id	sid	tid	token	lemma	pos
ejpam-4323	1	1	european	european	PROPN
ejpam-4323	1	2	journal	journal	PROPN
ejpam-4323	1	3	of	of	ADP
ejpam-4323	1	4	pure	pure	ADJ
ejpam-4323	1	5	and	and	CCONJ
ejpam-4323	1	6	applied	apply	VERB
ejpam-4323	1	7	mathematics	mathematic	NOUN
ejpam-4323	1	8	vol	vol	NOUN
ejpam-4323	1	9	.	.	PROPN
ejpam-4323	2	1	15	15	NUM
ejpam-4323	2	2	,	,	PUNCT
ejpam-4323	2	3	no	no	INTJ
ejpam-4323	2	4	.	.	NOUN
ejpam-4323	2	5	2	2	NUM
ejpam-4323	2	6	,	,	PUNCT
ejpam-4323	2	7	2022	2022	NUM
ejpam-4323	2	8	,	,	PUNCT
ejpam-4323	2	9	511	511	NUM
ejpam-4323	2	10	-	-	SYM
ejpam-4323	2	11	527	527	NUM
ejpam-4323	2	12	issn	issn	PROPN
ejpam-4323	2	13	1307	1307	NUM
ejpam-4323	2	14	-	-	SYM
ejpam-4323	2	15	5543	5543	NUM
ejpam-4323	2	16	–	–	PUNCT
ejpam-4323	2	17	ejpam.com	ejpam.com	X
ejpam-4323	2	18	published	publish	VERB
ejpam-4323	2	19	by	by	ADP
ejpam-4323	2	20	new	new	PROPN
ejpam-4323	2	21	york	york	PROPN
ejpam-4323	2	22	business	business	PROPN
ejpam-4323	2	23	global	global	ADJ
ejpam-4323	2	24	extensions	extension	NOUN
ejpam-4323	2	25	of	of	ADP
ejpam-4323	2	26	two	two	NUM
ejpam-4323	2	27	classical	classical	ADJ
ejpam-4323	2	28	poisson	poisson	NOUN
ejpam-4323	2	29	limit	limit	NOUN
ejpam-4323	2	30	laws	law	NOUN
ejpam-4323	2	31	to	to	ADP
ejpam-4323	2	32	non	non	ADJ
ejpam-4323	2	33	-	-	ADJ
ejpam-4323	2	34	stationary	stationary	ADJ
ejpam-4323	2	35	independent	independent	ADJ
ejpam-4323	2	36	sequences	sequence	NOUN
ejpam-4323	2	37	aladji	aladji	PROPN
ejpam-4323	2	38	babacar	babacar	PROPN
ejpam-4323	2	39	niang1	niang1	PROPN
ejpam-4323	2	40	,	,	PUNCT
ejpam-4323	2	41	harouna	harouna	PROPN
ejpam-4323	2	42	sangaré2	sangaré2	PROPN
ejpam-4323	2	43	,	,	PUNCT
ejpam-4323	2	44	tchilabalo	tchilabalo	NOUN
ejpam-4323	2	45	abozou	abozou	VERB
ejpam-4323	2	46	kpanzou3,∗	kpanzou3,∗	NOUN
ejpam-4323	2	47	,	,	PUNCT
ejpam-4323	2	48	gane	gane	NOUN
ejpam-4323	2	49	samb	samb	PROPN
ejpam-4323	2	50	lo4	lo4	PROPN
ejpam-4323	2	51	,	,	PUNCT
ejpam-4323	2	52	nafy	nafy	ADJ
ejpam-4323	2	53	ngom1	ngom1	PROPN
ejpam-4323	2	54	1lerstad	1lerstad	NUM
ejpam-4323	2	55	,	,	PUNCT
ejpam-4323	2	56	gaston	gaston	PROPN
ejpam-4323	2	57	berger	berger	PROPN
ejpam-4323	2	58	university	university	PROPN
ejpam-4323	2	59	,	,	PUNCT
ejpam-4323	2	60	saint	saint	NOUN
ejpam-4323	2	61	-	-	PUNCT
ejpam-4323	2	62	louis	louis	NOUN
ejpam-4323	2	63	,	,	PUNCT
ejpam-4323	2	64	sénégal	sénégal	PROPN
ejpam-4323	2	65	.	.	PUNCT
ejpam-4323	3	1	imhotep	imhotep	PROPN
ejpam-4323	3	2	mathematical	mathematical	PROPN
ejpam-4323	3	3	center	center	PROPN
ejpam-4323	3	4	(	(	PUNCT
ejpam-4323	3	5	imc	imc	PROPN
ejpam-4323	3	6	)	)	PUNCT
ejpam-4323	3	7	,	,	PUNCT
ejpam-4323	3	8	2der	2der	NUM
ejpam-4323	3	9	mi	mi	PROPN
ejpam-4323	3	10	,	,	PUNCT
ejpam-4323	3	11	fst	fst	NOUN
ejpam-4323	3	12	,	,	PUNCT
ejpam-4323	3	13	université	université	PROPN
ejpam-4323	3	14	des	des	PROPN
ejpam-4323	3	15	sciences	sciences	PROPN
ejpam-4323	3	16	,	,	PUNCT
ejpam-4323	3	17	des	des	X
ejpam-4323	3	18	techniques	technique	NOUN
ejpam-4323	3	19	et	et	PROPN
ejpam-4323	3	20	des	des	PROPN
ejpam-4323	3	21	technologies	technologies	PROPN
ejpam-4323	3	22	de	de	PROPN
ejpam-4323	3	23	bamako	bamako	PROPN
ejpam-4323	3	24	(	(	PUNCT
ejpam-4323	3	25	ustt	ustt	NOUN
ejpam-4323	3	26	-	-	PUNCT
ejpam-4323	3	27	b	b	NOUN
ejpam-4323	3	28	)	)	PUNCT
ejpam-4323	3	29	,	,	PUNCT
ejpam-4323	3	30	mali	mali	PROPN
ejpam-4323	3	31	.	.	PUNCT
ejpam-4323	4	1	affiliated	affiliate	VERB
ejpam-4323	4	2	to	to	ADP
ejpam-4323	4	3	lerstad	lerstad	PROPN
ejpam-4323	4	4	,	,	PUNCT
ejpam-4323	4	5	gaston	gaston	PROPN
ejpam-4323	4	6	berger	berger	PROPN
ejpam-4323	4	7	university	university	PROPN
ejpam-4323	4	8	,	,	PUNCT
ejpam-4323	4	9	saint	saint	NOUN
ejpam-4323	4	10	-	-	PUNCT
ejpam-4323	4	11	louis	louis	NOUN
ejpam-4323	4	12	,	,	PUNCT
ejpam-4323	4	13	sénégal	sénégal	PROPN
ejpam-4323	4	14	3	3	NUM
ejpam-4323	4	15	university	university	NOUN
ejpam-4323	4	16	of	of	ADP
ejpam-4323	4	17	kara	kara	PROPN
ejpam-4323	4	18	,	,	PUNCT
ejpam-4323	4	19	kara	kara	PROPN
ejpam-4323	4	20	,	,	PUNCT
ejpam-4323	4	21	togo	togo	PROPN
ejpam-4323	4	22	.	.	PUNCT
ejpam-4323	5	1	affiliated	affiliate	VERB
ejpam-4323	5	2	to	to	ADP
ejpam-4323	5	3	lerstad	lerstad	PROPN
ejpam-4323	5	4	,	,	PUNCT
ejpam-4323	5	5	gaston	gaston	PROPN
ejpam-4323	5	6	berger	berger	PROPN
ejpam-4323	5	7	university	university	PROPN
ejpam-4323	5	8	,	,	PUNCT
ejpam-4323	5	9	saintlouis	saintlouis	NOUN
ejpam-4323	5	10	,	,	PUNCT
ejpam-4323	5	11	sénégal	sénégal	ADJ
ejpam-4323	5	12	4	4	NUM
ejpam-4323	5	13	lerstad	lerstad	NOUN
ejpam-4323	5	14	,	,	PUNCT
ejpam-4323	5	15	gaston	gaston	PROPN
ejpam-4323	5	16	berger	berger	PROPN
ejpam-4323	5	17	university	university	PROPN
ejpam-4323	5	18	,	,	PUNCT
ejpam-4323	5	19	saint	saint	NOUN
ejpam-4323	5	20	-	-	PUNCT
ejpam-4323	5	21	louis	louis	NOUN
ejpam-4323	5	22	,	,	PUNCT
ejpam-4323	5	23	sénégal	sénégal	ADJ
ejpam-4323	5	24	(	(	PUNCT
ejpam-4323	5	25	main	main	ADJ
ejpam-4323	5	26	affiliation	affiliation	NOUN
ejpam-4323	5	27	)	)	PUNCT
ejpam-4323	5	28	department	department	NOUN
ejpam-4323	5	29	of	of	ADP
ejpam-4323	5	30	pure	pure	ADJ
ejpam-4323	5	31	and	and	CCONJ
ejpam-4323	5	32	applied	applied	ADJ
ejpam-4323	5	33	mathematics	mathematic	NOUN
ejpam-4323	5	34	,	,	PUNCT
ejpam-4323	5	35	african	african	ADJ
ejpam-4323	5	36	university	university	PROPN
ejpam-4323	5	37	of	of	ADP
ejpam-4323	5	38	science	science	NOUN
ejpam-4323	5	39	and	and	CCONJ
ejpam-4323	5	40	technology	technology	NOUN
ejpam-4323	5	41	,	,	PUNCT
ejpam-4323	5	42	abuja	abuja	PROPN
ejpam-4323	5	43	,	,	PUNCT
ejpam-4323	5	44	nigeria	nigeria	PROPN
ejpam-4323	5	45	lsta	lsta	ADV
ejpam-4323	5	46	,	,	PUNCT
ejpam-4323	5	47	pierre	pierre	PROPN
ejpam-4323	5	48	and	and	CCONJ
ejpam-4323	5	49	marie	marie	PROPN
ejpam-4323	5	50	curie	curie	PROPN
ejpam-4323	5	51	university	university	PROPN
ejpam-4323	5	52	,	,	PUNCT
ejpam-4323	5	53	paris	paris	PROPN
ejpam-4323	5	54	vi	vi	PROPN
ejpam-4323	5	55	,	,	PUNCT
ejpam-4323	5	56	france	france	PROPN
ejpam-4323	5	57	(	(	PUNCT
ejpam-4323	5	58	associated	associated	ADJ
ejpam-4323	5	59	researcher	researcher	NOUN
ejpam-4323	5	60	)	)	PUNCT
ejpam-4323	5	61	abstract	abstract	NOUN
ejpam-4323	5	62	.	.	PUNCT
ejpam-4323	6	1	in	in	ADP
ejpam-4323	6	2	earlier	early	ADJ
ejpam-4323	6	3	stages	stage	NOUN
ejpam-4323	6	4	in	in	ADP
ejpam-4323	6	5	the	the	DET
ejpam-4323	6	6	introduction	introduction	NOUN
ejpam-4323	6	7	to	to	ADP
ejpam-4323	6	8	asymptotic	asymptotic	ADJ
ejpam-4323	6	9	methods	method	NOUN
ejpam-4323	6	10	in	in	ADP
ejpam-4323	6	11	probability	probability	NOUN
ejpam-4323	6	12	theory	theory	NOUN
ejpam-4323	6	13	,	,	PUNCT
ejpam-4323	6	14	the	the	DET
ejpam-4323	6	15	weak	weak	ADJ
ejpam-4323	6	16	convergence	convergence	NOUN
ejpam-4323	6	17	of	of	ADP
ejpam-4323	6	18	sequences	sequence	NOUN
ejpam-4323	6	19	(	(	PUNCT
ejpam-4323	6	20	xn)n≥1	xn)n≥1	NOUN
ejpam-4323	6	21	of	of	ADP
ejpam-4323	6	22	binomial	binomial	ADJ
ejpam-4323	6	23	random	random	ADJ
ejpam-4323	6	24	variables	variable	NOUN
ejpam-4323	6	25	(	(	PUNCT
ejpam-4323	6	26	rv	rv	NOUN
ejpam-4323	6	27	’s	’s	ADV
ejpam-4323	6	28	)	)	PUNCT
ejpam-4323	6	29	to	to	ADP
ejpam-4323	6	30	a	a	DET
ejpam-4323	6	31	poisson	poisson	NOUN
ejpam-4323	6	32	law	law	NOUN
ejpam-4323	6	33	is	be	AUX
ejpam-4323	6	34	classical	classical	ADJ
ejpam-4323	6	35	and	and	CCONJ
ejpam-4323	6	36	easy	easy	ADJ
ejpam-4323	6	37	to	to	PART
ejpam-4323	6	38	prove	prove	VERB
ejpam-4323	6	39	.	.	PUNCT
ejpam-4323	7	1	a	a	DET
ejpam-4323	7	2	version	version	NOUN
ejpam-4323	7	3	of	of	ADP
ejpam-4323	7	4	such	such	DET
ejpam-4323	7	5	a	a	DET
ejpam-4323	7	6	result	result	NOUN
ejpam-4323	7	7	concerning	concern	VERB
ejpam-4323	7	8	sequences	sequence	NOUN
ejpam-4323	7	9	(	(	PUNCT
ejpam-4323	7	10	yn)n≥1	yn)n≥1	NOUN
ejpam-4323	7	11	of	of	ADP
ejpam-4323	7	12	negative	negative	ADJ
ejpam-4323	7	13	binomial	binomial	PROPN
ejpam-4323	8	1	rv	rv	PROPN
ejpam-4323	8	2	’s	’s	ADV
ejpam-4323	8	3	also	also	ADV
ejpam-4323	8	4	exists	exist	VERB
ejpam-4323	8	5	.	.	PUNCT
ejpam-4323	9	1	in	in	ADP
ejpam-4323	9	2	both	both	DET
ejpam-4323	9	3	cases	case	NOUN
ejpam-4323	9	4	,	,	PUNCT
ejpam-4323	9	5	xn	xn	PROPN
ejpam-4323	9	6	and	and	CCONJ
ejpam-4323	9	7	yn−n	yn−n	PROPN
ejpam-4323	9	8	are	be	AUX
ejpam-4323	9	9	by	by	ADP
ejpam-4323	9	10	-	-	PUNCT
ejpam-4323	9	11	row	row	NOUN
ejpam-4323	9	12	sums	sum	NOUN
ejpam-4323	9	13	sn[x	sn[x	NOUN
ejpam-4323	9	14	]	]	PUNCT
ejpam-4323	9	15	and	and	CCONJ
ejpam-4323	9	16	sn[y	sn[y	PROPN
ejpam-4323	9	17	]	]	PUNCT
ejpam-4323	9	18	of	of	ADP
ejpam-4323	9	19	arrays	array	NOUN
ejpam-4323	9	20	of	of	ADP
ejpam-4323	9	21	bernoulli	bernoulli	PROPN
ejpam-4323	9	22	rv	rv	PROPN
ejpam-4323	9	23	’s	’s	PART
ejpam-4323	9	24	and	and	CCONJ
ejpam-4323	9	25	corrected	correct	VERB
ejpam-4323	9	26	geometric	geometric	PROPN
ejpam-4323	9	27	rv	rv	PROPN
ejpam-4323	9	28	’s	’s	NOUN
ejpam-4323	9	29	respectively	respectively	ADV
ejpam-4323	9	30	.	.	PUNCT
ejpam-4323	10	1	when	when	SCONJ
ejpam-4323	10	2	considered	consider	VERB
ejpam-4323	10	3	in	in	ADP
ejpam-4323	10	4	the	the	DET
ejpam-4323	10	5	general	general	ADJ
ejpam-4323	10	6	frame	frame	NOUN
ejpam-4323	10	7	of	of	ADP
ejpam-4323	10	8	asymptotic	asymptotic	ADJ
ejpam-4323	10	9	theorems	theorem	NOUN
ejpam-4323	10	10	of	of	ADP
ejpam-4323	10	11	by	by	ADP
ejpam-4323	10	12	-	-	PUNCT
ejpam-4323	10	13	row	row	NOUN
ejpam-4323	10	14	sums	sum	NOUN
ejpam-4323	10	15	of	of	ADP
ejpam-4323	10	16	rv	rv	PROPN
ejpam-4323	10	17	’s	’s	NOUN
ejpam-4323	10	18	of	of	ADP
ejpam-4323	10	19	arrays	array	NOUN
ejpam-4323	10	20	,	,	PUNCT
ejpam-4323	10	21	these	these	DET
ejpam-4323	10	22	two	two	NUM
ejpam-4323	10	23	simple	simple	ADJ
ejpam-4323	10	24	results	result	NOUN
ejpam-4323	10	25	in	in	ADP
ejpam-4323	10	26	the	the	DET
ejpam-4323	10	27	independent	independent	ADJ
ejpam-4323	10	28	and	and	CCONJ
ejpam-4323	10	29	identically	identically	ADV
ejpam-4323	10	30	distributed	distribute	VERB
ejpam-4323	10	31	scheme	scheme	NOUN
ejpam-4323	10	32	can	can	AUX
ejpam-4323	10	33	be	be	AUX
ejpam-4323	10	34	generalized	generalize	VERB
ejpam-4323	10	35	to	to	ADP
ejpam-4323	10	36	non	non	ADJ
ejpam-4323	10	37	-	-	ADJ
ejpam-4323	10	38	stationary	stationary	ADJ
ejpam-4323	10	39	data	datum	NOUN
ejpam-4323	10	40	and	and	CCONJ
ejpam-4323	10	41	beyond	beyond	ADP
ejpam-4323	10	42	to	to	ADP
ejpam-4323	10	43	nonstationary	nonstationary	ADJ
ejpam-4323	10	44	and	and	CCONJ
ejpam-4323	10	45	dependent	dependent	ADJ
ejpam-4323	10	46	data	datum	NOUN
ejpam-4323	10	47	.	.	PUNCT
ejpam-4323	11	1	further	further	ADJ
ejpam-4323	11	2	generalizations	generalization	NOUN
ejpam-4323	11	3	give	give	VERB
ejpam-4323	11	4	interesting	interesting	ADJ
ejpam-4323	11	5	results	result	NOUN
ejpam-4323	11	6	that	that	PRON
ejpam-4323	11	7	would	would	AUX
ejpam-4323	11	8	not	not	PART
ejpam-4323	11	9	be	be	AUX
ejpam-4323	11	10	found	find	VERB
ejpam-4323	11	11	by	by	ADP
ejpam-4323	11	12	direct	direct	ADJ
ejpam-4323	11	13	methods	method	NOUN
ejpam-4323	11	14	.	.	PUNCT
ejpam-4323	12	1	in	in	ADP
ejpam-4323	12	2	this	this	DET
ejpam-4323	12	3	paper	paper	NOUN
ejpam-4323	12	4	,	,	PUNCT
ejpam-4323	12	5	we	we	PRON
ejpam-4323	12	6	focus	focus	VERB
ejpam-4323	12	7	on	on	ADP
ejpam-4323	12	8	generalizations	generalization	NOUN
ejpam-4323	12	9	to	to	ADP
ejpam-4323	12	10	the	the	DET
ejpam-4323	12	11	non	non	ADJ
ejpam-4323	12	12	-	-	ADJ
ejpam-4323	12	13	stationary	stationary	ADJ
ejpam-4323	12	14	independent	independent	ADJ
ejpam-4323	12	15	data	datum	NOUN
ejpam-4323	12	16	in	in	ADP
ejpam-4323	12	17	the	the	DET
ejpam-4323	12	18	frame	frame	NOUN
ejpam-4323	12	19	of	of	ADP
ejpam-4323	12	20	the	the	DET
ejpam-4323	12	21	central	central	ADJ
ejpam-4323	12	22	limit	limit	NOUN
ejpam-4323	12	23	theorem	theorem	VERB
ejpam-4323	12	24	for	for	ADP
ejpam-4323	12	25	independent	independent	ADJ
ejpam-4323	12	26	random	random	ADJ
ejpam-4323	12	27	variables	variable	NOUN
ejpam-4323	12	28	.	.	PUNCT
ejpam-4323	13	1	2020	2020	NUM
ejpam-4323	13	2	mathematics	mathematic	NOUN
ejpam-4323	13	3	subject	subject	NOUN
ejpam-4323	13	4	classifications	classification	NOUN
ejpam-4323	13	5	:	:	PUNCT
ejpam-4323	13	6	60b10	60b10	NOUN
ejpam-4323	13	7	,	,	PUNCT
ejpam-4323	13	8	60f05	60f05	NUM
ejpam-4323	13	9	,	,	PUNCT
ejpam-4323	13	10	60g70	60g70	NUM
ejpam-4323	13	11	,	,	PUNCT
ejpam-4323	13	12	62g30	62g30	NUM
ejpam-4323	13	13	key	key	ADJ
ejpam-4323	13	14	words	word	NOUN
ejpam-4323	13	15	and	and	CCONJ
ejpam-4323	13	16	phrases	phrase	NOUN
ejpam-4323	13	17	:	:	PUNCT
ejpam-4323	13	18	summands	summand	NOUN
ejpam-4323	13	19	of	of	ADP
ejpam-4323	13	20	independent	independent	ADJ
ejpam-4323	13	21	and	and	CCONJ
ejpam-4323	13	22	square	square	ADJ
ejpam-4323	13	23	integrable	integrable	ADJ
ejpam-4323	13	24	random	random	ADJ
ejpam-4323	13	25	variables	variable	NOUN
ejpam-4323	13	26	;	;	PUNCT
ejpam-4323	13	27	weak	weak	ADJ
ejpam-4323	13	28	convergence	convergence	NOUN
ejpam-4323	13	29	of	of	ADP
ejpam-4323	13	30	arrays	array	NOUN
ejpam-4323	13	31	;	;	PUNCT
ejpam-4323	13	32	poisson	poisson	NOUN
ejpam-4323	13	33	limits	limit	NOUN
ejpam-4323	13	34	,	,	PUNCT
ejpam-4323	13	35	binomial	binomial	ADJ
ejpam-4323	13	36	and	and	CCONJ
ejpam-4323	13	37	negative	negative	ADJ
ejpam-4323	13	38	binomial	binomial	ADJ
ejpam-4323	13	39	laws	law	NOUN
ejpam-4323	13	40	;	;	PUNCT
ejpam-4323	13	41	bernoulli	bernoulli	PROPN
ejpam-4323	13	42	and	and	CCONJ
ejpam-4323	13	43	corrected	correct	VERB
ejpam-4323	13	44	geometric	geometric	ADJ
ejpam-4323	13	45	laws	law	NOUN
ejpam-4323	13	46	;	;	PUNCT
ejpam-4323	13	47	non	non	ADJ
ejpam-4323	13	48	-	-	ADJ
ejpam-4323	13	49	stationary	stationary	ADJ
ejpam-4323	13	50	.	.	PUNCT
ejpam-4323	14	1	∗corresponding	∗corresponde	VERB
ejpam-4323	14	2	author	author	NOUN
ejpam-4323	14	3	.	.	PUNCT
ejpam-4323	15	1	doi	doi	NOUN
ejpam-4323	15	2	:	:	PUNCT
ejpam-4323	15	3	https://doi.org/10.29020/nybg.ejpam.v15i2.4323	https://doi.org/10.29020/nybg.ejpam.v15i2.4323	NUM
ejpam-4323	15	4	email	email	NOUN
ejpam-4323	15	5	addresses	address	NOUN
ejpam-4323	15	6	:	:	PUNCT
ejpam-4323	15	7	niang.aladji-babacar@ugb.edu.sn	niang.aladji-babacar@ugb.edu.sn	PROPN
ejpam-4323	15	8	(	(	PUNCT
ejpam-4323	15	9	ab	ab	PROPN
ejpam-4323	15	10	niang	niang	PROPN
ejpam-4323	15	11	)	)	PUNCT
ejpam-4323	15	12	,	,	PUNCT
ejpam-4323	15	13	harounasangare@fst-usttb-edu.ml	harounasangare@fst-usttb-edu.ml	PROPN
ejpam-4323	15	14	(	(	PUNCT
ejpam-4323	15	15	h	h	PROPN
ejpam-4323	15	16	sangaré	sangaré	PROPN
ejpam-4323	15	17	)	)	PUNCT
ejpam-4323	15	18	,	,	PUNCT
ejpam-4323	15	19	t.kpanzou@univkara.net	t.kpanzou@univkara.net	NOUN
ejpam-4323	15	20	(	(	PUNCT
ejpam-4323	15	21	ta	ta	PART
ejpam-4323	15	22	kpanzou	kpanzou	PROPN
ejpam-4323	15	23	)	)	PUNCT
ejpam-4323	15	24	,	,	PUNCT
ejpam-4323	15	25	gane-samb.lo@ugb.edu.sn	gane-samb.lo@ugb.edu.sn	PROPN
ejpam-4323	15	26	(	(	PUNCT
ejpam-4323	15	27	gs	gs	PROPN
ejpam-4323	15	28	lo	lo	PROPN
ejpam-4323	15	29	)	)	PUNCT
ejpam-4323	15	30	,	,	PUNCT
ejpam-4323	15	31	fany.ngom@ugb.edu.sn	fany.ngom@ugb.edu.sn	NOUN
ejpam-4323	15	32	(	(	PUNCT
ejpam-4323	15	33	n	n	CCONJ
ejpam-4323	15	34	ngom	ngom	ADJ
ejpam-4323	15	35	)	)	PUNCT
ejpam-4323	15	36	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4323	15	37	511	511	NUM
ejpam-4323	16	1	©	©	ADP
ejpam-4323	16	2	2022	2022	NUM
ejpam-4323	16	3	ejpam	ejpam	VERB
ejpam-4323	16	4	all	all	DET
ejpam-4323	16	5	rights	right	NOUN
ejpam-4323	16	6	reserved	reserve	VERB
ejpam-4323	16	7	.	.	PUNCT
ejpam-4323	17	1	ab	ab	PROPN
ejpam-4323	17	2	niang	niang	PROPN
ejpam-4323	17	3	et	et	PROPN
ejpam-4323	17	4	al	al	PROPN
ejpam-4323	17	5	.	.	PUNCT
ejpam-4323	17	6	/	/	SYM
ejpam-4323	17	7	eur	eur	PROPN
ejpam-4323	17	8	.	.	PUNCT
ejpam-4323	18	1	j.	j.	PROPN
ejpam-4323	18	2	pure	pure	PROPN
ejpam-4323	18	3	appl	appl	PROPN
ejpam-4323	18	4	.	.	PROPN
ejpam-4323	18	5	math	math	PROPN
ejpam-4323	18	6	,	,	PUNCT
ejpam-4323	18	7	15	15	NUM
ejpam-4323	18	8	(	(	PUNCT
ejpam-4323	18	9	2	2	NUM
ejpam-4323	18	10	)	)	PUNCT
ejpam-4323	18	11	(	(	PUNCT
ejpam-4323	18	12	2022	2022	NUM
ejpam-4323	18	13	)	)	PUNCT
ejpam-4323	18	14	,	,	PUNCT
ejpam-4323	18	15	511	511	NUM
ejpam-4323	18	16	-	-	SYM
ejpam-4323	18	17	527	527	NUM
ejpam-4323	18	18	512	512	NUM
ejpam-4323	18	19	1	1	NUM
ejpam-4323	18	20	.	.	PUNCT
ejpam-4323	19	1	introduction	introduction	NOUN
ejpam-4323	19	2	1.1	1.1	NUM
ejpam-4323	19	3	.	.	PUNCT
ejpam-4323	20	1	preliminaries	preliminary	NOUN
ejpam-4323	20	2	the	the	DET
ejpam-4323	20	3	approximation	approximation	NOUN
ejpam-4323	20	4	of	of	ADP
ejpam-4323	20	5	a	a	DET
ejpam-4323	20	6	sequence	sequence	NOUN
ejpam-4323	20	7	of	of	ADP
ejpam-4323	20	8	binomial	binomial	ADJ
ejpam-4323	20	9	probability	probability	NOUN
ejpam-4323	20	10	laws	law	NOUN
ejpam-4323	20	11	(	(	PUNCT
ejpam-4323	20	12	b(n	b(n	NOUN
ejpam-4323	20	13	,	,	PUNCT
ejpam-4323	20	14	pn))n≥1	pn))n≥1	VERB
ejpam-4323	20	15	associated	associate	VERB
ejpam-4323	20	16	to	to	ADP
ejpam-4323	20	17	a	a	DET
ejpam-4323	20	18	sequence	sequence	NOUN
ejpam-4323	20	19	of	of	ADP
ejpam-4323	20	20	r.v	r.v	PROPN
ejpam-4323	20	21	’s	’s	PART
ejpam-4323	20	22	(	(	PUNCT
ejpam-4323	20	23	zn)n≥1	zn)n≥1	NOUN
ejpam-4323	20	24	[	[	X
ejpam-4323	20	25	such	such	ADJ
ejpam-4323	20	26	that	that	SCONJ
ejpam-4323	20	27	the	the	DET
ejpam-4323	20	28	sequence	sequence	NOUN
ejpam-4323	20	29	of	of	ADP
ejpam-4323	20	30	probabilities	probability	NOUN
ejpam-4323	20	31	(	(	PUNCT
ejpam-4323	20	32	pn)n≥1	pn)n≥1	NOUN
ejpam-4323	20	33	converges	converge	NOUN
ejpam-4323	20	34	to	to	ADP
ejpam-4323	20	35	zero	zero	NUM
ejpam-4323	20	36	and	and	CCONJ
ejpam-4323	20	37	npn	npn	NOUN
ejpam-4323	20	38	→	→	SYM
ejpam-4323	20	39	λ	λ	X
ejpam-4323	20	40	>	>	X
ejpam-4323	20	41	0	0	PUNCT
ejpam-4323	20	42	as	as	ADP
ejpam-4323	20	43	n→	n→	ADV
ejpam-4323	20	44	+	+	PROPN
ejpam-4323	20	45	∞	∞	NOUN
ejpam-4323	20	46	]	]	PUNCT
ejpam-4323	20	47	to	to	ADP
ejpam-4323	20	48	a	a	DET
ejpam-4323	20	49	poisson	poisson	NOUN
ejpam-4323	20	50	law	law	NOUN
ejpam-4323	20	51	p(λ	p(λ	NOUN
ejpam-4323	20	52	)	)	PUNCT
ejpam-4323	20	53	is	be	AUX
ejpam-4323	20	54	a	a	DET
ejpam-4323	20	55	classical	classical	ADJ
ejpam-4323	20	56	and	and	CCONJ
ejpam-4323	20	57	easy	easy	ADJ
ejpam-4323	20	58	-	-	PUNCT
ejpam-4323	20	59	to	to	PART
ejpam-4323	20	60	-	-	PUNCT
ejpam-4323	20	61	prove	prove	VERB
ejpam-4323	20	62	result	result	NOUN
ejpam-4323	20	63	in	in	ADP
ejpam-4323	20	64	probability	probability	NOUN
ejpam-4323	20	65	theory	theory	NOUN
ejpam-4323	20	66	.	.	PUNCT
ejpam-4323	21	1	this	this	DET
ejpam-4323	21	2	approximation	approximation	NOUN
ejpam-4323	21	3	has	have	VERB
ejpam-4323	21	4	very	very	ADV
ejpam-4323	21	5	important	important	ADJ
ejpam-4323	21	6	applications	application	NOUN
ejpam-4323	21	7	in	in	ADP
ejpam-4323	21	8	reallife	reallife	PROPN
ejpam-4323	21	9	problems	problem	NOUN
ejpam-4323	21	10	,	,	PUNCT
ejpam-4323	21	11	especially	especially	ADV
ejpam-4323	21	12	in	in	ADP
ejpam-4323	21	13	lack	lack	NOUN
ejpam-4323	21	14	of	of	ADP
ejpam-4323	21	15	powerful	powerful	ADJ
ejpam-4323	21	16	computers	computer	NOUN
ejpam-4323	21	17	.	.	PUNCT
ejpam-4323	22	1	in	in	ADP
ejpam-4323	22	2	this	this	DET
ejpam-4323	22	3	simple	simple	ADJ
ejpam-4323	22	4	case	case	NOUN
ejpam-4323	22	5	,	,	PUNCT
ejpam-4323	22	6	each	each	DET
ejpam-4323	22	7	zn	zn	PROPN
ejpam-4323	22	8	is	be	AUX
ejpam-4323	22	9	a	a	DET
