id	sid	tid	token	lemma	pos
ejpam-3573	1	1	european	european	PROPN
ejpam-3573	1	2	journal	journal	PROPN
ejpam-3573	1	3	of	of	ADP
ejpam-3573	1	4	pure	pure	ADJ
ejpam-3573	1	5	and	and	CCONJ
ejpam-3573	1	6	applied	apply	VERB
ejpam-3573	1	7	mathematics	mathematic	NOUN
ejpam-3573	1	8	vol	vol	NOUN
ejpam-3573	1	9	.	.	PROPN
ejpam-3573	2	1	12	12	NUM
ejpam-3573	2	2	,	,	PUNCT
ejpam-3573	2	3	no	no	INTJ
ejpam-3573	2	4	.	.	NOUN
ejpam-3573	2	5	4	4	NUM
ejpam-3573	2	6	,	,	PUNCT
ejpam-3573	2	7	2019	2019	NUM
ejpam-3573	2	8	,	,	PUNCT
ejpam-3573	2	9	1689	1689	NUM
ejpam-3573	2	10	-	-	SYM
ejpam-3573	2	11	1700	1700	NUM
ejpam-3573	2	12	issn	issn	PROPN
ejpam-3573	2	13	1307	1307	NUM
ejpam-3573	2	14	-	-	SYM
ejpam-3573	2	15	5543	5543	NUM
ejpam-3573	2	16	–	–	PUNCT
ejpam-3573	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3573	2	18	published	publish	VERB
ejpam-3573	2	19	by	by	ADP
ejpam-3573	2	20	new	new	PROPN
ejpam-3573	2	21	york	york	PROPN
ejpam-3573	2	22	business	business	PROPN
ejpam-3573	2	23	global	global	ADJ
ejpam-3573	2	24	sensitivity	sensitivity	NOUN
ejpam-3573	2	25	of	of	ADP
ejpam-3573	2	26	fuzzy	fuzzy	ADJ
ejpam-3573	2	27	nonautonomous	nonautonomous	ADJ
ejpam-3573	2	28	dynamical	dynamical	ADJ
ejpam-3573	2	29	systems	system	NOUN
ejpam-3573	2	30	yaoyao	yaoyao	PROPN
ejpam-3573	2	31	lan	lan	PROPN
ejpam-3573	2	32	department	department	PROPN
ejpam-3573	2	33	of	of	ADP
ejpam-3573	2	34	mathematics	mathematics	PROPN
ejpam-3573	2	35	,	,	PUNCT
ejpam-3573	2	36	chongqing	chongqing	PROPN
ejpam-3573	2	37	university	university	PROPN
ejpam-3573	2	38	of	of	ADP
ejpam-3573	2	39	arts	art	NOUN
ejpam-3573	2	40	and	and	CCONJ
ejpam-3573	2	41	sciences	sciences	PROPN
ejpam-3573	2	42	,	,	PUNCT
ejpam-3573	2	43	yongchuan	yongchuan	PROPN
ejpam-3573	2	44	,	,	PUNCT
ejpam-3573	2	45	china	china	PROPN
ejpam-3573	2	46	abstract	abstract	PROPN
ejpam-3573	2	47	.	.	PUNCT
ejpam-3573	3	1	this	this	DET
ejpam-3573	3	2	paper	paper	NOUN
ejpam-3573	3	3	is	be	AUX
ejpam-3573	3	4	devoted	devote	VERB
ejpam-3573	3	5	to	to	ADP
ejpam-3573	3	6	a	a	DET
ejpam-3573	3	7	study	study	NOUN
ejpam-3573	3	8	of	of	ADP
ejpam-3573	3	9	relations	relation	NOUN
ejpam-3573	3	10	between	between	ADP
ejpam-3573	3	11	two	two	NUM
ejpam-3573	3	12	forms	form	NOUN
ejpam-3573	3	13	of	of	ADP
ejpam-3573	3	14	sensitivity	sensitivity	NOUN
ejpam-3573	3	15	of	of	ADP
ejpam-3573	3	16	nonautonomous	nonautonomous	ADJ
ejpam-3573	3	17	dynamical	dynamical	ADJ
ejpam-3573	3	18	system	system	NOUN
ejpam-3573	3	19	and	and	CCONJ
ejpam-3573	3	20	its	its	PRON
ejpam-3573	3	21	induced	induced	ADJ
ejpam-3573	3	22	fuzzy	fuzzy	ADJ
ejpam-3573	3	23	systems	system	NOUN
ejpam-3573	3	24	.	.	PUNCT
ejpam-3573	4	1	more	more	ADV
ejpam-3573	4	2	specially	specially	ADV
ejpam-3573	4	3	,	,	PUNCT
ejpam-3573	4	4	we	we	PRON
ejpam-3573	4	5	study	study	VERB
ejpam-3573	4	6	strong	strong	ADJ
ejpam-3573	4	7	sensitivity	sensitivity	NOUN
ejpam-3573	4	8	and	and	CCONJ
ejpam-3573	4	9	mean	mean	VERB
ejpam-3573	4	10	sensitivity	sensitivity	NOUN
ejpam-3573	4	11	in	in	ADP
ejpam-3573	4	12	an	an	DET
ejpam-3573	4	13	original	original	ADJ
ejpam-3573	4	14	nonautonomous	nonautonomous	ADJ
ejpam-3573	4	15	system	system	NOUN
ejpam-3573	4	16	and	and	CCONJ
ejpam-3573	4	17	its	its	PRON
ejpam-3573	4	18	connections	connection	NOUN
ejpam-3573	4	19	with	with	ADP
ejpam-3573	4	20	the	the	DET
ejpam-3573	4	21	same	same	ADJ
ejpam-3573	4	22	ones	one	NOUN
ejpam-3573	4	23	in	in	ADP
ejpam-3573	4	24	its	its	PRON
ejpam-3573	4	25	induced	induced	ADJ
ejpam-3573	4	26	systems	system	NOUN
ejpam-3573	4	27	,	,	PUNCT
ejpam-3573	4	28	including	include	VERB
ejpam-3573	4	29	set	set	NOUN
ejpam-3573	4	30	-	-	PUNCT
ejpam-3573	4	31	valued	value	VERB
ejpam-3573	4	32	system	system	NOUN
ejpam-3573	4	33	and	and	CCONJ
ejpam-3573	4	34	fuzzified	fuzzified	ADJ
ejpam-3573	4	35	system	system	NOUN
ejpam-3573	4	36	.	.	PUNCT
ejpam-3573	5	1	2010	2010	NUM
ejpam-3573	5	2	mathematics	mathematic	NOUN
ejpam-3573	5	3	subject	subject	NOUN
ejpam-3573	5	4	classifications	classification	NOUN
ejpam-3573	5	5	:	:	PUNCT
ejpam-3573	5	6	03e72	03e72	NUM
ejpam-3573	5	7	,	,	PUNCT
ejpam-3573	5	8	37b55	37b55	NUM
ejpam-3573	5	9	key	key	ADJ
ejpam-3573	5	10	words	word	NOUN
ejpam-3573	5	11	and	and	CCONJ
ejpam-3573	5	12	phrases	phrase	NOUN
ejpam-3573	5	13	:	:	PUNCT
ejpam-3573	5	14	nonautonomous	nonautonomous	ADJ
ejpam-3573	5	15	,	,	PUNCT
ejpam-3573	5	16	dynamical	dynamical	ADJ
ejpam-3573	5	17	systems	system	NOUN
ejpam-3573	5	18	,	,	PUNCT
ejpam-3573	5	19	fuzzy	fuzzy	ADJ
ejpam-3573	5	20	,	,	PUNCT
ejpam-3573	5	21	strong	strong	ADJ
ejpam-3573	5	22	sensitivity	sensitivity	NOUN
ejpam-3573	5	23	,	,	PUNCT
ejpam-3573	5	24	mean	mean	VERB
ejpam-3573	5	25	sensitivity	sensitivity	NOUN
ejpam-3573	5	26	1	1	NUM
ejpam-3573	5	27	.	.	PUNCT
ejpam-3573	6	1	introduction	introduction	NOUN
ejpam-3573	6	2	let	let	VERB
ejpam-3573	6	3	fn	fn	VERB
ejpam-3573	6	4	:	:	PUNCT
ejpam-3573	6	5	x	x	SYM
ejpam-3573	6	6	→	→	PUNCT
ejpam-3573	6	7	x	x	PUNCT
ejpam-3573	6	8	be	be	AUX
ejpam-3573	6	9	a	a	DET
ejpam-3573	6	10	sequence	sequence	NOUN
ejpam-3573	6	11	of	of	ADP
ejpam-3573	6	12	continuous	continuous	ADJ
ejpam-3573	6	13	maps	map	NOUN
ejpam-3573	6	14	acting	act	VERB
ejpam-3573	6	15	on	on	ADP
ejpam-3573	6	16	a	a	DET
ejpam-3573	6	17	compact	compact	ADJ
ejpam-3573	6	18	metric	metric	ADJ
ejpam-3573	6	19	space	space	NOUN
ejpam-3573	6	20	(	(	PUNCT
ejpam-3573	6	21	x	x	X
ejpam-3573	6	22	,	,	PUNCT
ejpam-3573	6	23	d	d	NOUN
ejpam-3573	6	24	)	)	PUNCT
ejpam-3573	6	25	.	.	PUNCT
ejpam-3573	7	1	a	a	DET
ejpam-3573	7	2	nonautonomous	nonautonomous	ADJ
ejpam-3573	7	3	discrete	discrete	ADJ
ejpam-3573	7	4	dynamical	dynamical	ADJ
ejpam-3573	7	5	systems	system	NOUN
ejpam-3573	7	6	is	be	AUX
ejpam-3573	7	7	a	a	DET
ejpam-3573	7	8	pair	pair	NOUN
ejpam-3573	7	9	(	(	PUNCT
ejpam-3573	7	10	x	x	X
ejpam-3573	7	11	,	,	PUNCT
ejpam-3573	7	12	{	{	PUNCT
ejpam-3573	7	13	fn}∞n=1	fn}∞n=1	X
ejpam-3573	7	14	)	)	PUNCT
ejpam-3573	7	15	defined	define	VERB
ejpam-3573	7	16	by	by	ADP
ejpam-3573	7	17	:	:	PUNCT
ejpam-3573	7	18	xn+1	xn+1	PROPN
ejpam-3573	7	19	=	=	SYM
ejpam-3573	7	20	fn(xn	fn(xn	PROPN
ejpam-3573	7	21	)	)	PUNCT
ejpam-3573	7	22	,	,	PUNCT
ejpam-3573	7	23	n	n	X
ejpam-3573	7	24	≥	≥	NOUN
ejpam-3573	7	25	1	1	NUM
ejpam-3573	7	26	,	,	PUNCT
ejpam-3573	7	27	(	(	PUNCT
ejpam-3573	7	28	1	1	X
ejpam-3573	7	29	)	)	PUNCT
ejpam-3573	7	30	note	note	NOUN
ejpam-3573	7	31	that	that	SCONJ
ejpam-3573	7	32	the	the	DET
ejpam-3573	7	33	autonomous	autonomous	ADJ
ejpam-3573	7	34	dynamical	dynamical	ADJ
ejpam-3573	7	35	system	system	NOUN
ejpam-3573	7	36	is	be	AUX
ejpam-3573	7	37	a	a	DET
ejpam-3573	7	38	special	special	ADJ
ejpam-3573	7	39	case	case	NOUN
ejpam-3573	7	40	of	of	ADP
ejpam-3573	7	41	system	system	NOUN
ejpam-3573	7	42	(	(	PUNCT
ejpam-3573	7	43	1	1	X
ejpam-3573	7	44	)	)	PUNCT
ejpam-3573	7	45	when	when	SCONJ
ejpam-3573	7	46	fn	fn	NOUN
ejpam-3573	7	47	=	=	SYM
ejpam-3573	7	48	f	f	PROPN
ejpam-3573	7	49	for	for	ADP
ejpam-3573	7	50	all	all	DET
ejpam-3573	7	51	n	n	PRON
ejpam-3573	7	52	≥	≥	NOUN
ejpam-3573	7	53	1	1	NUM
ejpam-3573	7	54	.	.	PUNCT
ejpam-3573	8	1	for	for	ADP
ejpam-3573	8	2	other	other	ADJ
ejpam-3573	8	3	notions	notion	NOUN
ejpam-3573	8	4	and	and	CCONJ
ejpam-3573	8	5	notations	notation	NOUN
ejpam-3573	8	6	mentioned	mention	VERB
ejpam-3573	8	7	in	in	ADP
ejpam-3573	8	8	this	this	DET
ejpam-3573	8	9	section	section	NOUN
ejpam-3573	8	10	,	,	PUNCT
ejpam-3573	8	11	we	we	PRON
ejpam-3573	8	12	refer	refer	VERB
ejpam-3573	8	13	to	to	ADP
ejpam-3573	8	14	section	section	NOUN
ejpam-3573	8	15	2	2	NUM
ejpam-3573	8	16	.	.	PUNCT
ejpam-3573	9	1	the	the	DET
ejpam-3573	9	2	dynamics	dynamic	NOUN
ejpam-3573	9	3	of	of	ADP
ejpam-3573	9	4	autonomous	autonomous	ADJ
ejpam-3573	9	5	dynamical	dynamical	ADJ
ejpam-3573	9	6	system	system	NOUN
ejpam-3573	9	7	have	have	AUX
ejpam-3573	9	8	been	be	AUX
ejpam-3573	9	9	extensively	extensively	ADV
ejpam-3573	9	10	studied	study	VERB
ejpam-3573	9	11	and	and	CCONJ
ejpam-3573	9	12	many	many	ADJ
ejpam-3573	9	13	elegant	elegant	ADJ
ejpam-3573	9	14	results	result	NOUN
ejpam-3573	9	15	have	have	AUX
ejpam-3573	9	16	been	be	AUX
ejpam-3573	9	17	obtained	obtain	VERB
ejpam-3573	9	18	[	[	X
ejpam-3573	9	19	1	1	NUM
ejpam-3573	9	20	,	,	PUNCT
ejpam-3573	9	21	2	2	NUM
ejpam-3573	9	22	,	,	PUNCT
ejpam-3573	9	23	and	and	CCONJ
ejpam-3573	9	24	the	the	DET
ejpam-3573	9	25	references	reference	NOUN
ejpam-3573	9	26	therein	therein	ADV
ejpam-3573	9	27	]	]	PUNCT
ejpam-3573	9	28	.	.	PUNCT
ejpam-3573	10	1	nonautonomous	nonautonomous	ADJ
ejpam-3573	10	2	systems	system	NOUN
ejpam-3573	10	3	,	,	PUNCT
ejpam-3573	10	4	also	also	ADV
ejpam-3573	10	5	called	call	VERB
ejpam-3573	10	6	sequences	sequence	NOUN
ejpam-3573	10	7	of	of	ADP
ejpam-3573	10	8	dynamical	dynamical	ADJ
ejpam-3573	10	9	systems	system	NOUN
ejpam-3573	10	10	,	,	PUNCT
ejpam-3573	10	11	present	present	ADJ
ejpam-3573	10	12	situations	situation	NOUN
ejpam-3573	10	13	that	that	PRON
ejpam-3573	10	14	the	the	DET
ejpam-3573	10	15	dynamics	dynamic	NOUN
ejpam-3573	10	16	vary	vary	VERB
ejpam-3573	10	17	with	with	ADP
ejpam-3573	10	18	time	time	NOUN
ejpam-3573	10	19	.	.	PUNCT
ejpam-3573	11	1	these	these	DET
ejpam-3573	11	2	systems	system	NOUN
ejpam-3573	11	3	can	can	AUX
ejpam-3573	11	4	be	be	AUX
ejpam-3573	11	5	very	very	ADV
ejpam-3573	11	6	complicated	complicated	ADJ
ejpam-3573	11	7	and	and	CCONJ
ejpam-3573	11	8	naturally	naturally	ADV
ejpam-3573	11	9	appear	appear	VERB
ejpam-3573	11	10	as	as	ADP
ejpam-3573	11	11	a	a	DET
ejpam-3573	11	12	suitable	suitable	ADJ
ejpam-3573	11	13	model	model	NOUN
ejpam-3573	11	14	to	to	PART
ejpam-3573	11	15	describe	describe	VERB
ejpam-3573	11	16	real	real	ADJ
ejpam-3573	11	17	processes	process	NOUN
ejpam-3573	11	18	.	.	PUNCT
ejpam-3573	12	1	the	the	DET
ejpam-3573	12	2	rich	rich	ADJ
ejpam-3573	12	3	dynamics	dynamic	NOUN
ejpam-3573	12	4	of	of	ADP
ejpam-3573	12	5	non	non	ADJ
ejpam-3573	12	6	-	-	ADJ
ejpam-3573	12	7	autonomous	autonomous	ADJ
ejpam-3573	12	8	discrete	discrete	ADJ
ejpam-3573	12	9	systems	system	NOUN
ejpam-3573	12	10	attract	attract	VERB
ejpam-3573	12	11	the	the	DET
ejpam-3573	12	12	interest	interest	NOUN
ejpam-3573	12	13	of	of	ADP
ejpam-3573	12	14	several	several	ADJ
ejpam-3573	12	15	researchers	researcher	NOUN
ejpam-3573	12	16	,	,	PUNCT
ejpam-3573	12	17	obtaining	obtain	VERB
ejpam-3573	12	18	results	result	NOUN
ejpam-3573	12	19	on	on	ADP
ejpam-3573	12	20	chaotic	chaotic	ADJ
ejpam-3573	12	21	properties	property	NOUN
ejpam-3573	12	22	[	[	X
ejpam-3573	12	23	3]-[7	3]-[7	NUM
ejpam-3573	12	24	]	]	PUNCT
ejpam-3573	12	25	.	.	PUNCT
ejpam-3573	13	1	sensitivity	sensitivity	NOUN
ejpam-3573	13	2	is	be	AUX
ejpam-3573	13	3	essential	essential	ADJ
ejpam-3573	13	4	for	for	ADP
ejpam-3573	13	5	the	the	DET
ejpam-3573	13	6	concept	concept	NOUN
ejpam-3573	13	7	of	of	ADP
ejpam-3573	13	8	chaos	chaos	NOUN
ejpam-3573	13	9	.	.	PUNCT
ejpam-3573	14	1	a	a	DET
ejpam-3573	14	2	study	study	NOUN
ejpam-3573	14	3	of	of	ADP
ejpam-3573	14	4	stronger	strong	ADJ
ejpam-3573	14	5	forms	form	NOUN
ejpam-3573	14	6	of	of	ADP
ejpam-3573	14	7	sensitivity	sensitivity	NOUN
ejpam-3573	14	8	has	have	AUX
ejpam-3573	14	9	been	be	AUX
ejpam-3573	14	10	initiated	initiate	VERB
ejpam-3573	14	11	by	by	ADP
ejpam-3573	14	12	moothathu	moothathu	NOUN
ejpam-3573	14	13	[	[	X
ejpam-3573	14	14	8	8	NUM
ejpam-3573	14	15	]	]	PUNCT
ejpam-3573	14	16	.	.	PUNCT
ejpam-3573	15	1	along	along	ADP
ejpam-3573	15	2	this	this	DET
ejpam-3573	15	3	line	line	NOUN
ejpam-3573	15	4	,	,	PUNCT
ejpam-3573	15	5	several	several	ADJ
ejpam-3573	15	6	elegant	elegant	ADJ
ejpam-3573	15	7	results	result	NOUN
ejpam-3573	15	8	have	have	AUX
ejpam-3573	15	9	been	be	AUX
ejpam-3573	15	10	obtained	obtain	VERB
ejpam-3573	15	11	[	[	PUNCT
ejpam-3573	15	12	9	9	NUM
ejpam-3573	15	13	,	,	PUNCT
ejpam-3573	15	14	10	10	NUM
ejpam-3573	15	15	]	]	PUNCT
ejpam-3573	15	16	.	.	PUNCT
ejpam-3573	16	1	a	a	DET
ejpam-3573	16	2	series	series	NOUN
ejpam-3573	16	3	of	of	ADP
ejpam-3573	16	4	research	research	NOUN
ejpam-3573	16	5	focus	focus	NOUN
ejpam-3573	16	6	on	on	ADP
ejpam-3573	16	7	mean	mean	NOUN
ejpam-3573	16	8	sensitivity	sensitivity	NOUN
ejpam-3573	16	9	[	[	X
ejpam-3573	16	10	11	11	NUM
ejpam-3573	16	11	,	,	PUNCT
ejpam-3573	16	12	12	12	NUM
ejpam-3573	16	13	]	]	PUNCT
ejpam-3573	16	14	.	.	PUNCT
ejpam-3573	17	1	until	until	ADP
ejpam-3573	17	2	very	very	ADV
ejpam-3573	17	3	recently	recently	ADV
ejpam-3573	17	4	,	,	PUNCT
ejpam-3573	17	5	sensitivity	sensitivity	NOUN
ejpam-3573	17	6	of	of	ADP
ejpam-3573	17	7	nonautonomous	nonautonomous	ADJ
ejpam-3573	17	8	dynamical	dynamical	ADJ
ejpam-3573	17	9	system	system	NOUN
ejpam-3573	17	10	has	have	AUX
ejpam-3573	17	11	been	be	AUX
ejpam-3573	17	12	discussed	discuss	VERB
ejpam-3573	17	13	[	[	PUNCT
ejpam-3573	17	14	13	13	NUM
ejpam-3573	17	15	]	]	PUNCT
ejpam-3573	17	16	.	.	PUNCT
ejpam-3573	18	1	motivated	motivate	VERB
ejpam-3573	18	2	by	by	ADP
ejpam-3573	18	3	the	the	DET
ejpam-3573	18	4	idea	idea	NOUN
ejpam-3573	18	5	in	in	ADP
ejpam-3573	18	6	[	[	X
ejpam-3573	18	7	9	9	NUM
ejpam-3573	18	8	]	]	PUNCT
ejpam-3573	18	9	,	,	PUNCT
ejpam-3573	18	10	we	we	PRON
ejpam-3573	18	11	discuss	discuss	VERB
ejpam-3573	18	12	different	different	ADJ
ejpam-3573	18	13	kinds	kind	NOUN
ejpam-3573	18	14	of	of	ADP
ejpam-3573	18	15	sensitivities	sensitivity	NOUN
ejpam-3573	18	16	in	in	ADP
ejpam-3573	18	17	nonautonomous	nonautonomous	ADJ
ejpam-3573	18	18	dynamical	dynamical	ADJ
ejpam-3573	18	19	systems	system	NOUN
ejpam-3573	18	20	in	in	ADP
ejpam-3573	18	21	this	this	DET
ejpam-3573	18	22	paper	paper	NOUN
ejpam-3573	18	23	.	.	PUNCT
ejpam-3573	19	1	doi	doi	NOUN
ejpam-3573	19	2	:	:	PUNCT
ejpam-3573	19	3	https://doi.org/10.29020/nybg.ejpam.v12i4.3573	https://doi.org/10.29020/nybg.ejpam.v12i4.3573	PRON
ejpam-3573	19	4	email	email	NOUN
ejpam-3573	19	5	addresses	address	NOUN
ejpam-3573	19	6	:	:	PUNCT
ejpam-3573	19	7	yylanmath@163.com	yylanmath@163.com	PROPN
ejpam-3573	19	8	(	(	PUNCT
ejpam-3573	19	9	y.	y.	PROPN
ejpam-3573	19	10	lan	lan	PROPN
ejpam-3573	19	11	)	)	PUNCT
ejpam-3573	19	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3573	20	1	1689	1689	NUM
ejpam-3573	20	2	c	c	X
ejpam-3573	20	3	©	©	PROPN
ejpam-3573	20	4	2019	2019	NUM
ejpam-3573	20	5	ejpam	ejpam	NOUN
ejpam-3573	20	6	all	all	DET
ejpam-3573	20	7	rights	right	NOUN
ejpam-3573	20	8	reserved	reserve	VERB
ejpam-3573	20	9	.	.	PUNCT
ejpam-3573	21	1	y.	y.	PROPN
ejpam-3573	21	2	lan	lan	PROPN
ejpam-3573	21	3	/	/	SYM
ejpam-3573	21	4	eur	eur	PROPN
ejpam-3573	21	5	.	.	PUNCT
ejpam-3573	22	1	j.	j.	PROPN
ejpam-3573	22	2	pure	pure	PROPN
ejpam-3573	22	3	appl	appl	PROPN
ejpam-3573	22	4	.	.	PROPN
ejpam-3573	22	5	math	math	PROPN
ejpam-3573	22	6	,	,	PUNCT
ejpam-3573	22	7	12	12	NUM
ejpam-3573	22	8	(	(	PUNCT
ejpam-3573	22	9	4	4	NUM
ejpam-3573	22	10	)	)	PUNCT
ejpam-3573	22	11	(	(	PUNCT
ejpam-3573	22	12	2019	2019	NUM
ejpam-3573	22	13	)	)	PUNCT
ejpam-3573	22	14	,	,	PUNCT
ejpam-3573	22	15	1689	1689	NUM
ejpam-3573	22	16	-	-	SYM
ejpam-3573	22	17	1700	1700	NUM
ejpam-3573	22	18	1690	1690	NUM
ejpam-3573	22	19	on	on	ADP
ejpam-3573	22	20	the	the	DET
ejpam-3573	22	21	other	other	ADJ
ejpam-3573	22	22	hand	hand	NOUN
ejpam-3573	22	23	,	,	PUNCT
ejpam-3573	22	24	it	it	PRON
ejpam-3573	22	25	is	be	AUX
ejpam-3573	22	26	well	well	ADV
ejpam-3573	22	27	known	know	VERB
ejpam-3573	22	28	that	that	SCONJ
ejpam-3573	22	29	every	every	DET
ejpam-3573	22	30	given	give	VERB
ejpam-3573	22	31	discrete	discrete	ADJ
ejpam-3573	22	32	dynamical	dynamical	ADJ
ejpam-3573	22	33	system	system	NOUN
ejpam-3573	22	34	uniquely	uniquely	ADV
ejpam-3573	22	35	induces	induce	VERB
ejpam-3573	22	36	its	its	PRON
ejpam-3573	22	37	fuzzified	fuzzified	ADJ
ejpam-3573	22	38	counterpart	counterpart	NOUN
ejpam-3573	22	39	,	,	PUNCT
ejpam-3573	22	40	i.e.	i.e.	X
ejpam-3573	22	41	,	,	PUNCT
ejpam-3573	22	42	a	a	DET
ejpam-3573	22	43	discrete	discrete	ADJ
ejpam-3573	22	44	system	system	NOUN
ejpam-3573	22	45	on	on	ADP
ejpam-3573	22	46	the	the	DET
ejpam-3573	22	47	space	space	NOUN
ejpam-3573	22	48	of	of	ADP
ejpam-3573	22	49	fuzzy	fuzzy	ADJ
ejpam-3573	22	50	sets	set	NOUN
ejpam-3573	22	51	.	.	PUNCT
ejpam-3573	23	1	it	it	PRON
ejpam-3573	23	2	is	be	AUX
ejpam-3573	23	3	natural	natural	ADJ
ejpam-3573	23	4	to	to	PART
ejpam-3573	23	5	investigate	investigate	VERB
ejpam-3573	23	6	the	the	DET
ejpam-3573	23	7	relation	relation	NOUN
ejpam-3573	23	8	between	between	ADP
ejpam-3573	23	9	dynamical	dynamical	ADJ
ejpam-3573	23	10	properties	property	NOUN
ejpam-3573	23	11	of	of	ADP
ejpam-3573	23	12	the	the	DET
ejpam-3573	23	13	original	original	ADJ
ejpam-3573	23	14	and	and	CCONJ
ejpam-3573	23	15	fuzzified	fuzzified	ADJ
ejpam-3573	23	16	systems	system	NOUN
ejpam-3573	23	17	.	.	PUNCT
ejpam-3573	24	1	actually	actually	ADV
ejpam-3573	24	2	,	,	PUNCT
ejpam-3573	24	3	there	there	PRON
ejpam-3573	24	4	are	be	VERB
ejpam-3573	24	5	quite	quite	DET
ejpam-3573	24	6	a	a	DET
ejpam-3573	24	7	few	few	ADJ
ejpam-3573	24	8	elegant	elegant	ADJ
ejpam-3573	24	9	results	result	NOUN
ejpam-3573	24	10	have	have	AUX
ejpam-3573	24	11	been	be	AUX
ejpam-3573	24	12	obtained	obtain	VERB
ejpam-3573	24	13	[	[	X
ejpam-3573	24	14	14][21	14][21	X
ejpam-3573	24	15	]	]	PUNCT
ejpam-3573	24	16	.	.	PUNCT
ejpam-3573	25	1	in	in	ADP
ejpam-3573	25	2	this	this	DET
ejpam-3573	25	3	paper	paper	NOUN
ejpam-3573	25	4	,	,	PUNCT
ejpam-3573	25	5	we	we	PRON
ejpam-3573	25	6	initiate	initiate	VERB
ejpam-3573	25	7	a	a	DET
ejpam-3573	25	8	preliminary	preliminary	ADJ
ejpam-3573	25	9	study	study	NOUN
ejpam-3573	25	10	of	of	ADP
ejpam-3573	25	11	relations	relation	NOUN
ejpam-3573	25	12	between	between	ADP
ejpam-3573	25	13	several	several	ADJ
ejpam-3573	25	14	forms	form	NOUN
ejpam-3573	25	15	of	of	ADP
ejpam-3573	25	16	sensitivity	sensitivity	NOUN
ejpam-3573	25	17	of	of	ADP
ejpam-3573	25	18	the	the	DET
ejpam-3573	25	19	original	original	ADJ
ejpam-3573	25	20	and	and	CCONJ
ejpam-3573	25	21	its	its	PRON
ejpam-3573	25	22	fuzzified	fuzzified	ADJ
ejpam-3573	25	23	nonautonomous	nonautonomous	ADJ
ejpam-3573	25	24	dynamical	dynamical	ADJ
ejpam-3573	25	25	systems	system	NOUN
ejpam-3573	25	26	.	.	PUNCT
ejpam-3573	26	1	below	below	ADV
ejpam-3573	26	2	,	,	PUNCT
ejpam-3573	26	3	basic	basic	ADJ
ejpam-3573	26	4	notions	notion	NOUN
ejpam-3573	26	5	are	be	AUX
ejpam-3573	26	6	introduced	introduce	VERB
ejpam-3573	26	7	in	in	ADP
ejpam-3573	26	8	section	section	NOUN
ejpam-3573	26	9	2	2	NUM
ejpam-3573	26	10	.	.	PUNCT
ejpam-3573	26	11	main	main	ADJ
ejpam-3573	26	12	results	result	NOUN
ejpam-3573	26	13	are	be	AUX
ejpam-3573	26	14	presented	present	VERB
ejpam-3573	26	15	in	in	ADP
ejpam-3573	26	16	section	section	NOUN
ejpam-3573	26	17	3	3	NUM
ejpam-3573	26	18	,	,	PUNCT
ejpam-3573	26	19	where	where	SCONJ
ejpam-3573	26	20	the	the	DET
ejpam-3573	26	21	relations	relation	NOUN
ejpam-3573	26	22	between	between	ADP
ejpam-3573	26	23	two	two	NUM
ejpam-3573	26	24	forms	form	NOUN
ejpam-3573	26	25	of	of	ADP
ejpam-3573	26	26	sensitivity	sensitivity	NOUN
ejpam-3573	26	27	of	of	ADP
ejpam-3573	26	28	the	the	DET
ejpam-3573	26	29	original	original	ADJ
ejpam-3573	26	30	and	and	CCONJ
ejpam-3573	26	31	fuzzified	fuzzifie	VERB
ejpam-3573	26	32	systems	system	NOUN
ejpam-3573	26	33	have	have	AUX
ejpam-3573	26	34	been	be	AUX
ejpam-3573	26	35	discussed	discuss	VERB
ejpam-3573	26	36	,	,	PUNCT
ejpam-3573	26	37	respectively	respectively	ADV
ejpam-3573	26	38	.	.	PUNCT
ejpam-3573	27	1	2	2	X
ejpam-3573	27	2	.	.	NUM
ejpam-3573	27	3	basic	basic	ADJ
ejpam-3573	27	4	concepts	concept	NOUN
ejpam-3573	27	5	and	and	CCONJ
ejpam-3573	27	6	notations	notation	NOUN
ejpam-3573	27	7	2.1	2.1	NUM
ejpam-3573	27	8	.	.	PUNCT
ejpam-3573	28	1	metric	metric	ADJ
ejpam-3573	28	2	space	space	NOUN
ejpam-3573	28	3	of	of	ADP
ejpam-3573	28	4	fuzzy	fuzzy	ADJ
ejpam-3573	28	5	sets	set	NOUN
ejpam-3573	28	6	let	let	AUX
ejpam-3573	28	7	(	(	PUNCT
ejpam-3573	28	8	x	x	NOUN
ejpam-3573	28	9	,	,	PUNCT
ejpam-3573	28	10	d	d	NOUN
ejpam-3573	28	11	)	)	PUNCT
ejpam-3573	28	12	denote	denote	VERB
ejpam-3573	28	13	a	a	DET
ejpam-3573	28	14	compact	compact	ADJ
ejpam-3573	28	15	metric	metric	ADJ
ejpam-3573	28	16	space	space	NOUN
ejpam-3573	28	17	and	and	CCONJ
ejpam-3573	28	18	let	let	VERB
ejpam-3573	28	19	k(x	k(x	PROPN
ejpam-3573	28	20	)	)	PUNCT
ejpam-3573	28	21	be	be	AUX
ejpam-3573	28	22	the	the	DET
ejpam-3573	28	23	class	class	NOUN
ejpam-3573	28	24	of	of	ADP
ejpam-3573	28	25	all	all	DET
ejpam-3573	28	26	non	non	ADJ
ejpam-3573	28	27	-	-	ADJ
ejpam-3573	28	28	empty	empty	ADJ
ejpam-3573	28	29	and	and	CCONJ
ejpam-3573	28	30	compact	compact	ADJ
ejpam-3573	28	31	subsets	subset	NOUN
ejpam-3573	28	32	of	of	ADP
ejpam-3573	28	33	x.	x.	NOUN
ejpam-3573	28	34	define	define	VERB
