id	sid	tid	token	lemma	pos
ejpam-3708	1	1	european	european	PROPN
ejpam-3708	1	2	journal	journal	PROPN
ejpam-3708	1	3	of	of	ADP
ejpam-3708	1	4	pure	pure	ADJ
ejpam-3708	1	5	and	and	CCONJ
ejpam-3708	1	6	applied	apply	VERB
ejpam-3708	1	7	mathematics	mathematic	NOUN
ejpam-3708	1	8	vol	vol	NOUN
ejpam-3708	1	9	.	.	PROPN
ejpam-3708	2	1	13	13	NUM
ejpam-3708	2	2	,	,	PUNCT
ejpam-3708	2	3	no	no	INTJ
ejpam-3708	2	4	.	.	NOUN
ejpam-3708	2	5	5	5	NUM
ejpam-3708	2	6	,	,	PUNCT
ejpam-3708	2	7	2020	2020	NUM
ejpam-3708	2	8	,	,	PUNCT
ejpam-3708	2	9	1131	1131	NUM
ejpam-3708	2	10	-	-	SYM
ejpam-3708	2	11	1148	1148	NUM
ejpam-3708	2	12	issn	issn	PROPN
ejpam-3708	2	13	1307	1307	NUM
ejpam-3708	2	14	-	-	SYM
ejpam-3708	2	15	5543	5543	NUM
ejpam-3708	2	16	–	–	PUNCT
ejpam-3708	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3708	2	18	published	publish	VERB
ejpam-3708	2	19	by	by	ADP
ejpam-3708	2	20	new	new	PROPN
ejpam-3708	2	21	york	york	PROPN
ejpam-3708	2	22	business	business	PROPN
ejpam-3708	2	23	global	global	ADJ
ejpam-3708	2	24	special	special	ADJ
ejpam-3708	2	25	issue	issue	NOUN
ejpam-3708	2	26	dedicated	dedicate	VERB
ejpam-3708	2	27	to	to	ADP
ejpam-3708	2	28	professor	professor	NOUN
ejpam-3708	2	29	hari	hari	PROPN
ejpam-3708	2	30	m.	m.	PROPN
ejpam-3708	2	31	srivastava	srivastava	PROPN
ejpam-3708	2	32	on	on	ADP
ejpam-3708	2	33	the	the	DET
ejpam-3708	2	34	occasion	occasion	NOUN
ejpam-3708	2	35	of	of	ADP
ejpam-3708	2	36	his	his	PRON
ejpam-3708	2	37	80th	80th	ADJ
ejpam-3708	2	38	birthday	birthday	NOUN
ejpam-3708	2	39	applications	application	NOUN
ejpam-3708	2	40	of	of	ADP
ejpam-3708	2	41	lacunary	lacunary	ADJ
ejpam-3708	2	42	sequences	sequence	NOUN
ejpam-3708	2	43	to	to	PART
ejpam-3708	2	44	develop	develop	VERB
ejpam-3708	2	45	fuzzy	fuzzy	ADJ
ejpam-3708	2	46	sequence	sequence	NOUN
ejpam-3708	2	47	spaces	space	NOUN
ejpam-3708	2	48	for	for	ADP
ejpam-3708	2	49	ideal	ideal	ADJ
ejpam-3708	2	50	convergence	convergence	NOUN
ejpam-3708	2	51	and	and	CCONJ
ejpam-3708	2	52	orlicz	orlicz	NOUN
ejpam-3708	2	53	function	function	PROPN
ejpam-3708	2	54	kuldip	kuldip	PROPN
ejpam-3708	2	55	raj1	raj1	PROPN
ejpam-3708	2	56	,	,	PUNCT
ejpam-3708	2	57	s.	s.	PROPN
ejpam-3708	2	58	a.	a.	PROPN
ejpam-3708	2	59	mohiuddine2,3,∗	mohiuddine2,3,∗	PROPN
ejpam-3708	2	60	1	1	NUM
ejpam-3708	2	61	school	school	NOUN
ejpam-3708	2	62	of	of	ADP
ejpam-3708	2	63	mathematics	mathematic	NOUN
ejpam-3708	2	64	,	,	PUNCT
ejpam-3708	2	65	shri	shri	PROPN
ejpam-3708	2	66	mata	mata	PROPN
ejpam-3708	2	67	vaishno	vaishno	PROPN
ejpam-3708	2	68	devi	devi	PROPN
ejpam-3708	2	69	university	university	PROPN
ejpam-3708	2	70	,	,	PUNCT
ejpam-3708	2	71	katra	katra	PROPN
ejpam-3708	2	72	182320	182320	NUM
ejpam-3708	2	73	,	,	PUNCT
ejpam-3708	2	74	j&k	j&k	PROPN
ejpam-3708	2	75	,	,	PUNCT
ejpam-3708	2	76	india	india	PROPN
ejpam-3708	2	77	2	2	NUM
ejpam-3708	2	78	department	department	NOUN
ejpam-3708	2	79	of	of	ADP
ejpam-3708	2	80	general	general	ADJ
ejpam-3708	2	81	required	require	VERB
ejpam-3708	2	82	courses	course	NOUN
ejpam-3708	2	83	,	,	PUNCT
ejpam-3708	2	84	mathematics	mathematic	NOUN
ejpam-3708	2	85	,	,	PUNCT
ejpam-3708	2	86	faculty	faculty	NOUN
ejpam-3708	2	87	of	of	ADP
ejpam-3708	2	88	applied	apply	VERB
ejpam-3708	2	89	studies	study	NOUN
ejpam-3708	2	90	,	,	PUNCT
ejpam-3708	2	91	king	king	PROPN
ejpam-3708	2	92	abdulaziz	abdulaziz	PROPN
ejpam-3708	2	93	university	university	PROPN
ejpam-3708	2	94	,	,	PUNCT
ejpam-3708	2	95	jeddah	jeddah	PROPN
ejpam-3708	2	96	21589	21589	NUM
ejpam-3708	2	97	,	,	PUNCT
ejpam-3708	2	98	saudi	saudi	PROPN
ejpam-3708	2	99	arabia	arabia	PROPN
ejpam-3708	2	100	3	3	NUM
ejpam-3708	2	101	operator	operator	NOUN
ejpam-3708	2	102	theory	theory	NOUN
ejpam-3708	2	103	and	and	CCONJ
ejpam-3708	2	104	applications	application	NOUN
ejpam-3708	2	105	research	research	NOUN
ejpam-3708	2	106	group	group	NOUN
ejpam-3708	2	107	,	,	PUNCT
ejpam-3708	2	108	department	department	NOUN
ejpam-3708	2	109	of	of	ADP
ejpam-3708	2	110	mathematics	mathematic	NOUN
ejpam-3708	2	111	,	,	PUNCT
ejpam-3708	2	112	king	king	PROPN
ejpam-3708	2	113	abdulaziz	abdulaziz	PROPN
ejpam-3708	2	114	university	university	PROPN
ejpam-3708	2	115	,	,	PUNCT
ejpam-3708	2	116	jeddah	jeddah	PROPN
ejpam-3708	2	117	21589	21589	NUM
ejpam-3708	2	118	,	,	PUNCT
ejpam-3708	2	119	saudi	saudi	PROPN
ejpam-3708	2	120	arabia	arabia	PROPN
ejpam-3708	2	121	abstract	abstract	NOUN
ejpam-3708	2	122	.	.	PUNCT
ejpam-3708	3	1	in	in	ADP
ejpam-3708	3	2	the	the	DET
ejpam-3708	3	3	present	present	ADJ
ejpam-3708	3	4	paper	paper	NOUN
ejpam-3708	3	5	,	,	PUNCT
ejpam-3708	3	6	we	we	PRON
ejpam-3708	3	7	introduce	introduce	VERB
ejpam-3708	3	8	and	and	CCONJ
ejpam-3708	3	9	study	study	VERB
ejpam-3708	3	10	ideal	ideal	ADJ
ejpam-3708	3	11	convergence	convergence	NOUN
ejpam-3708	3	12	of	of	ADP
ejpam-3708	3	13	some	some	DET
ejpam-3708	3	14	fuzzy	fuzzy	ADJ
ejpam-3708	3	15	sequence	sequence	NOUN
ejpam-3708	3	16	spaces	space	NOUN
ejpam-3708	3	17	via	via	ADP
ejpam-3708	3	18	lacunary	lacunary	ADJ
ejpam-3708	3	19	sequence	sequence	NOUN
ejpam-3708	3	20	,	,	PUNCT
ejpam-3708	3	21	infinite	infinite	ADJ
ejpam-3708	3	22	matrix	matrix	NOUN
ejpam-3708	3	23	and	and	CCONJ
ejpam-3708	3	24	orlicz	orlicz	ADJ
ejpam-3708	3	25	function	function	NOUN
ejpam-3708	3	26	.	.	PUNCT
ejpam-3708	4	1	we	we	PRON
ejpam-3708	4	2	study	study	VERB
ejpam-3708	4	3	some	some	DET
ejpam-3708	4	4	topological	topological	ADJ
ejpam-3708	4	5	and	and	CCONJ
ejpam-3708	4	6	algebraic	algebraic	ADJ
ejpam-3708	4	7	properties	property	NOUN
ejpam-3708	4	8	of	of	ADP
ejpam-3708	4	9	these	these	DET
ejpam-3708	4	10	spaces	space	NOUN
ejpam-3708	4	11	.	.	PUNCT
ejpam-3708	5	1	we	we	PRON
ejpam-3708	5	2	also	also	ADV
ejpam-3708	5	3	make	make	VERB
ejpam-3708	5	4	an	an	DET
ejpam-3708	5	5	effort	effort	NOUN
ejpam-3708	5	6	to	to	PART
ejpam-3708	5	7	show	show	VERB
ejpam-3708	5	8	that	that	SCONJ
ejpam-3708	5	9	these	these	DET
ejpam-3708	5	10	spaces	space	NOUN
ejpam-3708	5	11	are	be	AUX
ejpam-3708	5	12	normal	normal	ADJ
ejpam-3708	5	13	as	as	ADV
ejpam-3708	5	14	well	well	ADV
ejpam-3708	5	15	as	as	ADP
ejpam-3708	5	16	monotone	monotone	ADJ
ejpam-3708	5	17	.	.	PUNCT
ejpam-3708	6	1	further	far	ADV
ejpam-3708	6	2	,	,	PUNCT
ejpam-3708	6	3	it	it	PRON
ejpam-3708	6	4	is	be	AUX
ejpam-3708	6	5	very	very	ADV
ejpam-3708	6	6	interesting	interesting	ADJ
ejpam-3708	6	7	to	to	PART
ejpam-3708	6	8	show	show	VERB
ejpam-3708	6	9	that	that	SCONJ
ejpam-3708	6	10	if	if	SCONJ
ejpam-3708	6	11	i	i	PRON
ejpam-3708	6	12	is	be	AUX
ejpam-3708	6	13	not	not	PART
ejpam-3708	6	14	maximal	maximal	ADJ
ejpam-3708	6	15	ideal	ideal	NOUN
ejpam-3708	6	16	then	then	ADV
ejpam-3708	6	17	these	these	DET
ejpam-3708	6	18	spaces	space	NOUN
ejpam-3708	6	19	are	be	AUX
ejpam-3708	6	20	not	not	PART
ejpam-3708	6	21	symmetric	symmetric	ADJ
ejpam-3708	6	22	.	.	PUNCT
ejpam-3708	7	1	2020	2020	NUM
ejpam-3708	7	2	mathematics	mathematic	NOUN
ejpam-3708	7	3	subject	subject	NOUN
ejpam-3708	7	4	classifications	classification	NOUN
ejpam-3708	7	5	:	:	PUNCT
ejpam-3708	7	6	46a45	46a45	NUM
ejpam-3708	7	7	,	,	PUNCT
ejpam-3708	7	8	40a05	40a05	NUM
ejpam-3708	7	9	,	,	PUNCT
ejpam-3708	7	10	03e72	03e72	X
ejpam-3708	7	11	key	key	ADJ
ejpam-3708	7	12	words	word	NOUN
ejpam-3708	7	13	and	and	CCONJ
ejpam-3708	7	14	phrases	phrase	NOUN
ejpam-3708	7	15	:	:	PUNCT
ejpam-3708	7	16	lacunary	lacunary	ADJ
ejpam-3708	7	17	sequence	sequence	NOUN
ejpam-3708	7	18	,	,	PUNCT
ejpam-3708	7	19	ideal	ideal	ADJ
ejpam-3708	7	20	convergence	convergence	NOUN
ejpam-3708	7	21	,	,	PUNCT
ejpam-3708	7	22	orlicz	orlicz	ADJ
ejpam-3708	7	23	function	function	NOUN
ejpam-3708	7	24	,	,	PUNCT
ejpam-3708	7	25	sequence	sequence	NOUN
ejpam-3708	7	26	of	of	ADP
ejpam-3708	7	27	fuzzy	fuzzy	ADJ
ejpam-3708	7	28	numbers	number	NOUN
ejpam-3708	7	29	,	,	PUNCT
ejpam-3708	7	30	difference	difference	NOUN
ejpam-3708	7	31	sequence	sequence	NOUN
ejpam-3708	7	32	1	1	NUM
ejpam-3708	7	33	.	.	PUNCT
ejpam-3708	8	1	introduction	introduction	NOUN
ejpam-3708	8	2	and	and	CCONJ
ejpam-3708	8	3	preliminaries	preliminary	NOUN
ejpam-3708	8	4	the	the	DET
ejpam-3708	8	5	concept	concept	NOUN
ejpam-3708	8	6	of	of	ADP
ejpam-3708	8	7	ordinary	ordinary	ADJ
ejpam-3708	8	8	convergence	convergence	NOUN
ejpam-3708	8	9	of	of	ADP
ejpam-3708	8	10	a	a	DET
ejpam-3708	8	11	sequence	sequence	NOUN
ejpam-3708	8	12	of	of	ADP
ejpam-3708	8	13	fuzzy	fuzzy	ADJ
ejpam-3708	8	14	numbers	number	NOUN
ejpam-3708	8	15	was	be	AUX
ejpam-3708	8	16	introduced	introduce	VERB
ejpam-3708	8	17	by	by	ADP
ejpam-3708	8	18	matloka	matloka	NOUN
ejpam-3708	8	19	[	[	X
ejpam-3708	8	20	18	18	NUM
ejpam-3708	8	21	]	]	PUNCT
ejpam-3708	8	22	and	and	CCONJ
ejpam-3708	8	23	proved	prove	VERB
ejpam-3708	8	24	some	some	DET
ejpam-3708	8	25	basic	basic	ADJ
ejpam-3708	8	26	theorems	theorem	NOUN
ejpam-3708	8	27	for	for	ADP
ejpam-3708	8	28	sequences	sequence	NOUN
ejpam-3708	8	29	of	of	ADP
ejpam-3708	8	30	fuzzy	fuzzy	ADJ
ejpam-3708	8	31	numbers	number	NOUN
ejpam-3708	8	32	.	.	PUNCT
ejpam-3708	9	1	later	later	ADV
ejpam-3708	9	2	on	on	ADP
ejpam-3708	9	3	nanda	nanda	ADV
ejpam-3708	9	4	[	[	X
ejpam-3708	9	5	28	28	NUM
ejpam-3708	9	6	]	]	PUNCT
ejpam-3708	9	7	introduced	introduce	VERB
ejpam-3708	9	8	sequences	sequence	NOUN
ejpam-3708	9	9	of	of	ADP
ejpam-3708	9	10	fuzzy	fuzzy	ADJ
ejpam-3708	9	11	numbers	number	NOUN
ejpam-3708	9	12	and	and	CCONJ
ejpam-3708	9	13	studied	study	VERB
ejpam-3708	9	14	that	that	SCONJ
ejpam-3708	9	15	the	the	DET
ejpam-3708	9	16	set	set	NOUN
ejpam-3708	9	17	of	of	ADP
ejpam-3708	9	18	all	all	DET
ejpam-3708	9	19	convergent	convergent	ADJ
ejpam-3708	9	20	sequences	sequence	NOUN
ejpam-3708	9	21	of	of	ADP
ejpam-3708	9	22	fuzzy	fuzzy	ADJ
ejpam-3708	9	23	numbers	number	NOUN
ejpam-3708	9	24	forms	form	VERB
ejpam-3708	9	25	a	a	DET
ejpam-3708	9	26	complete	complete	ADJ
ejpam-3708	9	27	metric	metric	ADJ
ejpam-3708	9	28	space	space	NOUN
ejpam-3708	9	29	.	.	PUNCT
ejpam-3708	10	1	recently	recently	ADV
ejpam-3708	10	2	,	,	PUNCT
ejpam-3708	10	3	nuray	nuray	ADJ
ejpam-3708	10	4	∗corresponding	∗corresponde	VERB
ejpam-3708	10	5	author	author	NOUN
ejpam-3708	10	6	.	.	PUNCT
ejpam-3708	11	1	doi	doi	NOUN
ejpam-3708	11	2	:	:	PUNCT
ejpam-3708	11	3	https://doi.org/10.29020/nybg.ejpam.v13i5.3708	https://doi.org/10.29020/nybg.ejpam.v13i5.3708	ADJ
ejpam-3708	11	4	email	email	NOUN
ejpam-3708	11	5	addresses	address	NOUN
ejpam-3708	11	6	:	:	PUNCT
ejpam-3708	11	7	kuldipraj68@gmail.com	kuldipraj68@gmail.com	X
ejpam-3708	11	8	(	(	PUNCT
ejpam-3708	11	9	k.	k.	PROPN
ejpam-3708	11	10	raj	raj	PROPN
ejpam-3708	11	11	)	)	PUNCT
ejpam-3708	11	12	,	,	PUNCT
ejpam-3708	11	13	mohiuddine@gmail.com	mohiuddine@gmail.com	PROPN
ejpam-3708	11	14	(	(	PUNCT
ejpam-3708	11	15	s.	s.	PROPN
ejpam-3708	11	16	a.	a.	PROPN
ejpam-3708	11	17	mohiuddine	mohiuddine	PROPN
ejpam-3708	11	18	)	)	PUNCT
ejpam-3708	11	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3708	11	20	1131	1131	NUM
ejpam-3708	12	1	c	c	NOUN
ejpam-3708	12	2	©	©	PROPN
ejpam-3708	12	3	2020	2020	NUM
ejpam-3708	12	4	ejpam	ejpam	VERB
ejpam-3708	12	5	all	all	DET
ejpam-3708	12	6	rights	right	NOUN
ejpam-3708	12	7	reserved	reserve	VERB
ejpam-3708	12	8	.	.	PUNCT
ejpam-3708	13	1	k.	k.	PROPN
ejpam-3708	13	2	raj	raj	PROPN
ejpam-3708	13	3	,	,	PUNCT
ejpam-3708	13	4	s.	s.	PROPN
ejpam-3708	13	5	a.	a.	PROPN
ejpam-3708	13	6	mohiuddine	mohiuddine	PROPN
ejpam-3708	13	7	/	/	SYM
ejpam-3708	13	8	eur	eur	PROPN
ejpam-3708	13	9	.	.	PUNCT
ejpam-3708	14	1	j.	j.	PROPN
ejpam-3708	14	2	pure	pure	PROPN
ejpam-3708	14	3	appl	appl	PROPN
ejpam-3708	14	4	.	.	PROPN
ejpam-3708	14	5	math	math	PROPN
ejpam-3708	14	6	,	,	PUNCT
ejpam-3708	14	7	13	13	NUM
ejpam-3708	14	8	(	(	PUNCT
ejpam-3708	14	9	5	5	NUM
ejpam-3708	14	10	)	)	PUNCT
ejpam-3708	14	11	(	(	PUNCT
ejpam-3708	14	12	2020	2020	NUM
ejpam-3708	14	13	)	)	PUNCT
ejpam-3708	14	14	,	,	PUNCT
ejpam-3708	14	15	1131	1131	NUM
ejpam-3708	14	16	-	-	SYM
ejpam-3708	14	17	1148	1148	NUM
ejpam-3708	14	18	1132	1132	NUM
ejpam-3708	14	19	and	and	CCONJ
ejpam-3708	14	20	savaş	savaş	PROPN
ejpam-3708	14	21	[	[	X
ejpam-3708	14	22	30	30	NUM
ejpam-3708	14	23	]	]	PUNCT
ejpam-3708	14	24	studied	study	VERB
ejpam-3708	14	25	statistical	statistical	ADJ
ejpam-3708	14	26	convergence	convergence	NOUN
ejpam-3708	14	27	and	and	CCONJ
ejpam-3708	14	28	statistically	statistically	ADV
ejpam-3708	14	29	cauchy	cauchy	ADJ
ejpam-3708	14	30	for	for	ADP
ejpam-3708	14	31	sequence	sequence	NOUN
ejpam-3708	14	32	of	of	ADP
ejpam-3708	14	33	fuzzy	fuzzy	ADJ
ejpam-3708	14	34	numbers	number	NOUN
ejpam-3708	14	35	.	.	PUNCT
ejpam-3708	15	1	they	they	PRON
ejpam-3708	15	2	proved	prove	VERB
ejpam-3708	15	3	that	that	SCONJ
ejpam-3708	15	4	a	a	DET
ejpam-3708	15	5	sequence	sequence	NOUN
ejpam-3708	15	6	of	of	ADP
ejpam-3708	15	7	fuzzy	fuzzy	ADJ
ejpam-3708	15	8	numbers	number	NOUN
ejpam-3708	15	9	is	be	AUX
ejpam-3708	15	10	statistically	statistically	ADV
ejpam-3708	15	11	convergent	convergent	ADJ
ejpam-3708	15	12	if	if	SCONJ
ejpam-3708	15	13	and	and	CCONJ
ejpam-3708	15	14	only	only	ADV
ejpam-3708	15	15	if	if	SCONJ
ejpam-3708	15	16	it	it	PRON
ejpam-3708	15	17	is	be	AUX
ejpam-3708	15	18	statistically	statistically	ADV
ejpam-3708	15	19	cauchy	cauchy	PROPN
ejpam-3708	15	20	.	.	PUNCT
ejpam-3708	16	1	initially	initially	ADV
ejpam-3708	16	2	the	the	DET
ejpam-3708	16	3	idea	idea	NOUN
ejpam-3708	16	4	of	of	ADP
ejpam-3708	16	5	i	i	NOUN
ejpam-3708	16	6	-	-	PUNCT
ejpam-3708	16	7	convergence	convergence	NOUN
ejpam-3708	16	8	was	be	AUX
ejpam-3708	16	9	introduced	introduce	VERB
ejpam-3708	16	10	by	by	ADP
ejpam-3708	16	11	kostyrko	kostyrko	PROPN
ejpam-3708	16	12	et	et	PROPN
ejpam-3708	16	13	al	al	PROPN
ejpam-3708	16	14	.	.	PUNCT
ejpam-3708	17	1	[	[	X
ejpam-3708	17	2	15	15	NUM
ejpam-3708	17	3	]	]	PUNCT
ejpam-3708	17	4	.	.	PUNCT
ejpam-3708	18	1	a	a	DET
ejpam-3708	18	2	lot	lot	NOUN
ejpam-3708	18	3	of	of	ADP
ejpam-3708	18	4	developments	development	NOUN
ejpam-3708	18	5	have	have	AUX
ejpam-3708	18	6	been	be	AUX
ejpam-3708	18	7	made	make	VERB
ejpam-3708	18	8	in	in	ADP
ejpam-3708	18	9	this	this	DET
ejpam-3708	18	10	area	area	NOUN
ejpam-3708	18	11	,	,	PUNCT
ejpam-3708	18	12	one	one	PRON
ejpam-3708	18	13	may	may	AUX
ejpam-3708	18	14	refer	refer	VERB
ejpam-3708	18	15	to	to	ADP
ejpam-3708	18	16	the	the	DET
ejpam-3708	18	17	articles	article	NOUN
ejpam-3708	18	18	(	(	PUNCT
ejpam-3708	18	19	see	see	VERB
ejpam-3708	18	20	[	[	X
ejpam-3708	18	21	1–4	1–4	NUM
ejpam-3708	18	22	,	,	PUNCT
ejpam-3708	18	23	10	10	NUM
ejpam-3708	18	24	,	,	PUNCT
ejpam-3708	18	25	11	11	NUM
ejpam-3708	18	26	,	,	PUNCT
ejpam-3708	18	27	16	16	NUM
ejpam-3708	18	28	,	,	PUNCT
ejpam-3708	18	29	19	19	NUM
ejpam-3708	18	30	,	,	PUNCT
ejpam-3708	18	31	23	23	NUM
ejpam-3708	18	32	,	,	PUNCT
ejpam-3708	18	33	37	37	NUM
ejpam-3708	18	34	]	]	NUM
ejpam-3708	18	35	)	)	PUNCT
ejpam-3708	18	36	.	.	PUNCT
ejpam-3708	19	1	let	let	VERB
ejpam-3708	19	2	x	x	PRON
ejpam-3708	19	3	be	be	AUX
ejpam-3708	19	4	a	a	DET
ejpam-3708	19	5	non	non	X
ejpam-3708	19	6	empty	empty	ADJ
ejpam-3708	19	7	set	set	NOUN
ejpam-3708	19	8	.	.	PUNCT
ejpam-3708	20	1	then	then	ADV
ejpam-3708	20	2	a	a	DET
ejpam-3708	20	3	family	family	NOUN
ejpam-3708	20	4	of	of	ADP
ejpam-3708	20	5	sets	set	NOUN
ejpam-3708	20	6	i	i	PRON
ejpam-3708	20	7	⊆	⊆	NUM
ejpam-3708	20	8	2x	2x	NUM
ejpam-3708	20	9	(	(	PUNCT
ejpam-3708	20	10	power	power	NOUN
ejpam-3708	20	11	set	set	NOUN
ejpam-3708	20	12	of	of	ADP
ejpam-3708	20	13	x	x	NOUN
ejpam-3708	20	14	)	)	PUNCT
ejpam-3708	20	15	is	be	AUX
ejpam-3708	20	16	said	say	VERB
ejpam-3708	20	17	to	to	PART
ejpam-3708	20	18	be	be	AUX
ejpam-3708	20	19	an	an	DET
ejpam-3708	20	20	ideal	ideal	NOUN
ejpam-3708	20	21	if	if	SCONJ
ejpam-3708	20	22	i	i	PRON
ejpam-3708	20	23	is	be	AUX
ejpam-3708	20	24	additive	additive	VERB
ejpam-3708	20	25	i.e	i.e	DET
ejpam-3708	20	26	u1	u1	NOUN
ejpam-3708	20	27	,	,	PUNCT
ejpam-3708	20	28	u2	u2	PROPN
ejpam-3708	20	29	∈	∈	PROPN
ejpam-3708	20	30	i	i	PRON
ejpam-3708	20	31	⇒	⇒	VERB
ejpam-3708	20	32	u1	u1	PROPN
ejpam-3708	20	33	∪	∪	ADP
ejpam-3708	20	34	u2	u2	PROPN
ejpam-3708	20	35	∈	∈	PROPN
ejpam-3708	20	36	i	i	PRON
ejpam-3708	20	37	and	and	CCONJ
ejpam-3708	20	38	u1	u1	PROPN
ejpam-3708	20	39	∈	∈	PROPN
ejpam-3708	21	1	i	i	PROPN
ejpam-3708	21	2	,	,	PUNCT
ejpam-3708	21	3	u2	u2	PROPN
ejpam-3708	21	4	⊆	⊆	NUM
ejpam-3708	21	5	u1	u1	NOUN
ejpam-3708	21	6	⇒	⇒	NOUN
ejpam-3708	21	7	u2	u2	PROPN
ejpam-3708	21	8	∈	∈	PROPN
ejpam-3708	21	9	i.	i.	NOUN
ejpam-3708	21	10	a	a	DET
ejpam-3708	21	11	non	non	X
ejpam-3708	21	12	empty	empty	ADJ
ejpam-3708	21	13	family	family	NOUN
ejpam-3708	21	14	of	of	ADP
ejpam-3708	21	15	sets	set	NOUN
ejpam-3708	21	16	g	g	PROPN
ejpam-3708	21	17	⊆	⊆	NUM
ejpam-3708	21	18	2x	2x	NUM
ejpam-3708	21	19	is	be	AUX
ejpam-3708	21	20	said	say	VERB
ejpam-3708	21	21	to	to	PART
ejpam-3708	21	22	be	be	AUX
ejpam-3708	21	23	filter	filter	NOUN
ejpam-3708	21	24	on	on	ADP
ejpam-3708	21	25	x	x	SYM
ejpam-3708	21	26	if	if	SCONJ
ejpam-3708	21	27	and	and	CCONJ
ejpam-3708	21	28	only	only	ADV
ejpam-3708	21	29	if	if	SCONJ
ejpam-3708	21	30	φ	φ	PROPN
ejpam-3708	21	31	/∈	/∈	VERB
ejpam-3708	22	1	g	g	NOUN
ejpam-3708	22	2	,	,	PUNCT
ejpam-3708	22	3	for	for	ADP
ejpam-3708	22	4	u1	u1	NOUN
ejpam-3708	22	5	,	,	PUNCT
ejpam-3708	22	6	u2	u2	PROPN
ejpam-3708	22	7	∈	∈	PROPN
ejpam-3708	22	8	g	g	NOUN
ejpam-3708	22	9	we	we	PRON
ejpam-3708	22	10	have	have	VERB
ejpam-3708	22	11	u1	u1	NOUN
ejpam-3708	22	12	∩	∩	NOUN
ejpam-3708	22	13	u2	u2	PROPN
ejpam-3708	22	14	∈	∈	PROPN
ejpam-3708	22	15	g	g	NOUN
ejpam-3708	22	16	and	and	CCONJ
ejpam-3708	22	17	for	for	ADP
ejpam-3708	22	18	each	each	DET
ejpam-3708	22	19	u1	u1	NOUN
ejpam-3708	22	20	∈	∈	PROPN
ejpam-3708	22	21	g	g	NOUN
ejpam-3708	22	22	and	and	CCONJ
ejpam-3708	22	23	u1	u1	VERB
ejpam-3708	22	24	⊆	⊆	NUM
ejpam-3708	22	25	u2	u2	NOUN
ejpam-3708	22	26	implies	imply	VERB
ejpam-3708	22	27	u2	u2	PROPN
ejpam-3708	22	28	∈	∈	PROPN
ejpam-3708	22	29	g.	g.	NOUN
ejpam-3708	22	30	an	an	DET
ejpam-3708	22	31	ideal	ideal	NOUN
ejpam-3708	22	32	i	i	PRON
ejpam-3708	22	33	⊆	⊆	NUM
ejpam-3708	22	34	2x	2x	NUM
ejpam-3708	22	35	is	be	AUX
ejpam-3708	22	36	called	call	VERB
ejpam-3708	22	37	non	non	ADJ
ejpam-3708	22	38	trivial	trivial	ADJ
ejpam-3708	22	39	if	if	SCONJ
ejpam-3708	22	40	i	i	PRON
ejpam-3708	22	41	6=	6=	NUM
ejpam-3708	22	42	2x	2x	NUM
ejpam-3708	22	43	.	.	PUNCT
ejpam-3708	23	1	a	a	DET
ejpam-3708	23	2	non	non	ADJ
ejpam-3708	23	3	-	-	ADJ
ejpam-3708	23	4	trivial	trivial	ADJ
ejpam-3708	23	5	ideal	ideal	NOUN
ejpam-3708	23	6	i	i	PRON
ejpam-3708	23	7	⊆	⊆	NUM
ejpam-3708	23	8	2x	2x	NUM
ejpam-3708	23	9	is	be	AUX
ejpam-3708	23	10	called	call	VERB
ejpam-3708	23	11	admissible	admissible	ADJ
ejpam-3708	23	12	if	if	SCONJ
ejpam-3708	23	13	{	{	PUNCT
ejpam-3708	23	14	{	{	PUNCT
ejpam-3708	23	15	x	x	NOUN
ejpam-3708	23	16	}	}	PUNCT
ejpam-3708	23	17	:	:	PUNCT
ejpam-3708	24	1	x	x	SYM
ejpam-3708	24	2	∈	∈	NOUN
ejpam-3708	24	3	x	x	X
ejpam-3708	24	4	}	}	PUNCT
ejpam-3708	24	5	⊆	⊆	NUM
ejpam-3708	24	6	i.	i.	NOUN
ejpam-3708	24	7	a	a	DET
ejpam-3708	24	8	non	non	ADJ
ejpam-3708	24	9	-	-	ADJ
ejpam-3708	24	10	trivial	trivial	ADJ
ejpam-3708	24	11	ideal	ideal	NOUN
ejpam-3708	24	12	is	be	AUX
ejpam-3708	24	13	maximal	maximal	ADJ
ejpam-3708	24	14	if	if	SCONJ
ejpam-3708	24	15	there	there	PRON
ejpam-3708	24	16	can	can	AUX
ejpam-3708	24	17	not	not	PART
ejpam-3708	24	18	exist	exist	VERB
ejpam-3708	24	19	any	any	DET
ejpam-3708	24	20	non	non	ADJ
ejpam-3708	24	21	-	-	ADJ
ejpam-3708	24	22	trivial	trivial	ADJ
ejpam-3708	24	23	ideal	ideal	NOUN
ejpam-3708	24	24	j	j	PROPN
ejpam-3708	25	1	6=	6=	PROPN
ejpam-3708	25	2	i	i	PRON
ejpam-3708	25	3	containing	contain	VERB
ejpam-3708	25	4	i	i	PRON
ejpam-3708	25	5	as	as	ADP
ejpam-3708	25	6	a	a	DET
ejpam-3708	25	7	subset	subset	NOUN
ejpam-3708	25	8	.	.	PUNCT
ejpam-3708	26	1	a	a	DET
ejpam-3708	26	2	fuzzy	fuzzy	ADJ
ejpam-3708	26	3	number	number	NOUN
ejpam-3708	26	4	u	u	NOUN
ejpam-3708	26	5	is	be	AUX
ejpam-3708	26	6	a	a	DET
ejpam-3708	26	7	fuzzy	fuzzy	ADJ
ejpam-3708	26	8	set	set	NOUN
ejpam-3708	26	9	[	[	X
ejpam-3708	26	10	42	42	NUM
ejpam-3708	26	11	]	]	PUNCT
ejpam-3708	26	12	on	on	ADP
ejpam-3708	26	13	the	the	DET
ejpam-3708	26	14	real	real	ADJ
ejpam-3708	26	15	axis	axis	NOUN
ejpam-3708	26	16	,	,	PUNCT
ejpam-3708	26	17	i.e.	i.e.	X
ejpam-3708	26	18	,	,	PUNCT
ejpam-3708	26	19	a	a	DET
ejpam-3708	26	20	mapping	mapping	NOUN
ejpam-3708	26	21	u	u	NOUN
ejpam-3708	26	22	:	:	PUNCT
ejpam-3708	26	23	r	r	NOUN
ejpam-3708	26	24	→	→	SYM
ejpam-3708	26	25	[	[	X
ejpam-3708	26	26	0	0	NUM
ejpam-3708	26	27	,	,	PUNCT
ejpam-3708	26	28	1	1	NUM
ejpam-3708	26	29	]	]	PUNCT
ejpam-3708	26	30	which	which	PRON
ejpam-3708	26	31	satisfies	satisfy	VERB
ejpam-3708	26	32	the	the	DET
ejpam-3708	26	33	following	follow	VERB
ejpam-3708	26	34	conditions	condition	NOUN
ejpam-3708	26	35	:	:	PUNCT
ejpam-3708	26	36	(	(	PUNCT
ejpam-3708	26	37	i	i	NOUN
ejpam-3708	26	38	)	)	PUNCT
ejpam-3708	26	39	u	u	NOUN
ejpam-3708	26	40	is	be	AUX
ejpam-3708	26	41	normal	normal	ADJ
ejpam-3708	26	42	,	,	PUNCT
ejpam-3708	26	43	i.e.	i.e.	X
ejpam-3708	26	44	,	,	PUNCT
ejpam-3708	26	45	there	there	PRON
ejpam-3708	26	46	exist	exist	VERB
ejpam-3708	26	47	an	an	DET
ejpam-3708	26	48	x0	x0	PROPN
ejpam-3708	26	49	∈	∈	PROPN
ejpam-3708	26	50	r	r	NOUN
ejpam-3708	26	51	such	such	ADJ
ejpam-3708	26	52	that	that	DET
ejpam-3708	26	53	u(x0	u(x0	NOUN
ejpam-3708	26	54	)	)	PUNCT
ejpam-3708	26	55	=	=	SYM
ejpam-3708	26	56	1	1	NUM
ejpam-3708	26	57	;	;	PUNCT
ejpam-3708	26	58	(	(	PUNCT
ejpam-3708	26	59	ii	ii	NOUN
ejpam-3708	26	60	)	)	PUNCT
ejpam-3708	26	61	u	u	NOUN
ejpam-3708	26	62	is	be	AUX
ejpam-3708	26	63	fuzzy	fuzzy	ADJ
ejpam-3708	26	64	convex	convex	NOUN
ejpam-3708	26	65	,	,	PUNCT
ejpam-3708	26	66	i.e.	i.e.	X
ejpam-3708	26	67	,	,	PUNCT
ejpam-3708	26	68	for	for	ADP
ejpam-3708	26	69	x	x	X
ejpam-3708	26	70	,	,	PUNCT
ejpam-3708	26	71	y	y	PROPN
ejpam-3708	26	72	∈	∈	PROPN
ejpam-3708	26	73	r	r	NOUN
ejpam-3708	26	74	and	and	CCONJ
ejpam-3708	26	75	0	0	NUM
ejpam-3708	26	76	≤	≤	NUM
ejpam-3708	26	77	λ	λ	X
ejpam-3708	26	78	≤	≤	NOUN
ejpam-3708	26	79	1	1	NUM
ejpam-3708	26	80	,	,	PUNCT
ejpam-3708	26	81	u(λx+(1−λ)y	u(λx+(1−λ)y	NOUN
ejpam-3708	26	82	)	)	PUNCT
ejpam-3708	26	83	≥	≥	NOUN
ejpam-3708	26	84	min[u(x	min[u(x	NOUN
ejpam-3708	26	85	)	)	PUNCT
ejpam-3708	26	86	,	,	PUNCT
ejpam-3708	26	87	u(y	u(y	PROPN
ejpam-3708	26	88	)	)	PUNCT
ejpam-3708	26	89	]	]	PUNCT
ejpam-3708	26	90	;	;	PUNCT
ejpam-3708	26	91	(	(	PUNCT
ejpam-3708	26	92	iii	iii	X
ejpam-3708	26	93	)	)	PUNCT
ejpam-3708	26	94	u	u	NOUN
ejpam-3708	26	95	is	be	AUX
ejpam-3708	26	96	upper	upper	ADJ
ejpam-3708	26	97	semi	semi	ADJ
ejpam-3708	26	98	-	-	ADJ
ejpam-3708	26	99	continuous	continuous	ADJ
ejpam-3708	26	100	;	;	PUNCT
ejpam-3708	26	101	(	(	PUNCT
ejpam-3708	26	102	iv	iv	X
ejpam-3708	26	103	)	)	PUNCT
ejpam-3708	26	104	the	the	DET
ejpam-3708	26	105	closure	closure	NOUN
ejpam-3708	26	106	of	of	ADP
ejpam-3708	26	107	the	the	DET
ejpam-3708	26	108	set	set	NOUN
ejpam-3708	26	109	supp(u	supp(u	NOUN
ejpam-3708	26	110	)	)	PUNCT
ejpam-3708	26	111	is	be	AUX
ejpam-3708	26	112	compact	compact	ADJ
ejpam-3708	26	113	,	,	PUNCT
ejpam-3708	26	114	where	where	SCONJ
ejpam-3708	26	115	supp(u	supp(u	ADJ
ejpam-3708	26	116	)	)	PUNCT
ejpam-3708	26	117	=	=	SYM
ejpam-3708	27	1	{	{	PUNCT
ejpam-3708	27	2	x	x	PUNCT
ejpam-3708	27	3	∈	∈	PROPN
ejpam-3708	27	4	r	r	NOUN
ejpam-3708	27	5	:	:	PUNCT
ejpam-3708	27	6	u(x	u(x	PROPN
ejpam-3708	27	7	)	)	PUNCT
ejpam-3708	27	8	>	>	X
ejpam-3708	27	9	0	0	NUM
ejpam-3708	27	10	}	}	PUNCT
ejpam-3708	27	11	and	and	CCONJ
ejpam-3708	27	12	it	it	PRON
ejpam-3708	27	13	is	be	AUX
ejpam-3708	27	14	denoted	denote	VERB
ejpam-3708	27	15	by	by	ADP
ejpam-3708	27	16	[	[	X
ejpam-3708	27	17	u]0	u]0	NOUN
ejpam-3708	27	18	.	.	PUNCT
ejpam-3708	28	1	let	let	AUX
ejpam-3708	28	2	l(r	l(r	PROPN
ejpam-3708	28	3	)	)	PUNCT
ejpam-3708	28	4	denotes	denote	VERB
ejpam-3708	28	5	the	the	DET
ejpam-3708	28	6	set	set	NOUN
ejpam-3708	28	7	of	of	ADP
ejpam-3708	28	8	all	all	DET
ejpam-3708	28	9	fuzzy	fuzzy	ADJ
ejpam-3708	28	10	numbers	number	NOUN
ejpam-3708	28	11	.	.	PUNCT
ejpam-3708	29	1	the	the	DET
ejpam-3708	29	2	α	α	NOUN
ejpam-3708	29	3	-	-	PUNCT
ejpam-3708	29	4	level	level	NOUN
ejpam-3708	29	5	set	set	NOUN
ejpam-3708	29	6	of	of	ADP
ejpam-3708	29	7	a	a	DET
ejpam-3708	29	8	fuzzy	fuzzy	ADJ
ejpam-3708	29	9	real	real	ADJ
ejpam-3708	29	10	number	number	NOUN
ejpam-3708	29	11	u	u	NOUN
ejpam-3708	29	12	,	,	PUNCT
ejpam-3708	29	13	for	for	ADP
ejpam-3708	29	14	0	0	NUM
ejpam-3708	29	15	<	<	X
ejpam-3708	29	16	α	α	PROPN
ejpam-3708	29	17	≤	≤	ADV
ejpam-3708	29	18	1	1	NUM
ejpam-3708	29	19	denoted	denote	VERB
ejpam-3708	29	20	by	by	ADP
ejpam-3708	29	21	uα	uα	PROPN
ejpam-3708	29	22	is	be	AUX
ejpam-3708	29	23	defined	define	VERB
ejpam-3708	29	24	as	as	ADP
ejpam-3708	29	25	[	[	X
ejpam-3708	29	26	u]α	u]α	X
ejpam-3708	29	27	=	=	SYM
ejpam-3708	29	28	{	{	PUNCT
ejpam-3708	29	29	x	x	SYM
ejpam-3708	29	30	∈	∈	PROPN
ejpam-3708	29	31	r	r	NOUN
ejpam-3708	29	32	:	:	PUNCT
ejpam-3708	29	33	u(x	u(x	PROPN
ejpam-3708	29	34	)	)	PUNCT
ejpam-3708	29	35	≥	≥	NOUN
ejpam-3708	29	36	α	α	NOUN
ejpam-3708	29	37	}	}	PUNCT
ejpam-3708	29	38	,	,	PUNCT
ejpam-3708	29	39	for	for	ADP
ejpam-3708	29	40	α	α	NOUN
ejpam-3708	29	41	=	=	SYM
ejpam-3708	29	42	0	0	NUM
ejpam-3708	30	1	it	it	PRON
ejpam-3708	30	2	is	be	AUX
ejpam-3708	30	3	the	the	DET
ejpam-3708	30	4	closure	closure	NOUN
ejpam-3708	30	5	of	of	ADP
ejpam-3708	30	6	the	the	DET
ejpam-3708	30	7	strong	strong	ADJ
ejpam-3708	30	8	0	0	NUM
ejpam-3708	30	9	cut	cut	NOUN
ejpam-3708	30	10	(	(	PUNCT
ejpam-3708	30	11	i.e.	i.e.	X
ejpam-3708	30	12	closure	closure	NOUN
ejpam-3708	30	13	of	of	ADP
ejpam-3708	30	14	the	the	DET
ejpam-3708	30	15	set	set	NOUN
ejpam-3708	30	16	{	{	PUNCT
ejpam-3708	30	17	t	t	NOUN
ejpam-3708	30	18	∈	∈	PROPN
ejpam-3708	30	19	r	r	NOUN
ejpam-3708	30	20	:	:	PUNCT
ejpam-3708	30	21	u(t	u(t	NOUN
ejpam-3708	30	22	)	)	PUNCT
ejpam-3708	30	23	>	>	X
ejpam-3708	30	24	0	0	NUM
ejpam-3708	30	25	}	}	PUNCT
ejpam-3708	30	26	)	)	PUNCT
ejpam-3708	30	27	.	.	PUNCT
ejpam-3708	31	1	for	for	ADP
ejpam-3708	31	2	each	each	DET
ejpam-3708	31	3	r	r	NOUN
ejpam-3708	31	4	∈	∈	NOUN
ejpam-3708	31	5	r	r	NOUN
ejpam-3708	31	6	,	,	PUNCT
ejpam-3708	31	7	r	r	NOUN
ejpam-3708	31	8	∈	∈	NOUN
ejpam-3708	31	9	l(r	l(r	PROPN
ejpam-3708	31	10	)	)	PUNCT
ejpam-3708	31	11	is	be	AUX
ejpam-3708	31	12	defined	define	VERB
ejpam-3708	31	13	by	by	ADP
ejpam-3708	31	14	r̄(t	r̄(t	PROPN
ejpam-3708	31	15	)	)	PUNCT
ejpam-3708	32	1	=	=	PRON
ejpam-3708	32	2	{	{	PUNCT
ejpam-3708	32	3	1	1	NUM
ejpam-3708	32	4	,	,	PUNCT
ejpam-3708	32	5	if	if	SCONJ
ejpam-3708	32	6	t	t	NOUN
ejpam-3708	32	7	=	=	SYM
ejpam-3708	32	8	r	r	NOUN
ejpam-3708	32	9	;	;	PUNCT
ejpam-3708	32	10	0	0	NUM
ejpam-3708	32	11	,	,	PUNCT
ejpam-3708	32	12	if	if	SCONJ
ejpam-3708	32	13	t	t	PROPN
ejpam-3708	32	14	6=	6=	PRON
ejpam-3708	32	15	0	0	X
ejpam-3708	32	16	.	.	PUNCT
ejpam-3708	32	17	define	define	VERB
ejpam-3708	32	18	a	a	DET
ejpam-3708	32	19	map	map	NOUN
ejpam-3708	33	1	d	d	NOUN
ejpam-3708	33	2	:	:	PUNCT
ejpam-3708	33	3	l(r)×	l(r)×	INTJ
ejpam-3708	33	4	l(r)→	l(r)→	NUM
ejpam-3708	33	5	r	r	NOUN
ejpam-3708	33	6	by	by	ADP
ejpam-3708	33	7	d(x	d(x	PROPN
ejpam-3708	33	8	,	,	PUNCT
ejpam-3708	33	9	y	y	NOUN
ejpam-3708	33	10	)	)	PUNCT
ejpam-3708	33	11	=	=	SYM
ejpam-3708	33	12	sup	sup	NOUN
ejpam-3708	33	13	α∈[0,1	α∈[0,1	PROPN
ejpam-3708	33	14	]	]	X
ejpam-3708	33	15	{	{	PUNCT
ejpam-3708	33	16	max{|uα1	max{|uα1	PROPN
ejpam-3708	33	17	−	−	NOUN
ejpam-3708	34	1	vα1	vα1	NOUN
ejpam-3708	34	2	|	|	NOUN
ejpam-3708	34	3	,	,	PUNCT
ejpam-3708	34	4	|uα2	|uα2	PROPN
ejpam-3708	34	5	−	−	NOUN
ejpam-3708	34	6	vα2	vα2	NOUN
ejpam-3708	34	7	|	|	NOUN
ejpam-3708	34	8	}	}	PUNCT
ejpam-3708	34	9	}	}	PUNCT
ejpam-3708	34	10	,	,	PUNCT
ejpam-3708	34	11	where	where	SCONJ
ejpam-3708	34	12	uα	uα	NOUN
ejpam-3708	34	13	=	=	PUNCT
ejpam-3708	35	1	[	[	X
ejpam-3708	35	2	uα1	uα1	NOUN
ejpam-3708	35	3	,	,	PUNCT
ejpam-3708	35	4	u	u	NOUN
ejpam-3708	35	5	α	α	NOUN
ejpam-3708	35	6	2	2	NUM
ejpam-3708	35	7	]	]	PUNCT
ejpam-3708	35	8	and	and	CCONJ
ejpam-3708	35	9	vα	vα	X
ejpam-3708	35	10	=	=	PUNCT
ejpam-3708	36	1	[	[	X
ejpam-3708	36	2	vα1	vα1	NOUN
ejpam-3708	36	3	,	,	PUNCT
ejpam-3708	36	4	v	v	ADP
ejpam-3708	36	5	α	α	NOUN
ejpam-3708	36	6	2	2	NUM
ejpam-3708	36	7	]	]	PUNCT
ejpam-3708	36	8	.	.	PUNCT
ejpam-3708	37	1	in	in	ADP
ejpam-3708	37	2	this	this	DET
ejpam-3708	37	3	case	case	NOUN
ejpam-3708	37	4	,	,	PUNCT
ejpam-3708	37	5	(	(	PUNCT
ejpam-3708	37	6	l(r	l(r	PROPN
ejpam-3708	37	7	)	)	PUNCT
ejpam-3708	37	8	,	,	PUNCT
ejpam-3708	37	9	d	d	X
ejpam-3708	37	10	)	)	PUNCT
ejpam-3708	37	11	is	be	AUX
ejpam-3708	37	12	a	a	DET
ejpam-3708	37	13	complete	complete	ADJ
ejpam-3708	37	14	metric	metric	ADJ
ejpam-3708	37	15	space	space	NOUN
ejpam-3708	37	16	.	.	PUNCT
ejpam-3708	38	1	the	the	DET
ejpam-3708	38	2	additive	additive	ADJ
ejpam-3708	38	3	identity	identity	NOUN
ejpam-3708	38	4	and	and	CCONJ
ejpam-3708	38	5	multiplicative	multiplicative	ADJ
ejpam-3708	38	6	identity	identity	NOUN
ejpam-3708	38	7	in	in	ADP
ejpam-3708	38	8	l(r	l(r	PROPN
ejpam-3708	38	9	)	)	PUNCT
ejpam-3708	38	10	are	be	AUX
ejpam-3708	38	11	denoted	denote	VERB
ejpam-3708	38	12	by	by	ADP
ejpam-3708	38	13	0	0	NUM
ejpam-3708	38	14	and	and	CCONJ
ejpam-3708	38	15	1	1	NUM
ejpam-3708	38	16	,	,	PUNCT
ejpam-3708	38	17	respectively	respectively	ADV
ejpam-3708	38	18	.	.	PUNCT
ejpam-3708	39	1	an	an	DET
ejpam-3708	39	2	orlicz	orlicz	ADJ
ejpam-3708	39	3	function	function	NOUN
ejpam-3708	39	4	m	m	VERB
ejpam-3708	39	5	:	:	PUNCT
ejpam-3708	40	1	[	[	X
ejpam-3708	40	2	0,∞	0,∞	NOUN
ejpam-3708	40	3	)	)	PUNCT
ejpam-3708	40	4	→	→	PUNCT
ejpam-3708	41	1	[	[	X
ejpam-3708	41	2	0,∞	0,∞	NUM
ejpam-3708	41	3	)	)	PUNCT
ejpam-3708	41	4	is	be	AUX
ejpam-3708	41	5	convex	convex	ADJ
ejpam-3708	41	6	,	,	PUNCT
ejpam-3708	41	7	continuous	continuous	ADJ
ejpam-3708	41	8	and	and	CCONJ
ejpam-3708	41	9	non	non	ADJ
ejpam-3708	41	10	-	-	ADJ
ejpam-3708	41	11	decreasing	decrease	VERB
ejpam-3708	41	12	function	function	NOUN
ejpam-3708	41	13	which	which	PRON
ejpam-3708	41	14	also	also	ADV
ejpam-3708	41	15	satisfy	satisfy	VERB
ejpam-3708	41	16	m(0	m(0	PROPN
ejpam-3708	41	17	)	)	PUNCT
ejpam-3708	41	18	=	=	SYM
ejpam-3708	41	19	0	0	NUM
ejpam-3708	41	20	,	,	PUNCT
ejpam-3708	41	21	m(x	m(x	PROPN
ejpam-3708	41	22	)	)	PUNCT
ejpam-3708	41	23	>	>	X
ejpam-3708	41	24	0	0	PUNCT
ejpam-3708	42	1	for	for	ADP
ejpam-3708	42	2	x	x	PUNCT
ejpam-3708	42	3	>	>	X
ejpam-3708	42	4	0	0	NUM
ejpam-3708	42	5	and	and	CCONJ
ejpam-3708	42	6	m(x	m(x	NOUN
ejpam-3708	42	7	)	)	PUNCT
ejpam-3708	42	8	→	→	SYM
ejpam-3708	42	9	∞	∞	PROPN
ejpam-3708	42	10	as	as	ADP
ejpam-3708	42	11	x	x	X
ejpam-3708	42	12	→	→	SYM
ejpam-3708	42	13	∞.	∞.	PROPN
ejpam-3708	42	14	if	if	SCONJ
ejpam-3708	42	15	convexity	convexity	NOUN
ejpam-3708	42	16	of	of	ADP
ejpam-3708	42	17	orlicz	orlicz	ADJ
ejpam-3708	42	18	function	function	NOUN
ejpam-3708	42	19	is	be	AUX
ejpam-3708	42	20	replaced	replace	VERB
ejpam-3708	42	21	by	by	ADP
ejpam-3708	42	22	m(x+	m(x+	NUM
ejpam-3708	42	23	y	y	PROPN
ejpam-3708	42	24	)	)	PUNCT
ejpam-3708	42	25	≤	≤	NOUN
ejpam-3708	42	26	m(x	m(x	PROPN
ejpam-3708	42	27	)	)	PUNCT
ejpam-3708	42	28	+	+	NOUN
ejpam-3708	42	29	m(y	m(y	NOUN
ejpam-3708	42	30	)	)	PUNCT
ejpam-3708	42	31	,	,	PUNCT
ejpam-3708	42	32	then	then	ADV
ejpam-3708	42	33	this	this	DET
ejpam-3708	42	34	function	function	NOUN
ejpam-3708	42	35	is	be	AUX
ejpam-3708	42	36	called	call	VERB
ejpam-3708	42	37	the	the	DET
ejpam-3708	42	38	modulus	modulus	ADJ
ejpam-3708	42	39	function	function	NOUN
ejpam-3708	42	40	and	and	CCONJ
ejpam-3708	42	41	characterized	characterize	VERB
ejpam-3708	42	42	by	by	ADP
ejpam-3708	42	43	nakano	nakano	PROPN
ejpam-3708	42	44	[	[	X
ejpam-3708	42	45	27	27	NUM
ejpam-3708	42	46	]	]	PUNCT
ejpam-3708	42	47	and	and	CCONJ
ejpam-3708	42	48	followed	follow	VERB
ejpam-3708	42	49	by	by	ADP
ejpam-3708	42	50	ruckle	ruckle	NOUN
ejpam-3708	42	51	[	[	X
ejpam-3708	42	52	33	33	NUM
ejpam-3708	42	53	]	]	PUNCT
ejpam-3708	42	54	and	and	CCONJ
ejpam-3708	42	55	others	other	NOUN
ejpam-3708	42	56	.	.	PUNCT
ejpam-3708	43	1	an	an	DET
ejpam-3708	43	2	orlicz	orlicz	ADJ
ejpam-3708	43	3	function	function	NOUN
ejpam-3708	43	4	m	m	VERB
ejpam-3708	43	5	is	be	AUX
ejpam-3708	43	6	said	say	VERB
ejpam-3708	43	7	to	to	PART
ejpam-3708	43	8	satisfy	satisfy	VERB
ejpam-3708	43	9	∆2	∆2	NOUN
ejpam-3708	43	10	-	-	NOUN
ejpam-3708	43	11	condition	condition	NOUN
ejpam-3708	43	12	for	for	ADP
ejpam-3708	43	13	all	all	DET
ejpam-3708	43	14	values	value	NOUN
ejpam-3708	43	15	of	of	ADP
ejpam-3708	43	16	u	u	PROPN
ejpam-3708	43	17	,	,	PUNCT
ejpam-3708	43	18	k.	k.	PROPN
ejpam-3708	43	19	raj	raj	PROPN
ejpam-3708	43	20	,	,	PUNCT
ejpam-3708	43	21	s.	s.	PROPN
ejpam-3708	43	22	a.	a.	PROPN
ejpam-3708	43	23	mohiuddine	mohiuddine	PROPN
ejpam-3708	43	24	/	/	SYM
ejpam-3708	43	25	eur	eur	PROPN
ejpam-3708	43	26	.	.	PUNCT
ejpam-3708	44	1	j.	j.	PROPN
ejpam-3708	44	2	pure	pure	PROPN
ejpam-3708	44	3	appl	appl	PROPN
ejpam-3708	44	4	.	.	PROPN
ejpam-3708	44	5	math	math	PROPN
ejpam-3708	44	6	,	,	PUNCT
ejpam-3708	44	7	13	13	NUM
ejpam-3708	44	8	(	(	PUNCT
ejpam-3708	44	9	5	5	NUM
ejpam-3708	44	10	)	)	PUNCT
ejpam-3708	44	11	(	(	PUNCT
ejpam-3708	44	12	2020	2020	NUM
ejpam-3708	44	13	)	)	PUNCT
ejpam-3708	44	14	,	,	PUNCT
ejpam-3708	44	15	1131	1131	NUM
ejpam-3708	44	16	-	-	SYM
ejpam-3708	44	17	1148	1148	NUM
ejpam-3708	44	18	1133	1133	NUM
ejpam-3708	44	19	if	if	SCONJ
ejpam-3708	44	20	there	there	PRON
ejpam-3708	44	21	exists	exist	VERB
ejpam-3708	44	22	r	r	NOUN
ejpam-3708	44	23	>	>	X
ejpam-3708	44	24	0	0	NUM
ejpam-3708	44	25	such	such	ADJ
ejpam-3708	44	26	that	that	SCONJ
ejpam-3708	44	27	m(2u	m(2u	VERB
ejpam-3708	44	28	)	)	PUNCT
ejpam-3708	44	29	≤	≤	NOUN
ejpam-3708	44	30	rm(u	rm(u	X
ejpam-3708	44	31	)	)	PUNCT
ejpam-3708	44	32	,	,	PUNCT
ejpam-3708	44	33	u	u	NOUN
ejpam-3708	44	34	≥	≥	NOUN
ejpam-3708	44	35	0	0	NUM
ejpam-3708	44	36	.	.	PUNCT
ejpam-3708	45	1	lindenstrauss	lindenstrauss	ADJ
ejpam-3708	45	2	and	and	CCONJ
ejpam-3708	45	3	tzafriri	tzafriri	NOUN
ejpam-3708	46	1	[	[	X
ejpam-3708	46	2	17	17	NUM
ejpam-3708	46	3	]	]	PUNCT
ejpam-3708	46	4	used	use	VERB
ejpam-3708	46	5	the	the	DET
ejpam-3708	46	6	idea	idea	NOUN
ejpam-3708	46	7	of	of	ADP
ejpam-3708	46	8	orlicz	orlicz	ADJ
ejpam-3708	46	9	function	function	NOUN
ejpam-3708	46	10	to	to	PART
ejpam-3708	46	11	define	define	VERB
ejpam-3708	46	12	the	the	DET
ejpam-3708	46	13	following	follow	VERB
ejpam-3708	46	14	sequence	sequence	NOUN
ejpam-3708	46	15	space	space	NOUN
ejpam-3708	46	16	`	`	PUNCT
ejpam-3708	46	17	m	m	NOUN
ejpam-3708	46	18	=	=	PRON
ejpam-3708	46	19	{	{	PUNCT
ejpam-3708	46	20	x	x	PUNCT
ejpam-3708	46	21	∈	∈	PROPN
ejpam-3708	46	22	w	w	NOUN
ejpam-3708	46	23	:	:	PUNCT
ejpam-3708	46	24	∞∑	∞∑	NUM
ejpam-3708	47	1	k=1	k=1	PUNCT
ejpam-3708	47	2	m	m	INTJ
ejpam-3708	47	3	(	(	PUNCT
ejpam-3708	47	4	|xk|	|xk|	PROPN
ejpam-3708	47	5	ρ	ρ	PROPN
ejpam-3708	47	6	)	)	PUNCT
ejpam-3708	47	7	<	<	X
ejpam-3708	47	8	∞	∞	PROPN
ejpam-3708	47	9	,	,	PUNCT
ejpam-3708	47	10	for	for	ADP
ejpam-3708	47	11	some	some	DET
ejpam-3708	47	12	ρ	ρ	NOUN
ejpam-3708	47	13	>	>	X
ejpam-3708	47	14	0	0	NUM
ejpam-3708	47	15	}	}	PUNCT
ejpam-3708	47	16	which	which	PRON
ejpam-3708	47	17	is	be	AUX
ejpam-3708	47	18	called	call	VERB
ejpam-3708	47	19	as	as	ADP
ejpam-3708	47	20	an	an	DET