ejpam-4323	22	10	sum	sum	NOUN
ejpam-4323	22	11	of	of	ADP
ejpam-4323	22	12	n	n	CCONJ
ejpam-4323	22	13	independent	independent	ADJ
ejpam-4323	22	14	and	and	CCONJ
ejpam-4323	22	15	identically	identically	ADV
ejpam-4323	22	16	distributed	distribute	VERB
ejpam-4323	22	17	(	(	PUNCT
ejpam-4323	22	18	iid	iid	NOUN
ejpam-4323	22	19	)	)	PUNCT
ejpam-4323	22	20	bernoulli	bernoulli	PROPN
ejpam-4323	22	21	b(pn)-random	b(pn)-random	PROPN
ejpam-4323	22	22	variables	variable	NOUN
ejpam-4323	22	23	{	{	PUNCT
ejpam-4323	22	24	(	(	PUNCT
ejpam-4323	22	25	xj	xj	PROPN
ejpam-4323	22	26	,	,	PUNCT
ejpam-4323	22	27	n)1≤j≤n	n)1≤j≤n	PROPN
ejpam-4323	22	28	,	,	PUNCT
ejpam-4323	22	29	n	n	PRON
ejpam-4323	22	30	≥	≥	NOUN
ejpam-4323	22	31	1	1	NUM
ejpam-4323	22	32	}	}	PUNCT
ejpam-4323	22	33	,	,	PUNCT
ejpam-4323	22	34	i.e.	i.e.	X
ejpam-4323	22	35	,	,	PUNCT
ejpam-4323	22	36	zn	zn	X
ejpam-4323	22	37	=	=	SYM
ejpam-4323	22	38	x1,n	x1,n	PROPN
ejpam-4323	23	1	+	+	PUNCT
ejpam-4323	23	2	x2,n	x2,n	PROPN
ejpam-4323	23	3	+	+	X
ejpam-4323	23	4	·	·	PUNCT
ejpam-4323	23	5	·	·	PUNCT
ejpam-4323	23	6	·	·	PUNCT
ejpam-4323	23	7	+	+	NUM
ejpam-4323	23	8	xn	xn	NUM
ejpam-4323	23	9	,	,	PUNCT
ejpam-4323	23	10	n.	n.	NOUN
ejpam-4323	23	11	when	when	SCONJ
ejpam-4323	23	12	we	we	PRON
ejpam-4323	23	13	depart	depart	VERB
ejpam-4323	23	14	from	from	ADP
ejpam-4323	23	15	the	the	DET
ejpam-4323	23	16	identical	identical	ADJ
ejpam-4323	23	17	distributivity	distributivity	NOUN
ejpam-4323	23	18	assumption	assumption	NOUN
ejpam-4323	23	19	,	,	PUNCT
ejpam-4323	23	20	the	the	DET
ejpam-4323	23	21	problem	problem	NOUN
ejpam-4323	23	22	may	may	AUX
ejpam-4323	23	23	get	get	VERB
ejpam-4323	23	24	more	more	ADV
ejpam-4323	23	25	and	and	CCONJ
ejpam-4323	23	26	rapidly	rapidly	ADV
ejpam-4323	23	27	complex	complex	ADJ
ejpam-4323	23	28	,	,	PUNCT
ejpam-4323	23	29	even	even	ADV
ejpam-4323	23	30	if	if	SCONJ
ejpam-4323	23	31	the	the	DET
ejpam-4323	23	32	independence	independence	NOUN
ejpam-4323	23	33	assumption	assumption	NOUN
ejpam-4323	23	34	is	be	AUX
ejpam-4323	23	35	still	still	ADV
ejpam-4323	23	36	required	require	VERB
ejpam-4323	23	37	.	.	PUNCT
ejpam-4323	24	1	the	the	DET
ejpam-4323	24	2	situation	situation	NOUN
ejpam-4323	24	3	becomes	become	VERB
ejpam-4323	24	4	more	more	ADV
ejpam-4323	24	5	interesting	interesting	ADJ
ejpam-4323	24	6	if	if	SCONJ
ejpam-4323	24	7	the	the	DET
ejpam-4323	24	8	random	random	ADJ
ejpam-4323	24	9	variables	variable	NOUN
ejpam-4323	24	10	xj	xj	PROPN
ejpam-4323	24	11	,	,	PUNCT
ejpam-4323	24	12	n	n	PRON
ejpam-4323	24	13	are	be	AUX
ejpam-4323	24	14	non	non	ADJ
ejpam-4323	24	15	-	-	ADJ
ejpam-4323	24	16	stationary	stationary	ADJ
ejpam-4323	24	17	and	and	CCONJ
ejpam-4323	24	18	independent	independent	ADJ
ejpam-4323	24	19	.	.	PUNCT
ejpam-4323	25	1	for	for	ADP
ejpam-4323	25	2	the	the	DET
ejpam-4323	25	3	definition	definition	NOUN
ejpam-4323	25	4	and	and	CCONJ
ejpam-4323	25	5	more	more	ADJ
ejpam-4323	25	6	details	detail	NOUN
ejpam-4323	25	7	on	on	ADP
ejpam-4323	25	8	the	the	DET
ejpam-4323	25	9	binomial	binomial	ADJ
ejpam-4323	25	10	and	and	CCONJ
ejpam-4323	25	11	poisson	poisson	NOUN
ejpam-4323	25	12	laws	law	NOUN
ejpam-4323	25	13	,	,	PUNCT
ejpam-4323	25	14	see	see	VERB
ejpam-4323	25	15	[	[	X
ejpam-4323	25	16	4	4	NUM
ejpam-4323	25	17	]	]	PUNCT
ejpam-4323	25	18	.	.	PUNCT
ejpam-4323	26	1	in	in	ADP
ejpam-4323	26	2	this	this	DET
ejpam-4323	26	3	paper	paper	NOUN
ejpam-4323	26	4	,	,	PUNCT
ejpam-4323	26	5	we	we	PRON
ejpam-4323	26	6	aim	aim	VERB
ejpam-4323	26	7	at	at	ADP
ejpam-4323	26	8	giving	give	VERB
ejpam-4323	26	9	non	non	ADJ
ejpam-4323	26	10	trivial	trivial	ADJ
ejpam-4323	26	11	generalizations	generalization	NOUN
ejpam-4323	26	12	of	of	ADP
ejpam-4323	26	13	such	such	ADJ
ejpam-4323	26	14	results	result	NOUN
ejpam-4323	26	15	in	in	ADP
ejpam-4323	26	16	the	the	DET
ejpam-4323	26	17	frame	frame	NOUN
ejpam-4323	26	18	of	of	ADP
ejpam-4323	26	19	the	the	DET
ejpam-4323	26	20	central	central	ADJ
ejpam-4323	26	21	limit	limit	NOUN
ejpam-4323	26	22	theorem	theorem	VERB
ejpam-4323	26	23	for	for	ADP
ejpam-4323	26	24	independent	independent	ADJ
ejpam-4323	26	25	random	random	ADJ
ejpam-4323	26	26	variables	variable	NOUN
ejpam-4323	26	27	.	.	PUNCT
ejpam-4323	27	1	also	also	ADV
ejpam-4323	27	2	,	,	PUNCT
ejpam-4323	27	3	there	there	PRON
ejpam-4323	27	4	is	be	VERB
ejpam-4323	27	5	a	a	DET
ejpam-4323	27	6	negative	negative	ADJ
ejpam-4323	27	7	version	version	NOUN
ejpam-4323	27	8	of	of	ADP
ejpam-4323	27	9	the	the	DET
ejpam-4323	27	10	described	describe	VERB
ejpam-4323	27	11	result	result	NOUN
ejpam-4323	27	12	.	.	PUNCT
ejpam-4323	28	1	indeed	indeed	ADV
ejpam-4323	28	2	,	,	PUNCT
ejpam-4323	28	3	if	if	SCONJ
ejpam-4323	28	4	we	we	PRON
ejpam-4323	28	5	call	call	VERB
ejpam-4323	28	6	a	a	DET
ejpam-4323	28	7	binomial	binomial	ADJ
ejpam-4323	28	8	law	law	NOUN
ejpam-4323	28	9	as	as	ADP
ejpam-4323	28	10	a	a	DET
ejpam-4323	28	11	positive	positive	ADJ
ejpam-4323	28	12	binomial	binomial	ADJ
ejpam-4323	28	13	law	law	NOUN
ejpam-4323	28	14	pb(n	pb(n	NOUN
ejpam-4323	28	15	,	,	PUNCT
ejpam-4323	28	16	p	p	X
ejpam-4323	28	17	)	)	PUNCT
ejpam-4323	28	18	,	,	PUNCT
ejpam-4323	28	19	n	n	X
ejpam-4323	28	20	≥	≥	NOUN
ejpam-4323	28	21	1	1	NUM
ejpam-4323	28	22	,	,	PUNCT
ejpam-4323	28	23	0	0	PUNCT
ejpam-4323	28	24	<	<	X
ejpam-4323	28	25	p	p	X
ejpam-4323	28	26	<	<	X
ejpam-4323	28	27	1	1	NUM
ejpam-4323	28	28	in	in	ADP
ejpam-4323	28	29	opposition	opposition	NOUN
ejpam-4323	28	30	to	to	ADP
ejpam-4323	28	31	a	a	DET
ejpam-4323	28	32	negative	negative	ADJ
ejpam-4323	28	33	binomial	binomial	ADJ
ejpam-4323	28	34	law	law	NOUN
ejpam-4323	28	35	nb(n	nb(n	NOUN
ejpam-4323	28	36	,	,	PUNCT
ejpam-4323	28	37	p	p	X
ejpam-4323	28	38	)	)	PUNCT
ejpam-4323	28	39	,	,	PUNCT
ejpam-4323	28	40	we	we	PRON
ejpam-4323	28	41	have	have	VERB
ejpam-4323	28	42	the	the	DET
ejpam-4323	28	43	following	follow	VERB
ejpam-4323	28	44	two	two	NUM
ejpam-4323	28	45	results	result	NOUN
ejpam-4323	28	46	concerning	concern	VERB
ejpam-4323	28	47	positive	positive	ADJ
ejpam-4323	28	48	binomial	binomial	ADJ
ejpam-4323	28	49	and	and	CCONJ
ejpam-4323	28	50	negative	negative	ADJ
ejpam-4323	28	51	binomial	binomial	ADJ
ejpam-4323	28	52	laws	law	NOUN
ejpam-4323	28	53	respectively	respectively	ADV
ejpam-4323	28	54	.	.	PUNCT
ejpam-4323	29	1	let	let	VERB
ejpam-4323	29	2	us	we	PRON
ejpam-4323	29	3	make	make	VERB
ejpam-4323	29	4	this	this	DET
ejpam-4323	29	5	precision	precision	NOUN
ejpam-4323	29	6	for	for	ADP
ejpam-4323	29	7	once	once	ADV
ejpam-4323	29	8	:	:	PUNCT
ejpam-4323	29	9	throughout	throughout	ADP
ejpam-4323	29	10	this	this	DET
ejpam-4323	29	11	paper	paper	NOUN
ejpam-4323	29	12	,	,	PUNCT
ejpam-4323	29	13	all	all	DET
ejpam-4323	29	14	limits	limit	NOUN
ejpam-4323	29	15	are	be	AUX
ejpam-4323	29	16	meant	mean	VERB
ejpam-4323	29	17	as	as	ADP
ejpam-4323	29	18	n→	n→	ADV
ejpam-4323	29	19	+	+	PROPN
ejpam-4323	29	20	∞	∞	PROPN
ejpam-4323	29	21	unless	unless	SCONJ
ejpam-4323	29	22	the	the	DET
ejpam-4323	29	23	contrary	contrary	NOUN
ejpam-4323	29	24	is	be	AUX
ejpam-4323	29	25	specified	specify	VERB
ejpam-4323	29	26	.	.	PUNCT
ejpam-4323	30	1	proposition	proposition	NOUN
ejpam-4323	30	2	1	1	NUM
ejpam-4323	30	3	.	.	PUNCT
ejpam-4323	31	1	let	let	VERB
ejpam-4323	31	2	(	(	PUNCT
ejpam-4323	31	3	xn)n≥1	xn)n≥1	NOUN
ejpam-4323	31	4	be	be	AUX
ejpam-4323	31	5	a	a	DET
ejpam-4323	31	6	sequence	sequence	NOUN
ejpam-4323	31	7	of	of	ADP
ejpam-4323	31	8	random	random	ADJ
ejpam-4323	31	9	variables	variable	NOUN
ejpam-4323	31	10	in	in	ADP
ejpam-4323	31	11	some	some	DET
ejpam-4323	31	12	probability	probability	NOUN
ejpam-4323	31	13	space	space	NOUN
ejpam-4323	31	14	(	(	PUNCT
ejpam-4323	31	15	ω	ω	NOUN
ejpam-4323	31	16	,	,	PUNCT
ejpam-4323	31	17	a	a	DET
ejpam-4323	31	18	,	,	PUNCT
ejpam-4323	31	19	p	p	NOUN
ejpam-4323	31	20	)	)	PUNCT
ejpam-4323	32	1	such	such	ADJ
ejpam-4323	32	2	that	that	SCONJ
ejpam-4323	32	3	:	:	PUNCT
ejpam-4323	32	4	1	1	X
ejpam-4323	32	5	)	)	PUNCT
ejpam-4323	32	6	∀n	∀n	NUM
ejpam-4323	32	7	≥	≥	NOUN
ejpam-4323	32	8	1	1	NUM
ejpam-4323	32	9	,	,	PUNCT
ejpam-4323	32	10	xn	xn	PROPN
ejpam-4323	32	11	∼	∼	NOUN
ejpam-4323	32	12	b(n	b(n	PROPN
ejpam-4323	32	13	,	,	PUNCT
ejpam-4323	32	14	pn	pn	NOUN
ejpam-4323	32	15	)	)	PUNCT
ejpam-4323	32	16	,	,	PUNCT
ejpam-4323	32	17	n	n	PRON
ejpam-4323	32	18	≥	≥	NOUN
ejpam-4323	32	19	1	1	NUM
ejpam-4323	32	20	;	;	PUNCT
ejpam-4323	32	21	2	2	X
ejpam-4323	32	22	)	)	PUNCT
ejpam-4323	32	23	pn	pn	NOUN
ejpam-4323	32	24	→	→	SYM
ejpam-4323	32	25	0	0	NUM
ejpam-4323	32	26	and	and	CCONJ
ejpam-4323	32	27	npn	npn	NOUN
ejpam-4323	32	28	→	→	SYM
ejpam-4323	32	29	λ	λ	PROPN
ejpam-4323	32	30	∈	∈	PROPN
ejpam-4323	32	31	r+	r+	PUNCT
ejpam-4323	32	32	\	\	PUNCT
ejpam-4323	32	33	{	{	PUNCT
ejpam-4323	32	34	0	0	NUM
ejpam-4323	32	35	}	}	PUNCT
ejpam-4323	32	36	as	as	ADP
ejpam-4323	32	37	n→	n→	ADV
ejpam-4323	32	38	+	+	PROPN
ejpam-4323	32	39	∞.	∞.	PROPN
ejpam-4323	32	40	then	then	ADV
ejpam-4323	32	41	xn	xn	PROPN
ejpam-4323	32	42	p(λ	p(λ	PROPN
ejpam-4323	32	43	)	)	PUNCT
ejpam-4323	32	44	.	.	PUNCT
ejpam-4323	33	1	next	next	ADV
ejpam-4323	33	2	,	,	PUNCT
ejpam-4323	33	3	we	we	PRON
ejpam-4323	33	4	have	have	VERB
ejpam-4323	33	5	:	:	PUNCT
ejpam-4323	33	6	proposition	proposition	NOUN
ejpam-4323	33	7	2	2	NUM
ejpam-4323	33	8	.	.	PUNCT
ejpam-4323	34	1	let	let	VERB
ejpam-4323	34	2	(	(	PUNCT
ejpam-4323	34	3	xn)n≥1	xn)n≥1	NOUN
ejpam-4323	34	4	be	be	AUX
ejpam-4323	34	5	a	a	DET
ejpam-4323	34	6	sequence	sequence	NOUN
ejpam-4323	34	7	of	of	ADP
ejpam-4323	34	8	random	random	ADJ
ejpam-4323	34	9	variables	variable	NOUN
ejpam-4323	34	10	in	in	ADP
ejpam-4323	34	11	some	some	DET
ejpam-4323	34	12	probability	probability	NOUN
ejpam-4323	34	13	space	space	NOUN
ejpam-4323	34	14	(	(	PUNCT
ejpam-4323	34	15	ω	ω	NOUN
ejpam-4323	34	16	,	,	PUNCT
ejpam-4323	34	17	a	a	DET
ejpam-4323	34	18	,	,	PUNCT
ejpam-4323	34	19	p	p	NOUN
ejpam-4323	34	20	)	)	PUNCT
ejpam-4323	35	1	such	such	ADJ
ejpam-4323	35	2	that	that	SCONJ
ejpam-4323	35	3	:	:	PUNCT
ejpam-4323	35	4	ab	ab	PROPN
ejpam-4323	35	5	niang	niang	PROPN
ejpam-4323	35	6	et	et	PROPN
ejpam-4323	35	7	al	al	PROPN
ejpam-4323	35	8	.	.	PUNCT
ejpam-4323	35	9	/	/	SYM
ejpam-4323	35	10	eur	eur	PROPN
ejpam-4323	35	11	.	.	PUNCT
ejpam-4323	36	1	j.	j.	PROPN
ejpam-4323	36	2	pure	pure	PROPN
ejpam-4323	36	3	appl	appl	PROPN
ejpam-4323	36	4	.	.	PROPN
ejpam-4323	36	5	math	math	PROPN
ejpam-4323	36	6	,	,	PUNCT
ejpam-4323	36	7	15	15	NUM
ejpam-4323	36	8	(	(	PUNCT
ejpam-4323	36	9	2	2	NUM
ejpam-4323	36	10	)	)	PUNCT
ejpam-4323	36	11	(	(	PUNCT
ejpam-4323	36	12	2022	2022	NUM
ejpam-4323	36	13	)	)	PUNCT
ejpam-4323	36	14	,	,	PUNCT
ejpam-4323	36	15	511	511	NUM
ejpam-4323	36	16	-	-	SYM
ejpam-4323	36	17	527	527	NUM
ejpam-4323	36	18	513	513	NUM
ejpam-4323	36	19	1	1	NUM
ejpam-4323	36	20	)	)	PUNCT
ejpam-4323	36	21	∀n	∀n	NUM
ejpam-4323	36	22	≥	≥	NOUN
ejpam-4323	36	23	1	1	NUM
ejpam-4323	36	24	,	,	PUNCT
ejpam-4323	36	25	xn	xn	PROPN
ejpam-4323	36	26	∼	∼	NOUN
ejpam-4323	36	27	nb(n	nb(n	NOUN
ejpam-4323	36	28	,	,	PUNCT
ejpam-4323	36	29	pn	pn	PROPN
ejpam-4323	36	30	)	)	PUNCT
ejpam-4323	36	31	,	,	PUNCT
ejpam-4323	36	32	n	n	PRON
ejpam-4323	36	33	≥	≥	NOUN
ejpam-4323	36	34	1	1	NUM
ejpam-4323	36	35	;	;	PUNCT
ejpam-4323	36	36	2	2	NUM
ejpam-4323	36	37	)	)	PUNCT
ejpam-4323	36	38	(	(	PUNCT
ejpam-4323	36	39	1−	1−	NUM
ejpam-4323	36	40	pn	pn	NOUN
ejpam-4323	36	41	)	)	PUNCT
ejpam-4323	36	42	→	→	SYM
ejpam-4323	36	43	0	0	NUM
ejpam-4323	36	44	and	and	CCONJ
ejpam-4323	36	45	n(1−	n(1−	ADJ
ejpam-4323	36	46	pn	pn	PROPN
ejpam-4323	36	47	)	)	PUNCT
ejpam-4323	36	48	→	→	PUNCT
ejpam-4323	36	49	λ	λ	X
ejpam-4323	36	50	∈	∈	PROPN
ejpam-4323	36	51	r+	r+	PUNCT
ejpam-4323	36	52	\	\	PUNCT
ejpam-4323	36	53	{	{	PUNCT
ejpam-4323	36	54	0	0	NUM
ejpam-4323	36	55	}	}	PUNCT
ejpam-4323	36	56	as	as	ADP
ejpam-4323	36	57	n→	n→	ADV
ejpam-4323	36	58	+	+	PROPN
ejpam-4323	36	59	∞.	∞.	PROPN
ejpam-4323	36	60	then	then	ADV
ejpam-4323	36	61	xn	xn	PROPN
ejpam-4323	36	62	−	−	PROPN
ejpam-4323	36	63	n	n	PRON
ejpam-4323	36	64	p(λ	p(λ	NOUN
ejpam-4323	36	65	)	)	PUNCT
ejpam-4323	36	66	.	.	PUNCT
ejpam-4323	37	1	remark	remark	PROPN
ejpam-4323	37	2	.	.	PUNCT
ejpam-4323	38	1	these	these	DET
ejpam-4323	38	2	two	two	NUM
ejpam-4323	38	3	results	result	NOUN
ejpam-4323	38	4	are	be	AUX
ejpam-4323	38	5	proved	prove	VERB
ejpam-4323	38	6	in	in	ADP
ejpam-4323	38	7	[	[	X
ejpam-4323	38	8	5	5	NUM
ejpam-4323	38	9	]	]	PUNCT
ejpam-4323	38	10	.	.	PUNCT
ejpam-4323	39	1	although	although	SCONJ
ejpam-4323	39	2	the	the	DET
ejpam-4323	39	3	proofs	proof	NOUN
ejpam-4323	39	4	are	be	AUX
ejpam-4323	39	5	direct	direct	ADJ
ejpam-4323	39	6	,	,	PUNCT
ejpam-4323	39	7	we	we	PRON
ejpam-4323	39	8	do	do	AUX
ejpam-4323	39	9	not	not	PART
ejpam-4323	39	10	encounter	encounter	VERB
ejpam-4323	39	11	the	the	DET
ejpam-4323	39	12	second	second	ADJ
ejpam-4323	39	13	in	in	ADP
ejpam-4323	39	14	some	some	DET
ejpam-4323	39	15	classical	classical	ADJ
ejpam-4323	39	16	books	book	NOUN
ejpam-4323	39	17	as	as	ADP
ejpam-4323	39	18	[	[	X
ejpam-4323	39	19	1	1	NUM
ejpam-4323	39	20	,	,	PUNCT
ejpam-4323	39	21	2	2	NUM
ejpam-4323	39	22	]	]	PUNCT
ejpam-4323	39	23	,	,	PUNCT
ejpam-4323	39	24	[	[	X
ejpam-4323	39	25	3	3	NUM
ejpam-4323	39	26	]	]	PUNCT
ejpam-4323	39	27	,	,	PUNCT
ejpam-4323	39	28	[	[	X
ejpam-4323	39	29	6	6	NUM
ejpam-4323	39	30	]	]	PUNCT
ejpam-4323	39	31	.	.	PUNCT
ejpam-4323	40	1	for	for	ADP
ejpam-4323	40	2	that	that	DET
ejpam-4323	40	3	reason	reason	NOUN
ejpam-4323	40	4	,	,	PUNCT
ejpam-4323	40	5	we	we	PRON
ejpam-4323	40	6	give	give	VERB
ejpam-4323	40	7	it	it	PRON
ejpam-4323	40	8	below	below	ADV
ejpam-4323	40	9	.	.	PUNCT
ejpam-4323	41	1	proof	proof	NOUN
ejpam-4323	41	2	of	of	ADP
ejpam-4323	41	3	proposition	proposition	NOUN
ejpam-4323	41	4	2	2	NUM
ejpam-4323	41	5	.	.	PUNCT
ejpam-4323	41	6	let	let	VERB
ejpam-4323	41	7	us	we	PRON
ejpam-4323	41	8	use	use	VERB
ejpam-4323	41	9	the	the	DET
ejpam-4323	41	10	convergence	convergence	NOUN
ejpam-4323	41	11	of	of	ADP
ejpam-4323	41	12	characteristic	characteristic	ADJ
ejpam-4323	41	13	functions	function	NOUN
ejpam-4323	41	14	.	.	PUNCT
ejpam-4323	42	1	let	let	VERB
ejpam-4323	42	2	xn	xn	PUNCT
ejpam-4323	42	3	be	be	AUX
ejpam-4323	42	4	a	a	DET
ejpam-4323	42	5	sequence	sequence	NOUN
ejpam-4323	42	6	of	of	ADP
ejpam-4323	42	7	nb(n	nb(n	PROPN
ejpam-4323	42	8	,	,	PUNCT
ejpam-4323	42	9	pn)random	pn)random	VERB
ejpam-4323	42	10	variables	variable	NOUN
ejpam-4323	42	11	and	and	CCONJ
ejpam-4323	42	12	x	x	AUX
ejpam-4323	42	13	be	be	AUX
ejpam-4323	42	14	a	a	DET
ejpam-4323	42	15	p(λ	p(λ	NOUN
ejpam-4323	42	16	)	)	PUNCT
ejpam-4323	42	17	random	random	ADJ
ejpam-4323	42	18	variable	variable	NOUN
ejpam-4323	42	19	.	.	PUNCT
ejpam-4323	43	1	we	we	PRON
ejpam-4323	43	2	have	have	VERB
ejpam-4323	43	3	sn	sn	PROPN
ejpam-4323	43	4	=	=	SYM
ejpam-4323	43	5	xn	xn	PROPN
ejpam-4323	43	6	−	−	PROPN
ejpam-4323	43	7	n	n	NOUN
ejpam-4323	43	8	=	=	SYM
ejpam-4323	43	9	z1	z1	PROPN
ejpam-4323	43	10	+	+	CCONJ
ejpam-4323	43	11	·	·	PUNCT
ejpam-4323	43	12	·	·	PUNCT
ejpam-4323	43	13	·	·	PUNCT
ejpam-4323	44	1	+	+	CCONJ
ejpam-4323	44	2	zn	zn	NUM
ejpam-4323	44	3	,	,	PUNCT
ejpam-4323	44	4	where	where	SCONJ
ejpam-4323	44	5	z	z	NOUN
ejpam-4323	44	6	,	,	PUNCT
ejpam-4323	44	7	z1	z1	VERB
ejpam-4323	44	8	,	,	PUNCT
ejpam-4323	44	9	·	·	PUNCT
ejpam-4323	44	10	·	·	PUNCT
ejpam-4323	44	11	·	·	PUNCT
ejpam-4323	44	12	,	,	PUNCT
ejpam-4323	44	13	zn	zn	PROPN
ejpam-4323	44	14	are	be	AUX
ejpam-4323	44	15	independent	independent	ADJ
ejpam-4323	44	16	random	random	ADJ
ejpam-4323	44	17	variables	variable	NOUN
ejpam-4323	44	18	such	such	ADJ
ejpam-4323	44	19	that	that	SCONJ
ejpam-4323	44	20	each	each	DET
ejpam-4323	44	21	zi	zi	NOUN
ejpam-4323	45	1	+	+	CCONJ
ejpam-4323	45	2	1	1	NUM
ejpam-4323	45	3	follows	follow	VERB
ejpam-4323	45	4	a	a	DET
ejpam-4323	45	5	geometric	geometric	ADJ
ejpam-4323	45	6	law	law	NOUN
ejpam-4323	45	7	of	of	ADP
ejpam-4323	45	8	parameter	parameter	PROPN
ejpam-4323	45	9	pn	pn	PROPN
ejpam-4323	45	10	,	,	PUNCT
ejpam-4323	45	11	that	that	ADV
ejpam-4323	45	12	is	be	AUX
ejpam-4323	45	13	φz(t	φz(t	NOUN
ejpam-4323	45	14	)	)	PUNCT
ejpam-4323	45	15	=	=	SYM
ejpam-4323	45	16	pn	pn	PROPN
ejpam-4323	45	17	1−	1−	NUM
ejpam-4323	45	18	qneit	qneit	NOUN
ejpam-4323	45	19	,	,	PUNCT
ejpam-4323	45	20	t	t	PROPN
ejpam-4323	45	21	∈	∈	PROPN
ejpam-4323	45	22	r.	r.	PROPN
ejpam-4323	45	23	so	so	ADV
ejpam-4323	45	24	,	,	PUNCT
ejpam-4323	45	25	for	for	ADP
ejpam-4323	45	26	t	t	PROPN
ejpam-4323	45	27	∈	∈	PROPN
ejpam-4323	45	28	r	r	NOUN
ejpam-4323	45	29	fixed	fix	VERB
ejpam-4323	45	30	,	,	PUNCT
ejpam-4323	45	31	φsn(t	φsn(t	PROPN
ejpam-4323	45	32	)	)	PUNCT
ejpam-4323	45	33	=	=	NOUN
ejpam-4323	45	34	exp	exp	NOUN
ejpam-4323	45	35	(	(	PUNCT
ejpam-4323	45	36	n	n	CCONJ
ejpam-4323	45	37	(	(	PUNCT
ejpam-4323	45	38	log	log	VERB
ejpam-4323	45	39	pn	pn	PROPN
ejpam-4323	45	40	−	−	PROPN
ejpam-4323	45	41	log	log	NOUN
ejpam-4323	45	42	(	(	PUNCT
ejpam-4323	45	43	1−	1−	NUM
ejpam-4323	45	44	qne	qne	VERB
ejpam-4323	45	45	it	it	PRON
ejpam-4323	45	46	)	)	PUNCT
ejpam-4323	45	47	)	)	PUNCT
ejpam-4323	45	48	)	)	PUNCT
ejpam-4323	45	49	.	.	PUNCT
ejpam-4323	46	1	we	we	PRON
ejpam-4323	46	2	have	have	VERB
ejpam-4323	46	3	,	,	PUNCT
ejpam-4323	46	4	as	as	ADP
ejpam-4323	46	5	n→	n→	ADV
ejpam-4323	46	6	+	+	PROPN
ejpam-4323	46	7	∞	∞	PROPN
ejpam-4323	46	8	,	,	PUNCT
ejpam-4323	46	9	n	n	PRON
ejpam-4323	46	10	log	log	VERB
ejpam-4323	46	11	pn	pn	PROPN
ejpam-4323	46	12	=	=	SYM
ejpam-4323	46	13	n	n	PROPN
ejpam-4323	46	14	log(1−	log(1−	PROPN
ejpam-4323	46	15	qn	qn	PROPN
ejpam-4323	46	16	)	)	PUNCT
ejpam-4323	46	17	=	=	SYM
ejpam-4323	46	18	−nqn	−nqn	NOUN
ejpam-4323	46	19	+	+	CCONJ
ejpam-4323	46	20	o(nqn	o(nqn	PROPN
ejpam-4323	46	21	)	)	PUNCT
ejpam-4323	46	22	and	and	CCONJ
ejpam-4323	46	23	−n	−n	ADV
ejpam-4323	46	24	log	log	NOUN
ejpam-4323	46	25	(	(	PUNCT
ejpam-4323	46	26	1−	1−	NUM
ejpam-4323	46	27	qne	qne	VERB
ejpam-4323	46	28	it	it	PRON
ejpam-4323	46	29	)	)	PUNCT
ejpam-4323	47	1	=	=	SYM
ejpam-4323	47	2	nqne	nqne	VERB
ejpam-4323	47	3	it	it	PRON
ejpam-4323	47	4	+	+	CCONJ
ejpam-4323	47	5	o(nqn	o(nqn	PROPN
ejpam-4323	47	6	)	)	PUNCT
ejpam-4323	47	7	.	.	PUNCT
ejpam-4323	48	1	hence	hence	ADV
ejpam-4323	48	2	we	we	PRON
ejpam-4323	48	3	get	get	VERB
ejpam-4323	48	4	for	for	ADP
ejpam-4323	48	5	any	any	DET
ejpam-4323	48	6	t	t	NOUN
ejpam-4323	48	7	∈	∈	PROPN
ejpam-4323	48	8	r	r	NOUN
ejpam-4323	48	9	,	,	PUNCT
ejpam-4323	48	10	φsn(t	φsn(t	PROPN
ejpam-4323	48	11	)	)	PUNCT
ejpam-4323	48	12	=	=	NOUN
ejpam-4323	48	13	exp	exp	NOUN
ejpam-4323	48	14	(	(	PUNCT
ejpam-4323	48	15	nqn(e	nqn(e	NOUN
ejpam-4323	48	16	it	it	PRON
ejpam-4323	48	17	−	−	NUM
ejpam-4323	48	18	1	1	NUM
ejpam-4323	48	19	)	)	PUNCT
ejpam-4323	48	20	+	+	NUM
ejpam-4323	48	21	o(nqn	o(nqn	NOUN
ejpam-4323	48	22	)	)	PUNCT
ejpam-4323	48	23	)	)	PUNCT
ejpam-4323	49	1	→	→	SYM
ejpam-4323	49	2	eλ(e	eλ(e	X
ejpam-4323	49	3	it−1	it−1	NOUN
ejpam-4323	49	4	)	)	PUNCT
ejpam-4323	49	5	=	=	SYM
ejpam-4323	49	6	φp(λ)(t	φp(λ)(t	NUM
ejpam-4323	49	7	)	)	PUNCT
ejpam-4323	49	8	.	.	PUNCT
ejpam-4323	50	1	�	�	PROPN
ejpam-4323	50	2	ab	ab	PROPN
ejpam-4323	50	3	niang	niang	PROPN
ejpam-4323	50	4	et	et	PROPN
ejpam-4323	50	5	al	al	PROPN
ejpam-4323	50	6	.	.	PUNCT
ejpam-4323	50	7	/	/	SYM
ejpam-4323	50	8	eur	eur	PROPN
ejpam-4323	50	9	.	.	PUNCT
ejpam-4323	51	1	j.	j.	PROPN
