id	sid	tid	token	lemma	pos
ejpam-5608	1	1	european	european	PROPN
ejpam-5608	1	2	journal	journal	PROPN
ejpam-5608	1	3	of	of	ADP
ejpam-5608	1	4	pure	pure	ADJ
ejpam-5608	1	5	and	and	CCONJ
ejpam-5608	1	6	applied	applied	ADJ
ejpam-5608	1	7	mathematics	mathematic	NOUN
ejpam-5608	1	8	2025	2025	NUM
ejpam-5608	1	9	,	,	PUNCT
ejpam-5608	1	10	vol	vol	NOUN
ejpam-5608	1	11	.	.	PROPN
ejpam-5608	1	12	18	18	NUM
ejpam-5608	1	13	,	,	PUNCT
ejpam-5608	1	14	issue	issue	NOUN
ejpam-5608	1	15	1	1	NUM
ejpam-5608	1	16	,	,	PUNCT
ejpam-5608	1	17	article	article	NOUN
ejpam-5608	1	18	number	number	NOUN
ejpam-5608	1	19	5608	5608	NUM
ejpam-5608	1	20	issn	issn	VERB
ejpam-5608	1	21	1307	1307	NUM
ejpam-5608	1	22	-	-	SYM
ejpam-5608	1	23	5543	5543	NUM
ejpam-5608	1	24	–	–	PUNCT
ejpam-5608	1	25	ejpam.com	ejpam.com	X
ejpam-5608	1	26	published	publish	VERB
ejpam-5608	1	27	by	by	ADP
ejpam-5608	1	28	new	new	PROPN
ejpam-5608	1	29	york	york	PROPN
ejpam-5608	1	30	business	business	PROPN
ejpam-5608	1	31	global	global	ADJ
ejpam-5608	1	32	necessary	necessary	ADJ
ejpam-5608	1	33	and	and	CCONJ
ejpam-5608	1	34	sufficient	sufficient	ADJ
ejpam-5608	1	35	conditions	condition	NOUN
ejpam-5608	1	36	for	for	ADP
ejpam-5608	1	37	the	the	DET
ejpam-5608	1	38	equivalence	equivalence	NOUN
ejpam-5608	1	39	of	of	ADP
ejpam-5608	1	40	statistical	statistical	ADJ
ejpam-5608	1	41	,	,	PUNCT
ejpam-5608	1	42	ideal	ideal	ADJ
ejpam-5608	1	43	,	,	PUNCT
ejpam-5608	1	44	and	and	CCONJ
ejpam-5608	1	45	standard	standard	ADJ
ejpam-5608	1	46	convergence	convergence	NOUN
ejpam-5608	1	47	in	in	ADP
ejpam-5608	1	48	g	g	NOUN
ejpam-5608	1	49	-	-	PUNCT
ejpam-5608	1	50	metric	metric	ADJ
ejpam-5608	1	51	spaces	space	NOUN
ejpam-5608	1	52	manuharawati1,∗	manuharawati1,∗	NOUN
ejpam-5608	1	53	,	,	PUNCT
ejpam-5608	1	54	muhammad	muhammad	PROPN
ejpam-5608	1	55	jakfar1	jakfar1	PROPN
ejpam-5608	1	56	,	,	PUNCT
ejpam-5608	1	57	ahmad	ahmad	PROPN
ejpam-5608	1	58	taufik	taufik	PROPN
ejpam-5608	1	59	hamzah1	hamzah1	NOUN
ejpam-5608	1	60	1	1	NUM
ejpam-5608	1	61	department	department	NOUN
ejpam-5608	1	62	of	of	ADP
ejpam-5608	1	63	mathematics	mathematic	NOUN
ejpam-5608	1	64	,	,	PUNCT
ejpam-5608	1	65	faculty	faculty	NOUN
ejpam-5608	1	66	of	of	ADP
ejpam-5608	1	67	mathematics	mathematic	NOUN
ejpam-5608	1	68	and	and	CCONJ
ejpam-5608	1	69	natural	natural	ADJ
ejpam-5608	1	70	sciences	science	NOUN
ejpam-5608	1	71	,	,	PUNCT
ejpam-5608	1	72	universitas	universitas	PROPN
ejpam-5608	1	73	negeri	negeri	PROPN
ejpam-5608	1	74	surabaya	surabaya	PROPN
ejpam-5608	1	75	,	,	PUNCT
ejpam-5608	1	76	surabaya	surabaya	PROPN
ejpam-5608	1	77	,	,	PUNCT
ejpam-5608	1	78	indonesia	indonesia	PROPN
ejpam-5608	1	79	abstract	abstract	NOUN
ejpam-5608	1	80	.	.	PUNCT
ejpam-5608	2	1	this	this	DET
ejpam-5608	2	2	paper	paper	NOUN
ejpam-5608	2	3	investigates	investigate	VERB
ejpam-5608	2	4	the	the	DET
ejpam-5608	2	5	conditions	condition	NOUN
ejpam-5608	2	6	for	for	ADP
ejpam-5608	2	7	the	the	DET
ejpam-5608	2	8	equivalence	equivalence	NOUN
ejpam-5608	2	9	between	between	ADP
ejpam-5608	2	10	statistical	statistical	ADJ
ejpam-5608	2	11	convergence	convergence	NOUN
ejpam-5608	2	12	,	,	PUNCT
ejpam-5608	2	13	ideal	ideal	ADJ
ejpam-5608	2	14	convergence	convergence	NOUN
ejpam-5608	2	15	,	,	PUNCT
ejpam-5608	2	16	and	and	CCONJ
ejpam-5608	2	17	standard	standard	ADJ
ejpam-5608	2	18	convergence	convergence	NOUN
ejpam-5608	2	19	in	in	ADP
ejpam-5608	2	20	g	g	NOUN
ejpam-5608	2	21	-	-	PUNCT
ejpam-5608	2	22	metric	metric	ADJ
ejpam-5608	2	23	spaces	space	NOUN
ejpam-5608	2	24	.	.	PUNCT
ejpam-5608	3	1	although	although	SCONJ
ejpam-5608	3	2	statistical	statistical	ADJ
ejpam-5608	3	3	and	and	CCONJ
ejpam-5608	3	4	ideal	ideal	ADJ
ejpam-5608	3	5	convergence	convergence	NOUN
ejpam-5608	3	6	studies	study	NOUN
ejpam-5608	3	7	have	have	AUX
ejpam-5608	3	8	been	be	AUX
ejpam-5608	3	9	extensively	extensively	ADV
ejpam-5608	3	10	developed	develop	VERB
ejpam-5608	3	11	in	in	ADP
ejpam-5608	3	12	various	various	ADJ
ejpam-5608	3	13	settings	setting	NOUN
ejpam-5608	3	14	,	,	PUNCT
ejpam-5608	3	15	no	no	DET
ejpam-5608	3	16	prior	prior	ADJ
ejpam-5608	3	17	research	research	NOUN
ejpam-5608	3	18	has	have	AUX
ejpam-5608	3	19	explicitly	explicitly	ADV
ejpam-5608	3	20	explored	explore	VERB
ejpam-5608	3	21	the	the	DET
ejpam-5608	3	22	relationship	relationship	NOUN
ejpam-5608	3	23	between	between	ADP
ejpam-5608	3	24	statistical	statistical	ADJ
ejpam-5608	3	25	convergence	convergence	NOUN
ejpam-5608	3	26	and	and	CCONJ
ejpam-5608	3	27	standard	standard	ADJ
ejpam-5608	3	28	convergence	convergence	NOUN
ejpam-5608	3	29	within	within	ADP
ejpam-5608	3	30	g	g	NOUN
ejpam-5608	3	31	-	-	PUNCT
ejpam-5608	3	32	metric	metric	ADJ
ejpam-5608	3	33	spaces	space	NOUN
ejpam-5608	3	34	.	.	PUNCT
ejpam-5608	4	1	by	by	ADP
ejpam-5608	4	2	addressing	address	VERB
ejpam-5608	4	3	this	this	DET
ejpam-5608	4	4	gap	gap	NOUN
ejpam-5608	4	5	,	,	PUNCT
ejpam-5608	4	6	we	we	PRON
ejpam-5608	4	7	establish	establish	VERB
ejpam-5608	4	8	necessary	necessary	ADJ
ejpam-5608	4	9	and	and	CCONJ
ejpam-5608	4	10	sufficient	sufficient	ADJ
ejpam-5608	4	11	conditions	condition	NOUN
ejpam-5608	4	12	for	for	ADP
ejpam-5608	4	13	the	the	DET
ejpam-5608	4	14	equivalence	equivalence	NOUN
ejpam-5608	4	15	of	of	ADP
ejpam-5608	4	16	these	these	DET
ejpam-5608	4	17	types	type	NOUN
ejpam-5608	4	18	of	of	ADP
ejpam-5608	4	19	convergence	convergence	NOUN
ejpam-5608	4	20	in	in	ADP
ejpam-5608	4	21	g	g	NOUN
ejpam-5608	4	22	-	-	PUNCT
ejpam-5608	4	23	metric	metric	ADJ
ejpam-5608	4	24	spaces	space	NOUN
ejpam-5608	4	25	.	.	PUNCT
ejpam-5608	5	1	our	our	PRON
ejpam-5608	5	2	results	result	NOUN
ejpam-5608	5	3	contribute	contribute	VERB
ejpam-5608	5	4	to	to	ADP
ejpam-5608	5	5	a	a	DET
ejpam-5608	5	6	deeper	deep	ADJ
ejpam-5608	5	7	understanding	understanding	NOUN
ejpam-5608	5	8	of	of	ADP
ejpam-5608	5	9	the	the	DET
ejpam-5608	5	10	interplay	interplay	NOUN
ejpam-5608	5	11	between	between	ADP
ejpam-5608	5	12	these	these	DET
ejpam-5608	5	13	convergence	convergence	NOUN
ejpam-5608	5	14	notions	notion	NOUN
ejpam-5608	5	15	and	and	CCONJ
ejpam-5608	5	16	extend	extend	VERB
ejpam-5608	5	17	the	the	DET
ejpam-5608	5	18	theory	theory	NOUN
ejpam-5608	5	19	of	of	ADP
ejpam-5608	5	20	convergence	convergence	NOUN
ejpam-5608	5	21	in	in	ADP
ejpam-5608	5	22	generalized	generalized	ADJ
ejpam-5608	5	23	metric	metric	ADJ
ejpam-5608	5	24	spaces	space	NOUN
ejpam-5608	5	25	.	.	PUNCT
ejpam-5608	6	1	2020	2020	NUM
ejpam-5608	6	2	mathematics	mathematic	NOUN
ejpam-5608	6	3	subject	subject	NOUN
ejpam-5608	6	4	classifications	classification	NOUN
ejpam-5608	6	5	:	:	PUNCT
ejpam-5608	6	6	40a35	40a35	NUM
ejpam-5608	6	7	key	key	ADJ
ejpam-5608	6	8	words	word	NOUN
ejpam-5608	6	9	and	and	CCONJ
ejpam-5608	6	10	phrases	phrase	NOUN
ejpam-5608	6	11	:	:	PUNCT
ejpam-5608	6	12	statistical	statistical	ADJ
ejpam-5608	6	13	convergence	convergence	NOUN
ejpam-5608	6	14	,	,	PUNCT
ejpam-5608	6	15	ideal	ideal	ADJ
ejpam-5608	6	16	convergence	convergence	NOUN
ejpam-5608	6	17	,	,	PUNCT
ejpam-5608	6	18	standard	standard	ADJ
ejpam-5608	6	19	convergence	convergence	NOUN
ejpam-5608	6	20	,	,	PUNCT
ejpam-5608	6	21	g	g	NOUN
ejpam-5608	6	22	-	-	PUNCT
ejpam-5608	6	23	metric	metric	ADJ
ejpam-5608	6	24	spaces	space	NOUN
ejpam-5608	6	25	,	,	PUNCT
ejpam-5608	6	26	necessary	necessary	ADJ
ejpam-5608	6	27	and	and	CCONJ
ejpam-5608	6	28	sufficient	sufficient	ADJ
ejpam-5608	6	29	conditions	condition	NOUN
ejpam-5608	6	30	,	,	PUNCT
ejpam-5608	6	31	equivalence	equivalence	NOUN
ejpam-5608	6	32	theorems	theorem	NOUN
ejpam-5608	6	33	.	.	PUNCT
ejpam-5608	7	1	1	1	X
ejpam-5608	7	2	.	.	X
ejpam-5608	7	3	introduction	introduction	NOUN
ejpam-5608	7	4	the	the	DET
ejpam-5608	7	5	concept	concept	NOUN
ejpam-5608	7	6	of	of	ADP
ejpam-5608	7	7	convergence	convergence	NOUN
ejpam-5608	7	8	plays	play	VERB
ejpam-5608	7	9	a	a	DET
ejpam-5608	7	10	central	central	ADJ
ejpam-5608	7	11	role	role	NOUN
ejpam-5608	7	12	in	in	ADP
ejpam-5608	7	13	analysis	analysis	NOUN
ejpam-5608	7	14	and	and	CCONJ
ejpam-5608	7	15	its	its	PRON
ejpam-5608	7	16	applications	application	NOUN
ejpam-5608	7	17	,	,	PUNCT
ejpam-5608	7	18	with	with	ADP
ejpam-5608	7	19	various	various	ADJ
ejpam-5608	7	20	types	type	NOUN
ejpam-5608	7	21	of	of	ADP
ejpam-5608	7	22	convergence	convergence	NOUN
ejpam-5608	7	23	being	be	AUX
ejpam-5608	7	24	developed	develop	VERB
ejpam-5608	7	25	to	to	PART
ejpam-5608	7	26	generalize	generalize	VERB
ejpam-5608	7	27	the	the	DET
ejpam-5608	7	28	classical	classical	ADJ
ejpam-5608	7	29	notion	notion	NOUN
ejpam-5608	7	30	of	of	ADP
ejpam-5608	7	31	pointwise	pointwise	ADJ
ejpam-5608	7	32	convergence	convergence	NOUN
ejpam-5608	7	33	.	.	PUNCT
ejpam-5608	8	1	among	among	ADP
ejpam-5608	8	2	these	these	DET
ejpam-5608	8	3	generalizations	generalization	NOUN
ejpam-5608	8	4	,	,	PUNCT
ejpam-5608	8	5	statistical	statistical	ADJ
ejpam-5608	8	6	convergence	convergence	NOUN
ejpam-5608	8	7	and	and	CCONJ
ejpam-5608	8	8	ideal	ideal	ADJ
ejpam-5608	8	9	convergence	convergence	NOUN
ejpam-5608	8	10	have	have	AUX
ejpam-5608	8	11	attracted	attract	VERB
ejpam-5608	8	12	considerable	considerable	ADJ
ejpam-5608	8	13	attention	attention	NOUN
ejpam-5608	8	14	.	.	PUNCT
ejpam-5608	9	1	the	the	DET
ejpam-5608	9	2	notion	notion	NOUN
ejpam-5608	9	3	of	of	ADP
ejpam-5608	9	4	statistical	statistical	ADJ
ejpam-5608	9	5	convergence	convergence	NOUN
ejpam-5608	9	6	,	,	PUNCT
ejpam-5608	9	7	introduced	introduce	VERB
ejpam-5608	9	8	by	by	ADP
ejpam-5608	9	9	fast	fast	ADJ
ejpam-5608	9	10	[	[	X
ejpam-5608	9	11	3	3	NUM
ejpam-5608	9	12	]	]	PUNCT
ejpam-5608	9	13	and	and	CCONJ
ejpam-5608	9	14	further	far	ADV
ejpam-5608	9	15	studied	study	VERB
ejpam-5608	9	16	by	by	ADP
ejpam-5608	9	17	šalát	šalát	NOUN
ejpam-5608	10	1	[	[	X
ejpam-5608	10	2	32	32	NUM
ejpam-5608	10	3	]	]	PUNCT
ejpam-5608	10	4	,	,	PUNCT
ejpam-5608	10	5	provides	provide	VERB
ejpam-5608	10	6	a	a	DET
ejpam-5608	10	7	probabilistic	probabilistic	ADJ
ejpam-5608	10	8	framework	framework	NOUN
ejpam-5608	10	9	that	that	PRON
ejpam-5608	10	10	generalizes	generalize	VERB
ejpam-5608	10	11	classical	classical	ADJ
ejpam-5608	10	12	convergence	convergence	NOUN
ejpam-5608	10	13	by	by	ADP
ejpam-5608	10	14	considering	consider	VERB
ejpam-5608	10	15	the	the	DET
ejpam-5608	10	16	density	density	NOUN
ejpam-5608	10	17	of	of	ADP
ejpam-5608	10	18	indices	index	NOUN
ejpam-5608	10	19	at	at	ADP
ejpam-5608	10	20	which	which	PRON
ejpam-5608	10	21	a	a	DET
ejpam-5608	10	22	sequence	sequence	NOUN
ejpam-5608	10	23	fails	fail	VERB
ejpam-5608	10	24	to	to	PART
ejpam-5608	10	25	converge	converge	VERB
ejpam-5608	10	26	to	to	ADP
ejpam-5608	10	27	a	a	DET
ejpam-5608	10	28	limit	limit	NOUN
ejpam-5608	10	29	.	.	PUNCT
ejpam-5608	11	1	this	this	DET
ejpam-5608	11	2	approach	approach	NOUN
ejpam-5608	11	3	has	have	AUX
ejpam-5608	11	4	proven	prove	VERB
ejpam-5608	11	5	useful	useful	ADJ
ejpam-5608	11	6	in	in	ADP
ejpam-5608	11	7	various	various	ADJ
ejpam-5608	11	8	applications	application	NOUN
ejpam-5608	11	9	,	,	PUNCT
ejpam-5608	11	10	from	from	ADP
ejpam-5608	11	11	number	number	NOUN
ejpam-5608	11	12	theory	theory	NOUN
ejpam-5608	11	13	to	to	ADP
ejpam-5608	11	14	functional	functional	ADJ
ejpam-5608	11	15	analysis	analysis	NOUN
ejpam-5608	11	16	[	[	X
ejpam-5608	11	17	3	3	NUM
ejpam-5608	11	18	,	,	PUNCT
ejpam-5608	11	19	32	32	NUM
ejpam-5608	11	20	]	]	PUNCT
ejpam-5608	11	21	.	.	PUNCT
ejpam-5608	12	1	ideal	ideal	ADJ
ejpam-5608	12	2	convergence	convergence	NOUN
ejpam-5608	12	3	,	,	PUNCT
ejpam-5608	12	4	introduced	introduce	VERB
ejpam-5608	12	5	by	by	ADP
ejpam-5608	12	6	kostyrko	kostyrko	PROPN
ejpam-5608	12	7	et	et	PROPN
ejpam-5608	12	8	al	al	PROPN
ejpam-5608	12	9	.	.	PUNCT
ejpam-5608	13	1	in	in	ADP
ejpam-5608	13	2	[	[	X
ejpam-5608	13	3	20	20	NUM
ejpam-5608	13	4	]	]	PUNCT
ejpam-5608	13	5	,	,	PUNCT
ejpam-5608	13	6	extends	extend	VERB
ejpam-5608	13	7	statistical	statistical	ADJ
ejpam-5608	13	8	convergence	convergence	NOUN
ejpam-5608	13	9	by	by	ADP
ejpam-5608	13	10	incorporating	incorporate	VERB
ejpam-5608	13	11	ideals	ideal	NOUN
ejpam-5608	13	12	of	of	ADP
ejpam-5608	13	13	sets	set	NOUN
ejpam-5608	13	14	,	,	PUNCT
ejpam-5608	13	15	which	which	PRON
ejpam-5608	13	16	are	be	AUX
ejpam-5608	13	17	collections	collection	NOUN
ejpam-5608	13	18	of	of	ADP
ejpam-5608	13	19	subsets	subset	NOUN
ejpam-5608	13	20	of	of	ADP
ejpam-5608	13	21	natural	natural	ADJ
ejpam-5608	13	22	numbers	number	NOUN
ejpam-5608	13	23	closed	close	VERB
ejpam-5608	13	24	∗corresponding	∗corresponde	VERB
ejpam-5608	13	25	author	author	NOUN
ejpam-5608	13	26	.	.	PUNCT
ejpam-5608	14	1	doi	doi	NOUN
ejpam-5608	14	2	:	:	PUNCT
ejpam-5608	14	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5608	https://doi.org/10.29020/nybg.ejpam.v18i1.5608	NOUN
ejpam-5608	14	4	email	email	NOUN
ejpam-5608	14	5	addresses	address	NOUN
ejpam-5608	14	6	:	:	PUNCT
ejpam-5608	14	7	manuharawati@unesa.ac.id	manuharawati@unesa.ac.id	NOUN
ejpam-5608	14	8	(	(	PUNCT
ejpam-5608	14	9	manuharawati	manuharawati	NOUN
ejpam-5608	14	10	)	)	PUNCT
ejpam-5608	14	11	,	,	PUNCT
ejpam-5608	14	12	muhammadjakfar@unesa.ac.id	muhammadjakfar@unesa.ac.id	NOUN
ejpam-5608	14	13	(	(	PUNCT
ejpam-5608	14	14	m.	m.	NOUN
ejpam-5608	14	15	jakfar	jakfar	PROPN
ejpam-5608	14	16	)	)	PUNCT
ejpam-5608	14	17	,	,	PUNCT
ejpam-5608	14	18	taufikhamzahh26@gmail.com	taufikhamzahh26@gmail.com	X
ejpam-5608	14	19	(	(	PUNCT
ejpam-5608	14	20	a.	a.	PROPN
ejpam-5608	14	21	taufik	taufik	PROPN
ejpam-5608	14	22	hamzah	hamzah	PROPN
ejpam-5608	14	23	)	)	PUNCT
ejpam-5608	14	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5608	14	25	1	1	NUM
ejpam-5608	14	26	copyright	copyright	NOUN
ejpam-5608	14	27	:	:	PUNCT
ejpam-5608	15	1	©	©	PROPN
ejpam-5608	15	2	2025	2025	NUM
ejpam-5608	15	3	the	the	DET
ejpam-5608	15	4	author(s	author(s	NOUN
ejpam-5608	15	5	)	)	PUNCT
ejpam-5608	15	6	.	.	PUNCT
ejpam-5608	16	1	(	(	PUNCT
ejpam-5608	16	2	cc	cc	NOUN
ejpam-5608	16	3	by	by	ADP
ejpam-5608	16	4	-	-	PUNCT
ejpam-5608	16	5	nc	nc	PROPN
ejpam-5608	16	6	4.0	4.0	NUM
ejpam-5608	16	7	)	)	PUNCT
ejpam-5608	16	8	manuharawati	manuharawati	NOUN
ejpam-5608	16	9	,	,	PUNCT
ejpam-5608	16	10	m.jakfar	m.jakfar	ADV
ejpam-5608	16	11	,	,	PUNCT
ejpam-5608	16	12	a.	a.	PROPN
ejpam-5608	16	13	taufik	taufik	PROPN
ejpam-5608	16	14	hamzah	hamzah	PROPN
ejpam-5608	16	15	/	/	SYM
ejpam-5608	16	16	eur	eur	PROPN
ejpam-5608	16	17	.	.	PUNCT
ejpam-5608	17	1	j.	j.	PROPN
ejpam-5608	17	2	pure	pure	PROPN
ejpam-5608	17	3	appl	appl	PROPN
ejpam-5608	17	4	.	.	PROPN
ejpam-5608	17	5	math	math	PROPN
ejpam-5608	17	6	,	,	PUNCT
ejpam-5608	17	7	18	18	NUM
ejpam-5608	17	8	(	(	PUNCT
ejpam-5608	17	9	1	1	NUM
ejpam-5608	17	10	)	)	PUNCT
ejpam-5608	17	11	(	(	PUNCT
ejpam-5608	17	12	2025	2025	NUM
ejpam-5608	17	13	)	)	PUNCT
ejpam-5608	17	14	,	,	PUNCT
ejpam-5608	17	15	5608	5608	NUM
ejpam-5608	17	16	2	2	NUM
ejpam-5608	17	17	of	of	ADP
ejpam-5608	17	18	13	13	NUM
ejpam-5608	17	19	under	under	ADP
ejpam-5608	17	20	certain	certain	ADJ
ejpam-5608	17	21	set	set	NOUN
ejpam-5608	17	22	operations	operation	NOUN
ejpam-5608	17	23	.	.	PUNCT
ejpam-5608	18	1	ideal	ideal	ADJ
ejpam-5608	18	2	convergence	convergence	NOUN
ejpam-5608	18	3	provides	provide	VERB
ejpam-5608	18	4	a	a	DET
ejpam-5608	18	5	flexible	flexible	ADJ
ejpam-5608	18	6	framework	framework	NOUN
ejpam-5608	18	7	that	that	PRON
ejpam-5608	18	8	unifies	unify	VERB
ejpam-5608	18	9	several	several	ADJ
ejpam-5608	18	10	known	know	VERB
ejpam-5608	18	11	types	type	NOUN
ejpam-5608	18	12	of	of	ADP
ejpam-5608	18	13	convergence	convergence	NOUN
ejpam-5608	18	14	,	,	PUNCT
ejpam-5608	18	15	including	include	VERB
ejpam-5608	18	16	statistical	statistical	ADJ
ejpam-5608	18	17	convergence	convergence	NOUN
ejpam-5608	18	18	and	and	CCONJ
ejpam-5608	18	19	convergence	convergence	NOUN
ejpam-5608	18	20	with	with	ADP
ejpam-5608	18	21	respect	respect	NOUN
ejpam-5608	18	22	to	to	ADP
ejpam-5608	18	23	filters	filter	NOUN
ejpam-5608	18	24	[	[	X
ejpam-5608	18	25	20	20	NUM
ejpam-5608	18	26	]	]	PUNCT
ejpam-5608	18	27	.	.	PUNCT
ejpam-5608	19	1	ideal	ideal	ADJ
ejpam-5608	19	2	convergence	convergence	NOUN
ejpam-5608	19	3	has	have	AUX
ejpam-5608	19	4	been	be	AUX
ejpam-5608	19	5	studied	study	VERB
ejpam-5608	19	6	in	in	ADP
ejpam-5608	19	7	various	various	ADJ
ejpam-5608	19	8	contexts	contexts	NOUN
ejpam-5608	19	9	,	,	PUNCT
ejpam-5608	19	10	including	include	VERB
ejpam-5608	19	11	banach	banach	NOUN
ejpam-5608	19	12	spaces	space	NOUN
ejpam-5608	19	13	and	and	CCONJ
ejpam-5608	19	14	normed	normed	ADJ
ejpam-5608	19	15	spaces	space	NOUN
ejpam-5608	19	16	,	,	PUNCT
ejpam-5608	19	17	offering	offer	VERB
ejpam-5608	19	18	insights	insight	NOUN
ejpam-5608	19	19	into	into	ADP
ejpam-5608	19	20	the	the	DET
ejpam-5608	19	21	structure	structure	NOUN
ejpam-5608	19	22	of	of	ADP
ejpam-5608	19	23	function	function	NOUN
ejpam-5608	19	24	spaces	space	NOUN
ejpam-5608	19	25	and	and	CCONJ
ejpam-5608	19	26	the	the	DET
ejpam-5608	19	27	behaviour	behaviour	NOUN
ejpam-5608	19	28	of	of	ADP
ejpam-5608	19	29	sequences	sequence	NOUN
ejpam-5608	19	30	[	[	X
ejpam-5608	19	31	2	2	NUM
ejpam-5608	19	32	]	]	PUNCT
ejpam-5608	19	33	.	.	PUNCT
ejpam-5608	20	1	despite	despite	SCONJ
ejpam-5608	20	2	substantial	substantial	ADJ
ejpam-5608	20	3	progress	progress	NOUN
ejpam-5608	20	4	in	in	ADP
ejpam-5608	20	5	these	these	DET
ejpam-5608	20	6	areas	area	NOUN
ejpam-5608	20	7	,	,	PUNCT
ejpam-5608	20	8	research	research	NOUN
ejpam-5608	20	9	on	on	ADP
ejpam-5608	20	10	the	the	DET
ejpam-5608	20	11	relationship	relationship	NOUN
ejpam-5608	20	12	between	between	ADP
ejpam-5608	20	13	statistical	statistical	ADJ
ejpam-5608	20	14	convergence	convergence	NOUN
ejpam-5608	20	15	and	and	CCONJ
ejpam-5608	20	16	standard	standard	ADJ
ejpam-5608	20	17	convergence	convergence	NOUN
ejpam-5608	20	18	,	,	PUNCT
ejpam-5608	20	19	particularly	particularly	ADV
ejpam-5608	20	20	in	in	ADP
ejpam-5608	20	21	the	the	DET
ejpam-5608	20	22	setting	setting	NOUN
ejpam-5608	20	23	of	of	ADP
ejpam-5608	20	24	g	g	NOUN
ejpam-5608	20	25	-	-	PUNCT
ejpam-5608	20	26	metric	metric	ADJ
ejpam-5608	20	27	spaces	space	NOUN
ejpam-5608	20	28	,	,	PUNCT
ejpam-5608	20	29	remains	remain	VERB
ejpam-5608	20	30	limited	limited	ADJ
ejpam-5608	20	31	.	.	PUNCT
ejpam-5608	21	1	g	g	NOUN
ejpam-5608	21	2	-	-	PUNCT
ejpam-5608	21	3	metric	metric	ADJ
ejpam-5608	21	4	spaces	space	NOUN
ejpam-5608	21	5	,	,	PUNCT
ejpam-5608	21	6	introduced	introduce	VERB
ejpam-5608	21	7	by	by	ADP
ejpam-5608	21	8	mustafa	mustafa	PROPN
ejpam-5608	21	9	and	and	CCONJ
ejpam-5608	21	10	sims	sim	NOUN
ejpam-5608	21	11	[	[	X
ejpam-5608	21	12	27	27	NUM
ejpam-5608	21	13	]	]	PUNCT
ejpam-5608	21	14	,	,	PUNCT
ejpam-5608	21	15	generalize	generalize	VERB
ejpam-5608	21	16	the	the	DET
ejpam-5608	21	17	notion	notion	NOUN
ejpam-5608	21	18	of	of	ADP
ejpam-5608	21	19	a	a	DET
ejpam-5608	21	20	metric	metric	ADJ
ejpam-5608	21	21	space	space	NOUN
ejpam-5608	21	22	by	by	ADP
ejpam-5608	21	23	defining	define	VERB
ejpam-5608	21	24	a	a	DET
ejpam-5608	21	25	distance	distance	NOUN
ejpam-5608	21	26	function	function	NOUN
ejpam-5608	21	27	on	on	ADP
ejpam-5608	21	28	triplets	triplet	NOUN
ejpam-5608	21	29	of	of	ADP
ejpam-5608	21	30	points	point	NOUN
ejpam-5608	21	31	rather	rather	ADV
ejpam-5608	21	32	than	than	ADP
ejpam-5608	21	33	pairs	pair	NOUN
ejpam-5608	21	34	.	.	PUNCT
ejpam-5608	22	1	this	this	DET
ejpam-5608	22	2	structure	structure	NOUN
ejpam-5608	22	3	has	have	AUX
ejpam-5608	22	4	led	lead	VERB
ejpam-5608	22	5	to	to	ADP
ejpam-5608	22	6	the	the	DET
ejpam-5608	22	7	development	development	NOUN
ejpam-5608	22	8	of	of	ADP
ejpam-5608	22	9	various	various	ADJ
ejpam-5608	22	10	fixed	fix	VERB
ejpam-5608	22	11	-	-	PUNCT
ejpam-5608	22	12	point	point	NOUN
ejpam-5608	22	13	theorems	theorem	NOUN
ejpam-5608	22	14	and	and	CCONJ
ejpam-5608	22	15	applications	application	NOUN
ejpam-5608	22	16	in	in	ADP
ejpam-5608	22	17	nonlinear	nonlinear	ADJ
ejpam-5608	22	18	analysis	analysis	NOUN
ejpam-5608	22	19	[	[	X
ejpam-5608	22	20	27	27	NUM
ejpam-5608	22	21	]	]	PUNCT
ejpam-5608	22	22	.	.	PUNCT
ejpam-5608	23	1	many	many	ADJ
ejpam-5608	23	2	mathematicians	mathematician	NOUN
ejpam-5608	23	3	have	have	AUX
ejpam-5608	23	4	conducted	conduct	VERB
ejpam-5608	23	5	research	research	NOUN
ejpam-5608	23	6	on	on	ADP
ejpam-5608	23	7	g	g	NOUN
ejpam-5608	23	8	-	-	PUNCT
ejpam-5608	23	9	metric	metric	ADJ
ejpam-5608	23	10	spaces	space	NOUN
ejpam-5608	23	11	.	.	PUNCT
ejpam-5608	24	1	recent	recent	ADJ
ejpam-5608	24	2	results	result	NOUN
ejpam-5608	24	3	on	on	ADP
ejpam-5608	24	4	g	g	NOUN
ejpam-5608	24	5	-	-	PUNCT
ejpam-5608	24	6	metric	metric	ADJ
ejpam-5608	24	7	spaces	space	NOUN
ejpam-5608	24	8	include	include	VERB
ejpam-5608	24	9	,	,	PUNCT
ejpam-5608	24	10	among	among	ADP
ejpam-5608	24	11	others	other	NOUN
ejpam-5608	24	12	,	,	PUNCT
ejpam-5608	24	13	[	[	X
ejpam-5608	24	14	13	13	NUM
ejpam-5608	24	15	]	]	PUNCT
ejpam-5608	24	16	,	,	PUNCT
ejpam-5608	25	1	[	[	X
ejpam-5608	25	2	14	14	NUM
ejpam-5608	25	3	]	]	PUNCT
ejpam-5608	25	4	,	,	PUNCT
ejpam-5608	25	5	[	[	X
ejpam-5608	25	6	17	17	NUM
ejpam-5608	25	7	]	]	PUNCT
ejpam-5608	25	8	,	,	PUNCT
ejpam-5608	25	9	[	[	X
ejpam-5608	25	10	18	18	NUM
ejpam-5608	25	11	]	]	PUNCT
ejpam-5608	25	12	,	,	PUNCT
ejpam-5608	25	13	[	[	X
ejpam-5608	25	14	16	16	NUM
ejpam-5608	25	15	]	]	PUNCT
ejpam-5608	25	16	,	,	PUNCT
ejpam-5608	25	17	[	[	X
ejpam-5608	25	18	15	15	NUM
ejpam-5608	25	19	]	]	PUNCT
ejpam-5608	25	20	,	,	PUNCT
ejpam-5608	25	21	[	[	X
ejpam-5608	25	22	25	25	NUM
ejpam-5608	25	23	]	]	PUNCT
ejpam-5608	25	24	,	,	PUNCT
ejpam-5608	26	1	[	[	X
ejpam-5608	26	2	26	26	NUM
ejpam-5608	26	3	]	]	PUNCT
ejpam-5608	26	4	,	,	PUNCT
ejpam-5608	26	5	[	[	X
ejpam-5608	26	6	30	30	NUM
ejpam-5608	26	7	]	]	PUNCT
ejpam-5608	26	8	,	,	PUNCT
ejpam-5608	26	9	[	[	X
ejpam-5608	26	10	4	4	NUM
ejpam-5608	26	11	]	]	PUNCT
ejpam-5608	26	12	,	,	PUNCT
ejpam-5608	26	13	[	[	X
ejpam-5608	26	14	7	7	X
ejpam-5608	26	15	]	]	PUNCT
ejpam-5608	26	16	and	and	CCONJ
ejpam-5608	26	17	[	[	X
ejpam-5608	26	18	33	33	NUM
ejpam-5608	26	19	]	]	PUNCT
ejpam-5608	26	20	.	.	PUNCT
ejpam-5608	27	1	however	however	ADV
ejpam-5608	27	2	,	,	PUNCT
ejpam-5608	27	3	the	the	DET
ejpam-5608	27	4	interaction	interaction	NOUN
ejpam-5608	27	5	between	between	ADP
ejpam-5608	27	6	different	different	ADJ
ejpam-5608	27	7	types	type	NOUN
ejpam-5608	27	8	of	of	ADP
ejpam-5608	27	9	convergence	convergence	NOUN
ejpam-5608	27	10	,	,	PUNCT
ejpam-5608	27	11	such	such	ADJ
ejpam-5608	27	12	as	as	ADP
ejpam-5608	27	13	statistical	statistical	ADJ
ejpam-5608	27	14	and	and	CCONJ
ejpam-5608	27	15	standard	standard	ADJ
ejpam-5608	27	16	convergence	convergence	NOUN
ejpam-5608	27	17	(	(	PUNCT
ejpam-5608	27	18	[	[	X
ejpam-5608	27	19	10	10	NUM
ejpam-5608	27	20	]	]	PUNCT
ejpam-5608	27	21	,	,	PUNCT
ejpam-5608	27	22	[	[	X
ejpam-5608	27	23	11],[23	11],[23	NOUN
ejpam-5608	27	24	]	]	X
ejpam-5608	27	25	,	,	PUNCT
ejpam-5608	27	26	and	and	CCONJ
ejpam-5608	27	27	[	[	X
ejpam-5608	27	28	29	29	NUM
ejpam-5608	27	29	]	]	NUM
ejpam-5608	27	30	)	)	PUNCT
ejpam-5608	27	31	,	,	PUNCT
ejpam-5608	27	32	in	in	ADP
ejpam-5608	27	33	g	g	NOUN
ejpam-5608	27	34	-	-	PUNCT
ejpam-5608	27	35	metric	metric	ADJ
ejpam-5608	27	36	spaces	space	NOUN
ejpam-5608	27	37	has	have	AUX
ejpam-5608	27	38	not	not	PART
ejpam-5608	27	39	been	be	AUX
ejpam-5608	27	40	fully	fully	ADV
ejpam-5608	27	41	explored	explore	VERB
ejpam-5608	27	42	.	.	PUNCT
ejpam-5608	28	1	the	the	DET
ejpam-5608	28	2	concept	concept	NOUN
ejpam-5608	28	3	of	of	ADP
ejpam-5608	28	4	convergence	convergence	NOUN
ejpam-5608	28	5	,	,	PUNCT
ejpam-5608	28	6	particularly	particularly	ADV
ejpam-5608	28	7	in	in	ADP
ejpam-5608	28	8	g	g	NOUN
ejpam-5608	28	9	-	-	PUNCT
ejpam-5608	28	10	metric	metric	ADJ
ejpam-5608	28	11	spaces	space	NOUN
ejpam-5608	28	12	,	,	PUNCT
ejpam-5608	28	13	has	have	VERB
ejpam-5608	28	14	wide	wide	ADV
ejpam-5608	28	15	-	-	PUNCT
ejpam-5608	28	16	ranging	range	VERB
ejpam-5608	28	17	applications	application	NOUN
ejpam-5608	28	18	across	across	ADP
ejpam-5608	28	19	various	various	ADJ
ejpam-5608	28	20	fields	field	NOUN
ejpam-5608	28	21	.	.	PUNCT
ejpam-5608	29	1	in	in	ADP
ejpam-5608	29	2	machine	machine	NOUN
ejpam-5608	29	3	learning	learning	NOUN
ejpam-5608	29	4	and	and	CCONJ
ejpam-5608	29	5	data	datum	NOUN
ejpam-5608	29	6	analysis	analysis	NOUN
ejpam-5608	29	7	,	,	PUNCT
ejpam-5608	29	8	these	these	DET
ejpam-5608	29	9	results	result	NOUN
ejpam-5608	29	10	can	can	AUX
ejpam-5608	29	11	be	be	AUX
ejpam-5608	29	12	applied	apply	VERB
ejpam-5608	29	13	to	to	PART
ejpam-5608	29	14	understand	understand	VERB
ejpam-5608	29	15	the	the	DET
ejpam-5608	29	16	stability	stability	NOUN
ejpam-5608	29	17	of	of	ADP
ejpam-5608	29	18	algorithms	algorithm	NOUN
ejpam-5608	29	19	or	or	CCONJ
ejpam-5608	29	20	models	model	NOUN
ejpam-5608	29	21	operating	operate	VERB
ejpam-5608	29	22	within	within	ADP
ejpam-5608	29	23	complex	complex	ADJ
ejpam-5608	29	24	metric	metric	ADJ
ejpam-5608	29	25	structures	structure	NOUN
ejpam-5608	29	26	,	,	PUNCT
ejpam-5608	29	27	such	such	ADJ
ejpam-5608	29	28	as	as	ADP
ejpam-5608	29	29	g	g	NOUN
ejpam-5608	29	30	-	-	PUNCT
ejpam-5608	29	31	metric	metric	ADJ
ejpam-5608	29	32	spaces	space	NOUN
ejpam-5608	29	33	,	,	PUNCT
ejpam-5608	29	34	which	which	PRON
ejpam-5608	29	35	better	well	ADV
ejpam-5608	29	36	represent	represent	VERB
ejpam-5608	29	37	non	non	ADJ
ejpam-5608	29	38	-	-	ADJ
ejpam-5608	29	39	linear	linear	ADJ
ejpam-5608	29	40	data	datum	NOUN
ejpam-5608	29	41	relationships	relationship	NOUN
ejpam-5608	29	42	[	[	X
ejpam-5608	29	43	35	35	NUM
ejpam-5608	29	44	]	]	PUNCT
ejpam-5608	29	45	.	.	PUNCT
ejpam-5608	30	1	furthermore	furthermore	ADV
ejpam-5608	30	2	,	,	PUNCT
ejpam-5608	30	3	in	in	ADP
ejpam-5608	30	4	optimization	optimization	NOUN
ejpam-5608	30	5	theory	theory	NOUN
ejpam-5608	30	6	,	,	PUNCT
ejpam-5608	30	7	g	g	NOUN
ejpam-5608	30	8	-	-	PUNCT
ejpam-5608	30	9	metric	metric	ADJ
ejpam-5608	30	10	spaces	space	NOUN
ejpam-5608	30	11	provide	provide	VERB
ejpam-5608	30	12	a	a	DET
ejpam-5608	30	13	framework	framework	NOUN
ejpam-5608	30	14	for	for	ADP
ejpam-5608	30	15	analyzing	analyze	VERB
ejpam-5608	30	16	iterative	iterative	NOUN
ejpam-5608	30	17	algorithms	algorithm	NOUN
ejpam-5608	30	18	for	for	ADP
ejpam-5608	30	19	non	non	ADJ
ejpam-5608	30	20	-	-	ADJ
ejpam-5608	30	21	linear	linear	ADJ
ejpam-5608	30	22	problems	problem	NOUN
ejpam-5608	30	23	commonly	commonly	ADV
ejpam-5608	30	24	encountered	encounter	VERB
ejpam-5608	30	25	in	in	ADP
ejpam-5608	30	26	dynamic	dynamic	ADJ
ejpam-5608	30	27	programming	programming	NOUN
ejpam-5608	30	28	[	[	X
ejpam-5608	30	29	9	9	NUM
ejpam-5608	30	30	]	]	PUNCT
ejpam-5608	30	31	.	.	PUNCT
ejpam-5608	31	1	in	in	ADP
ejpam-5608	31	2	theoretical	theoretical	ADJ
ejpam-5608	31	3	physics	physics	NOUN
ejpam-5608	31	4	,	,	PUNCT
ejpam-5608	31	5	g	g	NOUN
ejpam-5608	31	6	-	-	PUNCT
ejpam-5608	31	7	metric	metric	ADJ
ejpam-5608	31	8	spaces	space	NOUN
ejpam-5608	31	9	aid	aid	VERB
ejpam-5608	31	10	in	in	ADP
ejpam-5608	31	11	modelling	model	VERB
ejpam-5608	31	12	systems	system	NOUN
ejpam-5608	31	13	with	with	ADP
ejpam-5608	31	14	multiple	multiple	ADJ
ejpam-5608	31	15	parameter	parameter	NOUN
ejpam-5608	31	16	interactions	interaction	NOUN
ejpam-5608	31	17	,	,	PUNCT
ejpam-5608	31	18	making	make	VERB
ejpam-5608	31	19	them	they	PRON
ejpam-5608	31	20	relevant	relevant	ADJ
ejpam-5608	31	21	for	for	ADP
ejpam-5608	31	22	studying	study	VERB
ejpam-5608	31	23	dynamical	dynamical	ADJ
ejpam-5608	31	24	systems	system	NOUN
ejpam-5608	31	25	and	and	CCONJ
ejpam-5608	31	26	physical	physical	ADJ
ejpam-5608	31	27	geometries	geometry	NOUN
ejpam-5608	31	28	[	[	X
ejpam-5608	31	29	28	28	NUM
ejpam-5608	31	30	]	]	PUNCT
ejpam-5608	31	31	.	.	PUNCT
ejpam-5608	32	1	finally	finally	ADV
ejpam-5608	32	2	,	,	PUNCT
ejpam-5608	32	3	in	in	ADP
ejpam-5608	32	4	mathematical	mathematical	ADJ
ejpam-5608	32	5	finance	finance	NOUN
ejpam-5608	32	6	,	,	PUNCT
ejpam-5608	32	7	this	this	DET
ejpam-5608	32	8	approach	approach	NOUN
ejpam-5608	32	9	enhances	enhance	VERB
ejpam-5608	32	10	the	the	DET
ejpam-5608	32	11	modelling	modelling	NOUN
ejpam-5608	32	12	of	of	ADP
ejpam-5608	32	13	complex	complex	ADJ
ejpam-5608	32	14	market	market	NOUN
ejpam-5608	32	15	data	datum	NOUN
ejpam-5608	32	16	through	through	ADP
ejpam-5608	32	17	statistical	statistical	ADJ
ejpam-5608	32	18	and	and	CCONJ
ejpam-5608	32	19	ideal	ideal	ADJ
ejpam-5608	32	20	convergence	convergence	NOUN
ejpam-5608	32	21	,	,	PUNCT
ejpam-5608	32	22	enabling	enable	VERB
ejpam-5608	32	23	more	more	ADV
ejpam-5608	32	24	robust	robust	ADJ
ejpam-5608	32	25	analysis	analysis	NOUN
ejpam-5608	32	26	of	of	ADP
ejpam-5608	32	27	economic	economic	ADJ
ejpam-5608	32	28	behaviour	behaviour	NOUN
ejpam-5608	32	29	[	[	X
ejpam-5608	32	30	16	16	NUM
ejpam-5608	32	31	]	]	PUNCT
ejpam-5608	32	32	.	.	PUNCT
ejpam-5608	33	1	thus	thus	ADV
ejpam-5608	33	2	,	,	PUNCT
ejpam-5608	33	3	this	this	DET
ejpam-5608	33	4	study	study	NOUN
ejpam-5608	33	5	not	not	PART
ejpam-5608	33	6	only	only	ADV
ejpam-5608	33	7	deepens	deepen	VERB
ejpam-5608	33	8	the	the	DET
ejpam-5608	33	9	theoretical	theoretical	ADJ
ejpam-5608	33	10	understanding	understanding	NOUN
ejpam-5608	33	11	of	of	ADP
ejpam-5608	33	12	convergence	convergence	NOUN
ejpam-5608	33	13	in	in	ADP
ejpam-5608	33	14	g	g	NOUN
ejpam-5608	33	15	-	-	PUNCT
ejpam-5608	33	16	metric	metric	ADJ
ejpam-5608	33	17	spaces	space	NOUN
ejpam-5608	33	18	,	,	PUNCT
ejpam-5608	33	19	but	but	CCONJ
ejpam-5608	33	20	also	also	ADV
ejpam-5608	33	21	opens	open	VERB
ejpam-5608	33	22	avenues	avenue	NOUN
ejpam-5608	33	23	for	for	ADP
ejpam-5608	33	24	its	its	PRON
ejpam-5608	33	25	application	application	NOUN
ejpam-5608	33	26	across	across	ADP
ejpam-5608	33	27	diverse	diverse	ADJ
ejpam-5608	33	28	scientific	scientific	ADJ
ejpam-5608	33	29	disciplines	discipline	NOUN
ejpam-5608	33	30	.	.	PUNCT
ejpam-5608	34	1	existing	exist	VERB
ejpam-5608	34	2	research	research	NOUN
ejpam-5608	34	3	has	have	AUX
ejpam-5608	34	4	focused	focus	VERB
ejpam-5608	34	5	mainly	mainly	ADV
ejpam-5608	34	6	on	on	ADP
ejpam-5608	34	7	the	the	DET
ejpam-5608	34	8	individual	individual	ADJ
ejpam-5608	34	9	properties	property	NOUN
ejpam-5608	34	10	of	of	ADP
ejpam-5608	34	11	statistical	statistical	ADJ
ejpam-5608	34	12	and	and	CCONJ
ejpam-5608	34	13	ideal	ideal	ADJ
ejpam-5608	34	14	convergence	convergence	NOUN
ejpam-5608	34	15	in	in	ADP
ejpam-5608	34	16	g	g	NOUN
ejpam-5608	34	17	-	-	PUNCT
ejpam-5608	34	18	metric	metric	ADJ
ejpam-5608	34	19	spaces	space	NOUN
ejpam-5608	34	20	[	[	X
ejpam-5608	34	21	12	12	NUM
ejpam-5608	34	22	,	,	PUNCT
ejpam-5608	34	23	31	31	NUM
ejpam-5608	34	24	]	]	PUNCT
