5	1995	1995	NUM
ejpam-1518	351	6	.	.	PUNCT
ejpam-1518	352	1	[	[	X
ejpam-1518	352	2	9	9	NUM
ejpam-1518	352	3	]	]	X
ejpam-1518	352	4	j	j	PROPN
ejpam-1518	352	5	fridy	fridy	PROPN
ejpam-1518	352	6	and	and	CCONJ
ejpam-1518	352	7	m	m	PROPN
ejpam-1518	352	8	khan	khan	PROPN
ejpam-1518	352	9	.	.	PUNCT
ejpam-1518	353	1	tauberian	tauberian	ADJ
ejpam-1518	353	2	theorems	theorem	NOUN
ejpam-1518	353	3	via	via	ADP
ejpam-1518	353	4	statistical	statistical	ADJ
ejpam-1518	353	5	convergence	convergence	NOUN
ejpam-1518	353	6	.	.	PUNCT
ejpam-1518	354	1	j.	j.	PROPN
ejpam-1518	354	2	math	math	PROPN
ejpam-1518	354	3	.	.	PUNCT
ejpam-1518	355	1	anal	anal	PROPN
ejpam-1518	355	2	.	.	PUNCT
ejpam-1518	356	1	appl	appl	PROPN
ejpam-1518	356	2	.	.	PROPN
ejpam-1518	356	3	,	,	PUNCT
ejpam-1518	357	1	228:73–95	228:73–95	NUM
ejpam-1518	357	2	,	,	PUNCT
ejpam-1518	357	3	1998	1998	NUM
ejpam-1518	357	4	.	.	PUNCT
ejpam-1518	358	1	[	[	X
ejpam-1518	358	2	10	10	NUM
ejpam-1518	358	3	]	]	X
ejpam-1518	358	4	j	j	PROPN
ejpam-1518	358	5	fridy	fridy	PROPN
ejpam-1518	358	6	and	and	CCONJ
ejpam-1518	358	7	h	h	PROPN
ejpam-1518	358	8	miller	miller	PROPN
ejpam-1518	358	9	.	.	PUNCT
ejpam-1518	359	1	a	a	DET
ejpam-1518	359	2	matrix	matrix	NOUN
ejpam-1518	359	3	characterization	characterization	NOUN
ejpam-1518	359	4	of	of	ADP
ejpam-1518	359	5	statistical	statistical	ADJ
ejpam-1518	359	6	convergence	convergence	NOUN
ejpam-1518	359	7	.	.	PUNCT
ejpam-1518	360	1	analysis	analysis	NOUN
ejpam-1518	360	2	,	,	PUNCT
ejpam-1518	360	3	11:59–66	11:59–66	NUM
ejpam-1518	360	4	,	,	PUNCT
ejpam-1518	360	5	1991	1991	NUM
ejpam-1518	360	6	.	.	PUNCT
ejpam-1518	361	1	references	reference	NOUN
ejpam-1518	361	2	186	186	NUM
ejpam-1518	361	3	[	[	X
ejpam-1518	361	4	11	11	NUM
ejpam-1518	361	5	]	]	X
ejpam-1518	361	6	j	j	PROPN
ejpam-1518	361	7	heinonen	heinonen	PROPN
ejpam-1518	361	8	.	.	PUNCT
ejpam-1518	362	1	lectures	lecture	NOUN
ejpam-1518	362	2	on	on	ADP
ejpam-1518	362	3	analysis	analysis	NOUN
ejpam-1518	362	4	on	on	ADP
ejpam-1518	362	5	metric	metric	ADJ
ejpam-1518	362	6	spaces	space	NOUN
ejpam-1518	362	7	.	.	PUNCT
ejpam-1518	363	1	springer	springer	NOUN
ejpam-1518	363	2	,	,	PUNCT
ejpam-1518	363	3	2001	2001	NUM
ejpam-1518	363	4	.	.	PUNCT
ejpam-1518	364	1	[	[	X
ejpam-1518	364	2	12	12	NUM
ejpam-1518	364	3	]	]	X
ejpam-1518	364	4	m	m	PROPN
ejpam-1518	364	5	küçükaslan	küçükaslan	NOUN
ejpam-1518	364	6	,	,	PUNCT
ejpam-1518	364	7	u	u	NOUN
ejpam-1518	364	8	değer	değer	NOUN
ejpam-1518	364	9	and	and	CCONJ
ejpam-1518	364	10	o	o	X
ejpam-1518	364	11	dovgoshey	dovgoshey	NOUN
ejpam-1518	364	12	.	.	PUNCT
ejpam-1518	365	1	on	on	ADP
ejpam-1518	365	2	statistical	statistical	ADJ
ejpam-1518	365	3	convergence	convergence	NOUN
ejpam-1518	365	4	of	of	ADP
ejpam-1518	365	5	metric	metric	ADJ
ejpam-1518	365	6	valued	value	VERB
ejpam-1518	365	7	sequences	sequence	NOUN
ejpam-1518	365	8	.	.	PUNCT
ejpam-1518	366	1	arxiv:1203.2584v1	arxiv:1203.2584v1	NOUN
ejpam-1518	367	1	[	[	X
ejpam-1518	367	2	math.fa	math.fa	PROPN
ejpam-1518	367	3	]	]	X
ejpam-1518	367	4	,	,	PUNCT
ejpam-1518	367	5	2011	2011	NUM
