id	sid	tid	token	lemma	pos
ejpam-3872	1	1	european	european	PROPN
ejpam-3872	1	2	journal	journal	PROPN
ejpam-3872	1	3	of	of	ADP
ejpam-3872	1	4	pure	pure	ADJ
ejpam-3872	1	5	and	and	CCONJ
ejpam-3872	1	6	applied	apply	VERB
ejpam-3872	1	7	mathematics	mathematic	NOUN
ejpam-3872	1	8	vol	vol	NOUN
ejpam-3872	1	9	.	.	PUNCT
ejpam-3872	2	1	14	14	NUM
ejpam-3872	2	2	,	,	PUNCT
ejpam-3872	2	3	no	no	INTJ
ejpam-3872	2	4	.	.	NOUN
ejpam-3872	2	5	1	1	NUM
ejpam-3872	2	6	,	,	PUNCT
ejpam-3872	2	7	2021	2021	NUM
ejpam-3872	2	8	,	,	PUNCT
ejpam-3872	2	9	19	19	NUM
ejpam-3872	2	10	-	-	SYM
ejpam-3872	2	11	42	42	NUM
ejpam-3872	2	12	issn	issn	PROPN
ejpam-3872	2	13	1307	1307	NUM
ejpam-3872	2	14	-	-	SYM
ejpam-3872	2	15	5543	5543	NUM
ejpam-3872	2	16	–	–	PUNCT
ejpam-3872	2	17	ejpam.com	ejpam.com	X
ejpam-3872	2	18	published	publish	VERB
ejpam-3872	2	19	by	by	ADP
ejpam-3872	2	20	new	new	PROPN
ejpam-3872	2	21	york	york	PROPN
ejpam-3872	2	22	business	business	PROPN
ejpam-3872	2	23	global	global	ADJ
ejpam-3872	2	24	asymptotic	asymptotic	ADJ
ejpam-3872	2	25	laws	law	NOUN
ejpam-3872	2	26	for	for	ADP
ejpam-3872	2	27	upper	upper	ADJ
ejpam-3872	2	28	and	and	CCONJ
ejpam-3872	2	29	strong	strong	ADJ
ejpam-3872	2	30	record	record	NOUN
ejpam-3872	2	31	values	value	NOUN
ejpam-3872	2	32	in	in	ADP
ejpam-3872	2	33	the	the	DET
ejpam-3872	2	34	extreme	extreme	ADJ
ejpam-3872	2	35	domain	domain	NOUN
ejpam-3872	2	36	of	of	ADP
ejpam-3872	2	37	attraction	attraction	NOUN
ejpam-3872	2	38	and	and	CCONJ
ejpam-3872	2	39	beyond	beyond	ADP
ejpam-3872	2	40	gane	gane	NOUN
ejpam-3872	2	41	samb	samb	PROPN
ejpam-3872	2	42	lo1,2,3,∗	lo1,2,3,∗	NOUN
ejpam-3872	2	43	,	,	PUNCT
ejpam-3872	2	44	mohammad	mohammad	PROPN
ejpam-3872	2	45	ahsanullah4	ahsanullah4	PROPN
ejpam-3872	2	46	,	,	PUNCT
ejpam-3872	2	47	moumouni	moumouni	PROPN
ejpam-3872	2	48	diallo5	diallo5	NOUN
ejpam-3872	2	49	,	,	PUNCT
ejpam-3872	2	50	modou	modou	NOUN
ejpam-3872	2	51	ngom1	ngom1	PROPN
ejpam-3872	2	52	1	1	NUM
ejpam-3872	2	53	lerstad	lerstad	PROPN
ejpam-3872	2	54	,	,	PUNCT
ejpam-3872	2	55	gaston	gaston	PROPN
ejpam-3872	2	56	berger	berger	PROPN
ejpam-3872	2	57	university	university	PROPN
ejpam-3872	2	58	,	,	PUNCT
ejpam-3872	2	59	saint	saint	NOUN
ejpam-3872	2	60	-	-	PUNCT
ejpam-3872	2	61	louis	louis	NOUN
ejpam-3872	2	62	,	,	PUNCT
ejpam-3872	2	63	sénégal	sénégal	ADJ
ejpam-3872	2	64	2	2	NUM
ejpam-3872	2	65	department	department	NOUN
ejpam-3872	2	66	of	of	ADP
ejpam-3872	2	67	pure	pure	ADJ
ejpam-3872	2	68	and	and	CCONJ
ejpam-3872	2	69	applied	applied	ADJ
ejpam-3872	2	70	mathematics	mathematic	NOUN
ejpam-3872	2	71	,	,	PUNCT
ejpam-3872	2	72	african	african	ADJ
ejpam-3872	2	73	university	university	PROPN
ejpam-3872	2	74	of	of	ADP
ejpam-3872	2	75	science	science	NOUN
ejpam-3872	2	76	and	and	CCONJ
ejpam-3872	2	77	technology	technology	NOUN
ejpam-3872	2	78	,	,	PUNCT
ejpam-3872	2	79	abuja	abuja	PROPN
ejpam-3872	2	80	,	,	PUNCT
ejpam-3872	2	81	nigeria	nigeria	PROPN
ejpam-3872	2	82	3	3	NUM
ejpam-3872	2	83	lsta	lsta	ADV
ejpam-3872	2	84	,	,	PUNCT
ejpam-3872	2	85	pierre	pierre	PROPN
ejpam-3872	2	86	and	and	CCONJ
ejpam-3872	2	87	marie	marie	PROPN
ejpam-3872	2	88	curie	curie	PROPN
ejpam-3872	2	89	university	university	PROPN
ejpam-3872	2	90	,	,	PUNCT
ejpam-3872	2	91	paris	paris	PROPN
ejpam-3872	2	92	vi	vi	PROPN
ejpam-3872	2	93	,	,	PUNCT
ejpam-3872	2	94	france	france	PROPN
ejpam-3872	2	95	4	4	NUM
ejpam-3872	2	96	department	department	NOUN
ejpam-3872	2	97	of	of	ADP
ejpam-3872	2	98	management	management	NOUN
ejpam-3872	2	99	sciences	sciences	PROPN
ejpam-3872	2	100	.	.	PUNCT
ejpam-3872	3	1	rider	rider	NOUN
ejpam-3872	3	2	university	university	PROPN
ejpam-3872	3	3	.	.	PUNCT
ejpam-3872	4	1	lawrenceville	lawrenceville	PROPN
ejpam-3872	4	2	,	,	PUNCT
ejpam-3872	4	3	new	new	PROPN
ejpam-3872	4	4	jersey	jersey	PROPN
ejpam-3872	4	5	,	,	PUNCT
ejpam-3872	4	6	usa	usa	PROPN
ejpam-3872	4	7	5	5	NUM
ejpam-3872	4	8	université	université	NOUN
ejpam-3872	4	9	des	des	PROPN
ejpam-3872	4	10	sciences	sciences	PROPN
ejpam-3872	4	11	sociale	sociale	PROPN
ejpam-3872	4	12	et	et	PROPN
ejpam-3872	4	13	de	de	X
ejpam-3872	4	14	gestion	gestion	PROPN
ejpam-3872	4	15	de	de	X
ejpam-3872	4	16	bamako	bamako	PROPN
ejpam-3872	4	17	(	(	PUNCT
ejpam-3872	4	18	ussgb	ussgb	PROPN
ejpam-3872	4	19	)	)	PUNCT
ejpam-3872	4	20	,	,	PUNCT
ejpam-3872	4	21	faculté	faculté	NOUN
ejpam-3872	4	22	des	des	PROPN
ejpam-3872	4	23	sciences	sciences	PROPN
ejpam-3872	4	24	économiques	économiques	PROPN
ejpam-3872	4	25	et	et	X
ejpam-3872	4	26	de	de	X
ejpam-3872	4	27	gestion	gestion	PROPN
ejpam-3872	4	28	(	(	PUNCT
ejpam-3872	4	29	fseg	fseg	NOUN
ejpam-3872	4	30	)	)	PUNCT
ejpam-3872	4	31	abstract	abstract	NOUN
ejpam-3872	4	32	.	.	PUNCT
ejpam-3872	5	1	asymptotic	asymptotic	ADJ
ejpam-3872	5	2	laws	law	NOUN
ejpam-3872	5	3	of	of	ADP
ejpam-3872	5	4	record	record	NOUN
ejpam-3872	5	5	values	value	NOUN
ejpam-3872	5	6	have	have	AUX
ejpam-3872	5	7	usually	usually	ADV
ejpam-3872	5	8	been	be	AUX
ejpam-3872	5	9	investigated	investigate	VERB
ejpam-3872	5	10	as	as	ADP
ejpam-3872	5	11	limits	limit	NOUN
ejpam-3872	5	12	in	in	ADP
ejpam-3872	5	13	type	type	NOUN
ejpam-3872	5	14	.	.	PUNCT
ejpam-3872	6	1	in	in	ADP
ejpam-3872	6	2	this	this	DET
ejpam-3872	6	3	paper	paper	NOUN
ejpam-3872	6	4	,	,	PUNCT
ejpam-3872	6	5	we	we	PRON
ejpam-3872	6	6	use	use	VERB
ejpam-3872	6	7	functional	functional	ADJ
ejpam-3872	6	8	representations	representation	NOUN
ejpam-3872	6	9	of	of	ADP
ejpam-3872	6	10	the	the	DET
ejpam-3872	6	11	tail	tail	NOUN
ejpam-3872	6	12	of	of	ADP
ejpam-3872	6	13	cumulative	cumulative	ADJ
ejpam-3872	6	14	distribution	distribution	NOUN
ejpam-3872	6	15	functions	function	NOUN
ejpam-3872	6	16	in	in	ADP
ejpam-3872	6	17	the	the	DET
ejpam-3872	6	18	extreme	extreme	ADJ
ejpam-3872	6	19	value	value	NOUN
ejpam-3872	6	20	domain	domain	NOUN
ejpam-3872	6	21	of	of	ADP
ejpam-3872	6	22	attraction	attraction	NOUN
ejpam-3872	6	23	to	to	PART
ejpam-3872	6	24	directly	directly	ADV
ejpam-3872	6	25	establish	establish	VERB
ejpam-3872	6	26	asymptotic	asymptotic	ADJ
ejpam-3872	6	27	laws	law	NOUN
ejpam-3872	6	28	of	of	ADP
ejpam-3872	6	29	record	record	NOUN
ejpam-3872	6	30	values	value	NOUN
ejpam-3872	6	31	,	,	PUNCT
ejpam-3872	6	32	not	not	PART
ejpam-3872	6	33	necessarily	necessarily	ADV
ejpam-3872	6	34	as	as	ADP
ejpam-3872	6	35	limits	limit	NOUN
ejpam-3872	6	36	in	in	ADP
ejpam-3872	6	37	type	type	NOUN
ejpam-3872	6	38	and	and	CCONJ
ejpam-3872	6	39	their	their	PRON
ejpam-3872	6	40	rates	rate	NOUN
ejpam-3872	6	41	of	of	ADP
ejpam-3872	6	42	convergences	convergence	NOUN
ejpam-3872	6	43	.	.	PUNCT
ejpam-3872	7	1	results	result	NOUN
ejpam-3872	7	2	beyond	beyond	ADP
ejpam-3872	7	3	the	the	DET
ejpam-3872	7	4	extreme	extreme	ADJ
ejpam-3872	7	5	value	value	NOUN
ejpam-3872	7	6	domain	domain	NOUN
ejpam-3872	7	7	are	be	AUX
ejpam-3872	7	8	provided	provide	VERB
ejpam-3872	7	9	.	.	PUNCT
ejpam-3872	8	1	explicit	explicit	ADJ
ejpam-3872	8	2	asymptotic	asymptotic	ADJ
ejpam-3872	8	3	laws	law	NOUN
ejpam-3872	8	4	concerning	concern	VERB
ejpam-3872	8	5	very	very	ADV
ejpam-3872	8	6	usual	usual	ADJ
ejpam-3872	8	7	laws	law	NOUN
ejpam-3872	8	8	and	and	CCONJ
ejpam-3872	8	9	related	related	ADJ
ejpam-3872	8	10	rates	rate	NOUN
ejpam-3872	8	11	of	of	ADP
ejpam-3872	8	12	convergence	convergence	NOUN
ejpam-3872	8	13	are	be	AUX
ejpam-3872	8	14	listed	list	VERB
ejpam-3872	8	15	as	as	ADV
ejpam-3872	8	16	well	well	ADV
ejpam-3872	8	17	.	.	PUNCT
ejpam-3872	9	1	some	some	PRON
ejpam-3872	9	2	of	of	ADP
ejpam-3872	9	3	these	these	DET
ejpam-3872	9	4	laws	law	NOUN
ejpam-3872	9	5	are	be	AUX
ejpam-3872	9	6	expected	expect	VERB
ejpam-3872	9	7	to	to	PART
ejpam-3872	9	8	be	be	AUX
ejpam-3872	9	9	used	use	VERB
ejpam-3872	9	10	in	in	ADP
ejpam-3872	9	11	fitting	fitting	ADJ
ejpam-3872	9	12	distribution	distribution	NOUN
ejpam-3872	9	13	.	.	PUNCT
ejpam-3872	10	1	2020	2020	NUM
ejpam-3872	10	2	mathematics	mathematic	NOUN
ejpam-3872	10	3	subject	subject	NOUN
ejpam-3872	10	4	classifications	classification	NOUN
ejpam-3872	10	5	:	:	PUNCT
ejpam-3872	10	6	62g30	62g30	NUM
ejpam-3872	10	7	,	,	PUNCT
ejpam-3872	10	8	60g70	60g70	NOUN
ejpam-3872	10	9	,	,	PUNCT
ejpam-3872	10	10	60fxx	60fxx	ADJ
ejpam-3872	10	11	key	key	ADJ
ejpam-3872	10	12	words	word	NOUN
ejpam-3872	10	13	and	and	CCONJ
ejpam-3872	10	14	phrases	phrase	NOUN
ejpam-3872	10	15	:	:	PUNCT
ejpam-3872	10	16	record	record	NOUN
ejpam-3872	10	17	values	value	NOUN
ejpam-3872	10	18	and	and	CCONJ
ejpam-3872	10	19	record	record	NOUN
ejpam-3872	10	20	times	time	NOUN
ejpam-3872	10	21	,	,	PUNCT
ejpam-3872	10	22	normal	normal	ADJ
ejpam-3872	10	23	asymptotic	asymptotic	ADJ
ejpam-3872	10	24	theory	theory	NOUN
ejpam-3872	10	25	,	,	PUNCT
ejpam-3872	10	26	extreme	extreme	ADJ
ejpam-3872	10	27	value	value	NOUN
ejpam-3872	10	28	theory	theory	NOUN
ejpam-3872	10	29	,	,	PUNCT
ejpam-3872	10	30	generalized	generalize	VERB
ejpam-3872	10	31	extreme	extreme	ADJ
ejpam-3872	10	32	values	value	NOUN
ejpam-3872	10	33	distributions	distribution	VERB
ejpam-3872	10	34	1	1	NUM
ejpam-3872	10	35	.	.	PUNCT
ejpam-3872	11	1	introduction	introduction	NOUN
ejpam-3872	11	2	let	let	VERB
ejpam-3872	11	3	x	x	PRON
ejpam-3872	11	4	,	,	PUNCT
ejpam-3872	11	5	x1	x1	PROPN
ejpam-3872	11	6	,	,	PUNCT
ejpam-3872	11	7	x2	x2	PROPN
ejpam-3872	11	8	,	,	PUNCT
ejpam-3872	11	9	·	·	PUNCT
ejpam-3872	11	10	·	·	PUNCT
ejpam-3872	11	11	·	·	PUNCT
ejpam-3872	11	12	be	be	AUX
ejpam-3872	11	13	a	a	DET
ejpam-3872	11	14	sequence	sequence	NOUN
ejpam-3872	11	15	of	of	ADP
ejpam-3872	11	16	independent	independent	ADJ
ejpam-3872	11	17	real	real	ADV
ejpam-3872	11	18	-	-	PUNCT
ejpam-3872	11	19	valued	value	VERB
ejpam-3872	11	20	randoms	random	NOUN
ejpam-3872	11	21	,	,	PUNCT
ejpam-3872	11	22	defined	define	VERB
ejpam-3872	11	23	on	on	ADP
ejpam-3872	11	24	the	the	DET
ejpam-3872	11	25	same	same	ADJ
ejpam-3872	11	26	probability	probability	NOUN
ejpam-3872	11	27	space	space	NOUN
ejpam-3872	11	28	(	(	PUNCT
ejpam-3872	11	29	ω	ω	NOUN
ejpam-3872	11	30	,	,	PUNCT
ejpam-3872	11	31	a	a	DET
ejpam-3872	11	32	,	,	PUNCT
ejpam-3872	11	33	p	p	NOUN
ejpam-3872	11	34	)	)	PUNCT
ejpam-3872	11	35	,	,	PUNCT
ejpam-3872	11	36	with	with	ADP
ejpam-3872	11	37	common	common	ADJ
ejpam-3872	11	38	cumulative	cumulative	ADJ
ejpam-3872	11	39	distribution	distribution	NOUN
ejpam-3872	11	40	function	function	NOUN
ejpam-3872	11	41	f	f	PROPN
ejpam-3872	11	42	,	,	PUNCT
ejpam-3872	11	43	which	which	PRON
ejpam-3872	11	44	has	have	VERB
ejpam-3872	11	45	the	the	DET
ejpam-3872	11	46	lower	low	ADJ
ejpam-3872	11	47	and	and	CCONJ
ejpam-3872	11	48	upper	upper	ADJ
ejpam-3872	11	49	endpoints	endpoint	NOUN
ejpam-3872	11	50	,	,	PUNCT
ejpam-3872	11	51	the	the	DET
ejpam-3872	11	52	first	first	ADJ
ejpam-3872	11	53	asymptotic	asymptotic	ADJ
ejpam-3872	11	54	moment	moment	NOUN
ejpam-3872	11	55	function	function	NOUN
ejpam-3872	11	56	and	and	CCONJ
ejpam-3872	11	57	the	the	DET
ejpam-3872	11	58	generalized	generalized	ADJ
ejpam-3872	11	59	inverse	inverse	NOUN
ejpam-3872	11	60	function	function	NOUN
ejpam-3872	11	61	defined	define	VERB
ejpam-3872	11	62	by	by	ADP
ejpam-3872	11	63	lep(f	lep(f	PROPN
ejpam-3872	11	64	)	)	PUNCT
ejpam-3872	12	1	=	=	PUNCT
ejpam-3872	12	2	inf{x	inf{x	NOUN
ejpam-3872	12	3	∈	∈	PROPN
ejpam-3872	12	4	r	r	NOUN
ejpam-3872	12	5	,	,	PUNCT
ejpam-3872	12	6	f	f	PROPN
ejpam-3872	12	7	(	(	PUNCT
ejpam-3872	12	8	x	x	X
ejpam-3872	12	9	)	)	PUNCT
ejpam-3872	12	10	>	>	X
ejpam-3872	12	11	0	0	NUM
ejpam-3872	12	12	}	}	PUNCT
ejpam-3872	12	13	,	,	PUNCT
ejpam-3872	12	14	uep(f	uep(f	PROPN
ejpam-3872	12	15	)	)	PUNCT
ejpam-3872	13	1	=	=	PUNCT
ejpam-3872	13	2	sup{x	sup{x	X
ejpam-3872	13	3	∈	∈	PROPN
ejpam-3872	13	4	r	r	NOUN
ejpam-3872	13	5	,	,	PUNCT
ejpam-3872	13	6	f	f	PROPN
ejpam-3872	13	7	(	(	PUNCT
ejpam-3872	13	8	x	x	X
ejpam-3872	13	9	)	)	PUNCT
ejpam-3872	13	10	<	<	X
ejpam-3872	13	11	1	1	NUM
ejpam-3872	13	12	}	}	PUNCT
ejpam-3872	13	13	,	,	PUNCT
ejpam-3872	13	14	r(x	r(x	PROPN
ejpam-3872	13	15	,	,	PUNCT
ejpam-3872	13	16	f	f	X
ejpam-3872	13	17	)	)	PUNCT
ejpam-3872	13	18	=	=	SYM
ejpam-3872	14	1	1	1	NUM
ejpam-3872	14	2	1−	1−	NUM
ejpam-3872	14	3	f	f	X
ejpam-3872	14	4	(	(	PUNCT
ejpam-3872	14	5	y	y	PROPN
ejpam-3872	14	6	)	)	PUNCT
ejpam-3872	14	7	∫	∫	PROPN
ejpam-3872	14	8	uep(f	uep(f	PROPN
ejpam-3872	14	9	)	)	PUNCT
ejpam-3872	14	10	x	x	X
ejpam-3872	14	11	(	(	PUNCT
ejpam-3872	14	12	1−	1−	NUM
ejpam-3872	14	13	f	f	X
ejpam-3872	14	14	(	(	PUNCT
ejpam-3872	14	15	y	y	NOUN
ejpam-3872	14	16	)	)	PUNCT
ejpam-3872	14	17	)	)	PUNCT
ejpam-3872	15	1	dy	dy	NOUN
ejpam-3872	15	2	,	,	PUNCT
ejpam-3872	15	3	x	x	PROPN
ejpam-3872	15	4	∈]lep(f	∈]lep(f	PROPN
ejpam-3872	15	5	)	)	PUNCT
ejpam-3872	15	6	,	,	PUNCT
ejpam-3872	15	7	uep(f	uep(f	PROPN
ejpam-3872	15	8	)	)	PUNCT
ejpam-3872	15	9	[	[	PUNCT
ejpam-3872	15	10	∗corresponding	∗corresponde	VERB
ejpam-3872	15	11	author	author	NOUN
ejpam-3872	15	12	.	.	PUNCT
ejpam-3872	16	1	doi	doi	NOUN
ejpam-3872	16	2	:	:	PUNCT
ejpam-3872	16	3	https://doi.org/10.29020/nybg.ejpam.v14i1.3872	https://doi.org/10.29020/nybg.ejpam.v14i1.3872	NOUN
ejpam-3872	16	4	email	email	NOUN
ejpam-3872	16	5	addresses	address	VERB
ejpam-3872	16	6	:	:	PUNCT
ejpam-3872	16	7	gane-samb.lo@ugb.edu.sn	gane-samb.lo@ugb.edu.sn	NUM
ejpam-3872	16	8	(	(	PUNCT
ejpam-3872	16	9	g.	g.	PROPN
ejpam-3872	16	10	s.	s.	PROPN
ejpam-3872	16	11	lo	lo	PROPN
ejpam-3872	16	12	)	)	PUNCT
ejpam-3872	16	13	,	,	PUNCT
ejpam-3872	16	14	ahsan@rider.edu	ahsan@rider.edu	PROPN
ejpam-3872	17	1	(	(	PUNCT
ejpam-3872	17	2	m.	m.	NOUN
ejpam-3872	17	3	ahsanullah	ahsanullah	PROPN
ejpam-3872	17	4	)	)	PUNCT
ejpam-3872	17	5	,	,	PUNCT
ejpam-3872	17	6	moudiallo1@gmail.com	moudiallo1@gmail.com	X
ejpam-3872	17	7	(	(	PUNCT
ejpam-3872	17	8	m.	m.	PROPN
ejpam-3872	17	9	diallo	diallo	PROPN
ejpam-3872	17	10	)	)	PUNCT
ejpam-3872	17	11	,	,	PUNCT
ejpam-3872	17	12	ngom.modou1@ugb.edu.sn	ngom.modou1@ugb.edu.sn	PROPN
ejpam-3872	17	13	(	(	PUNCT
ejpam-3872	17	14	m.	m.	NOUN
ejpam-3872	17	15	ngom	ngom	ADJ
ejpam-3872	17	16	)	)	PUNCT
ejpam-3872	17	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3872	18	1	19	19	NUM
ejpam-3872	18	2	c	c	X
ejpam-3872	18	3	©	©	PROPN
ejpam-3872	18	4	2021	2021	NUM
ejpam-3872	18	5	ejpam	ejpam	VERB
ejpam-3872	18	6	all	all	DET
ejpam-3872	18	7	rights	right	NOUN
ejpam-3872	18	8	reserved	reserve	VERB
ejpam-3872	18	9	.	.	PUNCT
ejpam-3872	19	1	g.	g.	PROPN
ejpam-3872	19	2	s.	s.	PROPN
ejpam-3872	19	3	lo	lo	PROPN
ejpam-3872	19	4	et	et	PROPN
ejpam-3872	19	5	al	al	PROPN
ejpam-3872	19	6	.	.	PUNCT
ejpam-3872	19	7	/	/	SYM
ejpam-3872	19	8	eur	eur	PROPN
ejpam-3872	19	9	.	.	PUNCT
ejpam-3872	20	1	j.	j.	PROPN
ejpam-3872	20	2	pure	pure	PROPN
ejpam-3872	20	3	appl	appl	PROPN
ejpam-3872	20	4	.	.	PROPN
ejpam-3872	20	5	math	math	PROPN
ejpam-3872	20	6	,	,	PUNCT
ejpam-3872	20	7	14	14	NUM
ejpam-3872	20	8	(	(	PUNCT
ejpam-3872	20	9	1	1	NUM
ejpam-3872	20	10	)	)	PUNCT
ejpam-3872	20	11	(	(	PUNCT
ejpam-3872	20	12	2021	2021	NUM
ejpam-3872	20	13	)	)	PUNCT
ejpam-3872	20	14	,	,	PUNCT
ejpam-3872	20	15	19	19	NUM
ejpam-3872	20	16	-	-	SYM
ejpam-3872	20	17	42	42	NUM
ejpam-3872	20	18	20	20	NUM
ejpam-3872	20	19	and	and	CCONJ
ejpam-3872	20	20	f−1(u	f−1(u	NOUN
ejpam-3872	20	21	)	)	PUNCT
ejpam-3872	20	22	=	=	PUNCT
ejpam-3872	20	23	inf{x	inf{x	NOUN
ejpam-3872	20	24	∈	∈	PROPN
ejpam-3872	20	25	r	r	NOUN
ejpam-3872	20	26	,	,	PUNCT
ejpam-3872	20	27	f	f	PROPN
ejpam-3872	20	28	(	(	PUNCT
ejpam-3872	20	29	x	x	NOUN
ejpam-3872	20	30	)	)	PUNCT
ejpam-3872	20	31	≥	≥	PROPN
ejpam-3872	20	32	u	u	NOUN
ejpam-3872	20	33	}	}	PUNCT
ejpam-3872	20	34	for	for	ADP
ejpam-3872	20	35	u	u	NOUN
ejpam-3872	20	36	∈]0	∈]0	X
ejpam-3872	20	37	,	,	PUNCT
ejpam-3872	20	38	1	1	NUM
ejpam-3872	20	39	[	[	PUNCT
ejpam-3872	20	40	and	and	CCONJ
ejpam-3872	20	41	f−1(0	f−1(0	PROPN
ejpam-3872	20	42	)	)	PUNCT
ejpam-3872	20	43	=	=	PUNCT
ejpam-3872	20	44	f−1(0	f−1(0	PROPN
ejpam-3872	20	45	+	+	NOUN
ejpam-3872	20	46	)	)	PUNCT
ejpam-3872	20	47	.	.	PUNCT
ejpam-3872	21	1	respectively	respectively	ADV
ejpam-3872	21	2	.	.	PUNCT
ejpam-3872	22	1	finally	finally	ADV
ejpam-3872	22	2	,	,	PUNCT
ejpam-3872	22	3	let	let	VERB
ejpam-3872	22	4	us	we	PRON
ejpam-3872	22	5	consider	consider	VERB
ejpam-3872	22	6	the	the	DET
ejpam-3872	22	7	sequence	sequence	NOUN
ejpam-3872	22	8	of	of	ADP
ejpam-3872	22	9	strong	strong	ADJ
ejpam-3872	22	10	record	record	NOUN
ejpam-3872	22	11	values	value	NOUN
ejpam-3872	22	12	x(1	x(1	PRON
ejpam-3872	22	13	)	)	PUNCT
ejpam-3872	23	1	=	=	SYM
ejpam-3872	23	2	x1	x1	PROPN
ejpam-3872	23	3	,	,	PUNCT
ejpam-3872	23	4	x	x	X
ejpam-3872	23	5	(	(	PUNCT
ejpam-3872	23	6	n	n	CCONJ
ejpam-3872	23	7	)	)	PUNCT
ejpam-3872	23	8	,	,	PUNCT
ejpam-3872	23	9	·	·	PUNCT
ejpam-3872	23	10	·	·	PUNCT
ejpam-3872	23	11	·	·	PUNCT
ejpam-3872	23	12	(	(	PUNCT
ejpam-3872	23	13	see	see	VERB
ejpam-3872	23	14	[	[	X
ejpam-3872	23	15	7	7	NUM
ejpam-3872	23	16	]	]	PUNCT
ejpam-3872	23	17	)	)	PUNCT
ejpam-3872	23	18	and	and	CCONJ
ejpam-3872	23	19	the	the	DET
ejpam-3872	23	20	sequence	sequence	NOUN
ejpam-3872	23	21	of	of	ADP
ejpam-3872	23	22	record	record	NOUN
ejpam-3872	23	23	times	times	PROPN
ejpam-3872	23	24	u(1	u(1	PROPN
ejpam-3872	23	25	)	)	PUNCT
ejpam-3872	23	26	=	=	SYM
ejpam-3872	23	27	1	1	NUM
ejpam-3872	23	28	,	,	PUNCT
ejpam-3872	23	29	u(2	u(2	NOUN
ejpam-3872	23	30	)	)	PUNCT
ejpam-3872	23	31	,	,	PUNCT
ejpam-3872	23	32	·	·	PUNCT
ejpam-3872	23	33	·	·	PUNCT
ejpam-3872	23	34	·	·	PUNCT
ejpam-3872	23	35	.	.	PUNCT
ejpam-3872	24	1	before	before	ADP
ejpam-3872	24	2	beginning	begin	VERB
ejpam-3872	24	3	an	an	DET
ejpam-3872	24	4	asymptotic	asymptotic	ADJ
ejpam-3872	24	5	theory	theory	NOUN
ejpam-3872	24	6	,	,	PUNCT
ejpam-3872	24	7	we	we	PRON
ejpam-3872	24	8	should	should	AUX
ejpam-3872	24	9	be	be	AUX
ejpam-3872	24	10	sure	sure	ADJ
ejpam-3872	24	11	that	that	SCONJ
ejpam-3872	24	12	we	we	PRON
ejpam-3872	24	13	have	have	VERB
ejpam-3872	24	14	an	an	DET
ejpam-3872	24	15	infinite	infinite	ADJ
ejpam-3872	24	16	sequence	sequence	NOUN
ejpam-3872	24	17	(	(	PUNCT
ejpam-3872	24	18	x(n))n≥1	x(n))n≥1	PROPN
ejpam-3872	24	19	.	.	PUNCT
ejpam-3872	25	1	for	for	ADP
ejpam-3872	25	2	a	a	DET
ejpam-3872	25	3	bounded	bound	VERB
ejpam-3872	25	4	random	random	ADJ
ejpam-3872	25	5	variable	variable	NOUN
ejpam-3872	25	6	with	with	ADP
ejpam-3872	25	7	finite	finite	PROPN
ejpam-3872	25	8	upper	upper	PROPN
ejpam-3872	25	9	bound	bind	VERB
ejpam-3872	25	10	uep(f	uep(f	PROPN
ejpam-3872	25	11	)	)	PUNCT
ejpam-3872	25	12	such	such	ADJ
ejpam-3872	25	13	that	that	DET
ejpam-3872	25	14	p(x	p(x	PROPN
ejpam-3872	25	15	=	=	SYM
ejpam-3872	25	16	uep(f	uep(f	PROPN
ejpam-3872	25	17	)	)	PUNCT
ejpam-3872	25	18	)	)	PUNCT
ejpam-3872	25	19	>	>	X
ejpam-3872	25	20	0	0	NUM
ejpam-3872	25	21	,	,	PUNCT
ejpam-3872	25	22	we	we	PRON
ejpam-3872	25	23	have	have	VERB
ejpam-3872	25	24	(	(	PUNCT
ejpam-3872	25	25	x(n	x(n	NOUN
ejpam-3872	25	26	)	)	PUNCT
ejpam-3872	25	27	<	<	X
ejpam-3872	25	28	uep(f	uep(f	PROPN
ejpam-3872	25	29	)	)	PUNCT
ejpam-3872	25	30	)	)	PUNCT
ejpam-3872	25	31	finitely	finitely	ADV
ejpam-3872	25	32	often	often	ADV
ejpam-3872	25	33	.	.	PUNCT
ejpam-3872	26	1	this	this	PRON
ejpam-3872	26	2	happens	happen	VERB
ejpam-3872	26	3	for	for	ADP
ejpam-3872	26	4	classical	classical	ADJ
ejpam-3872	26	5	integer	integer	NOUN
ejpam-3872	26	6	-	-	PUNCT
ejpam-3872	26	7	valued	value	VERB
ejpam-3872	26	8	and	and	CCONJ
ejpam-3872	26	9	bounded	bound	VERB
ejpam-3872	26	10	random	random	ADJ
ejpam-3872	26	11	variables	variable	NOUN
ejpam-3872	26	12	as	as	ADP
ejpam-3872	26	13	binomial	binomial	ADJ
ejpam-3872	26	14	laws	law	NOUN
ejpam-3872	26	15	.	.	PUNCT
ejpam-3872	27	1	in	in	ADP
ejpam-3872	27	2	such	such	ADJ
ejpam-3872	27	3	cases	case	NOUN
ejpam-3872	27	4	,	,	PUNCT
ejpam-3872	27	5	the	the	DET
ejpam-3872	27	6	asymptotic	asymptotic	ADJ
ejpam-3872	27	7	theory	theory	NOUN
ejpam-3872	27	8	is	be	AUX
ejpam-3872	27	9	meaningless	meaningless	ADJ
ejpam-3872	27	10	.	.	PUNCT
ejpam-3872	28	1	but	but	CCONJ
ejpam-3872	28	2	,	,	PUNCT
ejpam-3872	28	3	an	an	DET
ejpam-3872	28	4	interesting	interesting	ADJ
ejpam-3872	28	5	question	question	NOUN
ejpam-3872	28	6	would	would	AUX
ejpam-3872	28	7	be	be	AUX
ejpam-3872	28	8	the	the	DET
ejpam-3872	28	9	characterization	characterization	NOUN
ejpam-3872	28	10	the	the	DET
ejpam-3872	28	11	infinite	infinite	ADJ
ejpam-3872	28	12	random	random	ADJ
ejpam-3872	28	13	sequence	sequence	NOUN
ejpam-3872	28	14	(	(	PUNCT
ejpam-3872	28	15	nk)k≥1	nk)k≥1	NOUN
ejpam-3872	28	16	such	such	ADJ
ejpam-3872	28	17	that	that	SCONJ
ejpam-3872	28	18	xnk	xnk	PROPN
ejpam-3872	28	19	=	=	SYM
ejpam-3872	28	20	uep(f	uep(f	PROPN
ejpam-3872	28	21	)	)	PUNCT
ejpam-3872	28	22	for	for	ADP
ejpam-3872	28	23	all	all	DET
ejpam-3872	28	24	k	k	PROPN
ejpam-3872	28	25	≥	≥	NUM
ejpam-3872	28	26	1	1	NUM
ejpam-3872	28	27	.	.	PUNCT
ejpam-3872	29	1	in	in	ADP
ejpam-3872	29	2	all	all	DET
ejpam-3872	29	3	other	other	ADJ
ejpam-3872	29	4	cases	case	NOUN
ejpam-3872	29	5	,	,	PUNCT
ejpam-3872	29	6	even	even	ADV
ejpam-3872	29	7	if	if	SCONJ
ejpam-3872	29	8	uep(f	uep(f	PROPN
ejpam-3872	29	9	)	)	PUNCT
ejpam-3872	29	10	is	be	AUX
ejpam-3872	29	11	bounded	bound	VERB
ejpam-3872	29	12	,	,	PUNCT
ejpam-3872	29	13	the	the	DET
ejpam-3872	29	14	sequence	sequence	NOUN
ejpam-3872	29	15	(	(	PUNCT
ejpam-3872	29	16	x(n))n≥1	x(n))n≥1	PROPN
ejpam-3872	29	17	is	be	AUX
ejpam-3872	29	18	infinite	infinite	ADJ
ejpam-3872	29	19	.	.	PUNCT
ejpam-3872	30	1	so	so	ADV
ejpam-3872	30	2	,	,	PUNCT
ejpam-3872	30	3	the	the	DET
ejpam-3872	30	4	results	result	NOUN
ejpam-3872	30	5	of	of	ADP
ejpam-3872	30	6	this	this	DET
ejpam-3872	30	7	paper	paper	NOUN
ejpam-3872	30	8	apply	apply	VERB
ejpam-3872	30	9	to	to	ADP
ejpam-3872	30	10	cdf	cdf	PROPN
ejpam-3872	30	11	’s	’s	PART
ejpam-3872	30	12	f	f	PROPN
ejpam-3872	30	13	such	such	ADJ
ejpam-3872	30	14	that	that	DET
ejpam-3872	30	15	p(x	p(x	PROPN
ejpam-3872	30	16	=	=	SYM
ejpam-3872	30	17	uep(f	uep(f	PROPN
ejpam-3872	30	18	)	)	PUNCT
ejpam-3872	30	19	)	)	PUNCT
ejpam-3872	31	1	=	=	PUNCT
ejpam-3872	31	2	0	0	X
ejpam-3872	31	3	.	.	PUNCT
ejpam-3872	32	1	in	in	ADP
ejpam-3872	32	2	that	that	DET
ejpam-3872	32	3	context	context	NOUN
ejpam-3872	32	4	,	,	PUNCT
ejpam-3872	32	5	asymptotic	asymptotic	ADJ
ejpam-3872	32	6	laws	law	NOUN
ejpam-3872	32	7	have	have	AUX
ejpam-3872	32	8	been	be	AUX
ejpam-3872	32	9	proposed	propose	VERB
ejpam-3872	32	10	in	in	ADP
ejpam-3872	32	11	the	the	DET
ejpam-3872	32	12	literature	literature	NOUN
ejpam-3872	32	13	by	by	ADP
ejpam-3872	32	14	many	many	ADJ
ejpam-3872	32	15	authors	author	NOUN
ejpam-3872	32	16	like	like	ADP
ejpam-3872	32	17	[	[	X
ejpam-3872	32	18	8	8	NUM
ejpam-3872	32	19	]	]	PUNCT
ejpam-3872	32	20	,	,	PUNCT
ejpam-3872	32	21	[	[	X
ejpam-3872	32	22	10	10	NUM
ejpam-3872	32	23	]	]	PUNCT
ejpam-3872	32	24	,	,	PUNCT
ejpam-3872	33	1	[	[	X
ejpam-3872	33	2	9	9	NUM
ejpam-3872	33	3	]	]	PUNCT
ejpam-3872	33	4	,	,	PUNCT
ejpam-3872	33	5	etc	etc	X
ejpam-3872	33	6	.	.	X
ejpam-3872	33	7	,	,	PUNCT
ejpam-3872	33	8	in	in	ADP
ejpam-3872	33	9	relation	relation	NOUN
ejpam-3872	33	10	with	with	ADP
ejpam-3872	33	11	extreme	extreme	ADJ
ejpam-3872	33	12	value	value	NOUN
ejpam-3872	33	13	theory	theory	NOUN
ejpam-3872	33	14	,	,	PUNCT
ejpam-3872	33	15	as	as	SCONJ
ejpam-3872	33	16	limits	limit	NOUN
ejpam-3872	33	17	in	in	ADP
ejpam-3872	33	18	type	type	NOUN
ejpam-3872	33	19	in	in	ADP
ejpam-3872	33	20	the	the	DET
ejpam-3872	33	21	form	form	NOUN
ejpam-3872	33	22	(	(	PUNCT
ejpam-3872	33	23	∃(an)n≥1	∃(an)n≥1	VERB
ejpam-3872	33	24	⊂	⊂	PROPN
ejpam-3872	33	25	r+	r+	PUNCT
ejpam-3872	33	26	\	\	PROPN
ejpam-3872	33	27	{	{	PUNCT
ejpam-3872	33	28	0	0	NUM
ejpam-3872	33	29	}	}	PUNCT
ejpam-3872	33	30	)	)	PUNCT
ejpam-3872	33	31	,	,	PUNCT
ejpam-3872	33	32	∃	∃	PROPN
ejpam-3872	33	33	(	(	PUNCT
ejpam-3872	33	34	bn)n≥1	bn)n≥1	NOUN
ejpam-3872	33	35	⊂	⊂	PROPN
ejpam-3872	33	36	r	r	NOUN
ejpam-3872	33	37	,	,	PUNCT
ejpam-3872	33	38	x(n	x(n	NOUN
ejpam-3872	33	39	)	)	PUNCT
ejpam-3872	33	40	−bn	−bn	CCONJ
ejpam-3872	33	41	an	an	DET
ejpam-3872	33	42	z	z	NOUN
ejpam-3872	33	43	,	,	PUNCT
ejpam-3872	33	44	(	(	PUNCT
ejpam-3872	33	45	1	1	X
ejpam-3872	33	46	)	)	PUNCT
ejpam-3872	33	47	where	where	SCONJ
ejpam-3872	33	48	stands	stand	VERB
ejpam-3872	33	49	for	for	ADP
ejpam-3872	33	50	the	the	DET
ejpam-3872	33	51	convergence	convergence	NOUN
ejpam-3872	33	52	in	in	ADP
ejpam-3872	33	53	distribution	distribution	NOUN
ejpam-3872	33	54	and	and	CCONJ
ejpam-3872	33	55	z	z	NOUN
ejpam-3872	33	56	is	be	AUX
ejpam-3872	33	57	a	a	DET
ejpam-3872	33	58	non	non	ADJ
ejpam-3872	33	59	-	-	ADJ
ejpam-3872	33	60	degenerate	degenerate	ADJ
ejpam-3872	33	61	random	random	ADJ
ejpam-3872	33	62	variable	variable	NOUN
ejpam-3872	33	63	.	.	PUNCT
ejpam-3872	34	1	the	the	DET
ejpam-3872	34	2	motive	motive	NOUN
ejpam-3872	34	3	beneath	beneath	ADP
ejpam-3872	34	4	this	this	DET
ejpam-3872	34	5	search	search	NOUN
ejpam-3872	34	6	is	be	AUX
ejpam-3872	34	7	the	the	DET
ejpam-3872	34	8	following	following	NOUN
ejpam-3872	34	9	.	.	PUNCT
ejpam-3872	35	1	if	if	SCONJ
ejpam-3872	35	2	we	we	PRON
ejpam-3872	35	3	denote	denote	VERB
ejpam-3872	35	4	by	by	ADP
ejpam-3872	35	5	m(n	m(n	NOUN
ejpam-3872	35	6	)	)	PUNCT
ejpam-3872	35	7	=	=	PUNCT
ejpam-3872	36	1	max(x1	max(x1	PROPN
ejpam-3872	36	2	,	,	PUNCT
ejpam-3872	36	3	·	·	PUNCT
ejpam-3872	36	4	·	·	PUNCT
ejpam-3872	36	5	·	·	PUNCT
ejpam-3872	36	6	,	,	PUNCT
ejpam-3872	36	7	xn	xn	X
ejpam-3872	36	8	)	)	PUNCT
ejpam-3872	36	9	as	as	ADP
ejpam-3872	36	10	the	the	DET
ejpam-3872	36	11	n	n	CCONJ
ejpam-3872	36	12	-	-	PUNCT
ejpam-3872	36	13	th	th	X
ejpam-3872	36	14	maximum	maximum	NOUN
ejpam-3872	36	15	for	for	ADP
ejpam-3872	36	16	n	n	X
ejpam-3872	36	17	≥	≥	NOUN
ejpam-3872	36	18	1	1	NUM
ejpam-3872	36	19	,	,	PUNCT
ejpam-3872	36	20	it	it	PRON
ejpam-3872	36	21	is	be	AUX
ejpam-3872	36	22	clear	clear	ADJ
ejpam-3872	36	23	that	that	SCONJ
ejpam-3872	36	24	we	we	PRON
ejpam-3872	36	25	have	have	VERB
ejpam-3872	36	26	∀	∀	NOUN
ejpam-3872	36	27	n	n	PRON
ejpam-3872	36	28	≥	≥	NOUN
ejpam-3872	36	29	1	1	NUM
ejpam-3872	36	30	,	,	PUNCT
ejpam-3872	36	31	x(n	x(n	NOUN
ejpam-3872	36	32	)	)	PUNCT
ejpam-3872	36	33	=	=	SYM
ejpam-3872	36	34	m(u(n	m(u(n	PROPN
ejpam-3872	36	35	)	)	PUNCT
ejpam-3872	36	36	)	)	PUNCT
ejpam-3872	36	37	.	.	PUNCT
ejpam-3872	37	1	(	(	PUNCT
ejpam-3872	37	2	2	2	X
ejpam-3872	37	3	)	)	PUNCT
ejpam-3872	37	4	since	since	SCONJ
ejpam-3872	37	5	for	for	ADP
ejpam-3872	37	6	any	any	DET
ejpam-3872	37	7	f	f	NOUN
ejpam-3872	37	8	in	in	ADP
ejpam-3872	37	9	the	the	DET
ejpam-3872	37	10	extremal	extremal	ADJ
ejpam-3872	37	11	domain	domain	NOUN
ejpam-3872	37	12	of	of	ADP
ejpam-3872	37	13	attraction	attraction	NOUN
ejpam-3872	37	14	d	d	NOUN
ejpam-3872	37	15	,	,	PUNCT
ejpam-3872	37	16	we	we	PRON
ejpam-3872	37	17	have	have	VERB
ejpam-3872	37	18	that	that	PRON
ejpam-3872	37	19	for	for	ADP
ejpam-3872	37	20	some	some	DET
ejpam-3872	37	21	γ	γ	NOUN
ejpam-3872	37	22	∈	∈	PROPN
ejpam-3872	37	23	r	r	NOUN
ejpam-3872	37	24	,	,	PUNCT
ejpam-3872	37	25	(	(	PUNCT
ejpam-3872	37	26	∃(an)n≥1	∃(an)n≥1	VERB
ejpam-3872	37	27	⊂	⊂	PROPN
ejpam-3872	37	28	r+	r+	PUNCT
ejpam-3872	37	29	\	\	PROPN
ejpam-3872	37	30	{	{	PUNCT
ejpam-3872	37	31	0	0	NUM
ejpam-3872	37	32	}	}	PUNCT
ejpam-3872	37	33	)	)	PUNCT
ejpam-3872	37	34	,	,	PUNCT
ejpam-3872	37	35	(	(	PUNCT
ejpam-3872	37	36	∃(bn)n≥1	∃(bn)n≥1	VERB
ejpam-3872	37	37	⊂	⊂	NOUN
ejpam-3872	37	38	r	r	NOUN
ejpam-3872	37	39	,	,	PUNCT
ejpam-3872	37	40	m(n)−	m(n)−	NOUN
ejpam-3872	37	41	an	an	PRON
ejpam-3872	37	42	bn	bn	X
ejpam-3872	37	43	zγ	zγ	PROPN
ejpam-3872	37	44	,	,	PUNCT
ejpam-3872	37	45	(	(	PUNCT
ejpam-3872	37	46	3	3	X
ejpam-3872	37	47	)	)	PUNCT
ejpam-3872	37	48	where	where	SCONJ
ejpam-3872	37	49	the	the	DET
ejpam-3872	37	50	cdf	cdf	PROPN
ejpam-3872	37	51	of	of	ADP
ejpam-3872	37	52	zγ	zγ	PROPN
ejpam-3872	37	53	is	be	AUX
ejpam-3872	37	54	the	the	DET
ejpam-3872	37	55	generalized	generalize	VERB
ejpam-3872	37	56	extreme	extreme	ADJ
ejpam-3872	37	57	value	value	NOUN
ejpam-3872	37	58	distribution	distribution	NOUN
ejpam-3872	37	59	defined	define	VERB
ejpam-3872	37	60	by	by	ADP
ejpam-3872	37	61	gγ(x	gγ(x	NOUN
ejpam-3872	37	62	)	)	PUNCT
ejpam-3872	37	63	=	=	SYM
ejpam-3872	37	64	exp(−(1	exp(−(1	NOUN
ejpam-3872	38	1	+	+	CCONJ
ejpam-3872	38	2	γx)1	γx)1	ADJ
ejpam-3872	38	3	/	/	SYM
ejpam-3872	38	4	γ	γ	NOUN
ejpam-3872	38	5	)	)	PUNCT
ejpam-3872	38	6	,	,	PUNCT
ejpam-3872	38	7	with	with	ADP
ejpam-3872	38	8	1	1	NUM
ejpam-3872	38	9	+	+	CCONJ
ejpam-3872	38	10	γx	γx	NOUN
ejpam-3872	38	11	>	>	X
ejpam-3872	38	12	0	0	NUM
ejpam-3872	38	13	,	,	PUNCT
ejpam-3872	38	14	and	and	CCONJ
ejpam-3872	38	15	g0(x	g0(x	X
ejpam-3872	38	16	)	)	PUNCT
ejpam-3872	38	17	=	=	PROPN
ejpam-3872	39	1	exp(−	exp(−	PROPN
ejpam-3872	39	2	exp(−x	exp(−x	PROPN
ejpam-3872	39	3	)	)	PUNCT
ejpam-3872	39	4	)	)	PUNCT
ejpam-3872	40	1	for	for	ADP
ejpam-3872	40	2	x	x	PROPN
ejpam-3872	40	3	∈	∈	PROPN
ejpam-3872	40	4	r.	r.	PROPN
ejpam-3872	40	5	in	in	ADP
ejpam-3872	40	6	extreme	extreme	ADJ
ejpam-3872	40	7	value	value	NOUN
ejpam-3872	40	8	theory	theory	NOUN
ejpam-3872	40	9	,	,	PUNCT
ejpam-3872	40	10	formula	formula	NOUN
ejpam-3872	40	11	(	(	PUNCT
ejpam-3872	40	12	3	3	X
ejpam-3872	40	13	)	)	PUNCT
ejpam-3872	40	14	is	be	AUX
ejpam-3872	40	15	rephrased	rephrase	VERB
ejpam-3872	40	16	as	as	SCONJ
ejpam-3872	40	17	f	f	PROPN
ejpam-3872	40	18	is	be	AUX
ejpam-3872	40	19	attracted	attract	VERB
ejpam-3872	40	20	by	by	ADP
ejpam-3872	40	21	gγ	gγ	ADP
ejpam-3872	40	22	denoted	denote	VERB
ejpam-3872	40	23	by	by	ADP
ejpam-3872	40	24	f	f	PROPN
ejpam-3872	40	25	∈	∈	PROPN
ejpam-3872	40	26	d(gγ	d(gγ	PROPN
ejpam-3872	40	27	)	)	PUNCT
ejpam-3872	40	28	.	.	PUNCT
ejpam-3872	41	1	from	from	ADP
ejpam-3872	41	2	formulas	formula	NOUN
ejpam-3872	41	3	(	(	PUNCT
ejpam-3872	41	4	2	2	NUM
ejpam-3872	41	5	)	)	PUNCT
ejpam-3872	41	6	and	and	CCONJ
ejpam-3872	41	7	(	(	PUNCT
ejpam-3872	41	8	3	3	NUM
ejpam-3872	41	9	)	)	PUNCT
ejpam-3872	41	10	and	and	CCONJ
ejpam-3872	41	11	from	from	ADP
ejpam-3872	41	12	the	the	DET
ejpam-3872	41	13	fact	fact	NOUN
ejpam-3872	41	14	that	that	SCONJ
ejpam-3872	41	15	u(n	u(n	PROPN
ejpam-3872	41	16	)	)	PUNCT
ejpam-3872	41	17	→	→	PUNCT
ejpam-3872	42	1	+	+	NUM
ejpam-3872	42	2	∞	∞	PROPN
ejpam-3872	42	3	as	as	ADP
ejpam-3872	42	4	n	n	PROPN
ejpam-3872	42	5	→	→	SYM
ejpam-3872	42	6	+	+	PROPN
ejpam-3872	42	7	∞	∞	PROPN
ejpam-3872	42	8	,	,	PUNCT
ejpam-3872	42	9	the	the	DET
ejpam-3872	42	10	investigation	investigation	NOUN
ejpam-3872	42	11	of	of	ADP
ejpam-3872	42	12	the	the	DET
ejpam-3872	42	13	validity	validity	NOUN
ejpam-3872	42	14	of	of	ADP
ejpam-3872	42	15	(	(	PUNCT
ejpam-3872	42	16	1	1	X
ejpam-3872	42	17	)	)	PUNCT
ejpam-3872	42	18	was	be	AUX
ejpam-3872	42	19	justified	justify	VERB
ejpam-3872	42	20	enough	enough	ADV
ejpam-3872	42	21	.	.	PUNCT
ejpam-3872	43	1	the	the	DET
ejpam-3872	43	2	results	result	NOUN
ejpam-3872	43	3	of	of	ADP
ejpam-3872	43	4	the	the	DET
ejpam-3872	43	5	cited	cite	VERB
ejpam-3872	43	6	authors	author	NOUN
ejpam-3872	43	7	and	and	CCONJ
ejpam-3872	43	8	g.	g.	PROPN
ejpam-3872	43	9	s.	s.	PROPN
ejpam-3872	44	1	lo	lo	PROPN
ejpam-3872	44	2	et	et	PROPN
ejpam-3872	44	3	al	al	PROPN
ejpam-3872	44	4	.	.	PUNCT
ejpam-3872	44	5	/	/	SYM
ejpam-3872	44	6	eur	eur	PROPN
ejpam-3872	44	7	.	.	PUNCT
ejpam-3872	45	1	j.	j.	PROPN
ejpam-3872	45	2	pure	pure	PROPN
ejpam-3872	45	3	appl	appl	PROPN
ejpam-3872	45	4	.	.	PROPN
ejpam-3872	45	5	math	math	PROPN
ejpam-3872	45	6	,	,	PUNCT
ejpam-3872	45	7	14	14	NUM
ejpam-3872	45	8	(	(	PUNCT
ejpam-3872	45	9	1	1	NUM
ejpam-3872	45	10	)	)	PUNCT
ejpam-3872	45	11	(	(	PUNCT
ejpam-3872	45	12	2021	2021	NUM
ejpam-3872	45	13	)	)	PUNCT
ejpam-3872	45	14	,	,	PUNCT
ejpam-3872	45	15	19	19	NUM
ejpam-3872	45	16	-	-	SYM
ejpam-3872	45	17	42	42	NUM
ejpam-3872	45	18	21	21	NUM
ejpam-3872	45	19	others	other	NOUN
ejpam-3872	45	20	were	be	AUX
ejpam-3872	45	21	positive	positive	ADJ
ejpam-3872	45	22	with	with	ADP
ejpam-3872	45	23	the	the	DET
ejpam-3872	45	24	stunning	stunning	ADJ
ejpam-3872	45	25	result	result	NOUN
ejpam-3872	45	26	that	that	SCONJ
ejpam-3872	45	27	the	the	DET
ejpam-3872	45	28	cdf	cdf	PROPN
ejpam-3872	45	29	of	of	ADP
ejpam-3872	45	30	z	z	PROPN
ejpam-3872	45	31	should	should	AUX
ejpam-3872	45	32	be	be	AUX
ejpam-3872	45	33	on	on	ADP
ejpam-3872	45	34	the	the	DET
ejpam-3872	45	35	form	form	NOUN
ejpam-3872	45	36	φ(g(x	φ(g(x	PROPN
ejpam-3872	45	37	)	)	PUNCT
ejpam-3872	45	38	)	)	PUNCT
ejpam-3872	45	39	,	,	PUNCT
ejpam-3872	45	40	x	x	PUNCT
ejpam-3872	45	41	∈	∈	PROPN
ejpam-3872	45	42	r	r	NOUN
ejpam-3872	45	43	,	,	PUNCT
ejpam-3872	45	44	where	where	SCONJ
ejpam-3872	45	45	φ	φ	PROPN
ejpam-3872	45	46	is	be	AUX
ejpam-3872	45	47	the	the	DET
ejpam-3872	45	48	cdf	cdf	PROPN
ejpam-3872	45	49	of	of	ADP
ejpam-3872	45	50	the	the	DET
ejpam-3872	45	51	standard	standard	ADJ
ejpam-3872	45	52	normal	normal	ADJ
ejpam-3872	45	53	law	law	NOUN
ejpam-3872	45	54	and	and	CCONJ
ejpam-3872	45	55	g	g	NOUN
ejpam-3872	45	56	satisfies	satisfy	VERB
ejpam-3872	45	57	one	one	NUM
ejpam-3872	45	58	of	of	ADP
ejpam-3872	45	59	three	three	NUM
ejpam-3872	45	60	definitions	definition	NOUN
ejpam-3872	45	61	(	(	PUNCT
ejpam-3872	45	62	in	in	ADP
ejpam-3872	45	63	which	which	PRON
ejpam-3872	45	64	c	c	NOUN
ejpam-3872	45	65	is	be	AUX
ejpam-3872	45	66	a	a	DET
ejpam-3872	45	67	positive	positive	ADJ
ejpam-3872	45	68	constant	constant	ADJ
ejpam-3872	45	69	)	)	PUNCT
ejpam-3872	45	70	g(x	g(x	NOUN
ejpam-3872	45	71	)	)	PUNCT
ejpam-3872	46	1	=	=	SYM
ejpam-3872	46	2	x	x	X
ejpam-3872	46	3	,	,	PUNCT
ejpam-3872	46	4	x	x	PROPN
ejpam-3872	46	5	∈	∈	PROPN