ejpam-5608	34	25	.	.	PUNCT
ejpam-5608	35	1	these	these	DET
ejpam-5608	35	2	studies	study	NOUN
ejpam-5608	35	3	have	have	AUX
ejpam-5608	35	4	established	establish	VERB
ejpam-5608	35	5	important	important	ADJ
ejpam-5608	35	6	results	result	NOUN
ejpam-5608	35	7	concerning	concern	VERB
ejpam-5608	35	8	the	the	DET
ejpam-5608	35	9	behaviour	behaviour	NOUN
ejpam-5608	35	10	of	of	ADP
ejpam-5608	35	11	sequences	sequence	NOUN
ejpam-5608	35	12	and	and	CCONJ
ejpam-5608	35	13	functions	function	NOUN
ejpam-5608	35	14	in	in	ADP
ejpam-5608	35	15	such	such	ADJ
ejpam-5608	35	16	spaces	space	NOUN
ejpam-5608	35	17	.	.	PUNCT
ejpam-5608	36	1	however	however	ADV
ejpam-5608	36	2	,	,	PUNCT
ejpam-5608	36	3	no	no	DET
ejpam-5608	36	4	prior	prior	ADJ
ejpam-5608	36	5	study	study	NOUN
ejpam-5608	36	6	has	have	AUX
ejpam-5608	36	7	investigated	investigate	VERB
ejpam-5608	36	8	the	the	DET
ejpam-5608	36	9	precise	precise	ADJ
ejpam-5608	36	10	relationship	relationship	NOUN
ejpam-5608	36	11	between	between	ADP
ejpam-5608	36	12	statistical	statistical	ADJ
ejpam-5608	36	13	convergence	convergence	NOUN
ejpam-5608	36	14	and	and	CCONJ
ejpam-5608	36	15	standard	standard	ADJ
ejpam-5608	36	16	convergence	convergence	NOUN
ejpam-5608	36	17	in	in	ADP
ejpam-5608	36	18	g	g	NOUN
ejpam-5608	36	19	-	-	PUNCT
ejpam-5608	36	20	metric	metric	ADJ
ejpam-5608	36	21	spaces	space	NOUN
ejpam-5608	36	22	,	,	PUNCT
ejpam-5608	36	23	leaving	leave	VERB
ejpam-5608	36	24	a	a	DET
ejpam-5608	36	25	significant	significant	ADJ
ejpam-5608	36	26	gap	gap	NOUN
ejpam-5608	36	27	in	in	ADP
ejpam-5608	36	28	the	the	DET
ejpam-5608	36	29	literature	literature	NOUN
ejpam-5608	36	30	.	.	PUNCT
ejpam-5608	37	1	in	in	ADP
ejpam-5608	37	2	this	this	DET
ejpam-5608	37	3	paper	paper	NOUN
ejpam-5608	37	4	,	,	PUNCT
ejpam-5608	37	5	we	we	PRON
ejpam-5608	37	6	aim	aim	VERB
ejpam-5608	37	7	to	to	PART
ejpam-5608	37	8	bridge	bridge	VERB
ejpam-5608	37	9	this	this	DET
ejpam-5608	37	10	gap	gap	NOUN
ejpam-5608	37	11	by	by	ADP
ejpam-5608	37	12	studying	study	VERB
ejpam-5608	37	13	the	the	DET
ejpam-5608	37	14	conditions	condition	NOUN
ejpam-5608	37	15	under	under	ADP
ejpam-5608	37	16	which	which	PRON
ejpam-5608	37	17	statistical	statistical	ADJ
ejpam-5608	37	18	convergence	convergence	NOUN
ejpam-5608	37	19	,	,	PUNCT
ejpam-5608	37	20	ideal	ideal	ADJ
ejpam-5608	37	21	convergence	convergence	NOUN
ejpam-5608	37	22	,	,	PUNCT
ejpam-5608	37	23	and	and	CCONJ
ejpam-5608	37	24	standard	standard	ADJ
ejpam-5608	37	25	convergence	convergence	NOUN
ejpam-5608	37	26	are	be	AUX
ejpam-5608	37	27	equivalent	equivalent	ADJ
ejpam-5608	37	28	in	in	ADP
ejpam-5608	37	29	g	g	NOUN
ejpam-5608	37	30	-	-	PUNCT
ejpam-5608	37	31	metric	metric	ADJ
ejpam-5608	37	32	spaces	space	NOUN
ejpam-5608	37	33	.	.	PUNCT
ejpam-5608	38	1	our	our	PRON
ejpam-5608	38	2	main	main	ADJ
ejpam-5608	38	3	contribution	contribution	NOUN
ejpam-5608	38	4	is	be	AUX
ejpam-5608	38	5	the	the	DET
ejpam-5608	38	6	establishment	establishment	NOUN
ejpam-5608	38	7	of	of	ADP
ejpam-5608	38	8	necessary	necessary	ADJ
ejpam-5608	38	9	and	and	CCONJ
ejpam-5608	38	10	sufficient	sufficient	ADJ
ejpam-5608	38	11	conditions	condition	NOUN
ejpam-5608	38	12	for	for	ADP
ejpam-5608	38	13	this	this	DET
ejpam-5608	38	14	equivalence	equivalence	NOUN
ejpam-5608	38	15	,	,	PUNCT
ejpam-5608	38	16	which	which	PRON
ejpam-5608	38	17	provide	provide	VERB
ejpam-5608	38	18	a	a	DET
ejpam-5608	38	19	comprehensive	comprehensive	ADJ
ejpam-5608	38	20	framework	framework	NOUN
ejpam-5608	38	21	for	for	ADP
ejpam-5608	38	22	understanding	understand	VERB
ejpam-5608	38	23	how	how	SCONJ
ejpam-5608	38	24	these	these	DET
ejpam-5608	38	25	different	different	ADJ
ejpam-5608	38	26	convergence	convergence	NOUN
ejpam-5608	38	27	notions	notion	NOUN
ejpam-5608	38	28	relate	relate	VERB
ejpam-5608	38	29	to	to	ADP
ejpam-5608	38	30	one	one	NUM
ejpam-5608	38	31	another	another	DET
ejpam-5608	38	32	.	.	PUNCT
ejpam-5608	39	1	the	the	DET
ejpam-5608	39	2	results	result	NOUN
ejpam-5608	39	3	presented	present	VERB
ejpam-5608	39	4	in	in	ADP
ejpam-5608	39	5	this	this	DET
ejpam-5608	39	6	paper	paper	NOUN
ejpam-5608	39	7	extend	extend	VERB
ejpam-5608	39	8	the	the	DET
ejpam-5608	39	9	theory	theory	NOUN
ejpam-5608	39	10	of	of	ADP
ejpam-5608	39	11	convergence	convergence	NOUN
ejpam-5608	39	12	in	in	ADP
ejpam-5608	39	13	g	g	NOUN
ejpam-5608	39	14	-	-	PUNCT
ejpam-5608	39	15	metric	metric	ADJ
ejpam-5608	39	16	spaces	space	NOUN
ejpam-5608	39	17	and	and	CCONJ
ejpam-5608	39	18	offer	offer	VERB
ejpam-5608	39	19	new	new	ADJ
ejpam-5608	39	20	insights	insight	NOUN
ejpam-5608	39	21	into	into	ADP
ejpam-5608	39	22	the	the	DET
ejpam-5608	39	23	behaviour	behaviour	NOUN
ejpam-5608	39	24	of	of	ADP
ejpam-5608	39	25	sequences	sequence	NOUN
ejpam-5608	39	26	in	in	ADP
ejpam-5608	39	27	generalized	generalized	ADJ
ejpam-5608	39	28	metric	metric	ADJ
ejpam-5608	39	29	structures	structure	NOUN
ejpam-5608	39	30	.	.	PUNCT
ejpam-5608	40	1	this	this	DET
ejpam-5608	40	2	paper	paper	NOUN
ejpam-5608	40	3	is	be	AUX
ejpam-5608	40	4	organized	organize	VERB
ejpam-5608	40	5	as	as	SCONJ
ejpam-5608	40	6	follows	follow	VERB
ejpam-5608	40	7	.	.	PUNCT
ejpam-5608	41	1	in	in	ADP
ejpam-5608	41	2	section	section	NOUN
ejpam-5608	41	3	2	2	NUM
ejpam-5608	41	4	,	,	PUNCT
ejpam-5608	41	5	we	we	PRON
ejpam-5608	41	6	provide	provide	VERB
ejpam-5608	41	7	preliminary	preliminary	ADJ
ejpam-5608	41	8	definitions	definition	NOUN
ejpam-5608	41	9	and	and	CCONJ
ejpam-5608	41	10	review	review	VERB
ejpam-5608	41	11	key	key	ADJ
ejpam-5608	41	12	results	result	NOUN
ejpam-5608	41	13	concerning	concern	VERB
ejpam-5608	41	14	the	the	DET
ejpam-5608	41	15	statistical	statistical	ADJ
ejpam-5608	41	16	and	and	CCONJ
ejpam-5608	41	17	ideal	ideal	ADJ
ejpam-5608	41	18	convergence	convergence	NOUN
ejpam-5608	41	19	in	in	ADP
ejpam-5608	41	20	g	g	NOUN
ejpam-5608	41	21	-	-	PUNCT
ejpam-5608	41	22	metric	metric	ADJ
ejpam-5608	41	23	spaces	space	NOUN
ejpam-5608	41	24	.	.	PUNCT
ejpam-5608	42	1	section	section	NOUN
ejpam-5608	42	2	3	3	NUM
ejpam-5608	42	3	presents	present	VERB
ejpam-5608	42	4	the	the	DET
ejpam-5608	42	5	main	main	ADJ
ejpam-5608	42	6	theorems	theorem	NOUN
ejpam-5608	42	7	,	,	PUNCT
ejpam-5608	42	8	including	include	VERB
ejpam-5608	42	9	the	the	DET
ejpam-5608	42	10	necessary	necessary	ADJ
ejpam-5608	42	11	and	and	CCONJ
ejpam-5608	42	12	sufficient	sufficient	ADJ
ejpam-5608	42	13	conditions	condition	NOUN
ejpam-5608	42	14	for	for	ADP
ejpam-5608	42	15	manuharawati	manuharawati	NOUN
ejpam-5608	42	16	,	,	PUNCT
ejpam-5608	42	17	m.jakfar	m.jakfar	ADV
ejpam-5608	42	18	,	,	PUNCT
ejpam-5608	42	19	a.	a.	PROPN
ejpam-5608	42	20	taufik	taufik	PROPN
ejpam-5608	42	21	hamzah	hamzah	PROPN
ejpam-5608	42	22	/	/	SYM
ejpam-5608	42	23	eur	eur	PROPN
ejpam-5608	42	24	.	.	PUNCT
ejpam-5608	43	1	j.	j.	PROPN
ejpam-5608	43	2	pure	pure	PROPN
ejpam-5608	43	3	appl	appl	PROPN
ejpam-5608	43	4	.	.	PROPN
ejpam-5608	43	5	math	math	PROPN
ejpam-5608	43	6	,	,	PUNCT
ejpam-5608	43	7	18	18	NUM
ejpam-5608	43	8	(	(	PUNCT
ejpam-5608	43	9	1	1	NUM
ejpam-5608	43	10	)	)	PUNCT
ejpam-5608	43	11	(	(	PUNCT
ejpam-5608	43	12	2025	2025	NUM
ejpam-5608	43	13	)	)	PUNCT
ejpam-5608	43	14	,	,	PUNCT
ejpam-5608	43	15	5608	5608	NUM
ejpam-5608	43	16	3	3	NUM
ejpam-5608	43	17	of	of	ADP
ejpam-5608	43	18	13	13	NUM
ejpam-5608	43	19	the	the	DET
ejpam-5608	43	20	equivalence	equivalence	NOUN
ejpam-5608	43	21	of	of	ADP
ejpam-5608	43	22	statistical	statistical	ADJ
ejpam-5608	43	23	,	,	PUNCT
ejpam-5608	43	24	ideal	ideal	ADJ
ejpam-5608	43	25	,	,	PUNCT
ejpam-5608	43	26	and	and	CCONJ
ejpam-5608	43	27	standard	standard	ADJ
ejpam-5608	43	28	convergence	convergence	NOUN
ejpam-5608	43	29	in	in	ADP
ejpam-5608	43	30	g	g	NOUN
ejpam-5608	43	31	-	-	PUNCT
ejpam-5608	43	32	metric	metric	ADJ
ejpam-5608	43	33	spaces	space	NOUN
ejpam-5608	43	34	.	.	PUNCT
ejpam-5608	44	1	finally	finally	ADV
ejpam-5608	44	2	,	,	PUNCT
ejpam-5608	44	3	in	in	ADP
ejpam-5608	44	4	section	section	NOUN
ejpam-5608	44	5	4	4	NUM
ejpam-5608	44	6	,	,	PUNCT
ejpam-5608	44	7	we	we	PRON
ejpam-5608	44	8	conclude	conclude	VERB
ejpam-5608	44	9	with	with	ADP
ejpam-5608	44	10	a	a	DET
ejpam-5608	44	11	discussion	discussion	NOUN
ejpam-5608	44	12	of	of	ADP
ejpam-5608	44	13	the	the	DET
ejpam-5608	44	14	implications	implication	NOUN
ejpam-5608	44	15	of	of	ADP
ejpam-5608	44	16	our	our	PRON
ejpam-5608	44	17	results	result	NOUN
ejpam-5608	44	18	and	and	CCONJ
ejpam-5608	44	19	possible	possible	ADJ
ejpam-5608	44	20	directions	direction	NOUN
ejpam-5608	44	21	for	for	ADP
ejpam-5608	44	22	future	future	ADJ
ejpam-5608	44	23	research	research	NOUN
ejpam-5608	44	24	.	.	PUNCT
ejpam-5608	45	1	2	2	X
ejpam-5608	45	2	.	.	X
ejpam-5608	45	3	preliminary	preliminary	ADJ
ejpam-5608	45	4	definition	definition	NOUN
ejpam-5608	45	5	before	before	ADP
ejpam-5608	45	6	proceeding	proceed	VERB
ejpam-5608	45	7	with	with	ADP
ejpam-5608	45	8	the	the	DET
ejpam-5608	45	9	main	main	ADJ
ejpam-5608	45	10	discussion	discussion	NOUN
ejpam-5608	45	11	,	,	PUNCT
ejpam-5608	45	12	we	we	PRON
ejpam-5608	45	13	need	need	VERB
ejpam-5608	45	14	to	to	PART
ejpam-5608	45	15	establish	establish	VERB
ejpam-5608	45	16	several	several	ADJ
ejpam-5608	45	17	definitions	definition	NOUN
ejpam-5608	45	18	of	of	ADP
ejpam-5608	45	19	the	the	DET
ejpam-5608	45	20	key	key	ADJ
ejpam-5608	45	21	concepts	concept	NOUN
ejpam-5608	45	22	that	that	PRON
ejpam-5608	45	23	will	will	AUX
ejpam-5608	45	24	be	be	AUX
ejpam-5608	45	25	explored	explore	VERB
ejpam-5608	45	26	throughout	throughout	ADP
ejpam-5608	45	27	this	this	DET
ejpam-5608	45	28	research	research	NOUN
ejpam-5608	45	29	.	.	PUNCT
ejpam-5608	46	1	in	in	ADP
ejpam-5608	46	2	the	the	DET
ejpam-5608	46	3	following	following	ADJ
ejpam-5608	46	4	section	section	NOUN
ejpam-5608	46	5	,	,	PUNCT
ejpam-5608	46	6	we	we	PRON
ejpam-5608	46	7	will	will	AUX
ejpam-5608	46	8	provide	provide	VERB
ejpam-5608	46	9	the	the	DET
ejpam-5608	46	10	definitions	definition	NOUN
ejpam-5608	46	11	of	of	ADP
ejpam-5608	46	12	g	g	NOUN
ejpam-5608	46	13	-	-	PUNCT
ejpam-5608	46	14	metric	metric	ADJ
ejpam-5608	46	15	spaces	space	NOUN
ejpam-5608	46	16	and	and	CCONJ
ejpam-5608	46	17	the	the	DET
ejpam-5608	46	18	various	various	ADJ
ejpam-5608	46	19	types	type	NOUN
ejpam-5608	46	20	of	of	ADP
ejpam-5608	46	21	convergence	convergence	NOUN
ejpam-5608	46	22	within	within	ADP
ejpam-5608	46	23	g	g	NOUN
ejpam-5608	46	24	-	-	PUNCT
ejpam-5608	46	25	metric	metric	ADJ
ejpam-5608	46	26	spaces	space	NOUN
ejpam-5608	46	27	.	.	PUNCT
ejpam-5608	47	1	definition	definition	NOUN
ejpam-5608	47	2	1	1	NUM
ejpam-5608	47	3	.	.	PUNCT
ejpam-5608	48	1	[	[	X
ejpam-5608	48	2	27	27	NUM
ejpam-5608	48	3	]	]	PUNCT
ejpam-5608	48	4	let	let	VERB
ejpam-5608	48	5	x	x	PRON
ejpam-5608	48	6	be	be	AUX
ejpam-5608	48	7	a	a	DET
ejpam-5608	48	8	non	non	ADJ
ejpam-5608	48	9	-	-	ADJ
ejpam-5608	48	10	empty	empty	ADJ
ejpam-5608	48	11	set	set	NOUN
ejpam-5608	48	12	.	.	PUNCT
ejpam-5608	49	1	a	a	DET
ejpam-5608	49	2	function	function	NOUN
ejpam-5608	49	3	g	g	NOUN
ejpam-5608	49	4	:	:	PUNCT
ejpam-5608	49	5	x	x	PROPN
ejpam-5608	49	6	×x	×x	X
ejpam-5608	49	7	×x	×x	X
ejpam-5608	49	8	→	→	SYM
ejpam-5608	49	9	r+	r+	PRON
ejpam-5608	49	10	is	be	AUX
ejpam-5608	49	11	called	call	VERB
ejpam-5608	49	12	a	a	DET
ejpam-5608	49	13	g	g	NOUN
ejpam-5608	49	14	-	-	PUNCT
ejpam-5608	49	15	metric	metric	ADJ
ejpam-5608	49	16	if	if	SCONJ
ejpam-5608	49	17	,	,	PUNCT
ejpam-5608	49	18	for	for	ADP
ejpam-5608	49	19	all	all	DET
ejpam-5608	49	20	x	x	NOUN
ejpam-5608	49	21	,	,	PUNCT
ejpam-5608	49	22	y	y	PROPN
ejpam-5608	49	23	,	,	PUNCT
ejpam-5608	49	24	z	z	NOUN
ejpam-5608	49	25	∈	∈	PROPN
ejpam-5608	49	26	x	x	PUNCT
ejpam-5608	49	27	the	the	DET
ejpam-5608	49	28	following	follow	VERB
ejpam-5608	49	29	conditions	condition	NOUN
ejpam-5608	49	30	are	be	AUX
ejpam-5608	49	31	satisfied	satisfied	ADJ
ejpam-5608	49	32	:	:	PUNCT
ejpam-5608	49	33	(	(	PUNCT
ejpam-5608	49	34	i	i	NOUN
ejpam-5608	49	35	)	)	PUNCT
ejpam-5608	49	36	g(x	g(x	PROPN
ejpam-5608	49	37	,	,	PUNCT
ejpam-5608	49	38	y	y	PROPN
ejpam-5608	49	39	,	,	PUNCT
ejpam-5608	49	40	z	z	NOUN
ejpam-5608	49	41	)	)	PUNCT
ejpam-5608	49	42	=	=	SYM
ejpam-5608	49	43	0	0	PUNCT
ejpam-5608	50	1	if	if	SCONJ
ejpam-5608	50	2	and	and	CCONJ
ejpam-5608	50	3	only	only	ADV
ejpam-5608	50	4	if	if	SCONJ
ejpam-5608	50	5	x	x	NOUN
ejpam-5608	50	6	=	=	PUNCT
ejpam-5608	50	7	y	y	PROPN
ejpam-5608	50	8	=	=	SYM
ejpam-5608	50	9	z	z	PROPN
ejpam-5608	50	10	(	(	PUNCT
ejpam-5608	50	11	ii	ii	NOUN
ejpam-5608	50	12	)	)	PUNCT
ejpam-5608	50	13	g(x	g(x	PROPN
ejpam-5608	50	14	,	,	PUNCT
ejpam-5608	50	15	x	x	NOUN
ejpam-5608	50	16	,	,	PUNCT
ejpam-5608	50	17	y	y	PROPN
ejpam-5608	50	18	)	)	PUNCT
ejpam-5608	50	19	>	>	X
ejpam-5608	50	20	0	0	PUNCT
ejpam-5608	51	1	for	for	ADP
ejpam-5608	51	2	x	x	SYM
ejpam-5608	51	3	̸=	̸=	PROPN
ejpam-5608	51	4	y	y	PROPN
ejpam-5608	51	5	(	(	PUNCT
ejpam-5608	51	6	iii	iii	NOUN
ejpam-5608	51	7	)	)	PUNCT
ejpam-5608	51	8	g(x	g(x	NOUN
ejpam-5608	51	9	,	,	PUNCT
ejpam-5608	51	10	x	x	NOUN
ejpam-5608	51	11	,	,	PUNCT
ejpam-5608	51	12	y	y	NOUN
ejpam-5608	51	13	)	)	PUNCT
ejpam-5608	51	14	≤	≤	NOUN
ejpam-5608	51	15	g(x	g(x	NOUN
ejpam-5608	51	16	,	,	PUNCT
ejpam-5608	51	17	y	y	PROPN
ejpam-5608	51	18	,	,	PUNCT
ejpam-5608	51	19	z	z	NOUN
ejpam-5608	51	20	)	)	PUNCT
ejpam-5608	51	21	,	,	PUNCT
ejpam-5608	51	22	for	for	ADP
ejpam-5608	51	23	z	z	PROPN
ejpam-5608	51	24	̸=	̸=	PROPN
ejpam-5608	51	25	y	y	PROPN
ejpam-5608	51	26	(	(	PUNCT
ejpam-5608	51	27	iv	iv	X
ejpam-5608	51	28	)	)	PUNCT
ejpam-5608	51	29	g(x	g(x	PROPN
ejpam-5608	51	30	,	,	PUNCT
ejpam-5608	51	31	y	y	PROPN
ejpam-5608	51	32	,	,	PUNCT
ejpam-5608	51	33	z	z	NOUN
ejpam-5608	51	34	)	)	PUNCT
ejpam-5608	51	35	=	=	SYM
ejpam-5608	51	36	g(x	g(x	NOUN
ejpam-5608	51	37	,	,	PUNCT
ejpam-5608	51	38	z	z	NOUN
ejpam-5608	51	39	,	,	PUNCT
ejpam-5608	51	40	y	y	NOUN
ejpam-5608	51	41	)	)	PUNCT
ejpam-5608	51	42	=	=	PUNCT
ejpam-5608	52	1	g(y	g(y	PROPN
ejpam-5608	52	2	,	,	PUNCT
ejpam-5608	52	3	z	z	NOUN
ejpam-5608	52	4	,	,	PUNCT
ejpam-5608	52	5	x	x	NOUN
ejpam-5608	52	6	)	)	PUNCT
ejpam-5608	52	7	=	=	SYM
ejpam-5608	53	1	g(y	g(y	NOUN
ejpam-5608	53	2	,	,	PUNCT
ejpam-5608	53	3	x	x	X
ejpam-5608	53	4	,	,	PUNCT
ejpam-5608	53	5	z	z	NOUN
ejpam-5608	53	6	)	)	PUNCT
ejpam-5608	53	7	=	=	SYM
ejpam-5608	54	1	g(z	g(z	PROPN
ejpam-5608	54	2	,	,	PUNCT
ejpam-5608	54	3	x	x	X
ejpam-5608	54	4	,	,	PUNCT
ejpam-5608	54	5	y	y	NOUN
ejpam-5608	54	6	)	)	PUNCT
ejpam-5608	54	7	=	=	SYM
ejpam-5608	55	1	g(z	g(z	PROPN
ejpam-5608	55	2	,	,	PUNCT
ejpam-5608	55	3	y	y	PROPN
ejpam-5608	55	4	,	,	PUNCT
ejpam-5608	55	5	x	x	NOUN
ejpam-5608	55	6	)	)	PUNCT
ejpam-5608	55	7	(	(	PUNCT
ejpam-5608	55	8	v	v	NOUN
ejpam-5608	55	9	)	)	PUNCT
ejpam-5608	55	10	g(x	g(x	PROPN
ejpam-5608	55	11	,	,	PUNCT
ejpam-5608	55	12	y	y	PROPN
ejpam-5608	55	13	,	,	PUNCT
ejpam-5608	55	14	z	z	NOUN
ejpam-5608	55	15	)	)	PUNCT
ejpam-5608	55	16	≤	≤	NOUN
ejpam-5608	55	17	g(x	g(x	NOUN
ejpam-5608	55	18	,	,	PUNCT
ejpam-5608	55	19	a	a	PRON
ejpam-5608	55	20	,	,	PUNCT
ejpam-5608	55	21	a	a	NOUN
ejpam-5608	55	22	)	)	PUNCT
ejpam-5608	56	1	+	+	PROPN
ejpam-5608	56	2	g(a	g(a	PROPN
ejpam-5608	56	3	,	,	PUNCT
ejpam-5608	56	4	y	y	PROPN
ejpam-5608	56	5	,	,	PUNCT
ejpam-5608	56	6	z	z	NOUN
ejpam-5608	56	7	)	)	PUNCT
ejpam-5608	56	8	for	for	ADP
ejpam-5608	56	9	any	any	DET
ejpam-5608	56	10	a	a	DET
ejpam-5608	56	11	∈	∈	NOUN
ejpam-5608	56	12	x	x	PUNCT
ejpam-5608	56	13	a	a	DET
ejpam-5608	56	14	set	set	NOUN
ejpam-5608	56	15	x	x	PUNCT
ejpam-5608	56	16	equipped	equip	VERB
ejpam-5608	56	17	with	with	ADP
ejpam-5608	56	18	the	the	DET
ejpam-5608	56	19	function	function	NOUN
ejpam-5608	56	20	g	g	PROPN
ejpam-5608	56	21	is	be	AUX
ejpam-5608	56	22	called	call	VERB
ejpam-5608	56	23	a	a	DET
ejpam-5608	56	24	g	g	NOUN
ejpam-5608	56	25	-	-	PUNCT
ejpam-5608	56	26	metric	metric	ADJ
ejpam-5608	56	27	space	space	NOUN
ejpam-5608	56	28	and	and	CCONJ
ejpam-5608	56	29	is	be	AUX
ejpam-5608	56	30	denoted	denote	VERB
ejpam-5608	56	31	by	by	ADP
ejpam-5608	56	32	(	(	PUNCT
ejpam-5608	56	33	x	x	NOUN
ejpam-5608	56	34	,	,	PUNCT
ejpam-5608	56	35	g	g	NOUN
ejpam-5608	56	36	)	)	PUNCT
ejpam-5608	56	37	.	.	PUNCT
ejpam-5608	57	1	definition	definition	NOUN
ejpam-5608	57	2	2	2	NUM
ejpam-5608	57	3	.	.	PUNCT
ejpam-5608	58	1	[	[	X
ejpam-5608	58	2	6	6	NUM
ejpam-5608	58	3	]	]	PUNCT
ejpam-5608	58	4	let	let	VERB
ejpam-5608	58	5	(	(	PUNCT
ejpam-5608	58	6	x	x	NOUN
ejpam-5608	58	7	,	,	PUNCT
ejpam-5608	58	8	g	g	NOUN
ejpam-5608	58	9	)	)	PUNCT
ejpam-5608	58	10	be	be	AUX
ejpam-5608	58	11	a	a	DET
ejpam-5608	58	12	g	g	NOUN
ejpam-5608	58	13	-	-	PUNCT
ejpam-5608	58	14	metric	metric	ADJ
ejpam-5608	58	15	space	space	NOUN
ejpam-5608	58	16	and	and	CCONJ
ejpam-5608	58	17	(	(	PUNCT
ejpam-5608	58	18	xn	xn	X
ejpam-5608	58	19	)	)	PUNCT
ejpam-5608	58	20	be	be	VERB
ejpam-5608	58	21	a	a	DET
ejpam-5608	58	22	sequence	sequence	NOUN
ejpam-5608	58	23	in	in	ADP
ejpam-5608	58	24	x.	x.	NOUN
ejpam-5608	58	25	the	the	DET
ejpam-5608	58	26	sequence	sequence	NOUN
ejpam-5608	58	27	(	(	PUNCT
ejpam-5608	58	28	xn	xn	X
ejpam-5608	58	29	)	)	PUNCT
ejpam-5608	58	30	is	be	AUX
ejpam-5608	58	31	said	say	VERB
ejpam-5608	58	32	to	to	PART
ejpam-5608	58	33	converge	converge	VERB
ejpam-5608	58	34	to	to	ADP
ejpam-5608	58	35	x	x	PUNCT
ejpam-5608	58	36	∈	∈	PROPN
ejpam-5608	58	37	x	x	INTJ
ejpam-5608	58	38	if	if	SCONJ
ejpam-5608	58	39	lim	lim	PROPN
ejpam-5608	58	40	n	n	CCONJ
ejpam-5608	58	41	,	,	PUNCT
ejpam-5608	58	42	m→+∞	m→+∞	PROPN
ejpam-5608	58	43	g(x	g(x	PROPN
ejpam-5608	58	44	,	,	PUNCT
ejpam-5608	58	45	xn	xn	PROPN
ejpam-5608	58	46	,	,	PUNCT
ejpam-5608	58	47	xm	xm	PROPN
ejpam-5608	58	48	)	)	PUNCT
ejpam-5608	58	49	=	=	SYM
ejpam-5608	58	50	0	0	NUM
ejpam-5608	58	51	means	mean	VERB
ejpam-5608	58	52	that	that	SCONJ
ejpam-5608	58	53	for	for	ADP
ejpam-5608	58	54	every	every	DET
ejpam-5608	58	55	ε	ε	PROPN
ejpam-5608	58	56	>	>	X
ejpam-5608	58	57	0	0	PUNCT
ejpam-5608	58	58	there	there	PRON
ejpam-5608	58	59	exists	exist	VERB
ejpam-5608	58	60	n0	n0	PROPN
ejpam-5608	58	61	∈	∈	PROPN
ejpam-5608	58	62	n	n	PRON
ejpam-5608	58	63	such	such	ADJ
ejpam-5608	58	64	that	that	SCONJ
ejpam-5608	58	65	g(x	g(x	NOUN
ejpam-5608	58	66	,	,	PUNCT
ejpam-5608	58	67	xn	xn	PROPN
ejpam-5608	58	68	,	,	PUNCT
ejpam-5608	58	69	xm	xm	PROPN
ejpam-5608	58	70	)	)	PUNCT
ejpam-5608	58	71	<	<	X
ejpam-5608	58	72	ε	ε	PROPN
ejpam-5608	58	73	for	for	ADP
ejpam-5608	58	74	all	all	DET
ejpam-5608	58	75	n	n	CCONJ
ejpam-5608	58	76	,	,	PUNCT
ejpam-5608	58	77	m	m	PROPN
ejpam-5608	58	78	≥	≥	NOUN
ejpam-5608	58	79	n0	n0	NUM
ejpam-5608	58	80	.	.	PUNCT
ejpam-5608	59	1	x	x	PUNCT
ejpam-5608	59	2	in	in	ADP
ejpam-5608	59	3	this	this	DET
ejpam-5608	59	4	case	case	NOUN
ejpam-5608	59	5	,	,	PUNCT
ejpam-5608	59	6	x	x	PRON
ejpam-5608	59	7	is	be	AUX
ejpam-5608	59	8	called	call	VERB
ejpam-5608	59	9	the	the	DET
ejpam-5608	59	10	limit	limit	NOUN
ejpam-5608	59	11	of	of	ADP
ejpam-5608	59	12	the	the	DET
ejpam-5608	59	13	sequence	sequence	NOUN
ejpam-5608	59	14	(	(	PUNCT
ejpam-5608	59	15	xn	xn	X
ejpam-5608	59	16	)	)	PUNCT
ejpam-5608	59	17	denoted	denote	VERB
ejpam-5608	59	18	by	by	ADP
ejpam-5608	59	19	xn	xn	PROPN
ejpam-5608	59	20	→	→	SYM
ejpam-5608	59	21	x	x	X
ejpam-5608	59	22	or	or	CCONJ
ejpam-5608	59	23	lim	lim	PROPN
ejpam-5608	59	24	n→+∞	n→+∞	VERB
ejpam-5608	59	25	xn	xn	PUNCT
ejpam-5608	60	1	=	=	PUNCT
ejpam-5608	60	2	x.	x.	NOUN
ejpam-5608	60	3	definition	definition	NOUN
ejpam-5608	60	4	3	3	NUM
ejpam-5608	60	5	.	.	PUNCT
ejpam-5608	61	1	[	[	X
ejpam-5608	61	2	6	6	NUM
ejpam-5608	61	3	]	]	PUNCT
ejpam-5608	61	4	let	let	VERB
ejpam-5608	61	5	(	(	PUNCT
ejpam-5608	61	6	x	x	NOUN
ejpam-5608	61	7	,	,	PUNCT
ejpam-5608	61	8	g	g	NOUN
ejpam-5608	61	9	)	)	PUNCT
ejpam-5608	61	10	be	be	AUX
ejpam-5608	61	11	a	a	DET
ejpam-5608	61	12	g	g	NOUN
ejpam-5608	61	13	-	-	PUNCT
ejpam-5608	61	14	metric	metric	ADJ
ejpam-5608	61	15	space	space	NOUN
ejpam-5608	61	16	and	and	CCONJ
ejpam-5608	61	17	(	(	PUNCT
ejpam-5608	61	18	xn	xn	X
ejpam-5608	61	19	)	)	PUNCT
ejpam-5608	61	20	be	be	VERB
ejpam-5608	61	21	a	a	DET
ejpam-5608	61	22	sequence	sequence	NOUN
ejpam-5608	61	23	in	in	ADP
ejpam-5608	61	24	x.	x.	NOUN
ejpam-5608	61	25	the	the	DET
ejpam-5608	61	26	sequence	sequence	NOUN
ejpam-5608	61	27	(	(	PUNCT
ejpam-5608	61	28	xn	xn	X
ejpam-5608	61	29	)	)	PUNCT
ejpam-5608	61	30	is	be	AUX
ejpam-5608	61	31	said	say	VERB
ejpam-5608	61	32	to	to	PART
ejpam-5608	61	33	be	be	AUX
ejpam-5608	61	34	a	a	DET
ejpam-5608	61	35	cauchy	cauchy	ADJ
ejpam-5608	61	36	sequence	sequence	NOUN
ejpam-5608	61	37	in	in	ADP
ejpam-5608	61	38	the	the	DET
ejpam-5608	61	39	g	g	NOUN
ejpam-5608	61	40	-	-	PUNCT
ejpam-5608	61	41	metric	metric	ADJ
ejpam-5608	61	42	space	space	NOUN
ejpam-5608	61	43	if	if	SCONJ
ejpam-5608	61	44	for	for	ADP
ejpam-5608	61	45	every	every	DET
ejpam-5608	61	46	ε	ε	PROPN
ejpam-5608	61	47	>	>	X
ejpam-5608	61	48	0	0	PROPN
ejpam-5608	61	49	,	,	PUNCT
ejpam-5608	61	50	there	there	PRON
ejpam-5608	61	51	exists	exist	VERB
ejpam-5608	61	52	n0	n0	PROPN
ejpam-5608	61	53	∈	∈	PROPN
ejpam-5608	61	54	n	n	PRON
ejpam-5608	61	55	such	such	ADJ
ejpam-5608	61	56	that	that	PRON
ejpam-5608	61	57	for	for	ADP
ejpam-5608	61	58	all	all	DET
ejpam-5608	61	59	k	k	PROPN
ejpam-5608	61	60	,	,	PUNCT
ejpam-5608	61	61	n	n	CCONJ
ejpam-5608	61	62	,	,	PUNCT
ejpam-5608	61	63	m	m	PROPN
ejpam-5608	61	64	≥	≥	NOUN
ejpam-5608	61	65	n0	n0	PROPN
ejpam-5608	61	66	,	,	PUNCT
ejpam-5608	61	67	g	g	PROPN
ejpam-5608	61	68	(	(	PUNCT
ejpam-5608	61	69	xk	xk	PROPN
ejpam-5608	61	70	,	,	PUNCT
ejpam-5608	61	71	xn	xn	PROPN
ejpam-5608	61	72	,	,	PUNCT
ejpam-5608	61	73	xm	xm	PROPN
ejpam-5608	61	74	)	)	PUNCT
ejpam-5608	61	75	<	<	X
ejpam-5608	61	76	ε	ε	PROPN
ejpam-5608	61	77	.	.	PUNCT
ejpam-5608	61	78	theorem	theorem	NOUN
ejpam-5608	61	79	1	1	NUM
ejpam-5608	61	80	.	.	PUNCT
ejpam-5608	62	1	[	[	X
ejpam-5608	62	2	6	6	NUM
ejpam-5608	62	3	]	]	PUNCT
ejpam-5608	62	4	let	let	VERB
ejpam-5608	62	5	(	(	PUNCT
ejpam-5608	62	6	xn	xn	X
ejpam-5608	62	7	)	)	PUNCT
ejpam-5608	62	8	be	be	VERB
ejpam-5608	62	9	a	a	DET
ejpam-5608	62	10	sequence	sequence	NOUN
ejpam-5608	62	11	in	in	ADP
ejpam-5608	62	12	the	the	DET
ejpam-5608	62	13	g	g	NOUN
ejpam-5608	62	14	-	-	PUNCT
ejpam-5608	62	15	metric	metric	ADJ
ejpam-5608	62	16	space	space	NOUN
ejpam-5608	62	17	(	(	PUNCT
ejpam-5608	62	18	x	x	NOUN
ejpam-5608	62	19	,	,	PUNCT
ejpam-5608	62	20	g	g	NOUN
ejpam-5608	62	21	)	)	PUNCT
ejpam-5608	62	22	.	.	PUNCT
ejpam-5608	63	1	if	if	SCONJ
ejpam-5608	63	2	the	the	DET
ejpam-5608	63	3	sequence	sequence	NOUN
ejpam-5608	63	4	(	(	PUNCT
ejpam-5608	63	5	xn	xn	X
ejpam-5608	63	6	)	)	PUNCT
ejpam-5608	63	7	converges	converge	VERB
ejpam-5608	63	8	to	to	ADP
ejpam-5608	63	9	x	x	SYM
ejpam-5608	63	10	∈	∈	PROPN
ejpam-5608	63	11	r	r	NOUN
ejpam-5608	63	12	,	,	PUNCT
ejpam-5608	63	13	then	then	ADV
ejpam-5608	63	14	(	(	PUNCT
ejpam-5608	63	15	xn	xn	X
ejpam-5608	63	16	)	)	PUNCT
ejpam-5608	63	17	is	be	AUX
ejpam-5608	63	18	a	a	DET
ejpam-5608	63	19	cauchy	cauchy	ADJ
ejpam-5608	63	20	sequence	sequence	NOUN
ejpam-5608	63	21	.	.	PUNCT
ejpam-5608	64	1	definition	definition	NOUN
ejpam-5608	64	2	4	4	NUM
ejpam-5608	64	3	.	.	PUNCT
ejpam-5608	65	1	[	[	X
ejpam-5608	65	2	1	1	X
ejpam-5608	65	3	]	]	X
ejpam-5608	65	4	let	let	VERB
ejpam-5608	65	5	(	(	PUNCT
ejpam-5608	65	6	xn	xn	X
ejpam-5608	65	7	)	)	PUNCT
ejpam-5608	65	8	be	be	VERB
ejpam-5608	65	9	a	a	DET
ejpam-5608	65	10	sequence	sequence	NOUN
ejpam-5608	65	11	in	in	ADP
ejpam-5608	65	12	the	the	DET
ejpam-5608	65	13	g	g	NOUN
ejpam-5608	65	14	-	-	PUNCT
ejpam-5608	65	15	metric	metric	ADJ
ejpam-5608	65	16	space	space	NOUN
ejpam-5608	65	17	(	(	PUNCT
ejpam-5608	65	18	x	x	NOUN
ejpam-5608	65	19	,	,	PUNCT
ejpam-5608	65	20	g	g	NOUN
ejpam-5608	65	21	)	)	PUNCT
ejpam-5608	65	22	.	.	PUNCT
ejpam-5608	66	1	the	the	DET
ejpam-5608	66	2	sequence	sequence	NOUN
ejpam-5608	66	3	(	(	PUNCT
ejpam-5608	66	4	xn	xn	X
ejpam-5608	66	5	)	)	PUNCT
ejpam-5608	66	6	is	be	AUX
ejpam-5608	66	7	said	say	VERB
ejpam-5608	66	8	to	to	PART
ejpam-5608	66	9	converge	converge	VERB
ejpam-5608	66	10	statistically	statistically	ADV
ejpam-5608	66	11	to	to	ADP
ejpam-5608	66	12	x	x	PROPN
ejpam-5608	66	13	in	in	ADP
ejpam-5608	66	14	the	the	DET
ejpam-5608	66	15	g	g	NOUN
ejpam-5608	66	16	-	-	PUNCT
ejpam-5608	66	17	metric	metric	ADJ
ejpam-5608	66	18	space	space	NOUN
ejpam-5608	66	19	if	if	SCONJ
ejpam-5608	66	20	,	,	PUNCT
ejpam-5608	66	21	for	for	ADP
ejpam-5608	66	22	every	every	DET
ejpam-5608	66	23	real	real	ADJ
ejpam-5608	66	24	number	number	NOUN
ejpam-5608	66	25	ε	ε	PROPN
ejpam-5608	66	26	>	>	X
ejpam-5608	66	27	0	0	PROPN
ejpam-5608	66	28	,	,	PUNCT
ejpam-5608	66	29	we	we	PRON
ejpam-5608	66	30	have	have	VERB
ejpam-5608	66	31	lim	lim	PROPN
ejpam-5608	66	32	n→+∞	n→+∞	PROPN
ejpam-5608	66	33	(	(	PUNCT
ejpam-5608	66	34	2	2	NUM
ejpam-5608	66	35	n2	n2	ADJ
ejpam-5608	66	36	|{(n1	|{(n1	PROPN
ejpam-5608	66	37	,	,	PUNCT
ejpam-5608	66	38	n2	n2	ADJ
ejpam-5608	66	39	)	)	PUNCT
ejpam-5608	66	40	∈	∈	PROPN
ejpam-5608	66	41	n2	n2	NOUN
ejpam-5608	66	42	:	:	PUNCT
ejpam-5608	66	43	n1	n1	ADJ
ejpam-5608	66	44	,	,	PUNCT
ejpam-5608	66	45	n2	n2	ADJ
ejpam-5608	66	46	≤	≤	NUM
ejpam-5608	66	47	n	n	CCONJ
ejpam-5608	66	48	,	,	PUNCT
ejpam-5608	66	49	g(x	g(x	NOUN
ejpam-5608	66	50	,	,	PUNCT
ejpam-5608	66	51	xn1	xn1	NUM
ejpam-5608	66	52	,	,	PUNCT
ejpam-5608	66	53	xn2	xn2	PROPN
ejpam-5608	66	54	)	)	PUNCT
ejpam-5608	66	55	≥	≥	NUM
ejpam-5608	66	56	ε}|	ε}|	NOUN
ejpam-5608	66	57	)	)	PUNCT
ejpam-5608	66	58	=	=	SYM
ejpam-5608	66	59	0	0	PUNCT
ejpam-5608	67	1	and	and	CCONJ
ejpam-5608	67	2	this	this	PRON
ejpam-5608	67	3	is	be	AUX
ejpam-5608	67	4	denoted	denote	VERB
ejpam-5608	67	5	as	as	ADP
ejpam-5608	67	6	gs−	gs−	NUM
ejpam-5608	67	7	lim(xn	lim(xn	NOUN
ejpam-5608	67	8	)	)	PUNCT
ejpam-5608	67	9	=	=	SYM
ejpam-5608	67	10	x	x	SYM
ejpam-5608	67	11	manuharawati	manuharawati	NOUN
ejpam-5608	67	12	,	,	PUNCT
ejpam-5608	67	13	m.jakfar	m.jakfar	ADV
ejpam-5608	67	14	,	,	PUNCT
ejpam-5608	67	15	a.	a.	PROPN
ejpam-5608	67	16	taufik	taufik	PROPN
ejpam-5608	67	17	hamzah	hamzah	PROPN
ejpam-5608	67	18	/	/	SYM
ejpam-5608	67	19	eur	eur	PROPN
ejpam-5608	67	20	.	.	PUNCT
ejpam-5608	68	1	j.	j.	PROPN
ejpam-5608	68	2	pure	pure	PROPN
ejpam-5608	68	3	appl	appl	PROPN
ejpam-5608	68	4	.	.	PROPN
ejpam-5608	68	5	math	math	PROPN
ejpam-5608	68	6	,	,	PUNCT
ejpam-5608	68	7	18	18	NUM
ejpam-5608	68	8	(	(	PUNCT
ejpam-5608	68	9	1	1	NUM
ejpam-5608	68	10	)	)	PUNCT
ejpam-5608	68	11	(	(	PUNCT
ejpam-5608	68	12	2025	2025	NUM
ejpam-5608	68	13	)	)	PUNCT
ejpam-5608	68	14	,	,	PUNCT
ejpam-5608	68	15	5608	5608	NUM
ejpam-5608	68	16	4	4	NUM
ejpam-5608	68	17	of	of	ADP
ejpam-5608	68	18	13	13	NUM
ejpam-5608	68	19	definition	definition	NOUN
ejpam-5608	68	20	5	5	NUM
ejpam-5608	68	21	.	.	PUNCT
ejpam-5608	69	1	[	[	X
ejpam-5608	69	2	22	22	NUM
ejpam-5608	69	3	]	]	PUNCT
ejpam-5608	69	4	let	let	AUX
ejpam-5608	69	5	(	(	PUNCT
ejpam-5608	69	6	x	x	NOUN
ejpam-5608	69	7	,	,	PUNCT
ejpam-5608	69	8	g	g	NOUN
ejpam-5608	69	9	)	)	PUNCT
ejpam-5608	69	10	be	be	AUX
ejpam-5608	69	11	a	a	DET
ejpam-5608	69	12	g	g	NOUN
ejpam-5608	69	13	-	-	PUNCT
ejpam-5608	69	14	metric	metric	ADJ
ejpam-5608	69	15	space	space	NOUN
ejpam-5608	69	16	and	and	CCONJ
ejpam-5608	69	17	(	(	PUNCT
ejpam-5608	69	18	xn	xn	X
ejpam-5608	69	19	)	)	PUNCT
ejpam-5608	69	20	a	a	DET
ejpam-5608	69	21	sequence	sequence	NOUN
ejpam-5608	69	22	in	in	ADP
ejpam-5608	69	23	x.	x.	NOUN
ejpam-5608	69	24	the	the	DET
ejpam-5608	69	25	sequence	sequence	NOUN
ejpam-5608	69	26	(	(	PUNCT
ejpam-5608	69	27	xn	xn	X
ejpam-5608	69	28	)	)	PUNCT
ejpam-5608	69	29	is	be	AUX
ejpam-5608	69	30	said	say	VERB
ejpam-5608	69	31	to	to	PART
ejpam-5608	69	32	be	be	AUX
ejpam-5608	69	33	a	a	DET
ejpam-5608	69	34	statistical	statistical	ADJ
ejpam-5608	69	35	cauchy	cauchy	ADJ
ejpam-5608	69	36	sequence	sequence	NOUN
ejpam-5608	69	37	in	in	ADP
ejpam-5608	69	38	the	the	DET
ejpam-5608	69	39	g	g	NOUN
ejpam-5608	69	40	-	-	PUNCT
ejpam-5608	69	41	metric	metric	ADJ
ejpam-5608	69	42	space	space	NOUN
ejpam-5608	69	43	if	if	SCONJ
ejpam-5608	69	44	,	,	PUNCT
ejpam-5608	69	45	for	for	ADP
ejpam-5608	69	46	every	every	DET
ejpam-5608	69	47	ε	ε	PROPN
ejpam-5608	69	48	>	>	X
ejpam-5608	69	49	0	0	PROPN
ejpam-5608	69	50	,	,	PUNCT
ejpam-5608	69	51	there	there	PRON
ejpam-5608	69	52	exists	exist	VERB
ejpam-5608	69	53	i	i	PRON
ejpam-5608	69	54	∈	∈	PROPN
ejpam-5608	70	1	n	n	PRON
ejpam-5608	70	2	such	such	ADJ
ejpam-5608	71	1	that	that	SCONJ
ejpam-5608	71	2	lim	lim	PROPN
ejpam-5608	71	3	n→+∞	n→+∞	PROPN
ejpam-5608	71	4	(	(	PUNCT
ejpam-5608	71	5	2	2	NUM
ejpam-5608	71	6	n2	n2	ADJ
ejpam-5608	71	7	|{(n1	|{(n1	PROPN
ejpam-5608	71	8	,	,	PUNCT
ejpam-5608	71	9	n2	n2	ADJ
ejpam-5608	71	10	)	)	PUNCT
ejpam-5608	71	11	∈	∈	PROPN
ejpam-5608	71	12	n2	n2	NOUN
ejpam-5608	71	13	:	:	PUNCT
ejpam-5608	71	14	n1	n1	ADJ
ejpam-5608	71	15	,	,	PUNCT
ejpam-5608	71	16	n2	n2	ADJ
ejpam-5608	71	17	≤	≤	PUNCT
ejpam-5608	71	18	n	n	CCONJ
ejpam-5608	71	19	,	,	PUNCT
ejpam-5608	71	20	g(xi	g(xi	PROPN
ejpam-5608	71	21	,	,	PUNCT
ejpam-5608	71	22	xn1	xn1	NUM
ejpam-5608	71	23	,	,	PUNCT
ejpam-5608	71	24	xn2	xn2	PROPN
ejpam-5608	71	25	)	)	PUNCT
ejpam-5608	71	26	≥	≥	NUM
ejpam-5608	71	27	ε}|	ε}|	NOUN
ejpam-5608	71	28	)	)	PUNCT
ejpam-5608	72	1	=	=	SYM
ejpam-5608	72	2	0	0	PUNCT
ejpam-5608	72	3	let	let	VERB
ejpam-5608	72	4	i2	i2	PROPN
ejpam-5608	72	5	⊂	⊂	PROPN
ejpam-5608	72	6	2n	2n	X
ejpam-5608	72	7	2	2	NUM
ejpam-5608	72	8	be	be	AUX
ejpam-5608	72	9	a	a	DET
ejpam-5608	72	10	nontrivial	nontrivial	ADJ
ejpam-5608	72	11	ideal	ideal	NOUN
ejpam-5608	72	12	on	on	ADP
ejpam-5608	72	13	n2	n2	ADJ
ejpam-5608	72	14	,	,	PUNCT
ejpam-5608	72	15	where	where	SCONJ
ejpam-5608	72	16	a	a	DET
ejpam-5608	72	17	∈	∈	PROPN
ejpam-5608	72	18	i2	i2	NOUN
ejpam-5608	72	19	and	and	CCONJ
ejpam-5608	72	20	a	a	DET
ejpam-5608	72	21	=	=	X
ejpam-5608	72	22	{	{	PUNCT
ejpam-5608	72	23	(	(	PUNCT
ejpam-5608	72	24	n1	n1	NOUN
ejpam-5608	72	25	,	,	PUNCT
ejpam-5608	72	26	n2	n2	NOUN
ejpam-5608	72	27	)	)	PUNCT
ejpam-5608	72	28	:	:	PUNCT
ejpam-5608	73	1	n1	n1	NOUN
ejpam-5608	73	2	,	,	PUNCT
ejpam-5608	73	3	n2	n2	PROPN
ejpam-5608	73	4	∈	∈	PROPN
ejpam-5608	73	5	n	n	CCONJ
ejpam-5608	73	6	)	)	PUNCT
ejpam-5608	73	7	}	}	PUNCT
ejpam-5608	73	8	.	.	PUNCT
ejpam-5608	74	1	definition	definition	NOUN
ejpam-5608	74	2	6	6	NUM
ejpam-5608	74	3	.	.	PUNCT
ejpam-5608	75	1	[	[	X
ejpam-5608	75	2	22	22	NUM
ejpam-5608	75	3	]	]	X
ejpam-5608	75	4	let	let	AUX
ejpam-5608	75	5	i2	i2	PROPN
ejpam-5608	75	6	be	be	AUX
ejpam-5608	75	7	an	an	DET
ejpam-5608	75	8	ideal	ideal	NOUN
ejpam-5608	75	9	.	.	PUNCT
ejpam-5608	76	1	let	let	AUX
ejpam-5608	76	2	(	(	PUNCT
ejpam-5608	76	3	xn	xn	X
ejpam-5608	76	4	)	)	PUNCT
ejpam-5608	76	5	be	be	VERB