ejpam-3708	47	21	orlicz	orlicz	ADJ
ejpam-3708	47	22	sequence	sequence	NOUN
ejpam-3708	47	23	space	space	NOUN
ejpam-3708	47	24	.	.	PUNCT
ejpam-3708	48	1	the	the	DET
ejpam-3708	48	2	space	space	NOUN
ejpam-3708	48	3	`	`	PUNCT
ejpam-3708	48	4	m	m	NOUN
ejpam-3708	48	5	is	be	AUX
ejpam-3708	48	6	a	a	DET
ejpam-3708	48	7	banach	banach	NOUN
ejpam-3708	48	8	space	space	NOUN
ejpam-3708	48	9	with	with	ADP
ejpam-3708	48	10	the	the	DET
ejpam-3708	48	11	norm	norm	NOUN
ejpam-3708	48	12	||x||	||x||	NOUN
ejpam-3708	48	13	=	=	SYM
ejpam-3708	48	14	inf	inf	NOUN
ejpam-3708	48	15	{	{	PUNCT
ejpam-3708	48	16	ρ	ρ	PROPN
ejpam-3708	48	17	>	>	X
ejpam-3708	48	18	0	0	NUM
ejpam-3708	48	19	:	:	PUNCT
ejpam-3708	49	1	∞∑	∞∑	NUM
ejpam-3708	49	2	k=1	k=1	VERB
ejpam-3708	49	3	m	m	INTJ
ejpam-3708	49	4	(	(	PUNCT
ejpam-3708	49	5	|xk|	|xk|	PROPN
ejpam-3708	49	6	ρ	ρ	PROPN
ejpam-3708	49	7	)	)	PUNCT
ejpam-3708	49	8	≤	≤	NUM
ejpam-3708	49	9	1	1	NUM
ejpam-3708	49	10	}	}	PUNCT
ejpam-3708	49	11	.	.	PUNCT
ejpam-3708	50	1	an	an	DET
ejpam-3708	50	2	increasing	increase	VERB
ejpam-3708	50	3	non	non	ADJ
ejpam-3708	50	4	-	-	ADJ
ejpam-3708	50	5	negative	negative	ADJ
ejpam-3708	50	6	integer	integer	NOUN
ejpam-3708	50	7	sequence	sequence	NOUN
ejpam-3708	50	8	θ	θ	PROPN
ejpam-3708	50	9	=	=	SYM
ejpam-3708	50	10	(	(	PUNCT
ejpam-3708	50	11	ir	ir	NOUN
ejpam-3708	50	12	)	)	PUNCT
ejpam-3708	50	13	with	with	ADP
ejpam-3708	50	14	i0	i0	PROPN
ejpam-3708	50	15	=	=	SYM
ejpam-3708	50	16	0	0	NUM
ejpam-3708	50	17	and	and	CCONJ
ejpam-3708	50	18	hr	hr	NOUN
ejpam-3708	50	19	=	=	PUNCT
ejpam-3708	50	20	(	(	PUNCT
ejpam-3708	50	21	ir−ir−1)→	ir−ir−1)→	PROPN
ejpam-3708	50	22	∞	∞	NOUN
ejpam-3708	50	23	as	as	SCONJ
ejpam-3708	50	24	r	r	NOUN
ejpam-3708	50	25	→	→	SYM
ejpam-3708	50	26	∞	∞	PROPN
ejpam-3708	50	27	is	be	AUX
ejpam-3708	50	28	known	know	VERB
ejpam-3708	50	29	as	as	ADP
ejpam-3708	50	30	lacunary	lacunary	ADJ
ejpam-3708	50	31	sequence	sequence	NOUN
ejpam-3708	50	32	.	.	PUNCT
ejpam-3708	51	1	the	the	DET
ejpam-3708	51	2	intervals	interval	NOUN
ejpam-3708	51	3	determined	determine	VERB
ejpam-3708	51	4	by	by	ADP
ejpam-3708	51	5	θ	θ	PROPN
ejpam-3708	51	6	are	be	AUX
ejpam-3708	51	7	denoted	denote	VERB
ejpam-3708	51	8	by	by	ADP
ejpam-3708	51	9	ir	ir	PROPN
ejpam-3708	51	10	=	=	SYM
ejpam-3708	51	11	(	(	PUNCT
ejpam-3708	51	12	ir−1	ir−1	PROPN
ejpam-3708	51	13	,	,	PUNCT
ejpam-3708	51	14	ir	ir	PROPN
ejpam-3708	51	15	]	]	X
ejpam-3708	51	16	and	and	CCONJ
ejpam-3708	51	17	the	the	DET
ejpam-3708	51	18	ratio	ratio	NOUN
ejpam-3708	51	19	ir	ir	PROPN
ejpam-3708	51	20	/	/	AUX
ejpam-3708	51	21	ir−1	ir−1	PROPN
ejpam-3708	51	22	will	will	AUX
ejpam-3708	51	23	be	be	AUX
ejpam-3708	51	24	denoted	denote	VERB
ejpam-3708	51	25	by	by	ADP
ejpam-3708	51	26	qr	qr	PROPN
ejpam-3708	51	27	.	.	PUNCT
ejpam-3708	52	1	freedman	freedman	PROPN
ejpam-3708	52	2	et	et	PROPN
ejpam-3708	52	3	al	al	PROPN
ejpam-3708	52	4	.	.	PUNCT
ejpam-3708	53	1	[	[	X
ejpam-3708	53	2	7	7	X
ejpam-3708	53	3	]	]	PUNCT
ejpam-3708	53	4	defined	define	VERB
ejpam-3708	53	5	the	the	DET
ejpam-3708	53	6	space	space	NOUN
ejpam-3708	53	7	nθ	nθ	NOUN
ejpam-3708	53	8	in	in	ADP
ejpam-3708	53	9	the	the	DET
ejpam-3708	53	10	following	following	ADJ
ejpam-3708	53	11	way	way	NOUN
ejpam-3708	53	12	:	:	PUNCT
ejpam-3708	53	13	nθ	nθ	NOUN
ejpam-3708	53	14	=	=	PRON
ejpam-3708	53	15	{	{	PUNCT
ejpam-3708	53	16	x	x	SYM
ejpam-3708	53	17	=	=	SYM
ejpam-3708	53	18	(	(	PUNCT
ejpam-3708	53	19	xk	xk	PROPN
ejpam-3708	53	20	)	)	PUNCT
ejpam-3708	53	21	:	:	PUNCT
ejpam-3708	54	1	lim	lim	PROPN
ejpam-3708	54	2	r→∞	r→∞	PUNCT
ejpam-3708	54	3	1	1	NUM
ejpam-3708	54	4	hr	hr	NOUN
ejpam-3708	54	5	∑	∑	PUNCT
ejpam-3708	54	6	k∈ir	k∈ir	PROPN
ejpam-3708	54	7	|xk	|xk	NUM
ejpam-3708	54	8	−	−	NOUN
ejpam-3708	54	9	l|	l|	ADJ
ejpam-3708	54	10	=	=	X
ejpam-3708	54	11	0	0	NUM
ejpam-3708	54	12	for	for	ADP
ejpam-3708	54	13	some	some	DET
ejpam-3708	54	14	l	l	NOUN
ejpam-3708	54	15	}	}	PUNCT
ejpam-3708	54	16	.	.	PUNCT
ejpam-3708	55	1	fridy	fridy	ADJ
ejpam-3708	55	2	and	and	CCONJ
ejpam-3708	55	3	orhan	orhan	PROPN
ejpam-3708	56	1	[	[	X
ejpam-3708	56	2	8	8	NUM
ejpam-3708	56	3	]	]	PUNCT
ejpam-3708	56	4	defined	define	VERB
ejpam-3708	56	5	and	and	CCONJ
ejpam-3708	56	6	studied	study	VERB
ejpam-3708	56	7	the	the	DET
ejpam-3708	56	8	idea	idea	NOUN
ejpam-3708	56	9	of	of	ADP
ejpam-3708	56	10	lacunary	lacunary	ADJ
ejpam-3708	56	11	statistical	statistical	NOUN
ejpam-3708	56	12	for	for	ADP
ejpam-3708	56	13	sequence	sequence	NOUN
ejpam-3708	56	14	of	of	ADP
ejpam-3708	56	15	real	real	ADJ
ejpam-3708	56	16	number	number	NOUN
ejpam-3708	56	17	.	.	PUNCT
ejpam-3708	57	1	nuray	nuray	PROPN
ejpam-3708	58	1	[	[	X
ejpam-3708	58	2	29	29	NUM
ejpam-3708	58	3	]	]	PUNCT
ejpam-3708	58	4	and	and	CCONJ
ejpam-3708	58	5	mursaleen	mursaleen	NOUN
ejpam-3708	58	6	and	and	CCONJ
ejpam-3708	58	7	mohiuddine	mohiuddine	NOUN
ejpam-3708	58	8	[	[	X
ejpam-3708	58	9	25	25	NUM
ejpam-3708	58	10	]	]	PUNCT
ejpam-3708	58	11	defined	define	VERB
ejpam-3708	58	12	this	this	DET
ejpam-3708	58	13	notion	notion	NOUN
ejpam-3708	58	14	,	,	PUNCT
ejpam-3708	58	15	respectively	respectively	ADV
ejpam-3708	58	16	,	,	PUNCT
ejpam-3708	58	17	for	for	ADP
ejpam-3708	58	18	sequences	sequence	NOUN
ejpam-3708	58	19	of	of	ADP
ejpam-3708	58	20	fuzzy	fuzzy	ADJ
ejpam-3708	58	21	numbers	number	NOUN
ejpam-3708	58	22	and	and	CCONJ
ejpam-3708	58	23	in	in	ADP
ejpam-3708	58	24	the	the	DET
ejpam-3708	58	25	setting	setting	NOUN
ejpam-3708	58	26	of	of	ADP
ejpam-3708	58	27	intuitionistic	intuitionistic	ADJ
ejpam-3708	58	28	fuzzy	fuzzy	ADJ
ejpam-3708	58	29	normed	normed	ADJ
ejpam-3708	58	30	space	space	NOUN
ejpam-3708	58	31	.	.	PUNCT
ejpam-3708	59	1	most	most	ADV
ejpam-3708	59	2	recently	recently	ADV
ejpam-3708	59	3	,	,	PUNCT
ejpam-3708	59	4	mohiuddine	mohiuddine	NOUN
ejpam-3708	59	5	and	and	CCONJ
ejpam-3708	59	6	alamri	alamri	ADJ
ejpam-3708	59	7	[	[	X
ejpam-3708	59	8	20	20	NUM
ejpam-3708	59	9	]	]	PUNCT
ejpam-3708	59	10	defined	define	VERB
ejpam-3708	59	11	the	the	DET
ejpam-3708	59	12	notion	notion	NOUN
ejpam-3708	59	13	of	of	ADP
ejpam-3708	59	14	weighted	weight	VERB
ejpam-3708	59	15	lacunary	lacunary	ADJ
ejpam-3708	59	16	equistatistical	equistatistical	ADJ
ejpam-3708	59	17	convergence	convergence	NOUN
ejpam-3708	59	18	and	and	CCONJ
ejpam-3708	59	19	,	,	PUNCT
ejpam-3708	59	20	as	as	ADP
ejpam-3708	59	21	an	an	DET
ejpam-3708	59	22	application	application	NOUN
ejpam-3708	59	23	,	,	PUNCT
ejpam-3708	59	24	proved	prove	VERB
ejpam-3708	59	25	some	some	DET
ejpam-3708	59	26	approximation	approximation	NOUN
ejpam-3708	59	27	theorems	theorem	NOUN
ejpam-3708	59	28	.	.	PUNCT
ejpam-3708	60	1	in	in	ADP
ejpam-3708	60	2	[	[	X
ejpam-3708	60	3	14	14	NUM
ejpam-3708	60	4	]	]	X
ejpam-3708	60	5	kızmaz	kızmaz	NOUN
ejpam-3708	60	6	introduced	introduce	VERB
ejpam-3708	60	7	the	the	DET
ejpam-3708	60	8	notion	notion	NOUN
ejpam-3708	60	9	of	of	ADP
ejpam-3708	60	10	difference	difference	NOUN
ejpam-3708	60	11	sequence	sequence	NOUN
ejpam-3708	60	12	spaces	space	NOUN
ejpam-3708	60	13	and	and	CCONJ
ejpam-3708	60	14	studied	study	VERB
ejpam-3708	60	15	`	`	PUNCT
ejpam-3708	60	16	∞(∆	∞(∆	NOUN
ejpam-3708	60	17	)	)	PUNCT
ejpam-3708	60	18	,	,	PUNCT
ejpam-3708	60	19	c(∆	c(∆	PROPN
ejpam-3708	60	20	)	)	PUNCT
ejpam-3708	60	21	and	and	CCONJ
ejpam-3708	60	22	c0(∆	c0(∆	PROPN
ejpam-3708	60	23	)	)	PUNCT
ejpam-3708	60	24	which	which	PRON
ejpam-3708	60	25	has	have	AUX
ejpam-3708	60	26	been	be	AUX
ejpam-3708	60	27	recently	recently	ADV
ejpam-3708	60	28	used	use	VERB
ejpam-3708	60	29	to	to	PART
ejpam-3708	60	30	define	define	VERB
ejpam-3708	60	31	statistical	statistical	ADJ
ejpam-3708	60	32	convergence	convergence	NOUN
ejpam-3708	60	33	[	[	X
ejpam-3708	60	34	12	12	NUM
ejpam-3708	60	35	,	,	PUNCT
ejpam-3708	60	36	21	21	NUM
ejpam-3708	60	37	]	]	PUNCT
ejpam-3708	60	38	.	.	PUNCT
ejpam-3708	61	1	further	far	ADV
ejpam-3708	61	2	this	this	DET
ejpam-3708	61	3	notion	notion	NOUN
ejpam-3708	61	4	was	be	AUX
ejpam-3708	61	5	generalized	generalize	VERB
ejpam-3708	61	6	by	by	ADP
ejpam-3708	61	7	et	et	NOUN
ejpam-3708	61	8	and	and	CCONJ
ejpam-3708	61	9	çolak	çolak	VERB
ejpam-3708	62	1	[	[	X
ejpam-3708	62	2	6	6	NUM
ejpam-3708	62	3	]	]	PUNCT
ejpam-3708	62	4	by	by	ADP
ejpam-3708	62	5	introducing	introduce	VERB
ejpam-3708	62	6	the	the	DET
ejpam-3708	62	7	spaces	space	NOUN
ejpam-3708	62	8	`	`	PUNCT
ejpam-3708	62	9	∞(∆m	∞(∆m	NOUN
ejpam-3708	62	10	)	)	PUNCT
ejpam-3708	62	11	,	,	PUNCT
ejpam-3708	62	12	c(∆m	c(∆m	NOUN
ejpam-3708	62	13	)	)	PUNCT
ejpam-3708	62	14	and	and	CCONJ
ejpam-3708	62	15	c0(∆m	c0(∆m	ADJ
ejpam-3708	62	16	)	)	PUNCT
ejpam-3708	62	17	.	.	PUNCT
ejpam-3708	63	1	later	later	ADV
ejpam-3708	63	2	on	on	ADV
ejpam-3708	63	3	,	,	PUNCT
ejpam-3708	63	4	another	another	DET
ejpam-3708	63	5	type	type	NOUN
ejpam-3708	63	6	of	of	ADP
ejpam-3708	63	7	generalization	generalization	NOUN
ejpam-3708	63	8	of	of	ADP
ejpam-3708	63	9	the	the	DET
ejpam-3708	63	10	difference	difference	NOUN
ejpam-3708	63	11	sequence	sequence	NOUN
ejpam-3708	63	12	spaces	space	NOUN
ejpam-3708	63	13	is	be	AUX
ejpam-3708	63	14	due	due	ADJ
ejpam-3708	63	15	to	to	ADP
ejpam-3708	63	16	tripathy	tripathy	NOUN
ejpam-3708	63	17	and	and	CCONJ
ejpam-3708	63	18	esi	esi	NOUN
ejpam-3708	64	1	[	[	X
ejpam-3708	64	2	39	39	NUM
ejpam-3708	64	3	]	]	PUNCT
ejpam-3708	64	4	who	who	PRON
ejpam-3708	64	5	studied	study	VERB
ejpam-3708	64	6	the	the	DET
ejpam-3708	64	7	spaces	space	NOUN
ejpam-3708	64	8	`	`	PUNCT
ejpam-3708	64	9	∞(∆ν	∞(∆ν	NOUN
ejpam-3708	64	10	)	)	PUNCT
ejpam-3708	64	11	,	,	PUNCT
ejpam-3708	64	12	c(∆ν	c(∆ν	NOUN
ejpam-3708	64	13	)	)	PUNCT
ejpam-3708	64	14	and	and	CCONJ
ejpam-3708	64	15	c0(∆ν	c0(∆ν	PROPN
ejpam-3708	64	16	)	)	PUNCT
ejpam-3708	64	17	.	.	PUNCT
ejpam-3708	65	1	recently	recently	ADV
ejpam-3708	65	2	,	,	PUNCT
ejpam-3708	65	3	esi	esi	PROPN
ejpam-3708	65	4	et	et	PROPN
ejpam-3708	65	5	al	al	PROPN
ejpam-3708	65	6	.	.	PUNCT
ejpam-3708	66	1	[	[	X
ejpam-3708	66	2	5	5	NUM
ejpam-3708	66	3	]	]	PUNCT
ejpam-3708	66	4	and	and	CCONJ
ejpam-3708	66	5	tripathy	tripathy	NOUN
ejpam-3708	66	6	et	et	PROPN
ejpam-3708	66	7	al	al	PROPN
ejpam-3708	66	8	.	.	PUNCT
ejpam-3708	67	1	[	[	X
ejpam-3708	67	2	40	40	NUM
ejpam-3708	67	3	]	]	PUNCT
ejpam-3708	67	4	have	have	AUX
ejpam-3708	67	5	introduced	introduce	VERB
ejpam-3708	67	6	a	a	DET
ejpam-3708	67	7	new	new	ADJ
ejpam-3708	67	8	type	type	NOUN
ejpam-3708	67	9	of	of	ADP
ejpam-3708	67	10	generalized	generalized	ADJ
ejpam-3708	67	11	difference	difference	NOUN
ejpam-3708	67	12	operators	operator	NOUN
ejpam-3708	67	13	and	and	CCONJ
ejpam-3708	67	14	unified	unify	VERB
ejpam-3708	67	15	those	those	PRON
ejpam-3708	67	16	as	as	SCONJ
ejpam-3708	67	17	follows	follow	VERB
ejpam-3708	67	18	:	:	PUNCT
ejpam-3708	67	19	let	let	VERB
ejpam-3708	67	20	ν	ν	NOUN
ejpam-3708	67	21	,	,	PUNCT
ejpam-3708	67	22	m	m	VERB
ejpam-3708	67	23	be	be	VERB
ejpam-3708	67	24	non	non	ADJ
ejpam-3708	67	25	-	-	ADJ
ejpam-3708	67	26	negative	negative	ADJ
ejpam-3708	67	27	integers	integer	NOUN
ejpam-3708	67	28	,	,	PUNCT
ejpam-3708	67	29	then	then	ADV
ejpam-3708	67	30	for	for	ADP
ejpam-3708	67	31	z	z	PROPN
ejpam-3708	67	32	a	a	DET
ejpam-3708	67	33	given	give	VERB
ejpam-3708	67	34	sequence	sequence	NOUN
ejpam-3708	67	35	space	space	NOUN
ejpam-3708	67	36	,	,	PUNCT
ejpam-3708	67	37	we	we	PRON
ejpam-3708	67	38	have	have	VERB
ejpam-3708	67	39	z(∆m	z(∆m	ADJ
ejpam-3708	67	40	ν	ν	NOUN
ejpam-3708	67	41	)	)	PUNCT
ejpam-3708	68	1	=	=	PUNCT
ejpam-3708	68	2	{	{	PUNCT
ejpam-3708	68	3	x	x	SYM
ejpam-3708	68	4	=	=	SYM
ejpam-3708	68	5	(	(	PUNCT
ejpam-3708	68	6	xk	xk	ADJ
ejpam-3708	68	7	)	)	PUNCT
ejpam-3708	68	8	∈	∈	PROPN
ejpam-3708	68	9	w	w	NOUN
ejpam-3708	68	10	:	:	PUNCT
ejpam-3708	68	11	(	(	PUNCT
ejpam-3708	68	12	∆m	∆m	PROPN
ejpam-3708	68	13	ν	ν	PROPN
ejpam-3708	68	14	xk	xk	PROPN
ejpam-3708	68	15	)	)	PUNCT
ejpam-3708	68	16	∈	∈	PROPN
ejpam-3708	69	1	z	z	PROPN
ejpam-3708	69	2	}	}	PUNCT
ejpam-3708	69	3	for	for	ADP
ejpam-3708	69	4	z	z	NOUN
ejpam-3708	69	5	=	=	SYM
ejpam-3708	69	6	c	c	X
ejpam-3708	69	7	,	,	PUNCT
ejpam-3708	69	8	c0	c0	NOUN
ejpam-3708	69	9	and	and	CCONJ
ejpam-3708	69	10	`	`	PUNCT
ejpam-3708	69	11	∞	∞	PROPN
ejpam-3708	69	12	where	where	SCONJ
ejpam-3708	69	13	∆m	∆m	PROPN
ejpam-3708	69	14	ν	ν	X
ejpam-3708	69	15	x	x	SYM
ejpam-3708	69	16	=	=	SYM
ejpam-3708	69	17	(	(	PUNCT
ejpam-3708	69	18	∆m	∆m	PROPN
ejpam-3708	69	19	ν	ν	PROPN
ejpam-3708	69	20	xk	xk	PROPN
ejpam-3708	69	21	)	)	PUNCT
ejpam-3708	69	22	=	=	SYM
ejpam-3708	69	23	(	(	PUNCT
ejpam-3708	69	24	∆m−1	∆m−1	X
ejpam-3708	69	25	ν	ν	PROPN
ejpam-3708	69	26	xk	xk	PROPN
ejpam-3708	69	27	−∆m−1	−∆m−1	PROPN
ejpam-3708	69	28	ν	ν	PROPN
ejpam-3708	69	29	xk+1	xk+1	NUM
ejpam-3708	69	30	)	)	PUNCT
ejpam-3708	69	31	and	and	CCONJ
ejpam-3708	69	32	∆0	∆0	NUM
ejpam-3708	69	33	νxk	νxk	NOUN
ejpam-3708	69	34	=	=	SYM
ejpam-3708	69	35	xk	xk	PROPN
ejpam-3708	69	36	for	for	ADP
ejpam-3708	69	37	all	all	DET
ejpam-3708	69	38	k	k	PROPN
ejpam-3708	69	39	∈	∈	PROPN
ejpam-3708	69	40	n	n	CCONJ
ejpam-3708	69	41	,	,	PUNCT
ejpam-3708	69	42	which	which	PRON
ejpam-3708	69	43	is	be	AUX
ejpam-3708	69	44	equivalent	equivalent	ADJ
ejpam-3708	69	45	to	to	ADP
ejpam-3708	69	46	the	the	DET
ejpam-3708	69	47	following	follow	VERB
ejpam-3708	69	48	binomial	binomial	ADJ
ejpam-3708	69	49	representation	representation	NOUN
ejpam-3708	70	1	∆m	∆m	PROPN
ejpam-3708	70	2	ν	ν	X
ejpam-3708	70	3	xk	xk	X
ejpam-3708	70	4	=	=	PUNCT
ejpam-3708	70	5	m∑	m∑	NOUN
ejpam-3708	70	6	i=0	i=0	PROPN
ejpam-3708	70	7	(	(	PUNCT
ejpam-3708	70	8	−1)i	−1)i	X
ejpam-3708	70	9	(	(	PUNCT
ejpam-3708	70	10	m	m	VERB
ejpam-3708	70	11	i	i	NOUN
ejpam-3708	70	12	)	)	PUNCT
ejpam-3708	70	13	xk+νi	xk+νi	PROPN
ejpam-3708	70	14	.	.	PUNCT
ejpam-3708	71	1	taking	take	VERB
ejpam-3708	71	2	ν	ν	NOUN
ejpam-3708	71	3	=	=	SYM
ejpam-3708	71	4	1	1	NUM
ejpam-3708	71	5	,	,	PUNCT
ejpam-3708	71	6	we	we	PRON
ejpam-3708	71	7	get	get	VERB
ejpam-3708	71	8	the	the	DET
ejpam-3708	71	9	spaces	space	NOUN
ejpam-3708	71	10	`	`	PUNCT
ejpam-3708	71	11	∞(∆m	∞(∆m	NOUN
ejpam-3708	71	12	)	)	PUNCT
ejpam-3708	71	13	,	,	PUNCT
ejpam-3708	71	14	c(∆m	c(∆m	NOUN
ejpam-3708	71	15	)	)	PUNCT
ejpam-3708	71	16	and	and	CCONJ
ejpam-3708	71	17	c0(∆m	c0(∆m	PROPN
ejpam-3708	71	18	)	)	PUNCT
ejpam-3708	71	19	studied	study	VERB
ejpam-3708	71	20	by	by	ADP
ejpam-3708	71	21	et	et	NOUN
ejpam-3708	71	22	and	and	CCONJ
ejpam-3708	71	23	çolak	çolak	VERB
ejpam-3708	72	1	[	[	X
ejpam-3708	72	2	6	6	NUM
ejpam-3708	72	3	]	]	PUNCT
ejpam-3708	72	4	.	.	PUNCT
ejpam-3708	73	1	taking	take	VERB
ejpam-3708	73	2	m	m	NOUN
ejpam-3708	73	3	=	=	PUNCT
ejpam-3708	73	4	ν	ν	NOUN
ejpam-3708	73	5	=	=	SYM
ejpam-3708	73	6	1	1	NUM
ejpam-3708	73	7	,	,	PUNCT
ejpam-3708	73	8	we	we	PRON
ejpam-3708	73	9	get	get	VERB
ejpam-3708	73	10	the	the	DET
ejpam-3708	73	11	spaces	space	NOUN
ejpam-3708	73	12	`	`	PUNCT
ejpam-3708	73	13	∞(∆	∞(∆	NOUN
ejpam-3708	73	14	)	)	PUNCT
ejpam-3708	73	15	,	,	PUNCT
ejpam-3708	73	16	c(∆	c(∆	PROPN
ejpam-3708	73	17	)	)	PUNCT
ejpam-3708	73	18	and	and	CCONJ
ejpam-3708	73	19	c0(∆	c0(∆	NOUN
ejpam-3708	73	20	)	)	PUNCT
ejpam-3708	73	21	introduced	introduce	VERB
ejpam-3708	73	22	and	and	CCONJ
ejpam-3708	73	23	studied	study	VERB
ejpam-3708	73	24	by	by	ADP
ejpam-3708	73	25	kızmaz	kızmaz	NOUN
ejpam-3708	74	1	[	[	X
ejpam-3708	74	2	14	14	NUM
ejpam-3708	74	3	]	]	PUNCT
ejpam-3708	74	4	.	.	PUNCT
ejpam-3708	75	1	for	for	ADP
ejpam-3708	75	2	more	more	ADJ
ejpam-3708	75	3	details	detail	NOUN
ejpam-3708	75	4	about	about	ADP
ejpam-3708	75	5	sequence	sequence	NOUN
ejpam-3708	75	6	spaces	space	NOUN
ejpam-3708	75	7	(	(	PUNCT
ejpam-3708	75	8	see	see	VERB
ejpam-3708	75	9	[	[	X
ejpam-3708	75	10	9	9	NUM
ejpam-3708	75	11	,	,	PUNCT
ejpam-3708	75	12	31	31	NUM
ejpam-3708	75	13	,	,	PUNCT
ejpam-3708	75	14	32	32	NUM
ejpam-3708	75	15	,	,	PUNCT
ejpam-3708	75	16	34	34	NUM
ejpam-3708	75	17	,	,	PUNCT
ejpam-3708	75	18	36	36	NUM
ejpam-3708	75	19	,	,	PUNCT
ejpam-3708	75	20	38	38	NUM
ejpam-3708	75	21	,	,	PUNCT
ejpam-3708	75	22	41	41	NUM
ejpam-3708	75	23	]	]	PUNCT
ejpam-3708	75	24	)	)	PUNCT
ejpam-3708	75	25	and	and	CCONJ
ejpam-3708	75	26	references	reference	NOUN
ejpam-3708	75	27	therein	therein	ADV
ejpam-3708	75	28	.	.	PUNCT
ejpam-3708	76	1	k.	k.	PROPN
ejpam-3708	76	2	raj	raj	PROPN
ejpam-3708	76	3	,	,	PUNCT
ejpam-3708	76	4	s.	s.	PROPN
ejpam-3708	76	5	a.	a.	PROPN
ejpam-3708	76	6	mohiuddine	mohiuddine	PROPN
ejpam-3708	76	7	/	/	SYM
ejpam-3708	76	8	eur	eur	PROPN
ejpam-3708	76	9	.	.	PUNCT
ejpam-3708	77	1	j.	j.	PROPN
ejpam-3708	77	2	pure	pure	PROPN
ejpam-3708	77	3	appl	appl	PROPN
ejpam-3708	77	4	.	.	PROPN
ejpam-3708	77	5	math	math	PROPN
ejpam-3708	77	6	,	,	PUNCT
ejpam-3708	77	7	13	13	NUM
ejpam-3708	77	8	(	(	PUNCT
ejpam-3708	77	9	5	5	NUM
ejpam-3708	77	10	)	)	PUNCT
ejpam-3708	77	11	(	(	PUNCT
ejpam-3708	77	12	2020	2020	NUM
ejpam-3708	77	13	)	)	PUNCT
ejpam-3708	77	14	,	,	PUNCT
ejpam-3708	77	15	1131	1131	NUM
ejpam-3708	77	16	-	-	SYM
ejpam-3708	77	17	1148	1148	NUM
ejpam-3708	77	18	1134	1134	NUM
ejpam-3708	77	19	let	let	VERB
ejpam-3708	77	20	λ	λ	PROPN
ejpam-3708	77	21	and	and	CCONJ
ejpam-3708	77	22	η	η	PROPN
ejpam-3708	77	23	be	be	VERB
ejpam-3708	77	24	two	two	NUM
ejpam-3708	77	25	sequence	sequence	NOUN
ejpam-3708	77	26	spaces	space	NOUN
ejpam-3708	77	27	and	and	CCONJ
ejpam-3708	77	28	a	a	DET
ejpam-3708	77	29	=	=	SYM
ejpam-3708	77	30	(	(	PUNCT
ejpam-3708	77	31	ank	ank	PROPN
ejpam-3708	77	32	)	)	PUNCT
ejpam-3708	77	33	be	be	VERB
ejpam-3708	77	34	an	an	DET
ejpam-3708	77	35	infinite	infinite	ADJ
ejpam-3708	77	36	matrix	matrix	NOUN
ejpam-3708	77	37	of	of	ADP
ejpam-3708	77	38	real	real	ADJ
ejpam-3708	77	39	or	or	CCONJ
ejpam-3708	77	40	complex	complex	ADJ
ejpam-3708	77	41	numbers	number	NOUN
ejpam-3708	77	42	ank	ank	PROPN
ejpam-3708	77	43	,	,	PUNCT
ejpam-3708	77	44	where	where	SCONJ
ejpam-3708	77	45	n	n	X
ejpam-3708	77	46	,	,	PUNCT
ejpam-3708	77	47	k	k	PROPN
ejpam-3708	77	48	∈	∈	PROPN
ejpam-3708	77	49	n.	n.	NOUN
ejpam-3708	77	50	then	then	ADV
ejpam-3708	77	51	we	we	PRON
ejpam-3708	77	52	say	say	VERB
ejpam-3708	77	53	that	that	SCONJ
ejpam-3708	77	54	a	a	DET
ejpam-3708	77	55	defines	define	VERB
ejpam-3708	77	56	a	a	DET
ejpam-3708	77	57	matrix	matrix	NOUN
ejpam-3708	77	58	mapping	mapping	NOUN
ejpam-3708	77	59	from	from	ADP
ejpam-3708	77	60	λ	λ	PROPN
ejpam-3708	77	61	into	into	ADP
ejpam-3708	77	62	η	η	PROPN
ejpam-3708	77	63	if	if	SCONJ
ejpam-3708	77	64	for	for	ADP
ejpam-3708	77	65	every	every	DET
ejpam-3708	77	66	sequence	sequence	NOUN
ejpam-3708	77	67	x	x	PUNCT
ejpam-3708	78	1	=	=	SYM
ejpam-3708	78	2	(	(	PUNCT
ejpam-3708	78	3	xk	xk	PROPN
ejpam-3708	78	4	)	)	PUNCT
ejpam-3708	78	5	∞	∞	NUM
ejpam-3708	78	6	k=0	k=0	PROPN
ejpam-3708	78	7	∈	∈	PROPN
ejpam-3708	78	8	λ	λ	PROPN
ejpam-3708	78	9	,	,	PUNCT
ejpam-3708	78	10	the	the	DET
ejpam-3708	78	11	sequence	sequence	NOUN
ejpam-3708	78	12	ax	ax	NOUN
ejpam-3708	78	13	=	=	PUNCT
ejpam-3708	78	14	{	{	PUNCT
ejpam-3708	78	15	an(x)}∞n=0	an(x)}∞n=0	VERB
ejpam-3708	78	16	,	,	PUNCT
ejpam-3708	78	17	the	the	DET
ejpam-3708	78	18	a	a	DET
ejpam-3708	78	19	-	-	PUNCT
ejpam-3708	78	20	transform	transform	NOUN
ejpam-3708	78	21	of	of	ADP
ejpam-3708	78	22	x	x	NOUN
ejpam-3708	78	23	,	,	PUNCT
ejpam-3708	78	24	is	be	AUX
ejpam-3708	78	25	in	in	ADP
ejpam-3708	78	26	η	η	PROPN
ejpam-3708	78	27	,	,	PUNCT
ejpam-3708	78	28	where	where	SCONJ
ejpam-3708	78	29	an(x	an(x	VERB
ejpam-3708	78	30	)	)	PUNCT
ejpam-3708	78	31	=	=	SYM
ejpam-3708	79	1	∞∑	∞∑	NUM
ejpam-3708	79	2	k=0	k=0	PROPN
ejpam-3708	79	3	ankxk	ankxk	VERB
ejpam-3708	79	4	(	(	PUNCT
ejpam-3708	79	5	n	n	CCONJ
ejpam-3708	79	6	∈	∈	PROPN
ejpam-3708	79	7	n	n	CCONJ
ejpam-3708	79	8	)	)	PUNCT
ejpam-3708	79	9	.	.	PUNCT
ejpam-3708	80	1	(	(	PUNCT
ejpam-3708	80	2	1	1	X
ejpam-3708	80	3	)	)	PUNCT
ejpam-3708	80	4	by	by	ADP
ejpam-3708	80	5	(	(	PUNCT
ejpam-3708	80	6	λ	λ	PROPN
ejpam-3708	80	7	,	,	PUNCT
ejpam-3708	80	8	η	η	NOUN
ejpam-3708	80	9	)	)	PUNCT
ejpam-3708	80	10	,	,	PUNCT
ejpam-3708	80	11	we	we	PRON
ejpam-3708	80	12	denote	denote	VERB
ejpam-3708	80	13	the	the	DET
ejpam-3708	80	14	class	class	NOUN
ejpam-3708	80	15	of	of	ADP
ejpam-3708	80	16	all	all	DET
ejpam-3708	80	17	matrices	matrix	NOUN
ejpam-3708	80	18	a	a	DET
ejpam-3708	80	19	such	such	ADJ
ejpam-3708	80	20	that	that	SCONJ
ejpam-3708	80	21	a	a	DET
ejpam-3708	80	22	:	:	PUNCT
ejpam-3708	80	23	λ	λ	PROPN
ejpam-3708	80	24	→	→	SYM
ejpam-3708	80	25	η	η	PROPN
ejpam-3708	80	26	.	.	PROPN
ejpam-3708	80	27	thus	thus	ADV
ejpam-3708	80	28	,	,	PUNCT
ejpam-3708	80	29	a	a	DET
ejpam-3708	80	30	∈	∈	PROPN
ejpam-3708	80	31	(	(	PUNCT
ejpam-3708	80	32	λ	λ	PROPN
ejpam-3708	80	33	,	,	PUNCT
ejpam-3708	80	34	η	η	NOUN
ejpam-3708	80	35	)	)	PUNCT
ejpam-3708	80	36	if	if	SCONJ
ejpam-3708	80	37	and	and	CCONJ
ejpam-3708	80	38	only	only	ADV
ejpam-3708	80	39	if	if	SCONJ
ejpam-3708	80	40	the	the	DET
ejpam-3708	80	41	series	series	NOUN
ejpam-3708	80	42	on	on	ADP
ejpam-3708	80	43	the	the	DET
ejpam-3708	80	44	right	right	ADJ
ejpam-3708	80	45	-	-	PUNCT
ejpam-3708	80	46	hand	hand	NOUN
ejpam-3708	80	47	side	side	NOUN
ejpam-3708	80	48	of	of	ADP
ejpam-3708	80	49	(	(	PUNCT
ejpam-3708	80	50	1.1	1.1	NUM
ejpam-3708	80	51	)	)	PUNCT
ejpam-3708	80	52	converges	converge	NOUN
ejpam-3708	80	53	for	for	ADP
ejpam-3708	80	54	each	each	DET
ejpam-3708	80	55	n	n	PRON
ejpam-3708	80	56	∈	∈	PROPN
ejpam-3708	80	57	n	n	NOUN
ejpam-3708	80	58	and	and	CCONJ
ejpam-3708	80	59	every	every	DET
ejpam-3708	80	60	x	x	PROPN
ejpam-3708	80	61	∈	∈	PROPN
ejpam-3708	80	62	λ	λ	PROPN
ejpam-3708	80	63	.	.	PUNCT
ejpam-3708	81	1	the	the	DET
ejpam-3708	81	2	matrix	matrix	NOUN
ejpam-3708	81	3	domain	domain	NOUN
ejpam-3708	81	4	λa	λa	NOUN
ejpam-3708	81	5	of	of	ADP
ejpam-3708	81	6	an	an	DET
ejpam-3708	81	7	infinite	infinite	ADJ
ejpam-3708	81	8	matrix	matrix	NOUN
ejpam-3708	81	9	a	a	PRON
ejpam-3708	81	10	in	in	ADP
ejpam-3708	81	11	a	a	DET
ejpam-3708	81	12	sequence	sequence	NOUN
ejpam-3708	81	13	space	space	NOUN
ejpam-3708	81	14	λ	λ	PROPN
ejpam-3708	81	15	is	be	AUX
ejpam-3708	81	16	defined	define	VERB
ejpam-3708	81	17	by	by	ADP
ejpam-3708	81	18	λa	λa	NOUN
ejpam-3708	81	19	=	=	PUNCT
ejpam-3708	82	1	{	{	PUNCT
ejpam-3708	82	2	x	x	SYM
ejpam-3708	82	3	=	=	SYM
ejpam-3708	82	4	(	(	PUNCT
ejpam-3708	82	5	xk	xk	PROPN
ejpam-3708	82	6	)	)	PUNCT
ejpam-3708	82	7	:	:	PUNCT
ejpam-3708	82	8	ax	ax	NOUN
ejpam-3708	82	9	∈	∈	PROPN
ejpam-3708	82	10	λ	λ	PROPN
ejpam-3708	82	11	}	}	PUNCT
ejpam-3708	82	12	.	.	PUNCT
ejpam-3708	83	1	(	(	PUNCT
ejpam-3708	83	2	2	2	X
ejpam-3708	83	3	)	)	PUNCT
ejpam-3708	83	4	the	the	DET
ejpam-3708	83	5	approach	approach	NOUN
ejpam-3708	83	6	constructing	construct	VERB
ejpam-3708	83	7	a	a	DET
ejpam-3708	83	8	new	new	ADJ
ejpam-3708	83	9	sequence	sequence	NOUN
ejpam-3708	83	10	space	space	NOUN
ejpam-3708	83	11	by	by	ADP
ejpam-3708	83	12	means	mean	NOUN
ejpam-3708	83	13	of	of	ADP
ejpam-3708	83	14	the	the	DET
ejpam-3708	83	15	matrix	matrix	NOUN
ejpam-3708	83	16	domain	domain	NOUN
ejpam-3708	83	17	of	of	ADP
ejpam-3708	83	18	a	a	DET
ejpam-3708	83	19	particular	particular	ADJ
ejpam-3708	83	20	limitation	limitation	NOUN
ejpam-3708	83	21	method	method	NOUN
ejpam-3708	83	22	has	have	AUX
ejpam-3708	83	23	recently	recently	ADV
ejpam-3708	83	24	been	be	AUX
ejpam-3708	83	25	employed	employ	VERB
ejpam-3708	83	26	by	by	ADP
ejpam-3708	83	27	several	several	ADJ
ejpam-3708	83	28	authors	author	NOUN
ejpam-3708	83	29	(	(	PUNCT
ejpam-3708	83	30	see	see	VERB
ejpam-3708	83	31	[	[	X
ejpam-3708	83	32	35	35	NUM
ejpam-3708	83	33	]	]	SYM
ejpam-3708	83	34	)	)	PUNCT
ejpam-3708	83	35	.	.	PUNCT
ejpam-3708	84	1	kumar	kumar	PROPN
ejpam-3708	84	2	and	and	CCONJ
ejpam-3708	84	3	kumar	kumar	PROPN
ejpam-3708	85	1	[	[	X
ejpam-3708	85	2	16	16	NUM
ejpam-3708	85	3	]	]	PUNCT
ejpam-3708	85	4	defined	define	VERB
ejpam-3708	85	5	the	the	DET
ejpam-3708	85	6	notion	notion	NOUN
ejpam-3708	85	7	of	of	ADP
ejpam-3708	85	8	ideal	ideal	NOUN
ejpam-3708	85	9	(	(	PUNCT
ejpam-3708	85	10	or	or	CCONJ
ejpam-3708	85	11	,	,	PUNCT
ejpam-3708	85	12	i-	i-	X
ejpam-3708	85	13	)	)	PUNCT
ejpam-3708	85	14	convergence	convergence	NOUN
ejpam-3708	85	15	for	for	ADP
ejpam-3708	85	16	sequence	sequence	NOUN
ejpam-3708	85	17	of	of	ADP
ejpam-3708	85	18	fuzzy	fuzzy	ADJ
ejpam-3708	85	19	numbers	number	NOUN
ejpam-3708	85	20	and	and	CCONJ
ejpam-3708	85	21	recently	recently	ADV
ejpam-3708	85	22	studied	study	VERB
ejpam-3708	85	23	by	by	ADP
ejpam-3708	85	24	mursaleen	mursaleen	NOUN
ejpam-3708	85	25	and	and	CCONJ
ejpam-3708	85	26	mohiuddine	mohiuddine	NOUN
ejpam-3708	86	1	[	[	X
ejpam-3708	86	2	26	26	NUM
ejpam-3708	86	3	]	]	PUNCT
ejpam-3708	86	4	in	in	ADP
ejpam-3708	86	5	probabilistic	probabilistic	ADJ
ejpam-3708	86	6	normed	norme	VERB
ejpam-3708	86	7	spaces	space	NOUN
ejpam-3708	86	8	(	(	PUNCT
ejpam-3708	86	9	see	see	VERB
ejpam-3708	86	10	also	also	ADV
ejpam-3708	86	11	[	[	X
ejpam-3708	86	12	22	22	NUM
ejpam-3708	86	13	]	]	SYM
ejpam-3708	86	14	)	)	PUNCT
ejpam-3708	86	15	.	.	PUNCT
ejpam-3708	87	1	definition	definition	NOUN
ejpam-3708	87	2	1	1	NUM
ejpam-3708	87	3	.	.	PUNCT
ejpam-3708	88	1	a	a	DET
ejpam-3708	88	2	sequence	sequence	NOUN
ejpam-3708	88	3	x	x	PUNCT
ejpam-3708	88	4	=	=	SYM
ejpam-3708	88	5	(	(	PUNCT
ejpam-3708	88	6	xk	xk	NOUN
ejpam-3708	88	7	)	)	PUNCT
ejpam-3708	88	8	of	of	ADP
ejpam-3708	88	9	fuzzy	fuzzy	ADJ
ejpam-3708	88	10	numbers	number	NOUN
ejpam-3708	88	11	is	be	AUX
ejpam-3708	88	12	said	say	VERB
ejpam-3708	88	13	to	to	PART
ejpam-3708	88	14	be	be	AUX
ejpam-3708	88	15	i	i	NOUN
ejpam-3708	88	16	-	-	NOUN
ejpam-3708	88	17	convergent	convergent	ADJ
ejpam-3708	88	18	to	to	ADP
ejpam-3708	88	19	a	a	DET
ejpam-3708	88	20	fuzzy	fuzzy	ADJ
ejpam-3708	88	21	number	number	NOUN
ejpam-3708	88	22	x0	x0	PROPN
ejpam-3708	88	23	,	,	PUNCT
ejpam-3708	88	24	if	if	SCONJ
ejpam-3708	88	25	for	for	ADP
ejpam-3708	88	26	every	every	DET
ejpam-3708	88	27	ε	ε	PROPN
ejpam-3708	88	28	>	>	X
ejpam-3708	88	29	0	0	NUM
ejpam-3708	88	30	such	such	ADJ
ejpam-3708	88	31	that	that	SCONJ
ejpam-3708	88	32	{	{	PUNCT
ejpam-3708	88	33	k	k	PROPN
ejpam-3708	88	34	∈	∈	PROPN
ejpam-3708	88	35	n	n	CCONJ
ejpam-3708	88	36	:	:	PUNCT
ejpam-3708	88	37	d(xk	d(xk	PROPN
ejpam-3708	88	38	,	,	PUNCT
ejpam-3708	88	39	x0	x0	PROPN
ejpam-3708	88	40	)	)	PUNCT
ejpam-3708	88	41	≥	≥	X
ejpam-3708	88	42	ε	ε	PROPN
ejpam-3708	88	43	}	}	PUNCT
ejpam-3708	88	44	∈	∈	PROPN
ejpam-3708	88	45	i.	i.	NOUN
ejpam-3708	88	46	the	the	DET
ejpam-3708	88	47	fuzzy	fuzzy	ADJ
ejpam-3708	88	48	number	number	NOUN
ejpam-3708	88	49	x0	x0	PROPN
ejpam-3708	88	50	is	be	AUX
ejpam-3708	88	51	called	call	VERB
ejpam-3708	88	52	i	i	PRON
ejpam-3708	88	53	-	-	PUNCT
ejpam-3708	88	54	limit	limit	NOUN
ejpam-3708	88	55	of	of	ADP
ejpam-3708	88	56	the	the	DET
ejpam-3708	88	57	sequence	sequence	NOUN
ejpam-3708	88	58	(	(	PUNCT
ejpam-3708	88	59	xk	xk	NOUN
ejpam-3708	88	60	)	)	PUNCT
ejpam-3708	88	61	of	of	ADP
ejpam-3708	88	62	fuzzy	fuzzy	ADJ
ejpam-3708	88	63	numbers	number	NOUN
ejpam-3708	88	64	and	and	CCONJ
ejpam-3708	88	65	we	we	PRON
ejpam-3708	88	66	write	write	VERB
ejpam-3708	88	67	ilimxk	ilimxk	PROPN
ejpam-3708	89	1	=	=	PUNCT
ejpam-3708	89	2	x0	x0	PROPN
ejpam-3708	89	3	.	.	PUNCT
ejpam-3708	90	1	definition	definition	NOUN
ejpam-3708	90	2	2	2	NUM
ejpam-3708	90	3	.	.	PUNCT
ejpam-3708	91	1	a	a	DET
ejpam-3708	91	2	sequence	sequence	NOUN
ejpam-3708	91	3	x	x	PUNCT
ejpam-3708	91	4	=	=	SYM
ejpam-3708	91	5	(	(	PUNCT
ejpam-3708	91	6	xk	xk	NOUN
ejpam-3708	91	7	)	)	PUNCT
ejpam-3708	91	8	of	of	ADP
ejpam-3708	91	9	fuzzy	fuzzy	ADJ
ejpam-3708	91	10	numbers	number	NOUN
ejpam-3708	91	11	is	be	AUX
ejpam-3708	91	12	said	say	VERB
ejpam-3708	91	13	to	to	PART
ejpam-3708	91	14	be	be	AUX
ejpam-3708	91	15	i	i	PRON
ejpam-3708	91	16	-	-	PUNCT
ejpam-3708	91	17	bounded	bound	VERB
ejpam-3708	91	18	if	if	SCONJ
ejpam-3708	91	19	there	there	PRON
ejpam-3708	91	20	exists	exist	VERB
ejpam-3708	91	21	m	m	VERB
ejpam-3708	91	22	>	>	X
ejpam-3708	91	23	0	0	NUM
ejpam-3708	91	24	such	such	ADJ
ejpam-3708	91	25	that	that	SCONJ
ejpam-3708	91	26	{	{	PUNCT
ejpam-3708	91	27	k	k	PROPN
ejpam-3708	91	28	∈	∈	PROPN
ejpam-3708	91	29	n	n	CCONJ
ejpam-3708	91	30	:	:	PUNCT
ejpam-3708	91	31	d(xk	d(xk	PROPN
ejpam-3708	91	32	,	,	PUNCT
ejpam-3708	91	33	0	0	NUM
ejpam-3708	91	34	)	)	PUNCT
ejpam-3708	91	35	>	>	X
ejpam-3708	91	36	m	m	VERB
ejpam-3708	91	37	}	}	PUNCT
ejpam-3708	91	38	∈	∈	PROPN
ejpam-3708	91	39	i.	i.	NOUN
ejpam-3708	91	40	definition	definition	NOUN
ejpam-3708	91	41	3	3	X
ejpam-3708	91	42	.	.	PUNCT
ejpam-3708	92	1	let	let	VERB
ejpam-3708	92	2	θ	θ	PROPN
ejpam-3708	92	3	=	=	SYM
ejpam-3708	92	4	(	(	PUNCT
ejpam-3708	92	5	kr	kr	PROPN
ejpam-3708	92	6	)	)	PUNCT
ejpam-3708	92	7	be	be	AUX
ejpam-3708	92	8	lacunary	lacunary	ADJ
ejpam-3708	92	9	sequence	sequence	NOUN
ejpam-3708	92	10	.	.	PUNCT
ejpam-3708	93	1	then	then	ADV
ejpam-3708	93	2	a	a	DET
ejpam-3708	93	3	sequence	sequence	NOUN
ejpam-3708	93	4	(	(	PUNCT
ejpam-3708	93	5	xk	xk	NOUN
ejpam-3708	93	6	)	)	PUNCT
ejpam-3708	93	7	of	of	ADP
ejpam-3708	93	8	fuzzy	fuzzy	ADJ
ejpam-3708	93	9	numbers	number	NOUN
ejpam-3708	93	10	is	be	AUX
ejpam-3708	93	11	said	say	VERB
ejpam-3708	93	12	to	to	PART
ejpam-3708	93	13	be	be	AUX
ejpam-3708	93	14	lacunary	lacunary	ADJ
ejpam-3708	93	15	i	i	NOUN
ejpam-3708	93	16	-	-	PUNCT
ejpam-3708	93	17	convergent	convergent	NOUN
ejpam-3708	93	18	if	if	SCONJ
ejpam-3708	93	19	for	for	ADP
ejpam-3708	93	20	every	every	DET
ejpam-3708	93	21	ε	ε	PROPN
ejpam-3708	93	22	>	>	X
ejpam-3708	93	23	0	0	NUM
ejpam-3708	93	24	such	such	ADJ
ejpam-3708	93	25	that	that	SCONJ
ejpam-3708	93	26	{	{	PUNCT
ejpam-3708	93	27	r	r	NOUN
ejpam-3708	93	28	∈	∈	NOUN
ejpam-3708	93	29	n	n	NOUN
ejpam-3708	93	30	:	:	PUNCT
ejpam-3708	93	31	1	1	NUM
ejpam-3708	93	32	hr	hr	NOUN
ejpam-3708	93	33	∑	∑	PUNCT
ejpam-3708	93	34	k∈ir	k∈ir	PROPN
ejpam-3708	93	35	d(xk	d(xk	PROPN
ejpam-3708	93	36	,	,	PUNCT
ejpam-3708	93	37	x	x	NOUN
ejpam-3708	93	38	)	)	PUNCT
ejpam-3708	93	39	≥	≥	NOUN
ejpam-3708	93	40	ε	ε	PROPN
ejpam-3708	93	41	}	}	PUNCT
ejpam-3708	93	42	∈	∈	PROPN
ejpam-3708	93	43	i.	i.	NOUN
ejpam-3708	93	44	we	we	PRON
ejpam-3708	93	45	write	write	VERB
ejpam-3708	93	46	iθlimxk	iθlimxk	NOUN
ejpam-3708	93	47	=	=	PUNCT
ejpam-3708	93	48	x.	x.	NOUN
ejpam-3708	93	49	definition	definition	NOUN
ejpam-3708	93	50	4	4	NUM
ejpam-3708	93	51	.	.	PUNCT
ejpam-3708	94	1	let	let	VERB
ejpam-3708	94	2	ef	ef	PART
ejpam-3708	94	3	be	be	AUX
ejpam-3708	94	4	denote	denote	VERB
ejpam-3708	94	5	the	the	DET
ejpam-3708	94	6	sequence	sequence	NOUN
ejpam-3708	94	7	space	space	NOUN
ejpam-3708	94	8	of	of	ADP
ejpam-3708	94	9	fuzzy	fuzzy	ADJ
ejpam-3708	94	10	numbers	number	NOUN
ejpam-3708	94	11	.	.	PUNCT
ejpam-3708	95	1	then	then	ADV
ejpam-3708	95	2	ef	ef	PROPN
ejpam-3708	95	3	is	be	AUX
ejpam-3708	95	4	said	say	VERB
ejpam-3708	95	5	to	to	PART
ejpam-3708	95	6	be	be	AUX
ejpam-3708	95	7	solid	solid	ADJ
ejpam-3708	95	8	(	(	PUNCT
ejpam-3708	95	9	or	or	CCONJ
ejpam-3708	95	10	normal	normal	ADJ
ejpam-3708	95	11	)	)	PUNCT
ejpam-3708	95	12	if	if	SCONJ
ejpam-3708	95	13	(	(	PUNCT
ejpam-3708	95	14	yk	yk	NOUN
ejpam-3708	95	15	)	)	PUNCT
ejpam-3708	95	16	∈	∈	PROPN
ejpam-3708	95	17	ef	ef	X
ejpam-3708	95	18	whenever	whenever	SCONJ
ejpam-3708	95	19	(	(	PUNCT
ejpam-3708	95	20	xk	xk	ADJ
ejpam-3708	95	21	)	)	PUNCT
ejpam-3708	95	22	∈	∈	PROPN
ejpam-3708	95	23	ef	ef	PROPN
ejpam-3708	95	24	and	and	CCONJ
ejpam-3708	95	25	d(yk	d(yk	NOUN
ejpam-3708	95	26	,	,	PUNCT
ejpam-3708	95	27	0	0	NUM
ejpam-3708	95	28	)	)	PUNCT
ejpam-3708	95	29	≤	≤	NUM
ejpam-3708	95	30	d(xk	d(xk	PROPN
ejpam-3708	95	31	,	,	PUNCT
ejpam-3708	95	32	0	0	NUM
ejpam-3708	95	33	)	)	PUNCT
ejpam-3708	95	34	for	for	ADP
ejpam-3708	95	35	all	all	DET
ejpam-3708	95	36	k	k	PROPN
ejpam-3708	95	37	∈	∈	PROPN
ejpam-3708	95	38	n.	n.	PROPN
ejpam-3708	95	39	example	example	NOUN
ejpam-3708	96	1	1	1	X
ejpam-3708	96	2	.	.	PUNCT
ejpam-3708	97	1	(	(	PUNCT
ejpam-3708	97	2	i	i	NOUN
ejpam-3708	97	3	)	)	PUNCT
ejpam-3708	97	4	if	if	SCONJ
ejpam-3708	97	5	we	we	PRON
ejpam-3708	97	6	take	take	VERB
ejpam-3708	97	7	i	i	PRON
ejpam-3708	97	8	=	=	PUNCT
ejpam-3708	97	9	if	if	SCONJ
ejpam-3708	97	10	=	=	PRON
ejpam-3708	97	11	{	{	PUNCT
ejpam-3708	97	12	a	a	DET
ejpam-3708	97	13	⊆	⊆	NUM
ejpam-3708	97	14	n	n	NOUN
ejpam-3708	97	15	:	:	PUNCT
ejpam-3708	97	16	a	a	PRON
ejpam-3708	97	17	is	be	AUX
ejpam-3708	97	18	a	a	DET
ejpam-3708	97	19	finite	finite	NOUN
ejpam-3708	97	20	subset	subset	NOUN
ejpam-3708	97	21	}	}	PUNCT
ejpam-3708	97	22	.	.	PUNCT
ejpam-3708	98	1	then	then	ADV
ejpam-3708	98	2	if	if	SCONJ
ejpam-3708	98	3	is	be	AUX
ejpam-3708	98	4	a	a	DET
ejpam-3708	98	5	nontrival	nontrival	ADJ
ejpam-3708	98	6	admissible	admissible	ADJ
ejpam-3708	98	7	ideal	ideal	NOUN
ejpam-3708	98	8	of	of	ADP
ejpam-3708	98	9	n	n	NUM
ejpam-3708	98	10	and	and	CCONJ
ejpam-3708	98	11	the	the	DET
ejpam-3708	98	12	corresponding	correspond	VERB
ejpam-3708	98	13	convergence	convergence	NOUN
ejpam-3708	98	14	coincide	coincide	NOUN
ejpam-3708	98	15	with	with	ADP
ejpam-3708	98	16	the	the	DET
ejpam-3708	98	17	usual	usual	ADJ
ejpam-3708	98	18	convergence	convergence	NOUN
ejpam-3708	98	19	.	.	PUNCT
ejpam-3708	99	1	(	(	PUNCT
ejpam-3708	99	2	ii	ii	NOUN
ejpam-3708	99	3	)	)	PUNCT
ejpam-3708	99	4	if	if	SCONJ
ejpam-3708	99	5	we	we	PRON
ejpam-3708	99	6	take	take	VERB
ejpam-3708	99	7	i	i	PRON
ejpam-3708	99	8	=	=	PUNCT
ejpam-3708	99	9	iδ	iδ	NOUN
ejpam-3708	99	10	=	=	SYM
ejpam-3708	99	11	{	{	PUNCT
ejpam-3708	99	12	a	a	DET
ejpam-3708	99	13	⊆	⊆	NUM
ejpam-3708	99	14	n	n	NOUN
ejpam-3708	99	15	:	:	PUNCT
ejpam-3708	99	16	δ(a	δ(a	X
ejpam-3708	99	17	)	)	PUNCT
ejpam-3708	99	18	=	=	PUNCT
ejpam-3708	100	1	0	0	NUM
ejpam-3708	100	2	}	}	PUNCT
ejpam-3708	100	3	.	.	PUNCT
ejpam-3708	101	1	where	where	SCONJ
ejpam-3708	101	2	δ(a	δ(a	PROPN
ejpam-3708	101	3	)	)	PUNCT
ejpam-3708	101	4	denote	denote	VERB
ejpam-3708	101	5	the	the	DET
ejpam-3708	101	6	asymptotic	asymptotic	ADJ
ejpam-3708	101	7	density	density	NOUN
ejpam-3708	101	8	of	of	ADP
ejpam-3708	101	9	the	the	DET
ejpam-3708	101	10	set	set	NOUN
ejpam-3708	101	11	a.	a.	NOUN
ejpam-3708	101	12	then	then	ADV
ejpam-3708	101	13	iδ	iδ	PROPN
ejpam-3708	101	14	is	be	AUX
ejpam-3708	101	15	a	a	DET
ejpam-3708	101	16	non	non	ADJ
ejpam-3708	101	17	-	-	ADJ
ejpam-3708	101	18	trival	trival	ADJ
ejpam-3708	101	19	admissible	admissible	ADJ
ejpam-3708	101	20	ideal	ideal	NOUN
ejpam-3708	101	21	of	of	ADP
ejpam-3708	101	22	n	n	NUM
ejpam-3708	101	23	and	and	CCONJ
ejpam-3708	101	24	the	the	DET
ejpam-3708	101	25	corresponding	correspond	VERB
ejpam-3708	101	26	convergence	convergence	NOUN
ejpam-3708	101	27	coincide	coincide	NOUN
ejpam-3708	101	28	with	with	ADP
ejpam-3708	101	29	the	the	DET
ejpam-3708	101	30	statistical	statistical	ADJ
ejpam-3708	101	31	convergence	convergence	NOUN
ejpam-3708	101	32	.	.	PUNCT
ejpam-3708	102	1	k.	k.	PROPN
ejpam-3708	102	2	raj	raj	PROPN
ejpam-3708	102	3	,	,	PUNCT
ejpam-3708	102	4	s.	s.	PROPN
ejpam-3708	102	5	a.	a.	PROPN
ejpam-3708	102	6	mohiuddine	mohiuddine	PROPN
ejpam-3708	102	7	/	/	SYM
ejpam-3708	102	8	eur	eur	PROPN
ejpam-3708	102	9	.	.	PUNCT
ejpam-3708	103	1	j.	j.	PROPN
ejpam-3708	103	2	pure	pure	PROPN
ejpam-3708	103	3	appl	appl	PROPN
ejpam-3708	103	4	.	.	PROPN
ejpam-3708	103	5	math	math	PROPN
ejpam-3708	103	6	,	,	PUNCT
ejpam-3708	103	7	13	13	NUM
ejpam-3708	103	8	(	(	PUNCT
ejpam-3708	103	9	5	5	NUM
ejpam-3708	103	10	)	)	PUNCT
ejpam-3708	103	11	(	(	PUNCT