ejpam-4323	51	2	pure	pure	PROPN
ejpam-4323	51	3	appl	appl	PROPN
ejpam-4323	51	4	.	.	PROPN
ejpam-4323	51	5	math	math	PROPN
ejpam-4323	51	6	,	,	PUNCT
ejpam-4323	51	7	15	15	NUM
ejpam-4323	51	8	(	(	PUNCT
ejpam-4323	51	9	2	2	NUM
ejpam-4323	51	10	)	)	PUNCT
ejpam-4323	51	11	(	(	PUNCT
ejpam-4323	51	12	2022	2022	NUM
ejpam-4323	51	13	)	)	PUNCT
ejpam-4323	51	14	,	,	PUNCT
ejpam-4323	51	15	511	511	NUM
ejpam-4323	51	16	-	-	SYM
ejpam-4323	51	17	527	527	NUM
ejpam-4323	51	18	514	514	NUM
ejpam-4323	51	19	our	our	PRON
ejpam-4323	51	20	aim	aim	NOUN
ejpam-4323	51	21	here	here	ADV
ejpam-4323	51	22	is	be	AUX
ejpam-4323	51	23	to	to	PART
ejpam-4323	51	24	provide	provide	VERB
ejpam-4323	51	25	non	non	ADJ
ejpam-4323	51	26	-	-	ADJ
ejpam-4323	51	27	trivial	trivial	ADJ
ejpam-4323	51	28	generalizations	generalization	NOUN
ejpam-4323	51	29	of	of	ADP
ejpam-4323	51	30	such	such	ADJ
ejpam-4323	51	31	simple	simple	ADJ
ejpam-4323	51	32	results	result	NOUN
ejpam-4323	51	33	to	to	ADP
ejpam-4323	51	34	nonstationary	nonstationary	ADJ
ejpam-4323	51	35	and	and	CCONJ
ejpam-4323	51	36	independent	independent	ADJ
ejpam-4323	51	37	data	datum	NOUN
ejpam-4323	51	38	.	.	PUNCT
ejpam-4323	52	1	the	the	DET
ejpam-4323	52	2	used	use	VERB
ejpam-4323	52	3	methods	method	NOUN
ejpam-4323	52	4	will	will	AUX
ejpam-4323	52	5	later	later	ADV
ejpam-4323	52	6	allow	allow	VERB
ejpam-4323	52	7	further	further	ADJ
ejpam-4323	52	8	generalizations	generalization	NOUN
ejpam-4323	52	9	even	even	ADV
ejpam-4323	52	10	with	with	ADP
ejpam-4323	52	11	dependent	dependent	ADJ
ejpam-4323	52	12	data	datum	NOUN
ejpam-4323	52	13	.	.	PUNCT
ejpam-4323	53	1	let	let	VERB
ejpam-4323	53	2	us	we	PRON
ejpam-4323	53	3	prepare	prepare	VERB
ejpam-4323	53	4	generalizations	generalization	NOUN
ejpam-4323	53	5	by	by	ADP
ejpam-4323	53	6	transforming	transform	VERB
ejpam-4323	53	7	both	both	DET
ejpam-4323	53	8	results	result	NOUN
ejpam-4323	53	9	as	as	ADP
ejpam-4323	53	10	sums	sum	NOUN
ejpam-4323	53	11	of	of	ADP
ejpam-4323	53	12	random	random	ADJ
ejpam-4323	53	13	variables	variable	NOUN
ejpam-4323	53	14	.	.	PUNCT
ejpam-4323	54	1	1.2	1.2	NUM
ejpam-4323	54	2	.	.	PUNCT
ejpam-4323	55	1	the	the	DET
ejpam-4323	55	2	central	central	ADJ
ejpam-4323	55	3	limit	limit	NOUN
ejpam-4323	55	4	theorem	theorem	ADJ
ejpam-4323	55	5	frame	frame	NOUN
ejpam-4323	55	6	it	it	PRON
ejpam-4323	55	7	is	be	AUX
ejpam-4323	55	8	known	know	VERB
ejpam-4323	55	9	that	that	SCONJ
ejpam-4323	55	10	a	a	DET
ejpam-4323	55	11	binomial	binomial	ADJ
ejpam-4323	55	12	random	random	ADJ
ejpam-4323	55	13	variable	variable	NOUN
ejpam-4323	55	14	xn	xn	NOUN
ejpam-4323	55	15	∼	∼	NOUN
ejpam-4323	55	16	b(n	b(n	PROPN
ejpam-4323	55	17	,	,	PUNCT
ejpam-4323	55	18	pn	pn	NOUN
ejpam-4323	55	19	)	)	PUNCT
ejpam-4323	55	20	has	have	VERB
ejpam-4323	55	21	the	the	DET
ejpam-4323	55	22	same	same	ADJ
ejpam-4323	55	23	law	law	NOUN
ejpam-4323	55	24	as	as	ADP
ejpam-4323	55	25	a	a	DET
ejpam-4323	55	26	sum	sum	NOUN
ejpam-4323	55	27	of	of	ADP
ejpam-4323	55	28	n	n	PRON
ejpam-4323	55	29	iid	iid	VERB
ejpam-4323	55	30	bernoulli	bernoulli	NOUN
ejpam-4323	55	31	distributed	distribute	VERB
ejpam-4323	55	32	random	random	ADJ
ejpam-4323	55	33	variables	variable	NOUN
ejpam-4323	55	34	:	:	PUNCT
ejpam-4323	55	35	xn	xn	PUNCT
ejpam-4323	56	1	=	=	SYM
ejpam-4323	56	2	d	d	X
ejpam-4323	56	3	x1,n	x1,n	PROPN
ejpam-4323	56	4	+	+	CCONJ
ejpam-4323	56	5	·	·	PUNCT
ejpam-4323	56	6	·	·	PUNCT
ejpam-4323	56	7	·	·	PUNCT
ejpam-4323	56	8	+	+	NOUN
ejpam-4323	56	9	xn	xn	PROPN
ejpam-4323	56	10	,	,	PUNCT
ejpam-4323	56	11	n	n	CCONJ
ejpam-4323	56	12	,	,	PUNCT
ejpam-4323	56	13	where	where	SCONJ
ejpam-4323	56	14	x1,n	x1,n	PROPN
ejpam-4323	56	15	,	,	PUNCT
ejpam-4323	56	16	·	·	PUNCT
ejpam-4323	56	17	·	·	PUNCT
ejpam-4323	56	18	·	·	PUNCT
ejpam-4323	56	19	,	,	PUNCT
ejpam-4323	56	20	xn	xn	PROPN
ejpam-4323	56	21	,	,	PUNCT
ejpam-4323	56	22	n	n	PRON
ejpam-4323	56	23	are	be	AUX
ejpam-4323	56	24	independent	independent	ADJ
ejpam-4323	56	25	and	and	CCONJ
ejpam-4323	56	26	follow	follow	VERB
ejpam-4323	56	27	all	all	DET
ejpam-4323	56	28	the	the	DET
ejpam-4323	56	29	b(pn)-law	b(pn)-law	NOUN
ejpam-4323	56	30	.	.	PUNCT
ejpam-4323	57	1	also	also	ADV
ejpam-4323	57	2	xn	xn	PROPN
ejpam-4323	57	3	∼	∼	NOUN
ejpam-4323	57	4	nb(n	nb(n	NOUN
ejpam-4323	57	5	,	,	PUNCT
ejpam-4323	57	6	pn	pn	PROPN
ejpam-4323	57	7	)	)	PUNCT
ejpam-4323	57	8	has	have	VERB
ejpam-4323	57	9	the	the	DET
ejpam-4323	57	10	same	same	ADJ
ejpam-4323	57	11	law	law	NOUN
ejpam-4323	57	12	as	as	ADP
ejpam-4323	57	13	a	a	DET
ejpam-4323	57	14	sum	sum	NOUN
ejpam-4323	57	15	of	of	ADP
ejpam-4323	57	16	n	n	PRON
ejpam-4323	57	17	iid	iid	VERB
ejpam-4323	57	18	r.v	r.v	NOUN
ejpam-4323	57	19	’s	’s	NOUN
ejpam-4323	57	20	:	:	PUNCT
ejpam-4323	57	21	xn	xn	PUNCT
ejpam-4323	58	1	=	=	PUNCT
ejpam-4323	58	2	d	d	X
ejpam-4323	58	3	x∗	x∗	X
ejpam-4323	58	4	1,n	1,n	X
ejpam-4323	59	1	+	+	CCONJ
ejpam-4323	59	2	·	·	PUNCT
ejpam-4323	59	3	·	·	PUNCT
ejpam-4323	59	4	·	·	PUNCT
ejpam-4323	59	5	+	+	NOUN
ejpam-4323	59	6	x∗	x∗	PROPN
ejpam-4323	59	7	n	n	CCONJ
ejpam-4323	59	8	,	,	PUNCT
ejpam-4323	59	9	n	n	CCONJ
ejpam-4323	59	10	,	,	PUNCT
ejpam-4323	59	11	where	where	SCONJ
ejpam-4323	59	12	x∗	x∗	PROPN
ejpam-4323	59	13	1,n	1,n	AUX
ejpam-4323	59	14	,	,	PUNCT
ejpam-4323	59	15	·	·	PUNCT
ejpam-4323	59	16	·	·	PUNCT
ejpam-4323	59	17	·	·	PUNCT
ejpam-4323	59	18	,	,	PUNCT
ejpam-4323	59	19	x∗	x∗	PROPN
ejpam-4323	59	20	n	n	CCONJ
ejpam-4323	59	21	,	,	PUNCT
ejpam-4323	59	22	n	n	PRON
ejpam-4323	59	23	are	be	AUX
ejpam-4323	59	24	independent	independent	ADJ
ejpam-4323	59	25	and	and	CCONJ
ejpam-4323	59	26	each	each	DET
ejpam-4323	59	27	x∗	x∗	PROPN
ejpam-4323	59	28	j	j	PROPN
ejpam-4323	59	29	,	,	PUNCT
ejpam-4323	59	30	n	n	PRON
ejpam-4323	59	31	follows	follow	VERB
ejpam-4323	59	32	the	the	DET
ejpam-4323	59	33	geometric	geometric	ADJ
ejpam-4323	59	34	law	law	NOUN
ejpam-4323	59	35	g(pn	g(pn	NOUN
ejpam-4323	59	36	)	)	PUNCT
ejpam-4323	59	37	.	.	PUNCT
ejpam-4323	60	1	in	in	ADP
ejpam-4323	60	2	the	the	DET
ejpam-4323	60	3	second	second	NOUN
ejpam-4323	60	4	,	,	PUNCT
ejpam-4323	60	5	we	we	PRON
ejpam-4323	60	6	rather	rather	ADV
ejpam-4323	60	7	use	use	VERB
ejpam-4323	60	8	xn	xn	PROPN
ejpam-4323	60	9	−	−	PROPN
ejpam-4323	61	1	n	n	PROPN
ejpam-4323	61	2	=	=	SYM
ejpam-4323	61	3	n∑	n∑	NOUN
ejpam-4323	61	4	i=1	i=1	PROPN
ejpam-4323	62	1	(	(	PUNCT
ejpam-4323	62	2	x∗	x∗	PROPN
ejpam-4323	62	3	i	i	PRON
ejpam-4323	62	4	,	,	PUNCT
ejpam-4323	62	5	n	n	CCONJ
ejpam-4323	62	6	−	−	PROPN
ejpam-4323	62	7	1	1	NUM
ejpam-4323	62	8	)	)	PUNCT
ejpam-4323	63	1	=	=	NOUN
ejpam-4323	63	2	:	:	PUNCT
ejpam-4323	63	3	n∑	n∑	PROPN
ejpam-4323	63	4	i=1	i=1	X
ejpam-4323	63	5	xi	xi	PROPN
ejpam-4323	63	6	,	,	PUNCT
ejpam-4323	63	7	n	n	CCONJ
ejpam-4323	63	8	,	,	PUNCT
ejpam-4323	63	9	where	where	SCONJ
ejpam-4323	63	10	the	the	DET
ejpam-4323	63	11	xi	xi	PROPN
ejpam-4323	63	12	,	,	PUNCT
ejpam-4323	63	13	n	n	CCONJ
ejpam-4323	63	14	’s	’	VERB
ejpam-4323	63	15	are	be	AUX
ejpam-4323	63	16	independent	independent	ADJ
ejpam-4323	63	17	and	and	CCONJ
ejpam-4323	63	18	each	each	DET
ejpam-4323	63	19	xi	xi	PROPN
ejpam-4323	63	20	,	,	PUNCT
ejpam-4323	63	21	n	n	PRON
ejpam-4323	63	22	follows	follow	VERB
ejpam-4323	63	23	the	the	DET
ejpam-4323	63	24	law	law	NOUN
ejpam-4323	63	25	g∗(pn	g∗(pn	NOUN
ejpam-4323	63	26	)	)	PUNCT
ejpam-4323	63	27	=	=	SYM
ejpam-4323	63	28	g(pn	g(pn	NOUN
ejpam-4323	63	29	)	)	PUNCT
ejpam-4323	63	30	−	−	NUM
ejpam-4323	63	31	1	1	NUM
ejpam-4323	63	32	,	,	PUNCT
ejpam-4323	63	33	and	and	CCONJ
ejpam-4323	63	34	such	such	DET
ejpam-4323	63	35	a	a	DET
ejpam-4323	63	36	law	law	NOUN
ejpam-4323	63	37	is	be	AUX
ejpam-4323	63	38	called	call	VERB
ejpam-4323	63	39	a	a	DET
ejpam-4323	63	40	corrected	correct	VERB
ejpam-4323	63	41	geometric	geometric	ADJ
ejpam-4323	63	42	law	law	NOUN
ejpam-4323	63	43	,	,	PUNCT
ejpam-4323	63	44	for	for	ADP
ejpam-4323	63	45	convenience	convenience	NOUN
ejpam-4323	63	46	.	.	PUNCT
ejpam-4323	64	1	in	in	ADP
ejpam-4323	64	2	both	both	DET
ejpam-4323	64	3	cases	case	NOUN
ejpam-4323	64	4	,	,	PUNCT
ejpam-4323	64	5	we	we	PRON
ejpam-4323	64	6	have	have	VERB
ejpam-4323	64	7	to	to	PART
ejpam-4323	64	8	study	study	VERB
ejpam-4323	64	9	an	an	DET
ejpam-4323	64	10	array	array	NOUN
ejpam-4323	64	11	x	x	SYM
ejpam-4323	64	12	≡	≡	PROPN
ejpam-4323	64	13	{	{	PUNCT
ejpam-4323	64	14	{	{	PUNCT
ejpam-4323	64	15	xk	xk	PROPN
ejpam-4323	64	16	,	,	PUNCT
ejpam-4323	64	17	n	n	CCONJ
ejpam-4323	64	18	,	,	PUNCT
ejpam-4323	64	19	1	1	NUM
ejpam-4323	64	20	≤	≤	NUM
ejpam-4323	64	21	k	k	X
ejpam-4323	64	22	≤	≤	X
ejpam-4323	64	23	k(n	k(n	PROPN
ejpam-4323	64	24	)	)	PUNCT
ejpam-4323	64	25	}	}	PUNCT
ejpam-4323	64	26	,	,	PUNCT
ejpam-4323	64	27	n	n	X
ejpam-4323	64	28	≥	≥	NOUN
ejpam-4323	64	29	1	1	NUM
ejpam-4323	64	30	}	}	PUNCT
ejpam-4323	64	31	,	,	PUNCT
ejpam-4323	64	32	of	of	ADP
ejpam-4323	64	33	random	random	ADJ
ejpam-4323	64	34	variables	variable	NOUN
ejpam-4323	64	35	defined	define	VERB
ejpam-4323	64	36	in	in	ADP
ejpam-4323	64	37	the	the	DET
ejpam-4323	64	38	same	same	ADJ
ejpam-4323	64	39	probability	probability	NOUN
ejpam-4323	64	40	space	space	NOUN
ejpam-4323	64	41	(	(	PUNCT
ejpam-4323	64	42	ω	ω	NOUN
ejpam-4323	64	43	,	,	PUNCT
ejpam-4323	64	44	a	a	DET
ejpam-4323	64	45	,	,	PUNCT
ejpam-4323	64	46	p	p	NOUN
ejpam-4323	64	47	)	)	PUNCT
ejpam-4323	64	48	such	such	ADJ
ejpam-4323	64	49	that	that	SCONJ
ejpam-4323	64	50	here	here	ADV
ejpam-4323	64	51	:	:	PUNCT
ejpam-4323	64	52	1	1	X
ejpam-4323	64	53	)	)	PUNCT
ejpam-4323	64	54	∀n	∀n	NUM
ejpam-4323	64	55	≥	≥	NOUN
ejpam-4323	64	56	1	1	NUM
ejpam-4323	64	57	,	,	PUNCT
ejpam-4323	64	58	k(n	k(n	X
ejpam-4323	64	59	)	)	PUNCT
ejpam-4323	64	60	=	=	SYM
ejpam-4323	64	61	n	n	CCONJ
ejpam-4323	64	62	;	;	PUNCT
ejpam-4323	64	63	2	2	X
ejpam-4323	64	64	)	)	PUNCT
ejpam-4323	64	65	∀n	∀n	NUM
ejpam-4323	64	66	≥	≥	NOUN
ejpam-4323	64	67	1	1	NUM
ejpam-4323	64	68	,	,	PUNCT
ejpam-4323	64	69	the	the	DET
ejpam-4323	64	70	variables	variable	NOUN
ejpam-4323	64	71	x1,n	x1,n	PROPN
ejpam-4323	64	72	,	,	PUNCT
ejpam-4323	64	73	·	·	PUNCT
ejpam-4323	64	74	·	·	PUNCT
ejpam-4323	64	75	·	·	PUNCT
ejpam-4323	64	76	,	,	PUNCT
ejpam-4323	64	77	xk(n),n	xk(n),n	X
ejpam-4323	64	78	are	be	AUX
ejpam-4323	64	79	independent	independent	ADJ
ejpam-4323	64	80	;	;	PUNCT
ejpam-4323	64	81	3	3	X
ejpam-4323	64	82	)	)	PUNCT
ejpam-4323	64	83	the	the	DET
ejpam-4323	64	84	sequence	sequence	NOUN
ejpam-4323	64	85	x1,n	x1,n	PROPN
ejpam-4323	64	86	,	,	PUNCT
ejpam-4323	64	87	·	·	PUNCT
ejpam-4323	64	88	·	·	PUNCT
ejpam-4323	64	89	·	·	PUNCT
ejpam-4323	64	90	,	,	PUNCT
ejpam-4323	64	91	xk(n),n	xk(n),n	X
ejpam-4323	64	92	is	be	AUX
ejpam-4323	64	93	stationary	stationary	ADJ
ejpam-4323	64	94	for	for	ADP
ejpam-4323	64	95	n	n	X
ejpam-4323	64	96	≥	≥	NOUN
ejpam-4323	64	97	1	1	NUM
ejpam-4323	64	98	;	;	PUNCT
ejpam-4323	64	99	4	4	NUM
ejpam-4323	64	100	)	)	PUNCT
ejpam-4323	64	101	∀k	∀k	NOUN
ejpam-4323	64	102	∈	∈	PROPN
ejpam-4323	65	1	[	[	X
ejpam-4323	65	2	1	1	NUM
ejpam-4323	65	3	,	,	PUNCT
ejpam-4323	65	4	k(n	k(n	PROPN
ejpam-4323	65	5	)	)	PUNCT
ejpam-4323	65	6	]	]	PUNCT
ejpam-4323	65	7	,	,	PUNCT
ejpam-4323	65	8	xk	xk	PROPN
ejpam-4323	65	9	,	,	PUNCT
ejpam-4323	65	10	n	n	PRON
ejpam-4323	65	11	∼	∼	NOUN
ejpam-4323	65	12	b(pn	b(pn	NOUN
ejpam-4323	65	13	)	)	PUNCT
ejpam-4323	65	14	or	or	CCONJ
ejpam-4323	65	15	xk	xk	PROPN
ejpam-4323	65	16	,	,	PUNCT
ejpam-4323	65	17	n	n	PRON
ejpam-4323	65	18	∼	∼	NOUN
ejpam-4323	65	19	g(pn)−	g(pn)−	X
ejpam-4323	65	20	1	1	NUM
ejpam-4323	65	21	.	.	PUNCT
ejpam-4323	65	22	ab	ab	PROPN
ejpam-4323	65	23	niang	niang	PROPN
ejpam-4323	65	24	et	et	PROPN
ejpam-4323	65	25	al	al	PROPN
ejpam-4323	65	26	.	.	PUNCT
ejpam-4323	65	27	/	/	SYM
ejpam-4323	65	28	eur	eur	PROPN
ejpam-4323	65	29	.	.	PUNCT
ejpam-4323	66	1	j.	j.	PROPN
ejpam-4323	66	2	pure	pure	PROPN
ejpam-4323	66	3	appl	appl	PROPN
ejpam-4323	66	4	.	.	PROPN
ejpam-4323	66	5	math	math	PROPN
ejpam-4323	66	6	,	,	PUNCT
ejpam-4323	66	7	15	15	NUM
ejpam-4323	66	8	(	(	PUNCT
ejpam-4323	66	9	2	2	NUM
ejpam-4323	66	10	)	)	PUNCT
ejpam-4323	66	11	(	(	PUNCT
ejpam-4323	66	12	2022	2022	NUM
ejpam-4323	66	13	)	)	PUNCT
ejpam-4323	66	14	,	,	PUNCT
ejpam-4323	66	15	511	511	NUM
ejpam-4323	66	16	-	-	SYM
ejpam-4323	66	17	527	527	NUM
ejpam-4323	66	18	515	515	NUM
ejpam-4323	66	19	we	we	PRON
ejpam-4323	66	20	see	see	VERB
ejpam-4323	66	21	that	that	SCONJ
ejpam-4323	66	22	we	we	PRON
ejpam-4323	66	23	are	be	AUX
ejpam-4323	66	24	in	in	ADP
ejpam-4323	66	25	the	the	DET
ejpam-4323	66	26	clt	clt	NOUN
ejpam-4323	66	27	frame	frame	NOUN
ejpam-4323	66	28	and	and	CCONJ
ejpam-4323	66	29	each	each	PRON
ejpam-4323	66	30	of	of	ADP
ejpam-4323	66	31	points	point	NOUN
ejpam-4323	66	32	(	(	PUNCT
ejpam-4323	66	33	2	2	NUM
ejpam-4323	66	34	)	)	PUNCT
ejpam-4323	66	35	and	and	CCONJ
ejpam-4323	66	36	(	(	PUNCT
ejpam-4323	66	37	3	3	X
ejpam-4323	66	38	)	)	PUNCT
ejpam-4323	66	39	can	can	AUX
ejpam-4323	66	40	be	be	AUX
ejpam-4323	66	41	changed	change	VERB
ejpam-4323	66	42	to	to	PART
ejpam-4323	66	43	lead	lead	VERB
ejpam-4323	66	44	to	to	ADP
ejpam-4323	66	45	generalizations	generalization	NOUN
ejpam-4323	66	46	.	.	PUNCT
ejpam-4323	67	1	since	since	SCONJ
ejpam-4323	67	2	,	,	PUNCT
ejpam-4323	67	3	we	we	PRON
ejpam-4323	67	4	want	want	VERB
ejpam-4323	67	5	to	to	PART
ejpam-4323	67	6	generalize	generalize	VERB
ejpam-4323	67	7	the	the	DET
ejpam-4323	67	8	limiting	limit	VERB
ejpam-4323	67	9	binomial	binomial	ADJ
ejpam-4323	67	10	laws	law	NOUN
ejpam-4323	67	11	and	and	CCONJ
ejpam-4323	67	12	negative	negative	ADJ
ejpam-4323	67	13	binomial	binomial	ADJ
ejpam-4323	67	14	laws	law	NOUN
ejpam-4323	67	15	,	,	PUNCT
ejpam-4323	67	16	we	we	PRON
ejpam-4323	67	17	keep	keep	VERB
ejpam-4323	67	18	the	the	DET
ejpam-4323	67	19	same	same	ADJ
ejpam-4323	67	20	hypotheses	hypothesis	NOUN
ejpam-4323	67	21	on	on	ADP
ejpam-4323	67	22	the	the	DET
ejpam-4323	67	23	marginal	marginal	ADJ
ejpam-4323	67	24	laws	law	NOUN
ejpam-4323	67	25	∀k	∀k	X
ejpam-4323	67	26	∈	∈	PROPN
ejpam-4323	68	1	[	[	X
ejpam-4323	68	2	1	1	NUM
ejpam-4323	68	3	,	,	PUNCT
ejpam-4323	68	4	k(n	k(n	PROPN
ejpam-4323	68	5	)	)	PUNCT
ejpam-4323	68	6	]	]	PUNCT
ejpam-4323	68	7	,	,	PUNCT
ejpam-4323	68	8	xk	xk	PROPN
ejpam-4323	68	9	,	,	PUNCT
ejpam-4323	68	10	n	n	PRON
ejpam-4323	68	11	∼	∼	NOUN
ejpam-4323	68	12	b(pk	b(pk	NOUN
ejpam-4323	68	13	,	,	PUNCT
ejpam-4323	68	14	n	n	CCONJ
ejpam-4323	68	15	)	)	PUNCT
ejpam-4323	68	16	or	or	CCONJ
ejpam-4323	68	17	xk	xk	PROPN
ejpam-4323	68	18	,	,	PUNCT
ejpam-4323	68	19	n	n	PRON
ejpam-4323	68	20	∼	∼	NOUN
ejpam-4323	68	21	g(pk	g(pk	PROPN
ejpam-4323	68	22	,	,	PUNCT
ejpam-4323	68	23	n)−	n)−	PROPN
ejpam-4323	68	24	1	1	NUM
ejpam-4323	68	25	and	and	CCONJ
ejpam-4323	68	26	try	try	VERB
ejpam-4323	68	27	to	to	PART
ejpam-4323	68	28	answer	answer	VERB
ejpam-4323	68	29	to	to	ADP
ejpam-4323	68	30	the	the	DET
ejpam-4323	68	31	questions	question	NOUN
ejpam-4323	68	32	(	(	PUNCT
ejpam-4323	68	33	q1	q1	PROPN
ejpam-4323	68	34	)	)	PUNCT
ejpam-4323	68	35	and	and	CCONJ
ejpam-4323	68	36	(	(	PUNCT
ejpam-4323	68	37	q2	q2	NOUN
ejpam-4323	68	38	)	)	PUNCT
ejpam-4323	68	39	below	below	ADV
ejpam-4323	68	40	:	:	PUNCT
ejpam-4323	68	41	(	(	PUNCT
ejpam-4323	68	42	q1	q1	NOUN
ejpam-4323	68	43	)	)	PUNCT
ejpam-4323	68	44	given	give	VERB
ejpam-4323	68	45	an	an	DET
ejpam-4323	68	46	array	array	NOUN
ejpam-4323	68	47	x	x	PUNCT
ejpam-4323	68	48	of	of	ADP
ejpam-4323	68	49	random	random	ADJ
ejpam-4323	68	50	variables	variable	NOUN
ejpam-4323	68	51	with	with	ADP
ejpam-4323	68	52	k(n	k(n	PROPN
ejpam-4323	68	53	)	)	PUNCT
ejpam-4323	68	54	→	→	PUNCT
ejpam-4323	69	1	+	+	NUM
ejpam-4323	69	2	∞	∞	NUM
ejpam-4323	69	3	such	such	ADJ
ejpam-4323	69	4	that	that	SCONJ
ejpam-4323	69	5	the	the	DET
ejpam-4323	69	6	elements	element	NOUN
ejpam-4323	69	7	of	of	ADP
ejpam-4323	69	8	each	each	DET
ejpam-4323	69	9	row	row	NOUN
ejpam-4323	69	10	are	be	AUX
ejpam-4323	69	11	independent	independent	ADJ
ejpam-4323	69	12	and	and	CCONJ
ejpam-4323	69	13	b(pk	b(pk	NOUN
ejpam-4323	69	14	,	,	PUNCT
ejpam-4323	69	15	n)-r.v	n)-r.v	PROPN
ejpam-4323	69	16	’s	’s	PART
ejpam-4323	69	17	,	,	PUNCT
ejpam-4323	69	18	do	do	AUX
ejpam-4323	69	19	we	we	PRON
ejpam-4323	69	20	still	still	ADV
ejpam-4323	69	21	have	have	AUX
ejpam-4323	69	22	sn[x	sn[x	VERB
ejpam-4323	69	23	]	]	PUNCT
ejpam-4323	69	24	=	=	SYM
ejpam-4323	69	25	k(n)∑	k(n)∑	X
ejpam-4323	69	26	k=1	k=1	PROPN
ejpam-4323	70	1	xk	xk	PROPN
ejpam-4323	70	2	,	,	PUNCT
ejpam-4323	70	3	n	n	PRON
ejpam-4323	70	4	p(λ	p(λ	NOUN
ejpam-4323	70	5	)	)	PUNCT
ejpam-4323	70	6	,	,	PUNCT
ejpam-4323	70	7	(	(	PUNCT
ejpam-4323	70	8	1	1	X
ejpam-4323	70	9	)	)	PUNCT
ejpam-4323	70	10	when	when	SCONJ
ejpam-4323	70	11	some	some	PRON
ejpam-4323	70	12	of	of	ADP
ejpam-4323	70	13	the	the	DET
ejpam-4323	70	14	assumptions	assumption	NOUN
ejpam-4323	70	15	(	(	PUNCT
ejpam-4323	70	16	1	1	NUM
ejpam-4323	70	17	)	)	PUNCT
ejpam-4323	70	18	,	,	PUNCT
ejpam-4323	70	19	(	(	PUNCT
ejpam-4323	70	20	2	2	X
ejpam-4323	70	21	)	)	PUNCT
ejpam-4323	70	22	and	and	CCONJ
ejpam-4323	70	23	(	(	PUNCT
ejpam-4323	70	24	3	3	X
ejpam-4323	70	25	)	)	PUNCT
ejpam-4323	70	26	[	[	X
ejpam-4323	70	27	but	but	CCONJ
ejpam-4323	70	28	mainly	mainly	ADV
ejpam-4323	70	29	(	(	PUNCT
ejpam-4323	70	30	2	2	X
ejpam-4323	70	31	)	)	PUNCT
ejpam-4323	70	32	and	and	CCONJ
ejpam-4323	70	33	(	(	PUNCT
ejpam-4323	70	34	3	3	NUM
ejpam-4323	70	35	)	)	PUNCT
ejpam-4323	70	36	]	]	PUNCT
ejpam-4323	70	37	are	be	AUX
ejpam-4323	70	38	violated	violate	VERB
ejpam-4323	70	39	,	,	PUNCT
ejpam-4323	70	40	and	and	CCONJ
ejpam-4323	70	41	under	under	ADP
ejpam-4323	70	42	what	what	PRON
ejpam-4323	70	43	sufficient	sufficient	ADJ
ejpam-4323	70	44	conditions	condition	NOUN
ejpam-4323	70	45	this	this	PRON
ejpam-4323	70	46	should	should	AUX
ejpam-4323	70	47	hold	hold	VERB
ejpam-4323	70	48	?	?	PUNCT
ejpam-4323	71	1	(	(	PUNCT
ejpam-4323	71	2	q2	q2	NOUN
ejpam-4323	71	3	)	)	PUNCT
ejpam-4323	71	4	given	give	VERB
ejpam-4323	71	5	an	an	DET
ejpam-4323	71	6	array	array	NOUN
ejpam-4323	71	7	x	x	PUNCT
ejpam-4323	71	8	of	of	ADP
ejpam-4323	71	9	random	random	ADJ
ejpam-4323	71	10	variables	variable	NOUN
ejpam-4323	71	11	with	with	ADP
ejpam-4323	71	12	k(n	k(n	PROPN
ejpam-4323	71	13	)	)	PUNCT
ejpam-4323	71	14	→	→	PUNCT
ejpam-4323	72	1	+	+	NUM
ejpam-4323	72	2	∞	∞	NUM
ejpam-4323	72	3	such	such	ADJ
ejpam-4323	72	4	that	that	SCONJ
ejpam-4323	72	5	the	the	DET
ejpam-4323	72	6	elements	element	NOUN
ejpam-4323	72	7	of	of	ADP
ejpam-4323	72	8	each	each	DET
ejpam-4323	72	9	row	row	NOUN
ejpam-4323	72	10	are	be	AUX
ejpam-4323	72	11	independent	independent	ADJ
ejpam-4323	72	12	and	and	CCONJ
ejpam-4323	72	13	g∗(pk	g∗(pk	PROPN
ejpam-4323	72	14	,	,	PUNCT
ejpam-4323	72	15	n)-r.v	n)-r.v	PROPN
ejpam-4323	72	16	’s	’s	PART
ejpam-4323	72	17	,	,	PUNCT
ejpam-4323	72	18	do	do	AUX
ejpam-4323	72	19	we	we	PRON
ejpam-4323	72	20	still	still	ADV
ejpam-4323	72	21	have	have	VERB
ejpam-4323	72	22	(	(	PUNCT
ejpam-4323	72	23	1	1	X
ejpam-4323	72	24	)	)	PUNCT
ejpam-4323	72	25	when	when	SCONJ
ejpam-4323	72	26	some	some	PRON
ejpam-4323	72	27	of	of	ADP
ejpam-4323	72	28	the	the	DET
ejpam-4323	72	29	assumptions	assumption	NOUN
ejpam-4323	72	30	(	(	PUNCT
ejpam-4323	72	31	1	1	NUM
ejpam-4323	72	32	)	)	PUNCT
ejpam-4323	72	33	,	,	PUNCT
ejpam-4323	72	34	(	(	PUNCT
ejpam-4323	72	35	2	2	X
ejpam-4323	72	36	)	)	PUNCT
ejpam-4323	72	37	and	and	CCONJ
ejpam-4323	72	38	(	(	PUNCT