ejpam-5608	76	6	a	a	DET
ejpam-5608	76	7	sequence	sequence	NOUN
ejpam-5608	76	8	in	in	ADP
ejpam-5608	76	9	the	the	DET
ejpam-5608	76	10	g	g	NOUN
ejpam-5608	76	11	-	-	PUNCT
ejpam-5608	76	12	metric	metric	ADJ
ejpam-5608	76	13	space	space	NOUN
ejpam-5608	76	14	(	(	PUNCT
ejpam-5608	76	15	x	x	NOUN
ejpam-5608	76	16	,	,	PUNCT
ejpam-5608	76	17	g	g	NOUN
ejpam-5608	76	18	)	)	PUNCT
ejpam-5608	76	19	.	.	PUNCT
ejpam-5608	77	1	the	the	DET
ejpam-5608	77	2	sequence	sequence	NOUN
ejpam-5608	77	3	(	(	PUNCT
ejpam-5608	77	4	xn	xn	X
ejpam-5608	77	5	)	)	PUNCT
ejpam-5608	77	6	is	be	AUX
ejpam-5608	77	7	said	say	VERB
ejpam-5608	77	8	to	to	PART
ejpam-5608	77	9	be	be	AUX
ejpam-5608	77	10	ideally	ideally	ADV
ejpam-5608	77	11	convergent	convergent	ADJ
ejpam-5608	77	12	to	to	PART
ejpam-5608	77	13	x	x	VERB
ejpam-5608	77	14	if	if	SCONJ
ejpam-5608	77	15	,	,	PUNCT
ejpam-5608	77	16	for	for	ADP
ejpam-5608	77	17	every	every	DET
ejpam-5608	77	18	real	real	ADJ
ejpam-5608	77	19	number	number	NOUN
ejpam-5608	77	20	ε	ε	PROPN
ejpam-5608	77	21	>	>	X
ejpam-5608	77	22	0	0	PROPN
ejpam-5608	77	23	,	,	PUNCT
ejpam-5608	77	24	the	the	DET
ejpam-5608	77	25	set	set	NOUN
ejpam-5608	77	26	{	{	PUNCT
ejpam-5608	77	27	(	(	PUNCT
ejpam-5608	77	28	n1	n1	NOUN
ejpam-5608	77	29	,	,	PUNCT
ejpam-5608	77	30	n2	n2	ADJ
ejpam-5608	77	31	)	)	PUNCT
ejpam-5608	77	32	∈	∈	PROPN
ejpam-5608	77	33	n2	n2	NOUN
ejpam-5608	77	34	:	:	PUNCT
ejpam-5608	77	35	g	g	NOUN
ejpam-5608	77	36	(	(	PUNCT
ejpam-5608	77	37	x	x	X
ejpam-5608	77	38	,	,	PUNCT
ejpam-5608	77	39	xn1	xn1	NUM
ejpam-5608	77	40	,	,	PUNCT
ejpam-5608	77	41	xn2	xn2	PROPN
ejpam-5608	77	42	)	)	PUNCT
ejpam-5608	77	43	≥	≥	NOUN
ejpam-5608	77	44	ε	ε	PROPN
ejpam-5608	77	45	}	}	PUNCT
ejpam-5608	77	46	∈	∈	PROPN
ejpam-5608	77	47	i2	i2	NOUN
ejpam-5608	77	48	.	.	PUNCT
ejpam-5608	78	1	and	and	CCONJ
ejpam-5608	78	2	this	this	PRON
ejpam-5608	78	3	is	be	AUX
ejpam-5608	78	4	denoted	denote	VERB
ejpam-5608	78	5	as	as	ADP
ejpam-5608	78	6	gi	gi	NOUN
ejpam-5608	78	7	−	−	PROPN
ejpam-5608	78	8	lim(xn	lim(xn	NOUN
ejpam-5608	78	9	)	)	PUNCT
ejpam-5608	78	10	=	=	SYM
ejpam-5608	79	1	x	x	SYM
ejpam-5608	79	2	definition	definition	NOUN
ejpam-5608	79	3	7	7	NUM
ejpam-5608	79	4	.	.	PUNCT
ejpam-5608	80	1	[	[	X
ejpam-5608	80	2	22	22	NUM
ejpam-5608	80	3	]	]	PUNCT
ejpam-5608	80	4	let	let	AUX
ejpam-5608	80	5	(	(	PUNCT
ejpam-5608	80	6	x	x	NOUN
ejpam-5608	80	7	,	,	PUNCT
ejpam-5608	80	8	g	g	NOUN
ejpam-5608	80	9	)	)	PUNCT
ejpam-5608	80	10	be	be	AUX
ejpam-5608	80	11	a	a	DET
ejpam-5608	80	12	g	g	NOUN
ejpam-5608	80	13	-	-	PUNCT
ejpam-5608	80	14	metric	metric	ADJ
ejpam-5608	80	15	space	space	NOUN
ejpam-5608	80	16	and	and	CCONJ
ejpam-5608	80	17	i2	i2	PROPN
ejpam-5608	80	18	an	an	DET
ejpam-5608	80	19	ideal	ideal	NOUN
ejpam-5608	80	20	.	.	PUNCT
ejpam-5608	81	1	let	let	AUX
ejpam-5608	81	2	(	(	PUNCT
ejpam-5608	81	3	xn	xn	X
ejpam-5608	81	4	)	)	PUNCT
ejpam-5608	81	5	be	be	VERB
ejpam-5608	81	6	a	a	DET
ejpam-5608	81	7	sequence	sequence	NOUN
ejpam-5608	81	8	in	in	ADP
ejpam-5608	81	9	x.	x.	NOUN
ejpam-5608	81	10	the	the	DET
ejpam-5608	81	11	sequence	sequence	NOUN
ejpam-5608	81	12	(	(	PUNCT
ejpam-5608	81	13	xn	xn	X
ejpam-5608	81	14	)	)	PUNCT
ejpam-5608	81	15	is	be	AUX
ejpam-5608	81	16	said	say	VERB
ejpam-5608	81	17	to	to	PART
ejpam-5608	81	18	be	be	AUX
ejpam-5608	81	19	an	an	DET
ejpam-5608	81	20	ideal	ideal	ADJ
ejpam-5608	81	21	cauchy	cauchy	ADJ
ejpam-5608	81	22	sequence	sequence	NOUN
ejpam-5608	81	23	in	in	ADP
ejpam-5608	81	24	the	the	DET
ejpam-5608	81	25	g	g	NOUN
ejpam-5608	81	26	-	-	PUNCT
ejpam-5608	81	27	metric	metric	ADJ
ejpam-5608	81	28	space	space	NOUN
ejpam-5608	81	29	if	if	SCONJ
ejpam-5608	81	30	,	,	PUNCT
ejpam-5608	81	31	for	for	ADP
ejpam-5608	81	32	every	every	DET
ejpam-5608	81	33	ε	ε	PROPN
ejpam-5608	81	34	>	>	X
ejpam-5608	81	35	0	0	PROPN
ejpam-5608	81	36	,	,	PUNCT
ejpam-5608	81	37	there	there	PRON
ejpam-5608	81	38	exists	exist	VERB
ejpam-5608	81	39	i	i	PRON
ejpam-5608	81	40	∈	∈	PROPN
ejpam-5608	81	41	n	n	PRON
ejpam-5608	81	42	such	such	ADJ
ejpam-5608	81	43	that	that	SCONJ
ejpam-5608	81	44	{	{	PUNCT
ejpam-5608	81	45	(	(	PUNCT
ejpam-5608	81	46	n1	n1	NOUN
ejpam-5608	81	47	,	,	PUNCT
ejpam-5608	81	48	n2	n2	ADJ
ejpam-5608	81	49	)	)	PUNCT
ejpam-5608	81	50	∈	∈	PROPN
ejpam-5608	81	51	n2	n2	NOUN
ejpam-5608	81	52	:	:	PUNCT
ejpam-5608	81	53	g(xi	g(xi	ADJ
ejpam-5608	81	54	,	,	PUNCT
ejpam-5608	81	55	xn1	xn1	NUM
ejpam-5608	81	56	,	,	PUNCT
ejpam-5608	81	57	xn2	xn2	PROPN
ejpam-5608	81	58	)	)	PUNCT
ejpam-5608	81	59	≥	≥	NOUN
ejpam-5608	81	60	ε	ε	PROPN
ejpam-5608	81	61	}	}	PUNCT
ejpam-5608	81	62	∈	∈	PROPN
ejpam-5608	81	63	i2	i2	NOUN
ejpam-5608	81	64	.	.	PUNCT
ejpam-5608	82	1	3	3	X
ejpam-5608	82	2	.	.	X
ejpam-5608	82	3	main	main	ADJ
ejpam-5608	82	4	results	result	NOUN
ejpam-5608	82	5	in	in	ADP
ejpam-5608	82	6	this	this	DET
ejpam-5608	82	7	section	section	NOUN
ejpam-5608	82	8	,	,	PUNCT
ejpam-5608	82	9	we	we	PRON
ejpam-5608	82	10	discuss	discuss	VERB
ejpam-5608	82	11	the	the	DET
ejpam-5608	82	12	relationship	relationship	NOUN
ejpam-5608	82	13	between	between	ADP
ejpam-5608	82	14	standard	standard	ADJ
ejpam-5608	82	15	convergence	convergence	NOUN
ejpam-5608	82	16	,	,	PUNCT
ejpam-5608	82	17	statistical	statistical	ADJ
ejpam-5608	82	18	convergence	convergence	NOUN
ejpam-5608	82	19	,	,	PUNCT
ejpam-5608	82	20	and	and	CCONJ
ejpam-5608	82	21	ideal	ideal	ADJ
ejpam-5608	82	22	convergence	convergence	NOUN
ejpam-5608	82	23	in	in	ADP
ejpam-5608	82	24	the	the	DET
ejpam-5608	82	25	g	g	NOUN
ejpam-5608	82	26	-	-	PUNCT
ejpam-5608	82	27	metric	metric	ADJ
ejpam-5608	82	28	space	space	NOUN
ejpam-5608	82	29	(	(	PUNCT
ejpam-5608	82	30	r	r	NOUN
ejpam-5608	82	31	,	,	PUNCT
ejpam-5608	82	32	g	g	NOUN
ejpam-5608	82	33	)	)	PUNCT
ejpam-5608	82	34	.	.	PUNCT
ejpam-5608	83	1	theorem	theorem	NOUN
ejpam-5608	83	2	2	2	NUM
ejpam-5608	83	3	.	.	PUNCT
ejpam-5608	84	1	[	[	X
ejpam-5608	84	2	1	1	X
ejpam-5608	84	3	]	]	X
ejpam-5608	84	4	if	if	SCONJ
ejpam-5608	84	5	a	a	DET
ejpam-5608	84	6	sequence	sequence	NOUN
ejpam-5608	84	7	converges	converge	VERB
ejpam-5608	84	8	to	to	ADP
ejpam-5608	84	9	x	x	PUNCT
ejpam-5608	84	10	in	in	ADP
ejpam-5608	84	11	a	a	DET
ejpam-5608	84	12	g	g	NOUN
ejpam-5608	84	13	-	-	PUNCT
ejpam-5608	84	14	metric	metric	ADJ
ejpam-5608	84	15	space	space	NOUN
ejpam-5608	84	16	,	,	PUNCT
ejpam-5608	84	17	then	then	ADV
ejpam-5608	84	18	the	the	DET
ejpam-5608	84	19	sequence	sequence	NOUN
ejpam-5608	84	20	also	also	ADV
ejpam-5608	84	21	statistically	statistically	ADV
ejpam-5608	84	22	converges	converge	VERB
ejpam-5608	84	23	to	to	ADP
ejpam-5608	84	24	x	x	PUNCT
ejpam-5608	84	25	in	in	ADP
ejpam-5608	84	26	the	the	DET
ejpam-5608	84	27	g	g	NOUN
ejpam-5608	84	28	-	-	PUNCT
ejpam-5608	84	29	metric	metric	ADJ
ejpam-5608	84	30	space	space	NOUN
ejpam-5608	84	31	.	.	PUNCT
ejpam-5608	85	1	proof	proof	NOUN
ejpam-5608	85	2	.	.	PUNCT
ejpam-5608	86	1	let	let	AUX
ejpam-5608	86	2	(	(	PUNCT
ejpam-5608	86	3	xn	xn	X
ejpam-5608	86	4	)	)	PUNCT
ejpam-5608	86	5	be	be	VERB
ejpam-5608	86	6	a	a	DET
ejpam-5608	86	7	sequence	sequence	NOUN
ejpam-5608	86	8	that	that	PRON
ejpam-5608	86	9	converges	converge	VERB
ejpam-5608	86	10	to	to	ADP
ejpam-5608	86	11	x	x	PRON
ejpam-5608	86	12	in	in	ADP
ejpam-5608	86	13	a	a	DET
ejpam-5608	86	14	g	g	NOUN
ejpam-5608	86	15	-	-	PUNCT
ejpam-5608	86	16	metric	metric	ADJ
ejpam-5608	86	17	space	space	NOUN
ejpam-5608	86	18	.	.	PUNCT
ejpam-5608	87	1	this	this	PRON
ejpam-5608	87	2	means	mean	VERB
ejpam-5608	87	3	that	that	SCONJ
ejpam-5608	87	4	for	for	ADP
ejpam-5608	87	5	every	every	DET
ejpam-5608	87	6	real	real	ADJ
ejpam-5608	87	7	number	number	NOUN
ejpam-5608	87	8	ε	ε	PROPN
ejpam-5608	87	9	>	>	X
ejpam-5608	87	10	0	0	PROPN
ejpam-5608	87	11	,	,	PUNCT
ejpam-5608	87	12	there	there	PRON
ejpam-5608	87	13	exists	exist	VERB
ejpam-5608	87	14	an	an	DET
ejpam-5608	87	15	index	index	NOUN
ejpam-5608	87	16	j	j	PROPN
ejpam-5608	87	17	∈	∈	PROPN
ejpam-5608	87	18	n	n	PRON
ejpam-5608	87	19	such	such	ADJ
ejpam-5608	87	20	that	that	PRON
ejpam-5608	87	21	for	for	ADP
ejpam-5608	87	22	every	every	DET
ejpam-5608	87	23	n	n	CCONJ
ejpam-5608	87	24	,	,	PUNCT
ejpam-5608	87	25	m	m	PROPN
ejpam-5608	87	26	≥	≥	NOUN
ejpam-5608	87	27	j	j	NOUN
ejpam-5608	87	28	,	,	PUNCT
ejpam-5608	87	29	we	we	PRON
ejpam-5608	87	30	have	have	VERB
ejpam-5608	87	31	g(x	g(x	NOUN
ejpam-5608	87	32	,	,	PUNCT
ejpam-5608	87	33	xn	xn	PROPN
ejpam-5608	87	34	,	,	PUNCT
ejpam-5608	87	35	xm	xm	PROPN
ejpam-5608	87	36	)	)	PUNCT
ejpam-5608	87	37	<	<	X
ejpam-5608	88	1	ε	ε	PROPN
ejpam-5608	88	2	.	.	PUNCT
ejpam-5608	89	1	if	if	SCONJ
ejpam-5608	89	2	we	we	PRON
ejpam-5608	89	3	form	form	VERB
ejpam-5608	89	4	a	a	DET
ejpam-5608	89	5	set	set	NOUN
ejpam-5608	89	6	,	,	PUNCT
ejpam-5608	89	7	it	it	PRON
ejpam-5608	89	8	will	will	AUX
ejpam-5608	89	9	take	take	VERB
ejpam-5608	89	10	the	the	DET
ejpam-5608	89	11	following	follow	VERB
ejpam-5608	89	12	form	form	NOUN
ejpam-5608	89	13	:	:	PUNCT
ejpam-5608	89	14	a(j	a(j	PROPN
ejpam-5608	89	15	)	)	PUNCT
ejpam-5608	89	16	=	=	PRON
ejpam-5608	89	17	{	{	PUNCT
ejpam-5608	89	18	(	(	PUNCT
ejpam-5608	89	19	n	n	CCONJ
ejpam-5608	89	20	,	,	PUNCT
ejpam-5608	89	21	m	m	NOUN
ejpam-5608	89	22	)	)	PUNCT
ejpam-5608	89	23	∈	∈	PROPN
ejpam-5608	89	24	n2	n2	NOUN
ejpam-5608	89	25	:	:	PUNCT
ejpam-5608	89	26	n	n	CCONJ
ejpam-5608	89	27	,	,	PUNCT
ejpam-5608	89	28	m	m	PROPN
ejpam-5608	89	29	≥	≥	PROPN
ejpam-5608	89	30	j	j	PROPN
ejpam-5608	89	31	,	,	PUNCT
ejpam-5608	89	32	g(x	g(x	PROPN
ejpam-5608	89	33	,	,	PUNCT
ejpam-5608	89	34	xn	xn	PROPN
ejpam-5608	89	35	,	,	PUNCT
ejpam-5608	89	36	xm	xm	PROPN
ejpam-5608	89	37	)	)	PUNCT
ejpam-5608	89	38	<	<	X
ejpam-5608	89	39	ε	ε	PROPN
ejpam-5608	89	40	}	}	PUNCT
ejpam-5608	89	41	it	it	PRON
ejpam-5608	89	42	is	be	AUX
ejpam-5608	89	43	clear	clear	ADJ
ejpam-5608	89	44	that	that	SCONJ
ejpam-5608	89	45	because	because	SCONJ
ejpam-5608	89	46	there	there	PRON
ejpam-5608	89	47	exists	exist	VERB
ejpam-5608	89	48	j	j	PROPN
ejpam-5608	89	49	∈	∈	PROPN
ejpam-5608	89	50	n	n	PRON
ejpam-5608	89	51	such	such	ADJ
ejpam-5608	89	52	that	that	PRON
ejpam-5608	89	53	for	for	SCONJ
ejpam-5608	89	54	all	all	DET
ejpam-5608	89	55	n	n	CCONJ
ejpam-5608	89	56	,	,	PUNCT
ejpam-5608	89	57	m	m	VERB
ejpam-5608	89	58	≥	≥	NOUN
ejpam-5608	89	59	j	j	NOUN
ejpam-5608	89	60	then	then	ADV
ejpam-5608	89	61	g(x	g(x	PROPN
ejpam-5608	89	62	,	,	PUNCT
ejpam-5608	89	63	xn	xn	PROPN
ejpam-5608	89	64	,	,	PUNCT
ejpam-5608	89	65	xm	xm	PROPN
ejpam-5608	89	66	)	)	PUNCT
ejpam-5608	89	67	<	<	X
ejpam-5608	89	68	ε	ε	PROPN
ejpam-5608	89	69	.	.	PUNCT
ejpam-5608	90	1	thus	thus	ADV
ejpam-5608	90	2	,	,	PUNCT
ejpam-5608	90	3	|{n	|{n	NOUN
ejpam-5608	90	4	:	:	PUNCT
ejpam-5608	90	5	(	(	PUNCT
ejpam-5608	90	6	n	n	X
ejpam-5608	90	7	,	,	PUNCT
ejpam-5608	90	8	m	m	NOUN
ejpam-5608	90	9	)	)	PUNCT
ejpam-5608	90	10	∈	∈	PROPN
ejpam-5608	90	11	n2	n2	NOUN
ejpam-5608	90	12	,	,	PUNCT
ejpam-5608	90	13	g(x	g(x	PROPN
ejpam-5608	90	14	,	,	PUNCT
ejpam-5608	90	15	xn	xn	PROPN
ejpam-5608	90	16	,	,	PUNCT
ejpam-5608	90	17	xm	xm	PROPN
ejpam-5608	90	18	)	)	PUNCT
ejpam-5608	90	19	≥	≥	PROPN
ejpam-5608	90	20	ε}|or|{m	ε}|or|{m	NOUN
ejpam-5608	90	21	:	:	PUNCT
ejpam-5608	90	22	(	(	PUNCT
ejpam-5608	90	23	n	n	X
ejpam-5608	90	24	,	,	PUNCT
ejpam-5608	90	25	m	m	NOUN
ejpam-5608	90	26	)	)	PUNCT
ejpam-5608	90	27	∈	∈	PROPN
ejpam-5608	90	28	n2	n2	NOUN
ejpam-5608	90	29	,	,	PUNCT
ejpam-5608	90	30	g	g	PROPN
ejpam-5608	90	31	(	(	PUNCT
ejpam-5608	90	32	x	x	X
ejpam-5608	90	33	,	,	PUNCT
ejpam-5608	90	34	xn	xn	PROPN
ejpam-5608	90	35	,	,	PUNCT
ejpam-5608	90	36	xm	xm	PROPN
ejpam-5608	90	37	)	)	PUNCT
ejpam-5608	90	38	≥	≥	NUM
ejpam-5608	90	39	ε}|	ε}|	NOUN
ejpam-5608	90	40	is	be	AUX
ejpam-5608	90	41	at	at	ADP
ejpam-5608	90	42	most	most	ADJ
ejpam-5608	90	43	j	j	NOUN
ejpam-5608	90	44	−	−	PROPN
ejpam-5608	90	45	1	1	NUM
ejpam-5608	90	46	,	,	PUNCT
ejpam-5608	90	47	so	so	ADV
ejpam-5608	90	48	:	:	PUNCT
ejpam-5608	90	49	lim	lim	PROPN
ejpam-5608	90	50	n→+∞	n→+∞	PROPN
ejpam-5608	90	51	(	(	PUNCT
ejpam-5608	90	52	2	2	NUM
ejpam-5608	90	53	n2	n2	PROPN
ejpam-5608	90	54	|{(n	|{(n	PROPN
ejpam-5608	90	55	,	,	PUNCT
ejpam-5608	90	56	m	m	NOUN
ejpam-5608	90	57	)	)	PUNCT
ejpam-5608	90	58	∈	∈	PROPN
ejpam-5608	90	59	n2	n2	NOUN
ejpam-5608	90	60	:	:	PUNCT
ejpam-5608	90	61	n	n	CCONJ
ejpam-5608	90	62	,	,	PUNCT
ejpam-5608	90	63	m	m	PROPN
ejpam-5608	90	64	≥	≥	PROPN
ejpam-5608	90	65	j	j	PROPN
ejpam-5608	90	66	,	,	PUNCT
ejpam-5608	90	67	g(x	g(x	PROPN
ejpam-5608	90	68	,	,	PUNCT
ejpam-5608	90	69	xn	xn	PROPN
ejpam-5608	90	70	,	,	PUNCT
ejpam-5608	90	71	xm	xm	PROPN
ejpam-5608	90	72	)	)	PUNCT
ejpam-5608	90	73	<	<	X
ejpam-5608	90	74	ε}|	ε}|	NOUN
ejpam-5608	90	75	)	)	PUNCT
ejpam-5608	91	1	=	=	VERB
ejpam-5608	91	2	lim	lim	PROPN
ejpam-5608	91	3	n→+∞	n→+∞	PROPN
ejpam-5608	91	4	(	(	PUNCT
ejpam-5608	91	5	2(j	2(j	NUM
ejpam-5608	91	6	−	−	PROPN
ejpam-5608	91	7	1)n	1)n	X
ejpam-5608	91	8	n2	n2	NOUN
ejpam-5608	91	9	)	)	PUNCT
ejpam-5608	92	1	=	=	SYM
ejpam-5608	92	2	lim	lim	PROPN
ejpam-5608	92	3	n→+∞	n→+∞	VERB
ejpam-5608	92	4	2(j	2(j	NUM
ejpam-5608	92	5	−	−	NOUN
ejpam-5608	92	6	1	1	NUM
ejpam-5608	92	7	)	)	PUNCT
ejpam-5608	92	8	n	n	CCONJ
ejpam-5608	92	9	)	)	PUNCT
ejpam-5608	92	10	=	=	SYM
ejpam-5608	92	11	0	0	PUNCT
ejpam-5608	93	1	thus	thus	ADV
ejpam-5608	93	2	,	,	PUNCT
ejpam-5608	93	3	it	it	PRON
ejpam-5608	93	4	is	be	AUX
ejpam-5608	93	5	proven	prove	VERB
ejpam-5608	93	6	that	that	SCONJ
ejpam-5608	93	7	the	the	DET
ejpam-5608	93	8	sequence	sequence	NOUN
ejpam-5608	93	9	(	(	PUNCT
ejpam-5608	93	10	xn	xn	X
ejpam-5608	93	11	)	)	PUNCT
ejpam-5608	93	12	statistically	statistically	ADV
ejpam-5608	93	13	converges	converge	VERB
ejpam-5608	93	14	to	to	ADP
ejpam-5608	93	15	x	x	PUNCT
ejpam-5608	93	16	in	in	ADP
ejpam-5608	93	17	the	the	DET
ejpam-5608	93	18	g	g	NOUN
ejpam-5608	93	19	-	-	PUNCT
ejpam-5608	93	20	metric	metric	ADJ
ejpam-5608	93	21	space	space	NOUN
ejpam-5608	93	22	.	.	PUNCT
ejpam-5608	94	1	manuharawati	manuharawati	NOUN
ejpam-5608	94	2	,	,	PUNCT
ejpam-5608	94	3	m.jakfar	m.jakfar	ADV
ejpam-5608	94	4	,	,	PUNCT
ejpam-5608	94	5	a.	a.	PROPN
ejpam-5608	94	6	taufik	taufik	PROPN
ejpam-5608	94	7	hamzah	hamzah	PROPN
ejpam-5608	94	8	/	/	SYM
ejpam-5608	94	9	eur	eur	PROPN
ejpam-5608	94	10	.	.	PUNCT
ejpam-5608	95	1	j.	j.	PROPN
ejpam-5608	95	2	pure	pure	PROPN
ejpam-5608	95	3	appl	appl	PROPN
ejpam-5608	95	4	.	.	PROPN
ejpam-5608	95	5	math	math	PROPN
ejpam-5608	95	6	,	,	PUNCT
ejpam-5608	95	7	18	18	NUM
ejpam-5608	95	8	(	(	PUNCT
ejpam-5608	95	9	1	1	NUM
ejpam-5608	95	10	)	)	PUNCT
ejpam-5608	95	11	(	(	PUNCT
ejpam-5608	95	12	2025	2025	NUM
ejpam-5608	95	13	)	)	PUNCT
ejpam-5608	95	14	,	,	PUNCT
ejpam-5608	95	15	5608	5608	NUM
ejpam-5608	95	16	5	5	NUM
ejpam-5608	95	17	of	of	ADP
ejpam-5608	95	18	13	13	NUM
ejpam-5608	95	19	example	example	NOUN
ejpam-5608	95	20	1	1	NUM
ejpam-5608	95	21	.	.	X
ejpam-5608	95	22	consider	consider	VERB
ejpam-5608	95	23	the	the	DET
ejpam-5608	95	24	g	g	NOUN
ejpam-5608	95	25	-	-	PUNCT
ejpam-5608	95	26	metric	metric	ADJ
ejpam-5608	95	27	space	space	NOUN
ejpam-5608	95	28	(	(	PUNCT
ejpam-5608	95	29	r	r	NOUN
ejpam-5608	95	30	,	,	PUNCT
ejpam-5608	95	31	g	g	NOUN
ejpam-5608	95	32	)	)	PUNCT
ejpam-5608	95	33	,	,	PUNCT
ejpam-5608	95	34	where	where	SCONJ
ejpam-5608	95	35	for	for	ADP
ejpam-5608	95	36	all	all	DET
ejpam-5608	95	37	x	x	NOUN
ejpam-5608	95	38	,	,	PUNCT
ejpam-5608	95	39	y	y	PROPN
ejpam-5608	95	40	,	,	PUNCT
ejpam-5608	95	41	z	z	NOUN
ejpam-5608	95	42	∈	∈	PROPN
ejpam-5608	95	43	r	r	NOUN
ejpam-5608	95	44	,	,	PUNCT
ejpam-5608	95	45	the	the	DET
ejpam-5608	95	46	g	g	NOUN
ejpam-5608	95	47	-	-	PUNCT
ejpam-5608	95	48	metric	metric	ADJ
ejpam-5608	95	49	is	be	AUX
ejpam-5608	95	50	defined	define	VERB
ejpam-5608	95	51	as	as	ADP
ejpam-5608	95	52	:	:	PUNCT
ejpam-5608	95	53	g(x	g(x	PROPN
ejpam-5608	95	54	,	,	PUNCT
ejpam-5608	95	55	y	y	PROPN
ejpam-5608	95	56	,	,	PUNCT
ejpam-5608	95	57	z	z	NOUN
ejpam-5608	95	58	)	)	PUNCT
ejpam-5608	96	1	=	=	SYM
ejpam-5608	96	2	max{|x−	max{|x−	PROPN
ejpam-5608	96	3	y|+	y|+	PROPN
ejpam-5608	96	4	|x−	|x−	PROPN
ejpam-5608	96	5	z|+	z|+	NOUN
ejpam-5608	96	6	|y	|y	NOUN
ejpam-5608	96	7	−	−	PROPN
ejpam-5608	96	8	z|	z|	PROPN
ejpam-5608	96	9	}	}	PUNCT
ejpam-5608	96	10	.	.	PUNCT
ejpam-5608	97	1	the	the	DET
ejpam-5608	97	2	sequence	sequence	NOUN
ejpam-5608	97	3	(	(	PUNCT
ejpam-5608	97	4	1	1	NUM
ejpam-5608	97	5	n+1	n+1	DET
ejpam-5608	97	6	)	)	PUNCT
ejpam-5608	97	7	is	be	AUX
ejpam-5608	97	8	statistically	statistically	ADV
ejpam-5608	97	9	convergent	convergent	ADJ
ejpam-5608	97	10	to	to	ADP
ejpam-5608	97	11	0	0	NUM
ejpam-5608	97	12	in	in	ADP
ejpam-5608	97	13	the	the	DET
ejpam-5608	97	14	g	g	NOUN
ejpam-5608	97	15	-	-	PUNCT
ejpam-5608	97	16	metric	metric	ADJ
ejpam-5608	97	17	space	space	NOUN
ejpam-5608	97	18	.	.	PUNCT
ejpam-5608	98	1	we	we	PRON
ejpam-5608	98	2	can	can	AUX
ejpam-5608	98	3	investigate	investigate	VERB
ejpam-5608	98	4	whether	whether	SCONJ
ejpam-5608	98	5	the	the	DET
ejpam-5608	98	6	sequence	sequence	NOUN
ejpam-5608	98	7	(	(	PUNCT
ejpam-5608	98	8	1	1	NUM
ejpam-5608	98	9	n+1	n+1	PRON
ejpam-5608	98	10	)	)	PUNCT
ejpam-5608	98	11	also	also	ADV
ejpam-5608	98	12	converges	converge	VERB
ejpam-5608	98	13	to	to	ADP
ejpam-5608	98	14	0	0	NUM
ejpam-5608	98	15	in	in	ADP
ejpam-5608	98	16	the	the	DET
ejpam-5608	98	17	g	g	NOUN
ejpam-5608	98	18	-	-	PUNCT
ejpam-5608	98	19	metric	metric	ADJ
ejpam-5608	98	20	space	space	NOUN
ejpam-5608	98	21	.	.	PUNCT
ejpam-5608	99	1	according	accord	VERB
ejpam-5608	99	2	to	to	ADP
ejpam-5608	99	3	theorem	theorem	ADJ
ejpam-5608	99	4	2	2	NUM
ejpam-5608	99	5	,	,	PUNCT
ejpam-5608	99	6	the	the	DET
ejpam-5608	99	7	sequence	sequence	NOUN
ejpam-5608	99	8	(	(	PUNCT
ejpam-5608	99	9	1	1	NUM
ejpam-5608	99	10	n+1	n+1	PRON
ejpam-5608	99	11	)	)	PUNCT
ejpam-5608	99	12	is	be	AUX
ejpam-5608	99	13	statistically	statistically	ADV
ejpam-5608	99	14	convergent	convergent	ADJ
ejpam-5608	99	15	to	to	ADP
ejpam-5608	99	16	0	0	NUM
ejpam-5608	99	17	in	in	ADP
ejpam-5608	99	18	the	the	DET
ejpam-5608	99	19	g	g	NOUN
ejpam-5608	99	20	-	-	PUNCT
ejpam-5608	99	21	metric	metric	ADJ
ejpam-5608	99	22	space	space	NOUN
ejpam-5608	99	23	.	.	PUNCT
ejpam-5608	100	1	the	the	DET
ejpam-5608	100	2	proof	proof	NOUN
ejpam-5608	100	3	is	be	AUX
ejpam-5608	100	4	given	give	VERB
ejpam-5608	100	5	as	as	SCONJ
ejpam-5608	100	6	follows	follow	VERB
ejpam-5608	100	7	:	:	PUNCT
ejpam-5608	100	8	g(x	g(x	NOUN
ejpam-5608	100	9	,	,	PUNCT
ejpam-5608	100	10	xn	xn	PROPN
ejpam-5608	100	11	,	,	PUNCT
ejpam-5608	100	12	xm	xm	PROPN
ejpam-5608	100	13	)	)	PUNCT
ejpam-5608	101	1	=	=	PUNCT
ejpam-5608	101	2	max{|x−	max{|x−	PROPN
ejpam-5608	101	3	xn|	xn|	PROPN
ejpam-5608	101	4	,	,	PUNCT
ejpam-5608	101	5	|x−	|x−	PROPN
ejpam-5608	101	6	xm|	xm|	NOUN
ejpam-5608	101	7	,	,	PUNCT
ejpam-5608	101	8	|xn	|xn	X
ejpam-5608	101	9	−	−	PUNCT
ejpam-5608	101	10	xm|	xm|	NUM
ejpam-5608	101	11	}	}	PUNCT
ejpam-5608	101	12	=	=	SYM
ejpam-5608	101	13	max	max	X
ejpam-5608	101	14	{	{	PUNCT
ejpam-5608	101	15	∣∣∣∣0−	∣∣∣∣0−	NOUN
ejpam-5608	101	16	1	1	NUM
ejpam-5608	101	17	n+	n+	SYM
ejpam-5608	101	18	1	1	NUM
ejpam-5608	101	19	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5608	101	20	,	,	PUNCT
ejpam-5608	101	21	∣∣∣∣0−	∣∣∣∣0−	ADJ
ejpam-5608	101	22	1	1	NUM
ejpam-5608	101	23	m+	m+	NUM
ejpam-5608	101	24	1	1	NUM
ejpam-5608	101	25	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5608	101	26	,	,	PUNCT
ejpam-5608	101	27	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5608	101	28	1	1	NUM
ejpam-5608	101	29	n+	n+	ADP
ejpam-5608	101	30	1	1	NUM
ejpam-5608	101	31	−	−	NUM
ejpam-5608	101	32	1	1	NUM
ejpam-5608	101	33	m+	m+	NUM
ejpam-5608	101	34	1	1	NUM
ejpam-5608	101	35	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5608	101	36	}	}	PUNCT
ejpam-5608	101	37	≥	≥	NOUN
ejpam-5608	101	38	max	max	PROPN
ejpam-5608	101	39	{	{	PUNCT
ejpam-5608	101	40	1	1	NUM
ejpam-5608	101	41	n+	n+	NUM
ejpam-5608	101	42	1	1	NUM
ejpam-5608	101	43	,	,	PUNCT
ejpam-5608	101	44	1	1	NUM
ejpam-5608	101	45	m+	m+	NUM
ejpam-5608	101	46	1	1	NUM
ejpam-5608	101	47	,	,	PUNCT
ejpam-5608	101	48	1	1	NUM
ejpam-5608	101	49	n+	n+	SYM
ejpam-5608	101	50	1	1	NUM
ejpam-5608	101	51	−	−	NUM
ejpam-5608	101	52	1	1	NUM
ejpam-5608	101	53	m+	m+	NUM
ejpam-5608	101	54	1	1	NUM
ejpam-5608	101	55	}	}	PUNCT
ejpam-5608	101	56	≥	≥	NOUN
ejpam-5608	101	57	max	max	PROPN
ejpam-5608	101	58	{	{	PUNCT
ejpam-5608	101	59	1	1	NUM
ejpam-5608	101	60	n+	n+	NUM
ejpam-5608	101	61	1	1	NUM
ejpam-5608	101	62	,	,	PUNCT
ejpam-5608	101	63	1	1	NUM
ejpam-5608	101	64	m+	m+	NUM
ejpam-5608	101	65	1	1	NUM
ejpam-5608	101	66	}	}	PUNCT
ejpam-5608	101	67	let	let	VERB
ejpam-5608	101	68	k	k	PROPN
ejpam-5608	101	69	be	be	AUX
ejpam-5608	101	70	the	the	DET
ejpam-5608	101	71	largest	large	ADJ
ejpam-5608	101	72	integer	integer	NOUN
ejpam-5608	101	73	less	less	ADJ
ejpam-5608	101	74	than	than	ADP
ejpam-5608	101	75	or	or	CCONJ
ejpam-5608	101	76	equal	equal	ADJ
ejpam-5608	101	77	to	to	ADP
ejpam-5608	101	78	1	1	NUM
ejpam-5608	101	79	ε−1	ε−1	PROPN
ejpam-5608	101	80	,	,	PUNCT
ejpam-5608	101	81	for	for	ADP
ejpam-5608	101	82	any	any	DET
ejpam-5608	101	83	ε	ε	PROPN
ejpam-5608	101	84	>	>	X
ejpam-5608	101	85	0	0	PROPN
ejpam-5608	101	86	,	,	PUNCT
ejpam-5608	101	87	ε	ε	PROPN
ejpam-5608	101	88	∈	∈	PROPN
ejpam-5608	101	89	r.	r.	PROPN
ejpam-5608	101	90	then	then	ADV
ejpam-5608	101	91	:	:	PUNCT
ejpam-5608	101	92	lim	lim	PROPN
ejpam-5608	101	93	n→+∞	n→+∞	PROPN
ejpam-5608	101	94	(	(	PUNCT
ejpam-5608	101	95	2	2	NUM
ejpam-5608	101	96	n2	n2	ADJ
ejpam-5608	101	97	|{(n1	|{(n1	PROPN
ejpam-5608	101	98	,	,	PUNCT
ejpam-5608	101	99	n2	n2	ADJ
ejpam-5608	101	100	)	)	PUNCT
ejpam-5608	101	101	∈	∈	PROPN
ejpam-5608	101	102	n2	n2	NOUN
ejpam-5608	101	103	:	:	PUNCT
ejpam-5608	101	104	n1	n1	ADJ
ejpam-5608	101	105	,	,	PUNCT
ejpam-5608	101	106	n2	n2	ADJ
ejpam-5608	101	107	≤	≤	PUNCT
ejpam-5608	101	108	n	n	CCONJ
ejpam-5608	101	109	,	,	PUNCT
ejpam-5608	101	110	g(xi	g(xi	PROPN
ejpam-5608	101	111	,	,	PUNCT
ejpam-5608	101	112	xn1	xn1	NUM
ejpam-5608	101	113	,	,	PUNCT
ejpam-5608	101	114	xn2	xn2	PROPN
ejpam-5608	101	115	)	)	PUNCT
ejpam-5608	101	116	≥	≥	NUM
ejpam-5608	101	117	ε}|	ε}|	NOUN
ejpam-5608	101	118	)	)	PUNCT
ejpam-5608	102	1	=	=	VERB
ejpam-5608	102	2	lim	lim	PROPN
ejpam-5608	102	3	n→+∞	n→+∞	PROPN
ejpam-5608	102	4	(	(	PUNCT
ejpam-5608	102	5	2	2	NUM
ejpam-5608	102	6	n2	n2	NOUN
ejpam-5608	102	7	|{(1	|{(1	PROPN
ejpam-5608	102	8	,	,	PUNCT
ejpam-5608	102	9	1	1	NUM
ejpam-5608	102	10	)	)	PUNCT
ejpam-5608	102	11	,	,	PUNCT
ejpam-5608	102	12	(	(	PUNCT
ejpam-5608	102	13	1	1	NUM
ejpam-5608	102	14	,	,	PUNCT
ejpam-5608	102	15	2	2	NUM
ejpam-5608	102	16	)	)	PUNCT
ejpam-5608	102	17	,	,	PUNCT
ejpam-5608	102	18	(	(	PUNCT
ejpam-5608	102	19	1	1	NUM
ejpam-5608	102	20	,	,	PUNCT
ejpam-5608	102	21	3	3	NUM
ejpam-5608	102	22	)	)	PUNCT
ejpam-5608	102	23	,	,	PUNCT
ejpam-5608	102	24	.	.	PUNCT
ejpam-5608	102	25	.	.	PUNCT
ejpam-5608	102	26	.	.	PUNCT
ejpam-5608	103	1	,	,	PUNCT
ejpam-5608	103	2	(	(	PUNCT
ejpam-5608	103	3	k	k	NOUN
ejpam-5608	103	4	,	,	PUNCT
ejpam-5608	103	5	1	1	NUM
ejpam-5608	103	6	)	)	PUNCT
ejpam-5608	103	7	,	,	PUNCT
ejpam-5608	103	8	(	(	PUNCT
ejpam-5608	103	9	k	k	X
ejpam-5608	103	10	,	,	PUNCT
ejpam-5608	103	11	2	2	NUM
ejpam-5608	103	12	)	)	PUNCT
ejpam-5608	103	13	,	,	PUNCT
ejpam-5608	103	14	.	.	PUNCT
ejpam-5608	103	15	.	.	PUNCT
ejpam-5608	103	16	.	.	PUNCT
ejpam-5608	104	1	}	}	PUNCT
ejpam-5608	104	2	|	|	X
ejpam-5608	104	3	)	)	PUNCT
ejpam-5608	104	4	≤	≤	NOUN
ejpam-5608	104	5	lim	lim	PROPN
ejpam-5608	104	6	n→+∞	n→+∞	PROPN
ejpam-5608	104	7	(	(	PUNCT
ejpam-5608	104	8	2nk	2nk	ADJ
ejpam-5608	104	9	n2	n2	NOUN
ejpam-5608	104	10	)	)	PUNCT
ejpam-5608	104	11	≤	≤	NOUN
ejpam-5608	104	12	2k	2k	NUM
ejpam-5608	104	13	lim	lim	PROPN
ejpam-5608	104	14	n→+∞	n→+∞	PROPN
ejpam-5608	104	15	(	(	PUNCT
ejpam-5608	104	16	1	1	NUM
ejpam-5608	104	17	n	n	NOUN
ejpam-5608	104	18	)	)	PUNCT
ejpam-5608	104	19	=	=	SYM
ejpam-5608	105	1	2k.0	2k.0	NUM
ejpam-5608	106	1	=	=	SYM
ejpam-5608	106	2	0	0	NUM
ejpam-5608	107	1	next	next	ADV
ejpam-5608	107	2	,	,	PUNCT
ejpam-5608	107	3	we	we	PRON
ejpam-5608	107	4	investigate	investigate	VERB
ejpam-5608	107	5	whether	whether	SCONJ
ejpam-5608	107	6	a	a	DET
ejpam-5608	107	7	statistically	statistically	ADV
ejpam-5608	107	8	convergent	convergent	ADJ
ejpam-5608	107	9	sequence	sequence	NOUN
ejpam-5608	107	10	is	be	AUX
ejpam-5608	107	11	also	also	ADV
ejpam-5608	107	12	a	a	DET
ejpam-5608	107	13	standard	standard	ADJ
ejpam-5608	107	14	convergent	convergent	ADJ
ejpam-5608	107	15	sequence	sequence	NOUN
ejpam-5608	107	16	.	.	PUNCT
ejpam-5608	108	1	a	a	DET
ejpam-5608	108	2	statistically	statistically	ADV
ejpam-5608	108	3	convergent	convergent	ADJ
ejpam-5608	108	4	sequence	sequence	NOUN
ejpam-5608	108	5	in	in	ADP
ejpam-5608	108	6	the	the	DET
ejpam-5608	108	7	g	g	NOUN
ejpam-5608	108	8	-	-	PUNCT
ejpam-5608	108	9	metric	metric	ADJ
ejpam-5608	108	10	space	space	NOUN
ejpam-5608	108	11	is	be	AUX
ejpam-5608	108	12	not	not	PART
ejpam-5608	108	13	always	always	ADV
ejpam-5608	108	14	a	a	DET
ejpam-5608	108	15	standard	standard	ADJ
ejpam-5608	108	16	convergent	convergent	NOUN
ejpam-5608	108	17	sequence	sequence	NOUN
ejpam-5608	108	18	in	in	ADP
ejpam-5608	108	19	the	the	DET
ejpam-5608	108	20	g	g	NOUN
ejpam-5608	108	21	-	-	PUNCT
ejpam-5608	108	22	metric	metric	ADJ
ejpam-5608	108	23	space	space	NOUN
ejpam-5608	108	24	.	.	PUNCT
ejpam-5608	109	1	the	the	DET
ejpam-5608	109	2	following	follow	VERB
ejpam-5608	109	3	theorem	theorem	NOUN
ejpam-5608	109	4	provides	provide	VERB
ejpam-5608	109	5	the	the	DET
ejpam-5608	109	6	necessary	necessary	ADJ
ejpam-5608	109	7	condition	condition	NOUN
ejpam-5608	109	8	for	for	ADP
ejpam-5608	109	9	a	a	DET
ejpam-5608	109	10	sequence	sequence	NOUN
ejpam-5608	109	11	that	that	PRON
ejpam-5608	109	12	is	be	AUX
ejpam-5608	109	13	statistically	statistically	ADV
ejpam-5608	109	14	convergent	convergent	ADJ
ejpam-5608	109	15	in	in	ADP
ejpam-5608	109	16	a	a	DET
ejpam-5608	109	17	g	g	NOUN
ejpam-5608	109	18	-	-	PUNCT
ejpam-5608	109	19	metric	metric	ADJ
ejpam-5608	109	20	space	space	NOUN
ejpam-5608	109	21	to	to	PART
ejpam-5608	109	22	also	also	ADV
ejpam-5608	109	23	be	be	AUX
ejpam-5608	109	24	a	a	DET
ejpam-5608	109	25	standard	standard	ADJ
ejpam-5608	109	26	convergent	convergent	NOUN
ejpam-5608	109	27	sequence	sequence	NOUN
ejpam-5608	109	28	in	in	ADP
ejpam-5608	109	29	the	the	DET
ejpam-5608	109	30	same	same	ADJ
ejpam-5608	109	31	space	space	NOUN
ejpam-5608	109	32	.	.	PUNCT
ejpam-5608	110	1	theorem	theorem	NOUN
ejpam-5608	110	2	3	3	NUM
ejpam-5608	110	3	.	.	PUNCT
ejpam-5608	110	4	given	give	VERB
ejpam-5608	110	5	a	a	DET
ejpam-5608	110	6	sequence	sequence	NOUN
ejpam-5608	110	7	(	(	PUNCT
ejpam-5608	110	8	xn	xn	PROPN
ejpam-5608	110	9	)	)	PUNCT
ejpam-5608	110	10	that	that	PRON
ejpam-5608	110	11	is	be	AUX
ejpam-5608	110	12	statistically	statistically	ADV
ejpam-5608	110	13	convergent	convergent	ADJ
ejpam-5608	110	14	to	to	ADP
ejpam-5608	110	15	x	x	VERB
ejpam-5608	110	16	in	in	ADP
ejpam-5608	110	17	a	a	DET
ejpam-5608	110	18	g	g	NOUN
ejpam-5608	110	19	-	-	PUNCT
ejpam-5608	110	20	metric	metric	ADJ
ejpam-5608	110	21	space	space	NOUN
ejpam-5608	110	22	,	,	PUNCT
ejpam-5608	110	23	if	if	SCONJ
ejpam-5608	110	24	|a|	|a|	PROPN
ejpam-5608	110	25	=	=	SYM
ejpam-5608	110	26	|{n	|{n	NOUN
ejpam-5608	110	27	:	:	PUNCT
ejpam-5608	110	28	(	(	PUNCT
ejpam-5608	110	29	n	n	X
ejpam-5608	110	30	,	,	PUNCT
ejpam-5608	110	31	m	m	NOUN
ejpam-5608	110	32	)	)	PUNCT
ejpam-5608	110	33	∈	∈	PROPN
ejpam-5608	110	34	n2	n2	NOUN
ejpam-5608	110	35	,	,	PUNCT
ejpam-5608	110	36	g(x	g(x	PROPN
ejpam-5608	110	37	,	,	PUNCT
ejpam-5608	110	38	xn	xn	PROPN
ejpam-5608	110	39	,	,	PUNCT
ejpam-5608	110	40	xm	xm	PROPN
ejpam-5608	110	41	)	)	PUNCT
ejpam-5608	110	42	≥	≥	X
ejpam-5608	110	43	ε}|	ε}|	VERB
ejpam-5608	110	44	<	<	X
ejpam-5608	110	45	+	+	NOUN
ejpam-5608	110	46	∞	∞	NUM
ejpam-5608	110	47	or	or	CCONJ
ejpam-5608	110	48	|b|	|b|	PROPN
ejpam-5608	110	49	=	=	PUNCT
ejpam-5608	110	50	|{m	|{m	NOUN
ejpam-5608	110	51	:	:	PUNCT
ejpam-5608	110	52	(	(	PUNCT
ejpam-5608	110	53	n	n	X
ejpam-5608	110	54	,	,	PUNCT
ejpam-5608	110	55	m	m	NOUN
ejpam-5608	110	56	)	)	PUNCT
ejpam-5608	110	57	∈	∈	PROPN
ejpam-5608	110	58	n2	n2	NOUN
ejpam-5608	110	59	,	,	PUNCT
ejpam-5608	110	60	g(x	g(x	PROPN
ejpam-5608	110	61	,	,	PUNCT
ejpam-5608	110	62	xn	xn	PROPN
ejpam-5608	110	63	,	,	PUNCT
ejpam-5608	110	64	xm	xm	PROPN
ejpam-5608	110	65	)	)	PUNCT
ejpam-5608	110	66	≥	≥	X
ejpam-5608	110	67	ε}|	ε}|	VERB
ejpam-5608	110	68	<	<	X
ejpam-5608	110	69	+	+	NOUN
ejpam-5608	110	70	∞	∞	PROPN
ejpam-5608	110	71	then	then	ADV
ejpam-5608	110	72	the	the	DET
ejpam-5608	110	73	sequence	sequence	NOUN
ejpam-5608	110	74	is	be	AUX
ejpam-5608	110	75	standard	standard	ADJ
ejpam-5608	110	76	convergent	convergent	NOUN
ejpam-5608	110	77	to	to	ADP
ejpam-5608	110	78	x	x	PUNCT
ejpam-5608	110	79	in	in	ADP
ejpam-5608	110	80	the	the	DET
ejpam-5608	110	81	gmetric	gmetric	ADJ
ejpam-5608	110	82	space	space	NOUN
ejpam-5608	110	83	.	.	PUNCT
ejpam-5608	111	1	proof	proof	NOUN
ejpam-5608	111	2	.	.	PUNCT
ejpam-5608	112	1	the	the	DET
ejpam-5608	112	2	sequence	sequence	NOUN
ejpam-5608	112	3	(	(	PUNCT
ejpam-5608	112	4	xn	xn	X
ejpam-5608	112	5	)	)	PUNCT
ejpam-5608	112	6	is	be	AUX
ejpam-5608	112	7	statistically	statistically	ADV
ejpam-5608	112	8	convergent	convergent	ADJ
ejpam-5608	112	9	to	to	ADP
ejpam-5608	112	10	x	x	PRON
ejpam-5608	112	11	,	,	PUNCT
ejpam-5608	112	12	meaning	mean	VERB
ejpam-5608	112	13	that	that	SCONJ
ejpam-5608	112	14	for	for	ADP
ejpam-5608	112	15	every	every	DET
ejpam-5608	112	16	real	real	ADJ
ejpam-5608	112	17	number	number	NOUN
ejpam-5608	112	18	ε	ε	PROPN
ejpam-5608	112	19	>	>	X
ejpam-5608	112	20	0	0	PROPN
ejpam-5608	112	21	,	,	PUNCT
ejpam-5608	112	22	the	the	DET
ejpam-5608	112	23	following	follow	VERB
ejpam-5608	112	24	holds	hold	VERB
ejpam-5608	112	25	:	:	PUNCT
ejpam-5608	112	26	lim	lim	PROPN
ejpam-5608	112	27	n→+∞	n→+∞	PROPN
ejpam-5608	112	28	(	(	PUNCT
ejpam-5608	112	29	2	2	NUM
ejpam-5608	112	30	n2	n2	ADJ
ejpam-5608	112	31	|{(n1	|{(n1	PROPN
ejpam-5608	112	32	,	,	PUNCT
ejpam-5608	112	33	n2	n2	ADJ
ejpam-5608	112	34	)	)	PUNCT
ejpam-5608	112	35	∈	∈	PROPN
ejpam-5608	112	36	n2	n2	NOUN
ejpam-5608	112	37	:	:	PUNCT
ejpam-5608	112	38	n1	n1	ADJ
ejpam-5608	112	39	,	,	PUNCT
ejpam-5608	112	40	n2	n2	ADJ
ejpam-5608	112	41	≤	≤	PUNCT
ejpam-5608	112	42	n	n	CCONJ
ejpam-5608	112	43	:	:	PUNCT
ejpam-5608	112	44	g(x	g(x	NOUN
ejpam-5608	112	45	,	,	PUNCT
ejpam-5608	112	46	xn1	xn1	NUM
ejpam-5608	112	47	,	,	PUNCT
ejpam-5608	112	48	xn2	xn2	PROPN
ejpam-5608	112	49	)	)	PUNCT
ejpam-5608	112	50	≥	≥	NOUN
ejpam-5608	112	51	ε}|	ε}|	NOUN
ejpam-5608	112	52	)	)	PUNCT