ejpam-3573	28	35	the	the	DET
ejpam-3573	28	36	ε	ε	PROPN
ejpam-3573	28	37	-	-	PUNCT
ejpam-3573	28	38	neighborhood	neighborhood	NOUN
ejpam-3573	28	39	of	of	ADP
ejpam-3573	28	40	a	a	DET
ejpam-3573	28	41	nonempty	nonempty	NOUN
ejpam-3573	28	42	subset	subset	VERB
ejpam-3573	28	43	a	a	DET
ejpam-3573	28	44	in	in	ADP
ejpam-3573	28	45	x	x	PART
ejpam-3573	28	46	to	to	PART
ejpam-3573	28	47	be	be	AUX
ejpam-3573	28	48	the	the	DET
ejpam-3573	28	49	set	set	NOUN
ejpam-3573	28	50	ud(a	ud(a	PROPN
ejpam-3573	28	51	,	,	PUNCT
ejpam-3573	28	52	ε	ε	PROPN
ejpam-3573	28	53	)	)	PUNCT
ejpam-3573	28	54	=	=	PRON
ejpam-3573	29	1	{	{	PUNCT
ejpam-3573	29	2	x	x	X
ejpam-3573	29	3	|	|	ADV
ejpam-3573	29	4	d(x	d(x	PROPN
ejpam-3573	29	5	,	,	PUNCT
ejpam-3573	29	6	a	a	PRON
ejpam-3573	29	7	)	)	PUNCT
ejpam-3573	29	8	<	<	X
ejpam-3573	29	9	ε	ε	X
ejpam-3573	29	10	}	}	PUNCT
ejpam-3573	29	11	,	,	PUNCT
ejpam-3573	29	12	where	where	SCONJ
ejpam-3573	29	13	d(x	d(x	PROPN
ejpam-3573	29	14	,	,	PUNCT
ejpam-3573	29	15	a	a	PRON
ejpam-3573	29	16	)	)	PUNCT
ejpam-3573	29	17	=	=	SYM
ejpam-3573	29	18	infa∈a	infa∈a	NOUN
ejpam-3573	29	19	‖x−	‖x−	PROPN
ejpam-3573	29	20	a‖.	a‖.	NOUN
ejpam-3573	29	21	the	the	DET
ejpam-3573	29	22	hausdorff	hausdorff	NOUN
ejpam-3573	29	23	separation	separation	NOUN
ejpam-3573	29	24	ρ(a	ρ(a	PROPN
ejpam-3573	29	25	,	,	PUNCT
ejpam-3573	29	26	b	b	NOUN
ejpam-3573	29	27	)	)	PUNCT
ejpam-3573	29	28	of	of	ADP
ejpam-3573	29	29	a	a	DET
ejpam-3573	29	30	,	,	PUNCT
ejpam-3573	29	31	b	b	PROPN
ejpam-3573	29	32	∈	∈	PROPN
ejpam-3573	29	33	k(x	k(x	PROPN
ejpam-3573	29	34	)	)	PUNCT
ejpam-3573	29	35	is	be	AUX
ejpam-3573	29	36	defined	define	VERB
ejpam-3573	29	37	by	by	ADP
ejpam-3573	29	38	ρ(a	ρ(a	PROPN
ejpam-3573	29	39	,	,	PUNCT
ejpam-3573	29	40	b	b	NOUN
ejpam-3573	29	41	)	)	PUNCT
ejpam-3573	29	42	=	=	SYM
ejpam-3573	29	43	inf{ε	inf{ε	PROPN
ejpam-3573	29	44	>	>	X
ejpam-3573	29	45	0|	0|	NOUN
ejpam-3573	30	1	a	a	DET
ejpam-3573	30	2	⊆	⊆	NUM
ejpam-3573	30	3	u(b	u(b	NOUN
ejpam-3573	30	4	,	,	PUNCT
ejpam-3573	30	5	ε	ε	PROPN
ejpam-3573	30	6	)	)	PUNCT
ejpam-3573	30	7	}	}	PUNCT
ejpam-3573	31	1	,	,	PUNCT
ejpam-3573	31	2	the	the	DET
ejpam-3573	31	3	hausdorff	hausdorff	PROPN
ejpam-3573	31	4	metric	metric	PROPN
ejpam-3573	31	5	dh	dh	PROPN
ejpam-3573	31	6	on	on	ADP
ejpam-3573	31	7	k(x	k(x	PROPN
ejpam-3573	31	8	)	)	PUNCT
ejpam-3573	31	9	is	be	AUX
ejpam-3573	31	10	defined	define	VERB
ejpam-3573	31	11	by	by	ADP
ejpam-3573	31	12	letting	let	VERB
ejpam-3573	31	13	dh(a	dh(a	ADJ
ejpam-3573	31	14	,	,	PUNCT
ejpam-3573	31	15	b	b	NOUN
ejpam-3573	31	16	)	)	PUNCT
ejpam-3573	31	17	=	=	SYM
ejpam-3573	32	1	max{ρ(a	max{ρ(a	PROPN
ejpam-3573	32	2	,	,	PUNCT
ejpam-3573	32	3	b	b	NOUN
ejpam-3573	32	4	)	)	PUNCT
ejpam-3573	32	5	,	,	PUNCT
ejpam-3573	32	6	ρ(b	ρ(b	PROPN
ejpam-3573	32	7	,	,	PUNCT
ejpam-3573	32	8	a	a	PRON
ejpam-3573	32	9	)	)	PUNCT
ejpam-3573	32	10	}	}	PUNCT
ejpam-3573	32	11	.	.	PUNCT
ejpam-3573	33	1	for	for	ADP
ejpam-3573	33	2	a	a	DET
ejpam-3573	33	3	compact	compact	ADJ
ejpam-3573	33	4	metric	metric	ADJ
ejpam-3573	33	5	space	space	NOUN
ejpam-3573	33	6	x	x	NOUN
ejpam-3573	33	7	,	,	PUNCT
ejpam-3573	33	8	the	the	DET
ejpam-3573	33	9	topology	topology	NOUN
ejpam-3573	33	10	generated	generate	VERB
ejpam-3573	33	11	by	by	ADP
ejpam-3573	33	12	dh	dh	PROPN
ejpam-3573	33	13	coincides	coincide	VERB
ejpam-3573	33	14	with	with	ADP
ejpam-3573	33	15	the	the	DET
ejpam-3573	33	16	finite	finite	ADJ
ejpam-3573	33	17	topology	topology	NOUN
ejpam-3573	33	18	.	.	PUNCT
ejpam-3573	34	1	it	it	PRON
ejpam-3573	34	2	is	be	AUX
ejpam-3573	34	3	known	know	VERB
ejpam-3573	34	4	that	that	SCONJ
ejpam-3573	34	5	the	the	DET
ejpam-3573	34	6	set	set	NOUN
ejpam-3573	34	7	of	of	ADP
ejpam-3573	34	8	all	all	DET
ejpam-3573	34	9	finite	finite	ADJ
ejpam-3573	34	10	subsets	subset	NOUN
ejpam-3573	34	11	of	of	ADP
ejpam-3573	34	12	x	x	PRON
ejpam-3573	34	13	,	,	PUNCT
ejpam-3573	34	14	denote	denote	VERB
ejpam-3573	34	15	by	by	ADP
ejpam-3573	34	16	l(x	l(x	PROPN
ejpam-3573	34	17	)	)	PUNCT
ejpam-3573	34	18	,	,	PUNCT
ejpam-3573	34	19	is	be	AUX
ejpam-3573	34	20	dense	dense	ADJ
ejpam-3573	34	21	in	in	ADP
ejpam-3573	34	22	k(x	k(x	PROPN
ejpam-3573	34	23	)	)	PUNCT
ejpam-3573	34	24	.	.	PUNCT
ejpam-3573	35	1	define	define	VERB
ejpam-3573	35	2	f(x	f(x	PROPN
ejpam-3573	35	3	)	)	PUNCT
ejpam-3573	35	4	as	as	SCONJ
ejpam-3573	35	5	the	the	DET
ejpam-3573	35	6	class	class	NOUN
ejpam-3573	35	7	of	of	ADP
ejpam-3573	35	8	all	all	PRON
ejpam-3573	35	9	upper	upper	ADJ
ejpam-3573	35	10	semicontinuous	semicontinuous	ADJ
ejpam-3573	35	11	fuzzy	fuzzy	ADJ
ejpam-3573	35	12	sets	set	VERB
ejpam-3573	35	13	u	u	PRON
ejpam-3573	35	14	:	:	PUNCT
ejpam-3573	35	15	x	x	X
ejpam-3573	35	16	→	→	SYM
ejpam-3573	36	1	[	[	X
ejpam-3573	36	2	0	0	NUM
ejpam-3573	36	3	,	,	PUNCT
ejpam-3573	36	4	1	1	NUM
ejpam-3573	36	5	]	]	PUNCT
ejpam-3573	36	6	such	such	ADJ
ejpam-3573	36	7	that	that	SCONJ
ejpam-3573	36	8	[	[	X
ejpam-3573	36	9	u]α	u]α	X
ejpam-3573	36	10	∈	∈	PROPN
ejpam-3573	36	11	k(x	k(x	PROPN
ejpam-3573	36	12	)	)	PUNCT
ejpam-3573	36	13	,	,	PUNCT
ejpam-3573	36	14	where	where	SCONJ
ejpam-3573	36	15	α	α	NOUN
ejpam-3573	36	16	-	-	NOUN
ejpam-3573	36	17	cuts	cut	NOUN
ejpam-3573	36	18	and	and	CCONJ
ejpam-3573	36	19	the	the	DET
ejpam-3573	36	20	support	support	NOUN
ejpam-3573	36	21	of	of	ADP
ejpam-3573	36	22	u	u	NOUN
ejpam-3573	36	23	are	be	AUX
ejpam-3573	36	24	defined	define	VERB
ejpam-3573	36	25	by	by	ADP
ejpam-3573	36	26	[	[	PUNCT
ejpam-3573	36	27	u]α	u]α	X
ejpam-3573	36	28	=	=	SYM
ejpam-3573	36	29	{	{	PUNCT
ejpam-3573	36	30	x	x	PROPN
ejpam-3573	36	31	∈	∈	PROPN
ejpam-3573	36	32	x|u(x	x|u(x	PROPN
ejpam-3573	36	33	)	)	PUNCT
ejpam-3573	36	34	≥	≥	NUM
ejpam-3573	36	35	α	α	NOUN
ejpam-3573	36	36	}	}	PUNCT
ejpam-3573	36	37	,	,	PUNCT
ejpam-3573	36	38	α	α	PROPN
ejpam-3573	36	39	∈	∈	PROPN
ejpam-3573	37	1	[	[	X
ejpam-3573	37	2	0	0	NUM
ejpam-3573	37	3	,	,	PUNCT
ejpam-3573	37	4	1	1	NUM
ejpam-3573	37	5	]	]	PUNCT
ejpam-3573	37	6	,	,	PUNCT
ejpam-3573	37	7	and	and	CCONJ
ejpam-3573	37	8	supp(u	supp(u	X
ejpam-3573	37	9	)	)	PUNCT
ejpam-3573	37	10	=	=	SYM
ejpam-3573	37	11	{	{	PUNCT
ejpam-3573	37	12	x	x	PUNCT
ejpam-3573	37	13	∈	∈	PROPN
ejpam-3573	37	14	x|u(x	x|u(x	PROPN
ejpam-3573	37	15	)	)	PUNCT
ejpam-3573	37	16	>	>	X
ejpam-3573	37	17	0	0	NUM
ejpam-3573	37	18	}	}	PUNCT
ejpam-3573	37	19	,	,	PUNCT
ejpam-3573	37	20	respectively	respectively	ADV
ejpam-3573	37	21	.	.	PUNCT
ejpam-3573	38	1	moreover	moreover	ADV
ejpam-3573	38	2	,	,	PUNCT
ejpam-3573	38	3	for	for	ADP
ejpam-3573	38	4	each	each	DET
ejpam-3573	38	5	x	x	SYM
ejpam-3573	38	6	∈	∈	PROPN
ejpam-3573	38	7	x	x	X
ejpam-3573	38	8	,	,	PUNCT
ejpam-3573	38	9	we	we	PRON
ejpam-3573	38	10	denote	denote	VERB
ejpam-3573	38	11	x̂	x̂	PUNCT
ejpam-3573	39	1	the	the	DET
ejpam-3573	39	2	characteristic	characteristic	ADJ
ejpam-3573	39	3	function	function	NOUN
ejpam-3573	39	4	of	of	ADP
ejpam-3573	39	5	x	x	X
ejpam-3573	39	6	,	,	PUNCT
ejpam-3573	39	7	it	it	PRON
ejpam-3573	39	8	is	be	AUX
ejpam-3573	39	9	clear	clear	ADJ
ejpam-3573	39	10	that	that	SCONJ
ejpam-3573	39	11	for	for	ADP
ejpam-3573	39	12	for	for	ADP
ejpam-3573	39	13	all	all	PRON
ejpam-3573	39	14	x	x	SYM
ejpam-3573	39	15	∈	∈	PROPN
ejpam-3573	39	16	x	x	X
ejpam-3573	39	17	,	,	PUNCT
ejpam-3573	39	18	x̂	x̂	PUNCT
ejpam-3573	39	19	∈	∈	PROPN
ejpam-3573	39	20	f(x	f(x	PROPN
ejpam-3573	39	21	)	)	PUNCT
ejpam-3573	39	22	and	and	CCONJ
ejpam-3573	40	1	[	[	X
ejpam-3573	40	2	x̂]α	x̂]α	X
ejpam-3573	40	3	=	=	X
ejpam-3573	40	4	{	{	PUNCT
ejpam-3573	40	5	x	x	NOUN
ejpam-3573	40	6	}	}	PUNCT
ejpam-3573	40	7	for	for	ADP
ejpam-3573	40	8	α	α	DET
ejpam-3573	40	9	∈	∈	PROPN
ejpam-3573	40	10	(	(	PUNCT
ejpam-3573	40	11	0	0	NUM
ejpam-3573	40	12	,	,	PUNCT
ejpam-3573	40	13	1	1	NUM
ejpam-3573	40	14	]	]	PUNCT
ejpam-3573	40	15	.	.	PUNCT
ejpam-3573	41	1	denote	denote	PROPN
ejpam-3573	41	2	∅x	∅x	PROPN
ejpam-3573	41	3	the	the	DET
ejpam-3573	41	4	empty	empty	ADJ
ejpam-3573	41	5	fuzzy	fuzzy	ADJ
ejpam-3573	41	6	set	set	NOUN
ejpam-3573	41	7	(	(	PUNCT
ejpam-3573	41	8	∅x(x	∅x(x	NOUN
ejpam-3573	41	9	)	)	PUNCT
ejpam-3573	41	10	=	=	SYM
ejpam-3573	41	11	0	0	PUNCT
ejpam-3573	42	1	for	for	ADP
ejpam-3573	42	2	all	all	DET
ejpam-3573	42	3	x	x	SYM
ejpam-3573	42	4	∈	∈	PROPN
ejpam-3573	42	5	x	x	NOUN
ejpam-3573	42	6	)	)	PUNCT
ejpam-3573	42	7	.	.	PUNCT
ejpam-3573	43	1	a	a	DET
ejpam-3573	43	2	levelwise	levelwise	NOUN
ejpam-3573	43	3	metric	metric	ADJ
ejpam-3573	43	4	d∞	d∞	NOUN
ejpam-3573	43	5	on	on	ADP
ejpam-3573	43	6	f(x	f(x	PROPN
ejpam-3573	43	7	)	)	PUNCT
ejpam-3573	43	8	is	be	AUX
ejpam-3573	43	9	defined	define	VERB
ejpam-3573	43	10	by	by	ADP
ejpam-3573	43	11	d∞(u	d∞(u	PROPN
ejpam-3573	43	12	,	,	PUNCT
ejpam-3573	43	13	v	v	NOUN
ejpam-3573	43	14	)	)	PUNCT
ejpam-3573	43	15	=	=	SYM
ejpam-3573	43	16	sup	sup	NOUN
ejpam-3573	43	17	α∈[0,1	α∈[0,1	NUM
ejpam-3573	43	18	]	]	X
ejpam-3573	43	19	dh([u]α	dh([u]α	NOUN
ejpam-3573	43	20	,	,	PUNCT
ejpam-3573	43	21	[	[	X
ejpam-3573	43	22	v]α	v]α	ADJ
ejpam-3573	43	23	)	)	PUNCT
ejpam-3573	43	24	,	,	PUNCT
ejpam-3573	43	25	y.	y.	PROPN
ejpam-3573	43	26	lan	lan	PROPN
ejpam-3573	43	27	/	/	SYM
ejpam-3573	43	28	eur	eur	PROPN
ejpam-3573	43	29	.	.	PUNCT
ejpam-3573	44	1	j.	j.	PROPN
ejpam-3573	44	2	pure	pure	PROPN
ejpam-3573	44	3	appl	appl	PROPN
ejpam-3573	44	4	.	.	PROPN
ejpam-3573	44	5	math	math	PROPN
ejpam-3573	44	6	,	,	PUNCT
ejpam-3573	44	7	12	12	NUM
ejpam-3573	44	8	(	(	PUNCT
ejpam-3573	44	9	4	4	NUM
ejpam-3573	44	10	)	)	PUNCT
ejpam-3573	44	11	(	(	PUNCT
ejpam-3573	44	12	2019	2019	NUM
ejpam-3573	44	13	)	)	PUNCT
ejpam-3573	44	14	,	,	PUNCT
ejpam-3573	44	15	1689	1689	NUM
ejpam-3573	44	16	-	-	SYM
ejpam-3573	44	17	1700	1700	NUM
ejpam-3573	44	18	1691	1691	NUM
ejpam-3573	44	19	for	for	ADP
ejpam-3573	44	20	all	all	DET
ejpam-3573	44	21	u	u	NOUN
ejpam-3573	44	22	,	,	PUNCT
ejpam-3573	44	23	v	v	PROPN
ejpam-3573	44	24	∈	∈	PROPN
ejpam-3573	44	25	f(x	f(x	PROPN
ejpam-3573	44	26	)	)	PUNCT
ejpam-3573	44	27	.	.	PUNCT
ejpam-3573	45	1	it	it	PRON
ejpam-3573	45	2	is	be	AUX
ejpam-3573	45	3	well	well	ADV
ejpam-3573	45	4	known	know	VERB
ejpam-3573	45	5	that	that	SCONJ
ejpam-3573	45	6	if	if	SCONJ
ejpam-3573	45	7	(	(	PUNCT
ejpam-3573	45	8	x	x	NOUN
ejpam-3573	45	9	,	,	PUNCT
ejpam-3573	45	10	d	d	NOUN
ejpam-3573	45	11	)	)	PUNCT
ejpam-3573	45	12	is	be	AUX
ejpam-3573	45	13	complete	complete	ADJ
ejpam-3573	45	14	,	,	PUNCT
ejpam-3573	45	15	then	then	ADV
ejpam-3573	45	16	(	(	PUNCT
ejpam-3573	45	17	f(x	f(x	PROPN
ejpam-3573	45	18	)	)	PUNCT
ejpam-3573	45	19	,	,	PUNCT
ejpam-3573	45	20	d∞	d∞	PROPN
ejpam-3573	45	21	)	)	PUNCT
ejpam-3573	45	22	is	be	AUX
ejpam-3573	45	23	also	also	ADV
ejpam-3573	45	24	complete	complete	ADJ
ejpam-3573	45	25	but	but	CCONJ
ejpam-3573	45	26	is	be	AUX
ejpam-3573	45	27	not	not	PART
ejpam-3573	45	28	compact	compact	ADJ
ejpam-3573	45	29	and	and	CCONJ
ejpam-3573	45	30	is	be	AUX
ejpam-3573	45	31	not	not	PART
ejpam-3573	45	32	separable	separable	ADJ
ejpam-3573	45	33	.	.	PUNCT
ejpam-3573	46	1	2.2	2.2	NUM
ejpam-3573	46	2	.	.	PUNCT
ejpam-3573	47	1	zadeh	zadeh	PROPN
ejpam-3573	47	2	’s	’s	PART
ejpam-3573	47	3	and	and	CCONJ
ejpam-3573	47	4	set	set	NOUN
ejpam-3573	47	5	-	-	PUNCT
ejpam-3573	47	6	valued	value	VERB
ejpam-3573	47	7	extension	extension	NOUN
ejpam-3573	47	8	the	the	DET
ejpam-3573	47	9	set	set	NOUN
ejpam-3573	47	10	-	-	PUNCT
ejpam-3573	47	11	valued	value	VERB
ejpam-3573	47	12	extension	extension	NOUN
ejpam-3573	47	13	of	of	ADP
ejpam-3573	47	14	a	a	DET
ejpam-3573	47	15	discrete	discrete	ADJ
ejpam-3573	47	16	dynamical	dynamical	ADJ
ejpam-3573	47	17	system	system	NOUN
ejpam-3573	47	18	(	(	PUNCT
ejpam-3573	47	19	x	x	X
ejpam-3573	47	20	,	,	PUNCT
ejpam-3573	47	21	f	f	X
ejpam-3573	47	22	)	)	PUNCT
ejpam-3573	47	23	is	be	AUX
ejpam-3573	47	24	a	a	DET
ejpam-3573	47	25	map	map	NOUN
ejpam-3573	47	26	f̄	f̄	NOUN
ejpam-3573	47	27	:	:	PUNCT
ejpam-3573	47	28	k(x	k(x	PROPN
ejpam-3573	47	29	)	)	PUNCT
ejpam-3573	47	30	→	→	SYM
ejpam-3573	47	31	k(x	k(x	PROPN
ejpam-3573	47	32	)	)	PUNCT
ejpam-3573	47	33	defined	define	VERB
ejpam-3573	47	34	by	by	ADP
ejpam-3573	47	35	f̄(a	f̄(a	NOUN
ejpam-3573	47	36	)	)	PUNCT
ejpam-3573	47	37	=	=	SYM
ejpam-3573	47	38	f(a	f(a	PROPN
ejpam-3573	47	39	)	)	PUNCT
ejpam-3573	47	40	for	for	ADP
ejpam-3573	47	41	any	any	DET
ejpam-3573	47	42	a	a	DET
ejpam-3573	47	43	∈	∈	PROPN
ejpam-3573	47	44	k(x	k(x	PROPN
ejpam-3573	47	45	)	)	PUNCT
ejpam-3573	47	46	.	.	PUNCT
ejpam-3573	48	1	it	it	PRON
ejpam-3573	48	2	is	be	AUX
ejpam-3573	48	3	shown	show	VERB
ejpam-3573	48	4	that	that	SCONJ
ejpam-3573	48	5	f̄	f̄	PROPN
ejpam-3573	48	6	is	be	AUX
ejpam-3573	48	7	continuous	continuous	ADJ
ejpam-3573	48	8	in	in	ADP
ejpam-3573	48	9	hausdorff	hausdorff	NOUN
ejpam-3573	48	10	metric	metric	NOUN
ejpam-3573	48	11	if	if	SCONJ
ejpam-3573	48	12	and	and	CCONJ
ejpam-3573	48	13	only	only	ADV
ejpam-3573	48	14	if	if	SCONJ
ejpam-3573	48	15	f	f	PROPN
ejpam-3573	48	16	is	be	AUX
ejpam-3573	48	17	continuous	continuous	ADJ
ejpam-3573	48	18	[	[	X
ejpam-3573	48	19	14	14	NUM
ejpam-3573	48	20	]	]	PUNCT
ejpam-3573	48	21	.	.	PUNCT
ejpam-3573	49	1	the	the	DET
ejpam-3573	49	2	zadeh	zadeh	PROPN
ejpam-3573	49	3	’s	’s	PART
ejpam-3573	49	4	extension	extension	NOUN
ejpam-3573	49	5	of	of	ADP
ejpam-3573	49	6	(	(	PUNCT
ejpam-3573	49	7	x	x	NOUN
ejpam-3573	49	8	,	,	PUNCT
ejpam-3573	49	9	f	f	X
ejpam-3573	49	10	)	)	PUNCT
ejpam-3573	49	11	is	be	AUX
ejpam-3573	49	12	a	a	DET
ejpam-3573	49	13	map	map	NOUN
ejpam-3573	49	14	f̂	f̂	NUM
ejpam-3573	49	15	:	:	PUNCT
ejpam-3573	49	16	f(x)→	f(x)→	PUNCT
ejpam-3573	49	17	f(x	f(x	PROPN
ejpam-3573	49	18	)	)	PUNCT
ejpam-3573	49	19	defined	define	VERB
ejpam-3573	49	20	by	by	ADP
ejpam-3573	49	21	[	[	X
ejpam-3573	49	22	f̂(u)](x	f̂(u)](x	NOUN
ejpam-3573	49	23	)	)	PUNCT
ejpam-3573	49	24	=	=	SYM
ejpam-3573	49	25	sup	sup	NUM
ejpam-3573	49	26	y∈f−1(x	y∈f−1(x	NOUN
ejpam-3573	49	27	)	)	PUNCT
ejpam-3573	49	28	{	{	PUNCT
ejpam-3573	49	29	u(y	u(y	NOUN
ejpam-3573	49	30	)	)	PUNCT
ejpam-3573	49	31	}	}	PUNCT
ejpam-3573	49	32	for	for	ADP
ejpam-3573	49	33	any	any	DET
ejpam-3573	49	34	u	u	PROPN
ejpam-3573	49	35	∈	∈	PROPN
ejpam-3573	49	36	f(x	f(x	PROPN
ejpam-3573	49	37	)	)	PUNCT
ejpam-3573	49	38	and	and	CCONJ
ejpam-3573	50	1	x	x	PUNCT
ejpam-3573	50	2	∈	∈	NOUN
ejpam-3573	50	3	x.	x.	NOUN
ejpam-3573	51	1	it	it	PRON
ejpam-3573	51	2	is	be	AUX
ejpam-3573	51	3	known	know	VERB
ejpam-3573	51	4	that	that	SCONJ
ejpam-3573	51	5	for	for	ADP
ejpam-3573	51	6	compact	compact	ADJ
ejpam-3573	51	7	x	x	NOUN
ejpam-3573	51	8	,	,	PUNCT
ejpam-3573	51	9	f̂	f̂	NUM
ejpam-3573	51	10	:	:	PUNCT
ejpam-3573	51	11	f(x	f(x	PROPN
ejpam-3573	51	12	)	)	PUNCT
ejpam-3573	51	13	→	→	SYM
ejpam-3573	51	14	f(x	f(x	PROPN
ejpam-3573	51	15	)	)	PUNCT
ejpam-3573	51	16	is	be	AUX
ejpam-3573	51	17	continuous	continuous	ADJ
ejpam-3573	51	18	if	if	SCONJ
ejpam-3573	51	19	and	and	CCONJ
ejpam-3573	51	20	only	only	ADV
ejpam-3573	51	21	if	if	SCONJ
ejpam-3573	51	22	f	f	X
ejpam-3573	51	23	:	:	PUNCT
ejpam-3573	51	24	x	x	X
ejpam-3573	51	25	→	→	PUNCT
ejpam-3573	51	26	x	x	X
ejpam-3573	51	27	is	be	AUX
ejpam-3573	51	28	continuous	continuous	ADJ
ejpam-3573	51	29	[	[	X
ejpam-3573	51	30	15	15	NUM
ejpam-3573	51	31	]	]	PUNCT
ejpam-3573	51	32	.	.	PUNCT
ejpam-3573	52	1	lemma	lemma	PROPN
ejpam-3573	52	2	1	1	NUM
ejpam-3573	52	3	(	(	PUNCT
ejpam-3573	52	4	[	[	X
ejpam-3573	52	5	16],[17	16],[17	PROPN
ejpam-3573	52	6	]	]	X
ejpam-3573	52	7	)	)	PUNCT
ejpam-3573	52	8	.	.	PUNCT
ejpam-3573	53	1	let	let	VERB
ejpam-3573	53	2	x	x	PRON
ejpam-3573	53	3	be	be	AUX
ejpam-3573	53	4	a	a	DET
ejpam-3573	53	5	metric	metric	ADJ
ejpam-3573	53	6	space	space	NOUN
ejpam-3573	53	7	.	.	PUNCT
ejpam-3573	54	1	if	if	SCONJ
ejpam-3573	54	2	f	f	PROPN
ejpam-3573	54	3	:	:	PUNCT
ejpam-3573	54	4	x	x	X
ejpam-3573	54	5	→	→	PUNCT
ejpam-3573	54	6	x	x	X
ejpam-3573	54	7	is	be	AUX
ejpam-3573	54	8	continuous	continuous	ADJ
ejpam-3573	54	9	,	,	PUNCT
ejpam-3573	54	10	then	then	ADV
ejpam-3573	54	11	[	[	X
ejpam-3573	54	12	f̂(u)]α	f̂(u)]α	NOUN
ejpam-3573	54	13	=	=	SYM
ejpam-3573	54	14	f([u]α	f([u]α	NOUN
ejpam-3573	54	15	)	)	PUNCT
ejpam-3573	54	16	.	.	PUNCT
ejpam-3573	55	1	a	a	DET
ejpam-3573	55	2	fuzzy	fuzzy	ADJ
ejpam-3573	55	3	set	set	NOUN
ejpam-3573	55	4	u	u	NOUN
ejpam-3573	55	5	is	be	AUX
ejpam-3573	55	6	piecewise	piecewise	NOUN
ejpam-3573	55	7	constant	constant	ADJ
ejpam-3573	55	8	if	if	SCONJ
ejpam-3573	55	9	there	there	PRON
ejpam-3573	55	10	exists	exist	VERB
ejpam-3573	55	11	a	a	DET
ejpam-3573	55	12	strictly	strictly	ADV
ejpam-3573	55	13	decreasing	decrease	VERB
ejpam-3573	55	14	sequence	sequence	NOUN
ejpam-3573	55	15	of	of	ADP
ejpam-3573	55	16	closed	closed	ADJ
ejpam-3573	55	17	subsets	subset	NOUN
ejpam-3573	55	18	{	{	PUNCT
ejpam-3573	55	19	c1	c1	PROPN
ejpam-3573	55	20	,	,	PUNCT
ejpam-3573	55	21	c2	c2	PROPN
ejpam-3573	55	22	,	,	PUNCT
ejpam-3573	55	23	·	·	PUNCT
ejpam-3573	55	24	·	·	PUNCT
ejpam-3573	55	25	·	·	PUNCT
ejpam-3573	55	26	,	,	PUNCT
ejpam-3573	55	27	ck	ck	INTJ
ejpam-3573	55	28	}	}	PUNCT
ejpam-3573	55	29	of	of	ADP
ejpam-3573	55	30	x	x	X
ejpam-3573	55	31	and	and	CCONJ
ejpam-3573	55	32	a	a	DET
ejpam-3573	55	33	strictly	strictly	ADV
ejpam-3573	55	34	increasing	increase	VERB
ejpam-3573	55	35	sequence	sequence	NOUN
ejpam-3573	55	36	of	of	ADP
ejpam-3573	55	37	real	real	ADJ
ejpam-3573	55	38	numbers	number	NOUN
ejpam-3573	55	39	{	{	PUNCT
ejpam-3573	55	40	α1	α1	PROPN
ejpam-3573	55	41	,	,	PUNCT
ejpam-3573	55	42	α2	α2	ADJ
ejpam-3573	55	43	,	,	PUNCT
ejpam-3573	55	44	·	·	PUNCT
ejpam-3573	55	45	·	·	PUNCT
ejpam-3573	55	46	·	·	PUNCT
ejpam-3573	55	47	,	,	PUNCT
ejpam-3573	55	48	αk	αk	INTJ
ejpam-3573	55	49	}	}	PUNCT
ejpam-3573	55	50	⊆	⊆	NUM
ejpam-3573	55	51	(	(	PUNCT
ejpam-3573	55	52	0	0	NUM
ejpam-3573	55	53	,	,	PUNCT
ejpam-3573	55	54	1	1	NUM
ejpam-3573	55	55	]	]	PUNCT
ejpam-3573	55	56	such	such	ADJ
ejpam-3573	55	57	that	that	SCONJ
ejpam-3573	55	58	[	[	X
ejpam-3573	55	59	u]α	u]α	X
ejpam-3573	55	60	=	=	ADJ
ejpam-3573	55	61	ci+1	ci+1	PROPN
ejpam-3573	55	62	,	,	PUNCT
ejpam-3573	55	63	where	where	SCONJ
ejpam-3573	55	64	α	α	X
ejpam-3573	55	65	∈	∈	PROPN
ejpam-3573	55	66	(	(	PUNCT
ejpam-3573	55	67	αi	αi	NOUN
ejpam-3573	55	68	,	,	PUNCT
ejpam-3573	55	69	αi+1	αi+1	NOUN
ejpam-3573	55	70	]	]	PUNCT
ejpam-3573	55	71	.	.	PUNCT
ejpam-3573	56	1	lemma	lemma	PROPN
ejpam-3573	56	2	2	2	NUM
ejpam-3573	56	3	(	(	PUNCT
ejpam-3573	56	4	[	[	X
ejpam-3573	56	5	18	18	NUM
ejpam-3573	56	6	]	]	NUM
ejpam-3573	56	7	)	)	PUNCT
ejpam-3573	56	8	.	.	PUNCT
ejpam-3573	57	1	for	for	ADP
ejpam-3573	57	2	any	any	DET
ejpam-3573	57	3	v	v	PROPN
ejpam-3573	57	4	∈	∈	PROPN
ejpam-3573	57	5	f(x	f(x	PROPN
ejpam-3573	57	6	)	)	PUNCT
ejpam-3573	57	7	and	and	CCONJ
ejpam-3573	57	8	ε	ε	X
ejpam-3573	57	9	>	>	X
ejpam-3573	57	10	0	0	PUNCT
ejpam-3573	58	1	there	there	PRON
ejpam-3573	58	2	exists	exist	VERB
ejpam-3573	58	3	a	a	DET
ejpam-3573	58	4	piecewise	piecewise	NOUN
ejpam-3573	58	5	constant	constant	ADJ
ejpam-3573	58	6	u	u	PROPN
ejpam-3573	58	7	∈	∈	PROPN
ejpam-3573	58	8	f(x	f(x	PROPN
ejpam-3573	58	9	)	)	PUNCT
ejpam-3573	58	10	such	such	ADJ
ejpam-3573	58	11	that	that	SCONJ
ejpam-3573	58	12	d∞(u	d∞(u	NOUN
ejpam-3573	58	13	,	,	PUNCT
ejpam-3573	58	14	v	v	NOUN
ejpam-3573	58	15	)	)	PUNCT
ejpam-3573	58	16	<	<	X
ejpam-3573	58	17	ε	ε	PROPN
ejpam-3573	58	18	,	,	PUNCT
ejpam-3573	58	19	i.e.	i.e.	X
ejpam-3573	58	20	,	,	PUNCT
ejpam-3573	58	21	the	the	DET
ejpam-3573	58	22	set	set	NOUN
ejpam-3573	58	23	of	of	ADP
ejpam-3573	58	24	piecewise	piecewise	NOUN
ejpam-3573	58	25	constant	constant	ADJ
ejpam-3573	58	26	fuzzy	fuzzy	ADJ
ejpam-3573	58	27	sets	set	NOUN
ejpam-3573	58	28	is	be	AUX
ejpam-3573	58	29	dense	dense	ADJ
ejpam-3573	58	30	in	in	ADP
ejpam-3573	58	31	f(x	f(x	PROPN
ejpam-3573	58	32	)	)	PUNCT
ejpam-3573	58	33	.	.	PUNCT
ejpam-3573	59	1	denote	denote	VERB
ejpam-3573	59	2	by	by	ADP
ejpam-3573	59	3	sf(x	sf(x	NOUN
ejpam-3573	59	4	)	)	PUNCT
ejpam-3573	59	5	the	the	DET
ejpam-3573	59	6	set	set	NOUN
ejpam-3573	59	7	of	of	ADP
ejpam-3573	59	8	piecewise	piecewise	NOUN
ejpam-3573	59	9	constant	constant	ADJ
ejpam-3573	59	10	fuzzy	fuzzy	ADJ
ejpam-3573	59	11	sets	set	NOUN
ejpam-3573	59	12	.	.	PUNCT
ejpam-3573	60	1	2.3	2.3	NUM
ejpam-3573	60	2	.	.	PUNCT
ejpam-3573	61	1	nonautonomous	nonautonomous	ADJ
ejpam-3573	61	2	discrete	discrete	ADJ
ejpam-3573	61	3	dynamical	dynamical	ADJ
ejpam-3573	61	4	systems	system	NOUN
ejpam-3573	61	5	for	for	ADP
ejpam-3573	61	6	a	a	DET
ejpam-3573	61	7	compact	compact	ADJ
ejpam-3573	61	8	metric	metric	ADJ
ejpam-3573	61	9	space	space	NOUN
ejpam-3573	61	10	x	x	NOUN
ejpam-3573	61	11	,	,	PUNCT
ejpam-3573	61	12	let	let	VERB
ejpam-3573	61	13	{	{	PUNCT
ejpam-3573	61	14	fn}∞n=1	fn}∞n=1	PUNCT
ejpam-3573	61	15	be	be	AUX
ejpam-3573	61	16	a	a	DET
ejpam-3573	61	17	sequence	sequence	NOUN