ejpam-4323	72	39	3	3	X
ejpam-4323	72	40	)	)	PUNCT
ejpam-4323	73	1	[	[	X
ejpam-4323	73	2	but	but	CCONJ
ejpam-4323	73	3	mainly	mainly	ADV
ejpam-4323	73	4	(	(	PUNCT
ejpam-4323	73	5	2	2	X
ejpam-4323	73	6	)	)	PUNCT
ejpam-4323	73	7	and	and	CCONJ
ejpam-4323	73	8	(	(	PUNCT
ejpam-4323	73	9	3	3	NUM
ejpam-4323	73	10	)	)	PUNCT
ejpam-4323	73	11	]	]	PUNCT
ejpam-4323	73	12	are	be	AUX
ejpam-4323	73	13	violated	violate	VERB
ejpam-4323	73	14	,	,	PUNCT
ejpam-4323	73	15	and	and	CCONJ
ejpam-4323	73	16	under	under	ADP
ejpam-4323	73	17	what	what	PRON
ejpam-4323	73	18	sufficient	sufficient	ADJ
ejpam-4323	73	19	conditions	condition	NOUN
ejpam-4323	73	20	this	this	PRON
ejpam-4323	73	21	should	should	AUX
ejpam-4323	73	22	hold	hold	VERB
ejpam-4323	73	23	?	?	PUNCT
ejpam-4323	74	1	although	although	SCONJ
ejpam-4323	74	2	direct	direct	ADJ
ejpam-4323	74	3	handlings	handling	NOUN
ejpam-4323	74	4	of	of	ADP
ejpam-4323	74	5	these	these	DET
ejpam-4323	74	6	questions	question	NOUN
ejpam-4323	74	7	might	might	AUX
ejpam-4323	74	8	be	be	AUX
ejpam-4323	74	9	possible	possible	ADJ
ejpam-4323	74	10	,	,	PUNCT
ejpam-4323	74	11	we	we	PRON
ejpam-4323	74	12	think	think	VERB
ejpam-4323	74	13	that	that	SCONJ
ejpam-4323	74	14	a	a	DET
ejpam-4323	74	15	general	general	ADJ
ejpam-4323	74	16	and	and	CCONJ
ejpam-4323	74	17	extensible	extensible	ADJ
ejpam-4323	74	18	solution	solution	NOUN
ejpam-4323	74	19	resides	reside	VERB
ejpam-4323	74	20	in	in	ADP
ejpam-4323	74	21	the	the	DET
ejpam-4323	74	22	clt	clt	NOUN
ejpam-4323	74	23	frame	frame	NOUN
ejpam-4323	74	24	,	,	PUNCT
ejpam-4323	74	25	since	since	SCONJ
ejpam-4323	74	26	it	it	PRON
ejpam-4323	74	27	will	will	AUX
ejpam-4323	74	28	prepare	prepare	VERB
ejpam-4323	74	29	further	further	ADJ
ejpam-4323	74	30	generalizations	generalization	NOUN
ejpam-4323	74	31	for	for	ADP
ejpam-4323	74	32	dependent	dependent	ADJ
ejpam-4323	74	33	data	datum	NOUN
ejpam-4323	74	34	.	.	PUNCT
ejpam-4323	75	1	therefore	therefore	ADV
ejpam-4323	75	2	,	,	PUNCT
ejpam-4323	75	3	we	we	PRON
ejpam-4323	75	4	organize	organize	VERB
ejpam-4323	75	5	the	the	DET
ejpam-4323	75	6	paper	paper	NOUN
ejpam-4323	75	7	as	as	SCONJ
ejpam-4323	75	8	follows	follow	VERB
ejpam-4323	75	9	.	.	PUNCT
ejpam-4323	76	1	in	in	ADP
ejpam-4323	76	2	section	section	NOUN
ejpam-4323	76	3	2	2	NUM
ejpam-4323	76	4	,	,	PUNCT
ejpam-4323	76	5	we	we	PRON
ejpam-4323	76	6	recall	recall	VERB
ejpam-4323	76	7	the	the	DET
ejpam-4323	76	8	frame	frame	NOUN
ejpam-4323	76	9	of	of	ADP
ejpam-4323	76	10	the	the	DET
ejpam-4323	76	11	clt	clt	PROPN
ejpam-4323	76	12	problem	problem	NOUN
ejpam-4323	76	13	as	as	SCONJ
ejpam-4323	76	14	stated	state	VERB
ejpam-4323	76	15	in	in	ADP
ejpam-4323	76	16	[	[	X
ejpam-4323	76	17	6	6	NUM
ejpam-4323	76	18	]	]	PUNCT
ejpam-4323	76	19	.	.	PUNCT
ejpam-4323	77	1	in	in	ADP
ejpam-4323	77	2	section	section	NOUN
ejpam-4323	77	3	3	3	NUM
ejpam-4323	77	4	,	,	PUNCT
ejpam-4323	77	5	we	we	PRON
ejpam-4323	77	6	state	state	VERB
ejpam-4323	77	7	and	and	CCONJ
ejpam-4323	77	8	prove	prove	VERB
ejpam-4323	77	9	the	the	DET
ejpam-4323	77	10	results	result	NOUN
ejpam-4323	77	11	.	.	PUNCT
ejpam-4323	78	1	we	we	PRON
ejpam-4323	78	2	conclude	conclude	VERB
ejpam-4323	78	3	the	the	DET
ejpam-4323	78	4	paper	paper	NOUN
ejpam-4323	78	5	by	by	ADP
ejpam-4323	78	6	conclusive	conclusive	ADJ
ejpam-4323	78	7	remarks	remark	NOUN
ejpam-4323	78	8	in	in	ADP
ejpam-4323	78	9	section	section	NOUN
ejpam-4323	78	10	4	4	NUM
ejpam-4323	78	11	.	.	NOUN
ejpam-4323	78	12	2	2	NUM
ejpam-4323	78	13	.	.	X
ejpam-4323	78	14	notation	notation	NOUN
ejpam-4323	78	15	and	and	CCONJ
ejpam-4323	78	16	g	g	NOUN
ejpam-4323	78	17	-	-	PUNCT
ejpam-4323	78	18	clt	clt	NOUN
ejpam-4323	78	19	for	for	ADP
ejpam-4323	78	20	summands	summand	NOUN
ejpam-4323	78	21	of	of	ADP
ejpam-4323	78	22	independent	independent	ADJ
ejpam-4323	78	23	random	random	ADJ
ejpam-4323	78	24	variables	variable	NOUN
ejpam-4323	78	25	let	let	VERB
ejpam-4323	78	26	us	we	PRON
ejpam-4323	78	27	consider	consider	VERB
ejpam-4323	78	28	the	the	DET
ejpam-4323	78	29	array	array	NOUN
ejpam-4323	78	30	x	x	SYM
ejpam-4323	78	31	≡	≡	PROPN
ejpam-4323	78	32	{	{	PUNCT
ejpam-4323	78	33	{	{	PUNCT
ejpam-4323	78	34	xk	xk	PROPN
ejpam-4323	78	35	,	,	PUNCT
ejpam-4323	78	36	n	n	CCONJ
ejpam-4323	78	37	,	,	PUNCT
ejpam-4323	78	38	1	1	NUM
ejpam-4323	78	39	≤	≤	NUM
ejpam-4323	78	40	k	k	X
ejpam-4323	78	41	≤	≤	PROPN
ejpam-4323	78	42	kn	kn	NOUN
ejpam-4323	78	43	=	=	PUNCT
ejpam-4323	78	44	k(n	k(n	PROPN
ejpam-4323	78	45	)	)	PUNCT
ejpam-4323	78	46	}	}	PUNCT
ejpam-4323	78	47	,	,	PUNCT
ejpam-4323	78	48	n	n	X
ejpam-4323	78	49	≥	≥	NOUN
ejpam-4323	78	50	1	1	NUM
ejpam-4323	78	51	}	}	PUNCT
ejpam-4323	78	52	,	,	PUNCT
ejpam-4323	78	53	of	of	ADP
ejpam-4323	78	54	square	square	ADJ
ejpam-4323	78	55	integrable	integrable	ADJ
ejpam-4323	78	56	random	random	ADJ
ejpam-4323	78	57	variables	variable	NOUN
ejpam-4323	78	58	defined	define	VERB
ejpam-4323	78	59	on	on	ADP
ejpam-4323	78	60	the	the	DET
ejpam-4323	78	61	same	same	ADJ
ejpam-4323	78	62	probability	probability	NOUN
ejpam-4323	78	63	space	space	NOUN
ejpam-4323	78	64	(	(	PUNCT
ejpam-4323	78	65	ω	ω	NOUN
ejpam-4323	78	66	,	,	PUNCT
ejpam-4323	78	67	a	a	DET
ejpam-4323	78	68	,	,	PUNCT
ejpam-4323	78	69	p	p	NOUN
ejpam-4323	78	70	)	)	PUNCT
ejpam-4323	78	71	.	.	PUNCT
ejpam-4323	79	1	we	we	PRON
ejpam-4323	79	2	denote	denote	VERB
ejpam-4323	79	3	fk	fk	PROPN
ejpam-4323	79	4	,	,	PUNCT
ejpam-4323	79	5	n	n	CCONJ
ejpam-4323	79	6	as	as	ADP
ejpam-4323	79	7	the	the	DET
ejpam-4323	79	8	cumulative	cumulative	ADJ
ejpam-4323	79	9	distribution	distribution	NOUN
ejpam-4323	79	10	function	function	NOUN
ejpam-4323	79	11	(	(	PUNCT
ejpam-4323	79	12	cdf	cdf	PROPN
ejpam-4323	79	13	)	)	PUNCT
ejpam-4323	79	14	of	of	ADP
ejpam-4323	79	15	xk	xk	PROPN
ejpam-4323	79	16	,	,	PUNCT
ejpam-4323	79	17	n.	n.	PROPN
ejpam-4323	79	18	we	we	PRON
ejpam-4323	79	19	also	also	ADV
ejpam-4323	79	20	denote	denote	VERB
ejpam-4323	79	21	by	by	ADP
ejpam-4323	79	22	ak	ak	PROPN
ejpam-4323	79	23	,	,	PUNCT
ejpam-4323	79	24	n	n	PROPN
ejpam-4323	79	25	=	=	SYM
ejpam-4323	79	26	e(xk	e(xk	PROPN
ejpam-4323	79	27	,	,	PUNCT
ejpam-4323	79	28	n	n	CCONJ
ejpam-4323	79	29	)	)	PUNCT
ejpam-4323	79	30	and	and	CCONJ
ejpam-4323	79	31	σ2k	σ2k	NOUN
ejpam-4323	79	32	,	,	PUNCT
ejpam-4323	79	33	n	n	NOUN
ejpam-4323	79	34	=	=	SYM
ejpam-4323	79	35	var(xk	var(xk	X
ejpam-4323	79	36	,	,	PUNCT
ejpam-4323	79	37	n	n	CCONJ
ejpam-4323	79	38	)	)	PUNCT
ejpam-4323	79	39	,	,	PUNCT
ejpam-4323	79	40	1	1	NUM
ejpam-4323	79	41	≤	≤	NUM
ejpam-4323	79	42	k	k	X
ejpam-4323	79	43	≤	≤	X
ejpam-4323	79	44	k(n	k(n	X
ejpam-4323	79	45	)	)	PUNCT
ejpam-4323	79	46	,	,	PUNCT
ejpam-4323	79	47	if	if	SCONJ
ejpam-4323	79	48	these	these	DET
ejpam-4323	79	49	expectations	expectation	NOUN
ejpam-4323	79	50	or	or	CCONJ
ejpam-4323	79	51	variances	variance	NOUN
ejpam-4323	79	52	exist	exist	VERB
ejpam-4323	79	53	.	.	PUNCT
ejpam-4323	80	1	we	we	PRON
ejpam-4323	80	2	also	also	ADV
ejpam-4323	80	3	suppose	suppose	VERB
ejpam-4323	80	4	that	that	SCONJ
ejpam-4323	80	5	ab	ab	PROPN
ejpam-4323	80	6	niang	niang	PROPN
ejpam-4323	80	7	et	et	PROPN
ejpam-4323	80	8	al	al	PROPN
ejpam-4323	80	9	.	.	PUNCT
ejpam-4323	80	10	/	/	SYM
ejpam-4323	80	11	eur	eur	PROPN
ejpam-4323	80	12	.	.	PUNCT
ejpam-4323	81	1	j.	j.	PROPN
ejpam-4323	81	2	pure	pure	PROPN
ejpam-4323	81	3	appl	appl	PROPN
ejpam-4323	81	4	.	.	PROPN
ejpam-4323	81	5	math	math	PROPN
ejpam-4323	81	6	,	,	PUNCT
ejpam-4323	81	7	15	15	NUM
ejpam-4323	81	8	(	(	PUNCT
ejpam-4323	81	9	2	2	NUM
ejpam-4323	81	10	)	)	PUNCT
ejpam-4323	81	11	(	(	PUNCT
ejpam-4323	81	12	2022	2022	NUM
ejpam-4323	81	13	)	)	PUNCT
ejpam-4323	81	14	,	,	PUNCT
ejpam-4323	81	15	511	511	NUM
ejpam-4323	81	16	-	-	SYM
ejpam-4323	81	17	527	527	NUM
ejpam-4323	81	18	516	516	NUM
ejpam-4323	81	19	k(n	k(n	NOUN
ejpam-4323	81	20	)	)	PUNCT
ejpam-4323	81	21	→	→	PUNCT
ejpam-4323	82	1	+	+	NUM
ejpam-4323	82	2	∞	∞	NUM
ejpam-4323	82	3	as	as	ADP
ejpam-4323	82	4	n→	n→	ADV
ejpam-4323	82	5	+	+	PROPN
ejpam-4323	82	6	∞.	∞.	PROPN
ejpam-4323	82	7	the	the	DET
ejpam-4323	82	8	central	central	ADJ
ejpam-4323	82	9	limit	limit	NOUN
ejpam-4323	82	10	theorem	theorem	VERB
ejpam-4323	82	11	problem	problem	NOUN
ejpam-4323	82	12	consists	consist	VERB
ejpam-4323	82	13	in	in	ADP
ejpam-4323	82	14	finding	find	VERB
ejpam-4323	82	15	,	,	PUNCT
ejpam-4323	82	16	whenever	whenever	SCONJ
ejpam-4323	82	17	possible	possible	ADJ
ejpam-4323	82	18	,	,	PUNCT
ejpam-4323	82	19	the	the	DET
ejpam-4323	82	20	weak	weak	ADJ
ejpam-4323	82	21	limit	limit	NOUN
ejpam-4323	82	22	law	law	NOUN
ejpam-4323	82	23	(	(	PUNCT
ejpam-4323	82	24	in	in	ADP
ejpam-4323	82	25	type	type	NOUN
ejpam-4323	82	26	)	)	PUNCT
ejpam-4323	82	27	of	of	ADP
ejpam-4323	82	28	the	the	DET
ejpam-4323	82	29	by	by	ADP
ejpam-4323	82	30	-	-	PUNCT
ejpam-4323	82	31	row	row	NOUN
ejpam-4323	82	32	sums	sum	NOUN
ejpam-4323	82	33	of	of	ADP
ejpam-4323	82	34	the	the	DET
ejpam-4323	82	35	array	array	NOUN
ejpam-4323	82	36	x	x	NOUN
ejpam-4323	82	37	,	,	PUNCT
ejpam-4323	82	38	i.e.	i.e.	X
ejpam-4323	82	39	the	the	DET
ejpam-4323	82	40	summands	summand	NOUN
ejpam-4323	82	41	:	:	PUNCT
ejpam-4323	82	42	sn[x	sn[x	PUNCT
ejpam-4323	82	43	]	]	X
ejpam-4323	82	44	=	=	PUNCT
ejpam-4323	82	45	k(n)∑	k(n)∑	X
ejpam-4323	82	46	k=1	k=1	PROPN
ejpam-4323	82	47	xk	xk	PROPN
ejpam-4323	82	48	,	,	PUNCT
ejpam-4323	82	49	n	n	CCONJ
ejpam-4323	82	50	,	,	PUNCT
ejpam-4323	82	51	n	n	PRON
ejpam-4323	82	52	≥	≥	NOUN
ejpam-4323	82	53	1	1	NUM
ejpam-4323	82	54	.	.	PUNCT
ejpam-4323	83	1	historically	historically	ADV
ejpam-4323	83	2	,	,	PUNCT
ejpam-4323	83	3	the	the	DET
ejpam-4323	83	4	clt	clt	NOUN
ejpam-4323	83	5	was	be	AUX
ejpam-4323	83	6	discovered	discover	VERB
ejpam-4323	83	7	with	with	ADP
ejpam-4323	83	8	the	the	DET
ejpam-4323	83	9	convergence	convergence	NOUN
ejpam-4323	83	10	of	of	ADP
ejpam-4323	83	11	a	a	DET
ejpam-4323	83	12	binomial	binomial	ADJ
ejpam-4323	83	13	law	law	NOUN
ejpam-4323	83	14	(	(	PUNCT
ejpam-4323	83	15	which	which	PRON
ejpam-4323	83	16	has	have	VERB
ejpam-4323	83	17	the	the	DET
ejpam-4323	83	18	same	same	ADJ
ejpam-4323	83	19	law	law	NOUN
ejpam-4323	83	20	as	as	ADP
ejpam-4323	83	21	a	a	DET
ejpam-4323	83	22	sum	sum	NOUN
ejpam-4323	83	23	of	of	ADP
ejpam-4323	83	24	iid	iid	NOUN
ejpam-4323	83	25	bernoulli	bernoulli	NOUN
ejpam-4323	83	26	random	random	ADJ
ejpam-4323	83	27	variables	variable	NOUN
ejpam-4323	83	28	)	)	PUNCT
ejpam-4323	83	29	to	to	ADP
ejpam-4323	83	30	the	the	DET
ejpam-4323	83	31	standard	standard	ADJ
ejpam-4323	83	32	gaussian	gaussian	ADJ
ejpam-4323	83	33	law	law	NOUN
ejpam-4323	83	34	(	(	PUNCT
ejpam-4323	83	35	due	due	ADP
ejpam-4323	83	36	to	to	ADP
ejpam-4323	83	37	laplace	laplace	NOUN
ejpam-4323	83	38	,	,	PUNCT
ejpam-4323	83	39	de	de	ADP
ejpam-4323	83	40	moivre	moivre	NOUN
ejpam-4323	83	41	,	,	PUNCT
ejpam-4323	83	42	etc	etc	X
ejpam-4323	83	43	.	.	X
ejpam-4323	83	44	,	,	PUNCT
ejpam-4323	83	45	around	around	ADP
ejpam-4323	83	46	1731	1731	NUM
ejpam-4323	83	47	,	,	PUNCT
ejpam-4323	83	48	see	see	VERB
ejpam-4323	83	49	[	[	X
ejpam-4323	83	50	6	6	X
ejpam-4323	83	51	]	]	PUNCT
ejpam-4323	83	52	for	for	ADP
ejpam-4323	83	53	a	a	DET
ejpam-4323	83	54	review	review	NOUN
ejpam-4323	83	55	)	)	PUNCT
ejpam-4323	83	56	.	.	PUNCT
ejpam-4323	84	1	for	for	ADP
ejpam-4323	84	2	a	a	DET
ejpam-4323	84	3	long	long	ADJ
ejpam-4323	84	4	period	period	NOUN
ejpam-4323	84	5	,	,	PUNCT
ejpam-4323	84	6	the	the	DET
ejpam-4323	84	7	gaussian	gaussian	ADJ
ejpam-4323	84	8	limit	limit	NOUN
ejpam-4323	84	9	was	be	AUX
ejpam-4323	84	10	automatically	automatically	ADV
ejpam-4323	84	11	meant	mean	VERB
ejpam-4323	84	12	in	in	ADP
ejpam-4323	84	13	the	the	DET
ejpam-4323	84	14	clt	clt	PROPN
ejpam-4323	84	15	problem	problem	NOUN
ejpam-4323	84	16	.	.	PUNCT
ejpam-4323	85	1	many	many	ADJ
ejpam-4323	85	2	authors	author	NOUN
ejpam-4323	85	3	,	,	PUNCT
ejpam-4323	85	4	among	among	ADP
ejpam-4323	85	5	them	they	PRON
ejpam-4323	85	6	lévy	lévy	ADJ
ejpam-4323	85	7	,	,	PUNCT
ejpam-4323	85	8	gnedenko	gnedenko	PROPN
ejpam-4323	85	9	,	,	PUNCT
ejpam-4323	85	10	kolmogorov	kolmogorov	PROPN
ejpam-4323	85	11	,	,	PUNCT
ejpam-4323	85	12	etc	etc	X
ejpam-4323	85	13	.	.	X
ejpam-4323	85	14	,	,	PUNCT
ejpam-4323	85	15	characterized	characterize	VERB
ejpam-4323	85	16	the	the	DET
ejpam-4323	85	17	class	class	NOUN
ejpam-4323	85	18	of	of	ADP
ejpam-4323	85	19	possible	possible	ADJ
ejpam-4323	85	20	limit	limit	NOUN
ejpam-4323	85	21	laws	law	NOUN
ejpam-4323	85	22	under	under	ADP
ejpam-4323	85	23	the	the	DET
ejpam-4323	85	24	uniform	uniform	ADJ
ejpam-4323	85	25	asymptotic	asymptotic	ADJ
ejpam-4323	85	26	negligibility	negligibility	NOUN
ejpam-4323	85	27	(	(	PUNCT
ejpam-4323	85	28	uan	uan	PROPN
ejpam-4323	85	29	)	)	PUNCT
ejpam-4323	85	30	condition	condition	NOUN
ejpam-4323	85	31	,	,	PUNCT
ejpam-4323	85	32	exactly	exactly	ADV
ejpam-4323	85	33	as	as	ADP
ejpam-4323	85	34	the	the	DET
ejpam-4323	85	35	class	class	NOUN
ejpam-4323	85	36	of	of	ADP
ejpam-4323	85	37	infinitely	infinitely	ADV
ejpam-4323	85	38	decomposable	decomposable	ADJ
ejpam-4323	85	39	distributions	distribution	NOUN
ejpam-4323	85	40	.	.	PUNCT
ejpam-4323	86	1	the	the	DET
ejpam-4323	86	2	longtime	longtime	PROPN
ejpam-4323	86	3	association	association	NOUN
ejpam-4323	86	4	of	of	ADP
ejpam-4323	86	5	clt	clt	PROPN
ejpam-4323	86	6	’s	’s	ADV
ejpam-4323	86	7	with	with	ADP
ejpam-4323	86	8	gaussian	gaussian	ADJ
ejpam-4323	86	9	limits	limit	NOUN
ejpam-4323	86	10	explains	explain	VERB
ejpam-4323	86	11	that	that	SCONJ
ejpam-4323	86	12	some	some	DET
ejpam-4323	86	13	authors	author	NOUN
ejpam-4323	86	14	reserve	reserve	VERB
ejpam-4323	86	15	the	the	DET
ejpam-4323	86	16	vocable	vocable	ADJ
ejpam-4323	86	17	clt	clt	NOUN
ejpam-4323	86	18	for	for	ADP
ejpam-4323	86	19	gaussian	gaussian	ADJ
ejpam-4323	86	20	limits	limit	NOUN
ejpam-4323	86	21	and	and	CCONJ
ejpam-4323	86	22	for	for	ADP
ejpam-4323	86	23	other	other	ADJ
ejpam-4323	86	24	possible	possible	ADJ
ejpam-4323	86	25	limits	limit	NOUN
ejpam-4323	86	26	,	,	PUNCT
ejpam-4323	86	27	they	they	PRON
ejpam-4323	86	28	use	use	VERB
ejpam-4323	86	29	different	different	ADJ
ejpam-4323	86	30	vocables	vocable	NOUN
ejpam-4323	86	31	.	.	PUNCT
ejpam-4323	87	1	here	here	ADV
ejpam-4323	87	2	we	we	PRON
ejpam-4323	87	3	use	use	VERB
ejpam-4323	87	4	the	the	DET
ejpam-4323	87	5	vocable	vocable	NOUN
ejpam-4323	87	6	of	of	ADP
ejpam-4323	87	7	g	g	NOUN
ejpam-4323	87	8	-	-	PUNCT
ejpam-4323	87	9	clt	clt	NOUN
ejpam-4323	87	10	to	to	PART
ejpam-4323	87	11	cover	cover	VERB
ejpam-4323	87	12	all	all	DET
ejpam-4323	87	13	possible	possible	ADJ
ejpam-4323	87	14	limit	limit	NOUN
ejpam-4323	87	15	laws	law	NOUN
ejpam-4323	87	16	g	g	NOUN
ejpam-4323	87	17	beyond	beyond	ADP
ejpam-4323	87	18	the	the	DET
ejpam-4323	87	19	gaussian	gaussian	ADJ
ejpam-4323	87	20	law	law	NOUN
ejpam-4323	87	21	.	.	PUNCT
ejpam-4323	88	1	here	here	ADV
ejpam-4323	88	2	we	we	PRON
ejpam-4323	88	3	suppose	suppose	VERB
ejpam-4323	88	4	that	that	SCONJ
ejpam-4323	88	5	the	the	DET
ejpam-4323	88	6	xk	xk	PROPN
ejpam-4323	88	7	,	,	PUNCT
ejpam-4323	88	8	n	n	CCONJ
ejpam-4323	88	9	’s	’	VERB
ejpam-4323	88	10	are	be	AUX
ejpam-4323	88	11	integrable	integrable	ADJ
ejpam-4323	88	12	with	with	ADP
ejpam-4323	88	13	finite	finite	ADJ
ejpam-4323	88	14	variances	variance	NOUN
ejpam-4323	88	15	.	.	PUNCT
ejpam-4323	89	1	for	for	ADP
ejpam-4323	89	2	an	an	DET
ejpam-4323	89	3	array	array	NOUN
ejpam-4323	89	4	x	x	X
ejpam-4323	89	5	,	,	PUNCT
ejpam-4323	89	6	we	we	PRON
ejpam-4323	89	7	define	define	VERB
ejpam-4323	89	8	some	some	DET
ejpam-4323	89	9	important	important	ADJ
ejpam-4323	89	10	hypotheses	hypothesis	NOUN
ejpam-4323	89	11	used	use	VERB
ejpam-4323	89	12	in	in	ADP
ejpam-4323	89	13	the	the	DET
ejpam-4323	89	14	formulation	formulation	NOUN
ejpam-4323	89	15	of	of	ADP
ejpam-4323	89	16	the	the	DET
ejpam-4323	89	17	clt	clt	PROPN
ejpam-4323	89	18	problem	problem	NOUN
ejpam-4323	89	19	.	.	PUNCT
ejpam-4323	90	1	(	(	PUNCT
ejpam-4323	90	2	1	1	X
ejpam-4323	90	3	)	)	PUNCT
ejpam-4323	90	4	the	the	DET
ejpam-4323	90	5	uan	uan	PROPN
ejpam-4323	90	6	condition	condition	NOUN
ejpam-4323	90	7	:	:	PUNCT
ejpam-4323	90	8	for	for	ADP
ejpam-4323	90	9	any	any	DET
ejpam-4323	90	10	ε	ε	PROPN
ejpam-4323	90	11	>	>	X
ejpam-4323	90	12	0	0	PROPN
ejpam-4323	90	13	,	,	PUNCT
ejpam-4323	90	14	u(n	u(n	PROPN
ejpam-4323	90	15	,	,	PUNCT
ejpam-4323	90	16	ε	ε	PROPN
ejpam-4323	90	17	,	,	PUNCT
ejpam-4323	90	18	x	x	NOUN
ejpam-4323	90	19	)	)	PUNCT
ejpam-4323	90	20	=	=	SYM
ejpam-4323	90	21	sup	sup	NOUN
ejpam-4323	90	22	1≤k≤kn	1≤k≤kn	NUM
ejpam-4323	90	23	p(|xk	p(|xk	NUM
ejpam-4323	90	24	,	,	PUNCT
ejpam-4323	90	25	n	n	CCONJ
ejpam-4323	90	26	−	−	PROPN
ejpam-4323	90	27	ak	ak	PROPN
ejpam-4323	90	28	,	,	PUNCT
ejpam-4323	90	29	n|	n|	X
ejpam-4323	90	30	≥	≥	NOUN
ejpam-4323	90	31	ε	ε	NOUN
ejpam-4323	90	32	)	)	PUNCT
ejpam-4323	90	33	→	→	SYM
ejpam-4323	90	34	0	0	X
ejpam-4323	90	35	.	.	PUNCT
ejpam-4323	91	1	(	(	PUNCT
ejpam-4323	91	2	2	2	NUM
ejpam-4323	91	3	)	)	PUNCT
ejpam-4323	91	4	(	(	PUNCT
ejpam-4323	91	5	2	2	X
ejpam-4323	91	6	)	)	PUNCT
ejpam-4323	91	7	the	the	DET
ejpam-4323	91	8	bounded	bounded	ADJ
ejpam-4323	91	9	variance	variance	NOUN
ejpam-4323	91	10	hypothesis	hypothesis	NOUN
ejpam-4323	91	11	(	(	PUNCT
ejpam-4323	91	12	bvh	bvh	NOUN
ejpam-4323	91	13	):	):	PUNCT
ejpam-4323	91	14	there	there	PRON
ejpam-4323	91	15	exists	exist	VERB
ejpam-4323	91	16	a	a	DET
ejpam-4323	91	17	constant	constant	ADJ
ejpam-4323	91	18	c	c	NOUN
ejpam-4323	91	19	>	>	X
ejpam-4323	91	20	0	0	PROPN
ejpam-4323	91	21	,	,	PUNCT
ejpam-4323	91	22	such	such	ADJ
ejpam-4323	91	23	that	that	DET
ejpam-4323	91	24	sup	sup	PROPN
ejpam-4323	91	25	n≥1	n≥1	PROPN
ejpam-4323	91	26	mv	mv	PROPN
ejpam-4323	91	27	(	(	PUNCT
ejpam-4323	91	28	n	n	CCONJ
ejpam-4323	91	29	,	,	PUNCT
ejpam-4323	91	30	x	x	NOUN
ejpam-4323	91	31	)	)	PUNCT
ejpam-4323	91	32	≤	≤	NOUN
ejpam-4323	92	1	c	c	NOUN
ejpam-4323	92	2	,	,	PUNCT
ejpam-4323	92	3	where	where	SCONJ
ejpam-4323	92	4	mv	mv	PROPN
ejpam-4323	92	5	(	(	PUNCT
ejpam-4323	92	6	n	n	CCONJ
ejpam-4323	92	7	,	,	PUNCT
ejpam-4323	92	8	x	x	NOUN
ejpam-4323	92	9	)	)	PUNCT
ejpam-4323	92	10	=	=	SYM
ejpam-4323	92	11	var(sn[x	var(sn[x	NOUN
ejpam-4323	92	12	]	]	X
ejpam-4323	92	13	)	)	PUNCT
ejpam-4323	92	14	,	,	PUNCT
ejpam-4323	92	15	n	n	X
ejpam-4323	92	16	≥	≥	NOUN
ejpam-4323	92	17	1	1	NUM
ejpam-4323	92	18	.	.	PUNCT
ejpam-4323	93	1	(	(	PUNCT
ejpam-4323	93	2	3	3	X
ejpam-4323	93	3	)	)	PUNCT
ejpam-4323	93	4	the	the	DET
ejpam-4323	93	5	variance	variance	NOUN
ejpam-4323	93	6	convergence	convergence	NOUN
ejpam-4323	93	7	hypothesis	hypothesis	NOUN
ejpam-4323	93	8	(	(	PUNCT
ejpam-4323	93	9	vch	vch	PROPN
ejpam-4323	93	10	):	):	PUNCT
ejpam-4323	93	11	mv	mv	PROPN
ejpam-4323	93	12	(	(	PUNCT
ejpam-4323	93	13	n	n	CCONJ
ejpam-4323	93	14	,	,	PUNCT
ejpam-4323	93	15	x	x	NOUN
ejpam-4323	93	16	)	)	PUNCT
ejpam-4323	93	17	→	→	SYM
ejpam-4323	93	18	c	c	NOUN
ejpam-4323	93	19	∈]0,+∞	∈]0,+∞	PUNCT
ejpam-4323	93	20	[	[	X
ejpam-4323	93	21	.	.	PUNCT
ejpam-4323	94	1	ab	ab	PROPN
ejpam-4323	94	2	niang	niang	PROPN
ejpam-4323	94	3	et	et	PROPN
ejpam-4323	94	4	al	al	PROPN
ejpam-4323	94	5	.	.	PUNCT
ejpam-4323	94	6	/	/	SYM
ejpam-4323	94	7	eur	eur	PROPN
ejpam-4323	94	8	.	.	PUNCT
ejpam-4323	95	1	j.	j.	PROPN
ejpam-4323	95	2	pure	pure	PROPN
ejpam-4323	95	3	appl	appl	PROPN
ejpam-4323	95	4	.	.	PROPN