ejpam-5608	112	53	=	=	SYM
ejpam-5608	112	54	0	0	NUM
ejpam-5608	112	55	manuharawati	manuharawati	NOUN
ejpam-5608	112	56	,	,	PUNCT
ejpam-5608	112	57	m.jakfar	m.jakfar	ADV
ejpam-5608	112	58	,	,	PUNCT
ejpam-5608	112	59	a.	a.	PROPN
ejpam-5608	112	60	taufik	taufik	PROPN
ejpam-5608	112	61	hamzah	hamzah	PROPN
ejpam-5608	112	62	/	/	SYM
ejpam-5608	112	63	eur	eur	PROPN
ejpam-5608	112	64	.	.	PUNCT
ejpam-5608	113	1	j.	j.	PROPN
ejpam-5608	113	2	pure	pure	PROPN
ejpam-5608	113	3	appl	appl	PROPN
ejpam-5608	113	4	.	.	PROPN
ejpam-5608	113	5	math	math	PROPN
ejpam-5608	113	6	,	,	PUNCT
ejpam-5608	113	7	18	18	NUM
ejpam-5608	113	8	(	(	PUNCT
ejpam-5608	113	9	1	1	NUM
ejpam-5608	113	10	)	)	PUNCT
ejpam-5608	113	11	(	(	PUNCT
ejpam-5608	113	12	2025	2025	NUM
ejpam-5608	113	13	)	)	PUNCT
ejpam-5608	113	14	,	,	PUNCT
ejpam-5608	113	15	5608	5608	NUM
ejpam-5608	113	16	6	6	NUM
ejpam-5608	113	17	of	of	ADP
ejpam-5608	113	18	13	13	NUM
ejpam-5608	113	19	if	if	SCONJ
ejpam-5608	113	20	|a|	|a|	PROPN
ejpam-5608	113	21	=	=	SYM
ejpam-5608	113	22	|{n	|{n	NOUN
ejpam-5608	113	23	:	:	PUNCT
ejpam-5608	113	24	(	(	PUNCT
ejpam-5608	113	25	n	n	X
ejpam-5608	113	26	,	,	PUNCT
ejpam-5608	113	27	m	m	NOUN
ejpam-5608	113	28	)	)	PUNCT
ejpam-5608	113	29	∈	∈	PROPN
ejpam-5608	113	30	n2	n2	NOUN
ejpam-5608	113	31	,	,	PUNCT
ejpam-5608	113	32	g(x	g(x	PROPN
ejpam-5608	113	33	,	,	PUNCT
ejpam-5608	113	34	xn	xn	PROPN
ejpam-5608	113	35	,	,	PUNCT
ejpam-5608	113	36	xm	xm	PROPN
ejpam-5608	113	37	)	)	PUNCT
ejpam-5608	113	38	≥	≥	X
ejpam-5608	113	39	ε}|	ε}|	VERB
ejpam-5608	113	40	<	<	X
ejpam-5608	113	41	+	+	NOUN
ejpam-5608	113	42	∞	∞	PROPN
ejpam-5608	113	43	,	,	PUNCT
ejpam-5608	113	44	then	then	ADV
ejpam-5608	113	45	there	there	PRON
ejpam-5608	113	46	exists	exist	VERB
ejpam-5608	113	47	a	a	DET
ejpam-5608	113	48	sup(a	sup(a	NOUN
ejpam-5608	113	49	)	)	PUNCT
ejpam-5608	113	50	+	+	CCONJ
ejpam-5608	113	51	1	1	NUM
ejpam-5608	113	52	∈	∈	NOUN
ejpam-5608	113	53	n	n	PRON
ejpam-5608	113	54	such	such	ADJ
ejpam-5608	113	55	that	that	PRON
ejpam-5608	113	56	for	for	ADP
ejpam-5608	113	57	every	every	DET
ejpam-5608	113	58	n	n	CCONJ
ejpam-5608	113	59	,	,	PUNCT
ejpam-5608	113	60	m	m	PROPN
ejpam-5608	113	61	≥	≥	NOUN
ejpam-5608	113	62	sup(a	sup(a	NOUN
ejpam-5608	113	63	)	)	PUNCT
ejpam-5608	113	64	+	+	CCONJ
ejpam-5608	113	65	1	1	NUM
ejpam-5608	113	66	,	,	PUNCT
ejpam-5608	113	67	g(x	g(x	NOUN
ejpam-5608	113	68	,	,	PUNCT
ejpam-5608	113	69	xn	xn	PROPN
ejpam-5608	113	70	,	,	PUNCT
ejpam-5608	113	71	xm	xm	PROPN
ejpam-5608	113	72	)	)	PUNCT
ejpam-5608	113	73	<	<	X
ejpam-5608	113	74	ε	ε	PROPN
ejpam-5608	113	75	.	.	PROPN
ejpam-5608	114	1	in	in	ADP
ejpam-5608	114	2	other	other	ADJ
ejpam-5608	114	3	words	word	NOUN
ejpam-5608	114	4	,	,	PUNCT
ejpam-5608	114	5	the	the	DET
ejpam-5608	114	6	sequence	sequence	NOUN
ejpam-5608	114	7	(	(	PUNCT
ejpam-5608	114	8	xn	xn	X
ejpam-5608	114	9	)	)	PUNCT
ejpam-5608	114	10	is	be	AUX
ejpam-5608	114	11	convergent	convergent	ADJ
ejpam-5608	114	12	to	to	ADP
ejpam-5608	114	13	x	x	VERB
ejpam-5608	114	14	in	in	ADP
ejpam-5608	114	15	the	the	DET
ejpam-5608	114	16	g	g	NOUN
ejpam-5608	114	17	-	-	PUNCT
ejpam-5608	114	18	metric	metric	ADJ
ejpam-5608	114	19	space	space	NOUN
ejpam-5608	114	20	.	.	PUNCT
ejpam-5608	115	1	similary	similary	ADJ
ejpam-5608	115	2	,	,	PUNCT
ejpam-5608	115	3	if	if	SCONJ
ejpam-5608	115	4	|b|	|b|	PROPN
ejpam-5608	115	5	=	=	PUNCT
ejpam-5608	115	6	|{m	|{m	NOUN
ejpam-5608	115	7	:	:	PUNCT
ejpam-5608	115	8	(	(	PUNCT
ejpam-5608	115	9	n	n	X
ejpam-5608	115	10	,	,	PUNCT
ejpam-5608	115	11	m	m	NOUN
ejpam-5608	115	12	)	)	PUNCT
ejpam-5608	115	13	∈	∈	PROPN
ejpam-5608	115	14	n2	n2	NOUN
ejpam-5608	115	15	,	,	PUNCT
ejpam-5608	115	16	g(x	g(x	PROPN
ejpam-5608	115	17	,	,	PUNCT
ejpam-5608	115	18	xn	xn	PROPN
ejpam-5608	115	19	,	,	PUNCT
ejpam-5608	115	20	xm	xm	PROPN
ejpam-5608	115	21	)	)	PUNCT
ejpam-5608	115	22	≥	≥	X
ejpam-5608	115	23	ε}|	ε}|	VERB
ejpam-5608	115	24	<	<	X
ejpam-5608	115	25	+	+	NOUN
ejpam-5608	115	26	∞	∞	PROPN
ejpam-5608	115	27	,	,	PUNCT
ejpam-5608	115	28	then	then	ADV
ejpam-5608	115	29	there	there	PRON
ejpam-5608	115	30	exists	exist	VERB
ejpam-5608	115	31	a	a	DET
ejpam-5608	115	32	sup(b	sup(b	NOUN
ejpam-5608	115	33	)	)	PUNCT
ejpam-5608	116	1	+	+	CCONJ
ejpam-5608	116	2	1	1	NUM
ejpam-5608	116	3	∈	∈	NOUN
ejpam-5608	116	4	n	n	PRON
ejpam-5608	116	5	such	such	ADJ
ejpam-5608	116	6	that	that	PRON
ejpam-5608	116	7	for	for	ADP
ejpam-5608	116	8	every	every	DET
ejpam-5608	116	9	n	n	CCONJ
ejpam-5608	116	10	,	,	PUNCT
ejpam-5608	116	11	m	m	NOUN
ejpam-5608	116	12	≥	≥	NOUN
ejpam-5608	116	13	sup(b	sup(b	NOUN
ejpam-5608	116	14	)	)	PUNCT
ejpam-5608	117	1	+	+	CCONJ
ejpam-5608	117	2	1	1	NUM
ejpam-5608	117	3	,	,	PUNCT
ejpam-5608	117	4	g(x	g(x	NOUN
ejpam-5608	117	5	,	,	PUNCT
ejpam-5608	117	6	xn	xn	PROPN
ejpam-5608	117	7	,	,	PUNCT
ejpam-5608	117	8	xm	xm	PROPN
ejpam-5608	117	9	)	)	PUNCT
ejpam-5608	117	10	<	<	X
ejpam-5608	117	11	ε	ε	PROPN
ejpam-5608	117	12	,	,	PUNCT
ejpam-5608	117	13	and	and	CCONJ
ejpam-5608	117	14	hence	hence	ADV
ejpam-5608	117	15	the	the	DET
ejpam-5608	117	16	sequence	sequence	NOUN
ejpam-5608	117	17	(	(	PUNCT
ejpam-5608	117	18	xn	xn	X
ejpam-5608	117	19	)	)	PUNCT
ejpam-5608	117	20	is	be	AUX
ejpam-5608	117	21	standard	standard	ADJ
ejpam-5608	117	22	convergent	convergent	NOUN
ejpam-5608	117	23	to	to	ADP
ejpam-5608	117	24	x	x	VERB
ejpam-5608	117	25	in	in	ADP
ejpam-5608	117	26	the	the	DET
ejpam-5608	117	27	g	g	NOUN
ejpam-5608	117	28	-	-	PUNCT
ejpam-5608	117	29	metric	metric	ADJ
ejpam-5608	117	30	space	space	NOUN
ejpam-5608	117	31	.	.	PUNCT
ejpam-5608	118	1	example	example	NOUN
ejpam-5608	119	1	2	2	NUM
ejpam-5608	119	2	.	.	X
ejpam-5608	119	3	consider	consider	VERB
ejpam-5608	119	4	the	the	DET
ejpam-5608	119	5	g	g	NOUN
ejpam-5608	119	6	-	-	PUNCT
ejpam-5608	119	7	metric	metric	ADJ
ejpam-5608	119	8	space	space	NOUN
ejpam-5608	119	9	(	(	PUNCT
ejpam-5608	119	10	r	r	NOUN
ejpam-5608	119	11	,	,	PUNCT
ejpam-5608	119	12	g	g	NOUN
ejpam-5608	119	13	)	)	PUNCT
ejpam-5608	119	14	,	,	PUNCT
ejpam-5608	119	15	where	where	SCONJ
ejpam-5608	119	16	for	for	ADP
ejpam-5608	119	17	all	all	DET
ejpam-5608	119	18	x	x	NOUN
ejpam-5608	119	19	,	,	PUNCT
ejpam-5608	119	20	y	y	PROPN
ejpam-5608	119	21	,	,	PUNCT
ejpam-5608	119	22	z	z	NOUN
ejpam-5608	119	23	∈	∈	PROPN
ejpam-5608	119	24	r	r	NOUN
ejpam-5608	119	25	,	,	PUNCT
ejpam-5608	119	26	the	the	DET
ejpam-5608	119	27	g	g	NOUN
ejpam-5608	119	28	-	-	PUNCT
ejpam-5608	119	29	metric	metric	ADJ
ejpam-5608	119	30	is	be	AUX
ejpam-5608	119	31	defined	define	VERB
ejpam-5608	119	32	as	as	ADP
ejpam-5608	119	33	:	:	PUNCT
ejpam-5608	119	34	g(x	g(x	PROPN
ejpam-5608	119	35	,	,	PUNCT
ejpam-5608	119	36	y	y	PROPN
ejpam-5608	119	37	,	,	PUNCT
ejpam-5608	119	38	z	z	NOUN
ejpam-5608	119	39	)	)	PUNCT
ejpam-5608	119	40	=	=	SYM
ejpam-5608	119	41	|x−	|x−	NUM
ejpam-5608	119	42	y|+	y|+	PROPN
ejpam-5608	119	43	|x−	|x−	PROPN
ejpam-5608	119	44	z|+	z|+	PROPN
ejpam-5608	119	45	|y	|y	NOUN
ejpam-5608	119	46	−	−	PROPN
ejpam-5608	119	47	z|	z|	PROPN
ejpam-5608	119	48	.	.	PUNCT
ejpam-5608	120	1	the	the	DET
ejpam-5608	120	2	sequence	sequence	NOUN
ejpam-5608	120	3	(	(	PUNCT
ejpam-5608	120	4	xn	xn	PROPN
ejpam-5608	120	5	)	)	PUNCT
ejpam-5608	120	6	=	=	SYM
ejpam-5608	120	7	(	(	PUNCT
ejpam-5608	120	8	(	(	PUNCT
ejpam-5608	120	9	−1)n	−1)n	PROPN
ejpam-5608	120	10	n	n	CCONJ
ejpam-5608	120	11	)	)	PUNCT
ejpam-5608	120	12	converges	converge	VERB
ejpam-5608	120	13	to	to	ADP
ejpam-5608	120	14	0	0	NUM
ejpam-5608	120	15	in	in	ADP
ejpam-5608	120	16	the	the	DET
ejpam-5608	120	17	g	g	NOUN
ejpam-5608	120	18	-	-	PUNCT
ejpam-5608	120	19	metric	metric	ADJ
ejpam-5608	120	20	space	space	NOUN
ejpam-5608	120	21	.	.	PUNCT
ejpam-5608	121	1	it	it	PRON
ejpam-5608	121	2	will	will	AUX
ejpam-5608	121	3	be	be	AUX
ejpam-5608	121	4	proven	prove	VERB
ejpam-5608	121	5	that	that	SCONJ
ejpam-5608	121	6	the	the	DET
ejpam-5608	121	7	sequence	sequence	NOUN
ejpam-5608	121	8	(	(	PUNCT
ejpam-5608	121	9	xn	xn	PROPN
ejpam-5608	121	10	)	)	PUNCT
ejpam-5608	121	11	=	=	SYM
ejpam-5608	121	12	(	(	PUNCT
ejpam-5608	121	13	(	(	PUNCT
ejpam-5608	121	14	−1)n	−1)n	PROPN
ejpam-5608	121	15	n	n	CCONJ
ejpam-5608	121	16	)	)	PUNCT
ejpam-5608	121	17	statistically	statistically	ADV
ejpam-5608	121	18	converges	converge	VERB
ejpam-5608	121	19	to	to	ADP
ejpam-5608	121	20	0	0	NUM
ejpam-5608	121	21	in	in	ADP
ejpam-5608	121	22	a	a	DET
ejpam-5608	121	23	g	g	NOUN
ejpam-5608	121	24	-	-	PUNCT
ejpam-5608	121	25	metric	metric	ADJ
ejpam-5608	121	26	space	space	NOUN
ejpam-5608	121	27	.	.	PUNCT
ejpam-5608	122	1	let	let	VERB
ejpam-5608	122	2	j	j	PROPN
ejpam-5608	122	3	be	be	AUX
ejpam-5608	122	4	the	the	DET
ejpam-5608	122	5	largest	large	ADJ
ejpam-5608	122	6	natural	natural	ADJ
ejpam-5608	122	7	number	number	NOUN
ejpam-5608	122	8	less	less	ADJ
ejpam-5608	122	9	than	than	ADP
ejpam-5608	122	10	or	or	CCONJ
ejpam-5608	122	11	equal	equal	ADJ
ejpam-5608	122	12	to	to	ADP
ejpam-5608	122	13	2	2	NUM
ejpam-5608	122	14	ε	ε	NOUN
ejpam-5608	122	15	for	for	ADP
ejpam-5608	122	16	every	every	DET
ejpam-5608	122	17	ε	ε	PROPN
ejpam-5608	122	18	>	>	X
ejpam-5608	122	19	0	0	PROPN
ejpam-5608	122	20	,	,	PUNCT
ejpam-5608	122	21	ε	ε	PROPN
ejpam-5608	122	22	∈	∈	PROPN
ejpam-5608	122	23	r	r	NOUN
ejpam-5608	122	24	,	,	PUNCT
ejpam-5608	123	1	then	then	ADV
ejpam-5608	123	2	lim	lim	PROPN
ejpam-5608	123	3	n→+∞	n→+∞	PROPN
ejpam-5608	123	4	(	(	PUNCT
ejpam-5608	123	5	2	2	NUM
ejpam-5608	123	6	n2	n2	ADJ
ejpam-5608	123	7	|{(n1	|{(n1	PROPN
ejpam-5608	123	8	,	,	PUNCT
ejpam-5608	123	9	n2	n2	ADJ
ejpam-5608	123	10	)	)	PUNCT
ejpam-5608	123	11	∈	∈	PROPN
ejpam-5608	123	12	n2	n2	NOUN
ejpam-5608	123	13	:	:	PUNCT
ejpam-5608	123	14	n1	n1	ADJ
ejpam-5608	123	15	,	,	PUNCT
ejpam-5608	123	16	n2	n2	ADJ
ejpam-5608	123	17	≤	≤	PUNCT
ejpam-5608	123	18	n	n	CCONJ
ejpam-5608	123	19	,	,	PUNCT
ejpam-5608	123	20	g(xi	g(xi	PROPN
ejpam-5608	123	21	,	,	PUNCT
ejpam-5608	123	22	xn1	xn1	NUM
ejpam-5608	123	23	,	,	PUNCT
ejpam-5608	123	24	xn2	xn2	PROPN
ejpam-5608	123	25	)	)	PUNCT
ejpam-5608	123	26	≥	≥	NUM
ejpam-5608	123	27	ε}|	ε}|	NOUN
ejpam-5608	123	28	)	)	PUNCT
ejpam-5608	124	1	=	=	VERB
ejpam-5608	124	2	lim	lim	PROPN
ejpam-5608	124	3	n→+∞	n→+∞	PROPN
ejpam-5608	124	4	(	(	PUNCT
ejpam-5608	124	5	2	2	NUM
ejpam-5608	124	6	n2	n2	NOUN
ejpam-5608	124	7	|{(1	|{(1	PROPN
ejpam-5608	124	8	,	,	PUNCT
ejpam-5608	124	9	1	1	NUM
ejpam-5608	124	10	)	)	PUNCT
ejpam-5608	124	11	,	,	PUNCT
ejpam-5608	124	12	(	(	PUNCT
ejpam-5608	124	13	1	1	NUM
ejpam-5608	124	14	,	,	PUNCT
ejpam-5608	124	15	2	2	NUM
ejpam-5608	124	16	)	)	PUNCT
ejpam-5608	124	17	,	,	PUNCT
ejpam-5608	124	18	(	(	PUNCT
ejpam-5608	124	19	1	1	NUM
ejpam-5608	124	20	,	,	PUNCT
ejpam-5608	124	21	3	3	NUM
ejpam-5608	124	22	)	)	PUNCT
ejpam-5608	124	23	,	,	PUNCT
ejpam-5608	124	24	.	.	PUNCT
ejpam-5608	124	25	.	.	PUNCT
ejpam-5608	124	26	.	.	PUNCT
ejpam-5608	125	1	,	,	PUNCT
ejpam-5608	125	2	(	(	PUNCT
ejpam-5608	125	3	j	j	NOUN
ejpam-5608	125	4	,	,	PUNCT
ejpam-5608	125	5	1	1	NUM
ejpam-5608	125	6	)	)	PUNCT
ejpam-5608	125	7	,	,	PUNCT
ejpam-5608	125	8	(	(	PUNCT
ejpam-5608	125	9	j	j	NOUN
ejpam-5608	125	10	,	,	PUNCT
ejpam-5608	125	11	2	2	NUM
ejpam-5608	125	12	)	)	PUNCT
ejpam-5608	125	13	,	,	PUNCT
ejpam-5608	125	14	.	.	PUNCT
ejpam-5608	125	15	.	.	PUNCT
ejpam-5608	125	16	.	.	PUNCT
ejpam-5608	126	1	}	}	PUNCT
ejpam-5608	126	2	|	|	X
ejpam-5608	126	3	)	)	PUNCT
ejpam-5608	126	4	≤	≤	NOUN
ejpam-5608	126	5	lim	lim	PROPN
ejpam-5608	126	6	n→+∞	n→+∞	PROPN
ejpam-5608	126	7	(	(	PUNCT
ejpam-5608	126	8	2nj	2nj	ADJ
ejpam-5608	126	9	n2	n2	NOUN
ejpam-5608	126	10	)	)	PUNCT
ejpam-5608	126	11	≤	≤	NUM
ejpam-5608	126	12	2j	2j	NUM
ejpam-5608	126	13	lim	lim	PROPN
ejpam-5608	126	14	n→+∞	n→+∞	PROPN
ejpam-5608	126	15	(	(	PUNCT
ejpam-5608	126	16	1	1	NUM
ejpam-5608	126	17	n	n	NOUN
ejpam-5608	126	18	)	)	PUNCT
ejpam-5608	126	19	=	=	SYM
ejpam-5608	126	20	2j.0	2j.0	NOUN
ejpam-5608	126	21	=	=	SYM
ejpam-5608	126	22	0	0	NUM
ejpam-5608	126	23	theorem	theorem	NOUN
ejpam-5608	126	24	4	4	NUM
ejpam-5608	126	25	.	.	PUNCT
ejpam-5608	126	26	given	give	VERB
ejpam-5608	126	27	a	a	DET
ejpam-5608	126	28	sequence	sequence	NOUN
ejpam-5608	126	29	(	(	PUNCT
ejpam-5608	126	30	xn	xn	PROPN
ejpam-5608	126	31	)	)	PUNCT
ejpam-5608	126	32	that	that	PRON
ejpam-5608	126	33	converges	converge	VERB
ejpam-5608	126	34	statistically	statistically	ADV
ejpam-5608	126	35	to	to	ADP
ejpam-5608	126	36	x	x	PRON
ejpam-5608	126	37	in	in	ADP
ejpam-5608	126	38	a	a	DET
ejpam-5608	126	39	g	g	NOUN
ejpam-5608	126	40	-	-	PUNCT
ejpam-5608	126	41	metric	metric	ADJ
ejpam-5608	126	42	space	space	NOUN
ejpam-5608	126	43	,	,	PUNCT
ejpam-5608	126	44	if	if	SCONJ
ejpam-5608	126	45	the	the	DET
ejpam-5608	126	46	sequence	sequence	NOUN
ejpam-5608	126	47	(	(	PUNCT
ejpam-5608	126	48	xn	xn	X
ejpam-5608	126	49	)	)	PUNCT
ejpam-5608	126	50	is	be	AUX
ejpam-5608	126	51	monotonic	monotonic	ADJ
ejpam-5608	126	52	,	,	PUNCT
ejpam-5608	126	53	then	then	ADV
ejpam-5608	126	54	(	(	PUNCT
ejpam-5608	126	55	xn	xn	X
ejpam-5608	126	56	)	)	PUNCT
ejpam-5608	126	57	converges	converge	VERB
ejpam-5608	126	58	ordinarily	ordinarily	ADV
ejpam-5608	126	59	to	to	ADP
ejpam-5608	126	60	x	x	PROPN
ejpam-5608	126	61	in	in	ADP
ejpam-5608	126	62	the	the	DET
ejpam-5608	126	63	g	g	NOUN
ejpam-5608	126	64	-	-	PUNCT
ejpam-5608	126	65	metric	metric	ADJ
ejpam-5608	126	66	space	space	NOUN
ejpam-5608	126	67	.	.	PUNCT
ejpam-5608	127	1	proof	proof	NOUN
ejpam-5608	127	2	.	.	PUNCT
ejpam-5608	128	1	the	the	DET
ejpam-5608	128	2	sequence	sequence	NOUN
ejpam-5608	128	3	(	(	PUNCT
ejpam-5608	128	4	xn	xn	X
ejpam-5608	128	5	)	)	PUNCT
ejpam-5608	128	6	converging	converge	VERB
ejpam-5608	128	7	statistically	statistically	ADV
ejpam-5608	128	8	to	to	ADP
ejpam-5608	128	9	xmeans	xmean	NOUN
ejpam-5608	128	10	that	that	SCONJ
ejpam-5608	128	11	for	for	ADP
ejpam-5608	128	12	every	every	DET
ejpam-5608	128	13	real	real	ADJ
ejpam-5608	128	14	number	number	NOUN
ejpam-5608	128	15	ε	ε	PROPN
ejpam-5608	128	16	>	>	X
ejpam-5608	128	17	0	0	PROPN
ejpam-5608	128	18	,	,	PUNCT
ejpam-5608	128	19	the	the	DET
ejpam-5608	128	20	following	follow	VERB
ejpam-5608	128	21	holds	hold	VERB
ejpam-5608	128	22	:	:	PUNCT
ejpam-5608	128	23	lim	lim	PROPN
ejpam-5608	128	24	n→+∞	n→+∞	PROPN
ejpam-5608	128	25	(	(	PUNCT
ejpam-5608	128	26	2	2	NUM
ejpam-5608	128	27	n2	n2	ADJ
ejpam-5608	128	28	|{(n1	|{(n1	PROPN
ejpam-5608	128	29	,	,	PUNCT
ejpam-5608	128	30	n2	n2	ADJ
ejpam-5608	128	31	)	)	PUNCT
ejpam-5608	128	32	∈	∈	PROPN
ejpam-5608	128	33	n2	n2	NOUN
ejpam-5608	128	34	:	:	PUNCT
ejpam-5608	128	35	n1	n1	ADJ
ejpam-5608	128	36	,	,	PUNCT
ejpam-5608	128	37	n2	n2	ADJ
ejpam-5608	128	38	≤	≤	NUM
ejpam-5608	128	39	n	n	CCONJ
ejpam-5608	128	40	,	,	PUNCT
ejpam-5608	128	41	g(x	g(x	NOUN
ejpam-5608	128	42	,	,	PUNCT
ejpam-5608	128	43	xn1	xn1	NUM
ejpam-5608	128	44	,	,	PUNCT
ejpam-5608	128	45	xn2	xn2	PROPN
ejpam-5608	128	46	)	)	PUNCT
ejpam-5608	128	47	≥	≥	NUM
ejpam-5608	128	48	ε}|	ε}|	NOUN
ejpam-5608	128	49	)	)	PUNCT
ejpam-5608	129	1	=	=	SYM
ejpam-5608	129	2	0	0	PUNCT
ejpam-5608	130	1	a	a	DET
ejpam-5608	130	2	sequence	sequence	NOUN
ejpam-5608	130	3	(	(	PUNCT
ejpam-5608	130	4	xn	xn	X
ejpam-5608	130	5	)	)	PUNCT
ejpam-5608	130	6	is	be	AUX
ejpam-5608	130	7	monotonic	monotonic	ADV
ejpam-5608	130	8	increasing	increase	VERB
ejpam-5608	130	9	if	if	SCONJ
ejpam-5608	130	10	x1	x1	PROPN
ejpam-5608	130	11	≤	≤	NUM
ejpam-5608	130	12	x2	x2	ADJ
ejpam-5608	130	13	≤	≤	NOUN
ejpam-5608	130	14	·	·	PUNCT
ejpam-5608	130	15	·	·	PUNCT
ejpam-5608	130	16	·	·	PUNCT
ejpam-5608	131	1	≤	≤	NUM
ejpam-5608	131	2	xn	xn	X
ejpam-5608	131	3	≤	≤	NUM
ejpam-5608	131	4	xn+1	xn+1	NUM
ejpam-5608	131	5	≤	≤	NOUN
ejpam-5608	131	6	.	.	PUNCT
ejpam-5608	131	7	.	.	PUNCT
ejpam-5608	132	1	.	.	PUNCT
ejpam-5608	133	1	,	,	PUNCT
ejpam-5608	133	2	and	and	CCONJ
ejpam-5608	133	3	monotonic	monotonic	ADV
ejpam-5608	133	4	decreasing	decrease	VERB
ejpam-5608	133	5	if	if	SCONJ
ejpam-5608	133	6	x1	x1	PROPN
ejpam-5608	133	7	≥	≥	X
ejpam-5608	133	8	x2	x2	NOUN
ejpam-5608	133	9	≥	≥	NUM
ejpam-5608	133	10	.	.	PUNCT
ejpam-5608	133	11	.	.	PUNCT
ejpam-5608	133	12	.	.	PUNCT
ejpam-5608	134	1	xn	xn	PROPN
ejpam-5608	134	2	≥	≥	PROPN
ejpam-5608	134	3	xn+1	xn+1	NUM
ejpam-5608	134	4	≥	≥	PROPN
ejpam-5608	134	5	.	.	PUNCT
ejpam-5608	134	6	.	.	PUNCT
ejpam-5608	135	1	.	.	PUNCT
ejpam-5608	136	1	.	.	PUNCT
ejpam-5608	137	1	if	if	SCONJ
ejpam-5608	137	2	for	for	ADP
ejpam-5608	137	3	some	some	PRON
ejpam-5608	137	4	(	(	PUNCT
ejpam-5608	137	5	m	m	PROPN
ejpam-5608	137	6	,	,	PUNCT
ejpam-5608	137	7	n	n	CCONJ
ejpam-5608	137	8	)	)	PUNCT
ejpam-5608	137	9	∈	∈	PROPN
ejpam-5608	137	10	n2	n2	NOUN
ejpam-5608	137	11	,	,	PUNCT
ejpam-5608	137	12	g(x	g(x	PROPN
ejpam-5608	137	13	,	,	PUNCT
ejpam-5608	137	14	xm	xm	PROPN
ejpam-5608	137	15	,	,	PUNCT
ejpam-5608	137	16	xn	xn	PROPN
ejpam-5608	137	17	)	)	PUNCT
ejpam-5608	137	18	≥	≥	PRON
ejpam-5608	137	19	ε	ε	PROPN
ejpam-5608	137	20	,	,	PUNCT
ejpam-5608	137	21	then	then	ADV
ejpam-5608	137	22	for	for	ADP
ejpam-5608	137	23	every	every	DET
ejpam-5608	137	24	i	i	PRON
ejpam-5608	137	25	<	<	X
ejpam-5608	137	26	n	n	PROPN
ejpam-5608	137	27	and	and	CCONJ
ejpam-5608	137	28	k	k	X
ejpam-5608	137	29	<	<	X
ejpam-5608	137	30	m	m	PROPN
ejpam-5608	137	31	,	,	PUNCT
ejpam-5608	137	32	g(x	g(x	PROPN
ejpam-5608	137	33	,	,	PUNCT
ejpam-5608	137	34	xi	xi	PROPN
ejpam-5608	137	35	,	,	PUNCT
ejpam-5608	137	36	xk	xk	PROPN
ejpam-5608	137	37	)	)	PUNCT
ejpam-5608	137	38	≥	≥	X
ejpam-5608	137	39	ε	ε	PROPN
ejpam-5608	137	40	because	because	SCONJ
ejpam-5608	137	41	(	(	PUNCT
ejpam-5608	137	42	xn	xn	X
ejpam-5608	137	43	)	)	PUNCT
ejpam-5608	137	44	converges	converge	VERB
ejpam-5608	137	45	statistically	statistically	ADV
ejpam-5608	137	46	.	.	PUNCT
ejpam-5608	138	1	additionally	additionally	ADV
ejpam-5608	138	2	,	,	PUNCT
ejpam-5608	138	3	since	since	SCONJ
ejpam-5608	138	4	(	(	PUNCT
ejpam-5608	138	5	xn	xn	X
ejpam-5608	138	6	)	)	PUNCT
ejpam-5608	138	7	converges	converge	VERB
ejpam-5608	138	8	statistically	statistically	ADV
ejpam-5608	138	9	,	,	PUNCT
ejpam-5608	138	10	we	we	PRON
ejpam-5608	138	11	have	have	VERB
ejpam-5608	138	12	|a|	|a|	NOUN
ejpam-5608	138	13	=	=	PUNCT
ejpam-5608	138	14	|{n	|{n	NOUN
ejpam-5608	138	15	:	:	PUNCT
ejpam-5608	138	16	(	(	PUNCT
ejpam-5608	138	17	n	n	X
ejpam-5608	138	18	,	,	PUNCT
ejpam-5608	138	19	m	m	NOUN
ejpam-5608	138	20	)	)	PUNCT
ejpam-5608	138	21	∈	∈	PROPN
ejpam-5608	138	22	n2	n2	NOUN
ejpam-5608	138	23	,	,	PUNCT
ejpam-5608	138	24	g(x	g(x	PROPN
ejpam-5608	138	25	,	,	PUNCT
ejpam-5608	138	26	xn	xn	PROPN
ejpam-5608	138	27	,	,	PUNCT
ejpam-5608	138	28	xm	xm	PROPN
ejpam-5608	138	29	)	)	PUNCT
ejpam-5608	138	30	≥	≥	X
ejpam-5608	138	31	ε}|	ε}|	VERB
ejpam-5608	138	32	<	<	X
ejpam-5608	138	33	+	+	NOUN
ejpam-5608	138	34	∞	∞	PROPN
ejpam-5608	138	35	,	,	PUNCT
ejpam-5608	138	36	let	let	VERB
ejpam-5608	138	37	|a|	|a|	NOUN
ejpam-5608	138	38	=	=	PROPN
ejpam-5608	138	39	z	z	PROPN
ejpam-5608	138	40	or	or	CCONJ
ejpam-5608	138	41	|b|	|b|	PROPN
ejpam-5608	138	42	=	=	PUNCT
ejpam-5608	139	1	|{m	|{m	NOUN
ejpam-5608	139	2	:	:	PUNCT
ejpam-5608	139	3	(	(	PUNCT
ejpam-5608	139	4	n	n	X
ejpam-5608	139	5	,	,	PUNCT
ejpam-5608	139	6	m	m	NOUN
ejpam-5608	139	7	)	)	PUNCT
ejpam-5608	139	8	∈	∈	PROPN
ejpam-5608	139	9	n2	n2	NOUN
ejpam-5608	139	10	,	,	PUNCT
ejpam-5608	139	11	g(x	g(x	PROPN
ejpam-5608	139	12	,	,	PUNCT
ejpam-5608	139	13	xn	xn	PROPN
ejpam-5608	139	14	,	,	PUNCT
ejpam-5608	139	15	xm	xm	PROPN
ejpam-5608	139	16	)	)	PUNCT
ejpam-5608	139	17	≥	≥	X
ejpam-5608	139	18	ε}|	ε}|	VERB
ejpam-5608	139	19	<	<	X
ejpam-5608	139	20	+	+	NOUN
ejpam-5608	139	21	∞	∞	PROPN
ejpam-5608	139	22	,	,	PUNCT
ejpam-5608	139	23	let	let	VERB
ejpam-5608	139	24	|b|	|b|	PROPN
ejpam-5608	139	25	=	=	PUNCT
ejpam-5608	139	26	y.	y.	NOUN
ejpam-5608	139	27	if	if	SCONJ
ejpam-5608	139	28	|a|	|a|	PROPN
ejpam-5608	139	29	=	=	SYM
ejpam-5608	139	30	|{n	|{n	NOUN
ejpam-5608	139	31	:	:	PUNCT
ejpam-5608	139	32	(	(	PUNCT
ejpam-5608	139	33	n	n	X
ejpam-5608	139	34	,	,	PUNCT
ejpam-5608	139	35	m	m	NOUN
ejpam-5608	139	36	)	)	PUNCT
ejpam-5608	139	37	∈	∈	PROPN
ejpam-5608	139	38	n2	n2	NOUN
ejpam-5608	139	39	,	,	PUNCT
ejpam-5608	139	40	g(x	g(x	PROPN
ejpam-5608	139	41	,	,	PUNCT
ejpam-5608	139	42	xn	xn	PROPN
ejpam-5608	139	43	,	,	PUNCT
ejpam-5608	139	44	xm	xm	PROPN
ejpam-5608	139	45	)	)	PUNCT
ejpam-5608	139	46	≥	≥	X
ejpam-5608	139	47	ε}|	ε}|	VERB
ejpam-5608	139	48	<	<	X
ejpam-5608	139	49	+	+	NOUN
ejpam-5608	139	50	∞	∞	PROPN
ejpam-5608	139	51	,	,	PUNCT
ejpam-5608	139	52	then	then	ADV
ejpam-5608	139	53	there	there	PRON
ejpam-5608	139	54	exists	exist	VERB
ejpam-5608	139	55	z	z	NOUN
ejpam-5608	139	56	+	+	CCONJ
ejpam-5608	139	57	1	1	NUM
ejpam-5608	139	58	∈	∈	NOUN
ejpam-5608	139	59	n	n	PRON
ejpam-5608	139	60	such	such	ADJ
ejpam-5608	139	61	that	that	PRON
ejpam-5608	139	62	for	for	ADP
ejpam-5608	139	63	all	all	DET
ejpam-5608	139	64	n	n	CCONJ
ejpam-5608	139	65	,	,	PUNCT
ejpam-5608	139	66	m	m	VERB
ejpam-5608	139	67	≥	≥	NOUN
ejpam-5608	139	68	z	z	NOUN
ejpam-5608	139	69	+	+	CCONJ
ejpam-5608	139	70	1	1	NUM
ejpam-5608	139	71	,	,	PUNCT
ejpam-5608	139	72	g(x	g(x	NOUN
ejpam-5608	139	73	,	,	PUNCT
ejpam-5608	139	74	xn	xn	PROPN
ejpam-5608	139	75	,	,	PUNCT
ejpam-5608	139	76	xm	xm	PROPN
ejpam-5608	139	77	)	)	PUNCT
ejpam-5608	139	78	<	<	X
ejpam-5608	139	79	ε	ε	PROPN
ejpam-5608	139	80	,	,	PUNCT
ejpam-5608	139	81	or	or	CCONJ
ejpam-5608	139	82	in	in	ADP
ejpam-5608	139	83	other	other	ADJ
ejpam-5608	139	84	words	word	NOUN
ejpam-5608	139	85	,	,	PUNCT
ejpam-5608	139	86	the	the	DET
ejpam-5608	139	87	sequence	sequence	NOUN
ejpam-5608	139	88	(	(	PUNCT
ejpam-5608	139	89	xn	xn	X
ejpam-5608	139	90	)	)	PUNCT
ejpam-5608	139	91	converges	converge	VERB
ejpam-5608	139	92	ordinarily	ordinarily	ADV
ejpam-5608	139	93	to	to	ADP
ejpam-5608	139	94	x	x	PROPN
ejpam-5608	139	95	in	in	ADP
ejpam-5608	139	96	the	the	DET
ejpam-5608	139	97	g	g	NOUN
ejpam-5608	139	98	-	-	PUNCT
ejpam-5608	139	99	metric	metric	ADJ
ejpam-5608	139	100	space	space	NOUN
ejpam-5608	139	101	.	.	PUNCT
ejpam-5608	140	1	if	if	SCONJ
ejpam-5608	140	2	manuharawati	manuharawati	NOUN
ejpam-5608	140	3	,	,	PUNCT
ejpam-5608	140	4	m.jakfar	m.jakfar	ADV
ejpam-5608	140	5	,	,	PUNCT
ejpam-5608	140	6	a.	a.	PROPN
ejpam-5608	140	7	taufik	taufik	PROPN
ejpam-5608	140	8	hamzah	hamzah	PROPN
ejpam-5608	140	9	/	/	SYM
ejpam-5608	140	10	eur	eur	PROPN
ejpam-5608	140	11	.	.	PUNCT
ejpam-5608	141	1	j.	j.	PROPN
ejpam-5608	141	2	pure	pure	PROPN
ejpam-5608	141	3	appl	appl	PROPN
ejpam-5608	141	4	.	.	PROPN
ejpam-5608	141	5	math	math	PROPN
ejpam-5608	141	6	,	,	PUNCT
ejpam-5608	141	7	18	18	NUM
ejpam-5608	141	8	(	(	PUNCT
ejpam-5608	141	9	1	1	NUM
ejpam-5608	141	10	)	)	PUNCT
ejpam-5608	141	11	(	(	PUNCT
ejpam-5608	141	12	2025	2025	NUM
ejpam-5608	141	13	)	)	PUNCT
ejpam-5608	141	14	,	,	PUNCT
ejpam-5608	141	15	5608	5608	NUM
ejpam-5608	141	16	7	7	NUM
ejpam-5608	141	17	of	of	ADP
ejpam-5608	141	18	13	13	NUM
ejpam-5608	141	19	|b|	|b|	NOUN
ejpam-5608	141	20	=	=	PUNCT
ejpam-5608	141	21	|{m	|{m	NOUN
ejpam-5608	141	22	:	:	PUNCT
ejpam-5608	141	23	(	(	PUNCT
ejpam-5608	141	24	n	n	X
ejpam-5608	141	25	,	,	PUNCT
ejpam-5608	141	26	m	m	NOUN
ejpam-5608	141	27	)	)	PUNCT
ejpam-5608	141	28	∈	∈	PROPN
ejpam-5608	141	29	n2	n2	NOUN
ejpam-5608	141	30	,	,	PUNCT
ejpam-5608	141	31	g(x	g(x	PROPN
ejpam-5608	141	32	,	,	PUNCT
ejpam-5608	141	33	xn	xn	PROPN
ejpam-5608	141	34	,	,	PUNCT
ejpam-5608	141	35	xm	xm	PROPN
ejpam-5608	141	36	)	)	PUNCT
ejpam-5608	141	37	≥	≥	X
ejpam-5608	141	38	ε}|	ε}|	VERB
ejpam-5608	141	39	<	<	X
ejpam-5608	141	40	+	+	NOUN
ejpam-5608	141	41	∞	∞	PROPN
ejpam-5608	141	42	,	,	PUNCT
ejpam-5608	141	43	then	then	ADV
ejpam-5608	141	44	there	there	PRON
ejpam-5608	141	45	exists	exist	VERB
ejpam-5608	141	46	y	y	PROPN
ejpam-5608	141	47	+	+	CCONJ
ejpam-5608	141	48	1	1	NUM
ejpam-5608	141	49	∈	∈	NOUN
ejpam-5608	141	50	n	n	PRON
ejpam-5608	141	51	such	such	ADJ
ejpam-5608	141	52	that	that	PRON
ejpam-5608	141	53	for	for	ADP
ejpam-5608	141	54	all	all	DET
ejpam-5608	141	55	n	n	CCONJ
ejpam-5608	141	56	,	,	PUNCT
ejpam-5608	141	57	m	m	VERB
ejpam-5608	141	58	≥	≥	NOUN
ejpam-5608	141	59	y+1	y+1	NUM
ejpam-5608	141	60	,	,	PUNCT
ejpam-5608	141	61	g(x	g(x	PROPN
ejpam-5608	141	62	,	,	PUNCT
ejpam-5608	141	63	xn	xn	PROPN
ejpam-5608	141	64	,	,	PUNCT
ejpam-5608	141	65	xm	xm	PROPN
ejpam-5608	141	66	)	)	PUNCT
ejpam-5608	141	67	<	<	X
ejpam-5608	141	68	ε	ε	PROPN
ejpam-5608	141	69	,	,	PUNCT
ejpam-5608	141	70	or	or	CCONJ
ejpam-5608	141	71	in	in	ADP
ejpam-5608	141	72	other	other	ADJ
ejpam-5608	141	73	words	word	NOUN
ejpam-5608	141	74	,	,	PUNCT
ejpam-5608	141	75	the	the	DET
ejpam-5608	141	76	sequence	sequence	NOUN
ejpam-5608	141	77	(	(	PUNCT
ejpam-5608	141	78	xn	xn	X
ejpam-5608	141	79	)	)	PUNCT
ejpam-5608	141	80	converges	converge	VERB
ejpam-5608	141	81	ordinarily	ordinarily	ADV
ejpam-5608	141	82	to	to	ADP
ejpam-5608	141	83	x	x	PROPN
ejpam-5608	141	84	in	in	ADP
ejpam-5608	141	85	the	the	DET
ejpam-5608	141	86	g	g	NOUN
ejpam-5608	141	87	-	-	PUNCT
ejpam-5608	141	88	metric	metric	ADJ
ejpam-5608	141	89	space	space	NOUN
ejpam-5608	141	90	.	.	PUNCT
ejpam-5608	142	1	example	example	NOUN
ejpam-5608	143	1	3	3	NUM
ejpam-5608	143	2	.	.	PUNCT
ejpam-5608	143	3	given	give	VERB
ejpam-5608	143	4	a	a	DET
ejpam-5608	143	5	g	g	NOUN
ejpam-5608	143	6	-	-	PUNCT
ejpam-5608	143	7	metric	metric	ADJ
ejpam-5608	143	8	space	space	NOUN
ejpam-5608	143	9	,	,	PUNCT
ejpam-5608	143	10	(	(	PUNCT
ejpam-5608	143	11	r	r	NOUN
ejpam-5608	143	12	,	,	PUNCT
ejpam-5608	143	13	g	g	NOUN
ejpam-5608	143	14	)	)	PUNCT
ejpam-5608	143	15	,	,	PUNCT
ejpam-5608	143	16	and	and	CCONJ
ejpam-5608	143	17	for	for	ADP
ejpam-5608	143	18	every	every	DET
ejpam-5608	143	19	x	x	PROPN
ejpam-5608	143	20	,	,	PUNCT
ejpam-5608	143	21	y	y	PROPN
ejpam-5608	143	22	,	,	PUNCT
ejpam-5608	143	23	z	z	NOUN
ejpam-5608	143	24	∈	∈	PROPN
ejpam-5608	143	25	r	r	NOUN
ejpam-5608	143	26	,	,	PUNCT
ejpam-5608	143	27	the	the	DET
ejpam-5608	143	28	following	follow	VERB
ejpam-5608	143	29	condition	condition	NOUN
ejpam-5608	143	30	holds	hold	VERB
ejpam-5608	143	31	:	:	PUNCT
ejpam-5608	143	32	g	g	PROPN
ejpam-5608	143	33	(	(	PUNCT
ejpam-5608	143	34	x	x	PROPN
ejpam-5608	143	35	,	,	PUNCT
ejpam-5608	143	36	y	y	PROPN
ejpam-5608	143	37	,	,	PUNCT
ejpam-5608	143	38	z	z	NOUN
ejpam-5608	143	39	)	)	PUNCT
ejpam-5608	143	40	=	=	SYM
ejpam-5608	143	41	max{|x−	max{|x−	PROPN
ejpam-5608	143	42	y|+	y|+	PROPN
ejpam-5608	143	43	|x−	|x−	PROPN
ejpam-5608	143	44	z|+	z|+	NOUN
ejpam-5608	143	45	|y	|y	NOUN
ejpam-5608	143	46	−	−	PROPN
ejpam-5608	143	47	z|	z|	PROPN
ejpam-5608	143	48	}	}	PUNCT
ejpam-5608	143	49	the	the	DET
ejpam-5608	143	50	sequence	sequence	NOUN
ejpam-5608	143	51	(	(	PUNCT
ejpam-5608	143	52	xn	xn	PROPN
ejpam-5608	143	53	)	)	PUNCT
ejpam-5608	143	54	=	=	PUNCT
ejpam-5608	143	55	(	(	PUNCT
ejpam-5608	143	56	n	n	NOUN
ejpam-5608	143	57	n+1	n+1	X
ejpam-5608	143	58	)	)	PUNCT
ejpam-5608	143	59	converges	converge	VERB
ejpam-5608	143	60	to	to	ADP
ejpam-5608	143	61	1	1	NUM
ejpam-5608	143	62	in	in	ADP
ejpam-5608	143	63	the	the	DET
ejpam-5608	143	64	g	g	NOUN
ejpam-5608	143	65	-	-	PUNCT
ejpam-5608	143	66	metric	metric	ADJ
ejpam-5608	143	67	space	space	NOUN
ejpam-5608	143	68	.	.	PUNCT
ejpam-5608	144	1	clearly	clearly	ADV
ejpam-5608	144	2	,	,	PUNCT
ejpam-5608	144	3	(	(	PUNCT
ejpam-5608	144	4	xn	xn	X
ejpam-5608	144	5	)	)	PUNCT
ejpam-5608	144	6	is	be	AUX
ejpam-5608	144	7	an	an	DET
ejpam-5608	144	8	increasing	increase	VERB
ejpam-5608	144	9	sequence	sequence	NOUN
ejpam-5608	144	10	since	since	SCONJ
ejpam-5608	144	11	n	n	PROPN
ejpam-5608	144	12	n+1	n+1	PROPN
ejpam-5608	144	13	≤	≤	NOUN
ejpam-5608	144	14	n+1	n+1	PROPN
ejpam-5608	144	15	n+2	n+2	PROPN
ejpam-5608	144	16	.	.	PUNCT
ejpam-5608	145	1	next	next	ADV
ejpam-5608	145	2	,	,	PUNCT
ejpam-5608	145	3	it	it	PRON
ejpam-5608	145	4	will	will	AUX
ejpam-5608	145	5	be	be	AUX
ejpam-5608	145	6	proven	prove	VERB
ejpam-5608	145	7	that	that	SCONJ
ejpam-5608	145	8	the	the	DET
ejpam-5608	145	9	sequence	sequence	NOUN
ejpam-5608	145	10	(	(	PUNCT
ejpam-5608	145	11	xn	xn	X
ejpam-5608	145	12	)	)	PUNCT
ejpam-5608	145	13	statistically	statistically	ADV
ejpam-5608	145	14	converges	converge	VERB
ejpam-5608	145	15	to	to	ADP
ejpam-5608	145	16	1	1	NUM
ejpam-5608	145	17	in	in	ADP
ejpam-5608	145	18	the	the	DET
ejpam-5608	145	19	g	g	NOUN
ejpam-5608	145	20	-	-	PUNCT
ejpam-5608	145	21	metric	metric	ADJ
ejpam-5608	145	22	space	space	NOUN
ejpam-5608	145	23	.	.	PUNCT
ejpam-5608	146	1	let	let	VERB
ejpam-5608	146	2	i	i	PRON
ejpam-5608	146	3	be	be	AUX
ejpam-5608	146	4	the	the	DET
ejpam-5608	146	5	greatest	great	ADJ
ejpam-5608	146	6	integer	integer	NOUN
ejpam-5608	146	7	less	less	ADJ
ejpam-5608	146	8	than	than	ADP
ejpam-5608	146	9	or	or	CCONJ
ejpam-5608	146	10	equal	equal	ADJ
ejpam-5608	146	11	to	to	ADP
ejpam-5608	146	12	1	1	NUM
ejpam-5608	146	13	ε	ε	PROPN
ejpam-5608	146	14	−	−	PROPN
ejpam-5608	146	15	1	1	NUM
ejpam-5608	146	16	for	for	ADP
ejpam-5608	146	17	every	every	DET
ejpam-5608	146	18	ε	ε	PROPN
ejpam-5608	146	19	>	>	X
ejpam-5608	146	20	0	0	PROPN
ejpam-5608	146	21	,	,	PUNCT
ejpam-5608	146	22	ε	ε	PROPN
ejpam-5608	146	23	∈	∈	PROPN
ejpam-5608	146	24	r	r	NOUN
ejpam-5608	146	25	,	,	PUNCT
ejpam-5608	147	1	then	then	ADV
ejpam-5608	147	2	lim	lim	PROPN
ejpam-5608	147	3	n→+∞	n→+∞	PROPN
ejpam-5608	147	4	(	(	PUNCT
ejpam-5608	147	5	2	2	NUM
ejpam-5608	147	6	n2	n2	ADJ
ejpam-5608	147	7	|{(n1	|{(n1	PROPN
ejpam-5608	147	8	,	,	PUNCT
ejpam-5608	147	9	n2	n2	ADJ
ejpam-5608	147	10	)	)	PUNCT
ejpam-5608	147	11	∈	∈	PROPN
ejpam-5608	147	12	n2	n2	NOUN
ejpam-5608	147	13	:	:	PUNCT
ejpam-5608	147	14	n1	n1	ADJ
ejpam-5608	147	15	,	,	PUNCT
ejpam-5608	147	16	n2	n2	ADJ
ejpam-5608	147	17	≤	≤	PUNCT
ejpam-5608	147	18	n	n	CCONJ
ejpam-5608	147	19	,	,	PUNCT
ejpam-5608	147	20	g(xi	g(xi	PROPN
ejpam-5608	147	21	,	,	PUNCT
ejpam-5608	147	22	xn1	xn1	NUM
ejpam-5608	147	23	,	,	PUNCT
ejpam-5608	147	24	xn2	xn2	PROPN
ejpam-5608	147	25	)	)	PUNCT
ejpam-5608	147	26	≥	≥	NUM
ejpam-5608	147	27	ε}|	ε}|	NOUN
ejpam-5608	147	28	)	)	PUNCT
ejpam-5608	148	1	=	=	VERB
ejpam-5608	148	2	lim	lim	PROPN
ejpam-5608	148	3	n→+∞	n→+∞	PROPN
ejpam-5608	148	4	(	(	PUNCT
ejpam-5608	148	5	2	2	NUM
ejpam-5608	148	6	n2	n2	NOUN
ejpam-5608	148	7	|{(1	|{(1	PROPN
ejpam-5608	148	8	,	,	PUNCT
ejpam-5608	148	9	1	1	NUM
ejpam-5608	148	10	)	)	PUNCT
ejpam-5608	148	11	,	,	PUNCT
ejpam-5608	148	12	(	(	PUNCT
ejpam-5608	148	13	1	1	NUM
ejpam-5608	148	14	,	,	PUNCT
ejpam-5608	148	15	2	2	NUM
ejpam-5608	148	16	)	)	PUNCT
ejpam-5608	148	17	,	,	PUNCT
ejpam-5608	148	18	(	(	PUNCT
ejpam-5608	148	19	1	1	NUM
ejpam-5608	148	20	,	,	PUNCT
ejpam-5608	148	21	3	3	NUM
ejpam-5608	148	22	)	)	PUNCT
ejpam-5608	148	23	,	,	PUNCT
ejpam-5608	148	24	.	.	PUNCT
ejpam-5608	148	25	.	.	PUNCT