ejpam-3573	61	18	of	of	ADP
ejpam-3573	61	19	continuous	continuous	ADJ
ejpam-3573	61	20	maps	map	NOUN
ejpam-3573	61	21	,	,	PUNCT
ejpam-3573	61	22	where	where	SCONJ
ejpam-3573	61	23	fn	fn	NOUN
ejpam-3573	61	24	:	:	PUNCT
ejpam-3573	61	25	x	x	X
ejpam-3573	61	26	→	→	PUNCT
ejpam-3573	61	27	x.	x.	NOUN
ejpam-3573	61	28	an	an	DET
ejpam-3573	61	29	orbit	orbit	NOUN
ejpam-3573	61	30	{	{	PUNCT
ejpam-3573	61	31	xn}∞n=1	xn}∞n=1	X
ejpam-3573	61	32	of	of	ADP
ejpam-3573	61	33	a	a	DET
ejpam-3573	61	34	point	point	NOUN
ejpam-3573	61	35	x1	x1	NOUN
ejpam-3573	61	36	∈	∈	PROPN
ejpam-3573	61	37	x	x	PUNCT
ejpam-3573	61	38	is	be	AUX
ejpam-3573	61	39	defined	define	VERB
ejpam-3573	61	40	as	as	SCONJ
ejpam-3573	61	41	follows	follow	VERB
ejpam-3573	61	42	:	:	PUNCT
ejpam-3573	61	43	xn+1	xn+1	NUM
ejpam-3573	61	44	=	=	SYM
ejpam-3573	61	45	fn(xn	fn(xn	PROPN
ejpam-3573	61	46	)	)	PUNCT
ejpam-3573	61	47	,	,	PUNCT
ejpam-3573	61	48	n	n	NOUN
ejpam-3573	61	49	=	=	SYM
ejpam-3573	61	50	1	1	NUM
ejpam-3573	61	51	,	,	PUNCT
ejpam-3573	61	52	2	2	NUM
ejpam-3573	61	53	,	,	PUNCT
ejpam-3573	61	54	·	·	PUNCT
ejpam-3573	61	55	·	·	PUNCT
ejpam-3573	61	56	·	·	PUNCT
ejpam-3573	62	1	the	the	DET
ejpam-3573	62	2	set	set	NOUN
ejpam-3573	62	3	-	-	PUNCT
ejpam-3573	62	4	valued	value	VERB
ejpam-3573	62	5	extension	extension	NOUN
ejpam-3573	62	6	of	of	ADP
ejpam-3573	62	7	(	(	PUNCT
ejpam-3573	62	8	x	x	X
ejpam-3573	62	9	,	,	PUNCT
ejpam-3573	62	10	{	{	PUNCT
ejpam-3573	62	11	fn}∞n=1	fn}∞n=1	X
ejpam-3573	62	12	)	)	PUNCT
ejpam-3573	62	13	is	be	AUX
ejpam-3573	62	14	denoted	denote	VERB
ejpam-3573	62	15	by	by	ADP
ejpam-3573	62	16	(	(	PUNCT
ejpam-3573	62	17	k(x	k(x	PROPN
ejpam-3573	62	18	)	)	PUNCT
ejpam-3573	62	19	,	,	PUNCT
ejpam-3573	62	20	{	{	PUNCT
ejpam-3573	62	21	f̄n}∞n=1	f̄n}∞n=1	NOUN
ejpam-3573	62	22	)	)	PUNCT
ejpam-3573	62	23	.	.	PUNCT
ejpam-3573	63	1	denote	denote	VERB
ejpam-3573	63	2	fn	fn	INTJ
ejpam-3573	63	3	:	:	PUNCT
ejpam-3573	63	4	x	x	X
ejpam-3573	63	5	→	→	SYM
ejpam-3573	63	6	x	x	X
ejpam-3573	63	7	and	and	CCONJ
ejpam-3573	63	8	f̄n	f̄n	ADJ
ejpam-3573	63	9	:	:	PUNCT
ejpam-3573	63	10	k(x)→	k(x)→	PROPN
ejpam-3573	63	11	k(x	k(x	PROPN
ejpam-3573	63	12	)	)	PUNCT
ejpam-3573	63	13	by	by	ADP
ejpam-3573	63	14	fn(x	fn(x	NOUN
ejpam-3573	63	15	)	)	PUNCT
ejpam-3573	64	1	=	=	SYM
ejpam-3573	64	2	fn	fn	NOUN
ejpam-3573	64	3	◦	◦	NOUN
ejpam-3573	64	4	fn−1	fn−1	ADJ
ejpam-3573	64	5	·	·	PUNCT
ejpam-3573	64	6	·	·	PUNCT
ejpam-3573	64	7	·	·	PUNCT
ejpam-3573	65	1	◦	◦	VERB
ejpam-3573	65	2	f2	f2	ADV
ejpam-3573	65	3	◦	◦	NOUN
ejpam-3573	65	4	f1(x	f1(x	NUM
ejpam-3573	65	5	)	)	PUNCT
ejpam-3573	65	6	,	,	PUNCT
ejpam-3573	65	7	and	and	CCONJ
ejpam-3573	65	8	f̄n(x	f̄n(x	X
ejpam-3573	65	9	)	)	PUNCT
ejpam-3573	65	10	=	=	SYM
ejpam-3573	65	11	f̄n	f̄n	PROPN
ejpam-3573	65	12	◦	◦	NOUN
ejpam-3573	65	13	f̄n−1	f̄n−1	ADV
ejpam-3573	65	14	·	·	PUNCT
ejpam-3573	65	15	·	·	PUNCT
ejpam-3573	65	16	·	·	PUNCT
ejpam-3573	66	1	◦	◦	VERB
ejpam-3573	66	2	f̄2	f̄2	ADJ
ejpam-3573	66	3	◦	◦	NOUN
ejpam-3573	66	4	f̄1(x	f̄1(x	NUM
ejpam-3573	66	5	)	)	PUNCT
ejpam-3573	66	6	,	,	PUNCT
ejpam-3573	66	7	respectively	respectively	ADV
ejpam-3573	66	8	.	.	PUNCT
ejpam-3573	67	1	y.	y.	PROPN
ejpam-3573	67	2	lan	lan	PROPN
ejpam-3573	67	3	/	/	SYM
ejpam-3573	67	4	eur	eur	PROPN
ejpam-3573	67	5	.	.	PUNCT
ejpam-3573	68	1	j.	j.	PROPN
ejpam-3573	68	2	pure	pure	PROPN
ejpam-3573	68	3	appl	appl	PROPN
ejpam-3573	68	4	.	.	PROPN
ejpam-3573	68	5	math	math	PROPN
ejpam-3573	68	6	,	,	PUNCT
ejpam-3573	68	7	12	12	NUM
ejpam-3573	68	8	(	(	PUNCT
ejpam-3573	68	9	4	4	NUM
ejpam-3573	68	10	)	)	PUNCT
ejpam-3573	68	11	(	(	PUNCT
ejpam-3573	68	12	2019	2019	NUM
ejpam-3573	68	13	)	)	PUNCT
ejpam-3573	68	14	,	,	PUNCT
ejpam-3573	68	15	1689	1689	NUM
ejpam-3573	68	16	-	-	SYM
ejpam-3573	68	17	1700	1700	NUM
ejpam-3573	68	18	1692	1692	NUM
ejpam-3573	68	19	3	3	NUM
ejpam-3573	68	20	.	.	PUNCT
ejpam-3573	68	21	main	main	ADJ
ejpam-3573	68	22	results	result	NOUN
ejpam-3573	68	23	in	in	ADP
ejpam-3573	68	24	this	this	DET
ejpam-3573	68	25	section	section	NOUN
ejpam-3573	68	26	,	,	PUNCT
ejpam-3573	68	27	we	we	PRON
ejpam-3573	68	28	investigate	investigate	VERB
ejpam-3573	68	29	the	the	DET
ejpam-3573	68	30	relations	relation	NOUN
ejpam-3573	68	31	between	between	ADP
ejpam-3573	68	32	several	several	ADJ
ejpam-3573	68	33	forms	form	NOUN
ejpam-3573	68	34	of	of	ADP
ejpam-3573	68	35	sensitivity	sensitivity	NOUN
ejpam-3573	68	36	of	of	ADP
ejpam-3573	68	37	nonautonomous	nonautonomous	ADJ
ejpam-3573	68	38	dynamical	dynamical	ADJ
ejpam-3573	68	39	system	system	NOUN
ejpam-3573	68	40	and	and	CCONJ
ejpam-3573	68	41	its	its	PRON
ejpam-3573	68	42	induced	induced	ADJ
ejpam-3573	68	43	fuzzy	fuzzy	ADJ
ejpam-3573	68	44	systems	system	NOUN
ejpam-3573	68	45	.	.	PUNCT
ejpam-3573	69	1	let	let	VERB
ejpam-3573	69	2	(	(	PUNCT
ejpam-3573	69	3	x	x	NOUN
ejpam-3573	69	4	,	,	PUNCT
ejpam-3573	69	5	d	d	NOUN
ejpam-3573	69	6	)	)	PUNCT
ejpam-3573	69	7	be	be	AUX
ejpam-3573	69	8	a	a	DET
ejpam-3573	69	9	compact	compact	ADJ
ejpam-3573	69	10	metric	metric	ADJ
ejpam-3573	69	11	space	space	NOUN
ejpam-3573	69	12	and	and	CCONJ
ejpam-3573	69	13	{	{	PUNCT
ejpam-3573	69	14	fn}∞n=1	fn}∞n=1	X
ejpam-3573	69	15	be	be	AUX
ejpam-3573	69	16	a	a	DET
ejpam-3573	69	17	sequence	sequence	NOUN
ejpam-3573	69	18	of	of	ADP
ejpam-3573	69	19	continuous	continuous	ADJ
ejpam-3573	69	20	maps	map	NOUN
ejpam-3573	69	21	on	on	ADP
ejpam-3573	69	22	x.	x.	NOUN
ejpam-3573	69	23	for	for	ADP
ejpam-3573	69	24	(	(	PUNCT
ejpam-3573	69	25	x	x	X
ejpam-3573	69	26	,	,	PUNCT
ejpam-3573	69	27	{	{	PUNCT
ejpam-3573	69	28	f̂n}∞n=1	f̂n}∞n=1	PROPN
ejpam-3573	69	29	)	)	PUNCT
ejpam-3573	69	30	,	,	PUNCT
ejpam-3573	69	31	its	its	PRON
ejpam-3573	69	32	zadeh	zadeh	PROPN
ejpam-3573	69	33	’s	’s	PART
ejpam-3573	69	34	extension	extension	NOUN
ejpam-3573	69	35	(	(	PUNCT
ejpam-3573	69	36	or	or	CCONJ
ejpam-3573	69	37	fuzzification	fuzzification	NOUN
ejpam-3573	69	38	)	)	PUNCT
ejpam-3573	69	39	is	be	AUX
ejpam-3573	69	40	a	a	DET
ejpam-3573	69	41	sequence	sequence	NOUN
ejpam-3573	69	42	of	of	ADP
ejpam-3573	69	43	continuous	continuous	ADJ
ejpam-3573	69	44	maps	map	NOUN
ejpam-3573	69	45	f̂n	f̂n	NOUN
ejpam-3573	69	46	:	:	PUNCT
ejpam-3573	69	47	f(x)→	f(x)→	PUNCT
ejpam-3573	69	48	f(x	f(x	PROPN
ejpam-3573	69	49	)	)	PUNCT
ejpam-3573	69	50	defined	define	VERB
ejpam-3573	69	51	by	by	ADP
ejpam-3573	69	52	[	[	X
ejpam-3573	69	53	f̂n(u)](x	f̂n(u)](x	NOUN
ejpam-3573	69	54	)	)	PUNCT
ejpam-3573	69	55	=	=	SYM
ejpam-3573	69	56	supy∈f−1	supy∈f−1	NOUN
ejpam-3573	69	57	n	n	CCONJ
ejpam-3573	69	58	(	(	PUNCT
ejpam-3573	69	59	x){u(y	x){u(y	PROPN
ejpam-3573	69	60	)	)	PUNCT
ejpam-3573	69	61	}	}	PUNCT
ejpam-3573	69	62	,	,	PUNCT
ejpam-3573	69	63	for	for	ADP
ejpam-3573	69	64	any	any	DET
ejpam-3573	69	65	u	u	PROPN
ejpam-3573	69	66	∈	∈	PROPN
ejpam-3573	69	67	f(x	f(x	PROPN
ejpam-3573	69	68	)	)	PUNCT
ejpam-3573	69	69	and	and	CCONJ
ejpam-3573	69	70	x	x	PUNCT
ejpam-3573	69	71	∈	∈	NOUN
ejpam-3573	69	72	x.	x.	NOUN
ejpam-3573	70	1	an	an	DET
ejpam-3573	70	2	orbit	orbit	NOUN
ejpam-3573	70	3	{	{	PUNCT
ejpam-3573	70	4	un}∞n=1	un}∞n=1	NUM
ejpam-3573	70	5	of	of	ADP
ejpam-3573	70	6	a	a	DET
ejpam-3573	70	7	point	point	NOUN
ejpam-3573	70	8	u1	u1	NOUN
ejpam-3573	70	9	∈	∈	PROPN
ejpam-3573	70	10	f(x	f(x	PROPN
ejpam-3573	70	11	)	)	PUNCT
ejpam-3573	70	12	is	be	AUX
ejpam-3573	70	13	defined	define	VERB
ejpam-3573	70	14	as	as	SCONJ
ejpam-3573	70	15	follows	follow	VERB
ejpam-3573	70	16	:	:	PUNCT
ejpam-3573	70	17	un+1	un+1	PROPN
ejpam-3573	70	18	=	=	SYM
ejpam-3573	70	19	f̂n(un	f̂n(un	PROPN
ejpam-3573	70	20	)	)	PUNCT
ejpam-3573	70	21	,	,	PUNCT
ejpam-3573	70	22	n	n	NOUN
ejpam-3573	70	23	=	=	SYM
ejpam-3573	70	24	1	1	NUM
ejpam-3573	70	25	,	,	PUNCT
ejpam-3573	70	26	2	2	NUM
ejpam-3573	70	27	,	,	PUNCT
ejpam-3573	70	28	·	·	PUNCT
ejpam-3573	70	29	·	·	PUNCT
ejpam-3573	70	30	·	·	PUNCT
ejpam-3573	70	31	.	.	PUNCT
ejpam-3573	71	1	define	define	VERB
ejpam-3573	71	2	f̂n	f̂n	NOUN
ejpam-3573	71	3	:	:	PUNCT
ejpam-3573	71	4	f(x)→	f(x)→	PUNCT
ejpam-3573	71	5	f(x	f(x	PROPN
ejpam-3573	71	6	)	)	PUNCT
ejpam-3573	71	7	by	by	ADP
ejpam-3573	71	8	f̂n(u	f̂n(u	PROPN
ejpam-3573	71	9	)	)	PUNCT
ejpam-3573	72	1	=	=	SYM
ejpam-3573	72	2	f̂n	f̂n	NOUN
ejpam-3573	72	3	◦	◦	NOUN
ejpam-3573	72	4	f̂n−1	f̂n−1	NUM
ejpam-3573	72	5	·	·	PUNCT
ejpam-3573	72	6	·	·	PUNCT
ejpam-3573	72	7	·	·	PUNCT
ejpam-3573	72	8	◦	◦	NOUN
ejpam-3573	72	9	f̂2	f̂2	ADJ
ejpam-3573	72	10	◦	◦	NOUN
ejpam-3573	72	11	f̂1(u	f̂1(u	PROPN
ejpam-3573	72	12	)	)	PUNCT
ejpam-3573	72	13	,	,	PUNCT
ejpam-3573	72	14	for	for	ADP
ejpam-3573	72	15	any	any	DET
ejpam-3573	72	16	u	u	PROPN
ejpam-3573	72	17	∈	∈	PROPN
ejpam-3573	72	18	f(x	f(x	PROPN
ejpam-3573	72	19	)	)	PUNCT
ejpam-3573	72	20	.	.	PUNCT
ejpam-3573	73	1	definition	definition	NOUN
ejpam-3573	73	2	1	1	NUM
ejpam-3573	73	3	.	.	PUNCT
ejpam-3573	74	1	we	we	PRON
ejpam-3573	74	2	say	say	VERB
ejpam-3573	74	3	that	that	SCONJ
ejpam-3573	74	4	{	{	PUNCT
ejpam-3573	74	5	fn}∞n=1	fn}∞n=1	X
ejpam-3573	74	6	is	be	AUX
ejpam-3573	74	7	strong	strong	ADJ
ejpam-3573	74	8	sensitive	sensitive	ADJ
ejpam-3573	74	9	if	if	SCONJ
ejpam-3573	74	10	there	there	PRON
ejpam-3573	74	11	is	be	VERB
ejpam-3573	74	12	a	a	DET
ejpam-3573	74	13	constant	constant	ADJ
ejpam-3573	74	14	δ	δ	NOUN
ejpam-3573	74	15	>	>	X
ejpam-3573	74	16	0	0	NUM
ejpam-3573	74	17	such	such	ADJ
ejpam-3573	74	18	that	that	PRON
ejpam-3573	74	19	for	for	ADP
ejpam-3573	74	20	every	every	DET
ejpam-3573	74	21	point	point	NOUN
ejpam-3573	74	22	x	x	PUNCT
ejpam-3573	74	23	and	and	CCONJ
ejpam-3573	74	24	every	every	DET
ejpam-3573	74	25	neighborhood	neighborhood	NOUN
ejpam-3573	74	26	a	a	PRON
ejpam-3573	74	27	of	of	ADP
ejpam-3573	74	28	x	x	NOUN
ejpam-3573	74	29	,	,	PUNCT
ejpam-3573	74	30	there	there	PRON
ejpam-3573	74	31	is	be	VERB
ejpam-3573	74	32	a	a	DET
ejpam-3573	74	33	y	y	PROPN
ejpam-3573	74	34	∈	∈	PROPN
ejpam-3573	74	35	a	a	PRON
ejpam-3573	74	36	and	and	CCONJ
ejpam-3573	74	37	an	an	DET
ejpam-3573	74	38	integer	integer	NOUN
ejpam-3573	74	39	n0	n0	NOUN
ejpam-3573	74	40	such	such	ADJ
ejpam-3573	74	41	that	that	SCONJ
ejpam-3573	74	42	d(fk(x	d(fk(x	NOUN
ejpam-3573	74	43	)	)	PUNCT
ejpam-3573	74	44	,	,	PUNCT
ejpam-3573	74	45	fk(y	fk(y	NOUN
ejpam-3573	74	46	)	)	PUNCT
ejpam-3573	74	47	)	)	PUNCT
ejpam-3573	74	48	>	>	PUNCT
ejpam-3573	75	1	δ	δ	PROPN
ejpam-3573	75	2	for	for	ADP
ejpam-3573	75	3	every	every	DET
ejpam-3573	75	4	n	n	PRON
ejpam-3573	75	5	≥	≥	NOUN
ejpam-3573	75	6	n0	n0	NUM
ejpam-3573	75	7	.	.	PUNCT
ejpam-3573	76	1	mean	mean	VERB
ejpam-3573	76	2	sensitive	sensitive	ADJ
ejpam-3573	76	3	if	if	SCONJ
ejpam-3573	76	4	there	there	PRON
ejpam-3573	76	5	is	be	VERB
ejpam-3573	76	6	a	a	DET
ejpam-3573	76	7	constant	constant	ADJ
ejpam-3573	76	8	δ	δ	NOUN
ejpam-3573	76	9	>	>	X
ejpam-3573	76	10	0	0	NUM
ejpam-3573	77	1	such	such	ADJ
ejpam-3573	77	2	that	that	PRON
ejpam-3573	77	3	for	for	ADP
ejpam-3573	77	4	every	every	DET
ejpam-3573	77	5	point	point	NOUN
ejpam-3573	77	6	x	x	X
ejpam-3573	77	7	∈	∈	NOUN
ejpam-3573	77	8	x	x	X
ejpam-3573	77	9	and	and	CCONJ
ejpam-3573	77	10	every	every	DET
ejpam-3573	77	11	neighborhood	neighborhood	NOUN
ejpam-3573	77	12	a	a	PRON
ejpam-3573	77	13	of	of	ADP
ejpam-3573	77	14	x	x	NOUN
ejpam-3573	77	15	,	,	PUNCT
ejpam-3573	77	16	there	there	PRON
ejpam-3573	77	17	is	be	VERB
ejpam-3573	77	18	a	a	DET
ejpam-3573	77	19	y	y	PROPN
ejpam-3573	77	20	∈	∈	PROPN
ejpam-3573	77	21	a	a	DET
ejpam-3573	77	22	such	such	ADJ
ejpam-3573	77	23	that	that	SCONJ
ejpam-3573	77	24	lim	lim	PROPN
ejpam-3573	77	25	sup	sup	VERB
ejpam-3573	77	26	n→∞	n→∞	NUM
ejpam-3573	77	27	1	1	NUM
ejpam-3573	77	28	n	n	PROPN
ejpam-3573	77	29	n−1∑	n−1∑	NUM
ejpam-3573	77	30	i=0	i=0	PROPN
ejpam-3573	77	31	d(fi(x	d(fi(x	PROPN
ejpam-3573	77	32	)	)	PUNCT
ejpam-3573	77	33	,	,	PUNCT
ejpam-3573	77	34	fi(y	fi(y	NOUN
ejpam-3573	77	35	)	)	PUNCT
ejpam-3573	77	36	)	)	PUNCT
ejpam-3573	78	1	>	>	PUNCT
ejpam-3573	79	1	δ	δ	PROPN
ejpam-3573	79	2	.	.	PUNCT
ejpam-3573	80	1	we	we	PRON
ejpam-3573	80	2	call	call	VERB
ejpam-3573	80	3	(	(	PUNCT
ejpam-3573	80	4	x	x	NOUN
ejpam-3573	80	5	,	,	PUNCT
ejpam-3573	80	6	y	y	PROPN
ejpam-3573	80	7	)	)	PUNCT
ejpam-3573	80	8	a	a	DET
ejpam-3573	80	9	mean	mean	ADJ
ejpam-3573	80	10	sensitive	sensitive	ADJ
ejpam-3573	80	11	pair	pair	NOUN
ejpam-3573	80	12	.	.	PUNCT
ejpam-3573	81	1	definition	definition	NOUN
ejpam-3573	81	2	2	2	NUM
ejpam-3573	81	3	.	.	PUNCT
ejpam-3573	82	1	we	we	PRON
ejpam-3573	82	2	say	say	VERB
ejpam-3573	82	3	that	that	SCONJ
ejpam-3573	82	4	{	{	PUNCT
ejpam-3573	82	5	f̂n}∞n=0	f̂n}∞n=0	PROPN
ejpam-3573	82	6	is	be	AUX
ejpam-3573	82	7	strong	strong	ADJ
ejpam-3573	82	8	sensitive	sensitive	ADJ
ejpam-3573	82	9	if	if	SCONJ
ejpam-3573	82	10	there	there	PRON
ejpam-3573	82	11	is	be	VERB
ejpam-3573	82	12	a	a	DET
ejpam-3573	82	13	constant	constant	ADJ
ejpam-3573	82	14	δ	δ	NOUN
ejpam-3573	82	15	>	>	X
ejpam-3573	82	16	0	0	NUM
ejpam-3573	82	17	such	such	ADJ
ejpam-3573	82	18	that	that	PRON
ejpam-3573	82	19	for	for	ADP
ejpam-3573	82	20	every	every	DET
ejpam-3573	82	21	fuzzy	fuzzy	ADJ
ejpam-3573	82	22	set	set	VERB
ejpam-3573	82	23	u	u	PROPN
ejpam-3573	82	24	∈	∈	PROPN
ejpam-3573	82	25	f(x	f(x	PROPN
ejpam-3573	82	26	)	)	PUNCT
ejpam-3573	82	27	and	and	CCONJ
ejpam-3573	82	28	every	every	DET
ejpam-3573	82	29	neighborhood	neighborhood	NOUN
ejpam-3573	82	30	u	u	NOUN
ejpam-3573	82	31	about	about	ADP
ejpam-3573	82	32	u	u	NOUN
ejpam-3573	82	33	,	,	PUNCT
ejpam-3573	82	34	there	there	PRON
ejpam-3573	82	35	is	be	VERB
ejpam-3573	82	36	a	a	DET
ejpam-3573	82	37	v	v	NUM
ejpam-3573	82	38	∈	∈	NOUN
ejpam-3573	82	39	u	u	NOUN
ejpam-3573	82	40	and	and	CCONJ
ejpam-3573	82	41	an	an	DET
ejpam-3573	82	42	integer	integer	NOUN
ejpam-3573	82	43	n0	n0	NOUN
ejpam-3573	82	44	such	such	ADJ
ejpam-3573	82	45	that	that	SCONJ
ejpam-3573	82	46	d∞(f̂k(u	d∞(f̂k(u	NOUN
ejpam-3573	82	47	)	)	PUNCT
ejpam-3573	82	48	,	,	PUNCT
ejpam-3573	82	49	f̂k(v	f̂k(v	PROPN
ejpam-3573	82	50	)	)	PUNCT
ejpam-3573	82	51	)	)	PUNCT
ejpam-3573	82	52	≥	≥	PROPN
ejpam-3573	82	53	δ	δ	PROPN
ejpam-3573	82	54	for	for	ADP
ejpam-3573	82	55	every	every	DET
ejpam-3573	82	56	n	n	PRON
ejpam-3573	82	57	≥	≥	NOUN
ejpam-3573	82	58	n0	n0	NUM
ejpam-3573	82	59	.	.	PUNCT
ejpam-3573	83	1	mean	mean	VERB
ejpam-3573	83	2	sensitive	sensitive	ADJ
ejpam-3573	83	3	if	if	SCONJ
ejpam-3573	83	4	there	there	PRON
ejpam-3573	83	5	is	be	VERB
ejpam-3573	83	6	a	a	DET
ejpam-3573	83	7	constant	constant	ADJ
ejpam-3573	83	8	δ	δ	NOUN
ejpam-3573	83	9	>	>	X
ejpam-3573	83	10	0	0	NUM
ejpam-3573	84	1	such	such	ADJ
ejpam-3573	84	2	that	that	PRON
ejpam-3573	84	3	for	for	ADP
ejpam-3573	84	4	every	every	DET
ejpam-3573	84	5	fuzzy	fuzzy	ADJ
ejpam-3573	84	6	set	set	VERB
ejpam-3573	84	7	u	u	PROPN
ejpam-3573	84	8	∈	∈	PROPN
ejpam-3573	84	9	f(x	f(x	PROPN
ejpam-3573	84	10	)	)	PUNCT
ejpam-3573	84	11	and	and	CCONJ
ejpam-3573	84	12	every	every	DET
ejpam-3573	84	13	neighborhood	neighborhood	NOUN
ejpam-3573	84	14	u	u	NOUN
ejpam-3573	84	15	of	of	ADP
ejpam-3573	84	16	u	u	NOUN
ejpam-3573	84	17	,	,	PUNCT
ejpam-3573	84	18	there	there	PRON
ejpam-3573	84	19	is	be	VERB
ejpam-3573	84	20	a	a	DET
ejpam-3573	84	21	v	v	NUM
ejpam-3573	84	22	∈	∈	NOUN
ejpam-3573	84	23	u	u	NOUN
ejpam-3573	84	24	such	such	ADJ
ejpam-3573	84	25	that	that	SCONJ
ejpam-3573	84	26	lim	lim	PROPN
ejpam-3573	84	27	sup	sup	VERB
ejpam-3573	84	28	n→∞	n→∞	NUM
ejpam-3573	84	29	1	1	NUM
ejpam-3573	84	30	n	n	PROPN
ejpam-3573	84	31	n−1∑	n−1∑	NUM
ejpam-3573	84	32	i=0	i=0	ADJ
ejpam-3573	84	33	d∞(f̂i(u	d∞(f̂i(u	NOUN
ejpam-3573	84	34	)	)	PUNCT
ejpam-3573	84	35	,	,	PUNCT
ejpam-3573	84	36	f̂i(v	f̂i(v	PROPN
ejpam-3573	84	37	)	)	PUNCT
ejpam-3573	84	38	)	)	PUNCT
ejpam-3573	85	1	>	>	X
ejpam-3573	86	1	δ	δ	PROPN
ejpam-3573	86	2	.	.	PUNCT
ejpam-3573	87	1	proposition	proposition	NOUN
ejpam-3573	87	2	1	1	NUM
ejpam-3573	87	3	.	.	PUNCT
ejpam-3573	88	1	let	let	VERB
ejpam-3573	88	2	u	u	PRON
ejpam-3573	88	3	∈	∈	PROPN
ejpam-3573	88	4	f(x	f(x	PROPN
ejpam-3573	88	5	)	)	PUNCT
ejpam-3573	88	6	and	and	CCONJ
ejpam-3573	88	7	f̂n	f̂n	NOUN
ejpam-3573	88	8	:	:	PUNCT
ejpam-3573	88	9	f(x	f(x	PROPN
ejpam-3573	88	10	)	)	PUNCT
ejpam-3573	88	11	→	→	SYM
ejpam-3573	88	12	f(x	f(x	PROPN
ejpam-3573	88	13	)	)	PUNCT
ejpam-3573	88	14	.	.	PUNCT
ejpam-3573	89	1	then	then	ADV
ejpam-3573	89	2	[	[	X
ejpam-3573	89	3	f̂n(u)]α	f̂n(u)]α	PROPN
ejpam-3573	89	4	=	=	PUNCT
ejpam-3573	89	5	fn([u]α	fn([u]α	PROPN
ejpam-3573	89	6	)	)	PUNCT
ejpam-3573	89	7	for	for	ADP
ejpam-3573	89	8	α	α	PRON
ejpam-3573	89	9	∈	∈	PROPN
ejpam-3573	90	1	[	[	X
ejpam-3573	90	2	0	0	NUM
ejpam-3573	90	3	,	,	PUNCT
ejpam-3573	90	4	1	1	NUM
ejpam-3573	90	5	]	]	PUNCT
ejpam-3573	90	6	.	.	PUNCT
ejpam-3573	91	1	y.	y.	PROPN
ejpam-3573	91	2	lan	lan	PROPN
ejpam-3573	91	3	/	/	SYM
ejpam-3573	91	4	eur	eur	PROPN
ejpam-3573	91	5	.	.	PUNCT
ejpam-3573	92	1	j.	j.	PROPN
ejpam-3573	92	2	pure	pure	PROPN
ejpam-3573	92	3	appl	appl	PROPN
ejpam-3573	92	4	.	.	PROPN
ejpam-3573	92	5	math	math	PROPN
ejpam-3573	92	6	,	,	PUNCT
ejpam-3573	92	7	12	12	NUM
ejpam-3573	92	8	(	(	PUNCT
ejpam-3573	92	9	4	4	NUM
ejpam-3573	92	10	)	)	PUNCT
ejpam-3573	92	11	(	(	PUNCT
ejpam-3573	92	12	2019	2019	NUM
ejpam-3573	92	13	)	)	PUNCT
ejpam-3573	92	14	,	,	PUNCT
ejpam-3573	92	15	1689	1689	NUM
ejpam-3573	92	16	-	-	SYM
ejpam-3573	92	17	1700	1700	NUM
ejpam-3573	92	18	1693	1693	NUM
ejpam-3573	92	19	proof	proof	NOUN
ejpam-3573	92	20	.	.	PUNCT
ejpam-3573	93	1	take	take	VERB
ejpam-3573	93	2	u	u	NOUN
ejpam-3573	93	3	=	=	PROPN
ejpam-3573	93	4	ω1	ω1	PROPN
ejpam-3573	93	5	.	.	PUNCT
ejpam-3573	94	1	since	since	SCONJ
ejpam-3573	94	2	[	[	X
ejpam-3573	94	3	f̂(ω)]α	f̂(ω)]α	X
ejpam-3573	94	4	=	=	SYM
ejpam-3573	94	5	f([ω]α	f([ω]α	PROPN
ejpam-3573	94	6	)	)	PUNCT
ejpam-3573	94	7	and	and	CCONJ
ejpam-3573	94	8	f̂n(ωn	f̂n(ωn	PROPN
ejpam-3573	94	9	)	)	PUNCT
ejpam-3573	94	10	=	=	SYM
ejpam-3573	94	11	ωn+1	ωn+1	PROPN
ejpam-3573	94	12	for	for	ADP
ejpam-3573	94	13	n	n	NOUN
ejpam-3573	94	14	=	=	SYM
ejpam-3573	94	15	1	1	NUM
ejpam-3573	94	16	,	,	PUNCT
ejpam-3573	94	17	2	2	NUM
ejpam-3573	94	18	,	,	PUNCT
ejpam-3573	94	19	·	·	PUNCT
ejpam-3573	94	20	·	·	PUNCT
ejpam-3573	94	21	·	·	PUNCT
ejpam-3573	94	22	,	,	PUNCT
ejpam-3573	94	23	then	then	ADV
ejpam-3573	94	24	[	[	X
ejpam-3573	94	25	f̂n(u)]α	f̂n(u)]α	PROPN
ejpam-3573	94	26	=	=	PUNCT
ejpam-3573	95	1	[	[	X
ejpam-3573	95	2	f̂n(ω1)]α	f̂n(ω1)]α	X
ejpam-3573	95	3	=	=	NOUN
ejpam-3573	96	1	[	[	X
ejpam-3573	96	2	f̂n	f̂n	NOUN
ejpam-3573	96	3	◦	◦	VERB
ejpam-3573	96	4	f̂n−1	f̂n−1	NUM
ejpam-3573	96	5	◦	◦	NOUN
ejpam-3573	96	6	·	·	PUNCT
ejpam-3573	96	7	·	·	PUNCT
ejpam-3573	96	8	·	·	PUNCT
ejpam-3573	96	9	◦	◦	NOUN
ejpam-3573	96	10	f̂1(ω1)]α	f̂1(ω1)]α	PUNCT
ejpam-3573	96	11	)	)	PUNCT
ejpam-3573	96	12	=	=	NOUN
ejpam-3573	97	1	[	[	X
ejpam-3573	97	2	f̂n	f̂n	NOUN
ejpam-3573	97	3	◦	◦	VERB
ejpam-3573	97	4	f̂n−1	f̂n−1	NUM
ejpam-3573	97	5	◦	◦	NOUN
ejpam-3573	97	6	·	·	PUNCT
ejpam-3573	97	7	·	·	PUNCT
ejpam-3573	97	8	·	·	PUNCT
ejpam-3573	97	9	◦	◦	NOUN
ejpam-3573	97	10	f̂2(ω2)]α	f̂2(ω2)]α	NUM
ejpam-3573	97	11	)	)	PUNCT
ejpam-3573	97	12	=	=	NOUN
ejpam-3573	98	1	[	[	X
ejpam-3573	98	2	f̂n	f̂n	NOUN
ejpam-3573	98	3	◦	◦	VERB
ejpam-3573	98	4	f̂n−1	f̂n−1	NUM
ejpam-3573	98	5	◦	◦	NOUN
ejpam-3573	98	6	·	·	PUNCT
ejpam-3573	98	7	·	·	PUNCT
ejpam-3573	98	8	·	·	PUNCT
ejpam-3573	98	9	◦	◦	NOUN
ejpam-3573	98	10	f̂3(ω3)]α	f̂3(ω3)]α	NUM
ejpam-3573	98	11	)	)	PUNCT
ejpam-3573	98	12	=	=	SYM
ejpam-3573	98	13	·	·	PUNCT
ejpam-3573	98	14	·	·	PUNCT
ejpam-3573	98	15	·	·	PUNCT
ejpam-3573	99	1	=	=	PUNCT
ejpam-3573	100	1	[	[	X
ejpam-3573	100	2	f̂n(ωn)]α	f̂n(ωn)]α	NOUN
ejpam-3573	100	3	=	=	NOUN
ejpam-3573	100	4	fn([ωn]α	fn([ωn]α	NOUN
ejpam-3573	100	5	)	)	PUNCT
ejpam-3573	100	6	=	=	PUNCT
ejpam-3573	100	7	fn([f̂n−1(ωn−1)]α	fn([f̂n−1(ωn−1)]α	X
ejpam-3573	100	8	)	)	PUNCT
ejpam-3573	100	9	=	=	SYM
ejpam-3573	100	10	fn	fn	NOUN
ejpam-3573	100	11	◦	◦	NOUN
ejpam-3573	100	12	fn−1([ωn−1]α	fn−1([ωn−1]α	PUNCT
ejpam-3573	100	13	)	)	PUNCT
ejpam-3573	101	1	=	=	SYM
ejpam-3573	101	2	fn	fn	NOUN
ejpam-3573	101	3	◦	◦	NOUN
ejpam-3573	101	4	fn−1	fn−1	ADJ
ejpam-3573	101	5	◦	◦	NOUN
ejpam-3573	101	6	·	·	PUNCT
ejpam-3573	101	7	·	·	PUNCT
ejpam-3573	101	8	·	·	PUNCT
ejpam-3573	101	9	◦	◦	VERB
ejpam-3573	101	10	f1([ω1]α	f1([ω1]α	NUM
ejpam-3573	101	11	)	)	PUNCT
ejpam-3573	101	12	=	=	SYM
ejpam-3573	101	13	fn([ω1]α	fn([ω1]α	NOUN
ejpam-3573	101	14	)	)	PUNCT
ejpam-3573	101	15	=	=	SYM
ejpam-3573	101	16	fn([u]α	fn([u]α	NOUN
ejpam-3573	101	17	)	)	PUNCT
ejpam-3573	101	18	.	.	PUNCT
ejpam-3573	102	1	theorem	theorem	NOUN
ejpam-3573	102	2	1	1	NUM
ejpam-3573	102	3	.	.	PUNCT
ejpam-3573	103	1	if	if	SCONJ
ejpam-3573	103	2	{	{	PUNCT
ejpam-3573	103	3	f̂n}∞n=1	f̂n}∞n=1	PROPN
ejpam-3573	103	4	is	be	AUX
ejpam-3573	103	5	strongly	strongly	ADV
ejpam-3573	103	6	sensitive	sensitive	ADJ