ejpam-3708	103	12	2020	2020	NUM
ejpam-3708	103	13	)	)	PUNCT
ejpam-3708	103	14	,	,	PUNCT
ejpam-3708	103	15	1131	1131	NUM
ejpam-3708	103	16	-	-	SYM
ejpam-3708	103	17	1148	1148	NUM
ejpam-3708	103	18	1135	1135	NUM
ejpam-3708	103	19	lemma	lemma	PROPN
ejpam-3708	103	20	1	1	NUM
ejpam-3708	103	21	.	.	PUNCT
ejpam-3708	104	1	[	[	X
ejpam-3708	104	2	24	24	NUM
ejpam-3708	104	3	]	]	X
ejpam-3708	104	4	if	if	SCONJ
ejpam-3708	104	5	d	d	PROPN
ejpam-3708	104	6	is	be	AUX
ejpam-3708	104	7	a	a	DET
ejpam-3708	104	8	translation	translation	NOUN
ejpam-3708	104	9	invariant	invariant	ADJ
ejpam-3708	104	10	metric	metric	NOUN
ejpam-3708	104	11	.	.	PUNCT
ejpam-3708	105	1	then	then	ADV
ejpam-3708	105	2	(	(	PUNCT
ejpam-3708	105	3	i	i	NOUN
ejpam-3708	105	4	)	)	PUNCT
ejpam-3708	105	5	d(x	d(x	PROPN
ejpam-3708	106	1	+	+	CCONJ
ejpam-3708	106	2	y	y	PROPN
ejpam-3708	106	3	,	,	PUNCT
ejpam-3708	106	4	0	0	NUM
ejpam-3708	106	5	)	)	PUNCT
ejpam-3708	106	6	≤	≤	NOUN
ejpam-3708	106	7	d(x	d(x	NOUN
ejpam-3708	106	8	,	,	PUNCT
ejpam-3708	106	9	0	0	NUM
ejpam-3708	106	10	)	)	PUNCT
ejpam-3708	106	11	+	+	CCONJ
ejpam-3708	106	12	d(y	d(y	NOUN
ejpam-3708	106	13	,	,	PUNCT
ejpam-3708	106	14	0	0	NUM
ejpam-3708	106	15	)	)	PUNCT
ejpam-3708	106	16	,	,	PUNCT
ejpam-3708	106	17	(	(	PUNCT
ejpam-3708	106	18	ii	ii	NOUN
ejpam-3708	106	19	)	)	PUNCT
ejpam-3708	106	20	d(λx	d(λx	NOUN
ejpam-3708	106	21	,	,	PUNCT
ejpam-3708	106	22	0	0	NUM
ejpam-3708	106	23	)	)	PUNCT
ejpam-3708	106	24	≤	≤	NUM
ejpam-3708	106	25	|λ|d(x	|λ|d(x	PROPN
ejpam-3708	106	26	,	,	PUNCT
ejpam-3708	106	27	0	0	NUM
ejpam-3708	106	28	)	)	PUNCT
ejpam-3708	106	29	,	,	PUNCT
ejpam-3708	106	30	|λ|	|λ|	ADP
ejpam-3708	106	31	>	>	X
ejpam-3708	106	32	1	1	X
ejpam-3708	106	33	.	.	PUNCT
ejpam-3708	107	1	lemma	lemma	PROPN
ejpam-3708	107	2	2	2	NUM
ejpam-3708	107	3	.	.	PUNCT
ejpam-3708	108	1	a	a	DET
ejpam-3708	108	2	sequence	sequence	NOUN
ejpam-3708	108	3	space	space	NOUN
ejpam-3708	108	4	ef	ef	PROPN
ejpam-3708	108	5	is	be	AUX
ejpam-3708	108	6	normal	normal	ADJ
ejpam-3708	108	7	implies	imply	VERB
ejpam-3708	108	8	ef	ef	PROPN
ejpam-3708	108	9	is	be	AUX
ejpam-3708	108	10	monotone	monotone	ADJ
ejpam-3708	108	11	.	.	PUNCT
ejpam-3708	109	1	(	(	PUNCT
ejpam-3708	109	2	for	for	ADP
ejpam-3708	109	3	the	the	DET
ejpam-3708	109	4	crisp	crisp	ADJ
ejpam-3708	109	5	set	set	NOUN
ejpam-3708	109	6	case	case	NOUN
ejpam-3708	109	7	,	,	PUNCT
ejpam-3708	109	8	one	one	PRON
ejpam-3708	109	9	may	may	AUX
ejpam-3708	109	10	refer	refer	VERB
ejpam-3708	109	11	to	to	ADP
ejpam-3708	109	12	kamthan	kamthan	PROPN
ejpam-3708	109	13	and	and	CCONJ
ejpam-3708	109	14	gupta	gupta	NOUN
ejpam-3708	109	15	[	[	X
ejpam-3708	109	16	13	13	NUM
ejpam-3708	109	17	]	]	NUM
ejpam-3708	109	18	)	)	PUNCT
ejpam-3708	109	19	.	.	PUNCT
ejpam-3708	110	1	lemma	lemma	PROPN
ejpam-3708	110	2	3	3	X
ejpam-3708	110	3	.	.	PUNCT
ejpam-3708	111	1	[	[	X
ejpam-3708	111	2	15	15	NUM
ejpam-3708	111	3	]	]	X
ejpam-3708	111	4	if	if	SCONJ
ejpam-3708	111	5	i	i	PRON
ejpam-3708	111	6	⊂	⊂	PROPN
ejpam-3708	111	7	2n	2n	NUM
ejpam-3708	111	8	is	be	AUX
ejpam-3708	111	9	a	a	DET
ejpam-3708	111	10	maximal	maximal	ADJ
ejpam-3708	111	11	ideal	ideal	NOUN
ejpam-3708	111	12	then	then	ADV
ejpam-3708	111	13	for	for	ADP
ejpam-3708	111	14	each	each	DET
ejpam-3708	111	15	a	a	DET
ejpam-3708	111	16	∈	∈	PROPN
ejpam-3708	111	17	n	n	CCONJ
ejpam-3708	111	18	,	,	PUNCT
ejpam-3708	111	19	we	we	PRON
ejpam-3708	111	20	have	have	VERB
ejpam-3708	111	21	either	either	CCONJ
ejpam-3708	111	22	a	a	DET
ejpam-3708	111	23	∈	∈	ADJ
ejpam-3708	111	24	i	i	NOUN
ejpam-3708	111	25	or	or	CCONJ
ejpam-3708	111	26	n	n	CCONJ
ejpam-3708	111	27	\a	\a	ADJ
ejpam-3708	111	28	∈	∈	PROPN
ejpam-3708	111	29	i.	i.	NOUN
ejpam-3708	111	30	2	2	NUM
ejpam-3708	111	31	.	.	PUNCT
ejpam-3708	112	1	some	some	DET
ejpam-3708	112	2	fuzzy	fuzzy	ADJ
ejpam-3708	112	3	sequence	sequence	NOUN
ejpam-3708	112	4	spaces	space	NOUN
ejpam-3708	112	5	throughout	throughout	ADP
ejpam-3708	112	6	the	the	DET
ejpam-3708	112	7	paper	paper	NOUN
ejpam-3708	112	8	wf	wf	PROPN
ejpam-3708	112	9	denote	denote	VERB
ejpam-3708	112	10	the	the	DET
ejpam-3708	112	11	class	class	NOUN
ejpam-3708	112	12	of	of	ADP
ejpam-3708	112	13	all	all	DET
ejpam-3708	112	14	fuzzy	fuzzy	ADJ
ejpam-3708	112	15	real	real	ADV
ejpam-3708	112	16	-	-	PUNCT
ejpam-3708	112	17	valued	value	VERB
ejpam-3708	112	18	sequences	sequence	NOUN
ejpam-3708	112	19	.	.	PUNCT
ejpam-3708	113	1	by	by	ADP
ejpam-3708	113	2	n	n	CCONJ
ejpam-3708	113	3	and	and	CCONJ
ejpam-3708	113	4	r	r	NOUN
ejpam-3708	113	5	we	we	PRON
ejpam-3708	113	6	denote	denote	VERB
ejpam-3708	113	7	the	the	DET
ejpam-3708	113	8	set	set	NOUN
ejpam-3708	113	9	of	of	ADP
ejpam-3708	113	10	natural	natural	ADJ
ejpam-3708	113	11	and	and	CCONJ
ejpam-3708	113	12	real	real	ADJ
ejpam-3708	113	13	numbers	number	NOUN
ejpam-3708	113	14	respectively	respectively	ADV
ejpam-3708	113	15	.	.	PUNCT
ejpam-3708	114	1	let	let	VERB
ejpam-3708	114	2	i	i	PRON
ejpam-3708	114	3	be	be	AUX
ejpam-3708	114	4	an	an	DET
ejpam-3708	114	5	admissible	admissible	ADJ
ejpam-3708	114	6	ideal	ideal	NOUN
ejpam-3708	114	7	of	of	ADP
ejpam-3708	114	8	n	n	NUM
ejpam-3708	114	9	and	and	CCONJ
ejpam-3708	114	10	θ	θ	PROPN
ejpam-3708	115	1	=	=	SYM
ejpam-3708	115	2	(	(	PUNCT
ejpam-3708	115	3	ir	ir	AUX
ejpam-3708	115	4	)	)	PUNCT
ejpam-3708	115	5	be	be	AUX
ejpam-3708	115	6	lacunary	lacunary	ADJ
ejpam-3708	115	7	sequence	sequence	NOUN
ejpam-3708	115	8	.	.	PUNCT
ejpam-3708	116	1	suppose	suppose	VERB
ejpam-3708	116	2	p	p	PROPN
ejpam-3708	116	3	=	=	SYM
ejpam-3708	116	4	(	(	PUNCT
ejpam-3708	116	5	pk	pk	NOUN
ejpam-3708	116	6	)	)	PUNCT
ejpam-3708	116	7	is	be	AUX
ejpam-3708	116	8	a	a	DET
ejpam-3708	116	9	bounded	bounded	ADJ
ejpam-3708	116	10	sequence	sequence	NOUN
ejpam-3708	116	11	of	of	ADP
ejpam-3708	116	12	positive	positive	ADJ
ejpam-3708	116	13	real	real	ADJ
ejpam-3708	116	14	numbers	number	NOUN
ejpam-3708	116	15	,	,	PUNCT
ejpam-3708	116	16	u	u	NOUN
ejpam-3708	116	17	=	=	SYM
ejpam-3708	116	18	(	(	PUNCT
ejpam-3708	116	19	uk	uk	PROPN
ejpam-3708	116	20	)	)	PUNCT
ejpam-3708	116	21	be	be	VERB
ejpam-3708	116	22	a	a	DET
ejpam-3708	116	23	sequence	sequence	NOUN
ejpam-3708	116	24	of	of	ADP
ejpam-3708	116	25	nonzero	nonzero	NOUN
ejpam-3708	116	26	,	,	PUNCT
ejpam-3708	116	27	nonnegative	nonnegative	ADJ
ejpam-3708	116	28	real	real	ADJ
ejpam-3708	116	29	numbers	number	NOUN
ejpam-3708	116	30	,	,	PUNCT
ejpam-3708	116	31	a	a	DET
ejpam-3708	116	32	=	=	SYM
ejpam-3708	116	33	(	(	PUNCT
ejpam-3708	116	34	ank	ank	PROPN
ejpam-3708	116	35	)	)	PUNCT
ejpam-3708	116	36	an	an	DET
ejpam-3708	116	37	infinite	infinite	ADJ
ejpam-3708	116	38	matrix	matrix	NOUN
ejpam-3708	116	39	and	and	CCONJ
ejpam-3708	116	40	m	m	NOUN
ejpam-3708	116	41	=	=	SYM
ejpam-3708	116	42	(	(	PUNCT
ejpam-3708	116	43	mk	mk	X
ejpam-3708	116	44	)	)	PUNCT
ejpam-3708	116	45	be	be	VERB
ejpam-3708	116	46	a	a	DET
ejpam-3708	116	47	sequence	sequence	NOUN
ejpam-3708	116	48	of	of	ADP
ejpam-3708	116	49	orlicz	orlicz	ADJ
ejpam-3708	116	50	functions	function	NOUN
ejpam-3708	116	51	.	.	PUNCT
ejpam-3708	117	1	in	in	ADP
ejpam-3708	117	2	this	this	DET
ejpam-3708	117	3	paper	paper	NOUN
ejpam-3708	117	4	,	,	PUNCT
ejpam-3708	117	5	we	we	PRON
ejpam-3708	117	6	define	define	VERB
ejpam-3708	117	7	the	the	DET
ejpam-3708	117	8	following	follow	VERB
ejpam-3708	117	9	sequence	sequence	NOUN
ejpam-3708	117	10	spaces	space	NOUN
ejpam-3708	117	11	as	as	SCONJ
ejpam-3708	117	12	follows	follow	VERB
ejpam-3708	117	13	:	:	PUNCT
ejpam-3708	117	14	w	w	PROPN
ejpam-3708	117	15	i(f	i(f	NOUN
ejpam-3708	117	16	)	)	PUNCT
ejpam-3708	117	17	θ	θ	PROPN
ejpam-3708	118	1	[	[	X
ejpam-3708	118	2	a	a	X
ejpam-3708	118	3	,	,	PUNCT
ejpam-3708	118	4	m	m	PROPN
ejpam-3708	118	5	,	,	PUNCT
ejpam-3708	118	6	p	p	X
ejpam-3708	118	7	,	,	PUNCT
ejpam-3708	118	8	u,∆m	u,∆m	PROPN
ejpam-3708	118	9	v	v	NOUN
ejpam-3708	118	10	]	]	X
ejpam-3708	118	11	=	=	X
ejpam-3708	118	12	{	{	PUNCT
ejpam-3708	118	13	(	(	PUNCT
ejpam-3708	118	14	xk	xk	INTJ
ejpam-3708	118	15	)	)	PUNCT
ejpam-3708	118	16	∈	∈	PROPN
ejpam-3708	118	17	wf	wf	PROPN
ejpam-3708	118	18	:	:	PUNCT
ejpam-3708	118	19	∀ε	∀ε	X
ejpam-3708	118	20	>	>	X
ejpam-3708	118	21	0	0	NUM
ejpam-3708	118	22	,	,	PUNCT
ejpam-3708	118	23	{	{	PUNCT
ejpam-3708	118	24	n	n	CCONJ
ejpam-3708	118	25	,	,	PUNCT
ejpam-3708	118	26	r	r	NOUN
ejpam-3708	118	27	∈	∈	PROPN
ejpam-3708	118	28	n	n	CCONJ
ejpam-3708	118	29	:	:	PUNCT
ejpam-3708	118	30	1	1	NUM
ejpam-3708	118	31	hr	hr	NOUN
ejpam-3708	118	32	∑	∑	PUNCT
ejpam-3708	118	33	k∈ir	k∈ir	PROPN
ejpam-3708	118	34	ank	ank	PROPN
ejpam-3708	118	35	[	[	PUNCT
ejpam-3708	118	36	k−smk	k−smk	NOUN
ejpam-3708	118	37	(	(	PUNCT
ejpam-3708	118	38	d(uk∆	d(uk∆	PROPN
ejpam-3708	118	39	m	m	NOUN
ejpam-3708	118	40	v	v	NOUN
ejpam-3708	118	41	xk	xk	PROPN
ejpam-3708	118	42	,	,	PUNCT
ejpam-3708	118	43	x0	x0	PROPN
ejpam-3708	118	44	)	)	PUNCT
ejpam-3708	118	45	ρ	ρ	PROPN
ejpam-3708	118	46	)	)	PUNCT
ejpam-3708	118	47	]	]	PUNCT
ejpam-3708	118	48	pk	pk	NOUN
ejpam-3708	118	49	≥	≥	NOUN
ejpam-3708	118	50	ε	ε	PROPN
ejpam-3708	118	51	}	}	PUNCT
ejpam-3708	118	52	∈	∈	PROPN
ejpam-3708	118	53	i	i	PRON
ejpam-3708	118	54	,	,	PUNCT
ejpam-3708	118	55	for	for	ADP
ejpam-3708	118	56	some	some	DET
ejpam-3708	118	57	ρ	ρ	PROPN
ejpam-3708	118	58	>	>	X
ejpam-3708	118	59	0	0	NUM
ejpam-3708	118	60	,	,	PUNCT
ejpam-3708	118	61	s	s	VERB
ejpam-3708	118	62	≥	≥	NOUN
ejpam-3708	118	63	0	0	NUM
ejpam-3708	118	64	and	and	CCONJ
ejpam-3708	118	65	x0	x0	PROPN
ejpam-3708	118	66	∈	∈	PROPN
ejpam-3708	118	67	l(r	l(r	PROPN
ejpam-3708	118	68	)	)	PUNCT
ejpam-3708	118	69	}	}	PUNCT
ejpam-3708	118	70	,	,	PUNCT
ejpam-3708	118	71	w	w	NOUN
ejpam-3708	118	72	i(f	i(f	NOUN
ejpam-3708	118	73	)	)	PUNCT
ejpam-3708	118	74	θ	θ	PROPN
ejpam-3708	119	1	[	[	X
ejpam-3708	119	2	a	a	X
ejpam-3708	119	3	,	,	PUNCT
ejpam-3708	119	4	m	m	PROPN
ejpam-3708	119	5	,	,	PUNCT
ejpam-3708	119	6	p	p	X
ejpam-3708	119	7	,	,	PUNCT
ejpam-3708	119	8	u,∆m	u,∆m	PROPN
ejpam-3708	119	9	v	v	X
ejpam-3708	119	10	]	]	PUNCT
ejpam-3708	119	11	0	0	PUNCT
ejpam-3708	119	12	=	=	SYM
ejpam-3708	119	13	{	{	PUNCT
ejpam-3708	119	14	(	(	PUNCT
ejpam-3708	119	15	xk	xk	INTJ
ejpam-3708	119	16	)	)	PUNCT
ejpam-3708	119	17	∈	∈	PROPN
ejpam-3708	119	18	wf	wf	PROPN
ejpam-3708	119	19	:	:	PUNCT
ejpam-3708	119	20	∀ε	∀ε	X
ejpam-3708	119	21	>	>	X
ejpam-3708	119	22	0	0	NUM
ejpam-3708	119	23	,	,	PUNCT
ejpam-3708	119	24	{	{	PUNCT
ejpam-3708	119	25	n	n	CCONJ
ejpam-3708	119	26	,	,	PUNCT
ejpam-3708	119	27	r	r	NOUN
ejpam-3708	119	28	∈	∈	PROPN
ejpam-3708	119	29	n	n	CCONJ
ejpam-3708	119	30	:	:	PUNCT
ejpam-3708	119	31	1	1	NUM
ejpam-3708	119	32	hr	hr	NOUN
ejpam-3708	119	33	∑	∑	PUNCT
ejpam-3708	119	34	k∈ir	k∈ir	PROPN
ejpam-3708	119	35	ank	ank	PROPN
ejpam-3708	119	36	[	[	PUNCT
ejpam-3708	119	37	k−smk	k−smk	NOUN
ejpam-3708	119	38	(	(	PUNCT
ejpam-3708	119	39	d(uk∆	d(uk∆	PROPN
ejpam-3708	119	40	m	m	NOUN
ejpam-3708	119	41	v	v	NOUN
ejpam-3708	119	42	xk	xk	PROPN
ejpam-3708	119	43	,	,	PUNCT
ejpam-3708	119	44	0	0	NUM
ejpam-3708	119	45	)	)	PUNCT
ejpam-3708	119	46	ρ	ρ	NOUN
ejpam-3708	119	47	)	)	PUNCT
ejpam-3708	119	48	]	]	PUNCT
ejpam-3708	119	49	pk	pk	NOUN
ejpam-3708	119	50	≥	≥	NOUN
ejpam-3708	119	51	ε	ε	PROPN
ejpam-3708	119	52	}	}	PUNCT
ejpam-3708	119	53	∈	∈	PROPN
ejpam-3708	120	1	i	i	PRON
ejpam-3708	120	2	,	,	PUNCT
ejpam-3708	120	3	for	for	ADP
ejpam-3708	120	4	some	some	DET
ejpam-3708	120	5	ρ	ρ	NOUN
ejpam-3708	120	6	>	>	X
ejpam-3708	120	7	0	0	PUNCT
ejpam-3708	120	8	and	and	CCONJ
ejpam-3708	120	9	s	s	X
ejpam-3708	120	10	≥	≥	NOUN
ejpam-3708	120	11	0	0	NUM
ejpam-3708	120	12	}	}	PUNCT
ejpam-3708	120	13	,	,	PUNCT
ejpam-3708	120	14	wfθ	wfθ	NOUN
ejpam-3708	121	1	[	[	X
ejpam-3708	121	2	a	a	X
ejpam-3708	121	3	,	,	PUNCT
ejpam-3708	121	4	m	m	PROPN
ejpam-3708	121	5	,	,	PUNCT
ejpam-3708	121	6	p	p	X
ejpam-3708	121	7	,	,	PUNCT
ejpam-3708	121	8	u,∆m	u,∆m	PROPN
ejpam-3708	121	9	v	v	X
ejpam-3708	121	10	]	]	PUNCT
ejpam-3708	121	11	∞	∞	NUM
ejpam-3708	121	12	=	=	SYM
ejpam-3708	121	13	{	{	PUNCT
ejpam-3708	121	14	(	(	PUNCT
ejpam-3708	121	15	xk	xk	INTJ
ejpam-3708	121	16	)	)	PUNCT
ejpam-3708	121	17	∈	∈	PROPN
ejpam-3708	121	18	wf	wf	PROPN
ejpam-3708	121	19	:	:	PUNCT
ejpam-3708	121	20	sup	sup	PROPN
ejpam-3708	121	21	n	n	CCONJ
ejpam-3708	121	22	,	,	PUNCT
ejpam-3708	121	23	r	r	NOUN
ejpam-3708	121	24	1	1	NUM
ejpam-3708	121	25	hr	hr	NOUN
ejpam-3708	121	26	∑	∑	PUNCT
ejpam-3708	121	27	k∈ir	k∈ir	PROPN
ejpam-3708	121	28	ank	ank	PROPN
ejpam-3708	121	29	[	[	PUNCT
ejpam-3708	121	30	k−smk	k−smk	NOUN
ejpam-3708	121	31	(	(	PUNCT
ejpam-3708	121	32	d(uk∆	d(uk∆	PROPN
ejpam-3708	121	33	m	m	NOUN
ejpam-3708	121	34	v	v	NOUN
ejpam-3708	121	35	xk	xk	PROPN
ejpam-3708	121	36	,	,	PUNCT
ejpam-3708	121	37	0	0	NUM
ejpam-3708	121	38	)	)	PUNCT
ejpam-3708	121	39	ρ	ρ	NOUN
ejpam-3708	121	40	)	)	PUNCT
ejpam-3708	121	41	]	]	X
ejpam-3708	121	42	pk	pk	NOUN
ejpam-3708	121	43	<	<	X
ejpam-3708	121	44	∞	∞	PROPN
ejpam-3708	121	45	,	,	PUNCT
ejpam-3708	121	46	for	for	ADP
ejpam-3708	121	47	some	some	DET
ejpam-3708	121	48	ρ	ρ	NOUN
ejpam-3708	121	49	>	>	X
ejpam-3708	121	50	0	0	PUNCT
ejpam-3708	121	51	and	and	CCONJ
ejpam-3708	121	52	s	s	X
ejpam-3708	121	53	≥	≥	NOUN
ejpam-3708	121	54	0	0	NUM
ejpam-3708	121	55	}	}	PUNCT
ejpam-3708	121	56	,	,	PUNCT
ejpam-3708	121	57	k.	k.	PROPN
ejpam-3708	121	58	raj	raj	PROPN
ejpam-3708	121	59	,	,	PUNCT
ejpam-3708	121	60	s.	s.	PROPN
ejpam-3708	121	61	a.	a.	PROPN
ejpam-3708	121	62	mohiuddine	mohiuddine	PROPN
ejpam-3708	121	63	/	/	SYM
ejpam-3708	121	64	eur	eur	PROPN
ejpam-3708	121	65	.	.	PUNCT
ejpam-3708	122	1	j.	j.	PROPN
ejpam-3708	122	2	pure	pure	PROPN
ejpam-3708	122	3	appl	appl	PROPN
ejpam-3708	122	4	.	.	PROPN
ejpam-3708	122	5	math	math	PROPN
ejpam-3708	122	6	,	,	PUNCT
ejpam-3708	122	7	13	13	NUM
ejpam-3708	122	8	(	(	PUNCT
ejpam-3708	122	9	5	5	NUM
ejpam-3708	122	10	)	)	PUNCT
ejpam-3708	122	11	(	(	PUNCT
ejpam-3708	122	12	2020	2020	NUM
ejpam-3708	122	13	)	)	PUNCT
ejpam-3708	122	14	,	,	PUNCT
ejpam-3708	122	15	1131	1131	NUM
ejpam-3708	122	16	-	-	SYM
ejpam-3708	122	17	1148	1148	NUM
ejpam-3708	122	18	1136	1136	NUM
ejpam-3708	122	19	and	and	CCONJ
ejpam-3708	122	20	w	w	NOUN
ejpam-3708	122	21	i(f	i(f	NOUN
ejpam-3708	122	22	)	)	PUNCT
ejpam-3708	122	23	θ	θ	PROPN
ejpam-3708	123	1	[	[	X
ejpam-3708	123	2	a	a	X
ejpam-3708	123	3	,	,	PUNCT
ejpam-3708	123	4	m	m	PROPN
ejpam-3708	123	5	,	,	PUNCT
ejpam-3708	123	6	p	p	X
ejpam-3708	123	7	,	,	PUNCT
ejpam-3708	123	8	u,∆m	u,∆m	PROPN
ejpam-3708	123	9	v	v	X
ejpam-3708	123	10	]	]	PUNCT
ejpam-3708	123	11	∞	∞	NUM
ejpam-3708	123	12	=	=	SYM
ejpam-3708	123	13	{	{	PUNCT
ejpam-3708	123	14	(	(	PUNCT
ejpam-3708	123	15	xk	xk	INTJ
ejpam-3708	123	16	)	)	PUNCT
ejpam-3708	123	17	∈	∈	PROPN
ejpam-3708	123	18	wf	wf	PROPN
ejpam-3708	123	19	:	:	PUNCT
ejpam-3708	124	1	∃	∃	PROPN
ejpam-3708	124	2	k	k	PROPN
ejpam-3708	124	3	>	>	X
ejpam-3708	124	4	0	0	NUM
ejpam-3708	125	1	such	such	ADJ
ejpam-3708	125	2	that	that	SCONJ
ejpam-3708	125	3	{	{	PUNCT
ejpam-3708	125	4	n	n	X
ejpam-3708	125	5	,	,	PUNCT
ejpam-3708	125	6	r	r	NOUN
ejpam-3708	125	7	∈	∈	PROPN
ejpam-3708	125	8	n	n	CCONJ
ejpam-3708	125	9	:	:	PUNCT
ejpam-3708	125	10	1	1	NUM
ejpam-3708	125	11	hr	hr	NOUN
ejpam-3708	125	12	∑	∑	PUNCT
ejpam-3708	125	13	k∈ir	k∈ir	PROPN
ejpam-3708	125	14	ank	ank	PROPN
ejpam-3708	125	15	[	[	PUNCT
ejpam-3708	125	16	k−smk	k−smk	NOUN
ejpam-3708	125	17	(	(	PUNCT
ejpam-3708	125	18	d(uk∆	d(uk∆	PROPN
ejpam-3708	125	19	m	m	NOUN
ejpam-3708	125	20	v	v	NOUN
ejpam-3708	125	21	xk	xk	PROPN
ejpam-3708	125	22	,	,	PUNCT
ejpam-3708	125	23	x0	x0	PROPN
ejpam-3708	125	24	)	)	PUNCT
ejpam-3708	125	25	ρ	ρ	PROPN
ejpam-3708	125	26	)	)	PUNCT
ejpam-3708	125	27	]	]	PUNCT
ejpam-3708	125	28	pk	pk	NOUN
ejpam-3708	125	29	≥	≥	NOUN
ejpam-3708	125	30	k	k	NOUN
ejpam-3708	125	31	}	}	PUNCT
ejpam-3708	125	32	∈	∈	PROPN
ejpam-3708	125	33	i	i	PRON
ejpam-3708	125	34	,	,	PUNCT
ejpam-3708	125	35	for	for	ADP
ejpam-3708	125	36	some	some	DET
ejpam-3708	125	37	ρ	ρ	NOUN
ejpam-3708	125	38	>	>	X
ejpam-3708	125	39	0	0	PUNCT
ejpam-3708	125	40	and	and	CCONJ
ejpam-3708	125	41	s	s	X
ejpam-3708	125	42	≥	≥	NOUN
ejpam-3708	125	43	0	0	NUM
ejpam-3708	125	44	}	}	PUNCT
ejpam-3708	125	45	.	.	PUNCT
ejpam-3708	126	1	example	example	NOUN
ejpam-3708	127	1	2	2	NUM
ejpam-3708	127	2	.	.	PUNCT
ejpam-3708	127	3	let	let	VERB
ejpam-3708	127	4	xk(l	xk(l	PRON
ejpam-3708	127	5	)	)	PUNCT
ejpam-3708	127	6	=	=	SYM
ejpam-3708	128	1	1	1	NUM
ejpam-3708	128	2	for	for	ADP
ejpam-3708	128	3	k	k	NOUN
ejpam-3708	128	4	=	=	SYM
ejpam-3708	128	5	2q	2q	NUM
ejpam-3708	128	6	,	,	PUNCT
ejpam-3708	128	7	q	q	NOUN
ejpam-3708	128	8	=	=	SYM
ejpam-3708	128	9	1	1	NUM
ejpam-3708	128	10	,	,	PUNCT
ejpam-3708	128	11	2	2	NUM
ejpam-3708	128	12	,	,	PUNCT
ejpam-3708	128	13	3	3	NUM
ejpam-3708	128	14	.....	.....	PUNCT
ejpam-3708	128	15	otherwise	otherwise	ADV
ejpam-3708	128	16	,	,	PUNCT
ejpam-3708	128	17	xk(l	xk(l	PUNCT
ejpam-3708	128	18	)	)	PUNCT
ejpam-3708	128	19	=	=	PUNCT
ejpam-3708	129	1			PUNCT
ejpam-3708	129	2	k	k	NOUN
ejpam-3708	129	3	3	3	NUM
ejpam-3708	129	4	(	(	PUNCT
ejpam-3708	129	5	l	l	NOUN
ejpam-3708	129	6	−	−	PROPN
ejpam-3708	129	7	2	2	NUM
ejpam-3708	129	8	)	)	PUNCT
ejpam-3708	129	9	+	+	CCONJ
ejpam-3708	129	10	1	1	NUM
ejpam-3708	129	11	for	for	ADP
ejpam-3708	129	12	l	l	NOUN
ejpam-3708	129	13	∈	∈	PROPN
ejpam-3708	129	14	[	[	PUNCT
ejpam-3708	129	15	2k−3	2k−3	NUM
ejpam-3708	129	16	2	2	NUM
ejpam-3708	129	17	,	,	PUNCT
ejpam-3708	129	18	2	2	NUM
ejpam-3708	129	19	]	]	PUNCT
ejpam-3708	129	20	,	,	PUNCT
ejpam-3708	129	21	−k	−k	PROPN
ejpam-3708	129	22	3	3	NUM
ejpam-3708	129	23	(	(	PUNCT
ejpam-3708	129	24	l	l	NOUN
ejpam-3708	129	25	−	−	PROPN
ejpam-3708	129	26	2	2	NUM
ejpam-3708	129	27	)	)	PUNCT
ejpam-3708	129	28	+	+	CCONJ
ejpam-3708	129	29	1	1	NUM
ejpam-3708	129	30	for	for	ADP
ejpam-3708	129	31	l	l	NOUN
ejpam-3708	129	32	∈	∈	PROPN
ejpam-3708	129	33	[	[	PUNCT
ejpam-3708	129	34	2	2	NUM
ejpam-3708	129	35	,	,	PUNCT
ejpam-3708	129	36	2k+3	2k+3	NOUN
ejpam-3708	129	37	2	2	NUM
ejpam-3708	129	38	]	]	PUNCT
ejpam-3708	129	39	.	.	PUNCT
ejpam-3708	130	1	for	for	ADP
ejpam-3708	130	2	instance	instance	NOUN
ejpam-3708	130	3	take	take	VERB
ejpam-3708	130	4	m	m	NOUN
ejpam-3708	130	5	=	=	SYM
ejpam-3708	130	6	v	v	NOUN
ejpam-3708	130	7	=	=	SYM
ejpam-3708	130	8	1	1	NUM
ejpam-3708	130	9	,	,	PUNCT
ejpam-3708	130	10	then	then	ADV
ejpam-3708	130	11	the	the	DET
ejpam-3708	130	12	α−level	α−level	NOUN
ejpam-3708	130	13	sets	set	NOUN
ejpam-3708	130	14	of	of	ADP
ejpam-3708	130	15	(	(	PUNCT
ejpam-3708	130	16	xk	xk	ADJ
ejpam-3708	130	17	)	)	PUNCT
ejpam-3708	130	18	and	and	CCONJ
ejpam-3708	130	19	(	(	PUNCT
ejpam-3708	130	20	∆xk	∆xk	NOUN
ejpam-3708	130	21	)	)	PUNCT
ejpam-3708	130	22	are	be	AUX
ejpam-3708	130	23	[	[	X
ejpam-3708	130	24	xk	xk	X
ejpam-3708	130	25	]	]	X
ejpam-3708	130	26	α	α	NOUN
ejpam-3708	130	27	=	=	X
ejpam-3708	130	28	{	{	PUNCT
ejpam-3708	131	1	[	[	X
ejpam-3708	131	2	1	1	NUM
ejpam-3708	131	3	,	,	PUNCT
ejpam-3708	131	4	1	1	NUM
ejpam-3708	131	5	]	]	PUNCT
ejpam-3708	131	6	k	k	NOUN
ejpam-3708	131	7	=	=	SYM
ejpam-3708	131	8	2q	2q	NOUN
ejpam-3708	131	9	,	,	PUNCT
ejpam-3708	131	10	[	[	X
ejpam-3708	131	11	2−	2−	NUM
ejpam-3708	131	12	3	3	NUM
ejpam-3708	131	13	k	k	X
ejpam-3708	131	14	(	(	PUNCT
ejpam-3708	131	15	1−	1−	NUM
ejpam-3708	131	16	α	α	NOUN
ejpam-3708	131	17	)	)	PUNCT
ejpam-3708	131	18	,	,	PUNCT
ejpam-3708	131	19	2	2	NUM
ejpam-3708	131	20	+	+	SYM
ejpam-3708	131	21	3	3	NUM
ejpam-3708	131	22	k	k	X
ejpam-3708	131	23	(	(	PUNCT
ejpam-3708	131	24	1−	1−	NUM
ejpam-3708	131	25	α	α	NOUN
ejpam-3708	131	26	)	)	PUNCT
ejpam-3708	131	27	]	]	PUNCT
ejpam-3708	131	28	otherwise	otherwise	ADV
ejpam-3708	131	29	.	.	PUNCT
ejpam-3708	132	1	and	and	CCONJ
ejpam-3708	132	2	[	[	X
ejpam-3708	132	3	∆xk	∆xk	NOUN
ejpam-3708	132	4	]	]	X
ejpam-3708	132	5	α	α	NOUN
ejpam-3708	132	6	=	=	PUNCT
ejpam-3708	132	7			PUNCT
ejpam-3708	133	1	[	[	X
ejpam-3708	133	2	−1−	−1−	X
ejpam-3708	133	3	3	3	NUM
ejpam-3708	133	4	k	k	X
ejpam-3708	133	5	(	(	PUNCT
ejpam-3708	133	6	1−	1−	NUM
ejpam-3708	133	7	α),−1	α),−1	PRON
ejpam-3708	133	8	+	+	NUM
ejpam-3708	133	9	3	3	NUM
ejpam-3708	133	10	k	k	X
ejpam-3708	133	11	(	(	PUNCT
ejpam-3708	133	12	1−	1−	NUM
ejpam-3708	133	13	α	α	NOUN
ejpam-3708	133	14	)	)	PUNCT
ejpam-3708	133	15	]	]	PUNCT
ejpam-3708	133	16	k	k	X
ejpam-3708	134	1	=	=	PUNCT
ejpam-3708	134	2	2q	2q	NOUN
ejpam-3708	134	3	,	,	PUNCT
ejpam-3708	134	4	[	[	X
ejpam-3708	134	5	1−	1−	NUM
ejpam-3708	134	6	3	3	NUM
ejpam-3708	134	7	k	k	X
ejpam-3708	134	8	(	(	PUNCT
ejpam-3708	134	9	1−	1−	NUM
ejpam-3708	134	10	α	α	NOUN
ejpam-3708	134	11	)	)	PUNCT
ejpam-3708	134	12	,	,	PUNCT
ejpam-3708	134	13	1	1	NUM
ejpam-3708	134	14	+	+	SYM
ejpam-3708	134	15	3	3	NUM
ejpam-3708	134	16	k	k	X
ejpam-3708	134	17	(	(	PUNCT
ejpam-3708	134	18	1−	1−	NUM
ejpam-3708	134	19	α	α	NOUN
ejpam-3708	134	20	)	)	PUNCT
ejpam-3708	134	21	]	]	PUNCT
ejpam-3708	135	1	k	k	X
ejpam-3708	136	1	+	+	CCONJ
ejpam-3708	136	2	1	1	NUM
ejpam-3708	136	3	=	=	SYM
ejpam-3708	136	4	2q	2q	NOUN
ejpam-3708	136	5	.	.	PUNCT
ejpam-3708	137	1	[	[	X
ejpam-3708	137	2	(	(	PUNCT
ejpam-3708	137	3	3	3	NUM
ejpam-3708	137	4	k	k	NOUN
ejpam-3708	137	5	+	+	PROPN
ejpam-3708	137	6	3	3	NUM
ejpam-3708	137	7	k+1)(α−	k+1)(α−	NOUN
ejpam-3708	137	8	1	1	NUM
ejpam-3708	137	9	)	)	PUNCT
ejpam-3708	137	10	,	,	PUNCT
ejpam-3708	137	11	(	(	PUNCT
ejpam-3708	137	12	3	3	NUM
ejpam-3708	137	13	k	k	NOUN
ejpam-3708	137	14	+	+	PROPN
ejpam-3708	137	15	3	3	NUM
ejpam-3708	137	16	k+1)(1−	k+1)(1−	PROPN
ejpam-3708	137	17	α	α	NUM
ejpam-3708	137	18	)	)	PUNCT
ejpam-3708	137	19	]	]	PUNCT
ejpam-3708	137	20	otherwise	otherwise	ADV
ejpam-3708	137	21	.	.	PUNCT
ejpam-3708	138	1	let	let	VERB
ejpam-3708	138	2	a	a	DET
ejpam-3708	138	3	=	=	X
ejpam-3708	138	4	(	(	PUNCT
ejpam-3708	138	5	c	c	NOUN
ejpam-3708	138	6	,	,	PUNCT
ejpam-3708	138	7	1	1	NUM
ejpam-3708	138	8	)	)	PUNCT
ejpam-3708	138	9	,	,	PUNCT
ejpam-3708	138	10	the	the	DET
ejpam-3708	138	11	cesàro	cesàro	PROPN
ejpam-3708	138	12	matrix	matrix	NOUN
ejpam-3708	138	13	,	,	PUNCT
ejpam-3708	138	14	m(x	m(x	PROPN
ejpam-3708	138	15	)	)	PUNCT
ejpam-3708	138	16	=	=	SYM
ejpam-3708	139	1	x	x	X
ejpam-3708	139	2	,	,	PUNCT
ejpam-3708	139	3	s	s	PART
ejpam-3708	139	4	=	=	SYM
ejpam-3708	139	5	0	0	NUM
ejpam-3708	139	6	,	,	PUNCT
ejpam-3708	139	7	u	u	NOUN
ejpam-3708	139	8	=	=	SYM
ejpam-3708	139	9	(	(	PUNCT
ejpam-3708	139	10	uk	uk	PROPN
ejpam-3708	139	11	)	)	PUNCT
ejpam-3708	139	12	=	=	SYM
ejpam-3708	139	13	1	1	NUM
ejpam-3708	139	14	,	,	PUNCT
ejpam-3708	139	15	p	p	NOUN
ejpam-3708	139	16	=	=	SYM
ejpam-3708	139	17	(	(	PUNCT
ejpam-3708	139	18	pk	pk	NOUN
ejpam-3708	139	19	)	)	PUNCT
ejpam-3708	139	20	=	=	SYM
ejpam-3708	139	21	1	1	NUM
ejpam-3708	139	22	,	,	PUNCT
ejpam-3708	139	23	for	for	ADP
ejpam-3708	139	24	all	all	DET
ejpam-3708	139	25	k	k	PROPN
ejpam-3708	139	26	∈	∈	PROPN
ejpam-3708	139	27	n	n	CCONJ
ejpam-3708	139	28	,	,	PUNCT
ejpam-3708	139	29	ρ	ρ	PROPN
ejpam-3708	139	30	=	=	SYM
ejpam-3708	139	31	1	1	NUM
ejpam-3708	139	32	and	and	CCONJ
ejpam-3708	139	33	θ	θ	PROPN
ejpam-3708	139	34	=	=	SYM
ejpam-3708	139	35	2r	2r	NUM
ejpam-3708	139	36	,	,	PUNCT
ejpam-3708	139	37	we	we	PRON
ejpam-3708	139	38	have	have	VERB
ejpam-3708	139	39	sup	sup	NOUN
ejpam-3708	139	40	n	n	CCONJ
ejpam-3708	139	41	∑	∑	PROPN
ejpam-3708	139	42	k∈ir	k∈ir	PROPN
ejpam-3708	139	43	ank	ank	PROPN
ejpam-3708	139	44	[	[	PUNCT
ejpam-3708	139	45	mk	mk	PROPN
ejpam-3708	139	46	(	(	PUNCT
ejpam-3708	139	47	d(uk∆	d(uk∆	PROPN
ejpam-3708	139	48	m	m	NOUN
ejpam-3708	139	49	v	v	NOUN
ejpam-3708	139	50	xk	xk	PROPN
ejpam-3708	139	51	,	,	PUNCT
ejpam-3708	139	52	0	0	NUM
ejpam-3708	139	53	)	)	PUNCT
ejpam-3708	139	54	ρ	ρ	NOUN
ejpam-3708	139	55	)	)	PUNCT
ejpam-3708	139	56	]	]	PUNCT
ejpam-3708	139	57	pk	pk	NOUN
ejpam-3708	139	58	<	<	X
ejpam-3708	139	59	∞	∞	PROPN
ejpam-3708	139	60	thus	thus	ADV
ejpam-3708	139	61	,	,	PUNCT
ejpam-3708	139	62	(	(	PUNCT
ejpam-3708	139	63	xk	xk	ADJ
ejpam-3708	139	64	)	)	PUNCT
ejpam-3708	139	65	∈	∈	PROPN
ejpam-3708	139	66	wfθ	wfθ	NOUN
ejpam-3708	140	1	[	[	X
ejpam-3708	140	2	a	a	X
ejpam-3708	140	3	,	,	PUNCT
ejpam-3708	140	4	m	m	PROPN
ejpam-3708	140	5	,	,	PUNCT
ejpam-3708	140	6	p	p	X
ejpam-3708	140	7	,	,	PUNCT
ejpam-3708	140	8	u,∆m	u,∆m	PROPN
ejpam-3708	140	9	v	v	X
ejpam-3708	140	10	]	]	PUNCT
ejpam-3708	140	11	∞	∞	NUM
ejpam-3708	140	12	but	but	CCONJ
ejpam-3708	140	13	(	(	PUNCT
ejpam-3708	140	14	xk	xk	INTJ
ejpam-3708	140	15	)	)	PUNCT
ejpam-3708	140	16	is	be	AUX
ejpam-3708	140	17	not	not	PART
ejpam-3708	140	18	an	an	DET
ejpam-3708	140	19	ideal	ideal	ADJ
ejpam-3708	140	20	convergent	convergent	NOUN
ejpam-3708	140	21	.	.	PUNCT
ejpam-3708	141	1	let	let	VERB
ejpam-3708	141	2	us	we	PRON
ejpam-3708	141	3	consider	consider	VERB
ejpam-3708	141	4	a	a	DET
ejpam-3708	141	5	few	few	ADJ
ejpam-3708	141	6	special	special	ADJ
ejpam-3708	141	7	cases	case	NOUN
ejpam-3708	141	8	of	of	ADP
ejpam-3708	141	9	the	the	DET
ejpam-3708	141	10	above	above	ADJ
ejpam-3708	141	11	sequence	sequence	NOUN
ejpam-3708	141	12	spaces	space	VERB
ejpam-3708	141	13	:	:	PUNCT
ejpam-3708	141	14	(	(	PUNCT
ejpam-3708	141	15	i	i	NOUN
ejpam-3708	141	16	)	)	PUNCT
ejpam-3708	141	17	if	if	SCONJ
ejpam-3708	141	18	mk(x	mk(x	NOUN
ejpam-3708	141	19	)	)	PUNCT
ejpam-3708	141	20	=	=	SYM
ejpam-3708	142	1	x	x	X
ejpam-3708	142	2	for	for	ADP
ejpam-3708	142	3	all	all	DET
ejpam-3708	142	4	k	k	PROPN
ejpam-3708	142	5	∈	∈	PROPN
ejpam-3708	142	6	n	n	CCONJ
ejpam-3708	142	7	,	,	PUNCT
ejpam-3708	142	8	then	then	ADV
ejpam-3708	142	9	we	we	PRON
ejpam-3708	142	10	have	have	VERB
ejpam-3708	142	11	w	w	NOUN
ejpam-3708	142	12	i(f	i(f	NOUN
ejpam-3708	142	13	)	)	PUNCT
ejpam-3708	142	14	θ	θ	PROPN
ejpam-3708	143	1	[	[	X
ejpam-3708	143	2	a	a	X
ejpam-3708	143	3	,	,	PUNCT
ejpam-3708	143	4	m	m	PROPN
ejpam-3708	143	5	,	,	PUNCT
ejpam-3708	143	6	p	p	X
ejpam-3708	143	7	,	,	PUNCT
ejpam-3708	143	8	u,∆m	u,∆m	PROPN
ejpam-3708	143	9	v	v	NOUN
ejpam-3708	143	10	]	]	PUNCT
ejpam-3708	143	11	=	=	PUNCT
ejpam-3708	143	12	w	w	PROPN
ejpam-3708	143	13	i(f	i(f	NOUN
ejpam-3708	143	14	)	)	PUNCT
ejpam-3708	143	15	θ	θ	PROPN
ejpam-3708	144	1	[	[	X
ejpam-3708	144	2	a	a	X
ejpam-3708	144	3	,	,	PUNCT
ejpam-3708	144	4	p	p	X
ejpam-3708	144	5	,	,	PUNCT
ejpam-3708	144	6	u,∆m	u,∆m	PROPN
ejpam-3708	144	7	v	v	X
ejpam-3708	144	8	]	]	PUNCT
ejpam-3708	144	9	,	,	PUNCT
ejpam-3708	144	10	w	w	PROPN
ejpam-3708	144	11	i(f	i(f	NOUN
ejpam-3708	144	12	)	)	PUNCT
ejpam-3708	144	13	θ	θ	PROPN
ejpam-3708	145	1	[	[	X
ejpam-3708	145	2	a	a	X
ejpam-3708	145	3	,	,	PUNCT
ejpam-3708	145	4	m	m	PROPN
ejpam-3708	145	5	,	,	PUNCT
ejpam-3708	145	6	p	p	X
ejpam-3708	145	7	,	,	PUNCT
ejpam-3708	145	8	u,∆m	u,∆m	PROPN
ejpam-3708	145	9	v	v	X
ejpam-3708	145	10	]	]	PUNCT
ejpam-3708	145	11	0	0	PUNCT
ejpam-3708	145	12	=	=	SYM
ejpam-3708	145	13	w	w	PROPN
ejpam-3708	145	14	i(f	i(f	NOUN
ejpam-3708	145	15	)	)	PUNCT
ejpam-3708	145	16	θ	θ	PROPN
ejpam-3708	146	1	[	[	X
ejpam-3708	146	2	a	a	X
ejpam-3708	146	3	,	,	PUNCT
ejpam-3708	146	4	p	p	X
ejpam-3708	146	5	,	,	PUNCT
ejpam-3708	146	6	u,∆m	u,∆m	PROPN
ejpam-3708	146	7	v	v	X
ejpam-3708	146	8	]	]	PUNCT
ejpam-3708	146	9	0	0	NUM
ejpam-3708	146	10	,	,	PUNCT
ejpam-3708	146	11	w	w	PROPN
ejpam-3708	146	12	f	f	NOUN
ejpam-3708	146	13	θ	θ	PROPN
ejpam-3708	147	1	[	[	X
ejpam-3708	147	2	a	a	X
ejpam-3708	147	3	,	,	PUNCT
ejpam-3708	147	4	m	m	PROPN
ejpam-3708	147	5	,	,	PUNCT
ejpam-3708	147	6	p	p	X
ejpam-3708	147	7	,	,	PUNCT
ejpam-3708	147	8	u,∆m	u,∆m	PROPN
ejpam-3708	147	9	v	v	X
ejpam-3708	147	10	]	]	PUNCT
ejpam-3708	147	11	∞	∞	NUM
ejpam-3708	147	12	=	=	SYM
ejpam-3708	147	13	wfθ	wfθ	NOUN
ejpam-3708	148	1	[	[	X
ejpam-3708	148	2	a	a	X
ejpam-3708	148	3	,	,	PUNCT
ejpam-3708	148	4	p	p	X
ejpam-3708	148	5	,	,	PUNCT
ejpam-3708	148	6	u,∆m	u,∆m	PROPN
ejpam-3708	148	7	v	v	X
ejpam-3708	148	8	]	]	PUNCT
ejpam-3708	148	9	∞	∞	PROPN
ejpam-3708	148	10	and	and	CCONJ
ejpam-3708	148	11	w	w	NOUN
ejpam-3708	148	12	i(f	i(f	NOUN
ejpam-3708	148	13	)	)	PUNCT
ejpam-3708	148	14	θ	θ	PROPN
ejpam-3708	149	1	[	[	X
ejpam-3708	149	2	a	a	X
ejpam-3708	149	3	,	,	PUNCT
ejpam-3708	149	4	m	m	PROPN
ejpam-3708	149	5	,	,	PUNCT
ejpam-3708	149	6	p	p	X
ejpam-3708	149	7	,	,	PUNCT
ejpam-3708	149	8	u,∆m	u,∆m	PROPN
ejpam-3708	149	9	v	v	X
ejpam-3708	149	10	]	]	PUNCT
ejpam-3708	149	11	∞	∞	PUNCT
ejpam-3708	149	12	=	=	SYM
ejpam-3708	149	13	w	w	PROPN
ejpam-3708	149	14	i(f	i(f	NOUN
ejpam-3708	149	15	)	)	PUNCT
ejpam-3708	149	16	θ	θ	PROPN
ejpam-3708	150	1	[	[	X
ejpam-3708	150	2	a	a	X
ejpam-3708	150	3	,	,	PUNCT
ejpam-3708	150	4	p	p	X
ejpam-3708	150	5	,	,	PUNCT
ejpam-3708	150	6	u,∆m	u,∆m	PROPN
ejpam-3708	150	7	v	v	NOUN
ejpam-3708	150	8	]	]	X
ejpam-3708	150	9	∞.	∞.	PROPN
ejpam-3708	150	10	(	(	PUNCT
ejpam-3708	150	11	ii	ii	PROPN
ejpam-3708	150	12	)	)	PUNCT
ejpam-3708	150	13	if	if	SCONJ
ejpam-3708	150	14	p	p	NOUN
ejpam-3708	150	15	=	=	SYM
ejpam-3708	150	16	(	(	PUNCT
ejpam-3708	150	17	pk	pk	NOUN
ejpam-3708	150	18	)	)	PUNCT
ejpam-3708	150	19	=	=	SYM
ejpam-3708	150	20	1	1	NUM
ejpam-3708	150	21	,	,	PUNCT
ejpam-3708	150	22	for	for	ADP
ejpam-3708	150	23	all	all	DET
ejpam-3708	150	24	k	k	NOUN
ejpam-3708	150	25	,	,	PUNCT
ejpam-3708	150	26	then	then	ADV
ejpam-3708	150	27	we	we	PRON
ejpam-3708	150	28	have	have	VERB
ejpam-3708	150	29	w	w	NOUN
ejpam-3708	150	30	i(f	i(f	NOUN
ejpam-3708	150	31	)	)	PUNCT
ejpam-3708	150	32	θ	θ	PROPN
ejpam-3708	151	1	[	[	X
ejpam-3708	151	2	a	a	X
ejpam-3708	151	3	,	,	PUNCT
ejpam-3708	151	4	m	m	PROPN
ejpam-3708	151	5	,	,	PUNCT
ejpam-3708	151	6	p	p	X
ejpam-3708	151	7	,	,	PUNCT
ejpam-3708	151	8	u,∆m	u,∆m	PROPN
ejpam-3708	151	9	v	v	NOUN
ejpam-3708	151	10	]	]	PUNCT
ejpam-3708	151	11	=	=	PUNCT
ejpam-3708	151	12	w	w	PROPN
ejpam-3708	151	13	i(f	i(f	NOUN
ejpam-3708	151	14	)	)	PUNCT
ejpam-3708	151	15	θ	θ	PROPN
ejpam-3708	152	1	[	[	X
ejpam-3708	152	2	a	a	X
ejpam-3708	152	3	,	,	PUNCT
ejpam-3708	152	4	m	m	PROPN
ejpam-3708	152	5	,	,	PUNCT
ejpam-3708	152	6	u,∆m	u,∆m	PROPN
ejpam-3708	152	7	v	v	X
ejpam-3708	152	8	]	]	PUNCT
ejpam-3708	152	9	,	,	PUNCT
ejpam-3708	152	10	w	w	PROPN
ejpam-3708	152	11	i(f	i(f	NOUN
ejpam-3708	152	12	)	)	PUNCT
ejpam-3708	152	13	θ	θ	PROPN
ejpam-3708	153	1	[	[	X
ejpam-3708	153	2	a	a	X
ejpam-3708	153	3	,	,	PUNCT
ejpam-3708	153	4	m	m	PROPN
ejpam-3708	153	5	,	,	PUNCT
ejpam-3708	153	6	p	p	X
ejpam-3708	153	7	,	,	PUNCT
ejpam-3708	153	8	u,∆m	u,∆m	PROPN
ejpam-3708	153	9	v	v	X
ejpam-3708	153	10	]	]	PUNCT
ejpam-3708	153	11	0	0	PUNCT
ejpam-3708	153	12	=	=	SYM
ejpam-3708	153	13	w	w	PROPN
ejpam-3708	153	14	i(f	i(f	NOUN
ejpam-3708	153	15	)	)	PUNCT
ejpam-3708	153	16	θ	θ	PROPN
ejpam-3708	154	1	[	[	X
ejpam-3708	154	2	a	a	X
ejpam-3708	154	3	,	,	PUNCT
ejpam-3708	154	4	m	m	PROPN
ejpam-3708	154	5	,	,	PUNCT
ejpam-3708	154	6	u,∆m	u,∆m	PROPN
ejpam-3708	154	7	v	v	X
ejpam-3708	154	8	]	]	PUNCT
ejpam-3708	154	9	0	0	NUM
ejpam-3708	154	10	,	,	PUNCT
ejpam-3708	154	11	w	w	PROPN
ejpam-3708	154	12	f	f	NOUN
ejpam-3708	154	13	θ	θ	PROPN
ejpam-3708	155	1	[	[	X
ejpam-3708	155	2	a	a	X
ejpam-3708	155	3	,	,	PUNCT
ejpam-3708	155	4	m	m	PROPN
ejpam-3708	155	5	,	,	PUNCT
ejpam-3708	155	6	p	p	X
ejpam-3708	155	7	,	,	PUNCT
ejpam-3708	155	8	u,∆m	u,∆m	PROPN
ejpam-3708	155	9	v	v	X
ejpam-3708	155	10	]	]	PUNCT
ejpam-3708	155	11	∞	∞	NUM
ejpam-3708	155	12	=	=	SYM
ejpam-3708	155	13	wfθ	wfθ	NOUN
ejpam-3708	156	1	[	[	X
ejpam-3708	156	2	a	a	X
ejpam-3708	156	3	,	,	PUNCT
ejpam-3708	156	4	m	m	PROPN
ejpam-3708	156	5	,	,	PUNCT
ejpam-3708	156	6	u,∆m	u,∆m	PROPN
ejpam-3708	156	7	v	v	X
ejpam-3708	156	8	]	]	PUNCT
ejpam-3708	156	9	∞	∞	PROPN
ejpam-3708	156	10	and	and	CCONJ
ejpam-3708	156	11	w	w	NOUN
ejpam-3708	156	12	i(f	i(f	NOUN
ejpam-3708	156	13	)	)	PUNCT
ejpam-3708	156	14	θ	θ	PROPN
ejpam-3708	157	1	[	[	X
ejpam-3708	157	2	a	a	X
ejpam-3708	157	3	,	,	PUNCT
ejpam-3708	157	4	m	m	PROPN
ejpam-3708	157	5	,	,	PUNCT
ejpam-3708	157	6	p	p	X
ejpam-3708	157	7	,	,	PUNCT
ejpam-3708	157	8	u,∆m	u,∆m	PROPN
ejpam-3708	157	9	v	v	X
ejpam-3708	157	10	]	]	PUNCT
ejpam-3708	157	11	∞	∞	PUNCT
ejpam-3708	157	12	=	=	SYM
ejpam-3708	157	13	w	w	PROPN
ejpam-3708	157	14	i(f	i(f	NOUN
ejpam-3708	157	15	)	)	PUNCT
ejpam-3708	157	16	θ	θ	PROPN
ejpam-3708	158	1	[	[	X
ejpam-3708	158	2	a	a	X
ejpam-3708	158	3	,	,	PUNCT
ejpam-3708	158	4	m	m	PROPN
ejpam-3708	158	5	,	,	PUNCT
ejpam-3708	158	6	u,∆m	u,∆m	PROPN
ejpam-3708	158	7	v	v	NOUN
ejpam-3708	158	8	]	]	PUNCT
ejpam-3708	158	9	∞.	∞.	PROPN
ejpam-3708	158	10	k.	k.	PROPN
ejpam-3708	158	11	raj	raj	PROPN
ejpam-3708	158	12	,	,	PUNCT
ejpam-3708	158	13	s.	s.	PROPN
ejpam-3708	158	14	a.	a.	PROPN
ejpam-3708	158	15	mohiuddine	mohiuddine	PROPN
ejpam-3708	158	16	/	/	SYM
ejpam-3708	158	17	eur	eur	PROPN
ejpam-3708	158	18	.	.	PUNCT
ejpam-3708	159	1	j.	j.	PROPN
ejpam-3708	159	2	pure	pure	PROPN
ejpam-3708	159	3	appl	appl	PROPN
ejpam-3708	159	4	.	.	PROPN
ejpam-3708	159	5	math	math	PROPN
ejpam-3708	159	6	,	,	PUNCT
ejpam-3708	159	7	13	13	NUM
ejpam-3708	159	8	(	(	PUNCT
ejpam-3708	159	9	5	5	NUM
ejpam-3708	159	10	)	)	PUNCT
ejpam-3708	159	11	(	(	PUNCT
ejpam-3708	159	12	2020	2020	NUM
ejpam-3708	159	13	)	)	PUNCT
ejpam-3708	159	14	,	,	PUNCT
ejpam-3708	159	15	1131	1131	NUM
ejpam-3708	159	16	-	-	SYM
ejpam-3708	159	17	1148	1148	NUM
ejpam-3708	159	18	1137	1137	NUM
ejpam-3708	159	19	(	(	PUNCT
ejpam-3708	159	20	iii	iii	NOUN
ejpam-3708	159	21	)	)	PUNCT
ejpam-3708	159	22	if	if	SCONJ
ejpam-3708	159	23	we	we	PRON
ejpam-3708	159	24	take	take	VERB
ejpam-3708	159	25	a	a	DET
ejpam-3708	159	26	=	=	PUNCT
ejpam-3708	159	27	(	(	PUNCT
ejpam-3708	159	28	c	c	NOUN
ejpam-3708	159	29	,	,	PUNCT
ejpam-3708	159	30	1	1	NUM
ejpam-3708	159	31	)	)	PUNCT
ejpam-3708	159	32	,	,	PUNCT
ejpam-3708	159	33	i.e.	i.e.	X
ejpam-3708	159	34	,	,	PUNCT
ejpam-3708	159	35	the	the	DET
ejpam-3708	159	36	cesàro	cesàro	PROPN
ejpam-3708	159	37	matrix	matrix	NOUN
ejpam-3708	159	38	,	,	PUNCT
ejpam-3708	159	39	then	then	ADV
ejpam-3708	159	40	the	the	DET
ejpam-3708	159	41	above	above	ADJ
ejpam-3708	159	42	classes	class	NOUN
ejpam-3708	159	43	of	of	ADP
ejpam-3708	159	44	sequences	sequence	NOUN
ejpam-3708	159	45	are	be	AUX
ejpam-3708	159	46	denoted	denote	VERB
ejpam-3708	159	47	by	by	ADP
ejpam-3708	159	48	w	w	NOUN
ejpam-3708	159	49	i(f	i(f	NOUN
ejpam-3708	159	50	)	)	PUNCT
ejpam-3708	159	51	θ	θ	PROPN
ejpam-3708	160	1	[	[	X
ejpam-3708	160	2	w	w	PROPN
ejpam-3708	160	3	,	,	PUNCT
ejpam-3708	160	4	m	m	PROPN
ejpam-3708	160	5	,	,	PUNCT
ejpam-3708	160	6	p	p	X
ejpam-3708	160	7	,	,	PUNCT
ejpam-3708	160	8	u,∆m	u,∆m	PROPN
ejpam-3708	160	9	v	v	X
ejpam-3708	160	10	]	]	PUNCT
ejpam-3708	160	11	,	,	PUNCT
ejpam-3708	160	12	w	w	PROPN
ejpam-3708	160	13	i(f	i(f	NOUN
ejpam-3708	160	14	)	)	PUNCT
ejpam-3708	160	15	θ	θ	PROPN
ejpam-3708	161	1	[	[	X
ejpam-3708	161	2	w	w	PROPN
ejpam-3708	161	3	,	,	PUNCT
ejpam-3708	161	4	m	m	PROPN
ejpam-3708	161	5	,	,	PUNCT
ejpam-3708	161	6	p	p	X
ejpam-3708	161	7	,	,	PUNCT
ejpam-3708	161	8	u,∆m	u,∆m	PROPN
ejpam-3708	161	9	v	v	X
ejpam-3708	161	10	]	]	PUNCT
ejpam-3708	161	11	0	0	NUM
ejpam-3708	161	12	,	,	PUNCT
ejpam-3708	161	13	w	w	PROPN
ejpam-3708	161	14	f	f	NOUN
ejpam-3708	161	15	θ	θ	PROPN
ejpam-3708	162	1	[	[	X
ejpam-3708	162	2	w	w	PROPN
ejpam-3708	162	3	,	,	PUNCT
ejpam-3708	162	4	m	m	PROPN
ejpam-3708	162	5	,	,	PUNCT
ejpam-3708	162	6	p	p	X
ejpam-3708	162	7	,	,	PUNCT
ejpam-3708	162	8	u,∆m	u,∆m	PROPN
ejpam-3708	162	9	v	v	X
ejpam-3708	162	10	]	]	PUNCT
ejpam-3708	162	11	∞	∞	PROPN
ejpam-3708	162	12	and	and	CCONJ
ejpam-3708	162	13	w	w	NOUN
ejpam-3708	162	14	i(f	i(f	NOUN