ejpam-3872	46	6	r.	r.	PROPN
ejpam-3872	46	7	g(x	g(x	NOUN
ejpam-3872	46	8	)	)	PUNCT
ejpam-3872	47	1	=	=	SYM
ejpam-3872	47	2	−∞1(x<0	−∞1(x<0	ADJ
ejpam-3872	47	3	)	)	PUNCT
ejpam-3872	48	1	+	+	CCONJ
ejpam-3872	48	2	(	(	PUNCT
ejpam-3872	48	3	c	c	NOUN
ejpam-3872	48	4	log	log	VERB
ejpam-3872	48	5	x	x	SYM
ejpam-3872	48	6	)	)	PUNCT
ejpam-3872	48	7	1(x≥0	1(x≥0	NUM
ejpam-3872	48	8	)	)	PUNCT
ejpam-3872	48	9	,	,	PUNCT
ejpam-3872	48	10	x	x	PROPN
ejpam-3872	48	11	∈	∈	PROPN
ejpam-3872	48	12	r.	r.	PROPN
ejpam-3872	48	13	g(x	g(x	PROPN
ejpam-3872	48	14	)	)	PUNCT
ejpam-3872	49	1	=	=	PRON
ejpam-3872	49	2	(	(	PUNCT
ejpam-3872	49	3	−c	−c	NOUN
ejpam-3872	49	4	log−x	log−x	NOUN
ejpam-3872	49	5	)	)	PUNCT
ejpam-3872	49	6	1(x<0	1(x<0	NUM
ejpam-3872	49	7	)	)	PUNCT
ejpam-3872	50	1	+	+	NOUN
ejpam-3872	50	2	∞	∞	NOUN
ejpam-3872	50	3	1(x>0	1(x>0	NUM
ejpam-3872	50	4	)	)	PUNCT
ejpam-3872	50	5	,	,	PUNCT
ejpam-3872	50	6	x	x	PROPN
ejpam-3872	50	7	∈	∈	PROPN
ejpam-3872	50	8	r.	r.	PROPN
ejpam-3872	50	9	instead	instead	ADV
ejpam-3872	50	10	of	of	ADP
ejpam-3872	50	11	using	use	VERB
ejpam-3872	50	12	this	this	DET
ejpam-3872	50	13	mathematically	mathematically	ADV
ejpam-3872	50	14	appealing	appealing	ADJ
ejpam-3872	50	15	approach	approach	NOUN
ejpam-3872	50	16	based	base	VERB
ejpam-3872	50	17	on	on	ADP
ejpam-3872	50	18	functional	functional	ADJ
ejpam-3872	50	19	equations	equation	NOUN
ejpam-3872	50	20	,	,	PUNCT
ejpam-3872	50	21	an	an	DET
ejpam-3872	50	22	other	other	ADJ
ejpam-3872	50	23	approach	approach	NOUN
ejpam-3872	50	24	consisting	consist	VERB
ejpam-3872	50	25	in	in	ADP
ejpam-3872	50	26	directly	directly	ADV
ejpam-3872	50	27	finding	find	VERB
ejpam-3872	50	28	the	the	DET
ejpam-3872	50	29	asymptotic	asymptotic	ADJ
ejpam-3872	50	30	laws	law	NOUN
ejpam-3872	50	31	of	of	ADP
ejpam-3872	50	32	x(n	x(n	NOUN
ejpam-3872	50	33	)	)	PUNCT
ejpam-3872	50	34	,	,	PUNCT
ejpam-3872	50	35	not	not	PART
ejpam-3872	50	36	necessarily	necessarily	ADV
ejpam-3872	50	37	in	in	ADP
ejpam-3872	50	38	the	the	DET
ejpam-3872	50	39	form	form	NOUN
ejpam-3872	50	40	of	of	ADP
ejpam-3872	50	41	formula	formula	NOUN
ejpam-3872	50	42	(	(	PUNCT
ejpam-3872	50	43	1	1	X
ejpam-3872	50	44	)	)	PUNCT
ejpam-3872	50	45	is	be	AUX
ejpam-3872	50	46	possible	possible	ADJ
ejpam-3872	50	47	and	and	CCONJ
ejpam-3872	50	48	we	we	PRON
ejpam-3872	50	49	proceed	proceed	VERB
ejpam-3872	50	50	to	to	ADP
ejpam-3872	50	51	it	it	PRON
ejpam-3872	50	52	here	here	ADV
ejpam-3872	50	53	.	.	PUNCT
ejpam-3872	51	1	that	that	DET
ejpam-3872	51	2	approach	approach	NOUN
ejpam-3872	51	3	is	be	AUX
ejpam-3872	51	4	based	base	VERB
ejpam-3872	51	5	on	on	ADP
ejpam-3872	51	6	representations	representation	NOUN
ejpam-3872	51	7	of	of	ADP
ejpam-3872	51	8	f	f	PROPN
ejpam-3872	51	9	∈	∈	PROPN
ejpam-3872	51	10	d	d	PROPN
ejpam-3872	51	11	due	due	ADP
ejpam-3872	51	12	to	to	PART
ejpam-3872	51	13	karamata	karamata	VERB
ejpam-3872	51	14	and	and	CCONJ
ejpam-3872	51	15	to	to	ADP
ejpam-3872	51	16	de	de	X
ejpam-3872	51	17	haan	haan	PROPN
ejpam-3872	51	18	for	for	ADP
ejpam-3872	51	19	example	example	NOUN
ejpam-3872	51	20	.	.	PUNCT
ejpam-3872	52	1	our	our	PRON
ejpam-3872	52	2	achievement	achievement	NOUN
ejpam-3872	52	3	is	be	AUX
ejpam-3872	52	4	the	the	DET
ejpam-3872	52	5	finding	finding	NOUN
ejpam-3872	52	6	of	of	ADP
ejpam-3872	52	7	the	the	DET
ejpam-3872	52	8	asymptotic	asymptotic	ADJ
ejpam-3872	52	9	laws	law	NOUN
ejpam-3872	52	10	of	of	ADP
ejpam-3872	52	11	the	the	DET
ejpam-3872	52	12	records	record	NOUN
ejpam-3872	52	13	for	for	ADP
ejpam-3872	52	14	all	all	DET
ejpam-3872	52	15	f	f	PROPN
ejpam-3872	52	16	∈	∈	PROPN
ejpam-3872	52	17	d	d	PROPN
ejpam-3872	52	18	and	and	CCONJ
ejpam-3872	52	19	the	the	DET
ejpam-3872	52	20	related	related	ADJ
ejpam-3872	52	21	rates	rate	NOUN
ejpam-3872	52	22	of	of	ADP
ejpam-3872	52	23	convergence	convergence	NOUN
ejpam-3872	52	24	:	:	PUNCT
ejpam-3872	52	25	first	first	ADV
ejpam-3872	52	26	,	,	PUNCT
ejpam-3872	52	27	for	for	ADP
ejpam-3872	52	28	γ	γ	X
ejpam-3872	52	29	6=	6=	PROPN
ejpam-3872	52	30	0	0	NUM
ejpam-3872	52	31	,	,	PUNCT
ejpam-3872	52	32	outside	outside	ADP
ejpam-3872	52	33	the	the	DET
ejpam-3872	52	34	frame	frame	NOUN
ejpam-3872	52	35	of	of	ADP
ejpam-3872	52	36	formula	formula	NOUN
ejpam-3872	52	37	(	(	PUNCT
ejpam-3872	52	38	1	1	NUM
ejpam-3872	52	39	)	)	PUNCT
ejpam-3872	52	40	,	,	PUNCT
ejpam-3872	52	41	that	that	PRON
ejpam-3872	52	42	is	be	AUX
ejpam-3872	52	43	as	as	ADP
ejpam-3872	52	44	limits	limit	NOUN
ejpam-3872	52	45	in	in	ADP
ejpam-3872	52	46	type	type	NOUN
ejpam-3872	52	47	,	,	PUNCT
ejpam-3872	52	48	and	and	CCONJ
ejpam-3872	52	49	without	without	ADP
ejpam-3872	52	50	any	any	DET
ejpam-3872	52	51	further	further	ADJ
ejpam-3872	52	52	condition	condition	NOUN
ejpam-3872	52	53	and	and	CCONJ
ejpam-3872	52	54	secondly	secondly	ADV
ejpam-3872	52	55	,	,	PUNCT
ejpam-3872	52	56	for	for	ADP
ejpam-3872	52	57	γ	γ	X
ejpam-3872	52	58	=	=	SYM
ejpam-3872	52	59	0	0	NUM
ejpam-3872	52	60	,	,	PUNCT
ejpam-3872	52	61	within	within	ADP
ejpam-3872	52	62	the	the	DET
ejpam-3872	52	63	frame	frame	NOUN
ejpam-3872	52	64	of	of	ADP
ejpam-3872	52	65	formula	formula	NOUN
ejpam-3872	52	66	(	(	PUNCT
ejpam-3872	52	67	1	1	NUM
ejpam-3872	52	68	)	)	PUNCT
ejpam-3872	52	69	,	,	PUNCT
ejpam-3872	52	70	under	under	ADP
ejpam-3872	52	71	a	a	DET
ejpam-3872	52	72	general	general	ADJ
ejpam-3872	52	73	regularity	regularity	NOUN
ejpam-3872	52	74	condition	condition	NOUN
ejpam-3872	52	75	.	.	PUNCT
ejpam-3872	53	1	that	that	DET
ejpam-3872	53	2	regularity	regularity	NOUN
ejpam-3872	53	3	condition	condition	NOUN
ejpam-3872	53	4	generally	generally	ADV
ejpam-3872	53	5	holds	hold	VERB
ejpam-3872	53	6	for	for	ADP
ejpam-3872	53	7	usual	usual	ADJ
ejpam-3872	53	8	cdf	cdf	PROPN
ejpam-3872	53	9	’	'	PUNCT
ejpam-3872	53	10	s.	s.	PROPN
ejpam-3872	53	11	we	we	PRON
ejpam-3872	53	12	also	also	ADV
ejpam-3872	53	13	give	give	VERB
ejpam-3872	53	14	general	general	ADJ
ejpam-3872	53	15	conditions	condition	NOUN
ejpam-3872	53	16	to	to	PART
ejpam-3872	53	17	ensure	ensure	VERB
ejpam-3872	53	18	the	the	DET
ejpam-3872	53	19	asymptotic	asymptotic	ADJ
ejpam-3872	53	20	normality	normality	NOUN
ejpam-3872	53	21	of	of	ADP
ejpam-3872	53	22	the	the	DET
ejpam-3872	53	23	record	record	NOUN
ejpam-3872	53	24	values	value	NOUN
ejpam-3872	53	25	for	for	ADP
ejpam-3872	53	26	f	f	PROPN
ejpam-3872	53	27	not	not	PART
ejpam-3872	53	28	necessarily	necessarily	ADV
ejpam-3872	53	29	in	in	ADP
ejpam-3872	53	30	the	the	DET
ejpam-3872	53	31	extremal	extremal	ADJ
ejpam-3872	53	32	domain	domain	NOUN
ejpam-3872	53	33	.	.	PUNCT
ejpam-3872	54	1	as	as	ADV
ejpam-3872	54	2	well	well	ADV
ejpam-3872	54	3	general	general	ADJ
ejpam-3872	54	4	rates	rate	NOUN
ejpam-3872	54	5	of	of	ADP
ejpam-3872	54	6	convergence	convergence	NOUN
ejpam-3872	54	7	are	be	AUX
ejpam-3872	54	8	given	give	VERB
ejpam-3872	54	9	.	.	PUNCT
ejpam-3872	55	1	these	these	DET
ejpam-3872	55	2	rates	rate	NOUN
ejpam-3872	55	3	can	can	AUX
ejpam-3872	55	4	be	be	AUX
ejpam-3872	55	5	explicitly	explicitly	ADV
ejpam-3872	55	6	stated	state	VERB
ejpam-3872	55	7	for	for	ADP
ejpam-3872	55	8	usual	usual	ADJ
ejpam-3872	55	9	cdf	cdf	PROPN
ejpam-3872	55	10	’s	’s	X
ejpam-3872	55	11	in	in	ADP
ejpam-3872	55	12	d.	d.	PROPN
ejpam-3872	55	13	finally	finally	ADV
ejpam-3872	55	14	,	,	PUNCT
ejpam-3872	55	15	we	we	PRON
ejpam-3872	55	16	give	give	VERB
ejpam-3872	55	17	detailed	detailed	ADJ
ejpam-3872	55	18	asymptotic	asymptotic	ADJ
ejpam-3872	55	19	laws	law	NOUN
ejpam-3872	55	20	of	of	ADP
ejpam-3872	55	21	the	the	DET
ejpam-3872	55	22	records	record	NOUN
ejpam-3872	55	23	of	of	ADP
ejpam-3872	55	24	a	a	DET
ejpam-3872	55	25	list	list	NOUN
ejpam-3872	55	26	of	of	ADP
ejpam-3872	55	27	remarkable	remarkable	ADJ
ejpam-3872	55	28	cdf	cdf	PROPN
ejpam-3872	55	29	’s	’s	X
ejpam-3872	55	30	with	with	ADP
ejpam-3872	55	31	specific	specific	ADJ
ejpam-3872	55	32	coefficients	coefficient	NOUN
ejpam-3872	55	33	.	.	PUNCT
ejpam-3872	56	1	in	in	ADP
ejpam-3872	56	2	this	this	DET
ejpam-3872	56	3	paper	paper	NOUN
ejpam-3872	56	4	that	that	PRON
ejpam-3872	56	5	we	we	PRON
ejpam-3872	56	6	want	want	VERB
ejpam-3872	56	7	short	short	ADJ
ejpam-3872	56	8	,	,	PUNCT
ejpam-3872	56	9	we	we	PRON
ejpam-3872	56	10	use	use	VERB
ejpam-3872	56	11	many	many	ADJ
ejpam-3872	56	12	results	result	NOUN
ejpam-3872	56	13	from	from	ADP
ejpam-3872	56	14	extreme	extreme	ADJ
ejpam-3872	56	15	value	value	NOUN
ejpam-3872	56	16	theory	theory	NOUN
ejpam-3872	56	17	and	and	CCONJ
ejpam-3872	56	18	record	record	NOUN
ejpam-3872	56	19	values	value	NOUN
ejpam-3872	56	20	theory	theory	NOUN
ejpam-3872	56	21	.	.	PUNCT
ejpam-3872	57	1	so	so	ADV
ejpam-3872	57	2	,	,	PUNCT
ejpam-3872	57	3	for	for	ADP
ejpam-3872	57	4	more	more	ADJ
ejpam-3872	57	5	details	detail	NOUN
ejpam-3872	57	6	,	,	PUNCT
ejpam-3872	57	7	we	we	PRON
ejpam-3872	57	8	refer	refer	VERB
ejpam-3872	57	9	the	the	DET
ejpam-3872	57	10	reader	reader	NOUN
ejpam-3872	57	11	to	to	ADP
ejpam-3872	57	12	the	the	DET
ejpam-3872	57	13	books	book	NOUN
ejpam-3872	57	14	of	of	ADP
ejpam-3872	57	15	[	[	X
ejpam-3872	57	16	7	7	NUM
ejpam-3872	57	17	]	]	PUNCT
ejpam-3872	57	18	and	and	CCONJ
ejpam-3872	57	19	[	[	X
ejpam-3872	57	20	9	9	NUM
ejpam-3872	57	21	]	]	PUNCT
ejpam-3872	57	22	,	,	PUNCT
ejpam-3872	57	23	for	for	ADP
ejpam-3872	57	24	an	an	DET
ejpam-3872	57	25	easy	easy	ADJ
ejpam-3872	57	26	introduction	introduction	NOUN
ejpam-3872	57	27	to	to	ADP
ejpam-3872	57	28	records	record	NOUN
ejpam-3872	57	29	and	and	CCONJ
ejpam-3872	57	30	to	to	ADP
ejpam-3872	57	31	those	those	PRON
ejpam-3872	57	32	of	of	ADP
ejpam-3872	57	33	[	[	X
ejpam-3872	57	34	2	2	NUM
ejpam-3872	57	35	]	]	PUNCT
ejpam-3872	57	36	,	,	PUNCT
ejpam-3872	57	37	[	[	X
ejpam-3872	57	38	1	1	NUM
ejpam-3872	57	39	]	]	PUNCT
ejpam-3872	57	40	,	,	PUNCT
ejpam-3872	57	41	[	[	X
ejpam-3872	57	42	10	10	NUM
ejpam-3872	57	43	]	]	PUNCT
ejpam-3872	57	44	and	and	CCONJ
ejpam-3872	57	45	[	[	X
ejpam-3872	57	46	6	6	NUM
ejpam-3872	57	47	]	]	PUNCT
ejpam-3872	57	48	,	,	PUNCT
ejpam-3872	57	49	concerning	concern	VERB
ejpam-3872	57	50	extreme	extreme	ADJ
ejpam-3872	57	51	value	value	NOUN
ejpam-3872	57	52	theory	theory	NOUN
ejpam-3872	57	53	.	.	PUNCT
ejpam-3872	58	1	to	to	PART
ejpam-3872	58	2	end	end	VERB
ejpam-3872	58	3	this	this	DET
ejpam-3872	58	4	introduction	introduction	NOUN
ejpam-3872	58	5	,	,	PUNCT
ejpam-3872	58	6	we	we	PRON
ejpam-3872	58	7	recall	recall	VERB
ejpam-3872	58	8	two	two	NUM
ejpam-3872	58	9	important	important	ADJ
ejpam-3872	58	10	tools	tool	NOUN
ejpam-3872	58	11	of	of	ADP
ejpam-3872	58	12	extreme	extreme	ADJ
ejpam-3872	58	13	value	value	NOUN
ejpam-3872	58	14	theory	theory	NOUN
ejpam-3872	58	15	that	that	PRON
ejpam-3872	58	16	form	form	VERB
ejpam-3872	58	17	the	the	DET
ejpam-3872	58	18	basis	basis	NOUN
ejpam-3872	58	19	of	of	ADP
ejpam-3872	58	20	our	our	PRON
ejpam-3872	58	21	method	method	NOUN
ejpam-3872	58	22	.	.	PUNCT
ejpam-3872	59	1	the	the	DET
ejpam-3872	59	2	first	first	ADJ
ejpam-3872	59	3	is	be	AUX
ejpam-3872	59	4	the	the	DET
ejpam-3872	59	5	following	follow	VERB
ejpam-3872	59	6	proposition	proposition	NOUN
ejpam-3872	59	7	.	.	PUNCT
ejpam-3872	60	1	suppose	suppose	VERB
ejpam-3872	60	2	that	that	SCONJ
ejpam-3872	60	3	x	x	PROPN
ejpam-3872	60	4	≥	≥	NOUN
ejpam-3872	60	5	0	0	NUM
ejpam-3872	60	6	,	,	PUNCT
ejpam-3872	60	7	that	that	PRON
ejpam-3872	60	8	is	be	AUX
ejpam-3872	60	9	f	f	PROPN
ejpam-3872	60	10	(	(	PUNCT
ejpam-3872	60	11	0	0	NUM
ejpam-3872	60	12	)	)	PUNCT
ejpam-3872	60	13	=	=	NOUN
ejpam-3872	61	1	0	0	X
ejpam-3872	61	2	.	.	PUNCT
ejpam-3872	62	1	in	in	ADP
ejpam-3872	62	2	that	that	DET
ejpam-3872	62	3	case	case	NOUN
ejpam-3872	62	4	,	,	PUNCT
ejpam-3872	62	5	we	we	PRON
ejpam-3872	62	6	define	define	VERB
ejpam-3872	62	7	y	y	PROPN
ejpam-3872	62	8	=	=	PUNCT
ejpam-3872	62	9	logx	logx	PROPN
ejpam-3872	62	10	with	with	ADP
ejpam-3872	62	11	cdf	cdf	PROPN
ejpam-3872	62	12	g(x	g(x	NOUN
ejpam-3872	62	13	)	)	PUNCT
ejpam-3872	63	1	=	=	SYM
ejpam-3872	63	2	f	f	X
ejpam-3872	63	3	(	(	PUNCT
ejpam-3872	63	4	ex	ex	NOUN
ejpam-3872	63	5	)	)	PUNCT
ejpam-3872	63	6	,	,	PUNCT
ejpam-3872	63	7	x	x	PUNCT
ejpam-3872	63	8	∈	∈	NOUN
ejpam-3872	63	9	r	r	NOUN
ejpam-3872	63	10	and	and	CCONJ
ejpam-3872	63	11	we	we	PRON
ejpam-3872	63	12	have	have	VERB
ejpam-3872	63	13	the	the	DET
ejpam-3872	63	14	proposition	proposition	NOUN
ejpam-3872	63	15	below	below	ADV
ejpam-3872	63	16	,	,	PUNCT
ejpam-3872	63	17	proposition	proposition	NOUN
ejpam-3872	63	18	1	1	NUM
ejpam-3872	63	19	.	.	PUNCT
ejpam-3872	64	1	(	(	PUNCT
ejpam-3872	64	2	see	see	VERB
ejpam-3872	64	3	[	[	X
ejpam-3872	64	4	5	5	NUM
ejpam-3872	64	5	]	]	PUNCT
ejpam-3872	64	6	)	)	PUNCT
ejpam-3872	64	7	we	we	PRON
ejpam-3872	64	8	have	have	VERB
ejpam-3872	64	9	the	the	DET
ejpam-3872	64	10	following	follow	VERB
ejpam-3872	64	11	equivalences	equivalence	NOUN
ejpam-3872	64	12	.	.	PUNCT
ejpam-3872	65	1	(	(	PUNCT
ejpam-3872	65	2	1	1	X
ejpam-3872	65	3	)	)	PUNCT
ejpam-3872	65	4	if	if	SCONJ
ejpam-3872	65	5	γ	γ	X
ejpam-3872	65	6	>	>	X
ejpam-3872	65	7	0	0	PROPN
ejpam-3872	65	8	,	,	PUNCT
ejpam-3872	65	9	f	f	PROPN
ejpam-3872	65	10	∈	∈	PROPN
ejpam-3872	65	11	d(gγ	d(gγ	PROPN
ejpam-3872	65	12	)	)	PUNCT
ejpam-3872	65	13	⇔	⇔	NOUN
ejpam-3872	65	14	(	(	PUNCT
ejpam-3872	65	15	g	g	PROPN
ejpam-3872	65	16	∈	∈	PROPN
ejpam-3872	65	17	d(g0	d(g0	NOUN
ejpam-3872	65	18	)	)	PUNCT
ejpam-3872	65	19	and	and	CCONJ
ejpam-3872	65	20	r(x	r(x	PROPN
ejpam-3872	65	21	,	,	PUNCT
ejpam-3872	65	22	g)→	g)→	NOUN
ejpam-3872	65	23	γ	γ	X
ejpam-3872	65	24	as	as	ADP
ejpam-3872	65	25	x→	x→	PROPN
ejpam-3872	65	26	uep(g	uep(g	PROPN
ejpam-3872	65	27	)	)	PUNCT
ejpam-3872	65	28	)	)	PUNCT
ejpam-3872	65	29	.	.	PUNCT
ejpam-3872	66	1	(	(	PUNCT
ejpam-3872	66	2	2	2	X
ejpam-3872	66	3	)	)	PUNCT
ejpam-3872	66	4	if	if	SCONJ
ejpam-3872	66	5	γ	γ	X
ejpam-3872	66	6	=	=	SYM
ejpam-3872	66	7	0	0	NUM
ejpam-3872	66	8	,	,	PUNCT
ejpam-3872	67	1	g.	g.	PROPN
ejpam-3872	67	2	s.	s.	PROPN
ejpam-3872	67	3	lo	lo	PROPN
ejpam-3872	67	4	et	et	PROPN
ejpam-3872	67	5	al	al	PROPN
ejpam-3872	67	6	.	.	PUNCT
ejpam-3872	67	7	/	/	SYM
ejpam-3872	67	8	eur	eur	PROPN
ejpam-3872	67	9	.	.	PUNCT
ejpam-3872	68	1	j.	j.	PROPN
ejpam-3872	68	2	pure	pure	PROPN
ejpam-3872	68	3	appl	appl	PROPN
ejpam-3872	68	4	.	.	PROPN
ejpam-3872	68	5	math	math	PROPN
ejpam-3872	68	6	,	,	PUNCT
ejpam-3872	68	7	14	14	NUM
ejpam-3872	68	8	(	(	PUNCT
ejpam-3872	68	9	1	1	NUM
ejpam-3872	68	10	)	)	PUNCT
ejpam-3872	68	11	(	(	PUNCT
ejpam-3872	68	12	2021	2021	NUM
ejpam-3872	68	13	)	)	PUNCT
ejpam-3872	68	14	,	,	PUNCT
ejpam-3872	68	15	19	19	NUM
ejpam-3872	68	16	-	-	SYM
ejpam-3872	68	17	42	42	NUM
ejpam-3872	68	18	22	22	NUM
ejpam-3872	68	19	f	f	PROPN
ejpam-3872	68	20	∈	∈	PROPN
ejpam-3872	68	21	d(g0	d(g0	NOUN
ejpam-3872	68	22	)	)	PUNCT
ejpam-3872	68	23	⇔	⇔	PROPN
ejpam-3872	68	24	(	(	PUNCT
ejpam-3872	68	25	g	g	PROPN
ejpam-3872	68	26	∈	∈	PROPN
ejpam-3872	68	27	d(g0	d(g0	NOUN
ejpam-3872	68	28	)	)	PUNCT
ejpam-3872	68	29	and	and	CCONJ
ejpam-3872	68	30	r(x	r(x	PROPN
ejpam-3872	68	31	,	,	PUNCT
ejpam-3872	68	32	g)→	g)→	NOUN
ejpam-3872	68	33	0	0	NUM
ejpam-3872	68	34	as	as	ADP
ejpam-3872	68	35	x→	x→	PROPN
ejpam-3872	68	36	uep(g	uep(g	PROPN
ejpam-3872	68	37	)	)	PUNCT
ejpam-3872	68	38	)	)	PUNCT
ejpam-3872	68	39	.	.	PUNCT
ejpam-3872	69	1	(	(	PUNCT
ejpam-3872	69	2	3	3	X
ejpam-3872	69	3	)	)	PUNCT
ejpam-3872	69	4	if	if	SCONJ
ejpam-3872	69	5	γ	γ	X
ejpam-3872	69	6	<	<	X
ejpam-3872	69	7	0	0	PROPN
ejpam-3872	69	8	,	,	PUNCT
ejpam-3872	69	9	f	f	PROPN
ejpam-3872	69	10	∈	∈	PROPN
ejpam-3872	69	11	d(gγ	d(gγ	PROPN
ejpam-3872	69	12	)	)	PUNCT
ejpam-3872	69	13	⇔	⇔	NOUN
ejpam-3872	69	14	(	(	PUNCT
ejpam-3872	69	15	g	g	PROPN
ejpam-3872	69	16	∈	∈	PROPN
ejpam-3872	69	17	d(gγ	d(gγ	PROPN
ejpam-3872	69	18	)	)	PUNCT
ejpam-3872	69	19	)	)	PUNCT
ejpam-3872	69	20	.	.	PUNCT
ejpam-3872	70	1	in	in	ADP
ejpam-3872	70	2	the	the	DET
ejpam-3872	70	3	second	second	ADJ
ejpam-3872	70	4	place	place	NOUN
ejpam-3872	70	5	,	,	PUNCT
ejpam-3872	70	6	we	we	PRON
ejpam-3872	70	7	recall	recall	VERB
ejpam-3872	70	8	the	the	DET
ejpam-3872	70	9	following	follow	VERB
ejpam-3872	70	10	representations	representation	NOUN
ejpam-3872	70	11	of	of	ADP
ejpam-3872	70	12	cdf	cdf	PROPN
ejpam-3872	70	13	’s	’s	X
ejpam-3872	70	14	in	in	ADP
ejpam-3872	70	15	the	the	DET
ejpam-3872	70	16	extreme	extreme	ADJ
ejpam-3872	70	17	value	value	NOUN
ejpam-3872	70	18	domain	domain	NOUN
ejpam-3872	70	19	that	that	PRON
ejpam-3872	70	20	repeatedly	repeatedly	ADV
ejpam-3872	70	21	will	will	AUX
ejpam-3872	70	22	be	be	AUX
ejpam-3872	70	23	used	use	VERB
ejpam-3872	70	24	in	in	ADP
ejpam-3872	70	25	the	the	DET
ejpam-3872	70	26	sequel	sequel	NOUN
ejpam-3872	70	27	.	.	PUNCT
ejpam-3872	71	1	proposition	proposition	NOUN
ejpam-3872	71	2	2	2	NUM
ejpam-3872	71	3	.	.	PUNCT
ejpam-3872	72	1	(	(	PUNCT
ejpam-3872	72	2	[	[	X
ejpam-3872	72	3	3	3	X
ejpam-3872	72	4	]	]	PUNCT
ejpam-3872	72	5	and	and	CCONJ
ejpam-3872	72	6	[	[	X
ejpam-3872	72	7	1	1	NUM
ejpam-3872	72	8	]	]	PUNCT
ejpam-3872	72	9	)	)	PUNCT
ejpam-3872	72	10	we	we	PRON
ejpam-3872	72	11	have	have	VERB
ejpam-3872	72	12	the	the	DET
ejpam-3872	72	13	following	follow	VERB
ejpam-3872	72	14	characterizations	characterization	NOUN
ejpam-3872	72	15	for	for	ADP
ejpam-3872	72	16	the	the	DET
ejpam-3872	72	17	three	three	NUM
ejpam-3872	72	18	extremal	extremal	ADJ
ejpam-3872	72	19	domains	domain	NOUN
ejpam-3872	72	20	.	.	PUNCT
ejpam-3872	73	1	(	(	PUNCT
ejpam-3872	73	2	a	a	X
ejpam-3872	73	3	)	)	PUNCT
ejpam-3872	73	4	f	f	PROPN
ejpam-3872	73	5	∈	∈	PROPN
ejpam-3872	73	6	d(hγ	d(hγ	PROPN
ejpam-3872	73	7	)	)	PUNCT
ejpam-3872	73	8	,	,	PUNCT
ejpam-3872	73	9	γ	γ	X
ejpam-3872	73	10	>	>	X
ejpam-3872	73	11	0	0	NUM
ejpam-3872	73	12	,	,	PUNCT
ejpam-3872	73	13	if	if	SCONJ
ejpam-3872	73	14	and	and	CCONJ
ejpam-3872	73	15	only	only	ADV
ejpam-3872	73	16	if	if	SCONJ
ejpam-3872	73	17	there	there	PRON
ejpam-3872	73	18	exist	exist	VERB
ejpam-3872	73	19	a	a	DET
ejpam-3872	73	20	constant	constant	ADJ
ejpam-3872	73	21	c	c	NOUN
ejpam-3872	73	22	and	and	CCONJ
ejpam-3872	73	23	functions	function	NOUN
ejpam-3872	73	24	a(u	a(u	NOUN
ejpam-3872	73	25	)	)	PUNCT
ejpam-3872	73	26	and	and	CCONJ
ejpam-3872	73	27	`	`	PUNCT
ejpam-3872	73	28	(	(	PUNCT
ejpam-3872	73	29	u	u	NOUN
ejpam-3872	73	30	)	)	PUNCT
ejpam-3872	73	31	of	of	ADP
ejpam-3872	73	32	u→	u→	PROPN
ejpam-3872	73	33	u	u	NOUN
ejpam-3872	73	34	∈]0	∈]0	ADJ
ejpam-3872	73	35	,	,	PUNCT
ejpam-3872	73	36	1	1	X
ejpam-3872	73	37	]	]	X
ejpam-3872	73	38	satisfying	satisfying	NOUN
ejpam-3872	73	39	(	(	PUNCT
ejpam-3872	73	40	a(u	a(u	PROPN
ejpam-3872	73	41	)	)	PUNCT
ejpam-3872	73	42	,	,	PUNCT
ejpam-3872	73	43	`	`	PUNCT
ejpam-3872	73	44	(	(	PUNCT
ejpam-3872	73	45	u))→	u))→	INTJ
ejpam-3872	73	46	(	(	PUNCT
ejpam-3872	73	47	0	0	NUM
ejpam-3872	73	48	,	,	PUNCT
ejpam-3872	73	49	0	0	NUM
ejpam-3872	73	50	)	)	PUNCT
ejpam-3872	73	51	as	as	ADP
ejpam-3872	73	52	u→	u→	PROPN
ejpam-3872	73	53	0	0	NUM
ejpam-3872	73	54	,	,	PUNCT
ejpam-3872	73	55	such	such	ADJ
ejpam-3872	73	56	that	that	SCONJ
ejpam-3872	73	57	f−1	f−1	PROPN
ejpam-3872	73	58	admits	admit	VERB
ejpam-3872	73	59	the	the	DET
ejpam-3872	73	60	following	following	ADJ
ejpam-3872	73	61	representation	representation	NOUN
ejpam-3872	73	62	of	of	ADP
ejpam-3872	73	63	karamata	karamata	ADJ
ejpam-3872	73	64	f−1(1−	f−1(1−	PROPN
ejpam-3872	73	65	u	u	PROPN
ejpam-3872	73	66	)	)	PUNCT
ejpam-3872	73	67	=	=	PUNCT
ejpam-3872	73	68	c(1	c(1	PROPN
ejpam-3872	73	69	+	+	CCONJ
ejpam-3872	73	70	a(u))u−γ	a(u))u−γ	NOUN
ejpam-3872	73	71	exp	exp	NOUN
ejpam-3872	73	72	(	(	PUNCT
ejpam-3872	73	73	∫	∫	PROPN
ejpam-3872	73	74	1	1	NUM
ejpam-3872	73	75	u	u	PROPN
ejpam-3872	73	76	`	`	PUNCT
ejpam-3872	73	77	(	(	PUNCT
ejpam-3872	73	78	t	t	PROPN
ejpam-3872	73	79	)	)	PUNCT
ejpam-3872	73	80	t	t	NOUN
ejpam-3872	73	81	dt	dt	NOUN
ejpam-3872	73	82	)	)	PUNCT
ejpam-3872	73	83	.	.	PUNCT
ejpam-3872	74	1	(	(	PUNCT
ejpam-3872	74	2	4	4	NUM
ejpam-3872	74	3	)	)	PUNCT
ejpam-3872	74	4	(	(	PUNCT
ejpam-3872	74	5	b	b	X
ejpam-3872	74	6	)	)	PUNCT
ejpam-3872	74	7	f	f	PROPN
ejpam-3872	74	8	∈	∈	PROPN
ejpam-3872	74	9	d(hγ	d(hγ	PROPN
ejpam-3872	74	10	)	)	PUNCT
ejpam-3872	74	11	,	,	PUNCT
ejpam-3872	74	12	γ	γ	X
ejpam-3872	74	13	<	<	X
ejpam-3872	74	14	0	0	NUM
ejpam-3872	74	15	,	,	PUNCT
ejpam-3872	74	16	if	if	SCONJ
ejpam-3872	74	17	and	and	CCONJ
ejpam-3872	74	18	only	only	ADV
ejpam-3872	74	19	if	if	SCONJ
ejpam-3872	74	20	uep(f	uep(f	PROPN
ejpam-3872	74	21	)	)	PUNCT
ejpam-3872	75	1	<	<	X
ejpam-3872	76	1	+	+	X
ejpam-3872	76	2	∞	∞	PROPN
ejpam-3872	76	3	and	and	CCONJ
ejpam-3872	76	4	there	there	PRON
ejpam-3872	76	5	exist	exist	VERB
ejpam-3872	76	6	a	a	DET
ejpam-3872	76	7	constant	constant	ADJ
ejpam-3872	76	8	c	c	NOUN
ejpam-3872	76	9	and	and	CCONJ
ejpam-3872	76	10	functions	function	NOUN
ejpam-3872	76	11	a(u	a(u	NOUN
ejpam-3872	76	12	)	)	PUNCT
ejpam-3872	76	13	and	and	CCONJ
ejpam-3872	76	14	`	`	PUNCT
ejpam-3872	76	15	(	(	PUNCT
ejpam-3872	76	16	u	u	NOUN
ejpam-3872	76	17	)	)	PUNCT
ejpam-3872	76	18	of	of	ADP
ejpam-3872	76	19	u	u	PRON
ejpam-3872	76	20	∈]0	∈]0	X
ejpam-3872	76	21	,	,	PUNCT
ejpam-3872	76	22	1	1	X
ejpam-3872	76	23	]	]	X
ejpam-3872	76	24	satisfying	satisfying	NOUN
ejpam-3872	76	25	(	(	PUNCT
ejpam-3872	76	26	a(u	a(u	PROPN
ejpam-3872	76	27	)	)	PUNCT
ejpam-3872	76	28	,	,	PUNCT
ejpam-3872	76	29	`	`	PUNCT
ejpam-3872	76	30	(	(	PUNCT
ejpam-3872	76	31	u))→	u))→	INTJ
ejpam-3872	76	32	(	(	PUNCT
ejpam-3872	76	33	0	0	NUM
ejpam-3872	76	34	,	,	PUNCT
ejpam-3872	76	35	0	0	NUM
ejpam-3872	76	36	)	)	PUNCT
ejpam-3872	76	37	as	as	ADP
ejpam-3872	76	38	u→	u→	PROPN
ejpam-3872	76	39	0	0	NUM
ejpam-3872	76	40	,	,	PUNCT
ejpam-3872	76	41	such	such	ADJ
ejpam-3872	76	42	that	that	SCONJ
ejpam-3872	76	43	f−1	f−1	PROPN
ejpam-3872	76	44	admit	admit	VERB
ejpam-3872	76	45	the	the	DET
ejpam-3872	76	46	following	follow	VERB
ejpam-3872	76	47	representation	representation	NOUN
ejpam-3872	76	48	of	of	ADP
ejpam-3872	76	49	karamata	karamata	NOUN
ejpam-3872	76	50	uep(f	uep(f	PROPN
ejpam-3872	76	51	)	)	PUNCT
ejpam-3872	76	52	−	−	PROPN
ejpam-3872	76	53	f−1(1−	f−1(1−	PROPN
ejpam-3872	76	54	u	u	PROPN
ejpam-3872	76	55	)	)	PUNCT
ejpam-3872	76	56	=	=	PUNCT
ejpam-3872	76	57	c(1	c(1	PROPN
ejpam-3872	76	58	+	+	CCONJ
ejpam-3872	76	59	a(u))u−γ	a(u))u−γ	NOUN
ejpam-3872	76	60	exp	exp	NOUN
ejpam-3872	76	61	(	(	PUNCT
ejpam-3872	76	62	∫	∫	PROPN
ejpam-3872	76	63	1	1	NUM
ejpam-3872	76	64	u	u	PROPN
ejpam-3872	76	65	`	`	PUNCT
ejpam-3872	76	66	(	(	PUNCT
ejpam-3872	76	67	t	t	PROPN
ejpam-3872	76	68	)	)	PUNCT
ejpam-3872	76	69	t	t	NOUN
ejpam-3872	76	70	dt	dt	NOUN
ejpam-3872	76	71	)	)	PUNCT
ejpam-3872	76	72	.	.	PUNCT
ejpam-3872	77	1	(	(	PUNCT
ejpam-3872	77	2	5	5	NUM
ejpam-3872	77	3	)	)	PUNCT
ejpam-3872	77	4	(	(	PUNCT
ejpam-3872	77	5	c	c	X
ejpam-3872	77	6	)	)	PUNCT
ejpam-3872	77	7	f	f	PROPN
ejpam-3872	77	8	∈	∈	PROPN
ejpam-3872	77	9	d(h0	d(h0	NOUN
ejpam-3872	77	10	)	)	PUNCT
ejpam-3872	77	11	if	if	SCONJ
ejpam-3872	77	12	and	and	CCONJ
ejpam-3872	77	13	only	only	ADV
ejpam-3872	77	14	if	if	SCONJ
ejpam-3872	77	15	there	there	PRON
ejpam-3872	77	16	exist	exist	VERB
ejpam-3872	77	17	a	a	DET
ejpam-3872	77	18	constant	constant	ADJ
ejpam-3872	77	19	d	d	NOUN
ejpam-3872	77	20	and	and	CCONJ
ejpam-3872	77	21	a	a	DET
ejpam-3872	77	22	slowly	slowly	ADV
ejpam-3872	77	23	varying	vary	VERB
ejpam-3872	77	24	function	function	NOUN
ejpam-3872	77	25	s(u	s(u	PROPN
ejpam-3872	77	26	)	)	PUNCT
ejpam-3872	77	27	such	such	ADJ
ejpam-3872	77	28	that	that	SCONJ
ejpam-3872	77	29	f−1(1−	f−1(1−	PROPN
ejpam-3872	77	30	u	u	NOUN
ejpam-3872	77	31	)	)	PUNCT
ejpam-3872	77	32	=	=	SYM
ejpam-3872	77	33	d+	d+	NOUN
ejpam-3872	77	34	s(u	s(u	PROPN
ejpam-3872	77	35	)	)	PUNCT
ejpam-3872	77	36	+	+	CCONJ
ejpam-3872	77	37	∫	∫	PROPN
ejpam-3872	77	38	1	1	NUM
ejpam-3872	77	39	u	u	NOUN
ejpam-3872	77	40	s(t	s(t	PROPN
ejpam-3872	77	41	)	)	PUNCT
ejpam-3872	77	42	t	t	NOUN
ejpam-3872	77	43	dt	dt	PROPN
ejpam-3872	77	44	,	,	PUNCT
ejpam-3872	77	45	0	0	PUNCT
ejpam-3872	77	46	<	<	X
ejpam-3872	77	47	u	u	X
ejpam-3872	77	48	<	<	X
ejpam-3872	77	49	1	1	NUM
ejpam-3872	77	50	,	,	PUNCT
ejpam-3872	77	51	(	(	PUNCT
ejpam-3872	77	52	6	6	NUM
ejpam-3872	77	53	)	)	PUNCT
ejpam-3872	77	54	and	and	CCONJ
ejpam-3872	77	55	there	there	PRON
ejpam-3872	77	56	exist	exist	VERB
ejpam-3872	77	57	a	a	DET
ejpam-3872	77	58	constant	constant	ADJ
ejpam-3872	77	59	c	c	NOUN
ejpam-3872	77	60	and	and	CCONJ
ejpam-3872	77	61	functions	function	NOUN
ejpam-3872	77	62	a(u	a(u	NOUN
ejpam-3872	77	63	)	)	PUNCT
ejpam-3872	77	64	and	and	CCONJ
ejpam-3872	77	65	`	`	PUNCT
ejpam-3872	77	66	(	(	PUNCT
ejpam-3872	77	67	u	u	NOUN
ejpam-3872	77	68	)	)	PUNCT
ejpam-3872	77	69	of	of	ADP
ejpam-3872	77	70	u	u	PRON
ejpam-3872	77	71	∈]0	∈]0	X
ejpam-3872	77	72	,	,	PUNCT
ejpam-3872	77	73	1	1	X
ejpam-3872	77	74	]	]	X
ejpam-3872	77	75	satisfying	satisfying	NOUN
ejpam-3872	77	76	(	(	PUNCT
ejpam-3872	77	77	a(u	a(u	PROPN
ejpam-3872	77	78	)	)	PUNCT
ejpam-3872	77	79	,	,	PUNCT
ejpam-3872	77	80	`	`	PUNCT
ejpam-3872	77	81	(	(	PUNCT
ejpam-3872	77	82	u))→	u))→	INTJ
ejpam-3872	77	83	(	(	PUNCT
ejpam-3872	77	84	0	0	NUM
ejpam-3872	77	85	,	,	PUNCT
ejpam-3872	77	86	0	0	NUM
ejpam-3872	77	87	)	)	PUNCT
ejpam-3872	77	88	as	as	ADP
ejpam-3872	77	89	u→	u→	PROPN
ejpam-3872	77	90	0	0	NUM
ejpam-3872	77	91	,	,	PUNCT
ejpam-3872	78	1	g.	g.	PROPN
ejpam-3872	78	2	s.	s.	PROPN
ejpam-3872	78	3	lo	lo	PROPN
ejpam-3872	78	4	et	et	PROPN
ejpam-3872	78	5	al	al	PROPN
ejpam-3872	78	6	.	.	PUNCT
ejpam-3872	78	7	/	/	SYM
ejpam-3872	78	8	eur	eur	PROPN
ejpam-3872	78	9	.	.	PUNCT
ejpam-3872	79	1	j.	j.	PROPN
ejpam-3872	79	2	pure	pure	PROPN
ejpam-3872	79	3	appl	appl	PROPN
ejpam-3872	79	4	.	.	PROPN
ejpam-3872	79	5	math	math	PROPN
ejpam-3872	79	6	,	,	PUNCT
ejpam-3872	79	7	14	14	NUM
ejpam-3872	79	8	(	(	PUNCT
ejpam-3872	79	9	1	1	NUM
ejpam-3872	79	10	)	)	PUNCT
ejpam-3872	79	11	(	(	PUNCT
ejpam-3872	79	12	2021	2021	NUM
ejpam-3872	79	13	)	)	PUNCT
ejpam-3872	79	14	,	,	PUNCT
ejpam-3872	79	15	19	19	NUM
ejpam-3872	79	16	-	-	SYM
ejpam-3872	79	17	42	42	NUM
ejpam-3872	79	18	23	23	NUM
ejpam-3872	79	19	such	such	ADJ
ejpam-3872	79	20	that	that	SCONJ
ejpam-3872	79	21	the	the	DET
ejpam-3872	79	22	function	function	NOUN
ejpam-3872	79	23	s(u	s(u	PROPN
ejpam-3872	79	24	)	)	PUNCT
ejpam-3872	79	25	of	of	ADP
ejpam-3872	79	26	u	u	PRON
ejpam-3872	79	27	∈]0	∈]0	X
ejpam-3872	79	28	,	,	PUNCT
ejpam-3872	79	29	1	1	NUM
ejpam-3872	79	30	[	[	PUNCT
ejpam-3872	79	31	admits	admit	VERB
ejpam-3872	79	32	the	the	DET
ejpam-3872	79	33	representation	representation	NOUN
ejpam-3872	79	34	s(u	s(u	PROPN
ejpam-3872	79	35	)	)	PUNCT
ejpam-3872	79	36	=	=	PUNCT
ejpam-3872	79	37	c(1	c(1	PROPN
ejpam-3872	79	38	+	+	CCONJ
ejpam-3872	79	39	a(u	a(u	PROPN
ejpam-3872	79	40	)	)	PUNCT
ejpam-3872	79	41	)	)	PUNCT
ejpam-3872	79	42	exp	exp	NOUN
ejpam-3872	79	43	(	(	PUNCT
ejpam-3872	79	44	∫	∫	PROPN
ejpam-3872	79	45	1	1	NUM
ejpam-3872	79	46	u	u	PROPN
ejpam-3872	79	47	`	`	PUNCT
ejpam-3872	79	48	(	(	PUNCT
ejpam-3872	79	49	t	t	PROPN
ejpam-3872	79	50	)	)	PUNCT
ejpam-3872	79	51	t	t	NOUN
ejpam-3872	79	52	dt	dt	NOUN
ejpam-3872	79	53	)	)	PUNCT
ejpam-3872	79	54	.	.	PUNCT
ejpam-3872	80	1	(	(	PUNCT
ejpam-3872	80	2	7	7	X
ejpam-3872	80	3	)	)	PUNCT
ejpam-3872	80	4	moreover	moreover	ADV
ejpam-3872	80	5	,	,	PUNCT
ejpam-3872	80	6	if	if	SCONJ
ejpam-3872	80	7	f−1(1−	f−1(1−	PROPN
ejpam-3872	80	8	u	u	NOUN
ejpam-3872	80	9	)	)	PUNCT
ejpam-3872	80	10	is	be	AUX
ejpam-3872	80	11	differentiable	differentiable	ADJ
ejpam-3872	80	12	for	for	ADP
ejpam-3872	80	13	small	small	ADJ
ejpam-3872	80	14	values	value	NOUN
ejpam-3872	80	15	of	of	ADP
ejpam-3872	80	16	u	u	PRON
ejpam-3872	80	17	such	such	ADJ
ejpam-3872	80	18	that	that	SCONJ
ejpam-3872	80	19	r(u	r(u	PROPN
ejpam-3872	80	20	)	)	PUNCT
ejpam-3872	80	21	=	=	PUNCT
ejpam-3872	80	22	−u(f−1(1−	−u(f−1(1−	NOUN
ejpam-3872	80	23	u))′	u))′	PUNCT
ejpam-3872	80	24	=	=	SYM
ejpam-3872	80	25	u	u	NOUN
ejpam-3872	80	26	df−1(1−	df−1(1−	PROPN
ejpam-3872	80	27	u)/du	u)/du	PROPN
ejpam-3872	80	28	is	be	AUX
ejpam-3872	80	29	slowly	slowly	ADV
ejpam-3872	80	30	varying	vary	VERB
ejpam-3872	80	31	at	at	ADP
ejpam-3872	80	32	zero	zero	NUM
ejpam-3872	80	33	,	,	PUNCT
ejpam-3872	80	34	then	then	ADV
ejpam-3872	80	35	(	(	PUNCT
ejpam-3872	80	36	6	6	NUM
ejpam-3872	80	37	)	)	PUNCT
ejpam-3872	80	38	may	may	AUX
ejpam-3872	80	39	be	be	AUX
ejpam-3872	80	40	replaced	replace	VERB
ejpam-3872	80	41	by	by	ADP
ejpam-3872	80	42	f−1(1−	f−1(1−	PROPN
ejpam-3872	80	43	u	u	PROPN
ejpam-3872	80	44	)	)	PUNCT
ejpam-3872	80	45	=	=	PUNCT
ejpam-3872	81	1	d+	d+	PUNCT
ejpam-3872	81	2	∫	∫	PROPN
ejpam-3872	81	3	u0	u0	PROPN
ejpam-3872	81	4	u	u	PROPN
ejpam-3872	81	5	r(t	r(t	PROPN
ejpam-3872	81	6	)	)	PUNCT
ejpam-3872	81	7	t	t	PROPN
ejpam-3872	81	8	dt	dt	PROPN
ejpam-3872	81	9	,	,	PUNCT
ejpam-3872	81	10	0	0	PUNCT
ejpam-3872	81	11	<	<	X
ejpam-3872	81	12	u	u	X
ejpam-3872	81	13	<	<	X
ejpam-3872	81	14	u0	u0	X
ejpam-3872	81	15	<	<	X
ejpam-3872	81	16	1	1	NUM
ejpam-3872	81	17	,	,	PUNCT
ejpam-3872	81	18	(	(	PUNCT
ejpam-3872	81	19	8)	8)	NUM
ejpam-3872	81	20	which	which	PRON
ejpam-3872	81	21	will	will	AUX
ejpam-3872	81	22	be	be	AUX
ejpam-3872	81	23	called	call	VERB
ejpam-3872	81	24	a	a	DET
ejpam-3872	81	25	reduced	reduce	VERB
ejpam-3872	81	26	de	de	PROPN
ejpam-3872	81	27	haan	haan	PROPN
ejpam-3872	81	28	representation	representation	NOUN
ejpam-3872	81	29	of	of	ADP
ejpam-3872	81	30	f−1	f−1	PROPN
ejpam-3872	81	31	.	.	PUNCT
ejpam-3872	82	1	the	the	DET
ejpam-3872	82	2	rest	rest	NOUN
ejpam-3872	82	3	of	of	ADP
ejpam-3872	82	4	the	the	DET
ejpam-3872	82	5	paper	paper	NOUN
ejpam-3872	82	6	is	be	AUX
ejpam-3872	82	7	organized	organize	VERB
ejpam-3872	82	8	as	as	SCONJ
ejpam-3872	82	9	follows	follow	VERB
ejpam-3872	82	10	.	.	PUNCT
ejpam-3872	83	1	the	the	DET
ejpam-3872	83	2	results	result	NOUN
ejpam-3872	83	3	are	be	AUX
ejpam-3872	83	4	stated	state	VERB
ejpam-3872	83	5	in	in	ADP
ejpam-3872	83	6	section	section	NOUN
ejpam-3872	83	7	2	2	NUM
ejpam-3872	83	8	.	.	PUNCT
ejpam-3872	84	1	examples	example	NOUN
ejpam-3872	84	2	and	and	CCONJ
ejpam-3872	84	3	applications	application	NOUN
ejpam-3872	84	4	are	be	AUX
ejpam-3872	84	5	given	give	VERB
ejpam-3872	84	6	in	in	ADP
ejpam-3872	84	7	section	section	NOUN
ejpam-3872	84	8	3	3	NUM
ejpam-3872	84	9	.	.	PUNCT
ejpam-3872	85	1	the	the	DET
ejpam-3872	85	2	proofs	proof	NOUN
ejpam-3872	85	3	are	be	AUX
ejpam-3872	85	4	stated	state	VERB
ejpam-3872	85	5	in	in	ADP
ejpam-3872	85	6	section	section	NOUN
ejpam-3872	85	7	4	4	NUM
ejpam-3872	85	8	.	.	PUNCT
ejpam-3872	86	1	the	the	DET
ejpam-3872	86	2	computations	computation	NOUN
ejpam-3872	86	3	related	relate	VERB
ejpam-3872	86	4	to	to	ADP
ejpam-3872	86	5	examples	example	NOUN
ejpam-3872	86	6	in	in	ADP
ejpam-3872	86	7	section	section	NOUN
ejpam-3872	86	8	3	3	NUM
ejpam-3872	86	9	are	be	AUX
ejpam-3872	86	10	detailed	detail	VERB
ejpam-3872	86	11	in	in	ADP
ejpam-3872	86	12	the	the	DET
ejpam-3872	86	13	appendix	appendix	ADJ
ejpam-3872	86	14	section	section	NOUN
ejpam-3872	86	15	6	6	NUM
ejpam-3872	86	16	(	(	PUNCT
ejpam-3872	86	17	appendix	appendix	VERB
ejpam-3872	86	18	i	i	PRON
ejpam-3872	86	19	,	,	PUNCT
ejpam-3872	86	20	page	page	NOUN
ejpam-3872	86	21	37	37	NUM
ejpam-3872	86	22	)	)	PUNCT
ejpam-3872	86	23	.	.	PUNCT
ejpam-3872	87	1	the	the	DET
ejpam-3872	87	2	paper	paper	NOUN
ejpam-3872	87	3	is	be	AUX
ejpam-3872	87	4	closed	close	VERB
ejpam-3872	87	5	by	by	ADP
ejpam-3872	87	6	a	a	DET
ejpam-3872	87	7	conclusion	conclusion	NOUN
ejpam-3872	87	8	in	in	ADP
ejpam-3872	87	9	section	section	NOUN
ejpam-3872	87	10	5	5	NUM
ejpam-3872	87	11	.	.	NOUN
ejpam-3872	88	1	2	2	NUM
ejpam-3872	88	2	.	.	NOUN
ejpam-3872	88	3	results	result	NOUN
ejpam-3872	88	4	before	before	ADP
ejpam-3872	88	5	stating	state	VERB
ejpam-3872	88	6	our	our	PRON
ejpam-3872	88	7	results	result	NOUN
ejpam-3872	89	1	,	,	PUNCT
ejpam-3872	89	2	we	we	PRON
ejpam-3872	89	3	recall	recall	VERB
ejpam-3872	89	4	that	that	SCONJ
ejpam-3872	89	5	any	any	DET
ejpam-3872	89	6	f	f	PROPN
ejpam-3872	89	7	∈	∈	PROPN
ejpam-3872	89	8	d	d	NOUN
ejpam-3872	89	9	is	be	AUX
ejpam-3872	89	10	associated	associate	VERB
ejpam-3872	89	11	to	to	ADP
ejpam-3872	89	12	a	a	DET
ejpam-3872	89	13	pair	pair	NOUN
ejpam-3872	89	14	of	of	ADP
ejpam-3872	89	15	functions	function	NOUN
ejpam-3872	89	16	(	(	PUNCT
ejpam-3872	89	17	a(u	a(u	PROPN
ejpam-3872	89	18	)	)	PUNCT
ejpam-3872	89	19	,	,	PUNCT
ejpam-3872	89	20	b(u	b(u	PROPN
ejpam-3872	89	21	)	)	PUNCT
ejpam-3872	89	22	)	)	PUNCT
ejpam-3872	89	23	of	of	ADP
ejpam-3872	89	24	u	u	PROPN
ejpam-3872	89	25	∈	∈	PROPN
ejpam-3872	90	1	[	[	X
ejpam-3872	90	2	0	0	NUM
ejpam-3872	90	3	,	,	PUNCT
ejpam-3872	90	4	1	1	NUM
ejpam-3872	90	5	]	]	PUNCT
ejpam-3872	90	6	as	as	SCONJ
ejpam-3872	90	7	defined	define	VERB
ejpam-3872	90	8	in	in	ADP
ejpam-3872	90	9	the	the	DET
ejpam-3872	90	10	representations	representation	NOUN
ejpam-3872	90	11	of	of	ADP
ejpam-3872	90	12	proposition	proposition	NOUN
ejpam-3872	90	13	2	2	NUM
ejpam-3872	90	14	for	for	ADP
ejpam-3872	90	15	f	f	PROPN
ejpam-3872	90	16	∈	∈	PROPN
ejpam-3872	90	17	d(gγ	d(gγ	PROPN
ejpam-3872	90	18	)	)	PUNCT
ejpam-3872	90	19	,	,	PUNCT
ejpam-3872	90	20	γ	γ	PROPN
ejpam-3872	90	21	6=	6=	PROPN
ejpam-3872	90	22	0	0	NUM
ejpam-3872	90	23	.	.	PUNCT
ejpam-3872	91	1	in	in	ADP
ejpam-3872	91	2	the	the	DET
ejpam-3872	91	3	special	special	ADJ
ejpam-3872	91	4	case	case	NOUN
ejpam-3872	91	5	where	where	SCONJ
ejpam-3872	91	6	γ	γ	X
ejpam-3872	91	7	=	=	SYM
ejpam-3872	91	8	0	0	PROPN
ejpam-3872	91	9	,	,	PUNCT
ejpam-3872	91	10	the	the	DET
ejpam-3872	91	11	pair	pair	NOUN