ejpam-3573	103	7	,	,	PUNCT
ejpam-3573	103	8	then	then	ADV
ejpam-3573	103	9	{	{	PUNCT
ejpam-3573	103	10	fn}∞n=1	fn}∞n=1	X
ejpam-3573	103	11	is	be	AUX
ejpam-3573	103	12	strongly	strongly	ADV
ejpam-3573	103	13	sensitive	sensitive	ADJ
ejpam-3573	103	14	.	.	PUNCT
ejpam-3573	104	1	proof	proof	NOUN
ejpam-3573	104	2	.	.	PUNCT
ejpam-3573	105	1	let	let	VERB
ejpam-3573	105	2	x	x	SYM
ejpam-3573	105	3	∈	∈	PROPN
ejpam-3573	105	4	x.	x.	NOUN
ejpam-3573	105	5	take	take	VERB
ejpam-3573	105	6	u	u	NOUN
ejpam-3573	105	7	=	=	NOUN
ejpam-3573	105	8	x̂	x̂	NUM
ejpam-3573	105	9	∈	∈	PROPN
ejpam-3573	105	10	f(x	f(x	PROPN
ejpam-3573	105	11	)	)	PUNCT
ejpam-3573	105	12	.	.	PUNCT
ejpam-3573	106	1	since	since	SCONJ
ejpam-3573	106	2	{	{	PUNCT
ejpam-3573	106	3	f̂n}∞n=1	f̂n}∞n=1	PROPN
ejpam-3573	106	4	is	be	AUX
ejpam-3573	106	5	strongly	strongly	ADV
ejpam-3573	106	6	sensitive	sensitive	ADJ
ejpam-3573	106	7	,	,	PUNCT
ejpam-3573	106	8	there	there	PRON
ejpam-3573	106	9	exist	exist	VERB
ejpam-3573	106	10	δ	δ	PROPN
ejpam-3573	106	11	>	>	X
ejpam-3573	106	12	0	0	PUNCT
ejpam-3573	107	1	and	and	CCONJ
ejpam-3573	107	2	an	an	DET
ejpam-3573	107	3	integer	integer	NOUN
ejpam-3573	107	4	n0	n0	NOUN
ejpam-3573	107	5	such	such	ADJ
ejpam-3573	107	6	that	that	DET
ejpam-3573	107	7	d∞(f̂n(u	d∞(f̂n(u	NOUN
ejpam-3573	107	8	)	)	PUNCT
ejpam-3573	107	9	,	,	PUNCT
ejpam-3573	107	10	f̂n(ν	f̂n(ν	NOUN
ejpam-3573	107	11	)	)	PUNCT
ejpam-3573	107	12	)	)	PUNCT
ejpam-3573	108	1	=	=	PUNCT
ejpam-3573	108	2	d∞(f̂n(x̂	d∞(f̂n(x̂	NOUN
ejpam-3573	108	3	)	)	PUNCT
ejpam-3573	108	4	,	,	PUNCT
ejpam-3573	108	5	f̂n(ν	f̂n(ν	PROPN
ejpam-3573	108	6	)	)	PUNCT
ejpam-3573	108	7	)	)	PUNCT
ejpam-3573	109	1	=	=	SYM
ejpam-3573	109	2	sup	sup	NOUN
ejpam-3573	109	3	α∈[0,1	α∈[0,1	NUM
ejpam-3573	109	4	]	]	X
ejpam-3573	109	5	dh([f̂n(x̂)]α	dh([f̂n(x̂)]α	X
ejpam-3573	109	6	,	,	PUNCT
ejpam-3573	109	7	[	[	X
ejpam-3573	109	8	f̂n(ν)]α	f̂n(ν)]α	NOUN
ejpam-3573	109	9	)	)	PUNCT
ejpam-3573	109	10	=	=	SYM
ejpam-3573	109	11	sup	sup	PROPN
ejpam-3573	109	12	α∈[0,1	α∈[0,1	PROPN
ejpam-3573	109	13	]	]	X
ejpam-3573	109	14	dh(fn([x̂]α	dh(fn([x̂]α	PROPN
ejpam-3573	109	15	)	)	PUNCT
ejpam-3573	109	16	,	,	PUNCT
ejpam-3573	109	17	fn([ν]α	fn([ν]α	PROPN
ejpam-3573	109	18	)	)	PUNCT
ejpam-3573	109	19	)	)	PUNCT
ejpam-3573	110	1	=	=	SYM
ejpam-3573	110	2	sup	sup	NOUN
ejpam-3573	110	3	α∈[0,1	α∈[0,1	X
ejpam-3573	110	4	]	]	X
ejpam-3573	110	5	dh(f̄n({x	dh(f̄n({x	X
ejpam-3573	110	6	}	}	PUNCT
ejpam-3573	110	7	)	)	PUNCT
ejpam-3573	110	8	,	,	PUNCT
ejpam-3573	110	9	f̄n([ν]α	f̄n([ν]α	PROPN
ejpam-3573	110	10	)	)	PUNCT
ejpam-3573	110	11	)	)	PUNCT
ejpam-3573	111	1	=	=	SYM
ejpam-3573	111	2	sup	sup	NOUN
ejpam-3573	111	3	α∈[0,1	α∈[0,1	NOUN
ejpam-3573	111	4	]	]	X
ejpam-3573	111	5	{	{	PUNCT
ejpam-3573	111	6	sup	sup	NUM
ejpam-3573	111	7	y∈[ν]α	y∈[ν]α	NOUN
ejpam-3573	111	8	d(fn(x	d(fn(x	NOUN
ejpam-3573	111	9	)	)	PUNCT
ejpam-3573	111	10	,	,	PUNCT
ejpam-3573	111	11	fn(y	fn(y	PROPN
ejpam-3573	111	12	)	)	PUNCT
ejpam-3573	111	13	)	)	PUNCT
ejpam-3573	111	14	}	}	PUNCT
ejpam-3573	112	1	=	=	PUNCT
ejpam-3573	112	2	sup	sup	NOUN
ejpam-3573	112	3	y∈[ν]0	y∈[ν]0	PROPN
ejpam-3573	112	4	d(fn(x	d(fn(x	NOUN
ejpam-3573	112	5	)	)	PUNCT
ejpam-3573	112	6	,	,	PUNCT
ejpam-3573	112	7	fn(y	fn(y	PROPN
ejpam-3573	112	8	)	)	PUNCT
ejpam-3573	112	9	)	)	PUNCT
ejpam-3573	113	1	>	>	X
ejpam-3573	113	2	δ	δ	PROPN
ejpam-3573	113	3	.	.	PUNCT
ejpam-3573	114	1	for	for	ADP
ejpam-3573	114	2	all	all	DET
ejpam-3573	114	3	n	n	PRON
ejpam-3573	114	4	≥	≥	NOUN
ejpam-3573	114	5	n0	n0	NUM
ejpam-3573	114	6	.	.	PUNCT
ejpam-3573	115	1	thus	thus	ADV
ejpam-3573	115	2	it	it	PRON
ejpam-3573	115	3	follows	follow	VERB
ejpam-3573	115	4	from	from	ADP
ejpam-3573	115	5	the	the	DET
ejpam-3573	115	6	continuity	continuity	NOUN
ejpam-3573	115	7	of	of	ADP
ejpam-3573	115	8	{	{	PUNCT
ejpam-3573	115	9	fn}∞n=1	fn}∞n=1	PUNCT
ejpam-3573	115	10	and	and	CCONJ
ejpam-3573	115	11	the	the	DET
ejpam-3573	115	12	compactness	compactness	NOUN
ejpam-3573	115	13	of	of	ADP
ejpam-3573	115	14	[	[	X
ejpam-3573	115	15	ν]0	ν]0	X
ejpam-3573	115	16	that	that	SCONJ
ejpam-3573	115	17	there	there	PRON
ejpam-3573	115	18	exists	exist	VERB
ejpam-3573	115	19	y∗	y∗	PROPN
ejpam-3573	115	20	∈	∈	PROPN
ejpam-3573	116	1	[	[	X
ejpam-3573	116	2	ν]0	ν]0	X
ejpam-3573	116	3	such	such	ADJ
ejpam-3573	116	4	that	that	SCONJ
ejpam-3573	116	5	d∞(f̂n(x̂	d∞(f̂n(x̂	NOUN
ejpam-3573	116	6	)	)	PUNCT
ejpam-3573	116	7	,	,	PUNCT
ejpam-3573	116	8	f̂n(ν	f̂n(ν	PROPN
ejpam-3573	116	9	)	)	PUNCT
ejpam-3573	116	10	)	)	PUNCT
ejpam-3573	117	1	=	=	PUNCT
ejpam-3573	117	2	d(fn(x	d(fn(x	ADJ
ejpam-3573	117	3	)	)	PUNCT
ejpam-3573	117	4	,	,	PUNCT
ejpam-3573	117	5	fn(y∗	fn(y∗	NUM
ejpam-3573	117	6	)	)	PUNCT
ejpam-3573	117	7	)	)	PUNCT
ejpam-3573	117	8	>	>	PUNCT
ejpam-3573	118	1	δ	δ	PROPN
ejpam-3573	118	2	.	.	PUNCT
ejpam-3573	119	1	on	on	ADP
ejpam-3573	119	2	the	the	DET
ejpam-3573	119	3	other	other	ADJ
ejpam-3573	119	4	hand	hand	NOUN
ejpam-3573	119	5	,	,	PUNCT
ejpam-3573	119	6	since	since	SCONJ
ejpam-3573	119	7	ν	ν	PROPN
ejpam-3573	119	8	∈	∈	PROPN
ejpam-3573	119	9	ud∞(x̂	ud∞(x̂	PROPN
ejpam-3573	119	10	,	,	PUNCT
ejpam-3573	119	11	ε	ε	PROPN
ejpam-3573	119	12	)	)	PUNCT
ejpam-3573	119	13	,	,	PUNCT
ejpam-3573	119	14	we	we	PRON
ejpam-3573	119	15	have	have	VERB
ejpam-3573	119	16	[	[	X
ejpam-3573	119	17	ν]0	ν]0	PROPN
ejpam-3573	119	18	⊂	⊂	X
ejpam-3573	119	19	udh	udh	PROPN
ejpam-3573	119	20	(	(	PUNCT
ejpam-3573	119	21	{	{	PUNCT
ejpam-3573	119	22	x	x	NOUN
ejpam-3573	119	23	}	}	PUNCT
ejpam-3573	119	24	,	,	PUNCT
ejpam-3573	119	25	ε	ε	PROPN
ejpam-3573	119	26	)	)	PUNCT
ejpam-3573	119	27	and	and	CCONJ
ejpam-3573	119	28	then	then	ADV
ejpam-3573	119	29	y∗	y∗	PROPN
ejpam-3573	119	30	∈	∈	PROPN
ejpam-3573	119	31	ud(x	ud(x	X
ejpam-3573	119	32	,	,	PUNCT
ejpam-3573	119	33	ε	ε	PROPN
ejpam-3573	119	34	)	)	PUNCT
ejpam-3573	119	35	.	.	PUNCT
ejpam-3573	120	1	consequently	consequently	ADV
ejpam-3573	120	2	,	,	PUNCT
ejpam-3573	120	3	{	{	PUNCT
ejpam-3573	120	4	fn}∞n=1	fn}∞n=1	X
ejpam-3573	120	5	is	be	AUX
ejpam-3573	120	6	strongly	strongly	ADV
ejpam-3573	120	7	sensitive	sensitive	ADJ
ejpam-3573	120	8	in	in	ADP
ejpam-3573	120	9	x.	x.	NOUN
ejpam-3573	120	10	claim	claim	NOUN
ejpam-3573	120	11	1	1	NUM
ejpam-3573	120	12	if	if	SCONJ
ejpam-3573	120	13	{	{	PUNCT
ejpam-3573	120	14	f̄n}∞n=1	f̄n}∞n=1	NOUN
ejpam-3573	120	15	is	be	AUX
ejpam-3573	120	16	strongly	strongly	ADV
ejpam-3573	120	17	sensitive	sensitive	ADJ
ejpam-3573	120	18	in	in	ADP
ejpam-3573	120	19	l(x	l(x	PROPN
ejpam-3573	120	20	)	)	PUNCT
ejpam-3573	120	21	,	,	PUNCT
ejpam-3573	120	22	then	then	ADV
ejpam-3573	120	23	it	it	PRON
ejpam-3573	120	24	is	be	AUX
ejpam-3573	120	25	strongly	strongly	ADV
ejpam-3573	120	26	sensitive	sensitive	ADJ
ejpam-3573	120	27	in	in	ADP
ejpam-3573	120	28	k(x	k(x	PROPN
ejpam-3573	120	29	)	)	PUNCT
ejpam-3573	120	30	.	.	PUNCT
ejpam-3573	121	1	proof	proof	NOUN
ejpam-3573	121	2	.	.	PUNCT
ejpam-3573	122	1	let	let	VERB
ejpam-3573	122	2	b	b	NOUN
ejpam-3573	122	3	∈	∈	PROPN
ejpam-3573	122	4	l(x	l(x	PROPN
ejpam-3573	122	5	)	)	PUNCT
ejpam-3573	122	6	.	.	PUNCT
ejpam-3573	123	1	since	since	SCONJ
ejpam-3573	123	2	l(x	l(x	PROPN
ejpam-3573	123	3	)	)	PUNCT
ejpam-3573	123	4	is	be	AUX
ejpam-3573	123	5	dense	dense	ADJ
ejpam-3573	123	6	in	in	ADP
ejpam-3573	123	7	k(x	k(x	PROPN
ejpam-3573	123	8	)	)	PUNCT
ejpam-3573	123	9	,	,	PUNCT
ejpam-3573	123	10	for	for	ADP
ejpam-3573	123	11	any	any	DET
ejpam-3573	123	12	ε	ε	PROPN
ejpam-3573	123	13	>	>	X
ejpam-3573	123	14	0	0	PROPN
ejpam-3573	123	15	,	,	PUNCT
ejpam-3573	123	16	there	there	PRON
ejpam-3573	123	17	exists	exist	VERB
ejpam-3573	123	18	a	a	DET
ejpam-3573	123	19	∈	∈	NOUN
ejpam-3573	123	20	l(x	l(x	NOUN
ejpam-3573	123	21	)	)	PUNCT
ejpam-3573	123	22	such	such	ADJ
ejpam-3573	123	23	that	that	SCONJ
ejpam-3573	123	24	a	a	DET
ejpam-3573	123	25	∈	∈	PROPN
ejpam-3573	123	26	udh	udh	NOUN
ejpam-3573	123	27	(	(	PUNCT
ejpam-3573	123	28	b	b	NOUN
ejpam-3573	123	29	,	,	PUNCT
ejpam-3573	123	30	ε	ε	PROPN
ejpam-3573	123	31	)	)	PUNCT
ejpam-3573	123	32	.	.	PUNCT
ejpam-3573	124	1	due	due	ADP
ejpam-3573	124	2	to	to	ADP
ejpam-3573	124	3	the	the	DET
ejpam-3573	124	4	strong	strong	ADJ
ejpam-3573	124	5	sensitivity	sensitivity	NOUN
ejpam-3573	124	6	of	of	ADP
ejpam-3573	124	7	{	{	PUNCT
ejpam-3573	124	8	f̄n}∞n=1	f̄n}∞n=1	PROPN
ejpam-3573	124	9	in	in	ADP
ejpam-3573	124	10	l(x	l(x	PROPN
ejpam-3573	124	11	)	)	PUNCT
ejpam-3573	124	12	,	,	PUNCT
ejpam-3573	124	13	y.	y.	PROPN
ejpam-3573	124	14	lan	lan	PROPN
ejpam-3573	124	15	/	/	SYM
ejpam-3573	124	16	eur	eur	PROPN
ejpam-3573	124	17	.	.	PUNCT
ejpam-3573	125	1	j.	j.	PROPN
ejpam-3573	125	2	pure	pure	PROPN
ejpam-3573	125	3	appl	appl	PROPN
ejpam-3573	125	4	.	.	PROPN
ejpam-3573	125	5	math	math	PROPN
ejpam-3573	125	6	,	,	PUNCT
ejpam-3573	125	7	12	12	NUM
ejpam-3573	125	8	(	(	PUNCT
ejpam-3573	125	9	4	4	NUM
ejpam-3573	125	10	)	)	PUNCT
ejpam-3573	125	11	(	(	PUNCT
ejpam-3573	125	12	2019	2019	NUM
ejpam-3573	125	13	)	)	PUNCT
ejpam-3573	125	14	,	,	PUNCT
ejpam-3573	125	15	1689	1689	NUM
ejpam-3573	125	16	-	-	SYM
ejpam-3573	125	17	1700	1700	NUM
ejpam-3573	125	18	1694	1694	NUM
ejpam-3573	125	19	there	there	PRON
ejpam-3573	125	20	exist	exist	VERB
ejpam-3573	125	21	a	a	DET
ejpam-3573	125	22	constant	constant	ADJ
ejpam-3573	125	23	δ	δ	NOUN
ejpam-3573	125	24	>	>	X
ejpam-3573	125	25	0	0	PUNCT
ejpam-3573	126	1	and	and	CCONJ
ejpam-3573	126	2	an	an	DET
ejpam-3573	126	3	integer	integer	NOUN
ejpam-3573	126	4	n0	n0	NOUN
ejpam-3573	126	5	such	such	ADJ
ejpam-3573	126	6	that	that	SCONJ
ejpam-3573	126	7	dh(f̄k(a	dh(f̄k(a	NOUN
ejpam-3573	126	8	)	)	PUNCT
ejpam-3573	126	9	,	,	PUNCT
ejpam-3573	126	10	f̄k(b	f̄k(b	NOUN
ejpam-3573	126	11	)	)	PUNCT
ejpam-3573	126	12	)	)	PUNCT
ejpam-3573	126	13	≥	≥	X
ejpam-3573	126	14	δ	δ	PROPN
ejpam-3573	126	15	for	for	ADP
ejpam-3573	126	16	all	all	DET
ejpam-3573	126	17	n	n	PRON
ejpam-3573	126	18	≥	≥	NOUN
ejpam-3573	126	19	n0	n0	NUM
ejpam-3573	126	20	.	.	PUNCT
ejpam-3573	127	1	this	this	PRON
ejpam-3573	127	2	completes	complete	VERB
ejpam-3573	127	3	the	the	DET
ejpam-3573	127	4	proof	proof	NOUN
ejpam-3573	127	5	.	.	PUNCT
ejpam-3573	128	1	apply	apply	VERB
ejpam-3573	128	2	the	the	DET
ejpam-3573	128	3	similar	similar	ADJ
ejpam-3573	128	4	technique	technique	NOUN
ejpam-3573	128	5	to	to	ADP
ejpam-3573	128	6	(	(	PUNCT
ejpam-3573	128	7	f(x	f(x	PROPN
ejpam-3573	128	8	)	)	PUNCT
ejpam-3573	128	9	,	,	PUNCT
ejpam-3573	128	10	{	{	PUNCT
ejpam-3573	128	11	f̂n}∞n=1	f̂n}∞n=1	PROPN
ejpam-3573	128	12	)	)	PUNCT
ejpam-3573	128	13	,	,	PUNCT
ejpam-3573	128	14	the	the	DET
ejpam-3573	128	15	following	following	ADJ
ejpam-3573	128	16	result	result	NOUN
ejpam-3573	128	17	is	be	AUX
ejpam-3573	128	18	obtained	obtain	VERB
ejpam-3573	128	19	:	:	PUNCT
ejpam-3573	128	20	claim	claim	NOUN
ejpam-3573	128	21	2	2	NUM
ejpam-3573	128	22	if	if	SCONJ
ejpam-3573	128	23	{	{	PUNCT
ejpam-3573	128	24	f̂n}∞n=1	f̂n}∞n=1	PROPN
ejpam-3573	128	25	is	be	AUX
ejpam-3573	128	26	strongly	strongly	ADV
ejpam-3573	128	27	sensitive	sensitive	ADJ
ejpam-3573	128	28	in	in	ADP
ejpam-3573	128	29	sf(x	sf(x	NOUN
ejpam-3573	128	30	)	)	PUNCT
ejpam-3573	128	31	,	,	PUNCT
ejpam-3573	128	32	then	then	ADV
ejpam-3573	128	33	it	it	PRON
ejpam-3573	128	34	is	be	AUX
ejpam-3573	128	35	strongly	strongly	ADV
ejpam-3573	128	36	sensitive	sensitive	ADJ
ejpam-3573	128	37	in	in	ADP
ejpam-3573	128	38	f(x	f(x	PROPN
ejpam-3573	128	39	)	)	PUNCT
ejpam-3573	128	40	.	.	PUNCT
ejpam-3573	129	1	proposition	proposition	NOUN
ejpam-3573	129	2	2	2	NUM
ejpam-3573	129	3	.	.	PUNCT
ejpam-3573	130	1	the	the	DET
ejpam-3573	130	2	following	follow	VERB
ejpam-3573	130	3	conditions	condition	NOUN
ejpam-3573	130	4	are	be	AUX
ejpam-3573	130	5	equivalent	equivalent	ADJ
ejpam-3573	130	6	:	:	PUNCT
ejpam-3573	130	7	(	(	PUNCT
ejpam-3573	130	8	1	1	X
ejpam-3573	130	9	)	)	PUNCT
ejpam-3573	130	10	{	{	PUNCT
ejpam-3573	130	11	f̂n}∞n=1	f̂n}∞n=1	PROPN
ejpam-3573	130	12	is	be	AUX
ejpam-3573	130	13	strongly	strongly	ADV
ejpam-3573	130	14	sensitive	sensitive	ADJ
ejpam-3573	130	15	.	.	PUNCT
ejpam-3573	131	1	(	(	PUNCT
ejpam-3573	131	2	2	2	X
ejpam-3573	131	3	)	)	PUNCT
ejpam-3573	131	4	{	{	PUNCT
ejpam-3573	131	5	f̄n}∞n=1	f̄n}∞n=1	PROPN
ejpam-3573	131	6	is	be	AUX
ejpam-3573	131	7	strongly	strongly	ADV
ejpam-3573	131	8	sensitive	sensitive	ADJ
ejpam-3573	131	9	.	.	PUNCT
ejpam-3573	132	1	proof	proof	NOUN
ejpam-3573	132	2	.	.	PUNCT
ejpam-3573	133	1	(	(	PUNCT
ejpam-3573	133	2	1)⇒	1)⇒	NUM
ejpam-3573	133	3	(	(	PUNCT
ejpam-3573	133	4	2	2	NUM
ejpam-3573	133	5	)	)	PUNCT
ejpam-3573	133	6	since	since	SCONJ
ejpam-3573	133	7	l(x	l(x	PROPN
ejpam-3573	133	8	)	)	PUNCT
ejpam-3573	133	9	is	be	AUX
ejpam-3573	133	10	dense	dense	ADJ
ejpam-3573	133	11	in	in	ADP
ejpam-3573	133	12	k(x	k(x	PROPN
ejpam-3573	133	13	)	)	PUNCT
ejpam-3573	133	14	,	,	PUNCT
ejpam-3573	133	15	by	by	ADP
ejpam-3573	133	16	claim	claim	NOUN
ejpam-3573	133	17	1	1	NUM
ejpam-3573	133	18	,	,	PUNCT
ejpam-3573	133	19	it	it	PRON
ejpam-3573	133	20	is	be	AUX
ejpam-3573	133	21	sufficient	sufficient	ADJ
ejpam-3573	133	22	to	to	PART
ejpam-3573	133	23	show	show	VERB
ejpam-3573	133	24	that	that	SCONJ
ejpam-3573	133	25	{	{	PUNCT
ejpam-3573	133	26	f̄n}∞n=1	f̄n}∞n=1	PROPN
ejpam-3573	133	27	|l(x	|l(x	PROPN
ejpam-3573	133	28	)	)	PUNCT
ejpam-3573	133	29	is	be	AUX
ejpam-3573	133	30	strongly	strongly	ADV
ejpam-3573	133	31	sensitive	sensitive	ADJ
ejpam-3573	133	32	.	.	PUNCT
ejpam-3573	134	1	let	let	VERB
ejpam-3573	134	2	{	{	PUNCT
ejpam-3573	134	3	f̂n}∞n=1	f̂n}∞n=1	PROPN
ejpam-3573	134	4	be	be	AUX
ejpam-3573	134	5	strongly	strongly	ADV
ejpam-3573	134	6	sensitive	sensitive	ADJ
ejpam-3573	134	7	with	with	ADP
ejpam-3573	134	8	sensitive	sensitive	ADJ
ejpam-3573	134	9	constant	constant	ADJ
ejpam-3573	134	10	δ	δ	PROPN
ejpam-3573	134	11	and	and	CCONJ
ejpam-3573	134	12	a	a	PRON
ejpam-3573	134	13	=	=	X
ejpam-3573	134	14	{	{	PUNCT
ejpam-3573	134	15	x1	x1	PROPN
ejpam-3573	134	16	,	,	PUNCT
ejpam-3573	134	17	x2	x2	PROPN
ejpam-3573	134	18	,	,	PUNCT
ejpam-3573	134	19	·	·	PUNCT
ejpam-3573	134	20	·	·	PUNCT
ejpam-3573	134	21	·	·	PUNCT
ejpam-3573	134	22	,	,	PUNCT
ejpam-3573	134	23	xk	xk	ADJ
ejpam-3573	134	24	}	}	PUNCT
ejpam-3573	134	25	∈	∈	PROPN
ejpam-3573	134	26	l(x	l(x	PROPN
ejpam-3573	134	27	)	)	PUNCT
ejpam-3573	134	28	.	.	PUNCT
ejpam-3573	135	1	take	take	VERB
ejpam-3573	135	2	ui	ui	NOUN
ejpam-3573	135	3	=	=	PUNCT
ejpam-3573	135	4	x̂i	x̂i	PROPN
ejpam-3573	135	5	for	for	ADP
ejpam-3573	135	6	1	1	NUM
ejpam-3573	135	7	≤	≤	NUM
ejpam-3573	135	8	i	i	NOUN
ejpam-3573	135	9	≤	≤	PROPN
ejpam-3573	136	1	k	k	X
ejpam-3573	136	2	,	,	PUNCT
ejpam-3573	136	3	then	then	ADV
ejpam-3573	136	4	ui	ui	PROPN
ejpam-3573	136	5	∈	∈	PROPN
ejpam-3573	136	6	f(x	f(x	PROPN
ejpam-3573	136	7	)	)	PUNCT
ejpam-3573	136	8	.	.	PUNCT
ejpam-3573	137	1	since	since	SCONJ
ejpam-3573	137	2	{	{	PUNCT
ejpam-3573	137	3	f̂n}∞n=1	f̂n}∞n=1	PROPN
ejpam-3573	137	4	is	be	AUX
ejpam-3573	137	5	strongly	strongly	ADV
ejpam-3573	137	6	sensitive	sensitive	ADJ
ejpam-3573	137	7	,	,	PUNCT
ejpam-3573	137	8	for	for	ADP
ejpam-3573	137	9	each	each	DET
ejpam-3573	137	10	ui	ui	NOUN
ejpam-3573	137	11	,	,	PUNCT
ejpam-3573	137	12	there	there	PRON
ejpam-3573	137	13	exist	exist	VERB
ejpam-3573	137	14	vi	vi	PROPN
ejpam-3573	137	15	∈	∈	PROPN
ejpam-3573	137	16	ud∞(ui	ud∞(ui	PROPN
ejpam-3573	137	17	,	,	PUNCT
ejpam-3573	137	18	ε	ε	PROPN
ejpam-3573	137	19	)	)	PUNCT
ejpam-3573	137	20	and	and	CCONJ
ejpam-3573	137	21	an	an	DET
ejpam-3573	137	22	integer	integer	NOUN
ejpam-3573	137	23	ni	ni	PROPN
ejpam-3573	137	24	such	such	ADJ
ejpam-3573	137	25	that	that	SCONJ
ejpam-3573	137	26	d∞(f̂r(ui	d∞(f̂r(ui	NUM
ejpam-3573	137	27	)	)	PUNCT
ejpam-3573	137	28	,	,	PUNCT
ejpam-3573	137	29	f̂r(vi	f̂r(vi	ADJ
ejpam-3573	137	30	)	)	PUNCT
ejpam-3573	137	31	)	)	PUNCT
ejpam-3573	137	32	>	>	X
ejpam-3573	138	1	2δ	2δ	NUM
ejpam-3573	138	2	for	for	ADP
ejpam-3573	138	3	all	all	DET
ejpam-3573	138	4	r	r	NOUN
ejpam-3573	138	5	>	>	X
ejpam-3573	138	6	ni	ni	PROPN
ejpam-3573	138	7	,	,	PUNCT
ejpam-3573	138	8	where	where	SCONJ
ejpam-3573	138	9	i	i	PRON
ejpam-3573	138	10	=	=	NOUN
ejpam-3573	138	11	1	1	NUM
ejpam-3573	138	12	,	,	PUNCT
ejpam-3573	138	13	2	2	NUM
ejpam-3573	138	14	,	,	PUNCT
ejpam-3573	138	15	·	·	PUNCT
ejpam-3573	138	16	·	·	PUNCT
ejpam-3573	138	17	·	·	PUNCT
ejpam-3573	138	18	,	,	PUNCT
ejpam-3573	138	19	k.	k.	PROPN
ejpam-3573	138	20	set	set	VERB
ejpam-3573	138	21	n	n	PROPN
ejpam-3573	138	22	=	=	PUNCT
ejpam-3573	138	23	max{ni	max{ni	NOUN
ejpam-3573	138	24	:	:	PUNCT
ejpam-3573	138	25	1	1	X
ejpam-3573	138	26	≤	≤	NUM
ejpam-3573	138	27	i	i	X
ejpam-3573	138	28	≤	≤	PUNCT
ejpam-3573	139	1	k	k	X
ejpam-3573	139	2	}	}	PUNCT
ejpam-3573	139	3	.	.	PUNCT
ejpam-3573	140	1	now	now	ADV
ejpam-3573	140	2	we	we	PRON
ejpam-3573	140	3	show	show	VERB
ejpam-3573	140	4	that	that	SCONJ
ejpam-3573	140	5	dh(f̄n(a	dh(f̄n(a	NOUN
ejpam-3573	140	6	)	)	PUNCT
ejpam-3573	140	7	,	,	PUNCT
ejpam-3573	140	8	f̄n(b	f̄n(b	NOUN
ejpam-3573	140	9	)	)	PUNCT
ejpam-3573	140	10	)	)	PUNCT
ejpam-3573	140	11	>	>	PUNCT
ejpam-3573	141	1	δ	δ	PROPN
ejpam-3573	141	2	for	for	ADP
ejpam-3573	141	3	all	all	DET
ejpam-3573	141	4	b	b	PROPN
ejpam-3573	141	5	∈	∈	PROPN
ejpam-3573	141	6	udh	udh	NOUN
ejpam-3573	141	7	(	(	PUNCT
ejpam-3573	141	8	a	a	PRON
ejpam-3573	141	9	,	,	PUNCT
ejpam-3573	141	10	ε	ε	PROPN
ejpam-3573	141	11	)	)	PUNCT
ejpam-3573	141	12	and	and	CCONJ
ejpam-3573	141	13	n	n	CCONJ
ejpam-3573	141	14	>	>	X
ejpam-3573	141	15	n	n	CCONJ
ejpam-3573	141	16	.	.	PUNCT
ejpam-3573	142	1	let	let	VERB
ejpam-3573	142	2	n	n	PRON
ejpam-3573	142	3	>	>	X
ejpam-3573	142	4	n	n	PROPN
ejpam-3573	142	5	.	.	PUNCT
ejpam-3573	143	1	then	then	ADV
ejpam-3573	143	2	for	for	ADP
ejpam-3573	143	3	any	any	DET
ejpam-3573	143	4	ui	ui	NOUN
ejpam-3573	143	5	,	,	PUNCT
ejpam-3573	143	6	there	there	PRON
ejpam-3573	143	7	exists	exist	VERB
ejpam-3573	143	8	vi	vi	PROPN
ejpam-3573	143	9	∈	∈	PROPN
ejpam-3573	143	10	ud∞(ui	ud∞(ui	PROPN
ejpam-3573	143	11	,	,	PUNCT
ejpam-3573	143	12	ε	ε	PROPN
ejpam-3573	143	13	)	)	PUNCT
ejpam-3573	143	14	such	such	ADJ
ejpam-3573	143	15	that	that	DET
ejpam-3573	143	16	d∞(f̂n(ui	d∞(f̂n(ui	NOUN
ejpam-3573	143	17	)	)	PUNCT
ejpam-3573	143	18	,	,	PUNCT
ejpam-3573	143	19	f̂n(vi	f̂n(vi	PROPN
ejpam-3573	143	20	)	)	PUNCT
ejpam-3573	143	21	)	)	PUNCT
ejpam-3573	143	22	>	>	X
ejpam-3573	144	1	2δ	2δ	NUM
ejpam-3573	144	2	.	.	PUNCT
ejpam-3573	145	1	set	set	VERB
ejpam-3573	145	2	c	c	NOUN
ejpam-3573	145	3	=	=	PRON
ejpam-3573	145	4	{	{	PUNCT
ejpam-3573	145	5	wi}ki=1	wi}ki=1	PROPN
ejpam-3573	145	6	.	.	PUNCT
ejpam-3573	146	1	without	without	ADP
ejpam-3573	146	2	loss	loss	NOUN
ejpam-3573	146	3	of	of	ADP
ejpam-3573	146	4	generality	generality	NOUN
ejpam-3573	146	5	,	,	PUNCT
ejpam-3573	146	6	let	let	VERB
ejpam-3573	146	7	wi	wi	PROPN
ejpam-3573	146	8	=	=	PROPN
ejpam-3573	146	9	{	{	PUNCT
ejpam-3573	146	10	vi	vi	PROPN
ejpam-3573	146	11	,	,	PUNCT
ejpam-3573	146	12	if	if	SCONJ
ejpam-3573	146	13	d∞(f̂n(u1	d∞(f̂n(u1	PROPN
ejpam-3573	146	14	)	)	PUNCT
ejpam-3573	146	15	,	,	PUNCT
ejpam-3573	146	16	f̂n(ui	f̂n(ui	PROPN
ejpam-3573	146	17	)	)	PUNCT
ejpam-3573	146	18	)	)	PUNCT
ejpam-3573	147	1	≤	≤	NUM
ejpam-3573	147	2	δ	δ	PROPN
ejpam-3573	147	3	,	,	PUNCT
ejpam-3573	147	4	ui	ui	PROPN
ejpam-3573	147	5	,	,	PUNCT
ejpam-3573	147	6	if	if	SCONJ
ejpam-3573	147	7	d∞(f̂n(u1	d∞(f̂n(u1	PROPN
ejpam-3573	147	8	)	)	PUNCT
ejpam-3573	147	9	,	,	PUNCT
ejpam-3573	147	10	f̂n(ui	f̂n(ui	PROPN
ejpam-3573	147	11	)	)	PUNCT
ejpam-3573	147	12	)	)	PUNCT
ejpam-3573	147	13	>	>	PUNCT
ejpam-3573	147	14	δ	δ	PROPN
ejpam-3573	147	15	.	.	PUNCT
ejpam-3573	148	1	more	more	ADV
ejpam-3573	148	2	specifically	specifically	ADV
ejpam-3573	148	3	,	,	PUNCT
ejpam-3573	148	4	if	if	SCONJ
ejpam-3573	148	5	wi	wi	PROPN
ejpam-3573	148	6	=	=	SYM
ejpam-3573	148	7	ui	ui	PROPN
ejpam-3573	148	8	,	,	PUNCT
ejpam-3573	148	9	then	then	ADV
ejpam-3573	148	10	d∞(f̂n(u1	d∞(f̂n(u1	PROPN
ejpam-3573	148	11	)	)	PUNCT
ejpam-3573	148	12	,	,	PUNCT
ejpam-3573	148	13	f̂n(wi	f̂n(wi	NOUN
ejpam-3573	148	14	)	)	PUNCT
ejpam-3573	148	15	)	)	PUNCT
ejpam-3573	149	1	=	=	SYM
ejpam-3573	149	2	d∞(f̂n(u1	d∞(f̂n(u1	PROPN
ejpam-3573	149	3	)	)	PUNCT
ejpam-3573	149	4	,	,	PUNCT
ejpam-3573	149	5	f̂n(ui	f̂n(ui	PROPN
ejpam-3573	149	6	)	)	PUNCT
ejpam-3573	149	7	)	)	PUNCT
ejpam-3573	149	8	>	>	PUNCT
ejpam-3573	150	1	δ	δ	PROPN
ejpam-3573	150	2	;	;	PUNCT
ejpam-3573	150	3	if	if	SCONJ
ejpam-3573	150	4	wi	wi	PROPN
ejpam-3573	150	5	=	=	SYM
ejpam-3573	150	6	vi	vi	PROPN
ejpam-3573	150	7	,	,	PUNCT
ejpam-3573	150	8	then	then	ADV
ejpam-3573	150	9	2δ	2δ	NUM
ejpam-3573	150	10	<	<	X
ejpam-3573	150	11	d∞(f̂n(ui	d∞(f̂n(ui	NOUN
ejpam-3573	150	12	)	)	PUNCT
ejpam-3573	150	13	,	,	PUNCT
ejpam-3573	150	14	f̂n(vi	f̂n(vi	PROPN