ejpam-4323	95	5	math	math	PROPN
ejpam-4323	95	6	,	,	PUNCT
ejpam-4323	95	7	15	15	NUM
ejpam-4323	95	8	(	(	PUNCT
ejpam-4323	95	9	2	2	NUM
ejpam-4323	95	10	)	)	PUNCT
ejpam-4323	95	11	(	(	PUNCT
ejpam-4323	95	12	2022	2022	NUM
ejpam-4323	95	13	)	)	PUNCT
ejpam-4323	95	14	,	,	PUNCT
ejpam-4323	95	15	511	511	NUM
ejpam-4323	95	16	-	-	SYM
ejpam-4323	95	17	527	527	NUM
ejpam-4323	95	18	517	517	NUM
ejpam-4323	95	19	according	accord	VERB
ejpam-4323	95	20	to	to	ADP
ejpam-4323	95	21	the	the	DET
ejpam-4323	95	22	state	state	NOUN
ejpam-4323	95	23	of	of	ADP
ejpam-4323	95	24	the	the	DET
ejpam-4323	95	25	art	art	NOUN
ejpam-4323	95	26	in	in	ADP
ejpam-4323	95	27	clt	clt	PROPN
ejpam-4323	95	28	’s	’s	PART
ejpam-4323	95	29	theory	theory	NOUN
ejpam-4323	95	30	for	for	ADP
ejpam-4323	95	31	centered	center	VERB
ejpam-4323	95	32	,	,	PUNCT
ejpam-4323	95	33	square	square	ADJ
ejpam-4323	95	34	integrable	integrable	ADJ
ejpam-4323	95	35	and	and	CCONJ
ejpam-4323	95	36	independent	independent	ADJ
ejpam-4323	95	37	by	by	ADP
ejpam-4323	95	38	-	-	PUNCT
ejpam-4323	95	39	row	row	NOUN
ejpam-4323	95	40	arrays	array	NOUN
ejpam-4323	95	41	of	of	ADP
ejpam-4323	95	42	random	random	ADJ
ejpam-4323	95	43	variables	variable	NOUN
ejpam-4323	95	44	,	,	PUNCT
ejpam-4323	95	45	the	the	DET
ejpam-4323	95	46	summands	summand	NOUN
ejpam-4323	95	47	weakly	weakly	ADJ
ejpam-4323	95	48	converge	converge	NOUN
ejpam-4323	95	49	to	to	ADP
ejpam-4323	95	50	a	a	DET
ejpam-4323	95	51	probability	probability	NOUN
ejpam-4323	95	52	law	law	NOUN
ejpam-4323	95	53	associated	associate	VERB
ejpam-4323	95	54	to	to	ADP
ejpam-4323	95	55	the	the	DET
ejpam-4323	95	56	cdf	cdf	PROPN
ejpam-4323	95	57	g	g	NOUN
ejpam-4323	95	58	and	and	CCONJ
ejpam-4323	95	59	to	to	ADP
ejpam-4323	95	60	the	the	DET
ejpam-4323	95	61	characteristic	characteristic	ADJ
ejpam-4323	95	62	function	function	NOUN
ejpam-4323	95	63	(	(	PUNCT
ejpam-4323	95	64	cha.f	cha.f	PROPN
ejpam-4323	95	65	)	)	PUNCT
ejpam-4323	95	66	ψg	ψg	PROPN
ejpam-4323	95	67	under	under	ADP
ejpam-4323	95	68	the	the	DET
ejpam-4323	95	69	uan	uan	PROPN
ejpam-4323	95	70	condition	condition	NOUN
ejpam-4323	95	71	and	and	CCONJ
ejpam-4323	95	72	the	the	DET
ejpam-4323	95	73	bvh	bvh	NOUN
ejpam-4323	95	74	if	if	SCONJ
ejpam-4323	95	75	and	and	CCONJ
ejpam-4323	95	76	only	only	ADV
ejpam-4323	95	77	if	if	SCONJ
ejpam-4323	95	78	the	the	DET
ejpam-4323	95	79	sequence	sequence	NOUN
ejpam-4323	95	80	of	of	ADP
ejpam-4323	95	81	distribution	distribution	NOUN
ejpam-4323	95	82	functions	function	NOUN
ejpam-4323	95	83	(	(	PUNCT
ejpam-4323	95	84	df	df	PROPN
ejpam-4323	95	85	)	)	PUNCT
ejpam-4323	95	86	kn(x	kn(x	X
ejpam-4323	95	87	)	)	PUNCT
ejpam-4323	96	1	=	=	PUNCT
ejpam-4323	96	2	k(n)∑	k(n)∑	VERB
ejpam-4323	97	1	k=1	k=1	X
ejpam-4323	97	2	∫	∫	PROPN
ejpam-4323	97	3	x	x	PROPN
ejpam-4323	98	1	−∞	−∞	ADP
ejpam-4323	98	2	y2dfk	y2dfk	PROPN
ejpam-4323	98	3	,	,	PUNCT
ejpam-4323	98	4	n(y	n(y	PROPN
ejpam-4323	98	5	)	)	PUNCT
ejpam-4323	98	6	,	,	PUNCT
ejpam-4323	98	7	x	x	PUNCT
ejpam-4323	98	8	∈	∈	PROPN
ejpam-4323	98	9	r	r	NOUN
ejpam-4323	98	10	,	,	PUNCT
ejpam-4323	98	11	n	n	PRON
ejpam-4323	98	12	≥	≥	NOUN
ejpam-4323	98	13	1	1	NUM
ejpam-4323	98	14	,	,	PUNCT
ejpam-4323	98	15	pre	pre	ADJ
ejpam-4323	98	16	-	-	ADJ
ejpam-4323	98	17	weakly	weakly	ADJ
ejpam-4323	98	18	converges	converge	VERB
ejpam-4323	98	19	to	to	ADP
ejpam-4323	98	20	a	a	DET
ejpam-4323	98	21	df	df	PROPN
ejpam-4323	98	22	k	k	NOUN
ejpam-4323	98	23	,	,	PUNCT
ejpam-4323	98	24	denoted	denote	VERB
ejpam-4323	98	25	kn	kn	PROPN
ejpam-4323	98	26	pre	pre	X
ejpam-4323	98	27	k	k	PROPN
ejpam-4323	98	28	,	,	PUNCT
ejpam-4323	98	29	that	that	PRON
ejpam-4323	98	30	is	be	AUX
ejpam-4323	98	31	for	for	ADP
ejpam-4323	98	32	any	any	DET
ejpam-4323	98	33	continuity	continuity	NOUN
ejpam-4323	98	34	point	point	NOUN
ejpam-4323	98	35	x	x	PUNCT
ejpam-4323	98	36	of	of	ADP
ejpam-4323	98	37	k	k	PROPN
ejpam-4323	98	38	denoted	denote	VERB
ejpam-4323	98	39	as	as	ADP
ejpam-4323	98	40	[	[	X
ejpam-4323	98	41	x	x	X
ejpam-4323	98	42	∈	∈	PROPN
ejpam-4323	98	43	c(k	c(k	NOUN
ejpam-4323	98	44	)	)	PUNCT
ejpam-4323	98	45	]	]	PUNCT
ejpam-4323	98	46	,	,	PUNCT
ejpam-4323	98	47	we	we	PRON
ejpam-4323	98	48	have	have	VERB
ejpam-4323	98	49	kn(x	kn(x	X
ejpam-4323	98	50	)	)	PUNCT
ejpam-4323	98	51	→	→	SYM
ejpam-4323	98	52	k(x	k(x	PROPN
ejpam-4323	98	53	)	)	PUNCT
ejpam-4323	98	54	,	,	PUNCT
ejpam-4323	98	55	and	and	CCONJ
ejpam-4323	98	56	the	the	DET
ejpam-4323	98	57	cha.f	cha.f	PROPN
ejpam-4323	98	58	ψg	ψg	PROPN
ejpam-4323	98	59	(	(	PUNCT
ejpam-4323	98	60	◦	◦	NOUN
ejpam-4323	98	61	)	)	PUNCT
ejpam-4323	98	62	of	of	ADP
ejpam-4323	98	63	g	g	PROPN
ejpam-4323	98	64	is	be	AUX
ejpam-4323	98	65	given	give	VERB
ejpam-4323	98	66	by	by	ADP
ejpam-4323	98	67	exp(ψ[k	exp(ψ[k	NOUN
ejpam-4323	98	68	]	]	SYM
ejpam-4323	98	69	(	(	PUNCT
ejpam-4323	98	70	◦	◦	NOUN
ejpam-4323	98	71	)	)	PUNCT
ejpam-4323	98	72	)	)	PUNCT
ejpam-4323	98	73	with	with	ADP
ejpam-4323	98	74	∀u	∀u	NOUN
ejpam-4323	98	75	∈	∈	NOUN
ejpam-4323	98	76	r	r	NOUN
ejpam-4323	98	77	,	,	PUNCT
ejpam-4323	98	78	ψ[k](u	ψ[k](u	PROPN
ejpam-4323	98	79	)	)	PUNCT
ejpam-4323	99	1	=	=	SYM
ejpam-4323	99	2	∫	∫	PROPN
ejpam-4323	100	1	eiux	eiux	INTJ
ejpam-4323	101	1	−	−	PROPN
ejpam-4323	101	2	1−	1−	NUM
ejpam-4323	102	1	iux	iux	INTJ
ejpam-4323	102	2	x2	x2	PROPN
ejpam-4323	102	3	dk(x	dk(x	PRON
ejpam-4323	102	4	)	)	PUNCT
ejpam-4323	102	5	.	.	PUNCT
ejpam-4323	103	1	if	if	SCONJ
ejpam-4323	103	2	we	we	PRON
ejpam-4323	103	3	have	have	VERB
ejpam-4323	103	4	the	the	DET
ejpam-4323	103	5	vch	vch	PROPN
ejpam-4323	103	6	,	,	PUNCT
ejpam-4323	103	7	the	the	DET
ejpam-4323	103	8	convergence	convergence	NOUN
ejpam-4323	103	9	criterion	criterion	NOUN
ejpam-4323	103	10	is	be	AUX
ejpam-4323	103	11	replaced	replace	VERB
ejpam-4323	103	12	by	by	ADP
ejpam-4323	103	13	the	the	DET
ejpam-4323	103	14	weak	weak	ADJ
ejpam-4323	103	15	convergence	convergence	NOUN
ejpam-4323	103	16	kn	kn	PROPN
ejpam-4323	103	17	k.	k.	PROPN
ejpam-4323	104	1	moreover	moreover	ADV
ejpam-4323	104	2	,	,	PUNCT
ejpam-4323	104	3	the	the	DET
ejpam-4323	104	4	limit	limit	NOUN
ejpam-4323	104	5	law	law	NOUN
ejpam-4323	104	6	g	g	PROPN
ejpam-4323	104	7	is	be	AUX
ejpam-4323	104	8	necessarily	necessarily	ADV
ejpam-4323	104	9	an	an	DET
ejpam-4323	104	10	infinitely	infinitely	ADV
ejpam-4323	104	11	decomposable	decomposable	ADJ
ejpam-4323	104	12	law	law	NOUN
ejpam-4323	104	13	.	.	PUNCT
ejpam-4323	105	1	in	in	ADP
ejpam-4323	105	2	the	the	DET
ejpam-4323	105	3	non	non	NOUN
ejpam-4323	105	4	centered	center	VERB
ejpam-4323	105	5	case	case	NOUN
ejpam-4323	105	6	,	,	PUNCT
ejpam-4323	105	7	with	with	ADP
ejpam-4323	105	8	the	the	DET
ejpam-4323	105	9	same	same	ADJ
ejpam-4323	105	10	hypotheses	hypothesis	NOUN
ejpam-4323	105	11	above	above	ADV
ejpam-4323	105	12	on	on	ADP
ejpam-4323	105	13	the	the	DET
ejpam-4323	105	14	random	random	ADJ
ejpam-4323	105	15	variables	variable	NOUN
ejpam-4323	105	16	of	of	ADP
ejpam-4323	105	17	the	the	DET
ejpam-4323	105	18	array	array	NOUN
ejpam-4323	105	19	,	,	PUNCT
ejpam-4323	105	20	the	the	DET
ejpam-4323	105	21	summands	summand	NOUN
ejpam-4323	105	22	weakly	weakly	ADJ
ejpam-4323	105	23	converge	converge	NOUN
ejpam-4323	105	24	to	to	ADP
ejpam-4323	105	25	a	a	DET
ejpam-4323	105	26	probability	probability	NOUN
ejpam-4323	105	27	law	law	NOUN
ejpam-4323	105	28	associated	associate	VERB
ejpam-4323	105	29	to	to	ADP
ejpam-4323	105	30	the	the	DET
ejpam-4323	105	31	cdf	cdf	PROPN
ejpam-4323	105	32	g∗	g∗	NOUN
ejpam-4323	105	33	and	and	CCONJ
ejpam-4323	105	34	to	to	ADP
ejpam-4323	105	35	the	the	DET
ejpam-4323	105	36	cha.f	cha.f	PROPN
ejpam-4323	105	37	ψg∗	ψg∗	PUNCT
ejpam-4323	105	38	under	under	ADP
ejpam-4323	105	39	the	the	DET
ejpam-4323	105	40	uan	uan	PROPN
ejpam-4323	105	41	condition	condition	NOUN
ejpam-4323	105	42	and	and	CCONJ
ejpam-4323	105	43	the	the	DET
ejpam-4323	105	44	bvh	bvh	NOUN
ejpam-4323	105	45	if	if	SCONJ
ejpam-4323	105	46	and	and	CCONJ
ejpam-4323	105	47	only	only	ADV
ejpam-4323	105	48	if	if	SCONJ
ejpam-4323	105	49	k(n)∑	k(n)∑	PROPN
ejpam-4323	105	50	k=1	k=1	PROPN
ejpam-4323	105	51	ak	ak	PROPN
ejpam-4323	105	52	,	,	PUNCT
ejpam-4323	105	53	n	n	PROPN
ejpam-4323	105	54	→	→	SYM
ejpam-4323	105	55	a	a	X
ejpam-4323	105	56	,	,	PUNCT
ejpam-4323	105	57	a	a	DET
ejpam-4323	105	58	∈	∈	NOUN
ejpam-4323	105	59	r	r	NOUN
ejpam-4323	105	60	and	and	CCONJ
ejpam-4323	105	61	the	the	DET
ejpam-4323	105	62	sequence	sequence	NOUN
ejpam-4323	105	63	of	of	ADP
ejpam-4323	105	64	distribution	distribution	NOUN
ejpam-4323	105	65	functions	function	NOUN
ejpam-4323	105	66	(	(	PUNCT
ejpam-4323	105	67	df	df	PROPN
ejpam-4323	105	68	)	)	PUNCT
ejpam-4323	105	69	k∗	k∗	VERB
ejpam-4323	105	70	n(x	n(x	PROPN
ejpam-4323	105	71	)	)	PUNCT
ejpam-4323	105	72	=	=	PUNCT
ejpam-4323	106	1	k(n)∑	k(n)∑	NOUN
ejpam-4323	106	2	k=1	k=1	X
ejpam-4323	107	1	∫	∫	PROPN
ejpam-4323	107	2	x	x	PROPN
ejpam-4323	108	1	−∞	−∞	ADP
ejpam-4323	108	2	y2dfk	y2dfk	NOUN
ejpam-4323	108	3	,	,	PUNCT
ejpam-4323	108	4	n(y	n(y	PROPN
ejpam-4323	108	5	+	+	CCONJ
ejpam-4323	108	6	ak	ak	PROPN
ejpam-4323	108	7	,	,	PUNCT
ejpam-4323	108	8	n	n	CCONJ
ejpam-4323	108	9	)	)	PUNCT
ejpam-4323	108	10	,	,	PUNCT
ejpam-4323	108	11	x	x	PUNCT
ejpam-4323	108	12	∈	∈	PROPN
ejpam-4323	108	13	r	r	NOUN
ejpam-4323	108	14	,	,	PUNCT
ejpam-4323	108	15	n	n	PRON
ejpam-4323	108	16	≥	≥	NOUN
ejpam-4323	108	17	1	1	NUM
ejpam-4323	108	18	,	,	PUNCT
ejpam-4323	108	19	pre	pre	ADJ
ejpam-4323	108	20	-	-	ADJ
ejpam-4323	108	21	weakly	weakly	ADJ
ejpam-4323	108	22	converges	converge	VERB
ejpam-4323	108	23	to	to	ADP
ejpam-4323	108	24	a	a	DET
ejpam-4323	108	25	df	df	NOUN
ejpam-4323	108	26	k∗	k∗	NOUN
ejpam-4323	108	27	and	and	CCONJ
ejpam-4323	108	28	the	the	DET
ejpam-4323	108	29	cha.f	cha.f	PROPN
ejpam-4323	108	30	ψg∗	ψg∗	ADJ
ejpam-4323	108	31	(	(	PUNCT
ejpam-4323	108	32	◦	◦	NOUN
ejpam-4323	108	33	)	)	PUNCT
ejpam-4323	108	34	of	of	ADP
ejpam-4323	108	35	g∗	g∗	PROPN
ejpam-4323	108	36	is	be	AUX
ejpam-4323	108	37	given	give	VERB
ejpam-4323	108	38	by	by	ADP
ejpam-4323	108	39	exp(ψ[k∗	exp(ψ[k∗	NOUN
ejpam-4323	108	40	]	]	PUNCT
ejpam-4323	108	41	(	(	PUNCT
ejpam-4323	108	42	◦	◦	NOUN
ejpam-4323	108	43	)	)	PUNCT
ejpam-4323	108	44	)	)	PUNCT
ejpam-4323	108	45	with	with	ADP
ejpam-4323	108	46	∀u	∀u	NOUN
ejpam-4323	108	47	∈	∈	NOUN
ejpam-4323	108	48	r	r	NOUN
ejpam-4323	108	49	,	,	PUNCT
ejpam-4323	108	50	ψ[k∗](u	ψ[k∗](u	PROPN
ejpam-4323	108	51	)	)	PUNCT
ejpam-4323	108	52	=	=	SYM
ejpam-4323	109	1	∫	∫	PROPN
ejpam-4323	109	2	eiux	eiux	INTJ
ejpam-4323	110	1	−	−	PROPN
ejpam-4323	110	2	1−	1−	NUM
ejpam-4323	111	1	iux	iux	INTJ
ejpam-4323	111	2	x2	x2	ADJ
ejpam-4323	111	3	dk∗(x	dk∗(x	PROPN
ejpam-4323	111	4	)	)	PUNCT
ejpam-4323	111	5	.	.	PUNCT
ejpam-4323	112	1	ab	ab	PROPN
ejpam-4323	112	2	niang	niang	PROPN
ejpam-4323	112	3	et	et	PROPN
ejpam-4323	112	4	al	al	PROPN
ejpam-4323	112	5	.	.	PUNCT
ejpam-4323	112	6	/	/	SYM
ejpam-4323	112	7	eur	eur	PROPN
ejpam-4323	112	8	.	.	PUNCT
ejpam-4323	113	1	j.	j.	PROPN
ejpam-4323	113	2	pure	pure	PROPN
ejpam-4323	113	3	appl	appl	PROPN
ejpam-4323	113	4	.	.	PROPN
ejpam-4323	113	5	math	math	PROPN
ejpam-4323	113	6	,	,	PUNCT
ejpam-4323	113	7	15	15	NUM
ejpam-4323	113	8	(	(	PUNCT
ejpam-4323	113	9	2	2	NUM
ejpam-4323	113	10	)	)	PUNCT
ejpam-4323	113	11	(	(	PUNCT
ejpam-4323	113	12	2022	2022	NUM
ejpam-4323	113	13	)	)	PUNCT
ejpam-4323	113	14	,	,	PUNCT
ejpam-4323	113	15	511	511	NUM
ejpam-4323	113	16	-	-	SYM
ejpam-4323	113	17	527	527	NUM
ejpam-4323	113	18	518	518	NUM
ejpam-4323	113	19	if	if	SCONJ
ejpam-4323	113	20	we	we	PRON
ejpam-4323	113	21	have	have	VERB
ejpam-4323	113	22	the	the	DET
ejpam-4323	113	23	vch	vch	PROPN
ejpam-4323	113	24	,	,	PUNCT
ejpam-4323	113	25	the	the	DET
ejpam-4323	113	26	convergence	convergence	NOUN
ejpam-4323	113	27	criterion	criterion	NOUN
ejpam-4323	113	28	is	be	AUX
ejpam-4323	113	29	replaced	replace	VERB
ejpam-4323	113	30	by	by	ADP
ejpam-4323	113	31	the	the	DET
ejpam-4323	113	32	weak	weak	ADJ
ejpam-4323	113	33	convergence	convergence	NOUN
ejpam-4323	113	34	k∗	k∗	VERB
ejpam-4323	113	35	n	n	PRON
ejpam-4323	113	36	k∗.	k∗.	PROPN
ejpam-4323	113	37	moreover	moreover	ADV
ejpam-4323	113	38	,	,	PUNCT
ejpam-4323	113	39	the	the	DET
ejpam-4323	113	40	limit	limit	NOUN
ejpam-4323	113	41	law	law	NOUN
ejpam-4323	113	42	g∗	g∗	NOUN
ejpam-4323	113	43	is	be	AUX
ejpam-4323	113	44	of	of	ADP
ejpam-4323	113	45	the	the	DET
ejpam-4323	113	46	form	form	NOUN
ejpam-4323	113	47	g∗	g∗	NOUN
ejpam-4323	113	48	=	=	PUNCT
ejpam-4323	113	49	g	g	PROPN
ejpam-4323	113	50	+	+	NOUN
ejpam-4323	113	51	a	a	X
ejpam-4323	113	52	,	,	PUNCT
ejpam-4323	113	53	with	with	ADP
ejpam-4323	113	54	g	g	PROPN
ejpam-4323	113	55	is	be	AUX
ejpam-4323	113	56	necessarily	necessarily	ADV
ejpam-4323	113	57	a	a	DET
ejpam-4323	113	58	centered	center	VERB
ejpam-4323	113	59	and	and	CCONJ
ejpam-4323	113	60	infinitely	infinitely	ADV
ejpam-4323	113	61	decomposable	decomposable	ADJ
ejpam-4323	113	62	law	law	NOUN
ejpam-4323	113	63	.	.	PUNCT
ejpam-4323	114	1	by	by	ADP
ejpam-4323	114	2	specializing	specialize	VERB
ejpam-4323	114	3	the	the	DET
ejpam-4323	114	4	limit	limit	NOUN
ejpam-4323	114	5	law	law	NOUN
ejpam-4323	114	6	as	as	ADP
ejpam-4323	114	7	a	a	DET
ejpam-4323	114	8	gaussian	gaussian	ADJ
ejpam-4323	114	9	law	law	NOUN
ejpam-4323	114	10	or	or	CCONJ
ejpam-4323	114	11	a	a	DET
ejpam-4323	114	12	poisson	poisson	NOUN
ejpam-4323	114	13	law	law	NOUN
ejpam-4323	114	14	,	,	PUNCT
ejpam-4323	114	15	which	which	PRON
ejpam-4323	114	16	clearly	clearly	ADV
ejpam-4323	114	17	are	be	AUX
ejpam-4323	114	18	infinitely	infinitely	ADV
ejpam-4323	114	19	decomposable	decomposable	ADJ
ejpam-4323	114	20	laws	law	NOUN
ejpam-4323	114	21	,	,	PUNCT
ejpam-4323	114	22	we	we	PRON
ejpam-4323	114	23	have	have	VERB
ejpam-4323	114	24	the	the	DET
ejpam-4323	114	25	following	follow	VERB
ejpam-4323	114	26	characterizations	characterization	NOUN
ejpam-4323	114	27	.	.	PUNCT
ejpam-4323	115	1	c1	c1	PROPN
ejpam-4323	115	2	.	.	PUNCT
ejpam-4323	116	1	under	under	ADP
ejpam-4323	116	2	the	the	DET
ejpam-4323	116	3	conditions	condition	NOUN
ejpam-4323	116	4	(	(	PUNCT
ejpam-4323	116	5	∀n	∀n	X
ejpam-4323	116	6	≥	≥	NOUN
ejpam-4323	116	7	1	1	NUM
ejpam-4323	116	8	,	,	PUNCT
ejpam-4323	116	9	∀1	∀1	VERB
ejpam-4323	116	10	≤	≤	PUNCT
ejpam-4323	116	11	k	k	X
ejpam-4323	116	12	≤	≤	X
ejpam-4323	116	13	k(n	k(n	PROPN
ejpam-4323	116	14	)	)	PUNCT
ejpam-4323	116	15	,	,	PUNCT
ejpam-4323	116	16	ak	ak	PROPN
ejpam-4323	116	17	,	,	PUNCT
ejpam-4323	116	18	n	n	NOUN
ejpam-4323	116	19	=	=	SYM
ejpam-4323	116	20	0	0	NUM
ejpam-4323	116	21	)	)	PUNCT
ejpam-4323	116	22	and	and	CCONJ
ejpam-4323	116	23	k(n)∑	k(n)∑	VERB
ejpam-4323	116	24	k=1	k=1	PROPN
ejpam-4323	117	1	σ2k	σ2k	NOUN
ejpam-4323	117	2	,	,	PUNCT
ejpam-4323	117	3	n	n	NOUN
ejpam-4323	117	4	=	=	SYM
ejpam-4323	117	5	1	1	NUM
ejpam-4323	117	6	,	,	PUNCT
ejpam-4323	117	7	the	the	DET
ejpam-4323	117	8	summands	summand	NOUN
ejpam-4323	117	9	sn[x	sn[x	VERB
ejpam-4323	117	10	]	]	PUNCT
ejpam-4323	117	11	of	of	ADP
ejpam-4323	117	12	the	the	DET
ejpam-4323	117	13	arrayx	arrayx	NOUN
ejpam-4323	117	14	converges	converge	NOUN
ejpam-4323	117	15	to	to	ADP
ejpam-4323	117	16	standard	standard	ADJ
ejpam-4323	117	17	gaussian	gaussian	ADJ
ejpam-4323	117	18	law	law	NOUN
ejpam-4323	117	19	and	and	CCONJ
ejpam-4323	117	20	max1≤k≤k(n	max1≤k≤k(n	NOUN
ejpam-4323	117	21	)	)	PUNCT
ejpam-4323	117	22	σ	σ	PROPN
ejpam-4323	117	23	2	2	NUM
ejpam-4323	117	24	k	k	NOUN
ejpam-4323	117	25	,	,	PUNCT
ejpam-4323	117	26	n	n	PROPN
ejpam-4323	117	27	→	→	SYM
ejpam-4323	117	28	0	0	NUM
ejpam-4323	117	29	if	if	SCONJ
ejpam-4323	117	30	and	and	CCONJ
ejpam-4323	117	31	only	only	ADV
ejpam-4323	117	32	if	if	SCONJ
ejpam-4323	117	33	the	the	DET
ejpam-4323	117	34	following	follow	VERB
ejpam-4323	117	35	lynderberg	lynderberg	PROPN
ejpam-4323	117	36	-	-	PUNCT
ejpam-4323	117	37	gaussian	gaussian	NOUN
ejpam-4323	117	38	condition	condition	NOUN
ejpam-4323	117	39	holds	hold	VERB
ejpam-4323	117	40	:	:	PUNCT
ejpam-4323	117	41	∀ε	∀ε	X
ejpam-4323	117	42	>	>	X
ejpam-4323	117	43	0	0	NUM
ejpam-4323	117	44	,	,	PUNCT
ejpam-4323	117	45	ln	ln	ADJ
ejpam-4323	117	46	,	,	PUNCT
ejpam-4323	117	47	g(ε	g(ε	NOUN
ejpam-4323	117	48	)	)	PUNCT
ejpam-4323	117	49	=	=	PUNCT
ejpam-4323	118	1	k(n)∑	k(n)∑	X
ejpam-4323	118	2	k=1	k=1	X
ejpam-4323	118	3	∫	∫	PROPN
ejpam-4323	118	4	(	(	PUNCT
ejpam-4323	118	5	|x|≥ε	|x|≥ε	PROPN
ejpam-4323	118	6	)	)	PUNCT
ejpam-4323	118	7	x2	x2	PROPN
ejpam-4323	118	8	dfk	dfk	PROPN
ejpam-4323	118	9	,	,	PUNCT
ejpam-4323	118	10	n(x	n(x	PROPN
ejpam-4323	118	11	)	)	PUNCT
ejpam-4323	118	12	→	→	SYM
ejpam-4323	118	13	0	0	NUM
ejpam-4323	118	14	.	.	PUNCT
ejpam-4323	119	1	(	(	PUNCT
ejpam-4323	119	2	3	3	X
ejpam-4323	119	3	)	)	PUNCT
ejpam-4323	119	4	c2	c2	PROPN
ejpam-4323	119	5	.	.	PUNCT
ejpam-4323	120	1	under	under	ADP
ejpam-4323	120	2	the	the	DET
ejpam-4323	120	3	conditions	condition	NOUN
ejpam-4323	120	4	max	max	PROPN
ejpam-4323	120	5	1≤k≤k(n	1≤k≤k(n	NUM
ejpam-4323	120	6	)	)	PUNCT
ejpam-4323	120	7	σ2k	σ2k	NOUN
ejpam-4323	120	8	,	,	PUNCT
ejpam-4323	120	9	n	n	NOUN
ejpam-4323	120	10	→	→	SYM
ejpam-4323	120	11	0	0	NUM
ejpam-4323	120	12	and	and	CCONJ
ejpam-4323	120	13	k(n)∑	k(n)∑	VERB
ejpam-4323	120	14	k=1	k=1	PROPN
ejpam-4323	121	1	σ2k	σ2k	NOUN
ejpam-4323	121	2	,	,	PUNCT
ejpam-4323	121	3	n	n	PROPN
ejpam-4323	121	4	→	→	SYM
ejpam-4323	121	5	λ	λ	PROPN
ejpam-4323	121	6	,	,	PUNCT
ejpam-4323	121	7	λ	λ	X
ejpam-4323	121	8	>	>	X
ejpam-4323	121	9	0	0	PROPN
ejpam-4323	121	10	,	,	PUNCT
ejpam-4323	121	11	the	the	DET
ejpam-4323	121	12	summands	summand	NOUN
ejpam-4323	121	13	sn[x	sn[x	VERB
ejpam-4323	121	14	]	]	PUNCT
ejpam-4323	121	15	of	of	ADP
ejpam-4323	121	16	the	the	DET
ejpam-4323	121	17	array	array	NOUN
ejpam-4323	121	18	x	x	PUNCT
ejpam-4323	121	19	converges	converge	VERB
ejpam-4323	121	20	to	to	ADP
ejpam-4323	121	21	a	a	DET
ejpam-4323	121	22	translated	translate	VERB
ejpam-4323	121	23	poisson	poisson	NOUN
ejpam-4323	121	24	law	law	NOUN
ejpam-4323	121	25	p(a	p(a	PROPN
ejpam-4323	121	26	,	,	PUNCT
ejpam-4323	121	27	λ	λ	PROPN
ejpam-4323	121	28	)	)	PUNCT
ejpam-4323	121	29	≡	≡	PROPN
ejpam-4323	121	30	a+	a+	PUNCT
ejpam-4323	121	31	p(λ	p(λ	PROPN
ejpam-4323	121	32	)	)	PUNCT
ejpam-4323	121	33	,	,	PUNCT
ejpam-4323	121	34	a	a	DET
ejpam-4323	121	35	∈	∈	PROPN
ejpam-4323	121	36	r	r	NOUN
ejpam-4323	121	37	,	,	PUNCT
ejpam-4323	121	38	if	if	SCONJ
ejpam-4323	121	39	and	and	CCONJ
ejpam-4323	121	40	only	only	ADV
ejpam-4323	121	41	if	if	SCONJ
ejpam-4323	121	42	k(n)∑	k(n)∑	PROPN
ejpam-4323	121	43	k=1	k=1	PROPN
ejpam-4323	121	44	ak	ak	PROPN
ejpam-4323	121	45	,	,	PUNCT
ejpam-4323	121	46	n	n	PROPN
ejpam-4323	121	47	→	→	SYM
ejpam-4323	121	48	a+	a+	PUNCT
ejpam-4323	121	49	λ	λ	NOUN
ejpam-4323	121	50	and	and	CCONJ
ejpam-4323	121	51	the	the	DET
ejpam-4323	121	52	following	follow	VERB
ejpam-4323	121	53	lynderberg	lynderberg	PROPN
ejpam-4323	121	54	poisson	poisson	NOUN
ejpam-4323	121	55	-	-	PUNCT
ejpam-4323	121	56	type	type	NOUN
ejpam-4323	121	57	condition	condition	NOUN
ejpam-4323	121	58	holds	hold	VERB
ejpam-4323	121	59	:	:	PUNCT
ejpam-4323	121	60	∀ε	∀ε	X
ejpam-4323	121	61	>	>	X
ejpam-4323	121	62	0	0	NUM
ejpam-4323	121	63	,	,	PUNCT
ejpam-4323	121	64	ln	ln	ADJ
ejpam-4323	121	65	,	,	PUNCT
ejpam-4323	121	66	p	p	X
ejpam-4323	121	67	(	(	PUNCT
ejpam-4323	121	68	ε	ε	PROPN