ejpam-3872	91	12	of	of	ADP
ejpam-3872	91	13	functions	function	NOUN
ejpam-3872	91	14	(	(	PUNCT
ejpam-3872	91	15	a	a	DET
ejpam-3872	91	16	(	(	PUNCT
ejpam-3872	91	17	◦	◦	NOUN
ejpam-3872	91	18	)	)	PUNCT
ejpam-3872	91	19	,	,	PUNCT
ejpam-3872	91	20	b	b	X
ejpam-3872	91	21	(	(	PUNCT
ejpam-3872	91	22	◦	◦	NOUN
ejpam-3872	91	23	)	)	PUNCT
ejpam-3872	91	24	)	)	PUNCT
ejpam-3872	91	25	is	be	AUX
ejpam-3872	91	26	used	use	VERB
ejpam-3872	91	27	in	in	ADP
ejpam-3872	91	28	the	the	DET
ejpam-3872	91	29	representation	representation	NOUN
ejpam-3872	91	30	of	of	ADP
ejpam-3872	91	31	the	the	DET
ejpam-3872	91	32	function	function	NOUN
ejpam-3872	91	33	s(u	s(u	PROPN
ejpam-3872	91	34	)	)	PUNCT
ejpam-3872	91	35	of	of	ADP
ejpam-3872	91	36	u	u	PROPN
ejpam-3872	91	37	∈	∈	PROPN
ejpam-3872	91	38	[	[	X
ejpam-3872	91	39	0	0	NUM
ejpam-3872	91	40	,	,	PUNCT
ejpam-3872	91	41	1	1	NUM
ejpam-3872	91	42	]	]	PUNCT
ejpam-3872	91	43	in	in	ADP
ejpam-3872	91	44	equation	equation	NOUN
ejpam-3872	91	45	(	(	PUNCT
ejpam-3872	91	46	6	6	NUM
ejpam-3872	91	47	)	)	PUNCT
ejpam-3872	91	48	.	.	PUNCT
ejpam-3872	92	1	we	we	PRON
ejpam-3872	92	2	will	will	AUX
ejpam-3872	92	3	need	need	VERB
ejpam-3872	92	4	the	the	DET
ejpam-3872	92	5	following	follow	VERB
ejpam-3872	92	6	condition	condition	NOUN
ejpam-3872	92	7	.	.	PUNCT
ejpam-3872	93	1	let	let	VERB
ejpam-3872	93	2	us	we	PRON
ejpam-3872	93	3	define	define	VERB
ejpam-3872	93	4	,	,	PUNCT
ejpam-3872	93	5	for	for	ADP
ejpam-3872	93	6	any	any	DET
ejpam-3872	93	7	n	n	PRON
ejpam-3872	93	8	≥	≥	NOUN
ejpam-3872	93	9	1	1	NUM
ejpam-3872	93	10	,	,	PUNCT
ejpam-3872	93	11	a	a	DET
ejpam-3872	93	12	finite	finite	ADJ
ejpam-3872	93	13	sum	sum	NOUN
ejpam-3872	93	14	of	of	ADP
ejpam-3872	93	15	n	n	CCONJ
ejpam-3872	93	16	standard	standard	ADJ
ejpam-3872	93	17	exponential	exponential	ADJ
ejpam-3872	93	18	random	random	ADJ
ejpam-3872	93	19	variables	variable	NOUN
ejpam-3872	93	20	s(n	s(n	PROPN
ejpam-3872	93	21	)	)	PUNCT
ejpam-3872	94	1	=	=	SYM
ejpam-3872	94	2	e1,n	e1,n	PROPN
ejpam-3872	94	3	+	+	CCONJ
ejpam-3872	94	4	·	·	PUNCT
ejpam-3872	94	5	·	·	PUNCT
ejpam-3872	94	6	·	·	PUNCT
ejpam-3872	94	7	+	+	X
ejpam-3872	94	8	en	en	X
ejpam-3872	94	9	,	,	PUNCT
ejpam-3872	94	10	n	n	CCONJ
ejpam-3872	94	11	,	,	PUNCT
ejpam-3872	94	12	and	and	CCONJ
ejpam-3872	94	13	denote	denote	VERB
ejpam-3872	94	14	vn	vn	PROPN
ejpam-3872	94	15	=	=	SYM
ejpam-3872	94	16	exp(−s(n	exp(−s(n	PROPN
ejpam-3872	94	17	)	)	PUNCT
ejpam-3872	94	18	)	)	PUNCT
ejpam-3872	94	19	and	and	CCONJ
ejpam-3872	94	20	vn	vn	X
ejpam-3872	94	21	=	=	SYM
ejpam-3872	94	22	exp(−n	exp(−n	PROPN
ejpam-3872	94	23	)	)	PUNCT
ejpam-3872	94	24	,	,	PUNCT
ejpam-3872	94	25	n	n	X
ejpam-3872	94	26	≥	≥	NOUN
ejpam-3872	94	27	1	1	NUM
ejpam-3872	94	28	and	and	CCONJ
ejpam-3872	94	29	finally	finally	ADV
ejpam-3872	94	30	set	set	VERB
ejpam-3872	94	31	the	the	DET
ejpam-3872	94	32	hypothesis	hypothesis	NOUN
ejpam-3872	94	33	(	(	PUNCT
ejpam-3872	94	34	ha	ha	INTJ
ejpam-3872	94	35	)	)	PUNCT
ejpam-3872	94	36	:	:	PUNCT
ejpam-3872	94	37	sup	sup	X
ejpam-3872	94	38	{	{	PUNCT
ejpam-3872	94	39	∣∣∣u	∣∣∣u	PROPN
ejpam-3872	94	40	v	v	NOUN
ejpam-3872	94	41	−	−	PROPN
ejpam-3872	94	42	1	1	NUM
ejpam-3872	94	43	∣∣∣	∣∣∣	NOUN
ejpam-3872	94	44	,	,	PUNCT
ejpam-3872	94	45	min(vn	min(vn	PROPN
ejpam-3872	94	46	,	,	PUNCT
ejpam-3872	94	47	vn	vn	NOUN
ejpam-3872	94	48	)	)	PUNCT
ejpam-3872	94	49	≤	≤	NOUN
ejpam-3872	94	50	u	u	NOUN
ejpam-3872	94	51	,	,	PUNCT
ejpam-3872	94	52	v	v	ADJ
ejpam-3872	94	53	≤	≤	NUM
ejpam-3872	94	54	max(vn	max(vn	NOUN
ejpam-3872	94	55	,	,	PUNCT
ejpam-3872	94	56	vn	vn	PROPN
ejpam-3872	94	57	)	)	PUNCT
ejpam-3872	94	58	}	}	PUNCT
ejpam-3872	94	59	→p	→p	PROPN
ejpam-3872	94	60	0	0	NUM
ejpam-3872	94	61	as	as	ADP
ejpam-3872	94	62	n→	n→	ADV
ejpam-3872	94	63	+	+	PROPN
ejpam-3872	94	64	∞	∞	PROPN
ejpam-3872	94	65	,	,	PUNCT
ejpam-3872	94	66	(	(	PUNCT
ejpam-3872	94	67	hb	hb	X
ejpam-3872	94	68	)	)	PUNCT
ejpam-3872	94	69	:	:	PUNCT
ejpam-3872	94	70	(	(	PUNCT
ejpam-3872	94	71	∃α	∃α	X
ejpam-3872	94	72	>	>	X
ejpam-3872	94	73	0	0	NUM
ejpam-3872	94	74	)	)	PUNCT
ejpam-3872	94	75	,	,	PUNCT
ejpam-3872	94	76	√	√	PROPN
ejpam-3872	94	77	n	n	PRON
ejpam-3872	94	78	s(vn)→	s(vn)→	NOUN
ejpam-3872	94	79	α	α	NOUN
ejpam-3872	94	80	as	as	ADP
ejpam-3872	94	81	n→	n→	ADV
ejpam-3872	94	82	+	+	PROPN
ejpam-3872	94	83	∞	∞	PROPN
ejpam-3872	94	84	,	,	PUNCT
ejpam-3872	94	85	g.	g.	PROPN
ejpam-3872	94	86	s.	s.	PROPN
ejpam-3872	95	1	lo	lo	PROPN
ejpam-3872	95	2	et	et	PROPN
ejpam-3872	95	3	al	al	PROPN
ejpam-3872	95	4	.	.	PUNCT
ejpam-3872	95	5	/	/	SYM
ejpam-3872	95	6	eur	eur	PROPN
ejpam-3872	95	7	.	.	PUNCT
ejpam-3872	96	1	j.	j.	PROPN
ejpam-3872	96	2	pure	pure	PROPN
ejpam-3872	96	3	appl	appl	PROPN
ejpam-3872	96	4	.	.	PROPN
ejpam-3872	96	5	math	math	PROPN
ejpam-3872	96	6	,	,	PUNCT
ejpam-3872	96	7	14	14	NUM
ejpam-3872	96	8	(	(	PUNCT
ejpam-3872	96	9	1	1	NUM
ejpam-3872	96	10	)	)	PUNCT
ejpam-3872	96	11	(	(	PUNCT
ejpam-3872	96	12	2021	2021	NUM
ejpam-3872	96	13	)	)	PUNCT
ejpam-3872	96	14	,	,	PUNCT
ejpam-3872	96	15	19	19	NUM
ejpam-3872	96	16	-	-	SYM
ejpam-3872	96	17	42	42	NUM
ejpam-3872	96	18	24	24	NUM
ejpam-3872	96	19	where	where	SCONJ
ejpam-3872	96	20	→p	→p	PROPN
ejpam-3872	96	21	stands	stand	VERB
ejpam-3872	96	22	for	for	ADP
ejpam-3872	96	23	the	the	DET
ejpam-3872	96	24	convergence	convergence	NOUN
ejpam-3872	96	25	in	in	ADP
ejpam-3872	96	26	probability	probability	NOUN
ejpam-3872	96	27	.	.	PUNCT
ejpam-3872	97	1	here	here	ADV
ejpam-3872	97	2	are	be	AUX
ejpam-3872	97	3	our	our	PRON
ejpam-3872	97	4	results	result	NOUN
ejpam-3872	97	5	that	that	PRON
ejpam-3872	97	6	cover	cover	VERB
ejpam-3872	97	7	the	the	DET
ejpam-3872	97	8	whole	whole	ADJ
ejpam-3872	97	9	extreme	extreme	ADJ
ejpam-3872	97	10	value	value	NOUN
ejpam-3872	97	11	domain	domain	NOUN
ejpam-3872	97	12	of	of	ADP
ejpam-3872	97	13	attraction	attraction	NOUN
ejpam-3872	97	14	.	.	PUNCT
ejpam-3872	98	1	for	for	ADP
ejpam-3872	98	2	γ	γ	PROPN
ejpam-3872	98	3	6=	6=	PROPN
ejpam-3872	98	4	0	0	NUM
ejpam-3872	98	5	,	,	PUNCT
ejpam-3872	98	6	we	we	PRON
ejpam-3872	98	7	need	need	VERB
ejpam-3872	98	8	any	any	DET
ejpam-3872	98	9	condition	condition	NOUN
ejpam-3872	98	10	.	.	PUNCT
ejpam-3872	99	1	let	let	VERB
ejpam-3872	99	2	us	we	PRON
ejpam-3872	99	3	begin	begin	VERB
ejpam-3872	99	4	by	by	ADP
ejpam-3872	99	5	asymptotic	asymptotic	ADJ
ejpam-3872	99	6	laws	law	NOUN
ejpam-3872	99	7	for	for	ADP
ejpam-3872	99	8	f	f	PROPN
ejpam-3872	99	9	∈	∈	PROPN
ejpam-3872	99	10	d.	d.	PROPN
ejpam-3872	99	11	theorem	theorem	VERB
ejpam-3872	99	12	1	1	X
ejpam-3872	99	13	.	.	PUNCT
ejpam-3872	100	1	let	let	VERB
ejpam-3872	100	2	f	f	PROPN
ejpam-3872	100	3	∈	∈	PROPN
ejpam-3872	100	4	d(gγ	d(gγ	PROPN
ejpam-3872	100	5	)	)	PUNCT
ejpam-3872	100	6	,	,	PUNCT
ejpam-3872	100	7	γ	γ	PROPN
ejpam-3872	100	8	∈	∈	PROPN
ejpam-3872	100	9	r.	r.	NOUN
ejpam-3872	100	10	we	we	PRON
ejpam-3872	100	11	have	have	VERB
ejpam-3872	100	12	:	:	PUNCT
ejpam-3872	100	13	(	(	PUNCT
ejpam-3872	100	14	a	a	X
ejpam-3872	100	15	)	)	PUNCT
ejpam-3872	100	16	if	if	SCONJ
ejpam-3872	100	17	γ	γ	X
ejpam-3872	100	18	>	>	X
ejpam-3872	100	19	0	0	PROPN
ejpam-3872	100	20	,	,	PUNCT
ejpam-3872	100	21	the	the	DET
ejpam-3872	100	22	asymptotic	asymptotic	ADJ
ejpam-3872	100	23	law	law	NOUN
ejpam-3872	100	24	of	of	ADP
ejpam-3872	100	25	x(n	x(n	NOUN
ejpam-3872	100	26	)	)	PUNCT
ejpam-3872	100	27	is	be	AUX
ejpam-3872	100	28	lognormal	lognormal	ADJ
ejpam-3872	100	29	,	,	PUNCT
ejpam-3872	100	30	precisely	precisely	ADV
ejpam-3872	100	31	(	(	PUNCT
ejpam-3872	100	32	x(n	x(n	NOUN
ejpam-3872	100	33	)	)	PUNCT
ejpam-3872	100	34	f−1	f−1	PROPN
ejpam-3872	100	35	(	(	PUNCT
ejpam-3872	100	36	1−	1−	NUM
ejpam-3872	100	37	e−n	e−n	PROPN
ejpam-3872	100	38	)	)	PUNCT
ejpam-3872	100	39	)	)	PUNCT
ejpam-3872	100	40	n−1/2	n−1/2	PROPN
ejpam-3872	100	41	ln(0	ln(0	PROPN
ejpam-3872	100	42	,	,	PUNCT
ejpam-3872	100	43	γ2	γ2	NOUN
ejpam-3872	100	44	)	)	PUNCT
ejpam-3872	100	45	,	,	PUNCT
ejpam-3872	100	46	where	where	SCONJ
ejpam-3872	100	47	ln(m	ln(m	NOUN
ejpam-3872	100	48	,	,	PUNCT
ejpam-3872	100	49	σ2	σ2	PROPN
ejpam-3872	100	50	)	)	PUNCT
ejpam-3872	100	51	is	be	AUX
ejpam-3872	100	52	the	the	DET
ejpam-3872	100	53	lognormal	lognormal	ADJ
ejpam-3872	100	54	law	law	NOUN
ejpam-3872	100	55	of	of	ADP
ejpam-3872	100	56	parameters	parameter	NOUN
ejpam-3872	100	57	m	m	VERB
ejpam-3872	100	58	and	and	CCONJ
ejpam-3872	100	59	σ	σ	NOUN
ejpam-3872	100	60	>	>	X
ejpam-3872	100	61	0	0	NUM
ejpam-3872	100	62	.	.	PUNCT
ejpam-3872	101	1	(	(	PUNCT
ejpam-3872	101	2	b	b	X
ejpam-3872	101	3	)	)	PUNCT
ejpam-3872	101	4	if	if	SCONJ
ejpam-3872	101	5	γ	γ	X
ejpam-3872	101	6	>	>	X
ejpam-3872	101	7	0	0	PUNCT
ejpam-3872	102	1	and	and	CCONJ
ejpam-3872	102	2	x	x	ADJ
ejpam-3872	102	3	≥	≥	NOUN
ejpam-3872	102	4	0	0	NUM
ejpam-3872	102	5	,	,	PUNCT
ejpam-3872	102	6	y	y	PROPN
ejpam-3872	102	7	=	=	PUNCT
ejpam-3872	102	8	logx	logx	PROPN
ejpam-3872	102	9	∈	∈	PROPN
ejpam-3872	102	10	d(g0	d(g0	NOUN
ejpam-3872	102	11	)	)	PUNCT
ejpam-3872	102	12	)	)	PUNCT
ejpam-3872	103	1	and	and	CCONJ
ejpam-3872	103	2	r(x	r(x	PROPN
ejpam-3872	103	3	,	,	PUNCT
ejpam-3872	103	4	g	g	NOUN
ejpam-3872	103	5	)	)	PUNCT
ejpam-3872	103	6	→	→	SYM
ejpam-3872	103	7	γ	γ	X
ejpam-3872	103	8	as	as	ADP
ejpam-3872	103	9	x	x	X
ejpam-3872	103	10	→	→	SYM
ejpam-3872	103	11	uep(g	uep(g	NOUN
ejpam-3872	103	12	)	)	PUNCT
ejpam-3872	103	13	and	and	CCONJ
ejpam-3872	103	14	we	we	PRON
ejpam-3872	103	15	have	have	VERB
ejpam-3872	103	16	y	y	PROPN
ejpam-3872	103	17	(	(	PUNCT
ejpam-3872	103	18	n	n	CCONJ
ejpam-3872	103	19	)	)	PUNCT
ejpam-3872	103	20	−g−1	−g−1	X
ejpam-3872	103	21	(	(	PUNCT
ejpam-3872	103	22	1−	1−	NUM
ejpam-3872	103	23	e−n)√	e−n)√	NOUN
ejpam-3872	103	24	n	n	CCONJ
ejpam-3872	103	25	n	n	PROPN
ejpam-3872	103	26	(	(	PUNCT
ejpam-3872	103	27	0	0	NUM
ejpam-3872	103	28	,	,	PUNCT
ejpam-3872	103	29	γ2	γ2	NOUN
ejpam-3872	103	30	)	)	PUNCT
ejpam-3872	103	31	.	.	PUNCT
ejpam-3872	104	1	(	(	PUNCT
ejpam-3872	104	2	c	c	X
ejpam-3872	104	3	)	)	PUNCT
ejpam-3872	104	4	if	if	SCONJ
ejpam-3872	104	5	γ	γ	X
ejpam-3872	104	6	<	<	X
ejpam-3872	104	7	0	0	NUM
ejpam-3872	104	8	,	,	PUNCT
ejpam-3872	104	9	the	the	DET
ejpam-3872	104	10	asymptotic	asymptotic	ADJ
ejpam-3872	104	11	law	law	NOUN
ejpam-3872	104	12	of	of	ADP
ejpam-3872	104	13	x(n	x(n	NOUN
ejpam-3872	104	14	)	)	PUNCT
ejpam-3872	104	15	is	be	AUX
ejpam-3872	104	16	lognormal	lognormal	ADJ
ejpam-3872	104	17	,	,	PUNCT
ejpam-3872	104	18	precisely	precisely	ADV
ejpam-3872	104	19	(	(	PUNCT
ejpam-3872	104	20	uep(f	uep(f	PROPN
ejpam-3872	104	21	)	)	PUNCT
ejpam-3872	104	22	−x(n	−x(n	PROPN
ejpam-3872	104	23	)	)	PUNCT
ejpam-3872	104	24	uep(f	uep(f	PROPN
ejpam-3872	104	25	)	)	PUNCT
ejpam-3872	105	1	−	−	PROPN
ejpam-3872	105	2	f−1	f−1	PROPN
ejpam-3872	105	3	(	(	PUNCT
ejpam-3872	105	4	1−	1−	NUM
ejpam-3872	105	5	e−n	e−n	PROPN
ejpam-3872	105	6	)	)	PUNCT
ejpam-3872	105	7	)	)	PUNCT
ejpam-3872	106	1	n−1/2	n−1/2	PROPN
ejpam-3872	106	2	exp(n	exp(n	PROPN
ejpam-3872	106	3	(	(	PUNCT
ejpam-3872	106	4	0	0	NUM
ejpam-3872	106	5	,	,	PUNCT
ejpam-3872	106	6	γ2	γ2	NOUN
ejpam-3872	106	7	)	)	PUNCT
ejpam-3872	106	8	)	)	PUNCT
ejpam-3872	106	9	.	.	PUNCT
ejpam-3872	107	1	(	(	PUNCT
ejpam-3872	107	2	d	d	X
ejpam-3872	107	3	)	)	PUNCT
ejpam-3872	107	4	suppose	suppose	VERB
ejpam-3872	107	5	that	that	SCONJ
ejpam-3872	107	6	γ	γ	PROPN
ejpam-3872	107	7	=	=	SYM
ejpam-3872	107	8	0	0	PROPN
ejpam-3872	107	9	and	and	CCONJ
ejpam-3872	107	10	r(x	r(x	PROPN
ejpam-3872	107	11	,	,	PUNCT
ejpam-3872	107	12	g)→	g)→	NOUN
ejpam-3872	107	13	0	0	NUM
ejpam-3872	107	14	as	as	ADP
ejpam-3872	107	15	x→	x→	PROPN
ejpam-3872	107	16	uep(g	uep(g	PROPN
ejpam-3872	107	17	)	)	PUNCT
ejpam-3872	107	18	.	.	PUNCT
ejpam-3872	108	1	if	if	SCONJ
ejpam-3872	108	2	(	(	PUNCT
ejpam-3872	108	3	ha	ha	INTJ
ejpam-3872	108	4	)	)	PUNCT
ejpam-3872	108	5	and	and	CCONJ
ejpam-3872	108	6	(	(	PUNCT
ejpam-3872	108	7	hb	hb	X
ejpam-3872	108	8	)	)	PUNCT
ejpam-3872	108	9	hold	hold	VERB
ejpam-3872	108	10	both	both	PRON
ejpam-3872	108	11	,	,	PUNCT
ejpam-3872	108	12	we	we	PRON
ejpam-3872	108	13	have	have	VERB
ejpam-3872	108	14	x(n	x(n	NOUN
ejpam-3872	108	15	)	)	PUNCT
ejpam-3872	109	1	−	−	PROPN
ejpam-3872	109	2	f−1	f−1	PROPN
ejpam-3872	109	3	(	(	PUNCT
ejpam-3872	109	4	1−	1−	NUM
ejpam-3872	109	5	e−n	e−n	PROPN
ejpam-3872	109	6	)	)	PUNCT
ejpam-3872	109	7	n	n	CCONJ
ejpam-3872	109	8	(	(	PUNCT
ejpam-3872	109	9	0	0	NUM
ejpam-3872	109	10	,	,	PUNCT
ejpam-3872	109	11	α2	α2	ADJ
ejpam-3872	109	12	)	)	PUNCT
ejpam-3872	109	13	.	.	PUNCT
ejpam-3872	110	1	more	more	ADV
ejpam-3872	110	2	precisely	precisely	ADV
ejpam-3872	110	3	,	,	PUNCT
ejpam-3872	110	4	we	we	PRON
ejpam-3872	110	5	have	have	AUX
ejpam-3872	110	6	:	:	PUNCT
ejpam-3872	110	7	given	give	VERB
ejpam-3872	110	8	γ	γ	PROPN
ejpam-3872	110	9	=	=	SYM
ejpam-3872	110	10	0	0	NUM
ejpam-3872	110	11	,	,	PUNCT
ejpam-3872	110	12	r(x	r(x	NOUN
ejpam-3872	110	13	,	,	PUNCT
ejpam-3872	110	14	g)→	g)→	NOUN
ejpam-3872	110	15	0	0	NUM
ejpam-3872	110	16	as	as	ADP
ejpam-3872	110	17	x→	x→	PROPN
ejpam-3872	110	18	uep(g	uep(g	PROPN
ejpam-3872	110	19	)	)	PUNCT
ejpam-3872	110	20	and	and	CCONJ
ejpam-3872	110	21	(	(	PUNCT
ejpam-3872	110	22	ha	ha	INTJ
ejpam-3872	110	23	)	)	PUNCT
ejpam-3872	110	24	,	,	PUNCT
ejpam-3872	110	25	the	the	DET
ejpam-3872	110	26	above	above	ADJ
ejpam-3872	110	27	asymptotic	asymptotic	ADJ
ejpam-3872	110	28	normality	normality	NOUN
ejpam-3872	110	29	is	be	AUX
ejpam-3872	110	30	valid	valid	ADJ
ejpam-3872	110	31	if	if	SCONJ
ejpam-3872	110	32	and	and	CCONJ
ejpam-3872	110	33	only	only	ADV
ejpam-3872	110	34	if	if	SCONJ
ejpam-3872	110	35	(	(	PUNCT
ejpam-3872	110	36	hb	hb	NOUN
ejpam-3872	110	37	)	)	PUNCT
ejpam-3872	110	38	holds	hold	VERB
ejpam-3872	110	39	.	.	PUNCT
ejpam-3872	111	1	beyond	beyond	ADP
ejpam-3872	111	2	distributions	distribution	NOUN
ejpam-3872	111	3	in	in	ADP
ejpam-3872	111	4	d	d	PROPN
ejpam-3872	111	5	,	,	PUNCT
ejpam-3872	111	6	we	we	PRON
ejpam-3872	111	7	may	may	AUX
ejpam-3872	111	8	use	use	VERB
ejpam-3872	111	9	the	the	DET
ejpam-3872	111	10	delta	delta	NOUN
ejpam-3872	111	11	-	-	PUNCT
ejpam-3872	111	12	method	method	NOUN
ejpam-3872	111	13	as	as	SCONJ
ejpam-3872	111	14	follows	follow	VERB
ejpam-3872	111	15	.	.	PUNCT
ejpam-3872	112	1	drawing	draw	VERB
ejpam-3872	112	2	lessons	lesson	NOUN
ejpam-3872	112	3	from	from	ADP
ejpam-3872	112	4	theorem	theorem	NOUN
ejpam-3872	112	5	1	1	NUM
ejpam-3872	112	6	,	,	PUNCT
ejpam-3872	112	7	we	we	PRON
ejpam-3872	112	8	might	might	AUX
ejpam-3872	112	9	be	be	AUX
ejpam-3872	112	10	tempted	tempt	VERB
ejpam-3872	112	11	to	to	PART
ejpam-3872	112	12	generalize	generalize	VERB
ejpam-3872	112	13	point	point	NOUN
ejpam-3872	112	14	(	(	PUNCT
ejpam-3872	112	15	a	a	NOUN
ejpam-3872	112	16	)	)	PUNCT
ejpam-3872	112	17	by	by	ADP
ejpam-3872	112	18	imposing	impose	VERB
ejpam-3872	112	19	that	that	SCONJ
ejpam-3872	112	20	f−1	f−1	PROPN
ejpam-3872	112	21	satisfies	satisfy	VERB
ejpam-3872	112	22	,	,	PUNCT
ejpam-3872	112	23	for	for	ADP
ejpam-3872	112	24	some	some	DET
ejpam-3872	112	25	coefficient	coefficient	NOUN
ejpam-3872	112	26	γ	γ	NOUN
ejpam-3872	112	27	,	,	PUNCT
ejpam-3872	112	28	∀λ	∀λ	X
ejpam-3872	112	29	>	>	X
ejpam-3872	112	30	0	0	NUM
ejpam-3872	112	31	,	,	PUNCT
ejpam-3872	112	32	f−1(1−	f−1(1−	PROPN
ejpam-3872	112	33	λu)/f−1(1−	λu)/f−1(1−	PROPN
ejpam-3872	112	34	u	u	PROPN
ejpam-3872	112	35	)	)	PUNCT
ejpam-3872	112	36	=	=	PUNCT
ejpam-3872	113	1	λγ(1	λγ(1	X
ejpam-3872	113	2	+	+	NUM
ejpam-3872	113	3	o(1	o(1	NOUN
ejpam-3872	113	4	)	)	PUNCT
ejpam-3872	113	5	)	)	PUNCT
ejpam-3872	113	6	,	,	PUNCT
ejpam-3872	113	7	u	u	NOUN
ejpam-3872	113	8	∈]0	∈]0	ADJ
ejpam-3872	113	9	,	,	PUNCT
ejpam-3872	113	10	1	1	NUM
ejpam-3872	113	11	[	[	NOUN
ejpam-3872	113	12	.	.	PUNCT
ejpam-3872	114	1	but	but	CCONJ
ejpam-3872	114	2	,	,	PUNCT
ejpam-3872	114	3	by	by	ADP
ejpam-3872	114	4	extreme	extreme	ADJ
ejpam-3872	114	5	value	value	NOUN
ejpam-3872	114	6	theory	theory	NOUN
ejpam-3872	114	7	,	,	PUNCT
ejpam-3872	114	8	this	this	PRON
ejpam-3872	114	9	would	would	AUX
ejpam-3872	114	10	imply	imply	VERB
ejpam-3872	114	11	that	that	SCONJ
ejpam-3872	114	12	f	f	PROPN
ejpam-3872	114	13	∈	∈	PROPN
ejpam-3872	114	14	d(gγ	d(gγ	PROPN
ejpam-3872	114	15	)	)	PUNCT
ejpam-3872	114	16	and	and	CCONJ
ejpam-3872	114	17	nothing	nothing	PRON
ejpam-3872	114	18	new	new	ADJ
ejpam-3872	114	19	would	would	AUX
ejpam-3872	114	20	happen	happen	VERB
ejpam-3872	114	21	.	.	PUNCT
ejpam-3872	115	1	but	but	CCONJ
ejpam-3872	115	2	trying	try	VERB
ejpam-3872	115	3	a	a	DET
ejpam-3872	115	4	generalization	generalization	NOUN
ejpam-3872	115	5	from	from	ADP
ejpam-3872	115	6	point	point	NOUN
ejpam-3872	115	7	(	(	PUNCT
ejpam-3872	115	8	c	c	NOUN
ejpam-3872	115	9	)	)	PUNCT
ejpam-3872	115	10	would	would	AUX
ejpam-3872	115	11	be	be	AUX
ejpam-3872	115	12	successful	successful	ADJ
ejpam-3872	115	13	.	.	PUNCT
ejpam-3872	116	1	let	let	VERB
ejpam-3872	116	2	us	we	PRON
ejpam-3872	116	3	define	define	VERB
ejpam-3872	116	4	the	the	DET
ejpam-3872	116	5	g.	g.	NOUN
ejpam-3872	116	6	s.	s.	PROPN
ejpam-3872	117	1	lo	lo	PROPN
ejpam-3872	117	2	et	et	PROPN
ejpam-3872	117	3	al	al	PROPN
ejpam-3872	117	4	.	.	PUNCT
ejpam-3872	117	5	/	/	SYM
ejpam-3872	117	6	eur	eur	PROPN
ejpam-3872	117	7	.	.	PUNCT
ejpam-3872	118	1	j.	j.	PROPN
ejpam-3872	118	2	pure	pure	PROPN
ejpam-3872	118	3	appl	appl	PROPN
ejpam-3872	118	4	.	.	PROPN
ejpam-3872	118	5	math	math	PROPN
ejpam-3872	118	6	,	,	PUNCT
ejpam-3872	118	7	14	14	NUM
ejpam-3872	118	8	(	(	PUNCT
ejpam-3872	118	9	1	1	NUM
ejpam-3872	118	10	)	)	PUNCT
ejpam-3872	118	11	(	(	PUNCT
ejpam-3872	118	12	2021	2021	NUM
ejpam-3872	118	13	)	)	PUNCT
ejpam-3872	118	14	,	,	PUNCT
ejpam-3872	118	15	19	19	NUM
ejpam-3872	118	16	-	-	SYM
ejpam-3872	118	17	42	42	NUM
ejpam-3872	118	18	25	25	NUM
ejpam-3872	118	19	following	follow	VERB
ejpam-3872	118	20	hypothesis	hypothesis	NOUN
ejpam-3872	118	21	:	:	PUNCT
ejpam-3872	118	22	(	(	PUNCT
ejpam-3872	118	23	ga	ga	PROPN
ejpam-3872	118	24	)	)	PUNCT
ejpam-3872	118	25	f	f	PROPN
ejpam-3872	118	26	is	be	AUX
ejpam-3872	118	27	differentiable	differentiable	ADJ
ejpam-3872	118	28	in	in	ADP
ejpam-3872	118	29	some	some	DET
ejpam-3872	118	30	left	left	ADJ
ejpam-3872	118	31	neighborhood	neighborhood	NOUN
ejpam-3872	118	32	of	of	ADP
ejpam-3872	118	33	uep(f	uep(f	PROPN
ejpam-3872	118	34	)	)	PUNCT
ejpam-3872	118	35	.	.	PUNCT
ejpam-3872	119	1	(	(	PUNCT
ejpam-3872	119	2	gb	gb	X
ejpam-3872	119	3	)	)	PUNCT
ejpam-3872	119	4	the	the	DET
ejpam-3872	119	5	function	function	NOUN
ejpam-3872	119	6	s(x	s(x	PROPN
ejpam-3872	119	7	)	)	PUNCT
ejpam-3872	120	1	=	=	SYM
ejpam-3872	120	2	e−x	e−x	NOUN
ejpam-3872	120	3	[	[	PUNCT
ejpam-3872	120	4	f−1(1−	f−1(1−	PROPN
ejpam-3872	120	5	t	t	PROPN
ejpam-3872	120	6	)	)	PUNCT
ejpam-3872	120	7	]	]	PUNCT
ejpam-3872	120	8	′	′	NUM
ejpam-3872	120	9	t	t	PROPN
ejpam-3872	120	10	=	=	SYM
ejpam-3872	120	11	e−x	e−x	NOUN
ejpam-3872	120	12	,	,	PUNCT
ejpam-3872	120	13	ex	ex	X
ejpam-3872	120	14	<	<	X
ejpam-3872	120	15	u0	u0	X
ejpam-3872	120	16	<	<	X
ejpam-3872	120	17	1	1	NUM
ejpam-3872	120	18	,	,	PUNCT
ejpam-3872	120	19	for	for	ADP
ejpam-3872	120	20	some	some	DET
ejpam-3872	120	21	u0	u0	NOUN
ejpam-3872	120	22	∈]0	∈]0	ADJ
ejpam-3872	120	23	,	,	PUNCT
ejpam-3872	120	24	1	1	NUM
ejpam-3872	120	25	[	[	PUNCT
ejpam-3872	120	26	decreases	decrease	VERB
ejpam-3872	120	27	to	to	ADP
ejpam-3872	120	28	0	0	NUM
ejpam-3872	120	29	as	as	ADP
ejpam-3872	120	30	x→	x→	PUNCT
ejpam-3872	120	31	+	+	NOUN
ejpam-3872	120	32	∞	∞	NUM
ejpam-3872	120	33	and	and	CCONJ
ejpam-3872	120	34	is	be	AUX
ejpam-3872	120	35	such	such	ADJ
ejpam-3872	120	36	that	that	PRON
ejpam-3872	120	37	:	:	PUNCT
ejpam-3872	120	38	for	for	ADP
ejpam-3872	120	39	any	any	DET
ejpam-3872	120	40	sequence	sequence	NOUN
ejpam-3872	120	41	(	(	PUNCT
ejpam-3872	120	42	xn	xn	PROPN
ejpam-3872	120	43	,	,	PUNCT
ejpam-3872	120	44	yn)n≥1	yn)n≥1	VERB
ejpam-3872	120	45	such	such	ADJ
ejpam-3872	120	46	that	that	SCONJ
ejpam-3872	120	47	lim	lim	PROPN
ejpam-3872	120	48	sup	sup	PROPN
ejpam-3872	120	49	n→+∞	n→+∞	VERB
ejpam-3872	120	50	|xn	|xn	PRON
ejpam-3872	120	51	−	−	NOUN
ejpam-3872	120	52	yn|/	yn|/	NOUN
ejpam-3872	120	53	√	√	VERB
ejpam-3872	120	54	n	n	CCONJ
ejpam-3872	120	55	<	<	X
ejpam-3872	120	56	+	+	NOUN
ejpam-3872	120	57	∞	∞	PROPN
ejpam-3872	120	58	,	,	PUNCT
ejpam-3872	120	59	we	we	PRON
ejpam-3872	120	60	have	have	VERB
ejpam-3872	120	61	,	,	PUNCT
ejpam-3872	120	62	for	for	ADP
ejpam-3872	120	63	some	some	DET
ejpam-3872	120	64	α	α	NOUN
ejpam-3872	120	65	>	>	X
ejpam-3872	120	66	0	0	PROPN
ejpam-3872	120	67	,	,	PUNCT
ejpam-3872	120	68	lim	lim	PROPN
ejpam-3872	120	69	n→+∞	n→+∞	VERB
ejpam-3872	120	70	√	√	PROPN
ejpam-3872	120	71	n	n	PRON
ejpam-3872	120	72	s	s	X
ejpam-3872	120	73	(	(	PUNCT
ejpam-3872	120	74	exp(min(xn	exp(min(xn	PROPN
ejpam-3872	120	75	,	,	PUNCT
ejpam-3872	120	76	yn	yn	NOUN
ejpam-3872	120	77	)	)	PUNCT
ejpam-3872	120	78	)	)	PUNCT
ejpam-3872	120	79	)	)	PUNCT
ejpam-3872	121	1	=	=	NOUN
ejpam-3872	121	2	lim	lim	PROPN
ejpam-3872	121	3	n→+∞	n→+∞	VERB
ejpam-3872	121	4	√	√	PROPN
ejpam-3872	121	5	n	n	PRON
ejpam-3872	121	6	s	s	X
ejpam-3872	121	7	(	(	PUNCT
ejpam-3872	121	8	exp(max(xn	exp(max(xn	PROPN
ejpam-3872	121	9	,	,	PUNCT
ejpam-3872	121	10	yn	yn	PROPN
ejpam-3872	121	11	)	)	PUNCT
ejpam-3872	121	12	)	)	PUNCT
ejpam-3872	121	13	)	)	PUNCT
ejpam-3872	122	1	=	=	SYM
ejpam-3872	122	2	α	α	X
ejpam-3872	122	3	.	.	PUNCT
ejpam-3872	123	1	we	we	PRON
ejpam-3872	123	2	have	have	VERB
ejpam-3872	123	3	the	the	DET
ejpam-3872	123	4	following	follow	VERB
ejpam-3872	123	5	generalization	generalization	NOUN
ejpam-3872	123	6	.	.	PUNCT
ejpam-3872	124	1	theorem	theorem	NOUN
ejpam-3872	124	2	2	2	NUM
ejpam-3872	124	3	.	.	PUNCT
ejpam-3872	125	1	if	if	SCONJ
ejpam-3872	125	2	f	f	PROPN
ejpam-3872	125	3	satisfies	satisfy	VERB
ejpam-3872	125	4	assumptions	assumption	NOUN
ejpam-3872	125	5	(	(	PUNCT
ejpam-3872	125	6	ga	ga	NOUN
ejpam-3872	125	7	)	)	PUNCT
ejpam-3872	125	8	and	and	CCONJ
ejpam-3872	125	9	(	(	PUNCT
ejpam-3872	125	10	gb	gb	NOUN
ejpam-3872	125	11	)	)	PUNCT
ejpam-3872	125	12	,	,	PUNCT
ejpam-3872	125	13	then	then	ADV
ejpam-3872	125	14	we	we	PRON
ejpam-3872	125	15	have	have	VERB
ejpam-3872	125	16	x(n	x(n	NOUN
ejpam-3872	125	17	)	)	PUNCT
ejpam-3872	125	18	−	−	PROPN
ejpam-3872	125	19	f−1	f−1	PROPN
ejpam-3872	125	20	(	(	PUNCT
ejpam-3872	125	21	1−	1−	NUM
ejpam-3872	125	22	e−n	e−n	PROPN
ejpam-3872	125	23	)	)	PUNCT
ejpam-3872	125	24	n	n	CCONJ
ejpam-3872	125	25	(	(	PUNCT
ejpam-3872	125	26	0	0	NUM
ejpam-3872	125	27	,	,	PUNCT
ejpam-3872	125	28	α2	α2	ADJ
ejpam-3872	125	29	)	)	PUNCT
ejpam-3872	125	30	.	.	PUNCT
ejpam-3872	126	1	comments	comment	NOUN
ejpam-3872	126	2	i	i	PRON
ejpam-3872	126	3	.	.	PUNCT
ejpam-3872	127	1	a	a	DET
ejpam-3872	127	2	firm	firm	ADJ
ejpam-3872	127	3	look	look	NOUN
ejpam-3872	127	4	at	at	ADP
ejpam-3872	127	5	the	the	DET
ejpam-3872	127	6	results	result	NOUN
ejpam-3872	127	7	shows	show	VERB
ejpam-3872	127	8	that	that	SCONJ
ejpam-3872	127	9	for	for	ADP
ejpam-3872	127	10	any	any	DET
ejpam-3872	127	11	f	f	PROPN
ejpam-3872	127	12	∈	∈	PROPN
ejpam-3872	127	13	d	d	NOUN
ejpam-3872	127	14	,	,	PUNCT
ejpam-3872	127	15	we	we	PRON
ejpam-3872	127	16	found	find	VERB
ejpam-3872	127	17	the	the	DET
ejpam-3872	127	18	direct	direct	ADJ
ejpam-3872	127	19	asymptotic	asymptotic	ADJ
ejpam-3872	127	20	law	law	NOUN
ejpam-3872	127	21	of	of	ADP
ejpam-3872	127	22	x(n	x(n	NOUN
ejpam-3872	127	23	)	)	PUNCT
ejpam-3872	127	24	or	or	CCONJ
ejpam-3872	127	25	that	that	PRON
ejpam-3872	127	26	of	of	ADP
ejpam-3872	127	27	a	a	DET
ejpam-3872	127	28	function	function	NOUN
ejpam-3872	127	29	of	of	ADP
ejpam-3872	127	30	x(n	x(n	NOUN
ejpam-3872	127	31	)	)	PUNCT
ejpam-3872	127	32	,	,	PUNCT
ejpam-3872	127	33	mainly	mainly	ADV
ejpam-3872	127	34	logx(n	logx(n	NOUN
ejpam-3872	127	35	)	)	PUNCT
ejpam-3872	127	36	.	.	PUNCT
ejpam-3872	128	1	for	for	ADP
ejpam-3872	128	2	example	example	NOUN
ejpam-3872	128	3	,	,	PUNCT
ejpam-3872	128	4	point	point	NOUN
ejpam-3872	128	5	(	(	PUNCT
ejpam-3872	128	6	d	d	NOUN
ejpam-3872	128	7	)	)	PUNCT
ejpam-3872	128	8	of	of	ADP
ejpam-3872	128	9	theorem	theorem	NOUN
ejpam-3872	128	10	1	1	NUM
ejpam-3872	128	11	can	can	AUX
ejpam-3872	128	12	not	not	PART
ejpam-3872	128	13	be	be	AUX
ejpam-3872	128	14	applied	apply	VERB
ejpam-3872	128	15	when	when	SCONJ
ejpam-3872	128	16	x	x	PRON
ejpam-3872	128	17	follows	follow	VERB
ejpam-3872	128	18	a	a	DET
ejpam-3872	128	19	lognormal	lognormal	ADJ
ejpam-3872	128	20	law	law	NOUN
ejpam-3872	128	21	but	but	CCONJ
ejpam-3872	128	22	can	can	AUX
ejpam-3872	128	23	be	be	AUX
ejpam-3872	128	24	applied	apply	VERB
ejpam-3872	128	25	to	to	ADP
ejpam-3872	128	26	exp(x	exp(x	PROPN
ejpam-3872	128	27	)	)	PUNCT
ejpam-3872	128	28	.	.	PUNCT
ejpam-3872	129	1	this	this	PRON
ejpam-3872	129	2	leads	lead	VERB
ejpam-3872	129	3	to	to	ADP
ejpam-3872	129	4	the	the	DET
ejpam-3872	129	5	following	follow	VERB
ejpam-3872	129	6	rule	rule	NOUN
ejpam-3872	129	7	for	for	ADP
ejpam-3872	129	8	all	all	DET
ejpam-3872	129	9	f	f	PROPN
ejpam-3872	129	10	∈	∈	PROPN
ejpam-3872	130	1	d	d	NOUN
ejpam-3872	130	2	:	:	PUNCT
ejpam-3872	130	3	(	(	PUNCT
ejpam-3872	130	4	e	e	NOUN
ejpam-3872	130	5	)	)	PUNCT
ejpam-3872	130	6	if	if	SCONJ
ejpam-3872	130	7	f	f	PROPN
ejpam-3872	130	8	∈	∈	PROPN
ejpam-3872	130	9	d(gγ	d(gγ	PROPN
ejpam-3872	130	10	)	)	PUNCT
ejpam-3872	130	11	,	,	PUNCT
ejpam-3872	130	12	γ	γ	PROPN
ejpam-3872	130	13	6=	6=	PROPN
ejpam-3872	130	14	0	0	NUM
ejpam-3872	130	15	,	,	PUNCT
ejpam-3872	130	16	we	we	PRON
ejpam-3872	130	17	apply	apply	VERB
ejpam-3872	130	18	points	point	NOUN
ejpam-3872	130	19	(	(	PUNCT
ejpam-3872	130	20	a	a	NOUN
ejpam-3872	130	21	)	)	PUNCT
ejpam-3872	130	22	or	or	CCONJ
ejpam-3872	130	23	(	(	PUNCT
ejpam-3872	130	24	c	c	NOUN
ejpam-3872	130	25	)	)	PUNCT
ejpam-3872	130	26	without	without	ADP
ejpam-3872	130	27	any	any	DET
ejpam-3872	130	28	further	further	ADJ
ejpam-3872	130	29	condition	condition	NOUN
ejpam-3872	130	30	.	.	PUNCT
ejpam-3872	131	1	(	(	PUNCT
ejpam-3872	131	2	f	f	X
ejpam-3872	131	3	)	)	PUNCT
ejpam-3872	131	4	if	if	SCONJ
ejpam-3872	131	5	f	f	PROPN
ejpam-3872	131	6	∈	∈	PROPN
ejpam-3872	131	7	d(g0	d(g0	NOUN
ejpam-3872	131	8	)	)	PUNCT
ejpam-3872	131	9	and	and	CCONJ
ejpam-3872	131	10	exp(x	exp(x	PROPN
ejpam-3872	131	11	)	)	PUNCT
ejpam-3872	131	12	∈	∈	PROPN
ejpam-3872	131	13	d(gγ	d(gγ	PROPN
ejpam-3872	131	14	)	)	PUNCT
ejpam-3872	131	15	for	for	ADP
ejpam-3872	131	16	some	some	DET
ejpam-3872	131	17	γ	γ	NOUN
ejpam-3872	131	18	>	>	X
ejpam-3872	131	19	0	0	NUM
ejpam-3872	131	20	,	,	PUNCT
ejpam-3872	131	21	we	we	PRON
ejpam-3872	131	22	apply	apply	VERB
ejpam-3872	131	23	point	point	NOUN
ejpam-3872	131	24	(	(	PUNCT
ejpam-3872	131	25	b	b	NOUN
ejpam-3872	131	26	)	)	PUNCT
ejpam-3872	131	27	without	without	ADP
ejpam-3872	131	28	any	any	DET
ejpam-3872	131	29	further	further	ADJ
ejpam-3872	131	30	condition	condition	NOUN
ejpam-3872	131	31	.	.	PUNCT
ejpam-3872	132	1	(	(	PUNCT
ejpam-3872	132	2	g	g	NOUN
ejpam-3872	132	3	)	)	PUNCT
ejpam-3872	132	4	if	if	SCONJ
ejpam-3872	132	5	f	f	PROPN
ejpam-3872	132	6	∈	∈	PROPN
ejpam-3872	132	7	d(g0	d(g0	NOUN
ejpam-3872	132	8	)	)	PUNCT
ejpam-3872	132	9	and	and	CCONJ
ejpam-3872	132	10	s(u)→	s(u)→	PROPN
ejpam-3872	132	11	0	0	PUNCT
ejpam-3872	132	12	as	as	ADP
ejpam-3872	132	13	u→	u→	PROPN
ejpam-3872	132	14	0	0	NUM
ejpam-3872	132	15	.	.	PUNCT
ejpam-3872	133	1	if	if	SCONJ
ejpam-3872	133	2	(	(	PUNCT
ejpam-3872	133	3	ha	ha	INTJ
ejpam-3872	133	4	)	)	PUNCT
ejpam-3872	133	5	and	and	CCONJ
ejpam-3872	133	6	(	(	PUNCT
ejpam-3872	133	7	hb	hb	X
ejpam-3872	133	8	)	)	PUNCT
ejpam-3872	133	9	hold	hold	VERB
ejpam-3872	133	10	,	,	PUNCT
ejpam-3872	133	11	we	we	PRON
ejpam-3872	133	12	conclude	conclude	VERB
ejpam-3872	133	13	by	by	ADP
ejpam-3872	133	14	applying	apply	VERB
ejpam-3872	133	15	point	point	NOUN
ejpam-3872	133	16	(	(	PUNCT
ejpam-3872	133	17	d	d	NOUN
ejpam-3872	133	18	)	)	PUNCT
ejpam-3872	133	19	.	.	PUNCT
ejpam-3872	134	1	if	if	SCONJ
ejpam-3872	134	2	not	not	PART
ejpam-3872	134	3	(	(	PUNCT
ejpam-3872	134	4	as	as	SCONJ
ejpam-3872	134	5	it	it	PRON
ejpam-3872	134	6	is	be	AUX
ejpam-3872	134	7	for	for	ADP
ejpam-3872	134	8	a	a	DET
ejpam-3872	134	9	lognormal	lognormal	ADJ
ejpam-3872	134	10	law	law	NOUN
ejpam-3872	134	11	)	)	PUNCT
ejpam-3872	134	12	,	,	PUNCT
ejpam-3872	134	13	we	we	PRON
ejpam-3872	134	14	search	search	VERB
ejpam-3872	134	15	whether	whether	SCONJ
ejpam-3872	134	16	x1	x1	PROPN
ejpam-3872	134	17	=	=	SYM
ejpam-3872	134	18	exp(x	exp(x	PROPN
ejpam-3872	134	19	)	)	PUNCT
ejpam-3872	134	20	∈	∈	PROPN
ejpam-3872	134	21	d(gγ	d(gγ	PROPN
ejpam-3872	134	22	)	)	PUNCT
ejpam-3872	134	23	for	for	ADP
ejpam-3872	134	24	some	some	DET
ejpam-3872	134	25	γ	γ	NOUN
ejpam-3872	134	26	>	>	X
ejpam-3872	134	27	0	0	NUM
ejpam-3872	134	28	or	or	CCONJ
ejpam-3872	134	29	x1	x1	PROPN
ejpam-3872	134	30	=	=	SYM
ejpam-3872	134	31	exp(x	exp(x	PROPN
ejpam-3872	134	32	)	)	PUNCT
ejpam-3872	134	33	fulfills	fulfill	NOUN
ejpam-3872	134	34	(	(	PUNCT
ejpam-3872	134	35	ha	ha	INTJ
ejpam-3872	134	36	)	)	PUNCT
ejpam-3872	134	37	and	and	CCONJ
ejpam-3872	134	38	(	(	PUNCT
ejpam-3872	134	39	hb	hb	X
ejpam-3872	134	40	)	)	PUNCT
ejpam-3872	134	41	.	.	PUNCT
ejpam-3872	135	1	if	if	SCONJ
ejpam-3872	135	2	yes	yes	INTJ
ejpam-3872	135	3	,	,	PUNCT
ejpam-3872	135	4	we	we	PRON
ejpam-3872	135	5	conclude	conclude	VERB
ejpam-3872	135	6	by	by	ADP
ejpam-3872	135	7	point	point	NOUN
ejpam-3872	135	8	(	(	PUNCT
ejpam-3872	135	9	b	b	NOUN
ejpam-3872	135	10	)	)	PUNCT
ejpam-3872	135	11	or	or	CCONJ
ejpam-3872	135	12	by	by	ADP
ejpam-3872	135	13	point	point	NOUN
ejpam-3872	135	14	(	(	PUNCT
ejpam-3872	135	15	d	d	NOUN
ejpam-3872	135	16	)	)	PUNCT
ejpam-3872	135	17	.	.	PUNCT
ejpam-3872	136	1	if	if	SCONJ
ejpam-3872	136	2	not	not	PART
ejpam-3872	136	3	,	,	PUNCT
ejpam-3872	136	4	we	we	PRON
ejpam-3872	136	5	consider	consider	VERB
ejpam-3872	136	6	x2	x2	PROPN
ejpam-3872	136	7	=	=	PUNCT
ejpam-3872	136	8	exp(x1	exp(x1	ADJ
ejpam-3872	136	9	)	)	PUNCT
ejpam-3872	136	10	,	,	PUNCT
ejpam-3872	136	11	and	and	CCONJ
ejpam-3872	136	12	we	we	PRON
ejpam-3872	136	13	continue	continue	VERB
ejpam-3872	136	14	until	until	SCONJ
ejpam-3872	136	15	we	we	PRON
ejpam-3872	136	16	reach	reach	VERB
ejpam-3872	136	17	xp	xp	NOUN
ejpam-3872	136	18	=	=	SYM
ejpam-3872	136	19	exp(xp−1	exp(xp−1	PROPN
ejpam-3872	136	20	)	)	PUNCT
ejpam-3872	136	21	∈	∈	PROPN
ejpam-3872	136	22	d(gγ	d(gγ	PROPN
ejpam-3872	136	23	)	)	PUNCT
ejpam-3872	136	24	for	for	ADP
ejpam-3872	136	25	some	some	DET
ejpam-3872	136	26	γ	γ	NOUN
ejpam-3872	136	27	>	>	X
ejpam-3872	136	28	0	0	NUM
ejpam-3872	136	29	or	or	CCONJ
ejpam-3872	136	30	xp	xp	INTJ
ejpam-3872	136	31	=	=	SYM
ejpam-3872	136	32	exp(xp−1	exp(xp−1	PROPN
ejpam-3872	136	33	)	)	PUNCT
ejpam-3872	136	34	for	for	ADP
ejpam-3872	136	35	some	some	DET
ejpam-3872	136	36	p	p	NOUN
ejpam-3872	136	37	≥	≥	NOUN
ejpam-3872	136	38	1	1	NUM
ejpam-3872	136	39	.	.	PUNCT
ejpam-3872	137	1	finally	finally	ADV
ejpam-3872	137	2	,	,	PUNCT
ejpam-3872	137	3	we	we	PRON
ejpam-3872	137	4	handle	handle	VERB
ejpam-3872	137	5	the	the	DET
ejpam-3872	137	6	rates	rate	NOUN
ejpam-3872	137	7	of	of	ADP
ejpam-3872	137	8	convergences	convergence	NOUN
ejpam-3872	137	9	in	in	ADP
ejpam-3872	137	10	the	the	DET
ejpam-3872	137	11	theorems	theorem	NOUN
ejpam-3872	137	12	stated	state	VERB
ejpam-3872	137	13	above	above	ADV
ejpam-3872	137	14	.	.	PUNCT
ejpam-3872	138	1	let	let	VERB
ejpam-3872	138	2	us	we	PRON
ejpam-3872	138	3	introduce	introduce	VERB
ejpam-3872	138	4	the	the	DET
ejpam-3872	138	5	following	following	ADJ
ejpam-3872	138	6	notations	notation	NOUN
ejpam-3872	138	7	.	.	PUNCT
ejpam-3872	139	1	g.	g.	PROPN
ejpam-3872	139	2	s.	s.	PROPN
ejpam-3872	139	3	lo	lo	PROPN
ejpam-3872	139	4	et	et	PROPN
ejpam-3872	139	5	al	al	PROPN
ejpam-3872	139	6	.	.	PUNCT
ejpam-3872	139	7	/	/	SYM
ejpam-3872	139	8	eur	eur	PROPN
ejpam-3872	139	9	.	.	PUNCT
ejpam-3872	140	1	j.	j.	PROPN
ejpam-3872	140	2	pure	pure	PROPN
ejpam-3872	140	3	appl	appl	PROPN
ejpam-3872	140	4	.	.	PROPN
ejpam-3872	140	5	math	math	PROPN
ejpam-3872	140	6	,	,	PUNCT
ejpam-3872	140	7	14	14	NUM
ejpam-3872	140	8	(	(	PUNCT
ejpam-3872	140	9	1	1	NUM
ejpam-3872	140	10	)	)	PUNCT
ejpam-3872	140	11	(	(	PUNCT
ejpam-3872	140	12	2021	2021	NUM
ejpam-3872	140	13	)	)	PUNCT
ejpam-3872	140	14	,	,	PUNCT
ejpam-3872	140	15	19	19	NUM
ejpam-3872	140	16	-	-	SYM
ejpam-3872	140	17	42	42	NUM
ejpam-3872	140	18	26	26	NUM
ejpam-3872	140	19	theorem	theorem	NOUN
ejpam-3872	140	20	3	3	X
ejpam-3872	140	21	.	.	PUNCT
ejpam-3872	141	1	let	let	VERB
ejpam-3872	141	2	f	f	PROPN
ejpam-3872	141	3	∈	∈	PROPN
ejpam-3872	141	4	d(gγ	d(gγ	PROPN
ejpam-3872	141	5	)	)	PUNCT
ejpam-3872	141	6	,	,	PUNCT
ejpam-3872	141	7	γ	γ	PROPN
ejpam-3872	141	8	∈	∈	PROPN
ejpam-3872	141	9	r.	r.	PROPN
ejpam-3872	141	10	then	then	ADV
ejpam-3872	141	11	,	,	PUNCT
ejpam-3872	141	12	there	there	PRON
ejpam-3872	141	13	exists	exist	VERB
ejpam-3872	141	14	a	a	DET
ejpam-3872	141	15	probability	probability	NOUN
ejpam-3872	141	16	space	space	NOUN
ejpam-3872	141	17	(	(	PUNCT
ejpam-3872	141	18	ω	ω	NOUN
ejpam-3872	141	19	,	,	PUNCT
ejpam-3872	141	20	a	a	DET
ejpam-3872	141	21	,	,	PUNCT
ejpam-3872	141	22	p	p	NOUN
ejpam-3872	141	23	)	)	PUNCT
ejpam-3872	141	24	holding	hold	VERB
ejpam-3872	141	25	a	a	DET
ejpam-3872	141	26	sequence	sequence	NOUN
ejpam-3872	141	27	of	of	ADP
ejpam-3872	141	28	independent	independent	ADJ
ejpam-3872	141	29	standard	standard	ADJ
ejpam-3872	141	30	exponential	exponential	ADJ
ejpam-3872	141	31	random	random	ADJ
ejpam-3872	141	32	variables	variable	NOUN