ejpam-3573	150	15	)	)	PUNCT
ejpam-3573	150	16	)	)	PUNCT
ejpam-3573	150	17	=	=	SYM
ejpam-3573	150	18	d∞(f̂n(ui	d∞(f̂n(ui	NOUN
ejpam-3573	150	19	)	)	PUNCT
ejpam-3573	150	20	,	,	PUNCT
ejpam-3573	150	21	f̂n(wi	f̂n(wi	PROPN
ejpam-3573	150	22	)	)	PUNCT
ejpam-3573	150	23	)	)	PUNCT
ejpam-3573	151	1	<	<	X
ejpam-3573	151	2	d∞(f̂n(ui	d∞(f̂n(ui	NOUN
ejpam-3573	151	3	)	)	PUNCT
ejpam-3573	151	4	,	,	PUNCT
ejpam-3573	151	5	f̂n(u1	f̂n(u1	NOUN
ejpam-3573	151	6	)	)	PUNCT
ejpam-3573	151	7	)	)	PUNCT
ejpam-3573	152	1	+	+	CCONJ
ejpam-3573	152	2	d∞(f̂n(u1	d∞(f̂n(u1	NUM
ejpam-3573	152	3	)	)	PUNCT
ejpam-3573	152	4	,	,	PUNCT
ejpam-3573	152	5	f̂n(wi	f̂n(wi	NOUN
ejpam-3573	152	6	)	)	PUNCT
ejpam-3573	152	7	)	)	PUNCT
ejpam-3573	153	1	≤	≤	NUM
ejpam-3573	153	2	δ	δ	PROPN
ejpam-3573	153	3	+	+	CCONJ
ejpam-3573	153	4	d∞(f̂n(u1	d∞(f̂n(u1	PROPN
ejpam-3573	153	5	)	)	PUNCT
ejpam-3573	153	6	,	,	PUNCT
ejpam-3573	153	7	f̂n(wi	f̂n(wi	NOUN
ejpam-3573	153	8	)	)	PUNCT
ejpam-3573	153	9	)	)	PUNCT
ejpam-3573	153	10	.	.	PUNCT
ejpam-3573	154	1	thus	thus	ADV
ejpam-3573	154	2	d∞(f̂n(u1	d∞(f̂n(u1	NUM
ejpam-3573	154	3	)	)	PUNCT
ejpam-3573	154	4	,	,	PUNCT
ejpam-3573	154	5	f̂n(wi	f̂n(wi	NOUN
ejpam-3573	154	6	)	)	PUNCT
ejpam-3573	154	7	)	)	PUNCT
ejpam-3573	154	8	>	>	PUNCT
ejpam-3573	155	1	δ	δ	PROPN
ejpam-3573	155	2	and	and	CCONJ
ejpam-3573	155	3	then	then	ADV
ejpam-3573	155	4	d∞(f̂n(u1	d∞(f̂n(u1	PROPN
ejpam-3573	155	5	)	)	PUNCT
ejpam-3573	155	6	,	,	PUNCT
ejpam-3573	155	7	f̂n(wi	f̂n(wi	NOUN
ejpam-3573	155	8	)	)	PUNCT
ejpam-3573	155	9	)	)	PUNCT
ejpam-3573	156	1	=	=	SYM
ejpam-3573	156	2	d∞(f̂n(x̂1	d∞(f̂n(x̂1	NOUN
ejpam-3573	156	3	)	)	PUNCT
ejpam-3573	156	4	,	,	PUNCT
ejpam-3573	156	5	f̂n(wi	f̂n(wi	NOUN
ejpam-3573	156	6	)	)	PUNCT
ejpam-3573	156	7	)	)	PUNCT
ejpam-3573	157	1	=	=	SYM
ejpam-3573	157	2	sup	sup	NOUN
ejpam-3573	157	3	α∈[0,1	α∈[0,1	NOUN
ejpam-3573	157	4	]	]	X
ejpam-3573	157	5	dh([f̂n(x̂1)]α	dh([f̂n(x̂1)]α	PROPN
ejpam-3573	157	6	,	,	PUNCT
ejpam-3573	157	7	[	[	X
ejpam-3573	157	8	f̂n(wi)]α	f̂n(wi)]α	X
ejpam-3573	157	9	)	)	PUNCT
ejpam-3573	157	10	=	=	SYM
ejpam-3573	157	11	sup	sup	NOUN
ejpam-3573	157	12	α∈[0,1	α∈[0,1	NUM
ejpam-3573	157	13	]	]	X
ejpam-3573	157	14	dh(fn([x̂1]α	dh(fn([x̂1]α	NUM
ejpam-3573	157	15	)	)	PUNCT
ejpam-3573	157	16	,	,	PUNCT
ejpam-3573	157	17	fn([wi]α	fn([wi]α	PROPN
ejpam-3573	157	18	)	)	PUNCT
ejpam-3573	157	19	)	)	PUNCT
ejpam-3573	158	1	=	=	SYM
ejpam-3573	158	2	sup	sup	NOUN
ejpam-3573	158	3	α∈[0,1	α∈[0,1	NUM
ejpam-3573	158	4	]	]	X
ejpam-3573	158	5	dh({fn(x1	dh({fn(x1	NOUN
ejpam-3573	158	6	)	)	PUNCT
ejpam-3573	158	7	}	}	PUNCT
ejpam-3573	158	8	,	,	PUNCT
ejpam-3573	158	9	fn([wi]α	fn([wi]α	PROPN
ejpam-3573	158	10	)	)	PUNCT
ejpam-3573	158	11	)	)	PUNCT
ejpam-3573	158	12	>	>	PUNCT
ejpam-3573	159	1	δ	δ	PROPN
ejpam-3573	159	2	.	.	PUNCT
ejpam-3573	160	1	therefore	therefore	ADV
ejpam-3573	160	2	,	,	PUNCT
ejpam-3573	160	3	there	there	PRON
ejpam-3573	160	4	exists	exist	VERB
ejpam-3573	160	5	yi	yi	PROPN
ejpam-3573	160	6	∈	∈	PROPN
ejpam-3573	161	1	[	[	X
ejpam-3573	161	2	wi]α	wi]α	PROPN
ejpam-3573	161	3	such	such	ADJ
ejpam-3573	161	4	that	that	SCONJ
ejpam-3573	161	5	d(fn(x1	d(fn(x1	NOUN
ejpam-3573	161	6	)	)	PUNCT
ejpam-3573	161	7	,	,	PUNCT
ejpam-3573	161	8	fn(yi	fn(yi	NOUN
ejpam-3573	161	9	)	)	PUNCT
ejpam-3573	161	10	)	)	PUNCT
ejpam-3573	161	11	>	>	PUNCT
ejpam-3573	161	12	δ	δ	PROPN
ejpam-3573	161	13	for	for	ADP
ejpam-3573	161	14	each	each	DET
ejpam-3573	161	15	i.	i.	NOUN
ejpam-3573	161	16	take	take	VERB
ejpam-3573	161	17	b	b	NOUN
ejpam-3573	161	18	=	=	PRON
ejpam-3573	161	19	{	{	PUNCT
ejpam-3573	161	20	yi}ki=1	yi}ki=1	PROPN
ejpam-3573	161	21	.	.	PUNCT
ejpam-3573	162	1	then	then	ADV
ejpam-3573	162	2	dh(f̄n(a	dh(f̄n(a	PROPN
ejpam-3573	162	3	)	)	PUNCT
ejpam-3573	162	4	,	,	PUNCT
ejpam-3573	162	5	f̄n(b	f̄n(b	NOUN
ejpam-3573	162	6	)	)	PUNCT
ejpam-3573	162	7	)	)	PUNCT
ejpam-3573	162	8	>	>	PUNCT
ejpam-3573	163	1	δ	δ	PROPN
ejpam-3573	163	2	holds	hold	VERB
ejpam-3573	163	3	for	for	ADP
ejpam-3573	163	4	all	all	DET
ejpam-3573	163	5	b	b	PROPN
ejpam-3573	163	6	∈	∈	NOUN
ejpam-3573	163	7	udh	udh	NOUN
ejpam-3573	163	8	(	(	PUNCT
ejpam-3573	163	9	a	a	PRON
ejpam-3573	163	10	,	,	PUNCT
ejpam-3573	163	11	ε	ε	PROPN
ejpam-3573	163	12	)	)	PUNCT
ejpam-3573	163	13	and	and	CCONJ
ejpam-3573	163	14	n	n	CCONJ
ejpam-3573	163	15	>	>	X
ejpam-3573	163	16	n	n	X
ejpam-3573	163	17	.	.	PUNCT
ejpam-3573	164	1	(	(	PUNCT
ejpam-3573	164	2	2	2	X
ejpam-3573	164	3	)	)	PUNCT
ejpam-3573	164	4	⇒	⇒	NOUN
ejpam-3573	164	5	(	(	PUNCT
ejpam-3573	164	6	1	1	X
ejpam-3573	164	7	)	)	PUNCT
ejpam-3573	164	8	assume	assume	VERB
ejpam-3573	164	9	{	{	PUNCT
ejpam-3573	164	10	f̄n}∞n=1	f̄n}∞n=1	ADJ
ejpam-3573	164	11	is	be	AUX
ejpam-3573	164	12	strongly	strongly	ADV
ejpam-3573	164	13	sensitive	sensitive	ADJ
ejpam-3573	164	14	with	with	ADP
ejpam-3573	164	15	sensitive	sensitive	ADJ
ejpam-3573	164	16	constant	constant	ADJ
ejpam-3573	164	17	δ	δ	PROPN
ejpam-3573	164	18	.	.	PUNCT
ejpam-3573	165	1	to	to	PART
ejpam-3573	165	2	show	show	VERB
ejpam-3573	165	3	that	that	SCONJ
ejpam-3573	165	4	{	{	PUNCT
ejpam-3573	165	5	f̂n}∞n=1	f̂n}∞n=1	PROPN
ejpam-3573	165	6	is	be	AUX
ejpam-3573	165	7	strongly	strongly	ADV
ejpam-3573	165	8	sensitive	sensitive	ADJ
ejpam-3573	165	9	in	in	ADP
ejpam-3573	165	10	f(x	f(x	PROPN
ejpam-3573	165	11	)	)	PUNCT
ejpam-3573	165	12	,	,	PUNCT
ejpam-3573	165	13	it	it	PRON
ejpam-3573	165	14	is	be	AUX
ejpam-3573	165	15	sufficient	sufficient	ADJ
ejpam-3573	165	16	to	to	PART
ejpam-3573	165	17	prove	prove	VERB
ejpam-3573	165	18	that	that	SCONJ
ejpam-3573	165	19	{	{	PUNCT
ejpam-3573	165	20	f̂n}∞n=1	f̂n}∞n=1	PROPN
ejpam-3573	165	21	|sf(x	|sf(x	PROPN
ejpam-3573	165	22	)	)	PUNCT
ejpam-3573	165	23	y.	y.	PROPN
ejpam-3573	165	24	lan	lan	PROPN
ejpam-3573	165	25	/	/	SYM
ejpam-3573	165	26	eur	eur	PROPN
ejpam-3573	165	27	.	.	PUNCT
ejpam-3573	166	1	j.	j.	PROPN
ejpam-3573	166	2	pure	pure	PROPN
ejpam-3573	166	3	appl	appl	PROPN
ejpam-3573	166	4	.	.	PROPN
ejpam-3573	166	5	math	math	PROPN
ejpam-3573	166	6	,	,	PUNCT
ejpam-3573	166	7	12	12	NUM
ejpam-3573	166	8	(	(	PUNCT
ejpam-3573	166	9	4	4	NUM
ejpam-3573	166	10	)	)	PUNCT
ejpam-3573	166	11	(	(	PUNCT
ejpam-3573	166	12	2019	2019	NUM
ejpam-3573	166	13	)	)	PUNCT
ejpam-3573	166	14	,	,	PUNCT
ejpam-3573	166	15	1689	1689	NUM
ejpam-3573	166	16	-	-	SYM
ejpam-3573	166	17	1700	1700	NUM
ejpam-3573	166	18	1695	1695	NUM
ejpam-3573	166	19	is	be	AUX
ejpam-3573	166	20	strongly	strongly	ADV
ejpam-3573	166	21	sensitive	sensitive	ADJ
ejpam-3573	166	22	,	,	PUNCT
ejpam-3573	166	23	as	as	ADP
ejpam-3573	166	24	sf(x	sf(x	NOUN
ejpam-3573	166	25	)	)	PUNCT
ejpam-3573	167	1	is	be	AUX
ejpam-3573	167	2	dense	dense	ADJ
ejpam-3573	167	3	in	in	ADP
ejpam-3573	167	4	f(x	f(x	PROPN
ejpam-3573	167	5	)	)	PUNCT
ejpam-3573	167	6	.	.	PUNCT
ejpam-3573	168	1	let	let	VERB
ejpam-3573	168	2	u	u	PRON
ejpam-3573	168	3	∈	∈	PROPN
ejpam-3573	168	4	sf(x	sf(x	NOUN
ejpam-3573	168	5	)	)	PUNCT
ejpam-3573	168	6	,	,	PUNCT
ejpam-3573	168	7	then	then	ADV
ejpam-3573	168	8	there	there	PRON
ejpam-3573	168	9	exist	exist	VERB
ejpam-3573	168	10	a	a	DET
ejpam-3573	168	11	sequence	sequence	NOUN
ejpam-3573	168	12	of	of	ADP
ejpam-3573	168	13	nested	nested	ADJ
ejpam-3573	168	14	closed	closed	ADJ
ejpam-3573	168	15	subsets	subset	NOUN
ejpam-3573	168	16	{	{	PUNCT
ejpam-3573	168	17	a1	a1	PROPN
ejpam-3573	168	18	,	,	PUNCT
ejpam-3573	168	19	a2	a2	PROPN
ejpam-3573	168	20	,	,	PUNCT
ejpam-3573	168	21	·	·	PUNCT
ejpam-3573	168	22	·	·	PUNCT
ejpam-3573	169	1	·	·	PUNCT
ejpam-3573	169	2	,	,	PUNCT
ejpam-3573	169	3	ak	ak	PROPN
ejpam-3573	169	4	}	}	PUNCT
ejpam-3573	169	5	of	of	ADP
ejpam-3573	169	6	x	x	X
ejpam-3573	169	7	and	and	CCONJ
ejpam-3573	169	8	a	a	DET
ejpam-3573	169	9	sequence	sequence	NOUN
ejpam-3573	169	10	of	of	ADP
ejpam-3573	169	11	real	real	ADJ
ejpam-3573	169	12	numbers	number	NOUN
ejpam-3573	169	13	{	{	PUNCT
ejpam-3573	169	14	α1	α1	PROPN
ejpam-3573	169	15	,	,	PUNCT
ejpam-3573	169	16	α2	α2	ADJ
ejpam-3573	169	17	,	,	PUNCT
ejpam-3573	169	18	·	·	PUNCT
ejpam-3573	169	19	·	·	PUNCT
ejpam-3573	169	20	·	·	PUNCT
ejpam-3573	169	21	,	,	PUNCT
ejpam-3573	169	22	αk	αk	ADP
ejpam-3573	169	23	}	}	PUNCT
ejpam-3573	169	24	such	such	ADJ
ejpam-3573	169	25	that	that	SCONJ
ejpam-3573	169	26	[	[	X
ejpam-3573	169	27	u]α	u]α	X
ejpam-3573	169	28	=	=	ADJ
ejpam-3573	169	29	ai+1	ai+1	PROPN
ejpam-3573	169	30	,	,	PUNCT
ejpam-3573	169	31	where	where	SCONJ
ejpam-3573	169	32	α	α	X
ejpam-3573	169	33	∈	∈	PROPN
ejpam-3573	169	34	(	(	PUNCT
ejpam-3573	169	35	αi	αi	PROPN
ejpam-3573	169	36	,	,	PUNCT
ejpam-3573	169	37	αi+1	αi+1	NOUN
ejpam-3573	169	38	]	]	X
ejpam-3573	169	39	,	,	PUNCT
ejpam-3573	169	40	1	1	NUM
ejpam-3573	169	41	≤	≤	NUM
ejpam-3573	169	42	i	i	PRON
ejpam-3573	169	43	≤	≤	PROPN
ejpam-3573	169	44	k.	k.	INTJ
ejpam-3573	170	1	since	since	SCONJ
ejpam-3573	170	2	{	{	PUNCT
ejpam-3573	170	3	f̄n}∞n=1	f̄n}∞n=1	PROPN
ejpam-3573	170	4	is	be	AUX
ejpam-3573	170	5	strongly	strongly	ADV
ejpam-3573	170	6	sensitive	sensitive	ADJ
ejpam-3573	170	7	,	,	PUNCT
ejpam-3573	170	8	for	for	ADP
ejpam-3573	170	9	ak	ak	PROPN
ejpam-3573	170	10	and	and	CCONJ
ejpam-3573	170	11	any	any	DET
ejpam-3573	170	12	b	b	PROPN
ejpam-3573	170	13	∈	∈	PROPN
ejpam-3573	170	14	k(x	k(x	PROPN
ejpam-3573	170	15	)	)	PUNCT
ejpam-3573	170	16	with	with	ADP
ejpam-3573	170	17	b	b	PROPN
ejpam-3573	170	18	∈	∈	PROPN
ejpam-3573	170	19	udh	udh	PROPN
ejpam-3573	170	20	(	(	PUNCT
ejpam-3573	170	21	ak	ak	PROPN
ejpam-3573	170	22	,	,	PUNCT
ejpam-3573	170	23	ε	ε	PROPN
ejpam-3573	170	24	2	2	NUM
ejpam-3573	170	25	)	)	PUNCT
ejpam-3573	170	26	,	,	PUNCT
ejpam-3573	170	27	there	there	PRON
ejpam-3573	170	28	exists	exist	VERB
ejpam-3573	170	29	an	an	DET
ejpam-3573	170	30	integer	integer	NOUN
ejpam-3573	170	31	n0	n0	NOUN
ejpam-3573	170	32	such	such	ADJ
ejpam-3573	170	33	that	that	PRON
ejpam-3573	170	34	for	for	SCONJ
ejpam-3573	170	35	all	all	PRON
ejpam-3573	170	36	n	n	PROPN
ejpam-3573	170	37	>	>	X
ejpam-3573	170	38	n0	n0	PROPN
ejpam-3573	170	39	,	,	PUNCT
ejpam-3573	170	40	dh(f̄n(ak	dh(f̄n(ak	NOUN
ejpam-3573	170	41	)	)	PUNCT
ejpam-3573	170	42	,	,	PUNCT
ejpam-3573	170	43	f̄n(b	f̄n(b	NOUN
ejpam-3573	170	44	)	)	PUNCT
ejpam-3573	170	45	)	)	PUNCT
ejpam-3573	170	46	>	>	PUNCT
ejpam-3573	171	1	δ	δ	PROPN
ejpam-3573	171	2	.	.	PUNCT
ejpam-3573	172	1	(	(	PUNCT
ejpam-3573	172	2	2	2	X
ejpam-3573	172	3	)	)	PUNCT
ejpam-3573	172	4	set	set	VERB
ejpam-3573	172	5	x1	x1	NOUN
ejpam-3573	172	6	=	=	PUNCT
ejpam-3573	172	7	x	x	X
ejpam-3573	172	8	and	and	CCONJ
ejpam-3573	172	9	c1	c1	PROPN
ejpam-3573	172	10	=	=	SYM
ejpam-3573	172	11	u−1(αk	u−1(αk	PROPN
ejpam-3573	172	12	)	)	PUNCT
ejpam-3573	173	1	⋂	⋂	PROPN
ejpam-3573	173	2	x1	x1	PROPN
ejpam-3573	173	3	.	.	PUNCT
ejpam-3573	174	1	in	in	ADP
ejpam-3573	174	2	general	general	ADJ
ejpam-3573	174	3	,	,	PUNCT
ejpam-3573	174	4	define	define	VERB
ejpam-3573	174	5	{	{	PUNCT
ejpam-3573	174	6	xi}ki=1	xi}ki=1	PROPN
ejpam-3573	174	7	and	and	CCONJ
ejpam-3573	174	8	{	{	PUNCT
ejpam-3573	174	9	ci}ki=1	ci}ki=1	ADV
ejpam-3573	174	10	by	by	ADP
ejpam-3573	174	11	the	the	DET
ejpam-3573	174	12	following	follow	VERB
ejpam-3573	174	13	xi	xi	X
ejpam-3573	174	14	=	=	SYM
ejpam-3573	174	15	xi−1	xi−1	PROPN
ejpam-3573	174	16	\	\	PROPN
ejpam-3573	174	17	udh	udh	PROPN
ejpam-3573	174	18	(	(	PUNCT
ejpam-3573	174	19	ci−1	ci−1	PROPN
ejpam-3573	174	20	,	,	PUNCT
ejpam-3573	174	21	ε	ε	PROPN
ejpam-3573	174	22	4	4	NUM
ejpam-3573	174	23	)	)	PUNCT
ejpam-3573	174	24	,	,	PUNCT
ejpam-3573	174	25	ci	ci	PROPN
ejpam-3573	174	26	=	=	SYM
ejpam-3573	174	27	u−1(αk−i+1	u−1(αk−i+1	PROPN
ejpam-3573	174	28	)	)	PUNCT
ejpam-3573	174	29	⋂	⋂	PROPN
ejpam-3573	174	30	xi	xi	X
ejpam-3573	174	31	.	.	PUNCT
ejpam-3573	175	1	let	let	VERB
ejpam-3573	175	2	di	di	X
ejpam-3573	175	3	=	=	PUNCT
ejpam-3573	175	4	⋃i	⋃i	PROPN
ejpam-3573	175	5	j=1udh	j=1udh	PROPN
ejpam-3573	175	6	(	(	PUNCT
ejpam-3573	175	7	ci	ci	PROPN
ejpam-3573	175	8	,	,	PUNCT
ejpam-3573	175	9	ε	ε	PROPN
ejpam-3573	175	10	4	4	NUM
ejpam-3573	175	11	)	)	PUNCT
ejpam-3573	175	12	,	,	PUNCT
ejpam-3573	175	13	then	then	ADV
ejpam-3573	175	14	we	we	PRON
ejpam-3573	175	15	obtain	obtain	VERB
ejpam-3573	175	16	an	an	DET
ejpam-3573	175	17	incresing	increse	VERB
ejpam-3573	175	18	sequence	sequence	NOUN
ejpam-3573	175	19	d1	d1	PROPN
ejpam-3573	176	1	⊂	⊂	PROPN
ejpam-3573	176	2	d2	d2	PROPN
ejpam-3573	176	3	⊂	⊂	PROPN
ejpam-3573	176	4	·	·	PUNCT
ejpam-3573	176	5	·	·	PUNCT
ejpam-3573	176	6	·	·	PUNCT
ejpam-3573	177	1	⊂	⊂	PRON
ejpam-3573	177	2	dk	dk	PROPN
ejpam-3573	177	3	of	of	ADP
ejpam-3573	177	4	closed	closed	ADJ
ejpam-3573	177	5	sets	set	NOUN
ejpam-3573	177	6	in	in	ADP
ejpam-3573	177	7	k(x	k(x	PROPN
ejpam-3573	177	8	)	)	PUNCT
ejpam-3573	177	9	.	.	PUNCT
ejpam-3573	178	1	consequently	consequently	ADV
ejpam-3573	178	2	,	,	PUNCT
ejpam-3573	178	3	we	we	PRON
ejpam-3573	178	4	have	have	VERB
ejpam-3573	178	5	a	a	DET
ejpam-3573	178	6	piecewise	piecewise	NOUN
ejpam-3573	178	7	constant	constant	ADJ
ejpam-3573	178	8	fuzzy	fuzzy	ADJ
ejpam-3573	178	9	set	set	VERB
ejpam-3573	178	10	ω	ω	PROPN
ejpam-3573	178	11	∈	∈	PROPN
ejpam-3573	178	12	sf(x	sf(x	NOUN
ejpam-3573	178	13	)	)	PUNCT
ejpam-3573	178	14	satisfying	satisfy	VERB
ejpam-3573	179	1	[	[	X
ejpam-3573	179	2	ω]α	ω]α	X
ejpam-3573	179	3	=	=	SYM
ejpam-3573	179	4	di+1	di+1	NOUN
ejpam-3573	179	5	,	,	PUNCT
ejpam-3573	179	6	where	where	SCONJ
ejpam-3573	179	7	α	α	X
ejpam-3573	179	8	∈	∈	PROPN
ejpam-3573	179	9	(	(	PUNCT
ejpam-3573	179	10	αi	αi	NOUN
ejpam-3573	179	11	,	,	PUNCT
ejpam-3573	179	12	αi+1	αi+1	NOUN
ejpam-3573	179	13	]	]	PUNCT
ejpam-3573	179	14	.	.	PUNCT
ejpam-3573	180	1	it	it	PRON
ejpam-3573	180	2	follows	follow	VERB
ejpam-3573	180	3	from	from	ADP
ejpam-3573	180	4	the	the	DET
ejpam-3573	180	5	construction	construction	NOUN
ejpam-3573	180	6	and	and	CCONJ
ejpam-3573	180	7	lemma	lemma	PROPN
ejpam-3573	180	8	2.2	2.2	NUM
ejpam-3573	180	9	that	that	PRON
ejpam-3573	180	10	d∞(u	d∞(u	NOUN
ejpam-3573	180	11	,	,	PUNCT
ejpam-3573	180	12	ω	ω	NOUN
ejpam-3573	180	13	)	)	PUNCT
ejpam-3573	180	14	<	<	X
ejpam-3573	180	15	ε	ε	PROPN
ejpam-3573	180	16	4	4	NUM
ejpam-3573	180	17	.	.	PUNCT
ejpam-3573	181	1	(	(	PUNCT
ejpam-3573	181	2	3	3	X
ejpam-3573	181	3	)	)	PUNCT
ejpam-3573	181	4	thus	thus	ADV
ejpam-3573	181	5	we	we	PRON
ejpam-3573	181	6	have	have	VERB
ejpam-3573	181	7	for	for	ADP
ejpam-3573	181	8	each	each	DET
ejpam-3573	181	9	i	i	NOUN
ejpam-3573	181	10	=	=	NOUN
ejpam-3573	181	11	1	1	NUM
ejpam-3573	181	12	,	,	PUNCT
ejpam-3573	181	13	2	2	NUM
ejpam-3573	181	14	,	,	PUNCT
ejpam-3573	181	15	·	·	PUNCT
ejpam-3573	181	16	·	·	PUNCT
ejpam-3573	181	17	·	·	PUNCT
ejpam-3573	181	18	,	,	PUNCT
ejpam-3573	181	19	k	k	PROPN
ejpam-3573	181	20	,	,	PUNCT
ejpam-3573	181	21	dh(b	dh(b	PROPN
ejpam-3573	181	22	,	,	PUNCT
ejpam-3573	181	23	di	di	NOUN
ejpam-3573	181	24	)	)	PUNCT
ejpam-3573	181	25	≤	≤	NOUN
ejpam-3573	181	26	dh(b	dh(b	PROPN
ejpam-3573	181	27	,	,	PUNCT
ejpam-3573	181	28	ak	ak	PROPN
ejpam-3573	181	29	)	)	PUNCT
ejpam-3573	182	1	+	+	CCONJ
ejpam-3573	182	2	dh(ak	dh(ak	ADJ
ejpam-3573	182	3	,	,	PUNCT
ejpam-3573	182	4	di	di	NOUN
ejpam-3573	182	5	)	)	PUNCT
ejpam-3573	182	6	<	<	X
ejpam-3573	182	7	ε	ε	PROPN
ejpam-3573	182	8	2	2	NUM
ejpam-3573	182	9	+	+	CCONJ
ejpam-3573	182	10	ε	ε	PROPN
ejpam-3573	182	11	4	4	NUM
ejpam-3573	182	12	=	=	SYM
ejpam-3573	182	13	3ε	3ε	NUM
ejpam-3573	182	14	4	4	NUM
ejpam-3573	182	15	.	.	PUNCT
ejpam-3573	183	1	(	(	PUNCT
ejpam-3573	183	2	4	4	X
ejpam-3573	183	3	)	)	PUNCT
ejpam-3573	183	4	take	take	VERB
ejpam-3573	183	5	ν	ν	PRON
ejpam-3573	183	6	∈	∈	PROPN
ejpam-3573	183	7	sf(x	sf(x	NOUN
ejpam-3573	183	8	)	)	PUNCT
ejpam-3573	183	9	such	such	ADJ
ejpam-3573	183	10	that	that	SCONJ
ejpam-3573	183	11	[	[	X
ejpam-3573	183	12	ν]α	ν]α	X
ejpam-3573	183	13	=	=	SYM
ejpam-3573	183	14	{	{	PUNCT
ejpam-3573	183	15	b	b	NOUN
ejpam-3573	183	16	,	,	PUNCT
ejpam-3573	183	17	if	if	SCONJ
ejpam-3573	183	18	α	α	PRON
ejpam-3573	183	19	∈	∈	PROPN
ejpam-3573	183	20	(	(	PUNCT
ejpam-3573	183	21	αk−1	αk−1	NOUN
ejpam-3573	183	22	,	,	PUNCT
ejpam-3573	183	23	αk	αk	ADP
ejpam-3573	183	24	]	]	X
ejpam-3573	183	25	b	b	PROPN
ejpam-3573	183	26	⋃	⋃	NOUN
ejpam-3573	183	27	di	di	NOUN
ejpam-3573	183	28	,	,	PUNCT
ejpam-3573	183	29	if	if	SCONJ
ejpam-3573	183	30	α	α	PRON
ejpam-3573	183	31	∈	∈	PROPN
ejpam-3573	183	32	(	(	PUNCT
ejpam-3573	183	33	αi	αi	NOUN
ejpam-3573	183	34	,	,	PUNCT
ejpam-3573	183	35	αi+1	αi+1	NOUN
ejpam-3573	183	36	]	]	X
ejpam-3573	183	37	,	,	PUNCT
ejpam-3573	183	38	i	i	PRON
ejpam-3573	183	39	=	=	NOUN
ejpam-3573	183	40	1	1	NUM
ejpam-3573	183	41	,	,	PUNCT
ejpam-3573	183	42	2	2	NUM
ejpam-3573	183	43	,	,	PUNCT
ejpam-3573	183	44	·	·	PUNCT
ejpam-3573	183	45	·	·	PUNCT
ejpam-3573	183	46	·	·	PUNCT
ejpam-3573	183	47	,	,	PUNCT
ejpam-3573	183	48	k	k	PROPN
ejpam-3573	183	49	−	−	PROPN
ejpam-3573	183	50	2	2	NUM
ejpam-3573	183	51	then	then	ADV
ejpam-3573	183	52	from	from	ADP
ejpam-3573	183	53	(	(	PUNCT
ejpam-3573	183	54	4	4	NUM
ejpam-3573	183	55	)	)	PUNCT
ejpam-3573	183	56	,	,	PUNCT
ejpam-3573	183	57	we	we	PRON
ejpam-3573	183	58	have	have	AUX
ejpam-3573	183	59	d∞(ν	d∞(ν	VERB
ejpam-3573	183	60	,	,	PUNCT
ejpam-3573	183	61	ω	ω	NUM
ejpam-3573	183	62	)	)	PUNCT
ejpam-3573	183	63	<	<	X
ejpam-3573	183	64	3ε	3ε	NUM
ejpam-3573	183	65	4	4	NUM
ejpam-3573	183	66	.	.	PUNCT
ejpam-3573	184	1	(	(	PUNCT
ejpam-3573	184	2	5	5	NUM
ejpam-3573	184	3	)	)	PUNCT
ejpam-3573	184	4	hence	hence	ADV
ejpam-3573	184	5	it	it	PRON
ejpam-3573	184	6	follows	follow	VERB
ejpam-3573	184	7	from	from	ADP
ejpam-3573	184	8	(	(	PUNCT
ejpam-3573	184	9	3	3	NUM
ejpam-3573	184	10	)	)	PUNCT
ejpam-3573	184	11	and	and	CCONJ
ejpam-3573	184	12	(	(	PUNCT
ejpam-3573	184	13	5	5	NUM
ejpam-3573	184	14	)	)	PUNCT
ejpam-3573	185	1	that	that	SCONJ
ejpam-3573	185	2	d∞(u	d∞(u	NOUN
ejpam-3573	185	3	,	,	PUNCT
ejpam-3573	185	4	ν	ν	NOUN
ejpam-3573	185	5	)	)	PUNCT
ejpam-3573	185	6	<	<	X
ejpam-3573	185	7	d∞(u	d∞(u	PROPN
ejpam-3573	185	8	,	,	PUNCT
ejpam-3573	185	9	ω	ω	NOUN
ejpam-3573	185	10	)	)	PUNCT
ejpam-3573	185	11	+	+	NUM
ejpam-3573	185	12	d∞(ω	d∞(ω	NOUN
ejpam-3573	185	13	,	,	PUNCT
ejpam-3573	185	14	ν	ν	X
ejpam-3573	185	15	)	)	PUNCT
ejpam-3573	185	16	<	<	X
ejpam-3573	185	17	ε	ε	PROPN
ejpam-3573	185	18	4	4	NUM
ejpam-3573	185	19	+	+	NUM
ejpam-3573	185	20	3ε	3ε	NUM
ejpam-3573	185	21	4	4	NUM
ejpam-3573	185	22	=	=	SYM
ejpam-3573	185	23	ε	ε	PROPN
ejpam-3573	185	24	.	.	PROPN
ejpam-3573	185	25	on	on	ADP
ejpam-3573	185	26	the	the	DET
ejpam-3573	185	27	other	other	ADJ
ejpam-3573	185	28	hand	hand	NOUN
ejpam-3573	185	29	,	,	PUNCT
ejpam-3573	185	30	by	by	ADP
ejpam-3573	185	31	(	(	PUNCT
ejpam-3573	185	32	2	2	NUM
ejpam-3573	185	33	)	)	PUNCT
ejpam-3573	185	34	and	and	CCONJ
ejpam-3573	185	35	lemma	lemma	PROPN
ejpam-3573	185	36	2.1	2.1	NUM
ejpam-3573	185	37	,	,	PUNCT
ejpam-3573	185	38	the	the	DET
ejpam-3573	185	39	following	follow	VERB
ejpam-3573	185	40	d∞(f̂n(u	d∞(f̂n(u	NOUN
ejpam-3573	185	41	)	)	PUNCT
ejpam-3573	185	42	,	,	PUNCT
ejpam-3573	185	43	f̂n(ν	f̂n(ν	NOUN
ejpam-3573	185	44	)	)	PUNCT
ejpam-3573	185	45	)	)	PUNCT
ejpam-3573	186	1	=	=	SYM
ejpam-3573	186	2	sup	sup	NOUN
ejpam-3573	186	3	α∈[0,1	α∈[0,1	PROPN
ejpam-3573	186	4	]	]	X
ejpam-3573	186	5	dh([f̂n(u)]α	dh([f̂n(u)]α	PRON
ejpam-3573	186	6	,	,	PUNCT
ejpam-3573	186	7	[	[	X
ejpam-3573	186	8	f̂n(ν)]α	f̂n(ν)]α	NOUN
ejpam-3573	186	9	)	)	PUNCT
ejpam-3573	186	10	=	=	SYM
ejpam-3573	186	11	sup	sup	NOUN
ejpam-3573	186	12	α∈[0,1	α∈[0,1	NOUN
ejpam-3573	186	13	]	]	X
ejpam-3573	186	14	dh(fn([u]α	dh(fn([u]α	PROPN
ejpam-3573	186	15	)	)	PUNCT
ejpam-3573	186	16	,	,	PUNCT
ejpam-3573	186	17	fn([ν]α	fn([ν]α	PROPN
ejpam-3573	186	18	)	)	PUNCT
ejpam-3573	186	19	)	)	PUNCT
ejpam-3573	187	1	y.	y.	PROPN
ejpam-3573	187	2	lan	lan	PROPN
ejpam-3573	187	3	/	/	SYM
ejpam-3573	187	4	eur	eur	PROPN
ejpam-3573	187	5	.	.	PUNCT
ejpam-3573	188	1	j.	j.	PROPN
ejpam-3573	188	2	pure	pure	PROPN
ejpam-3573	188	3	appl	appl	PROPN
ejpam-3573	188	4	.	.	PROPN
ejpam-3573	188	5	math	math	PROPN
ejpam-3573	188	6	,	,	PUNCT
ejpam-3573	188	7	12	12	NUM
ejpam-3573	188	8	(	(	PUNCT
ejpam-3573	188	9	4	4	NUM
ejpam-3573	188	10	)	)	PUNCT
ejpam-3573	188	11	(	(	PUNCT
ejpam-3573	188	12	2019	2019	NUM
ejpam-3573	188	13	)	)	PUNCT
ejpam-3573	188	14	,	,	PUNCT
ejpam-3573	188	15	1689	1689	NUM
ejpam-3573	188	16	-	-	SYM
ejpam-3573	188	17	1700	1700	NUM
ejpam-3573	188	18	1696	1696	NUM
ejpam-3573	188	19	=	=	SYM
ejpam-3573	188	20	sup	sup	NOUN
ejpam-3573	188	21	α∈[0,1	α∈[0,1	NUM
ejpam-3573	188	22	]	]	PUNCT
ejpam-3573	188	23	dh(f̄n([u]α	dh(f̄n([u]α	X
ejpam-3573	188	24	)	)	PUNCT
ejpam-3573	188	25	,	,	PUNCT
ejpam-3573	188	26	f̄n([ν]α	f̄n([ν]α	PROPN
ejpam-3573	188	27	)	)	PUNCT
ejpam-3573	188	28	)	)	PUNCT
ejpam-3573	188	29	≥	≥	NOUN
ejpam-3573	188	30	dh(f̄n([u]αk	dh(f̄n([u]αk	NUM