ejpam-3708	162	15	)	)	PUNCT
ejpam-3708	162	16	θ	θ	PROPN
ejpam-3708	163	1	[	[	X
ejpam-3708	163	2	w	w	PROPN
ejpam-3708	163	3	,	,	PUNCT
ejpam-3708	163	4	m	m	PROPN
ejpam-3708	163	5	,	,	PUNCT
ejpam-3708	163	6	p	p	X
ejpam-3708	163	7	,	,	PUNCT
ejpam-3708	163	8	u,∆m	u,∆m	PROPN
ejpam-3708	163	9	v	v	X
ejpam-3708	163	10	]	]	PUNCT
ejpam-3708	163	11	∞	∞	NUM
ejpam-3708	163	12	respectively	respectively	ADV
ejpam-3708	163	13	.	.	PUNCT
ejpam-3708	164	1	(	(	PUNCT
ejpam-3708	164	2	iv	iv	X
ejpam-3708	164	3	)	)	PUNCT
ejpam-3708	164	4	if	if	SCONJ
ejpam-3708	164	5	we	we	PRON
ejpam-3708	164	6	take	take	VERB
ejpam-3708	164	7	a	a	DET
ejpam-3708	164	8	=	=	SYM
ejpam-3708	164	9	(	(	PUNCT
ejpam-3708	164	10	ank	ank	PROPN
ejpam-3708	164	11	)	)	PUNCT
ejpam-3708	164	12	a	a	DET
ejpam-3708	164	13	de	de	X
ejpam-3708	164	14	la	la	PROPN
ejpam-3708	164	15	vallée	vallée	PROPN
ejpam-3708	164	16	-	-	PUNCT
ejpam-3708	164	17	poussin	poussin	PROPN
ejpam-3708	164	18	mean	mean	NOUN
ejpam-3708	164	19	,	,	PUNCT
ejpam-3708	164	20	i.e.	i.e.	X
ejpam-3708	164	21	,	,	PUNCT
ejpam-3708	164	22	ank	ank	PROPN
ejpam-3708	164	23	=	=	X
ejpam-3708	164	24	{	{	PUNCT
ejpam-3708	164	25	1	1	NUM
ejpam-3708	164	26	λn	λn	NOUN
ejpam-3708	164	27	,	,	PUNCT
ejpam-3708	164	28	if	if	SCONJ
ejpam-3708	164	29	k	k	PROPN
ejpam-3708	164	30	∈	∈	PROPN
ejpam-3708	164	31	in	in	ADP
ejpam-3708	164	32	=	=	PUNCT
ejpam-3708	165	1	[	[	X
ejpam-3708	165	2	n−	n−	NOUN
ejpam-3708	165	3	λn	λn	NOUN
ejpam-3708	165	4	+	+	NOUN
ejpam-3708	165	5	1	1	NUM
ejpam-3708	165	6	,	,	PUNCT
ejpam-3708	165	7	n	n	CCONJ
ejpam-3708	165	8	]	]	PUNCT
ejpam-3708	165	9	;	;	PUNCT
ejpam-3708	165	10	0	0	NUM
ejpam-3708	165	11	,	,	PUNCT
ejpam-3708	165	12	otherwise	otherwise	ADV
ejpam-3708	165	13	.	.	PUNCT
ejpam-3708	166	1	where	where	SCONJ
ejpam-3708	166	2	(	(	PUNCT
ejpam-3708	166	3	λn	λn	NOUN
ejpam-3708	166	4	)	)	PUNCT
ejpam-3708	166	5	is	be	AUX
ejpam-3708	166	6	a	a	DET
ejpam-3708	166	7	non	non	ADJ
ejpam-3708	166	8	-	-	ADJ
ejpam-3708	166	9	decreasing	decrease	VERB
ejpam-3708	166	10	sequence	sequence	NOUN
ejpam-3708	166	11	of	of	ADP
ejpam-3708	166	12	positive	positive	ADJ
ejpam-3708	166	13	numbers	number	NOUN
ejpam-3708	166	14	tending	tend	VERB
ejpam-3708	166	15	to	to	ADP
ejpam-3708	166	16	∞	∞	PROPN
ejpam-3708	166	17	and	and	CCONJ
ejpam-3708	166	18	λn+1	λn+1	ADP
ejpam-3708	166	19	≤	≤	NUM
ejpam-3708	166	20	λn	λn	ADP
ejpam-3708	166	21	+	+	CCONJ
ejpam-3708	166	22	1	1	NUM
ejpam-3708	166	23	,	,	PUNCT
ejpam-3708	166	24	λ1	λ1	ADJ
ejpam-3708	166	25	=	=	SYM
ejpam-3708	166	26	1	1	NUM
ejpam-3708	166	27	,	,	PUNCT
ejpam-3708	166	28	then	then	ADV
ejpam-3708	166	29	the	the	DET
ejpam-3708	166	30	above	above	ADJ
ejpam-3708	166	31	classes	class	NOUN
ejpam-3708	166	32	of	of	ADP
ejpam-3708	166	33	sequences	sequence	NOUN
ejpam-3708	166	34	are	be	AUX
ejpam-3708	166	35	denoted	denote	VERB
ejpam-3708	166	36	by	by	ADP
ejpam-3708	166	37	w	w	NOUN
ejpam-3708	166	38	i(f	i(f	NOUN
ejpam-3708	166	39	)	)	PUNCT
ejpam-3708	166	40	λ	λ	PROPN
ejpam-3708	167	1	[	[	X
ejpam-3708	167	2	m	m	X
ejpam-3708	167	3	,	,	PUNCT
ejpam-3708	167	4	p	p	X
ejpam-3708	167	5	,	,	PUNCT
ejpam-3708	167	6	u,∆m	u,∆m	PROPN
ejpam-3708	167	7	v	v	X
ejpam-3708	167	8	]	]	PUNCT
ejpam-3708	167	9	,	,	PUNCT
ejpam-3708	167	10	w	w	PROPN
ejpam-3708	167	11	i(f	i(f	NOUN
ejpam-3708	167	12	)	)	PUNCT
ejpam-3708	168	1	λ	λ	PROPN
ejpam-3708	169	1	[	[	X
ejpam-3708	169	2	m	m	X
ejpam-3708	169	3	,	,	PUNCT
ejpam-3708	169	4	p	p	X
ejpam-3708	169	5	,	,	PUNCT
ejpam-3708	169	6	u,∆m	u,∆m	PROPN
ejpam-3708	169	7	v	v	X
ejpam-3708	169	8	]	]	PUNCT
ejpam-3708	169	9	0	0	NUM
ejpam-3708	169	10	,	,	PUNCT
ejpam-3708	169	11	w	w	PROPN
ejpam-3708	169	12	f	f	PROPN
ejpam-3708	169	13	λ	λ	PROPN
ejpam-3708	170	1	[	[	X
ejpam-3708	170	2	m	m	X
ejpam-3708	170	3	,	,	PUNCT
ejpam-3708	170	4	p	p	X
ejpam-3708	170	5	,	,	PUNCT
ejpam-3708	170	6	u,∆m	u,∆m	PROPN
ejpam-3708	170	7	v	v	X
ejpam-3708	170	8	]	]	PUNCT
ejpam-3708	170	9	∞	∞	PROPN
ejpam-3708	170	10	and	and	CCONJ
ejpam-3708	170	11	w	w	NOUN
ejpam-3708	170	12	i(f	i(f	NOUN
ejpam-3708	170	13	)	)	PUNCT
ejpam-3708	170	14	λ	λ	PROPN
ejpam-3708	171	1	[	[	X
ejpam-3708	171	2	m	m	X
ejpam-3708	171	3	,	,	PUNCT
ejpam-3708	171	4	p	p	X
ejpam-3708	171	5	,	,	PUNCT
ejpam-3708	171	6	u,∆m	u,∆m	PROPN
ejpam-3708	171	7	v	v	X
ejpam-3708	171	8	]	]	PUNCT
ejpam-3708	171	9	∞	∞	NUM
ejpam-3708	171	10	respectively	respectively	ADV
ejpam-3708	171	11	.	.	PUNCT
ejpam-3708	172	1	(	(	PUNCT
ejpam-3708	172	2	v	v	NOUN
ejpam-3708	172	3	)	)	PUNCT
ejpam-3708	172	4	if	if	SCONJ
ejpam-3708	172	5	i	i	PRON
ejpam-3708	172	6	=	=	PUNCT
ejpam-3708	173	1	if	if	SCONJ
ejpam-3708	173	2	then	then	ADV
ejpam-3708	173	3	we	we	PRON
ejpam-3708	173	4	obtain	obtain	VERB
ejpam-3708	173	5	wfθ	wfθ	NOUN
ejpam-3708	173	6	[	[	X
ejpam-3708	173	7	a	a	X
ejpam-3708	173	8	,	,	PUNCT
ejpam-3708	173	9	m	m	PROPN
ejpam-3708	173	10	,	,	PUNCT
ejpam-3708	173	11	p	p	X
ejpam-3708	173	12	,	,	PUNCT
ejpam-3708	173	13	u,∆m	u,∆m	PROPN
ejpam-3708	173	14	v	v	NOUN
ejpam-3708	173	15	]	]	X
ejpam-3708	173	16	=	=	X
ejpam-3708	173	17	{	{	PUNCT
ejpam-3708	173	18	(	(	PUNCT
ejpam-3708	173	19	xk	xk	INTJ
ejpam-3708	173	20	)	)	PUNCT
ejpam-3708	173	21	∈	∈	PROPN
ejpam-3708	173	22	wf	wf	PROPN
ejpam-3708	173	23	:	:	PUNCT
ejpam-3708	173	24	lim	lim	PROPN
ejpam-3708	173	25	n	n	CCONJ
ejpam-3708	173	26	,	,	PUNCT
ejpam-3708	173	27	r→∞	r→∞	NUM
ejpam-3708	173	28	1	1	NUM
ejpam-3708	173	29	hr	hr	NOUN
ejpam-3708	173	30	∑	∑	PUNCT
ejpam-3708	173	31	k∈ir	k∈ir	PROPN
ejpam-3708	173	32	ank	ank	PROPN
ejpam-3708	173	33	[	[	PUNCT
ejpam-3708	173	34	k−smk	k−smk	NOUN
ejpam-3708	173	35	(	(	PUNCT
ejpam-3708	173	36	d(uk∆	d(uk∆	PROPN
ejpam-3708	173	37	m	m	NOUN
ejpam-3708	173	38	v	v	NOUN
ejpam-3708	173	39	xk	xk	PROPN
ejpam-3708	173	40	,	,	PUNCT
ejpam-3708	173	41	x0	x0	PROPN
ejpam-3708	173	42	)	)	PUNCT
ejpam-3708	173	43	ρ	ρ	PROPN
ejpam-3708	173	44	)	)	PUNCT
ejpam-3708	173	45	]	]	PUNCT
ejpam-3708	173	46	pk	pk	X
ejpam-3708	173	47	=	=	NOUN
ejpam-3708	173	48	0	0	NUM
ejpam-3708	173	49	,	,	PUNCT
ejpam-3708	173	50	for	for	ADP
ejpam-3708	173	51	some	some	DET
ejpam-3708	173	52	ρ	ρ	NOUN
ejpam-3708	173	53	>	>	X
ejpam-3708	173	54	0	0	PUNCT
ejpam-3708	173	55	and	and	CCONJ
ejpam-3708	173	56	s	s	X
ejpam-3708	173	57	≥	≥	NOUN
ejpam-3708	173	58	0	0	NUM
ejpam-3708	173	59	,	,	PUNCT
ejpam-3708	173	60	x0	x0	PROPN
ejpam-3708	173	61	∈	∈	PROPN
ejpam-3708	173	62	l(r	l(r	PROPN
ejpam-3708	173	63	)	)	PUNCT
ejpam-3708	173	64	}	}	PUNCT
ejpam-3708	173	65	,	,	PUNCT
ejpam-3708	173	66	wfθ	wfθ	NOUN
ejpam-3708	174	1	[	[	X
ejpam-3708	174	2	a	a	X
ejpam-3708	174	3	,	,	PUNCT
ejpam-3708	174	4	m	m	PROPN
ejpam-3708	174	5	,	,	PUNCT
ejpam-3708	174	6	p	p	X
ejpam-3708	174	7	,	,	PUNCT
ejpam-3708	174	8	u,∆m	u,∆m	PROPN
ejpam-3708	174	9	v	v	X
ejpam-3708	174	10	]	]	PUNCT
ejpam-3708	174	11	0	0	PUNCT
ejpam-3708	174	12	=	=	SYM
ejpam-3708	174	13	{	{	PUNCT
ejpam-3708	174	14	(	(	PUNCT
ejpam-3708	174	15	xk	xk	INTJ
ejpam-3708	174	16	)	)	PUNCT
ejpam-3708	174	17	∈	∈	PROPN
ejpam-3708	174	18	wf	wf	PROPN
ejpam-3708	174	19	:	:	PUNCT
ejpam-3708	174	20	lim	lim	PROPN
ejpam-3708	174	21	n	n	CCONJ
ejpam-3708	174	22	,	,	PUNCT
ejpam-3708	174	23	r→∞	r→∞	NUM
ejpam-3708	174	24	1	1	NUM
ejpam-3708	174	25	hr	hr	NOUN
ejpam-3708	174	26	∑	∑	PUNCT
ejpam-3708	174	27	k∈ir	k∈ir	PROPN
ejpam-3708	174	28	ank	ank	PROPN
ejpam-3708	174	29	[	[	PUNCT
ejpam-3708	174	30	k−smk	k−smk	NOUN
ejpam-3708	174	31	(	(	PUNCT
ejpam-3708	174	32	d(uk∆	d(uk∆	PROPN
ejpam-3708	174	33	m	m	NOUN
ejpam-3708	174	34	v	v	NOUN
ejpam-3708	174	35	xk	xk	PROPN
ejpam-3708	174	36	,	,	PUNCT
ejpam-3708	174	37	x0	x0	PROPN
ejpam-3708	174	38	)	)	PUNCT
ejpam-3708	174	39	ρ	ρ	PROPN
ejpam-3708	174	40	)	)	PUNCT
ejpam-3708	174	41	]	]	PUNCT
ejpam-3708	174	42	pk	pk	X
ejpam-3708	174	43	=	=	NOUN
ejpam-3708	174	44	0	0	NUM
ejpam-3708	174	45	,	,	PUNCT
ejpam-3708	174	46	for	for	ADP
ejpam-3708	174	47	some	some	DET
ejpam-3708	174	48	ρ	ρ	NOUN
ejpam-3708	174	49	>	>	X
ejpam-3708	174	50	0	0	PUNCT
ejpam-3708	174	51	and	and	CCONJ
ejpam-3708	174	52	s	s	X
ejpam-3708	174	53	≥	≥	NOUN
ejpam-3708	174	54	0	0	NUM
ejpam-3708	174	55	}	}	PUNCT
ejpam-3708	174	56	,	,	PUNCT
ejpam-3708	174	57	wfθ	wfθ	NOUN
ejpam-3708	175	1	[	[	X
ejpam-3708	175	2	a	a	X
ejpam-3708	175	3	,	,	PUNCT
ejpam-3708	175	4	m	m	PROPN
ejpam-3708	175	5	,	,	PUNCT
ejpam-3708	175	6	p	p	X
ejpam-3708	175	7	,	,	PUNCT
ejpam-3708	175	8	u,∆m	u,∆m	PROPN
ejpam-3708	175	9	v	v	X
ejpam-3708	175	10	]	]	PUNCT
ejpam-3708	175	11	∞	∞	NUM
ejpam-3708	175	12	=	=	SYM
ejpam-3708	175	13	{	{	PUNCT
ejpam-3708	175	14	(	(	PUNCT
ejpam-3708	175	15	xk	xk	INTJ
ejpam-3708	175	16	)	)	PUNCT
ejpam-3708	175	17	∈	∈	PROPN
ejpam-3708	175	18	wf	wf	PROPN
ejpam-3708	175	19	:	:	PUNCT
ejpam-3708	175	20	lim	lim	PROPN
ejpam-3708	175	21	n	n	CCONJ
ejpam-3708	175	22	,	,	PUNCT
ejpam-3708	175	23	r→∞	r→∞	NUM
ejpam-3708	175	24	1	1	NUM
ejpam-3708	175	25	hr	hr	NOUN
ejpam-3708	175	26	∑	∑	PUNCT
ejpam-3708	175	27	k∈ir	k∈ir	PROPN
ejpam-3708	175	28	ank	ank	PROPN
ejpam-3708	175	29	[	[	PUNCT
ejpam-3708	175	30	k−smk	k−smk	NOUN
ejpam-3708	175	31	(	(	PUNCT
ejpam-3708	175	32	d(uk∆	d(uk∆	PROPN
ejpam-3708	175	33	m	m	NOUN
ejpam-3708	175	34	v	v	NOUN
ejpam-3708	175	35	xk	xk	PROPN
ejpam-3708	175	36	,	,	PUNCT
ejpam-3708	175	37	0	0	NUM
ejpam-3708	175	38	)	)	PUNCT
ejpam-3708	175	39	ρ	ρ	NOUN
ejpam-3708	175	40	)	)	PUNCT
ejpam-3708	175	41	]	]	X
ejpam-3708	175	42	pk	pk	NOUN
ejpam-3708	175	43	<	<	X
ejpam-3708	175	44	∞	∞	PROPN
ejpam-3708	175	45	,	,	PUNCT
ejpam-3708	175	46	for	for	ADP
ejpam-3708	175	47	some	some	DET
ejpam-3708	175	48	ρ	ρ	NOUN
ejpam-3708	175	49	>	>	X
ejpam-3708	175	50	0	0	PUNCT
ejpam-3708	175	51	and	and	CCONJ
ejpam-3708	175	52	s	s	X
ejpam-3708	175	53	≥	≥	NOUN
ejpam-3708	175	54	0	0	NUM
ejpam-3708	175	55	}	}	PUNCT
ejpam-3708	175	56	.	.	PUNCT
ejpam-3708	176	1	k.	k.	PROPN
ejpam-3708	176	2	raj	raj	PROPN
ejpam-3708	176	3	,	,	PUNCT
ejpam-3708	176	4	s.	s.	PROPN
ejpam-3708	176	5	a.	a.	PROPN
ejpam-3708	176	6	mohiuddine	mohiuddine	PROPN
ejpam-3708	176	7	/	/	SYM
ejpam-3708	176	8	eur	eur	PROPN
ejpam-3708	176	9	.	.	PUNCT
ejpam-3708	177	1	j.	j.	PROPN
ejpam-3708	177	2	pure	pure	PROPN
ejpam-3708	177	3	appl	appl	PROPN
ejpam-3708	177	4	.	.	PROPN
ejpam-3708	177	5	math	math	PROPN
ejpam-3708	177	6	,	,	PUNCT
ejpam-3708	177	7	13	13	NUM
ejpam-3708	177	8	(	(	PUNCT
ejpam-3708	177	9	5	5	NUM
ejpam-3708	177	10	)	)	PUNCT
ejpam-3708	177	11	(	(	PUNCT
ejpam-3708	177	12	2020	2020	NUM
ejpam-3708	177	13	)	)	PUNCT
ejpam-3708	177	14	,	,	PUNCT
ejpam-3708	177	15	1131	1131	NUM
ejpam-3708	177	16	-	-	SYM
ejpam-3708	177	17	1148	1148	NUM
ejpam-3708	177	18	1138	1138	NUM
ejpam-3708	177	19	(	(	PUNCT
ejpam-3708	177	20	vi	vi	NOUN
ejpam-3708	177	21	)	)	PUNCT
ejpam-3708	177	22	if	if	SCONJ
ejpam-3708	177	23	i	i	PRON
ejpam-3708	177	24	=	=	PRON
ejpam-3708	177	25	iδ	iδ	PROPN
ejpam-3708	177	26	is	be	AUX
ejpam-3708	177	27	an	an	DET
ejpam-3708	177	28	admissible	admissible	ADJ
ejpam-3708	177	29	ideal	ideal	NOUN
ejpam-3708	177	30	of	of	ADP
ejpam-3708	177	31	n	n	CCONJ
ejpam-3708	177	32	,	,	PUNCT
ejpam-3708	177	33	then	then	ADV
ejpam-3708	177	34	w	w	PROPN
ejpam-3708	177	35	i(f	i(f	NOUN
ejpam-3708	177	36	)	)	PUNCT
ejpam-3708	177	37	θ	θ	PROPN
ejpam-3708	178	1	[	[	X
ejpam-3708	178	2	a	a	X
ejpam-3708	178	3	,	,	PUNCT
ejpam-3708	178	4	m	m	PROPN
ejpam-3708	178	5	,	,	PUNCT
ejpam-3708	178	6	p	p	X
ejpam-3708	178	7	,	,	PUNCT
ejpam-3708	178	8	u,∆m	u,∆m	PROPN
ejpam-3708	178	9	v	v	NOUN
ejpam-3708	178	10	]	]	X
ejpam-3708	178	11	=	=	X
ejpam-3708	178	12	{	{	PUNCT
ejpam-3708	178	13	(	(	PUNCT
ejpam-3708	178	14	xk	xk	INTJ
ejpam-3708	178	15	)	)	PUNCT
ejpam-3708	178	16	∈	∈	PROPN
ejpam-3708	178	17	wf	wf	PROPN
ejpam-3708	178	18	:	:	PUNCT
ejpam-3708	178	19	∀ε	∀ε	X
ejpam-3708	178	20	>	>	X
ejpam-3708	178	21	0	0	NUM
ejpam-3708	178	22	,	,	PUNCT
ejpam-3708	178	23	{	{	PUNCT
ejpam-3708	178	24	n	n	CCONJ
ejpam-3708	178	25	,	,	PUNCT
ejpam-3708	178	26	r	r	NOUN
ejpam-3708	178	27	∈	∈	PROPN
ejpam-3708	178	28	n	n	CCONJ
ejpam-3708	178	29	:	:	PUNCT
ejpam-3708	178	30	1	1	NUM
ejpam-3708	178	31	hr	hr	NOUN
ejpam-3708	178	32	∑	∑	PUNCT
ejpam-3708	178	33	k∈ir	k∈ir	PROPN
ejpam-3708	178	34	ank	ank	PROPN
ejpam-3708	178	35	[	[	PUNCT
ejpam-3708	178	36	k−smk	k−smk	NOUN
ejpam-3708	178	37	(	(	PUNCT
ejpam-3708	178	38	d(uk∆	d(uk∆	PROPN
ejpam-3708	178	39	m	m	NOUN
ejpam-3708	178	40	v	v	NOUN
ejpam-3708	178	41	xk	xk	PROPN
ejpam-3708	178	42	,	,	PUNCT
ejpam-3708	178	43	x0	x0	PROPN
ejpam-3708	178	44	)	)	PUNCT
ejpam-3708	178	45	ρ	ρ	PROPN
ejpam-3708	178	46	)	)	PUNCT
ejpam-3708	178	47	]	]	PUNCT
ejpam-3708	178	48	pk	pk	NOUN
ejpam-3708	178	49	≥	≥	NOUN
ejpam-3708	178	50	ε	ε	PROPN
ejpam-3708	178	51	}	}	PUNCT
ejpam-3708	178	52	∈	∈	PROPN
ejpam-3708	178	53	iδ	iδ	PROPN
ejpam-3708	178	54	,	,	PUNCT
ejpam-3708	178	55	for	for	ADP
ejpam-3708	178	56	some	some	DET
ejpam-3708	178	57	ρ	ρ	PROPN
ejpam-3708	178	58	>	>	X
ejpam-3708	178	59	0	0	NUM
ejpam-3708	178	60	,	,	PUNCT
ejpam-3708	178	61	s	s	VERB
ejpam-3708	178	62	≥	≥	NOUN
ejpam-3708	178	63	0	0	NUM
ejpam-3708	178	64	and	and	CCONJ
ejpam-3708	178	65	x0	x0	PROPN
ejpam-3708	178	66	∈	∈	PROPN
ejpam-3708	178	67	l(r	l(r	PROPN
ejpam-3708	178	68	)	)	PUNCT
ejpam-3708	178	69	}	}	PUNCT
ejpam-3708	178	70	,	,	PUNCT
ejpam-3708	178	71	w	w	NOUN
ejpam-3708	178	72	i(f	i(f	NOUN
ejpam-3708	178	73	)	)	PUNCT
ejpam-3708	178	74	θ	θ	PROPN
ejpam-3708	179	1	[	[	X
ejpam-3708	179	2	a	a	X
ejpam-3708	179	3	,	,	PUNCT
ejpam-3708	179	4	m	m	PROPN
ejpam-3708	179	5	,	,	PUNCT
ejpam-3708	179	6	p	p	X
ejpam-3708	179	7	,	,	PUNCT
ejpam-3708	179	8	u,∆m	u,∆m	PROPN
ejpam-3708	179	9	v	v	X
ejpam-3708	179	10	]	]	PUNCT
ejpam-3708	179	11	0	0	PUNCT
ejpam-3708	179	12	=	=	SYM
ejpam-3708	179	13	{	{	PUNCT
ejpam-3708	179	14	(	(	PUNCT
ejpam-3708	179	15	xk	xk	INTJ
ejpam-3708	179	16	)	)	PUNCT
ejpam-3708	179	17	∈	∈	PROPN
ejpam-3708	179	18	wf	wf	PROPN
ejpam-3708	179	19	:	:	PUNCT
ejpam-3708	179	20	∀ε	∀ε	X
ejpam-3708	179	21	>	>	X
ejpam-3708	179	22	0	0	NUM
ejpam-3708	179	23	,	,	PUNCT
ejpam-3708	179	24	{	{	PUNCT
ejpam-3708	179	25	n	n	CCONJ
ejpam-3708	179	26	,	,	PUNCT
ejpam-3708	179	27	r	r	NOUN
ejpam-3708	179	28	∈	∈	PROPN
ejpam-3708	179	29	n	n	CCONJ
ejpam-3708	179	30	:	:	PUNCT
ejpam-3708	179	31	1	1	NUM
ejpam-3708	179	32	hr	hr	NOUN
ejpam-3708	179	33	∑	∑	PUNCT
ejpam-3708	179	34	k∈ir	k∈ir	PROPN
ejpam-3708	179	35	ank	ank	PROPN
ejpam-3708	179	36	[	[	PUNCT
ejpam-3708	179	37	k−smk	k−smk	NOUN
ejpam-3708	179	38	(	(	PUNCT
ejpam-3708	179	39	d(uk∆	d(uk∆	PROPN
ejpam-3708	179	40	m	m	NOUN
ejpam-3708	179	41	v	v	NOUN
ejpam-3708	179	42	xk	xk	PROPN
ejpam-3708	179	43	,	,	PUNCT
ejpam-3708	179	44	0	0	NUM
ejpam-3708	179	45	)	)	PUNCT
ejpam-3708	179	46	ρ	ρ	NOUN
ejpam-3708	179	47	)	)	PUNCT
ejpam-3708	179	48	]	]	PUNCT
ejpam-3708	179	49	pk	pk	NOUN
ejpam-3708	179	50	≥	≥	NOUN
ejpam-3708	179	51	ε	ε	PROPN
ejpam-3708	179	52	}	}	PUNCT
ejpam-3708	179	53	∈	∈	PROPN
ejpam-3708	179	54	iδ	iδ	PROPN
ejpam-3708	179	55	,	,	PUNCT
ejpam-3708	179	56	for	for	ADP
ejpam-3708	179	57	some	some	DET
ejpam-3708	179	58	ρ	ρ	NOUN
ejpam-3708	179	59	>	>	X
ejpam-3708	179	60	0	0	PUNCT
ejpam-3708	179	61	and	and	CCONJ
ejpam-3708	179	62	s	s	X
ejpam-3708	179	63	≥	≥	NOUN
ejpam-3708	179	64	0	0	NUM
ejpam-3708	179	65	}	}	PUNCT
ejpam-3708	179	66	,	,	PUNCT
ejpam-3708	179	67	and	and	CCONJ
ejpam-3708	179	68	w	w	PROPN
ejpam-3708	179	69	i(f	i(f	NOUN
ejpam-3708	179	70	)	)	PUNCT
ejpam-3708	179	71	θ	θ	PROPN
ejpam-3708	180	1	[	[	X
ejpam-3708	180	2	a	a	X
ejpam-3708	180	3	,	,	PUNCT
ejpam-3708	180	4	m	m	PROPN
ejpam-3708	180	5	,	,	PUNCT
ejpam-3708	180	6	p	p	X
ejpam-3708	180	7	,	,	PUNCT
ejpam-3708	180	8	u,∆m	u,∆m	PROPN
ejpam-3708	180	9	v	v	X
ejpam-3708	180	10	]	]	PUNCT
ejpam-3708	180	11	∞	∞	NUM
ejpam-3708	180	12	=	=	SYM
ejpam-3708	180	13	{	{	PUNCT
ejpam-3708	180	14	(	(	PUNCT
ejpam-3708	180	15	xk	xk	INTJ
ejpam-3708	180	16	)	)	PUNCT
ejpam-3708	180	17	∈	∈	PROPN
ejpam-3708	180	18	wf	wf	PROPN
ejpam-3708	180	19	:	:	PUNCT
ejpam-3708	181	1	∃	∃	PROPN
ejpam-3708	181	2	k	k	PROPN
ejpam-3708	181	3	>	>	X
ejpam-3708	181	4	0	0	NUM
ejpam-3708	182	1	such	such	ADJ
ejpam-3708	182	2	that	that	SCONJ
ejpam-3708	182	3	{	{	PUNCT
ejpam-3708	182	4	n	n	X
ejpam-3708	182	5	,	,	PUNCT
ejpam-3708	182	6	r	r	NOUN
ejpam-3708	182	7	∈	∈	PROPN
ejpam-3708	182	8	n	n	CCONJ
ejpam-3708	182	9	:	:	PUNCT
ejpam-3708	182	10	1	1	NUM
ejpam-3708	182	11	hr	hr	NOUN
ejpam-3708	182	12	∑	∑	PUNCT
ejpam-3708	182	13	k∈ir	k∈ir	PROPN
ejpam-3708	182	14	ank	ank	PROPN
ejpam-3708	182	15	[	[	PUNCT
ejpam-3708	182	16	k−smk	k−smk	NOUN
ejpam-3708	182	17	(	(	PUNCT
ejpam-3708	182	18	d(uk∆	d(uk∆	PROPN
ejpam-3708	182	19	m	m	NOUN
ejpam-3708	182	20	v	v	NOUN
ejpam-3708	182	21	xk	xk	PROPN
ejpam-3708	182	22	,	,	PUNCT
ejpam-3708	182	23	x0	x0	PROPN
ejpam-3708	182	24	)	)	PUNCT
ejpam-3708	182	25	ρ	ρ	PROPN
ejpam-3708	182	26	)	)	PUNCT
ejpam-3708	182	27	]	]	PUNCT
ejpam-3708	182	28	pk	pk	NOUN
ejpam-3708	182	29	≥	≥	NOUN
ejpam-3708	182	30	k	k	NOUN
ejpam-3708	182	31	}	}	PUNCT
ejpam-3708	182	32	∈	∈	PROPN
ejpam-3708	182	33	iδ	iδ	PROPN
ejpam-3708	182	34	,	,	PUNCT
ejpam-3708	182	35	for	for	ADP
ejpam-3708	182	36	some	some	DET
ejpam-3708	182	37	ρ	ρ	NOUN
ejpam-3708	182	38	>	>	X
ejpam-3708	182	39	0	0	PUNCT
ejpam-3708	182	40	and	and	CCONJ
ejpam-3708	182	41	s	s	X
ejpam-3708	182	42	≥	≥	NOUN
ejpam-3708	182	43	0	0	NUM
ejpam-3708	182	44	}	}	PUNCT
ejpam-3708	182	45	.	.	PUNCT
ejpam-3708	183	1	the	the	DET
ejpam-3708	183	2	following	follow	VERB
ejpam-3708	183	3	inequality	inequality	NOUN
ejpam-3708	183	4	will	will	AUX
ejpam-3708	183	5	be	be	AUX
ejpam-3708	183	6	used	use	VERB
ejpam-3708	183	7	throughout	throughout	ADP
ejpam-3708	183	8	the	the	DET
ejpam-3708	183	9	paper	paper	NOUN
ejpam-3708	183	10	.	.	PUNCT
ejpam-3708	184	1	let	let	VERB
ejpam-3708	184	2	p	p	NOUN
ejpam-3708	184	3	=	=	X
ejpam-3708	184	4	(	(	PUNCT
ejpam-3708	184	5	pk	pk	NOUN
ejpam-3708	184	6	)	)	PUNCT
ejpam-3708	184	7	be	be	AUX
ejpam-3708	184	8	a	a	DET
ejpam-3708	184	9	sequence	sequence	NOUN
ejpam-3708	184	10	of	of	ADP
ejpam-3708	184	11	positive	positive	ADJ
ejpam-3708	184	12	real	real	ADJ
ejpam-3708	184	13	numbers	number	NOUN
ejpam-3708	184	14	with	with	ADP
ejpam-3708	184	15	0	0	NUM
ejpam-3708	184	16	<	<	X
ejpam-3708	184	17	pk	pk	NOUN
ejpam-3708	184	18	≤	≤	X
ejpam-3708	184	19	supk	supk	PRON
ejpam-3708	184	20	pk	pk	NOUN
ejpam-3708	184	21	=	=	NOUN
ejpam-3708	184	22	h	h	NOUN
ejpam-3708	184	23	and	and	CCONJ
ejpam-3708	184	24	let	let	VERB
ejpam-3708	184	25	d	d	NOUN
ejpam-3708	184	26	=	=	SYM
ejpam-3708	184	27	max	max	PROPN
ejpam-3708	184	28	{	{	PUNCT
ejpam-3708	184	29	1	1	NUM
ejpam-3708	184	30	,	,	PUNCT
ejpam-3708	184	31	2h−1	2h−1	NUM
ejpam-3708	184	32	}	}	PUNCT
ejpam-3708	184	33	.	.	PUNCT
ejpam-3708	185	1	then	then	ADV
ejpam-3708	185	2	,	,	PUNCT
ejpam-3708	185	3	for	for	ADP
ejpam-3708	185	4	the	the	DET
ejpam-3708	185	5	factorable	factorable	ADJ
ejpam-3708	185	6	sequences	sequence	NOUN
ejpam-3708	185	7	(	(	PUNCT
ejpam-3708	185	8	ak	ak	PROPN
ejpam-3708	185	9	)	)	PUNCT
ejpam-3708	185	10	and	and	CCONJ
ejpam-3708	185	11	(	(	PUNCT
ejpam-3708	185	12	bk	bk	NOUN
ejpam-3708	185	13	)	)	PUNCT
ejpam-3708	185	14	in	in	ADP
ejpam-3708	185	15	the	the	DET
ejpam-3708	185	16	complex	complex	ADJ
ejpam-3708	185	17	plane	plane	NOUN
ejpam-3708	185	18	,	,	PUNCT
ejpam-3708	185	19	we	we	PRON
ejpam-3708	185	20	have	have	VERB
ejpam-3708	185	21	|ak	|ak	NUM
ejpam-3708	185	22	+	+	NUM
ejpam-3708	185	23	bk|pk	bk|pk	PROPN
ejpam-3708	185	24	≤	≤	NUM
ejpam-3708	185	25	d(|ak|pk	d(|ak|pk	NUM
ejpam-3708	185	26	+	+	CCONJ
ejpam-3708	185	27	|bk|pk	|bk|pk	NOUN
ejpam-3708	185	28	)	)	PUNCT
ejpam-3708	185	29	.	.	PUNCT
ejpam-3708	186	1	(	(	PUNCT
ejpam-3708	186	2	3	3	X
ejpam-3708	186	3	)	)	PUNCT
ejpam-3708	186	4	also	also	ADV
ejpam-3708	186	5	|ak|pk	|ak|pk	PUNCT
ejpam-3708	186	6	≤	≤	NUM
ejpam-3708	186	7	max	max	PROPN
ejpam-3708	186	8	{	{	PUNCT
ejpam-3708	186	9	1	1	NUM
ejpam-3708	186	10	,	,	PUNCT
ejpam-3708	186	11	|a|h	|a|h	NOUN
ejpam-3708	186	12	}	}	PUNCT
ejpam-3708	186	13	for	for	ADP
ejpam-3708	186	14	all	all	DET
ejpam-3708	186	15	a	a	DET
ejpam-3708	186	16	∈	∈	PROPN
ejpam-3708	186	17	c.	c.	NOUN
ejpam-3708	186	18	the	the	DET
ejpam-3708	186	19	main	main	ADJ
ejpam-3708	186	20	purpose	purpose	NOUN
ejpam-3708	186	21	of	of	ADP
ejpam-3708	186	22	this	this	DET
ejpam-3708	186	23	paper	paper	NOUN
ejpam-3708	186	24	is	be	AUX
ejpam-3708	186	25	to	to	PART
ejpam-3708	186	26	introduced	introduce	VERB
ejpam-3708	186	27	and	and	CCONJ
ejpam-3708	186	28	study	study	VERB
ejpam-3708	186	29	some	some	DET
ejpam-3708	186	30	lacunary	lacunary	ADJ
ejpam-3708	186	31	i	i	NOUN
ejpam-3708	186	32	-	-	PUNCT
ejpam-3708	186	33	convergent	convergent	NOUN
ejpam-3708	186	34	sequence	sequence	NOUN
ejpam-3708	186	35	spaces	space	NOUN
ejpam-3708	186	36	of	of	ADP
ejpam-3708	186	37	fuzzy	fuzzy	ADJ
ejpam-3708	186	38	numbers	number	NOUN
ejpam-3708	186	39	by	by	ADP
ejpam-3708	186	40	using	use	VERB
ejpam-3708	186	41	an	an	DET
ejpam-3708	186	42	infinite	infinite	ADJ
ejpam-3708	186	43	matrix	matrix	NOUN
ejpam-3708	186	44	and	and	CCONJ
ejpam-3708	186	45	a	a	DET
ejpam-3708	186	46	sequence	sequence	NOUN
ejpam-3708	186	47	of	of	ADP
ejpam-3708	186	48	orlicz	orlicz	ADJ
ejpam-3708	186	49	functions	function	NOUN
ejpam-3708	186	50	in	in	ADP
ejpam-3708	186	51	more	more	ADJ
ejpam-3708	186	52	general	general	ADJ
ejpam-3708	186	53	setting	setting	NOUN
ejpam-3708	186	54	.	.	PUNCT
ejpam-3708	187	1	we	we	PRON
ejpam-3708	187	2	also	also	ADV
ejpam-3708	187	3	make	make	VERB
ejpam-3708	187	4	an	an	DET
ejpam-3708	187	5	effort	effort	NOUN
ejpam-3708	187	6	to	to	PART
ejpam-3708	187	7	study	study	VERB
ejpam-3708	187	8	some	some	DET
ejpam-3708	187	9	properties	property	NOUN
ejpam-3708	187	10	like	like	ADP
ejpam-3708	187	11	linearity	linearity	NOUN
ejpam-3708	187	12	,	,	PUNCT
ejpam-3708	187	13	paranorm	paranorm	NOUN
ejpam-3708	187	14	,	,	PUNCT
ejpam-3708	187	15	solidity	solidity	NOUN
ejpam-3708	187	16	and	and	CCONJ
ejpam-3708	187	17	some	some	DET
ejpam-3708	187	18	interesting	interesting	ADJ
ejpam-3708	187	19	inclusion	inclusion	NOUN
ejpam-3708	187	20	relations	relation	NOUN
ejpam-3708	187	21	between	between	ADP
ejpam-3708	187	22	the	the	DET
ejpam-3708	187	23	spaces	space	NOUN
ejpam-3708	187	24	w	w	ADP
ejpam-3708	187	25	i(f	i(f	NOUN
ejpam-3708	187	26	)	)	PUNCT
ejpam-3708	187	27	θ	θ	PROPN
ejpam-3708	188	1	[	[	X
ejpam-3708	188	2	a	a	X
ejpam-3708	188	3	,	,	PUNCT
ejpam-3708	188	4	m	m	PROPN
ejpam-3708	188	5	,	,	PUNCT
ejpam-3708	188	6	p	p	X
ejpam-3708	188	7	,	,	PUNCT
ejpam-3708	188	8	u,∆m	u,∆m	PROPN
ejpam-3708	188	9	v	v	X
ejpam-3708	188	10	]	]	PUNCT
ejpam-3708	188	11	,	,	PUNCT
ejpam-3708	188	12	w	w	PROPN
ejpam-3708	188	13	i(f	i(f	NOUN
ejpam-3708	188	14	)	)	PUNCT
ejpam-3708	188	15	θ	θ	PROPN
ejpam-3708	189	1	[	[	X
ejpam-3708	189	2	a	a	X
ejpam-3708	189	3	,	,	PUNCT
ejpam-3708	189	4	m	m	PROPN
ejpam-3708	189	5	,	,	PUNCT
ejpam-3708	189	6	p	p	X
ejpam-3708	189	7	,	,	PUNCT
ejpam-3708	189	8	u,∆m	u,∆m	PROPN
ejpam-3708	189	9	v	v	X
ejpam-3708	189	10	]	]	SYM
ejpam-3708	189	11	0	0	NUM
ejpam-3708	189	12	,	,	PUNCT
ejpam-3708	189	13	wfθ	wfθ	NOUN
ejpam-3708	190	1	[	[	X
ejpam-3708	190	2	a	a	X
ejpam-3708	190	3	,	,	PUNCT
ejpam-3708	190	4	m	m	PROPN
ejpam-3708	190	5	,	,	PUNCT
ejpam-3708	190	6	p	p	X
ejpam-3708	190	7	,	,	PUNCT
ejpam-3708	190	8	u,∆m	u,∆m	PROPN
ejpam-3708	190	9	v	v	X
ejpam-3708	190	10	]	]	PUNCT
ejpam-3708	190	11	∞	∞	PROPN
ejpam-3708	190	12	and	and	CCONJ
ejpam-3708	190	13	w	w	NOUN
ejpam-3708	190	14	i(f	i(f	NOUN
ejpam-3708	190	15	)	)	PUNCT
ejpam-3708	190	16	θ	θ	PROPN
ejpam-3708	191	1	[	[	X
ejpam-3708	191	2	a	a	X
ejpam-3708	191	3	,	,	PUNCT
ejpam-3708	191	4	m	m	PROPN
ejpam-3708	191	5	,	,	PUNCT
ejpam-3708	191	6	p	p	X
ejpam-3708	191	7	,	,	PUNCT
ejpam-3708	191	8	u	u	PROPN
ejpam-3708	191	9	,	,	PUNCT
ejpam-3708	191	10	∆m	∆m	PROPN
ejpam-3708	191	11	v	v	X
ejpam-3708	191	12	]	]	PUNCT
ejpam-3708	191	13	∞.	∞.	PROPN
ejpam-3708	191	14	k.	k.	PROPN
ejpam-3708	191	15	raj	raj	PROPN
ejpam-3708	191	16	,	,	PUNCT
ejpam-3708	191	17	s.	s.	PROPN
ejpam-3708	191	18	a.	a.	PROPN
ejpam-3708	191	19	mohiuddine	mohiuddine	PROPN
ejpam-3708	191	20	/	/	SYM
ejpam-3708	191	21	eur	eur	PROPN
ejpam-3708	191	22	.	.	PUNCT
ejpam-3708	192	1	j.	j.	PROPN
ejpam-3708	192	2	pure	pure	PROPN
ejpam-3708	192	3	appl	appl	PROPN
ejpam-3708	192	4	.	.	PROPN
ejpam-3708	192	5	math	math	PROPN
ejpam-3708	192	6	,	,	PUNCT
ejpam-3708	192	7	13	13	NUM
ejpam-3708	192	8	(	(	PUNCT
ejpam-3708	192	9	5	5	NUM
ejpam-3708	192	10	)	)	PUNCT
ejpam-3708	192	11	(	(	PUNCT
ejpam-3708	192	12	2020	2020	NUM
ejpam-3708	192	13	)	)	PUNCT
ejpam-3708	192	14	,	,	PUNCT
ejpam-3708	192	15	1131	1131	NUM
ejpam-3708	192	16	-	-	SYM
ejpam-3708	192	17	1148	1148	NUM
ejpam-3708	192	18	1139	1139	NUM
ejpam-3708	192	19	3	3	NUM
ejpam-3708	192	20	.	.	PUNCT
ejpam-3708	192	21	main	main	ADJ
ejpam-3708	192	22	results	result	NOUN
ejpam-3708	192	23	in	in	ADP
ejpam-3708	192	24	the	the	DET
ejpam-3708	192	25	current	current	ADJ
ejpam-3708	192	26	section	section	NOUN
ejpam-3708	192	27	we	we	PRON
ejpam-3708	192	28	study	study	VERB
ejpam-3708	192	29	some	some	DET
ejpam-3708	192	30	topological	topological	ADJ
ejpam-3708	192	31	properties	property	NOUN
ejpam-3708	192	32	and	and	CCONJ
ejpam-3708	192	33	some	some	DET
ejpam-3708	192	34	inclusion	inclusion	NOUN
ejpam-3708	192	35	relations	relation	NOUN
ejpam-3708	192	36	between	between	ADP
ejpam-3708	192	37	the	the	DET
ejpam-3708	192	38	sequence	sequence	NOUN
ejpam-3708	192	39	spaces	space	NOUN
ejpam-3708	192	40	which	which	PRON
ejpam-3708	192	41	we	we	PRON
ejpam-3708	192	42	have	have	AUX
ejpam-3708	192	43	defined	define	VERB
ejpam-3708	192	44	above	above	ADV
ejpam-3708	192	45	.	.	PUNCT
ejpam-3708	193	1	theorem	theorem	NOUN
ejpam-3708	193	2	1	1	NUM
ejpam-3708	193	3	.	.	PUNCT
ejpam-3708	194	1	let	let	VERB
ejpam-3708	194	2	m	m	VERB
ejpam-3708	194	3	=	=	SYM
ejpam-3708	194	4	(	(	PUNCT
ejpam-3708	194	5	mk	mk	X
ejpam-3708	194	6	)	)	PUNCT
ejpam-3708	194	7	be	be	VERB
ejpam-3708	194	8	a	a	DET
ejpam-3708	194	9	sequence	sequence	NOUN
ejpam-3708	194	10	of	of	ADP
ejpam-3708	194	11	orlicz	orlicz	ADJ
ejpam-3708	194	12	functions	function	NOUN
ejpam-3708	194	13	,	,	PUNCT
ejpam-3708	194	14	p	p	NOUN
ejpam-3708	194	15	=	=	PUNCT
ejpam-3708	194	16	(	(	PUNCT
ejpam-3708	194	17	pk	pk	NOUN
ejpam-3708	194	18	)	)	PUNCT
ejpam-3708	194	19	be	be	AUX
ejpam-3708	194	20	a	a	DET
ejpam-3708	194	21	bounded	bounded	ADJ
ejpam-3708	194	22	sequence	sequence	NOUN
ejpam-3708	194	23	of	of	ADP
ejpam-3708	194	24	positive	positive	ADJ
ejpam-3708	194	25	real	real	ADJ
ejpam-3708	194	26	numbers	number	NOUN
ejpam-3708	194	27	and	and	CCONJ
ejpam-3708	194	28	u	u	NOUN
ejpam-3708	194	29	=	=	SYM
ejpam-3708	194	30	(	(	PUNCT
ejpam-3708	194	31	uk	uk	PROPN
ejpam-3708	194	32	)	)	PUNCT
ejpam-3708	194	33	be	be	VERB
ejpam-3708	194	34	a	a	DET
ejpam-3708	194	35	sequence	sequence	NOUN
ejpam-3708	194	36	of	of	ADP
ejpam-3708	194	37	strictly	strictly	ADV
ejpam-3708	194	38	positive	positive	ADJ
ejpam-3708	194	39	real	real	ADJ
ejpam-3708	194	40	numbers	number	NOUN
ejpam-3708	194	41	.	.	PUNCT
ejpam-3708	195	1	then	then	ADV
ejpam-3708	195	2	the	the	DET
ejpam-3708	195	3	spaces	space	NOUN
ejpam-3708	195	4	w	w	ADP
ejpam-3708	195	5	i(f	i(f	NOUN
ejpam-3708	195	6	)	)	PUNCT
ejpam-3708	195	7	θ	θ	PROPN
ejpam-3708	196	1	[	[	X
ejpam-3708	196	2	a	a	X
ejpam-3708	196	3	,	,	PUNCT
ejpam-3708	196	4	m	m	PROPN
ejpam-3708	196	5	,	,	PUNCT
ejpam-3708	196	6	p	p	X
ejpam-3708	196	7	,	,	PUNCT
ejpam-3708	196	8	u,∆m	u,∆m	PROPN
ejpam-3708	196	9	v	v	X
ejpam-3708	196	10	]	]	PUNCT
ejpam-3708	196	11	,	,	PUNCT
ejpam-3708	196	12	w	w	PROPN
ejpam-3708	196	13	i(f	i(f	NOUN
ejpam-3708	196	14	)	)	PUNCT
ejpam-3708	196	15	θ	θ	PROPN
ejpam-3708	197	1	[	[	X
ejpam-3708	197	2	a	a	X
ejpam-3708	197	3	,	,	PUNCT
ejpam-3708	197	4	m	m	PROPN
ejpam-3708	197	5	,	,	PUNCT
ejpam-3708	197	6	p	p	X
ejpam-3708	197	7	,	,	PUNCT
ejpam-3708	197	8	u,∆m	u,∆m	PROPN
ejpam-3708	197	9	v	v	X
ejpam-3708	197	10	]	]	PUNCT
ejpam-3708	197	11	0	0	NUM
ejpam-3708	197	12	and	and	CCONJ
ejpam-3708	197	13	w	w	NOUN
ejpam-3708	197	14	i(f	i(f	NOUN
ejpam-3708	198	1	)	)	PUNCT
ejpam-3708	198	2	θ	θ	PROPN
ejpam-3708	199	1	[	[	X
ejpam-3708	199	2	a	a	X
ejpam-3708	199	3	,	,	PUNCT
ejpam-3708	199	4	m	m	PROPN
ejpam-3708	199	5	,	,	PUNCT
ejpam-3708	199	6	p	p	X
ejpam-3708	199	7	,	,	PUNCT
ejpam-3708	199	8	u,∆m	u,∆m	PROPN
ejpam-3708	199	9	v	v	NOUN
ejpam-3708	199	10	]	]	PUNCT
ejpam-3708	199	11	∞	∞	NUM
ejpam-3708	199	12	are	be	AUX
ejpam-3708	199	13	linear	linear	ADJ
ejpam-3708	199	14	spaces	space	NOUN
ejpam-3708	199	15	over	over	ADP
ejpam-3708	199	16	the	the	DET
ejpam-3708	199	17	complex	complex	ADJ
ejpam-3708	199	18	field	field	NOUN
ejpam-3708	199	19	c.	c.	NOUN
ejpam-3708	199	20	proof	proof	NOUN
ejpam-3708	199	21	.	.	PUNCT
ejpam-3708	200	1	we	we	PRON
ejpam-3708	200	2	shall	shall	AUX
ejpam-3708	200	3	prove	prove	VERB
ejpam-3708	200	4	the	the	DET
ejpam-3708	200	5	result	result	NOUN
ejpam-3708	200	6	for	for	ADP
ejpam-3708	200	7	the	the	DET
ejpam-3708	200	8	space	space	NOUN
ejpam-3708	200	9	w	w	ADP
ejpam-3708	200	10	i(f	i(f	NOUN
ejpam-3708	200	11	)	)	PUNCT
ejpam-3708	200	12	θ	θ	PROPN
ejpam-3708	201	1	[	[	X
ejpam-3708	201	2	a	a	X
ejpam-3708	201	3	,	,	PUNCT
ejpam-3708	201	4	m	m	PROPN
ejpam-3708	201	5	,	,	PUNCT
ejpam-3708	201	6	p	p	X
ejpam-3708	201	7	,	,	PUNCT
ejpam-3708	201	8	u,∆m	u,∆m	PROPN
ejpam-3708	201	9	n	n	X
ejpam-3708	201	10	]	]	PUNCT
ejpam-3708	201	11	0	0	PUNCT
ejpam-3708	202	1	only	only	ADV
ejpam-3708	202	2	and	and	CCONJ
ejpam-3708	202	3	others	other	NOUN
ejpam-3708	202	4	can	can	AUX
ejpam-3708	202	5	be	be	AUX
ejpam-3708	202	6	proved	prove	VERB
ejpam-3708	202	7	in	in	ADP
ejpam-3708	202	8	the	the	DET
ejpam-3708	202	9	similar	similar	ADJ
ejpam-3708	202	10	way	way	NOUN
ejpam-3708	202	11	.	.	PUNCT
ejpam-3708	203	1	let	let	VERB
ejpam-3708	203	2	x	x	PUNCT
ejpam-3708	203	3	=	=	SYM
ejpam-3708	203	4	(	(	PUNCT
ejpam-3708	203	5	xk	xk	ADJ
ejpam-3708	203	6	)	)	PUNCT
ejpam-3708	203	7	and	and	CCONJ
ejpam-3708	203	8	y	y	PROPN
ejpam-3708	203	9	=	=	PRON
ejpam-3708	203	10	(	(	PUNCT
ejpam-3708	203	11	yk	yk	PROPN
ejpam-3708	203	12	)	)	PUNCT
ejpam-3708	203	13	be	be	VERB
ejpam-3708	203	14	two	two	NUM
ejpam-3708	203	15	elements	element	NOUN
ejpam-3708	203	16	in	in	ADP
ejpam-3708	203	17	w	w	NOUN
ejpam-3708	203	18	i(f	i(f	NOUN
ejpam-3708	203	19	)	)	PUNCT
ejpam-3708	203	20	θ	θ	PROPN
ejpam-3708	204	1	[	[	X
ejpam-3708	204	2	a	a	X
ejpam-3708	204	3	,	,	PUNCT
ejpam-3708	204	4	m	m	PROPN
ejpam-3708	204	5	,	,	PUNCT
ejpam-3708	204	6	p	p	X
ejpam-3708	204	7	,	,	PUNCT
ejpam-3708	204	8	u,∆m	u,∆m	PROPN
ejpam-3708	204	9	n	n	X
ejpam-3708	204	10	]	]	X
ejpam-3708	204	11	0	0	X
ejpam-3708	204	12	.	.	PUNCT
ejpam-3708	205	1	then	then	ADV
ejpam-3708	205	2	there	there	PRON
ejpam-3708	205	3	exists	exist	VERB
ejpam-3708	205	4	ρ1	ρ1	NOUN
ejpam-3708	205	5	>	>	X
ejpam-3708	205	6	0	0	PUNCT
ejpam-3708	206	1	and	and	CCONJ
ejpam-3708	206	2	ρ2	ρ2	VERB
ejpam-3708	206	3	>	>	X
ejpam-3708	206	4	0	0	NUM
ejpam-3708	207	1	such	such	ADJ
ejpam-3708	207	2	that	that	SCONJ
ejpam-3708	207	3	a	a	DET
ejpam-3708	207	4	ε	ε	PROPN
ejpam-3708	207	5	2	2	NUM
ejpam-3708	207	6	=	=	SYM
ejpam-3708	207	7	{	{	PUNCT
ejpam-3708	207	8	n	n	CCONJ
ejpam-3708	207	9	,	,	PUNCT
ejpam-3708	207	10	r	r	NOUN
ejpam-3708	207	11	∈	∈	PROPN
ejpam-3708	207	12	n	n	CCONJ
ejpam-3708	207	13	:	:	PUNCT
ejpam-3708	207	14	1	1	NUM
ejpam-3708	207	15	hr	hr	NOUN
ejpam-3708	207	16	∑	∑	PUNCT
ejpam-3708	207	17	k∈ir	k∈ir	PROPN
ejpam-3708	207	18	ank	ank	PROPN
ejpam-3708	207	19	[	[	PUNCT
ejpam-3708	207	20	k−smk	k−smk	NOUN
ejpam-3708	207	21	(	(	PUNCT
ejpam-3708	207	22	d(uk∆	d(uk∆	PROPN
ejpam-3708	207	23	m	m	NOUN
ejpam-3708	207	24	v	v	NOUN
ejpam-3708	207	25	xk	xk	PROPN
ejpam-3708	207	26	,	,	PUNCT
ejpam-3708	207	27	0	0	NUM
ejpam-3708	207	28	)	)	PUNCT
ejpam-3708	207	29	ρ1	ρ1	NOUN
ejpam-3708	207	30	)	)	PUNCT
ejpam-3708	207	31	]	]	PUNCT
ejpam-3708	207	32	pk	pk	NOUN
ejpam-3708	207	33	≥	≥	NOUN
ejpam-3708	207	34	ε	ε	PROPN
ejpam-3708	207	35	2	2	NUM
ejpam-3708	207	36	}	}	PUNCT
ejpam-3708	207	37	∈	∈	PROPN
ejpam-3708	208	1	i	i	PRON
ejpam-3708	208	2	and	and	CCONJ
ejpam-3708	208	3	b	b	NOUN
ejpam-3708	208	4	ε	ε	PROPN
ejpam-3708	208	5	2	2	NUM
ejpam-3708	208	6	=	=	SYM
ejpam-3708	208	7	{	{	PUNCT
ejpam-3708	208	8	n	n	CCONJ
ejpam-3708	208	9	,	,	PUNCT
ejpam-3708	208	10	r	r	NOUN
ejpam-3708	208	11	∈	∈	PROPN
ejpam-3708	208	12	n	n	CCONJ
ejpam-3708	208	13	:	:	PUNCT
ejpam-3708	208	14	1	1	NUM
ejpam-3708	208	15	hr	hr	NOUN
ejpam-3708	208	16	∑	∑	PUNCT
ejpam-3708	208	17	k∈ir	k∈ir	PROPN
ejpam-3708	208	18	ank	ank	PROPN
ejpam-3708	208	19	[	[	PUNCT
ejpam-3708	208	20	k−smk	k−smk	NOUN
ejpam-3708	208	21	(	(	PUNCT
ejpam-3708	208	22	d(uk∆	d(uk∆	PROPN
ejpam-3708	208	23	m	m	NOUN
ejpam-3708	208	24	v	v	ADP
ejpam-3708	208	25	yk	yk	PROPN
ejpam-3708	208	26	,	,	PUNCT
ejpam-3708	208	27	0	0	NUM
ejpam-3708	208	28	)	)	PUNCT
ejpam-3708	208	29	ρ2	ρ2	NOUN
ejpam-3708	208	30	)	)	PUNCT
ejpam-3708	208	31	]	]	X
ejpam-3708	208	32	pk	pk	NOUN
ejpam-3708	208	33	≥	≥	NOUN
ejpam-3708	208	34	ε	ε	PROPN
ejpam-3708	208	35	2	2	NUM
ejpam-3708	208	36	}	}	PUNCT
ejpam-3708	208	37	∈	∈	PROPN
ejpam-3708	208	38	i.	i.	NOUN
ejpam-3708	208	39	let	let	VERB
ejpam-3708	208	40	α	α	PRON
ejpam-3708	208	41	and	and	CCONJ
ejpam-3708	208	42	β	β	X
ejpam-3708	208	43	be	be	AUX
ejpam-3708	208	44	two	two	NUM
ejpam-3708	208	45	scalars	scalar	NOUN
ejpam-3708	208	46	.	.	PUNCT
ejpam-3708	209	1	then	then	ADV
ejpam-3708	209	2	by	by	ADP
ejpam-3708	209	3	using	use	VERB
ejpam-3708	209	4	the	the	DET
ejpam-3708	209	5	inequality	inequality	NOUN
ejpam-3708	209	6	(	(	PUNCT
ejpam-3708	209	7	3	3	NUM
ejpam-3708	209	8	)	)	PUNCT
ejpam-3708	209	9	and	and	CCONJ
ejpam-3708	209	10	continuity	continuity	NOUN
ejpam-3708	209	11	of	of	ADP
ejpam-3708	209	12	the	the	DET
ejpam-3708	209	13	function	function	NOUN
ejpam-3708	209	14	m	m	VERB
ejpam-3708	209	15	=	=	SYM
ejpam-3708	209	16	(	(	PUNCT
ejpam-3708	209	17	mk	mk	PROPN
ejpam-3708	209	18	)	)	PUNCT
ejpam-3708	209	19	,	,	PUNCT
ejpam-3708	209	20	we	we	PRON
ejpam-3708	209	21	have	have	VERB
ejpam-3708	209	22	1	1	NUM
ejpam-3708	209	23	hr	hr	NOUN
ejpam-3708	209	24	∑	∑	PUNCT
ejpam-3708	209	25	k∈ir	k∈ir	PROPN
ejpam-3708	209	26	ank	ank	PROPN
ejpam-3708	209	27	[	[	PUNCT
ejpam-3708	209	28	k−smk	k−smk	NOUN
ejpam-3708	209	29	(	(	PUNCT
ejpam-3708	209	30	d(αuk∆	d(αuk∆	PROPN
ejpam-3708	209	31	m	m	NOUN
ejpam-3708	209	32	v	v	NOUN
ejpam-3708	209	33	xk	xk	PROPN
ejpam-3708	210	1	+	+	CCONJ
ejpam-3708	210	2	βuk∆	βuk∆	NUM
ejpam-3708	210	3	m	m	VERB
ejpam-3708	210	4	v	v	ADP
ejpam-3708	210	5	yk	yk	PROPN
ejpam-3708	210	6	,	,	PUNCT
ejpam-3708	210	7	0	0	NUM
ejpam-3708	210	8	)	)	PUNCT
ejpam-3708	210	9	|α|ρ1	|α|ρ1	PROPN
ejpam-3708	211	1	+	+	NUM
ejpam-3708	211	2	|β|ρ2	|β|ρ2	NOUN
ejpam-3708	211	3	)	)	PUNCT
ejpam-3708	211	4	]	]	PUNCT
ejpam-3708	211	5	pk	pk	NOUN
ejpam-3708	211	6	≤	≤	NUM
ejpam-3708	211	7	d	d	SYM
ejpam-3708	211	8	1	1	NUM
ejpam-3708	211	9	hr	hr	NOUN
ejpam-3708	211	10	∑	∑	PUNCT
ejpam-3708	211	11	k∈ir	k∈ir	PROPN
ejpam-3708	211	12	ank	ank	PROPN
ejpam-3708	211	13	[	[	PUNCT
ejpam-3708	211	14	|α|	|α|	PROPN
ejpam-3708	211	15	|α|ρ1	|α|ρ1	PROPN
ejpam-3708	211	16	+	+	NUM
ejpam-3708	211	17	|β|ρ2	|β|ρ2	NOUN
ejpam-3708	211	18	k−smk	k−smk	NOUN
ejpam-3708	211	19	(	(	PUNCT
ejpam-3708	211	20	d(uk∆	d(uk∆	PROPN
ejpam-3708	211	21	m	m	NOUN
ejpam-3708	211	22	v	v	NOUN
ejpam-3708	211	23	xk	xk	PROPN
ejpam-3708	211	24	,	,	PUNCT
ejpam-3708	211	25	0	0	NUM
ejpam-3708	211	26	)	)	PUNCT
ejpam-3708	211	27	ρ1	ρ1	NOUN