ejpam-3872	141	33	(	(	PUNCT
ejpam-3872	141	34	en)n≥1	en)n≥1	VERB
ejpam-3872	141	35	and	and	CCONJ
ejpam-3872	141	36	a	a	DET
ejpam-3872	141	37	brownian	brownian	ADJ
ejpam-3872	141	38	process	process	NOUN
ejpam-3872	141	39	{	{	PUNCT
ejpam-3872	141	40	w	w	PROPN
ejpam-3872	141	41	(	(	PUNCT
ejpam-3872	141	42	t	t	PROPN
ejpam-3872	141	43	)	)	PUNCT
ejpam-3872	141	44	,	,	PUNCT
ejpam-3872	141	45	t	t	PROPN
ejpam-3872	141	46	≥	≥	NUM
ejpam-3872	141	47	0	0	NUM
ejpam-3872	141	48	}	}	PUNCT
ejpam-3872	141	49	such	such	ADJ
ejpam-3872	141	50	that	that	SCONJ
ejpam-3872	141	51	the	the	DET
ejpam-3872	141	52	record	record	NOUN
ejpam-3872	141	53	values	value	NOUN
ejpam-3872	141	54	x(n	x(n	NOUN
ejpam-3872	141	55	)	)	PUNCT
ejpam-3872	141	56	,	,	PUNCT
ejpam-3872	141	57	n	n	PRON
ejpam-3872	141	58	≥	≥	NOUN
ejpam-3872	141	59	1	1	NUM
ejpam-3872	141	60	,	,	PUNCT
ejpam-3872	141	61	of	of	ADP
ejpam-3872	141	62	the	the	DET
ejpam-3872	141	63	sequence	sequence	NOUN
ejpam-3872	141	64	xj	xj	PROPN
ejpam-3872	141	65	=	=	SYM
ejpam-3872	141	66	f−1	f−1	PROPN
ejpam-3872	141	67	(	(	PUNCT
ejpam-3872	141	68	1−	1−	NUM
ejpam-3872	141	69	eej	eej	PROPN
ejpam-3872	141	70	)	)	PUNCT
ejpam-3872	141	71	,	,	PUNCT
ejpam-3872	141	72	j	j	PROPN
ejpam-3872	141	73	≥	≥	NUM
ejpam-3872	141	74	1	1	NUM
ejpam-3872	141	75	,	,	PUNCT
ejpam-3872	141	76	satisfy	satisfy	VERB
ejpam-3872	141	77	the	the	DET
ejpam-3872	141	78	following	follow	VERB
ejpam-3872	141	79	representations	representation	NOUN
ejpam-3872	141	80	below	below	ADP
ejpam-3872	141	81	under	under	ADP
ejpam-3872	141	82	the	the	DET
ejpam-3872	141	83	appropriate	appropriate	ADJ
ejpam-3872	141	84	conditions	condition	NOUN
ejpam-3872	141	85	.	.	PUNCT
ejpam-3872	142	1	here	here	ADV
ejpam-3872	142	2	,	,	PUNCT
ejpam-3872	142	3	sn	sn	NOUN
ejpam-3872	142	4	=	=	SYM
ejpam-3872	142	5	e1	e1	PROPN
ejpam-3872	142	6	+	+	CCONJ
ejpam-3872	142	7	...	...	PUNCT
ejpam-3872	143	1	+	+	CCONJ
ejpam-3872	143	2	en	en	X
ejpam-3872	143	3	,	,	PUNCT
ejpam-3872	143	4	n	n	PRON
ejpam-3872	143	5	≥	≥	NOUN
ejpam-3872	143	6	1	1	NUM
ejpam-3872	143	7	,	,	PUNCT
ejpam-3872	143	8	are	be	AUX
ejpam-3872	143	9	the	the	DET
ejpam-3872	143	10	partial	partial	ADJ
ejpam-3872	143	11	sums	sum	NOUN
ejpam-3872	143	12	of	of	ADP
ejpam-3872	143	13	the	the	DET
ejpam-3872	143	14	sequence	sequence	NOUN
ejpam-3872	143	15	(	(	PUNCT
ejpam-3872	143	16	en)n≥1	en)n≥1	VERB
ejpam-3872	143	17	,	,	PUNCT
ejpam-3872	143	18	s∗n	s∗n	PUNCT
ejpam-3872	143	19	=	=	PUNCT
ejpam-3872	143	20	n−1/2(sn	n−1/2(sn	X
ejpam-3872	143	21	−	−	PROPN
ejpam-3872	143	22	n	n	CCONJ
ejpam-3872	143	23	)	)	PUNCT
ejpam-3872	143	24	,	,	PUNCT
ejpam-3872	143	25	vn	vn	PROPN
ejpam-3872	143	26	=	=	SYM
ejpam-3872	143	27	e−n	e−n	PROPN
ejpam-3872	143	28	and	and	CCONJ
ejpam-3872	143	29	vn	vn	PROPN
ejpam-3872	143	30	=	=	PROPN
ejpam-3872	143	31	e−sn	e−sn	PROPN
ejpam-3872	143	32	.	.	PUNCT
ejpam-3872	144	1	below	below	ADV
ejpam-3872	144	2	,	,	PUNCT
ejpam-3872	144	3	the	the	DET
ejpam-3872	144	4	function	function	NOUN
ejpam-3872	144	5	a(u	a(u	PROPN
ejpam-3872	144	6	)	)	PUNCT
ejpam-3872	144	7	,	,	PUNCT
ejpam-3872	144	8	b(u	b(u	PROPN
ejpam-3872	144	9	)	)	PUNCT
ejpam-3872	144	10	and	and	CCONJ
ejpam-3872	144	11	s(u	s(u	PROPN
ejpam-3872	144	12	)	)	PUNCT
ejpam-3872	144	13	of	of	ADP
ejpam-3872	144	14	u	u	PRON
ejpam-3872	144	15	∈]0	∈]0	X
ejpam-3872	144	16	,	,	PUNCT
ejpam-3872	144	17	1	1	NUM
ejpam-3872	144	18	[	[	PUNCT
ejpam-3872	144	19	are	be	AUX
ejpam-3872	144	20	those	those	PRON
ejpam-3872	144	21	in	in	ADP
ejpam-3872	144	22	the	the	DET
ejpam-3872	144	23	representations	representation	NOUN
ejpam-3872	144	24	in	in	ADP
ejpam-3872	144	25	proposition	proposition	NOUN
ejpam-3872	144	26	2	2	NUM
ejpam-3872	144	27	.	.	PUNCT
ejpam-3872	144	28	by	by	ADP
ejpam-3872	144	29	denoting	denote	VERB
ejpam-3872	144	30	w	w	PROPN
ejpam-3872	144	31	∗n	∗n	PROPN
ejpam-3872	144	32	=	=	SYM
ejpam-3872	144	33	n−1/2w	n−1/2w	PROPN
ejpam-3872	144	34	(	(	PUNCT
ejpam-3872	144	35	n	n	CCONJ
ejpam-3872	144	36	)	)	PUNCT
ejpam-3872	144	37	and	and	CCONJ
ejpam-3872	144	38	cn	cn	PROPN
ejpam-3872	144	39	=	=	PROPN
ejpam-3872	144	40	n−1/2	n−1/2	PROPN
ejpam-3872	144	41	log	log	NOUN
ejpam-3872	144	42	n	n	CCONJ
ejpam-3872	144	43	,	,	PUNCT
ejpam-3872	144	44	we	we	PRON
ejpam-3872	144	45	have	have	VERB
ejpam-3872	144	46	w	w	PROPN
ejpam-3872	144	47	∗n	∗n	PROPN
ejpam-3872	144	48	∼	∼	NOUN
ejpam-3872	144	49	n	n	CCONJ
ejpam-3872	144	50	(	(	PUNCT
ejpam-3872	144	51	0	0	NUM
ejpam-3872	144	52	,	,	PUNCT
ejpam-3872	144	53	1	1	NUM
ejpam-3872	144	54	)	)	PUNCT
ejpam-3872	144	55	and	and	CCONJ
ejpam-3872	144	56	|s∗n	|s∗n	PRON
ejpam-3872	144	57	−w	−w	ADV
ejpam-3872	144	58	∗n	∗n	PROPN
ejpam-3872	144	59	|	|	ADV
ejpam-3872	144	60	=	=	SYM
ejpam-3872	144	61	op(cn	op(cn	PROPN
ejpam-3872	144	62	)	)	PUNCT
ejpam-3872	144	63	.	.	PUNCT
ejpam-3872	145	1	further	far	ADV
ejpam-3872	145	2	,	,	PUNCT
ejpam-3872	145	3	we	we	PRON
ejpam-3872	145	4	have	have	VERB
ejpam-3872	145	5	the	the	DET
ejpam-3872	145	6	following	follow	VERB
ejpam-3872	145	7	results	result	NOUN
ejpam-3872	145	8	.	.	PUNCT
ejpam-3872	146	1	(	(	PUNCT
ejpam-3872	146	2	a	a	X
ejpam-3872	146	3	)	)	PUNCT
ejpam-3872	146	4	let	let	VERB
ejpam-3872	146	5	γ	γ	X
ejpam-3872	146	6	>	>	X
ejpam-3872	146	7	0	0	PROPN
ejpam-3872	146	8	.	.	PUNCT
ejpam-3872	146	9	suppose	suppose	VERB
ejpam-3872	147	1	that	that	SCONJ
ejpam-3872	147	2	1−	1−	NUM
ejpam-3872	147	3	1	1	NUM
ejpam-3872	147	4	+	+	NUM
ejpam-3872	147	5	a(vn	a(vn	NOUN
ejpam-3872	147	6	)	)	PUNCT
ejpam-3872	147	7	1	1	NUM
ejpam-3872	147	8	+	+	SYM
ejpam-3872	147	9	a(vn	a(vn	PROPN
ejpam-3872	147	10	)	)	PUNCT
ejpam-3872	147	11	=	=	SYM
ejpam-3872	147	12	o(an	o(an	PROPN
ejpam-3872	147	13	)	)	PUNCT
ejpam-3872	147	14	,	,	PUNCT
ejpam-3872	147	15	sup{|b(t)|	sup{|b(t)|	NOUN
ejpam-3872	147	16	,	,	PUNCT
ejpam-3872	147	17	0	0	NUM
ejpam-3872	147	18	≤	≤	NUM
ejpam-3872	147	19	t	t	PROPN
ejpam-3872	147	20	≤	≤	NUM
ejpam-3872	147	21	vn	vn	PROPN
ejpam-3872	147	22	∨	∨	NUM
ejpam-3872	147	23	vn	vn	PROPN
ejpam-3872	147	24	}	}	PUNCT
ejpam-3872	147	25	=	=	SYM
ejpam-3872	147	26	op(bn	op(bn	PROPN
ejpam-3872	147	27	)	)	PUNCT
ejpam-3872	148	1	.	.	PUNCT
ejpam-3872	149	1	(	(	PUNCT
ejpam-3872	149	2	9	9	NUM
ejpam-3872	149	3	)	)	PUNCT
ejpam-3872	149	4	then	then	ADV
ejpam-3872	149	5	,	,	PUNCT
ejpam-3872	149	6	we	we	PRON
ejpam-3872	149	7	have	have	VERB
ejpam-3872	149	8	(	(	PUNCT
ejpam-3872	149	9	x(n	x(n	NOUN
ejpam-3872	149	10	)	)	PUNCT
ejpam-3872	149	11	f−1	f−1	PROPN
ejpam-3872	149	12	(	(	PUNCT
ejpam-3872	149	13	1−	1−	NUM
ejpam-3872	149	14	e−n	e−n	PROPN
ejpam-3872	149	15	)	)	PUNCT
ejpam-3872	149	16	)	)	PUNCT
ejpam-3872	150	1	n−1/2	n−1/2	PROPN
ejpam-3872	150	2	=	=	SYM
ejpam-3872	150	3	exp(γs∗n	exp(γs∗n	PROPN
ejpam-3872	150	4	)	)	PUNCT
ejpam-3872	151	1	+	+	NOUN
ejpam-3872	151	2	op(an	op(an	PROPN
ejpam-3872	151	3	∨	∨	NUM
ejpam-3872	151	4	bn	bn	NOUN
ejpam-3872	151	5	)	)	PUNCT
ejpam-3872	151	6	=	=	PUNCT
ejpam-3872	151	7	exp(γw	exp(γw	VERB
ejpam-3872	151	8	∗n	∗n	PROPN
ejpam-3872	151	9	)	)	PUNCT
ejpam-3872	152	1	+	+	ADJ
ejpam-3872	152	2	op(an	op(an	PROPN
ejpam-3872	152	3	∨	∨	NUM
ejpam-3872	152	4	bn	bn	PROPN
ejpam-3872	152	5	∨	∨	NUM
ejpam-3872	152	6	cn	cn	PROPN
ejpam-3872	152	7	)	)	PUNCT
ejpam-3872	152	8	.	.	PUNCT
ejpam-3872	153	1	(	(	PUNCT
ejpam-3872	153	2	b	b	X
ejpam-3872	153	3	)	)	PUNCT
ejpam-3872	153	4	let	let	VERB
ejpam-3872	153	5	γ	γ	X
ejpam-3872	153	6	>	>	X
ejpam-3872	153	7	0	0	PUNCT
ejpam-3872	154	1	and	and	CCONJ
ejpam-3872	154	2	x	x	ADJ
ejpam-3872	154	3	≥	≥	NOUN
ejpam-3872	154	4	0	0	NUM
ejpam-3872	154	5	,	,	PUNCT
ejpam-3872	154	6	y	y	PROPN
ejpam-3872	154	7	=	=	PUNCT
ejpam-3872	154	8	logx	logx	PROPN
ejpam-3872	154	9	∈	∈	PROPN
ejpam-3872	154	10	d(g0	d(g0	NOUN
ejpam-3872	154	11	)	)	PUNCT
ejpam-3872	154	12	)	)	PUNCT
ejpam-3872	155	1	and	and	CCONJ
ejpam-3872	155	2	r(x	r(x	PROPN
ejpam-3872	155	3	,	,	PUNCT
ejpam-3872	155	4	g)→	g)→	NOUN
ejpam-3872	155	5	γ	γ	X
ejpam-3872	155	6	as	as	ADP
ejpam-3872	155	7	x→	x→	PROPN
ejpam-3872	155	8	uep(g	uep(g	PROPN
ejpam-3872	155	9	)	)	PUNCT
ejpam-3872	155	10	and	and	CCONJ
ejpam-3872	155	11	we	we	PRON
ejpam-3872	155	12	have	have	VERB
ejpam-3872	155	13	y	y	PROPN
ejpam-3872	155	14	(	(	PUNCT
ejpam-3872	155	15	n	n	CCONJ
ejpam-3872	155	16	)	)	PUNCT
ejpam-3872	155	17	−g−1	−g−1	X
ejpam-3872	156	1	(	(	PUNCT
ejpam-3872	156	2	1−	1−	NUM
ejpam-3872	156	3	e−n)√	e−n)√	NOUN
ejpam-3872	156	4	n	n	PROPN
ejpam-3872	156	5	=	=	SYM
ejpam-3872	156	6	γs∗n	γs∗n	NUM
ejpam-3872	156	7	+	+	NOUN
ejpam-3872	156	8	op(an	op(an	ADJ
ejpam-3872	156	9	∨	∨	NUM
ejpam-3872	156	10	bn	bn	NOUN
ejpam-3872	156	11	)	)	PUNCT
ejpam-3872	157	1	=	=	PRON
ejpam-3872	157	2	γw	γw	PRON
ejpam-3872	157	3	∗n	∗n	PROPN
ejpam-3872	157	4	+	+	SYM
ejpam-3872	157	5	op(an	op(an	PROPN
ejpam-3872	157	6	∨	∨	NUM
ejpam-3872	157	7	bn	bn	PROPN
ejpam-3872	157	8	∨	∨	NUM
ejpam-3872	157	9	cn	cn	PROPN
ejpam-3872	157	10	)	)	PUNCT
ejpam-3872	157	11	.	.	PUNCT
ejpam-3872	158	1	(	(	PUNCT
ejpam-3872	158	2	c	c	X
ejpam-3872	158	3	)	)	PUNCT
ejpam-3872	158	4	let	let	VERB
ejpam-3872	158	5	γ	γ	X
ejpam-3872	158	6	<	<	X
ejpam-3872	158	7	0	0	NUM
ejpam-3872	158	8	.	.	PUNCT
ejpam-3872	159	1	then	then	ADV
ejpam-3872	159	2	,	,	PUNCT
ejpam-3872	159	3	by	by	ADP
ejpam-3872	159	4	using	use	VERB
ejpam-3872	159	5	the	the	DET
ejpam-3872	159	6	rates	rate	NOUN
ejpam-3872	159	7	of	of	ADP
ejpam-3872	159	8	convergence	convergence	NOUN
ejpam-3872	159	9	in	in	ADP
ejpam-3872	159	10	formula	formula	NOUN
ejpam-3872	159	11	(	(	PUNCT
ejpam-3872	159	12	9	9	NUM
ejpam-3872	159	13	)	)	PUNCT
ejpam-3872	159	14	,	,	PUNCT
ejpam-3872	159	15	we	we	PRON
ejpam-3872	159	16	have	have	VERB
ejpam-3872	159	17	(	(	PUNCT
ejpam-3872	159	18	uep(f	uep(f	PROPN
ejpam-3872	159	19	)	)	PUNCT
ejpam-3872	159	20	−x(n	−x(n	PROPN
ejpam-3872	159	21	)	)	PUNCT
ejpam-3872	159	22	uep(f	uep(f	PROPN
ejpam-3872	159	23	)	)	PUNCT
ejpam-3872	160	1	−	−	PROPN
ejpam-3872	160	2	f−1	f−1	PROPN
ejpam-3872	160	3	(	(	PUNCT
ejpam-3872	160	4	1−	1−	NUM
ejpam-3872	160	5	e−n	e−n	PROPN
ejpam-3872	160	6	)	)	PUNCT
ejpam-3872	160	7	)	)	PUNCT
ejpam-3872	161	1	n−1/2	n−1/2	PROPN
ejpam-3872	161	2	=	=	SYM
ejpam-3872	161	3	exp(γs∗n	exp(γs∗n	PROPN
ejpam-3872	161	4	)	)	PUNCT
ejpam-3872	162	1	+	+	NOUN
ejpam-3872	162	2	op(an	op(an	PROPN
ejpam-3872	162	3	∨	∨	NUM
ejpam-3872	162	4	bn	bn	NOUN
ejpam-3872	162	5	)	)	PUNCT
ejpam-3872	162	6	=	=	PUNCT
ejpam-3872	162	7	exp(γw	exp(γw	VERB
ejpam-3872	162	8	∗n	∗n	PROPN
ejpam-3872	162	9	)	)	PUNCT
ejpam-3872	163	1	+	+	ADJ
ejpam-3872	163	2	op(an	op(an	PROPN
ejpam-3872	163	3	∨	∨	NUM
ejpam-3872	163	4	bn	bn	PROPN
ejpam-3872	163	5	∨	∨	NUM
ejpam-3872	163	6	cn	cn	PROPN
ejpam-3872	163	7	)	)	PUNCT
ejpam-3872	163	8	.	.	PUNCT
ejpam-3872	164	1	(	(	PUNCT
ejpam-3872	164	2	d	d	X
ejpam-3872	164	3	)	)	PUNCT
ejpam-3872	164	4	suppose	suppose	VERB
ejpam-3872	164	5	that	that	SCONJ
ejpam-3872	164	6	γ	γ	PROPN
ejpam-3872	164	7	=	=	SYM
ejpam-3872	164	8	0	0	PROPN
ejpam-3872	164	9	and	and	CCONJ
ejpam-3872	164	10	r(x	r(x	PROPN
ejpam-3872	164	11	,	,	PUNCT
ejpam-3872	164	12	g	g	NOUN
ejpam-3872	164	13	)	)	PUNCT
ejpam-3872	164	14	→	→	SYM
ejpam-3872	164	15	0	0	PUNCT
ejpam-3872	164	16	as	as	ADP
ejpam-3872	164	17	x	x	X
ejpam-3872	164	18	→	→	SYM
ejpam-3872	164	19	uep(g	uep(g	NOUN
ejpam-3872	164	20	)	)	PUNCT
ejpam-3872	164	21	.	.	PUNCT
ejpam-3872	165	1	suppose	suppose	VERB
ejpam-3872	165	2	that	that	SCONJ
ejpam-3872	165	3	(	(	PUNCT
ejpam-3872	165	4	ha	ha	INTJ
ejpam-3872	165	5	)	)	PUNCT
ejpam-3872	165	6	and	and	CCONJ
ejpam-3872	165	7	(	(	PUNCT
ejpam-3872	165	8	hb	hb	X
ejpam-3872	165	9	)	)	PUNCT
ejpam-3872	165	10	hold	hold	VERB
ejpam-3872	165	11	both	both	PRON
ejpam-3872	165	12	.	.	PUNCT
ejpam-3872	166	1	if	if	SCONJ
ejpam-3872	166	2	g.	g.	PROPN
ejpam-3872	166	3	s.	s.	PROPN
ejpam-3872	166	4	lo	lo	PROPN
ejpam-3872	166	5	et	et	PROPN
ejpam-3872	166	6	al	al	PROPN
ejpam-3872	166	7	.	.	PUNCT
ejpam-3872	166	8	/	/	SYM
ejpam-3872	166	9	eur	eur	PROPN
ejpam-3872	166	10	.	.	PUNCT
ejpam-3872	167	1	j.	j.	PROPN
ejpam-3872	167	2	pure	pure	PROPN
ejpam-3872	167	3	appl	appl	PROPN
ejpam-3872	167	4	.	.	PROPN
ejpam-3872	167	5	math	math	PROPN
ejpam-3872	167	6	,	,	PUNCT
ejpam-3872	167	7	14	14	NUM
ejpam-3872	167	8	(	(	PUNCT
ejpam-3872	167	9	1	1	NUM
ejpam-3872	167	10	)	)	PUNCT
ejpam-3872	167	11	(	(	PUNCT
ejpam-3872	167	12	2021	2021	NUM
ejpam-3872	167	13	)	)	PUNCT
ejpam-3872	167	14	,	,	PUNCT
ejpam-3872	167	15	19	19	NUM
ejpam-3872	167	16	-	-	SYM
ejpam-3872	167	17	42	42	NUM
ejpam-3872	167	18	27	27	NUM
ejpam-3872	167	19	sup	sup	NOUN
ejpam-3872	167	20	{	{	PUNCT
ejpam-3872	167	21	∣∣∣∣s(u	∣∣∣∣s(u	NOUN
ejpam-3872	167	22	)	)	PUNCT
ejpam-3872	167	23	s(v	s(v	PROPN
ejpam-3872	167	24	)	)	PUNCT
ejpam-3872	167	25	−	−	PROPN
ejpam-3872	167	26	1	1	NUM
ejpam-3872	167	27	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3872	167	28	,	,	PUNCT
ejpam-3872	167	29	min(vn	min(vn	PROPN
ejpam-3872	167	30	,	,	PUNCT
ejpam-3872	167	31	vn	vn	NOUN
ejpam-3872	167	32	)	)	PUNCT
ejpam-3872	167	33	≤	≤	NOUN
ejpam-3872	167	34	u	u	NOUN
ejpam-3872	167	35	,	,	PUNCT
ejpam-3872	167	36	v	v	ADJ
ejpam-3872	167	37	≤	≤	NUM
ejpam-3872	167	38	max(vn	max(vn	NOUN
ejpam-3872	167	39	,	,	PUNCT
ejpam-3872	167	40	vn	vn	PROPN
ejpam-3872	167	41	)	)	PUNCT
ejpam-3872	167	42	}	}	PUNCT
ejpam-3872	167	43	=	=	SYM
ejpam-3872	167	44	op(dn	op(dn	PROPN
ejpam-3872	167	45	)	)	PUNCT
ejpam-3872	167	46	,	,	PUNCT
ejpam-3872	167	47	and	and	CCONJ
ejpam-3872	167	48	√	√	PROPN
ejpam-3872	167	49	ns(vn)−α	ns(vn)−α	PROPN
ejpam-3872	167	50	=	=	SYM
ejpam-3872	167	51	o(en	o(en	PROPN
ejpam-3872	167	52	)	)	PUNCT
ejpam-3872	167	53	,	,	PUNCT
ejpam-3872	167	54	we	we	PRON
ejpam-3872	167	55	have	have	VERB
ejpam-3872	167	56	x(n	x(n	NOUN
ejpam-3872	167	57	)	)	PUNCT
ejpam-3872	168	1	−	−	PROPN
ejpam-3872	168	2	f−1	f−1	PROPN
ejpam-3872	168	3	(	(	PUNCT
ejpam-3872	168	4	1−	1−	NUM
ejpam-3872	168	5	e−n	e−n	PROPN
ejpam-3872	168	6	)	)	PUNCT
ejpam-3872	168	7	=	=	PUNCT
ejpam-3872	168	8	αs∗n	αs∗n	NUM
ejpam-3872	168	9	+	+	NOUN
ejpam-3872	168	10	op(∨dn	op(∨dn	PROPN
ejpam-3872	168	11	∨	∨	NUM
ejpam-3872	168	12	en	en	X
ejpam-3872	168	13	)	)	PUNCT
ejpam-3872	168	14	=	=	SYM
ejpam-3872	168	15	αw	αw	ADP
ejpam-3872	168	16	∗n	∗n	PROPN
ejpam-3872	168	17	+	+	PROPN
ejpam-3872	168	18	op(cn	op(cn	PROPN
ejpam-3872	168	19	∨	∨	NUM
ejpam-3872	168	20	dn	dn	PROPN
ejpam-3872	168	21	∨	∨	PROPN
ejpam-3872	168	22	en	en	X
ejpam-3872	168	23	)	)	PUNCT
ejpam-3872	168	24	.	.	PUNCT
ejpam-3872	169	1	comments	comment	NOUN
ejpam-3872	169	2	ii	ii	PROPN
ejpam-3872	169	3	.	.	PUNCT
ejpam-3872	170	1	in	in	ADP
ejpam-3872	170	2	the	the	DET
ejpam-3872	170	3	domain	domain	NOUN
ejpam-3872	170	4	of	of	ADP
ejpam-3872	170	5	extremal	extremal	ADJ
ejpam-3872	170	6	attraction	attraction	NOUN
ejpam-3872	170	7	,	,	PUNCT
ejpam-3872	170	8	most	most	ADJ
ejpam-3872	170	9	of	of	ADP
ejpam-3872	170	10	the	the	DET
ejpam-3872	170	11	cdf	cdf	PROPN
ejpam-3872	170	12	’s	’	VERB
ejpam-3872	170	13	which	which	PRON
ejpam-3872	170	14	are	be	AUX
ejpam-3872	170	15	used	use	VERB
ejpam-3872	170	16	in	in	ADP
ejpam-3872	170	17	applications	application	NOUN
ejpam-3872	170	18	are	be	AUX
ejpam-3872	170	19	differentiable	differentiable	ADJ
ejpam-3872	170	20	in	in	ADP
ejpam-3872	170	21	a	a	DET
ejpam-3872	170	22	left	left	ADJ
ejpam-3872	170	23	-	-	PUNCT
ejpam-3872	170	24	neighborhood	neighborhood	NOUN
ejpam-3872	170	25	of	of	ADP
ejpam-3872	170	26	the	the	DET
ejpam-3872	170	27	upper	upper	ADJ
ejpam-3872	170	28	endpoint	endpoint	NOUN
ejpam-3872	170	29	.	.	PUNCT
ejpam-3872	171	1	in	in	ADP
ejpam-3872	171	2	such	such	DET
ejpam-3872	171	3	a	a	DET
ejpam-3872	171	4	case	case	NOUN
ejpam-3872	171	5	,	,	PUNCT
ejpam-3872	171	6	we	we	PRON
ejpam-3872	171	7	may	may	AUX
ejpam-3872	171	8	take	take	VERB
ejpam-3872	171	9	a	a	DET
ejpam-3872	171	10	≡	≡	PROPN
ejpam-3872	171	11	0	0	NUM
ejpam-3872	171	12	in	in	ADP
ejpam-3872	171	13	representation	representation	NOUN
ejpam-3872	171	14	(	(	PUNCT
ejpam-3872	171	15	4	4	NUM
ejpam-3872	171	16	)	)	PUNCT
ejpam-3872	171	17	and	and	CCONJ
ejpam-3872	171	18	(	(	PUNCT
ejpam-3872	171	19	5	5	NUM
ejpam-3872	171	20	)	)	PUNCT
ejpam-3872	171	21	in	in	ADP
ejpam-3872	171	22	proposition	proposition	NOUN
ejpam-3872	171	23	2	2	NUM
ejpam-3872	171	24	.	.	PUNCT
ejpam-3872	171	25	by	by	ADP
ejpam-3872	171	26	solving	solve	VERB
ejpam-3872	171	27	easy	easy	ADJ
ejpam-3872	171	28	differential	differential	ADJ
ejpam-3872	171	29	equations	equation	NOUN
ejpam-3872	171	30	,	,	PUNCT
ejpam-3872	171	31	we	we	PRON
ejpam-3872	171	32	have	have	VERB
ejpam-3872	171	33	the	the	DET
ejpam-3872	171	34	representation	representation	NOUN
ejpam-3872	171	35	for	for	ADP
ejpam-3872	171	36	b(u	b(u	PROPN
ejpam-3872	171	37	)	)	PUNCT
ejpam-3872	171	38	=	=	PUNCT
ejpam-3872	172	1	−u(g−1(1−	−u(g−1(1−	PROPN
ejpam-3872	172	2	u))′	u))′	X
ejpam-3872	172	3	−	−	PROPN
ejpam-3872	172	4	γ	γ	X
ejpam-3872	172	5	,	,	PUNCT
ejpam-3872	172	6	u	u	NOUN
ejpam-3872	172	7	∈	∈	PROPN
ejpam-3872	172	8	(	(	PUNCT
ejpam-3872	172	9	0	0	NUM
ejpam-3872	172	10	,	,	PUNCT
ejpam-3872	172	11	1	1	NUM
ejpam-3872	172	12	)	)	PUNCT
ejpam-3872	172	13	and	and	CCONJ
ejpam-3872	172	14	a	a	DET
ejpam-3872	172	15	≡	≡	PROPN
ejpam-3872	172	16	0	0	NUM
ejpam-3872	172	17	(	(	PUNCT
ejpam-3872	172	18	10	10	NUM
ejpam-3872	172	19	)	)	PUNCT
ejpam-3872	172	20	for	for	ADP
ejpam-3872	172	21	γ	γ	X
ejpam-3872	172	22	>	>	X
ejpam-3872	172	23	0	0	NUM
ejpam-3872	172	24	and	and	CCONJ
ejpam-3872	172	25	b(u	b(u	PROPN
ejpam-3872	172	26	)	)	PUNCT
ejpam-3872	172	27	=	=	SYM
ejpam-3872	172	28	u(uep(f	u(uep(f	PROPN
ejpam-3872	172	29	)	)	PUNCT
ejpam-3872	172	30	−	−	PROPN
ejpam-3872	173	1	f−1(1−	f−1(1−	PROPN
ejpam-3872	173	2	u	u	PROPN
ejpam-3872	173	3	)	)	PUNCT
ejpam-3872	173	4	)	)	PUNCT
ejpam-3872	174	1	f	f	PROPN
ejpam-3872	175	1	′(f−1(1−	′(f−1(1−	PROPN
ejpam-3872	175	2	u	u	NOUN
ejpam-3872	175	3	)	)	PUNCT
ejpam-3872	175	4	)	)	PUNCT
ejpam-3872	175	5	,	,	PUNCT
ejpam-3872	175	6	u	u	PROPN
ejpam-3872	175	7	∈	∈	PROPN
ejpam-3872	175	8	(	(	PUNCT
ejpam-3872	175	9	0	0	NUM
ejpam-3872	175	10	,	,	PUNCT
ejpam-3872	175	11	1	1	NUM
ejpam-3872	175	12	)	)	PUNCT
ejpam-3872	175	13	(	(	PUNCT
ejpam-3872	175	14	11	11	NUM
ejpam-3872	175	15	)	)	PUNCT
ejpam-3872	175	16	for	for	ADP
ejpam-3872	175	17	γ	γ	X
ejpam-3872	175	18	<	<	X
ejpam-3872	175	19	0	0	PROPN
ejpam-3872	175	20	,	,	PUNCT
ejpam-3872	175	21	whenever	whenever	SCONJ
ejpam-3872	175	22	we	we	PRON
ejpam-3872	175	23	have	have	VERB
ejpam-3872	175	24	b(u)→	b(u)→	NOUN
ejpam-3872	175	25	0	0	PUNCT
ejpam-3872	175	26	as	as	ADP
ejpam-3872	175	27	u→	u→	PROPN
ejpam-3872	175	28	0	0	NUM
ejpam-3872	175	29	.	.	PUNCT
ejpam-3872	176	1	consequently	consequently	ADV
ejpam-3872	176	2	,	,	PUNCT
ejpam-3872	176	3	the	the	DET
ejpam-3872	176	4	rate	rate	NOUN
ejpam-3872	176	5	of	of	ADP
ejpam-3872	176	6	convergence	convergence	NOUN
ejpam-3872	176	7	is	be	AUX
ejpam-3872	176	8	reduced	reduce	VERB
ejpam-3872	176	9	to	to	ADP
ejpam-3872	176	10	op(bn	op(bn	PROPN
ejpam-3872	176	11	∨	∨	NUM
ejpam-3872	176	12	cn	cn	PROPN
ejpam-3872	176	13	)	)	PUNCT
ejpam-3872	176	14	.	.	PUNCT
ejpam-3872	177	1	for	for	ADP
ejpam-3872	177	2	γ	γ	X
ejpam-3872	177	3	=	=	SYM
ejpam-3872	177	4	0	0	NUM
ejpam-3872	177	5	,	,	PUNCT
ejpam-3872	177	6	representation	representation	NOUN
ejpam-3872	177	7	(	(	PUNCT
ejpam-3872	177	8	8)	8)	NUM
ejpam-3872	177	9	in	in	ADP
ejpam-3872	177	10	proposition	proposition	NOUN
ejpam-3872	177	11	2	2	NUM
ejpam-3872	177	12	holds	hold	VERB
ejpam-3872	177	13	for	for	ADP
ejpam-3872	177	14	s(u	s(u	NOUN
ejpam-3872	177	15	)	)	PUNCT
ejpam-3872	177	16	=	=	PUNCT
ejpam-3872	178	1	−u(f−1(1−	−u(f−1(1−	NOUN
ejpam-3872	178	2	u))′	u))′	PROPN
ejpam-3872	178	3	,	,	PUNCT
ejpam-3872	178	4	0	0	NUM
ejpam-3872	178	5	<	<	X
ejpam-3872	178	6	u	u	X
ejpam-3872	178	7	<	<	X
ejpam-3872	178	8	1	1	NUM
ejpam-3872	178	9	,	,	PUNCT
ejpam-3872	178	10	whenever	whenever	SCONJ
ejpam-3872	178	11	it	it	PRON
ejpam-3872	178	12	is	be	AUX
ejpam-3872	178	13	slowly	slowly	ADV
ejpam-3872	178	14	varying	vary	VERB
ejpam-3872	178	15	at	at	ADP
ejpam-3872	178	16	zero	zero	NUM
ejpam-3872	178	17	and	and	CCONJ
ejpam-3872	178	18	the	the	DET
ejpam-3872	178	19	rate	rate	NOUN
ejpam-3872	178	20	of	of	ADP
ejpam-3872	178	21	convergence	convergence	NOUN
ejpam-3872	178	22	dn	dn	NOUN
ejpam-3872	178	23	becomes	become	VERB
ejpam-3872	178	24	useless	useless	ADJ
ejpam-3872	178	25	.	.	PUNCT
ejpam-3872	179	1	in	in	ADP
ejpam-3872	179	2	such	such	ADJ
ejpam-3872	179	3	cases	case	NOUN
ejpam-3872	179	4	,	,	PUNCT
ejpam-3872	179	5	the	the	DET
ejpam-3872	179	6	rate	rate	NOUN
ejpam-3872	179	7	of	of	ADP
ejpam-3872	179	8	convergence	convergence	NOUN
ejpam-3872	179	9	is	be	AUX
ejpam-3872	179	10	reduced	reduce	VERB
ejpam-3872	179	11	to	to	ADP
ejpam-3872	179	12	op(dn	op(dn	PROPN
ejpam-3872	179	13	∨	∨	NUM
ejpam-3872	179	14	cn	cn	PROPN
ejpam-3872	179	15	)	)	PUNCT
ejpam-3872	179	16	.	.	PUNCT
ejpam-3872	180	1	furthermore	furthermore	ADV
ejpam-3872	180	2	,	,	PUNCT
ejpam-3872	180	3	based	base	VERB
ejpam-3872	180	4	on	on	ADP
ejpam-3872	180	5	the	the	DET
ejpam-3872	180	6	limit	limit	NOUN
ejpam-3872	180	7	sn	sn	PROPN
ejpam-3872	180	8	/	/	SYM
ejpam-3872	180	9	n→	n→	ADV
ejpam-3872	180	10	1	1	NUM
ejpam-3872	180	11	as	as	ADP
ejpam-3872	180	12	n→	n→	ADV
ejpam-3872	180	13	+	+	PROPN
ejpam-3872	180	14	∞	∞	PROPN
ejpam-3872	180	15	,	,	PUNCT
ejpam-3872	180	16	we	we	PRON
ejpam-3872	180	17	get	get	VERB
ejpam-3872	180	18	that	that	PRON
ejpam-3872	180	19	have	have	VERB
ejpam-3872	180	20	for	for	ADP
ejpam-3872	180	21	any	any	DET
ejpam-3872	180	22	η	η	NOUN
ejpam-3872	180	23	∈]0	∈]0	X
ejpam-3872	180	24	,	,	PUNCT
ejpam-3872	180	25	1	1	NUM
ejpam-3872	180	26	[	[	X
ejpam-3872	180	27	,	,	PUNCT
ejpam-3872	180	28	lim	lim	PROPN
ejpam-3872	180	29	inf	inf	PROPN
ejpam-3872	180	30	n→+∞	n→+∞	VERB
ejpam-3872	180	31	p	p	X
ejpam-3872	180	32	(	(	PUNCT
ejpam-3872	180	33	e−n	e−n	PROPN
ejpam-3872	180	34	/	/	SYM
ejpam-3872	180	35	η	η	PROPN
ejpam-3872	180	36	≤	≤	PROPN
ejpam-3872	180	37	e−sn	e−sn	PROPN
ejpam-3872	180	38	≤	≤	ADJ
ejpam-3872	180	39	e−ηn	e−ηn	NOUN
ejpam-3872	180	40	)	)	PUNCT
ejpam-3872	181	1	=	=	SYM
ejpam-3872	181	2	1	1	X
ejpam-3872	181	3	.	.	PUNCT
ejpam-3872	181	4	(	(	PUNCT
ejpam-3872	181	5	12	12	NUM
ejpam-3872	181	6	)	)	PUNCT
ejpam-3872	181	7	so	so	SCONJ
ejpam-3872	181	8	we	we	PRON
ejpam-3872	181	9	may	may	AUX
ejpam-3872	181	10	replace	replace	VERB
ejpam-3872	181	11	the	the	DET
ejpam-3872	181	12	rates	rate	NOUN
ejpam-3872	181	13	of	of	ADP
ejpam-3872	181	14	convergence	convergence	NOUN
ejpam-3872	181	15	dn	dn	NOUN
ejpam-3872	181	16	and	and	CCONJ
ejpam-3872	181	17	bn	bn	INTJ
ejpam-3872	181	18	by	by	ADP
ejpam-3872	181	19	dn(η	dn(η	NOUN
ejpam-3872	181	20	)	)	PUNCT
ejpam-3872	181	21	and	and	CCONJ
ejpam-3872	181	22	bn(η	bn(η	ADV
ejpam-3872	181	23	)	)	PUNCT
ejpam-3872	181	24	defined	define	VERB
ejpam-3872	181	25	as	as	ADP
ejpam-3872	181	26	follows	follow	VERB
ejpam-3872	181	27	,	,	PUNCT
ejpam-3872	181	28	for	for	ADP
ejpam-3872	181	29	η	η	PROPN
ejpam-3872	181	30	∈]0	∈]0	X
ejpam-3872	181	31	,	,	PUNCT
ejpam-3872	181	32	1	1	NUM
ejpam-3872	181	33	[	[	NOUN
ejpam-3872	181	34	,	,	PUNCT
ejpam-3872	181	35	sup{|b(t)|	sup{|b(t)|	NOUN
ejpam-3872	181	36	,	,	PUNCT
ejpam-3872	181	37	0	0	NUM
ejpam-3872	181	38	≤	≤	NUM
ejpam-3872	181	39	t	t	PROPN
ejpam-3872	181	40	≤	≤	ADJ
ejpam-3872	181	41	e−ηn	e−ηn	NOUN
ejpam-3872	181	42	}	}	PUNCT
ejpam-3872	181	43	=	=	PUNCT
ejpam-3872	181	44	o(bn(η	o(bn(η	ADJ
ejpam-3872	181	45	)	)	PUNCT
ejpam-3872	181	46	)	)	PUNCT
ejpam-3872	182	1	(	(	PUNCT
ejpam-3872	182	2	13	13	NUM
ejpam-3872	182	3	)	)	PUNCT
ejpam-3872	182	4	g.	g.	PROPN
ejpam-3872	182	5	s.	s.	PROPN
ejpam-3872	182	6	lo	lo	PROPN
ejpam-3872	182	7	et	et	PROPN
ejpam-3872	182	8	al	al	PROPN
ejpam-3872	182	9	.	.	PUNCT
ejpam-3872	182	10	/	/	SYM
ejpam-3872	182	11	eur	eur	PROPN
ejpam-3872	182	12	.	.	PUNCT
ejpam-3872	183	1	j.	j.	PROPN
ejpam-3872	183	2	pure	pure	PROPN
ejpam-3872	183	3	appl	appl	PROPN
ejpam-3872	183	4	.	.	PROPN
ejpam-3872	183	5	math	math	PROPN
ejpam-3872	183	6	,	,	PUNCT
ejpam-3872	183	7	14	14	NUM
ejpam-3872	183	8	(	(	PUNCT
ejpam-3872	183	9	1	1	NUM
ejpam-3872	183	10	)	)	PUNCT
ejpam-3872	183	11	(	(	PUNCT
ejpam-3872	183	12	2021	2021	NUM
ejpam-3872	183	13	)	)	PUNCT
ejpam-3872	183	14	,	,	PUNCT
ejpam-3872	183	15	19	19	NUM
ejpam-3872	183	16	-	-	SYM
ejpam-3872	183	17	42	42	NUM
ejpam-3872	183	18	28	28	NUM
ejpam-3872	183	19	and	and	CCONJ
ejpam-3872	183	20	sup	sup	PROPN
ejpam-3872	183	21	{	{	PUNCT
ejpam-3872	183	22	∣∣∣∣s(u	∣∣∣∣s(u	PROPN
ejpam-3872	183	23	)	)	PUNCT
ejpam-3872	183	24	s(v	s(v	PROPN
ejpam-3872	183	25	)	)	PUNCT
ejpam-3872	183	26	−	−	PROPN
ejpam-3872	183	27	1	1	NUM
ejpam-3872	183	28	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3872	183	29	,	,	PUNCT
ejpam-3872	183	30	e−n	e−n	PROPN
ejpam-3872	183	31	/	/	SYM
ejpam-3872	183	32	η	η	PROPN
ejpam-3872	183	33	≤	≤	PROPN
ejpam-3872	183	34	u	u	PROPN
ejpam-3872	183	35	,	,	PUNCT
ejpam-3872	183	36	v	v	ADJ
ejpam-3872	183	37	≤	≤	NUM
ejpam-3872	183	38	e−ηn	e−ηn	NOUN
ejpam-3872	183	39	}	}	PUNCT
ejpam-3872	183	40	=	=	SYM
ejpam-3872	183	41	o(dn(η	o(dn(η	ADJ
ejpam-3872	183	42	)	)	PUNCT
ejpam-3872	183	43	)	)	PUNCT
ejpam-3872	183	44	..	..	PUNCT
ejpam-3872	184	1	(	(	PUNCT
ejpam-3872	184	2	14	14	X
ejpam-3872	184	3	)	)	PUNCT
ejpam-3872	184	4	specific	specific	ADJ
ejpam-3872	184	5	rates	rate	NOUN
ejpam-3872	184	6	of	of	ADP
ejpam-3872	184	7	convergence	convergence	NOUN
ejpam-3872	184	8	will	will	AUX
ejpam-3872	184	9	be	be	AUX
ejpam-3872	184	10	given	give	VERB
ejpam-3872	184	11	in	in	ADP
ejpam-3872	184	12	the	the	DET
ejpam-3872	184	13	examples	example	NOUN
ejpam-3872	184	14	below	below	ADV
ejpam-3872	184	15	as	as	ADP
ejpam-3872	184	16	illustrations	illustration	NOUN
ejpam-3872	184	17	♦	♦	PROPN
ejpam-3872	184	18	3	3	NUM
ejpam-3872	184	19	.	.	PUNCT
ejpam-3872	185	1	examples	example	NOUN
ejpam-3872	185	2	and	and	CCONJ
ejpam-3872	185	3	applications	application	NOUN
ejpam-3872	185	4	let	let	VERB
ejpam-3872	185	5	us	we	PRON
ejpam-3872	185	6	begin	begin	VERB
ejpam-3872	185	7	to	to	PART
ejpam-3872	185	8	explain	explain	VERB
ejpam-3872	185	9	how	how	SCONJ
ejpam-3872	185	10	to	to	PART
ejpam-3872	185	11	apply	apply	VERB
ejpam-3872	185	12	the	the	DET
ejpam-3872	185	13	results	result	NOUN
ejpam-3872	185	14	for	for	ADP
ejpam-3872	185	15	γ	γ	X
ejpam-3872	185	16	=	=	SYM
ejpam-3872	185	17	0	0	NUM
ejpam-3872	185	18	.	.	PUNCT
ejpam-3872	186	1	generally	generally	ADV
ejpam-3872	186	2	,	,	PUNCT
ejpam-3872	186	3	we	we	PRON
ejpam-3872	186	4	may	may	AUX
ejpam-3872	186	5	find	find	VERB
ejpam-3872	186	6	the	the	DET
ejpam-3872	186	7	function	function	NOUN
ejpam-3872	186	8	s(u	s(u	PROPN
ejpam-3872	186	9	)	)	PUNCT
ejpam-3872	186	10	,	,	PUNCT
ejpam-3872	186	11	with	with	ADP
ejpam-3872	186	12	u	u	NOUN
ejpam-3872	186	13	∈]0	∈]0	NOUN
ejpam-3872	186	14	,	,	PUNCT
ejpam-3872	186	15	1	1	NUM
ejpam-3872	186	16	[	[	X
ejpam-3872	186	17	,	,	PUNCT
ejpam-3872	186	18	by	by	ADP
ejpam-3872	186	19	the	the	DET
ejpam-3872	186	20	π	π	PROPN
ejpam-3872	186	21	-	-	PUNCT
ejpam-3872	186	22	variation	variation	NOUN
ejpam-3872	186	23	formula	formula	NOUN
ejpam-3872	186	24	∀	∀	X
ejpam-3872	186	25	λ	λ	X
ejpam-3872	186	26	>	>	X
ejpam-3872	186	27	0	0	PROPN
ejpam-3872	186	28	,	,	PUNCT
ejpam-3872	186	29	f−1(1−	f−1(1−	PROPN
ejpam-3872	186	30	λu)−	λu)−	ADP
ejpam-3872	186	31	f−1(1−	f−1(1−	PROPN
ejpam-3872	186	32	u	u	NOUN
ejpam-3872	186	33	)	)	PUNCT
ejpam-3872	186	34	s(u	s(u	PROPN
ejpam-3872	186	35	)	)	PUNCT
ejpam-3872	186	36	→	→	SYM
ejpam-3872	186	37	−	−	PROPN
ejpam-3872	186	38	log	log	NOUN
ejpam-3872	186	39	λ	λ	PROPN
ejpam-3872	186	40	as	as	ADP
ejpam-3872	186	41	u→	u→	PROPN
ejpam-3872	186	42	0	0	NUM
ejpam-3872	186	43	.	.	PUNCT
ejpam-3872	187	1	another	another	DET
ejpam-3872	187	2	method	method	NOUN
ejpam-3872	187	3	concerns	concern	VERB
ejpam-3872	187	4	the	the	DET
ejpam-3872	187	5	special	special	ADJ
ejpam-3872	187	6	case	case	NOUN
ejpam-3872	187	7	where	where	SCONJ
ejpam-3872	187	8	f	f	PROPN
ejpam-3872	187	9	is	be	AUX
ejpam-3872	187	10	differentiable	differentiable	ADJ
ejpam-3872	187	11	on	on	ADP
ejpam-3872	187	12	a	a	DET
ejpam-3872	187	13	left	left	ADJ
ejpam-3872	187	14	neighborhood	neighborhood	NOUN
ejpam-3872	187	15	of	of	ADP
ejpam-3872	187	16	uep(f	uep(f	PROPN
ejpam-3872	187	17	)	)	PUNCT
ejpam-3872	187	18	.	.	PUNCT
ejpam-3872	188	1	it	it	PRON
ejpam-3872	188	2	is	be	AUX
ejpam-3872	188	3	proved	prove	VERB
ejpam-3872	188	4	in	in	ADP
ejpam-3872	188	5	[	[	X
ejpam-3872	188	6	5	5	NUM
ejpam-3872	188	7	]	]	PUNCT
ejpam-3872	188	8	that	that	SCONJ
ejpam-3872	188	9	if	if	SCONJ
ejpam-3872	188	10	u	u	PROPN
ejpam-3872	188	11	(	(	PUNCT
ejpam-3872	188	12	f−1(1−	f−1(1−	PROPN
ejpam-3872	188	13	u	u	NOUN
ejpam-3872	188	14	)	)	PUNCT
ejpam-3872	188	15	)	)	PUNCT
ejpam-3872	188	16	′	′	NUM
ejpam-3872	188	17	is	be	AUX
ejpam-3872	188	18	slowly	slowly	ADV
ejpam-3872	188	19	varying	vary	VERB
ejpam-3872	188	20	at	at	ADP
ejpam-3872	188	21	zero	zero	NUM
ejpam-3872	188	22	,	,	PUNCT
ejpam-3872	188	23	we	we	PRON
ejpam-3872	188	24	have	have	VERB
ejpam-3872	188	25	for	for	ADP
ejpam-3872	188	26	some	some	DET
ejpam-3872	188	27	u0	u0	NOUN
ejpam-3872	188	28	∈]0	∈]0	ADJ
ejpam-3872	188	29	,	,	PUNCT
ejpam-3872	188	30	1	1	NUM
ejpam-3872	188	31	[	[	X
ejpam-3872	188	32	,	,	PUNCT
ejpam-3872	188	33	s(u	s(u	PROPN
ejpam-3872	188	34	)	)	PUNCT
ejpam-3872	189	1	=	=	SYM
ejpam-3872	189	2	−u	−u	NOUN
ejpam-3872	189	3	(	(	PUNCT
ejpam-3872	189	4	f−1(1−	f−1(1−	PROPN
ejpam-3872	189	5	u	u	NOUN
ejpam-3872	189	6	)	)	PUNCT
ejpam-3872	189	7	)	)	PUNCT
ejpam-3872	189	8	′	′	NUM
ejpam-3872	190	1	for	for	ADP
ejpam-3872	190	2	u	u	PROPN
ejpam-3872	190	3	∈]0	∈]0	X
ejpam-3872	190	4	,	,	PUNCT
ejpam-3872	190	5	u0	u0	PROPN
ejpam-3872	190	6	[	[	X
ejpam-3872	190	7	.	.	PUNCT
ejpam-3872	190	8	checking	check	VERB
ejpam-3872	190	9	hypothesis	hypothesis	NOUN
ejpam-3872	190	10	,	,	PUNCT
ejpam-3872	190	11	(	(	PUNCT
ejpam-3872	190	12	ha	ha	INTJ
ejpam-3872	190	13	)	)	PUNCT
ejpam-3872	190	14	and	and	CCONJ
ejpam-3872	190	15	(	(	PUNCT
ejpam-3872	190	16	hb	hb	X
ejpam-3872	190	17	)	)	PUNCT
ejpam-3872	190	18	can	can	AUX
ejpam-3872	190	19	be	be	AUX
ejpam-3872	190	20	done	do	VERB
ejpam-3872	190	21	with	with	ADP
ejpam-3872	190	22	the	the	DET
ejpam-3872	190	23	function	function	NOUN
ejpam-3872	190	24	s(u	s(u	PROPN
ejpam-3872	190	25	)	)	PUNCT
ejpam-3872	190	26	with	with	ADP
ejpam-3872	190	27	u	u	PRON
ejpam-3872	190	28	∈]0	∈]0	NOUN
ejpam-3872	190	29	,	,	PUNCT
ejpam-3872	190	30	1	1	NUM
ejpam-3872	190	31	[	[	X
ejpam-3872	190	32	,	,	PUNCT
ejpam-3872	190	33	as	as	SCONJ
ejpam-3872	190	34	explained	explain	VERB
ejpam-3872	190	35	above	above	ADV
ejpam-3872	190	36	.	.	PUNCT
ejpam-3872	191	1	here	here	ADV
ejpam-3872	191	2	are	be	AUX
ejpam-3872	191	3	some	some	DET
ejpam-3872	191	4	specific	specific	ADJ
ejpam-3872	191	5	examples	example	NOUN
ejpam-3872	191	6	of	of	ADP
ejpam-3872	191	7	asymptotic	asymptotic	ADJ
ejpam-3872	191	8	laws	law	NOUN
ejpam-3872	191	9	and	and	CCONJ
ejpam-3872	191	10	related	related	ADJ
ejpam-3872	191	11	rates	rate	NOUN
ejpam-3872	191	12	of	of	ADP
ejpam-3872	191	13	convergence	convergence	NOUN
ejpam-3872	191	14	.	.	PUNCT
ejpam-3872	192	1	the	the	DET
ejpam-3872	192	2	details	detail	NOUN
ejpam-3872	192	3	for	for	ADP
ejpam-3872	192	4	each	each	DET
ejpam-3872	192	5	case	case	NOUN
ejpam-3872	192	6	are	be	AUX
ejpam-3872	192	7	given	give	VERB
ejpam-3872	192	8	in	in	ADP
ejpam-3872	192	9	the	the	DET
ejpam-3872	192	10	appendix	appendix	NOUN
ejpam-3872	192	11	(	(	PUNCT
ejpam-3872	192	12	section	section	NOUN
ejpam-3872	192	13	6	6	NUM
ejpam-3872	192	14	)	)	PUNCT
ejpam-3872	192	15	.	.	PUNCT
ejpam-3872	193	1	let	let	VERB
ejpam-3872	193	2	us	we	PRON
ejpam-3872	193	3	recall	recall	VERB
ejpam-3872	193	4	that	that	SCONJ
ejpam-3872	193	5	{	{	PUNCT
ejpam-3872	193	6	w	w	PROPN
ejpam-3872	193	7	(	(	PUNCT
ejpam-3872	193	8	t	t	PROPN
ejpam-3872	193	9	)	)	PUNCT
ejpam-3872	193	10	,	,	PUNCT
ejpam-3872	193	11	t	t	PROPN
ejpam-3872	193	12	≥	≥	NUM
ejpam-3872	193	13	1	1	NUM
ejpam-3872	193	14	}	}	PUNCT
ejpam-3872	193	15	is	be	AUX
ejpam-3872	193	16	a	a	DET
ejpam-3872	193	17	brownian	brownian	ADJ
ejpam-3872	193	18	motion	motion	NOUN
ejpam-3872	193	19	defined	define	VERB
ejpam-3872	193	20	on	on	ADP
ejpam-3872	193	21	the	the	DET
ejpam-3872	193	22	same	same	ADJ
ejpam-3872	193	23	probability	probability	NOUN
ejpam-3872	193	24	space	space	NOUN
ejpam-3872	193	25	as	as	ADP
ejpam-3872	193	26	the	the	DET
ejpam-3872	193	27	sequence	sequence	NOUN
ejpam-3872	193	28	of	of	ADP
ejpam-3872	193	29	records	record	NOUN
ejpam-3872	193	30	.	.	PUNCT
ejpam-3872	194	1	we	we	PRON
ejpam-3872	194	2	begin	begin	VERB
ejpam-3872	194	3	for	for	ADP
ejpam-3872	194	4	light	light	ADJ
ejpam-3872	194	5	tails	tail	NOUN
ejpam-3872	194	6	:	:	PUNCT
ejpam-3872	195	1	i	i	PRON
ejpam-3872	195	2	f	f	PROPN
ejpam-3872	195	3	∈	∈	PROPN
ejpam-3872	195	4	d(g0	d(g0	NOUN
ejpam-3872	195	5	)	)	PUNCT
ejpam-3872	195	6	.	.	PUNCT
ejpam-3872	196	1	(	(	PUNCT
ejpam-3872	196	2	1	1	X
ejpam-3872	196	3	)	)	PUNCT
ejpam-3872	196	4	x	x	PRON
ejpam-3872	196	5	follows	follow	VERB
ejpam-3872	196	6	an	an	DET
ejpam-3872	196	7	exponential	exponential	ADJ
ejpam-3872	196	8	law	law	NOUN
ejpam-3872	196	9	e(λ	e(λ	PROPN
ejpam-3872	196	10	)	)	PUNCT
ejpam-3872	196	11	,	,	PUNCT
ejpam-3872	196	12	λ	λ	X
ejpam-3872	196	13	>	>	X
ejpam-3872	196	14	0	0	NUM
ejpam-3872	196	15	.	.	PUNCT
ejpam-3872	197	1	by	by	ADP
ejpam-3872	197	2	point	point	NOUN
ejpam-3872	197	3	(	(	PUNCT
ejpam-3872	197	4	b	b	NOUN
ejpam-3872	197	5	)	)	PUNCT
ejpam-3872	197	6	of	of	ADP