ejpam-3573	188	31	)	)	PUNCT
ejpam-3573	188	32	,	,	PUNCT
ejpam-3573	188	33	f̄n([ν]αk	f̄n([ν]αk	NUM
ejpam-3573	188	34	)	)	PUNCT
ejpam-3573	188	35	)	)	PUNCT
ejpam-3573	189	1	=	=	PRON
ejpam-3573	189	2	dh(f̄n(ak	dh(f̄n(ak	NOUN
ejpam-3573	189	3	)	)	PUNCT
ejpam-3573	189	4	,	,	PUNCT
ejpam-3573	189	5	f̄n(b	f̄n(b	NOUN
ejpam-3573	189	6	)	)	PUNCT
ejpam-3573	189	7	)	)	PUNCT
ejpam-3573	189	8	>	>	PUNCT
ejpam-3573	190	1	δ	δ	PROPN
ejpam-3573	190	2	holds	hold	VERB
ejpam-3573	190	3	,	,	PUNCT
ejpam-3573	190	4	the	the	DET
ejpam-3573	190	5	strong	strong	ADJ
ejpam-3573	190	6	sensitivity	sensitivity	NOUN
ejpam-3573	190	7	of	of	ADP
ejpam-3573	190	8	{	{	PUNCT
ejpam-3573	190	9	f̂n}∞n=1	f̂n}∞n=1	PROPN
ejpam-3573	190	10	follows	follow	VERB
ejpam-3573	190	11	.	.	PUNCT
ejpam-3573	191	1	theorem	theorem	NOUN
ejpam-3573	191	2	2	2	NUM
ejpam-3573	191	3	.	.	PUNCT
ejpam-3573	192	1	if	if	SCONJ
ejpam-3573	192	2	(	(	PUNCT
ejpam-3573	192	3	f(x	f(x	PROPN
ejpam-3573	192	4	)	)	PUNCT
ejpam-3573	192	5	,	,	PUNCT
ejpam-3573	192	6	{	{	PUNCT
ejpam-3573	192	7	f̂n}∞n=1	f̂n}∞n=1	PROPN
ejpam-3573	192	8	)	)	PUNCT
ejpam-3573	192	9	is	be	AUX
ejpam-3573	192	10	mean	mean	ADV
ejpam-3573	192	11	sensitive	sensitive	ADJ
ejpam-3573	192	12	,	,	PUNCT
ejpam-3573	192	13	then	then	ADV
ejpam-3573	192	14	(	(	PUNCT
ejpam-3573	192	15	x	x	X
ejpam-3573	192	16	,	,	PUNCT
ejpam-3573	192	17	{	{	PUNCT
ejpam-3573	192	18	fn}∞n=1	fn}∞n=1	X
ejpam-3573	192	19	)	)	PUNCT
ejpam-3573	192	20	is	be	AUX
ejpam-3573	192	21	also	also	ADV
ejpam-3573	192	22	mean	mean	ADJ
ejpam-3573	192	23	sensitive	sensitive	ADJ
ejpam-3573	192	24	.	.	PUNCT
ejpam-3573	193	1	proof	proof	NOUN
ejpam-3573	193	2	.	.	PUNCT
ejpam-3573	194	1	let	let	VERB
ejpam-3573	194	2	(	(	PUNCT
ejpam-3573	194	3	f(x	f(x	PROPN
ejpam-3573	194	4	)	)	PUNCT
ejpam-3573	194	5	,	,	PUNCT
ejpam-3573	194	6	{	{	PUNCT
ejpam-3573	194	7	f̂n}∞n=1	f̂n}∞n=1	PROPN
ejpam-3573	194	8	)	)	PUNCT
ejpam-3573	194	9	be	be	VERB
ejpam-3573	194	10	mean	mean	ADV
ejpam-3573	194	11	sensitive	sensitive	ADJ
ejpam-3573	194	12	with	with	ADP
ejpam-3573	194	13	sensitive	sensitive	ADJ
ejpam-3573	194	14	constant	constant	ADJ
ejpam-3573	194	15	δ	δ	PROPN
ejpam-3573	194	16	,	,	PUNCT
ejpam-3573	194	17	then	then	ADV
ejpam-3573	194	18	for	for	ADP
ejpam-3573	194	19	every	every	DET
ejpam-3573	194	20	u	u	PROPN
ejpam-3573	194	21	∈	∈	PROPN
ejpam-3573	194	22	f(x	f(x	PROPN
ejpam-3573	194	23	)	)	PUNCT
ejpam-3573	194	24	and	and	CCONJ
ejpam-3573	194	25	every	every	DET
ejpam-3573	194	26	ε	ε	PROPN
ejpam-3573	194	27	>	>	X
ejpam-3573	194	28	0	0	PUNCT
ejpam-3573	194	29	there	there	PRON
ejpam-3573	194	30	exists	exist	VERB
ejpam-3573	194	31	v1	v1	PROPN
ejpam-3573	194	32	∈	∈	PROPN
ejpam-3573	194	33	ud∞(u	ud∞(u	X
ejpam-3573	194	34	,	,	PUNCT
ejpam-3573	194	35	ε	ε	PROPN
ejpam-3573	194	36	)	)	PUNCT
ejpam-3573	194	37	such	such	ADJ
ejpam-3573	194	38	that	that	SCONJ
ejpam-3573	194	39	lim	lim	PROPN
ejpam-3573	194	40	sup	sup	VERB
ejpam-3573	194	41	n→∞	n→∞	NUM
ejpam-3573	194	42	1	1	NUM
ejpam-3573	194	43	n	n	PROPN
ejpam-3573	194	44	n−1∑	n−1∑	NUM
ejpam-3573	194	45	i=0	i=0	PROPN
ejpam-3573	194	46	d∞(f̂iu	d∞(f̂iu	PROPN
ejpam-3573	194	47	,	,	PUNCT
ejpam-3573	194	48	f̂iv1	f̂iv1	PROPN
ejpam-3573	194	49	)	)	PUNCT
ejpam-3573	194	50	>	>	X
ejpam-3573	195	1	δ	δ	PROPN
ejpam-3573	195	2	.	.	PUNCT
ejpam-3573	196	1	taking	take	VERB
ejpam-3573	196	2	u	u	NOUN
ejpam-3573	196	3	=	=	NOUN
ejpam-3573	196	4	x̂	x̂	NUM
ejpam-3573	196	5	∈	∈	PROPN
ejpam-3573	196	6	f(x	f(x	PROPN
ejpam-3573	196	7	)	)	PUNCT
ejpam-3573	196	8	we	we	PRON
ejpam-3573	196	9	have	have	VERB
ejpam-3573	196	10	that	that	PRON
ejpam-3573	196	11	lim	lim	PROPN
ejpam-3573	196	12	sup	sup	VERB
ejpam-3573	196	13	n→∞	n→∞	NUM
ejpam-3573	197	1	1	1	NUM
ejpam-3573	197	2	n	n	PROPN
ejpam-3573	197	3	n−1∑	n−1∑	NUM
ejpam-3573	197	4	i=0	i=0	PROPN
ejpam-3573	197	5	d∞(f̂ix̂	d∞(f̂ix̂	PROPN
ejpam-3573	197	6	,	,	PUNCT
ejpam-3573	197	7	f̂iv1	f̂iv1	PROPN
ejpam-3573	197	8	)	)	PUNCT
ejpam-3573	197	9	=	=	SYM
ejpam-3573	197	10	lim	lim	PROPN
ejpam-3573	197	11	sup	sup	VERB
ejpam-3573	197	12	n→∞	n→∞	NUM
ejpam-3573	197	13	1	1	NUM
ejpam-3573	197	14	n	n	PROPN
ejpam-3573	197	15	n−1∑	n−1∑	NUM
ejpam-3573	197	16	i=0	i=0	PROPN
ejpam-3573	197	17	sup	sup	NOUN
ejpam-3573	197	18	α∈[0,1	α∈[0,1	NUM
ejpam-3573	197	19	]	]	X
ejpam-3573	197	20	dh([f̂i(x̂)]α	dh([f̂i(x̂)]α	X
ejpam-3573	197	21	,	,	PUNCT
ejpam-3573	197	22	[	[	X
ejpam-3573	197	23	f̂i(v1)]α	f̂i(v1)]α	X
ejpam-3573	197	24	)	)	PUNCT
ejpam-3573	197	25	=	=	SYM
ejpam-3573	197	26	lim	lim	PROPN
ejpam-3573	197	27	sup	sup	VERB
ejpam-3573	197	28	n→∞	n→∞	NUM
ejpam-3573	197	29	1	1	NUM
ejpam-3573	197	30	n	n	PROPN
ejpam-3573	197	31	n−1∑	n−1∑	NUM
ejpam-3573	197	32	i=0	i=0	PROPN
ejpam-3573	197	33	sup	sup	NOUN
ejpam-3573	197	34	α∈[0,1	α∈[0,1	NOUN
ejpam-3573	197	35	]	]	X
ejpam-3573	197	36	dh(fi([x]α	dh(fi([x]α	NOUN
ejpam-3573	197	37	)	)	PUNCT
ejpam-3573	197	38	,	,	PUNCT
ejpam-3573	197	39	fi([v1]α	fi([v1]α	PROPN
ejpam-3573	197	40	)	)	PUNCT
ejpam-3573	197	41	)	)	PUNCT
ejpam-3573	198	1	=	=	SYM
ejpam-3573	198	2	lim	lim	PROPN
ejpam-3573	198	3	sup	sup	VERB
ejpam-3573	198	4	n→∞	n→∞	NUM
ejpam-3573	198	5	1	1	NUM
ejpam-3573	198	6	n	n	PROPN
ejpam-3573	198	7	n−1∑	n−1∑	NUM
ejpam-3573	198	8	i=0	i=0	PROPN
ejpam-3573	198	9	sup	sup	NOUN
ejpam-3573	198	10	α∈[0,1	α∈[0,1	NOUN
ejpam-3573	198	11	]	]	X
ejpam-3573	198	12	dh(f̄i({x	dh(f̄i({x	NOUN
ejpam-3573	198	13	}	}	PUNCT
ejpam-3573	198	14	)	)	PUNCT
ejpam-3573	198	15	,	,	PUNCT
ejpam-3573	198	16	f̄i([v1]α	f̄i([v1]α	NOUN
ejpam-3573	198	17	)	)	PUNCT
ejpam-3573	198	18	)	)	PUNCT
ejpam-3573	199	1	=	=	SYM
ejpam-3573	199	2	lim	lim	PROPN
ejpam-3573	199	3	sup	sup	VERB
ejpam-3573	199	4	n→∞	n→∞	NUM
ejpam-3573	199	5	1	1	NUM
ejpam-3573	199	6	n	n	NOUN
ejpam-3573	199	7	n−1∑	n−1∑	NUM
ejpam-3573	199	8	i=0	i=0	ADJ
ejpam-3573	199	9	sup	sup	NOUN
ejpam-3573	199	10	y∈[v1]0	y∈[v1]0	PROPN
ejpam-3573	199	11	d(fi(x	d(fi(x	PROPN
ejpam-3573	199	12	)	)	PUNCT
ejpam-3573	199	13	,	,	PUNCT
ejpam-3573	199	14	fi(y	fi(y	NOUN
ejpam-3573	199	15	)	)	PUNCT
ejpam-3573	199	16	)	)	PUNCT
ejpam-3573	199	17	>	>	PUNCT
ejpam-3573	200	1	δ	δ	PROPN
ejpam-3573	200	2	.	.	PUNCT
ejpam-3573	201	1	thus	thus	ADV
ejpam-3573	201	2	it	it	PRON
ejpam-3573	201	3	follows	follow	VERB
ejpam-3573	201	4	from	from	ADP
ejpam-3573	201	5	the	the	DET
ejpam-3573	201	6	continuity	continuity	NOUN
ejpam-3573	201	7	of	of	ADP
ejpam-3573	201	8	{	{	PUNCT
ejpam-3573	201	9	fn}∞n=1	fn}∞n=1	PUNCT
ejpam-3573	201	10	and	and	CCONJ
ejpam-3573	201	11	the	the	DET
ejpam-3573	201	12	compactness	compactness	NOUN
ejpam-3573	201	13	of	of	ADP
ejpam-3573	201	14	[	[	X
ejpam-3573	201	15	v1]0	v1]0	NOUN
ejpam-3573	201	16	that	that	SCONJ
ejpam-3573	201	17	there	there	PRON
ejpam-3573	201	18	exist	exist	VERB
ejpam-3573	201	19	y1	y1	PROPN
ejpam-3573	201	20	∈	∈	PROPN
ejpam-3573	202	1	[	[	X
ejpam-3573	202	2	v1]0	v1]0	NOUN
ejpam-3573	202	3	and	and	CCONJ
ejpam-3573	202	4	an	an	DET
ejpam-3573	202	5	integer	integer	NOUN
ejpam-3573	202	6	n1	n1	NOUN
ejpam-3573	202	7	such	such	ADJ
ejpam-3573	202	8	that	that	SCONJ
ejpam-3573	202	9	n1−1∑	n1−1∑	PROPN
ejpam-3573	202	10	i=0	i=0	PROPN
ejpam-3573	202	11	d(fi(x	d(fi(x	PROPN
ejpam-3573	202	12	)	)	PUNCT
ejpam-3573	202	13	,	,	PUNCT
ejpam-3573	202	14	fi(y1	fi(y1	NOUN
ejpam-3573	202	15	)	)	PUNCT
ejpam-3573	202	16	)	)	PUNCT
ejpam-3573	202	17	>	>	PUNCT
ejpam-3573	203	1	n1δ	n1δ	NOUN
ejpam-3573	203	2	.	.	PUNCT
ejpam-3573	204	1	if	if	SCONJ
ejpam-3573	204	2	(	(	PUNCT
ejpam-3573	204	3	x	x	NOUN
ejpam-3573	204	4	,	,	PUNCT
ejpam-3573	204	5	y1	y1	NOUN
ejpam-3573	204	6	)	)	PUNCT
ejpam-3573	204	7	forms	form	VERB
ejpam-3573	204	8	a	a	DET
ejpam-3573	204	9	mean	mean	ADJ
ejpam-3573	204	10	sensitive	sensitive	ADJ
ejpam-3573	204	11	pair	pair	NOUN
ejpam-3573	204	12	,	,	PUNCT
ejpam-3573	204	13	then	then	ADV
ejpam-3573	204	14	the	the	DET
ejpam-3573	204	15	proof	proof	NOUN
ejpam-3573	204	16	is	be	AUX
ejpam-3573	204	17	done	do	VERB
ejpam-3573	204	18	.	.	PUNCT
ejpam-3573	205	1	if	if	SCONJ
ejpam-3573	205	2	not	not	PART
ejpam-3573	205	3	,	,	PUNCT
ejpam-3573	205	4	then	then	ADV
ejpam-3573	205	5	there	there	PRON
ejpam-3573	205	6	exists	exist	VERB
ejpam-3573	205	7	an	an	DET
ejpam-3573	205	8	integer	integer	NOUN
ejpam-3573	205	9	k1	k1	NOUN
ejpam-3573	205	10	with	with	ADP
ejpam-3573	205	11	k1	k1	PROPN
ejpam-3573	205	12	>	>	X
ejpam-3573	205	13	n1	n1	PROPN
ejpam-3573	205	14	such	such	ADJ
ejpam-3573	205	15	that	that	SCONJ
ejpam-3573	205	16	∑n−1	∑n−1	ADP
ejpam-3573	205	17	i=0	i=0	PROPN
ejpam-3573	205	18	d(fi(x	d(fi(x	PROPN
ejpam-3573	205	19	)	)	PUNCT
ejpam-3573	205	20	,	,	PUNCT
ejpam-3573	205	21	fi(y1	fi(y1	NOUN
ejpam-3573	205	22	)	)	PUNCT
ejpam-3573	205	23	)	)	PUNCT
ejpam-3573	205	24	≤	≤	NUM
ejpam-3573	205	25	n1δ	n1δ	NOUN
ejpam-3573	205	26	for	for	ADP
ejpam-3573	205	27	all	all	DET
ejpam-3573	205	28	n	n	PRON
ejpam-3573	205	29	≥	≥	NOUN
ejpam-3573	205	30	k1	k1	NOUN
ejpam-3573	205	31	.	.	PUNCT
ejpam-3573	206	1	thus	thus	ADV
ejpam-3573	206	2	we	we	PRON
ejpam-3573	206	3	can	can	AUX
ejpam-3573	206	4	find	find	VERB
ejpam-3573	206	5	a	a	DET
ejpam-3573	206	6	neighborhood	neighborhood	NOUN
ejpam-3573	206	7	u1	u1	NOUN
ejpam-3573	206	8	of	of	ADP
ejpam-3573	206	9	y1	y1	PROPN
ejpam-3573	206	10	with	with	ADP
ejpam-3573	206	11	u1	u1	PROPN
ejpam-3573	206	12	⊂	⊂	PROPN
ejpam-3573	206	13	ud(x	ud(x	ADV
ejpam-3573	206	14	,	,	PUNCT
ejpam-3573	206	15	ε	ε	PROPN
ejpam-3573	206	16	)	)	PUNCT
ejpam-3573	206	17	such	such	ADJ
ejpam-3573	206	18	that	that	SCONJ
ejpam-3573	206	19	∑n1−1	∑n1−1	VERB
ejpam-3573	206	20	i=0	i=0	PROPN
ejpam-3573	206	21	d(fi(x	d(fi(x	PROPN
ejpam-3573	206	22	)	)	PUNCT
ejpam-3573	206	23	,	,	PUNCT
ejpam-3573	206	24	fi(z	fi(z	NOUN
ejpam-3573	206	25	)	)	PUNCT
ejpam-3573	206	26	)	)	PUNCT
ejpam-3573	207	1	>	>	PUNCT
ejpam-3573	208	1	n1δ	n1δ	NOUN
ejpam-3573	208	2	for	for	ADP
ejpam-3573	208	3	all	all	DET
ejpam-3573	208	4	z	z	NOUN
ejpam-3573	208	5	∈	∈	PROPN
ejpam-3573	208	6	u1	u1	NOUN
ejpam-3573	208	7	.	.	PUNCT
ejpam-3573	209	1	furthermore	furthermore	ADV
ejpam-3573	209	2	,	,	PUNCT
ejpam-3573	209	3	there	there	PRON
ejpam-3573	209	4	exists	exist	VERB
ejpam-3573	209	5	ε1	ε1	VERB
ejpam-3573	209	6	>	>	X
ejpam-3573	209	7	0	0	NUM
ejpam-3573	209	8	such	such	ADJ
ejpam-3573	209	9	that	that	SCONJ
ejpam-3573	209	10	ud(y1	ud(y1	NOUN
ejpam-3573	209	11	,	,	PUNCT
ejpam-3573	209	12	ε1	ε1	PROPN
ejpam-3573	209	13	)	)	PUNCT
ejpam-3573	209	14	⊂	⊂	PROPN
ejpam-3573	209	15	u1	u1	PROPN
ejpam-3573	209	16	.	.	PUNCT
ejpam-3573	210	1	using	use	VERB
ejpam-3573	210	2	the	the	DET
ejpam-3573	210	3	mean	mean	ADJ
ejpam-3573	210	4	sensitivity	sensitivity	NOUN
ejpam-3573	210	5	of	of	ADP
ejpam-3573	210	6	{	{	PUNCT
ejpam-3573	210	7	f̂n}∞n=1	f̂n}∞n=1	PROPN
ejpam-3573	210	8	again	again	ADV
ejpam-3573	210	9	,	,	PUNCT
ejpam-3573	210	10	we	we	PRON
ejpam-3573	210	11	have	have	VERB
ejpam-3573	210	12	v2	v2	PROPN
ejpam-3573	210	13	∈	∈	PROPN
ejpam-3573	210	14	ud∞(ŷ1	ud∞(ŷ1	PROPN
ejpam-3573	210	15	,	,	PUNCT
ejpam-3573	210	16	ε1	ε1	PROPN
ejpam-3573	210	17	)	)	PUNCT
ejpam-3573	210	18	such	such	ADJ
ejpam-3573	210	19	that	that	SCONJ
ejpam-3573	210	20	(	(	PUNCT
ejpam-3573	210	21	ŷ1	ŷ1	ADJ
ejpam-3573	210	22	,	,	PUNCT
ejpam-3573	210	23	v2	v2	PROPN
ejpam-3573	210	24	)	)	PUNCT
ejpam-3573	210	25	is	be	AUX
ejpam-3573	210	26	a	a	DET
ejpam-3573	210	27	mean	mean	ADJ
ejpam-3573	210	28	sensitive	sensitive	ADJ
ejpam-3573	210	29	pair	pair	NOUN
ejpam-3573	210	30	,	,	PUNCT
ejpam-3573	210	31	that	that	ADV
ejpam-3573	210	32	is	is	ADV
ejpam-3573	210	33	,	,	PUNCT
ejpam-3573	210	34	lim	lim	PROPN
ejpam-3573	210	35	sup	sup	VERB
ejpam-3573	210	36	n→∞	n→∞	NUM
ejpam-3573	210	37	1	1	NUM
ejpam-3573	210	38	n	n	PROPN
ejpam-3573	210	39	n−1∑	n−1∑	PROPN
ejpam-3573	210	40	i=0	i=0	PROPN
ejpam-3573	210	41	d∞(f̂iŷ1	d∞(f̂iŷ1	PROPN
ejpam-3573	210	42	,	,	PUNCT
ejpam-3573	210	43	f̂iv2	f̂iv2	PROPN
ejpam-3573	210	44	)	)	PUNCT
ejpam-3573	211	1	=	=	SYM
ejpam-3573	211	2	lim	lim	PROPN
ejpam-3573	211	3	sup	sup	VERB
ejpam-3573	211	4	n→∞	n→∞	NUM
ejpam-3573	211	5	1	1	NUM
ejpam-3573	211	6	n	n	PROPN
ejpam-3573	211	7	n−1∑	n−1∑	NUM
ejpam-3573	211	8	i=0	i=0	PROPN
ejpam-3573	211	9	sup	sup	NOUN
ejpam-3573	211	10	α∈[0,1	α∈[0,1	NOUN
ejpam-3573	211	11	]	]	X
ejpam-3573	211	12	dh([f̂i(ŷ1)]α	dh([f̂i(ŷ1)]α	PROPN
ejpam-3573	211	13	,	,	PUNCT
ejpam-3573	211	14	[	[	X
ejpam-3573	211	15	f̂i(v2)]α	f̂i(v2)]α	X
ejpam-3573	211	16	)	)	PUNCT
ejpam-3573	211	17	y.	y.	PROPN
ejpam-3573	211	18	lan	lan	PROPN
ejpam-3573	211	19	/	/	SYM
ejpam-3573	211	20	eur	eur	PROPN
ejpam-3573	211	21	.	.	PUNCT
ejpam-3573	212	1	j.	j.	PROPN
ejpam-3573	212	2	pure	pure	PROPN
ejpam-3573	212	3	appl	appl	PROPN
ejpam-3573	212	4	.	.	PROPN
ejpam-3573	212	5	math	math	PROPN
ejpam-3573	212	6	,	,	PUNCT
ejpam-3573	212	7	12	12	NUM
ejpam-3573	212	8	(	(	PUNCT
ejpam-3573	212	9	4	4	NUM
ejpam-3573	212	10	)	)	PUNCT
ejpam-3573	212	11	(	(	PUNCT
ejpam-3573	212	12	2019	2019	NUM
ejpam-3573	212	13	)	)	PUNCT
ejpam-3573	212	14	,	,	PUNCT
ejpam-3573	212	15	1689	1689	NUM
ejpam-3573	212	16	-	-	SYM
ejpam-3573	212	17	1700	1700	NUM
ejpam-3573	212	18	1697	1697	NUM
ejpam-3573	212	19	=	=	SYM
ejpam-3573	212	20	lim	lim	PROPN
ejpam-3573	212	21	sup	sup	VERB
ejpam-3573	212	22	n→∞	n→∞	NUM
ejpam-3573	212	23	1	1	NUM
ejpam-3573	212	24	n	n	PROPN
ejpam-3573	212	25	n−1∑	n−1∑	NUM
ejpam-3573	212	26	i=0	i=0	PROPN
ejpam-3573	212	27	sup	sup	NOUN
ejpam-3573	212	28	α∈[0,1	α∈[0,1	NOUN
ejpam-3573	212	29	]	]	X
ejpam-3573	212	30	dh(f̄i(y1	dh(f̄i(y1	PROPN
ejpam-3573	212	31	)	)	PUNCT
ejpam-3573	212	32	,	,	PUNCT
ejpam-3573	212	33	f̄i([v2]α	f̄i([v2]α	NUM
ejpam-3573	212	34	)	)	PUNCT
ejpam-3573	212	35	)	)	PUNCT
ejpam-3573	213	1	=	=	SYM
ejpam-3573	213	2	lim	lim	PROPN
ejpam-3573	213	3	sup	sup	VERB
ejpam-3573	213	4	n→∞	n→∞	NUM
ejpam-3573	213	5	1	1	NUM
ejpam-3573	213	6	n	n	PROPN
ejpam-3573	213	7	n−1∑	n−1∑	NUM
ejpam-3573	213	8	i=0	i=0	PROPN
ejpam-3573	213	9	sup	sup	NOUN
ejpam-3573	213	10	y∈[v2]0	y∈[v2]0	PROPN
ejpam-3573	213	11	d(fi(y1	d(fi(y1	NOUN
ejpam-3573	213	12	)	)	PUNCT
ejpam-3573	213	13	,	,	PUNCT
ejpam-3573	213	14	fi(y	fi(y	NOUN
ejpam-3573	213	15	)	)	PUNCT
ejpam-3573	213	16	)	)	PUNCT
ejpam-3573	213	17	>	>	PUNCT
ejpam-3573	214	1	δ	δ	PROPN
ejpam-3573	214	2	.	.	PUNCT
ejpam-3573	215	1	therefore	therefore	ADV
ejpam-3573	215	2	,	,	PUNCT
ejpam-3573	215	3	there	there	PRON
ejpam-3573	215	4	exist	exist	VERB
ejpam-3573	215	5	y2	y2	NOUN
ejpam-3573	215	6	∈	∈	PROPN
ejpam-3573	216	1	[	[	X
ejpam-3573	216	2	v2]0	v2]0	PUNCT
ejpam-3573	216	3	and	and	CCONJ
ejpam-3573	216	4	an	an	DET
ejpam-3573	216	5	integer	integer	NOUN
ejpam-3573	216	6	n2	n2	NOUN
ejpam-3573	216	7	>	>	X
ejpam-3573	216	8	k1	k1	PROPN
ejpam-3573	216	9	>	>	X
ejpam-3573	216	10	n1	n1	PROPN
ejpam-3573	216	11	such	such	ADJ
ejpam-3573	216	12	that	that	SCONJ
ejpam-3573	216	13	n2−1∑	n2−1∑	ADJ
ejpam-3573	216	14	i=0	i=0	ADJ
ejpam-3573	216	15	d(fi(y1	d(fi(y1	NOUN
ejpam-3573	216	16	)	)	PUNCT
ejpam-3573	216	17	,	,	PUNCT
ejpam-3573	216	18	fi(y2	fi(y2	NOUN
ejpam-3573	216	19	)	)	PUNCT
ejpam-3573	216	20	)	)	PUNCT
ejpam-3573	216	21	>	>	X
ejpam-3573	217	1	n2δ	n2δ	PROPN
ejpam-3573	217	2	,	,	PUNCT
ejpam-3573	217	3	and	and	CCONJ
ejpam-3573	217	4	then	then	ADV
ejpam-3573	217	5	n2−1∑	n2−1∑	VERB
ejpam-3573	217	6	i=0	i=0	PROPN
ejpam-3573	217	7	d(fi(x	d(fi(x	PROPN
ejpam-3573	217	8	)	)	PUNCT
ejpam-3573	217	9	,	,	PUNCT
ejpam-3573	217	10	fi(y2	fi(y2	NOUN
ejpam-3573	217	11	)	)	PUNCT
ejpam-3573	217	12	)	)	PUNCT
ejpam-3573	217	13	>	>	PUNCT
ejpam-3573	217	14	n2−1∑	n2−1∑	PROPN
ejpam-3573	217	15	i=0	i=0	ADJ
ejpam-3573	217	16	d(fi(y1	d(fi(y1	NOUN
ejpam-3573	217	17	)	)	PUNCT
ejpam-3573	217	18	,	,	PUNCT
ejpam-3573	217	19	fi(y2))−	fi(y2))−	PROPN
ejpam-3573	217	20	n2−1∑	n2−1∑	PROPN
ejpam-3573	217	21	i=0	i=0	PROPN
ejpam-3573	217	22	d(fi(x	d(fi(x	PROPN
ejpam-3573	217	23	)	)	PUNCT
ejpam-3573	217	24	,	,	PUNCT
ejpam-3573	217	25	fi(y1	fi(y1	NOUN
ejpam-3573	217	26	)	)	PUNCT
ejpam-3573	217	27	)	)	PUNCT
ejpam-3573	217	28	≥	≥	PROPN
ejpam-3573	217	29	(	(	PUNCT
ejpam-3573	217	30	n2	n2	ADJ
ejpam-3573	217	31	−	−	PROPN
ejpam-3573	217	32	n1)δ	n1)δ	ADJ
ejpam-3573	217	33	.	.	PUNCT
ejpam-3573	218	1	if	if	SCONJ
ejpam-3573	218	2	(	(	PUNCT
ejpam-3573	218	3	x	x	NOUN
ejpam-3573	218	4	,	,	PUNCT
ejpam-3573	218	5	y2	y2	PROPN
ejpam-3573	218	6	)	)	PUNCT
ejpam-3573	218	7	forms	form	VERB
ejpam-3573	218	8	a	a	DET
ejpam-3573	218	9	mean	mean	ADJ
ejpam-3573	218	10	sensitive	sensitive	ADJ
ejpam-3573	218	11	pair	pair	NOUN
ejpam-3573	218	12	,	,	PUNCT
ejpam-3573	218	13	then	then	ADV
ejpam-3573	218	14	the	the	DET
ejpam-3573	218	15	proof	proof	NOUN
ejpam-3573	218	16	is	be	AUX
ejpam-3573	218	17	done	do	VERB
ejpam-3573	218	18	.	.	PUNCT
ejpam-3573	219	1	if	if	SCONJ
ejpam-3573	219	2	not	not	PART
ejpam-3573	219	3	,	,	PUNCT
ejpam-3573	219	4	then	then	ADV
ejpam-3573	219	5	there	there	PRON
ejpam-3573	219	6	exists	exist	VERB
ejpam-3573	219	7	an	an	DET
ejpam-3573	219	8	integer	integer	NOUN
ejpam-3573	219	9	k2	k2	NOUN
ejpam-3573	219	10	with	with	ADP
ejpam-3573	219	11	k2	k2	PROPN
ejpam-3573	219	12	>	>	X
ejpam-3573	219	13	n2	n2	PROPN
ejpam-3573	219	14	such	such	ADJ
ejpam-3573	219	15	that	that	SCONJ
ejpam-3573	219	16	∑n−1	∑n−1	ADP
ejpam-3573	219	17	i=0	i=0	PROPN
ejpam-3573	219	18	d(fi(x	d(fi(x	PROPN
ejpam-3573	219	19	)	)	PUNCT
ejpam-3573	219	20	,	,	PUNCT
ejpam-3573	219	21	fi(y2	fi(y2	ADJ
ejpam-3573	219	22	)	)	PUNCT
ejpam-3573	219	23	)	)	PUNCT
ejpam-3573	219	24	≤	≤	NOUN
ejpam-3573	219	25	(	(	PUNCT
ejpam-3573	219	26	n2	n2	ADJ
ejpam-3573	219	27	−	−	PROPN
ejpam-3573	219	28	n1)δ	n1)δ	NOUN
ejpam-3573	219	29	for	for	ADP
ejpam-3573	219	30	all	all	DET
ejpam-3573	219	31	n	n	PRON
ejpam-3573	219	32	≥	≥	NOUN
ejpam-3573	219	33	k2	k2	PROPN
ejpam-3573	219	34	.	.	PUNCT
ejpam-3573	220	1	again	again	ADV
ejpam-3573	220	2	,	,	PUNCT
ejpam-3573	220	3	we	we	PRON
ejpam-3573	220	4	can	can	AUX
ejpam-3573	220	5	find	find	VERB
ejpam-3573	220	6	a	a	DET
ejpam-3573	220	7	neighborhood	neighborhood	NOUN
ejpam-3573	220	8	u2	u2	NOUN
ejpam-3573	220	9	of	of	ADP
ejpam-3573	220	10	y2	y2	PROPN
ejpam-3573	220	11	with	with	ADP
ejpam-3573	220	12	u2	u2	PROPN
ejpam-3573	220	13	⊂	⊂	PROPN
ejpam-3573	220	14	ud(y1	ud(y1	PROPN
ejpam-3573	220	15	,	,	PUNCT
ejpam-3573	220	16	ε1	ε1	PROPN
ejpam-3573	220	17	)	)	PUNCT
ejpam-3573	220	18	such	such	DET
ejpam-3573	220	19	that∑n2−1	that∑n2−1	DET
ejpam-3573	220	20	i=0	i=0	PROPN
ejpam-3573	220	21	d(fi(x	d(fi(x	PROPN
ejpam-3573	220	22	)	)	PUNCT
ejpam-3573	220	23	,	,	PUNCT
ejpam-3573	220	24	fi(z	fi(z	NOUN
ejpam-3573	220	25	)	)	PUNCT
ejpam-3573	220	26	)	)	PUNCT
ejpam-3573	220	27	>	>	PUNCT
ejpam-3573	221	1	(	(	PUNCT
ejpam-3573	221	2	n2	n2	ADJ
ejpam-3573	221	3	−	−	PROPN
ejpam-3573	221	4	n1)δ	n1)δ	NOUN
ejpam-3573	221	5	for	for	ADP
ejpam-3573	221	6	all	all	DET
ejpam-3573	221	7	z	z	NOUN
ejpam-3573	221	8	∈	∈	PROPN
ejpam-3573	221	9	u2	u2	NOUN
ejpam-3573	221	10	.	.	PUNCT
ejpam-3573	222	1	thus	thus	ADV
ejpam-3573	222	2	,	,	PUNCT
ejpam-3573	222	3	there	there	PRON
ejpam-3573	222	4	exists	exist	VERB
ejpam-3573	222	5	ε2	ε2	ADV
ejpam-3573	222	6	>	>	X
ejpam-3573	222	7	0	0	NUM
ejpam-3573	222	8	such	such	ADJ
ejpam-3573	222	9	that	that	SCONJ
ejpam-3573	222	10	ud(y2	ud(y2	ADJ
ejpam-3573	222	11	,	,	PUNCT
ejpam-3573	222	12	ε2	ε2	ADJ
ejpam-3573	222	13	)	)	PUNCT
ejpam-3573	222	14	⊂	⊂	PROPN
ejpam-3573	222	15	u2	u2	PROPN
ejpam-3573	222	16	.	.	PUNCT
ejpam-3573	223	1	proceeding	proceed	VERB
ejpam-3573	223	2	inductively	inductively	ADV
ejpam-3573	223	3	,	,	PUNCT
ejpam-3573	223	4	we	we	PRON
ejpam-3573	223	5	eventually	eventually	ADV
ejpam-3573	223	6	obtain	obtain	VERB
ejpam-3573	223	7	either	either	CCONJ
ejpam-3573	223	8	the	the	DET
ejpam-3573	223	9	mean	mean	ADJ
ejpam-3573	223	10	sensitive	sensitive	ADJ
ejpam-3573	223	11	pair	pair	NOUN
ejpam-3573	223	12	(	(	PUNCT
ejpam-3573	223	13	x	x	NOUN
ejpam-3573	223	14	,	,	PUNCT
ejpam-3573	223	15	yk	yk	PROPN
ejpam-3573	223	16	)	)	PUNCT
ejpam-3573	223	17	or	or	CCONJ
ejpam-3573	223	18	a	a	DET
ejpam-3573	223	19	sequence	sequence	NOUN
ejpam-3573	223	20	{	{	PUNCT
ejpam-3573	223	21	yn	yn	NOUN
ejpam-3573	223	22	}	}	PUNCT
ejpam-3573	223	23	in	in	ADP
ejpam-3573	223	24	ud(x	ud(x	PROPN
ejpam-3573	223	25	,	,	PUNCT
ejpam-3573	223	26	ε	ε	PROPN
ejpam-3573	223	27	)	)	PUNCT
ejpam-3573	223	28	.	.	PUNCT
ejpam-3573	224	1	it	it	PRON
ejpam-3573	224	2	follows	follow	VERB
ejpam-3573	224	3	from	from	ADP
ejpam-3573	224	4	the	the	DET
ejpam-3573	224	5	construction	construction	NOUN
ejpam-3573	224	6	that	that	SCONJ
ejpam-3573	224	7	the	the	DET
ejpam-3573	224	8	sequence	sequence	NOUN
ejpam-3573	224	9	{	{	PUNCT
ejpam-3573	224	10	yn	yn	NOUN
ejpam-3573	224	11	}	}	PUNCT
ejpam-3573	224	12	converges	converge	VERB
ejpam-3573	224	13	to	to	ADP
ejpam-3573	224	14	a	a	DET
ejpam-3573	224	15	point	point	NOUN
ejpam-3573	224	16	y0	y0	NOUN