ejpam-3708	211	28	)	)	PUNCT
ejpam-3708	211	29	]	]	PUNCT
ejpam-3708	211	30	pk	pk	NOUN
ejpam-3708	211	31	+	+	CCONJ
ejpam-3708	211	32	d	d	SYM
ejpam-3708	211	33	1	1	NUM
ejpam-3708	211	34	hr	hr	NOUN
ejpam-3708	211	35	∑	∑	PUNCT
ejpam-3708	211	36	k∈ir	k∈ir	PROPN
ejpam-3708	211	37	ank	ank	PROPN
ejpam-3708	211	38	[	[	PUNCT
ejpam-3708	211	39	|β|	|β|	X
ejpam-3708	211	40	|α|ρ1	|α|ρ1	PROPN
ejpam-3708	211	41	+	+	NUM
ejpam-3708	211	42	|β|ρ2	|β|ρ2	NOUN
ejpam-3708	211	43	k−smk	k−smk	NOUN
ejpam-3708	211	44	(	(	PUNCT
ejpam-3708	211	45	d(uk∆	d(uk∆	PROPN
ejpam-3708	211	46	m	m	NOUN
ejpam-3708	211	47	v	v	ADP
ejpam-3708	211	48	yk	yk	PROPN
ejpam-3708	211	49	,	,	PUNCT
ejpam-3708	211	50	0	0	NUM
ejpam-3708	211	51	)	)	PUNCT
ejpam-3708	211	52	ρ2	ρ2	NOUN
ejpam-3708	211	53	)	)	PUNCT
ejpam-3708	211	54	]	]	PUNCT
ejpam-3708	211	55	pk	pk	NOUN
ejpam-3708	211	56	≤	≤	PUNCT
ejpam-3708	211	57	dk	dk	PRON
ejpam-3708	211	58	1	1	NUM
ejpam-3708	211	59	hr	hr	NOUN
ejpam-3708	211	60	∑	∑	PUNCT
ejpam-3708	211	61	k∈ir	k∈ir	PROPN
ejpam-3708	211	62	ank	ank	PROPN
ejpam-3708	211	63	[	[	PUNCT
ejpam-3708	211	64	k−smk	k−smk	NOUN
ejpam-3708	211	65	(	(	PUNCT
ejpam-3708	211	66	d(uk∆	d(uk∆	PROPN
ejpam-3708	211	67	m	m	NOUN
ejpam-3708	211	68	v	v	NOUN
ejpam-3708	211	69	xk	xk	PROPN
ejpam-3708	211	70	,	,	PUNCT
ejpam-3708	211	71	0	0	NUM
ejpam-3708	211	72	)	)	PUNCT
ejpam-3708	211	73	ρ1	ρ1	NOUN
ejpam-3708	211	74	)	)	PUNCT
ejpam-3708	211	75	]	]	PUNCT
ejpam-3708	211	76	pk	pk	NOUN
ejpam-3708	211	77	+	+	CCONJ
ejpam-3708	211	78	dk	dk	PROPN
ejpam-3708	211	79	1	1	NUM
ejpam-3708	211	80	hr	hr	NOUN
ejpam-3708	211	81	∑	∑	PUNCT
ejpam-3708	211	82	k∈ir	k∈ir	PROPN
ejpam-3708	211	83	ank	ank	PROPN
ejpam-3708	211	84	[	[	PUNCT
ejpam-3708	211	85	k−smk	k−smk	NOUN
ejpam-3708	211	86	(	(	PUNCT
ejpam-3708	211	87	d(uk∆	d(uk∆	PROPN
ejpam-3708	211	88	m	m	NOUN
ejpam-3708	211	89	v	v	ADP
ejpam-3708	211	90	yk	yk	PROPN
ejpam-3708	211	91	,	,	PUNCT
ejpam-3708	211	92	0	0	NUM
ejpam-3708	211	93	)	)	PUNCT
ejpam-3708	211	94	ρ2	ρ2	NOUN
ejpam-3708	211	95	)	)	PUNCT
ejpam-3708	211	96	]	]	X
ejpam-3708	211	97	pk	pk	NOUN
ejpam-3708	211	98	,	,	PUNCT
ejpam-3708	211	99	where	where	SCONJ
ejpam-3708	211	100	k	k	PROPN
ejpam-3708	211	101	=	=	SYM
ejpam-3708	211	102	max	max	PROPN
ejpam-3708	211	103	{	{	PUNCT
ejpam-3708	211	104	1	1	NUM
ejpam-3708	211	105	,	,	PUNCT
ejpam-3708	211	106	(	(	PUNCT
ejpam-3708	211	107	|α|	|α|	PROPN
ejpam-3708	211	108	|α|ρ1+|β|ρ2	|α|ρ1+|β|ρ2	NUM
ejpam-3708	211	109	)	)	PUNCT
ejpam-3708	211	110	h	h	NOUN
ejpam-3708	211	111	,	,	PUNCT
ejpam-3708	211	112	(	(	PUNCT
ejpam-3708	211	113	|β|	|β|	X
ejpam-3708	211	114	|α|ρ1+|β|ρ2	|α|ρ1+|β|ρ2	X
ejpam-3708	211	115	)	)	PUNCT
ejpam-3708	211	116	h	h	NOUN
ejpam-3708	211	117	}	}	PUNCT
ejpam-3708	211	118	.	.	PUNCT
ejpam-3708	212	1	from	from	ADP
ejpam-3708	212	2	the	the	DET
ejpam-3708	212	3	above	above	ADJ
ejpam-3708	212	4	relation	relation	NOUN
ejpam-3708	212	5	we	we	PRON
ejpam-3708	212	6	obtain	obtain	VERB
ejpam-3708	212	7	the	the	DET
ejpam-3708	212	8	following	following	NOUN
ejpam-3708	212	9	:	:	PUNCT
ejpam-3708	212	10	k.	k.	PROPN
ejpam-3708	212	11	raj	raj	PROPN
ejpam-3708	212	12	,	,	PUNCT
ejpam-3708	212	13	s.	s.	PROPN
ejpam-3708	212	14	a.	a.	PROPN
ejpam-3708	212	15	mohiuddine	mohiuddine	PROPN
ejpam-3708	212	16	/	/	SYM
ejpam-3708	212	17	eur	eur	PROPN
ejpam-3708	212	18	.	.	PUNCT
ejpam-3708	213	1	j.	j.	PROPN
ejpam-3708	213	2	pure	pure	PROPN
ejpam-3708	213	3	appl	appl	PROPN
ejpam-3708	213	4	.	.	PROPN
ejpam-3708	213	5	math	math	PROPN
ejpam-3708	213	6	,	,	PUNCT
ejpam-3708	213	7	13	13	NUM
ejpam-3708	213	8	(	(	PUNCT
ejpam-3708	213	9	5	5	NUM
ejpam-3708	213	10	)	)	PUNCT
ejpam-3708	213	11	(	(	PUNCT
ejpam-3708	213	12	2020	2020	NUM
ejpam-3708	213	13	)	)	PUNCT
ejpam-3708	213	14	,	,	PUNCT
ejpam-3708	213	15	1131	1131	NUM
ejpam-3708	213	16	-	-	SYM
ejpam-3708	213	17	1148	1148	NUM
ejpam-3708	213	18	1140	1140	NUM
ejpam-3708	213	19	{	{	PUNCT
ejpam-3708	213	20	n	n	X
ejpam-3708	213	21	,	,	PUNCT
ejpam-3708	213	22	r	r	NOUN
ejpam-3708	213	23	∈	∈	PROPN
ejpam-3708	213	24	n	n	CCONJ
ejpam-3708	213	25	:	:	PUNCT
ejpam-3708	213	26	1	1	NUM
ejpam-3708	213	27	hr	hr	NOUN
ejpam-3708	213	28	∑	∑	PUNCT
ejpam-3708	213	29	k∈ir	k∈ir	PROPN
ejpam-3708	213	30	ank	ank	PROPN
ejpam-3708	213	31	[	[	PUNCT
ejpam-3708	213	32	k−smk	k−smk	NOUN
ejpam-3708	213	33	(	(	PUNCT
ejpam-3708	213	34	d(αuk∆m	d(αuk∆m	PROPN
ejpam-3708	213	35	v	v	ADP
ejpam-3708	213	36	xk+βuk∆m	xk+βuk∆m	PROPN
ejpam-3708	213	37	v	v	PROPN
ejpam-3708	213	38	yk,0	yk,0	PROPN
ejpam-3708	213	39	)	)	PUNCT
ejpam-3708	213	40	|α|ρ1+|β|ρ2	|α|ρ1+|β|ρ2	X
ejpam-3708	213	41	)	)	PUNCT
ejpam-3708	213	42	]	]	PUNCT
ejpam-3708	213	43	pk	pk	NOUN
ejpam-3708	213	44	≥	≥	NOUN
ejpam-3708	213	45	ε	ε	PROPN
ejpam-3708	213	46	}	}	PUNCT
ejpam-3708	213	47	⊆	⊆	NUM
ejpam-3708	213	48	{	{	PUNCT
ejpam-3708	213	49	n	n	CCONJ
ejpam-3708	213	50	,	,	PUNCT
ejpam-3708	213	51	r	r	NOUN
ejpam-3708	213	52	∈	∈	PROPN
ejpam-3708	213	53	n	n	NOUN
ejpam-3708	213	54	:	:	PUNCT
ejpam-3708	213	55	dk	dk	PROPN
ejpam-3708	213	56	1	1	NUM
ejpam-3708	213	57	hr	hr	NOUN
ejpam-3708	213	58	∑	∑	PUNCT
ejpam-3708	213	59	k∈ir	k∈ir	PROPN
ejpam-3708	213	60	ank	ank	PROPN
ejpam-3708	213	61	[	[	PUNCT
ejpam-3708	213	62	k−smk	k−smk	NOUN
ejpam-3708	213	63	(	(	PUNCT
ejpam-3708	213	64	d(uk∆	d(uk∆	PROPN
ejpam-3708	213	65	m	m	NOUN
ejpam-3708	213	66	v	v	NOUN
ejpam-3708	213	67	xk	xk	PROPN
ejpam-3708	213	68	,	,	PUNCT
ejpam-3708	213	69	0	0	NUM
ejpam-3708	213	70	)	)	PUNCT
ejpam-3708	213	71	ρ1	ρ1	NOUN
ejpam-3708	213	72	)	)	PUNCT
ejpam-3708	213	73	]	]	PUNCT
ejpam-3708	213	74	pk	pk	NOUN
ejpam-3708	213	75	≥	≥	NOUN
ejpam-3708	213	76	ε	ε	PROPN
ejpam-3708	213	77	2	2	NUM
ejpam-3708	213	78	}	}	PUNCT
ejpam-3708	213	79	∪	∪	X
ejpam-3708	213	80	{	{	PUNCT
ejpam-3708	213	81	n	n	NOUN
ejpam-3708	213	82	,	,	PUNCT
ejpam-3708	213	83	r	r	NOUN
ejpam-3708	213	84	∈	∈	PROPN
ejpam-3708	213	85	n	n	NOUN
ejpam-3708	213	86	:	:	PUNCT
ejpam-3708	213	87	dk	dk	PROPN
ejpam-3708	213	88	1	1	NUM
ejpam-3708	213	89	hr	hr	NOUN
ejpam-3708	213	90	∑	∑	PUNCT
ejpam-3708	213	91	k∈ir	k∈ir	PROPN
ejpam-3708	213	92	ank	ank	PROPN
ejpam-3708	213	93	[	[	PUNCT
ejpam-3708	213	94	k−smk	k−smk	NOUN
ejpam-3708	213	95	(	(	PUNCT
ejpam-3708	213	96	d(uk∆	d(uk∆	PROPN
ejpam-3708	213	97	m	m	NOUN
ejpam-3708	213	98	v	v	ADP
ejpam-3708	213	99	yk	yk	PROPN
ejpam-3708	213	100	,	,	PUNCT
ejpam-3708	213	101	0	0	NUM
ejpam-3708	213	102	)	)	PUNCT
ejpam-3708	213	103	ρ2	ρ2	NOUN
ejpam-3708	213	104	)	)	PUNCT
ejpam-3708	213	105	]	]	X
ejpam-3708	213	106	pk	pk	NOUN
ejpam-3708	213	107	≥	≥	NOUN
ejpam-3708	213	108	ε	ε	PROPN
ejpam-3708	213	109	2	2	NUM
ejpam-3708	213	110	}	}	PUNCT
ejpam-3708	213	111	∈	∈	PROPN
ejpam-3708	213	112	i.	i.	NOUN
ejpam-3708	213	113	this	this	PRON
ejpam-3708	213	114	completes	complete	VERB
ejpam-3708	213	115	the	the	DET
ejpam-3708	213	116	proof	proof	NOUN
ejpam-3708	213	117	.	.	PUNCT
ejpam-3708	214	1	theorem	theorem	NOUN
ejpam-3708	214	2	2	2	NUM
ejpam-3708	214	3	.	.	PUNCT
ejpam-3708	215	1	let	let	AUX
ejpam-3708	215	2	m	m	VERB
ejpam-3708	215	3	=	=	SYM
ejpam-3708	215	4	(	(	PUNCT
ejpam-3708	215	5	mk	mk	X
ejpam-3708	215	6	)	)	PUNCT
ejpam-3708	215	7	be	be	VERB
ejpam-3708	215	8	a	a	DET
ejpam-3708	215	9	sequence	sequence	NOUN
ejpam-3708	215	10	of	of	ADP
ejpam-3708	215	11	orlicz	orlicz	ADJ
ejpam-3708	215	12	functions	function	NOUN
ejpam-3708	215	13	,	,	PUNCT
ejpam-3708	215	14	p	p	NOUN
ejpam-3708	215	15	=	=	PUNCT
ejpam-3708	215	16	(	(	PUNCT
ejpam-3708	215	17	pk	pk	NOUN
ejpam-3708	215	18	)	)	PUNCT
ejpam-3708	215	19	be	be	AUX
ejpam-3708	215	20	a	a	DET
ejpam-3708	215	21	bounded	bounded	ADJ
ejpam-3708	215	22	sequence	sequence	NOUN
ejpam-3708	215	23	of	of	ADP
ejpam-3708	215	24	positive	positive	ADJ
ejpam-3708	215	25	real	real	ADJ
ejpam-3708	215	26	numbers	number	NOUN
ejpam-3708	215	27	and	and	CCONJ
ejpam-3708	215	28	u	u	NOUN
ejpam-3708	215	29	=	=	SYM
ejpam-3708	215	30	(	(	PUNCT
ejpam-3708	215	31	uk	uk	PROPN
ejpam-3708	215	32	)	)	PUNCT
ejpam-3708	215	33	be	be	VERB
ejpam-3708	215	34	a	a	DET
ejpam-3708	215	35	sequence	sequence	NOUN
ejpam-3708	215	36	of	of	ADP
ejpam-3708	215	37	strictly	strictly	ADV
ejpam-3708	215	38	positive	positive	ADJ
ejpam-3708	215	39	real	real	ADJ
ejpam-3708	215	40	numbers	number	NOUN
ejpam-3708	215	41	.	.	PUNCT
ejpam-3708	216	1	then	then	ADV
ejpam-3708	216	2	the	the	DET
ejpam-3708	216	3	spaces	space	NOUN
ejpam-3708	216	4	w	w	ADP
ejpam-3708	216	5	i(f	i(f	NOUN
ejpam-3708	216	6	)	)	PUNCT
ejpam-3708	216	7	θ	θ	PROPN
ejpam-3708	217	1	[	[	X
ejpam-3708	217	2	a	a	X
ejpam-3708	217	3	,	,	PUNCT
ejpam-3708	217	4	m	m	PROPN
ejpam-3708	217	5	,	,	PUNCT
ejpam-3708	217	6	p	p	X
ejpam-3708	217	7	,	,	PUNCT
ejpam-3708	217	8	u,∆m	u,∆m	PROPN
ejpam-3708	217	9	v	v	X
ejpam-3708	217	10	]	]	PUNCT
ejpam-3708	217	11	,	,	PUNCT
ejpam-3708	217	12	w	w	PROPN
ejpam-3708	217	13	i(f	i(f	NOUN
ejpam-3708	217	14	)	)	PUNCT
ejpam-3708	217	15	θ	θ	PROPN
ejpam-3708	218	1	[	[	X
ejpam-3708	218	2	a	a	X
ejpam-3708	218	3	,	,	PUNCT
ejpam-3708	218	4	m	m	PROPN
ejpam-3708	218	5	,	,	PUNCT
ejpam-3708	218	6	p	p	X
ejpam-3708	218	7	,	,	PUNCT
ejpam-3708	218	8	u,∆m	u,∆m	PROPN
ejpam-3708	218	9	v	v	X
ejpam-3708	218	10	]	]	PUNCT
ejpam-3708	218	11	0	0	NUM
ejpam-3708	218	12	and	and	CCONJ
ejpam-3708	218	13	w	w	NOUN
ejpam-3708	218	14	i(f	i(f	NOUN
ejpam-3708	219	1	)	)	PUNCT
ejpam-3708	219	2	θ	θ	PROPN
ejpam-3708	220	1	[	[	X
ejpam-3708	220	2	a	a	X
ejpam-3708	220	3	,	,	PUNCT
ejpam-3708	220	4	m	m	PROPN
ejpam-3708	220	5	,	,	PUNCT
ejpam-3708	220	6	p	p	X
ejpam-3708	220	7	,	,	PUNCT
ejpam-3708	220	8	u,∆m	u,∆m	PROPN
ejpam-3708	220	9	v	v	NOUN
ejpam-3708	220	10	]	]	PUNCT
ejpam-3708	220	11	∞	∞	NUM
ejpam-3708	220	12	are	be	AUX
ejpam-3708	220	13	paranormed	paranorme	VERB
ejpam-3708	220	14	spaces	space	NOUN
ejpam-3708	220	15	with	with	ADP
ejpam-3708	220	16	the	the	DET
ejpam-3708	220	17	paranorm	paranorm	NOUN
ejpam-3708	220	18	g∆	g∆	NOUN
ejpam-3708	220	19	defined	define	VERB
ejpam-3708	220	20	by	by	ADP
ejpam-3708	220	21	g∆(x	g∆(x	PRON
ejpam-3708	220	22	)	)	PUNCT
ejpam-3708	220	23	=	=	SYM
ejpam-3708	220	24	inf	inf	NOUN
ejpam-3708	220	25	{	{	PUNCT
ejpam-3708	220	26	(	(	PUNCT
ejpam-3708	220	27	ρ	ρ	NOUN
ejpam-3708	220	28	)	)	PUNCT
ejpam-3708	220	29	pn	pn	PROPN
ejpam-3708	220	30	h	h	NOUN
ejpam-3708	220	31	:	:	PUNCT
ejpam-3708	220	32	(	(	PUNCT
ejpam-3708	220	33	1	1	NUM
ejpam-3708	220	34	hr	hr	NOUN
ejpam-3708	220	35	∑	∑	PUNCT
ejpam-3708	220	36	k∈ir	k∈ir	PROPN
ejpam-3708	220	37	ank	ank	PROPN
ejpam-3708	220	38	[	[	PUNCT
ejpam-3708	220	39	k−smk	k−smk	NOUN
ejpam-3708	220	40	(	(	PUNCT
ejpam-3708	220	41	d(uk∆	d(uk∆	PROPN
ejpam-3708	220	42	m	m	NOUN
ejpam-3708	220	43	v	v	NOUN
ejpam-3708	220	44	xk	xk	PROPN
ejpam-3708	220	45	,	,	PUNCT
ejpam-3708	220	46	0	0	NUM
ejpam-3708	220	47	)	)	PUNCT
ejpam-3708	220	48	ρ	ρ	NOUN
ejpam-3708	220	49	)	)	PUNCT
ejpam-3708	220	50	]	]	SYM
ejpam-3708	220	51	pk	pk	NOUN
ejpam-3708	220	52	)	)	PUNCT
ejpam-3708	220	53	1	1	NUM
ejpam-3708	220	54	h	h	NOUN
ejpam-3708	220	55	≤	≤	NUM
ejpam-3708	220	56	1	1	NUM
ejpam-3708	220	57	,	,	PUNCT
ejpam-3708	220	58	for	for	ADP
ejpam-3708	220	59	some	some	DET
ejpam-3708	220	60	ρ	ρ	NOUN
ejpam-3708	220	61	>	>	X
ejpam-3708	220	62	0	0	PUNCT
ejpam-3708	220	63	and	and	CCONJ
ejpam-3708	220	64	s	s	X
ejpam-3708	220	65	≥	≥	NOUN
ejpam-3708	220	66	0	0	NUM
ejpam-3708	220	67	,	,	PUNCT
ejpam-3708	220	68	n	n	NOUN
ejpam-3708	220	69	=	=	SYM
ejpam-3708	220	70	1	1	NUM
ejpam-3708	220	71	,	,	PUNCT
ejpam-3708	220	72	2	2	NUM
ejpam-3708	220	73	,	,	PUNCT
ejpam-3708	220	74	....	....	PUNCT
ejpam-3708	221	1	r	r	NOUN
ejpam-3708	221	2	∈	∈	PROPN
ejpam-3708	221	3	n	n	NOUN
ejpam-3708	221	4	}	}	PUNCT
ejpam-3708	221	5	where	where	SCONJ
ejpam-3708	221	6	h	h	NOUN
ejpam-3708	221	7	=	=	PUNCT
ejpam-3708	221	8	max{1	max{1	NOUN
ejpam-3708	221	9	,	,	PUNCT
ejpam-3708	221	10	sup	sup	NOUN
ejpam-3708	221	11	k	k	PROPN
ejpam-3708	221	12	pk	pk	PROPN
ejpam-3708	221	13	}	}	PUNCT
ejpam-3708	221	14	.	.	PUNCT
ejpam-3708	222	1	proof	proof	NOUN
ejpam-3708	222	2	.	.	PUNCT
ejpam-3708	223	1	clearly	clearly	ADV
ejpam-3708	223	2	,	,	PUNCT
ejpam-3708	223	3	g∆(−x	g∆(−x	NOUN
ejpam-3708	223	4	)	)	PUNCT
ejpam-3708	223	5	=	=	SYM
ejpam-3708	223	6	g∆(x	g∆(x	PROPN
ejpam-3708	223	7	)	)	PUNCT
ejpam-3708	223	8	and	and	CCONJ
ejpam-3708	223	9	g∆(θ	g∆(θ	NOUN
ejpam-3708	223	10	)	)	PUNCT
ejpam-3708	224	1	=	=	SYM
ejpam-3708	224	2	0	0	X
ejpam-3708	224	3	.	.	PUNCT
ejpam-3708	225	1	let	let	VERB
ejpam-3708	225	2	x	x	PUNCT
ejpam-3708	225	3	=	=	SYM
ejpam-3708	225	4	(	(	PUNCT
ejpam-3708	225	5	xk	xk	ADJ
ejpam-3708	225	6	)	)	PUNCT
ejpam-3708	225	7	and	and	CCONJ
ejpam-3708	225	8	y	y	PROPN
ejpam-3708	225	9	=	=	PRON
ejpam-3708	225	10	(	(	PUNCT
ejpam-3708	225	11	yk	yk	PROPN
ejpam-3708	225	12	)	)	PUNCT
ejpam-3708	225	13	be	be	VERB
ejpam-3708	225	14	two	two	NUM
ejpam-3708	225	15	elements	element	NOUN
ejpam-3708	225	16	in	in	ADP
ejpam-3708	225	17	w	w	NOUN
ejpam-3708	225	18	i(f	i(f	NOUN
ejpam-3708	225	19	)	)	PUNCT
ejpam-3708	225	20	θ	θ	PROPN
ejpam-3708	226	1	[	[	X
ejpam-3708	226	2	a	a	X
ejpam-3708	226	3	,	,	PUNCT
ejpam-3708	226	4	m	m	PROPN
ejpam-3708	226	5	,	,	PUNCT
ejpam-3708	226	6	p	p	X
ejpam-3708	226	7	,	,	PUNCT
ejpam-3708	226	8	u,∆m	u,∆m	PROPN
ejpam-3708	226	9	v	v	X
ejpam-3708	226	10	]	]	PUNCT
ejpam-3708	226	11	0	0	X
ejpam-3708	226	12	.	.	PUNCT
ejpam-3708	227	1	then	then	ADV
ejpam-3708	227	2	for	for	ADP
ejpam-3708	227	3	every	every	DET
ejpam-3708	227	4	ρ	ρ	PROPN
ejpam-3708	227	5	>	>	X
ejpam-3708	227	6	0	0	NUM
ejpam-3708	227	7	we	we	PRON
ejpam-3708	227	8	write	write	VERB
ejpam-3708	227	9	a1	a1	NOUN
ejpam-3708	227	10	=	=	PUNCT
ejpam-3708	227	11	{	{	PUNCT
ejpam-3708	227	12	ρ	ρ	PROPN
ejpam-3708	227	13	>	>	X
ejpam-3708	227	14	0	0	NUM
ejpam-3708	228	1	:	:	PUNCT
ejpam-3708	228	2	(	(	PUNCT
ejpam-3708	228	3	1	1	NUM
ejpam-3708	228	4	hr	hr	NOUN
ejpam-3708	228	5	∑	∑	PUNCT
ejpam-3708	228	6	k∈ir	k∈ir	PROPN
ejpam-3708	228	7	ank	ank	PROPN
ejpam-3708	228	8	[	[	PUNCT
ejpam-3708	228	9	k−smk	k−smk	NOUN
ejpam-3708	228	10	(	(	PUNCT
ejpam-3708	228	11	d(uk∆	d(uk∆	PROPN
ejpam-3708	228	12	m	m	NOUN
ejpam-3708	228	13	v	v	NOUN
ejpam-3708	228	14	xk	xk	PROPN
ejpam-3708	228	15	,	,	PUNCT
ejpam-3708	228	16	0	0	NUM
ejpam-3708	228	17	)	)	PUNCT
ejpam-3708	228	18	ρ	ρ	NOUN
ejpam-3708	228	19	)	)	PUNCT
ejpam-3708	228	20	]	]	SYM
ejpam-3708	228	21	pk	pk	NOUN
ejpam-3708	228	22	)	)	PUNCT
ejpam-3708	228	23	1	1	NUM
ejpam-3708	228	24	h	h	NOUN
ejpam-3708	228	25	≤	≤	NUM
ejpam-3708	228	26	1	1	NUM
ejpam-3708	228	27	}	}	PUNCT
ejpam-3708	228	28	and	and	CCONJ
ejpam-3708	228	29	a2	a2	PROPN
ejpam-3708	228	30	=	=	SYM
ejpam-3708	228	31	{	{	PUNCT
ejpam-3708	228	32	ρ	ρ	PROPN
ejpam-3708	228	33	>	>	X
ejpam-3708	228	34	0	0	NUM
ejpam-3708	228	35	:	:	PUNCT
ejpam-3708	228	36	(	(	PUNCT
ejpam-3708	228	37	1	1	NUM
ejpam-3708	228	38	hr	hr	NOUN
ejpam-3708	228	39	∑	∑	PUNCT
ejpam-3708	228	40	k∈ir	k∈ir	PROPN
ejpam-3708	228	41	ank	ank	PROPN
ejpam-3708	228	42	[	[	PUNCT
ejpam-3708	228	43	k−smk	k−smk	NOUN
ejpam-3708	228	44	(	(	PUNCT
ejpam-3708	228	45	d(uk∆	d(uk∆	PROPN
ejpam-3708	228	46	m	m	NOUN
ejpam-3708	228	47	v	v	ADP
ejpam-3708	228	48	yk	yk	PROPN
ejpam-3708	228	49	,	,	PUNCT
ejpam-3708	228	50	0	0	NUM
ejpam-3708	228	51	)	)	PUNCT
ejpam-3708	228	52	ρ	ρ	NOUN
ejpam-3708	228	53	)	)	PUNCT
ejpam-3708	228	54	]	]	SYM
ejpam-3708	228	55	pk	pk	NOUN
ejpam-3708	228	56	)	)	PUNCT
ejpam-3708	228	57	1	1	NUM
ejpam-3708	228	58	h	h	NOUN
ejpam-3708	228	59	≤	≤	NUM
ejpam-3708	228	60	1	1	NUM
ejpam-3708	228	61	}	}	PUNCT
ejpam-3708	228	62	.	.	PUNCT
ejpam-3708	229	1	let	let	VERB
ejpam-3708	229	2	ρ1	ρ1	NOUN
ejpam-3708	229	3	∈	∈	NOUN
ejpam-3708	229	4	a1	a1	NOUN
ejpam-3708	229	5	and	and	CCONJ
ejpam-3708	229	6	ρ2	ρ2	PROPN
ejpam-3708	229	7	∈	∈	PROPN
ejpam-3708	229	8	a2	a2	PROPN
ejpam-3708	229	9	.	.	PUNCT
ejpam-3708	230	1	if	if	SCONJ
ejpam-3708	230	2	ρ	ρ	PROPN
ejpam-3708	230	3	=	=	SYM
ejpam-3708	230	4	ρ1	ρ1	PROPN
ejpam-3708	230	5	+	+	CCONJ
ejpam-3708	230	6	ρ2	ρ2	NOUN
ejpam-3708	230	7	,	,	PUNCT
ejpam-3708	230	8	then	then	ADV
ejpam-3708	230	9	we	we	PRON
ejpam-3708	230	10	get	get	VERB
ejpam-3708	230	11	the	the	DET
ejpam-3708	230	12	following	follow	VERB
ejpam-3708	230	13	(	(	PUNCT
ejpam-3708	230	14	1	1	NUM
ejpam-3708	230	15	hr	hr	NOUN
ejpam-3708	230	16	∑	∑	PUNCT
ejpam-3708	230	17	k∈ir	k∈ir	PROPN
ejpam-3708	230	18	ank	ank	PROPN
ejpam-3708	230	19	[	[	PUNCT
ejpam-3708	230	20	k−smk	k−smk	NOUN
ejpam-3708	230	21	(	(	PUNCT
ejpam-3708	230	22	d(uk∆m	d(uk∆m	PROPN
ejpam-3708	230	23	v	v	NOUN
ejpam-3708	230	24	(	(	PUNCT
ejpam-3708	230	25	xk+yk),0	xk+yk),0	PROPN
ejpam-3708	230	26	)	)	PUNCT
ejpam-3708	230	27	)	)	PUNCT
ejpam-3708	230	28	ρ	ρ	PROPN
ejpam-3708	230	29	)	)	PUNCT
ejpam-3708	230	30	]	]	PUNCT
ejpam-3708	230	31	)	)	PUNCT
ejpam-3708	230	32	≤	≤	NUM
ejpam-3708	230	33	ρ1	ρ1	NOUN
ejpam-3708	230	34	ρ1	ρ1	NOUN
ejpam-3708	230	35	+	+	CCONJ
ejpam-3708	230	36	ρ2	ρ2	NOUN
ejpam-3708	230	37	(	(	PUNCT
ejpam-3708	230	38	1	1	NUM
ejpam-3708	230	39	hr	hr	NOUN
ejpam-3708	230	40	∑	∑	PUNCT
ejpam-3708	230	41	k∈ir	k∈ir	PROPN
ejpam-3708	230	42	ank	ank	PROPN
ejpam-3708	230	43	[	[	PUNCT
ejpam-3708	230	44	k−smk	k−smk	NOUN
ejpam-3708	230	45	(	(	PUNCT
ejpam-3708	230	46	d(uk∆	d(uk∆	PROPN
ejpam-3708	230	47	m	m	NOUN
ejpam-3708	230	48	v	v	NOUN
ejpam-3708	230	49	xk	xk	PROPN
ejpam-3708	230	50	,	,	PUNCT
ejpam-3708	230	51	0	0	NUM
ejpam-3708	230	52	)	)	PUNCT
ejpam-3708	230	53	ρ1	ρ1	NOUN
ejpam-3708	230	54	)	)	PUNCT
ejpam-3708	230	55	]	]	PUNCT
ejpam-3708	230	56	)	)	PUNCT
ejpam-3708	230	57	k.	k.	PROPN
ejpam-3708	230	58	raj	raj	PROPN
ejpam-3708	230	59	,	,	PUNCT
ejpam-3708	230	60	s.	s.	PROPN
ejpam-3708	230	61	a.	a.	PROPN
ejpam-3708	230	62	mohiuddine	mohiuddine	PROPN
ejpam-3708	230	63	/	/	SYM
ejpam-3708	230	64	eur	eur	PROPN
ejpam-3708	230	65	.	.	PUNCT
ejpam-3708	231	1	j.	j.	PROPN
ejpam-3708	231	2	pure	pure	PROPN
ejpam-3708	231	3	appl	appl	PROPN
ejpam-3708	231	4	.	.	PROPN
ejpam-3708	231	5	math	math	PROPN
ejpam-3708	231	6	,	,	PUNCT
ejpam-3708	231	7	13	13	NUM
ejpam-3708	231	8	(	(	PUNCT
ejpam-3708	231	9	5	5	NUM
ejpam-3708	231	10	)	)	PUNCT
ejpam-3708	231	11	(	(	PUNCT
ejpam-3708	231	12	2020	2020	NUM
ejpam-3708	231	13	)	)	PUNCT
ejpam-3708	231	14	,	,	PUNCT
ejpam-3708	231	15	1131	1131	NUM
ejpam-3708	231	16	-	-	SYM
ejpam-3708	231	17	1148	1148	NUM
ejpam-3708	231	18	1141	1141	NUM
ejpam-3708	231	19	+	+	CCONJ
ejpam-3708	231	20	ρ2	ρ2	NOUN
ejpam-3708	231	21	ρ1	ρ1	NOUN
ejpam-3708	231	22	+	+	CCONJ
ejpam-3708	231	23	ρ2	ρ2	NOUN
ejpam-3708	231	24	(	(	PUNCT
ejpam-3708	231	25	1	1	NUM
ejpam-3708	231	26	hr	hr	NOUN
ejpam-3708	231	27	∑	∑	PUNCT
ejpam-3708	231	28	k∈ir	k∈ir	PROPN
ejpam-3708	231	29	ank	ank	PROPN
ejpam-3708	231	30	[	[	PUNCT
ejpam-3708	231	31	k−smk	k−smk	NOUN
ejpam-3708	231	32	(	(	PUNCT
ejpam-3708	231	33	d(uk∆	d(uk∆	PROPN
ejpam-3708	231	34	m	m	NOUN
ejpam-3708	231	35	v	v	ADP
ejpam-3708	231	36	yk	yk	PROPN
ejpam-3708	231	37	,	,	PUNCT
ejpam-3708	231	38	0	0	NUM
ejpam-3708	231	39	)	)	PUNCT
ejpam-3708	231	40	ρ2	ρ2	NOUN
ejpam-3708	231	41	)	)	PUNCT
ejpam-3708	231	42	]	]	PUNCT
ejpam-3708	231	43	)	)	PUNCT
ejpam-3708	231	44	.	.	PUNCT
ejpam-3708	232	1	thus	thus	ADV
ejpam-3708	232	2	,	,	PUNCT
ejpam-3708	232	3	we	we	PRON
ejpam-3708	232	4	have	have	VERB
ejpam-3708	232	5	1	1	NUM
ejpam-3708	232	6	hr	hr	NOUN
ejpam-3708	232	7	∑	∑	PUNCT
ejpam-3708	232	8	k∈ir	k∈ir	PROPN
ejpam-3708	232	9	ank	ank	PROPN
ejpam-3708	232	10	[	[	PUNCT
ejpam-3708	232	11	k−smk	k−smk	NOUN
ejpam-3708	232	12	(	(	PUNCT
ejpam-3708	232	13	d(uk∆	d(uk∆	PROPN
ejpam-3708	232	14	m	m	PROPN
ejpam-3708	232	15	v	v	NOUN
ejpam-3708	232	16	(	(	PUNCT
ejpam-3708	232	17	xk	xk	PROPN
ejpam-3708	232	18	+	+	CCONJ
ejpam-3708	232	19	yk	yk	PROPN
ejpam-3708	232	20	)	)	PUNCT
ejpam-3708	232	21	,	,	PUNCT
ejpam-3708	232	22	0	0	X
ejpam-3708	232	23	)	)	PUNCT
ejpam-3708	232	24	ρ	ρ	NOUN
ejpam-3708	232	25	)	)	PUNCT
ejpam-3708	232	26	]	]	PUNCT
ejpam-3708	232	27	pk	pk	NOUN
ejpam-3708	232	28	≤	≤	ADV
ejpam-3708	232	29	1	1	NUM
ejpam-3708	232	30	and	and	CCONJ
ejpam-3708	232	31	g∆(x	g∆(x	X
ejpam-3708	232	32	+	+	NUM
ejpam-3708	232	33	y	y	PROPN
ejpam-3708	232	34	)	)	PUNCT
ejpam-3708	233	1	=	=	SYM
ejpam-3708	233	2	inf{(ρ1	inf{(ρ1	NOUN
ejpam-3708	233	3	+	+	CCONJ
ejpam-3708	233	4	ρ2	ρ2	NOUN
ejpam-3708	233	5	)	)	PUNCT
ejpam-3708	233	6	pn	pn	PROPN
ejpam-3708	233	7	h	h	NOUN
ejpam-3708	233	8	:	:	PUNCT
ejpam-3708	233	9	ρ1	ρ1	PROPN
ejpam-3708	233	10	∈	∈	PROPN
ejpam-3708	233	11	a1	a1	NOUN
ejpam-3708	233	12	,	,	PUNCT
ejpam-3708	233	13	ρ2	ρ2	PROPN
ejpam-3708	233	14	∈	∈	PROPN
ejpam-3708	233	15	a2	a2	PROPN
ejpam-3708	233	16	}	}	PUNCT
ejpam-3708	233	17	≤	≤	NUM
ejpam-3708	233	18	inf{(ρ1	inf{(ρ1	NOUN
ejpam-3708	233	19	)	)	PUNCT
ejpam-3708	234	1	pn	pn	PROPN
ejpam-3708	234	2	h	h	NOUN
ejpam-3708	234	3	:	:	PUNCT
ejpam-3708	234	4	ρ1	ρ1	PROPN
ejpam-3708	234	5	∈	∈	PROPN
ejpam-3708	234	6	a1}+	a1}+	ADJ
ejpam-3708	234	7	inf{(ρ2	inf{(ρ2	NOUN
ejpam-3708	234	8	)	)	PUNCT
ejpam-3708	234	9	pn	pn	PROPN
ejpam-3708	234	10	h	h	NOUN
ejpam-3708	234	11	:	:	PUNCT
ejpam-3708	234	12	ρ2	ρ2	PROPN
ejpam-3708	234	13	∈	∈	PROPN
ejpam-3708	234	14	a2	a2	PROPN
ejpam-3708	234	15	}	}	PUNCT
ejpam-3708	234	16	=	=	SYM
ejpam-3708	234	17	g∆(x	g∆(x	NOUN
ejpam-3708	234	18	)	)	PUNCT
ejpam-3708	235	1	+	+	CCONJ
ejpam-3708	235	2	g∆(y	g∆(y	X
ejpam-3708	235	3	)	)	PUNCT
ejpam-3708	235	4	.	.	PUNCT
ejpam-3708	236	1	let	let	VERB
ejpam-3708	236	2	tmk	tmk	PROPN
ejpam-3708	236	3	→	→	SYM
ejpam-3708	236	4	t	t	PROPN
ejpam-3708	236	5	,	,	PUNCT
ejpam-3708	236	6	where	where	SCONJ
ejpam-3708	236	7	tmk	tmk	PROPN
ejpam-3708	236	8	,	,	PUNCT
ejpam-3708	236	9	t	t	PROPN
ejpam-3708	236	10	∈	∈	PROPN
ejpam-3708	236	11	c	c	NOUN
ejpam-3708	236	12	,	,	PUNCT
ejpam-3708	236	13	and	and	CCONJ
ejpam-3708	236	14	let	let	VERB
ejpam-3708	236	15	g∆(xm	g∆(xm	PROPN
ejpam-3708	236	16	k	k	PROPN
ejpam-3708	236	17	−	−	PROPN
ejpam-3708	236	18	xk	xk	PROPN
ejpam-3708	236	19	)	)	PUNCT
ejpam-3708	236	20	→	→	SYM
ejpam-3708	236	21	0	0	NUM
ejpam-3708	236	22	as	as	SCONJ
ejpam-3708	236	23	m	m	PROPN
ejpam-3708	236	24	→	→	SYM
ejpam-3708	236	25	∞.	∞.	PROPN
ejpam-3708	236	26	to	to	PART
ejpam-3708	236	27	prove	prove	VERB
ejpam-3708	236	28	that	that	SCONJ
ejpam-3708	236	29	g∆(tmk	g∆(tmk	NOUN
ejpam-3708	236	30	x	x	PUNCT
ejpam-3708	237	1	m	m	AUX
ejpam-3708	237	2	k	k	X
ejpam-3708	237	3	−	−	NOUN
ejpam-3708	237	4	txk)→	txk)→	NOUN
ejpam-3708	237	5	0	0	PUNCT
ejpam-3708	237	6	as	as	SCONJ
ejpam-3708	237	7	m→∞.	m→∞.	NOUN
ejpam-3708	237	8	let	let	VERB
ejpam-3708	237	9	tk	tk	PROPN
ejpam-3708	237	10	→	→	SYM
ejpam-3708	237	11	t	t	PROPN
ejpam-3708	237	12	,	,	PUNCT
ejpam-3708	237	13	where	where	SCONJ
ejpam-3708	237	14	tk	tk	PROPN
ejpam-3708	237	15	,	,	PUNCT
ejpam-3708	237	16	t	t	PROPN
ejpam-3708	237	17	∈	∈	PROPN
ejpam-3708	237	18	c	c	X
ejpam-3708	237	19	,	,	PUNCT
ejpam-3708	237	20	and	and	CCONJ
ejpam-3708	238	1	g∆(xm	g∆(xm	PROPN
ejpam-3708	238	2	k	k	PROPN
ejpam-3708	238	3	−xk)→	−xk)→	PROPN
ejpam-3708	238	4	0	0	PUNCT
ejpam-3708	238	5	as	as	ADP
ejpam-3708	238	6	m→∞.	m→∞.	PROPN
ejpam-3708	238	7	we	we	PRON
ejpam-3708	238	8	have	have	VERB
ejpam-3708	238	9	a3	a3	NOUN
ejpam-3708	238	10	=	=	PUNCT
ejpam-3708	238	11	{	{	PUNCT
ejpam-3708	238	12	ρk	ρk	INTJ
ejpam-3708	238	13	>	>	X
ejpam-3708	238	14	0	0	NUM
ejpam-3708	238	15	:	:	SYM
ejpam-3708	238	16	1	1	NUM
ejpam-3708	238	17	hr	hr	NOUN
ejpam-3708	238	18	∑	∑	PUNCT
ejpam-3708	238	19	k∈ir	k∈ir	PROPN
ejpam-3708	238	20	ank	ank	PROPN
ejpam-3708	238	21	[	[	PUNCT
ejpam-3708	238	22	k−smk	k−smk	NOUN
ejpam-3708	238	23	(	(	PUNCT
ejpam-3708	238	24	d(uk∆	d(uk∆	PROPN
ejpam-3708	238	25	m	m	NOUN
ejpam-3708	238	26	v	v	NOUN
ejpam-3708	238	27	xk	xk	PROPN
ejpam-3708	238	28	,	,	PUNCT
ejpam-3708	238	29	0	0	NUM
ejpam-3708	238	30	)	)	PUNCT
ejpam-3708	238	31	ρk	ρk	NOUN
ejpam-3708	238	32	)	)	PUNCT
ejpam-3708	238	33	]	]	PUNCT
ejpam-3708	238	34	pk	pk	NOUN
ejpam-3708	238	35	≤	≤	ADV
ejpam-3708	238	36	1	1	NUM
ejpam-3708	238	37	}	}	PUNCT
ejpam-3708	238	38	and	and	CCONJ
ejpam-3708	238	39	a4	a4	NOUN
ejpam-3708	238	40	=	=	SYM
ejpam-3708	238	41	{	{	PUNCT
ejpam-3708	238	42	ρ′k	ρ′k	ADV
ejpam-3708	238	43	>	>	X
ejpam-3708	238	44	0	0	NUM
ejpam-3708	238	45	:	:	SYM
ejpam-3708	238	46	1	1	NUM
ejpam-3708	238	47	hr	hr	NOUN
ejpam-3708	238	48	∑	∑	PUNCT
ejpam-3708	238	49	k∈ir	k∈ir	PROPN
ejpam-3708	238	50	ank	ank	PROPN
ejpam-3708	238	51	[	[	PUNCT
ejpam-3708	238	52	k−smk	k−smk	NOUN
ejpam-3708	238	53	(	(	PUNCT
ejpam-3708	238	54	d(uk∆	d(uk∆	PROPN
ejpam-3708	238	55	m	m	NOUN
ejpam-3708	238	56	v	v	ADP
ejpam-3708	238	57	yk	yk	PROPN
ejpam-3708	238	58	,	,	PUNCT
ejpam-3708	238	59	0	0	NUM
ejpam-3708	238	60	)	)	PUNCT
ejpam-3708	238	61	ρ′k	ρ′k	NOUN
ejpam-3708	238	62	)	)	PUNCT
ejpam-3708	238	63	]	]	PUNCT
ejpam-3708	238	64	pk	pk	NOUN
ejpam-3708	238	65	≤	≤	ADV
ejpam-3708	238	66	1	1	NUM
ejpam-3708	238	67	}	}	PUNCT
ejpam-3708	238	68	.	.	PUNCT
ejpam-3708	239	1	if	if	SCONJ
ejpam-3708	239	2	ρk	ρk	PROPN
ejpam-3708	239	3	∈	∈	PROPN
ejpam-3708	239	4	a3	a3	NOUN
ejpam-3708	239	5	and	and	CCONJ
ejpam-3708	239	6	ρ′k	ρ′k	NOUN
ejpam-3708	239	7	∈	∈	ADJ
ejpam-3708	239	8	a4	a4	NOUN
ejpam-3708	239	9	then	then	ADV
ejpam-3708	239	10	by	by	ADP
ejpam-3708	239	11	inequality	inequality	NOUN
ejpam-3708	239	12	(	(	PUNCT
ejpam-3708	239	13	3	3	NUM
ejpam-3708	239	14	)	)	PUNCT
ejpam-3708	239	15	and	and	CCONJ
ejpam-3708	239	16	continuity	continuity	NOUN
ejpam-3708	239	17	of	of	ADP
ejpam-3708	239	18	the	the	DET
ejpam-3708	239	19	function	function	NOUN
ejpam-3708	239	20	m	m	VERB
ejpam-3708	239	21	=	=	SYM
ejpam-3708	239	22	(	(	PUNCT
ejpam-3708	239	23	mk	mk	PROPN
ejpam-3708	239	24	)	)	PUNCT
ejpam-3708	239	25	,	,	PUNCT
ejpam-3708	239	26	we	we	PRON
ejpam-3708	239	27	have	have	VERB
ejpam-3708	239	28	that	that	DET
ejpam-3708	239	29	k−smk	k−smk	NOUN
ejpam-3708	239	30	(	(	PUNCT
ejpam-3708	239	31	d(uk∆m	d(uk∆m	PROPN
ejpam-3708	239	32	v	v	NOUN
ejpam-3708	239	33	(	(	PUNCT
ejpam-3708	239	34	tmxm	tmxm	NOUN
ejpam-3708	239	35	k	k	PROPN
ejpam-3708	239	36	−tx,0	−tx,0	PROPN
ejpam-3708	239	37	)	)	PUNCT
ejpam-3708	239	38	)	)	PUNCT
ejpam-3708	239	39	|tm−t|ρk+|t|ρ′k	|tm−t|ρk+|t|ρ′k	NOUN
ejpam-3708	239	40	)	)	PUNCT
ejpam-3708	239	41	≤	≤	NUM
ejpam-3708	239	42	k−smk	k−smk	NOUN
ejpam-3708	239	43	(	(	PUNCT
ejpam-3708	239	44	d(uk∆	d(uk∆	PROPN
ejpam-3708	239	45	m	m	PROPN
ejpam-3708	239	46	v	v	NOUN
ejpam-3708	239	47	(	(	PUNCT
ejpam-3708	239	48	tmxm	tmxm	NOUN
ejpam-3708	239	49	k	k	PROPN
ejpam-3708	239	50	−	−	PROPN
ejpam-3708	239	51	txk	txk	PROPN
ejpam-3708	239	52	)	)	PUNCT
ejpam-3708	239	53	,	,	PUNCT
ejpam-3708	239	54	0	0	NUM
ejpam-3708	239	55	)	)	PUNCT
ejpam-3708	240	1	|tm	|tm	ADP
ejpam-3708	240	2	−	−	PROPN
ejpam-3708	240	3	t|ρk	t|ρk	NOUN
ejpam-3708	241	1	+	+	CCONJ
ejpam-3708	241	2	|t|ρ′k	|t|ρ′k	NOUN
ejpam-3708	241	3	)	)	PUNCT
ejpam-3708	242	1	+	+	CCONJ
ejpam-3708	242	2	k−smk	k−smk	NOUN
ejpam-3708	242	3	(	(	PUNCT
ejpam-3708	242	4	d(uk∆	d(uk∆	PROPN
ejpam-3708	242	5	m	m	NOUN
ejpam-3708	242	6	v	v	NOUN
ejpam-3708	242	7	(	(	PUNCT
ejpam-3708	242	8	txk	txk	NOUN
ejpam-3708	242	9	−	−	PROPN
ejpam-3708	242	10	tx	tx	PROPN
ejpam-3708	242	11	,	,	PUNCT
ejpam-3708	242	12	0	0	NUM
ejpam-3708	242	13	)	)	PUNCT
ejpam-3708	242	14	)	)	PUNCT
ejpam-3708	243	1	|tm	|tm	ADP
ejpam-3708	243	2	−	−	NUM
ejpam-3708	243	3	t|ρk	t|ρk	NOUN
ejpam-3708	244	1	+	+	CCONJ
ejpam-3708	244	2	|t|ρ′k	|t|ρ′k	NOUN
ejpam-3708	244	3	)	)	PUNCT
ejpam-3708	244	4	≤	≤	NOUN
ejpam-3708	245	1	|tm	|tm	ADP
ejpam-3708	245	2	−	−	NUM
ejpam-3708	245	3	t|ρk	t|ρk	NOUN
ejpam-3708	246	1	|tm	|tm	ADP
ejpam-3708	246	2	−	−	NUM
ejpam-3708	246	3	t|ρk	t|ρk	NOUN
ejpam-3708	247	1	+	+	CCONJ
ejpam-3708	247	2	|t|ρ′k	|t|ρ′k	NOUN
ejpam-3708	247	3	k−smk	k−smk	NOUN
ejpam-3708	247	4	(	(	PUNCT
ejpam-3708	247	5	d(uk∆	d(uk∆	PROPN
ejpam-3708	247	6	m	m	NOUN
ejpam-3708	247	7	v	v	NOUN
ejpam-3708	247	8	x	x	SYM
ejpam-3708	247	9	m	m	VERB
ejpam-3708	247	10	k	k	NOUN
ejpam-3708	247	11	,	,	PUNCT
ejpam-3708	247	12	0	0	X
ejpam-3708	247	13	)	)	PUNCT
ejpam-3708	247	14	ρk	ρk	NOUN
ejpam-3708	247	15	)	)	PUNCT
ejpam-3708	248	1	+	+	CCONJ
ejpam-3708	248	2	|t|ρ′k	|t|ρ′k	NOUN
ejpam-3708	248	3	|tm	|tm	ADP
ejpam-3708	248	4	−	−	PROPN
ejpam-3708	248	5	t|ρk	t|ρk	NOUN
ejpam-3708	249	1	+	+	CCONJ
ejpam-3708	249	2	|t|ρ′k	|t|ρ′k	NOUN
ejpam-3708	249	3	k−smk	k−smk	NOUN
ejpam-3708	249	4	(	(	PUNCT
ejpam-3708	249	5	d(uk∆	d(uk∆	PROPN
ejpam-3708	249	6	m	m	NOUN
ejpam-3708	249	7	v	v	NOUN
ejpam-3708	249	8	(	(	PUNCT
ejpam-3708	249	9	xm	xm	PROPN
ejpam-3708	249	10	k	k	PROPN
ejpam-3708	249	11	−xk	−xk	PROPN
ejpam-3708	249	12	)	)	PUNCT
ejpam-3708	249	13	,	,	PUNCT
ejpam-3708	249	14	0	0	NUM
ejpam-3708	249	15	)	)	PUNCT
ejpam-3708	249	16	ρ′k	ρ′k	NOUN
ejpam-3708	249	17	)	)	PUNCT
ejpam-3708	249	18	.	.	PUNCT
ejpam-3708	250	1	from	from	ADP
ejpam-3708	250	2	the	the	DET
ejpam-3708	250	3	above	above	ADJ
ejpam-3708	250	4	inequality	inequality	NOUN
ejpam-3708	250	5	it	it	PRON
ejpam-3708	250	6	follows	follow	VERB
ejpam-3708	250	7	that	that	SCONJ
ejpam-3708	250	8	1	1	NUM
ejpam-3708	250	9	hr	hr	NOUN
ejpam-3708	250	10	∑	∑	PUNCT
ejpam-3708	250	11	k∈ir	k∈ir	PROPN
ejpam-3708	250	12	ank	ank	PROPN
ejpam-3708	250	13	[	[	PUNCT
ejpam-3708	250	14	k−smk	k−smk	NOUN
ejpam-3708	250	15	(	(	PUNCT
ejpam-3708	250	16	d(uk∆	d(uk∆	PROPN
ejpam-3708	250	17	m	m	PROPN
ejpam-3708	250	18	v	v	NOUN
ejpam-3708	250	19	(	(	PUNCT
ejpam-3708	250	20	tmxm	tmxm	NOUN
ejpam-3708	250	21	k	k	PROPN
ejpam-3708	250	22	−	−	PROPN
ejpam-3708	250	23	tx	tx	PROPN
ejpam-3708	250	24	)	)	PUNCT
ejpam-3708	250	25	,	,	PUNCT
ejpam-3708	250	26	0	0	NUM
ejpam-3708	250	27	)	)	PUNCT
ejpam-3708	251	1	|tm	|tm	ADP
ejpam-3708	251	2	−	−	PROPN
ejpam-3708	251	3	t|ρk	t|ρk	NOUN
ejpam-3708	252	1	+	+	CCONJ
ejpam-3708	252	2	|t|ρ′k	|t|ρ′k	NOUN
ejpam-3708	252	3	)	)	PUNCT
ejpam-3708	252	4	]	]	PUNCT
ejpam-3708	252	5	pk	pk	NOUN
ejpam-3708	252	6	≤	≤	ADV
ejpam-3708	252	7	1	1	NUM
ejpam-3708	252	8	k.	k.	PROPN
ejpam-3708	252	9	raj	raj	PROPN
ejpam-3708	252	10	,	,	PUNCT
ejpam-3708	252	11	s.	s.	PROPN
ejpam-3708	252	12	a.	a.	PROPN
ejpam-3708	252	13	mohiuddine	mohiuddine	PROPN
ejpam-3708	252	14	/	/	SYM
ejpam-3708	252	15	eur	eur	PROPN
ejpam-3708	252	16	.	.	PUNCT
ejpam-3708	253	1	j.	j.	PROPN
ejpam-3708	253	2	pure	pure	PROPN
ejpam-3708	253	3	appl	appl	PROPN
ejpam-3708	253	4	.	.	PROPN
ejpam-3708	253	5	math	math	PROPN
ejpam-3708	253	6	,	,	PUNCT
ejpam-3708	253	7	13	13	NUM
ejpam-3708	253	8	(	(	PUNCT
ejpam-3708	253	9	5	5	NUM
ejpam-3708	253	10	)	)	PUNCT
ejpam-3708	253	11	(	(	PUNCT
ejpam-3708	253	12	2020	2020	NUM
ejpam-3708	253	13	)	)	PUNCT
ejpam-3708	253	14	,	,	PUNCT
ejpam-3708	253	15	1131	1131	NUM
ejpam-3708	253	16	-	-	SYM
ejpam-3708	253	17	1148	1148	NUM
ejpam-3708	253	18	1142	1142	NUM
ejpam-3708	253	19	and	and	CCONJ
ejpam-3708	253	20	consequently	consequently	ADV
ejpam-3708	253	21	,	,	PUNCT
ejpam-3708	253	22	g∆(tmk	g∆(tmk	PROPN
ejpam-3708	253	23	xk	xk	PROPN
ejpam-3708	254	1	+	+	CCONJ
ejpam-3708	254	2	tx	tx	PROPN
ejpam-3708	254	3	)	)	PUNCT
ejpam-3708	254	4	=	=	NOUN
ejpam-3708	254	5	inf{(|tmk	inf{(|tmk	NOUN
ejpam-3708	254	6	−	−	NUM
ejpam-3708	254	7	t|ρk	t|ρk	NOUN
ejpam-3708	255	1	+	+	CCONJ
ejpam-3708	255	2	|t|ρ′k	|t|ρ′k	NOUN
ejpam-3708	255	3	}	}	PUNCT
ejpam-3708	255	4	)	)	PUNCT
ejpam-3708	256	1	pn	pn	PROPN
ejpam-3708	256	2	h	h	NOUN
ejpam-3708	256	3	:	:	PUNCT
ejpam-3708	256	4	ρk	ρk	PROPN
ejpam-3708	256	5	∈	∈	PROPN
ejpam-3708	256	6	a3	a3	NOUN
ejpam-3708	256	7	,	,	PUNCT
ejpam-3708	256	8	ρ	ρ	PROPN
ejpam-3708	256	9	′	′	NUM
ejpam-3708	256	10	k	k	PROPN
ejpam-3708	256	11	∈	∈	PROPN
ejpam-3708	256	12	a4	a4	PROPN
ejpam-3708	256	13	}	}	PUNCT
ejpam-3708	256	14	≤	≤	NOUN
ejpam-3708	256	15	|tmk	|tmk	PROPN
ejpam-3708	256	16	−	−	PROPN
ejpam-3708	256	17	t|ρ	t|ρ	PROPN
ejpam-3708	257	1	pn	pn	PROPN
ejpam-3708	257	2	h	h	PROPN
ejpam-3708	257	3	k	k	PROPN
ejpam-3708	257	4	inf{(ρk	inf{(ρk	PROPN
ejpam-3708	257	5	)	)	PUNCT
ejpam-3708	257	6	pn	pn	PROPN
ejpam-3708	257	7	h	h	NOUN
ejpam-3708	257	8	:	:	PUNCT
ejpam-3708	257	9	ρk	ρk	ADP
ejpam-3708	257	10	∈	∈	PROPN
ejpam-3708	257	11	a3}+	a3}+	AUX
ejpam-3708	257	12	|t|ρ′k	|t|ρ′k	NOUN
ejpam-3708	257	13	inf{(ρ′k	inf{(ρ′k	PROPN
ejpam-3708	257	14	)	)	PUNCT
ejpam-3708	257	15	pn	pn	PROPN
ejpam-3708	257	16	h	h	NOUN
ejpam-3708	257	17	:	:	PUNCT
ejpam-3708	257	18	ρ′k	ρ′k	PROPN
ejpam-3708	257	19	∈	∈	PROPN
ejpam-3708	257	20	a4	a4	PROPN
ejpam-3708	257	21	}	}	PUNCT
ejpam-3708	257	22	≤	≤	NUM
ejpam-3708	257	23	max{|t|	max{|t|	NOUN
ejpam-3708	257	24	,	,	PUNCT
ejpam-3708	257	25	|t|	|t|	VERB
ejpam-3708	257	26	pn	pn	PROPN
ejpam-3708	257	27	h	h	PROPN
ejpam-3708	257	28	}	}	PUNCT
ejpam-3708	257	29	g∆(xm	g∆(xm	PROPN
ejpam-3708	257	30	k	k	PROPN
ejpam-3708	257	31	−xk	−xk	PROPN
ejpam-3708	257	32	)	)	PUNCT
ejpam-3708	257	33	.	.	PUNCT
ejpam-3708	258	1	note	note	VERB
ejpam-3708	258	2	that	that	SCONJ
ejpam-3708	258	3	g∆(xm	g∆(xm	PROPN
ejpam-3708	258	4	k	k	PROPN
ejpam-3708	258	5	)	)	PUNCT
ejpam-3708	258	6	≤	≤	NUM
ejpam-3708	258	7	g∆(xm	g∆(xm	NOUN
ejpam-3708	258	8	)	)	PUNCT
ejpam-3708	259	1	+	+	CCONJ
ejpam-3708	259	2	g∆(xm	g∆(xm	PROPN
ejpam-3708	259	3	k	k	PROPN
ejpam-3708	259	4	−xm	−xm	PROPN
ejpam-3708	259	5	)	)	PUNCT
ejpam-3708	259	6	,	,	PUNCT
ejpam-3708	259	7	for	for	ADP
ejpam-3708	259	8	all	all	DET
ejpam-3708	259	9	k	k	PROPN
ejpam-3708	259	10	∈	∈	PROPN
ejpam-3708	259	11	n.	n.	NOUN
ejpam-3708	259	12	hence	hence	ADV
ejpam-3708	259	13	,	,	PUNCT
ejpam-3708	259	14	by	by	ADP
ejpam-3708	259	15	our	our	PRON
ejpam-3708	259	16	assumption	assumption	NOUN
ejpam-3708	259	17	the	the	DET
ejpam-3708	259	18	right	right	ADJ
ejpam-3708	259	19	hand	hand	NOUN
ejpam-3708	259	20	tends	tend	VERB
ejpam-3708	259	21	to	to	ADP
ejpam-3708	259	22	0	0	NUM
ejpam-3708	259	23	as	as	ADP
ejpam-3708	259	24	m→∞.	m→∞.	PROPN
ejpam-3708	259	25	this	this	PRON
ejpam-3708	259	26	completes	complete	VERB
ejpam-3708	259	27	the	the	DET
ejpam-3708	259	28	proof	proof	NOUN
ejpam-3708	259	29	.	.	PUNCT
ejpam-3708	260	1	theorem	theorem	NOUN
ejpam-3708	260	2	3	3	X
ejpam-3708	260	3	.	.	PUNCT
ejpam-3708	261	1	let	let	AUX
ejpam-3708	261	2	m	m	VERB
ejpam-3708	261	3	=	=	SYM
ejpam-3708	261	4	(	(	PUNCT
ejpam-3708	261	5	mk	mk	X
ejpam-3708	261	6	)	)	PUNCT
ejpam-3708	261	7	be	be	VERB
ejpam-3708	261	8	a	a	DET
ejpam-3708	261	9	sequence	sequence	NOUN
ejpam-3708	261	10	of	of	ADP
ejpam-3708	261	11	orlicz	orlicz	ADJ
ejpam-3708	261	12	functions	function	NOUN
ejpam-3708	261	13	,	,	PUNCT
ejpam-3708	261	14	p	p	NOUN
ejpam-3708	261	15	=	=	PUNCT
ejpam-3708	261	16	(	(	PUNCT
ejpam-3708	261	17	pk	pk	NOUN
ejpam-3708	261	18	)	)	PUNCT
ejpam-3708	261	19	be	be	AUX
ejpam-3708	261	20	a	a	DET
ejpam-3708	261	21	bounded	bounded	ADJ
ejpam-3708	261	22	sequence	sequence	NOUN
ejpam-3708	261	23	of	of	ADP
ejpam-3708	261	24	positive	positive	ADJ
ejpam-3708	261	25	real	real	ADJ
ejpam-3708	261	26	numbers	number	NOUN
ejpam-3708	261	27	,	,	PUNCT
ejpam-3708	261	28	(	(	PUNCT
ejpam-3708	261	29	i	i	NOUN
ejpam-3708	261	30	)	)	PUNCT
ejpam-3708	261	31	let	let	VERB
ejpam-3708	261	32	0	0	PUNCT
ejpam-3708	261	33	<	<	X
ejpam-3708	261	34	inf	inf	PROPN
ejpam-3708	261	35	pk	pk	NOUN
ejpam-3708	261	36	≤	≤	X
ejpam-3708	261	37	pk	pk	NOUN
ejpam-3708	261	38	≤	≤	ADJ
ejpam-3708	261	39	1	1	NUM
ejpam-3708	261	40	.	.	PUNCT
ejpam-3708	262	1	then	then	ADV
ejpam-3708	262	2	w	w	PROPN
ejpam-3708	262	3	i(f	i(f	NOUN
ejpam-3708	262	4	)	)	PUNCT
ejpam-3708	263	1	θ	θ	PROPN
ejpam-3708	264	1	[	[	X
ejpam-3708	264	2	a	a	X
ejpam-3708	264	3	,	,	PUNCT
ejpam-3708	264	4	m	m	PROPN
ejpam-3708	264	5	,	,	PUNCT
ejpam-3708	264	6	p	p	X
ejpam-3708	264	7	,	,	PUNCT
ejpam-3708	264	8	u,∆m	u,∆m	PROPN
ejpam-3708	264	9	v	v	NOUN