ejpam-3872	197	7	theorem	theorem	ADJ
ejpam-3872	197	8	1	1	NUM
ejpam-3872	197	9	,	,	PUNCT
ejpam-3872	197	10	x(n	x(n	NOUN
ejpam-3872	197	11	)	)	PUNCT
ejpam-3872	197	12	−	−	ADP
ejpam-3872	197	13	n√	n√	SYM
ejpam-3872	197	14	n	n	CCONJ
ejpam-3872	197	15	n	n	CCONJ
ejpam-3872	197	16	(	(	PUNCT
ejpam-3872	197	17	0	0	NUM
ejpam-3872	197	18	,	,	PUNCT
ejpam-3872	197	19	λ−2	λ−2	PROPN
ejpam-3872	197	20	)	)	PUNCT
ejpam-3872	197	21	.	.	PUNCT
ejpam-3872	198	1	but	but	CCONJ
ejpam-3872	198	2	for	for	ADP
ejpam-3872	198	3	a	a	DET
ejpam-3872	198	4	fixed	fixed	ADJ
ejpam-3872	198	5	n	n	CCONJ
ejpam-3872	198	6	,	,	PUNCT
ejpam-3872	198	7	we	we	PRON
ejpam-3872	198	8	have	have	VERB
ejpam-3872	198	9	for	for	ADP
ejpam-3872	198	10	a	a	DET
ejpam-3872	198	11	random	random	ADJ
ejpam-3872	198	12	variable	variable	NOUN
ejpam-3872	198	13	v	v	NOUN
ejpam-3872	198	14	following	follow	VERB
ejpam-3872	198	15	a	a	DET
ejpam-3872	198	16	gamma	gamma	NOUN
ejpam-3872	198	17	law	law	NOUN
ejpam-3872	198	18	of	of	ADP
ejpam-3872	198	19	parameters	parameter	NOUN
ejpam-3872	198	20	n	n	PRON
ejpam-3872	198	21	≥	≥	NOUN
ejpam-3872	198	22	1	1	NUM
ejpam-3872	198	23	and	and	CCONJ
ejpam-3872	198	24	1	1	NUM
ejpam-3872	198	25	,	,	PUNCT
ejpam-3872	198	26	x(n	x(n	NOUN
ejpam-3872	198	27	)	)	PUNCT
ejpam-3872	198	28	−	−	ADP
ejpam-3872	198	29	n√	n√	SYM
ejpam-3872	198	30	n	n	ADV
ejpam-3872	198	31	∼	∼	NOUN
ejpam-3872	198	32	v	v	ADP
ejpam-3872	198	33	−	−	PROPN
ejpam-3872	198	34	e(v	e(v	NOUN
ejpam-3872	198	35	)	)	PUNCT
ejpam-3872	199	1	var(v	var(v	PROPN
ejpam-3872	199	2	)	)	PUNCT
ejpam-3872	199	3	1/2	1/2	NUM
ejpam-3872	199	4	.	.	PUNCT
ejpam-3872	200	1	g.	g.	PROPN
ejpam-3872	200	2	s.	s.	PROPN
ejpam-3872	200	3	lo	lo	PROPN
ejpam-3872	200	4	et	et	PROPN
ejpam-3872	200	5	al	al	PROPN
ejpam-3872	200	6	.	.	PUNCT
ejpam-3872	200	7	/	/	SYM
ejpam-3872	200	8	eur	eur	PROPN
ejpam-3872	200	9	.	.	PUNCT
ejpam-3872	201	1	j.	j.	PROPN
ejpam-3872	201	2	pure	pure	PROPN
ejpam-3872	201	3	appl	appl	PROPN
ejpam-3872	201	4	.	.	PROPN
ejpam-3872	201	5	math	math	PROPN
ejpam-3872	201	6	,	,	PUNCT
ejpam-3872	201	7	14	14	NUM
ejpam-3872	201	8	(	(	PUNCT
ejpam-3872	201	9	1	1	NUM
ejpam-3872	201	10	)	)	PUNCT
ejpam-3872	201	11	(	(	PUNCT
ejpam-3872	201	12	2021	2021	NUM
ejpam-3872	201	13	)	)	PUNCT
ejpam-3872	201	14	,	,	PUNCT
ejpam-3872	201	15	19	19	NUM
ejpam-3872	201	16	-	-	SYM
ejpam-3872	201	17	42	42	NUM
ejpam-3872	201	18	29	29	NUM
ejpam-3872	201	19	the	the	DET
ejpam-3872	201	20	rate	rate	NOUN
ejpam-3872	201	21	of	of	ADP
ejpam-3872	201	22	convergence	convergence	NOUN
ejpam-3872	201	23	is	be	AUX
ejpam-3872	201	24	x(n	x(n	NOUN
ejpam-3872	201	25	)	)	PUNCT
ejpam-3872	201	26	−	−	ADP
ejpam-3872	201	27	n√	n√	SYM
ejpam-3872	201	28	n	n	NOUN
ejpam-3872	201	29	=	=	SYM
ejpam-3872	201	30	s∗n	s∗n	NUM
ejpam-3872	201	31	=	=	SYM
ejpam-3872	202	1	w	w	ADP
ejpam-3872	202	2	∗n	∗n	PROPN
ejpam-3872	202	3	+	+	SYM
ejpam-3872	202	4	op(n−1	op(n−1	PROPN
ejpam-3872	202	5	log	log	NOUN
ejpam-3872	202	6	n	n	CCONJ
ejpam-3872	202	7	)	)	PUNCT
ejpam-3872	202	8	.	.	PUNCT
ejpam-3872	203	1	(	(	PUNCT
ejpam-3872	203	2	2	2	X
ejpam-3872	203	3	)	)	PUNCT
ejpam-3872	203	4	x	x	PRON
ejpam-3872	203	5	follows	follow	VERB
ejpam-3872	203	6	a	a	DET
ejpam-3872	203	7	standard	standard	ADJ
ejpam-3872	203	8	normal	normal	ADJ
ejpam-3872	203	9	law	law	NOUN
ejpam-3872	203	10	n	n	CCONJ
ejpam-3872	203	11	(	(	PUNCT
ejpam-3872	203	12	0	0	NUM
ejpam-3872	203	13	,	,	PUNCT
ejpam-3872	203	14	1	1	NUM
ejpam-3872	203	15	)	)	PUNCT
ejpam-3872	203	16	.	.	PUNCT
ejpam-3872	204	1	by	by	ADP
ejpam-3872	204	2	point	point	NOUN
ejpam-3872	204	3	(	(	PUNCT
ejpam-3872	204	4	d	d	NOUN
ejpam-3872	204	5	)	)	PUNCT
ejpam-3872	204	6	of	of	ADP
ejpam-3872	204	7	theorem	theorem	ADJ
ejpam-3872	204	8	1	1	NUM
ejpam-3872	204	9	,	,	PUNCT
ejpam-3872	204	10	x(n	x(n	NOUN
ejpam-3872	204	11	)	)	PUNCT
ejpam-3872	204	12	−	−	PROPN
ejpam-3872	204	13	(	(	PUNCT
ejpam-3872	204	14	2n)1/2	2n)1/2	NUM
ejpam-3872	204	15	n	n	CCONJ
ejpam-3872	204	16	(	(	PUNCT
ejpam-3872	204	17	0	0	NUM
ejpam-3872	204	18	,	,	PUNCT
ejpam-3872	204	19	1/2	1/2	NUM
ejpam-3872	204	20	)	)	PUNCT
ejpam-3872	204	21	.	.	PUNCT
ejpam-3872	205	1	the	the	DET
ejpam-3872	205	2	rate	rate	NOUN
ejpam-3872	205	3	of	of	ADP
ejpam-3872	205	4	convergence	convergence	NOUN
ejpam-3872	205	5	is	be	AUX
ejpam-3872	205	6	given	give	VERB
ejpam-3872	205	7	by	by	ADP
ejpam-3872	205	8	x(n	x(n	NOUN
ejpam-3872	205	9	)	)	PUNCT
ejpam-3872	206	1	−	−	PROPN
ejpam-3872	206	2	(	(	PUNCT
ejpam-3872	206	3	2n)1/2	2n)1/2	NUM
ejpam-3872	206	4	=	=	SYM
ejpam-3872	206	5	s∗n	s∗n	NUM
ejpam-3872	207	1	+	+	NOUN
ejpam-3872	207	2	op	op	NOUN
ejpam-3872	207	3	(	(	PUNCT
ejpam-3872	207	4	(	(	PUNCT
ejpam-3872	207	5	log	log	PROPN
ejpam-3872	207	6	n)2	n)2	NOUN
ejpam-3872	207	7	n	n	NOUN
ejpam-3872	207	8	)	)	PUNCT
ejpam-3872	207	9	=	=	PUNCT
ejpam-3872	208	1	w	w	ADP
ejpam-3872	208	2	∗n	∗n	PROPN
ejpam-3872	208	3	+	+	NOUN
ejpam-3872	208	4	op	op	NOUN
ejpam-3872	208	5	(	(	PUNCT
ejpam-3872	208	6	log	log	NOUN
ejpam-3872	208	7	n	n	CCONJ
ejpam-3872	208	8	n	n	NOUN
ejpam-3872	208	9	)	)	PUNCT
ejpam-3872	208	10	.	.	PUNCT
ejpam-3872	209	1	(	(	PUNCT
ejpam-3872	209	2	3	3	X
ejpam-3872	209	3	)	)	PUNCT
ejpam-3872	209	4	x	x	PRON
ejpam-3872	209	5	follows	follow	VERB
ejpam-3872	209	6	a	a	DET
ejpam-3872	209	7	rayleigh	rayleigh	PROPN
ejpam-3872	209	8	law	law	NOUN
ejpam-3872	209	9	of	of	ADP
ejpam-3872	209	10	parameter	parameter	PROPN
ejpam-3872	209	11	ρ	ρ	PROPN
ejpam-3872	209	12	>	>	X
ejpam-3872	209	13	0	0	NUM
ejpam-3872	209	14	,	,	PUNCT
ejpam-3872	209	15	with	with	ADP
ejpam-3872	209	16	cdf	cdf	PROPN
ejpam-3872	209	17	1−	1−	NUM
ejpam-3872	209	18	f	f	X
ejpam-3872	209	19	(	(	PUNCT
ejpam-3872	209	20	x	x	NOUN
ejpam-3872	209	21	)	)	PUNCT
ejpam-3872	209	22	=	=	SYM
ejpam-3872	209	23	exp(−ρx2	exp(−ρx2	PROPN
ejpam-3872	209	24	)	)	PUNCT
ejpam-3872	209	25	,	,	PUNCT
ejpam-3872	209	26	x	x	X
ejpam-3872	209	27	≥	≥	NOUN
ejpam-3872	209	28	0	0	NUM
ejpam-3872	209	29	.	.	PUNCT
ejpam-3872	210	1	by	by	ADP
ejpam-3872	210	2	point	point	NOUN
ejpam-3872	210	3	(	(	PUNCT
ejpam-3872	210	4	d	d	NOUN
ejpam-3872	210	5	)	)	PUNCT
ejpam-3872	210	6	of	of	ADP
ejpam-3872	210	7	theorem	theorem	NOUN
ejpam-3872	210	8	1	1	NUM
ejpam-3872	210	9	,	,	PUNCT
ejpam-3872	210	10	we	we	PRON
ejpam-3872	210	11	have	have	VERB
ejpam-3872	210	12	x(n	x(n	NOUN
ejpam-3872	210	13	)	)	PUNCT
ejpam-3872	211	1	−	−	PROPN
ejpam-3872	211	2	(	(	PUNCT
ejpam-3872	211	3	n	n	NOUN
ejpam-3872	211	4	ρ	ρ	NOUN
ejpam-3872	211	5	)	)	PUNCT
ejpam-3872	211	6	1/2	1/2	NUM
ejpam-3872	211	7	n	n	CCONJ
ejpam-3872	211	8	(	(	PUNCT
ejpam-3872	211	9	0	0	NUM
ejpam-3872	211	10	,	,	PUNCT
ejpam-3872	211	11	ρ−1/4	ρ−1/4	NOUN
ejpam-3872	211	12	)	)	PUNCT
ejpam-3872	211	13	.	.	PUNCT
ejpam-3872	212	1	we	we	PRON
ejpam-3872	212	2	also	also	ADV
ejpam-3872	212	3	have	have	VERB
ejpam-3872	212	4	x(n	x(n	NOUN
ejpam-3872	212	5	)	)	PUNCT
ejpam-3872	213	1	−	−	PROPN
ejpam-3872	213	2	(	(	PUNCT
ejpam-3872	213	3	n	n	NOUN
ejpam-3872	213	4	ρ	ρ	NOUN
ejpam-3872	213	5	)	)	PUNCT
ejpam-3872	213	6	1/2	1/2	NUM
ejpam-3872	213	7	=	=	PUNCT
ejpam-3872	213	8	ρ−1/2s∗n	ρ−1/2s∗n	PROPN
ejpam-3872	214	1	+	+	NOUN
ejpam-3872	214	2	op	op	NOUN
ejpam-3872	214	3	(	(	PUNCT
ejpam-3872	214	4	1√	1√	NOUN
ejpam-3872	214	5	n	n	NOUN
ejpam-3872	214	6	)	)	PUNCT
ejpam-3872	214	7	.	.	PUNCT
ejpam-3872	215	1	(	(	PUNCT
ejpam-3872	215	2	4	4	X
ejpam-3872	215	3	)	)	PUNCT
ejpam-3872	215	4	x	x	PRON
ejpam-3872	215	5	follows	follow	VERB
ejpam-3872	215	6	the	the	DET
ejpam-3872	215	7	logistic	logistic	ADJ
ejpam-3872	215	8	law	law	NOUN
ejpam-3872	215	9	,	,	PUNCT
ejpam-3872	215	10	with	with	ADP
ejpam-3872	215	11	cdf	cdf	PROPN
ejpam-3872	215	12	f	f	PROPN
ejpam-3872	215	13	(	(	PUNCT
ejpam-3872	215	14	x	x	NOUN
ejpam-3872	215	15	)	)	PUNCT
ejpam-3872	215	16	=	=	SYM
ejpam-3872	215	17	1	1	NUM
ejpam-3872	215	18	1	1	NUM
ejpam-3872	215	19	+	+	CCONJ
ejpam-3872	215	20	e−x	e−x	NOUN
ejpam-3872	215	21	,	,	PUNCT
ejpam-3872	215	22	x	x	PROPN
ejpam-3872	215	23	∈	∈	PROPN
ejpam-3872	215	24	r.	r.	NOUN
ejpam-3872	215	25	by	by	ADP
ejpam-3872	215	26	point	point	NOUN
ejpam-3872	215	27	(	(	PUNCT
ejpam-3872	215	28	b	b	NOUN
ejpam-3872	215	29	)	)	PUNCT
ejpam-3872	215	30	of	of	ADP
ejpam-3872	215	31	theorem	theorem	NOUN
ejpam-3872	215	32	1	1	NUM
ejpam-3872	215	33	,	,	PUNCT
ejpam-3872	215	34	we	we	PRON
ejpam-3872	215	35	have	have	VERB
ejpam-3872	215	36	x(n	x(n	NOUN
ejpam-3872	215	37	)	)	PUNCT
ejpam-3872	216	1	−	−	ADP
ejpam-3872	216	2	n√	n√	SYM
ejpam-3872	216	3	n	n	CCONJ
ejpam-3872	216	4	n	n	CCONJ
ejpam-3872	216	5	(	(	PUNCT
ejpam-3872	216	6	0	0	NUM
ejpam-3872	216	7	,	,	PUNCT
ejpam-3872	216	8	1	1	NUM
ejpam-3872	216	9	)	)	PUNCT
ejpam-3872	216	10	.	.	PUNCT
ejpam-3872	217	1	g.	g.	PROPN
ejpam-3872	217	2	s.	s.	PROPN
ejpam-3872	217	3	lo	lo	PROPN
ejpam-3872	217	4	et	et	PROPN
ejpam-3872	217	5	al	al	PROPN
ejpam-3872	217	6	.	.	PUNCT
ejpam-3872	217	7	/	/	SYM
ejpam-3872	217	8	eur	eur	PROPN
ejpam-3872	217	9	.	.	PUNCT
ejpam-3872	218	1	j.	j.	PROPN
ejpam-3872	218	2	pure	pure	PROPN
ejpam-3872	218	3	appl	appl	PROPN
ejpam-3872	218	4	.	.	PROPN
ejpam-3872	218	5	math	math	PROPN
ejpam-3872	218	6	,	,	PUNCT
ejpam-3872	218	7	14	14	NUM
ejpam-3872	218	8	(	(	PUNCT
ejpam-3872	218	9	1	1	NUM
ejpam-3872	218	10	)	)	PUNCT
ejpam-3872	218	11	(	(	PUNCT
ejpam-3872	218	12	2021	2021	NUM
ejpam-3872	218	13	)	)	PUNCT
ejpam-3872	218	14	,	,	PUNCT
ejpam-3872	218	15	19	19	NUM
ejpam-3872	218	16	-	-	SYM
ejpam-3872	218	17	42	42	NUM
ejpam-3872	218	18	30	30	NUM
ejpam-3872	218	19	the	the	DET
ejpam-3872	218	20	rate	rate	NOUN
ejpam-3872	218	21	of	of	ADP
ejpam-3872	218	22	convergence	convergence	NOUN
ejpam-3872	218	23	is	be	AUX
ejpam-3872	218	24	given	give	VERB
ejpam-3872	218	25	,	,	PUNCT
ejpam-3872	218	26	for	for	ADP
ejpam-3872	218	27	any	any	DET
ejpam-3872	218	28	η	η	NOUN
ejpam-3872	218	29	∈]0	∈]0	X
ejpam-3872	218	30	,	,	PUNCT
ejpam-3872	218	31	1	1	NUM
ejpam-3872	218	32	[	[	X
ejpam-3872	218	33	,	,	PUNCT
ejpam-3872	218	34	x(n	x(n	NOUN
ejpam-3872	218	35	)	)	PUNCT
ejpam-3872	218	36	−	−	ADP
ejpam-3872	218	37	n√	n√	SYM
ejpam-3872	218	38	n	n	NOUN
ejpam-3872	218	39	=	=	SYM
ejpam-3872	218	40	s∗n	s∗n	NUM
ejpam-3872	218	41	+	+	NOUN
ejpam-3872	218	42	op	op	NOUN
ejpam-3872	218	43	(	(	PUNCT
ejpam-3872	218	44	e−nη	e−nη	NOUN
ejpam-3872	218	45	1−	1−	NUM
ejpam-3872	218	46	e−n	e−n	PROPN
ejpam-3872	218	47	/	/	SYM
ejpam-3872	218	48	η	η	PROPN
ejpam-3872	218	49	)	)	PUNCT
ejpam-3872	218	50	.	.	PUNCT
ejpam-3872	219	1	(	(	PUNCT
ejpam-3872	219	2	5	5	X
ejpam-3872	219	3	)	)	PUNCT
ejpam-3872	219	4	x	x	X
ejpam-3872	219	5	>	>	X
ejpam-3872	219	6	0	0	NUM
ejpam-3872	219	7	follows	follow	VERB
ejpam-3872	219	8	a	a	DET
ejpam-3872	219	9	standard	standard	ADJ
ejpam-3872	219	10	lognormal	lognormal	ADJ
ejpam-3872	219	11	law	law	NOUN
ejpam-3872	219	12	,	,	PUNCT
ejpam-3872	219	13	that	that	PRON
ejpam-3872	219	14	is	is	ADV
ejpam-3872	219	15	logx	logx	PROPN
ejpam-3872	219	16	follows	follow	VERB
ejpam-3872	219	17	a	a	DET
ejpam-3872	219	18	standard	standard	ADJ
ejpam-3872	219	19	normal	normal	ADJ
ejpam-3872	219	20	law	law	NOUN
ejpam-3872	219	21	.	.	PUNCT
ejpam-3872	220	1	we	we	PRON
ejpam-3872	220	2	have	have	VERB
ejpam-3872	220	3	logx(n	logx(n	NOUN
ejpam-3872	220	4	)	)	PUNCT
ejpam-3872	221	1	−	−	PROPN
ejpam-3872	221	2	(	(	PUNCT
ejpam-3872	221	3	2n)1/2	2n)1/2	NUM
ejpam-3872	221	4	n	n	CCONJ
ejpam-3872	221	5	(	(	PUNCT
ejpam-3872	221	6	0	0	NUM
ejpam-3872	221	7	,	,	PUNCT
ejpam-3872	221	8	1/2	1/2	NUM
ejpam-3872	221	9	)	)	PUNCT
ejpam-3872	221	10	.	.	PUNCT
ejpam-3872	222	1	the	the	DET
ejpam-3872	222	2	rate	rate	NOUN
ejpam-3872	222	3	of	of	ADP
ejpam-3872	222	4	convergence	convergence	NOUN
ejpam-3872	222	5	is	be	AUX
ejpam-3872	222	6	given	give	VERB
ejpam-3872	222	7	by	by	ADP
ejpam-3872	222	8	logx(n	logx(n	NOUN
ejpam-3872	222	9	)	)	PUNCT
ejpam-3872	222	10	−	−	PROPN
ejpam-3872	222	11	(	(	PUNCT
ejpam-3872	222	12	2n)1/2	2n)1/2	NUM
ejpam-3872	222	13	=	=	SYM
ejpam-3872	222	14	s∗n	s∗n	NUM
ejpam-3872	222	15	+	+	ADP
ejpam-3872	222	16	op(n−1(log	op(n−1(log	PROPN
ejpam-3872	222	17	n)2	n)2	NOUN
ejpam-3872	222	18	)	)	PUNCT
ejpam-3872	222	19	.	.	PUNCT
ejpam-3872	223	1	(	(	PUNCT
ejpam-3872	223	2	6	6	NUM
ejpam-3872	223	3	)	)	PUNCT
ejpam-3872	223	4	x	x	X
ejpam-3872	223	5	>	>	X
ejpam-3872	223	6	0	0	NUM
ejpam-3872	223	7	follows	follow	VERB
ejpam-3872	223	8	a	a	DET
ejpam-3872	223	9	gumbel	gumbel	PROPN
ejpam-3872	223	10	law	law	NOUN
ejpam-3872	223	11	with	with	ADP
ejpam-3872	223	12	cdf	cdf	PROPN
ejpam-3872	223	13	f	f	PROPN
ejpam-3872	223	14	(	(	PUNCT
ejpam-3872	223	15	x	x	NOUN
ejpam-3872	223	16	)	)	PUNCT
ejpam-3872	223	17	=	=	SYM
ejpam-3872	223	18	exp	exp	NOUN
ejpam-3872	223	19	(	(	PUNCT
ejpam-3872	223	20	−e−x	−e−x	PROPN
ejpam-3872	223	21	)	)	PUNCT
ejpam-3872	223	22	,	,	PUNCT
ejpam-3872	223	23	x	x	PUNCT
ejpam-3872	223	24	∈	∈	PROPN
ejpam-3872	223	25	r.	r.	PROPN
ejpam-3872	223	26	by	by	ADP
ejpam-3872	223	27	point	point	NOUN
ejpam-3872	223	28	(	(	PUNCT
ejpam-3872	223	29	b	b	NOUN
ejpam-3872	223	30	)	)	PUNCT
ejpam-3872	223	31	of	of	ADP
ejpam-3872	223	32	theorem	theorem	NOUN
ejpam-3872	223	33	1	1	NUM
ejpam-3872	223	34	,	,	PUNCT
ejpam-3872	223	35	we	we	PRON
ejpam-3872	223	36	have	have	VERB
ejpam-3872	223	37	x(n	x(n	NOUN
ejpam-3872	223	38	)	)	PUNCT
ejpam-3872	224	1	−	−	ADP
ejpam-3872	224	2	n√	n√	SYM
ejpam-3872	224	3	n	n	CCONJ
ejpam-3872	224	4	n	n	CCONJ
ejpam-3872	224	5	(	(	PUNCT
ejpam-3872	224	6	0	0	NUM
ejpam-3872	224	7	,	,	PUNCT
ejpam-3872	224	8	1	1	NUM
ejpam-3872	224	9	)	)	PUNCT
ejpam-3872	224	10	.	.	PUNCT
ejpam-3872	225	1	the	the	DET
ejpam-3872	225	2	rate	rate	NOUN
ejpam-3872	225	3	of	of	ADP
ejpam-3872	225	4	convergence	convergence	NOUN
ejpam-3872	225	5	is	be	AUX
ejpam-3872	225	6	given	give	VERB
ejpam-3872	225	7	,	,	PUNCT
ejpam-3872	225	8	for	for	ADP
ejpam-3872	225	9	any	any	DET
ejpam-3872	225	10	η	η	NOUN
ejpam-3872	225	11	∈]0	∈]0	X
ejpam-3872	225	12	,	,	PUNCT
ejpam-3872	225	13	1	1	NUM
ejpam-3872	225	14	[	[	X
ejpam-3872	225	15	,	,	PUNCT
ejpam-3872	225	16	by	by	ADP
ejpam-3872	225	17	x(n	x(n	NOUN
ejpam-3872	225	18	)	)	PUNCT
ejpam-3872	225	19	−	−	ADP
ejpam-3872	225	20	n√	n√	SYM
ejpam-3872	225	21	n	n	NOUN
ejpam-3872	225	22	=	=	SYM
ejpam-3872	225	23	s∗n	s∗n	NUM
ejpam-3872	226	1	+	+	NOUN
ejpam-3872	226	2	o	o	X
ejpam-3872	226	3	(	(	PUNCT
ejpam-3872	226	4	e−ηn	e−ηn	PROPN
ejpam-3872	226	5	)	)	PUNCT
ejpam-3872	226	6	.	.	PUNCT
ejpam-3872	227	1	ii	ii	PROPN
ejpam-3872	227	2	f	f	PROPN
ejpam-3872	227	3	∈	∈	PROPN
ejpam-3872	227	4	d(gγ	d(gγ	PROPN
ejpam-3872	227	5	)	)	PUNCT
ejpam-3872	227	6	,	,	PUNCT
ejpam-3872	227	7	γ	γ	X
ejpam-3872	227	8	>	>	X
ejpam-3872	227	9	0	0	NUM
ejpam-3872	227	10	.	.	PUNCT
ejpam-3872	228	1	(	(	PUNCT
ejpam-3872	228	2	7	7	X
ejpam-3872	228	3	)	)	PUNCT
ejpam-3872	228	4	x	x	PRON
ejpam-3872	228	5	follows	follow	VERB
ejpam-3872	228	6	a	a	DET
ejpam-3872	228	7	log	log	NOUN
ejpam-3872	228	8	-	-	PUNCT
ejpam-3872	228	9	logistic	logistic	NOUN
ejpam-3872	228	10	law	law	NOUN
ejpam-3872	228	11	of	of	ADP
ejpam-3872	228	12	parameter	parameter	NOUN
ejpam-3872	228	13	p	p	PROPN
ejpam-3872	228	14	>	>	X
ejpam-3872	228	15	0	0	NUM
ejpam-3872	228	16	,	,	PUNCT
ejpam-3872	228	17	with	with	ADP
ejpam-3872	228	18	cdf	cdf	PROPN
ejpam-3872	228	19	f	f	PROPN
ejpam-3872	228	20	(	(	PUNCT
ejpam-3872	228	21	x	x	NOUN
ejpam-3872	228	22	)	)	PUNCT
ejpam-3872	228	23	=	=	SYM
ejpam-3872	228	24	xp	xp	NOUN
ejpam-3872	228	25	1	1	NUM
ejpam-3872	229	1	+	+	CCONJ
ejpam-3872	229	2	xp	xp	INTJ
ejpam-3872	229	3	,	,	PUNCT
ejpam-3872	229	4	x	x	X
ejpam-3872	229	5	≥	≥	NOUN
ejpam-3872	229	6	0	0	NUM
ejpam-3872	229	7	.	.	PUNCT
ejpam-3872	230	1	by	by	ADP
ejpam-3872	230	2	point	point	NOUN
ejpam-3872	230	3	(	(	PUNCT
ejpam-3872	230	4	a	a	NOUN
ejpam-3872	230	5	)	)	PUNCT
ejpam-3872	230	6	of	of	ADP
ejpam-3872	230	7	theorem	theorem	NOUN
ejpam-3872	230	8	1	1	NUM
ejpam-3872	230	9	,	,	PUNCT
ejpam-3872	231	1	g.	g.	PROPN
ejpam-3872	231	2	s.	s.	PROPN
ejpam-3872	231	3	lo	lo	PROPN
ejpam-3872	231	4	et	et	PROPN
ejpam-3872	231	5	al	al	PROPN
ejpam-3872	231	6	.	.	PUNCT
ejpam-3872	231	7	/	/	SYM
ejpam-3872	231	8	eur	eur	PROPN
ejpam-3872	231	9	.	.	PUNCT
ejpam-3872	232	1	j.	j.	PROPN
ejpam-3872	232	2	pure	pure	PROPN
ejpam-3872	232	3	appl	appl	PROPN
ejpam-3872	232	4	.	.	PROPN
ejpam-3872	232	5	math	math	PROPN
ejpam-3872	232	6	,	,	PUNCT
ejpam-3872	232	7	14	14	NUM
ejpam-3872	232	8	(	(	PUNCT
ejpam-3872	232	9	1	1	NUM
ejpam-3872	232	10	)	)	PUNCT
ejpam-3872	232	11	(	(	PUNCT
ejpam-3872	232	12	2021	2021	NUM
ejpam-3872	232	13	)	)	PUNCT
ejpam-3872	232	14	,	,	PUNCT
ejpam-3872	232	15	19	19	NUM
ejpam-3872	232	16	-	-	SYM
ejpam-3872	232	17	42	42	NUM
ejpam-3872	232	18	31	31	NUM
ejpam-3872	232	19	(	(	PUNCT
ejpam-3872	232	20	e−n	e−n	PROPN
ejpam-3872	232	21	/	/	SYM
ejpam-3872	232	22	px(n	px(n	NOUN
ejpam-3872	232	23	)	)	PUNCT
ejpam-3872	232	24	)	)	PUNCT
ejpam-3872	232	25	−1/2	−1/2	PROPN
ejpam-3872	232	26	ln(0	ln(0	NOUN
ejpam-3872	232	27	,	,	PUNCT
ejpam-3872	232	28	p2	p2	NOUN
ejpam-3872	232	29	)	)	PUNCT
ejpam-3872	232	30	.	.	PUNCT
ejpam-3872	233	1	for	for	ADP
ejpam-3872	233	2	the	the	DET
ejpam-3872	233	3	rate	rate	NOUN
ejpam-3872	233	4	of	of	ADP
ejpam-3872	233	5	convergence	convergence	NOUN
ejpam-3872	233	6	,	,	PUNCT
ejpam-3872	233	7	we	we	PRON
ejpam-3872	233	8	take	take	VERB
ejpam-3872	233	9	η	η	PROPN
ejpam-3872	233	10	∈]0	∈]0	X
ejpam-3872	233	11	,	,	PUNCT
ejpam-3872	233	12	1	1	NUM
ejpam-3872	233	13	[	[	PUNCT
ejpam-3872	233	14	and	and	CCONJ
ejpam-3872	233	15	bn(η	bn(η	ADV
ejpam-3872	233	16	)	)	PUNCT
ejpam-3872	234	1	=	=	SYM
ejpam-3872	234	2	e−ηn	e−ηn	ADJ
ejpam-3872	234	3	p	p	X
ejpam-3872	234	4	(	(	PUNCT
ejpam-3872	234	5	1−	1−	NUM
ejpam-3872	234	6	e−n	e−n	PROPN
ejpam-3872	234	7	/	/	SYM
ejpam-3872	234	8	η	η	PROPN
ejpam-3872	234	9	)	)	PUNCT
ejpam-3872	234	10	.	.	PUNCT
ejpam-3872	235	1	we	we	PRON
ejpam-3872	235	2	have	have	VERB
ejpam-3872	235	3	(	(	PUNCT
ejpam-3872	235	4	e−n	e−n	PROPN
ejpam-3872	235	5	/	/	SYM
ejpam-3872	235	6	px(n	px(n	NOUN
ejpam-3872	235	7	)	)	PUNCT
ejpam-3872	235	8	)	)	PUNCT
ejpam-3872	236	1	−1/2	−1/2	VERB
ejpam-3872	236	2	−	−	PROPN
ejpam-3872	236	3	exp	exp	NOUN
ejpam-3872	236	4	(	(	PUNCT
ejpam-3872	236	5	s∗n	s∗n	NUM
ejpam-3872	236	6	)	)	PUNCT
ejpam-3872	236	7	=	=	SYM
ejpam-3872	236	8	op(bn	op(bn	PROPN
ejpam-3872	236	9	)	)	PUNCT
ejpam-3872	236	10	.	.	PUNCT
ejpam-3872	237	1	(	(	PUNCT
ejpam-3872	237	2	8)	8)	NUM
ejpam-3872	237	3	x	x	PRON
ejpam-3872	237	4	follows	follow	VERB
ejpam-3872	237	5	a	a	DET
ejpam-3872	237	6	sing	sing	NOUN
ejpam-3872	237	7	-	-	PUNCT
ejpam-3872	237	8	maddala	maddala	NOUN
ejpam-3872	237	9	law	law	NOUN
ejpam-3872	237	10	of	of	ADP
ejpam-3872	237	11	parameters	parameter	NOUN
ejpam-3872	237	12	a	a	DET
ejpam-3872	237	13	>	>	X
ejpam-3872	237	14	0	0	NUM
ejpam-3872	237	15	,	,	PUNCT
ejpam-3872	237	16	b	b	X
ejpam-3872	237	17	>	>	X
ejpam-3872	237	18	0	0	PUNCT
ejpam-3872	237	19	and	and	CCONJ
ejpam-3872	237	20	c	c	X
ejpam-3872	237	21	>	>	X
ejpam-3872	237	22	0	0	NUM
ejpam-3872	237	23	,	,	PUNCT
ejpam-3872	237	24	with	with	ADP
ejpam-3872	237	25	cdf	cdf	PROPN
ejpam-3872	237	26	1−	1−	NUM
ejpam-3872	237	27	f	f	X
ejpam-3872	237	28	(	(	PUNCT
ejpam-3872	237	29	x	x	NOUN
ejpam-3872	237	30	)	)	PUNCT
ejpam-3872	237	31	=	=	SYM
ejpam-3872	238	1	(	(	PUNCT
ejpam-3872	238	2	1	1	NUM
ejpam-3872	238	3	1	1	NUM
ejpam-3872	238	4	+	+	NUM
ejpam-3872	238	5	axb	axb	NOUN
ejpam-3872	238	6	)	)	PUNCT
ejpam-3872	239	1	c	c	NOUN
ejpam-3872	239	2	,	,	PUNCT
ejpam-3872	239	3	x	x	X
ejpam-3872	239	4	≥	≥	NOUN
ejpam-3872	239	5	0	0	NUM
ejpam-3872	239	6	.	.	PUNCT
ejpam-3872	240	1	by	by	ADP
ejpam-3872	240	2	point	point	NOUN
ejpam-3872	240	3	(	(	PUNCT
ejpam-3872	240	4	a	a	NOUN
ejpam-3872	240	5	)	)	PUNCT
ejpam-3872	240	6	of	of	ADP
ejpam-3872	240	7	theorem	theorem	NOUN
ejpam-3872	240	8	1	1	NUM
ejpam-3872	240	9	,	,	PUNCT
ejpam-3872	240	10	we	we	PRON
ejpam-3872	240	11	have	have	VERB
ejpam-3872	240	12	(	(	PUNCT
ejpam-3872	240	13	a1	a1	PROPN
ejpam-3872	240	14	/	/	SYM
ejpam-3872	240	15	b	b	NOUN
ejpam-3872	240	16	exp(−n/(bc))x(n	exp(−n/(bc))x(n	PROPN
ejpam-3872	240	17	)	)	PUNCT
ejpam-3872	240	18	)	)	PUNCT
ejpam-3872	241	1	1/√n	1/√n	NUM
ejpam-3872	241	2	ln(0	ln(0	NOUN
ejpam-3872	241	3	,	,	PUNCT
ejpam-3872	241	4	(	(	PUNCT
ejpam-3872	241	5	bc)−2	bc)−2	X
ejpam-3872	241	6	)	)	PUNCT
ejpam-3872	241	7	.	.	PUNCT
ejpam-3872	242	1	the	the	DET
ejpam-3872	242	2	rate	rate	NOUN
ejpam-3872	242	3	of	of	ADP
ejpam-3872	242	4	convergence	convergence	NOUN
ejpam-3872	242	5	is	be	AUX
ejpam-3872	242	6	given	give	VERB
ejpam-3872	242	7	as	as	SCONJ
ejpam-3872	242	8	follows	follow	VERB
ejpam-3872	242	9	.	.	PUNCT
ejpam-3872	243	1	let	let	VERB
ejpam-3872	243	2	η	η	PROPN
ejpam-3872	243	3	∈]0	∈]0	X
ejpam-3872	243	4	,	,	PUNCT
ejpam-3872	243	5	1	1	NUM
ejpam-3872	243	6	[	[	NOUN
ejpam-3872	243	7	,	,	PUNCT
ejpam-3872	243	8	and	and	CCONJ
ejpam-3872	243	9	bn(η	bn(η	ADV
ejpam-3872	243	10	)	)	PUNCT
ejpam-3872	244	1	=	=	SYM
ejpam-3872	244	2	e−ηn	e−ηn	ADJ
ejpam-3872	244	3	/	/	SYM
ejpam-3872	244	4	c	c	PROPN
ejpam-3872	244	5	b	b	PROPN
ejpam-3872	244	6	(	(	PUNCT
ejpam-3872	244	7	1−	1−	NUM
ejpam-3872	244	8	e−n/(cη	e−n/(cη	ADV
ejpam-3872	244	9	)	)	PUNCT
ejpam-3872	244	10	)	)	PUNCT
ejpam-3872	244	11	.	.	PUNCT
ejpam-3872	245	1	we	we	PRON
ejpam-3872	245	2	have	have	VERB
ejpam-3872	245	3	(	(	PUNCT
ejpam-3872	245	4	a1	a1	PROPN
ejpam-3872	245	5	/	/	SYM
ejpam-3872	245	6	b	b	NOUN
ejpam-3872	245	7	exp(−n/(bc))x(n	exp(−n/(bc))x(n	PROPN
ejpam-3872	245	8	)	)	PUNCT
ejpam-3872	245	9	)	)	PUNCT
ejpam-3872	245	10	1/√n	1/√n	NUM
ejpam-3872	245	11	=	=	PUNCT
ejpam-3872	245	12	exp(s∗n	exp(s∗n	PROPN
ejpam-3872	245	13	)	)	PUNCT
ejpam-3872	245	14	+	+	NOUN
ejpam-3872	245	15	op(bn(η	op(bn(η	ADJ
ejpam-3872	245	16	)	)	PUNCT
ejpam-3872	245	17	)	)	PUNCT
ejpam-3872	245	18	.	.	PUNCT
ejpam-3872	246	1	4	4	X
ejpam-3872	246	2	.	.	X
ejpam-3872	246	3	proofs	proof	NOUN
ejpam-3872	246	4	(	(	PUNCT
ejpam-3872	246	5	i	i	NOUN
ejpam-3872	246	6	)	)	PUNCT
ejpam-3872	246	7	proof	proof	NOUN
ejpam-3872	246	8	of	of	ADP
ejpam-3872	246	9	theorem	theorem	NOUN
ejpam-3872	246	10	1	1	X
ejpam-3872	246	11	.	.	X
ejpam-3872	247	1	we	we	PRON
ejpam-3872	247	2	begin	begin	VERB
ejpam-3872	247	3	by	by	ADP
ejpam-3872	247	4	describing	describe	VERB
ejpam-3872	247	5	the	the	DET
ejpam-3872	247	6	main	main	ADJ
ejpam-3872	247	7	tools	tool	NOUN
ejpam-3872	247	8	which	which	PRON
ejpam-3872	247	9	are	be	AUX
ejpam-3872	247	10	based	base	VERB
ejpam-3872	247	11	on	on	ADP
ejpam-3872	247	12	following	follow	VERB
ejpam-3872	247	13	results	result	NOUN
ejpam-3872	247	14	of	of	ADP
ejpam-3872	247	15	record	record	NOUN
ejpam-3872	247	16	theory	theory	NOUN
ejpam-3872	247	17	.	.	PUNCT
ejpam-3872	248	1	suppose	suppose	VERB
ejpam-3872	248	2	that	that	SCONJ
ejpam-3872	248	3	{	{	PUNCT
ejpam-3872	248	4	t	t	PROPN
ejpam-3872	248	5	,	,	PUNCT
ejpam-3872	248	6	tj	tj	X
ejpam-3872	248	7	>	>	X
ejpam-3872	248	8	0	0	PROPN
ejpam-3872	248	9	,	,	PUNCT
ejpam-3872	248	10	1	1	NUM
ejpam-3872	248	11	≤	≤	NUM
ejpam-3872	248	12	j	j	PROPN
ejpam-3872	248	13	≤	≤	PROPN
ejpam-3872	248	14	k	k	PROPN
ejpam-3872	248	15	}	}	PUNCT
ejpam-3872	248	16	are	be	AUX
ejpam-3872	248	17	(	(	PUNCT
ejpam-3872	248	18	k	k	X
ejpam-3872	249	1	+	+	PROPN
ejpam-3872	249	2	1	1	X
ejpam-3872	249	3	)	)	PUNCT
ejpam-3872	249	4	non	non	ADJ
ejpam-3872	249	5	-	-	ADJ
ejpam-3872	249	6	negative	negative	ADJ
ejpam-3872	249	7	real	real	ADV
ejpam-3872	249	8	-	-	PUNCT
ejpam-3872	249	9	valued	value	VERB
ejpam-3872	249	10	,	,	PUNCT
ejpam-3872	249	11	iid	iid	VERB
ejpam-3872	249	12	random	random	ADJ
ejpam-3872	249	13	variables	variable	NOUN
ejpam-3872	249	14	and	and	CCONJ
ejpam-3872	249	15	define	define	VERB
ejpam-3872	249	16	x0	x0	PROPN
ejpam-3872	249	17	=	=	SYM
ejpam-3872	249	18	0	0	NUM
ejpam-3872	249	19	,	,	PUNCT
ejpam-3872	249	20	tj	tj	PROPN
ejpam-3872	249	21	=	=	PUNCT
ejpam-3872	249	22	xj	xj	PROPN
ejpam-3872	249	23	−xj−1	−xj−1	NOUN
ejpam-3872	249	24	,	,	PUNCT
ejpam-3872	249	25	1	1	NUM
ejpam-3872	249	26	≤	≤	NUM
ejpam-3872	249	27	j	j	PROPN
ejpam-3872	249	28	≤	≤	PROPN
ejpam-3872	250	1	k.	k.	PROPN
ejpam-3872	250	2	g.	g.	PROPN
ejpam-3872	251	1	s.	s.	PROPN
ejpam-3872	251	2	lo	lo	PROPN
ejpam-3872	251	3	et	et	PROPN
ejpam-3872	251	4	al	al	PROPN
ejpam-3872	251	5	.	.	PUNCT
ejpam-3872	251	6	/	/	SYM
ejpam-3872	251	7	eur	eur	PROPN
ejpam-3872	251	8	.	.	PUNCT
ejpam-3872	252	1	j.	j.	PROPN
ejpam-3872	252	2	pure	pure	PROPN
ejpam-3872	252	3	appl	appl	PROPN
ejpam-3872	252	4	.	.	PROPN
ejpam-3872	252	5	math	math	PROPN
ejpam-3872	252	6	,	,	PUNCT
ejpam-3872	252	7	14	14	NUM
ejpam-3872	252	8	(	(	PUNCT
ejpam-3872	252	9	1	1	NUM
ejpam-3872	252	10	)	)	PUNCT
ejpam-3872	252	11	(	(	PUNCT
ejpam-3872	252	12	2021	2021	NUM
ejpam-3872	252	13	)	)	PUNCT
ejpam-3872	252	14	,	,	PUNCT
ejpam-3872	252	15	19	19	NUM
ejpam-3872	252	16	-	-	SYM
ejpam-3872	252	17	42	42	NUM
ejpam-3872	252	18	32	32	NUM
ejpam-3872	253	1	it	it	PRON
ejpam-3872	253	2	is	be	AUX
ejpam-3872	253	3	clear	clear	ADJ
ejpam-3872	253	4	that	that	SCONJ
ejpam-3872	253	5	if	if	SCONJ
ejpam-3872	253	6	t	t	PROPN
ejpam-3872	253	7	∼	∼	NOUN
ejpam-3872	253	8	e(λ	e(λ	NOUN
ejpam-3872	253	9	)	)	PUNCT
ejpam-3872	253	10	,	,	PUNCT
ejpam-3872	253	11	λ	λ	X
ejpam-3872	253	12	>	>	X
ejpam-3872	253	13	0	0	PROPN
ejpam-3872	253	14	,	,	PUNCT
ejpam-3872	253	15	then	then	ADV
ejpam-3872	253	16	the	the	DET
ejpam-3872	253	17	absolutely	absolutely	ADV
ejpam-3872	253	18	continuous	continuous	ADJ
ejpam-3872	253	19	pdf	pdf	NOUN
ejpam-3872	253	20	of	of	ADP
ejpam-3872	253	21	t	t	PROPN
ejpam-3872	253	22	=	=	SYM
ejpam-3872	253	23	(	(	PUNCT
ejpam-3872	253	24	t1	t1	PROPN
ejpam-3872	253	25	,	,	PUNCT
ejpam-3872	253	26	·	·	PUNCT
ejpam-3872	253	27	·	·	PUNCT
ejpam-3872	253	28	·	·	PUNCT
ejpam-3872	253	29	,	,	PUNCT
ejpam-3872	253	30	tk)t	tk)t	PROPN
ejpam-3872	253	31	is	be	AUX
ejpam-3872	253	32	given	give	VERB
ejpam-3872	253	33	by	by	ADP
ejpam-3872	253	34	ft	ft	PROPN
ejpam-3872	253	35	(	(	PUNCT
ejpam-3872	253	36	t1	t1	PROPN
ejpam-3872	253	37	,	,	PUNCT
ejpam-3872	253	38	·	·	PUNCT
ejpam-3872	253	39	·	·	PUNCT
ejpam-3872	253	40	·	·	PUNCT
ejpam-3872	253	41	,	,	PUNCT
ejpam-3872	253	42	tk	tk	PROPN
ejpam-3872	253	43	)	)	PUNCT
ejpam-3872	253	44	=	=	SYM
ejpam-3872	253	45	λke−λtk	λke−λtk	NOUN
ejpam-3872	253	46	1(0≤t1≤···≤tk	1(0≤t1≤···≤tk	NUM
ejpam-3872	253	47	)	)	PUNCT
ejpam-3872	253	48	.	.	PUNCT
ejpam-3872	254	1	(	(	PUNCT
ejpam-3872	254	2	15	15	X
ejpam-3872	254	3	)	)	PUNCT
ejpam-3872	254	4	suppose	suppose	VERB
ejpam-3872	254	5	if	if	SCONJ
ejpam-3872	254	6	tj	tj	PROPN
ejpam-3872	254	7	’s	’	VERB
ejpam-3872	254	8	are	be	AUX
ejpam-3872	254	9	independent	independent	ADJ
ejpam-3872	254	10	and	and	CCONJ
ejpam-3872	254	11	follow	follow	VERB
ejpam-3872	254	12	an	an	DET
ejpam-3872	254	13	exponential	exponential	ADJ
ejpam-3872	254	14	law	law	NOUN
ejpam-3872	254	15	e(λ	e(λ	PROPN
ejpam-3872	254	16	)	)	PUNCT
ejpam-3872	254	17	,	,	PUNCT
ejpam-3872	254	18	λ	λ	X
ejpam-3872	254	19	>	>	X
ejpam-3872	254	20	0	0	NUM
ejpam-3872	254	21	,	,	PUNCT
ejpam-3872	254	22	we	we	PRON
ejpam-3872	254	23	have	have	VERB
ejpam-3872	254	24	r(x	r(x	NOUN
ejpam-3872	254	25	)	)	PUNCT
ejpam-3872	254	26	=	=	SYM
ejpam-3872	254	27	df	df	PROPN
ejpam-3872	254	28	(	(	PUNCT
ejpam-3872	254	29	x)/dx	x)/dx	PROPN
ejpam-3872	254	30	1−	1−	NUM
ejpam-3872	254	31	f	f	PROPN
ejpam-3872	254	32	(	(	PUNCT
ejpam-3872	254	33	x	x	NOUN
ejpam-3872	254	34	)	)	PUNCT
ejpam-3872	254	35	=	=	SYM
ejpam-3872	254	36	λ	λ	PROPN
ejpam-3872	254	37	and	and	CCONJ
ejpam-3872	254	38	f(x	f(x	PROPN
ejpam-3872	254	39	)	)	PUNCT
ejpam-3872	254	40	=	=	PUNCT
ejpam-3872	255	1	λe−λx	λe−λx	NOUN
ejpam-3872	255	2	,	,	PUNCT
ejpam-3872	255	3	x	x	X
ejpam-3872	255	4	≥	≥	NOUN
ejpam-3872	255	5	0	0	NUM
ejpam-3872	255	6	.	.	PUNCT
ejpam-3872	256	1	as	as	SCONJ
ejpam-3872	256	2	stated	state	VERB
ejpam-3872	256	3	in	in	ADP
ejpam-3872	256	4	page	page	NOUN
ejpam-3872	256	5	3	3	NUM
ejpam-3872	256	6	of	of	ADP
ejpam-3872	256	7	[	[	X
ejpam-3872	256	8	7	7	NUM
ejpam-3872	256	9	]	]	PUNCT
ejpam-3872	256	10	,	,	PUNCT
ejpam-3872	256	11	the	the	DET
ejpam-3872	256	12	joint	joint	ADJ
ejpam-3872	256	13	distribution	distribution	NOUN
ejpam-3872	256	14	of	of	ADP
ejpam-3872	256	15	the	the	DET
ejpam-3872	256	16	k	k	PROPN
ejpam-3872	256	17	first	first	ADJ
ejpam-3872	256	18	record	record	NOUN
ejpam-3872	256	19	values	value	NOUN
ejpam-3872	256	20	(	(	PUNCT
ejpam-3872	256	21	t	t	NOUN
ejpam-3872	256	22	(	(	PUNCT
ejpam-3872	256	23	1	1	NUM
ejpam-3872	256	24	)	)	PUNCT
ejpam-3872	256	25	,	,	PUNCT
ejpam-3872	256	26	·	·	PUNCT
ejpam-3872	256	27	·	·	PUNCT
ejpam-3872	256	28	·	·	PUNCT
ejpam-3872	256	29	,	,	PUNCT
ejpam-3872	256	30	t	t	PROPN
ejpam-3872	256	31	(	(	PUNCT
ejpam-3872	256	32	k	k	NOUN
ejpam-3872	256	33	)	)	PUNCT
ejpam-3872	256	34	)	)	PUNCT
ejpam-3872	256	35	of	of	ADP
ejpam-3872	256	36	the	the	DET
ejpam-3872	256	37	sequence	sequence	NOUN
ejpam-3872	256	38	(	(	PUNCT
ejpam-3872	256	39	tn)n≥1	tn)n≥1	NOUN
ejpam-3872	256	40	is	be	AUX
ejpam-3872	256	41	the	the	DET
ejpam-3872	256	42	one	one	NOUN
ejpam-3872	256	43	given	give	VERB
ejpam-3872	256	44	in	in	ADP
ejpam-3872	256	45	formula	formula	NOUN
ejpam-3872	256	46	(	(	PUNCT
ejpam-3872	256	47	15	15	NUM
ejpam-3872	256	48	)	)	PUNCT
ejpam-3872	256	49	.	.	PUNCT
ejpam-3872	257	1	as	as	ADP
ejpam-3872	257	2	a	a	DET
ejpam-3872	257	3	consequence	consequence	NOUN
ejpam-3872	257	4	,	,	PUNCT
ejpam-3872	257	5	we	we	PRON
ejpam-3872	257	6	have	have	VERB
ejpam-3872	257	7	fact	fact	NOUN
ejpam-3872	257	8	1	1	NUM
ejpam-3872	257	9	.	.	PUNCT
ejpam-3872	258	1	if	if	SCONJ
ejpam-3872	258	2	the	the	DET
ejpam-3872	258	3	tj	tj	NOUN
ejpam-3872	258	4	’s	’s	PART
ejpam-3872	258	5	are	be	AUX
ejpam-3872	258	6	independent	independent	ADJ
ejpam-3872	258	7	and	and	CCONJ
ejpam-3872	258	8	follow	follow	VERB
ejpam-3872	258	9	an	an	DET
ejpam-3872	258	10	exponential	exponential	ADJ
ejpam-3872	258	11	law	law	NOUN
ejpam-3872	258	12	e(λ	e(λ	PROPN
ejpam-3872	258	13	)	)	PUNCT
ejpam-3872	258	14	,	,	PUNCT
ejpam-3872	258	15	then	then	ADV
ejpam-3872	258	16	the	the	DET
ejpam-3872	258	17	k	k	NOUN
ejpam-3872	258	18	-	-	PUNCT
ejpam-3872	258	19	th	th	VERB
ejpam-3872	258	20	record	record	NOUN
ejpam-3872	258	21	value	value	NOUN
ejpam-3872	258	22	,	,	PUNCT
ejpam-3872	258	23	k	k	PROPN
ejpam-3872	258	24	≥	≥	NUM
ejpam-3872	258	25	1	1	NUM
ejpam-3872	258	26	,	,	PUNCT
ejpam-3872	258	27	has	have	VERB
ejpam-3872	258	28	the	the	DET
ejpam-3872	258	29	same	same	ADJ
ejpam-3872	258	30	law	law	NOUN
ejpam-3872	258	31	as	as	ADP
ejpam-3872	258	32	the	the	DET
ejpam-3872	258	33	sum	sum	NOUN
ejpam-3872	258	34	of	of	ADP
ejpam-3872	258	35	k	k	PROPN
ejpam-3872	258	36	independent	independent	PROPN
ejpam-3872	258	37	e(λ)-random	e(λ)-random	PROPN
ejpam-3872	258	38	variables	variable	VERB
ejpam-3872	258	39	e1,k	e1,k	PROPN
ejpam-3872	258	40	,	,	PUNCT
ejpam-3872	258	41	·	·	PUNCT
ejpam-3872	258	42	·	·	PUNCT
ejpam-3872	258	43	·	·	PUNCT
ejpam-3872	258	44	,	,	PUNCT
ejpam-3872	258	45	ek	ek	PROPN
ejpam-3872	258	46	,	,	PUNCT
ejpam-3872	258	47	k	k	PROPN
ejpam-3872	258	48	,	,	PUNCT
ejpam-3872	258	49	i.e.	i.e.	X
ejpam-3872	258	50	t	t	PROPN
ejpam-3872	258	51	(	(	PUNCT
ejpam-3872	258	52	k	k	NOUN
ejpam-3872	258	53	)	)	PUNCT
ejpam-3872	258	54	=	=	PROPN
ejpam-3872	258	55	d	d	X
ejpam-3872	258	56	e1,k	e1,k	PROPN
ejpam-3872	258	57	+	+	CCONJ
ejpam-3872	258	58	·	·	PUNCT
ejpam-3872	258	59	·	·	PUNCT
ejpam-3872	258	60	·	·	PUNCT
ejpam-3872	258	61	+	+	CCONJ
ejpam-3872	258	62	ek	ek	PROPN
ejpam-3872	258	63	,	,	PUNCT
ejpam-3872	258	64	k	k	NOUN
ejpam-3872	258	65	,	,	PUNCT
ejpam-3872	258	66	where	where	SCONJ
ejpam-3872	258	67	=	=	NOUN
ejpam-3872	258	68	d	d	X
ejpam-3872	258	69	stands	stand	VERB
ejpam-3872	258	70	for	for	ADP
ejpam-3872	258	71	the	the	DET
ejpam-3872	258	72	equality	equality	NOUN
ejpam-3872	258	73	in	in	ADP
ejpam-3872	258	74	distribution	distribution	NOUN
ejpam-3872	258	75	.	.	PUNCT
ejpam-3872	259	1	by	by	ADP
ejpam-3872	259	2	the	the	DET
ejpam-3872	259	3	renyi	renyi	PROPN
ejpam-3872	259	4	’s	’s	PART
ejpam-3872	259	5	representation	representation	NOUN
ejpam-3872	259	6	,	,	PUNCT
ejpam-3872	259	7	we	we	PRON
ejpam-3872	259	8	can	can	AUX
ejpam-3872	259	9	represente	represente	VERB
ejpam-3872	259	10	the	the	DET
ejpam-3872	259	11	random	random	ADJ
ejpam-3872	259	12	variable	variable	NOUN
ejpam-3872	259	13	x	x	PUNCT
ejpam-3872	259	14	of	of	ADP
ejpam-3872	259	15	cdf	cdf	PROPN
ejpam-3872	259	16	f	f	X
ejpam-3872	259	17	by	by	ADP
ejpam-3872	259	18	a	a	DET
ejpam-3872	259	19	standard	standard	ADJ
ejpam-3872	259	20	exponential	exponential	ADJ
ejpam-3872	259	21	random	random	ADJ
ejpam-3872	259	22	variable	variable	NOUN
ejpam-3872	259	23	e	e	NOUN
ejpam-3872	259	24	x	x	X
ejpam-3872	259	25	=	=	SYM
ejpam-3872	259	26	d	d	X
ejpam-3872	259	27	f	f	NUM
ejpam-3872	259	28	−1	−1	NOUN
ejpam-3872	259	29	(	(	PUNCT
ejpam-3872	259	30	1−	1−	NUM
ejpam-3872	259	31	e−e	e−e	NOUN
ejpam-3872	259	32	)	)	PUNCT
ejpam-3872	259	33	.	.	PUNCT
ejpam-3872	260	1	it	it	PRON
ejpam-3872	260	2	comes	come	VERB
ejpam-3872	260	3	that	that	SCONJ
ejpam-3872	260	4	,	,	PUNCT
ejpam-3872	260	5	by	by	ADP
ejpam-3872	260	6	considering	consider	VERB
ejpam-3872	260	7	iid	iid	VERB
ejpam-3872	260	8	sequence	sequence	NOUN
ejpam-3872	260	9	(	(	PUNCT
ejpam-3872	260	10	xn)n≥1	xn)n≥1	PROPN
ejpam-3872	260	11	and	and	CCONJ
ejpam-3872	260	12	(	(	PUNCT
ejpam-3872	260	13	en)n≥1	en)n≥1	VERB
ejpam-3872	260	14	from	from	ADP
ejpam-3872	260	15	x	x	PUNCT
ejpam-3872	260	16	and	and	CCONJ
ejpam-3872	260	17	e	e	NOUN
ejpam-3872	260	18	,	,	PUNCT
ejpam-3872	260	19	and	and	CCONJ
ejpam-3872	260	20	by	by	ADP
ejpam-3872	260	21	denoting	denote	VERB