ejpam-5608	148	26	.	.	PUNCT
ejpam-5608	149	1	,	,	PUNCT
ejpam-5608	149	2	(	(	PUNCT
ejpam-5608	149	3	i	i	NOUN
ejpam-5608	149	4	,	,	PUNCT
ejpam-5608	149	5	1	1	NUM
ejpam-5608	149	6	)	)	PUNCT
ejpam-5608	149	7	,	,	PUNCT
ejpam-5608	149	8	(	(	PUNCT
ejpam-5608	149	9	i	i	NOUN
ejpam-5608	149	10	,	,	PUNCT
ejpam-5608	149	11	2	2	NUM
ejpam-5608	149	12	)	)	PUNCT
ejpam-5608	149	13	,	,	PUNCT
ejpam-5608	149	14	.	.	PUNCT
ejpam-5608	149	15	.	.	PUNCT
ejpam-5608	149	16	.	.	PUNCT
ejpam-5608	150	1	}	}	PUNCT
ejpam-5608	150	2	|	|	X
ejpam-5608	150	3	)	)	PUNCT
ejpam-5608	150	4	≤	≤	NOUN
ejpam-5608	150	5	lim	lim	PROPN
ejpam-5608	150	6	n→+∞	n→+∞	PROPN
ejpam-5608	150	7	(	(	PUNCT
ejpam-5608	150	8	2ni	2ni	ADJ
ejpam-5608	150	9	n2	n2	NOUN
ejpam-5608	150	10	)	)	PUNCT
ejpam-5608	150	11	≤	≤	NOUN
ejpam-5608	150	12	2i	2i	NUM
ejpam-5608	150	13	lim	lim	PROPN
ejpam-5608	150	14	n→+∞	n→+∞	PROPN
ejpam-5608	150	15	(	(	PUNCT
ejpam-5608	150	16	1	1	NUM
ejpam-5608	150	17	n	n	NOUN
ejpam-5608	150	18	)	)	PUNCT
ejpam-5608	150	19	=	=	SYM
ejpam-5608	151	1	2i.0	2i.0	NOUN
ejpam-5608	151	2	=	=	SYM
ejpam-5608	151	3	0	0	PUNCT
ejpam-5608	152	1	the	the	DET
ejpam-5608	152	2	statement	statement	NOUN
ejpam-5608	152	3	(	(	PUNCT
ejpam-5608	152	4	xn	xn	PROPN
ejpam-5608	152	5	)	)	PUNCT
ejpam-5608	152	6	=	=	PUNCT
ejpam-5608	152	7	(	(	PUNCT
ejpam-5608	152	8	n	n	NOUN
ejpam-5608	152	9	n+1	n+1	PROPN
ejpam-5608	152	10	)	)	PUNCT
ejpam-5608	152	11	is	be	AUX
ejpam-5608	152	12	statistically	statistically	ADV
ejpam-5608	152	13	convergent	convergent	ADJ
ejpam-5608	152	14	to	to	ADP
ejpam-5608	152	15	1	1	NUM
ejpam-5608	152	16	in	in	ADP
ejpam-5608	152	17	the	the	DET
ejpam-5608	152	18	g	g	NOUN
ejpam-5608	152	19	-	-	PUNCT
ejpam-5608	152	20	metric	metric	ADJ
ejpam-5608	152	21	space	space	NOUN
ejpam-5608	152	22	”	"	PUNCT
ejpam-5608	152	23	has	have	AUX
ejpam-5608	152	24	been	be	AUX
ejpam-5608	152	25	proven	prove	VERB
ejpam-5608	152	26	.	.	PUNCT
ejpam-5608	153	1	since	since	SCONJ
ejpam-5608	153	2	(	(	PUNCT
ejpam-5608	153	3	xn	xn	X
ejpam-5608	153	4	)	)	PUNCT
ejpam-5608	153	5	=	=	PUNCT
ejpam-5608	153	6	(	(	PUNCT
ejpam-5608	153	7	n	n	NOUN
ejpam-5608	153	8	n+1	n+1	PROPN
ejpam-5608	153	9	)	)	PUNCT
ejpam-5608	153	10	is	be	AUX
ejpam-5608	153	11	statistically	statistically	ADV
ejpam-5608	153	12	convergent	convergent	ADJ
ejpam-5608	153	13	to	to	ADP
ejpam-5608	153	14	1	1	NUM
ejpam-5608	153	15	in	in	ADP
ejpam-5608	153	16	the	the	DET
ejpam-5608	153	17	g	g	NOUN
ejpam-5608	153	18	-	-	PUNCT
ejpam-5608	153	19	metric	metric	ADJ
ejpam-5608	153	20	space	space	NOUN
ejpam-5608	153	21	and	and	CCONJ
ejpam-5608	153	22	is	be	AUX
ejpam-5608	153	23	a	a	DET
ejpam-5608	153	24	monotonic	monotonic	ADJ
ejpam-5608	153	25	sequence	sequence	NOUN
ejpam-5608	153	26	,	,	PUNCT
ejpam-5608	153	27	by	by	ADP
ejpam-5608	153	28	theorem	theorem	NOUN
ejpam-5608	153	29	4	4	NUM
ejpam-5608	153	30	,	,	PUNCT
ejpam-5608	153	31	(	(	PUNCT
ejpam-5608	153	32	xn	xn	X
ejpam-5608	153	33	)	)	PUNCT
ejpam-5608	154	1	=	=	PUNCT
ejpam-5608	154	2	(	(	PUNCT
ejpam-5608	154	3	n	n	NOUN
ejpam-5608	154	4	n+1	n+1	X
ejpam-5608	154	5	)	)	PUNCT
ejpam-5608	154	6	converges	converge	VERB
ejpam-5608	154	7	to	to	ADP
ejpam-5608	154	8	1	1	NUM
ejpam-5608	154	9	in	in	ADP
ejpam-5608	154	10	the	the	DET
ejpam-5608	154	11	g	g	NOUN
ejpam-5608	154	12	-	-	PUNCT
ejpam-5608	154	13	metric	metric	ADJ
ejpam-5608	154	14	space	space	NOUN
ejpam-5608	154	15	.	.	PUNCT
ejpam-5608	155	1	theorem	theorem	ADJ
ejpam-5608	155	2	5	5	NUM
ejpam-5608	155	3	.	.	PUNCT
ejpam-5608	156	1	[	[	X
ejpam-5608	156	2	19	19	NUM
ejpam-5608	156	3	]	]	PUNCT
ejpam-5608	156	4	given	give	VERB
ejpam-5608	156	5	an	an	DET
ejpam-5608	156	6	admissible	admissible	ADJ
ejpam-5608	156	7	ideal	ideal	ADJ
ejpam-5608	156	8	i2	i2	PROPN
ejpam-5608	156	9	.	.	PUNCT
ejpam-5608	157	1	if	if	SCONJ
ejpam-5608	157	2	a	a	DET
ejpam-5608	157	3	sequence	sequence	NOUN
ejpam-5608	157	4	converges	converge	VERB
ejpam-5608	157	5	to	to	ADP
ejpam-5608	157	6	x	x	PUNCT
ejpam-5608	157	7	in	in	ADP
ejpam-5608	157	8	a	a	DET
ejpam-5608	157	9	g	g	NOUN
ejpam-5608	157	10	-	-	PUNCT
ejpam-5608	157	11	metric	metric	ADJ
ejpam-5608	157	12	space	space	NOUN
ejpam-5608	157	13	,	,	PUNCT
ejpam-5608	157	14	then	then	ADV
ejpam-5608	157	15	the	the	DET
ejpam-5608	157	16	sequence	sequence	NOUN
ejpam-5608	157	17	converges	converge	VERB
ejpam-5608	157	18	ideally	ideally	ADV
ejpam-5608	157	19	to	to	ADP
ejpam-5608	157	20	x	x	VERB
ejpam-5608	157	21	in	in	ADP
ejpam-5608	157	22	the	the	DET
ejpam-5608	157	23	g	g	NOUN
ejpam-5608	157	24	-	-	PUNCT
ejpam-5608	157	25	metric	metric	ADJ
ejpam-5608	157	26	space	space	NOUN
ejpam-5608	157	27	with	with	ADP
ejpam-5608	157	28	the	the	DET
ejpam-5608	157	29	ideal	ideal	PROPN
ejpam-5608	157	30	i2	i2	PROPN
ejpam-5608	157	31	.	.	PUNCT
ejpam-5608	158	1	proof	proof	NOUN
ejpam-5608	158	2	.	.	PUNCT
ejpam-5608	159	1	let	let	AUX
ejpam-5608	159	2	(	(	PUNCT
ejpam-5608	159	3	xn	xn	X
ejpam-5608	159	4	)	)	PUNCT
ejpam-5608	159	5	be	be	VERB
ejpam-5608	159	6	a	a	DET
ejpam-5608	159	7	sequence	sequence	NOUN
ejpam-5608	159	8	that	that	PRON
ejpam-5608	159	9	converges	converge	VERB
ejpam-5608	159	10	to	to	ADP
ejpam-5608	159	11	x	x	PUNCT
ejpam-5608	159	12	in	in	ADP
ejpam-5608	159	13	the	the	DET
ejpam-5608	159	14	g	g	NOUN
ejpam-5608	159	15	-	-	PUNCT
ejpam-5608	159	16	metric	metric	ADJ
ejpam-5608	159	17	space	space	NOUN
ejpam-5608	159	18	(	(	PUNCT
ejpam-5608	159	19	r	r	NOUN
ejpam-5608	159	20	,	,	PUNCT
ejpam-5608	159	21	g	g	NOUN
ejpam-5608	159	22	)	)	PUNCT
ejpam-5608	159	23	.	.	PUNCT
ejpam-5608	160	1	this	this	PRON
ejpam-5608	160	2	means	mean	VERB
ejpam-5608	160	3	that	that	SCONJ
ejpam-5608	160	4	for	for	ADP
ejpam-5608	160	5	every	every	DET
ejpam-5608	160	6	real	real	ADJ
ejpam-5608	160	7	number	number	NOUN
ejpam-5608	160	8	ε	ε	PROPN
ejpam-5608	160	9	>	>	X
ejpam-5608	160	10	0	0	PROPN
ejpam-5608	160	11	,	,	PUNCT
ejpam-5608	160	12	there	there	PRON
ejpam-5608	160	13	exists	exist	VERB
ejpam-5608	160	14	n0	n0	PROPN
ejpam-5608	160	15	∈	∈	PROPN
ejpam-5608	160	16	n	n	PRON
ejpam-5608	160	17	such	such	ADJ
ejpam-5608	160	18	that	that	PRON
ejpam-5608	160	19	for	for	ADP
ejpam-5608	160	20	every	every	DET
ejpam-5608	160	21	natural	natural	ADJ
ejpam-5608	160	22	number	number	NOUN
ejpam-5608	160	23	n	n	CCONJ
ejpam-5608	160	24	,	,	PUNCT
ejpam-5608	160	25	m	m	PROPN
ejpam-5608	160	26	≥	≥	NOUN
ejpam-5608	160	27	n0	n0	NUM
ejpam-5608	160	28	,	,	PUNCT
ejpam-5608	160	29	we	we	PRON
ejpam-5608	160	30	have	have	VERB
ejpam-5608	160	31	g	g	NOUN
ejpam-5608	160	32	(	(	PUNCT
ejpam-5608	160	33	x	x	X
ejpam-5608	160	34	,	,	PUNCT
ejpam-5608	160	35	xn	xn	PROPN
ejpam-5608	160	36	,	,	PUNCT
ejpam-5608	160	37	xm	xm	PROPN
ejpam-5608	160	38	)	)	PUNCT
ejpam-5608	160	39	<	<	X
ejpam-5608	160	40	ε	ε	PROPN
ejpam-5608	160	41	.	.	PUNCT
ejpam-5608	161	1	if	if	SCONJ
ejpam-5608	161	2	we	we	PRON
ejpam-5608	161	3	define	define	VERB
ejpam-5608	161	4	a	a	DET
ejpam-5608	161	5	set	set	NOUN
ejpam-5608	161	6	,	,	PUNCT
ejpam-5608	161	7	it	it	PRON
ejpam-5608	161	8	will	will	AUX
ejpam-5608	161	9	form	form	VERB
ejpam-5608	161	10	the	the	DET
ejpam-5608	161	11	following	follow	VERB
ejpam-5608	161	12	set	set	NOUN
ejpam-5608	161	13	:	:	PUNCT
ejpam-5608	161	14	a	a	DET
ejpam-5608	161	15	(	(	PUNCT
ejpam-5608	161	16	n0	n0	NUM
ejpam-5608	161	17	)	)	PUNCT
ejpam-5608	161	18	=	=	PRON
ejpam-5608	161	19	{	{	PUNCT
ejpam-5608	161	20	(	(	PUNCT
ejpam-5608	161	21	n	n	CCONJ
ejpam-5608	161	22	,	,	PUNCT
ejpam-5608	161	23	m	m	NOUN
ejpam-5608	161	24	)	)	PUNCT
ejpam-5608	161	25	∈	∈	PROPN
ejpam-5608	161	26	n2	n2	NOUN
ejpam-5608	161	27	:	:	PUNCT
ejpam-5608	161	28	n	n	CCONJ
ejpam-5608	161	29	,	,	PUNCT
ejpam-5608	161	30	m	m	PROPN
ejpam-5608	161	31	≥	≥	NOUN
ejpam-5608	161	32	n0	n0	PROPN
ejpam-5608	161	33	,	,	PUNCT
ejpam-5608	161	34	g	g	PROPN
ejpam-5608	161	35	(	(	PUNCT
ejpam-5608	161	36	x	x	X
ejpam-5608	161	37	,	,	PUNCT
ejpam-5608	161	38	xn	xn	PROPN
ejpam-5608	161	39	,	,	PUNCT
ejpam-5608	161	40	xm	xm	PROPN
ejpam-5608	161	41	)	)	PUNCT
ejpam-5608	161	42	<	<	X
ejpam-5608	161	43	ε	ε	PROPN
ejpam-5608	161	44	}	}	PUNCT
ejpam-5608	161	45	it	it	PRON
ejpam-5608	161	46	is	be	AUX
ejpam-5608	161	47	clear	clear	ADJ
ejpam-5608	161	48	that	that	SCONJ
ejpam-5608	161	49	|a	|a	NOUN
ejpam-5608	161	50	(	(	PUNCT
ejpam-5608	161	51	n0)|	n0)|	NOUN
ejpam-5608	161	52	=	=	SYM
ejpam-5608	161	53	+	+	NOUN
ejpam-5608	161	54	∞	∞	PROPN
ejpam-5608	161	55	since	since	SCONJ
ejpam-5608	161	56	there	there	PRON
ejpam-5608	161	57	exists	exist	VERB
ejpam-5608	161	58	n0	n0	PROPN
ejpam-5608	161	59	∈	∈	PROPN
ejpam-5608	161	60	n	n	PRON
ejpam-5608	161	61	such	such	ADJ
ejpam-5608	161	62	that	that	PRON
ejpam-5608	161	63	for	for	ADP
ejpam-5608	161	64	every	every	DET
ejpam-5608	161	65	n	n	CCONJ
ejpam-5608	161	66	,	,	PUNCT
ejpam-5608	161	67	m	m	PROPN
ejpam-5608	161	68	≥	≥	NOUN
ejpam-5608	161	69	n0	n0	PROPN
ejpam-5608	161	70	,	,	PUNCT
ejpam-5608	161	71	g	g	PROPN
ejpam-5608	161	72	(	(	PUNCT
ejpam-5608	161	73	x	x	X
ejpam-5608	161	74	,	,	PUNCT
ejpam-5608	161	75	xn	xn	PROPN
ejpam-5608	161	76	,	,	PUNCT
ejpam-5608	161	77	xm	xm	PROPN
ejpam-5608	161	78	)	)	PUNCT
ejpam-5608	161	79	<	<	X
ejpam-5608	161	80	ε	ε	PROPN
ejpam-5608	161	81	,	,	PUNCT
ejpam-5608	161	82	the	the	DET
ejpam-5608	161	83	number	number	NOUN
ejpam-5608	161	84	of	of	ADP
ejpam-5608	161	85	n	n	CCONJ
ejpam-5608	161	86	,	,	PUNCT
ejpam-5608	161	87	m	m	VERB
ejpam-5608	161	88	∈	∈	ADJ
ejpam-5608	161	89	n	n	CCONJ
ejpam-5608	161	90	that	that	PRON
ejpam-5608	161	91	satisfy	satisfy	VERB
ejpam-5608	161	92	g	g	PROPN
ejpam-5608	161	93	(	(	PUNCT
ejpam-5608	161	94	x	x	X
ejpam-5608	161	95	,	,	PUNCT
ejpam-5608	161	96	xn	xn	PROPN
ejpam-5608	161	97	,	,	PUNCT
ejpam-5608	161	98	xm	xm	PROPN
ejpam-5608	161	99	)	)	PUNCT
ejpam-5608	161	100	≥	≥	PROPN
ejpam-5608	161	101	ε	ε	PROPN
ejpam-5608	161	102	is	be	AUX
ejpam-5608	161	103	at	at	ADP
ejpam-5608	161	104	most	most	ADJ
ejpam-5608	161	105	j2	j2	NOUN
ejpam-5608	161	106	,	,	PUNCT
ejpam-5608	161	107	or	or	CCONJ
ejpam-5608	161	108	in	in	ADP
ejpam-5608	161	109	other	other	ADJ
ejpam-5608	161	110	words	word	NOUN
ejpam-5608	161	111	,	,	PUNCT
ejpam-5608	161	112	it	it	PRON
ejpam-5608	161	113	is	be	AUX
ejpam-5608	161	114	finite	finite	ADJ
ejpam-5608	161	115	.	.	PUNCT
ejpam-5608	162	1	thus	thus	ADV
ejpam-5608	162	2	,	,	PUNCT
ejpam-5608	162	3	a	a	DET
ejpam-5608	162	4	(	(	PUNCT
ejpam-5608	162	5	ε	ε	PROPN
ejpam-5608	162	6	)	)	PUNCT
ejpam-5608	162	7	∈	∈	PROPN
ejpam-5608	162	8	i2	i2	PROPN
ejpam-5608	162	9	therefore	therefore	ADV
ejpam-5608	162	10	,	,	PUNCT
ejpam-5608	162	11	the	the	DET
ejpam-5608	162	12	sequence	sequence	NOUN
ejpam-5608	162	13	(	(	PUNCT
ejpam-5608	162	14	xn	xn	X
ejpam-5608	162	15	)	)	PUNCT
ejpam-5608	162	16	is	be	AUX
ejpam-5608	162	17	ideally	ideally	ADV
ejpam-5608	162	18	convergent	convergent	ADJ
ejpam-5608	162	19	to	to	ADP
ejpam-5608	162	20	x.	x.	PROPN
ejpam-5608	162	21	manuharawati	manuharawati	PROPN
ejpam-5608	162	22	,	,	PUNCT
ejpam-5608	162	23	m.jakfar	m.jakfar	ADV
ejpam-5608	162	24	,	,	PUNCT
ejpam-5608	162	25	a.	a.	PROPN
ejpam-5608	162	26	taufik	taufik	PROPN
ejpam-5608	162	27	hamzah	hamzah	PROPN
ejpam-5608	162	28	/	/	SYM
ejpam-5608	162	29	eur	eur	PROPN
ejpam-5608	162	30	.	.	PUNCT
ejpam-5608	163	1	j.	j.	PROPN
ejpam-5608	163	2	pure	pure	PROPN
ejpam-5608	163	3	appl	appl	PROPN
ejpam-5608	163	4	.	.	PROPN
ejpam-5608	163	5	math	math	PROPN
ejpam-5608	163	6	,	,	PUNCT
ejpam-5608	163	7	18	18	NUM
ejpam-5608	163	8	(	(	PUNCT
ejpam-5608	163	9	1	1	NUM
ejpam-5608	163	10	)	)	PUNCT
ejpam-5608	163	11	(	(	PUNCT
ejpam-5608	163	12	2025	2025	NUM
ejpam-5608	163	13	)	)	PUNCT
ejpam-5608	163	14	,	,	PUNCT
ejpam-5608	163	15	5608	5608	NUM
ejpam-5608	163	16	8	8	NUM
ejpam-5608	163	17	of	of	ADP
ejpam-5608	163	18	13	13	NUM
ejpam-5608	163	19	we	we	PRON
ejpam-5608	163	20	know	know	VERB
ejpam-5608	163	21	that	that	SCONJ
ejpam-5608	163	22	the	the	DET
ejpam-5608	163	23	sequence	sequence	NOUN
ejpam-5608	163	24	(	(	PUNCT
ejpam-5608	163	25	xn	xn	PROPN
ejpam-5608	163	26	)	)	PUNCT
ejpam-5608	163	27	=	=	PRON
ejpam-5608	163	28	(	(	PUNCT
ejpam-5608	163	29	1	1	NUM
ejpam-5608	163	30	n	n	NOUN
ejpam-5608	163	31	)	)	PUNCT
ejpam-5608	163	32	is	be	AUX
ejpam-5608	163	33	ideally	ideally	ADV
ejpam-5608	163	34	convergent	convergent	ADJ
ejpam-5608	163	35	to	to	ADP
ejpam-5608	163	36	0	0	NUM
ejpam-5608	163	37	in	in	ADP
ejpam-5608	163	38	the	the	DET
ejpam-5608	163	39	g	g	NOUN
ejpam-5608	163	40	-	-	PUNCT
ejpam-5608	163	41	metric	metric	ADJ
ejpam-5608	163	42	space	space	NOUN
ejpam-5608	163	43	with	with	ADP
ejpam-5608	163	44	one	one	NUM
ejpam-5608	163	45	of	of	ADP
ejpam-5608	163	46	the	the	DET
ejpam-5608	163	47	admissible	admissible	ADJ
ejpam-5608	163	48	ideals	ideal	NOUN
ejpam-5608	163	49	,	,	PUNCT
ejpam-5608	163	50	and	and	CCONJ
ejpam-5608	163	51	it	it	PRON
ejpam-5608	163	52	also	also	ADV
ejpam-5608	163	53	converges	converge	VERB
ejpam-5608	163	54	ordinarily	ordinarily	ADV
ejpam-5608	163	55	to	to	ADP
ejpam-5608	163	56	0	0	NUM
ejpam-5608	163	57	in	in	ADP
ejpam-5608	163	58	the	the	DET
ejpam-5608	163	59	g	g	NOUN
ejpam-5608	163	60	-	-	PUNCT
ejpam-5608	163	61	metric	metric	ADJ
ejpam-5608	163	62	space	space	NOUN
ejpam-5608	163	63	.	.	PUNCT
ejpam-5608	164	1	theorem	theorem	ADJ
ejpam-5608	164	2	6	6	NUM
ejpam-5608	164	3	.	.	PUNCT
ejpam-5608	165	1	let	let	AUX
ejpam-5608	165	2	(	(	PUNCT
ejpam-5608	165	3	xn	xn	X
ejpam-5608	165	4	)	)	PUNCT
ejpam-5608	165	5	be	be	VERB
ejpam-5608	165	6	a	a	DET
ejpam-5608	165	7	sequence	sequence	NOUN
ejpam-5608	165	8	that	that	PRON
ejpam-5608	165	9	ideally	ideally	ADV
ejpam-5608	165	10	converges	converge	VERB
ejpam-5608	165	11	to	to	ADP
ejpam-5608	165	12	l	l	NOUN
ejpam-5608	165	13	in	in	ADP
ejpam-5608	165	14	a	a	DET
ejpam-5608	165	15	g	g	NOUN
ejpam-5608	165	16	-	-	PUNCT
ejpam-5608	165	17	metric	metric	ADJ
ejpam-5608	165	18	space	space	NOUN
ejpam-5608	165	19	with	with	ADP
ejpam-5608	165	20	the	the	DET
ejpam-5608	165	21	ideal	ideal	PROPN
ejpam-5608	165	22	i2	i2	PROPN
ejpam-5608	165	23	.	.	PUNCT
ejpam-5608	166	1	if	if	SCONJ
ejpam-5608	166	2	for	for	ADP
ejpam-5608	166	3	every	every	DET
ejpam-5608	166	4	a	a	DET
ejpam-5608	166	5	∈	∈	PROPN
ejpam-5608	166	6	i2	i2	NOUN
ejpam-5608	166	7	,	,	PUNCT
ejpam-5608	166	8	|a|	|a|	PROPN
ejpam-5608	166	9	<	<	X
ejpam-5608	166	10	lim	lim	PROPN
ejpam-5608	166	11	n→+∞	n→+∞	PROPN
ejpam-5608	166	12	(	(	PUNCT
ejpam-5608	166	13	n2	n2	PROPN
ejpam-5608	166	14	)	)	PUNCT
ejpam-5608	166	15	,	,	PUNCT
ejpam-5608	166	16	then	then	ADV
ejpam-5608	166	17	the	the	DET
ejpam-5608	166	18	sequence	sequence	NOUN
ejpam-5608	166	19	(	(	PUNCT
ejpam-5608	166	20	xn	xn	X
ejpam-5608	166	21	)	)	PUNCT
ejpam-5608	166	22	statistically	statistically	ADV
ejpam-5608	166	23	converges	converge	VERB
ejpam-5608	166	24	to	to	ADP
ejpam-5608	166	25	l	l	NOUN
ejpam-5608	166	26	in	in	ADP
ejpam-5608	166	27	the	the	DET
ejpam-5608	166	28	g	g	NOUN
ejpam-5608	166	29	-	-	PUNCT
ejpam-5608	166	30	metric	metric	ADJ
ejpam-5608	166	31	space	space	NOUN
ejpam-5608	166	32	.	.	PUNCT
ejpam-5608	167	1	proof	proof	NOUN
ejpam-5608	167	2	.	.	PUNCT
ejpam-5608	168	1	it	it	PRON
ejpam-5608	168	2	is	be	AUX
ejpam-5608	168	3	known	know	VERB
ejpam-5608	168	4	that	that	SCONJ
ejpam-5608	168	5	the	the	DET
ejpam-5608	168	6	sequence	sequence	NOUN
ejpam-5608	168	7	(	(	PUNCT
ejpam-5608	168	8	xn	xn	X
ejpam-5608	168	9	)	)	PUNCT
ejpam-5608	168	10	is	be	AUX
ejpam-5608	168	11	ideally	ideally	ADV
ejpam-5608	168	12	convergent	convergent	ADJ
ejpam-5608	168	13	to	to	ADP
ejpam-5608	168	14	l	l	NOUN
ejpam-5608	168	15	,	,	PUNCT
ejpam-5608	168	16	which	which	PRON
ejpam-5608	168	17	means	mean	VERB
ejpam-5608	168	18	that	that	SCONJ
ejpam-5608	168	19	for	for	ADP
ejpam-5608	168	20	every	every	DET
ejpam-5608	168	21	ε	ε	PROPN
ejpam-5608	168	22	>	>	X
ejpam-5608	168	23	0	0	PROPN
ejpam-5608	168	24	,	,	PUNCT
ejpam-5608	168	25	we	we	PRON
ejpam-5608	168	26	have	have	VERB
ejpam-5608	168	27	aε	aε	NOUN
ejpam-5608	168	28	=	=	SYM
ejpam-5608	168	29	(	(	PUNCT
ejpam-5608	168	30	n	n	CCONJ
ejpam-5608	168	31	,	,	PUNCT
ejpam-5608	168	32	m	m	NOUN
ejpam-5608	168	33	)	)	PUNCT
ejpam-5608	168	34	∈	∈	PROPN
ejpam-5608	168	35	n2	n2	NOUN
ejpam-5608	168	36	:	:	PUNCT
ejpam-5608	168	37	g	g	PROPN
ejpam-5608	168	38	(	(	PUNCT
ejpam-5608	168	39	l	l	NOUN
ejpam-5608	168	40	,	,	PUNCT
ejpam-5608	168	41	xn	xn	PROPN
ejpam-5608	168	42	,	,	PUNCT
ejpam-5608	168	43	xm	xm	PROPN
ejpam-5608	168	44	)	)	PUNCT
ejpam-5608	168	45	≥	≥	NOUN
ejpam-5608	168	46	ε	ε	PROPN
ejpam-5608	168	47	∈	∈	PROPN
ejpam-5608	168	48	i2	i2	PROPN
ejpam-5608	168	49	.	.	PUNCT
ejpam-5608	169	1	since	since	SCONJ
ejpam-5608	169	2	|a|	|a|	PROPN
ejpam-5608	169	3	<	<	X
ejpam-5608	169	4	lim	lim	PROPN
ejpam-5608	169	5	n→+∞	n→+∞	PROPN
ejpam-5608	169	6	(	(	PUNCT
ejpam-5608	169	7	n2	n2	PROPN
ejpam-5608	169	8	)	)	PUNCT
ejpam-5608	169	9	for	for	ADP
ejpam-5608	169	10	every	every	DET
ejpam-5608	169	11	a	a	DET
ejpam-5608	169	12	∈	∈	PROPN
ejpam-5608	169	13	i2	i2	NOUN
ejpam-5608	169	14	it	it	PRON
ejpam-5608	169	15	follows	follow	VERB
ejpam-5608	169	16	that	that	SCONJ
ejpam-5608	169	17	|aε|	|aε|	PRON
ejpam-5608	169	18	<	<	X
ejpam-5608	170	1	+	+	NOUN
ejpam-5608	170	2	∞.	∞.	PROPN
ejpam-5608	170	3	let	let	VERB
ejpam-5608	170	4	|aε|	|aε|	NOUN
ejpam-5608	170	5	=	=	PRON
ejpam-5608	170	6	lim	lim	PROPN
ejpam-5608	170	7	n→+∞	n→+∞	PROPN
ejpam-5608	170	8	(	(	PUNCT
ejpam-5608	170	9	nj	nj	PROPN
ejpam-5608	170	10	)	)	PUNCT
ejpam-5608	170	11	,	,	PUNCT
ejpam-5608	170	12	with	with	ADP
ejpam-5608	170	13	j	j	PROPN
ejpam-5608	170	14	∈	∈	PROPN
ejpam-5608	170	15	n	n	CCONJ
ejpam-5608	170	16	,	,	PUNCT
ejpam-5608	170	17	so	so	SCONJ
ejpam-5608	170	18	that	that	SCONJ
ejpam-5608	170	19	for	for	ADP
ejpam-5608	170	20	every	every	DET
ejpam-5608	170	21	ε	ε	PROPN
ejpam-5608	170	22	>	>	X
ejpam-5608	170	23	0	0	PROPN
ejpam-5608	170	24	,	,	PUNCT
ejpam-5608	170	25	the	the	DET
ejpam-5608	170	26	following	follow	VERB
ejpam-5608	170	27	holds	hold	VERB
ejpam-5608	170	28	:	:	PUNCT
ejpam-5608	170	29	lim	lim	PROPN
ejpam-5608	170	30	n→+∞	n→+∞	PROPN
ejpam-5608	170	31	(	(	PUNCT
ejpam-5608	170	32	2	2	NUM
ejpam-5608	170	33	n2	n2	PROPN
ejpam-5608	170	34	|{(n	|{(n	PROPN
ejpam-5608	170	35	,	,	PUNCT
ejpam-5608	170	36	m	m	NOUN
ejpam-5608	170	37	)	)	PUNCT
ejpam-5608	170	38	∈	∈	PROPN
ejpam-5608	170	39	n2	n2	NOUN
ejpam-5608	170	40	:	:	PUNCT
ejpam-5608	170	41	n	n	CCONJ
ejpam-5608	170	42	,	,	PUNCT
ejpam-5608	170	43	m	m	VERB
ejpam-5608	170	44	≥	≥	NOUN
ejpam-5608	170	45	n	n	CCONJ
ejpam-5608	170	46	,	,	PUNCT
ejpam-5608	170	47	g(0	g(0	PROPN
ejpam-5608	170	48	,	,	PUNCT
ejpam-5608	170	49	xn	xn	PROPN
ejpam-5608	170	50	,	,	PUNCT
ejpam-5608	170	51	xm	xm	PROPN
ejpam-5608	170	52	)	)	PUNCT
ejpam-5608	171	1	<	<	X
ejpam-5608	171	2	ε}|	ε}|	NOUN
ejpam-5608	171	3	)	)	PUNCT
ejpam-5608	172	1	<	<	X
ejpam-5608	172	2	lim	lim	PROPN
ejpam-5608	172	3	n→+∞	n→+∞	PROPN
ejpam-5608	172	4	(	(	PUNCT
ejpam-5608	172	5	nj	nj	PROPN
ejpam-5608	172	6	n2	n2	PROPN
ejpam-5608	172	7	)	)	PUNCT
ejpam-5608	173	1	<	<	X
ejpam-5608	174	1	lim	lim	PROPN
ejpam-5608	175	1	n→+∞	n→+∞	PROPN
ejpam-5608	175	2	(	(	PUNCT
ejpam-5608	175	3	j	j	PROPN
ejpam-5608	175	4	n	n	CCONJ
ejpam-5608	175	5	)	)	PUNCT
ejpam-5608	176	1	=	=	SYM
ejpam-5608	176	2	0	0	PUNCT
ejpam-5608	177	1	so	so	ADV
ejpam-5608	177	2	,	,	PUNCT
ejpam-5608	177	3	the	the	DET
ejpam-5608	177	4	sequence	sequence	NOUN
ejpam-5608	177	5	(	(	PUNCT
ejpam-5608	177	6	xn	xn	X
ejpam-5608	177	7	)	)	PUNCT
ejpam-5608	177	8	statistically	statistically	ADV
ejpam-5608	177	9	converges	converge	VERB
ejpam-5608	177	10	to	to	ADP
ejpam-5608	177	11	l.	l.	PROPN
ejpam-5608	177	12	example	example	NOUN
ejpam-5608	177	13	4	4	X
ejpam-5608	177	14	.	.	PUNCT
ejpam-5608	178	1	it	it	PRON
ejpam-5608	178	2	will	will	AUX
ejpam-5608	178	3	be	be	AUX
ejpam-5608	178	4	proven	prove	VERB
ejpam-5608	178	5	that	that	SCONJ
ejpam-5608	178	6	the	the	DET
ejpam-5608	178	7	sequence	sequence	NOUN
ejpam-5608	178	8	(	(	PUNCT
ejpam-5608	178	9	1	1	NUM
ejpam-5608	178	10	n	n	CCONJ
ejpam-5608	178	11	)	)	PUNCT
ejpam-5608	178	12	statistically	statistically	ADV
ejpam-5608	178	13	converges	converge	VERB
ejpam-5608	178	14	to	to	ADP
ejpam-5608	178	15	0	0	NUM
ejpam-5608	178	16	in	in	ADP
ejpam-5608	178	17	the	the	DET
ejpam-5608	178	18	g	g	NOUN
ejpam-5608	178	19	-	-	PUNCT
ejpam-5608	178	20	metric	metric	ADJ
ejpam-5608	178	21	space	space	NOUN
ejpam-5608	178	22	.	.	PUNCT
ejpam-5608	179	1	it	it	PRON
ejpam-5608	179	2	has	have	AUX
ejpam-5608	179	3	been	be	AUX
ejpam-5608	179	4	known	know	VERB
ejpam-5608	179	5	that	that	SCONJ
ejpam-5608	179	6	the	the	DET
ejpam-5608	179	7	sequence	sequence	NOUN
ejpam-5608	179	8	(	(	PUNCT
ejpam-5608	179	9	1	1	NUM
ejpam-5608	179	10	n	n	NOUN
ejpam-5608	179	11	)	)	PUNCT
ejpam-5608	179	12	converges	converge	VERB
ejpam-5608	179	13	ideally	ideally	ADV
ejpam-5608	179	14	to	to	ADP
ejpam-5608	179	15	0	0	NUM
ejpam-5608	179	16	in	in	ADP
ejpam-5608	179	17	the	the	DET
ejpam-5608	179	18	g	g	NOUN
ejpam-5608	179	19	-	-	PUNCT
ejpam-5608	179	20	metric	metric	ADJ
ejpam-5608	179	21	space	space	NOUN
ejpam-5608	179	22	with	with	ADP
ejpam-5608	179	23	the	the	DET
ejpam-5608	179	24	ideal	ideal	NOUN
ejpam-5608	180	1	i	i	PRON
ejpam-5608	180	2	=	=	PUNCT
ejpam-5608	180	3	a	a	DET
ejpam-5608	180	4	⊂	⊂	PROPN
ejpam-5608	180	5	n2	n2	NOUN
ejpam-5608	180	6	:	:	PUNCT
ejpam-5608	180	7	|a|	|a|	PROPN
ejpam-5608	180	8	<	<	X
ejpam-5608	180	9	lim	lim	PROPN
ejpam-5608	180	10	n→+∞	n→+∞	PROPN
ejpam-5608	180	11	(	(	PUNCT
ejpam-5608	180	12	n2	n2	PROPN
ejpam-5608	180	13	)	)	PUNCT
ejpam-5608	180	14	.	.	PUNCT
ejpam-5608	181	1	it	it	PRON
ejpam-5608	181	2	will	will	AUX
ejpam-5608	181	3	also	also	ADV
ejpam-5608	181	4	be	be	AUX
ejpam-5608	181	5	shown	show	VERB
ejpam-5608	181	6	that	that	SCONJ
ejpam-5608	181	7	the	the	DET
ejpam-5608	181	8	sequence	sequence	NOUN
ejpam-5608	181	9	(	(	PUNCT
ejpam-5608	181	10	1	1	NUM
ejpam-5608	181	11	n	n	CCONJ
ejpam-5608	181	12	)	)	PUNCT
ejpam-5608	181	13	statistically	statistically	ADV
ejpam-5608	181	14	converges	converge	VERB
ejpam-5608	181	15	to	to	ADP
ejpam-5608	181	16	0	0	NUM
ejpam-5608	181	17	in	in	ADP
ejpam-5608	181	18	the	the	DET
ejpam-5608	181	19	g	g	NOUN
ejpam-5608	181	20	-	-	PUNCT
ejpam-5608	181	21	metric	metric	ADJ
ejpam-5608	181	22	space	space	NOUN
ejpam-5608	181	23	.	.	PUNCT
ejpam-5608	182	1	preliminary	preliminary	ADJ
ejpam-5608	182	2	analysis	analysis	NOUN
ejpam-5608	182	3	g	g	PROPN
ejpam-5608	182	4	(	(	PUNCT
ejpam-5608	182	5	x	x	X
ejpam-5608	182	6	,	,	PUNCT
ejpam-5608	182	7	xn1	xn1	NUM
ejpam-5608	182	8	,	,	PUNCT
ejpam-5608	182	9	xn2	xn2	PROPN
ejpam-5608	182	10	)	)	PUNCT
ejpam-5608	183	1	=	=	PUNCT
ejpam-5608	183	2	∣∣∣∣0−	∣∣∣∣0−	ADP
ejpam-5608	183	3	1	1	NUM
ejpam-5608	183	4	n1	n1	NOUN
ejpam-5608	183	5	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-5608	183	6	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5608	183	7	1n1	1n1	NUM
ejpam-5608	183	8	−	−	PROPN
ejpam-5608	183	9	1	1	NUM
ejpam-5608	183	10	n2	n2	PROPN
ejpam-5608	183	11	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-5608	183	12	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5608	183	13	1n2	1n2	NUM
ejpam-5608	183	14	−	−	NOUN
ejpam-5608	183	15	0	0	NUM
ejpam-5608	183	16	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5608	183	17	=	=	SYM
ejpam-5608	183	18	1	1	NUM
ejpam-5608	183	19	n1	n1	NOUN
ejpam-5608	183	20	+	+	CCONJ
ejpam-5608	183	21	1	1	NUM
ejpam-5608	183	22	n2	n2	NOUN
ejpam-5608	183	23	+	+	CCONJ
ejpam-5608	183	24	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5608	183	25	1n1	1n1	NUM
ejpam-5608	183	26	−	−	PROPN
ejpam-5608	183	27	1	1	NUM
ejpam-5608	183	28	n2	n2	NOUN
ejpam-5608	183	29	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5608	183	30	≥	≥	PROPN
ejpam-5608	183	31	1	1	NUM
ejpam-5608	183	32	n1	n1	NOUN
ejpam-5608	183	33	+	+	CCONJ
ejpam-5608	183	34	1	1	NUM
ejpam-5608	183	35	n2	n2	NOUN
ejpam-5608	183	36	+	+	CCONJ
ejpam-5608	183	37	(	(	PUNCT
ejpam-5608	183	38	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5608	183	39	1n1	1n1	NUM
ejpam-5608	183	40	∣∣∣∣−	∣∣∣∣−	PROPN
ejpam-5608	183	41	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5608	183	42	1n2	1n2	NUM
ejpam-5608	183	43	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5608	183	44	)	)	PUNCT
ejpam-5608	183	45	≥	≥	NOUN
ejpam-5608	183	46	2	2	NUM
ejpam-5608	183	47	n1	n1	NOUN
ejpam-5608	183	48	to	to	PART
ejpam-5608	183	49	ensure	ensure	VERB
ejpam-5608	183	50	2	2	NUM
ejpam-5608	183	51	n1	n1	PROPN
ejpam-5608	183	52	≥	≥	NOUN
ejpam-5608	183	53	ε	ε	NOUN
ejpam-5608	183	54	,	,	PUNCT
ejpam-5608	183	55	then	then	ADV
ejpam-5608	183	56	n1	n1	PROPN
ejpam-5608	183	57	must	must	AUX
ejpam-5608	183	58	be	be	AUX
ejpam-5608	183	59	a	a	DET
ejpam-5608	183	60	natural	natural	ADJ
ejpam-5608	183	61	number	number	NOUN
ejpam-5608	183	62	k	k	NOUN
ejpam-5608	183	63	such	such	ADJ
ejpam-5608	183	64	that	that	SCONJ
ejpam-5608	183	65	k	k	PROPN
ejpam-5608	183	66	≤	≤	ADV
ejpam-5608	183	67	2	2	NUM
ejpam-5608	183	68	ε	ε	PROPN
ejpam-5608	183	69	.	.	PUNCT
ejpam-5608	184	1	therefore	therefore	ADV
ejpam-5608	184	2	,	,	PUNCT
ejpam-5608	184	3	for	for	ADP
ejpam-5608	184	4	manuharawati	manuharawati	NOUN
ejpam-5608	184	5	,	,	PUNCT
ejpam-5608	184	6	m.jakfar	m.jakfar	ADV
ejpam-5608	184	7	,	,	PUNCT
ejpam-5608	184	8	a.	a.	PROPN
ejpam-5608	184	9	taufik	taufik	PROPN
ejpam-5608	184	10	hamzah	hamzah	PROPN
ejpam-5608	184	11	/	/	SYM
ejpam-5608	184	12	eur	eur	PROPN
ejpam-5608	184	13	.	.	PUNCT
ejpam-5608	185	1	j.	j.	PROPN
ejpam-5608	185	2	pure	pure	PROPN
ejpam-5608	185	3	appl	appl	PROPN
ejpam-5608	185	4	.	.	PROPN
ejpam-5608	185	5	math	math	PROPN
ejpam-5608	185	6	,	,	PUNCT
ejpam-5608	185	7	18	18	NUM
ejpam-5608	185	8	(	(	PUNCT
ejpam-5608	185	9	1	1	NUM
ejpam-5608	185	10	)	)	PUNCT
ejpam-5608	185	11	(	(	PUNCT
ejpam-5608	185	12	2025	2025	NUM
ejpam-5608	185	13	)	)	PUNCT
ejpam-5608	185	14	,	,	PUNCT
ejpam-5608	185	15	5608	5608	NUM
ejpam-5608	185	16	9	9	NUM
ejpam-5608	185	17	of	of	ADP
ejpam-5608	185	18	13	13	NUM
ejpam-5608	185	19	every	every	DET
ejpam-5608	185	20	real	real	ADJ
ejpam-5608	185	21	number	number	NOUN
ejpam-5608	185	22	ε	ε	PROPN
ejpam-5608	185	23	>	>	X
ejpam-5608	185	24	0	0	PROPN
ejpam-5608	185	25	,	,	PUNCT
ejpam-5608	185	26	the	the	DET
ejpam-5608	185	27	following	follow	VERB
ejpam-5608	185	28	holds	hold	VERB
ejpam-5608	185	29	:	:	PUNCT
ejpam-5608	186	1	lim	lim	PROPN
ejpam-5608	186	2	n→+∞	n→+∞	PROPN
ejpam-5608	186	3	(	(	PUNCT
ejpam-5608	186	4	2	2	NUM
ejpam-5608	186	5	n2	n2	ADJ
ejpam-5608	186	6	|{(n1	|{(n1	PROPN
ejpam-5608	186	7	,	,	PUNCT
ejpam-5608	186	8	n2	n2	ADJ
ejpam-5608	186	9	)	)	PUNCT
ejpam-5608	186	10	∈	∈	PROPN
ejpam-5608	186	11	n2	n2	NOUN
ejpam-5608	186	12	:	:	PUNCT
ejpam-5608	186	13	n1	n1	ADJ
ejpam-5608	186	14	,	,	PUNCT
ejpam-5608	186	15	n2	n2	ADJ
ejpam-5608	186	16	≤	≤	PUNCT
ejpam-5608	186	17	n	n	CCONJ
ejpam-5608	186	18	,	,	PUNCT
ejpam-5608	186	19	g(xi	g(xi	PROPN
ejpam-5608	186	20	,	,	PUNCT
ejpam-5608	186	21	xn1	xn1	NUM
ejpam-5608	186	22	,	,	PUNCT
ejpam-5608	186	23	xn2	xn2	PROPN
ejpam-5608	186	24	)	)	PUNCT
ejpam-5608	186	25	≥	≥	NUM
ejpam-5608	186	26	ε}|	ε}|	NOUN
ejpam-5608	186	27	)	)	PUNCT
ejpam-5608	187	1	=	=	VERB
ejpam-5608	187	2	lim	lim	PROPN
ejpam-5608	187	3	n→+∞	n→+∞	PROPN
ejpam-5608	187	4	(	(	PUNCT
ejpam-5608	187	5	2	2	NUM
ejpam-5608	187	6	n2	n2	NOUN
ejpam-5608	187	7	|{(1	|{(1	PROPN
ejpam-5608	187	8	,	,	PUNCT
ejpam-5608	187	9	1	1	NUM
ejpam-5608	187	10	)	)	PUNCT
ejpam-5608	187	11	,	,	PUNCT
ejpam-5608	187	12	(	(	PUNCT
ejpam-5608	187	13	1	1	NUM
ejpam-5608	187	14	,	,	PUNCT
ejpam-5608	187	15	2	2	NUM
ejpam-5608	187	16	)	)	PUNCT
ejpam-5608	187	17	,	,	PUNCT
ejpam-5608	187	18	(	(	PUNCT
ejpam-5608	187	19	1	1	NUM
ejpam-5608	187	20	,	,	PUNCT
ejpam-5608	187	21	3	3	NUM
ejpam-5608	187	22	)	)	PUNCT
ejpam-5608	187	23	,	,	PUNCT
ejpam-5608	187	24	.	.	PUNCT
ejpam-5608	187	25	.	.	PUNCT
ejpam-5608	187	26	.	.	PUNCT
ejpam-5608	188	1	,	,	PUNCT
ejpam-5608	188	2	(	(	PUNCT
ejpam-5608	188	3	k	k	NOUN
ejpam-5608	188	4	,	,	PUNCT
ejpam-5608	188	5	1	1	NUM
ejpam-5608	188	6	)	)	PUNCT
ejpam-5608	188	7	,	,	PUNCT
ejpam-5608	188	8	(	(	PUNCT
ejpam-5608	188	9	k	k	X
ejpam-5608	188	10	,	,	PUNCT
ejpam-5608	188	11	2	2	NUM
ejpam-5608	188	12	)	)	PUNCT
ejpam-5608	188	13	,	,	PUNCT
ejpam-5608	188	14	.	.	PUNCT
ejpam-5608	188	15	.	.	PUNCT
ejpam-5608	188	16	.	.	PUNCT
ejpam-5608	189	1	}	}	PUNCT
ejpam-5608	189	2	|	|	X
ejpam-5608	189	3	)	)	PUNCT
ejpam-5608	189	4	≤	≤	NOUN
ejpam-5608	189	5	lim	lim	PROPN
ejpam-5608	189	6	n→+∞	n→+∞	PROPN
ejpam-5608	189	7	(	(	PUNCT
ejpam-5608	189	8	2nk	2nk	ADJ
ejpam-5608	189	9	n2	n2	NOUN
ejpam-5608	189	10	)	)	PUNCT
ejpam-5608	189	11	≤	≤	NOUN
ejpam-5608	189	12	2k	2k	NUM
ejpam-5608	189	13	lim	lim	PROPN
ejpam-5608	189	14	n→+∞	n→+∞	PROPN
ejpam-5608	189	15	(	(	PUNCT
ejpam-5608	189	16	1	1	NUM
ejpam-5608	189	17	n	n	NOUN
ejpam-5608	189	18	)	)	PUNCT
ejpam-5608	189	19	=	=	SYM
ejpam-5608	190	1	2k.0	2k.0	NUM
ejpam-5608	190	2	=	=	SYM
ejpam-5608	190	3	0	0	PUNCT
ejpam-5608	191	1	thus	thus	ADV
ejpam-5608	191	2	,	,	PUNCT
ejpam-5608	191	3	the	the	DET
ejpam-5608	191	4	sequence	sequence	NOUN
ejpam-5608	191	5	(	(	PUNCT
ejpam-5608	191	6	1	1	NUM
ejpam-5608	191	7	n	n	NOUN
ejpam-5608	191	8	)	)	PUNCT
ejpam-5608	191	9	is	be	AUX
ejpam-5608	191	10	also	also	ADV
ejpam-5608	191	11	statistically	statistically	ADV
ejpam-5608	191	12	proven	prove	VERB
ejpam-5608	191	13	to	to	PART
ejpam-5608	191	14	converge	converge	VERB
ejpam-5608	191	15	to	to	ADP
ejpam-5608	191	16	0	0	NUM
ejpam-5608	191	17	in	in	ADP
ejpam-5608	191	18	the	the	DET
ejpam-5608	191	19	g	g	NOUN
ejpam-5608	191	20	-	-	PUNCT
ejpam-5608	191	21	metric	metric	ADJ
ejpam-5608	191	22	space	space	NOUN
ejpam-5608	191	23	.	.	PUNCT
ejpam-5608	192	1	theorem	theorem	VERB
ejpam-5608	192	2	7	7	NUM
ejpam-5608	192	3	.	.	PUNCT
ejpam-5608	193	1	[	[	X
ejpam-5608	193	2	19	19	NUM
ejpam-5608	193	3	]	]	PUNCT
ejpam-5608	193	4	given	give	VERB
ejpam-5608	193	5	a	a	DET
ejpam-5608	193	6	sequence	sequence	NOUN
ejpam-5608	193	7	(	(	PUNCT
ejpam-5608	193	8	xn	xn	PROPN
ejpam-5608	193	9	)	)	PUNCT
ejpam-5608	193	10	that	that	PRON
ejpam-5608	193	11	statistically	statistically	ADV
ejpam-5608	193	12	converges	converge	VERB
ejpam-5608	193	13	to	to	ADP
ejpam-5608	193	14	x	x	PUNCT
ejpam-5608	193	15	in	in	ADP
ejpam-5608	193	16	the	the	DET
ejpam-5608	193	17	g	g	NOUN
ejpam-5608	193	18	-	-	PUNCT
ejpam-5608	193	19	metric	metric	ADJ
ejpam-5608	193	20	space	space	NOUN
ejpam-5608	193	21	and	and	CCONJ
ejpam-5608	193	22	the	the	DET
ejpam-5608	193	23	ideal	ideal	PROPN
ejpam-5608	193	24	i2	i2	PROPN
ejpam-5608	193	25	,	,	PUNCT
ejpam-5608	193	26	where	where	SCONJ
ejpam-5608	193	27	i2	i2	PROPN
ejpam-5608	193	28	=	=	PROPN
ejpam-5608	193	29	a	a	PRON
ejpam-5608	193	30	:	:	PUNCT
ejpam-5608	193	31	δ(a	δ(a	PROPN