ejpam-3708	264	10	]	]	PUNCT
ejpam-3708	264	11	⊆	⊆	NUM
ejpam-3708	264	12	wi(f	wi(f	NOUN
ejpam-3708	264	13	)	)	PUNCT
ejpam-3708	264	14	θ	θ	PROPN
ejpam-3708	265	1	[	[	X
ejpam-3708	265	2	a	a	X
ejpam-3708	265	3	,	,	PUNCT
ejpam-3708	265	4	m	m	PROPN
ejpam-3708	265	5	,	,	PUNCT
ejpam-3708	265	6	u,∆m	u,∆m	PROPN
ejpam-3708	265	7	v	v	X
ejpam-3708	265	8	]	]	PUNCT
ejpam-3708	265	9	,	,	PUNCT
ejpam-3708	265	10	w	w	PROPN
ejpam-3708	265	11	i(f	i(f	NOUN
ejpam-3708	265	12	)	)	PUNCT
ejpam-3708	265	13	θ	θ	PROPN
ejpam-3708	266	1	[	[	X
ejpam-3708	266	2	a	a	X
ejpam-3708	266	3	,	,	PUNCT
ejpam-3708	266	4	m	m	PROPN
ejpam-3708	266	5	,	,	PUNCT
ejpam-3708	266	6	p	p	X
ejpam-3708	266	7	,	,	PUNCT
ejpam-3708	266	8	u,∆m	u,∆m	PROPN
ejpam-3708	266	9	v	v	X
ejpam-3708	266	10	]	]	PUNCT
ejpam-3708	266	11	0	0	NUM
ejpam-3708	266	12	⊆	⊆	NUM
ejpam-3708	266	13	wi(f	wi(f	NOUN
ejpam-3708	266	14	)	)	PUNCT
ejpam-3708	266	15	θ	θ	PROPN
ejpam-3708	267	1	[	[	X
ejpam-3708	267	2	a	a	X
ejpam-3708	267	3	,	,	PUNCT
ejpam-3708	267	4	m	m	PROPN
ejpam-3708	267	5	,	,	PUNCT
ejpam-3708	267	6	u,∆m	u,∆m	PROPN
ejpam-3708	267	7	v	v	X
ejpam-3708	267	8	]	]	PUNCT
ejpam-3708	267	9	0	0	NUM
ejpam-3708	267	10	.	.	PUNCT
ejpam-3708	267	11	(	(	PUNCT
ejpam-3708	267	12	ii	ii	NOUN
ejpam-3708	267	13	)	)	PUNCT
ejpam-3708	267	14	let	let	VERB
ejpam-3708	267	15	1	1	NUM
ejpam-3708	267	16	≤	≤	NUM
ejpam-3708	267	17	pk	pk	NOUN
ejpam-3708	267	18	≤	≤	NUM
ejpam-3708	267	19	sup	sup	NOUN
ejpam-3708	267	20	pk	pk	NOUN
ejpam-3708	267	21	<	<	X
ejpam-3708	267	22	∞.	∞.	PROPN
ejpam-3708	267	23	then	then	ADV
ejpam-3708	267	24	w	w	PROPN
ejpam-3708	267	25	i(f	i(f	PROPN
ejpam-3708	267	26	)	)	PUNCT
ejpam-3708	267	27	θ	θ	PROPN
ejpam-3708	268	1	[	[	X
ejpam-3708	268	2	a	a	X
ejpam-3708	268	3	,	,	PUNCT
ejpam-3708	268	4	m	m	PROPN
ejpam-3708	268	5	,	,	PUNCT
ejpam-3708	268	6	u,∆m	u,∆m	PROPN
ejpam-3708	268	7	v	v	X
ejpam-3708	268	8	]	]	PUNCT
ejpam-3708	268	9	⊆	⊆	NUM
ejpam-3708	268	10	wi(f	wi(f	NOUN
ejpam-3708	268	11	)	)	PUNCT
ejpam-3708	268	12	θ	θ	PROPN
ejpam-3708	269	1	[	[	X
ejpam-3708	269	2	a	a	X
ejpam-3708	269	3	,	,	PUNCT
ejpam-3708	269	4	m	m	PROPN
ejpam-3708	269	5	,	,	PUNCT
ejpam-3708	269	6	p	p	X
ejpam-3708	269	7	,	,	PUNCT
ejpam-3708	269	8	u,∆m	u,∆m	PROPN
ejpam-3708	269	9	v	v	X
ejpam-3708	269	10	]	]	PUNCT
ejpam-3708	269	11	,	,	PUNCT
ejpam-3708	269	12	w	w	PROPN
ejpam-3708	269	13	i(f	i(f	NOUN
ejpam-3708	269	14	)	)	PUNCT
ejpam-3708	269	15	θ	θ	PROPN
ejpam-3708	270	1	[	[	X
ejpam-3708	270	2	a	a	X
ejpam-3708	270	3	,	,	PUNCT
ejpam-3708	270	4	m	m	PROPN
ejpam-3708	270	5	,	,	PUNCT
ejpam-3708	270	6	u,∆m	u,∆m	PROPN
ejpam-3708	270	7	v	v	X
ejpam-3708	270	8	]	]	PUNCT
ejpam-3708	270	9	0	0	NUM
ejpam-3708	270	10	⊆	⊆	NUM
ejpam-3708	270	11	wi(f	wi(f	NOUN
ejpam-3708	270	12	)	)	PUNCT
ejpam-3708	270	13	θ	θ	PROPN
ejpam-3708	271	1	[	[	X
ejpam-3708	271	2	a	a	X
ejpam-3708	271	3	,	,	PUNCT
ejpam-3708	271	4	m	m	PROPN
ejpam-3708	271	5	,	,	PUNCT
ejpam-3708	271	6	p	p	X
ejpam-3708	271	7	,	,	PUNCT
ejpam-3708	271	8	u,∆m	u,∆m	PROPN
ejpam-3708	271	9	v	v	X
ejpam-3708	271	10	]	]	SYM
ejpam-3708	271	11	0	0	X
ejpam-3708	271	12	.	.	PUNCT
ejpam-3708	272	1	proof	proof	NOUN
ejpam-3708	272	2	.	.	PUNCT
ejpam-3708	273	1	(	(	PUNCT
ejpam-3708	273	2	i	i	NOUN
ejpam-3708	273	3	)	)	PUNCT
ejpam-3708	273	4	let	let	VERB
ejpam-3708	273	5	x	x	PUNCT
ejpam-3708	273	6	=	=	SYM
ejpam-3708	273	7	(	(	PUNCT
ejpam-3708	273	8	xk	xk	INTJ
ejpam-3708	273	9	)	)	PUNCT
ejpam-3708	273	10	be	be	AUX
ejpam-3708	273	11	an	an	DET
ejpam-3708	273	12	element	element	NOUN
ejpam-3708	273	13	in	in	ADP
ejpam-3708	273	14	w	w	NOUN
ejpam-3708	273	15	i(f	i(f	NOUN
ejpam-3708	273	16	)	)	PUNCT
ejpam-3708	273	17	θ	θ	PROPN
ejpam-3708	274	1	[	[	X
ejpam-3708	274	2	a	a	X
ejpam-3708	274	3	,	,	PUNCT
ejpam-3708	274	4	m	m	PROPN
ejpam-3708	274	5	,	,	PUNCT
ejpam-3708	274	6	p	p	X
ejpam-3708	274	7	,	,	PUNCT
ejpam-3708	274	8	u,∆m	u,∆m	PROPN
ejpam-3708	274	9	v	v	NOUN
ejpam-3708	274	10	]	]	PUNCT
ejpam-3708	274	11	.	.	PUNCT
ejpam-3708	275	1	since	since	SCONJ
ejpam-3708	275	2	0	0	NUM
ejpam-3708	275	3	<	<	X
ejpam-3708	275	4	inf	inf	PROPN
ejpam-3708	275	5	pk	pk	NOUN
ejpam-3708	275	6	≤	≤	X
ejpam-3708	275	7	pk	pk	NOUN
ejpam-3708	275	8	≤	≤	ADV
ejpam-3708	275	9	1	1	NUM
ejpam-3708	275	10	we	we	PRON
ejpam-3708	275	11	have	have	VERB
ejpam-3708	275	12	1	1	NUM
ejpam-3708	275	13	hr	hr	NOUN
ejpam-3708	275	14	∑	∑	PUNCT
ejpam-3708	275	15	k∈ir	k∈ir	PROPN
ejpam-3708	275	16	ank	ank	PROPN
ejpam-3708	275	17	[	[	PUNCT
ejpam-3708	275	18	k−smk	k−smk	NOUN
ejpam-3708	275	19	(	(	PUNCT
ejpam-3708	275	20	d(uk∆	d(uk∆	PROPN
ejpam-3708	275	21	m	m	NOUN
ejpam-3708	275	22	v	v	NOUN
ejpam-3708	275	23	xk	xk	PROPN
ejpam-3708	275	24	,	,	PUNCT
ejpam-3708	275	25	x0	x0	PROPN
ejpam-3708	275	26	)	)	PUNCT
ejpam-3708	275	27	ρ	ρ	PROPN
ejpam-3708	275	28	)	)	PUNCT
ejpam-3708	275	29	]	]	PUNCT
ejpam-3708	276	1	≤	≤	NUM
ejpam-3708	276	2	1	1	NUM
ejpam-3708	276	3	hr	hr	NOUN
ejpam-3708	276	4	∑	∑	PUNCT
ejpam-3708	276	5	k∈ir	k∈ir	PROPN
ejpam-3708	276	6	ank	ank	PROPN
ejpam-3708	276	7	[	[	PUNCT
ejpam-3708	276	8	k−smk	k−smk	NOUN
ejpam-3708	276	9	(	(	PUNCT
ejpam-3708	276	10	d(uk∆	d(uk∆	PROPN
ejpam-3708	276	11	m	m	NOUN
ejpam-3708	276	12	v	v	NOUN
ejpam-3708	276	13	xk	xk	PROPN
ejpam-3708	276	14	,	,	PUNCT
ejpam-3708	276	15	x0	x0	PROPN
ejpam-3708	276	16	)	)	PUNCT
ejpam-3708	276	17	ρ	ρ	PROPN
ejpam-3708	276	18	)	)	PUNCT
ejpam-3708	276	19	]	]	SYM
ejpam-3708	276	20	pk	pk	NOUN
ejpam-3708	276	21	.	.	PUNCT
ejpam-3708	277	1	therefore	therefore	ADV
ejpam-3708	277	2	,	,	PUNCT
ejpam-3708	277	3	{	{	PUNCT
ejpam-3708	277	4	n	n	CCONJ
ejpam-3708	277	5	,	,	PUNCT
ejpam-3708	277	6	r	r	NOUN
ejpam-3708	277	7	∈	∈	PROPN
ejpam-3708	277	8	n	n	CCONJ
ejpam-3708	277	9	:	:	PUNCT
ejpam-3708	277	10	1	1	NUM
ejpam-3708	277	11	hr	hr	NOUN
ejpam-3708	277	12	∑	∑	PUNCT
ejpam-3708	277	13	k∈ir	k∈ir	PROPN
ejpam-3708	277	14	ank	ank	PROPN
ejpam-3708	277	15	[	[	PUNCT
ejpam-3708	277	16	k−smk	k−smk	NOUN
ejpam-3708	277	17	(	(	PUNCT
ejpam-3708	277	18	d(uk∆m	d(uk∆m	PROPN
ejpam-3708	277	19	v	v	PROPN
ejpam-3708	277	20	xk	xk	PROPN
ejpam-3708	277	21	,	,	PUNCT
ejpam-3708	277	22	x0	x0	PROPN
ejpam-3708	277	23	)	)	PUNCT
ejpam-3708	277	24	ρ	ρ	PROPN
ejpam-3708	277	25	)	)	PUNCT
ejpam-3708	277	26	]	]	PUNCT
ejpam-3708	277	27	≥	≥	X
ejpam-3708	277	28	ε	ε	PROPN
ejpam-3708	277	29	}	}	PUNCT
ejpam-3708	277	30	⊆	⊆	NUM
ejpam-3708	277	31	{	{	PUNCT
ejpam-3708	277	32	n	n	CCONJ
ejpam-3708	277	33	,	,	PUNCT
ejpam-3708	277	34	r	r	NOUN
ejpam-3708	277	35	∈	∈	PROPN
ejpam-3708	277	36	n	n	CCONJ
ejpam-3708	277	37	:	:	PUNCT
ejpam-3708	277	38	1	1	NUM
ejpam-3708	277	39	hr	hr	NOUN
ejpam-3708	277	40	∑	∑	PUNCT
ejpam-3708	277	41	k∈ir	k∈ir	PROPN
ejpam-3708	277	42	ank	ank	PROPN
ejpam-3708	277	43	[	[	PUNCT
ejpam-3708	277	44	k−smk	k−smk	NOUN
ejpam-3708	277	45	(	(	PUNCT
ejpam-3708	277	46	d(uk∆	d(uk∆	PROPN
ejpam-3708	277	47	m	m	NOUN
ejpam-3708	277	48	v	v	NOUN
ejpam-3708	277	49	xk	xk	PROPN
ejpam-3708	277	50	,	,	PUNCT
ejpam-3708	277	51	x0	x0	PROPN
ejpam-3708	277	52	)	)	PUNCT
ejpam-3708	277	53	ρ	ρ	PROPN
ejpam-3708	277	54	)	)	PUNCT
ejpam-3708	277	55	]	]	PUNCT
ejpam-3708	277	56	pk	pk	NOUN
ejpam-3708	277	57	≥	≥	NOUN
ejpam-3708	277	58	ε	ε	PROPN
ejpam-3708	277	59	}	}	PUNCT
ejpam-3708	277	60	∈	∈	PROPN
ejpam-3708	277	61	i.	i.	NOUN
ejpam-3708	277	62	the	the	DET
ejpam-3708	277	63	other	other	ADJ
ejpam-3708	277	64	part	part	NOUN
ejpam-3708	277	65	can	can	AUX
ejpam-3708	277	66	be	be	AUX
ejpam-3708	277	67	proved	prove	VERB
ejpam-3708	277	68	in	in	ADP
ejpam-3708	277	69	the	the	DET
ejpam-3708	277	70	same	same	ADJ
ejpam-3708	277	71	way	way	NOUN
ejpam-3708	277	72	.	.	PUNCT
ejpam-3708	278	1	(	(	PUNCT
ejpam-3708	278	2	ii	ii	NOUN
ejpam-3708	278	3	)	)	PUNCT
ejpam-3708	278	4	let	let	VERB
ejpam-3708	278	5	x	x	PUNCT
ejpam-3708	278	6	=	=	SYM
ejpam-3708	278	7	(	(	PUNCT
ejpam-3708	278	8	xk	xk	INTJ
ejpam-3708	278	9	)	)	PUNCT
ejpam-3708	278	10	be	be	AUX
ejpam-3708	278	11	an	an	DET
ejpam-3708	278	12	element	element	NOUN
ejpam-3708	278	13	in	in	ADP
ejpam-3708	278	14	w	w	NOUN
ejpam-3708	278	15	i(f	i(f	NOUN
ejpam-3708	278	16	)	)	PUNCT
ejpam-3708	278	17	θ	θ	PROPN
ejpam-3708	279	1	[	[	X
ejpam-3708	279	2	a	a	X
ejpam-3708	279	3	,	,	PUNCT
ejpam-3708	279	4	m	m	PROPN
ejpam-3708	279	5	,	,	PUNCT
ejpam-3708	279	6	u,∆m	u,∆m	PROPN
ejpam-3708	279	7	v	v	NOUN
ejpam-3708	279	8	]	]	PUNCT
ejpam-3708	279	9	.	.	PUNCT
ejpam-3708	280	1	since	since	SCONJ
ejpam-3708	280	2	1	1	NUM
ejpam-3708	280	3	≤	≤	NUM
ejpam-3708	280	4	pk	pk	NOUN
ejpam-3708	280	5	≤	≤	NUM
ejpam-3708	280	6	sup	sup	NOUN
ejpam-3708	280	7	pk	pk	NOUN
ejpam-3708	280	8	<	<	X
ejpam-3708	280	9	∞.	∞.	PROPN
ejpam-3708	280	10	then	then	ADV
ejpam-3708	280	11	for	for	ADP
ejpam-3708	280	12	each	each	PRON
ejpam-3708	280	13	0	0	NUM
ejpam-3708	280	14	<	<	X
ejpam-3708	280	15	ε	ε	X
ejpam-3708	280	16	<	<	X
ejpam-3708	280	17	1	1	NUM
ejpam-3708	280	18	there	there	ADV
ejpam-3708	280	19	exists	exist	VERB
ejpam-3708	280	20	a	a	DET
ejpam-3708	280	21	positive	positive	ADJ
ejpam-3708	280	22	integer	integer	NOUN
ejpam-3708	280	23	n0	n0	NOUN
ejpam-3708	280	24	such	such	ADJ
ejpam-3708	280	25	that	that	SCONJ
ejpam-3708	280	26	1	1	NUM
ejpam-3708	280	27	hr	hr	NOUN
ejpam-3708	280	28	∑	∑	PUNCT
ejpam-3708	280	29	k∈ir	k∈ir	PROPN
ejpam-3708	280	30	ank	ank	PROPN
ejpam-3708	280	31	[	[	PUNCT
ejpam-3708	280	32	k−smk	k−smk	NOUN
ejpam-3708	280	33	(	(	PUNCT
ejpam-3708	280	34	d(uk∆	d(uk∆	PROPN
ejpam-3708	280	35	m	m	NOUN
ejpam-3708	280	36	v	v	NOUN
ejpam-3708	280	37	xk	xk	PROPN
ejpam-3708	280	38	,	,	PUNCT
ejpam-3708	280	39	x0	x0	PROPN
ejpam-3708	280	40	)	)	PUNCT
ejpam-3708	280	41	ρ	ρ	PROPN
ejpam-3708	280	42	)	)	PUNCT
ejpam-3708	280	43	]	]	PUNCT
ejpam-3708	280	44	≤	≤	X
ejpam-3708	280	45	ε	ε	X
ejpam-3708	280	46	<	<	X
ejpam-3708	280	47	1	1	NUM
ejpam-3708	280	48	for	for	ADP
ejpam-3708	280	49	all	all	DET
ejpam-3708	280	50	n	n	PRON
ejpam-3708	280	51	≥	≥	NOUN
ejpam-3708	280	52	n0	n0	NUM
ejpam-3708	280	53	.	.	PUNCT
ejpam-3708	281	1	this	this	PRON
ejpam-3708	281	2	implies	imply	VERB
ejpam-3708	281	3	that	that	SCONJ
ejpam-3708	281	4	1	1	NUM
ejpam-3708	281	5	hr	hr	NOUN
ejpam-3708	281	6	∑	∑	PUNCT
ejpam-3708	281	7	k∈ir	k∈ir	PROPN
ejpam-3708	281	8	ank	ank	PROPN
ejpam-3708	281	9	[	[	PUNCT
ejpam-3708	281	10	k−smk	k−smk	NOUN
ejpam-3708	281	11	(	(	PUNCT
ejpam-3708	281	12	d(uk∆	d(uk∆	PROPN
ejpam-3708	281	13	m	m	NOUN
ejpam-3708	281	14	v	v	NOUN
ejpam-3708	281	15	xk	xk	PROPN
ejpam-3708	281	16	,	,	PUNCT
ejpam-3708	281	17	x0	x0	PROPN
ejpam-3708	281	18	)	)	PUNCT
ejpam-3708	281	19	ρ	ρ	PROPN
ejpam-3708	281	20	)	)	PUNCT
ejpam-3708	281	21	]	]	PUNCT
ejpam-3708	281	22	pk	pk	NOUN
ejpam-3708	281	23	≤	≤	ADV
ejpam-3708	281	24	1	1	NUM
ejpam-3708	281	25	hr	hr	NOUN
ejpam-3708	281	26	∑	∑	PUNCT
ejpam-3708	281	27	k∈ir	k∈ir	PROPN
ejpam-3708	281	28	ank	ank	PROPN
ejpam-3708	281	29	[	[	PUNCT
ejpam-3708	281	30	k−smk	k−smk	NOUN
ejpam-3708	281	31	(	(	PUNCT
ejpam-3708	281	32	d(uk∆	d(uk∆	PROPN
ejpam-3708	281	33	m	m	NOUN
ejpam-3708	281	34	v	v	NOUN
ejpam-3708	281	35	xk	xk	PROPN
ejpam-3708	281	36	,	,	PUNCT
ejpam-3708	281	37	x0	x0	PROPN
ejpam-3708	281	38	)	)	PUNCT
ejpam-3708	281	39	ρ	ρ	PROPN
ejpam-3708	281	40	)	)	PUNCT
ejpam-3708	281	41	]	]	PUNCT
ejpam-3708	281	42	.	.	PUNCT
ejpam-3708	282	1	k.	k.	PROPN
ejpam-3708	282	2	raj	raj	PROPN
ejpam-3708	282	3	,	,	PUNCT
ejpam-3708	282	4	s.	s.	PROPN
ejpam-3708	282	5	a.	a.	PROPN
ejpam-3708	282	6	mohiuddine	mohiuddine	PROPN
ejpam-3708	282	7	/	/	SYM
ejpam-3708	282	8	eur	eur	PROPN
ejpam-3708	282	9	.	.	PUNCT
ejpam-3708	283	1	j.	j.	PROPN
ejpam-3708	283	2	pure	pure	PROPN
ejpam-3708	283	3	appl	appl	PROPN
ejpam-3708	283	4	.	.	PROPN
ejpam-3708	283	5	math	math	PROPN
ejpam-3708	283	6	,	,	PUNCT
ejpam-3708	283	7	13	13	NUM
ejpam-3708	283	8	(	(	PUNCT
ejpam-3708	283	9	5	5	NUM
ejpam-3708	283	10	)	)	PUNCT
ejpam-3708	283	11	(	(	PUNCT
ejpam-3708	283	12	2020	2020	NUM
ejpam-3708	283	13	)	)	PUNCT
ejpam-3708	283	14	,	,	PUNCT
ejpam-3708	283	15	1131	1131	NUM
ejpam-3708	283	16	-	-	SYM
ejpam-3708	283	17	1148	1148	NUM
ejpam-3708	283	18	1143	1143	NUM
ejpam-3708	283	19	therefore	therefore	ADV
ejpam-3708	283	20	,	,	PUNCT
ejpam-3708	283	21	we	we	PRON
ejpam-3708	283	22	have	have	VERB
ejpam-3708	283	23	{	{	PUNCT
ejpam-3708	283	24	n	n	X
ejpam-3708	283	25	,	,	PUNCT
ejpam-3708	283	26	r	r	NOUN
ejpam-3708	283	27	∈	∈	PROPN
ejpam-3708	284	1	n	n	CCONJ
ejpam-3708	284	2	:	:	PUNCT
ejpam-3708	284	3	1	1	NUM
ejpam-3708	284	4	hr	hr	NOUN
ejpam-3708	284	5	∑	∑	PUNCT
ejpam-3708	284	6	k∈ir	k∈ir	PROPN
ejpam-3708	284	7	ank	ank	PROPN
ejpam-3708	284	8	[	[	PUNCT
ejpam-3708	284	9	k−smk	k−smk	NOUN
ejpam-3708	284	10	(	(	PUNCT
ejpam-3708	284	11	d(uk∆m	d(uk∆m	PROPN
ejpam-3708	284	12	v	v	PROPN
ejpam-3708	284	13	xk	xk	PROPN
ejpam-3708	284	14	,	,	PUNCT
ejpam-3708	284	15	x0	x0	PROPN
ejpam-3708	284	16	)	)	PUNCT
ejpam-3708	284	17	ρ	ρ	PROPN
ejpam-3708	284	18	)	)	PUNCT
ejpam-3708	285	1	]	]	PUNCT
ejpam-3708	285	2	pk	pk	NOUN
ejpam-3708	285	3	≥	≥	NOUN
ejpam-3708	285	4	ε	ε	PROPN
ejpam-3708	285	5	}	}	PUNCT
ejpam-3708	285	6	⊆	⊆	NUM
ejpam-3708	285	7	{	{	PUNCT
ejpam-3708	285	8	n	n	CCONJ
ejpam-3708	285	9	,	,	PUNCT
ejpam-3708	285	10	r	r	NOUN
ejpam-3708	285	11	∈	∈	PROPN
ejpam-3708	285	12	n	n	CCONJ
ejpam-3708	285	13	:	:	PUNCT
ejpam-3708	285	14	1	1	NUM
ejpam-3708	285	15	hr	hr	NOUN
ejpam-3708	285	16	∑	∑	PUNCT
ejpam-3708	285	17	k∈ir	k∈ir	PROPN
ejpam-3708	285	18	ank	ank	PROPN
ejpam-3708	285	19	[	[	PUNCT
ejpam-3708	285	20	k−smk	k−smk	NOUN
ejpam-3708	285	21	(	(	PUNCT
ejpam-3708	285	22	d(uk∆	d(uk∆	PROPN
ejpam-3708	285	23	m	m	NOUN
ejpam-3708	285	24	v	v	NOUN
ejpam-3708	285	25	xk	xk	PROPN
ejpam-3708	285	26	,	,	PUNCT
ejpam-3708	285	27	x0	x0	PROPN
ejpam-3708	285	28	)	)	PUNCT
ejpam-3708	285	29	ρ	ρ	PROPN
ejpam-3708	285	30	)	)	PUNCT
ejpam-3708	285	31	]	]	PUNCT
ejpam-3708	285	32	≥	≥	X
ejpam-3708	285	33	ε	ε	PROPN
ejpam-3708	285	34	}	}	PUNCT
ejpam-3708	285	35	∈	∈	PROPN
ejpam-3708	285	36	i.	i.	NOUN
ejpam-3708	285	37	the	the	DET
ejpam-3708	285	38	other	other	ADJ
ejpam-3708	285	39	part	part	NOUN
ejpam-3708	285	40	can	can	AUX
ejpam-3708	285	41	be	be	AUX
ejpam-3708	285	42	proved	prove	VERB
ejpam-3708	285	43	in	in	ADP
ejpam-3708	285	44	the	the	DET
ejpam-3708	285	45	similar	similar	ADJ
ejpam-3708	285	46	way	way	NOUN
ejpam-3708	285	47	.	.	PUNCT
ejpam-3708	286	1	this	this	PRON
ejpam-3708	286	2	completes	complete	VERB
ejpam-3708	286	3	the	the	DET
ejpam-3708	286	4	proof	proof	NOUN
ejpam-3708	286	5	.	.	PUNCT
ejpam-3708	287	1	theorem	theorem	ADJ
ejpam-3708	287	2	4	4	NUM
ejpam-3708	287	3	.	.	PUNCT
ejpam-3708	288	1	let	let	VERB
ejpam-3708	288	2	x	x	PUNCT
ejpam-3708	288	3	=	=	SYM
ejpam-3708	288	4	(	(	PUNCT
ejpam-3708	288	5	xk	xk	INTJ
ejpam-3708	288	6	)	)	PUNCT
ejpam-3708	288	7	be	be	AUX
ejpam-3708	288	8	a	a	DET
ejpam-3708	288	9	sequence	sequence	NOUN
ejpam-3708	288	10	of	of	ADP
ejpam-3708	288	11	fuzzy	fuzzy	ADJ
ejpam-3708	288	12	numbers	number	NOUN
ejpam-3708	288	13	,	,	PUNCT
ejpam-3708	288	14	m	m	VERB
ejpam-3708	288	15	=	=	SYM
ejpam-3708	288	16	(	(	PUNCT
ejpam-3708	288	17	mk	mk	X
ejpam-3708	288	18	)	)	PUNCT
ejpam-3708	288	19	be	be	VERB
ejpam-3708	288	20	a	a	DET
ejpam-3708	288	21	sequence	sequence	NOUN
ejpam-3708	288	22	of	of	ADP
ejpam-3708	288	23	orlicz	orlicz	ADJ
ejpam-3708	288	24	functions	function	NOUN
ejpam-3708	288	25	,	,	PUNCT
ejpam-3708	288	26	p	p	NOUN
ejpam-3708	288	27	=	=	PUNCT
ejpam-3708	288	28	(	(	PUNCT
ejpam-3708	288	29	pk	pk	NOUN
ejpam-3708	288	30	)	)	PUNCT
ejpam-3708	288	31	be	be	AUX
ejpam-3708	288	32	a	a	DET
ejpam-3708	288	33	bounded	bounded	ADJ
ejpam-3708	288	34	sequence	sequence	NOUN
ejpam-3708	288	35	of	of	ADP
ejpam-3708	288	36	positive	positive	ADJ
ejpam-3708	288	37	real	real	ADJ
ejpam-3708	288	38	numbers	number	NOUN
ejpam-3708	288	39	and	and	CCONJ
ejpam-3708	288	40	u	u	NOUN
ejpam-3708	288	41	=	=	SYM
ejpam-3708	288	42	(	(	PUNCT
ejpam-3708	288	43	uk	uk	PROPN
ejpam-3708	288	44	)	)	PUNCT
ejpam-3708	288	45	be	be	VERB
ejpam-3708	288	46	a	a	DET
ejpam-3708	288	47	sequence	sequence	NOUN
ejpam-3708	288	48	of	of	ADP
ejpam-3708	288	49	strictly	strictly	ADV
ejpam-3708	288	50	positive	positive	ADJ
ejpam-3708	288	51	real	real	ADJ
ejpam-3708	288	52	numbers	number	NOUN
ejpam-3708	288	53	.	.	PUNCT
ejpam-3708	289	1	then	then	ADV
ejpam-3708	289	2	w	w	PROPN
ejpam-3708	289	3	i(f	i(f	NOUN
ejpam-3708	289	4	)	)	PUNCT
ejpam-3708	290	1	θ	θ	PROPN
ejpam-3708	291	1	[	[	X
ejpam-3708	291	2	a	a	X
ejpam-3708	291	3	,	,	PUNCT
ejpam-3708	291	4	m	m	PROPN
ejpam-3708	291	5	,	,	PUNCT
ejpam-3708	291	6	p	p	X
ejpam-3708	291	7	,	,	PUNCT
ejpam-3708	291	8	u,∆m	u,∆m	PROPN
ejpam-3708	291	9	v	v	X
ejpam-3708	291	10	]	]	PUNCT
ejpam-3708	291	11	0	0	PUNCT
ejpam-3708	291	12	⊂	⊂	NOUN
ejpam-3708	291	13	wi(f	wi(f	X
ejpam-3708	291	14	)	)	PUNCT
ejpam-3708	291	15	θ	θ	PROPN
ejpam-3708	292	1	[	[	X
ejpam-3708	292	2	a	a	X
ejpam-3708	292	3	,	,	PUNCT
ejpam-3708	292	4	m	m	PROPN
ejpam-3708	292	5	,	,	PUNCT
ejpam-3708	292	6	p	p	X
ejpam-3708	292	7	,	,	PUNCT
ejpam-3708	292	8	u,∆m	u,∆m	PROPN
ejpam-3708	292	9	v	v	NOUN
ejpam-3708	292	10	]	]	PUNCT
ejpam-3708	292	11	⊂	⊂	PRON
ejpam-3708	292	12	wfθ	wfθ	NOUN
ejpam-3708	293	1	[	[	X
ejpam-3708	293	2	a	a	X
ejpam-3708	293	3	,	,	PUNCT
ejpam-3708	293	4	m	m	PROPN
ejpam-3708	293	5	,	,	PUNCT
ejpam-3708	293	6	p	p	X
ejpam-3708	293	7	,	,	PUNCT
ejpam-3708	293	8	u,∆m	u,∆m	PROPN
ejpam-3708	293	9	v	v	NOUN
ejpam-3708	293	10	]	]	PUNCT
ejpam-3708	293	11	∞.	∞.	PROPN
ejpam-3708	293	12	proof	proof	NOUN
ejpam-3708	293	13	.	.	PUNCT
ejpam-3708	294	1	the	the	DET
ejpam-3708	294	2	inclusion	inclusion	NOUN
ejpam-3708	294	3	w	w	ADP
ejpam-3708	294	4	i(f	i(f	NOUN
ejpam-3708	294	5	)	)	PUNCT
ejpam-3708	294	6	θ	θ	PROPN
ejpam-3708	295	1	[	[	X
ejpam-3708	295	2	a	a	X
ejpam-3708	295	3	,	,	PUNCT
ejpam-3708	295	4	m	m	PROPN
ejpam-3708	295	5	,	,	PUNCT
ejpam-3708	295	6	p	p	X
ejpam-3708	295	7	,	,	PUNCT
ejpam-3708	295	8	u,∆m	u,∆m	PROPN
ejpam-3708	295	9	v	v	X
ejpam-3708	295	10	]	]	PUNCT
ejpam-3708	295	11	0	0	PUNCT
ejpam-3708	295	12	⊂	⊂	PROPN
ejpam-3708	295	13	w	w	PROPN
ejpam-3708	295	14	i(f	i(f	NOUN
ejpam-3708	295	15	)	)	PUNCT
ejpam-3708	295	16	θ	θ	PROPN
ejpam-3708	296	1	[	[	X
ejpam-3708	296	2	a	a	X
ejpam-3708	296	3	,	,	PUNCT
ejpam-3708	296	4	m	m	PROPN
ejpam-3708	296	5	,	,	PUNCT
ejpam-3708	296	6	p	p	X
ejpam-3708	296	7	,	,	PUNCT
ejpam-3708	296	8	u,∆m	u,∆m	PROPN
ejpam-3708	296	9	v	v	NOUN
ejpam-3708	296	10	]	]	PUNCT
ejpam-3708	296	11	is	be	AUX
ejpam-3708	296	12	obvious	obvious	ADJ
ejpam-3708	296	13	.	.	PUNCT
ejpam-3708	297	1	let	let	VERB
ejpam-3708	297	2	x	x	PUNCT
ejpam-3708	297	3	=	=	SYM
ejpam-3708	297	4	(	(	PUNCT
ejpam-3708	297	5	xk	xk	ADJ
ejpam-3708	297	6	)	)	PUNCT
ejpam-3708	297	7	∈	∈	PROPN
ejpam-3708	297	8	w	w	NOUN
ejpam-3708	297	9	i(f	i(f	NOUN
ejpam-3708	297	10	)	)	PUNCT
ejpam-3708	297	11	θ	θ	PROPN
ejpam-3708	298	1	[	[	X
ejpam-3708	298	2	a	a	X
ejpam-3708	298	3	,	,	PUNCT
ejpam-3708	298	4	m	m	PROPN
ejpam-3708	298	5	,	,	PUNCT
ejpam-3708	298	6	p	p	X
ejpam-3708	298	7	,	,	PUNCT
ejpam-3708	298	8	u,∆m	u,∆m	PROPN
ejpam-3708	298	9	v	v	NOUN
ejpam-3708	298	10	]	]	PUNCT
ejpam-3708	298	11	.	.	PUNCT
ejpam-3708	299	1	then	then	ADV
ejpam-3708	299	2	there	there	PRON
ejpam-3708	299	3	is	be	VERB
ejpam-3708	299	4	some	some	DET
ejpam-3708	299	5	fuzzy	fuzzy	ADJ
ejpam-3708	299	6	number	number	NOUN
ejpam-3708	299	7	x0	x0	PROPN
ejpam-3708	299	8	,	,	PUNCT
ejpam-3708	299	9	such	such	ADJ
ejpam-3708	299	10	that	that	SCONJ
ejpam-3708	299	11	1	1	NUM
ejpam-3708	299	12	hr	hr	NOUN
ejpam-3708	299	13	∑	∑	PUNCT
ejpam-3708	299	14	k∈ir	k∈ir	PROPN
ejpam-3708	299	15	ank	ank	PROPN
ejpam-3708	299	16	[	[	PUNCT
ejpam-3708	299	17	k−smk	k−smk	NOUN
ejpam-3708	299	18	(	(	PUNCT
ejpam-3708	299	19	d(uk∆	d(uk∆	PROPN
ejpam-3708	299	20	m	m	NOUN
ejpam-3708	299	21	v	v	NOUN
ejpam-3708	299	22	xk	xk	PROPN
ejpam-3708	299	23	,	,	PUNCT
ejpam-3708	299	24	x0	x0	PROPN
ejpam-3708	299	25	)	)	PUNCT
ejpam-3708	299	26	ρ	ρ	PROPN
ejpam-3708	299	27	)	)	PUNCT
ejpam-3708	299	28	]	]	PUNCT
ejpam-3708	299	29	pk	pk	X
ejpam-3708	299	30	≥	≥	NOUN
ejpam-3708	299	31	ε	ε	PROPN
ejpam-3708	299	32	.	.	PUNCT
ejpam-3708	300	1	now	now	ADV
ejpam-3708	300	2	,	,	PUNCT
ejpam-3708	300	3	by	by	ADP
ejpam-3708	300	4	inequality	inequality	NOUN
ejpam-3708	300	5	(	(	PUNCT
ejpam-3708	300	6	3	3	NUM
ejpam-3708	300	7	)	)	PUNCT
ejpam-3708	300	8	,	,	PUNCT
ejpam-3708	300	9	we	we	PRON
ejpam-3708	300	10	have	have	VERB
ejpam-3708	300	11	1	1	NUM
ejpam-3708	300	12	hr	hr	NOUN
ejpam-3708	300	13	∑	∑	PUNCT
ejpam-3708	300	14	k∈ir	k∈ir	PROPN
ejpam-3708	300	15	ank	ank	PROPN
ejpam-3708	300	16	[	[	PUNCT
ejpam-3708	300	17	k−smk	k−smk	NOUN
ejpam-3708	300	18	(	(	PUNCT
ejpam-3708	300	19	d(uk∆	d(uk∆	PROPN
ejpam-3708	300	20	m	m	NOUN
ejpam-3708	300	21	v	v	NOUN
ejpam-3708	300	22	xk	xk	PROPN
ejpam-3708	300	23	,	,	PUNCT
ejpam-3708	300	24	0	0	NUM
ejpam-3708	300	25	)	)	PUNCT
ejpam-3708	300	26	ρ	ρ	NOUN
ejpam-3708	300	27	)	)	PUNCT
ejpam-3708	300	28	]	]	PUNCT
ejpam-3708	300	29	pk	pk	NOUN
ejpam-3708	300	30	≤	≤	NUM
ejpam-3708	300	31	d	d	SYM
ejpam-3708	300	32	1	1	NUM
ejpam-3708	300	33	hr	hr	NOUN
ejpam-3708	300	34	∑	∑	PUNCT
ejpam-3708	300	35	k∈ir	k∈ir	PROPN
ejpam-3708	300	36	ank	ank	PROPN
ejpam-3708	300	37	[	[	PUNCT
ejpam-3708	300	38	k−smk	k−smk	NOUN
ejpam-3708	300	39	(	(	PUNCT
ejpam-3708	300	40	d(uk∆	d(uk∆	PROPN
ejpam-3708	300	41	m	m	NOUN
ejpam-3708	300	42	v	v	NOUN
ejpam-3708	300	43	xk	xk	PROPN
ejpam-3708	300	44	,	,	PUNCT
ejpam-3708	300	45	x0	x0	PROPN
ejpam-3708	300	46	)	)	PUNCT
ejpam-3708	300	47	ρ	ρ	PROPN
ejpam-3708	300	48	)	)	PUNCT
ejpam-3708	300	49	]	]	PUNCT
ejpam-3708	300	50	pk	pk	NOUN
ejpam-3708	300	51	+	+	CCONJ
ejpam-3708	300	52	d	d	SYM
ejpam-3708	300	53	1	1	NUM
ejpam-3708	300	54	hr	hr	NOUN
ejpam-3708	300	55	∑	∑	PUNCT
ejpam-3708	300	56	k∈ir	k∈ir	PROPN
ejpam-3708	300	57	ank	ank	PROPN
ejpam-3708	300	58	[	[	PUNCT
ejpam-3708	300	59	k−smk	k−smk	NOUN
ejpam-3708	300	60	(	(	PUNCT
ejpam-3708	300	61	d(x0	d(x0	NOUN
ejpam-3708	300	62	,	,	PUNCT
ejpam-3708	300	63	0	0	NUM
ejpam-3708	300	64	)	)	PUNCT
ejpam-3708	300	65	ρ	ρ	NOUN
ejpam-3708	300	66	)	)	PUNCT
ejpam-3708	300	67	]	]	X
ejpam-3708	300	68	pk	pk	NOUN
ejpam-3708	300	69	.	.	PUNCT
ejpam-3708	301	1	this	this	PRON
ejpam-3708	301	2	implies	imply	VERB
ejpam-3708	301	3	that	that	SCONJ
ejpam-3708	301	4	x	x	SYM
ejpam-3708	301	5	=	=	SYM
ejpam-3708	301	6	(	(	PUNCT
ejpam-3708	301	7	xk	xk	NOUN
ejpam-3708	301	8	)	)	PUNCT
ejpam-3708	301	9	∈	∈	PROPN
ejpam-3708	301	10	wfθ	wfθ	NOUN
ejpam-3708	302	1	[	[	X
ejpam-3708	302	2	a	a	X
ejpam-3708	302	3	,	,	PUNCT
ejpam-3708	302	4	m	m	PROPN
ejpam-3708	302	5	,	,	PUNCT
ejpam-3708	302	6	p	p	X
ejpam-3708	302	7	,	,	PUNCT
ejpam-3708	302	8	u,∆m	u,∆m	PROPN
ejpam-3708	302	9	v	v	NOUN
ejpam-3708	302	10	]	]	PUNCT
ejpam-3708	302	11	∞.	∞.	PROPN
ejpam-3708	302	12	this	this	PRON
ejpam-3708	302	13	completes	complete	VERB
ejpam-3708	302	14	the	the	DET
ejpam-3708	302	15	proof	proof	NOUN
ejpam-3708	302	16	.	.	PUNCT
ejpam-3708	303	1	theorem	theorem	ADJ
ejpam-3708	303	2	5	5	NUM
ejpam-3708	303	3	.	.	PUNCT
ejpam-3708	304	1	let	let	VERB
ejpam-3708	304	2	m	m	VERB
ejpam-3708	304	3	=	=	SYM
ejpam-3708	304	4	(	(	PUNCT
ejpam-3708	304	5	mk	mk	PROPN
ejpam-3708	304	6	)	)	PUNCT
ejpam-3708	304	7	and	and	CCONJ
ejpam-3708	304	8	s	s	NOUN
ejpam-3708	304	9	=	=	PUNCT
ejpam-3708	304	10	(	(	PUNCT
ejpam-3708	304	11	sk	sk	INTJ
ejpam-3708	304	12	)	)	PUNCT
ejpam-3708	304	13	be	be	AUX
ejpam-3708	304	14	a	a	DET
ejpam-3708	304	15	sequence	sequence	NOUN
ejpam-3708	304	16	of	of	ADP
ejpam-3708	304	17	orlicz	orlicz	ADJ
ejpam-3708	304	18	functions	function	NOUN
ejpam-3708	304	19	.	.	PUNCT
ejpam-3708	305	1	then	then	ADV
ejpam-3708	305	2	w	w	PROPN
ejpam-3708	305	3	i(f	i(f	NOUN
ejpam-3708	305	4	)	)	PUNCT
ejpam-3708	306	1	θ	θ	PROPN
ejpam-3708	307	1	[	[	X
ejpam-3708	307	2	a	a	X
ejpam-3708	307	3	,	,	PUNCT
ejpam-3708	307	4	m	m	PROPN
ejpam-3708	307	5	,	,	PUNCT
ejpam-3708	307	6	p	p	X
ejpam-3708	307	7	,	,	PUNCT
ejpam-3708	307	8	u,∆m	u,∆m	PROPN
ejpam-3708	307	9	v	v	NOUN
ejpam-3708	307	10	]	]	PUNCT
ejpam-3708	307	11	∩	∩	NOUN
ejpam-3708	307	12	wi(f	wi(f	NUM
ejpam-3708	307	13	)	)	PUNCT
ejpam-3708	307	14	θ	θ	PROPN
ejpam-3708	308	1	[	[	X
ejpam-3708	308	2	a	a	X
ejpam-3708	308	3	,	,	PUNCT
ejpam-3708	308	4	s	s	NOUN
ejpam-3708	308	5	,	,	PUNCT
ejpam-3708	308	6	p	p	X
ejpam-3708	308	7	,	,	PUNCT
ejpam-3708	308	8	u,∆m	u,∆m	PROPN
ejpam-3708	308	9	v	v	NOUN
ejpam-3708	308	10	]	]	PUNCT
ejpam-3708	308	11	⊂	⊂	X
ejpam-3708	308	12	wi(f	wi(f	X
ejpam-3708	308	13	)	)	PUNCT
ejpam-3708	308	14	θ	θ	PROPN
ejpam-3708	309	1	[	[	X
ejpam-3708	309	2	a	a	X
ejpam-3708	309	3	,	,	PUNCT
ejpam-3708	309	4	m+	m+	NUM
ejpam-3708	309	5	s	s	NOUN
ejpam-3708	309	6	,	,	PUNCT
ejpam-3708	309	7	p	p	X
ejpam-3708	309	8	,	,	PUNCT
ejpam-3708	309	9	u,∆m	u,∆m	PROPN
ejpam-3708	309	10	v	v	NOUN
ejpam-3708	309	11	]	]	PUNCT
ejpam-3708	309	12	.	.	PUNCT
ejpam-3708	310	1	proof	proof	NOUN
ejpam-3708	310	2	.	.	PUNCT
ejpam-3708	311	1	let	let	VERB
ejpam-3708	311	2	x	x	PUNCT
ejpam-3708	311	3	=	=	SYM
ejpam-3708	311	4	(	(	PUNCT
ejpam-3708	311	5	xk	xk	ADJ
ejpam-3708	311	6	)	)	PUNCT
ejpam-3708	311	7	∈	∈	PROPN
ejpam-3708	311	8	w	w	NOUN
ejpam-3708	311	9	i(f	i(f	NOUN
ejpam-3708	311	10	)	)	PUNCT
ejpam-3708	311	11	θ	θ	PROPN
ejpam-3708	312	1	[	[	X
ejpam-3708	312	2	a	a	X
ejpam-3708	312	3	,	,	PUNCT
ejpam-3708	312	4	m	m	PROPN
ejpam-3708	312	5	,	,	PUNCT
ejpam-3708	312	6	p	p	X
ejpam-3708	312	7	,	,	PUNCT
ejpam-3708	312	8	u,∆m	u,∆m	PROPN
ejpam-3708	312	9	v	v	NOUN
ejpam-3708	312	10	]	]	PUNCT
ejpam-3708	312	11	∩wi(f	∩wi(f	ADV
ejpam-3708	312	12	)	)	PUNCT
ejpam-3708	312	13	θ	θ	PROPN
ejpam-3708	313	1	[	[	X
ejpam-3708	313	2	a	a	X
ejpam-3708	313	3	,	,	PUNCT
ejpam-3708	313	4	s	s	NOUN
ejpam-3708	313	5	,	,	PUNCT
ejpam-3708	313	6	p	p	X
ejpam-3708	313	7	,	,	PUNCT
ejpam-3708	313	8	u,∆m	u,∆m	PROPN
ejpam-3708	313	9	v	v	NOUN
ejpam-3708	313	10	]	]	PUNCT
ejpam-3708	313	11	using	use	VERB
ejpam-3708	313	12	the	the	DET
ejpam-3708	313	13	inequality	inequality	NOUN
ejpam-3708	313	14	(	(	PUNCT
ejpam-3708	313	15	3	3	NUM
ejpam-3708	313	16	)	)	PUNCT
ejpam-3708	313	17	,	,	PUNCT
ejpam-3708	313	18	we	we	PRON
ejpam-3708	313	19	have	have	VERB
ejpam-3708	313	20	1	1	NUM
ejpam-3708	313	21	hr	hr	NOUN
ejpam-3708	313	22	∑	∑	PUNCT
ejpam-3708	313	23	k∈ir	k∈ir	PROPN
ejpam-3708	313	24	ank	ank	PROPN
ejpam-3708	313	25	[	[	PUNCT
ejpam-3708	313	26	k−s(mk	k−s(mk	PROPN
ejpam-3708	313	27	+	+	CCONJ
ejpam-3708	313	28	sk	sk	NOUN
ejpam-3708	313	29	)	)	PUNCT
ejpam-3708	313	30	(	(	PUNCT
ejpam-3708	313	31	d(uk∆m	d(uk∆m	PROPN
ejpam-3708	313	32	v	v	PROPN
ejpam-3708	313	33	xk	xk	PROPN
ejpam-3708	313	34	,	,	PUNCT
ejpam-3708	313	35	x0	x0	PROPN
ejpam-3708	313	36	)	)	PUNCT
ejpam-3708	313	37	ρ	ρ	PROPN
ejpam-3708	313	38	)	)	PUNCT
ejpam-3708	313	39	]	]	PUNCT
ejpam-3708	313	40	pk	pk	NOUN
ejpam-3708	313	41	=	=	SYM
ejpam-3708	313	42	1	1	NUM
ejpam-3708	313	43	hr	hr	NOUN
ejpam-3708	313	44	∑	∑	PUNCT
ejpam-3708	313	45	k∈ir	k∈ir	PROPN
ejpam-3708	313	46	ank	ank	PROPN
ejpam-3708	313	47	[	[	PUNCT
ejpam-3708	313	48	k−smk	k−smk	NOUN
ejpam-3708	313	49	(	(	PUNCT
ejpam-3708	313	50	d(uk∆	d(uk∆	PROPN
ejpam-3708	313	51	m	m	NOUN
ejpam-3708	313	52	v	v	NOUN
ejpam-3708	313	53	xk	xk	PROPN
ejpam-3708	313	54	,	,	PUNCT
ejpam-3708	313	55	x0	x0	PROPN
ejpam-3708	313	56	)	)	PUNCT
ejpam-3708	313	57	ρ	ρ	PROPN
ejpam-3708	313	58	)	)	PUNCT
ejpam-3708	314	1	+	+	CCONJ
ejpam-3708	314	2	k−ssk	k−ssk	NOUN
ejpam-3708	314	3	(	(	PUNCT
ejpam-3708	314	4	d(uk∆	d(uk∆	PROPN
ejpam-3708	314	5	m	m	NOUN
ejpam-3708	314	6	v	v	NOUN
ejpam-3708	314	7	xk	xk	PROPN
ejpam-3708	314	8	,	,	PUNCT
ejpam-3708	314	9	x0	x0	PROPN
ejpam-3708	314	10	)	)	PUNCT
ejpam-3708	314	11	ρ	ρ	PROPN
ejpam-3708	314	12	)	)	PUNCT
ejpam-3708	314	13	]	]	PUNCT
ejpam-3708	314	14	pk	pk	PROPN
ejpam-3708	314	15	k.	k.	PROPN
ejpam-3708	314	16	raj	raj	PROPN
ejpam-3708	314	17	,	,	PUNCT
ejpam-3708	314	18	s.	s.	PROPN
ejpam-3708	314	19	a.	a.	PROPN
ejpam-3708	314	20	mohiuddine	mohiuddine	PROPN
ejpam-3708	314	21	/	/	SYM
ejpam-3708	314	22	eur	eur	PROPN
ejpam-3708	314	23	.	.	PUNCT
ejpam-3708	315	1	j.	j.	PROPN
ejpam-3708	315	2	pure	pure	PROPN
ejpam-3708	315	3	appl	appl	PROPN
ejpam-3708	315	4	.	.	PROPN
ejpam-3708	315	5	math	math	PROPN
ejpam-3708	315	6	,	,	PUNCT
ejpam-3708	315	7	13	13	NUM
ejpam-3708	315	8	(	(	PUNCT
ejpam-3708	315	9	5	5	NUM
ejpam-3708	315	10	)	)	PUNCT
ejpam-3708	315	11	(	(	PUNCT
ejpam-3708	315	12	2020	2020	NUM
ejpam-3708	315	13	)	)	PUNCT
ejpam-3708	315	14	,	,	PUNCT
ejpam-3708	315	15	1131	1131	NUM
ejpam-3708	315	16	-	-	SYM
ejpam-3708	315	17	1148	1148	NUM
ejpam-3708	315	18	1144	1144	NUM
ejpam-3708	315	19	≤	≤	PROPN
ejpam-3708	316	1	d	d	NOUN
ejpam-3708	316	2	{	{	PUNCT
ejpam-3708	316	3	1	1	NUM
ejpam-3708	316	4	hr	hr	NOUN
ejpam-3708	316	5	∑	∑	PUNCT
ejpam-3708	316	6	k∈ir	k∈ir	PROPN
ejpam-3708	316	7	ank	ank	PROPN
ejpam-3708	316	8	[	[	PUNCT
ejpam-3708	316	9	k−smk	k−smk	NOUN
ejpam-3708	316	10	(	(	PUNCT
ejpam-3708	316	11	d(uk∆	d(uk∆	PROPN
ejpam-3708	316	12	m	m	NOUN
ejpam-3708	316	13	v	v	NOUN
ejpam-3708	316	14	xk	xk	PROPN
ejpam-3708	316	15	,	,	PUNCT
ejpam-3708	316	16	x0	x0	PROPN
ejpam-3708	316	17	)	)	PUNCT
ejpam-3708	316	18	ρ	ρ	PROPN
ejpam-3708	316	19	)	)	PUNCT
ejpam-3708	316	20	]	]	SYM
ejpam-3708	316	21	pk	pk	NOUN
ejpam-3708	316	22	+	+	NOUN
ejpam-3708	316	23	1	1	NUM
ejpam-3708	316	24	hr	hr	NOUN
ejpam-3708	316	25	∞∑	∞∑	NUM
ejpam-3708	316	26	k∈ir	k∈ir	PROPN
ejpam-3708	316	27	ank	ank	PROPN
ejpam-3708	316	28	[	[	PUNCT
ejpam-3708	316	29	k−ssk	k−ssk	NOUN
ejpam-3708	316	30	(	(	PUNCT
ejpam-3708	316	31	d(uk∆	d(uk∆	PROPN
ejpam-3708	316	32	m	m	NOUN
ejpam-3708	316	33	v	v	NOUN
ejpam-3708	316	34	xk	xk	PROPN
ejpam-3708	316	35	,	,	PUNCT
ejpam-3708	316	36	x0	x0	PROPN
ejpam-3708	316	37	)	)	PUNCT
ejpam-3708	316	38	ρ	ρ	PROPN
ejpam-3708	316	39	)	)	PUNCT
ejpam-3708	316	40	]	]	X
ejpam-3708	316	41	pk	pk	NOUN
ejpam-3708	316	42	}	}	PUNCT
ejpam-3708	316	43	.	.	PUNCT
ejpam-3708	317	1	thus	thus	ADV
ejpam-3708	317	2	,	,	PUNCT
ejpam-3708	317	3	x	x	SYM
ejpam-3708	317	4	=	=	SYM
ejpam-3708	317	5	(	(	PUNCT
ejpam-3708	317	6	xk	xk	ADJ
ejpam-3708	317	7	)	)	PUNCT
ejpam-3708	317	8	∈	∈	PROPN
ejpam-3708	317	9	w	w	NOUN
ejpam-3708	317	10	i(f	i(f	NOUN
ejpam-3708	317	11	)	)	PUNCT
ejpam-3708	317	12	θ	θ	PROPN
ejpam-3708	318	1	[	[	X
ejpam-3708	318	2	a	a	X
ejpam-3708	318	3	,	,	PUNCT
ejpam-3708	318	4	m+	m+	NUM
ejpam-3708	318	5	s	s	NOUN
ejpam-3708	318	6	,	,	PUNCT
ejpam-3708	318	7	p	p	X
ejpam-3708	318	8	,	,	PUNCT
ejpam-3708	318	9	u,∆m	u,∆m	PROPN
ejpam-3708	318	10	v	v	NOUN
ejpam-3708	318	11	]	]	PUNCT
ejpam-3708	318	12	.	.	PUNCT
ejpam-3708	319	1	this	this	PRON
ejpam-3708	319	2	completes	complete	VERB
ejpam-3708	319	3	the	the	DET
ejpam-3708	319	4	proof	proof	NOUN
ejpam-3708	319	5	.	.	PUNCT
ejpam-3708	320	1	theorem	theorem	VERB
ejpam-3708	320	2	6	6	NUM
ejpam-3708	320	3	.	.	PUNCT
ejpam-3708	321	1	the	the	DET
ejpam-3708	321	2	sequence	sequence	NOUN
ejpam-3708	321	3	spaces	space	VERB
ejpam-3708	321	4	w	w	ADP
ejpam-3708	321	5	i(f	i(f	NOUN
ejpam-3708	321	6	)	)	PUNCT
ejpam-3708	321	7	θ	θ	PROPN
ejpam-3708	322	1	[	[	X
ejpam-3708	322	2	a	a	X
ejpam-3708	322	3	,	,	PUNCT
ejpam-3708	322	4	m	m	PROPN
ejpam-3708	322	5	,	,	PUNCT
ejpam-3708	322	6	p	p	X
ejpam-3708	322	7	,	,	PUNCT
ejpam-3708	322	8	u,∆m	u,∆m	PROPN
ejpam-3708	322	9	v	v	X
ejpam-3708	322	10	]	]	PUNCT
ejpam-3708	322	11	0	0	NUM
ejpam-3708	322	12	and	and	CCONJ
ejpam-3708	322	13	w	w	NOUN
ejpam-3708	322	14	i(f	i(f	NOUN
ejpam-3708	323	1	)	)	PUNCT
ejpam-3708	323	2	θ	θ	PROPN
ejpam-3708	324	1	[	[	X
ejpam-3708	324	2	a	a	X
ejpam-3708	324	3	,	,	PUNCT
ejpam-3708	324	4	m	m	PROPN
ejpam-3708	324	5	,	,	PUNCT
ejpam-3708	324	6	p	p	X
ejpam-3708	324	7	,	,	PUNCT
ejpam-3708	324	8	u,∆m	u,∆m	PROPN
ejpam-3708	324	9	v	v	NOUN
ejpam-3708	324	10	]	]	PUNCT
ejpam-3708	324	11	∞	∞	NUM
ejpam-3708	324	12	are	be	AUX
ejpam-3708	324	13	normal	normal	ADJ
ejpam-3708	324	14	as	as	ADV
ejpam-3708	324	15	well	well	ADV
ejpam-3708	324	16	as	as	ADP
ejpam-3708	324	17	monotone	monotone	ADJ
ejpam-3708	324	18	.	.	PUNCT
ejpam-3708	325	1	proof	proof	NOUN
ejpam-3708	325	2	.	.	PUNCT
ejpam-3708	326	1	we	we	PRON
ejpam-3708	326	2	give	give	VERB
ejpam-3708	326	3	the	the	DET
ejpam-3708	326	4	proof	proof	NOUN
ejpam-3708	326	5	of	of	ADP
ejpam-3708	326	6	the	the	DET
ejpam-3708	326	7	theorem	theorem	NOUN
ejpam-3708	326	8	for	for	ADP
ejpam-3708	326	9	w	w	NOUN
ejpam-3708	326	10	i(f	i(f	NOUN
ejpam-3708	326	11	)	)	PUNCT
ejpam-3708	326	12	θ	θ	PROPN
ejpam-3708	327	1	[	[	X
ejpam-3708	327	2	a	a	X
ejpam-3708	327	3	,	,	PUNCT
ejpam-3708	327	4	m	m	PROPN
ejpam-3708	327	5	,	,	PUNCT
ejpam-3708	327	6	p	p	X
ejpam-3708	327	7	,	,	PUNCT
ejpam-3708	327	8	u,∆m	u,∆m	PROPN
ejpam-3708	327	9	v	v	X
ejpam-3708	327	10	]	]	PUNCT
ejpam-3708	327	11	0	0	NUM
ejpam-3708	328	1	only	only	ADV
ejpam-3708	328	2	.	.	PUNCT
ejpam-3708	329	1	let	let	VERB
ejpam-3708	329	2	x	x	PUNCT
ejpam-3708	329	3	=	=	SYM
ejpam-3708	329	4	(	(	PUNCT
ejpam-3708	329	5	xk	xk	ADJ
ejpam-3708	329	6	)	)	PUNCT
ejpam-3708	329	7	∈	∈	PROPN
ejpam-3708	329	8	w	w	NOUN
ejpam-3708	329	9	i(f	i(f	NOUN
ejpam-3708	329	10	)	)	PUNCT
ejpam-3708	329	11	θ	θ	PROPN
ejpam-3708	330	1	[	[	X
ejpam-3708	330	2	a	a	X
ejpam-3708	330	3	,	,	PUNCT
ejpam-3708	330	4	m	m	PROPN
ejpam-3708	330	5	,	,	PUNCT
ejpam-3708	330	6	p	p	X
ejpam-3708	330	7	,	,	PUNCT
ejpam-3708	330	8	u,∆m	u,∆m	PROPN
ejpam-3708	330	9	v	v	X
ejpam-3708	330	10	]	]	PUNCT
ejpam-3708	330	11	0	0	NUM
ejpam-3708	330	12	and	and	CCONJ
ejpam-3708	330	13	y	y	PROPN
ejpam-3708	330	14	=	=	SYM
ejpam-3708	330	15	(	(	PUNCT
ejpam-3708	330	16	yk	yk	PROPN
ejpam-3708	330	17	)	)	PUNCT
ejpam-3708	330	18	be	be	AUX
ejpam-3708	330	19	such	such	ADJ
ejpam-3708	330	20	that	that	SCONJ
ejpam-3708	330	21	d(yk	d(yk	NOUN
ejpam-3708	330	22	,	,	PUNCT
ejpam-3708	330	23	0	0	NUM
ejpam-3708	330	24	)	)	PUNCT
ejpam-3708	330	25	≤	≤	NUM
ejpam-3708	330	26	d(xk	d(xk	PROPN
ejpam-3708	330	27	,	,	PUNCT
ejpam-3708	330	28	0	0	NUM
ejpam-3708	330	29	)	)	PUNCT
ejpam-3708	330	30	for	for	ADP
ejpam-3708	330	31	all	all	DET
ejpam-3708	330	32	k	k	PROPN
ejpam-3708	330	33	∈	∈	PROPN
ejpam-3708	330	34	n.	n.	NOUN
ejpam-3708	330	35	then	then	ADV
ejpam-3708	330	36	for	for	ADP
ejpam-3708	330	37	given	give	VERB
ejpam-3708	330	38	ε	ε	PROPN
ejpam-3708	330	39	>	>	X
ejpam-3708	330	40	0	0	NUM
ejpam-3708	331	1	we	we	PRON
ejpam-3708	331	2	have	have	VERB
ejpam-3708	331	3	b	b	NOUN
ejpam-3708	331	4	=	=	SYM
ejpam-3708	331	5	{	{	PUNCT
ejpam-3708	331	6	n	n	CCONJ
ejpam-3708	331	7	,	,	PUNCT
ejpam-3708	331	8	r	r	NOUN
ejpam-3708	331	9	∈	∈	PROPN
ejpam-3708	331	10	n	n	CCONJ
ejpam-3708	331	11	:	:	PUNCT
ejpam-3708	331	12	1	1	NUM
ejpam-3708	331	13	hr	hr	NOUN
ejpam-3708	331	14	∑	∑	PUNCT
ejpam-3708	331	15	k∈ir	k∈ir	PROPN
ejpam-3708	331	16	ank	ank	PROPN
ejpam-3708	331	17	[	[	PUNCT
ejpam-3708	331	18	k−smk	k−smk	NOUN
ejpam-3708	331	19	(	(	PUNCT
ejpam-3708	331	20	d(uk∆	d(uk∆	PROPN
ejpam-3708	331	21	m	m	NOUN
ejpam-3708	331	22	v	v	NOUN
ejpam-3708	331	23	xk	xk	PROPN
ejpam-3708	331	24	,	,	PUNCT
ejpam-3708	331	25	0	0	NUM
ejpam-3708	331	26	)	)	PUNCT
ejpam-3708	331	27	ρ	ρ	NOUN
ejpam-3708	331	28	)	)	PUNCT
ejpam-3708	331	29	]	]	PUNCT
ejpam-3708	331	30	pk	pk	NOUN
ejpam-3708	331	31	≥	≥	NOUN
ejpam-3708	331	32	ε	ε	PROPN
ejpam-3708	331	33	}	}	PUNCT
ejpam-3708	331	34	∈	∈	PROPN
ejpam-3708	332	1	i	i	PRON
ejpam-3708	332	2	,	,	PUNCT
ejpam-3708	332	3	again	again	ADV
ejpam-3708	332	4	the	the	DET
ejpam-3708	332	5	set	set	ADJ
ejpam-3708	332	6	b1	b1	NOUN
ejpam-3708	332	7	=	=	SYM
ejpam-3708	332	8	{	{	PUNCT
ejpam-3708	332	9	n	n	CCONJ
ejpam-3708	332	10	,	,	PUNCT
ejpam-3708	332	11	r	r	NOUN