ejpam-3573	224	17	.	.	PUNCT
ejpam-3573	225	1	thus	thus	ADV
ejpam-3573	225	2	y0	y0	PROPN
ejpam-3573	225	3	∈	∈	NOUN
ejpam-3573	225	4	ud(yi	ud(yi	NOUN
ejpam-3573	225	5	,	,	PUNCT
ejpam-3573	225	6	εi	εi	VERB
ejpam-3573	225	7	)	)	PUNCT
ejpam-3573	225	8	⊂	⊂	PROPN
ejpam-3573	225	9	ud(yi	ud(yi	PROPN
ejpam-3573	225	10	,	,	PUNCT
ejpam-3573	225	11	εi	εi	VERB
ejpam-3573	225	12	)	)	PUNCT
ejpam-3573	225	13	⊂	⊂	PROPN
ejpam-3573	225	14	ui	ui	PROPN
ejpam-3573	226	1	⊂	⊂	PROPN
ejpam-3573	226	2	ud(x	ud(x	ADV
ejpam-3573	226	3	,	,	PUNCT
ejpam-3573	226	4	ε	ε	PROPN
ejpam-3573	226	5	)	)	PUNCT
ejpam-3573	226	6	.	.	PUNCT
ejpam-3573	227	1	hence	hence	ADV
ejpam-3573	227	2	for	for	ADP
ejpam-3573	227	3	each	each	DET
ejpam-3573	227	4	i	i	PRON
ejpam-3573	227	5	,	,	PUNCT
ejpam-3573	227	6	we	we	PRON
ejpam-3573	227	7	have	have	AUX
ejpam-3573	227	8	ni−1∑	ni−1∑	VERB
ejpam-3573	227	9	i=0	i=0	PROPN
ejpam-3573	227	10	d(fi(x	d(fi(x	PROPN
ejpam-3573	227	11	)	)	PUNCT
ejpam-3573	227	12	,	,	PUNCT
ejpam-3573	227	13	fi(y0	fi(y0	NOUN
ejpam-3573	227	14	)	)	PUNCT
ejpam-3573	227	15	)	)	PUNCT
ejpam-3573	227	16	>	>	PUNCT
ejpam-3573	228	1	riδ	riδ	NOUN
ejpam-3573	228	2	,	,	PUNCT
ejpam-3573	228	3	where	where	SCONJ
ejpam-3573	228	4	ri	ri	NOUN
ejpam-3573	228	5	=	=	PUNCT
ejpam-3573	228	6	{	{	PUNCT
ejpam-3573	228	7	∑i	∑i	INTJ
ejpam-3573	228	8	k=1(−1)k−1nk	k=1(−1)k−1nk	ADJ
ejpam-3573	228	9	,	,	PUNCT
ejpam-3573	228	10	i	i	PRON
ejpam-3573	228	11	=	=	SYM
ejpam-3573	228	12	2m−	2m−	PROPN
ejpam-3573	228	13	1∑i	1∑i	NUM
ejpam-3573	228	14	k=1(−1)knk	k=1(−1)knk	NOUN
ejpam-3573	228	15	,	,	PUNCT
ejpam-3573	228	16	i	i	PRON
ejpam-3573	228	17	=	=	NOUN
ejpam-3573	228	18	2	2	NUM
ejpam-3573	228	19	m.	m.	NOUN
ejpam-3573	228	20	therefore	therefore	ADV
ejpam-3573	228	21	,	,	PUNCT
ejpam-3573	228	22	lim	lim	PROPN
ejpam-3573	228	23	sup	sup	VERB
ejpam-3573	228	24	n→∞	n→∞	NUM
ejpam-3573	228	25	1	1	NUM
ejpam-3573	228	26	n	n	PROPN
ejpam-3573	228	27	n−1∑	n−1∑	NUM
ejpam-3573	228	28	i=0	i=0	PROPN
ejpam-3573	228	29	d∞(fi(x	d∞(fi(x	PROPN
ejpam-3573	228	30	)	)	PUNCT
ejpam-3573	228	31	,	,	PUNCT
ejpam-3573	228	32	fi(y0	fi(y0	NOUN
ejpam-3573	228	33	)	)	PUNCT
ejpam-3573	228	34	)	)	PUNCT
ejpam-3573	229	1	>	>	PUNCT
ejpam-3573	230	1	δ	δ	PROPN
ejpam-3573	231	1	and	and	CCONJ
ejpam-3573	231	2	then	then	ADV
ejpam-3573	231	3	{	{	PUNCT
ejpam-3573	231	4	fn}∞n=1	fn}∞n=1	PROPN
ejpam-3573	231	5	is	be	AUX
ejpam-3573	231	6	mean	mean	ADJ
ejpam-3573	231	7	sensitive	sensitive	ADJ
ejpam-3573	231	8	.	.	PUNCT
ejpam-3573	232	1	the	the	DET
ejpam-3573	232	2	following	follow	VERB
ejpam-3573	232	3	example	example	NOUN
ejpam-3573	232	4	shows	show	VERB
ejpam-3573	232	5	that	that	SCONJ
ejpam-3573	232	6	,	,	PUNCT
ejpam-3573	232	7	in	in	ADP
ejpam-3573	232	8	general	general	ADJ
ejpam-3573	232	9	,	,	PUNCT
ejpam-3573	232	10	the	the	DET
ejpam-3573	232	11	converse	converse	NOUN
ejpam-3573	232	12	of	of	ADP
ejpam-3573	232	13	theorem	theorem	NOUN
ejpam-3573	232	14	3.4	3.4	NUM
ejpam-3573	232	15	is	be	AUX
ejpam-3573	232	16	not	not	PART
ejpam-3573	232	17	true	true	ADJ
ejpam-3573	232	18	.	.	PUNCT
ejpam-3573	233	1	y.	y.	PROPN
ejpam-3573	233	2	lan	lan	PROPN
ejpam-3573	233	3	/	/	SYM
ejpam-3573	233	4	eur	eur	PROPN
ejpam-3573	233	5	.	.	PUNCT
ejpam-3573	234	1	j.	j.	PROPN
ejpam-3573	234	2	pure	pure	PROPN
ejpam-3573	234	3	appl	appl	PROPN
ejpam-3573	234	4	.	.	PROPN
ejpam-3573	234	5	math	math	PROPN
ejpam-3573	234	6	,	,	PUNCT
ejpam-3573	234	7	12	12	NUM
ejpam-3573	234	8	(	(	PUNCT
ejpam-3573	234	9	4	4	NUM
ejpam-3573	234	10	)	)	PUNCT
ejpam-3573	234	11	(	(	PUNCT
ejpam-3573	234	12	2019	2019	NUM
ejpam-3573	234	13	)	)	PUNCT
ejpam-3573	234	14	,	,	PUNCT
ejpam-3573	234	15	1689	1689	NUM
ejpam-3573	234	16	-	-	SYM
ejpam-3573	234	17	1700	1700	NUM
ejpam-3573	234	18	1698	1698	NUM
ejpam-3573	234	19	example	example	NOUN
ejpam-3573	234	20	1	1	NUM
ejpam-3573	234	21	.	.	PUNCT
ejpam-3573	235	1	let	let	VERB
ejpam-3573	235	2	s1	s1	NOUN
ejpam-3573	235	3	be	be	AUX
ejpam-3573	235	4	a	a	DET
ejpam-3573	235	5	circle	circle	NOUN
ejpam-3573	235	6	.	.	PUNCT
ejpam-3573	236	1	it	it	PRON
ejpam-3573	236	2	is	be	AUX
ejpam-3573	236	3	known	know	VERB
ejpam-3573	236	4	that	that	SCONJ
ejpam-3573	236	5	the	the	DET
ejpam-3573	236	6	denjoy	denjoy	NOUN
ejpam-3573	236	7	map	map	NOUN
ejpam-3573	236	8	dλ	dλ	PROPN
ejpam-3573	236	9	:	:	PUNCT
ejpam-3573	236	10	s∗	s∗	PROPN
ejpam-3573	236	11	→	→	SYM
ejpam-3573	236	12	s∗	s∗	PROPN
ejpam-3573	236	13	is	be	AUX
ejpam-3573	236	14	an	an	DET
ejpam-3573	236	15	orientation	orientation	NOUN
ejpam-3573	236	16	preserving	preserve	VERB
ejpam-3573	236	17	homeomorphism	homeomorphism	NOUN
ejpam-3573	236	18	of	of	ADP
ejpam-3573	236	19	the	the	DET
ejpam-3573	236	20	constructed	construct	VERB
ejpam-3573	236	21	circle	circle	NOUN
ejpam-3573	236	22	s∗.	s∗.	VERB
ejpam-3573	236	23	there	there	PRON
ejpam-3573	236	24	exists	exist	VERB
ejpam-3573	236	25	a	a	DET
ejpam-3573	236	26	cantor	cantor	NOUN
ejpam-3573	236	27	set	set	NOUN
ejpam-3573	236	28	cλ	cλ	PROPN
ejpam-3573	236	29	⊂	⊂	PROPN
ejpam-3573	236	30	s∗	s∗	PROPN
ejpam-3573	236	31	on	on	ADP
ejpam-3573	236	32	which	which	PRON
ejpam-3573	236	33	dλ	dλ	NOUN
ejpam-3573	236	34	acts	act	VERB
ejpam-3573	236	35	minimally	minimally	ADV
ejpam-3573	236	36	.	.	PUNCT
ejpam-3573	237	1	there	there	PRON
ejpam-3573	237	2	exists	exist	VERB
ejpam-3573	237	3	a	a	DET
ejpam-3573	237	4	continuous	continuous	ADJ
ejpam-3573	237	5	surjection	surjection	NOUN
ejpam-3573	237	6	hλ	hλ	NOUN
ejpam-3573	237	7	:	:	PUNCT
ejpam-3573	237	8	s∗	s∗	PROPN
ejpam-3573	237	9	→	→	SYM
ejpam-3573	237	10	s1	s1	PROPN
ejpam-3573	237	11	that	that	SCONJ
ejpam-3573	237	12	semi	semi	NOUN
ejpam-3573	237	13	-	-	NOUN
ejpam-3573	237	14	conjugates	conjugate	NOUN
ejpam-3573	237	15	dλ	dλ	NOUN
ejpam-3573	237	16	with	with	ADP
ejpam-3573	237	17	rλ	rλ	NOUN
ejpam-3573	237	18	.	.	PUNCT
ejpam-3573	238	1	in	in	ADP
ejpam-3573	238	2	[	[	X
ejpam-3573	238	3	22	22	NUM
ejpam-3573	238	4	]	]	PUNCT
ejpam-3573	238	5	,	,	PUNCT
ejpam-3573	238	6	the	the	DET
ejpam-3573	238	7	authors	author	NOUN
ejpam-3573	238	8	show	show	VERB
ejpam-3573	238	9	that	that	SCONJ
ejpam-3573	238	10	the	the	DET
ejpam-3573	238	11	system	system	NOUN
ejpam-3573	238	12	(	(	PUNCT
ejpam-3573	238	13	k(cλ	k(cλ	PROPN
ejpam-3573	238	14	)	)	PUNCT
ejpam-3573	238	15	,	,	PUNCT
ejpam-3573	238	16	dλ	dλ	NOUN
ejpam-3573	238	17	)	)	PUNCT
ejpam-3573	238	18	is	be	AUX
ejpam-3573	238	19	not	not	PART
ejpam-3573	238	20	sensitive	sensitive	ADJ
ejpam-3573	238	21	.	.	PUNCT
ejpam-3573	239	1	hence	hence	ADV
ejpam-3573	239	2	it	it	PRON
ejpam-3573	239	3	is	be	AUX
ejpam-3573	239	4	not	not	PART
ejpam-3573	239	5	mean	mean	ADJ
ejpam-3573	239	6	sensitive	sensitive	ADJ
ejpam-3573	239	7	,	,	PUNCT
ejpam-3573	239	8	as	as	SCONJ
ejpam-3573	239	9	the	the	DET
ejpam-3573	239	10	mean	mean	ADJ
ejpam-3573	239	11	sensitivity	sensitivity	NOUN
ejpam-3573	239	12	is	be	AUX
ejpam-3573	239	13	stronger	strong	ADJ
ejpam-3573	239	14	than	than	ADP
ejpam-3573	239	15	sensitivity	sensitivity	NOUN
ejpam-3573	239	16	.	.	PUNCT
ejpam-3573	240	1	let	let	VERB
ejpam-3573	240	2	fn	fn	NOUN
ejpam-3573	240	3	=	=	VERB
ejpam-3573	240	4	dλ	dλ	NOUN
ejpam-3573	240	5	,	,	PUNCT
ejpam-3573	240	6	n	n	NOUN
ejpam-3573	240	7	=	=	SYM
ejpam-3573	240	8	1	1	NUM
ejpam-3573	240	9	,	,	PUNCT
ejpam-3573	240	10	2	2	NUM
ejpam-3573	240	11	,	,	PUNCT
ejpam-3573	240	12	·	·	PUNCT
ejpam-3573	240	13	·	·	PUNCT
ejpam-3573	240	14	·	·	PUNCT
ejpam-3573	240	15	.	.	PUNCT
ejpam-3573	241	1	define	define	VERB
ejpam-3573	241	2	iλ	iλ	PROPN
ejpam-3573	241	3	:	:	PUNCT
ejpam-3573	241	4	k(cλ	k(cλ	PROPN
ejpam-3573	241	5	)	)	PUNCT
ejpam-3573	241	6	→	→	SYM
ejpam-3573	241	7	f(cλ	f(cλ	NUM
ejpam-3573	241	8	)	)	PUNCT
ejpam-3573	241	9	by	by	ADP
ejpam-3573	241	10	iλ(k	iλ(k	NOUN
ejpam-3573	241	11	)	)	PUNCT
ejpam-3573	241	12	=	=	PUNCT
ejpam-3573	242	1	λχk	λχk	ADP
ejpam-3573	242	2	for	for	ADP
ejpam-3573	242	3	any	any	DET
ejpam-3573	242	4	k	k	PROPN
ejpam-3573	242	5	∈	∈	PROPN
ejpam-3573	242	6	k(cλ	k(cλ	PROPN
ejpam-3573	242	7	)	)	PUNCT
ejpam-3573	242	8	and	and	CCONJ
ejpam-3573	242	9	any	any	DET
ejpam-3573	242	10	λ	λ	PROPN
ejpam-3573	242	11	∈	∈	PROPN
ejpam-3573	242	12	(	(	PUNCT
ejpam-3573	242	13	0	0	NUM
ejpam-3573	242	14	,	,	PUNCT
ejpam-3573	242	15	1	1	NUM
ejpam-3573	242	16	]	]	PUNCT
ejpam-3573	242	17	,	,	PUNCT
ejpam-3573	242	18	where	where	SCONJ
ejpam-3573	242	19	χk	χk	PROPN
ejpam-3573	242	20	is	be	AUX
ejpam-3573	242	21	the	the	DET
ejpam-3573	242	22	characteristic	characteristic	ADJ
ejpam-3573	242	23	function	function	NOUN
ejpam-3573	242	24	of	of	ADP
ejpam-3573	242	25	k.	k.	PROPN
ejpam-3573	242	26	hence	hence	ADV
ejpam-3573	242	27	,	,	PUNCT
ejpam-3573	242	28	iλ	iλ	PROPN
ejpam-3573	242	29	◦	◦	NOUN
ejpam-3573	242	30	dλ	dλ	NOUN
ejpam-3573	242	31	=	=	SYM
ejpam-3573	242	32	d̂λ	d̂λ	ADP
ejpam-3573	242	33	◦	◦	NOUN
ejpam-3573	242	34	iλ	iλ	NOUN
ejpam-3573	242	35	.	.	PUNCT
ejpam-3573	243	1	note	note	VERB
ejpam-3573	243	2	that	that	SCONJ
ejpam-3573	243	3	iλ	iλ	NOUN
ejpam-3573	243	4	is	be	AUX
ejpam-3573	243	5	continuous	continuous	ADJ
ejpam-3573	243	6	.	.	PUNCT
ejpam-3573	244	1	we	we	PRON
ejpam-3573	244	2	show	show	VERB
ejpam-3573	244	3	that	that	SCONJ
ejpam-3573	244	4	the	the	DET
ejpam-3573	244	5	mean	mean	ADJ
ejpam-3573	244	6	sensitivity	sensitivity	NOUN
ejpam-3573	244	7	of	of	ADP
ejpam-3573	244	8	dλ	dλ	NOUN
ejpam-3573	244	9	can	can	AUX
ejpam-3573	244	10	not	not	PART
ejpam-3573	244	11	be	be	AUX
ejpam-3573	244	12	inherited	inherit	VERB
ejpam-3573	244	13	by	by	ADP
ejpam-3573	244	14	d̂λ	d̂λ	PROPN
ejpam-3573	244	15	as	as	SCONJ
ejpam-3573	244	16	follows	follow	VERB
ejpam-3573	244	17	.	.	PUNCT
ejpam-3573	245	1	since	since	SCONJ
ejpam-3573	245	2	(	(	PUNCT
ejpam-3573	245	3	k(cλ	k(cλ	PROPN
ejpam-3573	245	4	)	)	PUNCT
ejpam-3573	245	5	,	,	PUNCT
ejpam-3573	245	6	dλ	dλ	NOUN
ejpam-3573	245	7	)	)	PUNCT
ejpam-3573	245	8	is	be	AUX
ejpam-3573	245	9	not	not	PART
ejpam-3573	245	10	mean	mean	ADV
ejpam-3573	245	11	sensitive	sensitive	ADJ
ejpam-3573	245	12	,	,	PUNCT
ejpam-3573	245	13	for	for	ADP
ejpam-3573	245	14	every	every	DET
ejpam-3573	245	15	δ	δ	PROPN
ejpam-3573	245	16	>	>	X
ejpam-3573	245	17	0	0	PROPN
ejpam-3573	245	18	,	,	PUNCT
ejpam-3573	245	19	there	there	PRON
ejpam-3573	245	20	exist	exist	VERB
ejpam-3573	245	21	a	a	DET
ejpam-3573	245	22	nonempty	nonempty	NOUN
ejpam-3573	245	23	set	set	VERB
ejpam-3573	245	24	a	a	DET
ejpam-3573	245	25	∈	∈	PROPN
ejpam-3573	245	26	k(cλ	k(cλ	PROPN
ejpam-3573	245	27	)	)	PUNCT
ejpam-3573	245	28	and	and	CCONJ
ejpam-3573	245	29	a	a	DET
ejpam-3573	245	30	neighborhood	neighborhood	NOUN
ejpam-3573	245	31	u	u	NOUN
ejpam-3573	245	32	of	of	ADP
ejpam-3573	245	33	a	a	DET
ejpam-3573	245	34	such	such	ADJ
ejpam-3573	245	35	that	that	PRON
ejpam-3573	245	36	for	for	ADP
ejpam-3573	245	37	all	all	DET
ejpam-3573	245	38	b	b	PROPN
ejpam-3573	245	39	∈	∈	PROPN
ejpam-3573	245	40	u	u	NOUN
ejpam-3573	245	41	,	,	PUNCT
ejpam-3573	245	42	lim	lim	PROPN
ejpam-3573	245	43	sup	sup	VERB
ejpam-3573	245	44	n→∞	n→∞	NUM
ejpam-3573	245	45	1	1	NUM
ejpam-3573	245	46	n	n	PROPN
ejpam-3573	245	47	n−1∑	n−1∑	NUM
ejpam-3573	245	48	i=0	i=0	PROPN
ejpam-3573	245	49	dh(d	dh(d	X
ejpam-3573	245	50	n	n	PRON
ejpam-3573	245	51	λ(a	λ(a	NOUN
ejpam-3573	245	52	)	)	PUNCT
ejpam-3573	245	53	,	,	PUNCT
ejpam-3573	246	1	d	d	PROPN
ejpam-3573	246	2	n	n	PRON
ejpam-3573	246	3	λ(b	λ(b	NOUN
ejpam-3573	246	4	)	)	PUNCT
ejpam-3573	246	5	)	)	PUNCT
ejpam-3573	247	1	≤	≤	NUM
ejpam-3573	247	2	δ	δ	PROPN
ejpam-3573	247	3	.	.	PUNCT
ejpam-3573	248	1	(	(	PUNCT
ejpam-3573	248	2	6	6	X
ejpam-3573	248	3	)	)	PUNCT
ejpam-3573	248	4	suppose	suppose	VERB
ejpam-3573	248	5	u	u	PRON
ejpam-3573	248	6	∈	∈	PROPN
ejpam-3573	248	7	e(a	e(a	PROPN
ejpam-3573	248	8	)	)	PUNCT
ejpam-3573	248	9	(	(	PUNCT
ejpam-3573	248	10	recall	recall	VERB
ejpam-3573	248	11	that	that	PRON
ejpam-3573	248	12	e(a	e(a	PROPN
ejpam-3573	248	13	)	)	PUNCT
ejpam-3573	248	14	=	=	SYM
ejpam-3573	248	15	{	{	PUNCT
ejpam-3573	248	16	u	u	NOUN
ejpam-3573	248	17	∈	∈	PROPN
ejpam-3573	248	18	f(cλ	f(cλ	PROPN
ejpam-3573	248	19	)	)	PUNCT
ejpam-3573	249	1	|	|	ADV
ejpam-3573	250	1	[	[	X
ejpam-3573	250	2	u]0	u]0	NOUN
ejpam-3573	250	3	⊆	⊆	NUM
ejpam-3573	250	4	a	a	PRON
ejpam-3573	250	5	}	}	PUNCT
ejpam-3573	250	6	)	)	PUNCT
ejpam-3573	250	7	,	,	PUNCT
ejpam-3573	250	8	by	by	ADP
ejpam-3573	250	9	continuity	continuity	NOUN
ejpam-3573	250	10	of	of	ADP
ejpam-3573	250	11	iλ	iλ	PROPN
ejpam-3573	250	12	and	and	CCONJ
ejpam-3573	250	13	(	(	PUNCT
ejpam-3573	250	14	3.5	3.5	NUM
ejpam-3573	250	15	)	)	PUNCT
ejpam-3573	250	16	,	,	PUNCT
ejpam-3573	250	17	we	we	PRON
ejpam-3573	250	18	have	have	VERB
ejpam-3573	250	19	lim	lim	PROPN
ejpam-3573	250	20	sup	sup	VERB
ejpam-3573	250	21	n→∞	n→∞	NUM
ejpam-3573	250	22	1	1	NUM
ejpam-3573	250	23	n	n	PROPN
ejpam-3573	250	24	n−1∑	n−1∑	NUM
ejpam-3573	250	25	i=0	i=0	PROPN
ejpam-3573	250	26	dh(d	dh(d	X
ejpam-3573	250	27	n	n	X
ejpam-3573	250	28	λ([u]0	λ([u]0	NUM
ejpam-3573	250	29	)	)	PUNCT
ejpam-3573	250	30	,	,	PUNCT
ejpam-3573	251	1	d	d	PROPN
ejpam-3573	251	2	n	n	PRON
ejpam-3573	251	3	λ(b	λ(b	NOUN
ejpam-3573	251	4	)	)	PUNCT
ejpam-3573	251	5	)	)	PUNCT
ejpam-3573	252	1	≤	≤	NUM
ejpam-3573	253	1	δ	δ	PROPN
ejpam-3573	253	2	⇒	⇒	PROPN
ejpam-3573	253	3	lim	lim	PROPN
ejpam-3573	253	4	sup	sup	VERB
ejpam-3573	253	5	n→∞	n→∞	NUM
ejpam-3573	253	6	1	1	NUM
ejpam-3573	253	7	n	n	PROPN
ejpam-3573	253	8	n−1∑	n−1∑	NUM
ejpam-3573	253	9	i=0	i=0	PROPN
ejpam-3573	253	10	dh(iλ	dh(iλ	PROPN
ejpam-3573	253	11	◦	◦	NOUN
ejpam-3573	253	12	d	d	PROPN
ejpam-3573	253	13	n	n	NOUN
ejpam-3573	253	14	λ([u]0	λ([u]0	NUM
ejpam-3573	253	15	)	)	PUNCT
ejpam-3573	253	16	,	,	PUNCT
ejpam-3573	253	17	iλ	iλ	PROPN
ejpam-3573	253	18	◦	◦	PROPN
ejpam-3573	253	19	d	d	X
ejpam-3573	253	20	n	n	PRON
ejpam-3573	253	21	λ(b	λ(b	NOUN
ejpam-3573	253	22	)	)	PUNCT
ejpam-3573	253	23	)	)	PUNCT
ejpam-3573	254	1	≤	≤	NUM
ejpam-3573	255	1	δ	δ	PROPN
ejpam-3573	255	2	⇒	⇒	PROPN
ejpam-3573	255	3	lim	lim	PROPN
ejpam-3573	255	4	sup	sup	VERB
ejpam-3573	255	5	n→∞	n→∞	NUM
ejpam-3573	255	6	1	1	NUM
ejpam-3573	255	7	n	n	PROPN
ejpam-3573	255	8	n−1∑	n−1∑	PROPN
ejpam-3573	255	9	i=0	i=0	PROPN
ejpam-3573	255	10	d∞(d̂λ	d∞(d̂λ	X
ejpam-3573	255	11	n	n	PRON
ejpam-3573	255	12	◦	◦	NOUN
ejpam-3573	255	13	iλ([u]0	iλ([u]0	PROPN
ejpam-3573	255	14	)	)	PUNCT
ejpam-3573	255	15	,	,	PUNCT
ejpam-3573	255	16	d̂λ	d̂λ	ADP
ejpam-3573	255	17	n	n	PRON
ejpam-3573	255	18	◦	◦	NOUN
ejpam-3573	255	19	iλ(b	iλ(b	NOUN
ejpam-3573	255	20	)	)	PUNCT
ejpam-3573	255	21	)	)	PUNCT
ejpam-3573	256	1	=	=	SYM
ejpam-3573	256	2	lim	lim	PROPN
ejpam-3573	256	3	sup	sup	VERB
ejpam-3573	256	4	n→∞	n→∞	NUM
ejpam-3573	256	5	1	1	NUM
ejpam-3573	256	6	n	n	PROPN
ejpam-3573	256	7	n−1∑	n−1∑	PROPN
ejpam-3573	256	8	i=0	i=0	PROPN
ejpam-3573	256	9	d∞(d̂λ	d∞(d̂λ	X
ejpam-3573	256	10	n	n	PROPN
ejpam-3573	256	11	(	(	PUNCT
ejpam-3573	256	12	u	u	NOUN
ejpam-3573	256	13	)	)	PUNCT
ejpam-3573	256	14	,	,	PUNCT
ejpam-3573	256	15	d̂λ	d̂λ	ADP
ejpam-3573	256	16	n	n	PRON
ejpam-3573	256	17	(	(	PUNCT
ejpam-3573	256	18	ν	ν	NOUN
ejpam-3573	256	19	)	)	PUNCT
ejpam-3573	256	20	)	)	PUNCT
ejpam-3573	257	1	≤	≤	NUM
ejpam-3573	257	2	δ	δ	PROPN
ejpam-3573	257	3	,	,	PUNCT
ejpam-3573	257	4	where	where	SCONJ
ejpam-3573	257	5	ν	ν	X
ejpam-3573	257	6	=	=	SYM
ejpam-3573	257	7	iλ(b	iλ(b	PROPN
ejpam-3573	257	8	)	)	PUNCT
ejpam-3573	257	9	∈	∈	PROPN
ejpam-3573	257	10	f(cλ	f(cλ	PROPN
ejpam-3573	257	11	)	)	PUNCT
ejpam-3573	257	12	.	.	PUNCT
ejpam-3573	258	1	it	it	PRON
ejpam-3573	258	2	follows	follow	VERB
ejpam-3573	258	3	that	that	SCONJ
ejpam-3573	258	4	(	(	PUNCT
ejpam-3573	258	5	f(cλ	f(cλ	NUM
ejpam-3573	258	6	)	)	PUNCT
ejpam-3573	258	7	,	,	PUNCT
ejpam-3573	258	8	d̂λ	d̂λ	X
ejpam-3573	258	9	)	)	PUNCT
ejpam-3573	258	10	is	be	AUX
ejpam-3573	258	11	not	not	PART
ejpam-3573	258	12	mean	mean	ADJ
ejpam-3573	258	13	sensitive	sensitive	ADJ
ejpam-3573	258	14	.	.	PUNCT
ejpam-3573	259	1	4	4	X
ejpam-3573	259	2	.	.	X
ejpam-3573	259	3	conclusions	conclusion	NOUN
ejpam-3573	259	4	in	in	ADP
ejpam-3573	259	5	this	this	DET
ejpam-3573	259	6	paper	paper	NOUN
ejpam-3573	259	7	,	,	PUNCT
ejpam-3573	259	8	we	we	PRON
ejpam-3573	259	9	introduce	introduce	VERB
ejpam-3573	259	10	the	the	DET
ejpam-3573	259	11	notions	notion	NOUN
ejpam-3573	259	12	of	of	ADP
ejpam-3573	259	13	strong	strong	ADJ
ejpam-3573	259	14	sensitivity	sensitivity	NOUN
ejpam-3573	259	15	and	and	CCONJ
ejpam-3573	259	16	mean	mean	VERB
ejpam-3573	259	17	sensitivity	sensitivity	NOUN
ejpam-3573	259	18	for	for	ADP
ejpam-3573	259	19	nonautonomous	nonautonomous	ADJ
ejpam-3573	259	20	systems	system	NOUN
ejpam-3573	259	21	and	and	CCONJ
ejpam-3573	259	22	investigate	investigate	VERB
ejpam-3573	259	23	these	these	DET
ejpam-3573	259	24	two	two	NUM
ejpam-3573	259	25	forms	form	NOUN
ejpam-3573	259	26	of	of	ADP
ejpam-3573	259	27	sensitivity	sensitivity	NOUN
ejpam-3573	259	28	in	in	ADP
ejpam-3573	259	29	an	an	DET
ejpam-3573	259	30	original	original	ADJ
ejpam-3573	259	31	nonautonomous	nonautonomous	ADJ
ejpam-3573	259	32	system	system	NOUN
ejpam-3573	259	33	and	and	CCONJ
ejpam-3573	259	34	its	its	PRON
ejpam-3573	259	35	connections	connection	NOUN
ejpam-3573	259	36	with	with	ADP
ejpam-3573	259	37	the	the	DET
ejpam-3573	259	38	same	same	ADJ
ejpam-3573	259	39	ones	one	NOUN
ejpam-3573	259	40	in	in	ADP
ejpam-3573	259	41	its	its	PRON
ejpam-3573	259	42	fuzzified	fuzzified	ADJ
ejpam-3573	259	43	system	system	NOUN
ejpam-3573	259	44	.	.	PUNCT
ejpam-3573	260	1	more	more	ADV
ejpam-3573	260	2	precisely	precisely	ADV
ejpam-3573	260	3	,	,	PUNCT
ejpam-3573	260	4	we	we	PRON
ejpam-3573	260	5	prove	prove	VERB
ejpam-3573	260	6	that	that	SCONJ
ejpam-3573	260	7	the	the	DET
ejpam-3573	260	8	strong	strong	ADJ
ejpam-3573	260	9	sensitivity	sensitivity	NOUN
ejpam-3573	260	10	of	of	ADP
ejpam-3573	260	11	original	original	ADJ
ejpam-3573	260	12	system	system	NOUN
ejpam-3573	260	13	and	and	CCONJ
ejpam-3573	260	14	its	its	PRON
ejpam-3573	260	15	induced	induced	ADJ
ejpam-3573	260	16	systems	system	NOUN
ejpam-3573	260	17	,	,	PUNCT
ejpam-3573	260	18	including	include	VERB
ejpam-3573	260	19	set	set	NOUN
ejpam-3573	260	20	-	-	PUNCT
ejpam-3573	260	21	valued	value	VERB
ejpam-3573	260	22	system	system	NOUN
ejpam-3573	260	23	and	and	CCONJ
ejpam-3573	260	24	fuzzified	fuzzified	ADJ
ejpam-3573	260	25	system	system	NOUN
ejpam-3573	260	26	,	,	PUNCT
ejpam-3573	260	27	are	be	AUX
ejpam-3573	260	28	equivalent	equivalent	ADJ
ejpam-3573	260	29	.	.	PUNCT
ejpam-3573	261	1	the	the	DET
ejpam-3573	261	2	mean	mean	ADJ
ejpam-3573	261	3	sensitivity	sensitivity	NOUN
ejpam-3573	261	4	of	of	ADP
ejpam-3573	261	5	induced	induced	ADJ
ejpam-3573	261	6	fuzzy	fuzzy	ADJ
ejpam-3573	261	7	system	system	NOUN
ejpam-3573	261	8	implies	imply	VERB
ejpam-3573	261	9	the	the	DET
ejpam-3573	261	10	same	same	ADJ
ejpam-3573	261	11	one	one	NUM
ejpam-3573	261	12	in	in	ADP
ejpam-3573	261	13	original	original	ADJ
ejpam-3573	261	14	nonautonomous	nonautonomous	ADJ
ejpam-3573	261	15	system	system	NOUN
ejpam-3573	261	16	,	,	PUNCT
ejpam-3573	261	17	however	however	ADV
ejpam-3573	261	18	,	,	PUNCT
ejpam-3573	261	19	the	the	DET
ejpam-3573	261	20	converse	converse	NOUN
ejpam-3573	261	21	is	be	AUX
ejpam-3573	261	22	not	not	PART
ejpam-3573	261	23	true	true	ADJ
ejpam-3573	261	24	.	.	PUNCT
ejpam-3573	262	1	references	reference	NOUN
ejpam-3573	262	2	1699	1699	NUM
ejpam-3573	262	3	acknowledgements	acknowledgement	NOUN
ejpam-3573	262	4	this	this	DET
ejpam-3573	262	5	work	work	NOUN
ejpam-3573	262	6	was	be	AUX
ejpam-3573	262	7	supported	support	VERB
ejpam-3573	262	8	by	by	ADP
ejpam-3573	262	9	the	the	DET
ejpam-3573	262	10	national	national	ADJ
ejpam-3573	262	11	natural	natural	PROPN
ejpam-3573	262	12	science	science	PROPN
ejpam-3573	262	13	foundation	foundation	PROPN
ejpam-3573	262	14	of	of	ADP
ejpam-3573	262	15	china	china	PROPN
ejpam-3573	262	16	(	(	PUNCT
ejpam-3573	262	17	no	no	INTJ
ejpam-3573	262	18	.	.	NOUN
ejpam-3573	262	19	11601051	11601051	NUM
ejpam-3573	262	20	)	)	PUNCT
ejpam-3573	262	21	and	and	CCONJ
ejpam-3573	262	22	china	china	PROPN
ejpam-3573	262	23	scholarship	scholarship	PROPN
ejpam-3573	262	24	council	council	PROPN
ejpam-3573	262	25	contract	contract	NOUN
ejpam-3573	262	26	(	(	PUNCT
ejpam-3573	262	27	no	no	INTJ
ejpam-3573	262	28	.	.	NOUN
ejpam-3573	262	29	201608505146	201608505146	NUM
ejpam-3573	262	30	)	)	PUNCT
ejpam-3573	262	31	.	.	PUNCT
ejpam-3573	263	1	references	reference	NOUN
ejpam-3573	263	2	[	[	X
ejpam-3573	263	3	1	1	NUM
ejpam-3573	263	4	]	]	X
ejpam-3573	263	5	n.c	n.c	PROPN
ejpam-3573	263	6	.	.	PROPN
ejpam-3573	263	7	bernardes	bernardes	PROPN
ejpam-3573	263	8	jr	jr	PROPN
ejpam-3573	263	9	.	.	PROPN
ejpam-3573	263	10	,	,	PUNCT
ejpam-3573	263	11	a.	a.	NOUN
ejpam-3573	263	12	bonilla	bonilla	PROPN