ejpam-5608	193	32	)	)	PUNCT
ejpam-5608	194	1	=	=	PUNCT
ejpam-5608	194	2	0	0	NUM
ejpam-5608	194	3	,	,	PUNCT
ejpam-5608	194	4	the	the	DET
ejpam-5608	194	5	sequence	sequence	NOUN
ejpam-5608	194	6	(	(	PUNCT
ejpam-5608	194	7	xn	xn	X
ejpam-5608	194	8	)	)	PUNCT
ejpam-5608	194	9	ideally	ideally	ADV
ejpam-5608	194	10	converges	converge	VERB
ejpam-5608	194	11	to	to	ADP
ejpam-5608	194	12	x	x	PUNCT
ejpam-5608	194	13	in	in	ADP
ejpam-5608	194	14	the	the	DET
ejpam-5608	194	15	g	g	NOUN
ejpam-5608	194	16	-	-	PUNCT
ejpam-5608	194	17	metric	metric	ADJ
ejpam-5608	194	18	space	space	NOUN
ejpam-5608	194	19	.	.	PUNCT
ejpam-5608	195	1	proof	proof	NOUN
ejpam-5608	195	2	.	.	PUNCT
ejpam-5608	196	1	a	a	DET
ejpam-5608	196	2	sequence	sequence	NOUN
ejpam-5608	196	3	(	(	PUNCT
ejpam-5608	196	4	xn	xn	X
ejpam-5608	196	5	)	)	PUNCT
ejpam-5608	196	6	is	be	AUX
ejpam-5608	196	7	said	say	VERB
ejpam-5608	196	8	to	to	PART
ejpam-5608	196	9	statistically	statistically	ADV
ejpam-5608	196	10	converge	converge	VERB
ejpam-5608	196	11	to	to	ADP
ejpam-5608	196	12	x	x	PUNCT
ejpam-5608	196	13	in	in	ADP
ejpam-5608	196	14	a	a	DET
ejpam-5608	196	15	g	g	NOUN
ejpam-5608	196	16	-	-	PUNCT
ejpam-5608	196	17	metric	metric	ADJ
ejpam-5608	196	18	space	space	NOUN
ejpam-5608	196	19	if	if	SCONJ
ejpam-5608	196	20	lim	lim	PROPN
ejpam-5608	196	21	n→+∞	n→+∞	PROPN
ejpam-5608	196	22	(	(	PUNCT
ejpam-5608	196	23	2	2	NUM
ejpam-5608	196	24	n2	n2	NOUN
ejpam-5608	196	25	∣∣(n1	∣∣(n1	PROPN
ejpam-5608	196	26	,	,	PUNCT
ejpam-5608	196	27	n2	n2	ADJ
ejpam-5608	196	28	)	)	PUNCT
ejpam-5608	196	29	∈	∈	PROPN
ejpam-5608	196	30	n2	n2	NOUN
ejpam-5608	196	31	:	:	PUNCT
ejpam-5608	196	32	n1	n1	ADJ
ejpam-5608	196	33	,	,	PUNCT
ejpam-5608	196	34	n2	n2	ADJ
ejpam-5608	196	35	≤	≤	PUNCT
ejpam-5608	196	36	n	n	CCONJ
ejpam-5608	196	37	,	,	PUNCT
ejpam-5608	196	38	g	g	PROPN
ejpam-5608	196	39	(	(	PUNCT
ejpam-5608	196	40	x	x	X
ejpam-5608	196	41	,	,	PUNCT
ejpam-5608	196	42	xn1	xn1	NUM
ejpam-5608	196	43	,	,	PUNCT
ejpam-5608	196	44	xn2	xn2	PROPN
ejpam-5608	196	45	)	)	PUNCT
ejpam-5608	196	46	≥	≥	NOUN
ejpam-5608	196	47	ε	ε	X
ejpam-5608	196	48	∣∣	∣∣	X
ejpam-5608	196	49	)	)	PUNCT
ejpam-5608	196	50	=	=	PUNCT
ejpam-5608	196	51	0	0	PUNCT
ejpam-5608	197	1	thus	thus	ADV
ejpam-5608	197	2	,	,	PUNCT
ejpam-5608	197	3	the	the	DET
ejpam-5608	197	4	set	set	NOUN
ejpam-5608	197	5	{	{	PUNCT
ejpam-5608	197	6	(	(	PUNCT
ejpam-5608	197	7	n1	n1	NOUN
ejpam-5608	197	8	,	,	PUNCT
ejpam-5608	197	9	n2	n2	ADJ
ejpam-5608	197	10	)	)	PUNCT
ejpam-5608	197	11	∈	∈	PROPN
ejpam-5608	197	12	n2	n2	NOUN
ejpam-5608	197	13	:	:	PUNCT
ejpam-5608	197	14	g	g	NOUN
ejpam-5608	197	15	(	(	PUNCT
ejpam-5608	197	16	x	x	X
ejpam-5608	197	17	,	,	PUNCT
ejpam-5608	197	18	xn1	xn1	NUM
ejpam-5608	197	19	,	,	PUNCT
ejpam-5608	197	20	xn2	xn2	PROPN
ejpam-5608	197	21	)	)	PUNCT
ejpam-5608	197	22	≥	≥	X
ejpam-5608	197	23	ε	ε	PROPN
ejpam-5608	197	24	}	}	PUNCT
ejpam-5608	197	25	has	have	VERB
ejpam-5608	197	26	asymptotic	asymptotic	ADJ
ejpam-5608	197	27	density	density	NOUN
ejpam-5608	197	28	0	0	NUM
ejpam-5608	197	29	.	.	PUNCT
ejpam-5608	198	1	this	this	PRON
ejpam-5608	198	2	means	mean	VERB
ejpam-5608	198	3	(	(	PUNCT
ejpam-5608	198	4	xn	xn	X
ejpam-5608	198	5	)	)	PUNCT
ejpam-5608	198	6	∈	∈	PROPN
ejpam-5608	198	7	i2	i2	PROPN
ejpam-5608	198	8	,	,	PUNCT
ejpam-5608	198	9	or	or	CCONJ
ejpam-5608	198	10	equivalently	equivalently	ADV
ejpam-5608	198	11	,	,	PUNCT
ejpam-5608	198	12	(	(	PUNCT
ejpam-5608	198	13	xn	xn	X
ejpam-5608	198	14	)	)	PUNCT
ejpam-5608	198	15	converges	converge	VERB
ejpam-5608	198	16	ideally	ideally	ADV
ejpam-5608	198	17	to	to	ADP
ejpam-5608	198	18	x	x	VERB
ejpam-5608	198	19	in	in	ADP
ejpam-5608	198	20	the	the	DET
ejpam-5608	198	21	g	g	NOUN
ejpam-5608	198	22	-	-	PUNCT
ejpam-5608	198	23	metric	metric	ADJ
ejpam-5608	198	24	space	space	NOUN
ejpam-5608	198	25	.	.	PUNCT
ejpam-5608	199	1	theorem	theorem	VERB
ejpam-5608	199	2	8	8	NUM
ejpam-5608	199	3	.	.	PUNCT
ejpam-5608	200	1	[	[	X
ejpam-5608	200	2	1	1	X
ejpam-5608	200	3	]	]	X
ejpam-5608	200	4	if	if	SCONJ
ejpam-5608	200	5	(	(	PUNCT
ejpam-5608	200	6	xn	xn	X
ejpam-5608	200	7	)	)	PUNCT
ejpam-5608	200	8	statistically	statistically	ADV
ejpam-5608	200	9	converges	converge	VERB
ejpam-5608	200	10	in	in	ADP
ejpam-5608	200	11	a	a	DET
ejpam-5608	200	12	g	g	NOUN
ejpam-5608	200	13	-	-	PUNCT
ejpam-5608	200	14	metric	metric	ADJ
ejpam-5608	200	15	space	space	NOUN
ejpam-5608	200	16	,	,	PUNCT
ejpam-5608	200	17	then	then	ADV
ejpam-5608	200	18	(	(	PUNCT
ejpam-5608	200	19	xn	xn	X
ejpam-5608	200	20	)	)	PUNCT
ejpam-5608	200	21	is	be	AUX
ejpam-5608	200	22	a	a	DET
ejpam-5608	200	23	statistically	statistically	ADV
ejpam-5608	200	24	cauchy	cauchy	ADJ
ejpam-5608	200	25	sequence	sequence	NOUN
ejpam-5608	200	26	in	in	ADP
ejpam-5608	200	27	the	the	DET
ejpam-5608	200	28	g	g	NOUN
ejpam-5608	200	29	-	-	PUNCT
ejpam-5608	200	30	metric	metric	ADJ
ejpam-5608	200	31	space	space	NOUN
ejpam-5608	200	32	.	.	PUNCT
ejpam-5608	201	1	proof	proof	NOUN
ejpam-5608	201	2	.	.	PUNCT
ejpam-5608	202	1	let	let	VERB
ejpam-5608	202	2	ε	ε	PROPN
ejpam-5608	202	3	>	>	X
ejpam-5608	202	4	0	0	PUNCT
ejpam-5608	202	5	be	be	AUX
ejpam-5608	202	6	any	any	DET
ejpam-5608	202	7	real	real	ADJ
ejpam-5608	202	8	number	number	NOUN
ejpam-5608	202	9	.	.	PUNCT
ejpam-5608	203	1	suppose	suppose	VERB
ejpam-5608	203	2	gs	gs	INTJ
ejpam-5608	203	3	−	−	PROPN
ejpam-5608	203	4	lim(xn	lim(xn	NOUN
ejpam-5608	203	5	)	)	PUNCT
ejpam-5608	203	6	=	=	PUNCT
ejpam-5608	204	1	x.	x.	NOUN
ejpam-5608	204	2	since	since	SCONJ
ejpam-5608	204	3	ε	ε	PROPN
ejpam-5608	204	4	is	be	AUX
ejpam-5608	204	5	a	a	DET
ejpam-5608	204	6	real	real	ADJ
ejpam-5608	204	7	number	number	NOUN
ejpam-5608	204	8	and	and	CCONJ
ejpam-5608	204	9	ε	ε	PROPN
ejpam-5608	204	10	>	>	X
ejpam-5608	204	11	0	0	PROPN
ejpam-5608	204	12	,	,	PUNCT
ejpam-5608	204	13	then	then	ADV
ejpam-5608	204	14	ε	ε	PROPN
ejpam-5608	204	15	6	6	NUM
ejpam-5608	204	16	is	be	AUX
ejpam-5608	204	17	also	also	ADV
ejpam-5608	204	18	a	a	DET
ejpam-5608	204	19	real	real	ADJ
ejpam-5608	204	20	number	number	NOUN
ejpam-5608	204	21	and	and	CCONJ
ejpam-5608	204	22	greater	great	ADJ
ejpam-5608	204	23	than	than	ADP
ejpam-5608	204	24	0	0	NUM
ejpam-5608	204	25	.	.	PUNCT
ejpam-5608	205	1	therefore	therefore	ADV
ejpam-5608	205	2	,	,	PUNCT
ejpam-5608	205	3	the	the	DET
ejpam-5608	205	4	set	set	NOUN
ejpam-5608	205	5	{	{	PUNCT
ejpam-5608	205	6	(	(	PUNCT
ejpam-5608	205	7	n1	n1	NOUN
ejpam-5608	205	8	,	,	PUNCT
ejpam-5608	205	9	n2	n2	ADJ
ejpam-5608	205	10	)	)	PUNCT
ejpam-5608	205	11	∈	∈	PROPN
ejpam-5608	205	12	n2	n2	NOUN
ejpam-5608	205	13	:	:	PUNCT
ejpam-5608	205	14	g	g	NOUN
ejpam-5608	205	15	(	(	PUNCT
ejpam-5608	205	16	x	x	X
ejpam-5608	205	17	,	,	PUNCT
ejpam-5608	205	18	xn1	xn1	NUM
ejpam-5608	205	19	,	,	PUNCT
ejpam-5608	205	20	xn2	xn2	PROPN
ejpam-5608	205	21	)	)	PUNCT
ejpam-5608	205	22	≥	≥	NOUN
ejpam-5608	205	23	ε	ε	PROPN
ejpam-5608	205	24	6	6	NUM
ejpam-5608	205	25	}	}	PUNCT
ejpam-5608	205	26	has	have	VERB
ejpam-5608	205	27	asymptotic	asymptotic	ADJ
ejpam-5608	205	28	density	density	NOUN
ejpam-5608	205	29	0	0	NUM
ejpam-5608	205	30	.	.	PUNCT
ejpam-5608	206	1	let	let	VERB
ejpam-5608	206	2	m	m	PRON
ejpam-5608	206	3	∈	∈	PROPN
ejpam-5608	206	4	n	n	AUX
ejpam-5608	206	5	be	be	AUX
ejpam-5608	206	6	chosen	choose	VERB
ejpam-5608	206	7	such	such	ADJ
ejpam-5608	206	8	that	that	SCONJ
ejpam-5608	206	9	g	g	PROPN
ejpam-5608	206	10	(	(	PUNCT
ejpam-5608	206	11	x	x	X
ejpam-5608	206	12	,	,	PUNCT
ejpam-5608	206	13	xn1	xn1	NUM
ejpam-5608	206	14	,	,	PUNCT
ejpam-5608	206	15	xm	xm	PROPN
ejpam-5608	206	16	)	)	PUNCT
ejpam-5608	206	17	≥	≥	PROPN
ejpam-5608	206	18	ε	ε	PROPN
ejpam-5608	206	19	6	6	NUM
ejpam-5608	206	20	.	.	PUNCT
ejpam-5608	207	1	then	then	ADV
ejpam-5608	207	2	g	g	PROPN
ejpam-5608	207	3	(	(	PUNCT
ejpam-5608	207	4	xm	xm	PROPN
ejpam-5608	207	5	,	,	PUNCT
ejpam-5608	207	6	xn1	xn1	NUM
ejpam-5608	207	7	,	,	PUNCT
ejpam-5608	207	8	xn2	xn2	PROPN
ejpam-5608	207	9	)	)	PUNCT
ejpam-5608	207	10	≤	≤	NOUN
ejpam-5608	207	11	g	g	PROPN
ejpam-5608	207	12	(	(	PUNCT
ejpam-5608	207	13	xm	xm	PROPN
ejpam-5608	207	14	,	,	PUNCT
ejpam-5608	207	15	x	x	NOUN
ejpam-5608	207	16	,	,	PUNCT
ejpam-5608	207	17	x	x	X
ejpam-5608	207	18	)	)	PUNCT
ejpam-5608	208	1	+	+	ADP
ejpam-5608	208	2	g	g	PROPN
ejpam-5608	208	3	(	(	PUNCT
ejpam-5608	208	4	x	x	X
ejpam-5608	208	5	,	,	PUNCT
ejpam-5608	208	6	xn1	xn1	NUM
ejpam-5608	208	7	,	,	PUNCT
ejpam-5608	208	8	x	x	X
ejpam-5608	208	9	)	)	PUNCT
ejpam-5608	208	10	+	+	ADP
ejpam-5608	208	11	g	g	NOUN
ejpam-5608	208	12	(	(	PUNCT
ejpam-5608	208	13	x	x	X
ejpam-5608	208	14	,	,	PUNCT
ejpam-5608	208	15	x	x	X
ejpam-5608	208	16	,	,	PUNCT
ejpam-5608	208	17	xn2	xn2	PROPN
ejpam-5608	208	18	)	)	PUNCT
ejpam-5608	208	19	≤	≤	NOUN
ejpam-5608	208	20	2(g	2(g	NUM
ejpam-5608	208	21	(	(	PUNCT
ejpam-5608	208	22	x	x	NOUN
ejpam-5608	208	23	,	,	PUNCT
ejpam-5608	208	24	xn1	xn1	NUM
ejpam-5608	208	25	,	,	PUNCT
ejpam-5608	208	26	xn2	xn2	PROPN
ejpam-5608	208	27	)	)	PUNCT
ejpam-5608	209	1	+	+	ADP
ejpam-5608	209	2	g	g	PROPN
ejpam-5608	209	3	(	(	PUNCT
ejpam-5608	209	4	x	x	X
ejpam-5608	209	5	,	,	PUNCT
ejpam-5608	209	6	xn1	xn1	NUM
ejpam-5608	209	7	,	,	PUNCT
ejpam-5608	209	8	xn2	xn2	PROPN
ejpam-5608	209	9	)	)	PUNCT
ejpam-5608	210	1	+	+	ADP
ejpam-5608	210	2	g	g	PROPN
ejpam-5608	210	3	(	(	PUNCT
ejpam-5608	210	4	x	x	X
ejpam-5608	210	5	,	,	PUNCT
ejpam-5608	210	6	xn1	xn1	NUM
ejpam-5608	210	7	,	,	PUNCT
ejpam-5608	210	8	xm	xm	PROPN
ejpam-5608	210	9	)	)	PUNCT
ejpam-5608	210	10	)	)	PUNCT
ejpam-5608	210	11	<	<	X
ejpam-5608	210	12	2	2	NUM
ejpam-5608	210	13	(	(	PUNCT
ejpam-5608	210	14	ε	ε	PROPN
ejpam-5608	210	15	6	6	NUM
ejpam-5608	210	16	+	+	CCONJ
ejpam-5608	210	17	ε	ε	PROPN
ejpam-5608	210	18	6	6	NUM
ejpam-5608	210	19	+	+	CCONJ
ejpam-5608	210	20	ε	ε	PROPN
ejpam-5608	210	21	6	6	NUM
ejpam-5608	210	22	)	)	PUNCT
ejpam-5608	210	23	=	=	SYM
ejpam-5608	210	24	ε	ε	PROPN
ejpam-5608	210	25	thus	thus	ADV
ejpam-5608	210	26	,	,	PUNCT
ejpam-5608	210	27	the	the	DET
ejpam-5608	210	28	set	set	NOUN
ejpam-5608	210	29	{	{	PUNCT
ejpam-5608	210	30	(	(	PUNCT
ejpam-5608	210	31	n1	n1	NOUN
ejpam-5608	210	32	,	,	PUNCT
ejpam-5608	210	33	n2	n2	ADJ
ejpam-5608	210	34	)	)	PUNCT
ejpam-5608	210	35	∈	∈	PROPN
ejpam-5608	210	36	n2	n2	NOUN
ejpam-5608	210	37	:	:	PUNCT
ejpam-5608	210	38	g	g	PROPN
ejpam-5608	210	39	(	(	PUNCT
ejpam-5608	210	40	xm	xm	PROPN
ejpam-5608	210	41	,	,	PUNCT
ejpam-5608	210	42	xn1	xn1	NUM
ejpam-5608	210	43	,	,	PUNCT
ejpam-5608	210	44	xn2	xn2	PROPN
ejpam-5608	210	45	)	)	PUNCT
ejpam-5608	210	46	≥	≥	X
ejpam-5608	210	47	ε	ε	PROPN
ejpam-5608	210	48	}	}	PUNCT
ejpam-5608	210	49	has	have	VERB
ejpam-5608	210	50	asymptotic	asymptotic	ADJ
ejpam-5608	210	51	density	density	NOUN
ejpam-5608	210	52	0	0	NUM
ejpam-5608	210	53	,	,	PUNCT
ejpam-5608	210	54	meaning	mean	VERB
ejpam-5608	210	55	that	that	SCONJ
ejpam-5608	210	56	(	(	PUNCT
ejpam-5608	210	57	xn	xn	X
ejpam-5608	210	58	)	)	PUNCT
ejpam-5608	210	59	is	be	AUX
ejpam-5608	210	60	an	an	DET
ejpam-5608	210	61	is	be	AUX
ejpam-5608	210	62	a	a	DET
ejpam-5608	210	63	statistically	statistically	ADV
ejpam-5608	210	64	cauchy	cauchy	ADJ
ejpam-5608	210	65	sequence	sequence	NOUN
ejpam-5608	210	66	.	.	PUNCT
ejpam-5608	211	1	theorem	theorem	VERB
ejpam-5608	211	2	9	9	NUM
ejpam-5608	211	3	.	.	PUNCT
ejpam-5608	212	1	[	[	X
ejpam-5608	212	2	19	19	NUM
ejpam-5608	212	3	]	]	X
ejpam-5608	212	4	if	if	SCONJ
ejpam-5608	212	5	(	(	PUNCT
ejpam-5608	212	6	xn	xn	X
ejpam-5608	212	7	)	)	PUNCT
ejpam-5608	212	8	ideally	ideally	ADV
ejpam-5608	212	9	converges	converge	VERB
ejpam-5608	212	10	in	in	ADP
ejpam-5608	212	11	a	a	DET
ejpam-5608	212	12	g	g	NOUN
ejpam-5608	212	13	-	-	PUNCT
ejpam-5608	212	14	metric	metric	ADJ
ejpam-5608	212	15	space	space	NOUN
ejpam-5608	212	16	,	,	PUNCT
ejpam-5608	212	17	then	then	ADV
ejpam-5608	212	18	(	(	PUNCT
ejpam-5608	212	19	xn	xn	X
ejpam-5608	212	20	)	)	PUNCT
ejpam-5608	212	21	is	be	AUX
ejpam-5608	212	22	an	an	DET
ejpam-5608	212	23	ideal	ideal	ADJ
ejpam-5608	212	24	cauchy	cauchy	ADJ
ejpam-5608	212	25	sequence	sequence	NOUN
ejpam-5608	212	26	in	in	ADP
ejpam-5608	212	27	the	the	DET
ejpam-5608	212	28	g	g	NOUN
ejpam-5608	212	29	-	-	PUNCT
ejpam-5608	212	30	metric	metric	ADJ
ejpam-5608	212	31	space	space	NOUN
ejpam-5608	212	32	.	.	PUNCT
ejpam-5608	213	1	manuharawati	manuharawati	NOUN
ejpam-5608	213	2	,	,	PUNCT
ejpam-5608	213	3	m.jakfar	m.jakfar	ADV
ejpam-5608	213	4	,	,	PUNCT
ejpam-5608	213	5	a.	a.	PROPN
ejpam-5608	213	6	taufik	taufik	PROPN
ejpam-5608	213	7	hamzah	hamzah	PROPN
ejpam-5608	213	8	/	/	SYM
ejpam-5608	213	9	eur	eur	PROPN
ejpam-5608	213	10	.	.	PUNCT
ejpam-5608	214	1	j.	j.	PROPN
ejpam-5608	214	2	pure	pure	PROPN
ejpam-5608	214	3	appl	appl	PROPN
ejpam-5608	214	4	.	.	PROPN
ejpam-5608	214	5	math	math	PROPN
ejpam-5608	214	6	,	,	PUNCT
ejpam-5608	214	7	18	18	NUM
ejpam-5608	214	8	(	(	PUNCT
ejpam-5608	214	9	1	1	NUM
ejpam-5608	214	10	)	)	PUNCT
ejpam-5608	214	11	(	(	PUNCT
ejpam-5608	214	12	2025	2025	NUM
ejpam-5608	214	13	)	)	PUNCT
ejpam-5608	214	14	,	,	PUNCT
ejpam-5608	214	15	5608	5608	NUM
ejpam-5608	214	16	10	10	NUM
ejpam-5608	214	17	of	of	ADP
ejpam-5608	214	18	13	13	NUM
ejpam-5608	214	19	proof	proof	NOUN
ejpam-5608	214	20	.	.	PUNCT
ejpam-5608	215	1	let	let	VERB
ejpam-5608	215	2	ε	ε	PROPN
ejpam-5608	215	3	>	>	X
ejpam-5608	215	4	0	0	PUNCT
ejpam-5608	215	5	be	be	AUX
ejpam-5608	215	6	any	any	DET
ejpam-5608	215	7	real	real	ADJ
ejpam-5608	215	8	number	number	NOUN
ejpam-5608	215	9	.	.	PUNCT
ejpam-5608	216	1	suppose	suppose	VERB
ejpam-5608	216	2	gi	gi	INTJ
ejpam-5608	216	3	−	−	NOUN
ejpam-5608	216	4	lim(xn	lim(xn	NOUN
ejpam-5608	216	5	)	)	PUNCT
ejpam-5608	216	6	=	=	PUNCT
ejpam-5608	217	1	x.	x.	NOUN
ejpam-5608	217	2	since	since	SCONJ
ejpam-5608	217	3	ε	ε	PROPN
ejpam-5608	217	4	is	be	AUX
ejpam-5608	217	5	a	a	DET
ejpam-5608	217	6	real	real	ADJ
ejpam-5608	217	7	number	number	NOUN
ejpam-5608	217	8	and	and	CCONJ
ejpam-5608	217	9	ε	ε	PROPN
ejpam-5608	217	10	>	>	X
ejpam-5608	217	11	0	0	PROPN
ejpam-5608	217	12	,	,	PUNCT
ejpam-5608	217	13	then	then	ADV
ejpam-5608	217	14	ε	ε	PROPN
ejpam-5608	217	15	6	6	NUM
ejpam-5608	217	16	is	be	AUX
ejpam-5608	217	17	also	also	ADV
ejpam-5608	217	18	a	a	DET
ejpam-5608	217	19	real	real	ADJ
ejpam-5608	217	20	number	number	NOUN
ejpam-5608	217	21	and	and	CCONJ
ejpam-5608	217	22	greater	great	ADJ
ejpam-5608	217	23	than	than	ADP
ejpam-5608	217	24	0	0	NUM
ejpam-5608	217	25	.	.	PUNCT
ejpam-5608	218	1	therefore	therefore	ADV
ejpam-5608	218	2	,	,	PUNCT
ejpam-5608	218	3	the	the	DET
ejpam-5608	218	4	set	set	NOUN
ejpam-5608	218	5	{	{	PUNCT
ejpam-5608	218	6	(	(	PUNCT
ejpam-5608	218	7	n1	n1	NOUN
ejpam-5608	218	8	,	,	PUNCT
ejpam-5608	218	9	n2	n2	ADJ
ejpam-5608	218	10	)	)	PUNCT
ejpam-5608	218	11	∈	∈	PROPN
ejpam-5608	218	12	n2	n2	NOUN
ejpam-5608	218	13	:	:	PUNCT
ejpam-5608	218	14	g	g	NOUN
ejpam-5608	218	15	(	(	PUNCT
ejpam-5608	218	16	x	x	X
ejpam-5608	218	17	,	,	PUNCT
ejpam-5608	218	18	xn1	xn1	NUM
ejpam-5608	218	19	,	,	PUNCT
ejpam-5608	218	20	xn2	xn2	PROPN
ejpam-5608	218	21	)	)	PUNCT
ejpam-5608	218	22	≥	≥	NOUN
ejpam-5608	218	23	ε	ε	PROPN
ejpam-5608	218	24	6	6	NUM
ejpam-5608	218	25	}	}	PUNCT
ejpam-5608	218	26	∈	∈	PROPN
ejpam-5608	218	27	i.	i.	NOUN
ejpam-5608	218	28	let	let	VERB
ejpam-5608	218	29	m	m	PRON
ejpam-5608	218	30	∈	∈	PROPN
ejpam-5608	218	31	n	n	AUX
ejpam-5608	218	32	be	be	AUX
ejpam-5608	218	33	chosen	choose	VERB
ejpam-5608	218	34	such	such	ADJ
ejpam-5608	218	35	that	that	SCONJ
ejpam-5608	218	36	g	g	PROPN
ejpam-5608	218	37	(	(	PUNCT
ejpam-5608	218	38	x	x	X
ejpam-5608	218	39	,	,	PUNCT
ejpam-5608	218	40	xn1	xn1	NUM
ejpam-5608	218	41	,	,	PUNCT
ejpam-5608	218	42	xm	xm	PROPN
ejpam-5608	218	43	)	)	PUNCT
ejpam-5608	218	44	≥	≥	PROPN
ejpam-5608	218	45	ε	ε	PROPN
ejpam-5608	218	46	6	6	NUM
ejpam-5608	218	47	.	.	PUNCT
ejpam-5608	219	1	then	then	ADV
ejpam-5608	219	2	g	g	PROPN
ejpam-5608	219	3	(	(	PUNCT
ejpam-5608	219	4	xm	xm	PROPN
ejpam-5608	219	5	,	,	PUNCT
ejpam-5608	219	6	xn1	xn1	NUM
ejpam-5608	219	7	,	,	PUNCT
ejpam-5608	219	8	xn2	xn2	PROPN
ejpam-5608	219	9	)	)	PUNCT
ejpam-5608	219	10	≤	≤	NOUN
ejpam-5608	219	11	g	g	PROPN
ejpam-5608	219	12	(	(	PUNCT
ejpam-5608	219	13	xm	xm	PROPN
ejpam-5608	219	14	,	,	PUNCT
ejpam-5608	219	15	x	x	NOUN
ejpam-5608	219	16	,	,	PUNCT
ejpam-5608	219	17	x	x	X
ejpam-5608	219	18	)	)	PUNCT
ejpam-5608	220	1	+	+	ADP
ejpam-5608	220	2	g	g	PROPN
ejpam-5608	220	3	(	(	PUNCT
ejpam-5608	220	4	x	x	X
ejpam-5608	220	5	,	,	PUNCT
ejpam-5608	220	6	xn1	xn1	NUM
ejpam-5608	220	7	,	,	PUNCT
ejpam-5608	220	8	x	x	X
ejpam-5608	220	9	)	)	PUNCT
ejpam-5608	220	10	+	+	ADP
ejpam-5608	220	11	g	g	NOUN
ejpam-5608	220	12	(	(	PUNCT
ejpam-5608	220	13	x	x	X
ejpam-5608	220	14	,	,	PUNCT
ejpam-5608	220	15	x	x	X
ejpam-5608	220	16	,	,	PUNCT
ejpam-5608	220	17	xn2	xn2	PROPN
ejpam-5608	220	18	)	)	PUNCT
ejpam-5608	220	19	≤	≤	NOUN
ejpam-5608	220	20	2(g	2(g	NUM
ejpam-5608	220	21	(	(	PUNCT
ejpam-5608	220	22	x	x	NOUN
ejpam-5608	220	23	,	,	PUNCT
ejpam-5608	220	24	xn1	xn1	NUM
ejpam-5608	220	25	,	,	PUNCT
ejpam-5608	220	26	xn2	xn2	PROPN
ejpam-5608	220	27	)	)	PUNCT
ejpam-5608	221	1	+	+	ADP
ejpam-5608	221	2	g	g	PROPN
ejpam-5608	221	3	(	(	PUNCT
ejpam-5608	221	4	x	x	X
ejpam-5608	221	5	,	,	PUNCT
ejpam-5608	221	6	xn1	xn1	NUM
ejpam-5608	221	7	,	,	PUNCT
ejpam-5608	221	8	xn2	xn2	PROPN
ejpam-5608	221	9	)	)	PUNCT
ejpam-5608	222	1	+	+	ADP
ejpam-5608	222	2	g	g	PROPN
ejpam-5608	222	3	(	(	PUNCT
ejpam-5608	222	4	x	x	X
ejpam-5608	222	5	,	,	PUNCT
ejpam-5608	222	6	xn1	xn1	NUM
ejpam-5608	222	7	,	,	PUNCT
ejpam-5608	222	8	xm	xm	PROPN
ejpam-5608	222	9	)	)	PUNCT
ejpam-5608	222	10	)	)	PUNCT
ejpam-5608	222	11	<	<	X
ejpam-5608	222	12	2	2	NUM
ejpam-5608	222	13	(	(	PUNCT
ejpam-5608	222	14	ε	ε	PROPN
ejpam-5608	222	15	6	6	NUM
ejpam-5608	222	16	+	+	CCONJ
ejpam-5608	222	17	ε	ε	PROPN
ejpam-5608	222	18	6	6	NUM
ejpam-5608	222	19	+	+	CCONJ
ejpam-5608	222	20	ε	ε	PROPN
ejpam-5608	222	21	6	6	NUM
ejpam-5608	222	22	)	)	PUNCT
ejpam-5608	222	23	=	=	SYM
ejpam-5608	222	24	ε	ε	PROPN
ejpam-5608	222	25	thus	thus	ADV
ejpam-5608	222	26	,	,	PUNCT
ejpam-5608	222	27	the	the	DET
ejpam-5608	222	28	set	set	NOUN
ejpam-5608	222	29	{	{	PUNCT
ejpam-5608	222	30	(	(	PUNCT
ejpam-5608	222	31	n1	n1	NOUN
ejpam-5608	222	32	,	,	PUNCT
ejpam-5608	222	33	n2	n2	ADJ
ejpam-5608	222	34	)	)	PUNCT
ejpam-5608	222	35	∈	∈	PROPN
ejpam-5608	222	36	n2	n2	NOUN
ejpam-5608	222	37	:	:	PUNCT
ejpam-5608	222	38	g	g	PROPN
ejpam-5608	222	39	(	(	PUNCT
ejpam-5608	222	40	xm	xm	PROPN
ejpam-5608	222	41	,	,	PUNCT
ejpam-5608	222	42	xn1	xn1	NUM
ejpam-5608	222	43	,	,	PUNCT
ejpam-5608	222	44	xn2	xn2	PROPN
ejpam-5608	222	45	)	)	PUNCT
ejpam-5608	222	46	≥	≥	NOUN
ejpam-5608	222	47	ε	ε	PROPN
ejpam-5608	222	48	}	}	PUNCT
ejpam-5608	222	49	∈	∈	PROPN
ejpam-5608	222	50	i	i	PRON
ejpam-5608	222	51	,	,	PUNCT
ejpam-5608	222	52	which	which	PRON
ejpam-5608	222	53	means	mean	VERB
ejpam-5608	222	54	(	(	PUNCT
ejpam-5608	222	55	xn	xn	X
ejpam-5608	222	56	)	)	PUNCT
ejpam-5608	222	57	is	be	AUX
ejpam-5608	222	58	an	an	DET
ejpam-5608	222	59	ideal	ideal	ADJ
ejpam-5608	222	60	cauchy	cauchy	ADJ
ejpam-5608	222	61	sequence	sequence	NOUN
ejpam-5608	222	62	.	.	PUNCT
ejpam-5608	223	1	theorems	theorems	PROPN
ejpam-5608	223	2	1	1	NUM
ejpam-5608	223	3	,	,	PUNCT
ejpam-5608	223	4	2	2	NUM
ejpam-5608	223	5	,	,	PUNCT
ejpam-5608	223	6	5	5	NUM
ejpam-5608	223	7	,	,	PUNCT
ejpam-5608	223	8	8	8	NUM
ejpam-5608	223	9	,	,	PUNCT
ejpam-5608	223	10	and	and	CCONJ
ejpam-5608	223	11	9	9	NUM
ejpam-5608	223	12	yield	yield	VERB
ejpam-5608	223	13	the	the	DET
ejpam-5608	223	14	following	follow	VERB
ejpam-5608	223	15	corollaries	corollary	NOUN
ejpam-5608	223	16	:	:	PUNCT
ejpam-5608	224	1	corollary	corollary	ADJ
ejpam-5608	224	2	1	1	NUM
ejpam-5608	224	3	.	.	PUNCT
ejpam-5608	225	1	if	if	SCONJ
ejpam-5608	225	2	the	the	DET
ejpam-5608	225	3	sequence	sequence	NOUN
ejpam-5608	225	4	(	(	PUNCT
ejpam-5608	225	5	xn	xn	X
ejpam-5608	225	6	)	)	PUNCT
ejpam-5608	225	7	is	be	AUX
ejpam-5608	225	8	a	a	DET
ejpam-5608	225	9	cauchy	cauchy	ADJ
ejpam-5608	225	10	sequence	sequence	NOUN
ejpam-5608	225	11	in	in	ADP
ejpam-5608	225	12	a	a	DET
ejpam-5608	225	13	g	g	NOUN
ejpam-5608	225	14	-	-	PUNCT
ejpam-5608	225	15	metric	metric	ADJ
ejpam-5608	225	16	space	space	NOUN
ejpam-5608	225	17	,	,	PUNCT
ejpam-5608	225	18	then	then	ADV
ejpam-5608	225	19	the	the	DET
ejpam-5608	225	20	sequence	sequence	NOUN
ejpam-5608	225	21	(	(	PUNCT
ejpam-5608	225	22	xn	xn	X
ejpam-5608	225	23	)	)	PUNCT
ejpam-5608	225	24	is	be	AUX
ejpam-5608	225	25	statistically	statistically	ADV
ejpam-5608	225	26	cauchy	cauchy	ADJ
ejpam-5608	225	27	in	in	ADP
ejpam-5608	225	28	the	the	DET
ejpam-5608	225	29	g	g	NOUN
ejpam-5608	225	30	-	-	PUNCT
ejpam-5608	225	31	metric	metric	ADJ
ejpam-5608	225	32	space	space	NOUN
ejpam-5608	225	33	.	.	PUNCT
ejpam-5608	226	1	proof	proof	NOUN
ejpam-5608	226	2	.	.	PUNCT
ejpam-5608	227	1	based	base	VERB
ejpam-5608	227	2	on	on	ADP
ejpam-5608	227	3	theorem	theorem	NOUN
ejpam-5608	227	4	1	1	NUM
ejpam-5608	227	5	,	,	PUNCT
ejpam-5608	227	6	it	it	PRON
ejpam-5608	227	7	can	can	AUX
ejpam-5608	227	8	be	be	AUX
ejpam-5608	227	9	observed	observe	VERB
ejpam-5608	227	10	that	that	SCONJ
ejpam-5608	227	11	a	a	DET
ejpam-5608	227	12	normally	normally	ADV
ejpam-5608	227	13	convergent	convergent	ADJ
ejpam-5608	227	14	sequence	sequence	NOUN
ejpam-5608	227	15	in	in	ADP
ejpam-5608	227	16	a	a	DET
ejpam-5608	227	17	g	g	NOUN
ejpam-5608	227	18	-	-	PUNCT
ejpam-5608	227	19	metric	metric	ADJ
ejpam-5608	227	20	space	space	NOUN
ejpam-5608	227	21	is	be	AUX
ejpam-5608	227	22	a	a	DET
ejpam-5608	227	23	cauchy	cauchy	ADJ
ejpam-5608	227	24	sequence	sequence	NOUN
ejpam-5608	227	25	in	in	ADP
ejpam-5608	227	26	the	the	DET
ejpam-5608	227	27	g	g	NOUN
ejpam-5608	227	28	-	-	PUNCT
ejpam-5608	227	29	metric	metric	ADJ
ejpam-5608	227	30	space	space	NOUN
ejpam-5608	227	31	.	.	PUNCT
ejpam-5608	228	1	according	accord	VERB
ejpam-5608	228	2	to	to	ADP
ejpam-5608	228	3	theorem	theorem	ADJ
ejpam-5608	228	4	2	2	NUM
ejpam-5608	228	5	,	,	PUNCT
ejpam-5608	228	6	if	if	SCONJ
ejpam-5608	228	7	a	a	DET
ejpam-5608	228	8	sequence	sequence	NOUN
ejpam-5608	228	9	is	be	AUX
ejpam-5608	228	10	normally	normally	ADV
ejpam-5608	228	11	convergent	convergent	ADJ
ejpam-5608	228	12	in	in	ADP
ejpam-5608	228	13	a	a	DET
ejpam-5608	228	14	g	g	NOUN
ejpam-5608	228	15	-	-	PUNCT
ejpam-5608	228	16	metric	metric	ADJ
ejpam-5608	228	17	space	space	NOUN
ejpam-5608	228	18	,	,	PUNCT
ejpam-5608	228	19	then	then	ADV
ejpam-5608	228	20	it	it	PRON
ejpam-5608	228	21	is	be	AUX
ejpam-5608	228	22	statistically	statistically	ADV
ejpam-5608	228	23	convergent	convergent	ADJ
ejpam-5608	228	24	in	in	ADP
ejpam-5608	228	25	the	the	DET
ejpam-5608	228	26	g	g	NOUN
ejpam-5608	228	27	-	-	PUNCT
ejpam-5608	228	28	metric	metric	ADJ
ejpam-5608	228	29	space	space	NOUN
ejpam-5608	228	30	.	.	PUNCT
ejpam-5608	229	1	theorem	theorem	VERB
ejpam-5608	229	2	8	8	NUM
ejpam-5608	229	3	states	state	NOUN
ejpam-5608	229	4	that	that	SCONJ
ejpam-5608	229	5	a	a	DET
ejpam-5608	229	6	statistically	statistically	ADV
ejpam-5608	229	7	convergent	convergent	ADJ
ejpam-5608	229	8	sequence	sequence	NOUN
ejpam-5608	229	9	in	in	ADP
ejpam-5608	229	10	a	a	DET
ejpam-5608	229	11	g	g	NOUN
ejpam-5608	229	12	-	-	PUNCT
ejpam-5608	229	13	metric	metric	ADJ
ejpam-5608	229	14	space	space	NOUN
ejpam-5608	229	15	is	be	AUX
ejpam-5608	229	16	a	a	DET
ejpam-5608	229	17	statistically	statistically	ADV
ejpam-5608	229	18	cauchy	cauchy	ADJ
ejpam-5608	229	19	sequence	sequence	NOUN
ejpam-5608	229	20	in	in	ADP
ejpam-5608	229	21	the	the	DET
ejpam-5608	229	22	g	g	NOUN
ejpam-5608	229	23	-	-	PUNCT
ejpam-5608	229	24	metric	metric	ADJ
ejpam-5608	229	25	space	space	NOUN
ejpam-5608	229	26	.	.	PUNCT
ejpam-5608	230	1	from	from	ADP
ejpam-5608	230	2	these	these	DET
ejpam-5608	230	3	three	three	NUM
ejpam-5608	230	4	theorems	theorem	NOUN
ejpam-5608	230	5	,	,	PUNCT
ejpam-5608	230	6	it	it	PRON
ejpam-5608	230	7	can	can	AUX
ejpam-5608	230	8	be	be	AUX
ejpam-5608	230	9	concluded	conclude	VERB
ejpam-5608	230	10	that	that	SCONJ
ejpam-5608	230	11	a	a	DET
ejpam-5608	230	12	cauchy	cauchy	ADJ
ejpam-5608	230	13	sequence	sequence	NOUN
ejpam-5608	230	14	in	in	ADP
ejpam-5608	230	15	a	a	DET
ejpam-5608	230	16	g	g	NOUN
ejpam-5608	230	17	-	-	PUNCT
ejpam-5608	230	18	metric	metric	ADJ
ejpam-5608	230	19	space	space	NOUN
ejpam-5608	230	20	is	be	AUX
ejpam-5608	230	21	a	a	DET
ejpam-5608	230	22	statistically	statistically	ADV
ejpam-5608	230	23	cauchy	cauchy	ADJ
ejpam-5608	230	24	sequence	sequence	NOUN
ejpam-5608	230	25	in	in	ADP
ejpam-5608	230	26	the	the	DET
ejpam-5608	230	27	g	g	NOUN
ejpam-5608	230	28	-	-	PUNCT
ejpam-5608	230	29	metric	metric	ADJ
ejpam-5608	230	30	space	space	NOUN
ejpam-5608	230	31	.	.	PUNCT
ejpam-5608	231	1	corollary	corollary	ADJ
ejpam-5608	231	2	2	2	NUM
ejpam-5608	231	3	.	.	PUNCT
ejpam-5608	231	4	given	give	VERB
ejpam-5608	231	5	an	an	DET
ejpam-5608	231	6	admissible	admissible	ADJ
ejpam-5608	231	7	ideal	ideal	NOUN
ejpam-5608	232	1	i	i	PRON
ejpam-5608	232	2	,	,	PUNCT
ejpam-5608	232	3	if	if	SCONJ
ejpam-5608	232	4	the	the	DET
ejpam-5608	232	5	sequence	sequence	NOUN
ejpam-5608	232	6	(	(	PUNCT
ejpam-5608	232	7	xn	xn	X
ejpam-5608	232	8	)	)	PUNCT
ejpam-5608	232	9	is	be	AUX
ejpam-5608	232	10	a	a	DET
ejpam-5608	232	11	cauchy	cauchy	ADJ
ejpam-5608	232	12	sequence	sequence	NOUN
ejpam-5608	232	13	,	,	PUNCT
ejpam-5608	232	14	then	then	ADV
ejpam-5608	232	15	the	the	DET
ejpam-5608	232	16	sequence	sequence	NOUN
ejpam-5608	232	17	(	(	PUNCT
ejpam-5608	232	18	xn	xn	X
ejpam-5608	232	19	)	)	PUNCT
ejpam-5608	232	20	is	be	AUX
ejpam-5608	232	21	an	an	DET
ejpam-5608	232	22	ideal	ideal	ADJ
ejpam-5608	232	23	cauchy	cauchy	ADJ
ejpam-5608	232	24	sequence	sequence	NOUN
ejpam-5608	232	25	.	.	PUNCT
ejpam-5608	233	1	proof	proof	NOUN
ejpam-5608	233	2	.	.	PUNCT
ejpam-5608	234	1	according	accord	VERB
ejpam-5608	234	2	to	to	ADP
ejpam-5608	234	3	theorem	theorem	NOUN
ejpam-5608	234	4	1	1	NUM
ejpam-5608	234	5	,	,	PUNCT
ejpam-5608	234	6	a	a	DET
ejpam-5608	234	7	normally	normally	ADV
ejpam-5608	234	8	convergent	convergent	ADJ
ejpam-5608	234	9	sequence	sequence	NOUN
ejpam-5608	234	10	in	in	ADP
ejpam-5608	234	11	a	a	DET
ejpam-5608	234	12	g	g	NOUN
ejpam-5608	234	13	-	-	PUNCT
ejpam-5608	234	14	metric	metric	ADJ
ejpam-5608	234	15	space	space	NOUN
ejpam-5608	234	16	is	be	AUX
ejpam-5608	234	17	a	a	DET
ejpam-5608	234	18	cauchy	cauchy	ADJ
ejpam-5608	234	19	sequence	sequence	NOUN
ejpam-5608	234	20	in	in	ADP
ejpam-5608	234	21	the	the	DET
ejpam-5608	234	22	g	g	NOUN
ejpam-5608	234	23	-	-	PUNCT
ejpam-5608	234	24	metric	metric	ADJ
ejpam-5608	234	25	space	space	NOUN
ejpam-5608	234	26	.	.	PUNCT
ejpam-5608	235	1	based	base	VERB
ejpam-5608	235	2	on	on	ADP
ejpam-5608	235	3	theorem	theorem	NOUN
ejpam-5608	235	4	5	5	NUM
ejpam-5608	235	5	,	,	PUNCT
ejpam-5608	235	6	if	if	SCONJ
ejpam-5608	235	7	a	a	DET
ejpam-5608	235	8	sequence	sequence	NOUN
ejpam-5608	235	9	is	be	AUX
ejpam-5608	235	10	normally	normally	ADV
ejpam-5608	235	11	convergent	convergent	ADJ
ejpam-5608	235	12	in	in	ADP
ejpam-5608	235	13	a	a	DET
ejpam-5608	235	14	g	g	NOUN
ejpam-5608	235	15	-	-	PUNCT
ejpam-5608	235	16	metric	metric	ADJ
ejpam-5608	235	17	space	space	NOUN
ejpam-5608	235	18	,	,	PUNCT
ejpam-5608	235	19	then	then	ADV
ejpam-5608	235	20	it	it	PRON
ejpam-5608	235	21	is	be	AUX
ejpam-5608	235	22	ideal	ideal	ADJ
ejpam-5608	235	23	convergent	convergent	NOUN
ejpam-5608	235	24	in	in	ADP
ejpam-5608	235	25	the	the	DET
ejpam-5608	235	26	g	g	NOUN
ejpam-5608	235	27	-	-	PUNCT
ejpam-5608	235	28	metric	metric	ADJ
ejpam-5608	235	29	space	space	NOUN
ejpam-5608	235	30	with	with	ADP
ejpam-5608	235	31	respect	respect	NOUN
ejpam-5608	235	32	to	to	ADP
ejpam-5608	235	33	the	the	DET
ejpam-5608	235	34	admissible	admissible	ADJ
ejpam-5608	235	35	ideal	ideal	NOUN
ejpam-5608	235	36	.	.	PUNCT
ejpam-5608	236	1	theorem	theorem	VERB
ejpam-5608	236	2	9	9	NUM
ejpam-5608	236	3	states	state	NOUN
ejpam-5608	236	4	that	that	SCONJ
ejpam-5608	236	5	an	an	DET
ejpam-5608	236	6	ideal	ideal	ADJ
ejpam-5608	236	7	convergent	convergent	NOUN
ejpam-5608	236	8	sequence	sequence	NOUN
ejpam-5608	236	9	in	in	ADP
ejpam-5608	236	10	a	a	DET
ejpam-5608	236	11	g	g	NOUN
ejpam-5608	236	12	-	-	PUNCT
ejpam-5608	236	13	metric	metric	ADJ
ejpam-5608	236	14	space	space	NOUN
ejpam-5608	236	15	is	be	AUX
ejpam-5608	236	16	an	an	DET
ejpam-5608	236	17	ideal	ideal	ADJ
ejpam-5608	236	18	cauchy	cauchy	ADJ
ejpam-5608	236	19	sequence	sequence	NOUN
ejpam-5608	236	20	in	in	ADP
ejpam-5608	236	21	the	the	DET
ejpam-5608	236	22	g	g	NOUN
ejpam-5608	236	23	-	-	PUNCT
ejpam-5608	236	24	metric	metric	ADJ
ejpam-5608	236	25	space	space	NOUN
ejpam-5608	236	26	.	.	PUNCT
ejpam-5608	237	1	from	from	ADP
ejpam-5608	237	2	these	these	DET
ejpam-5608	237	3	three	three	NUM
ejpam-5608	237	4	theorems	theorem	NOUN
ejpam-5608	237	5	,	,	PUNCT
ejpam-5608	237	6	it	it	PRON
ejpam-5608	237	7	can	can	AUX
ejpam-5608	237	8	be	be	AUX
ejpam-5608	237	9	concluded	conclude	VERB
ejpam-5608	237	10	that	that	SCONJ
ejpam-5608	237	11	a	a	DET
ejpam-5608	237	12	cauchy	cauchy	ADJ
ejpam-5608	237	13	sequence	sequence	NOUN
ejpam-5608	237	14	in	in	ADP
ejpam-5608	237	15	a	a	DET
ejpam-5608	237	16	g	g	NOUN
ejpam-5608	237	17	-	-	PUNCT
ejpam-5608	237	18	metric	metric	ADJ
ejpam-5608	237	19	space	space	NOUN
ejpam-5608	237	20	.	.	PUNCT
ejpam-5608	238	1	theorem	theorem	ADJ
ejpam-5608	238	2	10	10	NUM
ejpam-5608	238	3	.	.	PUNCT
ejpam-5608	239	1	given	give	VERB
ejpam-5608	239	2	(	(	PUNCT
ejpam-5608	239	3	xn	xn	X
ejpam-5608	239	4	)	)	PUNCT
ejpam-5608	239	5	is	be	AUX
ejpam-5608	239	6	a	a	DET
ejpam-5608	239	7	sequence	sequence	NOUN
ejpam-5608	239	8	of	of	ADP
ejpam-5608	239	9	real	real	ADJ
ejpam-5608	239	10	numbers	number	NOUN
ejpam-5608	239	11	with	with	ADP
ejpam-5608	239	12	an	an	DET
ejpam-5608	239	13	admissible	admissible	ADJ
ejpam-5608	239	14	ideal	ideal	ADJ
ejpam-5608	239	15	i2	i2	PROPN
ejpam-5608	239	16	.	.	PUNCT
ejpam-5608	240	1	if	if	SCONJ
ejpam-5608	240	2	(	(	PUNCT
ejpam-5608	240	3	xn	xn	X
ejpam-5608	240	4	)	)	PUNCT
ejpam-5608	240	5	is	be	AUX
ejpam-5608	240	6	ideal	ideal	ADJ
ejpam-5608	240	7	convergent	convergent	NOUN
ejpam-5608	240	8	to	to	ADP
ejpam-5608	240	9	l	l	NOUN
ejpam-5608	240	10	in	in	ADP
ejpam-5608	240	11	the	the	DET
ejpam-5608	240	12	g	g	NOUN
ejpam-5608	240	13	-	-	PUNCT
ejpam-5608	240	14	metric	metric	ADJ
ejpam-5608	240	15	space	space	NOUN
ejpam-5608	240	16	,	,	PUNCT
ejpam-5608	240	17	then	then	ADV
ejpam-5608	240	18	there	there	PRON
ejpam-5608	240	19	exists	exist	VERB
ejpam-5608	240	20	a	a	DET
ejpam-5608	240	21	sequence	sequence	NOUN
ejpam-5608	240	22	(	(	PUNCT
ejpam-5608	240	23	yn	yn	NOUN
ejpam-5608	240	24	)	)	PUNCT