ejpam-3872	260	22	the	the	DET
ejpam-3872	260	23	two	two	NUM
ejpam-3872	260	24	n	n	CCONJ
ejpam-3872	260	25	-	-	PUNCT
ejpam-3872	260	26	th	th	NOUN
ejpam-3872	260	27	record	record	NOUN
ejpam-3872	260	28	values	value	NOUN
ejpam-3872	260	29	x(n	x(n	NOUN
ejpam-3872	260	30	)	)	PUNCT
ejpam-3872	260	31	and	and	CCONJ
ejpam-3872	260	32	e(n	e(n	PROPN
ejpam-3872	260	33	)	)	PUNCT
ejpam-3872	260	34	from	from	ADP
ejpam-3872	260	35	the	the	DET
ejpam-3872	260	36	two	two	NUM
ejpam-3872	260	37	sequences	sequence	NOUN
ejpam-3872	260	38	respectively	respectively	ADV
ejpam-3872	260	39	,	,	PUNCT
ejpam-3872	260	40	we	we	PRON
ejpam-3872	260	41	have	have	VERB
ejpam-3872	260	42	the	the	DET
ejpam-3872	260	43	following	follow	VERB
ejpam-3872	260	44	representations	representation	NOUN
ejpam-3872	260	45	x(n	x(n	NOUN
ejpam-3872	260	46	)	)	PUNCT
ejpam-3872	261	1	=	=	SYM
ejpam-3872	261	2	d	d	NOUN
ejpam-3872	261	3	f	f	NOUN
ejpam-3872	261	4	−1	−1	NOUN
ejpam-3872	261	5	(	(	PUNCT
ejpam-3872	261	6	1−	1−	NUM
ejpam-3872	261	7	e−e(n	e−e(n	NOUN
ejpam-3872	261	8	)	)	PUNCT
ejpam-3872	261	9	)	)	PUNCT
ejpam-3872	261	10	,	,	PUNCT
ejpam-3872	261	11	where	where	SCONJ
ejpam-3872	261	12	e(n	e(n	ADJ
ejpam-3872	261	13	)	)	PUNCT
ejpam-3872	261	14	=	=	SYM
ejpam-3872	261	15	e1,n	e1,n	PROPN
ejpam-3872	261	16	+	+	CCONJ
ejpam-3872	261	17	·	·	PUNCT
ejpam-3872	261	18	·	·	PUNCT
ejpam-3872	261	19	·	·	PUNCT
ejpam-3872	261	20	+	+	SYM
ejpam-3872	261	21	en	en	X
ejpam-3872	261	22	,	,	PUNCT
ejpam-3872	261	23	n	n	NOUN
ejpam-3872	261	24	=	=	SYM
ejpam-3872	261	25	s(n	s(n	PROPN
ejpam-3872	261	26	)	)	PUNCT
ejpam-3872	261	27	.	.	PUNCT
ejpam-3872	262	1	in	in	ADP
ejpam-3872	262	2	the	the	DET
ejpam-3872	262	3	sequel	sequel	NOUN
ejpam-3872	262	4	,	,	PUNCT
ejpam-3872	262	5	we	we	PRON
ejpam-3872	262	6	can	can	AUX
ejpam-3872	262	7	and	and	CCONJ
ejpam-3872	262	8	do	do	AUX
ejpam-3872	262	9	use	use	VERB
ejpam-3872	262	10	the	the	DET
ejpam-3872	262	11	equality	equality	NOUN
ejpam-3872	262	12	:	:	PUNCT
ejpam-3872	262	13	x(n	x(n	NOUN
ejpam-3872	262	14	)	)	PUNCT
ejpam-3872	263	1	=	=	SYM
ejpam-3872	263	2	f−1	f−1	PROPN
ejpam-3872	263	3	(	(	PUNCT
ejpam-3872	263	4	1−	1−	NUM
ejpam-3872	263	5	e−s(n	e−s(n	NOUN
ejpam-3872	263	6	)	)	PUNCT
ejpam-3872	263	7	)	)	PUNCT
ejpam-3872	263	8	.	.	PUNCT
ejpam-3872	264	1	let	let	VERB
ejpam-3872	264	2	us	we	PRON
ejpam-3872	264	3	apply	apply	VERB
ejpam-3872	264	4	the	the	DET
ejpam-3872	264	5	representations	representation	NOUN
ejpam-3872	264	6	by	by	ADP
ejpam-3872	264	7	using	use	VERB
ejpam-3872	264	8	the	the	DET
ejpam-3872	264	9	simple	simple	ADJ
ejpam-3872	264	10	central	central	ADJ
ejpam-3872	264	11	limit	limit	NOUN
ejpam-3872	264	12	theorem	theorem	ADJ
ejpam-3872	264	13	s(n	s(n	NOUN
ejpam-3872	264	14	)	)	PUNCT
ejpam-3872	264	15	−	−	ADP
ejpam-3872	264	16	n√	n√	SYM
ejpam-3872	264	17	n	n	CCONJ
ejpam-3872	264	18	n	n	CCONJ
ejpam-3872	264	19	(	(	PUNCT
ejpam-3872	264	20	0	0	NUM
ejpam-3872	264	21	,	,	PUNCT
ejpam-3872	264	22	1	1	NUM
ejpam-3872	264	23	)	)	PUNCT
ejpam-3872	264	24	as	as	ADP
ejpam-3872	264	25	n→	n→	ADV
ejpam-3872	264	26	+	+	PROPN
ejpam-3872	264	27	∞.	∞.	PROPN
ejpam-3872	264	28	in	in	ADP
ejpam-3872	264	29	the	the	DET
ejpam-3872	264	30	sequel	sequel	NOUN
ejpam-3872	264	31	,	,	PUNCT
ejpam-3872	264	32	any	any	DET
ejpam-3872	264	33	unspecified	unspecified	ADJ
ejpam-3872	264	34	limit	limit	NOUN
ejpam-3872	264	35	is	be	AUX
ejpam-3872	264	36	meant	mean	VERB
ejpam-3872	264	37	as	as	ADP
ejpam-3872	264	38	n→	n→	ADV
ejpam-3872	264	39	+	+	PROPN
ejpam-3872	265	1	∞.	∞.	PROPN
ejpam-3872	265	2	g.	g.	PROPN
ejpam-3872	265	3	s.	s.	PROPN
ejpam-3872	265	4	lo	lo	PROPN
ejpam-3872	265	5	et	et	PROPN
ejpam-3872	265	6	al	al	PROPN
ejpam-3872	265	7	.	.	PUNCT
ejpam-3872	265	8	/	/	SYM
ejpam-3872	265	9	eur	eur	PROPN
ejpam-3872	265	10	.	.	PUNCT
ejpam-3872	266	1	j.	j.	PROPN
ejpam-3872	266	2	pure	pure	PROPN
ejpam-3872	266	3	appl	appl	PROPN
ejpam-3872	266	4	.	.	PROPN
ejpam-3872	266	5	math	math	PROPN
ejpam-3872	266	6	,	,	PUNCT
ejpam-3872	266	7	14	14	NUM
ejpam-3872	266	8	(	(	PUNCT
ejpam-3872	266	9	1	1	NUM
ejpam-3872	266	10	)	)	PUNCT
ejpam-3872	266	11	(	(	PUNCT
ejpam-3872	266	12	2021	2021	NUM
ejpam-3872	266	13	)	)	PUNCT
ejpam-3872	266	14	,	,	PUNCT
ejpam-3872	266	15	19	19	NUM
ejpam-3872	266	16	-	-	SYM
ejpam-3872	266	17	42	42	NUM
ejpam-3872	266	18	33	33	NUM
ejpam-3872	266	19	let	let	VERB
ejpam-3872	266	20	us	we	PRON
ejpam-3872	266	21	suppose	suppose	VERB
ejpam-3872	266	22	that	that	SCONJ
ejpam-3872	266	23	x	x	PROPN
ejpam-3872	266	24	∈	∈	PROPN
ejpam-3872	266	25	d(g1	d(g1	NOUN
ejpam-3872	266	26	/	/	SYM
ejpam-3872	266	27	γ	γ	NOUN
ejpam-3872	266	28	)	)	PUNCT
ejpam-3872	266	29	.	.	PUNCT
ejpam-3872	267	1	if	if	SCONJ
ejpam-3872	267	2	x	x	X
ejpam-3872	267	3	≥	≥	NOUN
ejpam-3872	267	4	0	0	NUM
ejpam-3872	267	5	,	,	PUNCT
ejpam-3872	267	6	we	we	PRON
ejpam-3872	267	7	will	will	AUX
ejpam-3872	267	8	consider	consider	VERB
ejpam-3872	267	9	y	y	NOUN
ejpam-3872	267	10	=	=	PUNCT
ejpam-3872	267	11	logx	logx	PROPN
ejpam-3872	267	12	of	of	ADP
ejpam-3872	267	13	cdf	cdf	PROPN
ejpam-3872	267	14	g	g	PROPN
ejpam-3872	267	15	defined	define	VERB
ejpam-3872	267	16	by	by	ADP
ejpam-3872	267	17	g(x	g(x	NOUN
ejpam-3872	267	18	)	)	PUNCT
ejpam-3872	268	1	=	=	SYM
ejpam-3872	268	2	f	f	X
ejpam-3872	268	3	(	(	PUNCT
ejpam-3872	268	4	ex	ex	NOUN
ejpam-3872	268	5	)	)	PUNCT
ejpam-3872	268	6	,	,	PUNCT
ejpam-3872	268	7	x	x	PROPN
ejpam-3872	268	8	∈	∈	PROPN
ejpam-3872	268	9	r.	r.	NOUN
ejpam-3872	268	10	let	let	VERB
ejpam-3872	268	11	us	we	PRON
ejpam-3872	268	12	prove	prove	VERB
ejpam-3872	268	13	the	the	DET
ejpam-3872	268	14	theorem	theorem	NOUN
ejpam-3872	268	15	1	1	NUM
ejpam-3872	268	16	.	.	PUNCT
ejpam-3872	269	1	(	(	PUNCT
ejpam-3872	269	2	a	a	X
ejpam-3872	269	3	)	)	PUNCT
ejpam-3872	269	4	asymptotic	asymptotic	ADJ
ejpam-3872	269	5	law	law	NOUN
ejpam-3872	269	6	of	of	ADP
ejpam-3872	269	7	x(n	x(n	NOUN
ejpam-3872	269	8	)	)	PUNCT
ejpam-3872	269	9	for	for	ADP
ejpam-3872	269	10	γ	γ	X
ejpam-3872	269	11	>	>	X
ejpam-3872	269	12	0	0	NUM
ejpam-3872	269	13	.	.	PUNCT
ejpam-3872	270	1	we	we	PRON
ejpam-3872	270	2	recall	recall	VERB
ejpam-3872	270	3	that	that	DET
ejpam-3872	270	4	vn	vn	PROPN
ejpam-3872	270	5	=	=	SYM
ejpam-3872	270	6	e−s(n	e−s(n	PROPN
ejpam-3872	270	7	)	)	PUNCT
ejpam-3872	270	8	and	and	CCONJ
ejpam-3872	270	9	vn	vn	X
ejpam-3872	270	10	=	=	SYM
ejpam-3872	270	11	e−n	e−n	PROPN
ejpam-3872	270	12	,	,	PUNCT
ejpam-3872	270	13	n	n	PRON
ejpam-3872	270	14	≥	≥	NOUN
ejpam-3872	270	15	1	1	NUM
ejpam-3872	270	16	.	.	PUNCT
ejpam-3872	270	17	by	by	ADP
ejpam-3872	270	18	representation	representation	NOUN
ejpam-3872	270	19	(	(	PUNCT
ejpam-3872	270	20	4	4	NUM
ejpam-3872	270	21	)	)	PUNCT
ejpam-3872	270	22	,	,	PUNCT
ejpam-3872	270	23	we	we	PRON
ejpam-3872	270	24	have	have	VERB
ejpam-3872	270	25	f−1	f−1	PROPN
ejpam-3872	270	26	(	(	PUNCT
ejpam-3872	270	27	1−	1−	NUM
ejpam-3872	270	28	e−s(n	e−s(n	NOUN
ejpam-3872	270	29	)	)	PUNCT
ejpam-3872	270	30	)	)	PUNCT
ejpam-3872	271	1	=	=	PUNCT
ejpam-3872	271	2	(	(	PUNCT
ejpam-3872	271	3	1	1	NUM
ejpam-3872	271	4	+	+	NUM
ejpam-3872	271	5	a(vn))v	a(vn))v	NOUN
ejpam-3872	271	6	−γn	−γn	NOUN
ejpam-3872	271	7	exp	exp	NOUN
ejpam-3872	271	8	(	(	PUNCT
ejpam-3872	271	9	∫	∫	PROPN
ejpam-3872	271	10	1	1	NUM
ejpam-3872	271	11	vn	vn	PROPN
ejpam-3872	271	12	b(t	b(t	PROPN
ejpam-3872	271	13	)	)	PUNCT
ejpam-3872	271	14	t	t	PROPN
ejpam-3872	271	15	dt	dt	PROPN
ejpam-3872	271	16	)	)	PUNCT
ejpam-3872	271	17	,	,	PUNCT
ejpam-3872	271	18	n	n	CCONJ
ejpam-3872	271	19	≥	≥	NOUN
ejpam-3872	271	20	1	1	NUM
ejpam-3872	271	21	and	and	CCONJ
ejpam-3872	271	22	f−1	f−1	PROPN
ejpam-3872	271	23	(	(	PUNCT
ejpam-3872	271	24	1−	1−	NUM
ejpam-3872	271	25	e−n	e−n	PROPN
ejpam-3872	271	26	)	)	PUNCT
ejpam-3872	271	27	=	=	PUNCT
ejpam-3872	272	1	(	(	PUNCT
ejpam-3872	272	2	1	1	NUM
ejpam-3872	272	3	+	+	NUM
ejpam-3872	272	4	a(vn))v−γn	a(vn))v−γn	PROPN
ejpam-3872	272	5	exp	exp	NOUN
ejpam-3872	272	6	(	(	PUNCT
ejpam-3872	272	7	∫	∫	PROPN
ejpam-3872	272	8	1	1	NUM
ejpam-3872	272	9	vn	vn	PROPN
ejpam-3872	272	10	b(t	b(t	PROPN
ejpam-3872	272	11	)	)	PUNCT
ejpam-3872	272	12	t	t	PROPN
ejpam-3872	272	13	dt	dt	PROPN
ejpam-3872	272	14	)	)	PUNCT
ejpam-3872	272	15	,	,	PUNCT
ejpam-3872	272	16	n	n	X
ejpam-3872	272	17	≥	≥	NOUN
ejpam-3872	272	18	1	1	NUM
ejpam-3872	272	19	.	.	PUNCT
ejpam-3872	273	1	we	we	PRON
ejpam-3872	273	2	get	get	VERB
ejpam-3872	273	3	that	that	PRON
ejpam-3872	273	4	vn	vn	PROPN
ejpam-3872	273	5	→p	→p	PROPN
ejpam-3872	273	6	0	0	NUM
ejpam-3872	273	7	,	,	PUNCT
ejpam-3872	273	8	(	(	PUNCT
ejpam-3872	273	9	1	1	NUM
ejpam-3872	273	10	+	+	NUM
ejpam-3872	273	11	a(vn))/(1	a(vn))/(1	PROPN
ejpam-3872	273	12	+	+	CCONJ
ejpam-3872	273	13	a(vn	a(vn	PROPN
ejpam-3872	273	14	)	)	PUNCT
ejpam-3872	273	15	)	)	PUNCT
ejpam-3872	274	1	≡	≡	PROPN
ejpam-3872	274	2	1	1	NUM
ejpam-3872	275	1	+	+	CCONJ
ejpam-3872	275	2	pn	pn	PROPN
ejpam-3872	275	3	→p	→p	PROPN
ejpam-3872	275	4	1	1	NUM
ejpam-3872	275	5	.	.	PUNCT
ejpam-3872	276	1	we	we	PRON
ejpam-3872	276	2	get	get	VERB
ejpam-3872	276	3	log	log	NOUN
ejpam-3872	276	4	(	(	PUNCT
ejpam-3872	276	5	x(n	x(n	NOUN
ejpam-3872	276	6	)	)	PUNCT
ejpam-3872	276	7	f−1	f−1	PROPN
ejpam-3872	276	8	(	(	PUNCT
ejpam-3872	276	9	1−	1−	NUM
ejpam-3872	276	10	e−n	e−n	PROPN
ejpam-3872	276	11	)	)	PUNCT
ejpam-3872	276	12	)	)	PUNCT
ejpam-3872	277	1	=	=	PUNCT
ejpam-3872	278	1	pn(1	pn(1	NOUN
ejpam-3872	278	2	+	+	CCONJ
ejpam-3872	278	3	op(1))−	op(1))−	ADP
ejpam-3872	278	4	γ(s(n	γ(s(n	PROPN
ejpam-3872	278	5	)	)	PUNCT
ejpam-3872	278	6	−	−	NOUN
ejpam-3872	278	7	n	n	CCONJ
ejpam-3872	278	8	)	)	PUNCT
ejpam-3872	278	9	+	+	CCONJ
ejpam-3872	278	10	∫	∫	PROPN
ejpam-3872	278	11	vn	vn	PROPN
ejpam-3872	278	12	vn	vn	PROPN
ejpam-3872	278	13	b(t	b(t	PROPN
ejpam-3872	278	14	)	)	PUNCT
ejpam-3872	278	15	t	t	PROPN
ejpam-3872	278	16	dt	dt	PROPN
ejpam-3872	278	17	.	.	PUNCT
ejpam-3872	279	1	(	(	PUNCT
ejpam-3872	279	2	16	16	NUM
ejpam-3872	279	3	)	)	PUNCT
ejpam-3872	279	4	we	we	PRON
ejpam-3872	279	5	have	have	VERB
ejpam-3872	279	6	∣∣∣∣∫	∣∣∣∣∫	PRON
ejpam-3872	279	7	1	1	NUM
ejpam-3872	279	8	vn	vn	PROPN
ejpam-3872	279	9	b(t	b(t	PROPN
ejpam-3872	279	10	)	)	PUNCT
ejpam-3872	279	11	t	t	PROPN
ejpam-3872	279	12	dt	dt	NOUN
ejpam-3872	279	13	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3872	279	14	≤	≤	PROPN
ejpam-3872	279	15	(	(	PUNCT
ejpam-3872	279	16	sup	sup	NOUN
ejpam-3872	279	17	0≤t≤(vn∨vn	0≤t≤(vn∨vn	ADJ
ejpam-3872	279	18	)	)	PUNCT
ejpam-3872	279	19	|b(t)|	|b(t)|	ADJ
ejpam-3872	279	20	)	)	PUNCT
ejpam-3872	279	21	|s(n	|s(n	PROPN
ejpam-3872	279	22	)	)	PUNCT
ejpam-3872	279	23	−	−	PROPN
ejpam-3872	279	24	n|	n|	X
ejpam-3872	279	25	.	.	PUNCT
ejpam-3872	280	1	(	(	PUNCT
ejpam-3872	280	2	17	17	NUM
ejpam-3872	280	3	)	)	PUNCT
ejpam-3872	280	4	by	by	ADP
ejpam-3872	280	5	combining	combine	VERB
ejpam-3872	280	6	the	the	DET
ejpam-3872	280	7	two	two	NUM
ejpam-3872	280	8	last	last	ADJ
ejpam-3872	280	9	formulae	formulae	NOUN
ejpam-3872	280	10	,	,	PUNCT
ejpam-3872	280	11	we	we	PRON
ejpam-3872	280	12	have	have	VERB
ejpam-3872	280	13	n−1/2	n−1/2	NOUN
ejpam-3872	280	14	log	log	NOUN
ejpam-3872	280	15	(	(	PUNCT
ejpam-3872	280	16	x(n	x(n	NOUN
ejpam-3872	280	17	)	)	PUNCT
ejpam-3872	280	18	f−1	f−1	PROPN
ejpam-3872	280	19	(	(	PUNCT
ejpam-3872	280	20	1−	1−	NUM
ejpam-3872	280	21	e−n	e−n	PROPN
ejpam-3872	280	22	)	)	PUNCT
ejpam-3872	280	23	)	)	PUNCT
ejpam-3872	281	1	n	n	CCONJ
ejpam-3872	281	2	(	(	PUNCT
ejpam-3872	281	3	0	0	NUM
ejpam-3872	281	4	,	,	PUNCT
ejpam-3872	281	5	γ2	γ2	NOUN
ejpam-3872	281	6	)	)	PUNCT
ejpam-3872	281	7	.	.	PUNCT
ejpam-3872	282	1	(	(	PUNCT
ejpam-3872	282	2	b	b	X
ejpam-3872	282	3	)	)	PUNCT
ejpam-3872	282	4	asymptotic	asymptotic	ADJ
ejpam-3872	282	5	law	law	NOUN
ejpam-3872	282	6	of	of	ADP
ejpam-3872	282	7	y	y	PROPN
ejpam-3872	282	8	(	(	PUNCT
ejpam-3872	282	9	n	n	CCONJ
ejpam-3872	282	10	)	)	PUNCT
ejpam-3872	282	11	for	for	ADP
ejpam-3872	282	12	γ	γ	X
ejpam-3872	282	13	>	>	X
ejpam-3872	282	14	0	0	NUM
ejpam-3872	282	15	.	.	PUNCT
ejpam-3872	283	1	from	from	ADP
ejpam-3872	283	2	the	the	DET
ejpam-3872	283	3	previous	previous	ADJ
ejpam-3872	283	4	theorem	theorem	NOUN
ejpam-3872	283	5	,	,	PUNCT
ejpam-3872	283	6	it	it	PRON
ejpam-3872	283	7	is	be	AUX
ejpam-3872	283	8	immediate	immediate	ADJ
ejpam-3872	283	9	for	for	ADP
ejpam-3872	283	10	the	the	DET
ejpam-3872	283	11	following	follow	VERB
ejpam-3872	283	12	result	result	NOUN
ejpam-3872	283	13	.	.	PUNCT
ejpam-3872	284	1	it	it	PRON
ejpam-3872	284	2	is	be	AUX
ejpam-3872	284	3	clear	clear	ADJ
ejpam-3872	284	4	that	that	SCONJ
ejpam-3872	284	5	g−1	g−1	PROPN
ejpam-3872	284	6	=	=	SYM
ejpam-3872	284	7	logf−1	logf−1	PROPN
ejpam-3872	284	8	.	.	PUNCT
ejpam-3872	285	1	so	so	ADV
ejpam-3872	285	2	,	,	PUNCT
ejpam-3872	285	3	the	the	DET
ejpam-3872	285	4	previous	previous	ADJ
ejpam-3872	285	5	theorem	theorem	NOUN
ejpam-3872	285	6	implies	imply	VERB
ejpam-3872	285	7	n−1/2	n−1/2	PROPN
ejpam-3872	285	8	(	(	PUNCT
ejpam-3872	285	9	y	y	PROPN
ejpam-3872	285	10	(	(	PUNCT
ejpam-3872	285	11	n	n	CCONJ
ejpam-3872	285	12	)	)	PUNCT
ejpam-3872	285	13	−g−1	−g−1	X
ejpam-3872	285	14	(	(	PUNCT
ejpam-3872	285	15	1−	1−	NUM
ejpam-3872	285	16	e−n	e−n	PROPN
ejpam-3872	285	17	)	)	PUNCT
ejpam-3872	285	18	)	)	PUNCT
ejpam-3872	286	1	n	n	CCONJ
ejpam-3872	286	2	(	(	PUNCT
ejpam-3872	286	3	0	0	NUM
ejpam-3872	286	4	,	,	PUNCT
ejpam-3872	286	5	γ2	γ2	NOUN
ejpam-3872	286	6	)	)	PUNCT
ejpam-3872	286	7	.	.	PUNCT
ejpam-3872	287	1	here	here	ADV
ejpam-3872	287	2	,	,	PUNCT
ejpam-3872	287	3	it	it	PRON
ejpam-3872	287	4	is	be	AUX
ejpam-3872	287	5	clear	clear	ADJ
ejpam-3872	287	6	that	that	SCONJ
ejpam-3872	287	7	y	y	PROPN
ejpam-3872	287	8	∈	∈	PROPN
ejpam-3872	287	9	d(g0	d(g0	NOUN
ejpam-3872	287	10	)	)	PUNCT
ejpam-3872	287	11	and	and	CCONJ
ejpam-3872	287	12	r(x	r(x	PROPN
ejpam-3872	287	13	,	,	PUNCT
ejpam-3872	287	14	g)→	g)→	NOUN
ejpam-3872	287	15	γ	γ	X
ejpam-3872	287	16	as	as	ADP
ejpam-3872	287	17	x→	x→	PROPN
ejpam-3872	287	18	uep(g	uep(g	PROPN
ejpam-3872	287	19	)	)	PUNCT
ejpam-3872	287	20	.	.	PUNCT
ejpam-3872	288	1	hence	hence	ADV
ejpam-3872	288	2	this	this	DET
ejpam-3872	288	3	result	result	NOUN
ejpam-3872	288	4	says	say	VERB
ejpam-3872	288	5	that	that	SCONJ
ejpam-3872	288	6	n−1/2	n−1/2	PROPN
ejpam-3872	288	7	(	(	PUNCT
ejpam-3872	288	8	x(n	x(n	PROPN
ejpam-3872	288	9	)	)	PUNCT
ejpam-3872	288	10	−	−	PROPN
ejpam-3872	289	1	f−1	f−1	PROPN
ejpam-3872	289	2	(	(	PUNCT
ejpam-3872	289	3	1−	1−	NUM
ejpam-3872	289	4	e−n	e−n	PROPN
ejpam-3872	289	5	)	)	PUNCT
ejpam-3872	289	6	)	)	PUNCT
ejpam-3872	290	1	n	n	CCONJ
ejpam-3872	290	2	(	(	PUNCT
ejpam-3872	290	3	0	0	NUM
ejpam-3872	290	4	,	,	PUNCT
ejpam-3872	290	5	γ2	γ2	NOUN
ejpam-3872	290	6	)	)	PUNCT
ejpam-3872	290	7	,	,	PUNCT
ejpam-3872	290	8	if	if	SCONJ
ejpam-3872	290	9	f	f	PROPN
ejpam-3872	290	10	∈	∈	PROPN
ejpam-3872	290	11	d(g0	d(g0	NOUN
ejpam-3872	290	12	)	)	PUNCT
ejpam-3872	290	13	and	and	CCONJ
ejpam-3872	290	14	r(x	r(x	PROPN
ejpam-3872	290	15	,	,	PUNCT
ejpam-3872	290	16	f	f	NOUN
ejpam-3872	290	17	)	)	PUNCT
ejpam-3872	290	18	→	→	SYM
ejpam-3872	290	19	γ	γ	PROPN
ejpam-3872	290	20	as	as	ADP
ejpam-3872	290	21	x→	x→	X
ejpam-3872	290	22	uep(f	uep(f	PROPN
ejpam-3872	290	23	)	)	PUNCT
ejpam-3872	290	24	.	.	PUNCT
ejpam-3872	291	1	g.	g.	PROPN
ejpam-3872	292	1	s.	s.	PROPN
ejpam-3872	292	2	lo	lo	PROPN
ejpam-3872	292	3	et	et	PROPN
ejpam-3872	292	4	al	al	PROPN
ejpam-3872	292	5	.	.	PUNCT
ejpam-3872	292	6	/	/	SYM
ejpam-3872	292	7	eur	eur	PROPN
ejpam-3872	292	8	.	.	PUNCT
ejpam-3872	293	1	j.	j.	PROPN
ejpam-3872	293	2	pure	pure	PROPN
ejpam-3872	293	3	appl	appl	PROPN
ejpam-3872	293	4	.	.	PROPN
ejpam-3872	293	5	math	math	PROPN
ejpam-3872	293	6	,	,	PUNCT
ejpam-3872	293	7	14	14	NUM
ejpam-3872	293	8	(	(	PUNCT
ejpam-3872	293	9	1	1	NUM
ejpam-3872	293	10	)	)	PUNCT
ejpam-3872	293	11	(	(	PUNCT
ejpam-3872	293	12	2021	2021	NUM
ejpam-3872	293	13	)	)	PUNCT
ejpam-3872	293	14	,	,	PUNCT
ejpam-3872	293	15	19	19	NUM
ejpam-3872	293	16	-	-	SYM
ejpam-3872	293	17	42	42	NUM
ejpam-3872	293	18	34	34	NUM
ejpam-3872	293	19	(	(	PUNCT
ejpam-3872	293	20	c	c	NOUN
ejpam-3872	293	21	)	)	PUNCT
ejpam-3872	293	22	asymptotic	asymptotic	ADJ
ejpam-3872	293	23	law	law	NOUN
ejpam-3872	293	24	of	of	ADP
ejpam-3872	293	25	y	y	PROPN
ejpam-3872	293	26	(	(	PUNCT
ejpam-3872	293	27	n	n	CCONJ
ejpam-3872	293	28	)	)	PUNCT
ejpam-3872	293	29	for	for	ADP
ejpam-3872	293	30	γ	γ	X
ejpam-3872	293	31	<	<	X
ejpam-3872	293	32	0	0	NUM
ejpam-3872	293	33	.	.	PUNCT
ejpam-3872	294	1	we	we	PRON
ejpam-3872	294	2	have	have	VERB
ejpam-3872	294	3	p(x	p(x	PROPN
ejpam-3872	294	4	=	=	SYM
ejpam-3872	294	5	uep(f	uep(f	PROPN
ejpam-3872	294	6	)	)	PUNCT
ejpam-3872	294	7	)	)	PUNCT
ejpam-3872	295	1	=	=	PUNCT
ejpam-3872	295	2	0	0	X
ejpam-3872	295	3	.	.	PUNCT
ejpam-3872	295	4	by	by	ADP
ejpam-3872	295	5	using	use	VERB
ejpam-3872	295	6	representation	representation	NOUN
ejpam-3872	295	7	(	(	PUNCT
ejpam-3872	295	8	5	5	NUM
ejpam-3872	295	9	)	)	PUNCT
ejpam-3872	295	10	,	,	PUNCT
ejpam-3872	295	11	we	we	PRON
ejpam-3872	295	12	may	may	AUX
ejpam-3872	295	13	and	and	CCONJ
ejpam-3872	295	14	do	do	AUX
ejpam-3872	295	15	prove	prove	VERB
ejpam-3872	295	16	this	this	DET
ejpam-3872	295	17	point	point	NOUN
ejpam-3872	295	18	exactly	exactly	ADV
ejpam-3872	295	19	as	as	ADP
ejpam-3872	295	20	for	for	ADP
ejpam-3872	295	21	point	point	NOUN
ejpam-3872	295	22	(	(	PUNCT
ejpam-3872	295	23	a	a	NOUN
ejpam-3872	295	24	)	)	PUNCT
ejpam-3872	295	25	.	.	PUNCT
ejpam-3872	296	1	(	(	PUNCT
ejpam-3872	296	2	d	d	X
ejpam-3872	296	3	)	)	PUNCT
ejpam-3872	296	4	asymptotic	asymptotic	ADJ
ejpam-3872	296	5	law	law	NOUN
ejpam-3872	296	6	of	of	ADP
ejpam-3872	296	7	y	y	PROPN
ejpam-3872	296	8	(	(	PUNCT
ejpam-3872	296	9	n	n	CCONJ
ejpam-3872	296	10	)	)	PUNCT
ejpam-3872	296	11	for	for	ADP
ejpam-3872	296	12	γ	γ	X
ejpam-3872	296	13	=	=	SYM
ejpam-3872	296	14	0	0	NUM
ejpam-3872	296	15	.	.	PUNCT
ejpam-3872	297	1	we	we	PRON
ejpam-3872	297	2	did	do	AUX
ejpam-3872	297	3	not	not	PART
ejpam-3872	297	4	have	have	VERB
ejpam-3872	297	5	yet	yet	ADV
ejpam-3872	297	6	the	the	DET
ejpam-3872	297	7	general	general	ADJ
ejpam-3872	297	8	law	law	NOUN
ejpam-3872	297	9	.	.	PUNCT
ejpam-3872	298	1	let	let	VERB
ejpam-3872	298	2	us	we	PRON
ejpam-3872	298	3	learn	learn	VERB
ejpam-3872	298	4	for	for	ADP
ejpam-3872	298	5	a	a	DET
ejpam-3872	298	6	no	no	ADV
ejpam-3872	298	7	-	-	PUNCT
ejpam-3872	298	8	trivial	trivial	ADJ
ejpam-3872	298	9	example	example	NOUN
ejpam-3872	298	10	.	.	PUNCT
ejpam-3872	299	1	(	(	PUNCT
ejpam-3872	299	2	a	a	X
ejpam-3872	299	3	)	)	PUNCT
ejpam-3872	299	4	x	x	SYM
ejpam-3872	299	5	∼	∼	NOUN
ejpam-3872	299	6	n	n	CCONJ
ejpam-3872	299	7	(	(	PUNCT
ejpam-3872	299	8	0	0	NUM
ejpam-3872	299	9	,	,	PUNCT
ejpam-3872	299	10	1	1	NUM
ejpam-3872	299	11	)	)	PUNCT
ejpam-3872	299	12	.	.	PUNCT
ejpam-3872	300	1	let	let	VERB
ejpam-3872	300	2	us	we	PRON
ejpam-3872	300	3	recall	recall	VERB
ejpam-3872	300	4	the	the	DET
ejpam-3872	300	5	expansion	expansion	NOUN
ejpam-3872	300	6	of	of	ADP
ejpam-3872	300	7	the	the	DET
ejpam-3872	300	8	tail	tail	NOUN
ejpam-3872	300	9	of	of	ADP
ejpam-3872	300	10	f	f	PROPN
ejpam-3872	300	11	as	as	SCONJ
ejpam-3872	300	12	follows	follow	VERB
ejpam-3872	300	13	f−1(1−	f−1(1−	PROPN
ejpam-3872	300	14	s	s	PART
ejpam-3872	300	15	)	)	PUNCT
ejpam-3872	300	16	=	=	SYM
ejpam-3872	300	17	(	(	PUNCT
ejpam-3872	300	18	2	2	NUM
ejpam-3872	300	19	log(1	log(1	NOUN
ejpam-3872	300	20	/	/	SYM
ejpam-3872	301	1	s))1/2	s))1/2	PROPN
ejpam-3872	302	1	−	−	PROPN
ejpam-3872	302	2	log	log	NOUN
ejpam-3872	302	3	4π	4π	NUM
ejpam-3872	302	4	+	+	CCONJ
ejpam-3872	302	5	log	log	VERB
ejpam-3872	302	6	log(1	log(1	NOUN
ejpam-3872	302	7	/	/	SYM
ejpam-3872	302	8	s	s	NOUN
ejpam-3872	302	9	)	)	PUNCT
ejpam-3872	302	10	2(2	2(2	NUM
ejpam-3872	302	11	log(1	log(1	NOUN
ejpam-3872	302	12	/	/	SYM
ejpam-3872	302	13	s))1/2	s))1/2	PROPN
ejpam-3872	302	14	(	(	PUNCT
ejpam-3872	302	15	18	18	NUM
ejpam-3872	302	16	)	)	PUNCT
ejpam-3872	302	17	+	+	CCONJ
ejpam-3872	302	18	o((log	o((log	PROPN
ejpam-3872	302	19	log(1	log(1	NOUN
ejpam-3872	302	20	/	/	SYM
ejpam-3872	302	21	s))2(log	s))2(log	PROPN
ejpam-3872	302	22	1	1	NUM
ejpam-3872	302	23	/	/	SYM
ejpam-3872	302	24	s)−1/2	s)−1/2	PROPN
ejpam-3872	302	25	)	)	PUNCT
ejpam-3872	302	26	.	.	PUNCT
ejpam-3872	303	1	we	we	PRON
ejpam-3872	303	2	get	get	VERB
ejpam-3872	303	3	x(n	x(n	NOUN
ejpam-3872	303	4	)	)	PUNCT
ejpam-3872	303	5	=	=	SYM
ejpam-3872	303	6	(	(	PUNCT
ejpam-3872	303	7	2s(n	2s(n	NUM
ejpam-3872	303	8	)	)	PUNCT
ejpam-3872	303	9	)	)	PUNCT
ejpam-3872	304	1	1/2	1/2	NUM
ejpam-3872	304	2	−	−	NOUN
ejpam-3872	304	3	log	log	NOUN
ejpam-3872	304	4	4π	4π	NUM
ejpam-3872	304	5	+	+	CCONJ
ejpam-3872	304	6	logs(n	logs(n	PROPN
ejpam-3872	304	7	)	)	PUNCT
ejpam-3872	304	8	2(2s(n)))1/2	2(2s(n)))1/2	NUM
ejpam-3872	305	1	+	+	PROPN
ejpam-3872	305	2	o(s	o(s	PROPN
ejpam-3872	305	3	−1/2	−1/2	ADJ
ejpam-3872	305	4	(	(	PUNCT
ejpam-3872	305	5	n	n	CCONJ
ejpam-3872	305	6	)	)	PUNCT
ejpam-3872	305	7	logs(n	logs(n	PROPN
ejpam-3872	305	8	)	)	PUNCT
ejpam-3872	305	9	)	)	PUNCT
ejpam-3872	306	1	=	=	SYM
ejpam-3872	306	2	(	(	PUNCT
ejpam-3872	306	3	2s(n	2s(n	NUM
ejpam-3872	306	4	)	)	PUNCT
ejpam-3872	306	5	)	)	PUNCT
ejpam-3872	307	1	1/2	1/2	NUM
ejpam-3872	307	2	−	−	NOUN
ejpam-3872	307	3	log	log	NOUN
ejpam-3872	307	4	4π	4π	NUM
ejpam-3872	307	5	+	+	CCONJ
ejpam-3872	307	6	logs(n	logs(n	PROPN
ejpam-3872	307	7	)	)	PUNCT
ejpam-3872	307	8	2(2s(n))1/2	2(2s(n))1/2	NUM
ejpam-3872	308	1	+	+	ADJ
ejpam-3872	308	2	op(n−1(log	op(n−1(log	PROPN
ejpam-3872	308	3	n)2	n)2	NOUN
ejpam-3872	308	4	)	)	PUNCT
ejpam-3872	308	5	(	(	PUNCT
ejpam-3872	308	6	19	19	NUM
ejpam-3872	308	7	)	)	PUNCT
ejpam-3872	308	8	=	=	NOUN
ejpam-3872	308	9	(	(	PUNCT
ejpam-3872	308	10	2s(n	2s(n	NUM
ejpam-3872	308	11	)	)	PUNCT
ejpam-3872	308	12	)	)	PUNCT
ejpam-3872	309	1	1/2	1/2	NUM
ejpam-3872	310	1	+	+	NUM
ejpam-3872	310	2	op(n−1/2	op(n−1/2	ADJ
ejpam-3872	310	3	log	log	NOUN
ejpam-3872	310	4	n	n	CCONJ
ejpam-3872	310	5	)	)	PUNCT
ejpam-3872	310	6	.	.	PUNCT
ejpam-3872	311	1	(	(	PUNCT
ejpam-3872	311	2	20	20	NUM
ejpam-3872	311	3	)	)	PUNCT
ejpam-3872	311	4	furthermore	furthermore	ADV
ejpam-3872	311	5	f−1(1−	f−1(1−	PROPN
ejpam-3872	311	6	e−n	e−n	PROPN
ejpam-3872	311	7	)	)	PUNCT
ejpam-3872	311	8	=	=	PUNCT
ejpam-3872	311	9	(	(	PUNCT
ejpam-3872	311	10	2n)1/2	2n)1/2	NUM
ejpam-3872	311	11	−	−	NOUN
ejpam-3872	311	12	log	log	NOUN
ejpam-3872	311	13	4π	4π	NUM
ejpam-3872	311	14	+	+	CCONJ
ejpam-3872	311	15	log	log	VERB
ejpam-3872	311	16	n	n	PRON
ejpam-3872	311	17	2(2n)1/2	2(2n)1/2	NUM
ejpam-3872	311	18	+	+	ADV
ejpam-3872	311	19	op(n−1(log	op(n−1(log	NOUN
ejpam-3872	311	20	n)2	n)2	NOUN
ejpam-3872	311	21	)	)	PUNCT
ejpam-3872	311	22	(	(	PUNCT
ejpam-3872	311	23	21	21	NUM
ejpam-3872	311	24	)	)	PUNCT
ejpam-3872	311	25	=	=	NOUN
ejpam-3872	311	26	(	(	PUNCT
ejpam-3872	311	27	2n)1/2	2n)1/2	NUM
ejpam-3872	312	1	+	+	NOUN
ejpam-3872	312	2	op(n−1/2	op(n−1/2	VERB
ejpam-3872	312	3	log	log	NOUN
ejpam-3872	312	4	n	n	CCONJ
ejpam-3872	312	5	)	)	PUNCT
ejpam-3872	312	6	.	.	PUNCT
ejpam-3872	313	1	(	(	PUNCT
ejpam-3872	313	2	22	22	X
ejpam-3872	313	3	)	)	PUNCT
ejpam-3872	313	4	combining	combine	VERB
ejpam-3872	313	5	relations	relation	NOUN
ejpam-3872	313	6	(	(	PUNCT
ejpam-3872	313	7	20	20	NUM
ejpam-3872	313	8	)	)	PUNCT
ejpam-3872	313	9	and	and	CCONJ
ejpam-3872	313	10	(	(	PUNCT
ejpam-3872	313	11	22	22	NUM
ejpam-3872	313	12	)	)	PUNCT
ejpam-3872	313	13	leads	lead	VERB
ejpam-3872	313	14	to	to	ADP
ejpam-3872	313	15	x(n	x(n	NOUN
ejpam-3872	313	16	)	)	PUNCT
ejpam-3872	314	1	−	−	PROPN
ejpam-3872	314	2	f−1(1−	f−1(1−	PROPN
ejpam-3872	314	3	e−n	e−n	PROPN
ejpam-3872	314	4	)	)	PUNCT
ejpam-3872	314	5	=	=	SYM
ejpam-3872	314	6	1√	1√	PROPN
ejpam-3872	314	7	2	2	NUM
ejpam-3872	314	8	s(n	s(n	NOUN
ejpam-3872	314	9	)	)	PUNCT
ejpam-3872	314	10	−	−	ADP
ejpam-3872	314	11	n√	n√	SYM
ejpam-3872	314	12	n	n	CCONJ
ejpam-3872	314	13	(	(	PUNCT
ejpam-3872	314	14	n	n	CCONJ
ejpam-3872	314	15	/	/	SYM
ejpam-3872	314	16	ζn)1/2	ζn)1/2	ADJ
ejpam-3872	314	17	+	+	PROPN
ejpam-3872	314	18	op(n−1(log	op(n−1(log	ADJ
ejpam-3872	314	19	n)2	n)2	NOUN
ejpam-3872	314	20	)	)	PUNCT
ejpam-3872	314	21	,	,	PUNCT
ejpam-3872	314	22	(	(	PUNCT
ejpam-3872	314	23	23	23	NUM
ejpam-3872	314	24	)	)	PUNCT
ejpam-3872	314	25	with	with	ADP
ejpam-3872	314	26	n∧s(n	n∧s(n	PROPN
ejpam-3872	314	27	)	)	PUNCT
ejpam-3872	314	28	<	<	X
ejpam-3872	314	29	ζn	ζn	X
ejpam-3872	314	30	<	<	X
ejpam-3872	314	31	n∨s(n	n∨s(n	PROPN
ejpam-3872	314	32	)	)	PUNCT
ejpam-3872	314	33	and	and	CCONJ
ejpam-3872	314	34	next	next	ADV
ejpam-3872	314	35	,	,	PUNCT
ejpam-3872	314	36	by	by	ADP
ejpam-3872	314	37	the	the	DET
ejpam-3872	314	38	weak	weak	ADJ
ejpam-3872	314	39	law	law	NOUN
ejpam-3872	314	40	of	of	ADP
ejpam-3872	314	41	large	large	ADJ
ejpam-3872	314	42	numbers	number	NOUN
ejpam-3872	314	43	,	,	PUNCT
ejpam-3872	314	44	(	(	PUNCT
ejpam-3872	314	45	n	n	CCONJ
ejpam-3872	314	46	/	/	SYM
ejpam-3872	314	47	ζn)1/2	ζn)1/2	ADJ
ejpam-3872	314	48	→p	→p	PROPN
ejpam-3872	314	49	1	1	NUM
ejpam-3872	314	50	and	and	CCONJ
ejpam-3872	314	51	thus	thus	ADV
ejpam-3872	314	52	x(n	x(n	NOUN
ejpam-3872	314	53	)	)	PUNCT
ejpam-3872	315	1	−	−	PROPN
ejpam-3872	315	2	(	(	PUNCT
ejpam-3872	315	3	2n)1/2	2n)1/2	NUM
ejpam-3872	315	4	n	n	CCONJ
ejpam-3872	315	5	(	(	PUNCT
ejpam-3872	315	6	0	0	NUM
ejpam-3872	315	7	,	,	PUNCT
ejpam-3872	315	8	1/2	1/2	NUM
ejpam-3872	315	9	)	)	PUNCT
ejpam-3872	315	10	.	.	PUNCT
ejpam-3872	316	1	(	(	PUNCT
ejpam-3872	316	2	24	24	NUM
ejpam-3872	316	3	)	)	PUNCT
ejpam-3872	316	4	(	(	PUNCT
ejpam-3872	316	5	b	b	X
ejpam-3872	316	6	)	)	PUNCT
ejpam-3872	316	7	general	general	ADJ
ejpam-3872	316	8	proof	proof	NOUN
ejpam-3872	316	9	.	.	PUNCT
ejpam-3872	317	1	it	it	PRON
ejpam-3872	317	2	is	be	AUX
ejpam-3872	317	3	known	know	VERB
ejpam-3872	317	4	that	that	SCONJ
ejpam-3872	317	5	s(u	s(u	NOUN
ejpam-3872	317	6	)	)	PUNCT
ejpam-3872	317	7	∼	∼	VERB
ejpam-3872	317	8	r(f−1(1	r(f−1(1	ADJ
ejpam-3872	317	9	−	−	PROPN
ejpam-3872	317	10	u	u	NOUN
ejpam-3872	317	11	)	)	PUNCT
ejpam-3872	317	12	,	,	PUNCT
ejpam-3872	317	13	f	f	PROPN
ejpam-3872	317	14	)	)	PUNCT
ejpam-3872	317	15	and	and	CCONJ
ejpam-3872	317	16	so	so	ADV
ejpam-3872	317	17	,	,	PUNCT
ejpam-3872	317	18	s(u	s(u	PROPN
ejpam-3872	317	19	)	)	PUNCT
ejpam-3872	317	20	→	→	SYM
ejpam-3872	317	21	0	0	NUM
ejpam-3872	317	22	as	as	ADP
ejpam-3872	317	23	u→	u→	PROPN
ejpam-3872	317	24	0	0	NUM
ejpam-3872	317	25	.	.	PUNCT
ejpam-3872	318	1	by	by	ADP
ejpam-3872	318	2	representation	representation	NOUN
ejpam-3872	318	3	(	(	PUNCT
ejpam-3872	318	4	6	6	NUM
ejpam-3872	318	5	)	)	PUNCT
ejpam-3872	318	6	of	of	ADP
ejpam-3872	318	7	proposition	proposition	NOUN
ejpam-3872	318	8	2	2	NUM
ejpam-3872	318	9	and	and	CCONJ
ejpam-3872	318	10	hypothesis	hypothesis	NOUN
ejpam-3872	318	11	(	(	PUNCT
ejpam-3872	318	12	ha	ha	INTJ
ejpam-3872	318	13	)	)	PUNCT
ejpam-3872	318	14	together	together	ADV
ejpam-3872	318	15	lead	lead	VERB
ejpam-3872	318	16	to	to	ADP
ejpam-3872	318	17	g.	g.	PROPN
ejpam-3872	318	18	s.	s.	PROPN
ejpam-3872	319	1	lo	lo	PROPN
ejpam-3872	319	2	et	et	PROPN
ejpam-3872	319	3	al	al	PROPN
ejpam-3872	319	4	.	.	PUNCT
ejpam-3872	319	5	/	/	SYM
ejpam-3872	319	6	eur	eur	PROPN
ejpam-3872	319	7	.	.	PUNCT
ejpam-3872	320	1	j.	j.	PROPN
ejpam-3872	320	2	pure	pure	PROPN
ejpam-3872	320	3	appl	appl	PROPN
ejpam-3872	320	4	.	.	PROPN
ejpam-3872	320	5	math	math	PROPN
ejpam-3872	320	6	,	,	PUNCT
ejpam-3872	320	7	14	14	NUM
ejpam-3872	320	8	(	(	PUNCT
ejpam-3872	320	9	1	1	NUM
ejpam-3872	320	10	)	)	PUNCT
ejpam-3872	320	11	(	(	PUNCT
ejpam-3872	320	12	2021	2021	NUM
ejpam-3872	320	13	)	)	PUNCT
ejpam-3872	320	14	,	,	PUNCT
ejpam-3872	320	15	19	19	NUM
ejpam-3872	320	16	-	-	SYM
ejpam-3872	320	17	42	42	NUM
ejpam-3872	320	18	35	35	NUM
ejpam-3872	320	19	x(n	x(n	NOUN
ejpam-3872	320	20	)	)	PUNCT
ejpam-3872	320	21	−	−	PROPN
ejpam-3872	321	1	f−1(1−	f−1(1−	PROPN
ejpam-3872	321	2	en	en	X
ejpam-3872	321	3	)	)	PUNCT
ejpam-3872	321	4	=	=	NOUN
ejpam-3872	321	5	s(vn)−	s(vn)−	NOUN
ejpam-3872	321	6	s(vn	s(vn	PROPN
ejpam-3872	321	7	)	)	PUNCT
ejpam-3872	322	1	+	+	NUM
ejpam-3872	322	2	∫	∫	PROPN
ejpam-3872	322	3	vn	vn	PROPN
ejpam-3872	322	4	vn	vn	PROPN
ejpam-3872	322	5	s(u	s(u	PROPN
ejpam-3872	322	6	)	)	PUNCT
ejpam-3872	322	7	u	u	PROPN
ejpam-3872	322	8	du	du	X
ejpam-3872	322	9	(	(	PUNCT
ejpam-3872	322	10	25	25	NUM
ejpam-3872	322	11	)	)	PUNCT
ejpam-3872	322	12	=	=	SYM
ejpam-3872	322	13	s(vn	s(vn	PROPN
ejpam-3872	322	14	)	)	PUNCT
ejpam-3872	322	15	(	(	PUNCT
ejpam-3872	322	16	s(vn	s(vn	PROPN
ejpam-3872	322	17	)	)	PUNCT
ejpam-3872	322	18	s(vn	s(vn	PROPN
ejpam-3872	322	19	)	)	PUNCT
ejpam-3872	322	20	−	−	PROPN
ejpam-3872	322	21	1	1	NUM
ejpam-3872	322	22	)	)	PUNCT
ejpam-3872	322	23	+	+	CCONJ
ejpam-3872	322	24	(	(	PUNCT
ejpam-3872	322	25	1	1	NUM
ejpam-3872	322	26	+	+	NUM
ejpam-3872	322	27	op(dn))s(vn)(s(n	op(dn))s(vn)(s(n	ADJ
ejpam-3872	322	28	)	)	PUNCT
ejpam-3872	322	29	−	−	NOUN
ejpam-3872	322	30	n	n	CCONJ
ejpam-3872	322	31	)	)	PUNCT
ejpam-3872	322	32	.	.	PUNCT
ejpam-3872	323	1	=	=	PRON
ejpam-3872	323	2	{	{	PUNCT
ejpam-3872	323	3	s(vn	s(vn	PROPN
ejpam-3872	323	4	)	)	PUNCT
ejpam-3872	323	5	√	√	NUM
ejpam-3872	323	6	n	n	CCONJ
ejpam-3872	323	7	}	}	PUNCT
ejpam-3872	323	8	(	(	PUNCT
ejpam-3872	323	9	1√	1√	PROPN
ejpam-3872	323	10	n	n	CCONJ
ejpam-3872	323	11	(	(	PUNCT
ejpam-3872	323	12	s(vn	s(vn	PROPN
ejpam-3872	323	13	)	)	PUNCT
ejpam-3872	323	14	s(vn	s(vn	PROPN
ejpam-3872	323	15	)	)	PUNCT
ejpam-3872	323	16	−	−	PROPN
ejpam-3872	323	17	1	1	NUM
ejpam-3872	323	18	)	)	PUNCT
ejpam-3872	323	19	)	)	PUNCT
ejpam-3872	324	1	+	+	CCONJ
ejpam-3872	324	2	{	{	PUNCT
ejpam-3872	324	3	s(vn	s(vn	PROPN
ejpam-3872	324	4	)	)	PUNCT
ejpam-3872	324	5	√	√	PUNCT
ejpam-3872	324	6	n}(1	n}(1	PRON
ejpam-3872	325	1	+	+	PROPN
ejpam-3872	325	2	op(dn	op(dn	PROPN
ejpam-3872	325	3	)	)	PUNCT
ejpam-3872	325	4	)	)	PUNCT
ejpam-3872	325	5	s∗n	s∗n	NUM
ejpam-3872	326	1	=	=	SYM
ejpam-3872	326	2	(	(	PUNCT
ejpam-3872	326	3	α+op(en	α+op(en	NUM
ejpam-3872	326	4	)	)	PUNCT
ejpam-3872	326	5	)	)	PUNCT
ejpam-3872	327	1	(	(	PUNCT
ejpam-3872	327	2	1√	1√	NUM
ejpam-3872	327	3	n	n	CCONJ
ejpam-3872	327	4	(	(	PUNCT
ejpam-3872	327	5	s(vn	s(vn	PROPN
ejpam-3872	327	6	)	)	PUNCT
ejpam-3872	327	7	s(vn	s(vn	PROPN
ejpam-3872	327	8	)	)	PUNCT
ejpam-3872	327	9	−	−	PROPN
ejpam-3872	327	10	1	1	NUM
ejpam-3872	327	11	)	)	PUNCT
ejpam-3872	327	12	)	)	PUNCT
ejpam-3872	328	1	+	+	CCONJ
ejpam-3872	328	2	(	(	PUNCT
ejpam-3872	328	3	α+op(en))(1	α+op(en))(1	NUM
ejpam-3872	328	4	+	+	NOUN
ejpam-3872	328	5	op(dn))s∗n	op(dn))s∗n	NOUN
ejpam-3872	328	6	=	=	SYM
ejpam-3872	328	7	αs∗n	αs∗n	SYM
ejpam-3872	328	8	+	+	NUM
ejpam-3872	328	9	op(en	op(en	PROPN
ejpam-3872	328	10	∨	∨	NUM
ejpam-3872	328	11	dn	dn	PROPN
ejpam-3872	328	12	)	)	PUNCT
ejpam-3872	328	13	=	=	PRON
ejpam-3872	328	14	αw	αw	ADP
ejpam-3872	328	15	∗n	∗n	PROPN
ejpam-3872	328	16	+	+	CCONJ
ejpam-3872	328	17	op(cn	op(cn	PROPN
ejpam-3872	328	18	∨	∨	NUM
ejpam-3872	328	19	en	en	X
ejpam-3872	328	20	∨	∨	NUM
ejpam-3872	328	21	dn	dn	PROPN
ejpam-3872	328	22	)	)	PUNCT
ejpam-3872	328	23	.	.	PUNCT
ejpam-3872	329	1	(	(	PUNCT
ejpam-3872	329	2	26	26	NUM
ejpam-3872	329	3	)	)	PUNCT
ejpam-3872	329	4	from	from	ADP
ejpam-3872	329	5	there	there	ADV
ejpam-3872	329	6	,	,	PUNCT
ejpam-3872	329	7	the	the	DET
ejpam-3872	329	8	conclusion	conclusion	NOUN
ejpam-3872	329	9	is	be	AUX
ejpam-3872	329	10	immediate	immediate	ADJ
ejpam-3872	329	11	by	by	ADP
ejpam-3872	329	12	using	use	VERB
ejpam-3872	329	13	hypothesis	hypothesis	NOUN
ejpam-3872	329	14	(	(	PUNCT
ejpam-3872	329	15	hb	hb	PROPN
ejpam-3872	329	16	)	)	PUNCT
ejpam-3872	329	17	�	�	PROPN
ejpam-3872	329	18	(	(	PUNCT
ejpam-3872	329	19	ii	ii	NOUN
ejpam-3872	329	20	)	)	PUNCT
ejpam-3872	329	21	proof	proof	NOUN
ejpam-3872	329	22	of	of	ADP
ejpam-3872	329	23	theorem	theorem	NOUN
ejpam-3872	329	24	2	2	X
ejpam-3872	329	25	.	.	X
ejpam-3872	330	1	we	we	PRON
ejpam-3872	330	2	have	have	VERB
ejpam-3872	330	3	g(x	g(x	NOUN
ejpam-3872	330	4	)	)	PUNCT
ejpam-3872	330	5	=	=	PUNCT
ejpam-3872	330	6	f−1(1	f−1(1	X
ejpam-3872	330	7	−	−	PROPN
ejpam-3872	330	8	e−x	e−x	NOUN
ejpam-3872	330	9	)	)	PUNCT
ejpam-3872	330	10	,	,	PUNCT
ejpam-3872	330	11	g′(x	g′(x	NOUN
ejpam-3872	330	12	)	)	PUNCT
ejpam-3872	330	13	=	=	SYM
ejpam-3872	330	14	s(x	s(x	PROPN
ejpam-3872	330	15	)	)	PUNCT
ejpam-3872	330	16	,	,	PUNCT
ejpam-3872	330	17	x	x	PUNCT
ejpam-3872	330	18	∈	∈	PROPN
ejpam-3872	330	19	]	]	PUNCT
ejpam-3872	330	20	lep(f	lep(f	PROPN
ejpam-3872	330	21	)	)	PUNCT
ejpam-3872	330	22	,	,	PUNCT
ejpam-3872	330	23	uep(f	uep(f	PROPN
ejpam-3872	330	24	)	)	PUNCT
ejpam-3872	331	1	[	[	X
ejpam-3872	331	2	.	.	PUNCT
ejpam-3872	332	1	the	the	DET
ejpam-3872	332	2	mean	mean	ADJ
ejpam-3872	332	3	value	value	NOUN
ejpam-3872	332	4	theorem	theorem	NOUN
ejpam-3872	332	5	gives	give	NOUN
ejpam-3872	332	6	,	,	PUNCT
ejpam-3872	332	7	for	for	ADP
ejpam-3872	332	8	∀n	∀n	NUM
ejpam-3872	332	9	>	>	X
ejpam-3872	332	10	0	0	NUM
ejpam-3872	332	11	,	,	PUNCT
ejpam-3872	332	12	x(n	x(n	NOUN
ejpam-3872	332	13	)	)	PUNCT
ejpam-3872	332	14	−	−	PROPN
ejpam-3872	332	15	f−1(1−	f−1(1−	PROPN
ejpam-3872	332	16	e−n	e−n	PROPN
ejpam-3872	332	17	)	)	PUNCT
ejpam-3872	332	18	=	=	SYM
ejpam-3872	332	19	s(n	s(n	NOUN
ejpam-3872	332	20	)	)	PUNCT
ejpam-3872	332	21	−	−	ADP
ejpam-3872	332	22	n√	n√	SYM
ejpam-3872	332	23	n	n	CCONJ
ejpam-3872	332	24	(	(	PUNCT
ejpam-3872	332	25	√	√	NUM
ejpam-3872	332	26	ns(exp(−ζn	ns(exp(−ζn	NUM
ejpam-3872	332	27	)	)	PUNCT
ejpam-3872	332	28	)	)	PUNCT
ejpam-3872	332	29	)	)	PUNCT
ejpam-3872	332	30	,	,	PUNCT
ejpam-3872	332	31	(	(	PUNCT