ejpam-3573	263	13	,	,	PUNCT
ejpam-3573	263	14	a.	a.	PROPN
ejpam-3573	263	15	peris	peris	PROPN
ejpam-3573	263	16	,	,	PUNCT
ejpam-3573	263	17	x.	x.	PROPN
ejpam-3573	263	18	wu	wu	PROPN
ejpam-3573	263	19	.	.	PUNCT
ejpam-3573	264	1	distributional	distributional	ADJ
ejpam-3573	264	2	chaos	chaos	NOUN
ejpam-3573	264	3	for	for	ADP
ejpam-3573	264	4	operators	operator	NOUN
ejpam-3573	264	5	on	on	ADP
ejpam-3573	264	6	banach	banach	NOUN
ejpam-3573	264	7	spaces	space	NOUN
ejpam-3573	264	8	.	.	PUNCT
ejpam-3573	265	1	journal	journal	NOUN
ejpam-3573	265	2	of	of	ADP
ejpam-3573	265	3	mathematical	mathematical	ADJ
ejpam-3573	265	4	analysis	analysis	NOUN
ejpam-3573	265	5	and	and	CCONJ
ejpam-3573	265	6	applications	application	NOUN
ejpam-3573	265	7	,	,	PUNCT
ejpam-3573	265	8	459:797–821	459:797–821	NUM
ejpam-3573	265	9	,	,	PUNCT
ejpam-3573	265	10	2018	2018	NUM
ejpam-3573	265	11	.	.	PUNCT
ejpam-3573	266	1	[	[	X
ejpam-3573	266	2	2	2	NUM
ejpam-3573	266	3	]	]	X
ejpam-3573	266	4	n.c	n.c	PROPN
ejpam-3573	266	5	.	.	PROPN
ejpam-3573	266	6	bernardes	bernardes	PROPN
ejpam-3573	266	7	jr	jr	PROPN
ejpam-3573	266	8	.	.	PROPN
ejpam-3573	266	9	,	,	PUNCT
ejpam-3573	266	10	r.	r.	PROPN
ejpam-3573	266	11	m.	m.	PROPN
ejpam-3573	266	12	vermersch	vermersch	PROPN
ejpam-3573	266	13	.	.	PUNCT
ejpam-3573	267	1	on	on	ADP
ejpam-3573	267	2	the	the	DET
ejpam-3573	267	3	dynamics	dynamic	NOUN
ejpam-3573	267	4	of	of	ADP
ejpam-3573	267	5	induced	induced	ADJ
ejpam-3573	267	6	maps	map	NOUN
ejpam-3573	267	7	on	on	ADP
ejpam-3573	267	8	the	the	DET
ejpam-3573	267	9	space	space	NOUN
ejpam-3573	267	10	of	of	ADP
ejpam-3573	267	11	probability	probability	NOUN
ejpam-3573	267	12	measures	measure	NOUN
ejpam-3573	267	13	.	.	PUNCT
ejpam-3573	268	1	transactions	transaction	NOUN
ejpam-3573	268	2	of	of	ADP
ejpam-3573	268	3	the	the	DET
ejpam-3573	268	4	american	american	PROPN
ejpam-3573	268	5	mathematical	mathematical	PROPN
ejpam-3573	268	6	society	society	NOUN
ejpam-3573	268	7	,	,	PUNCT
ejpam-3573	268	8	368:7703–7725	368:7703–7725	PROPN
ejpam-3573	268	9	,	,	PUNCT
ejpam-3573	268	10	2016	2016	NUM
ejpam-3573	268	11	.	.	PUNCT
ejpam-3573	269	1	[	[	X
ejpam-3573	269	2	3	3	X
ejpam-3573	269	3	]	]	PUNCT
ejpam-3573	269	4	m.	m.	NOUN
ejpam-3573	269	5	murillo	murillo	PROPN
ejpam-3573	269	6	-	-	PUNCT
ejpam-3573	269	7	arcila	arcila	PROPN
ejpam-3573	269	8	,	,	PUNCT
ejpam-3573	269	9	a.	a.	PROPN
ejpam-3573	269	10	peris	peris	PROPN
ejpam-3573	269	11	.	.	PUNCT
ejpam-3573	270	1	mixing	mix	VERB
ejpam-3573	270	2	properties	property	NOUN
ejpam-3573	270	3	for	for	ADP
ejpam-3573	270	4	nonautonomous	nonautonomous	ADJ
ejpam-3573	270	5	linear	linear	ADJ
ejpam-3573	270	6	dynamics	dynamic	NOUN
ejpam-3573	270	7	and	and	CCONJ
ejpam-3573	270	8	invariant	invariant	ADJ
ejpam-3573	270	9	sets	set	NOUN
ejpam-3573	270	10	.	.	PUNCT
ejpam-3573	271	1	applied	apply	VERB
ejpam-3573	271	2	mathematics	mathematics	NOUN
ejpam-3573	271	3	letters	letter	NOUN
ejpam-3573	271	4	,	,	PUNCT
ejpam-3573	271	5	26:215–218	26:215–218	PROPN
ejpam-3573	271	6	,	,	PUNCT
ejpam-3573	271	7	2013	2013	NUM
ejpam-3573	271	8	.	.	PUNCT
ejpam-3573	272	1	[	[	X
ejpam-3573	272	2	4	4	X
ejpam-3573	272	3	]	]	X
ejpam-3573	272	4	y.	y.	PROPN
ejpam-3573	272	5	shi	shi	PROPN
ejpam-3573	272	6	,	,	PUNCT
ejpam-3573	272	7	g.	g.	PROPN
ejpam-3573	272	8	chen	chen	PROPN
ejpam-3573	272	9	.	.	PUNCT
ejpam-3573	273	1	chaos	chaos	NOUN
ejpam-3573	273	2	of	of	ADP
ejpam-3573	273	3	time	time	NOUN
ejpam-3573	273	4	-	-	PUNCT
ejpam-3573	273	5	varying	vary	VERB
ejpam-3573	273	6	discrete	discrete	ADJ
ejpam-3573	273	7	dynamical	dynamical	ADJ
ejpam-3573	273	8	systems	system	NOUN
ejpam-3573	273	9	.	.	PUNCT
ejpam-3573	274	1	journal	journal	NOUN
ejpam-3573	274	2	of	of	ADP
ejpam-3573	274	3	difference	difference	NOUN
ejpam-3573	274	4	equations	equation	NOUN
ejpam-3573	274	5	and	and	CCONJ
ejpam-3573	274	6	applications	application	NOUN
ejpam-3573	274	7	,	,	PUNCT
ejpam-3573	274	8	15	15	NUM
ejpam-3573	274	9	:	:	SYM
ejpam-3573	274	10	429–449	429–449	NUM
ejpam-3573	274	11	,	,	PUNCT
ejpam-3573	274	12	2009	2009	NUM
ejpam-3573	274	13	.	.	PUNCT
ejpam-3573	275	1	[	[	X
ejpam-3573	275	2	5	5	X
ejpam-3573	275	3	]	]	X
ejpam-3573	275	4	jose	jose	PROPN
ejpam-3573	275	5	s.	s.	PROPN
ejpam-3573	275	6	cánovas	cánovas	PROPN
ejpam-3573	275	7	.	.	PUNCT
ejpam-3573	275	8	li	li	PROPN
ejpam-3573	275	9	-	-	PROPN
ejpam-3573	275	10	yorke	yorke	PROPN
ejpam-3573	275	11	chaos	chaos	NOUN
ejpam-3573	275	12	in	in	ADP
ejpam-3573	275	13	a	a	DET
ejpam-3573	275	14	class	class	NOUN
ejpam-3573	275	15	of	of	ADP
ejpam-3573	275	16	nonautonomous	nonautonomous	ADJ
ejpam-3573	275	17	discrete	discrete	ADJ
ejpam-3573	275	18	systems	system	NOUN
ejpam-3573	275	19	.	.	PUNCT
ejpam-3573	276	1	journal	journal	NOUN
ejpam-3573	276	2	of	of	ADP
ejpam-3573	276	3	difference	difference	NOUN
ejpam-3573	276	4	equations	equation	NOUN
ejpam-3573	276	5	and	and	CCONJ
ejpam-3573	276	6	applications	application	NOUN
ejpam-3573	276	7	,	,	PUNCT
ejpam-3573	276	8	17:479–486	17:479–486	NUM
ejpam-3573	276	9	,	,	PUNCT
ejpam-3573	276	10	2011	2011	NUM
ejpam-3573	276	11	.	.	PUNCT
ejpam-3573	277	1	[	[	X
ejpam-3573	277	2	6	6	NUM
ejpam-3573	277	3	]	]	PUNCT
ejpam-3573	277	4	j.	j.	PROPN
ejpam-3573	277	5	dvor̆áková.	dvor̆áková.	PROPN
ejpam-3573	277	6	chaos	chaos	NOUN
ejpam-3573	277	7	in	in	ADP
ejpam-3573	277	8	nonautonomous	nonautonomous	ADJ
ejpam-3573	277	9	discrete	discrete	ADJ
ejpam-3573	277	10	dynamical	dynamical	ADJ
ejpam-3573	277	11	systems	system	NOUN
ejpam-3573	277	12	.	.	PUNCT
ejpam-3573	278	1	communications	communication	NOUN
ejpam-3573	278	2	in	in	ADP
ejpam-3573	278	3	nonlinear	nonlinear	ADJ
ejpam-3573	278	4	science	science	NOUN
ejpam-3573	278	5	and	and	CCONJ
ejpam-3573	278	6	numerical	numerical	PROPN
ejpam-3573	278	7	simulation	simulation	PROPN
ejpam-3573	278	8	,	,	PUNCT
ejpam-3573	278	9	17:4649–4652	17:4649–4652	NUM
ejpam-3573	278	10	,	,	PUNCT
ejpam-3573	278	11	2012	2012	NUM
ejpam-3573	278	12	.	.	PUNCT
ejpam-3573	279	1	[	[	X
ejpam-3573	279	2	7	7	X
ejpam-3573	279	3	]	]	X
ejpam-3573	279	4	f.	f.	PROPN
ejpam-3573	279	5	balibrea	balibrea	PROPN
ejpam-3573	279	6	,	,	PUNCT
ejpam-3573	279	7	p.oprocha	p.oprocha	NUM
ejpam-3573	279	8	.	.	PUNCT
ejpam-3573	280	1	weak	weak	ADJ
ejpam-3573	280	2	mixing	mixing	NOUN
ejpam-3573	280	3	and	and	CCONJ
ejpam-3573	280	4	chaos	chaos	NOUN
ejpam-3573	280	5	in	in	ADP
ejpam-3573	280	6	nonautonomous	nonautonomous	ADJ
ejpam-3573	280	7	discrete	discrete	ADJ
ejpam-3573	280	8	system	system	NOUN
ejpam-3573	280	9	.	.	PUNCT
ejpam-3573	281	1	applied	apply	VERB
ejpam-3573	281	2	mathematics	mathematics	NOUN
ejpam-3573	281	3	letter	letter	NOUN
ejpam-3573	281	4	,	,	PUNCT
ejpam-3573	281	5	25:1135–1141	25:1135–1141	NUM
ejpam-3573	281	6	,	,	PUNCT
ejpam-3573	281	7	2012	2012	NUM
ejpam-3573	281	8	.	.	PUNCT
ejpam-3573	282	1	[	[	X
ejpam-3573	282	2	8	8	NUM
ejpam-3573	282	3	]	]	PUNCT
ejpam-3573	282	4	t	t	PROPN
ejpam-3573	282	5	k	k	PROPN
ejpam-3573	282	6	subrahmonian	subrahmonian	PROPN
ejpam-3573	282	7	moothathu	moothathu	NOUN
ejpam-3573	282	8	.	.	PUNCT
ejpam-3573	283	1	stronger	strong	ADJ
ejpam-3573	283	2	forms	form	NOUN
ejpam-3573	283	3	of	of	ADP
ejpam-3573	283	4	sensitivity	sensitivity	NOUN
ejpam-3573	283	5	for	for	ADP
ejpam-3573	283	6	dynamical	dynamical	ADJ
ejpam-3573	283	7	systems	system	NOUN
ejpam-3573	283	8	.	.	PUNCT
ejpam-3573	284	1	nonlinearity	nonlinearity	NOUN
ejpam-3573	284	2	,	,	PUNCT
ejpam-3573	284	3	20:2115–2126	20:2115–2126	NUM
ejpam-3573	284	4	,	,	PUNCT
ejpam-3573	284	5	2007	2007	NUM
ejpam-3573	284	6	.	.	PUNCT
ejpam-3573	285	1	[	[	X
ejpam-3573	285	2	9	9	NUM
ejpam-3573	285	3	]	]	X
ejpam-3573	285	4	puneet	puneet	NOUN
ejpam-3573	285	5	sharma	sharma	PROPN
ejpam-3573	285	6	,	,	PUNCT
ejpam-3573	285	7	anima	anima	PROPN
ejpam-3573	285	8	nagar	nagar	NOUN
ejpam-3573	285	9	.	.	PUNCT
ejpam-3573	286	1	inducing	induce	VERB
ejpam-3573	286	2	sensitivity	sensitivity	NOUN
ejpam-3573	286	3	on	on	ADP
ejpam-3573	286	4	hyperspaces	hyperspace	NOUN
ejpam-3573	286	5	.	.	PUNCT
ejpam-3573	286	6	topology	topology	NOUN
ejpam-3573	286	7	and	and	CCONJ
ejpam-3573	286	8	its	its	PRON
ejpam-3573	286	9	applications	application	NOUN
ejpam-3573	286	10	,	,	PUNCT
ejpam-3573	286	11	157:2052–2058	157:2052–2058	NUM
ejpam-3573	286	12	,	,	PUNCT
ejpam-3573	286	13	2010	2010	NUM
ejpam-3573	286	14	.	.	PUNCT
ejpam-3573	287	1	[	[	X
ejpam-3573	287	2	10	10	NUM
ejpam-3573	287	3	]	]	X
ejpam-3573	287	4	risong	risong	PROPN
ejpam-3573	287	5	li	li	PROPN
ejpam-3573	287	6	.	.	PUNCT
ejpam-3573	288	1	a	a	DET
ejpam-3573	288	2	note	note	NOUN
ejpam-3573	288	3	on	on	ADP
ejpam-3573	288	4	stronger	strong	ADJ
ejpam-3573	288	5	forms	form	NOUN
ejpam-3573	288	6	of	of	ADP
ejpam-3573	288	7	sensitivity	sensitivity	NOUN
ejpam-3573	288	8	for	for	ADP
ejpam-3573	288	9	dynamical	dynamical	ADJ
ejpam-3573	288	10	systems	system	NOUN
ejpam-3573	288	11	.	.	PUNCT
ejpam-3573	289	1	chaos	chaos	NOUN
ejpam-3573	289	2	,	,	PUNCT
ejpam-3573	289	3	solitons	soliton	NOUN
ejpam-3573	289	4	&	&	CCONJ
ejpam-3573	289	5	fractals	fractal	NOUN
ejpam-3573	289	6	,	,	PUNCT
ejpam-3573	289	7	45:753–758	45:753–758	NUM
ejpam-3573	289	8	,	,	PUNCT
ejpam-3573	289	9	2012	2012	NUM
ejpam-3573	289	10	.	.	PUNCT
ejpam-3573	290	1	[	[	X
ejpam-3573	290	2	11	11	NUM
ejpam-3573	290	3	]	]	PUNCT
ejpam-3573	290	4	j.	j.	PROPN
ejpam-3573	290	5	li	li	PROPN
ejpam-3573	290	6	,	,	PUNCT
ejpam-3573	290	7	s.m	s.m	PROPN
ejpam-3573	290	8	.	.	PROPN
ejpam-3573	290	9	tu	tu	PROPN
ejpam-3573	290	10	,	,	PUNCT
ejpam-3573	290	11	x.d	x.d	PROPN
ejpam-3573	290	12	.	.	PROPN
ejpam-3573	290	13	ye	ye	PROPN
ejpam-3573	290	14	.	.	NOUN
ejpam-3573	290	15	mean	mean	ADJ
ejpam-3573	290	16	equicontinuity	equicontinuity	NOUN
ejpam-3573	290	17	and	and	CCONJ
ejpam-3573	290	18	mean	mean	ADJ
ejpam-3573	290	19	sensitivity	sensitivity	NOUN
ejpam-3573	290	20	.	.	PUNCT
ejpam-3573	291	1	ergodic	ergodic	ADJ
ejpam-3573	291	2	theory	theory	NOUN
ejpam-3573	291	3	dynamical	dynamical	ADJ
ejpam-3573	291	4	systems	system	NOUN
ejpam-3573	291	5	,	,	PUNCT
ejpam-3573	291	6	35:2587–2612	35:2587–2612	NUM
ejpam-3573	291	7	,	,	PUNCT
ejpam-3573	291	8	2015	2015	NUM
ejpam-3573	291	9	.	.	PUNCT
ejpam-3573	292	1	[	[	X
ejpam-3573	292	2	12	12	NUM
ejpam-3573	292	3	]	]	X
ejpam-3573	292	4	f.	f.	PROPN
ejpam-3573	292	5	garcia	garcia	PROPN
ejpam-3573	292	6	-	-	PUNCT
ejpam-3573	292	7	ramos	ramos	PROPN
ejpam-3573	292	8	,	,	PUNCT
ejpam-3573	292	9	l.	l.	PROPN
ejpam-3573	292	10	jin	jin	PROPN
ejpam-3573	292	11	.	.	PUNCT
ejpam-3573	293	1	mean	mean	VERB
ejpam-3573	293	2	proximality	proximality	NOUN
ejpam-3573	293	3	and	and	CCONJ
ejpam-3573	293	4	mean	mean	VERB
ejpam-3573	293	5	li	li	PROPN
ejpam-3573	293	6	-	-	PROPN
ejpam-3573	293	7	yorke	yorke	PROPN
ejpam-3573	293	8	chaos	chaos	NOUN
ejpam-3573	293	9	.	.	PUNCT
ejpam-3573	294	1	proceedings	proceeding	NOUN
ejpam-3573	294	2	of	of	ADP
ejpam-3573	294	3	the	the	DET
ejpam-3573	294	4	american	american	PROPN
ejpam-3573	294	5	mathematical	mathematical	PROPN
ejpam-3573	294	6	society	society	NOUN
ejpam-3573	294	7	,	,	PUNCT
ejpam-3573	294	8	145:2959–2969	145:2959–2969	NUM
ejpam-3573	294	9	,	,	PUNCT
ejpam-3573	294	10	2017	2017	NUM
ejpam-3573	294	11	.	.	PUNCT
ejpam-3573	295	1	[	[	X
ejpam-3573	295	2	13	13	NUM
ejpam-3573	295	3	]	]	X
ejpam-3573	295	4	q.l	q.l	PROPN
ejpam-3573	295	5	.	.	PROPN
ejpam-3573	295	6	huang	huang	PROPN
ejpam-3573	295	7	,	,	PUNCT
ejpam-3573	295	8	y.m	y.m	PROPN
ejpam-3573	295	9	.	.	PROPN
ejpam-3573	295	10	shi	shi	PROPN
ejpam-3573	295	11	,	,	PUNCT
ejpam-3573	295	12	l.j	l.j	PROPN
ejpam-3573	295	13	.	.	PROPN
ejpam-3573	295	14	zhang	zhang	PROPN
ejpam-3573	295	15	.	.	PUNCT
ejpam-3573	296	1	sensitivity	sensitivity	NOUN
ejpam-3573	296	2	of	of	ADP
ejpam-3573	296	3	non	non	ADJ
ejpam-3573	296	4	-	-	ADJ
ejpam-3573	296	5	autonomous	autonomous	ADJ
ejpam-3573	296	6	discrete	discrete	ADJ
ejpam-3573	296	7	dynamical	dynamical	ADJ
ejpam-3573	296	8	systems	system	NOUN
ejpam-3573	296	9	.	.	PUNCT
ejpam-3573	297	1	applied	apply	VERB
ejpam-3573	297	2	mathematics	mathematics	NOUN
ejpam-3573	297	3	letters	letter	NOUN
ejpam-3573	297	4	,	,	PUNCT
ejpam-3573	297	5	39:31–34	39:31–34	NUM
ejpam-3573	297	6	,	,	PUNCT
ejpam-3573	297	7	2015	2015	NUM
ejpam-3573	297	8	.	.	PUNCT
ejpam-3573	298	1	references	reference	NOUN
ejpam-3573	298	2	1700	1700	NUM
ejpam-3573	298	3	[	[	X
ejpam-3573	298	4	14	14	NUM
ejpam-3573	298	5	]	]	X
ejpam-3573	298	6	h.román	h.román	ADJ
ejpam-3573	298	7	-	-	PUNCT
ejpam-3573	298	8	flores	flore	NOUN
ejpam-3573	298	9	,	,	PUNCT
ejpam-3573	298	10	y.chalco	y.chalco	NOUN
ejpam-3573	298	11	-	-	PUNCT
ejpam-3573	298	12	cano	cano	PROPN
ejpam-3573	298	13	.	.	PUNCT
ejpam-3573	299	1	robinson	robinson	PROPN
ejpam-3573	299	2	’s	’s	PART
ejpam-3573	299	3	chaos	chaos	NOUN
ejpam-3573	299	4	in	in	ADP
ejpam-3573	299	5	set	set	NOUN
ejpam-3573	299	6	-	-	PUNCT
ejpam-3573	299	7	valued	value	VERB
ejpam-3573	299	8	discrete	discrete	ADJ
ejpam-3573	299	9	sysyems	sysyem	NOUN
ejpam-3573	299	10	.	.	PUNCT
ejpam-3573	300	1	chaos	chaos	NOUN
ejpam-3573	300	2	solitons	soliton	NOUN
ejpam-3573	300	3	&	&	CCONJ
ejpam-3573	300	4	fractals	fractal	NOUN
ejpam-3573	300	5	,	,	PUNCT
ejpam-3573	300	6	25:33–42	25:33–42	NUM
ejpam-3573	300	7	,	,	PUNCT
ejpam-3573	300	8	2005	2005	NUM
ejpam-3573	300	9	.	.	PUNCT
ejpam-3573	301	1	[	[	X
ejpam-3573	301	2	15	15	NUM
ejpam-3573	301	3	]	]	X
ejpam-3573	301	4	h.román	h.román	ADJ
ejpam-3573	301	5	-	-	PUNCT
ejpam-3573	301	6	flores	flore	NOUN
ejpam-3573	301	7	,	,	PUNCT
ejpam-3573	301	8	y.chalco	y.chalco	NOUN
ejpam-3573	301	9	-	-	PUNCT
ejpam-3573	301	10	cano	cano	PROPN
ejpam-3573	301	11	.	.	PUNCT
ejpam-3573	302	1	some	some	DET
ejpam-3573	302	2	chaotic	chaotic	ADJ
ejpam-3573	302	3	properties	property	NOUN
ejpam-3573	302	4	of	of	ADP
ejpam-3573	302	5	zadeh	zadeh	PROPN
ejpam-3573	302	6	’s	’s	PART
ejpam-3573	302	7	extension	extension	NOUN
ejpam-3573	302	8	.	.	PUNCT
ejpam-3573	303	1	chaos	chaos	NOUN
ejpam-3573	303	2	solitons	soliton	NOUN
ejpam-3573	303	3	&	&	CCONJ
ejpam-3573	303	4	fractals	fractal	NOUN
ejpam-3573	303	5	,	,	PUNCT
ejpam-3573	303	6	35:452–459	35:452–459	NUM
ejpam-3573	303	7	,	,	PUNCT
ejpam-3573	303	8	2008	2008	NUM
ejpam-3573	303	9	.	.	PUNCT
ejpam-3573	304	1	[	[	X
ejpam-3573	304	2	16	16	NUM
ejpam-3573	304	3	]	]	X
ejpam-3573	304	4	h.román	h.román	ADJ
ejpam-3573	304	5	-	-	PUNCT
ejpam-3573	304	6	flores	flore	NOUN
ejpam-3573	304	7	,	,	PUNCT
ejpam-3573	304	8	laécio	laécio	NUM
ejpam-3573	304	9	c.	c.	PROPN
ejpam-3573	304	10	barros	barros	PROPN
ejpam-3573	304	11	,	,	PUNCT
ejpam-3573	304	12	rodney	rodney	PROPN
ejpam-3573	304	13	c.	c.	PROPN
ejpam-3573	304	14	bassanezi	bassanezi	PROPN
ejpam-3573	304	15	.	.	PUNCT
ejpam-3573	305	1	a	a	DET
ejpam-3573	305	2	note	note	NOUN
ejpam-3573	305	3	on	on	ADP
ejpam-3573	305	4	zadeh	zadeh	PROPN
ejpam-3573	305	5	’s	’s	PART
ejpam-3573	305	6	extensions	extension	NOUN
ejpam-3573	305	7	.	.	PUNCT
ejpam-3573	306	1	fuzzy	fuzzy	ADJ
ejpam-3573	306	2	sets	set	NOUN
ejpam-3573	306	3	and	and	CCONJ
ejpam-3573	306	4	systems	system	NOUN
ejpam-3573	306	5	,	,	PUNCT
ejpam-3573	306	6	117:327–331	117:327–331	NUM
ejpam-3573	306	7	,	,	PUNCT
ejpam-3573	306	8	2001	2001	NUM
ejpam-3573	306	9	.	.	PUNCT
ejpam-3573	307	1	[	[	X
ejpam-3573	307	2	17	17	NUM
ejpam-3573	307	3	]	]	X
ejpam-3573	307	4	p.	p.	NOUN
ejpam-3573	307	5	diamond	diamond	NOUN
ejpam-3573	307	6	,	,	PUNCT
ejpam-3573	307	7	a.	a.	PROPN
ejpam-3573	307	8	pokrovdkii	pokrovdkii	PROPN
ejpam-3573	307	9	.	.	PUNCT
ejpam-3573	308	1	chaos	chaos	NOUN
ejpam-3573	308	2	,	,	PUNCT
ejpam-3573	308	3	entropy	entropy	NOUN
ejpam-3573	308	4	and	and	CCONJ
ejpam-3573	308	5	a	a	DET
ejpam-3573	308	6	generalized	generalized	ADJ
ejpam-3573	308	7	extension	extension	NOUN
ejpam-3573	308	8	principle	principle	NOUN
ejpam-3573	308	9	.	.	PUNCT
ejpam-3573	309	1	fuzzy	fuzzy	ADJ
ejpam-3573	309	2	sets	set	NOUN
ejpam-3573	309	3	and	and	CCONJ
ejpam-3573	309	4	systems	system	NOUN
ejpam-3573	309	5	,	,	PUNCT
ejpam-3573	309	6	61:277–283	61:277–283	PROPN
ejpam-3573	309	7	,	,	PUNCT
ejpam-3573	309	8	1994	1994	NUM
ejpam-3573	309	9	.	.	PUNCT
ejpam-3573	310	1	[	[	X
ejpam-3573	310	2	18	18	NUM
ejpam-3573	310	3	]	]	PUNCT
ejpam-3573	310	4	jir̆́ı	jir̆́ı	PROPN
ejpam-3573	310	5	kupka	kupka	PROPN
ejpam-3573	310	6	.	.	PUNCT
ejpam-3573	311	1	on	on	ADP
ejpam-3573	311	2	devaney	devaney	PROPN
ejpam-3573	311	3	chaotic	chaotic	ADJ
ejpam-3573	311	4	induced	induce	VERB
ejpam-3573	311	5	fuzzy	fuzzy	ADJ
ejpam-3573	311	6	and	and	CCONJ
ejpam-3573	311	7	set	set	NOUN
ejpam-3573	311	8	-	-	PUNCT
ejpam-3573	311	9	valued	value	VERB
ejpam-3573	311	10	dynamical	dynamical	ADJ
ejpam-3573	311	11	systems	system	NOUN
ejpam-3573	311	12	.	.	PUNCT
ejpam-3573	312	1	fuzzy	fuzzy	ADJ
ejpam-3573	312	2	sets	set	NOUN
ejpam-3573	312	3	and	and	CCONJ
ejpam-3573	312	4	systems	system	NOUN
ejpam-3573	312	5	,	,	PUNCT
ejpam-3573	312	6	117:34–44	117:34–44	NUM
ejpam-3573	312	7	,	,	PUNCT
ejpam-3573	312	8	2011	2011	NUM
ejpam-3573	312	9	.	.	PUNCT
ejpam-3573	313	1	[	[	X
ejpam-3573	313	2	19	19	NUM
ejpam-3573	313	3	]	]	PUNCT
ejpam-3573	313	4	jir̆́ı	jir̆́ı	PROPN
ejpam-3573	313	5	kupka	kupka	PROPN
ejpam-3573	313	6	.	.	PUNCT
ejpam-3573	314	1	on	on	ADP
ejpam-3573	314	2	fuzzifications	fuzzification	NOUN
ejpam-3573	314	3	of	of	ADP
ejpam-3573	314	4	discrete	discrete	ADJ
ejpam-3573	314	5	dynamical	dynamical	ADJ
ejpam-3573	314	6	systems	system	NOUN
ejpam-3573	314	7	.	.	PUNCT
ejpam-3573	315	1	information	information	NOUN
ejpam-3573	315	2	sciences	sciences	PROPN
ejpam-3573	315	3	,	,	PUNCT
ejpam-3573	315	4	181:2858–2872	181:2858–2872	NUM
ejpam-3573	315	5	,	,	PUNCT
ejpam-3573	315	6	2011	2011	NUM
ejpam-3573	315	7	.	.	PUNCT
ejpam-3573	316	1	[	[	X
ejpam-3573	316	2	20	20	NUM
ejpam-3573	316	3	]	]	X
ejpam-3573	316	4	jose	jose	PROPN
ejpam-3573	316	5	s.cánovasa	s.cánovasa	PROPN
ejpam-3573	316	6	,	,	PUNCT
ejpam-3573	316	7	jir̆́ı	jir̆́ı	PROPN
ejpam-3573	316	8	kupka	kupka	PROPN
ejpam-3573	316	9	.	.	PUNCT
ejpam-3573	317	1	on	on	ADP
ejpam-3573	317	2	fuzzy	fuzzy	ADJ
ejpam-3573	317	3	entropy	entropy	NOUN
ejpam-3573	317	4	and	and	CCONJ
ejpam-3573	317	5	topological	topological	ADJ
ejpam-3573	317	6	entropy	entropy	NOUN
ejpam-3573	317	7	of	of	ADP
ejpam-3573	317	8	fuzzy	fuzzy	ADJ
ejpam-3573	317	9	extensions	extension	NOUN
ejpam-3573	317	10	of	of	ADP
ejpam-3573	317	11	dynamical	dynamical	ADJ
ejpam-3573	317	12	systems	system	NOUN
ejpam-3573	317	13	.	.	PUNCT
ejpam-3573	318	1	fuzzy	fuzzy	ADJ
ejpam-3573	318	2	sets	set	NOUN
ejpam-3573	318	3	and	and	CCONJ
ejpam-3573	318	4	systems	system	NOUN
ejpam-3573	318	5	,	,	PUNCT
ejpam-3573	318	6	309:115–130	309:115–130	NUM
ejpam-3573	318	7	,	,	PUNCT
ejpam-3573	318	8	2017	2017	NUM
ejpam-3573	318	9	.	.	PUNCT
ejpam-3573	319	1	[	[	X
ejpam-3573	319	2	21	21	NUM
ejpam-3573	319	3	]	]	X
ejpam-3573	319	4	x.x	x.x	PROPN
ejpam-3573	319	5	.	.	PROPN
ejpam-3573	319	6	wu	wu	PROPN
ejpam-3573	319	7	,	,	PUNCT
ejpam-3573	319	8	g.r	g.r	PROPN
ejpam-3573	319	9	.	.	PUNCT
ejpam-3573	319	10	chen	chen	PROPN
ejpam-3573	319	11	.	.	PUNCT
ejpam-3573	320	1	sensitivity	sensitivity	NOUN
ejpam-3573	320	2	and	and	CCONJ
ejpam-3573	320	3	transitivity	transitivity	NOUN
ejpam-3573	320	4	of	of	ADP
ejpam-3573	320	5	fuzzified	fuzzified	ADJ
ejpam-3573	320	6	dynamical	dynamical	ADJ
ejpam-3573	320	7	systems	system	NOUN
ejpam-3573	320	8	.	.	PUNCT
ejpam-3573	321	1	information	information	NOUN
ejpam-3573	321	2	sciences	sciences	PROPN
ejpam-3573	321	3	,	,	PUNCT
ejpam-3573	321	4	396:14–23	396:14–23	NUM
ejpam-3573	321	5	,	,	PUNCT
ejpam-3573	321	6	2017	2017	NUM
ejpam-3573	321	7	.	.	PUNCT
ejpam-3573	322	1	[	[	X
ejpam-3573	322	2	22	22	NUM
ejpam-3573	322	3	]	]	X
ejpam-3573	322	4	h.	h.	PROPN
ejpam-3573	322	5	liu	liu	PROPN
ejpam-3573	322	6	,	,	PUNCT
ejpam-3573	322	7	e.h	e.h	PROPN
ejpam-3573	322	8	.	.	PROPN
ejpam-3573	322	9	shi	shi	PROPN
ejpam-3573	322	10	,	,	PUNCT
ejpam-3573	322	11	g.f	g.f	PROPN
ejpam-3573	322	12	.	.	PROPN
ejpam-3573	322	13	liao	liao	PROPN
ejpam-3573	322	14	.	.	PROPN
ejpam-3573	322	15	sensitivity	sensitivity	NOUN
ejpam-3573	322	16	of	of	ADP
ejpam-3573	322	17	set	set	NOUN
ejpam-3573	322	18	-	-	PUNCT
ejpam-3573	322	19	valued	value	VERB
ejpam-3573	322	20	discrete	discrete	ADJ
ejpam-3573	322	21	systems	system	NOUN
ejpam-3573	322	22	.	.	PUNCT
ejpam-3573	323	1	nonlinear	nonlinear	ADJ
ejpam-3573	323	2	analysis	analysis	NOUN
ejpam-3573	323	3	:	:	PUNCT
ejpam-3573	323	4	theory	theory	NOUN
ejpam-3573	323	5	,	,	PUNCT
ejpam-3573	323	6	methods	method	NOUN
ejpam-3573	323	7	and	and	CCONJ
ejpam-3573	323	8	applications	application	NOUN
ejpam-3573	323	9	,	,	PUNCT
ejpam-3573	323	10	71:6122–6125	71:6122–6125	NUM
ejpam-3573	323	11	,	,	PUNCT
ejpam-3573	323	12	2009	2009	NUM
ejpam-3573	323	13	.	.	PUNCT