ejpam-5608	240	25	that	that	PRON
ejpam-5608	240	26	is	be	AUX
ejpam-5608	240	27	statistically	statistically	ADV
ejpam-5608	240	28	convergent	convergent	ADJ
ejpam-5608	240	29	to	to	ADP
ejpam-5608	240	30	l	l	NOUN
ejpam-5608	240	31	in	in	ADP
ejpam-5608	240	32	the	the	DET
ejpam-5608	240	33	g	g	NOUN
ejpam-5608	240	34	-	-	PUNCT
ejpam-5608	240	35	metric	metric	ADJ
ejpam-5608	240	36	space	space	NOUN
ejpam-5608	240	37	,	,	PUNCT
ejpam-5608	240	38	such	such	ADJ
ejpam-5608	240	39	that	that	SCONJ
ejpam-5608	240	40	(	(	PUNCT
ejpam-5608	240	41	|xn−	|xn−	PROPN
ejpam-5608	240	42	yn|	yn|	NOUN
ejpam-5608	240	43	)	)	PUNCT
ejpam-5608	240	44	is	be	AUX
ejpam-5608	240	45	ideal	ideal	ADJ
ejpam-5608	240	46	convergent	convergent	NOUN
ejpam-5608	240	47	to	to	ADP
ejpam-5608	240	48	0	0	NUM
ejpam-5608	240	49	in	in	ADP
ejpam-5608	240	50	the	the	DET
ejpam-5608	240	51	g	g	NOUN
ejpam-5608	240	52	-	-	PUNCT
ejpam-5608	240	53	metric	metric	ADJ
ejpam-5608	240	54	space	space	NOUN
ejpam-5608	240	55	.	.	PUNCT
ejpam-5608	241	1	proof	proof	NOUN
ejpam-5608	241	2	.	.	PUNCT
ejpam-5608	242	1	let	let	VERB
ejpam-5608	242	2	ε	ε	PROPN
ejpam-5608	242	3	>	>	X
ejpam-5608	242	4	0	0	PUNCT
ejpam-5608	242	5	be	be	AUX
ejpam-5608	242	6	a	a	DET
ejpam-5608	242	7	given	give	VERB
ejpam-5608	242	8	real	real	ADJ
ejpam-5608	242	9	number	number	NOUN
ejpam-5608	242	10	.	.	PUNCT
ejpam-5608	243	1	the	the	DET
ejpam-5608	243	2	sequence	sequence	NOUN
ejpam-5608	243	3	(	(	PUNCT
ejpam-5608	243	4	xn	xn	X
ejpam-5608	243	5	)	)	PUNCT
ejpam-5608	243	6	is	be	AUX
ejpam-5608	243	7	ideal	ideal	ADJ
ejpam-5608	243	8	convergent	convergent	NOUN
ejpam-5608	243	9	to	to	ADP
ejpam-5608	243	10	x	x	PRON
ejpam-5608	243	11	,	,	PUNCT
ejpam-5608	243	12	which	which	PRON
ejpam-5608	243	13	means	mean	VERB
ejpam-5608	243	14	that	that	SCONJ
ejpam-5608	243	15	for	for	ADP
ejpam-5608	243	16	each	each	DET
ejpam-5608	243	17	such	such	ADJ
ejpam-5608	243	18	ε	ε	PROPN
ejpam-5608	243	19	,	,	PUNCT
ejpam-5608	243	20	the	the	DET
ejpam-5608	243	21	set	set	NOUN
ejpam-5608	243	22	(	(	PUNCT
ejpam-5608	243	23	n1	n1	NOUN
ejpam-5608	243	24	,	,	PUNCT
ejpam-5608	243	25	n2	n2	ADJ
ejpam-5608	243	26	)	)	PUNCT
ejpam-5608	243	27	∈	∈	PROPN
ejpam-5608	243	28	n2	n2	NOUN
ejpam-5608	243	29	:	:	PUNCT
ejpam-5608	243	30	g	g	NOUN
ejpam-5608	243	31	(	(	PUNCT
ejpam-5608	243	32	x	x	X
ejpam-5608	243	33	,	,	PUNCT
ejpam-5608	243	34	xn1	xn1	NUM
ejpam-5608	243	35	,	,	PUNCT
ejpam-5608	243	36	xn2	xn2	PROPN
ejpam-5608	243	37	)	)	PUNCT
ejpam-5608	243	38	≥	≥	NOUN
ejpam-5608	243	39	ε	ε	PROPN
ejpam-5608	243	40	∈	∈	PROPN
ejpam-5608	243	41	i2	i2	PROPN
ejpam-5608	243	42	.	.	PUNCT
ejpam-5608	244	1	the	the	DET
ejpam-5608	244	2	sequence	sequence	NOUN
ejpam-5608	244	3	(	(	PUNCT
ejpam-5608	244	4	yn	yn	NOUN
ejpam-5608	244	5	)	)	PUNCT
ejpam-5608	244	6	is	be	AUX
ejpam-5608	244	7	statistically	statistically	ADV
ejpam-5608	244	8	convergent	convergent	ADJ
ejpam-5608	244	9	to	to	ADP
ejpam-5608	244	10	x	x	PRON
ejpam-5608	244	11	,	,	PUNCT
ejpam-5608	244	12	which	which	PRON
ejpam-5608	244	13	means	mean	VERB
ejpam-5608	244	14	that	that	SCONJ
ejpam-5608	244	15	for	for	ADP
ejpam-5608	244	16	each	each	DET
ejpam-5608	244	17	such	such	ADJ
ejpam-5608	244	18	ε	ε	PROPN
ejpam-5608	244	19	,	,	PUNCT
ejpam-5608	244	20	the	the	DET
ejpam-5608	244	21	following	follow	VERB
ejpam-5608	244	22	holds	hold	NOUN
ejpam-5608	244	23	:	:	PUNCT
ejpam-5608	244	24	lim	lim	PROPN
ejpam-5608	244	25	n→+∞	n→+∞	PROPN
ejpam-5608	244	26	(	(	PUNCT
ejpam-5608	244	27	2	2	NUM
ejpam-5608	244	28	n2	n2	NOUN
ejpam-5608	244	29	∣∣(n1	∣∣(n1	PROPN
ejpam-5608	244	30	,	,	PUNCT
ejpam-5608	244	31	n2	n2	ADJ
ejpam-5608	244	32	)	)	PUNCT
ejpam-5608	244	33	∈	∈	PROPN
ejpam-5608	244	34	n2	n2	NOUN
ejpam-5608	244	35	:	:	PUNCT
ejpam-5608	244	36	n1	n1	ADJ
ejpam-5608	244	37	,	,	PUNCT
ejpam-5608	244	38	n2	n2	ADJ
ejpam-5608	244	39	≤	≤	PUNCT
ejpam-5608	244	40	n	n	CCONJ
ejpam-5608	244	41	:	:	PUNCT
ejpam-5608	244	42	g	g	NOUN
ejpam-5608	244	43	(	(	PUNCT
ejpam-5608	244	44	x	x	NOUN
ejpam-5608	244	45	,	,	PUNCT
ejpam-5608	244	46	yn1	yn1	NOUN
ejpam-5608	244	47	,	,	PUNCT
ejpam-5608	244	48	yn2	yn2	NOUN
ejpam-5608	244	49	)	)	PUNCT
ejpam-5608	244	50	≥	≥	NOUN
ejpam-5608	244	51	ε	ε	X
ejpam-5608	244	52	∣∣	∣∣	X
ejpam-5608	244	53	)	)	PUNCT
ejpam-5608	244	54	=	=	SYM
ejpam-5608	244	55	0	0	NUM
ejpam-5608	244	56	manuharawati	manuharawati	NOUN
ejpam-5608	244	57	,	,	PUNCT
ejpam-5608	244	58	m.jakfar	m.jakfar	ADV
ejpam-5608	244	59	,	,	PUNCT
ejpam-5608	244	60	a.	a.	PROPN
ejpam-5608	244	61	taufik	taufik	PROPN
ejpam-5608	244	62	hamzah	hamzah	PROPN
ejpam-5608	244	63	/	/	SYM
ejpam-5608	244	64	eur	eur	PROPN
ejpam-5608	244	65	.	.	PUNCT
ejpam-5608	245	1	j.	j.	PROPN
ejpam-5608	245	2	pure	pure	PROPN
ejpam-5608	245	3	appl	appl	PROPN
ejpam-5608	245	4	.	.	PROPN
ejpam-5608	245	5	math	math	PROPN
ejpam-5608	245	6	,	,	PUNCT
ejpam-5608	245	7	18	18	NUM
ejpam-5608	245	8	(	(	PUNCT
ejpam-5608	245	9	1	1	NUM
ejpam-5608	245	10	)	)	PUNCT
ejpam-5608	245	11	(	(	PUNCT
ejpam-5608	245	12	2025	2025	NUM
ejpam-5608	245	13	)	)	PUNCT
ejpam-5608	245	14	,	,	PUNCT
ejpam-5608	245	15	5608	5608	NUM
ejpam-5608	245	16	11	11	NUM
ejpam-5608	245	17	of	of	ADP
ejpam-5608	245	18	13	13	NUM
ejpam-5608	245	19	let	let	VERB
ejpam-5608	245	20	{	{	PUNCT
ejpam-5608	245	21	(	(	PUNCT
ejpam-5608	245	22	n1	n1	NOUN
ejpam-5608	245	23	,	,	PUNCT
ejpam-5608	245	24	n2	n2	ADJ
ejpam-5608	245	25	)	)	PUNCT
ejpam-5608	245	26	∈	∈	PROPN
ejpam-5608	245	27	n2	n2	NOUN
ejpam-5608	245	28	:	:	PUNCT
ejpam-5608	245	29	n1	n1	ADJ
ejpam-5608	245	30	,	,	PUNCT
ejpam-5608	245	31	n2	n2	ADJ
ejpam-5608	245	32	≤	≤	PUNCT
ejpam-5608	245	33	n	n	CCONJ
ejpam-5608	245	34	:	:	PUNCT
ejpam-5608	245	35	g(x	g(x	NOUN
ejpam-5608	245	36	,	,	PUNCT
ejpam-5608	245	37	yn1	yn1	NOUN
ejpam-5608	245	38	,	,	PUNCT
ejpam-5608	245	39	yn2	yn2	NOUN
ejpam-5608	245	40	)	)	PUNCT
ejpam-5608	245	41	≥	≥	X
ejpam-5608	245	42	ε	ε	NOUN
ejpam-5608	245	43	}	}	PUNCT
ejpam-5608	245	44	=	=	SYM
ejpam-5608	245	45	aε	aε	NOUN
ejpam-5608	245	46	.	.	PUNCT
ejpam-5608	246	1	if	if	SCONJ
ejpam-5608	246	2	the	the	DET
ejpam-5608	246	3	sequence	sequence	NOUN
ejpam-5608	246	4	(	(	PUNCT
ejpam-5608	246	5	yn	yn	NOUN
ejpam-5608	246	6	)	)	PUNCT
ejpam-5608	246	7	satisfies	satisfie	NOUN
ejpam-5608	246	8	aε	aε	ADP
ejpam-5608	246	9	∈	∈	PROPN
ejpam-5608	246	10	i	i	PRON
ejpam-5608	246	11	for	for	ADP
ejpam-5608	246	12	each	each	DET
ejpam-5608	246	13	given	give	VERB
ejpam-5608	246	14	ε	ε	PROPN
ejpam-5608	246	15	,	,	PUNCT
ejpam-5608	246	16	then	then	ADV
ejpam-5608	246	17	g	g	PROPN
ejpam-5608	246	18	(	(	PUNCT
ejpam-5608	246	19	x	x	X
ejpam-5608	246	20	,	,	PUNCT
ejpam-5608	246	21	xn1	xn1	NUM
ejpam-5608	246	22	,	,	PUNCT
ejpam-5608	246	23	xn2)−g	xn2)−g	X
ejpam-5608	246	24	(	(	PUNCT
ejpam-5608	246	25	x	x	NOUN
ejpam-5608	246	26	,	,	PUNCT
ejpam-5608	246	27	yn1	yn1	NOUN
ejpam-5608	246	28	,	,	PUNCT
ejpam-5608	246	29	yn2	yn2	NOUN
ejpam-5608	246	30	)	)	PUNCT
ejpam-5608	246	31	=	=	SYM
ejpam-5608	246	32	g	g	PROPN
ejpam-5608	246	33	(	(	PUNCT
ejpam-5608	246	34	0	0	NUM
ejpam-5608	246	35	,	,	PUNCT
ejpam-5608	246	36	xn1	xn1	PRON
ejpam-5608	246	37	−	−	PROPN
ejpam-5608	246	38	yn1	yn1	NOUN
ejpam-5608	246	39	,	,	PUNCT
ejpam-5608	246	40	xn2	xn2	PROPN
ejpam-5608	247	1	−	−	NOUN
ejpam-5608	247	2	yn2	yn2	NOUN
ejpam-5608	247	3	)	)	PUNCT
ejpam-5608	247	4	thus	thus	ADV
ejpam-5608	247	5	,	,	PUNCT
ejpam-5608	247	6	the	the	DET
ejpam-5608	247	7	set	set	NOUN
ejpam-5608	247	8	{	{	PUNCT
ejpam-5608	247	9	(	(	PUNCT
ejpam-5608	247	10	n1	n1	NOUN
ejpam-5608	247	11	,	,	PUNCT
ejpam-5608	247	12	n2	n2	ADJ
ejpam-5608	247	13	)	)	PUNCT
ejpam-5608	247	14	∈	∈	PROPN
ejpam-5608	247	15	n2	n2	NOUN
ejpam-5608	247	16	:	:	PUNCT
ejpam-5608	247	17	n1	n1	ADJ
ejpam-5608	247	18	,	,	PUNCT
ejpam-5608	247	19	n2	n2	ADJ
ejpam-5608	247	20	≤	≤	PUNCT
ejpam-5608	247	21	n	n	CCONJ
ejpam-5608	247	22	:	:	PUNCT
ejpam-5608	247	23	g	g	PROPN
ejpam-5608	247	24	(	(	PUNCT
ejpam-5608	247	25	0	0	NUM
ejpam-5608	247	26	,	,	PUNCT
ejpam-5608	247	27	xn1	xn1	PRON
ejpam-5608	247	28	−	−	NOUN
ejpam-5608	247	29	yn1	yn1	NOUN
ejpam-5608	247	30	,	,	PUNCT
ejpam-5608	247	31	xn2	xn2	PROPN
ejpam-5608	247	32	−	−	X
ejpam-5608	247	33	yn2	yn2	NOUN
ejpam-5608	247	34	)	)	PUNCT
ejpam-5608	247	35	≥	≥	X
ejpam-5608	247	36	ε	ε	PROPN
ejpam-5608	247	37	}	}	PUNCT
ejpam-5608	247	38	∈	∈	PROPN
ejpam-5608	247	39	i.	i.	NOUN
ejpam-5608	247	40	therefore	therefore	ADV
ejpam-5608	247	41	,	,	PUNCT
ejpam-5608	247	42	the	the	DET
ejpam-5608	247	43	sequence	sequence	NOUN
ejpam-5608	247	44	(	(	PUNCT
ejpam-5608	247	45	|xn	|xn	NOUN
ejpam-5608	247	46	−	−	PROPN
ejpam-5608	247	47	yn|	yn|	NOUN
ejpam-5608	247	48	)	)	PUNCT
ejpam-5608	247	49	is	be	AUX
ejpam-5608	247	50	ideal	ideal	ADJ
ejpam-5608	247	51	convergent	convergent	NOUN
ejpam-5608	247	52	to	to	ADP
ejpam-5608	247	53	0	0	NUM
ejpam-5608	247	54	.	.	PUNCT
ejpam-5608	248	1	theorem	theorem	NOUN
ejpam-5608	248	2	11	11	NUM
ejpam-5608	248	3	.	.	PUNCT
ejpam-5608	249	1	let	let	VERB
ejpam-5608	249	2	i	i	PRON
ejpam-5608	249	3	be	be	AUX
ejpam-5608	249	4	a	a	DET
ejpam-5608	249	5	non	non	ADJ
ejpam-5608	249	6	-	-	ADJ
ejpam-5608	249	7	trivial	trivial	ADJ
ejpam-5608	249	8	ideal	ideal	NOUN
ejpam-5608	249	9	on	on	ADP
ejpam-5608	249	10	n2	n2	ADJ
ejpam-5608	249	11	.	.	PUNCT
ejpam-5608	250	1	if	if	SCONJ
ejpam-5608	250	2	the	the	DET
ejpam-5608	250	3	sequence	sequence	NOUN
ejpam-5608	250	4	of	of	ADP
ejpam-5608	250	5	real	real	ADJ
ejpam-5608	250	6	numbers	number	NOUN
ejpam-5608	250	7	(	(	PUNCT
ejpam-5608	250	8	xn	xn	X
ejpam-5608	250	9	)	)	PUNCT
ejpam-5608	250	10	ideal	ideal	ADJ
ejpam-5608	250	11	converges	converge	NOUN
ejpam-5608	250	12	to	to	ADP
ejpam-5608	250	13	l	l	NOUN
ejpam-5608	250	14	in	in	ADP
ejpam-5608	250	15	the	the	DET
ejpam-5608	250	16	metric	metric	ADJ
ejpam-5608	250	17	-	-	PUNCT
ejpam-5608	250	18	g	g	NOUN
ejpam-5608	250	19	space	space	NOUN
ejpam-5608	250	20	,	,	PUNCT
ejpam-5608	250	21	then	then	ADV
ejpam-5608	250	22	there	there	PRON
ejpam-5608	250	23	exists	exist	VERB
ejpam-5608	250	24	a	a	DET
ejpam-5608	250	25	subsequence	subsequence	NOUN
ejpam-5608	250	26	(	(	PUNCT
ejpam-5608	250	27	xnk	xnk	PROPN
ejpam-5608	250	28	)	)	PUNCT
ejpam-5608	250	29	of	of	ADP
ejpam-5608	250	30	(	(	PUNCT
ejpam-5608	250	31	xn	xn	X
ejpam-5608	250	32	)	)	PUNCT
ejpam-5608	250	33	that	that	PRON
ejpam-5608	250	34	converges	converge	VERB
ejpam-5608	250	35	to	to	ADP
ejpam-5608	250	36	x	x	PRON
ejpam-5608	250	37	in	in	ADP
ejpam-5608	250	38	the	the	DET
ejpam-5608	250	39	usual	usual	ADJ
ejpam-5608	250	40	sense	sense	NOUN
ejpam-5608	250	41	in	in	ADP
ejpam-5608	250	42	the	the	DET
ejpam-5608	250	43	metric	metric	ADJ
ejpam-5608	250	44	-	-	PUNCT
ejpam-5608	250	45	g	g	NOUN
ejpam-5608	250	46	space	space	NOUN
ejpam-5608	250	47	,	,	PUNCT
ejpam-5608	250	48	and	and	CCONJ
ejpam-5608	250	49	there	there	PRON
ejpam-5608	250	50	exists	exist	VERB
ejpam-5608	250	51	a	a	DET
ejpam-5608	250	52	subsequence	subsequence	NOUN
ejpam-5608	250	53	(	(	PUNCT
ejpam-5608	250	54	xmk	xmk	PROPN
ejpam-5608	250	55	)	)	PUNCT
ejpam-5608	250	56	that	that	PRON
ejpam-5608	250	57	converges	converge	VERB
ejpam-5608	250	58	statistically	statistically	ADV
ejpam-5608	250	59	to	to	ADP
ejpam-5608	250	60	l	l	NOUN
ejpam-5608	250	61	in	in	ADP
ejpam-5608	250	62	the	the	DET
ejpam-5608	250	63	metric	metric	ADJ
ejpam-5608	250	64	-	-	PUNCT
ejpam-5608	250	65	g	g	NOUN
ejpam-5608	250	66	space	space	NOUN
ejpam-5608	250	67	.	.	PUNCT
ejpam-5608	251	1	proof	proof	NOUN
ejpam-5608	251	2	.	.	PUNCT
ejpam-5608	252	1	let	let	VERB
ejpam-5608	252	2	ε	ε	PROPN
ejpam-5608	252	3	>	>	X
ejpam-5608	252	4	0	0	PUNCT
ejpam-5608	252	5	be	be	AUX
ejpam-5608	252	6	an	an	DET
ejpam-5608	252	7	arbitrary	arbitrary	ADJ
ejpam-5608	252	8	real	real	ADJ
ejpam-5608	252	9	number	number	NOUN
ejpam-5608	252	10	.	.	PUNCT
ejpam-5608	253	1	the	the	DET
ejpam-5608	253	2	fact	fact	NOUN
ejpam-5608	253	3	that	that	SCONJ
ejpam-5608	253	4	(	(	PUNCT
ejpam-5608	253	5	xn	xn	X
ejpam-5608	253	6	)	)	PUNCT
ejpam-5608	253	7	ideal	ideal	ADJ
ejpam-5608	253	8	converges	converge	NOUN
ejpam-5608	253	9	to	to	ADP
ejpam-5608	253	10	l	l	NOUN
ejpam-5608	253	11	means	mean	VERB
ejpam-5608	253	12	that	that	SCONJ
ejpam-5608	253	13	for	for	ADP
ejpam-5608	253	14	any	any	DET
ejpam-5608	253	15	ε	ε	PROPN
ejpam-5608	253	16	,	,	PUNCT
ejpam-5608	253	17	the	the	DET
ejpam-5608	253	18	set	set	NOUN
ejpam-5608	253	19	(	(	PUNCT
ejpam-5608	253	20	n	n	CCONJ
ejpam-5608	253	21	,	,	PUNCT
ejpam-5608	253	22	m	m	NOUN
ejpam-5608	253	23	)	)	PUNCT
ejpam-5608	253	24	∈	∈	PROPN
ejpam-5608	253	25	n2	n2	NOUN
ejpam-5608	253	26	:	:	PUNCT
ejpam-5608	253	27	g	g	PROPN
ejpam-5608	253	28	(	(	PUNCT
ejpam-5608	253	29	l	l	NOUN
ejpam-5608	253	30	,	,	PUNCT
ejpam-5608	253	31	xn	xn	PROPN
ejpam-5608	253	32	,	,	PUNCT
ejpam-5608	253	33	xm	xm	PROPN
ejpam-5608	253	34	)	)	PUNCT
ejpam-5608	253	35	≥	≥	NOUN
ejpam-5608	253	36	ε	ε	PROPN
ejpam-5608	253	37	∈	∈	PROPN
ejpam-5608	253	38	i.	i.	NOUN
ejpam-5608	253	39	if	if	SCONJ
ejpam-5608	253	40	we	we	PRON
ejpam-5608	253	41	select	select	VERB
ejpam-5608	253	42	a	a	DET
ejpam-5608	253	43	subsequence	subsequence	NOUN
ejpam-5608	253	44	(	(	PUNCT
ejpam-5608	253	45	xnk	xnk	PROPN
ejpam-5608	253	46	)	)	PUNCT
ejpam-5608	253	47	of	of	ADP
ejpam-5608	253	48	(	(	PUNCT
ejpam-5608	253	49	xn	xn	X
ejpam-5608	253	50	)	)	PUNCT
ejpam-5608	253	51	such	such	ADJ
ejpam-5608	253	52	that	that	SCONJ
ejpam-5608	253	53	its	its	PRON
ejpam-5608	253	54	members	member	NOUN
ejpam-5608	253	55	satisfy	satisfy	VERB
ejpam-5608	253	56	g	g	PROPN
ejpam-5608	253	57	(	(	PUNCT
ejpam-5608	253	58	l	l	PROPN
ejpam-5608	253	59	,	,	PUNCT
ejpam-5608	253	60	xn	xn	PROPN
ejpam-5608	253	61	,	,	PUNCT
ejpam-5608	253	62	xm	xm	PROPN
ejpam-5608	253	63	)	)	PUNCT
ejpam-5608	253	64	<	<	X
ejpam-5608	253	65	ε	ε	PROPN
ejpam-5608	253	66	,	,	PUNCT
ejpam-5608	253	67	then	then	ADV
ejpam-5608	253	68	clearly	clearly	ADV
ejpam-5608	253	69	(	(	PUNCT
ejpam-5608	253	70	xnk	xnk	PROPN
ejpam-5608	253	71	)	)	PUNCT
ejpam-5608	253	72	converges	converge	VERB
ejpam-5608	253	73	to	to	ADP
ejpam-5608	253	74	l.	l.	PROPN
ejpam-5608	253	75	similarly	similarly	ADV
ejpam-5608	253	76	,	,	PUNCT
ejpam-5608	253	77	we	we	PRON
ejpam-5608	253	78	can	can	AUX
ejpam-5608	253	79	choose	choose	VERB
ejpam-5608	253	80	a	a	DET
ejpam-5608	253	81	subsequence	subsequence	NOUN
ejpam-5608	253	82	(	(	PUNCT
ejpam-5608	253	83	xmk	xmk	PROPN
ejpam-5608	253	84	)	)	PUNCT
ejpam-5608	253	85	of	of	ADP
ejpam-5608	253	86	(	(	PUNCT
ejpam-5608	253	87	xn	xn	X
ejpam-5608	253	88	)	)	PUNCT
ejpam-5608	254	1	such	such	ADJ
ejpam-5608	254	2	that	that	SCONJ
ejpam-5608	254	3	lim	lim	PROPN
ejpam-5608	254	4	n→+∞	n→+∞	PROPN
ejpam-5608	254	5	(	(	PUNCT
ejpam-5608	254	6	2	2	NUM
ejpam-5608	254	7	n2	n2	ADJ
ejpam-5608	254	8	|{(n1	|{(n1	PROPN
ejpam-5608	254	9	,	,	PUNCT
ejpam-5608	254	10	n2	n2	ADJ
ejpam-5608	254	11	)	)	PUNCT
ejpam-5608	254	12	∈	∈	PROPN
ejpam-5608	254	13	n2	n2	NOUN
ejpam-5608	254	14	:	:	PUNCT
ejpam-5608	254	15	n1	n1	ADJ
ejpam-5608	254	16	,	,	PUNCT
ejpam-5608	254	17	n2	n2	ADJ
ejpam-5608	254	18	≤	≤	PUNCT
ejpam-5608	254	19	n	n	CCONJ
ejpam-5608	254	20	,	,	PUNCT
ejpam-5608	254	21	g(xi	g(xi	PROPN
ejpam-5608	254	22	,	,	PUNCT
ejpam-5608	254	23	xn1	xn1	NUM
ejpam-5608	254	24	,	,	PUNCT
ejpam-5608	254	25	xn2	xn2	PROPN
ejpam-5608	254	26	)	)	PUNCT
ejpam-5608	254	27	≥	≥	PROPN
ejpam-5608	254	28	ε}|	ε}|	NOUN
ejpam-5608	254	29	)	)	PUNCT
ejpam-5608	254	30	which	which	PRON
ejpam-5608	254	31	implies	imply	VERB
ejpam-5608	254	32	that	that	SCONJ
ejpam-5608	254	33	the	the	DET
ejpam-5608	254	34	sequence	sequence	NOUN
ejpam-5608	254	35	converges	converge	VERB
ejpam-5608	254	36	statistically	statistically	ADV
ejpam-5608	254	37	to	to	ADP
ejpam-5608	254	38	l.	l.	PROPN
ejpam-5608	254	39	4	4	NUM
ejpam-5608	254	40	.	.	PUNCT
ejpam-5608	254	41	conclusion	conclusion	NOUN
ejpam-5608	254	42	in	in	ADP
ejpam-5608	254	43	this	this	DET
ejpam-5608	254	44	study	study	NOUN
ejpam-5608	254	45	,	,	PUNCT
ejpam-5608	254	46	several	several	ADJ
ejpam-5608	254	47	significant	significant	ADJ
ejpam-5608	254	48	theorems	theorem	NOUN
ejpam-5608	254	49	regarding	regard	VERB
ejpam-5608	254	50	the	the	DET
ejpam-5608	254	51	convergence	convergence	NOUN
ejpam-5608	254	52	properties	property	NOUN
ejpam-5608	254	53	of	of	ADP
ejpam-5608	254	54	sequences	sequence	NOUN
ejpam-5608	254	55	in	in	ADP
ejpam-5608	254	56	g	g	NOUN
ejpam-5608	254	57	-	-	PUNCT
ejpam-5608	254	58	metric	metric	ADJ
ejpam-5608	254	59	spaces	space	NOUN
ejpam-5608	254	60	have	have	AUX
ejpam-5608	254	61	been	be	AUX
ejpam-5608	254	62	established	establish	VERB
ejpam-5608	254	63	.	.	PUNCT
ejpam-5608	255	1	the	the	DET
ejpam-5608	255	2	results	result	NOUN
ejpam-5608	255	3	demonstrate	demonstrate	VERB
ejpam-5608	255	4	a	a	DET
ejpam-5608	255	5	strong	strong	ADJ
ejpam-5608	255	6	connection	connection	NOUN
ejpam-5608	255	7	between	between	ADP
ejpam-5608	255	8	different	different	ADJ
ejpam-5608	255	9	types	type	NOUN
ejpam-5608	255	10	of	of	ADP
ejpam-5608	255	11	convergence	convergence	NOUN
ejpam-5608	255	12	—	—	PUNCT
ejpam-5608	255	13	statistical	statistical	ADJ
ejpam-5608	255	14	,	,	PUNCT
ejpam-5608	255	15	ideal	ideal	ADJ
ejpam-5608	255	16	,	,	PUNCT
ejpam-5608	255	17	and	and	CCONJ
ejpam-5608	255	18	standard	standard	NOUN
ejpam-5608	255	19	—	—	PUNCT
ejpam-5608	255	20	within	within	ADP
ejpam-5608	255	21	the	the	DET
ejpam-5608	255	22	framework	framework	NOUN
ejpam-5608	255	23	of	of	ADP
ejpam-5608	255	24	g	g	NOUN
ejpam-5608	255	25	-	-	PUNCT
ejpam-5608	255	26	metric	metric	ADJ
ejpam-5608	255	27	spaces	space	NOUN
ejpam-5608	255	28	.	.	PUNCT
ejpam-5608	256	1	overall	overall	ADV
ejpam-5608	256	2	,	,	PUNCT
ejpam-5608	256	3	this	this	DET
ejpam-5608	256	4	research	research	NOUN
ejpam-5608	256	5	enhances	enhance	VERB
ejpam-5608	256	6	our	our	PRON
ejpam-5608	256	7	understanding	understanding	NOUN
ejpam-5608	256	8	of	of	ADP
ejpam-5608	256	9	the	the	DET
ejpam-5608	256	10	behaviour	behaviour	NOUN
ejpam-5608	256	11	of	of	ADP
ejpam-5608	256	12	sequences	sequence	NOUN
ejpam-5608	256	13	in	in	ADP
ejpam-5608	256	14	g	g	NOUN
ejpam-5608	256	15	-	-	PUNCT
ejpam-5608	256	16	metric	metric	ADJ
ejpam-5608	256	17	spaces	space	NOUN
ejpam-5608	256	18	and	and	CCONJ
ejpam-5608	256	19	the	the	DET
ejpam-5608	256	20	interplay	interplay	NOUN
ejpam-5608	256	21	between	between	ADP
ejpam-5608	256	22	different	different	ADJ
ejpam-5608	256	23	convergence	convergence	NOUN
ejpam-5608	256	24	concepts	concept	NOUN
ejpam-5608	256	25	,	,	PUNCT
ejpam-5608	256	26	paving	pave	VERB
ejpam-5608	256	27	the	the	DET
ejpam-5608	256	28	way	way	NOUN
ejpam-5608	256	29	for	for	ADP
ejpam-5608	256	30	further	further	ADJ
ejpam-5608	256	31	exploration	exploration	NOUN
ejpam-5608	256	32	in	in	ADP
ejpam-5608	256	33	this	this	DET
ejpam-5608	256	34	area	area	NOUN
ejpam-5608	256	35	of	of	ADP
ejpam-5608	256	36	metric	metric	ADJ
ejpam-5608	256	37	space	space	NOUN
ejpam-5608	256	38	theory	theory	NOUN
ejpam-5608	256	39	.	.	PUNCT
ejpam-5608	257	1	future	future	ADJ
ejpam-5608	257	2	research	research	NOUN
ejpam-5608	257	3	directions	direction	NOUN
ejpam-5608	257	4	could	could	AUX
ejpam-5608	257	5	include	include	VERB
ejpam-5608	257	6	extending	extend	VERB
ejpam-5608	257	7	these	these	DET
ejpam-5608	257	8	results	result	NOUN
ejpam-5608	257	9	to	to	ADP
ejpam-5608	257	10	more	more	ADV
ejpam-5608	257	11	generalized	generalized	ADJ
ejpam-5608	257	12	metric	metric	ADJ
ejpam-5608	257	13	spaces	space	NOUN
ejpam-5608	257	14	,	,	PUNCT
ejpam-5608	257	15	such	such	ADJ
ejpam-5608	257	16	as	as	ADP
ejpam-5608	257	17	cone	cone	NOUN
ejpam-5608	257	18	g	g	NOUN
ejpam-5608	257	19	-	-	PUNCT
ejpam-5608	257	20	metric	metric	ADJ
ejpam-5608	257	21	spaces	space	NOUN
ejpam-5608	257	22	or	or	CCONJ
ejpam-5608	257	23	fuzzy	fuzzy	ADJ
ejpam-5608	257	24	g	g	NOUN
ejpam-5608	257	25	-	-	PUNCT
ejpam-5608	257	26	metric	metric	ADJ
ejpam-5608	257	27	spaces	space	NOUN
ejpam-5608	257	28	,	,	PUNCT
ejpam-5608	257	29	to	to	PART
ejpam-5608	257	30	explore	explore	VERB
ejpam-5608	257	31	whether	whether	SCONJ
ejpam-5608	257	32	similar	similar	ADJ
ejpam-5608	257	33	equivalences	equivalence	NOUN
ejpam-5608	257	34	and	and	CCONJ
ejpam-5608	257	35	relationships	relationship	NOUN
ejpam-5608	257	36	hold	hold	VERB
ejpam-5608	257	37	.	.	PUNCT
ejpam-5608	258	1	another	another	DET
ejpam-5608	258	2	promising	promising	ADJ
ejpam-5608	258	3	avenue	avenue	NOUN
ejpam-5608	258	4	would	would	AUX
ejpam-5608	258	5	be	be	AUX
ejpam-5608	258	6	to	to	PART
ejpam-5608	258	7	investigate	investigate	VERB
ejpam-5608	258	8	the	the	DET
ejpam-5608	258	9	applications	application	NOUN
ejpam-5608	258	10	of	of	ADP
ejpam-5608	258	11	these	these	DET
ejpam-5608	258	12	convergence	convergence	NOUN
ejpam-5608	258	13	properties	property	NOUN
ejpam-5608	258	14	in	in	ADP
ejpam-5608	258	15	solving	solve	VERB
ejpam-5608	258	16	fixed	fix	VERB
ejpam-5608	258	17	point	point	NOUN
ejpam-5608	258	18	problems	problem	NOUN
ejpam-5608	258	19	or	or	CCONJ
ejpam-5608	258	20	optimization	optimization	NOUN
ejpam-5608	258	21	problems	problem	NOUN
ejpam-5608	258	22	,	,	PUNCT
ejpam-5608	258	23	where	where	SCONJ
ejpam-5608	258	24	g	g	NOUN
ejpam-5608	258	25	-	-	PUNCT
ejpam-5608	258	26	metric	metric	ADJ
ejpam-5608	258	27	spaces	space	NOUN
ejpam-5608	258	28	often	often	ADV
ejpam-5608	258	29	provide	provide	VERB
ejpam-5608	258	30	a	a	DET
ejpam-5608	258	31	natural	natural	ADJ
ejpam-5608	258	32	framework	framework	NOUN
ejpam-5608	258	33	.	.	PUNCT
ejpam-5608	259	1	additionally	additionally	ADV
ejpam-5608	259	2	,	,	PUNCT
ejpam-5608	259	3	studying	study	VERB
ejpam-5608	259	4	the	the	DET
ejpam-5608	259	5	implications	implication	NOUN
ejpam-5608	259	6	of	of	ADP
ejpam-5608	259	7	these	these	DET
ejpam-5608	259	8	results	result	NOUN
ejpam-5608	259	9	in	in	ADP
ejpam-5608	259	10	functional	functional	ADJ
ejpam-5608	259	11	analysis	analysis	NOUN
ejpam-5608	259	12	or	or	CCONJ
ejpam-5608	259	13	dynamical	dynamical	ADJ
ejpam-5608	259	14	systems	system	NOUN
ejpam-5608	259	15	may	may	AUX
ejpam-5608	259	16	yield	yield	VERB
ejpam-5608	259	17	new	new	ADJ
ejpam-5608	259	18	insights	insight	NOUN
ejpam-5608	259	19	into	into	ADP
ejpam-5608	259	20	stability	stability	NOUN
ejpam-5608	259	21	and	and	CCONJ
ejpam-5608	259	22	convergence	convergence	NOUN
ejpam-5608	259	23	behaviours	behaviour	NOUN
ejpam-5608	259	24	in	in	ADP
ejpam-5608	259	25	broader	broad	ADJ
ejpam-5608	259	26	mathematical	mathematical	ADJ
ejpam-5608	259	27	contexts	contexts	NOUN
ejpam-5608	259	28	.	.	PUNCT
ejpam-5608	260	1	finally	finally	ADV
ejpam-5608	260	2	,	,	PUNCT
ejpam-5608	260	3	integrating	integrate	VERB
ejpam-5608	260	4	these	these	DET
ejpam-5608	260	5	findings	finding	NOUN
ejpam-5608	260	6	with	with	ADP
ejpam-5608	260	7	probabilistic	probabilistic	ADJ
ejpam-5608	260	8	and	and	CCONJ
ejpam-5608	260	9	stochastic	stochastic	ADJ
ejpam-5608	260	10	settings	setting	NOUN
ejpam-5608	260	11	could	could	AUX
ejpam-5608	260	12	open	open	VERB
ejpam-5608	260	13	new	new	ADJ
ejpam-5608	260	14	paths	path	NOUN
ejpam-5608	260	15	for	for	ADP
ejpam-5608	260	16	exploring	explore	VERB
ejpam-5608	260	17	the	the	DET
ejpam-5608	260	18	role	role	NOUN
ejpam-5608	260	19	of	of	ADP
ejpam-5608	260	20	convergence	convergence	NOUN
ejpam-5608	260	21	in	in	ADP
ejpam-5608	260	22	real	real	ADJ
ejpam-5608	260	23	-	-	PUNCT
ejpam-5608	260	24	world	world	NOUN
ejpam-5608	260	25	applications	application	NOUN
ejpam-5608	260	26	,	,	PUNCT
ejpam-5608	260	27	such	such	ADJ
ejpam-5608	260	28	as	as	ADP
ejpam-5608	260	29	data	datum	NOUN
ejpam-5608	260	30	science	science	NOUN
ejpam-5608	260	31	or	or	CCONJ
ejpam-5608	260	32	machine	machine	NOUN
ejpam-5608	260	33	learning	learning	NOUN
ejpam-5608	260	34	.	.	PUNCT
ejpam-5608	261	1	manuharawati	manuharawati	NOUN
ejpam-5608	261	2	,	,	PUNCT
ejpam-5608	261	3	m.jakfar	m.jakfar	ADV
ejpam-5608	261	4	,	,	PUNCT
ejpam-5608	261	5	a.	a.	PROPN
ejpam-5608	261	6	taufik	taufik	PROPN
ejpam-5608	261	7	hamzah	hamzah	PROPN
ejpam-5608	261	8	/	/	SYM
ejpam-5608	261	9	eur	eur	PROPN
ejpam-5608	261	10	.	.	PUNCT
ejpam-5608	262	1	j.	j.	PROPN
ejpam-5608	262	2	pure	pure	PROPN
ejpam-5608	262	3	appl	appl	PROPN
ejpam-5608	262	4	.	.	PROPN
ejpam-5608	262	5	math	math	PROPN
ejpam-5608	262	6	,	,	PUNCT
ejpam-5608	262	7	18	18	NUM
ejpam-5608	262	8	(	(	PUNCT
ejpam-5608	262	9	1	1	NUM
ejpam-5608	262	10	)	)	PUNCT
ejpam-5608	262	11	(	(	PUNCT
ejpam-5608	262	12	2025	2025	NUM
ejpam-5608	262	13	)	)	PUNCT
ejpam-5608	262	14	,	,	PUNCT
ejpam-5608	262	15	5608	5608	NUM
ejpam-5608	262	16	12	12	NUM
ejpam-5608	262	17	of	of	ADP
ejpam-5608	262	18	13	13	NUM
ejpam-5608	262	19	references	reference	NOUN
ejpam-5608	262	20	[	[	X
ejpam-5608	262	21	1	1	NUM
ejpam-5608	262	22	]	]	X
ejpam-5608	262	23	r	r	NOUN
ejpam-5608	262	24	abazari	abazari	X
ejpam-5608	262	25	.	.	PUNCT
ejpam-5608	263	1	statistical	statistical	ADJ
ejpam-5608	263	2	convergence	convergence	NOUN
ejpam-5608	263	3	in	in	ADP
ejpam-5608	263	4	g	g	NOUN
ejpam-5608	263	5	-	-	PUNCT
ejpam-5608	263	6	metric	metric	ADJ
ejpam-5608	263	7	spaces	space	NOUN
ejpam-5608	263	8	.	.	PUNCT
ejpam-5608	264	1	filomat	filomat	NOUN
ejpam-5608	264	2	,	,	PUNCT
ejpam-5608	264	3	36(5):1461–1468	36(5):1461–1468	PROPN
ejpam-5608	264	4	,	,	PUNCT
ejpam-5608	264	5	2022	2022	NUM
ejpam-5608	264	6	.	.	PUNCT
ejpam-5608	265	1	[	[	X
ejpam-5608	265	2	2	2	X
ejpam-5608	265	3	]	]	X
ejpam-5608	265	4	p	p	X
ejpam-5608	265	5	das	das	PROPN
ejpam-5608	265	6	,	,	PUNCT
ejpam-5608	265	7	e	e	X
ejpam-5608	265	8	savas	savas	PROPN
ejpam-5608	265	9	,	,	PUNCT
ejpam-5608	265	10	and	and	CCONJ
ejpam-5608	265	11	r	r	NOUN
ejpam-5608	265	12	savaş.	savaş.	VERB
ejpam-5608	265	13	on	on	ADP
ejpam-5608	265	14	statistical	statistical	ADJ
ejpam-5608	265	15	convergence	convergence	NOUN
ejpam-5608	265	16	of	of	ADP
ejpam-5608	265	17	sequences	sequence	NOUN
ejpam-5608	265	18	in	in	ADP
ejpam-5608	265	19	normed	normed	ADJ
ejpam-5608	265	20	spaces	space	NOUN
ejpam-5608	265	21	.	.	PUNCT
ejpam-5608	266	1	journal	journal	PROPN
ejpam-5608	266	2	of	of	ADP
ejpam-5608	266	3	mathematical	mathematical	ADJ
ejpam-5608	266	4	analysis	analysis	NOUN
ejpam-5608	266	5	and	and	CCONJ
ejpam-5608	266	6	applications	application	NOUN
ejpam-5608	266	7	,	,	PUNCT
ejpam-5608	266	8	304(1):508–522	304(1):508–522	ADV
ejpam-5608	266	9	,	,	PUNCT
ejpam-5608	266	10	2005	2005	NUM
ejpam-5608	266	11	.	.	PUNCT
ejpam-5608	267	1	[	[	X
ejpam-5608	267	2	3	3	X
ejpam-5608	267	3	]	]	X
ejpam-5608	267	4	h	h	NOUN
ejpam-5608	267	5	fast	fast	ADV
ejpam-5608	267	6	.	.	PUNCT
ejpam-5608	268	1	sur	sur	PROPN
ejpam-5608	268	2	la	la	PROPN
ejpam-5608	268	3	convergence	convergence	NOUN
ejpam-5608	268	4	statistique	statistique	NOUN
ejpam-5608	268	5	.	.	PUNCT
ejpam-5608	269	1	in	in	ADP
ejpam-5608	269	2	colloquium	colloquium	NOUN
ejpam-5608	269	3	mathematicae	mathematicae	PROPN
ejpam-5608	269	4	,	,	PUNCT
ejpam-5608	269	5	volume	volume	NOUN
ejpam-5608	269	6	2	2	NUM
ejpam-5608	269	7	,	,	PUNCT
ejpam-5608	269	8	pages	page	NOUN
ejpam-5608	269	9	241–244	241–244	NUM
ejpam-5608	269	10	,	,	PUNCT
ejpam-5608	269	11	1951	1951	NUM
ejpam-5608	269	12	.	.	PUNCT
ejpam-5608	270	1	[	[	X
ejpam-5608	270	2	4	4	NUM
ejpam-5608	270	3	]	]	X
ejpam-5608	270	4	d	d	PROPN
ejpam-5608	270	5	francis	francis	PROPN
ejpam-5608	270	6	,	,	PUNCT
ejpam-5608	270	7	ga	ga	PROPN
ejpam-5608	270	8	okeke	okeke	PROPN
ejpam-5608	270	9	,	,	PUNCT
ejpam-5608	270	10	and	and	CCONJ
ejpam-5608	270	11	hg	hg	PROPN
ejpam-5608	270	12	hyun	hyun	PROPN
ejpam-5608	270	13	.	.	PUNCT
ejpam-5608	271	1	on	on	ADP
ejpam-5608	271	2	fixed	fix	VERB
ejpam-5608	271	3	point	point	NOUN
ejpam-5608	271	4	theorems	theorem	NOUN
ejpam-5608	271	5	satisfying	satisfy	VERB
ejpam-5608	271	6	compatibility	compatibility	NOUN
ejpam-5608	271	7	property	property	NOUN
ejpam-5608	271	8	in	in	ADP
ejpam-5608	271	9	modular	modular	ADJ
ejpam-5608	271	10	g	g	NOUN
ejpam-5608	271	11	-	-	PUNCT
ejpam-5608	271	12	metric	metric	ADJ
ejpam-5608	271	13	spaces	space	NOUN
ejpam-5608	271	14	.	.	PUNCT
ejpam-5608	272	1	nonlinear	nonlinear	ADJ
ejpam-5608	272	2	functional	functional	ADJ
ejpam-5608	272	3	analysis	analysis	NOUN
ejpam-5608	272	4	and	and	CCONJ
ejpam-5608	272	5	applications	application	NOUN
ejpam-5608	272	6	,	,	PUNCT
ejpam-5608	272	7	29(2):361–391	29(2):361–391	PROPN
ejpam-5608	272	8	,	,	PUNCT
ejpam-5608	272	9	2024	2024	NUM
ejpam-5608	272	10	.	.	PUNCT
ejpam-5608	273	1	[	[	X
ejpam-5608	273	2	5	5	NUM
ejpam-5608	273	3	]	]	X
ejpam-5608	273	4	j	j	PROPN
ejpam-5608	273	5	a	a	DET
ejpam-5608	273	6	fridy	fridy	NOUN
ejpam-5608	273	7	.	.	PUNCT
ejpam-5608	274	1	on	on	ADP
ejpam-5608	274	2	statistical	statistical	ADJ
ejpam-5608	274	3	convergence	convergence	NOUN
ejpam-5608	274	4	.	.	PUNCT
ejpam-5608	275	1	analysis	analysis	NOUN
ejpam-5608	275	2	,	,	PUNCT
ejpam-5608	275	3	5(4):301–314	5(4):301–314	NUM
ejpam-5608	275	4	,	,	PUNCT
ejpam-5608	275	5	1985	1985	NUM
ejpam-5608	275	6	.	.	PUNCT
ejpam-5608	276	1	[	[	X
ejpam-5608	276	2	6	6	NUM
ejpam-5608	276	3	]	]	PUNCT
ejpam-5608	276	4	y	y	PROPN
ejpam-5608	276	5	u	u	PROPN
ejpam-5608	276	6	gaba	gaba	PROPN
ejpam-5608	276	7	.	.	PUNCT
ejpam-5608	277	1	fixed	fix	VERB
ejpam-5608	277	2	point	point	NOUN
ejpam-5608	277	3	theorems	theorem	NOUN
ejpam-5608	277	4	in	in	ADP
ejpam-5608	277	5	g	g	NOUN
ejpam-5608	277	6	-	-	PUNCT
ejpam-5608	277	7	metric	metric	ADJ
ejpam-5608	277	8	spaces	space	NOUN
ejpam-5608	277	9	.	.	PUNCT
ejpam-5608	278	1	journal	journal	NOUN
ejpam-5608	278	2	of	of	ADP
ejpam-5608	278	3	mathematical	mathematical	ADJ
ejpam-5608	278	4	analysis	analysis	NOUN
ejpam-5608	278	5	and	and	CCONJ
ejpam-5608	278	6	applications	application	NOUN
ejpam-5608	278	7	,	,	PUNCT
ejpam-5608	278	8	455(1):528–537	455(1):528–537	NOUN
ejpam-5608	278	9	,	,	PUNCT
ejpam-5608	278	10	2017	2017	NUM
ejpam-5608	278	11	.	.	PUNCT
ejpam-5608	279	1	[	[	X
ejpam-5608	279	2	7	7	X
ejpam-5608	279	3	]	]	PUNCT
ejpam-5608	279	4	aj	aj	PROPN
ejpam-5608	279	5	gnanaprakasam	gnanaprakasam	PROPN
ejpam-5608	279	6	,	,	PUNCT
ejpam-5608	279	7	g	g	NOUN
ejpam-5608	279	8	mani	mani	NOUN
ejpam-5608	279	9	,	,	PUNCT
ejpam-5608	279	10	and	and	CCONJ
ejpam-5608	279	11	s	s	VERB
ejpam-5608	279	12	kumar	kumar	PROPN
ejpam-5608	279	13	.	.	PROPN
ejpam-5608	279	14	technique	technique	NOUN
ejpam-5608	279	15	of	of	ADP
ejpam-5608	279	16	tripled	triple	VERB
ejpam-5608	279	17	fixed	fix	VERB
ejpam-5608	279	18	point	point	NOUN
ejpam-5608	279	19	results	result	NOUN
ejpam-5608	279	20	on	on	ADP
ejpam-5608	279	21	orthogonal	orthogonal	ADJ
ejpam-5608	279	22	g	g	NOUN
ejpam-5608	279	23	-	-	PUNCT
ejpam-5608	279	24	metric	metric	ADJ
ejpam-5608	279	25	spaces	space	NOUN
ejpam-5608	279	26	.	.	PUNCT
ejpam-5608	280	1	journal	journal	NOUN
ejpam-5608	280	2	of	of	ADP
ejpam-5608	280	3	applied	apply	VERB