ejpam-3872	332	32	27	27	NUM
ejpam-3872	332	33	)	)	PUNCT
ejpam-3872	332	34	where	where	SCONJ
ejpam-3872	332	35	ζn	ζn	PRON
ejpam-3872	332	36	∈	∈	PROPN
ejpam-3872	332	37	]	]	X
ejpam-3872	332	38	min(n	min(n	PROPN
ejpam-3872	332	39	,	,	PUNCT
ejpam-3872	332	40	s(n	s(n	PROPN
ejpam-3872	332	41	)	)	PUNCT
ejpam-3872	332	42	)	)	PUNCT
ejpam-3872	332	43	,	,	PUNCT
ejpam-3872	332	44	max(n	max(n	PROPN
ejpam-3872	332	45	,	,	PUNCT
ejpam-3872	332	46	s(n	s(n	PROPN
ejpam-3872	332	47	)	)	PUNCT
ejpam-3872	332	48	)	)	PUNCT
ejpam-3872	333	1	[	[	X
ejpam-3872	333	2	.	.	PUNCT
ejpam-3872	334	1	from	from	ADP
ejpam-3872	334	2	there	there	ADV
ejpam-3872	334	3	,	,	PUNCT
ejpam-3872	334	4	the	the	DET
ejpam-3872	334	5	conclusion	conclusion	NOUN
ejpam-3872	334	6	is	be	AUX
ejpam-3872	334	7	direct	direct	ADJ
ejpam-3872	334	8	�	�	NOUN
ejpam-3872	334	9	proof	proof	NOUN
ejpam-3872	334	10	of	of	ADP
ejpam-3872	334	11	theorem	theorem	NOUN
ejpam-3872	334	12	3	3	X
ejpam-3872	334	13	.	.	PUNCT
ejpam-3872	335	1	we	we	PRON
ejpam-3872	335	2	will	will	AUX
ejpam-3872	335	3	prove	prove	VERB
ejpam-3872	335	4	that	that	SCONJ
ejpam-3872	335	5	theorem	theorem	NOUN
ejpam-3872	335	6	in	in	ADP
ejpam-3872	335	7	a	a	DET
ejpam-3872	335	8	special	special	ADJ
ejpam-3872	335	9	space	space	NOUN
ejpam-3872	335	10	but	but	CCONJ
ejpam-3872	335	11	it	it	PRON
ejpam-3872	335	12	will	will	AUX
ejpam-3872	335	13	be	be	AUX
ejpam-3872	335	14	valid	valid	ADJ
ejpam-3872	335	15	in	in	ADP
ejpam-3872	335	16	any	any	DET
ejpam-3872	335	17	probability	probability	NOUN
ejpam-3872	335	18	space	space	NOUN
ejpam-3872	335	19	.	.	PUNCT
ejpam-3872	336	1	following	follow	VERB
ejpam-3872	336	2	[	[	X
ejpam-3872	336	3	4	4	NUM
ejpam-3872	336	4	]	]	PUNCT
ejpam-3872	336	5	,	,	PUNCT
ejpam-3872	336	6	we	we	PRON
ejpam-3872	336	7	consider	consider	VERB
ejpam-3872	336	8	the	the	DET
ejpam-3872	336	9	probability	probability	NOUN
ejpam-3872	336	10	space	space	NOUN
ejpam-3872	336	11	(	(	PUNCT
ejpam-3872	336	12	ω	ω	NOUN
ejpam-3872	336	13	,	,	PUNCT
ejpam-3872	336	14	a	a	DET
ejpam-3872	336	15	,	,	PUNCT
ejpam-3872	336	16	p	p	NOUN
ejpam-3872	336	17	)	)	PUNCT
ejpam-3872	336	18	holding	hold	VERB
ejpam-3872	336	19	a	a	DET
ejpam-3872	336	20	sequence	sequence	NOUN
ejpam-3872	336	21	(	(	PUNCT
ejpam-3872	336	22	en)n≥1	en)n≥1	VERB
ejpam-3872	336	23	and	and	CCONJ
ejpam-3872	336	24	a	a	DET
ejpam-3872	336	25	wiener	wiener	NOUN
ejpam-3872	336	26	process	process	NOUN
ejpam-3872	336	27	w	w	ADP
ejpam-3872	336	28	such	such	ADJ
ejpam-3872	336	29	that	that	SCONJ
ejpam-3872	336	30	|(sn	|(sn	PROPN
ejpam-3872	336	31	−	−	PROPN
ejpam-3872	336	32	n)−w	n)−w	NUM
ejpam-3872	336	33	(	(	PUNCT
ejpam-3872	336	34	n)|√	n)|√	PROPN
ejpam-3872	336	35	n	n	NOUN
ejpam-3872	336	36	=	=	SYM
ejpam-3872	336	37	o	o	X
ejpam-3872	336	38	(	(	PUNCT
ejpam-3872	336	39	log	log	VERB
ejpam-3872	336	40	n√	n√	NOUN
ejpam-3872	336	41	n	n	NUM
ejpam-3872	336	42	)	)	PUNCT
ejpam-3872	336	43	.	.	PUNCT
ejpam-3872	337	1	(	(	PUNCT
ejpam-3872	337	2	28	28	X
ejpam-3872	337	3	)	)	PUNCT
ejpam-3872	337	4	we	we	PRON
ejpam-3872	337	5	set	set	VERB
ejpam-3872	337	6	un	un	PROPN
ejpam-3872	337	7	=	=	NOUN
ejpam-3872	337	8	1	1	NUM
ejpam-3872	337	9	−	−	PROPN
ejpam-3872	337	10	exp(−en	exp(−en	PROPN
ejpam-3872	337	11	)	)	PUNCT
ejpam-3872	337	12	,	,	PUNCT
ejpam-3872	337	13	n	n	PRON
ejpam-3872	337	14	≥	≥	NOUN
ejpam-3872	337	15	1	1	NUM
ejpam-3872	337	16	and	and	CCONJ
ejpam-3872	337	17	finally	finally	ADV
ejpam-3872	337	18	xn	xn	PROPN
ejpam-3872	337	19	=	=	SYM
ejpam-3872	337	20	f−1(1	f−1(1	X
ejpam-3872	337	21	−	−	PROPN
ejpam-3872	338	1	exp(−en	exp(−en	PROPN
ejpam-3872	339	1	)	)	PUNCT
ejpam-3872	340	1	)	)	PUNCT
ejpam-3872	340	2	,	,	PUNCT
ejpam-3872	341	1	n	n	PRON
ejpam-3872	341	2	≥	≥	NOUN
ejpam-3872	341	3	1	1	NUM
ejpam-3872	341	4	.	.	PUNCT
ejpam-3872	342	1	from	from	ADP
ejpam-3872	342	2	that	that	DET
ejpam-3872	342	3	point	point	NOUN
ejpam-3872	342	4	,	,	PUNCT
ejpam-3872	342	5	all	all	DET
ejpam-3872	342	6	the	the	DET
ejpam-3872	342	7	notations	notation	NOUN
ejpam-3872	342	8	above	above	ADV
ejpam-3872	342	9	remain	remain	VERB
ejpam-3872	342	10	valid	valid	ADJ
ejpam-3872	342	11	.	.	PUNCT
ejpam-3872	343	1	the	the	DET
ejpam-3872	343	2	proofs	proof	NOUN
ejpam-3872	343	3	of	of	ADP
ejpam-3872	343	4	the	the	DET
ejpam-3872	343	5	different	different	ADJ
ejpam-3872	343	6	points	point	NOUN
ejpam-3872	343	7	of	of	ADP
ejpam-3872	343	8	the	the	DET
ejpam-3872	343	9	theorems	theorem	NOUN
ejpam-3872	343	10	derive	derive	VERB
ejpam-3872	343	11	easily	easily	ADV
ejpam-3872	343	12	from	from	ADP
ejpam-3872	343	13	the	the	DET
ejpam-3872	343	14	proof	proof	NOUN
ejpam-3872	343	15	of	of	ADP
ejpam-3872	343	16	the	the	DET
ejpam-3872	343	17	same	same	ADJ
ejpam-3872	343	18	points	point	NOUN
ejpam-3872	343	19	in	in	ADP
ejpam-3872	343	20	theorem	theorem	NOUN
ejpam-3872	343	21	1	1	X
ejpam-3872	343	22	.	.	PUNCT
ejpam-3872	344	1	here	here	ADV
ejpam-3872	344	2	are	be	AUX
ejpam-3872	344	3	the	the	DET
ejpam-3872	344	4	details	detail	NOUN
ejpam-3872	344	5	.	.	PUNCT
ejpam-3872	345	1	g.	g.	PROPN
ejpam-3872	345	2	s.	s.	PROPN
ejpam-3872	345	3	lo	lo	PROPN
ejpam-3872	345	4	et	et	PROPN
ejpam-3872	345	5	al	al	PROPN
ejpam-3872	345	6	.	.	PUNCT
ejpam-3872	345	7	/	/	SYM
ejpam-3872	345	8	eur	eur	PROPN
ejpam-3872	345	9	.	.	PUNCT
ejpam-3872	346	1	j.	j.	PROPN
ejpam-3872	346	2	pure	pure	PROPN
ejpam-3872	346	3	appl	appl	PROPN
ejpam-3872	346	4	.	.	PROPN
ejpam-3872	346	5	math	math	PROPN
ejpam-3872	346	6	,	,	PUNCT
ejpam-3872	346	7	14	14	NUM
ejpam-3872	346	8	(	(	PUNCT
ejpam-3872	346	9	1	1	NUM
ejpam-3872	346	10	)	)	PUNCT
ejpam-3872	346	11	(	(	PUNCT
ejpam-3872	346	12	2021	2021	NUM
ejpam-3872	346	13	)	)	PUNCT
ejpam-3872	346	14	,	,	PUNCT
ejpam-3872	346	15	19	19	NUM
ejpam-3872	346	16	-	-	SYM
ejpam-3872	346	17	42	42	NUM
ejpam-3872	346	18	36	36	NUM
ejpam-3872	346	19	proof	proof	NOUN
ejpam-3872	346	20	of	of	ADP
ejpam-3872	346	21	points	point	NOUN
ejpam-3872	346	22	(	(	PUNCT
ejpam-3872	346	23	a	a	NOUN
ejpam-3872	346	24	)	)	PUNCT
ejpam-3872	346	25	and	and	CCONJ
ejpam-3872	346	26	(	(	PUNCT
ejpam-3872	346	27	b	b	NOUN
ejpam-3872	346	28	)	)	PUNCT
ejpam-3872	346	29	.	.	PUNCT
ejpam-3872	347	1	by	by	ADP
ejpam-3872	347	2	combining	combine	VERB
ejpam-3872	347	3	formulas	formula	NOUN
ejpam-3872	347	4	(	(	PUNCT
ejpam-3872	347	5	16	16	NUM
ejpam-3872	347	6	)	)	PUNCT
ejpam-3872	347	7	and	and	CCONJ
ejpam-3872	347	8	(	(	PUNCT
ejpam-3872	347	9	17	17	NUM
ejpam-3872	347	10	)	)	PUNCT
ejpam-3872	347	11	with	with	ADP
ejpam-3872	347	12	formula	formula	NOUN
ejpam-3872	347	13	(	(	PUNCT
ejpam-3872	347	14	28	28	NUM
ejpam-3872	347	15	)	)	PUNCT
ejpam-3872	347	16	approximation	approximation	NOUN
ejpam-3872	347	17	,	,	PUNCT
ejpam-3872	347	18	we	we	PRON
ejpam-3872	347	19	easily	easily	ADV
ejpam-3872	347	20	isolate	isolate	VERB
ejpam-3872	347	21	a	a	DET
ejpam-3872	347	22	multiple	multiple	NOUN
ejpam-3872	347	23	of	of	ADP
ejpam-3872	347	24	s∗n	s∗n	NUM
ejpam-3872	347	25	or	or	CCONJ
ejpam-3872	347	26	of	of	ADP
ejpam-3872	347	27	w	w	NOUN
ejpam-3872	347	28	∗n	∗n	PROPN
ejpam-3872	347	29	and	and	CCONJ
ejpam-3872	347	30	find	find	VERB
ejpam-3872	347	31	the	the	DET
ejpam-3872	347	32	rates	rate	NOUN
ejpam-3872	347	33	of	of	ADP
ejpam-3872	347	34	convergence	convergence	NOUN
ejpam-3872	347	35	as	as	SCONJ
ejpam-3872	347	36	stated	state	VERB
ejpam-3872	347	37	for	for	ADP
ejpam-3872	347	38	point	point	NOUN
ejpam-3872	347	39	(	(	PUNCT
ejpam-3872	347	40	b	b	NOUN
ejpam-3872	347	41	)	)	PUNCT
ejpam-3872	347	42	.	.	PUNCT
ejpam-3872	348	1	point	point	NOUN
ejpam-3872	348	2	(	(	PUNCT
ejpam-3872	348	3	a	a	X
ejpam-3872	348	4	)	)	PUNCT
ejpam-3872	348	5	is	be	AUX
ejpam-3872	348	6	obtained	obtain	VERB
ejpam-3872	348	7	by	by	ADP
ejpam-3872	348	8	an	an	DET
ejpam-3872	348	9	exponential	exponential	ADJ
ejpam-3872	348	10	transformation	transformation	NOUN
ejpam-3872	348	11	.	.	PUNCT
ejpam-3872	349	1	proof	proof	NOUN
ejpam-3872	349	2	of	of	ADP
ejpam-3872	349	3	point	point	NOUN
ejpam-3872	349	4	(	(	PUNCT
ejpam-3872	349	5	c	c	NOUN
ejpam-3872	349	6	)	)	PUNCT
ejpam-3872	349	7	.	.	PUNCT
ejpam-3872	350	1	this	this	PRON
ejpam-3872	350	2	is	be	AUX
ejpam-3872	350	3	proved	prove	VERB
ejpam-3872	350	4	exactly	exactly	ADV
ejpam-3872	350	5	as	as	ADP
ejpam-3872	350	6	point	point	NOUN
ejpam-3872	350	7	(	(	PUNCT
ejpam-3872	350	8	a	a	NOUN
ejpam-3872	350	9	)	)	PUNCT
ejpam-3872	350	10	.	.	PUNCT
ejpam-3872	351	1	proof	proof	NOUN
ejpam-3872	351	2	of	of	ADP
ejpam-3872	351	3	point	point	NOUN
ejpam-3872	351	4	(	(	PUNCT
ejpam-3872	351	5	d	d	NOUN
ejpam-3872	351	6	)	)	PUNCT
ejpam-3872	351	7	.	.	PUNCT
ejpam-3872	352	1	from	from	ADP
ejpam-3872	352	2	formulas	formula	NOUN
ejpam-3872	352	3	(	(	PUNCT
ejpam-3872	352	4	25	25	NUM
ejpam-3872	352	5	)	)	PUNCT
ejpam-3872	352	6	and	and	CCONJ
ejpam-3872	352	7	(	(	PUNCT
ejpam-3872	352	8	28	28	NUM
ejpam-3872	352	9	)	)	PUNCT
ejpam-3872	352	10	,	,	PUNCT
ejpam-3872	352	11	we	we	PRON
ejpam-3872	352	12	simply	simply	ADV
ejpam-3872	352	13	use	use	VERB
ejpam-3872	352	14	the	the	DET
ejpam-3872	352	15	rates	rate	NOUN
ejpam-3872	352	16	of	of	ADP
ejpam-3872	352	17	convergence	convergence	NOUN
ejpam-3872	352	18	in	in	ADP
ejpam-3872	352	19	hypothesis	hypothesis	NOUN
ejpam-3872	352	20	(	(	PUNCT
ejpam-3872	352	21	ha	ha	INTJ
ejpam-3872	352	22	)	)	PUNCT
ejpam-3872	352	23	and	and	CCONJ
ejpam-3872	352	24	(	(	PUNCT
ejpam-3872	352	25	hb	hb	X
ejpam-3872	352	26	)	)	PUNCT
ejpam-3872	352	27	to	to	PART
ejpam-3872	352	28	conclude	conclude	VERB
ejpam-3872	352	29	�	�	PROPN
ejpam-3872	352	30	5	5	NUM
ejpam-3872	352	31	.	.	PUNCT
ejpam-3872	352	32	conclusion	conclusion	NOUN
ejpam-3872	352	33	after	after	ADP
ejpam-3872	352	34	the	the	DET
ejpam-3872	352	35	statements	statement	NOUN
ejpam-3872	352	36	of	of	ADP
ejpam-3872	352	37	the	the	DET
ejpam-3872	352	38	asymptotic	asymptotic	ADJ
ejpam-3872	352	39	laws	law	NOUN
ejpam-3872	352	40	of	of	ADP
ejpam-3872	352	41	the	the	DET
ejpam-3872	352	42	strong	strong	ADJ
ejpam-3872	352	43	record	record	NOUN
ejpam-3872	352	44	values	value	NOUN
ejpam-3872	352	45	from	from	ADP
ejpam-3872	352	46	iid	iid	VERB
ejpam-3872	352	47	random	random	ADJ
ejpam-3872	352	48	variables	variable	NOUN
ejpam-3872	352	49	and	and	CCONJ
ejpam-3872	352	50	their	their	PRON
ejpam-3872	352	51	rates	rate	NOUN
ejpam-3872	352	52	of	of	ADP
ejpam-3872	352	53	convergences	convergence	NOUN
ejpam-3872	352	54	,	,	PUNCT
ejpam-3872	352	55	and	and	CCONJ
ejpam-3872	352	56	after	after	SCONJ
ejpam-3872	352	57	some	some	DET
ejpam-3872	352	58	examples	example	NOUN
ejpam-3872	352	59	have	have	AUX
ejpam-3872	352	60	been	be	AUX
ejpam-3872	352	61	given	give	VERB
ejpam-3872	352	62	,	,	PUNCT
ejpam-3872	352	63	it	it	PRON
ejpam-3872	352	64	should	should	AUX
ejpam-3872	352	65	be	be	AUX
ejpam-3872	352	66	interesting	interesting	ADJ
ejpam-3872	352	67	to	to	PART
ejpam-3872	352	68	have	have	VERB
ejpam-3872	352	69	a	a	DET
ejpam-3872	352	70	review	review	NOUN
ejpam-3872	352	71	of	of	ADP
ejpam-3872	352	72	such	such	ADJ
ejpam-3872	352	73	asymptotic	asymptotic	ADJ
ejpam-3872	352	74	laws	law	NOUN
ejpam-3872	352	75	for	for	ADP
ejpam-3872	352	76	cdf	cdf	PROPN
ejpam-3872	352	77	’s	’	VERB
ejpam-3872	352	78	as	as	ADV
ejpam-3872	352	79	much	much	ADV
ejpam-3872	352	80	as	as	ADP
ejpam-3872	352	81	possible	possible	ADJ
ejpam-3872	352	82	,	,	PUNCT
ejpam-3872	353	1	f	f	PROPN
ejpam-3872	353	2	∈	∈	PROPN
ejpam-3872	353	3	d.	d.	PROPN
ejpam-3872	353	4	g.	g.	PROPN
ejpam-3872	353	5	s.	s.	PROPN
ejpam-3872	354	1	lo	lo	PROPN
ejpam-3872	354	2	et	et	PROPN
ejpam-3872	354	3	al	al	PROPN
ejpam-3872	354	4	.	.	PUNCT
ejpam-3872	354	5	/	/	SYM
ejpam-3872	354	6	eur	eur	PROPN
ejpam-3872	354	7	.	.	PUNCT
ejpam-3872	355	1	j.	j.	PROPN
ejpam-3872	355	2	pure	pure	PROPN
ejpam-3872	355	3	appl	appl	PROPN
ejpam-3872	355	4	.	.	PROPN
ejpam-3872	355	5	math	math	PROPN
ejpam-3872	355	6	,	,	PUNCT
ejpam-3872	355	7	14	14	NUM
ejpam-3872	355	8	(	(	PUNCT
ejpam-3872	355	9	1	1	NUM
ejpam-3872	355	10	)	)	PUNCT
ejpam-3872	355	11	(	(	PUNCT
ejpam-3872	355	12	2021	2021	NUM
ejpam-3872	355	13	)	)	PUNCT
ejpam-3872	355	14	,	,	PUNCT
ejpam-3872	355	15	19	19	NUM
ejpam-3872	355	16	-	-	SYM
ejpam-3872	355	17	42	42	NUM
ejpam-3872	355	18	37	37	NUM
ejpam-3872	355	19	6	6	NUM
ejpam-3872	355	20	.	.	PUNCT
ejpam-3872	356	1	appendix	appendix	VERB
ejpam-3872	356	2	appendix	appendix	NOUN
ejpam-3872	356	3	.	.	PUNCT
ejpam-3872	357	1	let	let	VERB
ejpam-3872	357	2	us	we	PRON
ejpam-3872	357	3	give	give	VERB
ejpam-3872	357	4	the	the	DET
ejpam-3872	357	5	details	detail	NOUN
ejpam-3872	357	6	concerning	concern	VERB
ejpam-3872	357	7	the	the	DET
ejpam-3872	357	8	results	result	NOUN
ejpam-3872	357	9	listed	list	VERB
ejpam-3872	357	10	in	in	ADP
ejpam-3872	357	11	section	section	NOUN
ejpam-3872	357	12	3	3	NUM
ejpam-3872	357	13	.	.	PUNCT
ejpam-3872	358	1	(	(	PUNCT
ejpam-3872	358	2	1	1	X
ejpam-3872	358	3	)	)	PUNCT
ejpam-3872	358	4	x	x	PRON
ejpam-3872	358	5	follows	follow	VERB
ejpam-3872	358	6	an	an	DET
ejpam-3872	358	7	exponential	exponential	ADJ
ejpam-3872	358	8	law	law	NOUN
ejpam-3872	358	9	e(λ	e(λ	PROPN
ejpam-3872	358	10	)	)	PUNCT
ejpam-3872	358	11	,	,	PUNCT
ejpam-3872	358	12	λ	λ	X
ejpam-3872	358	13	>	>	X
ejpam-3872	358	14	0	0	X
ejpam-3872	358	15	.	.	PUNCT
ejpam-3872	359	1	we	we	PRON
ejpam-3872	359	2	have	have	VERB
ejpam-3872	359	3	exp(x	exp(x	PROPN
ejpam-3872	359	4	)	)	PUNCT
ejpam-3872	359	5	∈	∈	PROPN
ejpam-3872	359	6	d(g−1	d(g−1	PROPN
ejpam-3872	359	7	)	)	PUNCT
ejpam-3872	359	8	and	and	CCONJ
ejpam-3872	359	9	f−1(1−	f−1(1−	PROPN
ejpam-3872	359	10	e−n	e−n	PROPN
ejpam-3872	359	11	)	)	PUNCT
ejpam-3872	359	12	=	=	VERB
ejpam-3872	360	1	n.	n.	NOUN
ejpam-3872	360	2	we	we	PRON
ejpam-3872	360	3	apply	apply	VERB
ejpam-3872	360	4	point	point	NOUN
ejpam-3872	360	5	(	(	PUNCT
ejpam-3872	360	6	b	b	NOUN
ejpam-3872	360	7	)	)	PUNCT
ejpam-3872	360	8	to	to	PART
ejpam-3872	360	9	conclude	conclude	VERB
ejpam-3872	360	10	that	that	PRON
ejpam-3872	360	11	x(n	x(n	NOUN
ejpam-3872	360	12	)	)	PUNCT
ejpam-3872	361	1	−	−	ADP
ejpam-3872	361	2	n√	n√	SYM
ejpam-3872	361	3	n	n	CCONJ
ejpam-3872	361	4	n	n	CCONJ
ejpam-3872	361	5	(	(	PUNCT
ejpam-3872	361	6	0	0	NUM
ejpam-3872	361	7	,	,	PUNCT
ejpam-3872	361	8	λ−2	λ−2	PROPN
ejpam-3872	361	9	)	)	PUNCT
ejpam-3872	361	10	.	.	PUNCT
ejpam-3872	362	1	the	the	DET
ejpam-3872	362	2	rate	rate	NOUN
ejpam-3872	362	3	of	of	ADP
ejpam-3872	362	4	convergence	convergence	NOUN
ejpam-3872	362	5	is	be	AUX
ejpam-3872	362	6	the	the	DET
ejpam-3872	362	7	one	one	NUM
ejpam-3872	362	8	in	in	ADP
ejpam-3872	362	9	the	the	DET
ejpam-3872	362	10	approximation	approximation	NOUN
ejpam-3872	362	11	between	between	ADP
ejpam-3872	362	12	s∗n	s∗n	NUM
ejpam-3872	362	13	and	and	CCONJ
ejpam-3872	362	14	w	w	PROPN
ejpam-3872	362	15	∗n	∗n	PROPN
ejpam-3872	362	16	which	which	PRON
ejpam-3872	362	17	is	be	AUX
ejpam-3872	362	18	cn	cn	PROPN
ejpam-3872	362	19	.	.	PUNCT
ejpam-3872	363	1	(	(	PUNCT
ejpam-3872	363	2	2	2	X
ejpam-3872	363	3	)	)	PUNCT
ejpam-3872	363	4	x	x	PRON
ejpam-3872	363	5	follows	follow	VERB
ejpam-3872	363	6	a	a	DET
ejpam-3872	363	7	standard	standard	ADJ
ejpam-3872	363	8	normal	normal	ADJ
ejpam-3872	363	9	law	law	NOUN
ejpam-3872	363	10	n	n	CCONJ
ejpam-3872	363	11	(	(	PUNCT
ejpam-3872	363	12	0	0	NUM
ejpam-3872	363	13	,	,	PUNCT
ejpam-3872	363	14	1	1	NUM
ejpam-3872	363	15	)	)	PUNCT
ejpam-3872	363	16	.	.	PUNCT
ejpam-3872	364	1	the	the	DET
ejpam-3872	364	2	result	result	NOUN
ejpam-3872	364	3	of	of	ADP
ejpam-3872	364	4	this	this	DET
ejpam-3872	364	5	point	point	NOUN
ejpam-3872	364	6	is	be	AUX
ejpam-3872	364	7	justified	justify	VERB
ejpam-3872	364	8	by	by	ADP
ejpam-3872	364	9	formula	formula	NOUN
ejpam-3872	364	10	24	24	NUM
ejpam-3872	364	11	,	,	PUNCT
ejpam-3872	364	12	page	page	NOUN
ejpam-3872	364	13	34	34	NUM
ejpam-3872	364	14	.	.	PUNCT
ejpam-3872	364	15	to	to	PART
ejpam-3872	364	16	find	find	VERB
ejpam-3872	364	17	the	the	DET
ejpam-3872	364	18	rate	rate	NOUN
ejpam-3872	364	19	of	of	ADP
ejpam-3872	364	20	convergence	convergence	NOUN
ejpam-3872	364	21	,	,	PUNCT
ejpam-3872	364	22	we	we	PRON
ejpam-3872	364	23	proceed	proceed	VERB
ejpam-3872	364	24	to	to	ADP
ejpam-3872	364	25	a	a	DET
ejpam-3872	364	26	direct	direct	ADJ
ejpam-3872	364	27	proof	proof	NOUN
ejpam-3872	364	28	based	base	VERB
ejpam-3872	364	29	on	on	ADP
ejpam-3872	364	30	formulas	formula	NOUN
ejpam-3872	364	31	(	(	PUNCT
ejpam-3872	364	32	19	19	NUM
ejpam-3872	364	33	)	)	PUNCT
ejpam-3872	364	34	and	and	CCONJ
ejpam-3872	364	35	(	(	PUNCT
ejpam-3872	364	36	21	21	NUM
ejpam-3872	364	37	)	)	PUNCT
ejpam-3872	364	38	.	.	PUNCT
ejpam-3872	365	1	we	we	PRON
ejpam-3872	365	2	get	get	VERB
ejpam-3872	365	3	x(n	x(n	NOUN
ejpam-3872	365	4	)	)	PUNCT
ejpam-3872	366	1	−	−	PROPN
ejpam-3872	366	2	f−1(1−	f−1(1−	PROPN
ejpam-3872	366	3	e−n	e−n	PROPN
ejpam-3872	366	4	)	)	PUNCT
ejpam-3872	366	5	=	=	PUNCT
ejpam-3872	366	6	(	(	PUNCT
ejpam-3872	366	7	2s(n	2s(n	NUM
ejpam-3872	366	8	)	)	PUNCT
ejpam-3872	366	9	)	)	PUNCT
ejpam-3872	367	1	1/2(2n)1/2	1/2(2n)1/2	PROPN
ejpam-3872	367	2	(	(	PUNCT
ejpam-3872	367	3	l1	l1	PROPN
ejpam-3872	367	4	)	)	PUNCT
ejpam-3872	367	5	−	−	PROPN
ejpam-3872	368	1	(	(	PUNCT
ejpam-3872	368	2	log	log	VERB
ejpam-3872	368	3	4π	4π	NUM
ejpam-3872	368	4	+	+	CCONJ
ejpam-3872	368	5	logs(n	logs(n	PROPN
ejpam-3872	368	6	)	)	PUNCT
ejpam-3872	368	7	2(2s(n)))1/2	2(2s(n)))1/2	NUM
ejpam-3872	368	8	−	−	PROPN
ejpam-3872	369	1	log	log	NOUN
ejpam-3872	369	2	4π	4π	NUM
ejpam-3872	369	3	+	+	CCONJ
ejpam-3872	369	4	logs(n	logs(n	PROPN
ejpam-3872	369	5	)	)	PUNCT
ejpam-3872	369	6	2(2s(n))1/2	2(2s(n))1/2	NUM
ejpam-3872	369	7	)	)	PUNCT
ejpam-3872	369	8	(	(	PUNCT
ejpam-3872	369	9	l2	l2	NOUN
ejpam-3872	369	10	)	)	PUNCT
ejpam-3872	370	1	+	+	CCONJ
ejpam-3872	370	2	op(n−(log	op(n−(log	ADP
ejpam-3872	370	3	n)2	n)2	PROPN
ejpam-3872	370	4	)	)	PUNCT
ejpam-3872	370	5	.	.	PUNCT
ejpam-3872	371	1	(	(	PUNCT
ejpam-3872	371	2	l3	l3	PROPN
ejpam-3872	371	3	)	)	PUNCT
ejpam-3872	371	4	by	by	ADP
ejpam-3872	371	5	using	use	VERB
ejpam-3872	371	6	the	the	DET
ejpam-3872	371	7	result	result	NOUN
ejpam-3872	371	8	of	of	ADP
ejpam-3872	371	9	the	the	DET
ejpam-3872	371	10	application	application	NOUN
ejpam-3872	371	11	of	of	ADP
ejpam-3872	371	12	the	the	DET
ejpam-3872	371	13	mean	mean	ADJ
ejpam-3872	371	14	value	value	NOUN
ejpam-3872	371	15	theorem	theorem	VERB
ejpam-3872	371	16	in	in	ADP
ejpam-3872	371	17	formula	formula	NOUN
ejpam-3872	371	18	(	(	PUNCT
ejpam-3872	371	19	23	23	NUM
ejpam-3872	371	20	)	)	PUNCT
ejpam-3872	371	21	(	(	PUNCT
ejpam-3872	371	22	page	page	NOUN
ejpam-3872	371	23	34	34	NUM
ejpam-3872	371	24	)	)	PUNCT
ejpam-3872	371	25	in	in	ADP
ejpam-3872	371	26	line	line	NOUN
ejpam-3872	371	27	(	(	PUNCT
ejpam-3872	371	28	l1	l1	PROPN
ejpam-3872	371	29	)	)	PUNCT
ejpam-3872	371	30	,	,	PUNCT
ejpam-3872	371	31	by	by	ADP
ejpam-3872	371	32	applying	apply	VERB
ejpam-3872	371	33	the	the	DET
ejpam-3872	371	34	mean	mean	ADJ
ejpam-3872	371	35	value	value	NOUN
ejpam-3872	371	36	theorem	theorem	VERB
ejpam-3872	371	37	in	in	ADP
ejpam-3872	371	38	line	line	NOUN
ejpam-3872	371	39	(	(	PUNCT
ejpam-3872	371	40	l2	l2	NOUN
ejpam-3872	371	41	)	)	PUNCT
ejpam-3872	371	42	above	above	ADV
ejpam-3872	371	43	and	and	CCONJ
ejpam-3872	371	44	by	by	ADP
ejpam-3872	371	45	using	use	VERB
ejpam-3872	371	46	the	the	DET
ejpam-3872	371	47	fact	fact	NOUN
ejpam-3872	371	48	(	(	PUNCT
ejpam-3872	371	49	n	n	CCONJ
ejpam-3872	371	50	/	/	SYM
ejpam-3872	371	51	ζn)→	ζn)→	NOUN
ejpam-3872	371	52	1	1	NUM
ejpam-3872	371	53	,	,	PUNCT
ejpam-3872	371	54	we	we	PRON
ejpam-3872	371	55	get	get	VERB
ejpam-3872	371	56	x(n	x(n	NOUN
ejpam-3872	371	57	)	)	PUNCT
ejpam-3872	372	1	−	−	PROPN
ejpam-3872	372	2	f−1(1−	f−1(1−	PROPN
ejpam-3872	372	3	e−n	e−n	PROPN
ejpam-3872	372	4	)	)	PUNCT
ejpam-3872	372	5	=	=	SYM
ejpam-3872	372	6	1√	1√	PROPN
ejpam-3872	372	7	2	2	NUM
ejpam-3872	372	8	s(n	s(n	NOUN
ejpam-3872	372	9	)	)	PUNCT
ejpam-3872	372	10	−	−	ADP
ejpam-3872	372	11	n√	n√	SYM
ejpam-3872	372	12	n	n	CCONJ
ejpam-3872	372	13	+	+	CCONJ
ejpam-3872	372	14	1√	1√	PROPN
ejpam-3872	372	15	2	2	NUM
ejpam-3872	372	16	s(n	s(n	NOUN
ejpam-3872	372	17	)	)	PUNCT
ejpam-3872	372	18	−	−	ADP
ejpam-3872	372	19	n√	n√	SYM
ejpam-3872	372	20	n	n	CCONJ
ejpam-3872	372	21	(	(	PUNCT
ejpam-3872	372	22	(	(	PUNCT
ejpam-3872	372	23	n	n	CCONJ
ejpam-3872	372	24	/	/	SYM
ejpam-3872	372	25	ζn)1/2	ζn)1/2	ADJ
ejpam-3872	372	26	−	−	PROPN
ejpam-3872	372	27	1	1	NUM
ejpam-3872	372	28	)	)	PUNCT
ejpam-3872	372	29	−	−	NOUN
ejpam-3872	372	30	op(n−1(log	op(n−1(log	PROPN
ejpam-3872	372	31	n	n	CCONJ
ejpam-3872	372	32	)	)	PUNCT
ejpam-3872	372	33	)	)	PUNCT
ejpam-3872	373	1	+	+	CCONJ
ejpam-3872	373	2	op(n−1/2	op(n−1/2	VERB
ejpam-3872	373	3	log	log	NOUN
ejpam-3872	373	4	n	n	CCONJ
ejpam-3872	373	5	)	)	PUNCT
ejpam-3872	373	6	.	.	PUNCT
ejpam-3872	374	1	finally	finally	ADV
ejpam-3872	374	2	,	,	PUNCT
ejpam-3872	374	3	by	by	ADP
ejpam-3872	374	4	using	use	VERB
ejpam-3872	374	5	(	(	PUNCT
ejpam-3872	374	6	n	n	CCONJ
ejpam-3872	374	7	/	/	SYM
ejpam-3872	374	8	ζn)−1	ζn)−1	NOUN
ejpam-3872	374	9	=	=	PUNCT
ejpam-3872	374	10	op(n−1(log	op(n−1(log	NOUN
ejpam-3872	374	11	n	n	CCONJ
ejpam-3872	374	12	)	)	PUNCT
ejpam-3872	374	13	)	)	PUNCT
ejpam-3872	374	14	and	and	CCONJ
ejpam-3872	374	15	(	(	PUNCT
ejpam-3872	374	16	sn−n)/	sn−n)/	PROPN
ejpam-3872	374	17	√	√	PROPN
ejpam-3872	374	18	n	n	PROPN
ejpam-3872	374	19	=	=	PUNCT
ejpam-3872	374	20	op(1	op(1	PROPN
ejpam-3872	374	21	)	)	PUNCT
ejpam-3872	374	22	,	,	PUNCT
ejpam-3872	374	23	we	we	PRON
ejpam-3872	374	24	conclude	conclude	VERB
ejpam-3872	374	25	that	that	SCONJ
ejpam-3872	374	26	x(n	x(n	NOUN
ejpam-3872	374	27	)	)	PUNCT
ejpam-3872	374	28	−	−	PROPN
ejpam-3872	374	29	f−1(1−	f−1(1−	PROPN
ejpam-3872	374	30	e−n	e−n	PROPN
ejpam-3872	374	31	)	)	PUNCT
ejpam-3872	374	32	=	=	PUNCT
ejpam-3872	375	1	s∗n	s∗n	PUNCT
ejpam-3872	376	1	+	+	CCONJ
ejpam-3872	376	2	op(n−1/2	op(n−1/2	ADJ
ejpam-3872	376	3	log	log	NOUN
ejpam-3872	376	4	n	n	CCONJ
ejpam-3872	376	5	)	)	PUNCT
ejpam-3872	376	6	,	,	PUNCT
ejpam-3872	376	7	which	which	PRON
ejpam-3872	376	8	was	be	AUX
ejpam-3872	376	9	the	the	DET
ejpam-3872	376	10	target	target	NOUN
ejpam-3872	376	11	.	.	PUNCT
ejpam-3872	377	1	(	(	PUNCT
ejpam-3872	377	2	3	3	X
ejpam-3872	377	3	)	)	PUNCT
ejpam-3872	377	4	x	x	PRON
ejpam-3872	377	5	follows	follow	VERB
ejpam-3872	377	6	a	a	DET
ejpam-3872	377	7	rayleigh	rayleigh	PROPN
ejpam-3872	377	8	law	law	NOUN
ejpam-3872	377	9	of	of	ADP
ejpam-3872	377	10	parameter	parameter	PROPN
ejpam-3872	377	11	ρ	ρ	PROPN
ejpam-3872	377	12	>	>	X
ejpam-3872	377	13	0	0	NUM
ejpam-3872	377	14	.	.	PUNCT
ejpam-3872	378	1	we	we	PRON
ejpam-3872	378	2	have	have	VERB
ejpam-3872	378	3	g.	g.	PROPN
ejpam-3872	378	4	s.	s.	PROPN
ejpam-3872	379	1	lo	lo	PROPN
ejpam-3872	379	2	et	et	PROPN
ejpam-3872	379	3	al	al	PROPN
ejpam-3872	379	4	.	.	PUNCT
ejpam-3872	379	5	/	/	SYM
ejpam-3872	379	6	eur	eur	PROPN
ejpam-3872	379	7	.	.	PUNCT
ejpam-3872	380	1	j.	j.	PROPN
ejpam-3872	380	2	pure	pure	PROPN
ejpam-3872	380	3	appl	appl	PROPN
ejpam-3872	380	4	.	.	PROPN
ejpam-3872	380	5	math	math	PROPN
ejpam-3872	380	6	,	,	PUNCT
ejpam-3872	380	7	14	14	NUM
ejpam-3872	380	8	(	(	PUNCT
ejpam-3872	380	9	1	1	NUM
ejpam-3872	380	10	)	)	PUNCT
ejpam-3872	380	11	(	(	PUNCT
ejpam-3872	380	12	2021	2021	NUM
ejpam-3872	380	13	)	)	PUNCT
ejpam-3872	380	14	,	,	PUNCT
ejpam-3872	380	15	19	19	NUM
ejpam-3872	380	16	-	-	SYM
ejpam-3872	380	17	42	42	NUM
ejpam-3872	380	18	38	38	NUM
ejpam-3872	380	19	f−1(1−	f−1(1−	PROPN
ejpam-3872	380	20	u	u	NOUN
ejpam-3872	380	21	)	)	PUNCT
ejpam-3872	380	22	=	=	PRON
ejpam-3872	380	23	(	(	PUNCT
ejpam-3872	380	24	−1	−1	NOUN
ejpam-3872	380	25	ρ	ρ	PROPN
ejpam-3872	380	26	log	log	NOUN
ejpam-3872	380	27	u	u	PROPN
ejpam-3872	380	28	)	)	PUNCT
ejpam-3872	380	29	1/2	1/2	NUM
ejpam-3872	380	30	,	,	PUNCT
ejpam-3872	380	31	u	u	NOUN
ejpam-3872	380	32	∈]0	∈]0	ADJ
ejpam-3872	380	33	,	,	PUNCT
ejpam-3872	380	34	1	1	NUM
ejpam-3872	380	35	[	[	PUNCT
ejpam-3872	380	36	and	and	CCONJ
ejpam-3872	380	37	s(u	s(u	PROPN
ejpam-3872	380	38	)	)	PUNCT
ejpam-3872	380	39	=	=	SYM
ejpam-3872	380	40	−u	−u	NOUN
ejpam-3872	380	41	(	(	PUNCT
ejpam-3872	380	42	f−1(1−	f−1(1−	PROPN
ejpam-3872	380	43	u	u	NOUN
ejpam-3872	380	44	)	)	PUNCT
ejpam-3872	380	45	)	)	PUNCT
ejpam-3872	380	46	′	′	NUM
ejpam-3872	381	1	=	=	SYM
ejpam-3872	381	2	1	1	NUM
ejpam-3872	381	3	2ρ(−(1	2ρ(−(1	NUM
ejpam-3872	381	4	/	/	SYM
ejpam-3872	381	5	ρ	ρ	PROPN
ejpam-3872	381	6	)	)	PUNCT
ejpam-3872	381	7	log	log	NOUN
ejpam-3872	381	8	u)1/2	u)1/2	PROPN
ejpam-3872	381	9	→	→	SYM
ejpam-3872	381	10	0	0	PUNCT
ejpam-3872	381	11	as	as	ADP
ejpam-3872	381	12	u→	u→	PROPN
ejpam-3872	381	13	0	0	NUM
ejpam-3872	381	14	.	.	PUNCT
ejpam-3872	382	1	furthermore	furthermore	ADV
ejpam-3872	382	2	,	,	PUNCT
ejpam-3872	382	3	s(u	s(u	PROPN
ejpam-3872	382	4	)	)	PUNCT
ejpam-3872	382	5	is	be	AUX
ejpam-3872	382	6	decreasing	decrease	VERB
ejpam-3872	382	7	in	in	ADP
ejpam-3872	382	8	u	u	NOUN
ejpam-3872	382	9	∈]0	∈]0	NOUN
ejpam-3872	382	10	,	,	PUNCT
ejpam-3872	382	11	1	1	NUM
ejpam-3872	382	12	[	[	PUNCT
ejpam-3872	382	13	and	and	CCONJ
ejpam-3872	382	14	s(vn)/s(vn)→	s(vn)/s(vn)→	NOUN
ejpam-3872	382	15	0	0	PUNCT
ejpam-3872	382	16	as	as	ADP
ejpam-3872	382	17	n→	n→	ADV
ejpam-3872	382	18	+	+	PROPN
ejpam-3872	382	19	∞.	∞.	PROPN
ejpam-3872	382	20	finally	finally	ADV
ejpam-3872	382	21	,	,	PUNCT
ejpam-3872	382	22	√	√	PROPN
ejpam-3872	382	23	ns(vn)→	ns(vn)→	PROPN
ejpam-3872	382	24	ρ−1/2/2	ρ−1/2/2	PROPN
ejpam-3872	382	25	.	.	PUNCT
ejpam-3872	383	1	we	we	PRON
ejpam-3872	383	2	conclude	conclude	VERB
ejpam-3872	383	3	the	the	DET
ejpam-3872	383	4	case	case	NOUN
ejpam-3872	383	5	by	by	ADP
ejpam-3872	383	6	applying	apply	VERB
ejpam-3872	383	7	point	point	NOUN
ejpam-3872	383	8	(	(	PUNCT
ejpam-3872	383	9	d	d	NOUN
ejpam-3872	383	10	)	)	PUNCT
ejpam-3872	383	11	of	of	ADP
ejpam-3872	383	12	theorem	theorem	NOUN
ejpam-3872	383	13	1	1	NUM
ejpam-3872	383	14	.	.	PUNCT
ejpam-3872	383	15	for	for	ADP
ejpam-3872	383	16	finding	find	VERB
ejpam-3872	383	17	the	the	DET
ejpam-3872	383	18	rate	rate	NOUN
ejpam-3872	383	19	of	of	ADP
ejpam-3872	383	20	convergence	convergence	NOUN
ejpam-3872	383	21	,	,	PUNCT
ejpam-3872	383	22	we	we	PRON
ejpam-3872	383	23	have	have	VERB
ejpam-3872	383	24	en	en	X
ejpam-3872	383	25	=	=	SYM
ejpam-3872	383	26	0	0	PROPN
ejpam-3872	383	27	since	since	SCONJ
ejpam-3872	383	28	√	√	PROPN
ejpam-3872	383	29	n	n	PRON
ejpam-3872	383	30	s(vn	s(vn	NUM
ejpam-3872	383	31	)	)	PUNCT
ejpam-3872	383	32	=	=	PUNCT
ejpam-3872	383	33	(	(	PUNCT
ejpam-3872	383	34	2	2	NUM
ejpam-3872	383	35	√	√	NUM
ejpam-3872	383	36	ρ	ρ	NUM
ejpam-3872	383	37	)	)	PUNCT
ejpam-3872	384	1	=	=	SYM
ejpam-3872	384	2	α	α	X
ejpam-3872	384	3	.	.	PUNCT
ejpam-3872	385	1	the	the	DET
ejpam-3872	385	2	rate	rate	NOUN
ejpam-3872	385	3	of	of	ADP
ejpam-3872	385	4	convergence	convergence	NOUN
ejpam-3872	385	5	corresponding	correspond	VERB
ejpam-3872	385	6	to	to	ADP
ejpam-3872	385	7	dn	dn	PROPN
ejpam-3872	385	8	is	be	AUX
ejpam-3872	385	9	obtained	obtain	VERB
ejpam-3872	385	10	by	by	ADP
ejpam-3872	385	11	remarking	remark	VERB
ejpam-3872	385	12	that	that	SCONJ
ejpam-3872	385	13	s	s	PROPN
ejpam-3872	385	14	(	(	PUNCT
ejpam-3872	385	15	◦	◦	NOUN
ejpam-3872	385	16	)	)	PUNCT
ejpam-3872	385	17	is	be	AUX
ejpam-3872	385	18	decreasing	decrease	VERB
ejpam-3872	385	19	to	to	ADP
ejpam-3872	385	20	zero	zero	NUM
ejpam-3872	385	21	and	and	CCONJ
ejpam-3872	385	22	so	so	ADV
ejpam-3872	385	23	sup	sup	PROPN
ejpam-3872	385	24	{	{	PUNCT
ejpam-3872	385	25	∣∣∣u	∣∣∣u	PROPN
ejpam-3872	385	26	v	v	NOUN
ejpam-3872	385	27	−	−	PROPN
ejpam-3872	385	28	1	1	NUM
ejpam-3872	385	29	∣∣∣	∣∣∣	NOUN
ejpam-3872	385	30	,	,	PUNCT
ejpam-3872	385	31	min(vn	min(vn	PROPN
ejpam-3872	385	32	,	,	PUNCT
ejpam-3872	385	33	vn	vn	NOUN
ejpam-3872	385	34	)	)	PUNCT
ejpam-3872	385	35	≤	≤	NOUN
ejpam-3872	385	36	u	u	NOUN
ejpam-3872	385	37	,	,	PUNCT
ejpam-3872	385	38	v	v	ADJ
ejpam-3872	385	39	≤	≤	NUM
ejpam-3872	385	40	max(vn	max(vn	NOUN
ejpam-3872	385	41	,	,	PUNCT
ejpam-3872	385	42	vn	vn	PROPN
ejpam-3872	385	43	)	)	PUNCT
ejpam-3872	385	44	}	}	PUNCT
ejpam-3872	385	45	≤	≤	NUM
ejpam-3872	385	46	∣∣∣∣s(e−n	∣∣∣∣s(e−n	PROPN
ejpam-3872	385	47	∨	∨	NOUN
ejpam-3872	385	48	e−sn	e−sn	PROPN
ejpam-3872	385	49	)	)	PUNCT
ejpam-3872	385	50	s(e−n	s(e−n	NOUN
ejpam-3872	385	51	∧	∧	PROPN
ejpam-3872	385	52	e−sn	e−sn	PROPN
ejpam-3872	385	53	)	)	PUNCT
ejpam-3872	386	1	−	−	PROPN
ejpam-3872	386	2	1	1	NUM
ejpam-3872	386	3	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3872	386	4	∣∣∣∣s(e−n	∣∣∣∣s(e−n	PROPN
ejpam-3872	386	5	∨	∨	NOUN
ejpam-3872	386	6	e−sn	e−sn	PROPN
ejpam-3872	386	7	)	)	PUNCT
ejpam-3872	386	8	s(e−n	s(e−n	NOUN
ejpam-3872	386	9	∧	∧	PROPN
ejpam-3872	386	10	e−sn	e−sn	PROPN
ejpam-3872	386	11	)	)	PUNCT
ejpam-3872	386	12	−	−	PROPN
ejpam-3872	386	13	1	1	NUM
ejpam-3872	386	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3872	386	15	≤	≤	NOUN
ejpam-3872	386	16	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3872	386	17	(	(	PUNCT
ejpam-3872	386	18	sn	sn	PROPN
ejpam-3872	386	19	n	n	CCONJ
ejpam-3872	386	20	)	)	PUNCT
ejpam-3872	386	21	1/2	1/2	NUM
ejpam-3872	386	22	−	−	PROPN
ejpam-3872	386	23	1	1	NUM
ejpam-3872	386	24	∣∣∣∣∣+	∣∣∣∣∣+	PROPN
ejpam-3872	386	25	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3872	386	26	(	(	PUNCT
ejpam-3872	386	27	sn	sn	PROPN
ejpam-3872	386	28	n	n	CCONJ
ejpam-3872	386	29	)	)	PUNCT
ejpam-3872	386	30	−1/2	−1/2	VERB
ejpam-3872	386	31	−	−	NOUN
ejpam-3872	386	32	1	1	NUM
ejpam-3872	386	33	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-3872	386	34	=	=	PUNCT
ejpam-3872	386	35	or	or	CCONJ
ejpam-3872	386	36	(	(	PUNCT
ejpam-3872	386	37	1√	1√	PROPN
ejpam-3872	386	38	n	n	NOUN
ejpam-3872	386	39	)	)	PUNCT
ejpam-3872	386	40	.	.	PUNCT
ejpam-3872	387	1	this	this	PRON
ejpam-3872	387	2	closes	close	VERB
ejpam-3872	387	3	the	the	DET
ejpam-3872	387	4	discussions	discussion	NOUN
ejpam-3872	387	5	on	on	ADP
ejpam-3872	387	6	the	the	DET
ejpam-3872	387	7	rate	rate	NOUN
ejpam-3872	387	8	of	of	ADP
ejpam-3872	387	9	convergence	convergence	NOUN
ejpam-3872	387	10	.	.	PUNCT
ejpam-3872	388	1	(	(	PUNCT
ejpam-3872	388	2	4	4	X
ejpam-3872	388	3	)	)	PUNCT
ejpam-3872	388	4	x	x	PRON
ejpam-3872	388	5	follows	follow	VERB
ejpam-3872	388	6	the	the	DET
ejpam-3872	388	7	logistic	logistic	ADJ
ejpam-3872	388	8	law	law	NOUN
ejpam-3872	388	9	.	.	PUNCT
ejpam-3872	389	1	it	it	PRON
ejpam-3872	389	2	is	be	AUX
ejpam-3872	389	3	immediate	immediate	ADJ
ejpam-3872	389	4	that	that	SCONJ
ejpam-3872	389	5	exp(x	exp(x	PROPN
ejpam-3872	389	6	)	)	PUNCT
ejpam-3872	389	7	∈	∈	PROPN
ejpam-3872	389	8	d(g−1	d(g−1	PROPN
ejpam-3872	389	9	)	)	PUNCT
ejpam-3872	389	10	and	and	CCONJ
ejpam-3872	389	11	we	we	PRON
ejpam-3872	389	12	have	have	VERB
ejpam-3872	389	13	f−1(1−	f−1(1−	PROPN
ejpam-3872	389	14	u	u	NOUN
ejpam-3872	389	15	)	)	PUNCT
ejpam-3872	389	16	=	=	PUNCT
ejpam-3872	390	1	log(u/(1−	log(u/(1−	PROPN
ejpam-3872	390	2	u	u	NOUN
ejpam-3872	390	3	)	)	PUNCT
ejpam-3872	390	4	)	)	PUNCT
ejpam-3872	390	5	,	,	PUNCT
ejpam-3872	391	1	u	u	NOUN
ejpam-3872	391	2	∈]0	∈]0	ADJ
ejpam-3872	391	3	,	,	PUNCT
ejpam-3872	391	4	1	1	NUM
ejpam-3872	391	5	[	[	NOUN
ejpam-3872	391	6	.	.	PUNCT
ejpam-3872	392	1	we	we	PRON
ejpam-3872	392	2	conclude	conclude	VERB
ejpam-3872	392	3	with	with	ADP
ejpam-3872	392	4	point	point	NOUN
ejpam-3872	392	5	(	(	PUNCT
ejpam-3872	392	6	b	b	NOUN
ejpam-3872	392	7	)	)	PUNCT
ejpam-3872	392	8	of	of	ADP
ejpam-3872	392	9	theorem	theorem	NOUN
ejpam-3872	392	10	1	1	NUM
ejpam-3872	392	11	.	.	PUNCT
ejpam-3872	393	1	the	the	DET
ejpam-3872	393	2	rate	rate	NOUN
ejpam-3872	393	3	of	of	ADP
ejpam-3872	393	4	convergence	convergence	NOUN
ejpam-3872	393	5	can	can	AUX
ejpam-3872	393	6	be	be	AUX
ejpam-3872	393	7	found	find	VERB
ejpam-3872	393	8	from	from	ADP
ejpam-3872	393	9	that	that	DET
ejpam-3872	393	10	z	z	NOUN
ejpam-3872	393	11	=	=	SYM
ejpam-3872	393	12	exp(x	exp(x	PROPN
ejpam-3872	393	13	)	)	PUNCT
ejpam-3872	393	14	of	of	ADP
ejpam-3872	393	15	cdf	cdf	PROPN
ejpam-3872	393	16	h(t	h(t	NUM
ejpam-3872	393	17	)	)	PUNCT
ejpam-3872	394	1	=	=	SYM
ejpam-3872	395	1	t(1	t(1	NOUN
ejpam-3872	395	2	+	+	CCONJ
ejpam-3872	395	3	t)−1	t)−1	PROPN
ejpam-3872	395	4	,	,	PUNCT
ejpam-3872	395	5	t	t	X
ejpam-3872	395	6	>	>	X
ejpam-3872	395	7	0	0	PROPN
ejpam-3872	395	8	.	.	PUNCT
ejpam-3872	396	1	g.	g.	PROPN
ejpam-3872	396	2	s.	s.	PROPN
ejpam-3872	396	3	lo	lo	PROPN
ejpam-3872	396	4	et	et	PROPN
ejpam-3872	396	5	al	al	PROPN
ejpam-3872	396	6	.	.	PUNCT
ejpam-3872	396	7	/	/	SYM
ejpam-3872	396	8	eur	eur	PROPN
ejpam-3872	396	9	.	.	PUNCT
ejpam-3872	397	1	j.	j.	PROPN
ejpam-3872	397	2	pure	pure	PROPN
ejpam-3872	397	3	appl	appl	PROPN
ejpam-3872	397	4	.	.	PROPN
ejpam-3872	397	5	math	math	PROPN
ejpam-3872	397	6	,	,	PUNCT
ejpam-3872	397	7	14	14	NUM
ejpam-3872	397	8	(	(	PUNCT
ejpam-3872	397	9	1	1	NUM
ejpam-3872	397	10	)	)	PUNCT
ejpam-3872	397	11	(	(	PUNCT
ejpam-3872	397	12	2021	2021	NUM
ejpam-3872	397	13	)	)	PUNCT
ejpam-3872	397	14	,	,	PUNCT
ejpam-3872	397	15	19	19	NUM
ejpam-3872	397	16	-	-	SYM
ejpam-3872	397	17	42	42	NUM
ejpam-3872	397	18	39	39	NUM
ejpam-3872	397	19	we	we	PRON
ejpam-3872	397	20	have	have	VERB
ejpam-3872	397	21	that	that	DET
ejpam-3872	397	22	h	h	PROPN
ejpam-3872	397	23	∈	∈	PROPN
ejpam-3872	397	24	g1	g1	PROPN
ejpam-3872	397	25	and	and	CCONJ
ejpam-3872	397	26	,	,	PUNCT
ejpam-3872	397	27	for	for	ADP
ejpam-3872	397	28	γ	γ	X
ejpam-3872	397	29	=	=	SYM
ejpam-3872	397	30	1	1	NUM
ejpam-3872	397	31	,	,	PUNCT
ejpam-3872	397	32	−u(logh−1(1−	−u(logh−1(1−	NOUN
ejpam-3872	397	33	u))′	u))′	SYM