ejpam-3708	332	12	∈	∈	PROPN
ejpam-3708	332	13	n	n	CCONJ
ejpam-3708	332	14	:	:	PUNCT
ejpam-3708	332	15	1	1	NUM
ejpam-3708	332	16	hr	hr	NOUN
ejpam-3708	332	17	∑	∑	PUNCT
ejpam-3708	332	18	k∈ir	k∈ir	PROPN
ejpam-3708	332	19	ank	ank	PROPN
ejpam-3708	332	20	[	[	PUNCT
ejpam-3708	332	21	k−smk	k−smk	NOUN
ejpam-3708	332	22	(	(	PUNCT
ejpam-3708	332	23	d(uk∆	d(uk∆	PROPN
ejpam-3708	332	24	m	m	NOUN
ejpam-3708	332	25	v	v	ADP
ejpam-3708	332	26	yk	yk	PROPN
ejpam-3708	332	27	,	,	PUNCT
ejpam-3708	332	28	0	0	NUM
ejpam-3708	332	29	)	)	PUNCT
ejpam-3708	332	30	ρ	ρ	NOUN
ejpam-3708	332	31	)	)	PUNCT
ejpam-3708	332	32	]	]	PUNCT
ejpam-3708	332	33	pk	pk	NOUN
ejpam-3708	332	34	≥	≥	NOUN
ejpam-3708	332	35	ε	ε	PROPN
ejpam-3708	332	36	}	}	PUNCT
ejpam-3708	332	37	⊆	⊆	NUM
ejpam-3708	332	38	b.	b.	NOUN
ejpam-3708	332	39	hence	hence	ADV
ejpam-3708	332	40	,	,	PUNCT
ejpam-3708	332	41	b1	b1	NOUN
ejpam-3708	332	42	∈	∈	PROPN
ejpam-3708	333	1	i	i	PRON
ejpam-3708	333	2	and	and	CCONJ
ejpam-3708	333	3	so	so	ADV
ejpam-3708	333	4	y	y	PROPN
ejpam-3708	333	5	=	=	SYM
ejpam-3708	333	6	(	(	PUNCT
ejpam-3708	333	7	yk	yk	PROPN
ejpam-3708	333	8	)	)	PUNCT
ejpam-3708	333	9	∈	∈	PROPN
ejpam-3708	333	10	w	w	NOUN
ejpam-3708	333	11	i(f	i(f	NOUN
ejpam-3708	333	12	)	)	PUNCT
ejpam-3708	333	13	θ	θ	PROPN
ejpam-3708	334	1	[	[	X
ejpam-3708	334	2	a	a	X
ejpam-3708	334	3	,	,	PUNCT
ejpam-3708	334	4	m	m	PROPN
ejpam-3708	334	5	,	,	PUNCT
ejpam-3708	334	6	p	p	X
ejpam-3708	334	7	,	,	PUNCT
ejpam-3708	334	8	u,∆m	u,∆m	PROPN
ejpam-3708	334	9	v	v	X
ejpam-3708	334	10	]	]	PUNCT
ejpam-3708	334	11	0	0	NUM
ejpam-3708	334	12	.	.	PUNCT
ejpam-3708	335	1	thus	thus	ADV
ejpam-3708	335	2	,	,	PUNCT
ejpam-3708	335	3	the	the	DET
ejpam-3708	335	4	space	space	NOUN
ejpam-3708	335	5	w	w	ADP
ejpam-3708	335	6	i(f	i(f	NOUN
ejpam-3708	335	7	)	)	PUNCT
ejpam-3708	335	8	θ	θ	PROPN
ejpam-3708	336	1	[	[	X
ejpam-3708	336	2	a	a	X
ejpam-3708	336	3	,	,	PUNCT
ejpam-3708	336	4	m	m	PROPN
ejpam-3708	336	5	,	,	PUNCT
ejpam-3708	336	6	p	p	X
ejpam-3708	336	7	,	,	PUNCT
ejpam-3708	336	8	u,∆m	u,∆m	PROPN
ejpam-3708	336	9	v	v	X
ejpam-3708	336	10	]	]	PUNCT
ejpam-3708	336	11	0	0	NUM
ejpam-3708	336	12	is	be	AUX
ejpam-3708	336	13	normal	normal	ADJ
ejpam-3708	336	14	.	.	PUNCT
ejpam-3708	337	1	also	also	ADV
ejpam-3708	337	2	,	,	PUNCT
ejpam-3708	337	3	from	from	ADP
ejpam-3708	337	4	the	the	DET
ejpam-3708	337	5	lemma	lemma	PROPN
ejpam-3708	337	6	2	2	NUM
ejpam-3708	337	7	,	,	PUNCT
ejpam-3708	337	8	it	it	PRON
ejpam-3708	337	9	follows	follow	VERB
ejpam-3708	337	10	that	that	PRON
ejpam-3708	337	11	w	w	NOUN
ejpam-3708	337	12	i(f	i(f	NOUN
ejpam-3708	337	13	)	)	PUNCT
ejpam-3708	337	14	θ	θ	PROPN
ejpam-3708	338	1	[	[	X
ejpam-3708	338	2	a	a	X
ejpam-3708	338	3	,	,	PUNCT
ejpam-3708	338	4	m	m	PROPN
ejpam-3708	338	5	,	,	PUNCT
ejpam-3708	338	6	p	p	X
ejpam-3708	338	7	,	,	PUNCT
ejpam-3708	338	8	u,∆m	u,∆m	PROPN
ejpam-3708	338	9	v	v	X
ejpam-3708	338	10	]	]	PUNCT
ejpam-3708	338	11	0	0	NUM
ejpam-3708	338	12	is	be	AUX
ejpam-3708	338	13	monotone	monotone	ADJ
ejpam-3708	338	14	.	.	PUNCT
ejpam-3708	339	1	this	this	PRON
ejpam-3708	339	2	completes	complete	VERB
ejpam-3708	339	3	the	the	DET
ejpam-3708	339	4	proof	proof	NOUN
ejpam-3708	339	5	.	.	PUNCT
ejpam-3708	340	1	theorem	theorem	VERB
ejpam-3708	340	2	7	7	NUM
ejpam-3708	340	3	.	.	PUNCT
ejpam-3708	341	1	if	if	SCONJ
ejpam-3708	341	2	i	i	PRON
ejpam-3708	341	3	is	be	AUX
ejpam-3708	341	4	not	not	PART
ejpam-3708	341	5	maximal	maximal	ADJ
ejpam-3708	341	6	ideal	ideal	NOUN
ejpam-3708	341	7	then	then	ADV
ejpam-3708	341	8	the	the	DET
ejpam-3708	341	9	space	space	NOUN
ejpam-3708	341	10	w	w	ADP
ejpam-3708	341	11	i(f	i(f	NOUN
ejpam-3708	341	12	)	)	PUNCT
ejpam-3708	341	13	θ	θ	PROPN
ejpam-3708	342	1	[	[	X
ejpam-3708	342	2	a	a	X
ejpam-3708	342	3	,	,	PUNCT
ejpam-3708	342	4	m	m	PROPN
ejpam-3708	342	5	,	,	PUNCT
ejpam-3708	342	6	p	p	X
ejpam-3708	342	7	,	,	PUNCT
ejpam-3708	342	8	u,∆m	u,∆m	PROPN
ejpam-3708	342	9	v	v	NOUN
ejpam-3708	342	10	]	]	PUNCT
ejpam-3708	342	11	is	be	AUX
ejpam-3708	342	12	neither	neither	CCONJ
ejpam-3708	342	13	normal	normal	ADJ
ejpam-3708	342	14	nor	nor	CCONJ
ejpam-3708	342	15	monotone	monotone	ADJ
ejpam-3708	342	16	.	.	PUNCT
ejpam-3708	342	17	example	example	NOUN
ejpam-3708	343	1	3	3	X
ejpam-3708	343	2	.	.	PUNCT
ejpam-3708	343	3	let	let	VERB
ejpam-3708	343	4	us	we	PRON
ejpam-3708	343	5	consider	consider	VERB
ejpam-3708	343	6	a	a	DET
ejpam-3708	343	7	sequence	sequence	NOUN
ejpam-3708	343	8	of	of	ADP
ejpam-3708	343	9	fuzzy	fuzzy	ADJ
ejpam-3708	343	10	numbers	number	NOUN
ejpam-3708	343	11	xk(l	xk(l	PRON
ejpam-3708	343	12	)	)	PUNCT
ejpam-3708	343	13	=	=	PUNCT
ejpam-3708	344	1			X
ejpam-3708	344	2	1+l	1+l	NUM
ejpam-3708	344	3	2	2	NUM
ejpam-3708	344	4	−	−	PROPN
ejpam-3708	344	5	1	1	NUM
ejpam-3708	344	6	≤	≤	NUM
ejpam-3708	344	7	l	l	NOUN
ejpam-3708	344	8	≤	≤	NUM
ejpam-3708	344	9	1	1	NUM
ejpam-3708	344	10	,	,	PUNCT
ejpam-3708	344	11	3−l	3−l	NUM
ejpam-3708	344	12	2	2	NUM
ejpam-3708	344	13	1	1	NUM
ejpam-3708	344	14	≤	≤	NUM
ejpam-3708	344	15	l	l	NOUN
ejpam-3708	344	16	≤	≤	NUM
ejpam-3708	344	17	3	3	NUM
ejpam-3708	344	18	,	,	PUNCT
ejpam-3708	344	19	0	0	NUM
ejpam-3708	344	20	otherwise	otherwise	ADV
ejpam-3708	344	21	.	.	PUNCT
ejpam-3708	345	1	if	if	SCONJ
ejpam-3708	345	2	m	m	ADV
ejpam-3708	345	3	=	=	SYM
ejpam-3708	345	4	0	0	NUM
ejpam-3708	345	5	,	,	PUNCT
ejpam-3708	345	6	then	then	ADV
ejpam-3708	345	7	∆m	∆m	PROPN
ejpam-3708	345	8	v	v	ADP
ejpam-3708	345	9	xk	xk	PROPN
ejpam-3708	345	10	=	=	PUNCT
ejpam-3708	346	1	1	1	X
ejpam-3708	346	2	.	.	PUNCT
ejpam-3708	346	3	let	let	VERB
ejpam-3708	346	4	a	a	DET
ejpam-3708	346	5	=	=	X
ejpam-3708	346	6	(	(	PUNCT
ejpam-3708	346	7	c	c	NOUN
ejpam-3708	346	8	,	,	PUNCT
ejpam-3708	346	9	1	1	NUM
ejpam-3708	346	10	)	)	PUNCT
ejpam-3708	346	11	,	,	PUNCT
ejpam-3708	346	12	the	the	DET
ejpam-3708	346	13	cesàro	cesàro	PROPN
ejpam-3708	346	14	matrix	matrix	NOUN
ejpam-3708	346	15	,	,	PUNCT
ejpam-3708	346	16	m(x	m(x	PROPN
ejpam-3708	346	17	)	)	PUNCT
ejpam-3708	346	18	=	=	SYM
ejpam-3708	347	1	x	x	X
ejpam-3708	347	2	,	,	PUNCT
ejpam-3708	347	3	u	u	NOUN
ejpam-3708	347	4	=	=	SYM
ejpam-3708	347	5	(	(	PUNCT
ejpam-3708	347	6	uk	uk	PROPN
ejpam-3708	347	7	)	)	PUNCT
ejpam-3708	347	8	=	=	SYM
ejpam-3708	347	9	1	1	NUM
ejpam-3708	347	10	,	,	PUNCT
ejpam-3708	347	11	s	s	NOUN
ejpam-3708	347	12	=	=	NOUN
ejpam-3708	347	13	0	0	NUM
ejpam-3708	347	14	,	,	PUNCT
ejpam-3708	347	15	p	p	NOUN
ejpam-3708	347	16	=	=	PUNCT
ejpam-3708	347	17	(	(	PUNCT
ejpam-3708	347	18	pk	pk	NOUN
ejpam-3708	347	19	)	)	PUNCT
ejpam-3708	347	20	=	=	SYM
ejpam-3708	347	21	1	1	NUM
ejpam-3708	347	22	,	,	PUNCT
ejpam-3708	347	23	for	for	ADP
ejpam-3708	347	24	all	all	DET
ejpam-3708	347	25	k	k	PROPN
ejpam-3708	347	26	∈	∈	PROPN
ejpam-3708	347	27	n	n	CCONJ
ejpam-3708	347	28	,	,	PUNCT
ejpam-3708	347	29	ρ	ρ	PROPN
ejpam-3708	347	30	=	=	SYM
ejpam-3708	347	31	1	1	NUM
ejpam-3708	347	32	and	and	CCONJ
ejpam-3708	347	33	θ	θ	NOUN
ejpam-3708	347	34	=	=	SYM
ejpam-3708	348	1	2r	2r	NUM
ejpam-3708	348	2	then	then	ADV
ejpam-3708	348	3	we	we	PRON
ejpam-3708	348	4	have	have	VERB
ejpam-3708	348	5	(	(	PUNCT
ejpam-3708	348	6	xk	xk	ADJ
ejpam-3708	348	7	)	)	PUNCT
ejpam-3708	348	8	∈	∈	PROPN
ejpam-3708	348	9	w	w	NOUN
ejpam-3708	348	10	i(f	i(f	NOUN
ejpam-3708	348	11	)	)	PUNCT
ejpam-3708	348	12	θ	θ	PROPN
ejpam-3708	349	1	[	[	X
ejpam-3708	349	2	a	a	X
ejpam-3708	349	3	,	,	PUNCT
ejpam-3708	349	4	m	m	PROPN
ejpam-3708	349	5	,	,	PUNCT
ejpam-3708	349	6	p	p	X
ejpam-3708	349	7	,	,	PUNCT
ejpam-3708	349	8	u,∆m	u,∆m	PROPN
ejpam-3708	349	9	v	v	NOUN
ejpam-3708	349	10	]	]	PUNCT
ejpam-3708	349	11	.	.	PUNCT
ejpam-3708	350	1	since	since	SCONJ
ejpam-3708	350	2	i	i	PRON
ejpam-3708	350	3	is	be	AUX
ejpam-3708	350	4	not	not	PART
ejpam-3708	350	5	maximal	maximal	ADJ
ejpam-3708	350	6	by	by	ADP
ejpam-3708	350	7	lemma	lemma	PROPN
ejpam-3708	350	8	3	3	NUM
ejpam-3708	350	9	,	,	PUNCT
ejpam-3708	350	10	their	their	PRON
ejpam-3708	350	11	exist	exist	VERB
ejpam-3708	350	12	a	a	DET
ejpam-3708	350	13	subset	subset	NOUN
ejpam-3708	350	14	k	k	NOUN
ejpam-3708	350	15	of	of	ADP
ejpam-3708	350	16	n	n	PRON
ejpam-3708	350	17	such	such	ADJ
ejpam-3708	350	18	that	that	SCONJ
ejpam-3708	350	19	k	k	PROPN
ejpam-3708	350	20	/∈	/∈	PUNCT
ejpam-3708	351	1	i	i	PRON
ejpam-3708	351	2	and	and	CCONJ
ejpam-3708	351	3	n−k	n−k	PROPN
ejpam-3708	351	4	/∈	/∈	PUNCT
ejpam-3708	352	1	i.	i.	PROPN
ejpam-3708	352	2	let	let	VERB
ejpam-3708	352	3	us	we	PRON
ejpam-3708	352	4	define	define	VERB
ejpam-3708	352	5	sequence	sequence	NOUN
ejpam-3708	352	6	y	y	PROPN
ejpam-3708	352	7	=	=	SYM
ejpam-3708	352	8	(	(	PUNCT
ejpam-3708	352	9	yk	yk	PROPN
ejpam-3708	352	10	)	)	PUNCT
ejpam-3708	352	11	by	by	ADP
ejpam-3708	352	12	yk	yk	PROPN
ejpam-3708	352	13	=	=	PUNCT
ejpam-3708	352	14	{	{	PUNCT
ejpam-3708	353	1	xk	xk	PROPN
ejpam-3708	353	2	k	k	PROPN
ejpam-3708	353	3	∈	∈	PROPN
ejpam-3708	353	4	k	k	NOUN
ejpam-3708	353	5	0	0	PUNCT
ejpam-3708	354	1	otherwise	otherwise	ADV
ejpam-3708	354	2	.	.	PUNCT
ejpam-3708	355	1	k.	k.	PROPN
ejpam-3708	355	2	raj	raj	PROPN
ejpam-3708	355	3	,	,	PUNCT
ejpam-3708	355	4	s.	s.	PROPN
ejpam-3708	355	5	a.	a.	PROPN
ejpam-3708	355	6	mohiuddine	mohiuddine	PROPN
ejpam-3708	355	7	/	/	SYM
ejpam-3708	355	8	eur	eur	PROPN
ejpam-3708	355	9	.	.	PUNCT
ejpam-3708	356	1	j.	j.	PROPN
ejpam-3708	356	2	pure	pure	PROPN
ejpam-3708	356	3	appl	appl	PROPN
ejpam-3708	356	4	.	.	PROPN
ejpam-3708	356	5	math	math	PROPN
ejpam-3708	356	6	,	,	PUNCT
ejpam-3708	356	7	13	13	NUM
ejpam-3708	356	8	(	(	PUNCT
ejpam-3708	356	9	5	5	NUM
ejpam-3708	356	10	)	)	PUNCT
ejpam-3708	356	11	(	(	PUNCT
ejpam-3708	356	12	2020	2020	NUM
ejpam-3708	356	13	)	)	PUNCT
ejpam-3708	356	14	,	,	PUNCT
ejpam-3708	356	15	1131	1131	NUM
ejpam-3708	356	16	-	-	SYM
ejpam-3708	356	17	1148	1148	NUM
ejpam-3708	356	18	1145	1145	NUM
ejpam-3708	356	19	then	then	ADV
ejpam-3708	356	20	,	,	PUNCT
ejpam-3708	356	21	(	(	PUNCT
ejpam-3708	356	22	yk	yk	PROPN
ejpam-3708	356	23	)	)	PUNCT
ejpam-3708	356	24	belongs	belong	VERB
ejpam-3708	356	25	to	to	ADP
ejpam-3708	356	26	the	the	DET
ejpam-3708	356	27	canonical	canonical	ADJ
ejpam-3708	356	28	pre	pre	ADJ
ejpam-3708	356	29	image	image	NOUN
ejpam-3708	356	30	of	of	ADP
ejpam-3708	356	31	the	the	DET
ejpam-3708	356	32	k	k	ADJ
ejpam-3708	356	33	-	-	PUNCT
ejpam-3708	356	34	step	step	NOUN
ejpam-3708	356	35	spaces	space	NOUN
ejpam-3708	356	36	of	of	ADP
ejpam-3708	356	37	w	w	NOUN
ejpam-3708	356	38	i(f	i(f	NOUN
ejpam-3708	356	39	)	)	PUNCT
ejpam-3708	356	40	θ	θ	PROPN
ejpam-3708	357	1	[	[	X
ejpam-3708	357	2	a	a	X
ejpam-3708	357	3	,	,	PUNCT
ejpam-3708	357	4	m	m	PROPN
ejpam-3708	357	5	,	,	PUNCT
ejpam-3708	357	6	p	p	X
ejpam-3708	357	7	,	,	PUNCT
ejpam-3708	357	8	u,∆m	u,∆m	PROPN
ejpam-3708	357	9	v	v	NOUN
ejpam-3708	357	10	]	]	PUNCT
ejpam-3708	357	11	.	.	PUNCT
ejpam-3708	358	1	but	but	CCONJ
ejpam-3708	358	2	yk	yk	PROPN
ejpam-3708	358	3	/∈	/∈	PROPN
ejpam-3708	358	4	wi(f	wi(f	NUM
ejpam-3708	358	5	)	)	PUNCT
ejpam-3708	359	1	θ	θ	X
ejpam-3708	360	1	[	[	X
ejpam-3708	360	2	a	a	X
ejpam-3708	360	3	,	,	PUNCT
ejpam-3708	360	4	m	m	PROPN
ejpam-3708	360	5	,	,	PUNCT
ejpam-3708	360	6	p	p	X
ejpam-3708	360	7	,	,	PUNCT
ejpam-3708	360	8	u,∆m	u,∆m	PROPN
ejpam-3708	360	9	v	v	NOUN
ejpam-3708	360	10	]	]	PUNCT
ejpam-3708	360	11	.	.	PUNCT
ejpam-3708	361	1	hence	hence	ADV
ejpam-3708	361	2	,	,	PUNCT
ejpam-3708	361	3	w	w	PROPN
ejpam-3708	361	4	i(f	i(f	NOUN
ejpam-3708	361	5	)	)	PUNCT
ejpam-3708	361	6	θ	θ	PROPN
ejpam-3708	362	1	[	[	X
ejpam-3708	362	2	a	a	X
ejpam-3708	362	3	,	,	PUNCT
ejpam-3708	362	4	m	m	PROPN
ejpam-3708	362	5	,	,	PUNCT
ejpam-3708	362	6	p	p	X
ejpam-3708	362	7	,	,	PUNCT
ejpam-3708	362	8	u,∆m	u,∆m	PROPN
ejpam-3708	362	9	v	v	NOUN
ejpam-3708	362	10	]	]	PUNCT
ejpam-3708	362	11	is	be	AUX
ejpam-3708	362	12	not	not	PART
ejpam-3708	362	13	monotone	monotone	ADJ
ejpam-3708	362	14	.	.	PUNCT
ejpam-3708	363	1	therefore	therefore	ADV
ejpam-3708	363	2	,	,	PUNCT
ejpam-3708	363	3	by	by	ADP
ejpam-3708	363	4	lemma	lemma	PROPN
ejpam-3708	363	5	2	2	NUM
ejpam-3708	363	6	,	,	PUNCT
ejpam-3708	363	7	w	w	NOUN
ejpam-3708	363	8	i(f	i(f	NOUN
ejpam-3708	363	9	)	)	PUNCT
ejpam-3708	363	10	θ	θ	PROPN
ejpam-3708	364	1	[	[	X
ejpam-3708	364	2	a	a	X
ejpam-3708	364	3	,	,	PUNCT
ejpam-3708	364	4	m	m	PROPN
ejpam-3708	364	5	,	,	PUNCT
ejpam-3708	364	6	p	p	X
ejpam-3708	364	7	,	,	PUNCT
ejpam-3708	364	8	u,∆m	u,∆m	PROPN
ejpam-3708	364	9	v	v	NOUN
ejpam-3708	364	10	]	]	PUNCT
ejpam-3708	364	11	is	be	AUX
ejpam-3708	364	12	not	not	PART
ejpam-3708	364	13	normal	normal	ADJ
ejpam-3708	364	14	.	.	PUNCT
ejpam-3708	365	1	theorem	theorem	VERB
ejpam-3708	365	2	8	8	NUM
ejpam-3708	365	3	.	.	PUNCT
ejpam-3708	366	1	if	if	SCONJ
ejpam-3708	366	2	i	i	PRON
ejpam-3708	366	3	is	be	AUX
ejpam-3708	366	4	neither	neither	CCONJ
ejpam-3708	366	5	maximal	maximal	ADJ
ejpam-3708	366	6	nor	nor	CCONJ
ejpam-3708	366	7	i	i	PRON
ejpam-3708	366	8	=	=	NOUN
ejpam-3708	366	9	if	if	SCONJ
ejpam-3708	366	10	then	then	ADV
ejpam-3708	366	11	the	the	DET
ejpam-3708	366	12	spaces	space	NOUN
ejpam-3708	366	13	w	w	ADP
ejpam-3708	366	14	i(f	i(f	NOUN
ejpam-3708	366	15	)	)	PUNCT
ejpam-3708	366	16	θ	θ	PROPN
ejpam-3708	367	1	[	[	X
ejpam-3708	367	2	a	a	X
ejpam-3708	367	3	,	,	PUNCT
ejpam-3708	367	4	m	m	PROPN
ejpam-3708	367	5	,	,	PUNCT
ejpam-3708	367	6	p	p	X
ejpam-3708	367	7	,	,	PUNCT
ejpam-3708	367	8	u,∆m	u,∆m	PROPN
ejpam-3708	367	9	v	v	NOUN
ejpam-3708	367	10	]	]	PUNCT
ejpam-3708	367	11	and	and	CCONJ
ejpam-3708	367	12	w	w	NOUN
ejpam-3708	367	13	i(f	i(f	NOUN
ejpam-3708	367	14	)	)	PUNCT
ejpam-3708	367	15	θ	θ	PROPN
ejpam-3708	368	1	[	[	X
ejpam-3708	368	2	a	a	X
ejpam-3708	368	3	,	,	PUNCT
ejpam-3708	368	4	m	m	PROPN
ejpam-3708	368	5	,	,	PUNCT
ejpam-3708	368	6	p	p	X
ejpam-3708	368	7	,	,	PUNCT
ejpam-3708	368	8	u,∆m	u,∆m	PROPN
ejpam-3708	368	9	v	v	X
ejpam-3708	368	10	]	]	SYM
ejpam-3708	368	11	0	0	NUM
ejpam-3708	368	12	are	be	AUX
ejpam-3708	368	13	not	not	PART
ejpam-3708	368	14	symmetric	symmetric	ADJ
ejpam-3708	368	15	.	.	PUNCT
ejpam-3708	368	16	example	example	NOUN
ejpam-3708	369	1	4	4	NUM
ejpam-3708	369	2	.	.	PUNCT
ejpam-3708	369	3	let	let	VERB
ejpam-3708	369	4	us	we	PRON
ejpam-3708	369	5	consider	consider	VERB
ejpam-3708	369	6	a	a	DET
ejpam-3708	369	7	sequence	sequence	NOUN
ejpam-3708	369	8	of	of	ADP
ejpam-3708	369	9	fuzzy	fuzzy	ADJ
ejpam-3708	369	10	numbers	number	NOUN
ejpam-3708	369	11	xk(l	xk(l	PRON
ejpam-3708	369	12	)	)	PUNCT
ejpam-3708	369	13	=	=	PUNCT
ejpam-3708	370	1			PUNCT
ejpam-3708	370	2	l	l	NOUN
ejpam-3708	370	3	−	−	PROPN
ejpam-3708	370	4	2k	2k	NOUN
ejpam-3708	370	5	+	+	CCONJ
ejpam-3708	370	6	1	1	NUM
ejpam-3708	370	7	l	l	NOUN
ejpam-3708	370	8	∈	∈	NOUN
ejpam-3708	371	1	[	[	X
ejpam-3708	371	2	2k	2k	NOUN
ejpam-3708	371	3	−	−	PROPN
ejpam-3708	371	4	1	1	NUM
ejpam-3708	371	5	,	,	PUNCT
ejpam-3708	371	6	2k	2k	NUM
ejpam-3708	371	7	]	]	PUNCT
ejpam-3708	371	8	,	,	PUNCT
ejpam-3708	371	9	−l	−l	PROPN
ejpam-3708	371	10	+	+	CCONJ
ejpam-3708	371	11	2k	2k	NUM
ejpam-3708	371	12	+	+	CCONJ
ejpam-3708	371	13	1	1	NUM
ejpam-3708	371	14	l	l	NOUN
ejpam-3708	371	15	∈	∈	NOUN
ejpam-3708	372	1	[	[	X
ejpam-3708	372	2	2k	2k	NUM
ejpam-3708	372	3	,	,	PUNCT
ejpam-3708	372	4	2k	2k	NUM
ejpam-3708	372	5	+	+	CCONJ
ejpam-3708	372	6	1	1	NUM
ejpam-3708	372	7	]	]	PUNCT
ejpam-3708	372	8	,	,	PUNCT
ejpam-3708	372	9	0	0	NUM
ejpam-3708	372	10	otherwise	otherwise	ADV
ejpam-3708	372	11	.	.	PUNCT
ejpam-3708	373	1	if	if	SCONJ
ejpam-3708	373	2	m	m	VERB
ejpam-3708	373	3	=	=	SYM
ejpam-3708	373	4	1	1	NUM
ejpam-3708	373	5	,	,	PUNCT
ejpam-3708	373	6	v	v	NOUN
ejpam-3708	373	7	=	=	SYM
ejpam-3708	373	8	1	1	NUM
ejpam-3708	373	9	,	,	PUNCT
ejpam-3708	373	10	then	then	ADV
ejpam-3708	373	11	∆m	∆m	PROPN
ejpam-3708	373	12	v	v	PROPN
ejpam-3708	373	13	xk	xk	PROPN
ejpam-3708	373	14	=	=	SYM
ejpam-3708	373	15	∆xk	∆xk	PROPN
ejpam-3708	373	16	.	.	PUNCT
ejpam-3708	374	1	let	let	VERB
ejpam-3708	374	2	a	a	DET
ejpam-3708	374	3	=	=	X
ejpam-3708	374	4	(	(	PUNCT
ejpam-3708	374	5	c	c	NOUN
ejpam-3708	374	6	,	,	PUNCT
ejpam-3708	374	7	1	1	NUM
ejpam-3708	374	8	)	)	PUNCT
ejpam-3708	374	9	,	,	PUNCT
ejpam-3708	374	10	the	the	DET
ejpam-3708	374	11	cesàro	cesàro	PROPN
ejpam-3708	374	12	matrix	matrix	NOUN
ejpam-3708	374	13	,	,	PUNCT
ejpam-3708	374	14	m(x	m(x	PROPN
ejpam-3708	374	15	)	)	PUNCT
ejpam-3708	374	16	=	=	SYM
ejpam-3708	374	17	x2	x2	PROPN
ejpam-3708	374	18	,	,	PUNCT
ejpam-3708	374	19	u	u	NOUN
ejpam-3708	374	20	=	=	SYM
ejpam-3708	374	21	(	(	PUNCT
ejpam-3708	374	22	uk	uk	PROPN
ejpam-3708	374	23	)	)	PUNCT
ejpam-3708	374	24	=	=	SYM
ejpam-3708	374	25	1	1	NUM
ejpam-3708	374	26	,	,	PUNCT
ejpam-3708	374	27	s	s	PART
ejpam-3708	374	28	=	=	SYM
ejpam-3708	374	29	0	0	NUM
ejpam-3708	374	30	,	,	PUNCT
ejpam-3708	375	1	i	i	PRON
ejpam-3708	375	2	=	=	PUNCT
ejpam-3708	375	3	iδ	iδ	PROPN
ejpam-3708	375	4	,	,	PUNCT
ejpam-3708	375	5	p	p	NOUN
ejpam-3708	375	6	=	=	PUNCT
ejpam-3708	375	7	(	(	PUNCT
ejpam-3708	375	8	pk	pk	NOUN
ejpam-3708	375	9	)	)	PUNCT
ejpam-3708	375	10	=	=	SYM
ejpam-3708	375	11	1	1	NUM
ejpam-3708	375	12	,	,	PUNCT
ejpam-3708	375	13	for	for	ADP
ejpam-3708	375	14	all	all	DET
ejpam-3708	375	15	k	k	PROPN
ejpam-3708	375	16	∈	∈	PROPN
ejpam-3708	375	17	n	n	NOUN
ejpam-3708	375	18	and	and	CCONJ
ejpam-3708	375	19	θ	θ	PROPN
ejpam-3708	375	20	=	=	SYM
ejpam-3708	375	21	2r	2r	NUM
ejpam-3708	375	22	.	.	PUNCT
ejpam-3708	376	1	thus	thus	ADV
ejpam-3708	376	2	,	,	PUNCT
ejpam-3708	376	3	we	we	PRON
ejpam-3708	376	4	have	have	VERB
ejpam-3708	376	5	(	(	PUNCT
ejpam-3708	376	6	xk	xk	ADJ
ejpam-3708	376	7	)	)	PUNCT
ejpam-3708	376	8	∈	∈	PROPN
ejpam-3708	376	9	wi(f	wi(f	NOUN
ejpam-3708	376	10	)	)	PUNCT
ejpam-3708	377	1	[	[	X
ejpam-3708	377	2	a	a	X
ejpam-3708	377	3	,	,	PUNCT
ejpam-3708	377	4	m	m	PROPN
ejpam-3708	377	5	,	,	PUNCT
ejpam-3708	377	6	p	p	X
ejpam-3708	377	7	,	,	PUNCT
ejpam-3708	377	8	u,∆m	u,∆m	PROPN
ejpam-3708	377	9	v	v	NOUN
ejpam-3708	377	10	]	]	PUNCT
ejpam-3708	377	11	.	.	PUNCT
ejpam-3708	378	1	but	but	CCONJ
ejpam-3708	378	2	the	the	DET
ejpam-3708	378	3	rearrangement	rearrangement	NOUN
ejpam-3708	378	4	y	y	PROPN
ejpam-3708	378	5	=	=	PRON
ejpam-3708	378	6	(	(	PUNCT
ejpam-3708	378	7	yk	yk	PROPN
ejpam-3708	378	8	)	)	PUNCT
ejpam-3708	378	9	of	of	ADP
ejpam-3708	378	10	the	the	DET
ejpam-3708	378	11	sequence	sequence	NOUN
ejpam-3708	378	12	space	space	NOUN
ejpam-3708	378	13	(	(	PUNCT
ejpam-3708	378	14	xk	xk	NOUN
ejpam-3708	378	15	)	)	PUNCT
ejpam-3708	378	16	is	be	AUX
ejpam-3708	378	17	defined	define	VERB
ejpam-3708	378	18	as	as	ADP
ejpam-3708	378	19	yk	yk	NOUN
ejpam-3708	378	20	=	=	PUNCT
ejpam-3708	378	21	{	{	PUNCT
ejpam-3708	378	22	x1	x1	PROPN
ejpam-3708	378	23	,	,	PUNCT
ejpam-3708	378	24	x4	x4	PROPN
ejpam-3708	378	25	,	,	PUNCT
ejpam-3708	378	26	x2	x2	PROPN
ejpam-3708	378	27	,	,	PUNCT
ejpam-3708	378	28	x9	x9	PROPN
ejpam-3708	378	29	,	,	PUNCT
ejpam-3708	378	30	x3	x3	ADJ
ejpam-3708	378	31	,	,	PUNCT
ejpam-3708	378	32	x16	x16	PROPN
ejpam-3708	378	33	,	,	PUNCT
ejpam-3708	378	34	x5	x5	PROPN
ejpam-3708	378	35	,	,	PUNCT
ejpam-3708	378	36	x25	x25	NUM
ejpam-3708	378	37	,	,	PUNCT
ejpam-3708	378	38	x6	x6	PROPN
ejpam-3708	378	39	,	,	PUNCT
ejpam-3708	378	40	...	...	PUNCT
ejpam-3708	378	41	}	}	PUNCT
ejpam-3708	378	42	this	this	PRON
ejpam-3708	378	43	implies	imply	VERB
ejpam-3708	378	44	that	that	SCONJ
ejpam-3708	378	45	(	(	PUNCT
ejpam-3708	378	46	yk	yk	NOUN
ejpam-3708	378	47	)	)	PUNCT
ejpam-3708	378	48	∈	∈	PROPN
ejpam-3708	378	49	w	w	NOUN
ejpam-3708	378	50	i(f	i(f	NOUN
ejpam-3708	378	51	)	)	PUNCT
ejpam-3708	378	52	θ	θ	PROPN
ejpam-3708	379	1	[	[	X
ejpam-3708	379	2	a	a	X
ejpam-3708	379	3	,	,	PUNCT
ejpam-3708	379	4	m	m	PROPN
ejpam-3708	379	5	,	,	PUNCT
ejpam-3708	379	6	p	p	X
ejpam-3708	379	7	,	,	PUNCT
ejpam-3708	379	8	u,∆m	u,∆m	PROPN
ejpam-3708	379	9	v	v	NOUN
ejpam-3708	379	10	]	]	PUNCT
ejpam-3708	379	11	.	.	PUNCT
ejpam-3708	380	1	hence	hence	ADV
ejpam-3708	380	2	,	,	PUNCT
ejpam-3708	380	3	w	w	PROPN
ejpam-3708	380	4	i(f	i(f	NOUN
ejpam-3708	380	5	)	)	PUNCT
ejpam-3708	380	6	θ	θ	PROPN
ejpam-3708	381	1	[	[	X
ejpam-3708	381	2	a	a	X
ejpam-3708	381	3	,	,	PUNCT
ejpam-3708	381	4	m	m	PROPN
ejpam-3708	381	5	,	,	PUNCT
ejpam-3708	381	6	p	p	X
ejpam-3708	381	7	,	,	PUNCT
ejpam-3708	381	8	u,∆m	u,∆m	PROPN
ejpam-3708	381	9	v	v	NOUN
ejpam-3708	381	10	]	]	PUNCT
ejpam-3708	381	11	is	be	AUX
ejpam-3708	381	12	not	not	PART
ejpam-3708	381	13	symmetric	symmetric	ADJ
ejpam-3708	381	14	.	.	PUNCT
ejpam-3708	382	1	similarly	similarly	ADV
ejpam-3708	382	2	,	,	PUNCT
ejpam-3708	382	3	w	w	PROPN
ejpam-3708	382	4	i(f	i(f	NOUN
ejpam-3708	382	5	)	)	PUNCT
ejpam-3708	382	6	θ	θ	PROPN
ejpam-3708	383	1	[	[	X
ejpam-3708	383	2	a	a	X
ejpam-3708	383	3	,	,	PUNCT
ejpam-3708	383	4	m	m	PROPN
ejpam-3708	383	5	,	,	PUNCT
ejpam-3708	383	6	p	p	X
ejpam-3708	383	7	,	,	PUNCT
ejpam-3708	383	8	u,∆m	u,∆m	PROPN
ejpam-3708	383	9	v	v	X
ejpam-3708	383	10	]	]	PUNCT
ejpam-3708	383	11	0	0	NUM
ejpam-3708	383	12	is	be	AUX
ejpam-3708	383	13	not	not	PART
ejpam-3708	383	14	symmetric	symmetric	ADJ
ejpam-3708	383	15	.	.	PUNCT
ejpam-3708	384	1	theorem	theorem	VERB
ejpam-3708	384	2	9	9	NUM
ejpam-3708	384	3	.	.	PUNCT
ejpam-3708	385	1	the	the	DET
ejpam-3708	385	2	spaces	space	NOUN
ejpam-3708	385	3	w	w	ADP
ejpam-3708	385	4	i(f	i(f	NOUN
ejpam-3708	385	5	)	)	PUNCT
ejpam-3708	385	6	θ	θ	PROPN
ejpam-3708	386	1	[	[	X
ejpam-3708	386	2	a	a	X
ejpam-3708	386	3	,	,	PUNCT
ejpam-3708	386	4	m	m	PROPN
ejpam-3708	386	5	,	,	PUNCT
ejpam-3708	386	6	p	p	X
ejpam-3708	386	7	,	,	PUNCT
ejpam-3708	386	8	u,∆m	u,∆m	PROPN
ejpam-3708	386	9	v	v	NOUN
ejpam-3708	386	10	]	]	PUNCT
ejpam-3708	386	11	and	and	CCONJ
ejpam-3708	386	12	w	w	NOUN
ejpam-3708	386	13	i(f	i(f	NOUN
ejpam-3708	386	14	)	)	PUNCT
ejpam-3708	386	15	θ	θ	PROPN
ejpam-3708	387	1	[	[	X
ejpam-3708	387	2	a	a	X
ejpam-3708	387	3	,	,	PUNCT
ejpam-3708	387	4	m	m	PROPN
ejpam-3708	387	5	,	,	PUNCT
ejpam-3708	387	6	p	p	X
ejpam-3708	387	7	,	,	PUNCT
ejpam-3708	387	8	u,∆m	u,∆m	PROPN
ejpam-3708	387	9	v	v	X
ejpam-3708	387	10	]	]	SYM
ejpam-3708	387	11	0	0	NUM
ejpam-3708	387	12	are	be	AUX
ejpam-3708	387	13	not	not	PART
ejpam-3708	387	14	convergent	convergent	ADJ
ejpam-3708	387	15	free	free	ADJ
ejpam-3708	387	16	in	in	ADP
ejpam-3708	387	17	general	general	ADJ
ejpam-3708	387	18	.	.	PUNCT
ejpam-3708	387	19	example	example	NOUN
ejpam-3708	388	1	5	5	NUM
ejpam-3708	388	2	.	.	PUNCT
ejpam-3708	388	3	let	let	VERB
ejpam-3708	388	4	us	we	PRON
ejpam-3708	388	5	consider	consider	VERB
ejpam-3708	388	6	a	a	DET
ejpam-3708	388	7	sequence	sequence	NOUN
ejpam-3708	388	8	of	of	ADP
ejpam-3708	388	9	fuzzy	fuzzy	ADJ
ejpam-3708	388	10	numbers	number	NOUN
ejpam-3708	388	11	xk(l	xk(l	PRON
ejpam-3708	388	12	)	)	PUNCT
ejpam-3708	388	13	=	=	PUNCT
ejpam-3708	389	1			X
ejpam-3708	389	2	1+l	1+l	NUM
ejpam-3708	389	3	2	2	NUM
ejpam-3708	389	4	−	−	PROPN
ejpam-3708	389	5	1	1	NUM
ejpam-3708	389	6	≤	≤	NUM
ejpam-3708	389	7	l	l	NOUN
ejpam-3708	389	8	≤	≤	NUM
ejpam-3708	389	9	1	1	NUM
ejpam-3708	389	10	,	,	PUNCT
ejpam-3708	389	11	3−l	3−l	NUM
ejpam-3708	389	12	2	2	NUM
ejpam-3708	389	13	1	1	NUM
ejpam-3708	389	14	≤	≤	NUM
ejpam-3708	389	15	l	l	NOUN
ejpam-3708	389	16	≤	≤	NUM
ejpam-3708	389	17	3	3	NUM
ejpam-3708	389	18	,	,	PUNCT
ejpam-3708	389	19	0	0	NUM
ejpam-3708	389	20	otherwise	otherwise	ADV
ejpam-3708	389	21	.	.	PUNCT
ejpam-3708	390	1	if	if	SCONJ
ejpam-3708	390	2	m	m	ADV
ejpam-3708	390	3	=	=	SYM
ejpam-3708	390	4	0	0	NUM
ejpam-3708	390	5	,	,	PUNCT
ejpam-3708	390	6	then	then	ADV
ejpam-3708	390	7	∆m	∆m	PROPN
ejpam-3708	390	8	v	v	ADP
ejpam-3708	390	9	xk	xk	PROPN
ejpam-3708	390	10	=	=	PUNCT
ejpam-3708	391	1	1	1	X
ejpam-3708	391	2	.	.	PUNCT
ejpam-3708	391	3	let	let	VERB
ejpam-3708	391	4	a	a	DET
ejpam-3708	391	5	=	=	X
ejpam-3708	391	6	(	(	PUNCT
ejpam-3708	391	7	c	c	NOUN
ejpam-3708	391	8	,	,	PUNCT
ejpam-3708	391	9	1	1	NUM
ejpam-3708	391	10	)	)	PUNCT
ejpam-3708	391	11	,	,	PUNCT
ejpam-3708	391	12	the	the	DET
ejpam-3708	391	13	cesàro	cesàro	PROPN
ejpam-3708	391	14	matrix	matrix	NOUN
ejpam-3708	391	15	,	,	PUNCT
ejpam-3708	391	16	m(x	m(x	PROPN
ejpam-3708	391	17	)	)	PUNCT
ejpam-3708	391	18	=	=	SYM
ejpam-3708	392	1	x	x	X
ejpam-3708	392	2	,	,	PUNCT
ejpam-3708	392	3	u	u	NOUN
ejpam-3708	392	4	=	=	SYM
ejpam-3708	392	5	(	(	PUNCT
ejpam-3708	392	6	uk	uk	PROPN
ejpam-3708	392	7	)	)	PUNCT
ejpam-3708	392	8	=	=	SYM
ejpam-3708	392	9	1	1	NUM
ejpam-3708	392	10	,	,	PUNCT
ejpam-3708	392	11	s	s	NOUN
ejpam-3708	392	12	=	=	NOUN
ejpam-3708	392	13	0	0	NUM
ejpam-3708	392	14	,	,	PUNCT
ejpam-3708	392	15	p	p	NOUN
ejpam-3708	392	16	=	=	PUNCT
ejpam-3708	392	17	(	(	PUNCT
ejpam-3708	392	18	pk	pk	NOUN
ejpam-3708	392	19	)	)	PUNCT
ejpam-3708	392	20	=	=	SYM
ejpam-3708	392	21	1	1	NUM
ejpam-3708	392	22	,	,	PUNCT
ejpam-3708	392	23	for	for	ADP
ejpam-3708	392	24	all	all	DET
ejpam-3708	392	25	k	k	PROPN
ejpam-3708	392	26	∈	∈	PROPN
ejpam-3708	392	27	n	n	NOUN
ejpam-3708	392	28	and	and	CCONJ
ejpam-3708	392	29	ρ	ρ	NUM
ejpam-3708	392	30	=	=	SYM
ejpam-3708	392	31	1	1	NUM
ejpam-3708	392	32	then	then	ADV
ejpam-3708	392	33	we	we	PRON
ejpam-3708	392	34	have	have	VERB
ejpam-3708	392	35	(	(	PUNCT
ejpam-3708	392	36	xk	xk	ADJ
ejpam-3708	392	37	)	)	PUNCT
ejpam-3708	392	38	∈	∈	PROPN
ejpam-3708	392	39	wi(f	wi(f	NOUN
ejpam-3708	392	40	)	)	PUNCT
ejpam-3708	393	1	[	[	X
ejpam-3708	393	2	a	a	X
ejpam-3708	393	3	,	,	PUNCT
ejpam-3708	393	4	m	m	PROPN
ejpam-3708	393	5	,	,	PUNCT
ejpam-3708	393	6	p	p	X
ejpam-3708	393	7	,	,	PUNCT
ejpam-3708	393	8	u,∆m	u,∆m	PROPN
ejpam-3708	393	9	v	v	NOUN
ejpam-3708	393	10	]	]	PUNCT
ejpam-3708	393	11	.	.	PUNCT
ejpam-3708	394	1	let	let	VERB
ejpam-3708	394	2	yk(l	yk(l	NOUN
ejpam-3708	394	3	)	)	PUNCT
ejpam-3708	394	4	=	=	SYM
ejpam-3708	394	5	1	1	NUM
ejpam-3708	394	6	k	k	NOUN
ejpam-3708	394	7	for	for	ADP
ejpam-3708	394	8	all	all	DET
ejpam-3708	394	9	k	k	PROPN
ejpam-3708	394	10	∈	∈	PROPN
ejpam-3708	394	11	n.	n.	NOUN
ejpam-3708	394	12	then	then	ADV
ejpam-3708	394	13	(	(	PUNCT
ejpam-3708	394	14	yk	yk	PROPN
ejpam-3708	394	15	)	)	PUNCT
ejpam-3708	394	16	∈	∈	PROPN
ejpam-3708	394	17	w	w	NOUN
ejpam-3708	394	18	i(f	i(f	NOUN
ejpam-3708	394	19	)	)	PUNCT
ejpam-3708	394	20	θ	θ	PROPN
ejpam-3708	395	1	[	[	X
ejpam-3708	395	2	a	a	X
ejpam-3708	395	3	,	,	PUNCT
ejpam-3708	395	4	m	m	PROPN
ejpam-3708	395	5	,	,	PUNCT
ejpam-3708	395	6	p	p	X
ejpam-3708	395	7	,	,	PUNCT
ejpam-3708	395	8	u,∆m	u,∆m	PROPN
ejpam-3708	395	9	v	v	NOUN
ejpam-3708	395	10	]	]	PUNCT
ejpam-3708	395	11	.	.	PUNCT
ejpam-3708	396	1	but	but	CCONJ
ejpam-3708	396	2	xk	xk	PROPN
ejpam-3708	396	3	=	=	PUNCT
ejpam-3708	396	4	0	0	PROPN
ejpam-3708	396	5	does	do	AUX
ejpam-3708	396	6	not	not	PART
ejpam-3708	396	7	imply	imply	VERB
ejpam-3708	396	8	yk	yk	NOUN
ejpam-3708	396	9	=	=	PUNCT
ejpam-3708	396	10	0	0	X
ejpam-3708	396	11	.	.	PUNCT
ejpam-3708	397	1	hence	hence	ADV
ejpam-3708	397	2	,	,	PUNCT
ejpam-3708	397	3	w	w	PROPN
ejpam-3708	397	4	i(f	i(f	NOUN
ejpam-3708	397	5	)	)	PUNCT
ejpam-3708	397	6	θ	θ	PROPN
ejpam-3708	398	1	[	[	X
ejpam-3708	398	2	a	a	X
ejpam-3708	398	3	,	,	PUNCT
ejpam-3708	398	4	m	m	PROPN
ejpam-3708	398	5	,	,	PUNCT
ejpam-3708	398	6	p	p	X
ejpam-3708	398	7	,	,	PUNCT
ejpam-3708	398	8	u,∆m	u,∆m	PROPN
ejpam-3708	398	9	v	v	NOUN
ejpam-3708	398	10	]	]	PUNCT
ejpam-3708	398	11	is	be	AUX
ejpam-3708	398	12	not	not	PART
ejpam-3708	398	13	convergent	convergent	ADJ
ejpam-3708	398	14	free	free	ADJ
ejpam-3708	398	15	.	.	PUNCT
ejpam-3708	399	1	similarly	similarly	ADV
ejpam-3708	399	2	,	,	PUNCT
ejpam-3708	399	3	w	w	PROPN
ejpam-3708	399	4	i(f	i(f	NOUN
ejpam-3708	399	5	)	)	PUNCT
ejpam-3708	399	6	θ	θ	PROPN
ejpam-3708	400	1	[	[	X
ejpam-3708	400	2	a	a	X
ejpam-3708	400	3	,	,	PUNCT
ejpam-3708	400	4	m	m	PROPN
ejpam-3708	400	5	,	,	PUNCT
ejpam-3708	400	6	p	p	X
ejpam-3708	400	7	,	,	PUNCT
ejpam-3708	400	8	u,∆m	u,∆m	PROPN
ejpam-3708	400	9	v	v	X
ejpam-3708	400	10	]	]	PUNCT
ejpam-3708	400	11	0	0	NUM
ejpam-3708	400	12	is	be	AUX
ejpam-3708	400	13	not	not	PART
ejpam-3708	400	14	convergent	convergent	ADJ
ejpam-3708	400	15	free	free	ADJ
ejpam-3708	400	16	.	.	PUNCT
ejpam-3708	401	1	acknowledgements	acknowledgement	NOUN
ejpam-3708	401	2	the	the	DET
ejpam-3708	401	3	authors	author	NOUN
ejpam-3708	401	4	would	would	AUX
ejpam-3708	401	5	like	like	VERB
ejpam-3708	401	6	to	to	PART
ejpam-3708	401	7	thank	thank	VERB
ejpam-3708	401	8	the	the	DET
ejpam-3708	401	9	referees	referee	NOUN
ejpam-3708	401	10	for	for	ADP
ejpam-3708	401	11	their	their	PRON
ejpam-3708	401	12	invaluable	invaluable	ADJ
ejpam-3708	401	13	comments	comment	NOUN
ejpam-3708	401	14	and	and	CCONJ
ejpam-3708	401	15	corrections	correction	NOUN
ejpam-3708	401	16	which	which	PRON
ejpam-3708	401	17	led	lead	VERB
ejpam-3708	401	18	to	to	ADP
ejpam-3708	401	19	the	the	DET
ejpam-3708	401	20	improvement	improvement	NOUN
ejpam-3708	401	21	of	of	ADP
ejpam-3708	401	22	the	the	DET
ejpam-3708	401	23	manuscript	manuscript	NOUN
ejpam-3708	401	24	.	.	PUNCT
ejpam-3708	402	1	references	reference	NOUN
ejpam-3708	402	2	1146	1146	NUM
ejpam-3708	402	3	references	reference	NOUN
ejpam-3708	402	4	[	[	X
ejpam-3708	402	5	1	1	NUM
ejpam-3708	402	6	]	]	PUNCT
ejpam-3708	402	7	h	h	NOUN
ejpam-3708	402	8	altınok	altınok	ADV
ejpam-3708	402	9	,	,	PUNCT
ejpam-3708	402	10	r	r	NOUN
ejpam-3708	402	11	çolak	çolak	NOUN
ejpam-3708	402	12	,	,	PUNCT
ejpam-3708	402	13	and	and	CCONJ
ejpam-3708	402	14	m	m	VERB
ejpam-3708	402	15	et	et	NOUN
ejpam-3708	402	16	.	.	PUNCT
ejpam-3708	403	1	λ	λ	NOUN
ejpam-3708	403	2	-	-	PUNCT
ejpam-3708	403	3	difference	difference	NOUN
ejpam-3708	403	4	sequence	sequence	NOUN
ejpam-3708	403	5	spaces	space	NOUN
ejpam-3708	403	6	of	of	ADP
ejpam-3708	403	7	fuzzy	fuzzy	ADJ
ejpam-3708	403	8	numbers	number	NOUN
ejpam-3708	403	9	.	.	PUNCT
ejpam-3708	404	1	fuzzy	fuzzy	ADJ
ejpam-3708	404	2	sets	set	NOUN
ejpam-3708	404	3	and	and	CCONJ
ejpam-3708	404	4	systems	system	NOUN
ejpam-3708	404	5	,	,	PUNCT
ejpam-3708	404	6	160(21):3128–3139	160(21):3128–3139	NUM
ejpam-3708	404	7	,	,	PUNCT
ejpam-3708	404	8	2009	2009	NUM
ejpam-3708	404	9	.	.	PUNCT
ejpam-3708	405	1	[	[	X
ejpam-3708	405	2	2	2	NUM
ejpam-3708	405	3	]	]	X
ejpam-3708	405	4	c	c	NOUN
ejpam-3708	405	5	belen	belen	NOUN
ejpam-3708	405	6	and	and	CCONJ
ejpam-3708	405	7	s	s	VERB
ejpam-3708	405	8	a	a	DET
ejpam-3708	405	9	mohiuddine	mohiuddine	NOUN
ejpam-3708	405	10	.	.	PUNCT
ejpam-3708	406	1	generalized	generalize	VERB
ejpam-3708	406	2	weighted	weight	VERB
ejpam-3708	406	3	statistical	statistical	ADJ
ejpam-3708	406	4	convergence	convergence	NOUN
ejpam-3708	406	5	and	and	CCONJ
ejpam-3708	406	6	application	application	NOUN
ejpam-3708	406	7	.	.	PUNCT
ejpam-3708	407	1	applied	apply	VERB
ejpam-3708	407	2	mathematics	mathematic	NOUN
ejpam-3708	407	3	and	and	CCONJ
ejpam-3708	407	4	computation	computation	NOUN
ejpam-3708	407	5	,	,	PUNCT
ejpam-3708	407	6	219(18):9821–9826	219(18):9821–9826	NUM
ejpam-3708	407	7	,	,	PUNCT
ejpam-3708	407	8	2013	2013	NUM
ejpam-3708	407	9	.	.	PUNCT
ejpam-3708	408	1	[	[	X
ejpam-3708	408	2	3	3	X
ejpam-3708	408	3	]	]	PUNCT
ejpam-3708	408	4	n	n	PRON
ejpam-3708	408	5	l	l	NOUN
ejpam-3708	408	6	braha	braha	NOUN
ejpam-3708	408	7	,	,	PUNCT
ejpam-3708	409	1	h	h	PROPN
ejpam-3708	409	2	m	m	PROPN
ejpam-3708	409	3	srivastava	srivastava	PROPN
ejpam-3708	409	4	,	,	PUNCT
ejpam-3708	409	5	and	and	CCONJ
ejpam-3708	409	6	s	s	VERB
ejpam-3708	409	7	a	a	DET
ejpam-3708	409	8	mohiuddine	mohiuddine	NOUN
ejpam-3708	409	9	.	.	PUNCT
ejpam-3708	410	1	a	a	DET
ejpam-3708	410	2	korovkin	korovkin	NOUN
ejpam-3708	410	3	’s	’s	PART
ejpam-3708	410	4	type	type	NOUN
ejpam-3708	410	5	approximation	approximation	NOUN
ejpam-3708	410	6	theorem	theorem	NOUN
ejpam-3708	410	7	for	for	ADP
ejpam-3708	410	8	periodic	periodic	ADJ
ejpam-3708	410	9	functions	function	NOUN
ejpam-3708	410	10	via	via	ADP
ejpam-3708	410	11	the	the	DET
ejpam-3708	410	12	statistical	statistical	ADJ
ejpam-3708	410	13	summability	summability	NOUN
ejpam-3708	410	14	of	of	ADP
ejpam-3708	410	15	the	the	DET
ejpam-3708	410	16	generalized	generalize	VERB
ejpam-3708	410	17	de	de	PROPN
ejpam-3708	410	18	la	la	X
ejpam-3708	410	19	vallée	vallée	PROPN
ejpam-3708	410	20	poussin	poussin	PROPN
ejpam-3708	410	21	mean	mean	VERB
ejpam-3708	410	22	.	.	PUNCT
ejpam-3708	411	1	applied	apply	VERB
ejpam-3708	411	2	mathematics	mathematic	NOUN
ejpam-3708	411	3	and	and	CCONJ
ejpam-3708	411	4	computation	computation	NOUN
ejpam-3708	411	5	,	,	PUNCT
ejpam-3708	411	6	228:162–169	228:162–169	NUM
ejpam-3708	411	7	,	,	PUNCT
ejpam-3708	411	8	2014	2014	NUM
ejpam-3708	411	9	.	.	PUNCT
ejpam-3708	412	1	[	[	X
ejpam-3708	412	2	4	4	X
ejpam-3708	412	3	]	]	X
ejpam-3708	412	4	o	o	NOUN
ejpam-3708	412	5	h	h	NOUN
ejpam-3708	412	6	h	h	NOUN
ejpam-3708	412	7	edely	edely	ADV
ejpam-3708	412	8	,	,	PUNCT
ejpam-3708	412	9	s	s	VERB
ejpam-3708	412	10	a	a	DET
ejpam-3708	412	11	mohiuddine	mohiuddine	NOUN
ejpam-3708	412	12	,	,	PUNCT
ejpam-3708	412	13	and	and	CCONJ
ejpam-3708	412	14	a	a	DET
ejpam-3708	412	15	k	k	PROPN
ejpam-3708	412	16	noman	noman	PROPN
ejpam-3708	412	17	.	.	PUNCT
ejpam-3708	413	1	korovkin	korovkin	PROPN
ejpam-3708	413	2	type	type	NOUN
ejpam-3708	413	3	approximation	approximation	NOUN
ejpam-3708	413	4	theorems	theorem	NOUN
ejpam-3708	413	5	obtained	obtain	VERB
ejpam-3708	413	6	through	through	ADP
ejpam-3708	413	7	generalized	generalized	ADJ
ejpam-3708	413	8	statistical	statistical	ADJ
ejpam-3708	413	9	convergence	convergence	NOUN
ejpam-3708	413	10	.	.	PUNCT
ejpam-3708	414	1	applied	apply	VERB
ejpam-3708	414	2	mathematics	mathematics	NOUN
ejpam-3708	414	3	letters	letter	NOUN
ejpam-3708	414	4	,	,	PUNCT
ejpam-3708	414	5	23(11):1382–1387	23(11):1382–1387	NUM
ejpam-3708	414	6	,	,	PUNCT
ejpam-3708	414	7	2010	2010	NUM
ejpam-3708	414	8	.	.	PUNCT
ejpam-3708	415	1	[	[	X
ejpam-3708	415	2	5	5	NUM
ejpam-3708	415	3	]	]	PUNCT
ejpam-3708	415	4	a	a	DET
ejpam-3708	415	5	esi	esi	PROPN
ejpam-3708	415	6	,	,	PUNCT
ejpam-3708	415	7	b	b	PROPN
ejpam-3708	415	8	tripathy	tripathy	ADJ
ejpam-3708	415	9	,	,	PUNCT
ejpam-3708	415	10	and	and	CCONJ
ejpam-3708	415	11	b	b	X
ejpam-3708	415	12	sarma	sarma	NOUN
ejpam-3708	415	13	.	.	PUNCT
ejpam-3708	416	1	on	on	ADP
ejpam-3708	416	2	some	some	DET
ejpam-3708	416	3	new	new	ADJ
ejpam-3708	416	4	type	type	NOUN
ejpam-3708	416	5	generalized	generalized	ADJ
ejpam-3708	416	6	difference	difference	NOUN
ejpam-3708	416	7	sequence	sequence	NOUN
ejpam-3708	416	8	spaces	space	VERB
ejpam-3708	416	9	.	.	PUNCT
ejpam-3708	417	1	mathematica	mathematica	PROPN
ejpam-3708	417	2	slovaca	slovaca	PROPN
ejpam-3708	417	3	,	,	PUNCT
ejpam-3708	417	4	57(5):475–482	57(5):475–482	PROPN
ejpam-3708	417	5	,	,	PUNCT
ejpam-3708	417	6	2007	2007	NUM
ejpam-3708	417	7	.	.	PUNCT
ejpam-3708	418	1	[	[	X
ejpam-3708	418	2	6	6	NUM
ejpam-3708	418	3	]	]	X
ejpam-3708	418	4	m	m	VERB
ejpam-3708	418	5	et	et	NOUN
ejpam-3708	418	6	and	and	CCONJ
ejpam-3708	418	7	r	r	NOUN
ejpam-3708	418	8	çolak	çolak	NOUN
ejpam-3708	418	9	.	.	PUNCT
ejpam-3708	419	1	on	on	ADP
ejpam-3708	419	2	some	some	DET
ejpam-3708	419	3	generalized	generalized	ADJ
ejpam-3708	419	4	difference	difference	NOUN
ejpam-3708	419	5	sequence	sequence	NOUN
ejpam-3708	419	6	spaces	space	VERB
ejpam-3708	419	7	.	.	PUNCT
ejpam-3708	420	1	soochow	soochow	PROPN
ejpam-3708	420	2	journal	journal	PROPN
ejpam-3708	420	3	of	of	ADP
ejpam-3708	420	4	mathematics	mathematic	NOUN
ejpam-3708	420	5	,	,	PUNCT
ejpam-3708	420	6	21(4):377–386	21(4):377–386	NUM
ejpam-3708	420	7	,	,	PUNCT
ejpam-3708	420	8	1995	1995	NUM
ejpam-3708	420	9	.	.	PUNCT