ejpam-5608	280	4	mathematics	mathematic	NOUN
ejpam-5608	280	5	,	,	PUNCT
ejpam-5608	280	6	page	page	NOUN
ejpam-5608	280	7	article	article	NOUN
ejpam-5608	280	8	i	i	PROPN
ejpam-5608	280	9	d	d	PROPN
ejpam-5608	280	10	4702847	4702847	NUM
ejpam-5608	280	11	,	,	PUNCT
ejpam-5608	280	12	2024	2024	NUM
ejpam-5608	280	13	.	.	PUNCT
ejpam-5608	281	1	[	[	X
ejpam-5608	281	2	8	8	NUM
ejpam-5608	281	3	]	]	X
ejpam-5608	281	4	h	h	PROPN
ejpam-5608	281	5	goldstein	goldstein	PROPN
ejpam-5608	281	6	,	,	PUNCT
ejpam-5608	281	7	c	c	PROPN
ejpam-5608	281	8	poole	poole	NOUN
ejpam-5608	281	9	,	,	PUNCT
ejpam-5608	281	10	and	and	CCONJ
ejpam-5608	281	11	j	j	PROPN
ejpam-5608	281	12	safko	safko	NOUN
ejpam-5608	281	13	.	.	PUNCT
ejpam-5608	282	1	classical	classical	ADJ
ejpam-5608	282	2	mechanics	mechanic	NOUN
ejpam-5608	282	3	.	.	PUNCT
ejpam-5608	283	1	american	american	PROPN
ejpam-5608	283	2	association	association	PROPN
ejpam-5608	283	3	of	of	ADP
ejpam-5608	283	4	physics	physics	PROPN
ejpam-5608	283	5	teachers	teachers	PROPN
ejpam-5608	283	6	,	,	PUNCT
ejpam-5608	283	7	2002	2002	NUM
ejpam-5608	283	8	.	.	PUNCT
ejpam-5608	284	1	[	[	X
ejpam-5608	284	2	9	9	NUM
ejpam-5608	284	3	]	]	PUNCT
ejpam-5608	284	4	d	d	NOUN
ejpam-5608	284	5	gopal	gopal	NOUN
ejpam-5608	284	6	and	and	CCONJ
ejpam-5608	284	7	h	h	PROPN
ejpam-5608	284	8	k	k	PROPN
ejpam-5608	284	9	pathak	pathak	PROPN
ejpam-5608	284	10	.	.	PUNCT
ejpam-5608	285	1	fixed	fix	VERB
ejpam-5608	285	2	point	point	NOUN
ejpam-5608	285	3	results	result	NOUN
ejpam-5608	285	4	for	for	ADP
ejpam-5608	285	5	g	g	NOUN
ejpam-5608	285	6	-	-	PUNCT
ejpam-5608	285	7	contraction	contraction	NOUN
ejpam-5608	285	8	mappings	mapping	NOUN
ejpam-5608	285	9	in	in	ADP
ejpam-5608	285	10	g	g	NOUN
ejpam-5608	285	11	-	-	PUNCT
ejpam-5608	285	12	metric	metric	ADJ
ejpam-5608	285	13	spaces	space	NOUN
ejpam-5608	285	14	with	with	ADP
ejpam-5608	285	15	applications	application	NOUN
ejpam-5608	285	16	.	.	PUNCT
ejpam-5608	286	1	journal	journal	NOUN
ejpam-5608	286	2	of	of	ADP
ejpam-5608	286	3	fixed	fix	VERB
ejpam-5608	286	4	point	point	NOUN
ejpam-5608	286	5	theory	theory	NOUN
ejpam-5608	286	6	and	and	CCONJ
ejpam-5608	286	7	applications	application	NOUN
ejpam-5608	286	8	,	,	PUNCT
ejpam-5608	286	9	17:665	17:665	NUM
ejpam-5608	286	10	–	–	PUNCT
ejpam-5608	286	11	685	685	NUM
ejpam-5608	286	12	,	,	PUNCT
ejpam-5608	286	13	2015	2015	NUM
ejpam-5608	286	14	.	.	PUNCT
ejpam-5608	287	1	[	[	X
ejpam-5608	287	2	10	10	NUM
ejpam-5608	287	3	]	]	X
ejpam-5608	287	4	m	m	AUX
ejpam-5608	287	5	gürdal	gürdal	ADJ
ejpam-5608	287	6	.	.	PUNCT
ejpam-5608	288	1	some	some	DET
ejpam-5608	288	2	types	type	NOUN
ejpam-5608	288	3	of	of	ADP
ejpam-5608	288	4	convergence	convergence	NOUN
ejpam-5608	288	5	.	.	PUNCT
ejpam-5608	289	1	doctoral	doctoral	ADJ
ejpam-5608	289	2	dissertation	dissertation	NOUN
ejpam-5608	289	3	,	,	PUNCT
ejpam-5608	289	4	süleyman	süleyman	ADJ
ejpam-5608	289	5	demirel	demirel	NOUN
ejpam-5608	289	6	university	university	NOUN
ejpam-5608	289	7	,	,	PUNCT
ejpam-5608	289	8	2004	2004	NUM
ejpam-5608	289	9	.	.	PUNCT
ejpam-5608	290	1	[	[	X
ejpam-5608	290	2	11	11	NUM
ejpam-5608	290	3	]	]	X
ejpam-5608	290	4	m	m	VERB
ejpam-5608	290	5	gürdal	gürdal	NOUN
ejpam-5608	290	6	and	and	CCONJ
ejpam-5608	290	7	u	u	NOUN
ejpam-5608	290	8	yamancı	yamancı	NOUN
ejpam-5608	290	9	.	.	PUNCT
ejpam-5608	291	1	statistical	statistical	ADJ
ejpam-5608	291	2	convergence	convergence	NOUN
ejpam-5608	291	3	and	and	CCONJ
ejpam-5608	291	4	some	some	DET
ejpam-5608	291	5	questions	question	NOUN
ejpam-5608	291	6	of	of	ADP
ejpam-5608	291	7	operator	operator	NOUN
ejpam-5608	291	8	theory	theory	NOUN
ejpam-5608	291	9	.	.	PUNCT
ejpam-5608	292	1	dynamic	dynamic	ADJ
ejpam-5608	292	2	systems	system	NOUN
ejpam-5608	292	3	and	and	CCONJ
ejpam-5608	292	4	applications	application	NOUN
ejpam-5608	292	5	,	,	PUNCT
ejpam-5608	292	6	24(3):305–311	24(3):305–311	NUM
ejpam-5608	292	7	,	,	PUNCT
ejpam-5608	292	8	2015	2015	NUM
ejpam-5608	292	9	.	.	PUNCT
ejpam-5608	293	1	[	[	X
ejpam-5608	293	2	12	12	NUM
ejpam-5608	293	3	]	]	SYM
ejpam-5608	293	4	b	b	NOUN
ejpam-5608	293	5	hazarika	hazarika	NOUN
ejpam-5608	293	6	,	,	PUNCT
ejpam-5608	293	7	s	s	NOUN
ejpam-5608	293	8	pal	pal	NOUN
ejpam-5608	293	9	,	,	PUNCT
ejpam-5608	293	10	and	and	CCONJ
ejpam-5608	293	11	p	p	PROPN
ejpam-5608	293	12	das	das	PROPN
ejpam-5608	293	13	.	.	PUNCT
ejpam-5608	293	14	statistical	statistical	ADJ
ejpam-5608	293	15	convergence	convergence	NOUN
ejpam-5608	293	16	in	in	ADP
ejpam-5608	293	17	g	g	NOUN
ejpam-5608	293	18	-	-	PUNCT
ejpam-5608	293	19	metric	metric	ADJ
ejpam-5608	293	20	spaces	space	NOUN
ejpam-5608	293	21	.	.	PUNCT
ejpam-5608	294	1	journal	journal	PROPN
ejpam-5608	294	2	of	of	ADP
ejpam-5608	294	3	inequalities	inequality	NOUN
ejpam-5608	294	4	and	and	CCONJ
ejpam-5608	294	5	applications	application	NOUN
ejpam-5608	294	6	,	,	PUNCT
ejpam-5608	294	7	2015:1–11	2015:1–11	NUM
ejpam-5608	294	8	,	,	PUNCT
ejpam-5608	294	9	2015	2015	NUM
ejpam-5608	294	10	.	.	PUNCT
ejpam-5608	295	1	[	[	X
ejpam-5608	295	2	13	13	NUM
ejpam-5608	295	3	]	]	PUNCT
ejpam-5608	295	4	m	m	VERB
ejpam-5608	295	5	jakfar	jakfar	ADJ
ejpam-5608	295	6	,	,	PUNCT
ejpam-5608	295	7	y	y	PROPN
ejpam-5608	295	8	manuharawati	manuharawati	NOUN
ejpam-5608	295	9	,	,	PUNCT
ejpam-5608	295	10	dn	dn	PROPN
ejpam-5608	295	11	yunianti	yunianti	PROPN
ejpam-5608	295	12	,	,	PUNCT
ejpam-5608	295	13	and	and	CCONJ
ejpam-5608	295	14	md	md	PROPN
ejpam-5608	295	15	kumala	kumala	PROPN
ejpam-5608	295	16	.	.	PUNCT
ejpam-5608	296	1	metrics	metric	NOUN
ejpam-5608	296	2	on	on	ADP
ejpam-5608	296	3	a	a	DET
ejpam-5608	296	4	g	g	NOUN
ejpam-5608	296	5	-	-	PUNCT
ejpam-5608	296	6	metric	metric	ADJ
ejpam-5608	296	7	space	space	NOUN
ejpam-5608	296	8	.	.	PUNCT
ejpam-5608	297	1	journal	journal	PROPN
ejpam-5608	297	2	of	of	ADP
ejpam-5608	297	3	physics	physics	PROPN
ejpam-5608	297	4	:	:	PUNCT
ejpam-5608	297	5	conference	conference	NOUN
ejpam-5608	297	6	series	series	NOUN
ejpam-5608	297	7	,	,	PUNCT
ejpam-5608	297	8	1417(1):012023	1417(1):012023	NUM
ejpam-5608	297	9	,	,	PUNCT
ejpam-5608	297	10	2019	2019	NUM
ejpam-5608	297	11	.	.	PUNCT
ejpam-5608	298	1	[	[	X
ejpam-5608	298	2	14	14	NUM
ejpam-5608	298	3	]	]	X
ejpam-5608	298	4	ah	ah	INTJ
ejpam-5608	298	5	jan	jan	PROPN
ejpam-5608	298	6	and	and	CCONJ
ejpam-5608	298	7	t	t	PROPN
ejpam-5608	298	8	jalal	jalal	PROPN
ejpam-5608	298	9	.	.	PUNCT
ejpam-5608	299	1	on	on	ADP
ejpam-5608	299	2	lacunary	lacunary	ADJ
ejpam-5608	299	3	δm	δm	ADV
ejpam-5608	299	4	-	-	PUNCT
ejpam-5608	299	5	statistical	statistical	ADJ
ejpam-5608	299	6	convergence	convergence	NOUN
ejpam-5608	299	7	in	in	ADP
ejpam-5608	299	8	g	g	NOUN
ejpam-5608	299	9	-	-	PUNCT
ejpam-5608	299	10	metric	metric	ADJ
ejpam-5608	299	11	spaces	space	NOUN
ejpam-5608	299	12	.	.	PUNCT
ejpam-5608	300	1	korean	korean	ADJ
ejpam-5608	300	2	journal	journal	PROPN
ejpam-5608	300	3	of	of	ADP
ejpam-5608	300	4	mathematics	mathematic	NOUN
ejpam-5608	300	5	,	,	PUNCT
ejpam-5608	300	6	32(1):109–120	32(1):109–120	NUM
ejpam-5608	300	7	,	,	PUNCT
ejpam-5608	300	8	2024	2024	NUM
ejpam-5608	300	9	.	.	PUNCT
ejpam-5608	301	1	[	[	X
ejpam-5608	301	2	15	15	NUM
ejpam-5608	301	3	]	]	X
ejpam-5608	301	4	a	a	DET
ejpam-5608	301	5	kamal	kamal	PROPN
ejpam-5608	301	6	,	,	PUNCT
ejpam-5608	301	7	d	d	PROPN
ejpam-5608	301	8	rizk	rizk	PROPN
ejpam-5608	301	9	,	,	PUNCT
ejpam-5608	301	10	k	k	PROPN
ejpam-5608	301	11	maheshwaran	maheshwaran	NOUN
ejpam-5608	301	12	,	,	PUNCT
ejpam-5608	301	13	and	and	CCONJ
ejpam-5608	301	14	tc	tc	NUM
ejpam-5608	301	15	mujeeburahman	mujeeburahman	NOUN
ejpam-5608	301	16	.	.	PUNCT
ejpam-5608	302	1	convergence	convergence	NOUN
ejpam-5608	302	2	theorems	theorem	NOUN
ejpam-5608	302	3	in	in	ADP
ejpam-5608	302	4	g	g	NOUN
ejpam-5608	302	5	-	-	PUNCT
ejpam-5608	302	6	metric	metric	ADJ
ejpam-5608	302	7	spaces	space	NOUN
ejpam-5608	302	8	and	and	CCONJ
ejpam-5608	302	9	its	its	PRON
ejpam-5608	302	10	application	application	NOUN
ejpam-5608	302	11	.	.	PUNCT
ejpam-5608	303	1	advances	advance	NOUN
ejpam-5608	303	2	in	in	ADP
ejpam-5608	303	3	fixed	fix	VERB
ejpam-5608	303	4	point	point	NOUN
ejpam-5608	303	5	theory	theory	NOUN
ejpam-5608	303	6	,	,	PUNCT
ejpam-5608	303	7	14:41	14:41	NUM
ejpam-5608	303	8	,	,	PUNCT
ejpam-5608	303	9	2024	2024	NUM
ejpam-5608	303	10	.	.	PUNCT
ejpam-5608	304	1	[	[	X
ejpam-5608	304	2	16	16	NUM
ejpam-5608	304	3	]	]	X
ejpam-5608	304	4	va	va	PROPN
ejpam-5608	304	5	khan	khan	PROPN
ejpam-5608	304	6	and	and	CCONJ
ejpam-5608	304	7	ska	ska	PROPN
ejpam-5608	304	8	rahaman	rahaman	NOUN
ejpam-5608	304	9	.	.	PUNCT
ejpam-5608	305	1	statistical	statistical	ADJ
ejpam-5608	305	2	convergence	convergence	NOUN
ejpam-5608	305	3	in	in	ADP
ejpam-5608	305	4	intuitionistic	intuitionistic	ADJ
ejpam-5608	305	5	fuzzy	fuzzy	ADJ
ejpam-5608	305	6	g	g	NOUN
ejpam-5608	305	7	-	-	PUNCT
ejpam-5608	305	8	metric	metric	ADJ
ejpam-5608	305	9	spaces	space	NOUN
ejpam-5608	305	10	with	with	ADP
ejpam-5608	305	11	order	order	NOUN
ejpam-5608	305	12	n.	n.	NOUN
ejpam-5608	305	13	filomat	filomat	NOUN
ejpam-5608	305	14	,	,	PUNCT
ejpam-5608	305	15	38(8):2785–2812	38(8):2785–2812	NUM
ejpam-5608	305	16	,	,	PUNCT
ejpam-5608	305	17	2024	2024	NUM
ejpam-5608	305	18	.	.	PUNCT
ejpam-5608	306	1	[	[	X
ejpam-5608	306	2	17	17	NUM
ejpam-5608	306	3	]	]	PUNCT
ejpam-5608	306	4	ö	ö	ADP
ejpam-5608	306	5	kişi	kişi	NOUN
ejpam-5608	306	6	,	,	PUNCT
ejpam-5608	306	7	b	b	NOUN
ejpam-5608	306	8	çakal	çakal	NOUN
ejpam-5608	306	9	,	,	PUNCT
ejpam-5608	306	10	and	and	CCONJ
ejpam-5608	306	11	m	m	AUX
ejpam-5608	306	12	gürdal	gürdal	ADJ
ejpam-5608	306	13	.	.	PUNCT
ejpam-5608	307	1	on	on	ADP
ejpam-5608	307	2	generalized	generalized	ADJ
ejpam-5608	307	3	statistical	statistical	ADJ
ejpam-5608	307	4	convergence	convergence	NOUN
ejpam-5608	307	5	in	in	ADP
ejpam-5608	307	6	quaternionvalued	quaternionvalued	ADJ
ejpam-5608	307	7	generalized	generalize	VERB
ejpam-5608	307	8	metric	metric	ADJ
ejpam-5608	307	9	spaces	space	NOUN
ejpam-5608	307	10	.	.	PUNCT
ejpam-5608	308	1	bulletin	bulletin	NOUN
ejpam-5608	308	2	of	of	ADP
ejpam-5608	308	3	mathematical	mathematical	ADJ
ejpam-5608	308	4	analysis	analysis	NOUN
ejpam-5608	308	5	and	and	CCONJ
ejpam-5608	308	6	applications	application	NOUN
ejpam-5608	308	7	,	,	PUNCT
ejpam-5608	308	8	16(3):28–44	16(3):28–44	NUM
ejpam-5608	308	9	,	,	PUNCT
ejpam-5608	308	10	2024	2024	NUM
ejpam-5608	308	11	.	.	PUNCT
ejpam-5608	309	1	[	[	X
ejpam-5608	309	2	18	18	NUM
ejpam-5608	309	3	]	]	SYM
ejpam-5608	309	4	ö	ö	ADP
ejpam-5608	309	5	kişi	kişi	NOUN
ejpam-5608	309	6	,	,	PUNCT
ejpam-5608	309	7	b	b	NOUN
ejpam-5608	309	8	çakal	çakal	NOUN
ejpam-5608	309	9	,	,	PUNCT
ejpam-5608	309	10	and	and	CCONJ
ejpam-5608	309	11	m	m	AUX
ejpam-5608	309	12	gürdal	gürdal	ADJ
ejpam-5608	309	13	.	.	PUNCT
ejpam-5608	310	1	on	on	ADP
ejpam-5608	310	2	lacunary	lacunary	ADJ
ejpam-5608	310	3	i	i	PROPN
ejpam-5608	310	4	-	-	PUNCT
ejpam-5608	310	5	invariant	invariant	ADJ
ejpam-5608	310	6	convergence	convergence	NOUN
ejpam-5608	310	7	of	of	ADP
ejpam-5608	310	8	sequences	sequence	NOUN
ejpam-5608	310	9	in	in	ADP
ejpam-5608	310	10	quaternion	quaternion	NOUN
ejpam-5608	310	11	-	-	PUNCT
ejpam-5608	310	12	valued	value	VERB
ejpam-5608	310	13	generalized	generalized	ADJ
ejpam-5608	310	14	metric	metric	ADJ
ejpam-5608	310	15	spaces	space	NOUN
ejpam-5608	310	16	.	.	PUNCT
ejpam-5608	311	1	journal	journal	NOUN
ejpam-5608	311	2	of	of	ADP
ejpam-5608	311	3	classical	classical	ADJ
ejpam-5608	311	4	analysis	analysis	NOUN
ejpam-5608	311	5	,	,	PUNCT
ejpam-5608	311	6	24(2):111	24(2):111	NUM
ejpam-5608	311	7	–	–	PUNCT
ejpam-5608	311	8	132	132	NUM
ejpam-5608	311	9	,	,	PUNCT
ejpam-5608	311	10	2024	2024	NUM
ejpam-5608	311	11	.	.	PUNCT
ejpam-5608	312	1	[	[	X
ejpam-5608	312	2	19	19	NUM
ejpam-5608	312	3	]	]	X
ejpam-5608	312	4	s	s	PART
ejpam-5608	312	5	kolancı	kolancı	NOUN
ejpam-5608	312	6	and	and	CCONJ
ejpam-5608	312	7	m	m	PROPN
ejpam-5608	312	8	gurdal	gurdal	ADJ
ejpam-5608	312	9	.	.	PUNCT
ejpam-5608	313	1	on	on	ADP
ejpam-5608	313	2	ideal	ideal	ADJ
ejpam-5608	313	3	convergence	convergence	NOUN
ejpam-5608	313	4	in	in	ADP
ejpam-5608	313	5	generalized	generalized	ADJ
ejpam-5608	313	6	metric	metric	ADJ
ejpam-5608	313	7	spaces	space	NOUN
ejpam-5608	313	8	.	.	PUNCT
ejpam-5608	314	1	dera	dera	NOUN
ejpam-5608	314	2	manuharawati	manuharawati	NOUN
ejpam-5608	314	3	,	,	PUNCT
ejpam-5608	314	4	m.jakfar	m.jakfar	ADV
ejpam-5608	314	5	,	,	PUNCT
ejpam-5608	314	6	a.	a.	PROPN
ejpam-5608	314	7	taufik	taufik	PROPN
ejpam-5608	314	8	hamzah	hamzah	PROPN
ejpam-5608	314	9	/	/	SYM
ejpam-5608	314	10	eur	eur	PROPN
ejpam-5608	314	11	.	.	PUNCT
ejpam-5608	315	1	j.	j.	PROPN
ejpam-5608	315	2	pure	pure	PROPN
ejpam-5608	315	3	appl	appl	PROPN
ejpam-5608	315	4	.	.	PROPN
ejpam-5608	315	5	math	math	PROPN
ejpam-5608	315	6	,	,	PUNCT
ejpam-5608	315	7	18	18	NUM
ejpam-5608	315	8	(	(	PUNCT
ejpam-5608	315	9	1	1	NUM
ejpam-5608	315	10	)	)	PUNCT
ejpam-5608	315	11	(	(	PUNCT
ejpam-5608	315	12	2025	2025	NUM
ejpam-5608	315	13	)	)	PUNCT
ejpam-5608	315	14	,	,	PUNCT
ejpam-5608	315	15	5608	5608	NUM
ejpam-5608	315	16	13	13	NUM
ejpam-5608	315	17	of	of	ADP
ejpam-5608	315	18	13	13	NUM
ejpam-5608	315	19	natung	natung	NOUN
ejpam-5608	315	20	government	government	NOUN
ejpam-5608	315	21	college	college	PROPN
ejpam-5608	315	22	research	research	PROPN
ejpam-5608	315	23	journal	journal	PROPN
ejpam-5608	315	24	,	,	PUNCT
ejpam-5608	315	25	8(1):81–96	8(1):81–96	NUM
ejpam-5608	315	26	,	,	PUNCT
ejpam-5608	315	27	2023	2023	NUM
ejpam-5608	315	28	.	.	PUNCT
ejpam-5608	316	1	[	[	X
ejpam-5608	316	2	20	20	NUM
ejpam-5608	316	3	]	]	X
ejpam-5608	316	4	p	p	PROPN
ejpam-5608	316	5	kostyrko	kostyrko	PROPN
ejpam-5608	316	6	,	,	PUNCT
ejpam-5608	316	7	w	w	PROPN
ejpam-5608	316	8	wilczyński	wilczyński	NOUN
ejpam-5608	316	9	,	,	PUNCT
ejpam-5608	316	10	and	and	CCONJ
ejpam-5608	316	11	t	t	PROPN
ejpam-5608	316	12	šalát	šalát	PROPN
ejpam-5608	316	13	.	.	PUNCT
ejpam-5608	317	1	i	i	NOUN
ejpam-5608	317	2	-	-	PUNCT
ejpam-5608	317	3	convergence	convergence	NOUN
ejpam-5608	317	4	.	.	PUNCT
ejpam-5608	318	1	real	real	ADJ
ejpam-5608	318	2	analysis	analysis	NOUN
ejpam-5608	318	3	exchange	exchange	NOUN
ejpam-5608	318	4	,	,	PUNCT
ejpam-5608	318	5	pages	page	NOUN
ejpam-5608	318	6	669–685	669–685	NUM
ejpam-5608	318	7	,	,	PUNCT
ejpam-5608	318	8	2000	2000	NUM
ejpam-5608	318	9	.	.	PUNCT
ejpam-5608	319	1	[	[	X
ejpam-5608	319	2	21	21	NUM
ejpam-5608	319	3	]	]	X
ejpam-5608	319	4	e	e	PROPN
ejpam-5608	319	5	kreyszig	kreyszig	PROPN
ejpam-5608	319	6	.	.	PUNCT
ejpam-5608	320	1	introductory	introductory	ADJ
ejpam-5608	320	2	functional	functional	ADJ
ejpam-5608	320	3	analysis	analysis	NOUN
ejpam-5608	320	4	with	with	ADP
ejpam-5608	320	5	applications	application	NOUN
ejpam-5608	320	6	,	,	PUNCT
ejpam-5608	320	7	volume	volume	NOUN
ejpam-5608	320	8	17	17	NUM
ejpam-5608	320	9	.	.	PUNCT
ejpam-5608	321	1	john	john	PROPN
ejpam-5608	321	2	wiley	wiley	PROPN
ejpam-5608	321	3	&	&	CCONJ
ejpam-5608	321	4	sons	son	NOUN
ejpam-5608	321	5	,	,	PUNCT
ejpam-5608	321	6	1978	1978	NUM
ejpam-5608	321	7	.	.	PUNCT
ejpam-5608	322	1	[	[	X
ejpam-5608	322	2	22	22	NUM
ejpam-5608	322	3	]	]	PUNCT
ejpam-5608	322	4	ş	ş	PROPN
ejpam-5608	322	5	s	s	PART
ejpam-5608	322	6	küçük	küçük	NOUN
ejpam-5608	322	7	and	and	CCONJ
ejpam-5608	322	8	h	h	NOUN
ejpam-5608	322	9	gümüş.	gümüş.	VERB
ejpam-5608	322	10	the	the	DET
ejpam-5608	322	11	meaning	meaning	NOUN
ejpam-5608	322	12	of	of	ADP
ejpam-5608	322	13	the	the	DET
ejpam-5608	322	14	concept	concept	NOUN
ejpam-5608	322	15	of	of	ADP
ejpam-5608	322	16	lacunary	lacunary	ADJ
ejpam-5608	322	17	statistical	statistical	ADJ
ejpam-5608	322	18	convergence	convergence	NOUN
ejpam-5608	322	19	in	in	ADP
ejpam-5608	322	20	g	g	NOUN
ejpam-5608	322	21	-	-	PUNCT
ejpam-5608	322	22	metric	metric	ADJ
ejpam-5608	322	23	spaces	space	NOUN
ejpam-5608	322	24	.	.	PUNCT
ejpam-5608	323	1	korean	korean	ADJ
ejpam-5608	323	2	journal	journal	PROPN
ejpam-5608	323	3	of	of	ADP
ejpam-5608	323	4	mathematics	mathematic	NOUN
ejpam-5608	323	5	,	,	PUNCT
ejpam-5608	323	6	30(4):679–686	30(4):679–686	NUM
ejpam-5608	323	7	,	,	PUNCT
ejpam-5608	323	8	2022	2022	NUM
ejpam-5608	323	9	.	.	PUNCT
ejpam-5608	324	1	[	[	X
ejpam-5608	324	2	23	23	NUM
ejpam-5608	324	3	]	]	PUNCT
ejpam-5608	324	4	manuharawati	manuharawati	NOUN
ejpam-5608	324	5	,	,	PUNCT
ejpam-5608	324	6	d.n	d.n	PROPN
ejpam-5608	324	7	.	.	PROPN
ejpam-5608	324	8	yunianti	yunianti	PROPN
ejpam-5608	324	9	,	,	PUNCT
ejpam-5608	324	10	and	and	CCONJ
ejpam-5608	324	11	m.	m.	NOUN
ejpam-5608	324	12	jakfar	jakfar	PROPN
ejpam-5608	324	13	.	.	PUNCT
ejpam-5608	325	1	the	the	DET
ejpam-5608	325	2	new	new	ADJ
ejpam-5608	325	3	convergence	convergence	NOUN
ejpam-5608	325	4	definition	definition	NOUN
ejpam-5608	325	5	for	for	ADP
ejpam-5608	325	6	sequence	sequence	NOUN
ejpam-5608	325	7	of	of	ADP
ejpam-5608	325	8	k	k	ADJ
ejpam-5608	325	9	-	-	ADJ
ejpam-5608	325	10	dimensional	dimensional	ADJ
ejpam-5608	325	11	subspaces	subspace	NOUN
ejpam-5608	325	12	of	of	ADP
ejpam-5608	325	13	an	an	DET
ejpam-5608	325	14	inner	inner	ADJ
ejpam-5608	325	15	product	product	NOUN
ejpam-5608	325	16	space	space	NOUN
ejpam-5608	325	17	.	.	PUNCT
ejpam-5608	326	1	volume	volume	NOUN
ejpam-5608	326	2	1417	1417	NUM
ejpam-5608	326	3	,	,	PUNCT
ejpam-5608	326	4	2019	2019	NUM
ejpam-5608	326	5	.	.	PUNCT
ejpam-5608	327	1	cited	cite	VERB
ejpam-5608	327	2	by	by	ADP
ejpam-5608	327	3	:	:	PUNCT
ejpam-5608	327	4	2	2	NUM
ejpam-5608	327	5	;	;	PUNCT
ejpam-5608	327	6	all	all	DET
ejpam-5608	327	7	open	open	ADJ
ejpam-5608	327	8	access	access	NOUN
ejpam-5608	327	9	,	,	PUNCT
ejpam-5608	327	10	gold	gold	NOUN
ejpam-5608	327	11	open	open	ADJ
ejpam-5608	327	12	access	access	NOUN
ejpam-5608	327	13	.	.	PUNCT
ejpam-5608	328	1	[	[	X
ejpam-5608	328	2	24	24	NUM
ejpam-5608	328	3	]	]	X
ejpam-5608	328	4	n	n	PROPN
ejpam-5608	328	5	f	f	PROPN
ejpam-5608	328	6	mardlatillah	mardlatillah	ADJ
ejpam-5608	328	7	,	,	PUNCT
ejpam-5608	328	8	manuharawati	manuharawati	NOUN
ejpam-5608	328	9	,	,	PUNCT
ejpam-5608	328	10	and	and	CCONJ
ejpam-5608	328	11	m	m	PROPN
ejpam-5608	328	12	jakfar	jakfar	ADJ
ejpam-5608	328	13	.	.	PUNCT
ejpam-5608	329	1	some	some	DET
ejpam-5608	329	2	properties	property	NOUN
ejpam-5608	329	3	i	i	PRON
ejpam-5608	329	4	–	–	PUNCT
ejpam-5608	329	5	cauchy	cauchy	PROPN
ejpam-5608	329	6	and	and	CCONJ
ejpam-5608	329	7	i	i	PRON
ejpam-5608	329	8	–	–	PUNCT
ejpam-5608	329	9	localized	localize	VERB
ejpam-5608	329	10	sequence	sequence	NOUN
ejpam-5608	329	11	on	on	ADP
ejpam-5608	329	12	g	g	NOUN
ejpam-5608	329	13	-	-	PUNCT
ejpam-5608	329	14	metric	metric	ADJ
ejpam-5608	329	15	space	space	NOUN
ejpam-5608	329	16	.	.	PUNCT
ejpam-5608	330	1	international	international	ADJ
ejpam-5608	330	2	journal	journal	PROPN
ejpam-5608	330	3	of	of	ADP
ejpam-5608	330	4	scientific	scientific	ADJ
ejpam-5608	330	5	engineering	engineering	NOUN
ejpam-5608	330	6	and	and	CCONJ
ejpam-5608	330	7	science	science	NOUN
ejpam-5608	330	8	,	,	PUNCT
ejpam-5608	330	9	7:50–53	7:50–53	NOUN
ejpam-5608	330	10	,	,	PUNCT
ejpam-5608	330	11	2023	2023	NUM
ejpam-5608	330	12	.	.	PUNCT
ejpam-5608	331	1	[	[	X
ejpam-5608	331	2	25	25	NUM
ejpam-5608	331	3	]	]	PUNCT
ejpam-5608	331	4	a	a	DET
ejpam-5608	331	5	mishra	mishra	PROPN
ejpam-5608	331	6	and	and	CCONJ
ejpam-5608	331	7	h	h	PROPN
ejpam-5608	331	8	raja	raja	PROPN
ejpam-5608	331	9	.	.	PUNCT
ejpam-5608	332	1	study	study	NOUN
ejpam-5608	332	2	of	of	ADP
ejpam-5608	332	3	fixed	fix	VERB
ejpam-5608	332	4	-	-	PUNCT
ejpam-5608	332	5	point	point	NOUN
ejpam-5608	332	6	results	result	NOUN
ejpam-5608	332	7	in	in	ADP
ejpam-5608	332	8	g	g	NOUN
ejpam-5608	332	9	-	-	PUNCT
ejpam-5608	332	10	metric	metric	ADJ
ejpam-5608	332	11	space	space	NOUN
ejpam-5608	332	12	and	and	CCONJ
ejpam-5608	332	13	g	g	NOUN
ejpam-5608	332	14	-	-	PUNCT
ejpam-5608	332	15	cone	cone	NOUN
ejpam-5608	332	16	metric	metric	ADJ
ejpam-5608	332	17	space	space	NOUN
ejpam-5608	332	18	and	and	CCONJ
ejpam-5608	332	19	its	its	PRON
ejpam-5608	332	20	application	application	NOUN
ejpam-5608	332	21	.	.	PUNCT
ejpam-5608	333	1	in	in	ADP
ejpam-5608	333	2	2024	2024	NUM
ejpam-5608	333	3	opju	opju	PROPN
ejpam-5608	333	4	international	international	ADJ
ejpam-5608	333	5	technology	technology	NOUN
ejpam-5608	333	6	conference	conference	NOUN
ejpam-5608	333	7	on	on	ADP
ejpam-5608	333	8	smart	smart	ADJ
ejpam-5608	333	9	computing	computing	NOUN
ejpam-5608	333	10	for	for	ADP
ejpam-5608	333	11	innovation	innovation	NOUN
ejpam-5608	333	12	and	and	CCONJ
ejpam-5608	333	13	advancement	advancement	NOUN
ejpam-5608	333	14	in	in	ADP
ejpam-5608	333	15	industry	industry	NOUN
ejpam-5608	333	16	4.0	4.0	NUM
ejpam-5608	333	17	(	(	PUNCT
ejpam-5608	333	18	otcon	otcon	NOUN
ejpam-5608	333	19	2024	2024	NUM
ejpam-5608	333	20	)	)	PUNCT
ejpam-5608	333	21	,	,	PUNCT
ejpam-5608	333	22	2024	2024	NUM
ejpam-5608	333	23	.	.	PUNCT
ejpam-5608	334	1	[	[	X
ejpam-5608	334	2	26	26	NUM
ejpam-5608	334	3	]	]	X
ejpam-5608	334	4	mn	mn	PROPN
ejpam-5608	334	5	mohammedali	mohammedali	PROPN
ejpam-5608	334	6	.	.	PUNCT
ejpam-5608	335	1	a	a	DET
ejpam-5608	335	2	new	new	ADJ
ejpam-5608	335	3	approach	approach	NOUN
ejpam-5608	335	4	to	to	ADP
ejpam-5608	335	5	g	g	NOUN
ejpam-5608	335	6	-	-	PUNCT
ejpam-5608	335	7	metric	metric	ADJ
ejpam-5608	335	8	spaces	space	NOUN
ejpam-5608	335	9	:	:	PUNCT
ejpam-5608	335	10	algebra	algebra	VERB
ejpam-5608	335	11	g	g	NOUN
ejpam-5608	335	12	-	-	PUNCT
ejpam-5608	335	13	fuzzy	fuzzy	ADJ
ejpam-5608	335	14	metric	metric	ADJ
ejpam-5608	335	15	spaces	space	NOUN
ejpam-5608	335	16	.	.	PUNCT
ejpam-5608	336	1	in	in	ADP
ejpam-5608	336	2	aip	aip	PROPN
ejpam-5608	336	3	conference	conference	NOUN
ejpam-5608	336	4	proceedings	proceeding	NOUN
ejpam-5608	336	5	,	,	PUNCT
ejpam-5608	336	6	volume	volume	NOUN
ejpam-5608	336	7	2820	2820	NUM
ejpam-5608	336	8	,	,	PUNCT
ejpam-5608	336	9	page	page	NOUN
ejpam-5608	336	10	040006	040006	NUM
ejpam-5608	336	11	,	,	PUNCT
ejpam-5608	336	12	2023	2023	NUM
ejpam-5608	336	13	.	.	PUNCT
ejpam-5608	337	1	[	[	X
ejpam-5608	337	2	27	27	NUM
ejpam-5608	337	3	]	]	X
ejpam-5608	337	4	z	z	NOUN
ejpam-5608	337	5	mustafa	mustafa	PROPN
ejpam-5608	337	6	and	and	CCONJ
ejpam-5608	337	7	b	b	NOUN
ejpam-5608	337	8	sims	sim	NOUN
ejpam-5608	337	9	.	.	PUNCT
ejpam-5608	338	1	a	a	DET
ejpam-5608	338	2	new	new	ADJ
ejpam-5608	338	3	approach	approach	NOUN
ejpam-5608	338	4	to	to	ADP
ejpam-5608	338	5	generalized	generalize	VERB
ejpam-5608	338	6	metric	metric	ADJ
ejpam-5608	338	7	spaces	space	NOUN
ejpam-5608	338	8	.	.	PUNCT
ejpam-5608	339	1	journal	journal	PROPN
ejpam-5608	339	2	of	of	ADP
ejpam-5608	339	3	nonlinear	nonlinear	ADJ
ejpam-5608	339	4	and	and	CCONJ
ejpam-5608	339	5	convex	convex	ADJ
ejpam-5608	339	6	analysis	analysis	NOUN
ejpam-5608	339	7	,	,	PUNCT
ejpam-5608	339	8	7(2):289–297	7(2):289–297	NOUN
ejpam-5608	339	9	,	,	PUNCT
ejpam-5608	339	10	2006	2006	NUM
ejpam-5608	339	11	.	.	PUNCT
ejpam-5608	340	1	[	[	X
ejpam-5608	340	2	28	28	NUM
ejpam-5608	340	3	]	]	X
ejpam-5608	340	4	z	z	NOUN
ejpam-5608	340	5	mustafa	mustafa	PROPN
ejpam-5608	340	6	and	and	CCONJ
ejpam-5608	340	7	b	b	NOUN
ejpam-5608	340	8	sims	sim	NOUN
ejpam-5608	340	9	.	.	PUNCT
ejpam-5608	341	1	a	a	DET
ejpam-5608	341	2	new	new	ADJ
ejpam-5608	341	3	approach	approach	NOUN
ejpam-5608	341	4	to	to	ADP
ejpam-5608	341	5	generalized	generalize	VERB
ejpam-5608	341	6	metric	metric	ADJ
ejpam-5608	341	7	spaces	space	NOUN
ejpam-5608	341	8	.	.	PUNCT
ejpam-5608	342	1	journal	journal	PROPN
ejpam-5608	342	2	of	of	ADP
ejpam-5608	342	3	nonlinear	nonlinear	ADJ
ejpam-5608	342	4	and	and	CCONJ
ejpam-5608	342	5	convex	convex	ADJ
ejpam-5608	342	6	analysis	analysis	NOUN
ejpam-5608	342	7	,	,	PUNCT
ejpam-5608	342	8	7:289–297	7:289–297	NUM
ejpam-5608	342	9	,	,	PUNCT
ejpam-5608	342	10	2006	2006	NUM
ejpam-5608	342	11	.	.	PUNCT
ejpam-5608	343	1	[	[	X
ejpam-5608	343	2	29	29	NUM
ejpam-5608	343	3	]	]	X
ejpam-5608	343	4	a	a	DET
ejpam-5608	343	5	a	a	DET
ejpam-5608	343	6	nabiev	nabiev	NOUN
ejpam-5608	343	7	,	,	PUNCT
ejpam-5608	343	8	e	e	NOUN
ejpam-5608	343	9	savaş	savaş	PROPN
ejpam-5608	343	10	,	,	PUNCT
ejpam-5608	343	11	and	and	CCONJ
ejpam-5608	343	12	m	m	PROPN
ejpam-5608	343	13	gürdal	gürdal	NOUN
ejpam-5608	343	14	.	.	PUNCT
ejpam-5608	344	1	statistically	statistically	ADV
ejpam-5608	344	2	localized	localize	VERB
ejpam-5608	344	3	sequences	sequence	NOUN
ejpam-5608	344	4	in	in	ADP
ejpam-5608	344	5	metric	metric	ADJ
ejpam-5608	344	6	spaces	space	NOUN
ejpam-5608	344	7	.	.	PUNCT
ejpam-5608	345	1	journal	journal	NOUN
ejpam-5608	345	2	of	of	ADP
ejpam-5608	345	3	applied	apply	VERB
ejpam-5608	345	4	analysis	analysis	NOUN
ejpam-5608	345	5	and	and	CCONJ
ejpam-5608	345	6	computation	computation	NOUN
ejpam-5608	345	7	,	,	PUNCT
ejpam-5608	345	8	9(2):739–746	9(2):739–746	NUM
ejpam-5608	345	9	,	,	PUNCT
ejpam-5608	345	10	2019	2019	NUM
ejpam-5608	345	11	.	.	PUNCT
ejpam-5608	346	1	[	[	X
ejpam-5608	346	2	30	30	NUM
ejpam-5608	346	3	]	]	X
ejpam-5608	346	4	t	t	PROPN
ejpam-5608	346	5	nazir	nazir	PROPN
ejpam-5608	346	6	and	and	CCONJ
ejpam-5608	346	7	m	m	PROPN
ejpam-5608	346	8	abbas	abbas	NOUN
ejpam-5608	346	9	.	.	PUNCT
ejpam-5608	347	1	best	good	ADJ
ejpam-5608	347	2	proximity	proximity	NOUN
ejpam-5608	347	3	point	point	NOUN
ejpam-5608	347	4	problems	problem	NOUN
ejpam-5608	347	5	in	in	ADP
ejpam-5608	347	6	g	g	NOUN
ejpam-5608	347	7	-	-	PUNCT
ejpam-5608	347	8	metric	metric	ADJ
ejpam-5608	347	9	spaces	space	NOUN
ejpam-5608	347	10	and	and	CCONJ
ejpam-5608	347	11	its	its	PRON
ejpam-5608	347	12	applications	application	NOUN
ejpam-5608	347	13	.	.	PUNCT
ejpam-5608	348	1	industrial	industrial	ADJ
ejpam-5608	348	2	and	and	CCONJ
ejpam-5608	348	3	applied	apply	VERB
ejpam-5608	348	4	mathematics	mathematic	NOUN
ejpam-5608	348	5	,	,	PUNCT
ejpam-5608	348	6	part	part	NOUN
ejpam-5608	348	7	f3430:135–157	f3430:135–157	PROPN
ejpam-5608	348	8	,	,	PUNCT
ejpam-5608	348	9	2024	2024	NUM
ejpam-5608	348	10	.	.	PUNCT
ejpam-5608	349	1	[	[	X
ejpam-5608	349	2	31	31	NUM
ejpam-5608	349	3	]	]	X
ejpam-5608	349	4	s	s	X
ejpam-5608	349	5	pal	pal	NOUN
ejpam-5608	349	6	and	and	CCONJ
ejpam-5608	349	7	b	b	PROPN
ejpam-5608	349	8	tiwari	tiwari	PROPN
ejpam-5608	349	9	.	.	PUNCT
ejpam-5608	349	10	ideal	ideal	ADJ
ejpam-5608	349	11	convergence	convergence	NOUN
ejpam-5608	349	12	in	in	ADP
ejpam-5608	349	13	g	g	NOUN
ejpam-5608	349	14	-	-	PUNCT
ejpam-5608	349	15	metric	metric	ADJ
ejpam-5608	349	16	spaces	space	NOUN
ejpam-5608	349	17	.	.	PUNCT
ejpam-5608	350	1	mathematica	mathematica	PROPN
ejpam-5608	350	2	slovaca	slovaca	PROPN
ejpam-5608	350	3	,	,	PUNCT
ejpam-5608	350	4	68(6):1395–1407	68(6):1395–1407	NUM
ejpam-5608	350	5	,	,	PUNCT
ejpam-5608	350	6	2018	2018	NUM
ejpam-5608	350	7	.	.	PUNCT
ejpam-5608	351	1	[	[	X
ejpam-5608	351	2	32	32	NUM
ejpam-5608	351	3	]	]	PUNCT
ejpam-5608	351	4	t	t	PROPN
ejpam-5608	351	5	šalát	šalát	PROPN
ejpam-5608	351	6	.	.	PUNCT
ejpam-5608	352	1	on	on	ADP
ejpam-5608	352	2	statistically	statistically	ADV
ejpam-5608	352	3	convergent	convergent	ADJ
ejpam-5608	352	4	sequences	sequence	NOUN
ejpam-5608	352	5	of	of	ADP
ejpam-5608	352	6	real	real	ADJ
ejpam-5608	352	7	numbers	number	NOUN
ejpam-5608	352	8	.	.	PUNCT
ejpam-5608	353	1	mathematica	mathematica	PROPN
ejpam-5608	353	2	slovaca	slovaca	PROPN
ejpam-5608	353	3	,	,	PUNCT
ejpam-5608	353	4	30(2):139–150	30(2):139–150	PROPN
ejpam-5608	353	5	,	,	PUNCT
ejpam-5608	353	6	1980	1980	NUM
ejpam-5608	353	7	.	.	PUNCT
ejpam-5608	354	1	[	[	X
ejpam-5608	354	2	33	33	NUM
ejpam-5608	354	3	]	]	PUNCT
ejpam-5608	354	4	af	af	VERB
ejpam-5608	354	5	sayed	say	VERB
ejpam-5608	354	6	and	and	CCONJ
ejpam-5608	354	7	a	a	DET
ejpam-5608	354	8	alahmari	alahmari	NOUN
ejpam-5608	354	9	.	.	PUNCT
ejpam-5608	355	1	some	some	DET
ejpam-5608	355	2	new	new	ADJ
ejpam-5608	355	3	results	result	NOUN
ejpam-5608	355	4	of	of	ADP
ejpam-5608	355	5	fixed	fix	VERB
ejpam-5608	355	6	point	point	NOUN
ejpam-5608	355	7	in	in	ADP
ejpam-5608	355	8	fuzzy	fuzzy	ADJ
ejpam-5608	355	9	soft	soft	ADJ
ejpam-5608	355	10	g	g	NOUN
ejpam-5608	355	11	-	-	PUNCT
ejpam-5608	355	12	metric	metric	ADJ
ejpam-5608	355	13	spaces	space	NOUN
ejpam-5608	355	14	.	.	PUNCT
ejpam-5608	356	1	european	european	ADJ
ejpam-5608	356	2	journal	journal	PROPN
ejpam-5608	356	3	of	of	ADP
ejpam-5608	356	4	pure	pure	ADJ
ejpam-5608	356	5	and	and	CCONJ
ejpam-5608	356	6	applied	applied	ADJ
ejpam-5608	356	7	mathematics	mathematic	NOUN
ejpam-5608	356	8	,	,	PUNCT
ejpam-5608	356	9	14(3):923–941	14(3):923–941	PROPN
ejpam-5608	356	10	,	,	PUNCT
ejpam-5608	356	11	2021	2021	NUM
ejpam-5608	356	12	.	.	PUNCT
ejpam-5608	357	1	[	[	X
ejpam-5608	357	2	34	34	NUM
ejpam-5608	357	3	]	]	SYM
ejpam-5608	357	4	v	v	ADP
ejpam-5608	357	5	a	a	DET
ejpam-5608	357	6	tran	tran	NOUN
ejpam-5608	357	7	,	,	PUNCT
ejpam-5608	357	8	n	n	CCONJ
ejpam-5608	357	9	van	van	NOUN
ejpam-5608	357	10	dung	dung	NOUN
ejpam-5608	357	11	,	,	PUNCT
ejpam-5608	357	12	and	and	CCONJ
ejpam-5608	357	13	vt	vt	PROPN
ejpam-5608	357	14	le	le	X
ejpam-5608	357	15	hang	hang	PROPN
ejpam-5608	357	16	.	.	PUNCT
ejpam-5608	358	1	a	a	DET
ejpam-5608	358	2	new	new	ADJ
ejpam-5608	358	3	approach	approach	NOUN
ejpam-5608	358	4	to	to	ADP
ejpam-5608	358	5	fixed	fix	VERB
ejpam-5608	358	6	point	point	NOUN
ejpam-5608	358	7	theorems	theorem	NOUN
ejpam-5608	358	8	on	on	ADP
ejpam-5608	358	9	g	g	NOUN
ejpam-5608	358	10	-	-	PUNCT
ejpam-5608	358	11	metric	metric	ADJ
ejpam-5608	358	12	spaces	space	NOUN
ejpam-5608	358	13	.	.	PUNCT
ejpam-5608	359	1	topology	topology	NOUN
ejpam-5608	359	2	and	and	CCONJ
ejpam-5608	359	3	its	its	PRON
ejpam-5608	359	4	applications	application	NOUN
ejpam-5608	359	5	,	,	PUNCT
ejpam-5608	359	6	160(12):1486–1493	160(12):1486–1493	NUM
ejpam-5608	359	7	,	,	PUNCT
ejpam-5608	359	8	2013	2013	NUM
ejpam-5608	359	9	.	.	PUNCT
ejpam-5608	360	1	[	[	X
ejpam-5608	360	2	35	35	NUM
ejpam-5608	360	3	]	]	SYM
ejpam-5608	360	4	u	u	NOUN
ejpam-5608	360	5	yamancı	yamancı	NOUN
ejpam-5608	360	6	and	and	CCONJ
ejpam-5608	360	7	m	m	PROPN
ejpam-5608	360	8	gürdal	gürdal	NOUN
ejpam-5608	360	9	.	.	PUNCT
ejpam-5608	361	1	statistical	statistical	ADJ
ejpam-5608	361	2	convergence	convergence	NOUN
ejpam-5608	361	3	and	and	CCONJ
ejpam-5608	361	4	operators	operator	NOUN
ejpam-5608	361	5	on	on	ADP
ejpam-5608	361	6	fock	fock	ADJ
ejpam-5608	361	7	space	space	NOUN
ejpam-5608	361	8	.	.	PUNCT
ejpam-5608	362	1	new	new	PROPN
ejpam-5608	362	2	york	york	PROPN
ejpam-5608	362	3	journal	journal	PROPN
ejpam-5608	362	4	of	of	ADP
ejpam-5608	362	5	mathematics	mathematic	NOUN
ejpam-5608	362	6	,	,	PUNCT
ejpam-5608	362	7	22:199–207	22:199–207	PROPN
ejpam-5608	362	8	,	,	PUNCT
ejpam-5608	362	9	2016	2016	NUM
ejpam-5608	362	10	.	.	PUNCT