ejpam-3872	397	34	−	−	PROPN
ejpam-3872	397	35	γ	γ	X
ejpam-3872	397	36	=	=	SYM
ejpam-3872	397	37	u(1−	u(1−	NOUN
ejpam-3872	397	38	u)−1	u)−1	NOUN
ejpam-3872	397	39	.	.	PUNCT
ejpam-3872	398	1	by	by	ADP
ejpam-3872	398	2	applying	apply	VERB
ejpam-3872	398	3	point	point	NOUN
ejpam-3872	398	4	(	(	PUNCT
ejpam-3872	398	5	1	1	NUM
ejpam-3872	398	6	)	)	PUNCT
ejpam-3872	398	7	of	of	ADP
ejpam-3872	398	8	theorem	theorem	NOUN
ejpam-3872	398	9	3	3	NUM
ejpam-3872	398	10	,	,	PUNCT
ejpam-3872	398	11	we	we	PRON
ejpam-3872	398	12	take	take	VERB
ejpam-3872	398	13	for	for	ADP
ejpam-3872	398	14	any	any	DET
ejpam-3872	398	15	η	η	NOUN
ejpam-3872	398	16	∈]0	∈]0	X
ejpam-3872	398	17	,	,	PUNCT
ejpam-3872	398	18	1	1	NUM
ejpam-3872	398	19	[	[	PUNCT
ejpam-3872	398	20	and	and	CCONJ
ejpam-3872	398	21	bn(η	bn(η	ADV
ejpam-3872	398	22	)	)	PUNCT
ejpam-3872	399	1	=	=	SYM
ejpam-3872	399	2	e−ηn	e−ηn	ADJ
ejpam-3872	399	3	p	p	X
ejpam-3872	399	4	(	(	PUNCT
ejpam-3872	399	5	1−	1−	NUM
ejpam-3872	399	6	e−n	e−n	PROPN
ejpam-3872	399	7	/	/	SYM
ejpam-3872	399	8	η	η	PROPN
ejpam-3872	399	9	)	)	PUNCT
ejpam-3872	399	10	and	and	CCONJ
ejpam-3872	399	11	get	get	VERB
ejpam-3872	399	12	(	(	PUNCT
ejpam-3872	399	13	z(n	z(n	NOUN
ejpam-3872	399	14	)	)	PUNCT
ejpam-3872	399	15	n−	n−	PROPN
ejpam-3872	399	16	log(1−	log(1−	PROPN
ejpam-3872	399	17	e−n	e−n	PROPN
ejpam-3872	399	18	)	)	PUNCT
ejpam-3872	399	19	)	)	PUNCT
ejpam-3872	399	20	1/	1/	NUM
ejpam-3872	399	21	√	√	PROPN
ejpam-3872	399	22	n	n	PROPN
ejpam-3872	399	23	=	=	SYM
ejpam-3872	399	24	exp(s∗n	exp(s∗n	PROPN
ejpam-3872	399	25	)	)	PUNCT
ejpam-3872	399	26	+	+	NOUN
ejpam-3872	399	27	op(bn	op(bn	PROPN
ejpam-3872	399	28	)	)	PUNCT
ejpam-3872	399	29	.	.	PUNCT
ejpam-3872	400	1	(	(	PUNCT
ejpam-3872	400	2	5	5	X
ejpam-3872	400	3	)	)	PUNCT
ejpam-3872	400	4	x	x	X
ejpam-3872	400	5	>	>	X
ejpam-3872	400	6	0	0	NUM
ejpam-3872	400	7	follows	follow	VERB
ejpam-3872	400	8	a	a	DET
ejpam-3872	400	9	standard	standard	ADJ
ejpam-3872	400	10	lognormal	lognormal	ADJ
ejpam-3872	400	11	law	law	NOUN
ejpam-3872	400	12	,	,	PUNCT
ejpam-3872	400	13	that	that	PRON
ejpam-3872	400	14	is	is	ADV
ejpam-3872	400	15	logx	logx	PROPN
ejpam-3872	400	16	follows	follow	VERB
ejpam-3872	400	17	a	a	DET
ejpam-3872	400	18	standard	standard	ADJ
ejpam-3872	400	19	normal	normal	ADJ
ejpam-3872	400	20	law	law	NOUN
ejpam-3872	400	21	.	.	PUNCT
ejpam-3872	401	1	since	since	SCONJ
ejpam-3872	401	2	logx(n	logx(n	NOUN
ejpam-3872	401	3	)	)	PUNCT
ejpam-3872	401	4	has	have	VERB
ejpam-3872	401	5	the	the	DET
ejpam-3872	401	6	same	same	ADJ
ejpam-3872	401	7	law	law	NOUN
ejpam-3872	401	8	as	as	ADP
ejpam-3872	401	9	the	the	DET
ejpam-3872	401	10	n	n	CCONJ
ejpam-3872	401	11	-	-	PUNCT
ejpam-3872	401	12	th	th	X
ejpam-3872	401	13	record	record	NOUN
ejpam-3872	401	14	z(n	z(n	NOUN
ejpam-3872	401	15	)	)	PUNCT
ejpam-3872	401	16	from	from	ADP
ejpam-3872	401	17	iid	iid	NOUN
ejpam-3872	401	18	n	n	CCONJ
ejpam-3872	401	19	(	(	PUNCT
ejpam-3872	401	20	0	0	NUM
ejpam-3872	401	21	,	,	PUNCT
ejpam-3872	401	22	1	1	NUM
ejpam-3872	401	23	)	)	PUNCT
ejpam-3872	401	24	random	random	ADJ
ejpam-3872	401	25	variables	variable	NOUN
ejpam-3872	401	26	.	.	PUNCT
ejpam-3872	402	1	so	so	ADV
ejpam-3872	402	2	we	we	PRON
ejpam-3872	402	3	have	have	VERB
ejpam-3872	402	4	logx(n	logx(n	NOUN
ejpam-3872	402	5	)	)	PUNCT
ejpam-3872	403	1	−	−	PROPN
ejpam-3872	404	1	(	(	PUNCT
ejpam-3872	404	2	2n)1/2	2n)1/2	NUM
ejpam-3872	404	3	→	→	SYM
ejpam-3872	404	4	n	n	CCONJ
ejpam-3872	404	5	(	(	PUNCT
ejpam-3872	404	6	0	0	NUM
ejpam-3872	404	7	,	,	PUNCT
ejpam-3872	404	8	1/2	1/2	NUM
ejpam-3872	404	9	)	)	PUNCT
ejpam-3872	404	10	.	.	PUNCT
ejpam-3872	405	1	the	the	DET
ejpam-3872	405	2	conclusion	conclusion	NOUN
ejpam-3872	405	3	is	be	AUX
ejpam-3872	405	4	done	do	VERB
ejpam-3872	405	5	by	by	ADP
ejpam-3872	405	6	taking	take	VERB
ejpam-3872	405	7	the	the	DET
ejpam-3872	405	8	logarithm	logarithm	NOUN
ejpam-3872	405	9	of	of	ADP
ejpam-3872	405	10	both	both	DET
ejpam-3872	405	11	members	member	NOUN
ejpam-3872	405	12	.	.	PUNCT
ejpam-3872	406	1	we	we	PRON
ejpam-3872	406	2	still	still	ADV
ejpam-3872	406	3	can	can	AUX
ejpam-3872	406	4	use	use	VERB
ejpam-3872	406	5	the	the	DET
ejpam-3872	406	6	rate	rate	NOUN
ejpam-3872	406	7	of	of	ADP
ejpam-3872	406	8	convergence	convergence	NOUN
ejpam-3872	406	9	from	from	ADP
ejpam-3872	406	10	normal	normal	ADJ
ejpam-3872	406	11	records	record	NOUN
ejpam-3872	406	12	to	to	PART
ejpam-3872	406	13	have	have	VERB
ejpam-3872	406	14	:	:	PUNCT
ejpam-3872	406	15	logx(n	logx(n	PROPN
ejpam-3872	406	16	)	)	PUNCT
ejpam-3872	406	17	−	−	PROPN
ejpam-3872	407	1	(	(	PUNCT
ejpam-3872	407	2	2n)1/2	2n)1/2	NUM
ejpam-3872	407	3	=	=	SYM
ejpam-3872	407	4	s∗n	s∗n	NUM
ejpam-3872	407	5	+	+	ADP
ejpam-3872	407	6	op(n−1(log	op(n−1(log	PROPN
ejpam-3872	407	7	n)2	n)2	NOUN
ejpam-3872	407	8	)	)	PUNCT
ejpam-3872	407	9	.	.	PUNCT
ejpam-3872	408	1	(	(	PUNCT
ejpam-3872	408	2	6	6	NUM
ejpam-3872	408	3	)	)	PUNCT
ejpam-3872	408	4	x	x	X
ejpam-3872	408	5	>	>	X
ejpam-3872	408	6	0	0	NUM
ejpam-3872	408	7	follows	follow	VERB
ejpam-3872	408	8	a	a	DET
ejpam-3872	408	9	gumbel	gumbel	PROPN
ejpam-3872	408	10	law	law	NOUN
ejpam-3872	408	11	.	.	PUNCT
ejpam-3872	409	1	we	we	PRON
ejpam-3872	409	2	have	have	VERB
ejpam-3872	409	3	f−1(1−	f−1(1−	PROPN
ejpam-3872	409	4	u	u	NOUN
ejpam-3872	409	5	)	)	PUNCT
ejpam-3872	409	6	=	=	SYM
ejpam-3872	409	7	−	−	PROPN
ejpam-3872	409	8	log	log	NOUN
ejpam-3872	409	9	log(1/(1−	log(1/(1−	PROPN
ejpam-3872	409	10	u	u	NOUN
ejpam-3872	409	11	)	)	PUNCT
ejpam-3872	409	12	)	)	PUNCT
ejpam-3872	409	13	,	,	PUNCT
ejpam-3872	409	14	u	u	NOUN
ejpam-3872	409	15	∈]0	∈]0	ADJ
ejpam-3872	409	16	,	,	PUNCT
ejpam-3872	409	17	1	1	NUM
ejpam-3872	409	18	[	[	PUNCT
ejpam-3872	409	19	and	and	CCONJ
ejpam-3872	409	20	for	for	ADP
ejpam-3872	409	21	any	any	DET
ejpam-3872	409	22	λ	λ	PROPN
ejpam-3872	409	23	>	>	X
ejpam-3872	409	24	0	0	PROPN
ejpam-3872	409	25	,	,	PUNCT
ejpam-3872	409	26	f−1(1−	f−1(1−	PROPN
ejpam-3872	409	27	λu)−	λu)−	ADP
ejpam-3872	409	28	f−1(1−	f−1(1−	PROPN
ejpam-3872	409	29	u)→	u)→	PROPN
ejpam-3872	409	30	−	−	PROPN
ejpam-3872	409	31	log	log	PROPN
ejpam-3872	409	32	λ	λ	PROPN
ejpam-3872	409	33	as	as	ADP
ejpam-3872	409	34	u→	u→	PROPN
ejpam-3872	409	35	0	0	NUM
ejpam-3872	409	36	.	.	PUNCT
ejpam-3872	410	1	so	so	ADV
ejpam-3872	410	2	,	,	PUNCT
ejpam-3872	410	3	exp(x	exp(x	PROPN
ejpam-3872	410	4	)	)	PUNCT
ejpam-3872	410	5	∈	∈	PROPN
ejpam-3872	410	6	d(g1	d(g1	NOUN
ejpam-3872	410	7	)	)	PUNCT
ejpam-3872	410	8	.	.	PUNCT
ejpam-3872	411	1	from	from	ADP
ejpam-3872	411	2	there	there	ADV
ejpam-3872	411	3	,	,	PUNCT
ejpam-3872	411	4	an	an	DET
ejpam-3872	411	5	application	application	NOUN
ejpam-3872	411	6	of	of	ADP
ejpam-3872	411	7	point	point	NOUN
ejpam-3872	411	8	(	(	PUNCT
ejpam-3872	411	9	b	b	NOUN
ejpam-3872	411	10	)	)	PUNCT
ejpam-3872	411	11	of	of	ADP
ejpam-3872	411	12	theorem	theorem	ADJ
ejpam-3872	411	13	1	1	NUM
ejpam-3872	411	14	closes	close	VERB
ejpam-3872	411	15	the	the	DET
ejpam-3872	411	16	case	case	NOUN
ejpam-3872	411	17	.	.	PUNCT
ejpam-3872	412	1	the	the	DET
ejpam-3872	412	2	rate	rate	NOUN
ejpam-3872	412	3	of	of	ADP
ejpam-3872	412	4	convergence	convergence	NOUN
ejpam-3872	412	5	can	can	AUX
ejpam-3872	412	6	be	be	AUX
ejpam-3872	412	7	found	find	VERB
ejpam-3872	412	8	from	from	ADP
ejpam-3872	412	9	that	that	PRON
ejpam-3872	412	10	of	of	ADP
ejpam-3872	412	11	z	z	NOUN
ejpam-3872	412	12	=	=	SYM
ejpam-3872	412	13	exp(x	exp(x	PROPN
ejpam-3872	412	14	)	)	PUNCT
ejpam-3872	412	15	of	of	ADP
ejpam-3872	412	16	cdf	cdf	PROPN
ejpam-3872	413	1	g.	g.	PROPN
ejpam-3872	413	2	s.	s.	PROPN
ejpam-3872	413	3	lo	lo	PROPN
ejpam-3872	413	4	et	et	PROPN
ejpam-3872	413	5	al	al	PROPN
ejpam-3872	413	6	.	.	PUNCT
ejpam-3872	413	7	/	/	SYM
ejpam-3872	413	8	eur	eur	PROPN
ejpam-3872	413	9	.	.	PUNCT
ejpam-3872	414	1	j.	j.	PROPN
ejpam-3872	414	2	pure	pure	PROPN
ejpam-3872	414	3	appl	appl	PROPN
ejpam-3872	414	4	.	.	PROPN
ejpam-3872	414	5	math	math	PROPN
ejpam-3872	414	6	,	,	PUNCT
ejpam-3872	414	7	14	14	NUM
ejpam-3872	414	8	(	(	PUNCT
ejpam-3872	414	9	1	1	NUM
ejpam-3872	414	10	)	)	PUNCT
ejpam-3872	414	11	(	(	PUNCT
ejpam-3872	414	12	2021	2021	NUM
ejpam-3872	414	13	)	)	PUNCT
ejpam-3872	414	14	,	,	PUNCT
ejpam-3872	414	15	19	19	NUM
ejpam-3872	414	16	-	-	SYM
ejpam-3872	414	17	42	42	NUM
ejpam-3872	414	18	40	40	NUM
ejpam-3872	414	19	h(t	h(t	NUM
ejpam-3872	414	20	)	)	PUNCT
ejpam-3872	414	21	=	=	SYM
ejpam-3872	414	22	exp(−1	exp(−1	PROPN
ejpam-3872	414	23	/	/	SYM
ejpam-3872	414	24	t	t	PROPN
ejpam-3872	414	25	)	)	PUNCT
ejpam-3872	414	26	,	,	PUNCT
ejpam-3872	415	1	t	t	X
ejpam-3872	415	2	>	>	X
ejpam-3872	415	3	0	0	X
ejpam-3872	415	4	.	.	PUNCT
ejpam-3872	416	1	we	we	PRON
ejpam-3872	416	2	have	have	VERB
ejpam-3872	416	3	that	that	DET
ejpam-3872	416	4	h	h	PROPN
ejpam-3872	416	5	∈	∈	PROPN
ejpam-3872	416	6	g1	g1	PROPN
ejpam-3872	416	7	and	and	CCONJ
ejpam-3872	416	8	,	,	PUNCT
ejpam-3872	416	9	for	for	ADP
ejpam-3872	416	10	γ	γ	X
ejpam-3872	416	11	=	=	SYM
ejpam-3872	416	12	1	1	NUM
ejpam-3872	416	13	,	,	PUNCT
ejpam-3872	416	14	−u(logh−1(1−	−u(logh−1(1−	NOUN
ejpam-3872	416	15	u))′	u))′	PUNCT
ejpam-3872	416	16	=	=	PUNCT
ejpam-3872	416	17	−u	−u	PROPN
ejpam-3872	416	18	[	[	PUNCT
ejpam-3872	416	19	log	log	NOUN
ejpam-3872	416	20	1	1	NUM
ejpam-3872	416	21	−	−	PROPN
ejpam-3872	416	22	log(1−	log(1−	PROPN
ejpam-3872	416	23	u	u	PROPN
ejpam-3872	416	24	)	)	PUNCT
ejpam-3872	416	25	]	]	PUNCT
ejpam-3872	416	26	′	′	NUM
ejpam-3872	417	1	=	=	PUNCT
ejpam-3872	417	2	−u	−u	PROPN
ejpam-3872	417	3	(	(	PUNCT
ejpam-3872	417	4	1−	1−	NUM
ejpam-3872	417	5	u	u	NOUN
ejpam-3872	417	6	)	)	PUNCT
ejpam-3872	417	7	log(1−	log(1−	PROPN
ejpam-3872	417	8	u	u	NOUN
ejpam-3872	417	9	)	)	PUNCT
ejpam-3872	417	10	=	=	SYM
ejpam-3872	417	11	u	u	NOUN
ejpam-3872	417	12	(	(	PUNCT
ejpam-3872	417	13	1−	1−	NUM
ejpam-3872	417	14	u)(u−	u)(u−	PROPN
ejpam-3872	417	15	u2/2	u2/2	ADJ
ejpam-3872	417	16	+	+	NOUN
ejpam-3872	417	17	o(u3	o(u3	NOUN
ejpam-3872	417	18	)	)	PUNCT
ejpam-3872	417	19	)	)	PUNCT
ejpam-3872	418	1	=	=	SYM
ejpam-3872	418	2	1	1	NUM
ejpam-3872	418	3	(	(	PUNCT
ejpam-3872	418	4	1−	1−	NUM
ejpam-3872	418	5	3u/2	3u/2	NUM
ejpam-3872	418	6	+	+	ADJ
ejpam-3872	418	7	o(u2	o(u2	ADJ
ejpam-3872	418	8	)	)	PUNCT
ejpam-3872	418	9	)	)	PUNCT
ejpam-3872	418	10	.	.	PUNCT
ejpam-3872	419	1	hence	hence	ADV
ejpam-3872	419	2	−u(logh−1(1−	−u(logh−1(1−	PROPN
ejpam-3872	419	3	u))′	u))′	PROPN
ejpam-3872	419	4	−	−	PROPN
ejpam-3872	419	5	γ	γ	X
ejpam-3872	419	6	=	=	SYM
ejpam-3872	419	7	3u/2(1	3u/2(1	NUM
ejpam-3872	419	8	+	+	CCONJ
ejpam-3872	419	9	o(1	o(1	NOUN
ejpam-3872	419	10	)	)	PUNCT
ejpam-3872	419	11	)	)	PUNCT
ejpam-3872	419	12	.	.	PUNCT
ejpam-3872	420	1	by	by	ADP
ejpam-3872	420	2	applying	apply	VERB
ejpam-3872	420	3	point	point	NOUN
ejpam-3872	420	4	(	(	PUNCT
ejpam-3872	420	5	1	1	NUM
ejpam-3872	420	6	)	)	PUNCT
ejpam-3872	420	7	of	of	ADP
ejpam-3872	420	8	theorem	theorem	NOUN
ejpam-3872	420	9	3	3	NUM
ejpam-3872	420	10	,	,	PUNCT
ejpam-3872	420	11	we	we	PRON
ejpam-3872	420	12	take	take	VERB
ejpam-3872	420	13	for	for	ADP
ejpam-3872	420	14	any	any	DET
ejpam-3872	420	15	η	η	NOUN
ejpam-3872	420	16	∈]0	∈]0	X
ejpam-3872	420	17	,	,	PUNCT
ejpam-3872	420	18	1	1	NUM
ejpam-3872	420	19	[	[	PUNCT
ejpam-3872	420	20	and	and	CCONJ
ejpam-3872	420	21	bn(η	bn(η	ADV
ejpam-3872	420	22	)	)	PUNCT
ejpam-3872	420	23	=	=	SYM
ejpam-3872	421	1	1.5e−ηn	1.5e−ηn	ADV
ejpam-3872	421	2	and	and	CCONJ
ejpam-3872	421	3	get	get	VERB
ejpam-3872	421	4	(	(	PUNCT
ejpam-3872	421	5	z(n	z(n	NOUN
ejpam-3872	421	6	)	)	PUNCT
ejpam-3872	421	7	n−	n−	PROPN
ejpam-3872	421	8	log(1−	log(1−	PROPN
ejpam-3872	421	9	e−n	e−n	PROPN
ejpam-3872	421	10	)	)	PUNCT
ejpam-3872	421	11	)	)	PUNCT
ejpam-3872	422	1	1/	1/	NUM
ejpam-3872	422	2	√	√	PROPN
ejpam-3872	422	3	n	n	PROPN
ejpam-3872	422	4	=	=	SYM
ejpam-3872	422	5	exp(s∗n	exp(s∗n	PROPN
ejpam-3872	422	6	)	)	PUNCT
ejpam-3872	422	7	+	+	NOUN
ejpam-3872	422	8	op(bn	op(bn	PROPN
ejpam-3872	422	9	)	)	PUNCT
ejpam-3872	422	10	.	.	PUNCT
ejpam-3872	423	1	the	the	DET
ejpam-3872	423	2	conclusion	conclusion	NOUN
ejpam-3872	423	3	is	be	AUX
ejpam-3872	423	4	done	do	VERB
ejpam-3872	423	5	by	by	ADP
ejpam-3872	423	6	taking	take	VERB
ejpam-3872	423	7	the	the	DET
ejpam-3872	423	8	logarithm	logarithm	NOUN
ejpam-3872	423	9	of	of	ADP
ejpam-3872	423	10	both	both	DET
ejpam-3872	423	11	members	member	NOUN
ejpam-3872	423	12	.	.	PUNCT
ejpam-3872	424	1	(	(	PUNCT
ejpam-3872	424	2	7	7	X
ejpam-3872	424	3	)	)	PUNCT
ejpam-3872	424	4	x	x	PRON
ejpam-3872	424	5	follows	follow	VERB
ejpam-3872	424	6	a	a	DET
ejpam-3872	424	7	log	log	NOUN
ejpam-3872	424	8	-	-	PUNCT
ejpam-3872	424	9	logistic	logistic	NOUN
ejpam-3872	424	10	law	law	NOUN
ejpam-3872	424	11	of	of	ADP
ejpam-3872	424	12	parameter	parameter	NOUN
ejpam-3872	424	13	p	p	PROPN
ejpam-3872	424	14	>	>	X
ejpam-3872	424	15	0	0	NUM
ejpam-3872	424	16	,	,	PUNCT
ejpam-3872	424	17	with	with	ADP
ejpam-3872	424	18	cdf	cdf	PROPN
ejpam-3872	424	19	f	f	PROPN
ejpam-3872	424	20	(	(	PUNCT
ejpam-3872	424	21	x	x	NOUN
ejpam-3872	424	22	)	)	PUNCT
ejpam-3872	424	23	=	=	SYM
ejpam-3872	424	24	xp	xp	NOUN
ejpam-3872	424	25	1	1	NUM
ejpam-3872	425	1	+	+	CCONJ
ejpam-3872	425	2	xp	xp	INTJ
ejpam-3872	425	3	,	,	PUNCT
ejpam-3872	425	4	x	x	X
ejpam-3872	425	5	≥	≥	NOUN
ejpam-3872	425	6	0	0	NUM
ejpam-3872	425	7	.	.	PUNCT
ejpam-3872	426	1	we	we	PRON
ejpam-3872	426	2	have	have	VERB
ejpam-3872	426	3	f	f	PROPN
ejpam-3872	426	4	∈	∈	PROPN
ejpam-3872	426	5	d(g1	d(g1	NOUN
ejpam-3872	426	6	/	/	SYM
ejpam-3872	426	7	p	p	NOUN
ejpam-3872	426	8	)	)	PUNCT
ejpam-3872	426	9	since	since	SCONJ
ejpam-3872	426	10	f−1(1−	f−1(1−	PROPN
ejpam-3872	426	11	u	u	PROPN
ejpam-3872	426	12	)	)	PUNCT
ejpam-3872	426	13	=	=	SYM
ejpam-3872	427	1	u−1	u−1	PROPN
ejpam-3872	427	2	/	/	SYM
ejpam-3872	427	3	p(1−	p(1−	PROPN
ejpam-3872	427	4	u)1	u)1	PROPN
ejpam-3872	427	5	/	/	SYM
ejpam-3872	427	6	p	p	PROPN
ejpam-3872	427	7	,	,	PUNCT
ejpam-3872	427	8	u	u	NOUN
ejpam-3872	427	9	∈]0	∈]0	ADJ
ejpam-3872	427	10	,	,	PUNCT
ejpam-3872	427	11	1	1	NUM
ejpam-3872	427	12	[	[	NOUN
ejpam-3872	427	13	.	.	PUNCT
ejpam-3872	428	1	by	by	ADP
ejpam-3872	428	2	point	point	NOUN
ejpam-3872	428	3	(	(	PUNCT
ejpam-3872	428	4	a	a	NOUN
ejpam-3872	428	5	)	)	PUNCT
ejpam-3872	428	6	of	of	ADP
ejpam-3872	428	7	theorem	theorem	NOUN
ejpam-3872	428	8	1	1	NUM
ejpam-3872	428	9	,	,	PUNCT
ejpam-3872	429	1	g.	g.	PROPN
ejpam-3872	429	2	s.	s.	PROPN
ejpam-3872	429	3	lo	lo	PROPN
ejpam-3872	429	4	et	et	PROPN
ejpam-3872	429	5	al	al	PROPN
ejpam-3872	429	6	.	.	PUNCT
ejpam-3872	429	7	/	/	SYM
ejpam-3872	429	8	eur	eur	PROPN
ejpam-3872	429	9	.	.	PUNCT
ejpam-3872	430	1	j.	j.	PROPN
ejpam-3872	430	2	pure	pure	PROPN
ejpam-3872	430	3	appl	appl	PROPN
ejpam-3872	430	4	.	.	PROPN
ejpam-3872	430	5	math	math	PROPN
ejpam-3872	430	6	,	,	PUNCT
ejpam-3872	430	7	14	14	NUM
ejpam-3872	430	8	(	(	PUNCT
ejpam-3872	430	9	1	1	NUM
ejpam-3872	430	10	)	)	PUNCT
ejpam-3872	430	11	(	(	PUNCT
ejpam-3872	430	12	2021	2021	NUM
ejpam-3872	430	13	)	)	PUNCT
ejpam-3872	430	14	,	,	PUNCT
ejpam-3872	430	15	19	19	NUM
ejpam-3872	430	16	-	-	SYM
ejpam-3872	430	17	42	42	NUM
ejpam-3872	430	18	41	41	NUM
ejpam-3872	430	19	(	(	PUNCT
ejpam-3872	430	20	e−n	e−n	PROPN
ejpam-3872	430	21	/	/	SYM
ejpam-3872	430	22	px(n	px(n	NOUN
ejpam-3872	430	23	)	)	PUNCT
ejpam-3872	430	24	)	)	PUNCT
ejpam-3872	430	25	1/√n	1/√n	NUM
ejpam-3872	430	26	ln(0	ln(0	NOUN
ejpam-3872	430	27	,	,	PUNCT
ejpam-3872	430	28	p2	p2	PROPN
ejpam-3872	430	29	)	)	PUNCT
ejpam-3872	430	30	.	.	PUNCT
ejpam-3872	431	1	to	to	PART
ejpam-3872	431	2	find	find	VERB
ejpam-3872	431	3	the	the	DET
ejpam-3872	431	4	rate	rate	NOUN
ejpam-3872	431	5	of	of	ADP
ejpam-3872	431	6	convergence	convergence	NOUN
ejpam-3872	431	7	,	,	PUNCT
ejpam-3872	431	8	we	we	PRON
ejpam-3872	431	9	apply	apply	VERB
ejpam-3872	431	10	the	the	DET
ejpam-3872	431	11	recommendations	recommendation	NOUN
ejpam-3872	431	12	in	in	ADP
ejpam-3872	431	13	comments	comment	NOUN
ejpam-3872	431	14	ii	ii	PROPN
ejpam-3872	431	15	(	(	PUNCT
ejpam-3872	431	16	page	page	NOUN
ejpam-3872	431	17	27	27	NUM
ejpam-3872	431	18	)	)	PUNCT
ejpam-3872	431	19	.	.	PUNCT
ejpam-3872	432	1	we	we	PRON
ejpam-3872	432	2	have	have	VERB
ejpam-3872	432	3	b(u	b(u	PROPN
ejpam-3872	432	4	)	)	PUNCT
ejpam-3872	432	5	=	=	PUNCT
ejpam-3872	433	1	−u(g−1(1−	−u(g−1(1−	PROPN
ejpam-3872	433	2	u))′	u))′	X
ejpam-3872	433	3	−	−	PROPN
ejpam-3872	433	4	(	(	PUNCT
ejpam-3872	433	5	1	1	NUM
ejpam-3872	433	6	/	/	SYM
ejpam-3872	433	7	p	p	NOUN
ejpam-3872	433	8	)	)	PUNCT
ejpam-3872	433	9	=	=	PUNCT
ejpam-3872	433	10	u	u	PROPN
ejpam-3872	433	11	p(1−	p(1−	PROPN
ejpam-3872	433	12	u	u	PROPN
ejpam-3872	433	13	)	)	PUNCT
ejpam-3872	433	14	,	,	PUNCT
ejpam-3872	433	15	u	u	NOUN
ejpam-3872	433	16	∈]0	∈]0	ADJ
ejpam-3872	433	17	,	,	PUNCT
ejpam-3872	433	18	1	1	NUM
ejpam-3872	433	19	[	[	NOUN
ejpam-3872	433	20	.	.	PUNCT
ejpam-3872	434	1	for	for	ADP
ejpam-3872	434	2	any	any	DET
ejpam-3872	434	3	0	0	PUNCT
ejpam-3872	434	4	<	<	X
ejpam-3872	434	5	η	η	X
ejpam-3872	434	6	<	<	X
ejpam-3872	434	7	1	1	NUM
ejpam-3872	434	8	,	,	PUNCT
ejpam-3872	434	9	we	we	PRON
ejpam-3872	434	10	get	get	VERB
ejpam-3872	434	11	the	the	DET
ejpam-3872	434	12	rate	rate	NOUN
ejpam-3872	434	13	of	of	ADP
ejpam-3872	434	14	convergence	convergence	NOUN
ejpam-3872	434	15	bn(η	bn(η	PUNCT
ejpam-3872	434	16	)	)	PUNCT
ejpam-3872	435	1	=	=	SYM
ejpam-3872	435	2	e−ηn	e−ηn	ADJ
ejpam-3872	435	3	p	p	X
ejpam-3872	435	4	(	(	PUNCT
ejpam-3872	435	5	1−	1−	NUM
ejpam-3872	435	6	e−n	e−n	PROPN
ejpam-3872	435	7	/	/	SYM
ejpam-3872	435	8	η	η	PROPN
ejpam-3872	435	9	)	)	PUNCT
ejpam-3872	435	10	.	.	PUNCT
ejpam-3872	436	1	(	(	PUNCT
ejpam-3872	436	2	8)	8)	NUM
ejpam-3872	436	3	x	x	PRON
ejpam-3872	436	4	follows	follow	VERB
ejpam-3872	436	5	a	a	DET
ejpam-3872	436	6	sing	sing	NOUN
ejpam-3872	436	7	-	-	PUNCT
ejpam-3872	436	8	maddala	maddala	NOUN
ejpam-3872	436	9	law	law	NOUN
ejpam-3872	436	10	of	of	ADP
ejpam-3872	436	11	parameters	parameter	NOUN
ejpam-3872	436	12	a	a	DET
ejpam-3872	436	13	>	>	X
ejpam-3872	436	14	0	0	NUM
ejpam-3872	436	15	,	,	PUNCT
ejpam-3872	436	16	b	b	X
ejpam-3872	436	17	>	>	X
ejpam-3872	436	18	0	0	PUNCT
ejpam-3872	436	19	and	and	CCONJ
ejpam-3872	436	20	c	c	X
ejpam-3872	436	21	>	>	X
ejpam-3872	436	22	0	0	X
ejpam-3872	436	23	.	.	PUNCT
ejpam-3872	437	1	we	we	PRON
ejpam-3872	437	2	have	have	VERB
ejpam-3872	437	3	1−	1−	NUM
ejpam-3872	437	4	f	f	X
ejpam-3872	437	5	(	(	PUNCT
ejpam-3872	437	6	x	x	NOUN
ejpam-3872	437	7	)	)	PUNCT
ejpam-3872	437	8	=	=	SYM
ejpam-3872	437	9	x−bc(x−b	x−bc(x−b	NOUN
ejpam-3872	438	1	+	+	CCONJ
ejpam-3872	438	2	a)−c	a)−c	PROPN
ejpam-3872	438	3	≡	≡	PROPN
ejpam-3872	438	4	x−bcl(x	x−bcl(x	PROPN
ejpam-3872	438	5	)	)	PUNCT
ejpam-3872	438	6	,	,	PUNCT
ejpam-3872	438	7	x	x	X
ejpam-3872	438	8	≥	≥	NOUN
ejpam-3872	438	9	0	0	NUM
ejpam-3872	438	10	,	,	PUNCT
ejpam-3872	438	11	and	and	CCONJ
ejpam-3872	438	12	l	l	NOUN
ejpam-3872	438	13	is	be	AUX
ejpam-3872	438	14	a	a	DET
ejpam-3872	438	15	slowly	slowly	ADV
ejpam-3872	438	16	varying	vary	VERB
ejpam-3872	438	17	function	function	NOUN
ejpam-3872	438	18	at	at	ADP
ejpam-3872	438	19	+	+	NOUN
ejpam-3872	438	20	∞.	∞.	PROPN
ejpam-3872	439	1	so	so	ADV
ejpam-3872	439	2	f	f	PROPN
ejpam-3872	439	3	∈	∈	PROPN
ejpam-3872	439	4	g1/(bc	g1/(bc	PROPN
ejpam-3872	439	5	)	)	PUNCT
ejpam-3872	439	6	.	.	PUNCT
ejpam-3872	440	1	applying	apply	VERB
ejpam-3872	440	2	the	the	DET
ejpam-3872	440	3	point	point	NOUN
ejpam-3872	440	4	(	(	PUNCT
ejpam-3872	440	5	a	a	NOUN
ejpam-3872	440	6	)	)	PUNCT
ejpam-3872	440	7	of	of	ADP
ejpam-3872	440	8	theorem	theorem	NOUN
ejpam-3872	440	9	1	1	NUM
ejpam-3872	440	10	,	,	PUNCT
ejpam-3872	440	11	when	when	SCONJ
ejpam-3872	440	12	combined	combine	VERB
ejpam-3872	440	13	with	with	ADP
ejpam-3872	440	14	f−1(1−	f−1(1−	PROPN
ejpam-3872	440	15	u	u	PROPN
ejpam-3872	440	16	)	)	PUNCT
ejpam-3872	440	17	=	=	SYM
ejpam-3872	440	18	a−1	a−1	NOUN
ejpam-3872	440	19	/	/	SYM
ejpam-3872	440	20	bu−1/(bc)(1−	bu−1/(bc)(1−	NOUN
ejpam-3872	440	21	u1	u1	NOUN
ejpam-3872	440	22	/	/	SYM
ejpam-3872	440	23	c)1	c)1	PROPN
ejpam-3872	440	24	/	/	SYM
ejpam-3872	440	25	b	b	PROPN
ejpam-3872	440	26	,	,	PUNCT
ejpam-3872	440	27	u	u	NOUN
ejpam-3872	440	28	∈]0	∈]0	ADJ
ejpam-3872	440	29	,	,	PUNCT
ejpam-3872	440	30	1	1	NUM
ejpam-3872	440	31	[	[	NOUN
ejpam-3872	440	32	,	,	PUNCT
ejpam-3872	440	33	and	and	CCONJ
ejpam-3872	440	34	with	with	ADP
ejpam-3872	440	35	,	,	PUNCT
ejpam-3872	440	36	f−1(1−	f−1(1−	PROPN
ejpam-3872	440	37	e−n	e−n	PROPN
ejpam-3872	440	38	)	)	PUNCT
ejpam-3872	440	39	=	=	SYM
ejpam-3872	440	40	a−1	a−1	PROPN
ejpam-3872	440	41	/	/	SYM
ejpam-3872	440	42	ben/(bc)(1−	ben/(bc)(1−	PROPN
ejpam-3872	440	43	e−n	e−n	PROPN
ejpam-3872	440	44	/	/	SYM
ejpam-3872	440	45	c)1	c)1	PROPN
ejpam-3872	440	46	/	/	SYM
ejpam-3872	440	47	b	b	NOUN
ejpam-3872	440	48	,	,	PUNCT
ejpam-3872	440	49	for	for	ADP
ejpam-3872	440	50	n	n	PRON
ejpam-3872	440	51	≥	≥	NOUN
ejpam-3872	440	52	1	1	NUM
ejpam-3872	440	53	.	.	PUNCT
ejpam-3872	440	54	to	to	PART
ejpam-3872	440	55	find	find	VERB
ejpam-3872	440	56	the	the	DET
ejpam-3872	440	57	rate	rate	NOUN
ejpam-3872	440	58	of	of	ADP
ejpam-3872	440	59	convergence	convergence	NOUN
ejpam-3872	440	60	,	,	PUNCT
ejpam-3872	440	61	we	we	PRON
ejpam-3872	440	62	check	check	VERB
ejpam-3872	440	63	that	that	SCONJ
ejpam-3872	440	64	we	we	PRON
ejpam-3872	440	65	have	have	VERB
ejpam-3872	440	66	γ	γ	NOUN
ejpam-3872	440	67	=	=	SYM
ejpam-3872	440	68	1/(bc	1/(bc	NUM
ejpam-3872	440	69	)	)	PUNCT
ejpam-3872	440	70	and	and	CCONJ
ejpam-3872	440	71	b(u	b(u	PROPN
ejpam-3872	440	72	)	)	PUNCT
ejpam-3872	440	73	=	=	PUNCT
ejpam-3872	441	1	−u(g−1(1−	−u(g−1(1−	PROPN
ejpam-3872	441	2	u))′	u))′	X
ejpam-3872	441	3	−	−	PROPN
ejpam-3872	441	4	(	(	PUNCT
ejpam-3872	441	5	1/(bc	1/(bc	NUM
ejpam-3872	441	6	)	)	PUNCT
ejpam-3872	441	7	)	)	PUNCT
ejpam-3872	442	1	=	=	SYM
ejpam-3872	442	2	u1	u1	PROPN
ejpam-3872	442	3	/	/	SYM
ejpam-3872	442	4	c	c	NOUN
ejpam-3872	442	5	b(1−	b(1−	PROPN
ejpam-3872	442	6	u1	u1	PROPN
ejpam-3872	442	7	/	/	SYM
ejpam-3872	442	8	c	c	NOUN
ejpam-3872	442	9	)	)	PUNCT
ejpam-3872	442	10	,	,	PUNCT
ejpam-3872	442	11	u	u	NOUN
ejpam-3872	442	12	∈]0	∈]0	ADJ
ejpam-3872	442	13	,	,	PUNCT
ejpam-3872	442	14	1	1	NUM
ejpam-3872	442	15	[	[	NOUN
ejpam-3872	442	16	.	.	PUNCT
ejpam-3872	443	1	for	for	ADP
ejpam-3872	443	2	any	any	DET
ejpam-3872	443	3	0	0	PUNCT
ejpam-3872	443	4	<	<	X
ejpam-3872	443	5	η	η	X
ejpam-3872	443	6	<	<	X
ejpam-3872	443	7	1	1	NUM
ejpam-3872	443	8	,	,	PUNCT
ejpam-3872	443	9	we	we	PRON
ejpam-3872	443	10	get	get	VERB
ejpam-3872	443	11	the	the	DET
ejpam-3872	443	12	rate	rate	NOUN
ejpam-3872	443	13	of	of	ADP
ejpam-3872	443	14	convergence	convergence	NOUN
ejpam-3872	443	15	bn(η	bn(η	PUNCT
ejpam-3872	443	16	)	)	PUNCT
ejpam-3872	444	1	=	=	SYM
ejpam-3872	444	2	e−ηn	e−ηn	ADJ
ejpam-3872	444	3	/	/	SYM
ejpam-3872	444	4	c	c	PROPN
ejpam-3872	444	5	b	b	PROPN
ejpam-3872	444	6	(	(	PUNCT
ejpam-3872	444	7	1−	1−	NUM
ejpam-3872	444	8	e−n/(cη	e−n/(cη	ADV
ejpam-3872	444	9	)	)	PUNCT
ejpam-3872	444	10	)	)	PUNCT
ejpam-3872	444	11	�	�	PROPN
ejpam-3872	444	12	references	reference	VERB
ejpam-3872	444	13	42	42	NUM
ejpam-3872	444	14	references	reference	NOUN
ejpam-3872	444	15	[	[	X
ejpam-3872	444	16	1	1	NUM
ejpam-3872	444	17	]	]	PUNCT
ejpam-3872	444	18	l.	l.	PROPN
ejpam-3872	444	19	de	de	PROPN
ejpam-3872	444	20	haan	haan	PROPN
ejpam-3872	444	21	.	.	PUNCT
ejpam-3872	445	1	on	on	ADP
ejpam-3872	445	2	regular	regular	ADJ
ejpam-3872	445	3	variation	variation	NOUN
ejpam-3872	445	4	and	and	CCONJ
ejpam-3872	445	5	its	its	PRON
ejpam-3872	445	6	application	application	NOUN
ejpam-3872	445	7	to	to	ADP
ejpam-3872	445	8	the	the	DET
ejpam-3872	445	9	weak	weak	ADJ
ejpam-3872	445	10	convergence	convergence	NOUN
ejpam-3872	445	11	of	of	ADP
ejpam-3872	445	12	sample	sample	NOUN
ejpam-3872	445	13	extremes	extreme	NOUN
ejpam-3872	445	14	.	.	PUNCT
ejpam-3872	446	1	mathematical	mathematical	ADJ
ejpam-3872	446	2	center	center	NOUN
ejpam-3872	446	3	tracts	tract	NOUN
ejpam-3872	446	4	,	,	PUNCT
ejpam-3872	446	5	amsterdam	amsterdam	PROPN
ejpam-3872	446	6	.	.	PUNCT
ejpam-3872	447	1	(	(	PUNCT
ejpam-3872	447	2	mr0286156	mr0286156	PROPN
ejpam-3872	447	3	)	)	PUNCT
ejpam-3872	447	4	,	,	PUNCT
ejpam-3872	447	5	1970	1970	NUM
ejpam-3872	447	6	.	.	PUNCT
ejpam-3872	448	1	[	[	X
ejpam-3872	448	2	2	2	X
ejpam-3872	448	3	]	]	PUNCT
ejpam-3872	448	4	j.	j.	PROPN
ejpam-3872	448	5	galambos	galambos	PROPN
ejpam-3872	448	6	.	.	PUNCT
ejpam-3872	449	1	the	the	DET
ejpam-3872	449	2	asymptotic	asymptotic	ADJ
ejpam-3872	449	3	theory	theory	NOUN
ejpam-3872	449	4	of	of	ADP
ejpam-3872	449	5	extreme	extreme	ADJ
ejpam-3872	449	6	order	order	NOUN
ejpam-3872	449	7	statistics	statistic	NOUN
ejpam-3872	449	8	.	.	PUNCT
ejpam-3872	450	1	wiley	wiley	PROPN
ejpam-3872	450	2	,	,	PUNCT
ejpam-3872	450	3	nex	nex	PROPN
ejpam-3872	450	4	-	-	PUNCT
ejpam-3872	450	5	york	york	NOUN
ejpam-3872	450	6	.	.	PUNCT
ejpam-3872	451	1	(	(	PUNCT
ejpam-3872	451	2	mr0489334	mr0489334	PROPN
ejpam-3872	451	3	)	)	PUNCT
ejpam-3872	451	4	,	,	PUNCT
ejpam-3872	451	5	1985	1985	NUM
ejpam-3872	451	6	.	.	PUNCT
ejpam-3872	452	1	[	[	X
ejpam-3872	452	2	3	3	X
ejpam-3872	452	3	]	]	AUX
ejpam-3872	452	4	karamata	karamata	NOUN
ejpam-3872	452	5	j.	j.	PROPN
ejpam-3872	452	6	some	some	DET
ejpam-3872	452	7	theorems	theorem	NOUN
ejpam-3872	452	8	concerning	concern	VERB
ejpam-3872	452	9	slowly	slowly	ADV
ejpam-3872	452	10	varying	vary	VERB
ejpam-3872	452	11	.	.	PUNCT
ejpam-3872	453	1	mathematics	mathematic	NOUN
ejpam-3872	453	2	research	research	NOUN
ejpam-3872	453	3	center	center	NOUN
ejpam-3872	453	4	,	,	PUNCT
ejpam-3872	453	5	tech	tech	NOUN
ejpam-3872	453	6	.	.	PUNCT
ejpam-3872	454	1	rep	rep	PROPN
ejpam-3872	454	2	.	.	PROPN
ejpam-3872	454	3	,no	,no	PUNCT
ejpam-3872	454	4	369	369	NUM
ejpam-3872	454	5	.	.	PUNCT
ejpam-3872	455	1	university	university	NOUN
ejpam-3872	455	2	of	of	ADP
ejpam-3872	455	3	winconsin	winconsin	PROPN
ejpam-3872	455	4	,	,	PUNCT
ejpam-3872	455	5	madison	madison	PROPN
ejpam-3872	455	6	.	.	PROPN
ejpam-3872	455	7	,	,	PUNCT
ejpam-3872	455	8	1962	1962	NUM
ejpam-3872	455	9	.	.	PUNCT
ejpam-3872	456	1	[	[	X
ejpam-3872	456	2	4	4	X
ejpam-3872	456	3	]	]	X
ejpam-3872	456	4	komlós	komlós	PROPN
ejpam-3872	456	5	j.	j.	PROPN
ejpam-3872	456	6	,	,	PUNCT
ejpam-3872	456	7	major	major	ADJ
ejpam-3872	456	8	p.	p.	NOUN
ejpam-3872	456	9	,	,	PUNCT
ejpam-3872	456	10	and	and	CCONJ
ejpam-3872	456	11	tusnády	tusnády	NOUN
ejpam-3872	456	12	.	.	PUNCT
ejpam-3872	457	1	an	an	DET
ejpam-3872	457	2	approximation	approximation	NOUN
ejpam-3872	457	3	of	of	ADP
ejpam-3872	457	4	partial	partial	ADJ
ejpam-3872	457	5	sums	sum	NOUN
ejpam-3872	457	6	of	of	ADP
ejpam-3872	457	7	independent	independent	ADJ
ejpam-3872	457	8	rv	rv	PROPN
ejpam-3872	457	9	’s	’s	NOUN
ejpam-3872	457	10	and	and	CCONJ
ejpam-3872	457	11	the	the	DET
ejpam-3872	457	12	sample	sample	NOUN
ejpam-3872	457	13	df	df	PROPN
ejpam-3872	457	14	.	.	PUNCT
ejpam-3872	457	15	i.	i.	PROPN
ejpam-3872	457	16	z.	z.	PROPN
ejpam-3872	457	17	wahrsch	wahrsch	PROPN
ejpam-3872	457	18	.	.	PUNCT
ejpam-3872	458	1	verw	verw	PROPN
ejpam-3872	458	2	.	.	PUNCT
ejpam-3872	459	1	gebiete,32	gebiete,32	VERB
ejpam-3872	459	2	111x96	111x96	NUM
ejpam-3872	459	3	131	131	NUM
ejpam-3872	459	4	.	.	PUNCT
ejpam-3872	460	1	mr0375412	mr0375412	PROPN
ejpam-3872	460	2	,	,	PUNCT
ejpam-3872	460	3	1975	1975	NUM
ejpam-3872	460	4	.	.	PUNCT
ejpam-3872	461	1	[	[	X
ejpam-3872	461	2	5	5	NUM
ejpam-3872	461	3	]	]	X
ejpam-3872	461	4	g.s	g.s	PROPN
ejpam-3872	461	5	.	.	PROPN
ejpam-3872	461	6	lo	lo	PROPN
ejpam-3872	461	7	.	.	PUNCT
ejpam-3872	462	1	on	on	ADP
ejpam-3872	462	2	some	some	DET
ejpam-3872	462	3	estimators	estimator	NOUN
ejpam-3872	462	4	of	of	ADP
ejpam-3872	462	5	the	the	DET
ejpam-3872	462	6	index	index	NOUN
ejpam-3872	462	7	of	of	ADP
ejpam-3872	462	8	the	the	DET
ejpam-3872	462	9	pareto	pareto	ADJ
ejpam-3872	462	10	law	law	NOUN
ejpam-3872	462	11	and	and	CCONJ
ejpam-3872	462	12	limit	limit	VERB
ejpam-3872	462	13	theorems	theorem	NOUN
ejpam-3872	462	14	for	for	ADP
ejpam-3872	462	15	extreme	extreme	ADJ
ejpam-3872	462	16	value	value	NOUN
ejpam-3872	462	17	sums.phd	sums.phd	NOUN
ejpam-3872	462	18	thesis	thesis	NOUN
ejpam-3872	462	19	.	.	PUNCT
ejpam-3872	462	20	pierre	pierre	PROPN
ejpam-3872	462	21	and	and	CCONJ
ejpam-3872	462	22	marie	marie	PROPN
ejpam-3872	462	23	curie	curie	PROPN
ejpam-3872	462	24	university	university	PROPN
ejpam-3872	462	25	,	,	PUNCT
ejpam-3872	462	26	paris	paris	PROPN
ejpam-3872	462	27	vi	vi	PROPN
ejpam-3872	462	28	.	.	PROPN
ejpam-3872	462	29	france	france	PROPN
ejpam-3872	462	30	.	.	PROPN
ejpam-3872	462	31	,	,	PUNCT
ejpam-3872	462	32	1986	1986	NUM
ejpam-3872	462	33	.	.	PUNCT
ejpam-3872	463	1	[	[	X
ejpam-3872	463	2	6	6	NUM
ejpam-3872	463	3	]	]	X
ejpam-3872	463	4	g.s	g.s	PROPN
ejpam-3872	463	5	.	.	PROPN
ejpam-3872	463	6	lo	lo	PROPN
ejpam-3872	463	7	,	,	PUNCT
ejpam-3872	463	8	t.	t.	NOUN
ejpam-3872	463	9	a.	a.	NOUN
ejpam-3872	463	10	kpanzou	kpanzou	PROPN
ejpam-3872	463	11	,	,	PUNCT
ejpam-3872	463	12	m.	m.	NOUN
ejpam-3872	463	13	ngom	ngom	PROPN
ejpam-3872	463	14	,	,	PUNCT
ejpam-3872	463	15	and	and	CCONJ
ejpam-3872	463	16	m.	m.	PROPN
ejpam-3872	463	17	diallo	diallo	PROPN
ejpam-3872	463	18	.	.	PUNCT
ejpam-3872	464	1	weak	weak	ADJ
ejpam-3872	464	2	convergence	convergence	NOUN
ejpam-3872	464	3	(	(	PUNCT
ejpam-3872	464	4	iia	iia	NOUN
ejpam-3872	464	5	)	)	PUNCT
ejpam-3872	464	6	functional	functional	ADJ
ejpam-3872	464	7	and	and	CCONJ
ejpam-3872	464	8	random	random	ADJ
ejpam-3872	464	9	aspects	aspect	NOUN
ejpam-3872	464	10	of	of	ADP
ejpam-3872	464	11	the	the	DET
ejpam-3872	464	12	univariate	univariate	ADJ
ejpam-3872	464	13	extreme	extreme	ADJ
ejpam-3872	464	14	value	value	NOUN
ejpam-3872	464	15	theory	theory	NOUN
ejpam-3872	464	16	.	.	PUNCT
ejpam-3872	465	1	arxiv	arxiv	NOUN
ejpam-3872	465	2	:	:	PUNCT
ejpam-3872	465	3	1810.01625	1810.01625	NUM
ejpam-3872	465	4	,	,	PUNCT
ejpam-3872	465	5	2018	2018	NUM
ejpam-3872	465	6	.	.	PUNCT
ejpam-3872	466	1	[	[	X
ejpam-3872	466	2	7	7	X
ejpam-3872	466	3	]	]	PUNCT
ejpam-3872	466	4	ahsanullah	ahsanullah	PROPN
ejpam-3872	466	5	m.	m.	NOUN
ejpam-3872	466	6	record	record	NOUN
ejpam-3872	466	7	statistics	statistic	NOUN
ejpam-3872	466	8	.	.	PUNCT
ejpam-3872	467	1	nova	nova	PROPN
ejpam-3872	467	2	science	science	PROPN
ejpam-3872	467	3	publishers	publishers	PROPN
ejpam-3872	467	4	inc	inc	PROPN
ejpam-3872	467	5	.	.	PROPN
ejpam-3872	467	6	new	new	PROPN
ejpam-3872	467	7	-	-	PUNCT
ejpam-3872	467	8	york	york	PROPN
ejpam-3872	467	9	,	,	PUNCT
ejpam-3872	467	10	usa	usa	PROPN
ejpam-3872	467	11	,	,	PUNCT
ejpam-3872	467	12	1995	1995	NUM
ejpam-3872	467	13	.	.	PUNCT
ejpam-3872	468	1	[	[	X
ejpam-3872	468	2	8	8	X
ejpam-3872	468	3	]	]	X
ejpam-3872	468	4	tata	tata	PROPN
ejpam-3872	468	5	m.n	m.n	PROPN
ejpam-3872	468	6	.	.	PROPN
ejpam-3872	468	7	on	on	ADP
ejpam-3872	468	8	outstanding	outstanding	ADJ
ejpam-3872	468	9	values	value	NOUN
ejpam-3872	468	10	in	in	ADP
ejpam-3872	468	11	a	a	DET
ejpam-3872	468	12	sequence	sequence	NOUN
ejpam-3872	468	13	of	of	ADP
ejpam-3872	468	14	random	random	ADJ
ejpam-3872	468	15	variables	variable	NOUN
ejpam-3872	468	16	.	.	PUNCT
ejpam-3872	469	1	zeitschrift	zeitschrift	NOUN
ejpam-3872	469	2	.	.	PUNCT
ejpam-3872	470	1	wehrs	wehrs	PROPN
ejpam-3872	470	2	.	.	PUNCT
ejpam-3872	470	3	verw	verw	PROPN
ejpam-3872	470	4	.	.	PUNCT
ejpam-3872	471	1	gebiete	gebiete	NOUN
ejpam-3872	471	2	,	,	PUNCT
ejpam-3872	471	3	12,:09–20	12,:09–20	NUM
ejpam-3872	471	4	,	,	PUNCT
ejpam-3872	471	5	1969	1969	NUM
ejpam-3872	471	6	.	.	PUNCT
ejpam-3872	472	1	[	[	X
ejpam-3872	472	2	9	9	NUM
ejpam-3872	472	3	]	]	PUNCT
ejpam-3872	472	4	v.	v.	PROPN
ejpam-3872	472	5	b.	b.	PROPN
ejpam-3872	472	6	nevzorov	nevzorov	PROPN
ejpam-3872	472	7	.	.	PUNCT
ejpam-3872	473	1	records	record	NOUN
ejpam-3872	473	2	:	:	PUNCT
ejpam-3872	473	3	mathematical	mathematical	ADJ
ejpam-3872	473	4	theory.translation	theory.translation	NOUN
ejpam-3872	473	5	of	of	ADP
ejpam-3872	473	6	mathematical	mathematical	ADJ
ejpam-3872	473	7	monographs	monograph	NOUN
ejpam-3872	473	8	,	,	PUNCT
ejpam-3872	473	9	volume	volume	NOUN
ejpam-3872	473	10	194	194	NUM
ejpam-3872	473	11	.	.	PUNCT
ejpam-3872	474	1	american	american	PROPN
ejpam-3872	474	2	mathematical	mathematical	PROPN
ejpam-3872	474	3	society	society	NOUN
ejpam-3872	474	4	.	.	PUNCT
ejpam-3872	475	1	providence	providence	NOUN
ejpam-3872	475	2	,	,	PUNCT
ejpam-3872	475	3	ri	ri	PROPN
ejpam-3872	475	4	,	,	PUNCT
ejpam-3872	475	5	usa	usa	PROPN
ejpam-3872	475	6	,	,	PUNCT
ejpam-3872	475	7	2001	2001	NUM
ejpam-3872	475	8	.	.	PUNCT
ejpam-3872	476	1	[	[	X
ejpam-3872	476	2	10	10	NUM
ejpam-3872	476	3	]	]	X
ejpam-3872	476	4	s.i	s.i	PROPN
ejpam-3872	476	5	.	.	PROPN
ejpam-3872	476	6	resnick	resnick	PROPN
ejpam-3872	476	7	.	.	PUNCT
ejpam-3872	477	1	extreme	extreme	ADJ
ejpam-3872	477	2	values	value	NOUN
ejpam-3872	477	3	,	,	PUNCT
ejpam-3872	477	4	regular	regular	ADJ
ejpam-3872	477	5	variation	variation	NOUN
ejpam-3872	477	6	and	and	CCONJ
ejpam-3872	477	7	point	point	NOUN
ejpam-3872	477	8	processes	process	NOUN
ejpam-3872	477	9	.	.	PUNCT
ejpam-3872	478	1	springerverbag	springerverbag	PROPN
ejpam-3872	478	2	,	,	PUNCT
ejpam-3872	478	3	new	new	ADJ
ejpam-3872	478	4	-	-	PUNCT
ejpam-3872	478	5	york	york	NOUN
ejpam-3872	478	6	.	.	PUNCT
ejpam-3872	479	1	(	(	PUNCT
ejpam-3872	479	2	mr0900810	mr0900810	PROPN
ejpam-3872	479	3	)	)	PUNCT
ejpam-3872	479	4	,	,	PUNCT
ejpam-3872	479	5	1987	1987	NUM
ejpam-3872	479	6	.	.	PUNCT