ejpam-4323	121	69	)	)	PUNCT
ejpam-4323	121	70	=	=	PUNCT
ejpam-4323	122	1	k(n)∑	k(n)∑	X
ejpam-4323	122	2	k=1	k=1	X
ejpam-4323	122	3	∫	∫	PROPN
ejpam-4323	122	4	(	(	PUNCT
ejpam-4323	122	5	|x−1|≥ε	|x−1|≥ε	NOUN
ejpam-4323	122	6	)	)	PUNCT
ejpam-4323	122	7	x2	x2	PROPN
ejpam-4323	122	8	dfk	dfk	PROPN
ejpam-4323	122	9	,	,	PUNCT
ejpam-4323	122	10	n(x+	n(x+	PROPN
ejpam-4323	122	11	ak	ak	PROPN
ejpam-4323	122	12	,	,	PUNCT
ejpam-4323	122	13	n	n	CCONJ
ejpam-4323	122	14	)	)	PUNCT
ejpam-4323	123	1	→	→	SYM
ejpam-4323	123	2	0	0	X
ejpam-4323	123	3	.	.	PUNCT
ejpam-4323	124	1	(	(	PUNCT
ejpam-4323	124	2	4	4	NUM
ejpam-4323	124	3	)	)	PUNCT
ejpam-4323	124	4	3	3	NUM
ejpam-4323	124	5	.	.	PUNCT
ejpam-4323	124	6	statements	statement	NOUN
ejpam-4323	124	7	of	of	ADP
ejpam-4323	124	8	the	the	DET
ejpam-4323	124	9	results	result	NOUN
ejpam-4323	124	10	as	as	SCONJ
ejpam-4323	124	11	announced	announce	VERB
ejpam-4323	124	12	,	,	PUNCT
ejpam-4323	124	13	we	we	PRON
ejpam-4323	124	14	focus	focus	VERB
ejpam-4323	124	15	here	here	ADV
ejpam-4323	124	16	on	on	ADP
ejpam-4323	124	17	the	the	DET
ejpam-4323	124	18	non	non	ADJ
ejpam-4323	124	19	-	-	ADJ
ejpam-4323	124	20	stationary	stationary	ADJ
ejpam-4323	124	21	independent	independent	ADJ
ejpam-4323	124	22	scheme	scheme	NOUN
ejpam-4323	124	23	.	.	PUNCT
ejpam-4323	125	1	ab	ab	PROPN
ejpam-4323	125	2	niang	niang	PROPN
ejpam-4323	125	3	et	et	PROPN
ejpam-4323	125	4	al	al	PROPN
ejpam-4323	125	5	.	.	PUNCT
ejpam-4323	125	6	/	/	SYM
ejpam-4323	125	7	eur	eur	PROPN
ejpam-4323	125	8	.	.	PUNCT
ejpam-4323	126	1	j.	j.	PROPN
ejpam-4323	126	2	pure	pure	PROPN
ejpam-4323	126	3	appl	appl	PROPN
ejpam-4323	126	4	.	.	PROPN
ejpam-4323	126	5	math	math	PROPN
ejpam-4323	126	6	,	,	PUNCT
ejpam-4323	126	7	15	15	NUM
ejpam-4323	126	8	(	(	PUNCT
ejpam-4323	126	9	2	2	NUM
ejpam-4323	126	10	)	)	PUNCT
ejpam-4323	126	11	(	(	PUNCT
ejpam-4323	126	12	2022	2022	NUM
ejpam-4323	126	13	)	)	PUNCT
ejpam-4323	126	14	,	,	PUNCT
ejpam-4323	126	15	511	511	NUM
ejpam-4323	126	16	-	-	SYM
ejpam-4323	126	17	527	527	NUM
ejpam-4323	126	18	519	519	NUM
ejpam-4323	126	19	first	first	ADJ
ejpam-4323	126	20	,	,	PUNCT
ejpam-4323	126	21	we	we	PRON
ejpam-4323	126	22	consider	consider	VERB
ejpam-4323	126	23	uniform	uniform	ADJ
ejpam-4323	126	24	conditions	condition	NOUN
ejpam-4323	126	25	of	of	ADP
ejpam-4323	126	26	the	the	DET
ejpam-4323	126	27	convergence	convergence	NOUN
ejpam-4323	126	28	of	of	ADP
ejpam-4323	126	29	the	the	DET
ejpam-4323	126	30	probabilities	probability	NOUN
ejpam-4323	126	31	pk	pk	NOUN
ejpam-4323	126	32	,	,	PUNCT
ejpam-4323	126	33	n	n	CCONJ
ejpam-4323	126	34	(	(	PUNCT
ejpam-4323	126	35	in	in	ADP
ejpam-4323	126	36	the	the	DET
ejpam-4323	126	37	bernoulli	bernoulli	PROPN
ejpam-4323	126	38	case	case	NOUN
ejpam-4323	126	39	)	)	PUNCT
ejpam-4323	126	40	and	and	CCONJ
ejpam-4323	126	41	qk	qk	INTJ
ejpam-4323	126	42	,	,	PUNCT
ejpam-4323	126	43	n	n	CCONJ
ejpam-4323	126	44	(	(	PUNCT
ejpam-4323	126	45	in	in	ADP
ejpam-4323	126	46	the	the	DET
ejpam-4323	126	47	corrected	correct	VERB
ejpam-4323	126	48	geometric	geometric	ADJ
ejpam-4323	126	49	case	case	NOUN
ejpam-4323	126	50	)	)	PUNCT
ejpam-4323	126	51	to	to	ADP
ejpam-4323	126	52	zero	zero	NUM
ejpam-4323	126	53	to	to	AUX
ejpam-4323	126	54	unveil	unveil	ADJ
ejpam-4323	126	55	refined	refined	ADJ
ejpam-4323	126	56	versions	version	NOUN
ejpam-4323	126	57	of	of	ADP
ejpam-4323	126	58	the	the	DET
ejpam-4323	126	59	extensions	extension	NOUN
ejpam-4323	126	60	.	.	PUNCT
ejpam-4323	127	1	later	later	ADV
ejpam-4323	127	2	,	,	PUNCT
ejpam-4323	127	3	we	we	PRON
ejpam-4323	127	4	will	will	AUX
ejpam-4323	127	5	provide	provide	VERB
ejpam-4323	127	6	more	more	ADJ
ejpam-4323	127	7	general	general	ADJ
ejpam-4323	127	8	conditions	condition	NOUN
ejpam-4323	127	9	.	.	PUNCT
ejpam-4323	128	1	theorem	theorem	NOUN
ejpam-4323	128	2	1	1	NUM
ejpam-4323	128	3	.	.	PUNCT
ejpam-4323	129	1	let	let	VERB
ejpam-4323	129	2	x	x	PUNCT
ejpam-4323	129	3	=	=	PRON
ejpam-4323	129	4	{	{	PUNCT
ejpam-4323	129	5	{	{	PUNCT
ejpam-4323	129	6	xk	xk	PROPN
ejpam-4323	129	7	,	,	PUNCT
ejpam-4323	129	8	n	n	CCONJ
ejpam-4323	129	9	,	,	PUNCT
ejpam-4323	129	10	1	1	NUM
ejpam-4323	129	11	≤	≤	NUM
ejpam-4323	129	12	k	k	X
ejpam-4323	129	13	≤	≤	PROPN
ejpam-4323	130	1	kn	kn	NOUN
ejpam-4323	130	2	=	=	PUNCT
ejpam-4323	130	3	k(n	k(n	PROPN
ejpam-4323	130	4	)	)	PUNCT
ejpam-4323	130	5	}	}	PUNCT
ejpam-4323	130	6	,	,	PUNCT
ejpam-4323	130	7	n	n	X
ejpam-4323	130	8	≥	≥	NOUN
ejpam-4323	130	9	1	1	NUM
ejpam-4323	130	10	}	}	PUNCT
ejpam-4323	130	11	,	,	PUNCT
ejpam-4323	130	12	be	be	AUX
ejpam-4323	130	13	an	an	DET
ejpam-4323	130	14	array	array	NOUN
ejpam-4323	130	15	of	of	ADP
ejpam-4323	130	16	by	by	ADP
ejpam-4323	130	17	-	-	PUNCT
ejpam-4323	130	18	row	row	NOUN
ejpam-4323	130	19	independent	independent	ADJ
ejpam-4323	130	20	bernoulli	bernoulli	PROPN
ejpam-4323	130	21	random	random	ADJ
ejpam-4323	130	22	variables	variable	NOUN
ejpam-4323	130	23	,	,	PUNCT
ejpam-4323	130	24	that	that	PRON
ejpam-4323	130	25	is	be	AUX
ejpam-4323	130	26	:	:	PUNCT
ejpam-4323	130	27	(	(	PUNCT
ejpam-4323	130	28	1	1	X
ejpam-4323	130	29	)	)	PUNCT
ejpam-4323	130	30	∀n	∀n	NUM
ejpam-4323	130	31	≥	≥	NOUN
ejpam-4323	130	32	1	1	NUM
ejpam-4323	130	33	,	,	PUNCT
ejpam-4323	130	34	∀1	∀1	VERB
ejpam-4323	130	35	≤	≤	PUNCT
ejpam-4323	130	36	k	k	X
ejpam-4323	130	37	≤	≤	X
ejpam-4323	130	38	k(n	k(n	PROPN
ejpam-4323	130	39	)	)	PUNCT
ejpam-4323	130	40	,	,	PUNCT
ejpam-4323	130	41	xk	xk	PROPN
ejpam-4323	130	42	,	,	PUNCT
ejpam-4323	130	43	n	n	PRON
ejpam-4323	130	44	∼	∼	NOUN
ejpam-4323	130	45	b(pk	b(pk	NOUN
ejpam-4323	130	46	,	,	PUNCT
ejpam-4323	130	47	n	n	CCONJ
ejpam-4323	130	48	)	)	PUNCT
ejpam-4323	130	49	,	,	PUNCT
ejpam-4323	130	50	with	with	ADP
ejpam-4323	130	51	0	0	NUM
ejpam-4323	130	52	<	<	X
ejpam-4323	130	53	pk	pk	NOUN
ejpam-4323	130	54	,	,	PUNCT
ejpam-4323	130	55	n	n	CCONJ
ejpam-4323	130	56	<	<	X
ejpam-4323	130	57	1	1	NUM
ejpam-4323	130	58	and	and	CCONJ
ejpam-4323	130	59	:	:	PUNCT
ejpam-4323	130	60	(	(	PUNCT
ejpam-4323	130	61	2	2	X
ejpam-4323	130	62	)	)	PUNCT
ejpam-4323	130	63	sup1≤k≤k(n	sup1≤k≤k(n	NOUN
ejpam-4323	130	64	)	)	PUNCT
ejpam-4323	130	65	pk	pk	NOUN
ejpam-4323	130	66	,	,	PUNCT
ejpam-4323	130	67	n	n	PROPN
ejpam-4323	130	68	→	→	SYM
ejpam-4323	130	69	0	0	NUM
ejpam-4323	130	70	;	;	PUNCT
ejpam-4323	130	71	(	(	PUNCT
ejpam-4323	130	72	3	3	X
ejpam-4323	130	73	)	)	PUNCT
ejpam-4323	130	74	∑	∑	ADP
ejpam-4323	130	75	1≤k≤k(n	1≤k≤k(n	NUM
ejpam-4323	130	76	)	)	PUNCT
ejpam-4323	130	77	pk	pk	NOUN
ejpam-4323	130	78	,	,	PUNCT
ejpam-4323	130	79	n	n	PROPN
ejpam-4323	130	80	→	→	SYM
ejpam-4323	130	81	λ	λ	NOUN
ejpam-4323	130	82	∈]0	∈]0	X
ejpam-4323	130	83	,	,	PUNCT
ejpam-4323	130	84	+	+	NOUN
ejpam-4323	130	85	∞	∞	PROPN
ejpam-4323	130	86	[	[	X
ejpam-4323	130	87	.	.	PUNCT
ejpam-4323	131	1	then	then	ADV
ejpam-4323	131	2	we	we	PRON
ejpam-4323	131	3	have	have	AUX
ejpam-4323	131	4	sn[x	sn[x	VERB
ejpam-4323	131	5	]	]	PUNCT
ejpam-4323	131	6	p(λ	p(λ	NOUN
ejpam-4323	131	7	)	)	PUNCT
ejpam-4323	131	8	.	.	PUNCT
ejpam-4323	132	1	proof	proof	NOUN
ejpam-4323	132	2	of	of	ADP
ejpam-4323	132	3	theorem	theorem	NOUN
ejpam-4323	132	4	1	1	NUM
ejpam-4323	132	5	.	.	PUNCT
ejpam-4323	133	1	throughout	throughout	ADP
ejpam-4323	133	2	this	this	DET
ejpam-4323	133	3	proof	proof	NOUN
ejpam-4323	133	4	,	,	PUNCT
ejpam-4323	133	5	the	the	DET
ejpam-4323	133	6	notation	notation	NOUN
ejpam-4323	133	7	`	`	PUNCT
ejpam-4323	133	8	k	k	PROPN
ejpam-4323	133	9	,	,	PUNCT
ejpam-4323	133	10	n	n	PROPN
ejpam-4323	133	11	=	=	SYM
ejpam-4323	133	12	on(1	on(1	NOUN
ejpam-4323	133	13	)	)	PUNCT
ejpam-4323	133	14	,	,	PUNCT
ejpam-4323	133	15	for	for	ADP
ejpam-4323	133	16	k	k	PROPN
ejpam-4323	133	17	ranging	range	VERB
ejpam-4323	133	18	over	over	ADP
ejpam-4323	133	19	some	some	DET
ejpam-4323	133	20	set	set	NOUN
ejpam-4323	133	21	in	in	ADP
ejpam-4323	133	22	means	mean	NOUN
ejpam-4323	133	23	that	that	SCONJ
ejpam-4323	133	24	the	the	DET
ejpam-4323	133	25	sequence	sequence	NOUN
ejpam-4323	133	26	`	`	PUNCT
ejpam-4323	133	27	k	k	PROPN
ejpam-4323	133	28	,	,	PUNCT
ejpam-4323	133	29	n	n	PRON
ejpam-4323	133	30	goes	go	VERB
ejpam-4323	133	31	to	to	ADP
ejpam-4323	133	32	zero	zero	NUM
ejpam-4323	133	33	as	as	ADP
ejpam-4323	133	34	n	n	PROPN
ejpam-4323	133	35	→	→	SYM
ejpam-4323	133	36	+	+	NOUN
ejpam-4323	133	37	∞	∞	NOUN
ejpam-4323	133	38	uniformly	uniformly	ADV
ejpam-4323	133	39	in	in	ADP
ejpam-4323	133	40	k	k	PROPN
ejpam-4323	133	41	∈	∈	PROPN
ejpam-4323	133	42	in	in	ADP
ejpam-4323	133	43	.	.	PUNCT
ejpam-4323	134	1	so	so	ADV
ejpam-4323	134	2	assumption	assumption	NOUN
ejpam-4323	134	3	(	(	PUNCT
ejpam-4323	134	4	2	2	X
ejpam-4323	134	5	)	)	PUNCT
ejpam-4323	134	6	means	mean	VERB
ejpam-4323	134	7	that	that	SCONJ
ejpam-4323	134	8	pk	pk	NOUN
ejpam-4323	134	9	,	,	PUNCT
ejpam-4323	134	10	n	n	NOUN
ejpam-4323	134	11	=	=	SYM
ejpam-4323	134	12	on(1	on(1	NOUN
ejpam-4323	134	13	)	)	PUNCT
ejpam-4323	134	14	and	and	CCONJ
ejpam-4323	134	15	qk	qk	NOUN
ejpam-4323	134	16	,	,	PUNCT
ejpam-4323	134	17	n	n	PROPN
ejpam-4323	134	18	=	=	SYM
ejpam-4323	134	19	1−	1−	NUM
ejpam-4323	134	20	pk	pk	NOUN
ejpam-4323	134	21	,	,	PUNCT
ejpam-4323	134	22	n	n	NOUN
ejpam-4323	134	23	=	=	SYM
ejpam-4323	134	24	1	1	NUM
ejpam-4323	134	25	+	+	NUM
ejpam-4323	134	26	on(1	on(1	NOUN
ejpam-4323	134	27	)	)	PUNCT
ejpam-4323	134	28	.	.	PUNCT
ejpam-4323	135	1	we	we	PRON
ejpam-4323	135	2	have	have	VERB
ejpam-4323	135	3	to	to	PART
ejpam-4323	135	4	check	check	VERB
ejpam-4323	135	5	the	the	DET
ejpam-4323	135	6	uan	uan	PROPN
ejpam-4323	135	7	condition	condition	NOUN
ejpam-4323	135	8	.	.	PUNCT
ejpam-4323	136	1	by	by	ADP
ejpam-4323	136	2	using	use	VERB
ejpam-4323	136	3	chebychev	chebychev	NOUN
ejpam-4323	136	4	’s	’s	PART
ejpam-4323	136	5	inequality	inequality	NOUN
ejpam-4323	136	6	,	,	PUNCT
ejpam-4323	136	7	we	we	PRON
ejpam-4323	136	8	have	have	AUX
ejpam-4323	136	9	,	,	PUNCT
ejpam-4323	136	10	for	for	ADP
ejpam-4323	136	11	any	any	DET
ejpam-4323	136	12	ε	ε	PROPN
ejpam-4323	136	13	>	>	X
ejpam-4323	136	14	0	0	PROPN
ejpam-4323	136	15	,	,	PUNCT
ejpam-4323	136	16	u(n	u(n	PROPN
ejpam-4323	136	17	,	,	PUNCT
ejpam-4323	136	18	ε	ε	PROPN
ejpam-4323	136	19	,	,	PUNCT
ejpam-4323	136	20	x	x	NOUN
ejpam-4323	136	21	)	)	PUNCT
ejpam-4323	136	22	=	=	SYM
ejpam-4323	136	23	sup	sup	NOUN
ejpam-4323	136	24	1≤k≤kn	1≤k≤kn	NUM
ejpam-4323	136	25	p(|xk	p(|xk	NUM
ejpam-4323	136	26	,	,	PUNCT
ejpam-4323	136	27	n	n	CCONJ
ejpam-4323	136	28	−	−	PROPN
ejpam-4323	136	29	ak	ak	PROPN
ejpam-4323	136	30	,	,	PUNCT
ejpam-4323	136	31	n|	n|	X
ejpam-4323	136	32	≥	≥	NOUN
ejpam-4323	136	33	ε	ε	NOUN
ejpam-4323	136	34	)	)	PUNCT
ejpam-4323	136	35	≤	≤	NOUN
ejpam-4323	137	1	ε−2	ε−2	PROPN
ejpam-4323	137	2	sup	sup	NOUN
ejpam-4323	137	3	1≤k≤kn	1≤k≤kn	NUM
ejpam-4323	137	4	var(xk	var(xk	NOUN
ejpam-4323	137	5	,	,	PUNCT
ejpam-4323	137	6	n	n	CCONJ
ejpam-4323	137	7	)	)	PUNCT
ejpam-4323	138	1	=	=	SYM
ejpam-4323	138	2	ε−2	ε−2	PROPN
ejpam-4323	138	3	pk	pk	PROPN
ejpam-4323	138	4	,	,	PUNCT
ejpam-4323	138	5	n	n	PRON
ejpam-4323	138	6	qk	qk	NOUN
ejpam-4323	138	7	,	,	PUNCT
ejpam-4323	138	8	n	n	PROPN
ejpam-4323	138	9	=	=	SYM
ejpam-4323	138	10	ε−2	ε−2	PROPN
ejpam-4323	138	11	on(1)(1	on(1)(1	NUM
ejpam-4323	138	12	+	+	ADJ
ejpam-4323	138	13	on(1	on(1	NOUN
ejpam-4323	138	14	)	)	PUNCT
ejpam-4323	138	15	)	)	PUNCT
ejpam-4323	139	1	→	→	SYM
ejpam-4323	139	2	0	0	X
ejpam-4323	139	3	.	.	PUNCT
ejpam-4323	140	1	the	the	DET
ejpam-4323	140	2	vch	vch	PROPN
ejpam-4323	140	3	also	also	ADV
ejpam-4323	140	4	holds	hold	VERB
ejpam-4323	140	5	since	since	SCONJ
ejpam-4323	140	6	mv	mv	PROPN
ejpam-4323	140	7	(	(	PUNCT
ejpam-4323	140	8	n	n	CCONJ
ejpam-4323	140	9	,	,	PUNCT
ejpam-4323	140	10	x	x	NOUN
ejpam-4323	140	11	)	)	PUNCT
ejpam-4323	140	12	=	=	SYM
ejpam-4323	140	13	∑	∑	PUNCT
ejpam-4323	140	14	1≤k≤k(n	1≤k≤k(n	NUM
ejpam-4323	140	15	)	)	PUNCT
ejpam-4323	140	16	var(xk	var(xk	X
ejpam-4323	140	17	,	,	PUNCT
ejpam-4323	140	18	n	n	CCONJ
ejpam-4323	140	19	)	)	PUNCT
ejpam-4323	140	20	ab	ab	PROPN
ejpam-4323	140	21	niang	niang	PROPN
ejpam-4323	140	22	et	et	PROPN
ejpam-4323	140	23	al	al	PROPN
ejpam-4323	140	24	.	.	PUNCT
ejpam-4323	140	25	/	/	SYM
ejpam-4323	140	26	eur	eur	PROPN
ejpam-4323	140	27	.	.	PUNCT
ejpam-4323	141	1	j.	j.	PROPN
ejpam-4323	141	2	pure	pure	PROPN
ejpam-4323	141	3	appl	appl	PROPN
ejpam-4323	141	4	.	.	PROPN
ejpam-4323	141	5	math	math	PROPN
ejpam-4323	141	6	,	,	PUNCT
ejpam-4323	141	7	15	15	NUM
ejpam-4323	141	8	(	(	PUNCT
ejpam-4323	141	9	2	2	NUM
ejpam-4323	141	10	)	)	PUNCT
ejpam-4323	141	11	(	(	PUNCT
ejpam-4323	141	12	2022	2022	NUM
ejpam-4323	141	13	)	)	PUNCT
ejpam-4323	141	14	,	,	PUNCT
ejpam-4323	141	15	511	511	NUM
ejpam-4323	141	16	-	-	SYM
ejpam-4323	141	17	527	527	NUM
ejpam-4323	141	18	520	520	NUM
ejpam-4323	141	19	=	=	SYM
ejpam-4323	141	20	∑	∑	PART
ejpam-4323	141	21	1≤k≤k(n	1≤k≤k(n	NUM
ejpam-4323	141	22	)	)	PUNCT
ejpam-4323	141	23	pk	pk	NOUN
ejpam-4323	141	24	,	,	PUNCT
ejpam-4323	141	25	n	n	PRON
ejpam-4323	141	26	qk	qk	NOUN
ejpam-4323	141	27	,	,	PUNCT
ejpam-4323	141	28	n	n	NOUN
ejpam-4323	141	29	=	=	SYM
ejpam-4323	141	30	(	(	PUNCT
ejpam-4323	141	31	1	1	NUM
ejpam-4323	141	32	+	+	SYM
ejpam-4323	141	33	on(1	on(1	NOUN
ejpam-4323	141	34	)	)	PUNCT
ejpam-4323	141	35	)	)	PUNCT
ejpam-4323	141	36	∑	∑	PUNCT
ejpam-4323	141	37	1≤k≤k(n	1≤k≤k(n	NUM
ejpam-4323	141	38	)	)	PUNCT
ejpam-4323	141	39	pk	pk	NOUN
ejpam-4323	141	40	,	,	PUNCT
ejpam-4323	141	41	n	n	NOUN
ejpam-4323	141	42	→	→	SYM
ejpam-4323	141	43	λ	λ	X
ejpam-4323	141	44	.	.	PUNCT
ejpam-4323	142	1	besides	besides	SCONJ
ejpam-4323	142	2	∑	∑	ADP
ejpam-4323	142	3	1≤k≤k(n	1≤k≤k(n	NUM
ejpam-4323	142	4	)	)	PUNCT
ejpam-4323	142	5	e(xk	e(xk	PROPN
ejpam-4323	142	6	,	,	PUNCT
ejpam-4323	142	7	n	n	CCONJ
ejpam-4323	142	8	)	)	PUNCT
ejpam-4323	142	9	=	=	SYM
ejpam-4323	142	10	∑	∑	PUNCT
ejpam-4323	142	11	1≤k≤k(n	1≤k≤k(n	NUM
ejpam-4323	142	12	)	)	PUNCT
ejpam-4323	142	13	pk	pk	NOUN
ejpam-4323	142	14	,	,	PUNCT
ejpam-4323	142	15	n	n	NOUN
ejpam-4323	142	16	→	→	SYM
ejpam-4323	142	17	λ	λ	X
ejpam-4323	142	18	.	.	PUNCT
ejpam-4323	143	1	so	so	ADV
ejpam-4323	143	2	,	,	PUNCT
ejpam-4323	143	3	we	we	PRON
ejpam-4323	143	4	are	be	AUX
ejpam-4323	143	5	in	in	ADP
ejpam-4323	143	6	the	the	DET
ejpam-4323	143	7	position	position	NOUN
ejpam-4323	143	8	of	of	ADP
ejpam-4323	143	9	applying	apply	VERB
ejpam-4323	143	10	the	the	DET
ejpam-4323	143	11	conditions	condition	NOUN
ejpam-4323	143	12	of	of	ADP
ejpam-4323	143	13	weak	weak	ADJ
ejpam-4323	143	14	convergence	convergence	NOUN
ejpam-4323	143	15	to	to	ADP
ejpam-4323	143	16	a	a	DET
ejpam-4323	143	17	poisson	poisson	NOUN
ejpam-4323	143	18	law	law	NOUN
ejpam-4323	143	19	by	by	ADP
ejpam-4323	143	20	checking	check	VERB
ejpam-4323	143	21	the	the	DET
ejpam-4323	143	22	poisson	poisson	PROPN
ejpam-4323	143	23	lynderbeg	lynderbeg	PROPN
ejpam-4323	143	24	condition	condition	NOUN
ejpam-4323	143	25	(	(	PUNCT
ejpam-4323	143	26	4	4	NUM
ejpam-4323	143	27	)	)	PUNCT
ejpam-4323	143	28	.	.	PUNCT
ejpam-4323	144	1	we	we	PRON
ejpam-4323	144	2	have	have	VERB
ejpam-4323	144	3	for	for	ADP
ejpam-4323	144	4	any	any	DET
ejpam-4323	144	5	ε	ε	PROPN
ejpam-4323	144	6	>	>	X
ejpam-4323	144	7	0	0	PUNCT
ejpam-4323	145	1	ln	ln	ADJ
ejpam-4323	145	2	,	,	PUNCT
ejpam-4323	145	3	p	p	X
ejpam-4323	145	4	(	(	PUNCT
ejpam-4323	145	5	ε	ε	PROPN
ejpam-4323	145	6	)	)	PUNCT
ejpam-4323	145	7	=	=	NOUN
ejpam-4323	145	8	:	:	PUNCT
ejpam-4323	145	9	k(n)∑	k(n)∑	X
ejpam-4323	145	10	k=1	k=1	PROPN
ejpam-4323	146	1	ln	ln	INTJ
ejpam-4323	146	2	,	,	PUNCT
ejpam-4323	146	3	k	k	PROPN
ejpam-4323	146	4	,	,	PUNCT
ejpam-4323	146	5	p	p	X
ejpam-4323	146	6	(	(	PUNCT
ejpam-4323	146	7	ε	ε	PROPN
ejpam-4323	146	8	)	)	PUNCT
ejpam-4323	146	9	,	,	PUNCT
ejpam-4323	146	10	with	with	ADP
ejpam-4323	146	11	ln	ln	ADJ
ejpam-4323	146	12	,	,	PUNCT
ejpam-4323	146	13	k	k	NOUN
ejpam-4323	146	14	,	,	PUNCT
ejpam-4323	146	15	p	p	X
ejpam-4323	146	16	(	(	PUNCT
ejpam-4323	146	17	ε	ε	PROPN
ejpam-4323	146	18	)	)	PUNCT
ejpam-4323	146	19	=	=	SYM
ejpam-4323	146	20	∫	∫	PROPN
ejpam-4323	146	21	(	(	PUNCT
ejpam-4323	146	22	|x−1|≥ε	|x−1|≥ε	NOUN
ejpam-4323	146	23	)	)	PUNCT
ejpam-4323	146	24	x2	x2	PROPN
ejpam-4323	146	25	dfk	dfk	PROPN
ejpam-4323	146	26	,	,	PUNCT
ejpam-4323	146	27	n(x+	n(x+	ADV
ejpam-4323	146	28	pk	pk	NOUN
ejpam-4323	146	29	,	,	PUNCT
ejpam-4323	146	30	n	n	CCONJ
ejpam-4323	146	31	)	)	PUNCT
ejpam-4323	146	32	=	=	SYM
ejpam-4323	146	33	∫	∫	PROPN
ejpam-4323	146	34	(	(	PUNCT
ejpam-4323	146	35	|xk	|xk	X
ejpam-4323	146	36	,	,	PUNCT
ejpam-4323	146	37	n−pk	n−pk	NOUN
ejpam-4323	146	38	,	,	PUNCT
ejpam-4323	146	39	n−1|≥ε	n−1|≥ε	NOUN
ejpam-4323	146	40	)	)	PUNCT
ejpam-4323	146	41	|xk	|xk	NUM
ejpam-4323	146	42	,	,	PUNCT
ejpam-4323	146	43	n	n	CCONJ
ejpam-4323	146	44	−	−	PROPN
ejpam-4323	146	45	pk	pk	PROPN
ejpam-4323	146	46	,	,	PUNCT
ejpam-4323	146	47	n|2	n|2	PROPN
ejpam-4323	146	48	dpk	dpk	NOUN
ejpam-4323	146	49	,	,	PUNCT
ejpam-4323	146	50	n	n	NOUN
ejpam-4323	146	51	=	=	SYM
ejpam-4323	146	52	pk	pk	NOUN
ejpam-4323	146	53	,	,	PUNCT
ejpam-4323	146	54	n	n	CCONJ
ejpam-4323	146	55	(	(	PUNCT
ejpam-4323	146	56	1(|xk	1(|xk	NUM
ejpam-4323	146	57	,	,	PUNCT
ejpam-4323	146	58	n−pk	n−pk	NOUN
ejpam-4323	146	59	,	,	PUNCT
ejpam-4323	146	60	n−1|≥ε)|xk	n−1|≥ε)|xk	NOUN
ejpam-4323	146	61	,	,	PUNCT
ejpam-4323	146	62	n	n	CCONJ
ejpam-4323	146	63	−	−	PROPN
ejpam-4323	146	64	pk	pk	PROPN
ejpam-4323	146	65	,	,	PUNCT
ejpam-4323	146	66	n|2	n|2	NOUN
ejpam-4323	146	67	)	)	PUNCT
ejpam-4323	146	68	(	(	PUNCT
ejpam-4323	146	69	xk	xk	PROPN
ejpam-4323	146	70	,	,	PUNCT
ejpam-4323	146	71	n=1	n=1	PROPN
ejpam-4323	146	72	)	)	PUNCT
ejpam-4323	147	1	+	+	CCONJ
ejpam-4323	147	2	(	(	PUNCT
ejpam-4323	147	3	1−	1−	NUM
ejpam-4323	147	4	pk	pk	NOUN
ejpam-4323	147	5	,	,	PUNCT
ejpam-4323	147	6	n	n	CCONJ
ejpam-4323	147	7	)	)	PUNCT
ejpam-4323	147	8	(	(	PUNCT
ejpam-4323	147	9	1(|xk	1(|xk	NUM
ejpam-4323	147	10	,	,	PUNCT
ejpam-4323	147	11	n−pk	n−pk	NOUN
ejpam-4323	147	12	,	,	PUNCT
ejpam-4323	147	13	n−1|≥ε)|xk	n−1|≥ε)|xk	NOUN
ejpam-4323	147	14	,	,	PUNCT
ejpam-4323	147	15	n	n	CCONJ
ejpam-4323	147	16	−	−	PROPN
ejpam-4323	147	17	pk	pk	PROPN
ejpam-4323	147	18	,	,	PUNCT
ejpam-4323	147	19	n|2	n|2	NOUN
ejpam-4323	147	20	)	)	PUNCT
ejpam-4323	147	21	(	(	PUNCT
ejpam-4323	147	22	xk	xk	PROPN
ejpam-4323	147	23	,	,	PUNCT
ejpam-4323	147	24	n=0	n=0	NUM
ejpam-4323	147	25	)	)	PUNCT
ejpam-4323	147	26	=	=	SYM
ejpam-4323	147	27	pk	pk	PROPN
ejpam-4323	147	28	,	,	PUNCT
ejpam-4323	147	29	n1(|pk	n1(|pk	NOUN
ejpam-4323	147	30	,	,	PUNCT
ejpam-4323	147	31	n|≥ε	n|≥ε	ADJ
ejpam-4323	147	32	)	)	PUNCT
ejpam-4323	147	33	(	(	PUNCT
ejpam-4323	147	34	1−	1−	NUM
ejpam-4323	147	35	pk	pk	NOUN
ejpam-4323	147	36	,	,	PUNCT
ejpam-4323	147	37	n	n	CCONJ
ejpam-4323	147	38	)	)	PUNCT
ejpam-4323	147	39	2	2	NUM
ejpam-4323	148	1	+	+	CCONJ
ejpam-4323	148	2	(	(	PUNCT
ejpam-4323	148	3	1−	1−	NUM
ejpam-4323	148	4	pk	pk	NOUN
ejpam-4323	148	5	,	,	PUNCT
ejpam-4323	148	6	n)1(|pk	n)1(|pk	NOUN
ejpam-4323	148	7	,	,	PUNCT
ejpam-4323	148	8	n+1|≥ε	n+1|≥ε	PROPN
ejpam-4323	148	9	)	)	PUNCT
ejpam-4323	148	10	p	p	NOUN
ejpam-4323	148	11	2	2	NUM
ejpam-4323	148	12	k	k	NOUN
ejpam-4323	148	13	,	,	PUNCT
ejpam-4323	148	14	n	n	NOUN
ejpam-4323	148	15	=	=	SYM
ejpam-4323	148	16	pk	pk	NOUN
ejpam-4323	148	17	,	,	PUNCT
ejpam-4323	148	18	n1(|on(1)|≥ε)(1	n1(|on(1)|≥ε)(1	NOUN
ejpam-4323	148	19	+	+	CCONJ
ejpam-4323	148	20	on(1	on(1	NOUN