ejpam-1518	367	6	.	.	PUNCT
ejpam-1518	368	1	[	[	X
ejpam-1518	368	2	13	13	NUM
ejpam-1518	368	3	]	]	SYM
ejpam-1518	368	4	m	m	VERB
ejpam-1518	368	5	mačaj	mačaj	NOUN
ejpam-1518	368	6	and	and	CCONJ
ejpam-1518	368	7	t	t	NOUN
ejpam-1518	368	8	šalát	šalát	NOUN
ejpam-1518	368	9	.	.	PUNCT
ejpam-1518	369	1	statistical	statistical	ADJ
ejpam-1518	369	2	convergence	convergence	NOUN
ejpam-1518	369	3	of	of	ADP
ejpam-1518	369	4	subsequence	subsequence	NOUN
ejpam-1518	369	5	of	of	ADP
ejpam-1518	369	6	a	a	DET
ejpam-1518	369	7	given	give	VERB
ejpam-1518	369	8	sequence	sequence	NOUN
ejpam-1518	369	9	.	.	PUNCT
ejpam-1518	370	1	mathematica	mathematica	PROPN
ejpam-1518	370	2	bohemica	bohemica	PROPN
ejpam-1518	370	3	,	,	PUNCT
ejpam-1518	370	4	126:191–208	126:191–208	NUM
ejpam-1518	370	5	,	,	PUNCT
ejpam-1518	370	6	2001	2001	NUM
ejpam-1518	370	7	.	.	PUNCT
ejpam-1518	371	1	[	[	X
ejpam-1518	371	2	14	14	NUM
ejpam-1518	371	3	]	]	X
ejpam-1518	371	4	h	h	PROPN
ejpam-1518	371	5	miller	miller	PROPN
ejpam-1518	371	6	.	.	PUNCT
ejpam-1518	372	1	a	a	DET
ejpam-1518	372	2	measure	measure	NOUN
ejpam-1518	372	3	theoretical	theoretical	ADJ
ejpam-1518	372	4	subsequence	subsequence	NOUN
ejpam-1518	372	5	characterization	characterization	NOUN
ejpam-1518	372	6	of	of	ADP
ejpam-1518	372	7	statistical	statistical	ADJ
ejpam-1518	372	8	convergence	convergence	NOUN
ejpam-1518	372	9	.	.	PUNCT
ejpam-1518	373	1	transactions	transaction	NOUN
ejpam-1518	373	2	of	of	ADP
ejpam-1518	373	3	the	the	DET
ejpam-1518	373	4	ams	am	NOUN
ejpam-1518	373	5	,	,	PUNCT
ejpam-1518	373	6	347:1811–1819	347:1811–1819	NUM
ejpam-1518	373	7	,	,	PUNCT
ejpam-1518	373	8	1995	1995	NUM
ejpam-1518	373	9	.	.	PUNCT
ejpam-1518	374	1	[	[	X
ejpam-1518	374	2	15	15	NUM
ejpam-1518	374	3	]	]	X
ejpam-1518	374	4	t	t	NOUN
ejpam-1518	374	5	šalát	šalát	NOUN
ejpam-1518	374	6	.	.	PUNCT
ejpam-1518	375	1	on	on	ADP
ejpam-1518	375	2	statistically	statistically	ADV
ejpam-1518	375	3	convergent	convergent	ADJ
ejpam-1518	375	4	sequences	sequence	NOUN
ejpam-1518	375	5	of	of	ADP
ejpam-1518	375	6	real	real	ADJ
ejpam-1518	375	7	numbers	number	NOUN
ejpam-1518	375	8	.	.	PUNCT
ejpam-1518	376	1	math	math	NOUN
ejpam-1518	376	2	.	.	PUNCT
ejpam-1518	377	1	slovaca	slovaca	PROPN
ejpam-1518	377	2	,	,	PUNCT
ejpam-1518	377	3	30:139	30:139	NUM
ejpam-1518	377	4	–	–	PUNCT
ejpam-1518	377	5	150	150	NUM
ejpam-1518	377	6	,	,	PUNCT
ejpam-1518	377	7	1980	1980	NUM
ejpam-1518	377	8	.	.	PUNCT
ejpam-1518	378	1	[	[	X
ejpam-1518	378	2	16	16	NUM
ejpam-1518	378	3	]	]	PUNCT
ejpam-1518	378	4	a	a	DET
ejpam-1518	378	5	zygmund	zygmund	NOUN
ejpam-1518	378	6	.	.	PUNCT
ejpam-1518	379	1	trigonometric	trigonometric	PROPN
ejpam-1518	379	2	series	series	PROPN
ejpam-1518	379	3	.	.	PUNCT
ejpam-1518	380	1	cambridge	cambridge	PROPN
ejpam-1518	380	2	university	university	PROPN
ejpam-1518	380	3	press	press	PROPN
ejpam-1518	380	4	,	,	PUNCT
ejpam-1518	380	5	cambridge	cambridge	PROPN
ejpam-1518	380	6	,	,	PUNCT
ejpam-1518	380	7	uk	uk	PROPN
ejpam-1518	380	8	,	,	PUNCT
ejpam-1518	380	9	1979	1979	NUM
ejpam-1518	380	10	.	.	PUNCT