ejpam-3708	421	1	[	[	X
ejpam-3708	421	2	7	7	X
ejpam-3708	421	3	]	]	X
ejpam-3708	421	4	a	a	DET
ejpam-3708	421	5	r	r	NOUN
ejpam-3708	421	6	freedman	freedman	PROPN
ejpam-3708	421	7	,	,	PUNCT
ejpam-3708	421	8	j	j	PROPN
ejpam-3708	421	9	j	j	PROPN
ejpam-3708	421	10	sember	sember	PROPN
ejpam-3708	421	11	,	,	PUNCT
ejpam-3708	421	12	and	and	CCONJ
ejpam-3708	421	13	m	m	PROPN
ejpam-3708	421	14	raphael	raphael	PROPN
ejpam-3708	421	15	.	.	PUNCT
ejpam-3708	422	1	some	some	DET
ejpam-3708	422	2	cesàro	cesàro	ADJ
ejpam-3708	422	3	-	-	PUNCT
ejpam-3708	422	4	type	type	NOUN
ejpam-3708	422	5	summability	summability	NOUN
ejpam-3708	422	6	spaces	space	NOUN
ejpam-3708	422	7	.	.	PUNCT
ejpam-3708	423	1	proceedings	proceeding	NOUN
ejpam-3708	423	2	of	of	ADP
ejpam-3708	423	3	the	the	DET
ejpam-3708	423	4	london	london	PROPN
ejpam-3708	423	5	mathematical	mathematical	ADJ
ejpam-3708	423	6	society	society	NOUN
ejpam-3708	423	7	,	,	PUNCT
ejpam-3708	423	8	3(3):508–520	3(3):508–520	NUM
ejpam-3708	423	9	,	,	PUNCT
ejpam-3708	423	10	1978	1978	NUM
ejpam-3708	423	11	.	.	PUNCT
ejpam-3708	424	1	[	[	X
ejpam-3708	424	2	8	8	NUM
ejpam-3708	424	3	]	]	X
ejpam-3708	424	4	j	j	PROPN
ejpam-3708	424	5	a	a	DET
ejpam-3708	424	6	fridy	fridy	ADJ
ejpam-3708	424	7	and	and	CCONJ
ejpam-3708	424	8	c	c	PROPN
ejpam-3708	424	9	orhan	orhan	PROPN
ejpam-3708	424	10	.	.	PUNCT
ejpam-3708	425	1	lacunary	lacunary	ADJ
ejpam-3708	425	2	statistical	statistical	ADJ
ejpam-3708	425	3	convergence	convergence	NOUN
ejpam-3708	425	4	.	.	PUNCT
ejpam-3708	426	1	pacific	pacific	PROPN
ejpam-3708	426	2	journal	journal	PROPN
ejpam-3708	426	3	of	of	ADP
ejpam-3708	426	4	mathematics	mathematic	NOUN
ejpam-3708	426	5	,	,	PUNCT
ejpam-3708	426	6	160(1):43–51	160(1):43–51	NUM
ejpam-3708	426	7	,	,	PUNCT
ejpam-3708	426	8	1993	1993	NUM
ejpam-3708	426	9	.	.	PUNCT
ejpam-3708	427	1	[	[	X
ejpam-3708	427	2	9	9	NUM
ejpam-3708	427	3	]	]	SYM
ejpam-3708	427	4	b	b	NOUN
ejpam-3708	427	5	hazarika	hazarika	NOUN
ejpam-3708	427	6	.	.	PUNCT
ejpam-3708	428	1	lacunary	lacunary	ADJ
ejpam-3708	428	2	i−convergent	i−convergent	NUM
ejpam-3708	428	3	sequence	sequence	NOUN
ejpam-3708	428	4	of	of	ADP
ejpam-3708	428	5	fuzzy	fuzzy	ADJ
ejpam-3708	428	6	real	real	ADJ
ejpam-3708	428	7	numbers	number	NOUN
ejpam-3708	428	8	.	.	PUNCT
ejpam-3708	429	1	pacific	pacific	PROPN
ejpam-3708	429	2	journal	journal	PROPN
ejpam-3708	429	3	of	of	ADP
ejpam-3708	429	4	science	science	NOUN
ejpam-3708	429	5	and	and	CCONJ
ejpam-3708	429	6	technology	technology	NOUN
ejpam-3708	429	7	,	,	PUNCT
ejpam-3708	429	8	2009	2009	NUM
ejpam-3708	429	9	.	.	PUNCT
ejpam-3708	430	1	[	[	X
ejpam-3708	430	2	10	10	NUM
ejpam-3708	430	3	]	]	SYM
ejpam-3708	430	4	b	b	NOUN
ejpam-3708	430	5	hazarika	hazarika	NOUN
ejpam-3708	430	6	,	,	PUNCT
ejpam-3708	430	7	a	a	DET
ejpam-3708	430	8	alotaibi	alotaibi	NOUN
ejpam-3708	430	9	,	,	PUNCT
ejpam-3708	430	10	and	and	CCONJ
ejpam-3708	430	11	s	s	VERB
ejpam-3708	430	12	a	a	DET
ejpam-3708	430	13	mohiuddine	mohiuddine	NOUN
ejpam-3708	430	14	.	.	PUNCT
ejpam-3708	431	1	statistical	statistical	ADJ
ejpam-3708	431	2	convergence	convergence	NOUN
ejpam-3708	431	3	in	in	ADP
ejpam-3708	431	4	measure	measure	NOUN
ejpam-3708	431	5	for	for	ADP
ejpam-3708	431	6	double	double	ADJ
ejpam-3708	431	7	sequences	sequence	NOUN
ejpam-3708	431	8	of	of	ADP
ejpam-3708	431	9	fuzzy	fuzzy	ADV
ejpam-3708	431	10	-	-	PUNCT
ejpam-3708	431	11	valued	value	VERB
ejpam-3708	431	12	functions	function	NOUN
ejpam-3708	431	13	.	.	PUNCT
ejpam-3708	432	1	soft	soft	ADJ
ejpam-3708	432	2	computing	computing	NOUN
ejpam-3708	432	3	,	,	PUNCT
ejpam-3708	432	4	24:6613–6622	24:6613–6622	NUM
ejpam-3708	432	5	,	,	PUNCT
ejpam-3708	432	6	2020	2020	NUM
ejpam-3708	432	7	.	.	PUNCT
ejpam-3708	433	1	[	[	X
ejpam-3708	433	2	11	11	NUM
ejpam-3708	433	3	]	]	SYM
ejpam-3708	433	4	b	b	NOUN
ejpam-3708	433	5	hazarika	hazarika	NOUN
ejpam-3708	433	6	and	and	CCONJ
ejpam-3708	433	7	e	e	X
ejpam-3708	433	8	savas	savas	PROPN
ejpam-3708	433	9	.	.	PUNCT
ejpam-3708	434	1	some	some	PRON
ejpam-3708	434	2	i−convergent	i−convergent	VERB
ejpam-3708	434	3	lambda	lambda	ADJ
ejpam-3708	434	4	-	-	PUNCT
ejpam-3708	434	5	summable	summable	ADJ
ejpam-3708	434	6	difference	difference	NOUN
ejpam-3708	434	7	sequence	sequence	NOUN
ejpam-3708	434	8	spaces	space	NOUN
ejpam-3708	434	9	of	of	ADP
ejpam-3708	434	10	fuzzy	fuzzy	ADJ
ejpam-3708	434	11	real	real	ADJ
ejpam-3708	434	12	numbers	number	NOUN
ejpam-3708	434	13	defined	define	VERB
ejpam-3708	434	14	by	by	ADP
ejpam-3708	434	15	a	a	DET
ejpam-3708	434	16	sequence	sequence	NOUN
ejpam-3708	434	17	of	of	ADP
ejpam-3708	434	18	orlicz	orlicz	ADJ
ejpam-3708	434	19	functions	function	NOUN
ejpam-3708	434	20	.	.	PUNCT
ejpam-3708	435	1	mathematical	mathematical	ADJ
ejpam-3708	435	2	and	and	CCONJ
ejpam-3708	435	3	computer	computer	NOUN
ejpam-3708	435	4	modelling	modelling	NOUN
ejpam-3708	435	5	,	,	PUNCT
ejpam-3708	435	6	54:2986–2998	54:2986–2998	NUM
ejpam-3708	435	7	,	,	PUNCT
ejpam-3708	435	8	2011	2011	NUM
ejpam-3708	435	9	.	.	PUNCT
ejpam-3708	436	1	[	[	X
ejpam-3708	436	2	12	12	NUM
ejpam-3708	436	3	]	]	X
ejpam-3708	436	4	u	u	X
ejpam-3708	436	5	kadak	kadak	PROPN
ejpam-3708	436	6	and	and	CCONJ
ejpam-3708	436	7	s	s	VERB
ejpam-3708	436	8	a	a	DET
ejpam-3708	436	9	mohiuddine	mohiuddine	NOUN
ejpam-3708	436	10	.	.	PUNCT
ejpam-3708	437	1	generalized	generalize	VERB
ejpam-3708	437	2	statistically	statistically	ADV
ejpam-3708	437	3	almost	almost	ADV
ejpam-3708	437	4	convergence	convergence	NOUN
ejpam-3708	437	5	based	base	VERB
ejpam-3708	437	6	on	on	ADP
ejpam-3708	437	7	the	the	DET
ejpam-3708	437	8	difference	difference	NOUN
ejpam-3708	437	9	operator	operator	NOUN
ejpam-3708	437	10	which	which	PRON
ejpam-3708	437	11	includes	include	VERB
ejpam-3708	437	12	the	the	DET
ejpam-3708	437	13	(	(	PUNCT
ejpam-3708	437	14	p	p	NOUN
ejpam-3708	437	15	,	,	PUNCT
ejpam-3708	437	16	q)−gamma	q)−gamma	PROPN
ejpam-3708	437	17	function	function	NOUN
ejpam-3708	437	18	and	and	CCONJ
ejpam-3708	437	19	related	related	ADJ
ejpam-3708	437	20	approximation	approximation	NOUN
ejpam-3708	437	21	theorems	theorem	NOUN
ejpam-3708	437	22	.	.	PUNCT
ejpam-3708	437	23	results	result	NOUN
ejpam-3708	437	24	in	in	ADP
ejpam-3708	437	25	mathematics	mathematic	NOUN
ejpam-3708	437	26	,	,	PUNCT
ejpam-3708	437	27	73(1):article	73(1):article	PROPN
ejpam-3708	437	28	9	9	NUM
ejpam-3708	437	29	,	,	PUNCT
ejpam-3708	437	30	2018	2018	NUM
ejpam-3708	437	31	.	.	PUNCT
ejpam-3708	438	1	[	[	X
ejpam-3708	438	2	13	13	NUM
ejpam-3708	438	3	]	]	X
ejpam-3708	438	4	p	p	X
ejpam-3708	438	5	k	k	PROPN
ejpam-3708	438	6	kamthan	kamthan	PROPN
ejpam-3708	438	7	and	and	CCONJ
ejpam-3708	438	8	m.	m.	PROPN
ejpam-3708	438	9	gupta	gupta	PROPN
ejpam-3708	438	10	.	.	PUNCT
ejpam-3708	439	1	sequence	sequence	NOUN
ejpam-3708	439	2	spaces	space	NOUN
ejpam-3708	439	3	and	and	CCONJ
ejpam-3708	439	4	series	series	NOUN
ejpam-3708	439	5	.	.	PUNCT
ejpam-3708	440	1	marcel	marcel	PROPN
ejpam-3708	440	2	dekker	dekker	PROPN
ejpam-3708	440	3	,	,	PUNCT
ejpam-3708	440	4	1980	1980	NUM
ejpam-3708	440	5	.	.	PUNCT
ejpam-3708	441	1	[	[	X
ejpam-3708	441	2	14	14	NUM
ejpam-3708	441	3	]	]	X
ejpam-3708	441	4	h	h	PROPN
ejpam-3708	441	5	kizmaz	kizmaz	PROPN
ejpam-3708	441	6	.	.	PUNCT
ejpam-3708	442	1	on	on	ADP
ejpam-3708	442	2	certain	certain	ADJ
ejpam-3708	442	3	sequence	sequence	NOUN
ejpam-3708	442	4	spaces	space	NOUN
ejpam-3708	442	5	.	.	PUNCT
ejpam-3708	443	1	canadian	canadian	ADJ
ejpam-3708	443	2	mathematical	mathematical	ADJ
ejpam-3708	443	3	bulletin	bulletin	NOUN
ejpam-3708	443	4	,	,	PUNCT
ejpam-3708	443	5	24(2):169	24(2):169	NUM
ejpam-3708	443	6	–	–	PUNCT
ejpam-3708	443	7	176	176	NUM
ejpam-3708	443	8	,	,	PUNCT
ejpam-3708	443	9	1981	1981	NUM
ejpam-3708	443	10	.	.	PUNCT
ejpam-3708	444	1	[	[	X
ejpam-3708	444	2	15	15	NUM
ejpam-3708	444	3	]	]	X
ejpam-3708	444	4	p	p	X
ejpam-3708	444	5	kostyrko	kostyrko	PROPN
ejpam-3708	444	6	,	,	PUNCT
ejpam-3708	444	7	w	w	PROPN
ejpam-3708	444	8	wilczyński	wilczyński	NOUN
ejpam-3708	444	9	,	,	PUNCT
ejpam-3708	444	10	and	and	CCONJ
ejpam-3708	444	11	t	t	PROPN
ejpam-3708	444	12	šalát	šalát	PROPN
ejpam-3708	444	13	.	.	PUNCT
ejpam-3708	444	14	i−convergence	i−convergence	NOUN
ejpam-3708	444	15	.	.	PUNCT
ejpam-3708	445	1	real	real	ADJ
ejpam-3708	445	2	analysis	analysis	NOUN
ejpam-3708	445	3	exchange	exchange	NOUN
ejpam-3708	445	4	,	,	PUNCT
ejpam-3708	445	5	26(2):669–686	26(2):669–686	NUM
ejpam-3708	445	6	,	,	PUNCT
ejpam-3708	445	7	2000	2000	NUM
ejpam-3708	445	8	.	.	PUNCT
ejpam-3708	446	1	references	reference	NOUN
ejpam-3708	446	2	1147	1147	NUM
ejpam-3708	447	1	[	[	X
ejpam-3708	447	2	16	16	NUM
ejpam-3708	447	3	]	]	SYM
ejpam-3708	447	4	v	v	ADP
ejpam-3708	447	5	kumar	kumar	PROPN
ejpam-3708	447	6	and	and	CCONJ
ejpam-3708	447	7	k	k	PROPN
ejpam-3708	447	8	kumar	kumar	PROPN
ejpam-3708	447	9	.	.	PROPN
ejpam-3708	448	1	on	on	ADP
ejpam-3708	448	2	the	the	DET
ejpam-3708	448	3	ideal	ideal	ADJ
ejpam-3708	448	4	convergence	convergence	NOUN
ejpam-3708	448	5	of	of	ADP
ejpam-3708	448	6	sequences	sequence	NOUN
ejpam-3708	448	7	of	of	ADP
ejpam-3708	448	8	fuzzy	fuzzy	ADJ
ejpam-3708	448	9	numbers	number	NOUN
ejpam-3708	448	10	.	.	PUNCT
ejpam-3708	449	1	information	information	NOUN
ejpam-3708	449	2	sciences	sciences	PROPN
ejpam-3708	449	3	,	,	PUNCT
ejpam-3708	449	4	178(24):4670–4678	178(24):4670–4678	NUM
ejpam-3708	449	5	,	,	PUNCT
ejpam-3708	449	6	2008	2008	NUM
ejpam-3708	449	7	.	.	PUNCT
ejpam-3708	450	1	[	[	X
ejpam-3708	450	2	17	17	NUM
ejpam-3708	450	3	]	]	X
ejpam-3708	450	4	j	j	PROPN
ejpam-3708	450	5	lindenstrauss	lindenstrauss	ADJ
ejpam-3708	450	6	and	and	CCONJ
ejpam-3708	450	7	l	l	NOUN
ejpam-3708	450	8	tzafriri	tzafriri	NOUN
ejpam-3708	450	9	.	.	PUNCT
ejpam-3708	451	1	on	on	ADP
ejpam-3708	451	2	orlicz	orlicz	ADJ
ejpam-3708	451	3	sequence	sequence	NOUN
ejpam-3708	451	4	spaces	space	VERB
ejpam-3708	451	5	.	.	PUNCT
ejpam-3708	452	1	israel	israel	PROPN
ejpam-3708	452	2	journal	journal	PROPN
ejpam-3708	452	3	of	of	ADP
ejpam-3708	452	4	mathematics	mathematic	NOUN
ejpam-3708	452	5	,	,	PUNCT
ejpam-3708	452	6	10(3):379–390	10(3):379–390	NUM
ejpam-3708	452	7	,	,	PUNCT
ejpam-3708	452	8	1971	1971	NUM
ejpam-3708	452	9	.	.	PUNCT
ejpam-3708	453	1	[	[	X
ejpam-3708	453	2	18	18	NUM
ejpam-3708	453	3	]	]	PUNCT
ejpam-3708	453	4	m	m	NOUN
ejpam-3708	453	5	matloka	matloka	NOUN
ejpam-3708	453	6	.	.	PUNCT
ejpam-3708	454	1	sequences	sequence	NOUN
ejpam-3708	454	2	of	of	ADP
ejpam-3708	454	3	fuzzy	fuzzy	ADJ
ejpam-3708	454	4	numbers	number	NOUN
ejpam-3708	454	5	.	.	PUNCT
ejpam-3708	455	1	busefal	busefal	PROPN
ejpam-3708	455	2	,	,	PUNCT
ejpam-3708	455	3	28(1):28–37	28(1):28–37	NUM
ejpam-3708	455	4	,	,	PUNCT
ejpam-3708	455	5	1986	1986	NUM
ejpam-3708	455	6	.	.	PUNCT
ejpam-3708	456	1	[	[	X
ejpam-3708	456	2	19	19	NUM
ejpam-3708	456	3	]	]	X
ejpam-3708	456	4	s	s	VERB
ejpam-3708	456	5	a	a	DET
ejpam-3708	456	6	mohiuddine	mohiuddine	NOUN
ejpam-3708	456	7	.	.	PUNCT
ejpam-3708	457	1	statistical	statistical	ADJ
ejpam-3708	457	2	weighted	weight	VERB
ejpam-3708	457	3	a	a	DET
ejpam-3708	457	4	-	-	PUNCT
ejpam-3708	457	5	summability	summability	NOUN
ejpam-3708	457	6	with	with	ADP
ejpam-3708	457	7	application	application	NOUN
ejpam-3708	457	8	to	to	ADP
ejpam-3708	457	9	korovkin	korovkin	PROPN
ejpam-3708	457	10	’s	’s	PART
ejpam-3708	457	11	type	type	NOUN
ejpam-3708	457	12	approximation	approximation	NOUN
ejpam-3708	457	13	theorem	theorem	NOUN
ejpam-3708	457	14	.	.	PROPN
ejpam-3708	457	15	journal	journal	PROPN
ejpam-3708	457	16	of	of	ADP
ejpam-3708	457	17	inequalities	inequality	NOUN
ejpam-3708	457	18	and	and	CCONJ
ejpam-3708	457	19	applications	application	NOUN
ejpam-3708	457	20	,	,	PUNCT
ejpam-3708	457	21	2016	2016	NUM
ejpam-3708	457	22	:	:	PUNCT
ejpam-3708	457	23	article	article	NOUN
ejpam-3708	457	24	101	101	NUM
ejpam-3708	457	25	,	,	PUNCT
ejpam-3708	457	26	2016	2016	NUM
ejpam-3708	457	27	.	.	PUNCT
ejpam-3708	458	1	[	[	X
ejpam-3708	458	2	20	20	NUM
ejpam-3708	458	3	]	]	SYM
ejpam-3708	458	4	s	s	VERB
ejpam-3708	458	5	a	a	DET
ejpam-3708	458	6	mohiuddine	mohiuddine	NOUN
ejpam-3708	458	7	and	and	CCONJ
ejpam-3708	459	1	b	b	DET
ejpam-3708	459	2	a	a	PRON
ejpam-3708	459	3	s	s	NOUN
ejpam-3708	459	4	alamri	alamri	ADJ
ejpam-3708	459	5	.	.	PUNCT
ejpam-3708	460	1	generalization	generalization	NOUN
ejpam-3708	460	2	of	of	ADP
ejpam-3708	460	3	equi	equi	NOUN
ejpam-3708	460	4	-	-	PUNCT
ejpam-3708	460	5	statistical	statistical	ADJ
ejpam-3708	460	6	convergence	convergence	NOUN
ejpam-3708	460	7	via	via	ADP
ejpam-3708	460	8	weighted	weight	VERB
ejpam-3708	460	9	lacunary	lacunary	ADJ
ejpam-3708	460	10	sequence	sequence	NOUN
ejpam-3708	460	11	with	with	ADP
ejpam-3708	460	12	associated	associated	ADJ
ejpam-3708	460	13	korovkin	korovkin	NOUN
ejpam-3708	460	14	and	and	CCONJ
ejpam-3708	460	15	voronovskaya	voronovskaya	NOUN
ejpam-3708	460	16	type	type	NOUN
ejpam-3708	460	17	approximation	approximation	NOUN
ejpam-3708	460	18	theorems	theorem	NOUN
ejpam-3708	460	19	.	.	PUNCT
ejpam-3708	461	1	revista	revista	PROPN
ejpam-3708	461	2	de	de	X
ejpam-3708	461	3	la	la	PROPN
ejpam-3708	461	4	real	real	PROPN
ejpam-3708	461	5	academia	academia	PROPN
ejpam-3708	461	6	de	de	PROPN
ejpam-3708	461	7	ciencias	ciencias	PROPN
ejpam-3708	461	8	exactas	exacta	NOUN
ejpam-3708	461	9	,	,	PUNCT
ejpam-3708	461	10	f́ısicas	f́ısicas	PROPN
ejpam-3708	461	11	y	y	PROPN
ejpam-3708	461	12	naturales	naturale	NOUN
ejpam-3708	461	13	.	.	PUNCT
ejpam-3708	462	1	serie	serie	PROPN
ejpam-3708	462	2	a.	a.	PROPN
ejpam-3708	462	3	matemáticas	matemáticas	PROPN
ejpam-3708	462	4	,	,	PUNCT
ejpam-3708	462	5	113(3):1955–1973	113(3):1955–1973	NUM
ejpam-3708	462	6	,	,	PUNCT
ejpam-3708	462	7	2019	2019	NUM
ejpam-3708	462	8	.	.	PUNCT
ejpam-3708	463	1	[	[	X
ejpam-3708	463	2	21	21	NUM
ejpam-3708	463	3	]	]	X
ejpam-3708	463	4	s	s	VERB
ejpam-3708	463	5	a	a	DET
ejpam-3708	463	6	mohiuddine	mohiuddine	NOUN
ejpam-3708	463	7	,	,	PUNCT
ejpam-3708	463	8	a	a	DET
ejpam-3708	463	9	asiri	asiri	NOUN
ejpam-3708	463	10	,	,	PUNCT
ejpam-3708	463	11	and	and	CCONJ
ejpam-3708	463	12	b	b	X
ejpam-3708	463	13	hazarika	hazarika	NOUN
ejpam-3708	463	14	.	.	PUNCT
ejpam-3708	464	1	weighted	weight	VERB
ejpam-3708	464	2	statistical	statistical	ADJ
ejpam-3708	464	3	convergence	convergence	NOUN
ejpam-3708	464	4	through	through	ADP
ejpam-3708	464	5	difference	difference	NOUN
ejpam-3708	464	6	operator	operator	NOUN
ejpam-3708	464	7	of	of	ADP
ejpam-3708	464	8	sequences	sequence	NOUN
ejpam-3708	464	9	of	of	ADP
ejpam-3708	464	10	fuzzy	fuzzy	ADJ
ejpam-3708	464	11	numbers	number	NOUN
ejpam-3708	464	12	with	with	ADP
ejpam-3708	464	13	application	application	NOUN
ejpam-3708	464	14	to	to	ADP
ejpam-3708	464	15	fuzzy	fuzzy	ADJ
ejpam-3708	464	16	approximation	approximation	NOUN
ejpam-3708	464	17	theorems	theorem	NOUN
ejpam-3708	464	18	.	.	PUNCT
ejpam-3708	465	1	international	international	ADJ
ejpam-3708	465	2	journal	journal	PROPN
ejpam-3708	465	3	of	of	ADP
ejpam-3708	465	4	general	general	ADJ
ejpam-3708	465	5	systems	system	NOUN
ejpam-3708	465	6	,	,	PUNCT
ejpam-3708	465	7	48(5):492–506	48(5):492–506	NOUN
ejpam-3708	465	8	,	,	PUNCT
ejpam-3708	465	9	2019	2019	NUM
ejpam-3708	465	10	.	.	PUNCT
ejpam-3708	466	1	[	[	X
ejpam-3708	466	2	22	22	NUM
ejpam-3708	466	3	]	]	X
ejpam-3708	466	4	s	s	VERB
ejpam-3708	466	5	a	a	DET
ejpam-3708	466	6	mohiuddine	mohiuddine	NOUN
ejpam-3708	466	7	and	and	CCONJ
ejpam-3708	466	8	b	b	NOUN
ejpam-3708	466	9	hazarika	hazarika	NOUN
ejpam-3708	466	10	.	.	PUNCT
ejpam-3708	467	1	some	some	DET
ejpam-3708	467	2	classes	class	NOUN
ejpam-3708	467	3	of	of	ADP
ejpam-3708	467	4	ideal	ideal	ADJ
ejpam-3708	467	5	convergent	convergent	NOUN
ejpam-3708	467	6	sequences	sequence	NOUN
ejpam-3708	467	7	and	and	CCONJ
ejpam-3708	467	8	generalized	generalized	ADJ
ejpam-3708	467	9	difference	difference	NOUN
ejpam-3708	467	10	matrix	matrix	NOUN
ejpam-3708	467	11	operator	operator	NOUN
ejpam-3708	467	12	.	.	PUNCT
ejpam-3708	468	1	filomat	filomat	PROPN
ejpam-3708	468	2	,	,	PUNCT
ejpam-3708	468	3	31(6):1827–1834	31(6):1827–1834	NUM
ejpam-3708	468	4	,	,	PUNCT
ejpam-3708	468	5	2017	2017	NUM
ejpam-3708	468	6	.	.	PUNCT
ejpam-3708	469	1	[	[	X
ejpam-3708	469	2	23	23	NUM
ejpam-3708	469	3	]	]	X
ejpam-3708	469	4	s	s	VERB
ejpam-3708	469	5	a	a	DET
ejpam-3708	469	6	mohiuddine	mohiuddine	NOUN
ejpam-3708	469	7	,	,	PUNCT
ejpam-3708	469	8	b	b	NOUN
ejpam-3708	469	9	hazarika	hazarika	NOUN
ejpam-3708	469	10	,	,	PUNCT
ejpam-3708	469	11	and	and	CCONJ
ejpam-3708	469	12	m	m	VERB
ejpam-3708	469	13	a	a	DET
ejpam-3708	469	14	alghamdi	alghamdi	NOUN
ejpam-3708	469	15	.	.	PUNCT
ejpam-3708	470	1	ideal	ideal	ADJ
ejpam-3708	470	2	relatively	relatively	ADV
ejpam-3708	470	3	uniform	uniform	ADJ
ejpam-3708	470	4	convergence	convergence	NOUN
ejpam-3708	470	5	with	with	ADP
ejpam-3708	470	6	korovkin	korovkin	NOUN
ejpam-3708	470	7	and	and	CCONJ
ejpam-3708	470	8	voronovskaya	voronovskaya	NOUN
ejpam-3708	470	9	types	type	NOUN
ejpam-3708	470	10	approximation	approximation	NOUN
ejpam-3708	470	11	theorems	theorem	NOUN
ejpam-3708	470	12	.	.	PUNCT
ejpam-3708	471	1	filomat	filomat	NOUN
ejpam-3708	471	2	,	,	PUNCT
ejpam-3708	471	3	33(14):4549–4560	33(14):4549–4560	PROPN
ejpam-3708	471	4	,	,	PUNCT
ejpam-3708	471	5	2019	2019	NUM
ejpam-3708	471	6	.	.	PUNCT
ejpam-3708	472	1	[	[	X
ejpam-3708	472	2	24	24	NUM
ejpam-3708	472	3	]	]	X
ejpam-3708	472	4	m	m	VERB
ejpam-3708	472	5	mursaleen	mursaleen	ADJ
ejpam-3708	472	6	and	and	CCONJ
ejpam-3708	472	7	m	m	PROPN
ejpam-3708	472	8	başarir	başarir	NOUN
ejpam-3708	472	9	.	.	PUNCT
ejpam-3708	473	1	on	on	ADP
ejpam-3708	473	2	some	some	DET
ejpam-3708	473	3	new	new	ADJ
ejpam-3708	473	4	sequence	sequence	NOUN
ejpam-3708	473	5	spaces	space	NOUN
ejpam-3708	473	6	of	of	ADP
ejpam-3708	473	7	fuzzy	fuzzy	ADJ
ejpam-3708	473	8	numbers	number	NOUN
ejpam-3708	473	9	.	.	PUNCT
ejpam-3708	474	1	indian	indian	ADJ
ejpam-3708	474	2	journal	journal	PROPN
ejpam-3708	474	3	of	of	ADP
ejpam-3708	474	4	pure	pure	ADJ
ejpam-3708	474	5	and	and	CCONJ
ejpam-3708	474	6	applied	applied	ADJ
ejpam-3708	474	7	mathematics	mathematic	NOUN
ejpam-3708	474	8	,	,	PUNCT
ejpam-3708	474	9	34(9):1351–1357	34(9):1351–1357	NUM
ejpam-3708	474	10	,	,	PUNCT
ejpam-3708	474	11	2003	2003	NUM
ejpam-3708	474	12	.	.	PUNCT
ejpam-3708	475	1	[	[	X
ejpam-3708	475	2	25	25	NUM
ejpam-3708	475	3	]	]	X
ejpam-3708	475	4	m	m	VERB
ejpam-3708	475	5	mursaleen	mursaleen	ADJ
ejpam-3708	475	6	and	and	CCONJ
ejpam-3708	475	7	s	s	VERB
ejpam-3708	475	8	a	a	DET
ejpam-3708	475	9	mohiuddine	mohiuddine	NOUN
ejpam-3708	475	10	.	.	PUNCT
ejpam-3708	476	1	on	on	ADP
ejpam-3708	476	2	lacunary	lacunary	ADJ
ejpam-3708	476	3	statistical	statistical	ADJ
ejpam-3708	476	4	convergence	convergence	NOUN
ejpam-3708	476	5	with	with	ADP
ejpam-3708	476	6	respect	respect	NOUN
ejpam-3708	476	7	to	to	ADP
ejpam-3708	476	8	the	the	DET
ejpam-3708	476	9	intuitionistic	intuitionistic	ADJ
ejpam-3708	476	10	fuzzy	fuzzy	ADJ
ejpam-3708	476	11	normed	normed	ADJ
ejpam-3708	476	12	space	space	NOUN
ejpam-3708	476	13	.	.	PUNCT
ejpam-3708	477	1	journal	journal	PROPN
ejpam-3708	477	2	of	of	ADP
ejpam-3708	477	3	computational	computational	ADJ
ejpam-3708	477	4	and	and	CCONJ
ejpam-3708	477	5	applied	applied	ADJ
ejpam-3708	477	6	mathematics	mathematic	NOUN
ejpam-3708	477	7	,	,	PUNCT
ejpam-3708	477	8	233(2):142–149	233(2):142–149	NUM
ejpam-3708	477	9	,	,	PUNCT
ejpam-3708	477	10	2009	2009	NUM
ejpam-3708	477	11	.	.	PUNCT
ejpam-3708	478	1	[	[	X
ejpam-3708	478	2	26	26	NUM
ejpam-3708	478	3	]	]	X
ejpam-3708	478	4	m	m	VERB
ejpam-3708	478	5	mursaleen	mursaleen	ADJ
ejpam-3708	478	6	and	and	CCONJ
ejpam-3708	478	7	s	s	VERB
ejpam-3708	478	8	a	a	DET
ejpam-3708	478	9	mohiuddine	mohiuddine	NOUN
ejpam-3708	478	10	.	.	PUNCT
ejpam-3708	479	1	on	on	ADP
ejpam-3708	479	2	ideal	ideal	ADJ
ejpam-3708	479	3	convergence	convergence	NOUN
ejpam-3708	479	4	in	in	ADP
ejpam-3708	479	5	probabilistic	probabilistic	ADJ
ejpam-3708	479	6	normed	normed	ADJ
ejpam-3708	479	7	spaces	space	NOUN
ejpam-3708	479	8	.	.	PUNCT
ejpam-3708	480	1	mathematica	mathematica	PROPN
ejpam-3708	480	2	slovaca	slovaca	PROPN
ejpam-3708	480	3	,	,	PUNCT
ejpam-3708	480	4	62(1):49–62	62(1):49–62	NUM
ejpam-3708	480	5	,	,	PUNCT
ejpam-3708	480	6	2012	2012	NUM
ejpam-3708	480	7	.	.	PUNCT
ejpam-3708	481	1	[	[	X
ejpam-3708	481	2	27	27	NUM
ejpam-3708	481	3	]	]	X
ejpam-3708	481	4	h	h	PROPN
ejpam-3708	481	5	nakano	nakano	PROPN
ejpam-3708	481	6	.	.	PUNCT
ejpam-3708	482	1	concave	concave	PROPN
ejpam-3708	482	2	modulars	modular	NOUN
ejpam-3708	482	3	.	.	PUNCT
ejpam-3708	483	1	journal	journal	NOUN
ejpam-3708	483	2	of	of	ADP
ejpam-3708	483	3	the	the	DET
ejpam-3708	483	4	mathematical	mathematical	ADJ
ejpam-3708	483	5	society	society	NOUN
ejpam-3708	483	6	of	of	ADP
ejpam-3708	483	7	japan	japan	PROPN
ejpam-3708	483	8	,	,	PUNCT
ejpam-3708	483	9	5(1):29	5(1):29	NUM
ejpam-3708	483	10	–	–	PUNCT
ejpam-3708	483	11	49	49	NUM
ejpam-3708	483	12	,	,	PUNCT
ejpam-3708	483	13	1953	1953	NUM
ejpam-3708	483	14	.	.	PUNCT
ejpam-3708	484	1	[	[	X
ejpam-3708	484	2	28	28	NUM
ejpam-3708	484	3	]	]	X
ejpam-3708	484	4	s	s	VERB
ejpam-3708	484	5	nanda	nanda	ADJ
ejpam-3708	484	6	.	.	PUNCT
ejpam-3708	485	1	on	on	ADP
ejpam-3708	485	2	sequences	sequence	NOUN
ejpam-3708	485	3	of	of	ADP
ejpam-3708	485	4	fuzzy	fuzzy	ADJ
ejpam-3708	485	5	numbers	number	NOUN
ejpam-3708	485	6	.	.	PUNCT
ejpam-3708	486	1	fuzzy	fuzzy	ADJ
ejpam-3708	486	2	sets	set	NOUN
ejpam-3708	486	3	and	and	CCONJ
ejpam-3708	486	4	systems	system	NOUN
ejpam-3708	486	5	,	,	PUNCT
ejpam-3708	486	6	33:123–126	33:123–126	PROPN
ejpam-3708	486	7	,	,	PUNCT
ejpam-3708	486	8	1989	1989	NUM
ejpam-3708	486	9	.	.	PUNCT
ejpam-3708	487	1	[	[	X
ejpam-3708	487	2	29	29	NUM
ejpam-3708	487	3	]	]	X
ejpam-3708	487	4	f	f	PROPN
ejpam-3708	487	5	nuray	nuray	PROPN
ejpam-3708	487	6	.	.	PUNCT
ejpam-3708	488	1	lacunary	lacunary	ADJ
ejpam-3708	488	2	statistical	statistical	ADJ
ejpam-3708	488	3	convergence	convergence	NOUN
ejpam-3708	488	4	of	of	ADP
ejpam-3708	488	5	sequences	sequence	NOUN
ejpam-3708	488	6	of	of	ADP
ejpam-3708	488	7	fuzzy	fuzzy	ADJ
ejpam-3708	488	8	numbers	number	NOUN
ejpam-3708	488	9	.	.	PUNCT
ejpam-3708	489	1	fuzzy	fuzzy	ADJ
ejpam-3708	489	2	sets	set	NOUN
ejpam-3708	489	3	and	and	CCONJ
ejpam-3708	489	4	systems	system	NOUN
ejpam-3708	489	5	,	,	PUNCT
ejpam-3708	489	6	99(3):353–355	99(3):353–355	NUM
ejpam-3708	489	7	,	,	PUNCT
ejpam-3708	489	8	1998	1998	NUM
ejpam-3708	489	9	.	.	PUNCT
ejpam-3708	490	1	[	[	X
ejpam-3708	490	2	30	30	NUM
ejpam-3708	490	3	]	]	X
ejpam-3708	490	4	f	f	PROPN
ejpam-3708	490	5	nuray	nuray	NOUN
ejpam-3708	490	6	and	and	CCONJ
ejpam-3708	490	7	e	e	NOUN
ejpam-3708	490	8	savaş.	savaş.	ADJ
ejpam-3708	490	9	statistical	statistical	ADJ
ejpam-3708	490	10	convergence	convergence	NOUN
ejpam-3708	490	11	of	of	ADP
ejpam-3708	490	12	sequences	sequence	NOUN
ejpam-3708	490	13	of	of	ADP
ejpam-3708	490	14	fuzzy	fuzzy	ADJ
ejpam-3708	490	15	numbers	number	NOUN
ejpam-3708	490	16	.	.	PUNCT
ejpam-3708	491	1	mathematica	mathematica	PROPN
ejpam-3708	491	2	slovaca	slovaca	PROPN
ejpam-3708	491	3	,	,	PUNCT
ejpam-3708	491	4	45:269–273	45:269–273	NUM
ejpam-3708	491	5	,	,	PUNCT
ejpam-3708	491	6	1995	1995	NUM
ejpam-3708	491	7	.	.	PUNCT
ejpam-3708	492	1	references	reference	NOUN
ejpam-3708	492	2	1148	1148	NUM
ejpam-3708	493	1	[	[	X
ejpam-3708	493	2	31	31	NUM
ejpam-3708	493	3	]	]	SYM
ejpam-3708	493	4	s	s	PROPN
ejpam-3708	493	5	d	d	X
ejpam-3708	493	6	parashar	parashar	PROPN
ejpam-3708	493	7	and	and	CCONJ
ejpam-3708	493	8	b	b	PROPN
ejpam-3708	493	9	choudhary	choudhary	PROPN
ejpam-3708	493	10	.	.	PUNCT
ejpam-3708	494	1	sequence	sequence	NOUN
ejpam-3708	494	2	spaces	space	NOUN
ejpam-3708	494	3	defined	define	VERB
ejpam-3708	494	4	by	by	ADP
ejpam-3708	494	5	orlicz	orlicz	ADJ
ejpam-3708	494	6	functions	function	NOUN
ejpam-3708	494	7	.	.	PUNCT
ejpam-3708	495	1	indian	indian	ADJ
ejpam-3708	495	2	journal	journal	PROPN
ejpam-3708	495	3	of	of	ADP
ejpam-3708	495	4	pure	pure	ADJ
ejpam-3708	495	5	and	and	CCONJ
ejpam-3708	495	6	applied	applied	ADJ
ejpam-3708	495	7	mathematics	mathematic	NOUN
ejpam-3708	495	8	,	,	PUNCT
ejpam-3708	495	9	25:419–419	25:419–419	PROPN
ejpam-3708	495	10	,	,	PUNCT
ejpam-3708	495	11	1994	1994	NUM
ejpam-3708	495	12	.	.	PUNCT
ejpam-3708	496	1	[	[	X
ejpam-3708	496	2	32	32	NUM
ejpam-3708	496	3	]	]	X
ejpam-3708	496	4	k	k	PROPN
ejpam-3708	496	5	raj	raj	PROPN
ejpam-3708	496	6	and	and	CCONJ
ejpam-3708	496	7	a	a	DET
ejpam-3708	496	8	kılıçman	kılıçman	NOUN
ejpam-3708	496	9	.	.	PUNCT
ejpam-3708	497	1	on	on	ADP
ejpam-3708	497	2	certain	certain	ADJ
ejpam-3708	497	3	generalized	generalized	ADJ
ejpam-3708	497	4	paranormed	paranorme	VERB
ejpam-3708	497	5	spaces	space	NOUN
ejpam-3708	497	6	.	.	PUNCT
ejpam-3708	498	1	journal	journal	PROPN
ejpam-3708	498	2	of	of	ADP
ejpam-3708	498	3	inequalities	inequality	NOUN
ejpam-3708	498	4	and	and	CCONJ
ejpam-3708	498	5	applications	application	NOUN
ejpam-3708	498	6	,	,	PUNCT
ejpam-3708	498	7	2015(1):1–12	2015(1):1–12	NOUN
ejpam-3708	498	8	,	,	PUNCT
ejpam-3708	498	9	2015	2015	NUM
ejpam-3708	498	10	.	.	PUNCT
ejpam-3708	499	1	[	[	X
ejpam-3708	499	2	33	33	NUM
ejpam-3708	499	3	]	]	PUNCT
ejpam-3708	499	4	w	w	PROPN
ejpam-3708	499	5	h	h	PROPN
ejpam-3708	499	6	ruckle	ruckle	NOUN
ejpam-3708	499	7	.	.	PUNCT
ejpam-3708	500	1	fk	fk	NOUN
ejpam-3708	500	2	-	-	NOUN
ejpam-3708	500	3	spaces	space	NOUN
ejpam-3708	500	4	in	in	ADP
ejpam-3708	500	5	which	which	PRON
ejpam-3708	500	6	the	the	DET
ejpam-3708	500	7	sequence	sequence	NOUN
ejpam-3708	500	8	of	of	ADP
ejpam-3708	500	9	coordinate	coordinate	NOUN
ejpam-3708	500	10	vectors	vector	NOUN
ejpam-3708	500	11	is	be	AUX
ejpam-3708	500	12	bounded	bound	VERB
ejpam-3708	500	13	.	.	PUNCT
ejpam-3708	501	1	canadian	canadian	ADJ
ejpam-3708	501	2	journal	journal	PROPN
ejpam-3708	501	3	of	of	ADP
ejpam-3708	501	4	mathematics	mathematic	NOUN
ejpam-3708	501	5	,	,	PUNCT
ejpam-3708	501	6	25(5):973–978	25(5):973–978	PROPN
ejpam-3708	501	7	,	,	PUNCT
ejpam-3708	501	8	1973	1973	NUM
ejpam-3708	501	9	.	.	PUNCT
ejpam-3708	502	1	[	[	X
ejpam-3708	502	2	34	34	NUM
ejpam-3708	502	3	]	]	X
ejpam-3708	502	4	e	e	NOUN
ejpam-3708	502	5	savaş.	savaş.	VERB
ejpam-3708	502	6	some	some	DET
ejpam-3708	502	7	i−convergent	i−convergent	NUM
ejpam-3708	502	8	sequence	sequence	NOUN
ejpam-3708	502	9	spaces	space	NOUN
ejpam-3708	502	10	of	of	ADP
ejpam-3708	502	11	fuzzy	fuzzy	ADJ
ejpam-3708	502	12	numbers	number	NOUN
ejpam-3708	502	13	defined	define	VERB
ejpam-3708	502	14	by	by	ADP
ejpam-3708	502	15	infinite	infinite	ADJ
ejpam-3708	502	16	matrix	matrix	NOUN
ejpam-3708	502	17	.	.	PUNCT
ejpam-3708	503	1	mathematical	mathematical	ADJ
ejpam-3708	503	2	and	and	CCONJ
ejpam-3708	503	3	computational	computational	ADJ
ejpam-3708	503	4	applications	application	NOUN
ejpam-3708	503	5	,	,	PUNCT
ejpam-3708	503	6	18(2):84–93	18(2):84–93	NUM
ejpam-3708	503	7	,	,	PUNCT
ejpam-3708	503	8	2013	2013	NUM
ejpam-3708	503	9	.	.	PUNCT
ejpam-3708	504	1	[	[	X
ejpam-3708	504	2	35	35	NUM
ejpam-3708	504	3	]	]	X
ejpam-3708	504	4	e	e	X
ejpam-3708	504	5	savaş	savaş	NOUN
ejpam-3708	504	6	and	and	CCONJ
ejpam-3708	504	7	m	m	PROPN
ejpam-3708	504	8	mursaleen	mursaleen	PROPN
ejpam-3708	504	9	.	.	PUNCT
ejpam-3708	505	1	matrix	matrix	NOUN
ejpam-3708	505	2	transformations	transformation	NOUN
ejpam-3708	505	3	in	in	ADP
ejpam-3708	505	4	some	some	DET
ejpam-3708	505	5	sequence	sequence	NOUN
ejpam-3708	505	6	spaces	space	NOUN
ejpam-3708	505	7	.	.	PUNCT
ejpam-3708	506	1	i̇stanbul	i̇stanbul	PROPN
ejpam-3708	506	2	üniversitesi	üniversitesi	PROPN
ejpam-3708	506	3	fen	fen	PROPN
ejpam-3708	506	4	fakültesi	fakültesi	SYM
ejpam-3708	506	5	matematik	matematik	PROPN
ejpam-3708	506	6	dergisi	dergisi	PROPN
ejpam-3708	506	7	,	,	PUNCT
ejpam-3708	506	8	52:1–5	52:1–5	NUM
ejpam-3708	506	9	,	,	PUNCT
ejpam-3708	506	10	1993	1993	NUM
ejpam-3708	506	11	.	.	PUNCT
ejpam-3708	507	1	[	[	X
ejpam-3708	507	2	36	36	NUM
ejpam-3708	507	3	]	]	SYM
ejpam-3708	507	4	b	b	PROPN
ejpam-3708	507	5	c	c	NOUN
ejpam-3708	507	6	tripathy	tripathy	NOUN
ejpam-3708	507	7	and	and	CCONJ
ejpam-3708	507	8	a	a	DET
ejpam-3708	507	9	baruah	baruah	NOUN
ejpam-3708	507	10	.	.	PUNCT
ejpam-3708	508	1	lacunary	lacunary	ADJ
ejpam-3708	508	2	statically	statically	ADV
ejpam-3708	508	3	convergent	convergent	NOUN
ejpam-3708	508	4	and	and	CCONJ
ejpam-3708	508	5	lacunary	lacunary	ADJ
ejpam-3708	508	6	strongly	strongly	ADV
ejpam-3708	508	7	convergent	convergent	ADJ
ejpam-3708	508	8	generalized	generalized	ADJ
ejpam-3708	508	9	difference	difference	NOUN
ejpam-3708	508	10	sequences	sequence	NOUN
ejpam-3708	508	11	of	of	ADP
ejpam-3708	508	12	fuzzy	fuzzy	ADJ
ejpam-3708	508	13	real	real	ADJ
ejpam-3708	508	14	numbers	number	NOUN
ejpam-3708	508	15	.	.	PUNCT
ejpam-3708	509	1	kyungpook	kyungpook	PROPN
ejpam-3708	509	2	mathematical	mathematical	PROPN
ejpam-3708	509	3	journal	journal	NOUN
ejpam-3708	509	4	,	,	PUNCT
ejpam-3708	509	5	50:565–574	50:565–574	NUM
ejpam-3708	509	6	,	,	PUNCT
ejpam-3708	509	7	2010	2010	NUM
ejpam-3708	509	8	.	.	PUNCT
ejpam-3708	510	1	[	[	X
ejpam-3708	510	2	37	37	NUM
ejpam-3708	510	3	]	]	SYM
ejpam-3708	510	4	b	b	PROPN
ejpam-3708	510	5	c	c	NOUN
ejpam-3708	510	6	tripathy	tripathy	PROPN
ejpam-3708	510	7	and	and	CCONJ
ejpam-3708	510	8	a	a	DET
ejpam-3708	510	9	j	j	PROPN
ejpam-3708	510	10	dutta	dutta	PROPN
ejpam-3708	510	11	.	.	PUNCT
ejpam-3708	511	1	lacunary	lacunary	ADJ
ejpam-3708	511	2	i−convergent	i−convergent	NUM
ejpam-3708	511	3	sequences	sequence	NOUN
ejpam-3708	511	4	of	of	ADP
ejpam-3708	511	5	fuzzy	fuzzy	ADJ
ejpam-3708	511	6	real	real	ADJ
ejpam-3708	511	7	numbers	number	NOUN
ejpam-3708	511	8	.	.	PUNCT
ejpam-3708	512	1	proyecciones	proyeccione	NOUN
ejpam-3708	512	2	(	(	PUNCT
ejpam-3708	512	3	antofagasta	antofagasta	PROPN
ejpam-3708	512	4	)	)	PUNCT
ejpam-3708	512	5	,	,	PUNCT
ejpam-3708	512	6	34(3):205–218	34(3):205–218	NOUN
ejpam-3708	512	7	,	,	PUNCT
ejpam-3708	512	8	2015	2015	NUM
ejpam-3708	512	9	.	.	PUNCT
ejpam-3708	513	1	[	[	X
ejpam-3708	513	2	38	38	NUM
ejpam-3708	513	3	]	]	SYM
ejpam-3708	513	4	b	b	PROPN
ejpam-3708	513	5	c	c	X
ejpam-3708	513	6	tripathy	tripathy	NOUN
ejpam-3708	513	7	and	and	CCONJ
ejpam-3708	513	8	h	h	PROPN
ejpam-3708	513	9	dutta	dutta	PROPN
ejpam-3708	513	10	.	.	PUNCT
ejpam-3708	514	1	on	on	ADP
ejpam-3708	514	2	some	some	DET
ejpam-3708	514	3	lacunary	lacunary	ADJ
ejpam-3708	514	4	difference	difference	NOUN
ejpam-3708	514	5	sequence	sequence	NOUN
ejpam-3708	514	6	spaces	space	NOUN
ejpam-3708	514	7	defined	define	VERB
ejpam-3708	514	8	by	by	ADP
ejpam-3708	514	9	a	a	DET
ejpam-3708	514	10	sequence	sequence	NOUN
ejpam-3708	514	11	of	of	ADP
ejpam-3708	514	12	orlicz	orlicz	ADJ
ejpam-3708	514	13	functions	function	NOUN
ejpam-3708	514	14	and	and	CCONJ
ejpam-3708	514	15	q−lacunary	q−lacunary	NOUN
ejpam-3708	514	16	∆n	∆n	PROPN
ejpam-3708	514	17	m−statistical	m−statistical	ADJ
ejpam-3708	514	18	convergence	convergence	NOUN
ejpam-3708	514	19	.	.	PUNCT
ejpam-3708	515	1	analele	analele	PROPN
ejpam-3708	515	2	universitatii	universitatii	PROPN
ejpam-3708	515	3	ovidius	ovidius	PROPN
ejpam-3708	515	4	,	,	PUNCT
ejpam-3708	515	5	constanta	constanta	PROPN
ejpam-3708	515	6	-	-	PUNCT
ejpam-3708	515	7	seria	seria	PROPN
ejpam-3708	515	8	matematica	matematica	PROPN
ejpam-3708	515	9	,	,	PUNCT
ejpam-3708	515	10	20(1):417–430	20(1):417–430	PROPN
ejpam-3708	515	11	,	,	PUNCT
ejpam-3708	515	12	2012	2012	NUM
ejpam-3708	515	13	.	.	PUNCT
ejpam-3708	516	1	[	[	X
ejpam-3708	516	2	39	39	NUM
ejpam-3708	516	3	]	]	SYM
ejpam-3708	516	4	b	b	PROPN
ejpam-3708	516	5	c	c	NOUN
ejpam-3708	516	6	tripathy	tripathy	PROPN
ejpam-3708	516	7	and	and	CCONJ
ejpam-3708	516	8	a	a	DET
ejpam-3708	516	9	esi	esi	PROPN
ejpam-3708	516	10	.	.	PUNCT
ejpam-3708	517	1	a	a	DET
ejpam-3708	517	2	new	new	ADJ
ejpam-3708	517	3	type	type	NOUN
ejpam-3708	517	4	of	of	ADP
ejpam-3708	517	5	difference	difference	NOUN
ejpam-3708	517	6	sequence	sequence	NOUN
ejpam-3708	517	7	spaces	space	VERB
ejpam-3708	517	8	.	.	PUNCT
ejpam-3708	518	1	international	international	ADJ
ejpam-3708	518	2	journal	journal	PROPN
ejpam-3708	518	3	of	of	ADP
ejpam-3708	518	4	science	science	NOUN
ejpam-3708	518	5	and	and	CCONJ
ejpam-3708	518	6	technology	technology	NOUN
ejpam-3708	518	7	,	,	PUNCT
ejpam-3708	518	8	1(1):11–14	1(1):11–14	NUM
ejpam-3708	518	9	,	,	PUNCT
ejpam-3708	518	10	2006	2006	NUM
ejpam-3708	518	11	.	.	PUNCT
ejpam-3708	519	1	[	[	X
ejpam-3708	519	2	40	40	NUM
ejpam-3708	519	3	]	]	SYM
ejpam-3708	519	4	b	b	PROPN
ejpam-3708	519	5	c	c	X
ejpam-3708	519	6	tripathy	tripathy	PROPN
ejpam-3708	519	7	,	,	PUNCT
ejpam-3708	519	8	a	a	DET
ejpam-3708	519	9	esi	esi	NOUN
ejpam-3708	519	10	,	,	PUNCT
ejpam-3708	519	11	and	and	CCONJ
ejpam-3708	519	12	b	b	NOUN
ejpam-3708	519	13	tripathy	tripathy	ADJ
ejpam-3708	519	14	.	.	PUNCT
ejpam-3708	520	1	on	on	ADP
ejpam-3708	520	2	new	new	ADJ
ejpam-3708	520	3	types	type	NOUN
ejpam-3708	520	4	of	of	ADP
ejpam-3708	520	5	generalized	generalized	ADJ
ejpam-3708	520	6	difference	difference	NOUN
ejpam-3708	520	7	cesàro	cesàro	NOUN
ejpam-3708	520	8	sequence	sequence	NOUN
ejpam-3708	520	9	spaces	space	VERB
ejpam-3708	520	10	.	.	PUNCT
ejpam-3708	521	1	soochow	soochow	PROPN
ejpam-3708	521	2	journal	journal	PROPN
ejpam-3708	521	3	of	of	ADP
ejpam-3708	521	4	mathematics	mathematic	NOUN
ejpam-3708	521	5	,	,	PUNCT
ejpam-3708	521	6	31(3):333	31(3):333	NUM
ejpam-3708	521	7	,	,	PUNCT
ejpam-3708	521	8	2005	2005	NUM
ejpam-3708	521	9	.	.	PUNCT
ejpam-3708	522	1	[	[	X
ejpam-3708	522	2	41	41	NUM
ejpam-3708	522	3	]	]	X
ejpam-3708	522	4	b	b	NOUN
ejpam-3708	522	5	c	c	X
ejpam-3708	522	6	tripathy	tripathy	NOUN
ejpam-3708	522	7	and	and	CCONJ
ejpam-3708	522	8	s	s	VERB
ejpam-3708	522	9	mahanta	mahanta	ADJ
ejpam-3708	522	10	.	.	PUNCT
ejpam-3708	523	1	on	on	ADP
ejpam-3708	523	2	a	a	DET
ejpam-3708	523	3	class	class	NOUN
ejpam-3708	523	4	of	of	ADP
ejpam-3708	523	5	generalized	generalized	ADJ
ejpam-3708	523	6	lacunary	lacunary	ADJ
ejpam-3708	523	7	difference	difference	NOUN
ejpam-3708	523	8	sequence	sequence	NOUN
ejpam-3708	523	9	spaces	space	NOUN
ejpam-3708	523	10	defined	define	VERB
ejpam-3708	523	11	by	by	ADP
ejpam-3708	523	12	orlicz	orlicz	ADJ
ejpam-3708	523	13	functions	function	NOUN
ejpam-3708	523	14	.	.	PUNCT
ejpam-3708	524	1	acta	acta	PROPN
ejpam-3708	524	2	mathematicae	mathematicae	PROPN
ejpam-3708	524	3	applicatae	applicatae	PROPN
ejpam-3708	524	4	sinica	sinica	PROPN
ejpam-3708	524	5	,	,	PUNCT
ejpam-3708	524	6	english	english	ADJ
ejpam-3708	524	7	series	series	NOUN
ejpam-3708	524	8	,	,	PUNCT
ejpam-3708	524	9	20(2):231–238	20(2):231–238	PROPN
ejpam-3708	524	10	,	,	PUNCT
ejpam-3708	524	11	2004	2004	NUM
ejpam-3708	524	12	.	.	PUNCT
ejpam-3708	525	1	[	[	X
ejpam-3708	525	2	42	42	NUM
ejpam-3708	525	3	]	]	X
ejpam-3708	525	4	l	l	NOUN
ejpam-3708	525	5	a	a	DET
ejpam-3708	525	6	zadeh	zadeh	PROPN
ejpam-3708	525	7	.	.	PUNCT
ejpam-3708	525	8	fuzzy	fuzzy	ADJ
ejpam-3708	525	9	sets	set	NOUN
ejpam-3708	525	10	.	.	PUNCT
ejpam-3708	526	1	information	information	NOUN
ejpam-3708	526	2	and	and	CCONJ
ejpam-3708	526	3	control	control	NOUN
ejpam-3708	526	4	,	,	PUNCT
ejpam-3708	526	5	8:338353	8:338353	NUM
ejpam-3708	526	6	,	,	PUNCT
ejpam-3708	526	7	1965	1965	NUM
ejpam-3708	526	8	.	.	PUNCT