ejpam-4323	148	21	)	)	PUNCT
ejpam-4323	148	22	)	)	PUNCT
ejpam-4323	148	23	2	2	NUM
ejpam-4323	149	1	+	+	CCONJ
ejpam-4323	149	2	on(1)(1	on(1)(1	NUM
ejpam-4323	149	3	+	+	CCONJ
ejpam-4323	149	4	on(1))1(|on(1)+1|≥ε	on(1))1(|on(1)+1|≥ε	ADJ
ejpam-4323	149	5	)	)	PUNCT
ejpam-4323	149	6	pk	pk	NOUN
ejpam-4323	149	7	,	,	PUNCT
ejpam-4323	149	8	n.	n.	NOUN
ejpam-4323	149	9	we	we	PRON
ejpam-4323	149	10	only	only	ADV
ejpam-4323	149	11	need	need	VERB
ejpam-4323	149	12	to	to	PART
ejpam-4323	149	13	get	get	VERB
ejpam-4323	149	14	(	(	PUNCT
ejpam-4323	149	15	4	4	NUM
ejpam-4323	149	16	)	)	PUNCT
ejpam-4323	149	17	for	for	ADP
ejpam-4323	149	18	0	0	NUM
ejpam-4323	149	19	<	<	X
ejpam-4323	149	20	ε	ε	PROPN
ejpam-4323	149	21	<	<	X
ejpam-4323	149	22	ε0	ε0	PROPN
ejpam-4323	149	23	,	,	PUNCT
ejpam-4323	149	24	for	for	ADP
ejpam-4323	149	25	a	a	DET
ejpam-4323	149	26	fixed	fix	VERB
ejpam-4323	149	27	ε0	ε0	NOUN
ejpam-4323	149	28	>	>	X
ejpam-4323	149	29	0	0	X
ejpam-4323	149	30	.	.	PUNCT
ejpam-4323	150	1	let	let	VERB
ejpam-4323	150	2	us	we	PRON
ejpam-4323	150	3	fix	fix	VERB
ejpam-4323	150	4	ε0	ε0	NOUN
ejpam-4323	150	5	=	=	SYM
ejpam-4323	150	6	1/2	1/2	NUM
ejpam-4323	150	7	.	.	PUNCT
ejpam-4323	151	1	so	so	ADV
ejpam-4323	151	2	,	,	PUNCT
ejpam-4323	151	3	for	for	ADP
ejpam-4323	151	4	n	n	CCONJ
ejpam-4323	151	5	large	large	ADJ
ejpam-4323	151	6	enough	enough	ADV
ejpam-4323	151	7	,	,	PUNCT
ejpam-4323	151	8	1(|on(1)|≥ε	1(|on(1)|≥ε	NUM
ejpam-4323	151	9	)	)	PUNCT
ejpam-4323	151	10	=	=	SYM
ejpam-4323	151	11	0	0	NUM
ejpam-4323	151	12	and	and	CCONJ
ejpam-4323	151	13	1(|on(1)+1|≥ε	1(|on(1)+1|≥ε	NUM
ejpam-4323	151	14	)	)	PUNCT
ejpam-4323	152	1	=	=	SYM
ejpam-4323	152	2	1	1	NUM
ejpam-4323	152	3	and	and	CCONJ
ejpam-4323	152	4	hence	hence	ADV
ejpam-4323	152	5	k(n)∑	k(n)∑	X
ejpam-4323	153	1	k=1	k=1	PROPN
ejpam-4323	154	1	ln	ln	INTJ
ejpam-4323	154	2	,	,	PUNCT
ejpam-4323	154	3	k	k	PROPN
ejpam-4323	154	4	,	,	PUNCT
ejpam-4323	154	5	p	p	X
ejpam-4323	154	6	(	(	PUNCT
ejpam-4323	154	7	ε	ε	PROPN
ejpam-4323	154	8	)	)	PUNCT
ejpam-4323	154	9	=	=	PUNCT
ejpam-4323	154	10	on(1)(1	on(1)(1	NUM
ejpam-4323	154	11	+	+	ADJ
ejpam-4323	154	12	on(1	on(1	NOUN
ejpam-4323	154	13	)	)	PUNCT
ejpam-4323	154	14	)	)	PUNCT
ejpam-4323	155	1	k(n)∑	k(n)∑	VERB
ejpam-4323	156	1	k=1	k=1	PROPN
ejpam-4323	156	2	pk	pk	PROPN
ejpam-4323	156	3	,	,	PUNCT
ejpam-4323	156	4	n	n	PROPN
ejpam-4323	156	5	ab	ab	PROPN
ejpam-4323	156	6	niang	niang	PROPN
ejpam-4323	156	7	et	et	PROPN
ejpam-4323	156	8	al	al	PROPN
ejpam-4323	156	9	.	.	PUNCT
ejpam-4323	156	10	/	/	SYM
ejpam-4323	156	11	eur	eur	PROPN
ejpam-4323	156	12	.	.	PUNCT
ejpam-4323	157	1	j.	j.	PROPN
ejpam-4323	157	2	pure	pure	PROPN
ejpam-4323	157	3	appl	appl	PROPN
ejpam-4323	157	4	.	.	PROPN
ejpam-4323	157	5	math	math	PROPN
ejpam-4323	157	6	,	,	PUNCT
ejpam-4323	157	7	15	15	NUM
ejpam-4323	157	8	(	(	PUNCT
ejpam-4323	157	9	2	2	NUM
ejpam-4323	157	10	)	)	PUNCT
ejpam-4323	157	11	(	(	PUNCT
ejpam-4323	157	12	2022	2022	NUM
ejpam-4323	157	13	)	)	PUNCT
ejpam-4323	157	14	,	,	PUNCT
ejpam-4323	157	15	511	511	NUM
ejpam-4323	157	16	-	-	SYM
ejpam-4323	157	17	527	527	NUM
ejpam-4323	158	1	521	521	NUM
ejpam-4323	158	2	=	=	SYM
ejpam-4323	158	3	on(1)(1	on(1)(1	NUM
ejpam-4323	158	4	+	+	CCONJ
ejpam-4323	158	5	on(1))(λ+	on(1))(λ+	NOUN
ejpam-4323	158	6	o(1	o(1	NOUN
ejpam-4323	158	7	)	)	PUNCT
ejpam-4323	158	8	)	)	PUNCT
ejpam-4323	159	1	→	→	SYM
ejpam-4323	159	2	0	0	X
ejpam-4323	159	3	.	.	PUNCT
ejpam-4323	160	1	the	the	DET
ejpam-4323	160	2	proof	proof	NOUN
ejpam-4323	160	3	is	be	AUX
ejpam-4323	160	4	complete	complete	ADJ
ejpam-4323	160	5	.	.	PUNCT
ejpam-4323	161	1	�	�	PROPN
ejpam-4323	161	2	theorem	theorem	VERB
ejpam-4323	161	3	2	2	NUM
ejpam-4323	161	4	.	.	PUNCT
ejpam-4323	162	1	let	let	VERB
ejpam-4323	162	2	x	x	PUNCT
ejpam-4323	162	3	=	=	PRON
ejpam-4323	162	4	{	{	PUNCT
ejpam-4323	162	5	{	{	PUNCT
ejpam-4323	162	6	xk	xk	PROPN
ejpam-4323	162	7	,	,	PUNCT
ejpam-4323	162	8	n	n	CCONJ
ejpam-4323	162	9	,	,	PUNCT
ejpam-4323	162	10	1	1	NUM
ejpam-4323	162	11	≤	≤	NUM
ejpam-4323	162	12	k	k	X
ejpam-4323	162	13	≤	≤	PROPN
ejpam-4323	163	1	kn	kn	NOUN
ejpam-4323	163	2	=	=	PUNCT
ejpam-4323	163	3	k(n	k(n	PROPN
ejpam-4323	163	4	)	)	PUNCT
ejpam-4323	163	5	}	}	PUNCT
ejpam-4323	163	6	,	,	PUNCT
ejpam-4323	163	7	n	n	X
ejpam-4323	163	8	≥	≥	NOUN
ejpam-4323	163	9	1	1	NUM
ejpam-4323	163	10	}	}	PUNCT
ejpam-4323	163	11	,	,	PUNCT
ejpam-4323	163	12	be	be	AUX
ejpam-4323	163	13	an	an	DET
ejpam-4323	163	14	array	array	NOUN
ejpam-4323	163	15	of	of	ADP
ejpam-4323	163	16	by	by	ADP
ejpam-4323	163	17	-	-	PUNCT
ejpam-4323	163	18	row	row	NOUN
ejpam-4323	163	19	-	-	PUNCT
ejpam-4323	163	20	independent	independent	ADJ
ejpam-4323	163	21	corrected	correct	VERB
ejpam-4323	163	22	geometric	geometric	ADJ
ejpam-4323	163	23	random	random	ADJ
ejpam-4323	163	24	variables	variable	NOUN
ejpam-4323	163	25	,	,	PUNCT
ejpam-4323	163	26	that	that	PRON
ejpam-4323	163	27	is	be	AUX
ejpam-4323	163	28	:	:	PUNCT
ejpam-4323	163	29	(	(	PUNCT
ejpam-4323	163	30	1	1	X
ejpam-4323	163	31	)	)	PUNCT
ejpam-4323	163	32	∀n	∀n	NUM
ejpam-4323	163	33	≥	≥	NOUN
ejpam-4323	163	34	1	1	NUM
ejpam-4323	163	35	,	,	PUNCT
ejpam-4323	163	36	∀1	∀1	VERB
ejpam-4323	163	37	≤	≤	PUNCT
ejpam-4323	163	38	k	k	X
ejpam-4323	163	39	≤	≤	X
ejpam-4323	163	40	k(n	k(n	PROPN
ejpam-4323	163	41	)	)	PUNCT
ejpam-4323	163	42	,	,	PUNCT
ejpam-4323	163	43	xk	xk	PROPN
ejpam-4323	163	44	,	,	PUNCT
ejpam-4323	163	45	n	n	PRON
ejpam-4323	163	46	∼	∼	NOUN
ejpam-4323	163	47	g∗(pk	g∗(pk	NOUN
ejpam-4323	163	48	,	,	PUNCT
ejpam-4323	163	49	n	n	CCONJ
ejpam-4323	163	50	)	)	PUNCT
ejpam-4323	163	51	,	,	PUNCT
ejpam-4323	163	52	with	with	ADP
ejpam-4323	163	53	0	0	NUM
ejpam-4323	163	54	<	<	X
ejpam-4323	163	55	pk	pk	NOUN
ejpam-4323	163	56	,	,	PUNCT
ejpam-4323	163	57	n	n	NOUN
ejpam-4323	163	58	=	=	SYM
ejpam-4323	163	59	1−	1−	NUM
ejpam-4323	163	60	qk	qk	NOUN
ejpam-4323	163	61	,	,	PUNCT
ejpam-4323	163	62	n	n	CCONJ
ejpam-4323	163	63	<	<	X
ejpam-4323	163	64	1	1	NUM
ejpam-4323	163	65	and	and	CCONJ
ejpam-4323	163	66	:	:	PUNCT
ejpam-4323	163	67	(	(	PUNCT
ejpam-4323	163	68	2	2	X
ejpam-4323	163	69	)	)	PUNCT
ejpam-4323	163	70	sup1≤k≤k(n	sup1≤k≤k(n	NOUN
ejpam-4323	163	71	)	)	PUNCT
ejpam-4323	163	72	qk	qk	PROPN
ejpam-4323	163	73	,	,	PUNCT
ejpam-4323	163	74	n	n	PROPN
ejpam-4323	163	75	→	→	SYM
ejpam-4323	163	76	0	0	NUM
ejpam-4323	163	77	;	;	PUNCT
ejpam-4323	163	78	(	(	PUNCT
ejpam-4323	163	79	3	3	X
ejpam-4323	163	80	)	)	PUNCT
ejpam-4323	163	81	∑	∑	NOUN
ejpam-4323	163	82	1≤k≤k(n	1≤k≤k(n	NUM
ejpam-4323	163	83	)	)	PUNCT
ejpam-4323	163	84	qk	qk	PROPN
ejpam-4323	163	85	,	,	PUNCT
ejpam-4323	163	86	n	n	PROPN
ejpam-4323	163	87	→	→	SYM
ejpam-4323	163	88	λ	λ	NOUN
ejpam-4323	163	89	∈]0	∈]0	X
ejpam-4323	163	90	,	,	PUNCT
ejpam-4323	163	91	+	+	NOUN
ejpam-4323	163	92	∞	∞	PROPN
ejpam-4323	163	93	[	[	X
ejpam-4323	163	94	.	.	PUNCT
ejpam-4323	164	1	then	then	ADV
ejpam-4323	164	2	we	we	PRON
ejpam-4323	164	3	have	have	AUX
ejpam-4323	164	4	sn[x	sn[x	VERB
ejpam-4323	164	5	]	]	PUNCT
ejpam-4323	164	6	p(λ	p(λ	NOUN
ejpam-4323	164	7	)	)	PUNCT
ejpam-4323	164	8	.	.	PUNCT
ejpam-4323	165	1	proof	proof	NOUN
ejpam-4323	165	2	of	of	ADP
ejpam-4323	165	3	theorem	theorem	ADJ
ejpam-4323	165	4	2	2	NUM
ejpam-4323	165	5	.	.	NOUN
ejpam-4323	165	6	assumption	assumption	NOUN
ejpam-4323	165	7	(	(	PUNCT
ejpam-4323	165	8	2	2	NUM
ejpam-4323	165	9	)	)	PUNCT
ejpam-4323	165	10	of	of	ADP
ejpam-4323	165	11	the	the	DET
ejpam-4323	165	12	theorem	theorem	NOUN
ejpam-4323	165	13	means	mean	VERB
ejpam-4323	165	14	that	that	SCONJ
ejpam-4323	165	15	qk	qk	NOUN
ejpam-4323	165	16	,	,	PUNCT
ejpam-4323	165	17	n	n	PROPN
ejpam-4323	165	18	=	=	SYM
ejpam-4323	165	19	on(1	on(1	NOUN
ejpam-4323	165	20	)	)	PUNCT
ejpam-4323	165	21	,	,	PUNCT
ejpam-4323	165	22	pk	pk	NOUN
ejpam-4323	165	23	,	,	PUNCT
ejpam-4323	165	24	n	n	NOUN
ejpam-4323	165	25	=	=	SYM
ejpam-4323	165	26	1	1	NUM
ejpam-4323	165	27	+	+	NUM
ejpam-4323	165	28	on(1	on(1	NOUN
ejpam-4323	165	29	)	)	PUNCT
ejpam-4323	165	30	and	and	CCONJ
ejpam-4323	165	31	(	(	PUNCT
ejpam-4323	165	32	1	1	NUM
ejpam-4323	165	33	/	/	SYM
ejpam-4323	165	34	pk	pk	NOUN
ejpam-4323	165	35	,	,	PUNCT
ejpam-4323	165	36	n	n	CCONJ
ejpam-4323	165	37	)	)	PUNCT
ejpam-4323	165	38	i	i	PRON
ejpam-4323	165	39	=	=	NOUN
ejpam-4323	165	40	1	1	NUM
ejpam-4323	165	41	+	+	NUM
ejpam-4323	165	42	on(1	on(1	NOUN
ejpam-4323	165	43	)	)	PUNCT
ejpam-4323	165	44	,	,	PUNCT
ejpam-4323	165	45	i	i	PRON
ejpam-4323	165	46	=	=	NOUN
ejpam-4323	165	47	1	1	NUM
ejpam-4323	165	48	,	,	PUNCT
ejpam-4323	165	49	2	2	NUM
ejpam-4323	165	50	,	,	PUNCT
ejpam-4323	165	51	3	3	NUM
ejpam-4323	165	52	.	.	X
ejpam-4323	166	1	we	we	PRON
ejpam-4323	166	2	have	have	VERB
ejpam-4323	166	3	to	to	PART
ejpam-4323	166	4	check	check	VERB
ejpam-4323	166	5	the	the	DET
ejpam-4323	166	6	uan	uan	PROPN
ejpam-4323	166	7	condition	condition	NOUN
ejpam-4323	166	8	.	.	PUNCT
ejpam-4323	167	1	by	by	ADP
ejpam-4323	167	2	using	use	VERB
ejpam-4323	167	3	chebychev	chebychev	NOUN
ejpam-4323	167	4	’s	’s	PART
ejpam-4323	167	5	inequality	inequality	NOUN
ejpam-4323	167	6	,	,	PUNCT
ejpam-4323	167	7	we	we	PRON
ejpam-4323	167	8	have	have	AUX
ejpam-4323	167	9	,	,	PUNCT
ejpam-4323	167	10	for	for	ADP
ejpam-4323	167	11	any	any	DET
ejpam-4323	167	12	ε	ε	PROPN
ejpam-4323	167	13	>	>	X
ejpam-4323	167	14	0	0	PROPN
ejpam-4323	167	15	,	,	PUNCT
ejpam-4323	167	16	u(n	u(n	PROPN
ejpam-4323	167	17	,	,	PUNCT
ejpam-4323	167	18	ε	ε	PROPN
ejpam-4323	167	19	,	,	PUNCT
ejpam-4323	167	20	x	x	NOUN
ejpam-4323	167	21	)	)	PUNCT
ejpam-4323	167	22	=	=	SYM
ejpam-4323	167	23	sup	sup	NOUN
ejpam-4323	167	24	1≤k≤kn	1≤k≤kn	NUM
ejpam-4323	167	25	p(|xk	p(|xk	NUM
ejpam-4323	167	26	,	,	PUNCT
ejpam-4323	167	27	n	n	CCONJ
ejpam-4323	167	28	−	−	PROPN
ejpam-4323	167	29	ak	ak	PROPN
ejpam-4323	167	30	,	,	PUNCT
ejpam-4323	167	31	n|	n|	X
ejpam-4323	167	32	≥	≥	NOUN
ejpam-4323	167	33	ε	ε	NOUN
ejpam-4323	167	34	)	)	PUNCT
ejpam-4323	167	35	≤	≤	NOUN
ejpam-4323	168	1	ε−2	ε−2	PROPN
ejpam-4323	168	2	sup	sup	NOUN
ejpam-4323	168	3	1≤k≤kn	1≤k≤kn	NUM
ejpam-4323	168	4	var(xk	var(xk	NOUN
ejpam-4323	168	5	,	,	PUNCT
ejpam-4323	168	6	n	n	CCONJ
ejpam-4323	168	7	)	)	PUNCT
ejpam-4323	169	1	=	=	SYM
ejpam-4323	169	2	ε−2	ε−2	PROPN
ejpam-4323	169	3	sup	sup	NOUN
ejpam-4323	169	4	1≤k≤kn	1≤k≤kn	NUM
ejpam-4323	169	5	qk	qk	NOUN
ejpam-4323	169	6	,	,	PUNCT
ejpam-4323	169	7	n	n	PROPN
ejpam-4323	169	8	p2k	p2k	PROPN
ejpam-4323	169	9	,	,	PUNCT
ejpam-4323	169	10	n	n	PROPN
ejpam-4323	169	11	=	=	PUNCT
ejpam-4323	169	12	ε−2on(1)(1	ε−2on(1)(1	PROPN
ejpam-4323	169	13	+	+	X
ejpam-4323	169	14	on(1	on(1	NOUN
ejpam-4323	169	15	)	)	PUNCT
ejpam-4323	169	16	)	)	PUNCT
ejpam-4323	170	1	→	→	SYM
ejpam-4323	170	2	0	0	X
ejpam-4323	170	3	.	.	PUNCT
ejpam-4323	171	1	the	the	DET
ejpam-4323	171	2	vch	vch	PROPN
ejpam-4323	171	3	also	also	ADV
ejpam-4323	171	4	holds	hold	VERB
ejpam-4323	171	5	since	since	SCONJ
ejpam-4323	171	6	mv	mv	PROPN
ejpam-4323	171	7	(	(	PUNCT
ejpam-4323	171	8	n	n	CCONJ
ejpam-4323	171	9	,	,	PUNCT
ejpam-4323	171	10	x	x	NOUN
ejpam-4323	171	11	)	)	PUNCT
ejpam-4323	171	12	=	=	SYM
ejpam-4323	171	13	∑	∑	PUNCT
ejpam-4323	171	14	1≤k≤k(n	1≤k≤k(n	NUM
ejpam-4323	171	15	)	)	PUNCT
ejpam-4323	171	16	var(xk	var(xk	X
ejpam-4323	171	17	,	,	PUNCT
ejpam-4323	171	18	n	n	CCONJ
ejpam-4323	171	19	)	)	PUNCT
ejpam-4323	171	20	ab	ab	PROPN
ejpam-4323	171	21	niang	niang	PROPN
ejpam-4323	171	22	et	et	PROPN
ejpam-4323	171	23	al	al	PROPN
ejpam-4323	171	24	.	.	PUNCT
ejpam-4323	171	25	/	/	SYM
ejpam-4323	171	26	eur	eur	PROPN
ejpam-4323	171	27	.	.	PUNCT
ejpam-4323	172	1	j.	j.	PROPN
ejpam-4323	172	2	pure	pure	PROPN
ejpam-4323	172	3	appl	appl	PROPN
ejpam-4323	172	4	.	.	PROPN
ejpam-4323	172	5	math	math	PROPN
ejpam-4323	172	6	,	,	PUNCT
ejpam-4323	172	7	15	15	NUM
ejpam-4323	172	8	(	(	PUNCT
ejpam-4323	172	9	2	2	NUM
ejpam-4323	172	10	)	)	PUNCT
ejpam-4323	172	11	(	(	PUNCT
ejpam-4323	172	12	2022	2022	NUM
ejpam-4323	172	13	)	)	PUNCT
ejpam-4323	172	14	,	,	PUNCT
ejpam-4323	172	15	511	511	NUM
ejpam-4323	172	16	-	-	SYM
ejpam-4323	172	17	527	527	NUM
ejpam-4323	172	18	522	522	NUM
ejpam-4323	172	19	=	=	SYM
ejpam-4323	172	20	∑	∑	PUNCT
ejpam-4323	172	21	1≤k≤k(n	1≤k≤k(n	NUM
ejpam-4323	172	22	)	)	PUNCT
ejpam-4323	172	23	qk	qk	PROPN
ejpam-4323	172	24	,	,	PUNCT
ejpam-4323	172	25	n	n	PROPN
ejpam-4323	172	26	p2k	p2k	PROPN
ejpam-4323	172	27	,	,	PUNCT
ejpam-4323	172	28	n	n	NOUN
ejpam-4323	172	29	=	=	SYM
ejpam-4323	172	30	(	(	PUNCT
ejpam-4323	172	31	1	1	NUM
ejpam-4323	172	32	+	+	SYM
ejpam-4323	172	33	on(1	on(1	NOUN
ejpam-4323	172	34	)	)	PUNCT
ejpam-4323	172	35	)	)	PUNCT
ejpam-4323	172	36	∑	∑	PUNCT
ejpam-4323	172	37	1≤k≤k(n	1≤k≤k(n	X
ejpam-4323	172	38	)	)	PUNCT
ejpam-4323	172	39	qk	qk	PROPN
ejpam-4323	172	40	,	,	PUNCT
ejpam-4323	172	41	n	n	PROPN
ejpam-4323	172	42	→	→	SYM
ejpam-4323	172	43	λ	λ	X
ejpam-4323	172	44	.	.	PUNCT
ejpam-4323	173	1	besides	besides	SCONJ
ejpam-4323	173	2	∑	∑	ADP
ejpam-4323	173	3	1≤k≤k(n	1≤k≤k(n	NUM
ejpam-4323	173	4	)	)	PUNCT
ejpam-4323	173	5	e(xk	e(xk	PROPN
ejpam-4323	173	6	,	,	PUNCT
ejpam-4323	173	7	n	n	CCONJ
ejpam-4323	173	8	)	)	PUNCT
ejpam-4323	173	9	=	=	SYM
ejpam-4323	173	10	∑	∑	PUNCT
ejpam-4323	173	11	1≤k≤k(n	1≤k≤k(n	NUM
ejpam-4323	173	12	)	)	PUNCT
ejpam-4323	173	13	qk	qk	PROPN
ejpam-4323	173	14	,	,	PUNCT
ejpam-4323	173	15	n	n	PRON
ejpam-4323	173	16	pk	pk	NOUN
ejpam-4323	173	17	,	,	PUNCT
ejpam-4323	173	18	n	n	NOUN
ejpam-4323	173	19	=	=	SYM
ejpam-4323	173	20	(	(	PUNCT
ejpam-4323	173	21	1	1	NUM
ejpam-4323	173	22	+	+	SYM
ejpam-4323	173	23	on(1	on(1	NOUN
ejpam-4323	173	24	)	)	PUNCT
ejpam-4323	173	25	)	)	PUNCT
ejpam-4323	173	26	∑	∑	PUNCT
ejpam-4323	173	27	1≤k≤k(n	1≤k≤k(n	X
ejpam-4323	173	28	)	)	PUNCT
ejpam-4323	173	29	qk	qk	PROPN
ejpam-4323	173	30	,	,	PUNCT
ejpam-4323	173	31	n	n	PROPN
ejpam-4323	173	32	→	→	SYM
ejpam-4323	173	33	λ	λ	X
ejpam-4323	173	34	.	.	PUNCT
ejpam-4323	173	35	here	here	ADV
ejpam-4323	173	36	again	again	ADV
ejpam-4323	173	37	,	,	PUNCT
ejpam-4323	173	38	we	we	PRON
ejpam-4323	173	39	are	be	AUX
ejpam-4323	173	40	in	in	ADP
ejpam-4323	173	41	the	the	DET
ejpam-4323	173	42	position	position	NOUN
ejpam-4323	173	43	of	of	ADP
ejpam-4323	173	44	applying	apply	VERB
ejpam-4323	173	45	the	the	DET
ejpam-4323	173	46	conditions	condition	NOUN
ejpam-4323	173	47	of	of	ADP
ejpam-4323	173	48	weak	weak	ADJ
ejpam-4323	173	49	convergence	convergence	NOUN
ejpam-4323	173	50	to	to	ADP
ejpam-4323	173	51	a	a	DET
ejpam-4323	173	52	poisson	poisson	NOUN
ejpam-4323	173	53	law	law	NOUN
ejpam-4323	173	54	by	by	ADP
ejpam-4323	173	55	checking	check	VERB
ejpam-4323	173	56	the	the	DET
ejpam-4323	173	57	poisson	poisson	PROPN
ejpam-4323	173	58	lynderbeg	lynderbeg	PROPN
ejpam-4323	173	59	condition	condition	NOUN
ejpam-4323	173	60	(	(	PUNCT
ejpam-4323	173	61	4	4	NUM
ejpam-4323	173	62	)	)	PUNCT
ejpam-4323	173	63	.	.	PUNCT
ejpam-4323	174	1	we	we	PRON
ejpam-4323	174	2	have	have	VERB
ejpam-4323	174	3	for	for	ADP
ejpam-4323	174	4	any	any	DET
ejpam-4323	174	5	0	0	PUNCT
ejpam-4323	174	6	<	<	X
ejpam-4323	174	7	ε	ε	X
ejpam-4323	174	8	<	<	X
ejpam-4323	174	9	1/2	1/2	NUM
ejpam-4323	174	10	ln	ln	ADJ
ejpam-4323	174	11	,	,	PUNCT
ejpam-4323	174	12	p	p	X
ejpam-4323	174	13	(	(	PUNCT
ejpam-4323	174	14	ε	ε	PROPN
ejpam-4323	174	15	)	)	PUNCT
ejpam-4323	174	16	=	=	NOUN
ejpam-4323	174	17	:	:	PUNCT
ejpam-4323	174	18	k(n)∑	k(n)∑	X
ejpam-4323	174	19	k=1	k=1	PROPN
ejpam-4323	175	1	ln	ln	INTJ
ejpam-4323	175	2	,	,	PUNCT
ejpam-4323	175	3	k	k	PROPN
ejpam-4323	175	4	,	,	PUNCT
ejpam-4323	175	5	p	p	X
ejpam-4323	175	6	(	(	PUNCT
ejpam-4323	175	7	ε	ε	PROPN
ejpam-4323	175	8	)	)	PUNCT
ejpam-4323	175	9	,	,	PUNCT
ejpam-4323	175	10	with	with	ADP
ejpam-4323	175	11	ln	ln	ADJ
ejpam-4323	175	12	,	,	PUNCT
ejpam-4323	175	13	k	k	NOUN
ejpam-4323	175	14	,	,	PUNCT
ejpam-4323	175	15	p	p	X
ejpam-4323	175	16	(	(	PUNCT
ejpam-4323	175	17	ε	ε	PROPN
ejpam-4323	175	18	)	)	PUNCT
ejpam-4323	175	19	=	=	SYM
ejpam-4323	175	20	∫	∫	PROPN
ejpam-4323	175	21	(	(	PUNCT
ejpam-4323	175	22	|x−1|≥ε	|x−1|≥ε	NOUN
ejpam-4323	175	23	)	)	PUNCT
ejpam-4323	175	24	x2	x2	PROPN
ejpam-4323	175	25	dfk	dfk	PROPN
ejpam-4323	175	26	,	,	PUNCT
ejpam-4323	175	27	n(x+	n(x+	PROPN
ejpam-4323	175	28	ak	ak	PROPN
ejpam-4323	175	29	,	,	PUNCT
ejpam-4323	175	30	n	n	CCONJ
ejpam-4323	175	31	)	)	PUNCT
ejpam-4323	175	32	=	=	SYM
ejpam-4323	175	33	∫(∣∣∣∣xk	∫(∣∣∣∣xk	PROPN
ejpam-4323	175	34	,	,	PUNCT
ejpam-4323	175	35	n−	n−	PROPN
ejpam-4323	175	36	qk	qk	NOUN
ejpam-4323	175	37	,	,	PUNCT
ejpam-4323	175	38	n	n	PRON
ejpam-4323	175	39	pk	pk	NOUN
ejpam-4323	175	40	,	,	PUNCT
ejpam-4323	175	41	n	n	NOUN
ejpam-4323	175	42	−1	−1	NOUN
ejpam-4323	175	43	∣∣∣∣≥ε	∣∣∣∣≥ε	NOUN
ejpam-4323	175	44	)	)	PUNCT
ejpam-4323	175	45	∣∣∣∣xk	∣∣∣∣xk	PROPN
ejpam-4323	175	46	,	,	PUNCT
ejpam-4323	175	47	n	n	CCONJ
ejpam-4323	175	48	−	−	PROPN
ejpam-4323	175	49	qk	qk	PROPN
ejpam-4323	175	50	,	,	PUNCT
ejpam-4323	175	51	n	n	PRON
ejpam-4323	175	52	pk	pk	NOUN
ejpam-4323	175	53	,	,	PUNCT
ejpam-4323	175	54	n	n	PRON
ejpam-4323	175	55	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-4323	175	56	dpxk	dpxk	NOUN
ejpam-4323	175	57	,	,	PUNCT
ejpam-4323	175	58	n	n	X
ejpam-4323	175	59	=	=	PUNCT
ejpam-4323	176	1	+	+	ADP
ejpam-4323	176	2	∞∑	∞∑	PROPN
ejpam-4323	176	3	j=0	j=0	PROPN
ejpam-4323	176	4	pk	pk	NOUN
ejpam-4323	176	5	,	,	PUNCT
ejpam-4323	176	6	nq	nq	PROPN
ejpam-4323	176	7	j	j	PROPN
ejpam-4323	176	8	k	k	PROPN
ejpam-4323	176	9	,	,	PUNCT
ejpam-4323	176	10	n	n	PROPN
ejpam-4323	176	11	(	(	PUNCT
ejpam-4323	176	12	1(∣∣∣∣xk	1(∣∣∣∣xk	PROPN
ejpam-4323	176	13	,	,	PUNCT
ejpam-4323	176	14	n−	n−	PROPN
ejpam-4323	176	15	qk	qk	NOUN
ejpam-4323	176	16	,	,	PUNCT
ejpam-4323	176	17	n	n	PRON
ejpam-4323	176	18	pk	pk	NOUN
ejpam-4323	176	19	,	,	PUNCT
ejpam-4323	176	20	n	n	NOUN
ejpam-4323	176	21	−1	−1	NOUN
ejpam-4323	176	22	∣∣∣∣≥ε	∣∣∣∣≥ε	NOUN
ejpam-4323	176	23	)	)	PUNCT
ejpam-4323	176	24	∣∣∣∣xk	∣∣∣∣xk	PROPN
ejpam-4323	176	25	,	,	PUNCT
ejpam-4323	176	26	n	n	CCONJ
ejpam-4323	176	27	−	−	PROPN
ejpam-4323	176	28	qk	qk	PROPN
ejpam-4323	176	29	,	,	PUNCT
ejpam-4323	176	30	n	n	PRON
ejpam-4323	176	31	pk	pk	NOUN
ejpam-4323	176	32	,	,	PUNCT
ejpam-4323	176	33	n	n	PRON
ejpam-4323	176	34	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-4323	176	35	)	)	PUNCT
ejpam-4323	176	36	(	(	PUNCT
ejpam-4323	176	37	xk	xk	PROPN
ejpam-4323	176	38	,	,	PUNCT
ejpam-4323	176	39	n	n	CCONJ
ejpam-4323	176	40	=	=	SYM
ejpam-4323	176	41	j	j	NOUN
ejpam-4323	176	42	)	)	PUNCT
ejpam-4323	176	43	=	=	SYM
ejpam-4323	176	44	pk	pk	PROPN
ejpam-4323	176	45	,	,	PUNCT
ejpam-4323	176	46	n1(∣∣∣∣	n1(∣∣∣∣	PROPN
ejpam-4323	176	47	qk	qk	PROPN
ejpam-4323	176	48	,	,	PUNCT
ejpam-4323	176	49	npk	npk	NOUN
ejpam-4323	176	50	,	,	PUNCT
ejpam-4323	176	51	n	n	CCONJ
ejpam-4323	176	52	+1	+1	PROPN
ejpam-4323	176	53	∣∣∣∣≥ε	∣∣∣∣≥ε	X
ejpam-4323	176	54	)	)	PUNCT
ejpam-4323	176	55	(	(	PUNCT
ejpam-4323	176	56	qk	qk	PROPN
ejpam-4323	176	57	,	,	PUNCT
ejpam-4323	176	58	n	n	PRON
ejpam-4323	176	59	pk	pk	NOUN
ejpam-4323	176	60	,	,	PUNCT
ejpam-4323	176	61	n	n	CCONJ
ejpam-4323	176	62	)	)	PUNCT
ejpam-4323	176	63	2	2	NUM
ejpam-4323	176	64	(	(	PUNCT
ejpam-4323	176	65	for	for	ADP
ejpam-4323	176	66	j	j	PROPN
ejpam-4323	176	67	=	=	SYM
ejpam-4323	176	68	0	0	NUM
ejpam-4323	176	69	)	)	PUNCT
ejpam-4323	176	70	+	+	NUM
ejpam-4323	176	71	pk	pk	NOUN
ejpam-4323	176	72	,	,	PUNCT
ejpam-4323	176	73	nqk	nqk	NOUN
ejpam-4323	176	74	,	,	PUNCT
ejpam-4323	176	75	n1(∣∣∣∣	n1(∣∣∣∣	PROPN
ejpam-4323	176	76	qk	qk	PROPN
ejpam-4323	176	77	,	,	PUNCT
ejpam-4323	176	78	npk	npk	NOUN
ejpam-4323	176	79	,	,	PUNCT
ejpam-4323	176	80	n	n	NOUN
ejpam-4323	176	81	∣∣∣∣≥ε	∣∣∣∣≥ε	NOUN
ejpam-4323	176	82	)	)	PUNCT
ejpam-4323	176	83	(	(	PUNCT
ejpam-4323	176	84	1−	1−	NUM
ejpam-4323	176	85	qk	qk	NOUN
ejpam-4323	176	86	,	,	PUNCT
ejpam-4323	176	87	n	n	PRON
ejpam-4323	176	88	pk	pk	NOUN
ejpam-4323	176	89	,	,	PUNCT
ejpam-4323	176	90	n	n	CCONJ
ejpam-4323	176	91	)	)	PUNCT
ejpam-4323	176	92	2	2	NUM
ejpam-4323	176	93	(	(	PUNCT
ejpam-4323	176	94	for	for	ADP
ejpam-4323	176	95	j	j	PROPN
ejpam-4323	176	96	=	=	SYM
ejpam-4323	176	97	1	1	NUM
ejpam-4323	176	98	)	)	PUNCT
ejpam-4323	176	99	+	+	PUNCT
ejpam-4323	177	1	+	+	ADJ
ejpam-4323	177	2	∞∑	∞∑	PROPN
ejpam-4323	177	3	j=2	j=2	PROPN
ejpam-4323	177	4	pk	pk	NOUN
ejpam-4323	177	5	,	,	PUNCT
ejpam-4323	177	6	nq	nq	PROPN
ejpam-4323	177	7	j	j	PROPN
ejpam-4323	177	8	k	k	PROPN
ejpam-4323	177	9	,	,	PUNCT
ejpam-4323	177	10	n1	n1	PROPN
ejpam-4323	177	11	(	(	PUNCT
ejpam-4323	177	12	∣∣∣∣j−1−	∣∣∣∣j−1−	PROPN
ejpam-4323	177	13	qk	qk	PROPN
ejpam-4323	177	14	,	,	PUNCT
ejpam-4323	177	15	n	n	PRON
ejpam-4323	177	16	pk	pk	NOUN
ejpam-4323	177	17	,	,	PUNCT
ejpam-4323	177	18	n	n	X
ejpam-4323	177	19	∣∣∣∣≥ε	∣∣∣∣≥ε	NOUN
ejpam-4323	177	20	)	)	PUNCT
ejpam-4323	177	21	(	(	PUNCT
ejpam-4323	177	22	j	j	PROPN
ejpam-4323	177	23	−	−	PROPN
ejpam-4323	177	24	qk	qk	PROPN
ejpam-4323	177	25	,	,	PUNCT
ejpam-4323	177	26	n	n	PRON
ejpam-4323	177	27	pk	pk	NOUN
ejpam-4323	177	28	,	,	PUNCT
ejpam-4323	177	29	n	n	CCONJ
ejpam-4323	177	30	)	)	PUNCT
ejpam-4323	177	31	2	2	NUM
ejpam-4323	177	32	(	(	PUNCT
ejpam-4323	177	33	for	for	ADP
ejpam-4323	177	34	j	j	PROPN
ejpam-4323	177	35	≥	≥	PROPN
ejpam-4323	177	36	2	2	NUM
ejpam-4323	177	37	)	)	PUNCT
ejpam-4323	177	38	.	.	PUNCT
ejpam-4323	178	1	by	by	ADP
ejpam-4323	178	2	the	the	DET
ejpam-4323	178	3	same	same	ADJ
ejpam-4323	178	4	remarks	remark	NOUN
ejpam-4323	178	5	used	use	VERB
ejpam-4323	178	6	in	in	ADP
ejpam-4323	178	7	the	the	DET
ejpam-4323	178	8	precedent	precedent	NOUN
ejpam-4323	178	9	proof	proof	NOUN
ejpam-4323	178	10	,	,	PUNCT
ejpam-4323	178	11	we	we	PRON
ejpam-4323	178	12	have	have	VERB
ejpam-4323	178	13	for	for	ADP
ejpam-4323	178	14	n	n	X
ejpam-4323	178	15	large	large	ADJ
ejpam-4323	178	16	enough	enough	ADV
ejpam-4323	178	17	,	,	PUNCT
ejpam-4323	178	18	1(∣∣∣∣	1(∣∣∣∣	PROPN
ejpam-4323	178	19	qk	qk	PROPN
ejpam-4323	178	20	,	,	PUNCT
ejpam-4323	178	21	npk	npk	NOUN
ejpam-4323	178	22	,	,	PUNCT
ejpam-4323	178	23	n	n	CCONJ
ejpam-4323	178	24	+1	+1	NOUN
ejpam-4323	178	25	∣∣∣∣≥ε	∣∣∣∣≥ε	X
ejpam-4323	178	26	)	)	PUNCT
ejpam-4323	179	1	=	=	SYM
ejpam-4323	179	2	1(|on(1)(1+on(1))+1|≥ε	1(|on(1)(1+on(1))+1|≥ε	X
ejpam-4323	179	3	)	)	PUNCT
ejpam-4323	179	4	=	=	SYM
ejpam-4323	179	5	1	1	NUM
ejpam-4323	179	6	ab	ab	PROPN
ejpam-4323	179	7	niang	niang	PROPN
ejpam-4323	179	8	et	et	PROPN
ejpam-4323	179	9	al	al	PROPN
ejpam-4323	179	10	.	.	PUNCT
ejpam-4323	179	11	/	/	SYM
ejpam-4323	179	12	eur	eur	PROPN
ejpam-4323	179	13	.	.	PUNCT
ejpam-4323	180	1	j.	j.	PROPN
ejpam-4323	180	2	pure	pure	PROPN
ejpam-4323	180	3	appl	appl	PROPN
ejpam-4323	180	4	.	.	PROPN
ejpam-4323	180	5	math	math	PROPN
ejpam-4323	180	6	,	,	PUNCT
ejpam-4323	180	7	15	15	NUM
ejpam-4323	180	8	(	(	PUNCT
ejpam-4323	180	9	2	2	NUM
ejpam-4323	180	10	)	)	PUNCT
ejpam-4323	180	11	(	(	PUNCT
ejpam-4323	180	12	2022	2022	NUM
ejpam-4323	180	13	)	)	PUNCT
ejpam-4323	180	14	,	,	PUNCT
ejpam-4323	180	15	511	511	NUM
ejpam-4323	180	16	-	-	SYM
ejpam-4323	180	17	527	527	NUM
ejpam-4323	180	18	523	523	NUM
ejpam-4323	180	19	and	and	CCONJ
ejpam-4323	180	20	next	next	ADJ
ejpam-4323	180	21	pk	pk	PROPN
ejpam-4323	180	22	,	,	PUNCT
ejpam-4323	180	23	n1(∣∣∣∣	n1(∣∣∣∣	PROPN
ejpam-4323	180	24	qk	qk	PROPN
ejpam-4323	180	25	,	,	PUNCT
ejpam-4323	180	26	npk	npk	NOUN
ejpam-4323	180	27	,	,	PUNCT
ejpam-4323	180	28	n	n	CCONJ
ejpam-4323	180	29	+1	+1	PROPN
ejpam-4323	180	30	∣∣∣∣≥ε	∣∣∣∣≥ε	PROPN
ejpam-4323	180	31	)	)	PUNCT
ejpam-4323	180	32	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4323	180	33	qk	qk	PROPN
ejpam-4323	180	34	,	,	PUNCT
ejpam-4323	180	35	npk	npk	NOUN
ejpam-4323	180	36	,	,	PUNCT
ejpam-4323	180	37	n	n	NOUN
ejpam-4323	180	38	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-4323	180	39	=	=	SYM
ejpam-4323	180	40	(	(	PUNCT
ejpam-4323	180	41	1	1	NUM
ejpam-4323	180	42	+	+	NUM
ejpam-4323	180	43	on(1))q	on(1))q	NOUN
ejpam-4323	180	44	2	2	NUM
ejpam-4323	180	45	k	k	NOUN
ejpam-4323	180	46	,	,	PUNCT
ejpam-4323	180	47	n	n	NOUN
ejpam-4323	180	48	=	=	PUNCT
ejpam-4323	180	49	on(1)(1	on(1)(1	NUM
ejpam-4323	180	50	+	+	ADJ
ejpam-4323	180	51	on(1	on(1	NOUN
ejpam-4323	180	52	)	)	PUNCT
ejpam-4323	180	53	)	)	PUNCT
ejpam-4323	180	54	qk	qk	PROPN
ejpam-4323	180	55	,	,	PUNCT
ejpam-4323	180	56	n.	n.	PROPN
ejpam-4323	180	57	(	(	PUNCT
ejpam-4323	180	58	l1	l1	PROPN
ejpam-4323	180	59	)	)	PUNCT
ejpam-4323	180	60	also	also	ADV
ejpam-4323	180	61	,	,	PUNCT
ejpam-4323	180	62	we	we	PRON
ejpam-4323	180	63	have	have	VERB
ejpam-4323	180	64	for	for	ADP
ejpam-4323	180	65	n	n	X
ejpam-4323	180	66	large	large	ADJ
ejpam-4323	180	67	enough	enough	ADV
ejpam-4323	180	68	,	,	PUNCT
ejpam-4323	180	69	1(∣∣∣∣	1(∣∣∣∣	PROPN
ejpam-4323	180	70	qk	qk	PROPN
ejpam-4323	180	71	,	,	PUNCT
ejpam-4323	180	72	npk	npk	NOUN
ejpam-4323	180	73	,	,	PUNCT
ejpam-4323	180	74	n	n	NOUN
ejpam-4323	180	75	∣∣∣∣≥ε	∣∣∣∣≥ε	NOUN
ejpam-4323	180	76	)	)	PUNCT
ejpam-4323	180	77	=	=	SYM
ejpam-4323	180	78	1(|on(1)(1+on(1))|≥ε	1(|on(1)(1+on(1))|≥ε	NUM
ejpam-4323	180	79	)	)	PUNCT
ejpam-4323	180	80	=	=	SYM
ejpam-4323	180	81	0	0	NUM
ejpam-4323	180	82	and	and	CCONJ
ejpam-4323	180	83	next	next	ADJ
ejpam-4323	180	84	pk	pk	NOUN
ejpam-4323	180	85	,	,	PUNCT
ejpam-4323	180	86	nqk	nqk	NOUN
ejpam-4323	180	87	,	,	PUNCT
ejpam-4323	180	88	n1(∣∣∣∣	n1(∣∣∣∣	PROPN
ejpam-4323	180	89	qk	qk	PROPN
ejpam-4323	180	90	,	,	PUNCT
ejpam-4323	180	91	npk	npk	NOUN
ejpam-4323	180	92	,	,	PUNCT
ejpam-4323	180	93	n	n	NOUN
ejpam-4323	180	94	∣∣∣∣≥ε	∣∣∣∣≥ε	NOUN
ejpam-4323	180	95	)	)	PUNCT
ejpam-4323	180	96	(	(	PUNCT
ejpam-4323	180	97	1−	1−	NUM
ejpam-4323	180	98	qk	qk	NOUN
ejpam-4323	180	99	,	,	PUNCT
ejpam-4323	180	100	n	n	PRON
ejpam-4323	180	101	pk	pk	NOUN
ejpam-4323	180	102	,	,	PUNCT
ejpam-4323	180	103	n	n	CCONJ
ejpam-4323	180	104	)	)	PUNCT
ejpam-4323	180	105	2	2	NUM
ejpam-4323	180	106	=	=	SYM
ejpam-4323	180	107	0	0	NUM
ejpam-4323	180	108	.	.	PUNCT
ejpam-4323	181	1	(	(	PUNCT
ejpam-4323	181	2	l2	l2	NOUN
ejpam-4323	181	3	)	)	PUNCT
ejpam-4323	181	4	now	now	ADV
ejpam-4323	181	5	,	,	PUNCT
ejpam-4323	181	6	for	for	ADP
ejpam-4323	181	7	n	n	CCONJ
ejpam-4323	181	8	large	large	ADJ
ejpam-4323	181	9	enough	enough	ADV
ejpam-4323	181	10	and	and	CCONJ
ejpam-4323	181	11	for	for	ADP
ejpam-4323	181	12	any	any	DET
ejpam-4323	181	13	j	j	PROPN
ejpam-4323	181	14	≥	≥	NUM
ejpam-4323	181	15	2	2	NUM
ejpam-4323	181	16	,	,	PUNCT
ejpam-4323	181	17	1(|j−1+on(1)(1+on(1))|≥ε	1(|j−1+on(1)(1+on(1))|≥ε	NUM
ejpam-4323	181	18	)	)	PUNCT
ejpam-4323	181	19	=	=	SYM
ejpam-4323	181	20	1	1	NUM
ejpam-4323	181	21	and	and	CCONJ
ejpam-4323	181	22	thus	thus	ADV
ejpam-4323	181	23	,	,	PUNCT
ejpam-4323	181	24	aj	aj	PROPN
ejpam-4323	181	25	,	,	PUNCT
ejpam-4323	181	26	k	k	PROPN
ejpam-4323	181	27	,	,	PUNCT
ejpam-4323	181	28	n	n	PROPN
ejpam-4323	181	29	:	:	PUNCT
ejpam-4323	181	30	=	=	SYM
ejpam-4323	181	31	pk	pk	PROPN
ejpam-4323	181	32	,	,	PUNCT
ejpam-4323	181	33	nq	nq	PROPN
ejpam-4323	181	34	j	j	PROPN
ejpam-4323	181	35	k	k	PROPN
ejpam-4323	181	36	,	,	PUNCT
ejpam-4323	181	37	n1	n1	PROPN
ejpam-4323	181	38	(	(	PUNCT
ejpam-4323	181	39	∣∣∣∣j−1−	∣∣∣∣j−1−	PROPN
ejpam-4323	181	40	qk	qk	PROPN
ejpam-4323	181	41	,	,	PUNCT
ejpam-4323	181	42	n	n	PRON
ejpam-4323	181	43	pk	pk	NOUN
ejpam-4323	181	44	,	,	PUNCT
ejpam-4323	181	45	n	n	X
ejpam-4323	181	46	∣∣∣∣≥ε	∣∣∣∣≥ε	NOUN
ejpam-4323	181	47	)	)	PUNCT
ejpam-4323	181	48	(	(	PUNCT
ejpam-4323	181	49	j	j	PROPN
ejpam-4323	181	50	−	−	PROPN
ejpam-4323	181	51	qk	qk	PROPN
ejpam-4323	181	52	,	,	PUNCT
ejpam-4323	181	53	n	n	PRON
ejpam-4323	181	54	pk	pk	NOUN
ejpam-4323	181	55	,	,	PUNCT
ejpam-4323	181	56	n	n	NOUN
ejpam-4323	181	57	)	)	PUNCT
ejpam-4323	181	58	2	2	NUM
ejpam-4323	181	59	=	=	SYM
ejpam-4323	181	60	(	(	PUNCT
ejpam-4323	181	61	(	(	PUNCT
ejpam-4323	181	62	1	1	NUM
ejpam-4323	181	63	+	+	CCONJ
ejpam-4323	181	64	on(1))qk	on(1))qk	PROPN
ejpam-4323	181	65	,	,	PUNCT
ejpam-4323	181	66	n	n	CCONJ
ejpam-4323	181	67	)	)	PUNCT
ejpam-4323	181	68	qj−1	qj−1	PROPN
ejpam-4323	181	69	k	k	PROPN
ejpam-4323	181	70	,	,	PUNCT
ejpam-4323	181	71	n	n	PROPN
ejpam-4323	181	72	1(∣∣∣∣j−1+on(1)(1+on(1	1(∣∣∣∣j−1+on(1)(1+on(1	NUM
ejpam-4323	181	73	)	)	PUNCT
ejpam-4323	181	74	)	)	PUNCT
ejpam-4323	181	75	∣∣∣∣≥ε	∣∣∣∣≥ε	NOUN
ejpam-4323	181	76	)	)	PUNCT
ejpam-4323	181	77	(	(	PUNCT
ejpam-4323	181	78	j	j	NOUN
ejpam-4323	181	79	+	+	CCONJ
ejpam-4323	181	80	on(1)(1	on(1)(1	NUM
ejpam-4323	181	81	+	+	ADJ
ejpam-4323	181	82	on(1	on(1	NOUN
ejpam-4323	181	83	)	)	PUNCT
ejpam-4323	181	84	)	)	PUNCT
ejpam-4323	181	85	)	)	PUNCT
ejpam-4323	181	86	2	2	X
ejpam-4323	181	87	=	=	SYM
ejpam-4323	181	88	(	(	PUNCT
ejpam-4323	181	89	(	(	PUNCT
ejpam-4323	181	90	1	1	NUM
ejpam-4323	181	91	+	+	CCONJ
ejpam-4323	181	92	on(1))qk	on(1))qk	PROPN
ejpam-4323	181	93	,	,	PUNCT
ejpam-4323	181	94	n	n	CCONJ
ejpam-4323	181	95	)	)	PUNCT
ejpam-4323	181	96	qj−1	qj−1	PROPN
ejpam-4323	181	97	k	k	PROPN
ejpam-4323	181	98	,	,	PUNCT
ejpam-4323	181	99	n	n	PROPN
ejpam-4323	181	100	(	(	PUNCT
ejpam-4323	181	101	j	j	PROPN
ejpam-4323	181	102	+	+	CCONJ
ejpam-4323	181	103	on(1)(1	on(1)(1	NUM
ejpam-4323	181	104	+	+	ADJ
ejpam-4323	181	105	on(1	on(1	NOUN
ejpam-4323	181	106	)	)	PUNCT
ejpam-4323	181	107	)	)	PUNCT
ejpam-4323	181	108	)	)	PUNCT
ejpam-4323	181	109	2	2	NUM
ejpam-4323	181	110	≤	≤	NOUN
ejpam-4323	181	111	(	(	PUNCT
ejpam-4323	181	112	(	(	PUNCT
ejpam-4323	181	113	1	1	NUM
ejpam-4323	181	114	+	+	CCONJ
ejpam-4323	181	115	on(1))qk	on(1))qk	PROPN
ejpam-4323	181	116	,	,	PUNCT
ejpam-4323	181	117	n	n	CCONJ
ejpam-4323	181	118	)	)	PUNCT
ejpam-4323	181	119	qj−1	qj−1	PROPN
ejpam-4323	181	120	k	k	PROPN
ejpam-4323	181	121	,	,	PUNCT
ejpam-4323	181	122	n	n	PROPN
ejpam-4323	181	123	(	(	PUNCT
ejpam-4323	181	124	j	j	PROPN
ejpam-4323	181	125	+	+	CCONJ
ejpam-4323	181	126	1)2	1)2	NUM
ejpam-4323	181	127	≤	≤	NUM
ejpam-4323	181	128	2	2	NUM
ejpam-4323	181	129	(	(	PUNCT
ejpam-4323	181	130	(	(	PUNCT
ejpam-4323	181	131	1	1	NUM
ejpam-4323	181	132	+	+	CCONJ
ejpam-4323	181	133	on(1))qk	on(1))qk	PROPN
ejpam-4323	181	134	,	,	PUNCT
ejpam-4323	181	135	n	n	CCONJ
ejpam-4323	181	136	)	)	PUNCT
ejpam-4323	181	137	qj−1	qj−1	PROPN
ejpam-4323	181	138	k	k	PROPN
ejpam-4323	181	139	,	,	PUNCT
ejpam-4323	181	140	n	n	PROPN
ejpam-4323	181	141	(	(	PUNCT
ejpam-4323	181	142	j2	j2	PROPN
ejpam-4323	181	143	+	+	CCONJ
ejpam-4323	181	144	1	1	NUM
ejpam-4323	181	145	)	)	PUNCT
ejpam-4323	181	146	,	,	PUNCT
ejpam-4323	181	147	where	where	SCONJ
ejpam-4323	181	148	we	we	PRON
ejpam-4323	181	149	apply	apply	VERB
ejpam-4323	181	150	the	the	DET
ejpam-4323	181	151	c2	c2	PROPN
ejpam-4323	181	152	-	-	PUNCT
ejpam-4323	181	153	inequality	inequality	NOUN
ejpam-4323	181	154	in	in	ADP
ejpam-4323	181	155	the	the	DET
ejpam-4323	181	156	last	last	ADJ
ejpam-4323	181	157	line	line	NOUN
ejpam-4323	181	158	.	.	PUNCT
ejpam-4323	182	1	so	so	ADV
ejpam-4323	182	2	we	we	PRON
ejpam-4323	182	3	have	have	VERB
ejpam-4323	182	4	∑	∑	PROPN
ejpam-4323	182	5	j≥2	j≥2	PROPN
ejpam-4323	182	6	aj	aj	PROPN
ejpam-4323	182	7	,	,	PUNCT
ejpam-4323	182	8	k	k	PROPN
ejpam-4323	182	9	,	,	PUNCT
ejpam-4323	182	10	n	n	NOUN
ejpam-4323	182	11	≤	≤	NOUN
ejpam-4323	182	12	2(1	2(1	NUM
ejpam-4323	182	13	+	+	CCONJ
ejpam-4323	183	1	on(1	on(1	NOUN
ejpam-4323	183	2	)	)	PUNCT
ejpam-4323	183	3	)	)	PUNCT
ejpam-4323	184	1	qk	qk	PROPN
ejpam-4323	184	2	,	,	PUNCT
ejpam-4323	184	3	n	n	PRON
ejpam-4323	184	4	b(n	b(n	NOUN
ejpam-4323	184	5	,	,	PUNCT
ejpam-4323	184	6	k	k	NOUN
ejpam-4323	184	7	)	)	PUNCT
ejpam-4323	184	8	,	,	PUNCT
ejpam-4323	184	9	(	(	PUNCT
ejpam-4323	184	10	l3	l3	PROPN
ejpam-4323	184	11	)	)	PUNCT
ejpam-4323	184	12	with	with	ADP
ejpam-4323	184	13	ab	ab	PROPN
ejpam-4323	184	14	niang	niang	PROPN
ejpam-4323	184	15	et	et	PROPN
ejpam-4323	184	16	al	al	PROPN
ejpam-4323	184	17	.	.	PUNCT
ejpam-4323	184	18	/	/	SYM
ejpam-4323	184	19	eur	eur	PROPN
ejpam-4323	184	20	.	.	PUNCT
ejpam-4323	185	1	j.	j.	PROPN
ejpam-4323	185	2	pure	pure	PROPN
ejpam-4323	185	3	appl	appl	PROPN
ejpam-4323	185	4	.	.	PROPN
ejpam-4323	185	5	math	math	PROPN
ejpam-4323	185	6	,	,	PUNCT
ejpam-4323	185	7	15	15	NUM
ejpam-4323	185	8	(	(	PUNCT
ejpam-4323	185	9	2	2	NUM
ejpam-4323	185	10	)	)	PUNCT
ejpam-4323	185	11	(	(	PUNCT
ejpam-4323	185	12	2022	2022	NUM
ejpam-4323	185	13	)	)	PUNCT
ejpam-4323	185	14	,	,	PUNCT
ejpam-4323	185	15	511	511	NUM
ejpam-4323	185	16	-	-	SYM
ejpam-4323	185	17	527	527	NUM
ejpam-4323	185	18	524	524	NUM
ejpam-4323	185	19	b(n	b(n	PROPN
ejpam-4323	185	20	,	,	PUNCT
ejpam-4323	185	21	k	k	NOUN
ejpam-4323	185	22	)	)	PUNCT
ejpam-4323	185	23	=	=	PUNCT
ejpam-4323	185	24	∑	∑	PUNCT
ejpam-4323	185	25	j≥2	j≥2	PROPN
ejpam-4323	185	26	qj−1	qj−1	PROPN
ejpam-4323	185	27	k	k	PROPN
ejpam-4323	185	28	,	,	PUNCT
ejpam-4323	185	29	n	n	PROPN
ejpam-4323	185	30	+	+	CCONJ
ejpam-4323	185	31	∑	∑	PUNCT
ejpam-4323	185	32	j≥2	j≥2	ADJ
ejpam-4323	185	33	j2qj−1	j2qj−1	PROPN
ejpam-4323	185	34	k	k	PROPN
ejpam-4323	185	35	,	,	PUNCT
ejpam-4323	185	36	n	n	PROPN
ejpam-4323	185	37	=	=	NOUN
ejpam-4323	185	38	:	:	PUNCT
ejpam-4323	185	39	b(n	b(n	NOUN
ejpam-4323	185	40	,	,	PUNCT
ejpam-4323	185	41	k	k	NOUN
ejpam-4323	185	42	,	,	PUNCT
ejpam-4323	185	43	1	1	X
ejpam-4323	185	44	)	)	PUNCT
ejpam-4323	186	1	+	+	NOUN
ejpam-4323	186	2	b(n	b(n	PROPN
ejpam-4323	186	3	,	,	PUNCT
ejpam-4323	186	4	k	k	NOUN
ejpam-4323	186	5	,	,	PUNCT
ejpam-4323	186	6	2	2	NUM
ejpam-4323	186	7	)	)	PUNCT
ejpam-4323	186	8	.	.	PUNCT
ejpam-4323	187	1	we	we	PRON
ejpam-4323	187	2	have	have	VERB
ejpam-4323	187	3	b(n	b(n	PROPN
ejpam-4323	187	4	,	,	PUNCT
ejpam-4323	187	5	k	k	NOUN
ejpam-4323	187	6	,	,	PUNCT
ejpam-4323	187	7	1	1	NUM
ejpam-4323	187	8	)	)	PUNCT
ejpam-4323	187	9	=	=	SYM
ejpam-4323	187	10	(	(	PUNCT
ejpam-4323	187	11	∑	∑	PUNCT
ejpam-4323	187	12	j≥0	j≥0	PROPN
ejpam-4323	187	13	qjk	qjk	PROPN
ejpam-4323	187	14	,	,	PUNCT
ejpam-4323	187	15	n	n	CCONJ
ejpam-4323	187	16	)	)	PUNCT
ejpam-4323	187	17	−	−	PROPN
ejpam-4323	187	18	1	1	NUM
ejpam-4323	187	19	=	=	SYM
ejpam-4323	187	20	qk	qk	NOUN
ejpam-4323	187	21	,	,	PUNCT
ejpam-4323	187	22	n	n	PRON
ejpam-4323	187	23	pk	pk	NOUN
ejpam-4323	187	24	,	,	PUNCT
ejpam-4323	187	25	n	n	NOUN
ejpam-4323	187	26	=	=	SYM
ejpam-4323	187	27	on(1)(1	on(1)(1	NUM
ejpam-4323	187	28	+	+	ADJ
ejpam-4323	187	29	on(1	on(1	NOUN
ejpam-4323	187	30	)	)	PUNCT
ejpam-4323	187	31	)	)	PUNCT
ejpam-4323	187	32	.	.	PUNCT
ejpam-4323	188	1	(	(	PUNCT
ejpam-4323	188	2	l4a	l4a	PROPN
ejpam-4323	188	3	)	)	PUNCT
ejpam-4323	188	4	next	next	ADJ
ejpam-4323	188	5	b(n	b(n	PROPN
ejpam-4323	188	6	,	,	PUNCT
ejpam-4323	188	7	k	k	NOUN
ejpam-4323	188	8	,	,	PUNCT
ejpam-4323	188	9	2	2	NUM
ejpam-4323	188	10	)	)	PUNCT
ejpam-4323	188	11	=	=	PUNCT
ejpam-4323	188	12	∑	∑	PUNCT
ejpam-4323	188	13	j≥2	j≥2	PROPN
ejpam-4323	188	14	jqj−1	jqj−1	PROPN
ejpam-4323	188	15	k	k	PROPN
ejpam-4323	188	16	,	,	PUNCT
ejpam-4323	188	17	n	n	PROPN
ejpam-4323	188	18	+	+	CCONJ
ejpam-4323	188	19	∑	∑	PROPN
ejpam-4323	188	20	j≥2	j≥2	ADJ
ejpam-4323	188	21	j(j	j(j	PROPN
ejpam-4323	188	22	−	−	PROPN
ejpam-4323	188	23	1)qj−1	1)qj−1	NUM
ejpam-4323	188	24	k	k	NOUN
ejpam-4323	188	25	,	,	PUNCT
ejpam-4323	188	26	n	n	NOUN
ejpam-4323	188	27	=	=	SYM
ejpam-4323	188	28	(	(	PUNCT
ejpam-4323	188	29	+	+	ADJ
ejpam-4323	188	30	∞∑	∞∑	NUM
ejpam-4323	188	31	j=1	j=1	ADJ
ejpam-4323	188	32	jqj−1	jqj−1	PROPN
ejpam-4323	188	33	k	k	PROPN
ejpam-4323	188	34	,	,	PUNCT
ejpam-4323	188	35	n	n	PROPN
ejpam-4323	188	36	−	−	PROPN
ejpam-4323	188	37	1	1	NUM
ejpam-4323	188	38	)	)	PUNCT
ejpam-4323	189	1	+	+	CCONJ
ejpam-4323	189	2	(	(	PUNCT
ejpam-4323	189	3	qk	qk	INTJ
ejpam-4323	189	4	,	,	PUNCT
ejpam-4323	189	5	n	n	PROPN
ejpam-4323	189	6	+	+	ADJ
ejpam-4323	189	7	∞∑	∞∑	PROPN
ejpam-4323	189	8	j=2	j=2	PROPN
ejpam-4323	189	9	j(j	j(j	PROPN
ejpam-4323	189	10	−	−	PROPN
ejpam-4323	189	11	1)qj−2	1)qj−2	PROPN
ejpam-4323	190	1	k	k	NOUN
ejpam-4323	190	2	,	,	PUNCT
ejpam-4323	190	3	n	n	PROPN
ejpam-4323	190	4	)	)	PUNCT
ejpam-4323	191	1	=	=	SYM
ejpam-4323	191	2	(	(	PUNCT
ejpam-4323	191	3	{	{	PUNCT
ejpam-4323	191	4	+	+	ADP
ejpam-4323	191	5	∞∑	∞∑	NUM
ejpam-4323	191	6	j=0	j=0	ADJ
ejpam-4323	191	7	qjk	qjk	NOUN
ejpam-4323	191	8	,	,	PUNCT
ejpam-4323	191	9	n	n	PRON
ejpam-4323	191	10	}	}	PUNCT
ejpam-4323	191	11	′	′	NUM
ejpam-4323	192	1	−	−	NOUN
ejpam-4323	192	2	1	1	NUM
ejpam-4323	192	3	)	)	PUNCT
ejpam-4323	192	4	+	+	CCONJ
ejpam-4323	192	5	qk	qk	NOUN
ejpam-4323	192	6	,	,	PUNCT
ejpam-4323	192	7	n	n	CCONJ
ejpam-4323	192	8	{	{	PUNCT
ejpam-4323	192	9	+	+	ADP
ejpam-4323	192	10	∞∑	∞∑	NUM
ejpam-4323	192	11	j=0	j=0	ADJ
ejpam-4323	192	12	qjk	qjk	NOUN
ejpam-4323	192	13	,	,	PUNCT
ejpam-4323	192	14	n	n	CCONJ
ejpam-4323	192	15	}	}	PUNCT
ejpam-4323	192	16	′′	′′	PROPN
ejpam-4323	192	17	=	=	SYM
ejpam-4323	192	18	(	(	PUNCT
ejpam-4323	192	19	1	1	NUM
ejpam-4323	192	20	p2k	p2k	PROPN
ejpam-4323	192	21	,	,	PUNCT
ejpam-4323	192	22	n	n	CCONJ
ejpam-4323	192	23	−	−	PROPN
ejpam-4323	192	24	1	1	NUM
ejpam-4323	192	25	)	)	PUNCT
ejpam-4323	193	1	+	+	CCONJ
ejpam-4323	193	2	(	(	PUNCT
ejpam-4323	193	3	qk	qk	INTJ
ejpam-4323	193	4	,	,	PUNCT
ejpam-4323	193	5	n	n	PROPN
ejpam-4323	193	6	2	2	NUM
ejpam-4323	193	7	p3k	p3k	NOUN
ejpam-4323	193	8	,	,	PUNCT
ejpam-4323	193	9	n	n	NOUN
ejpam-4323	193	10	)	)	PUNCT
ejpam-4323	193	11	=	=	SYM
ejpam-4323	193	12	1−	1−	NUM
ejpam-4323	193	13	p2k	p2k	PROPN
ejpam-4323	193	14	,	,	PUNCT
ejpam-4323	193	15	n	n	PROPN
ejpam-4323	193	16	p2k	p2k	PROPN
ejpam-4323	193	17	,	,	PUNCT
ejpam-4323	193	18	n	n	PROPN
ejpam-4323	193	19	+	+	CCONJ
ejpam-4323	193	20	2qk	2qk	ADJ
ejpam-4323	193	21	,	,	PUNCT
ejpam-4323	193	22	n	n	PRON
ejpam-4323	193	23	p3k	p3k	NOUN
ejpam-4323	193	24	,	,	PUNCT
ejpam-4323	193	25	n	n	NOUN
ejpam-4323	193	26	=	=	SYM
ejpam-4323	193	27	pk	pk	PROPN
ejpam-4323	193	28	,	,	PUNCT
ejpam-4323	193	29	n(1−	n(1−	PROPN
ejpam-4323	193	30	p2k	p2k	PROPN
ejpam-4323	193	31	,	,	PUNCT
ejpam-4323	193	32	n	n	CCONJ
ejpam-4323	193	33	)	)	PUNCT
ejpam-4323	194	1	+	+	CCONJ
ejpam-4323	194	2	2qk	2qk	ADJ
ejpam-4323	194	3	,	,	PUNCT
ejpam-4323	194	4	n	n	PRON
ejpam-4323	194	5	p3k	p3k	NOUN
ejpam-4323	194	6	,	,	PUNCT
ejpam-4323	194	7	n	n	PROPN
ejpam-4323	194	8	=	=	SYM
ejpam-4323	194	9	pk	pk	NOUN
ejpam-4323	194	10	,	,	PUNCT
ejpam-4323	194	11	nqk	nqk	NOUN
ejpam-4323	194	12	,	,	PUNCT
ejpam-4323	194	13	n(1	n(1	PROPN
ejpam-4323	194	14	+	+	CCONJ
ejpam-4323	194	15	pk	pk	NOUN
ejpam-4323	194	16	,	,	PUNCT
ejpam-4323	194	17	n	n	CCONJ
ejpam-4323	194	18	)	)	PUNCT
ejpam-4323	195	1	+	+	CCONJ
ejpam-4323	195	2	2qk	2qk	ADJ
ejpam-4323	195	3	,	,	PUNCT
ejpam-4323	195	4	n	n	PRON
ejpam-4323	195	5	p3k	p3k	NOUN
ejpam-4323	195	6	,	,	PUNCT
ejpam-4323	195	7	n	n	NOUN
ejpam-4323	195	8	=	=	SYM
ejpam-4323	195	9	qk	qk	NOUN
ejpam-4323	195	10	,	,	PUNCT
ejpam-4323	195	11	n	n	PROPN
ejpam-4323	195	12	(	(	PUNCT
ejpam-4323	195	13	pk	pk	NOUN
ejpam-4323	195	14	,	,	PUNCT
ejpam-4323	195	15	n(1	n(1	NOUN
ejpam-4323	195	16	+	+	CCONJ
ejpam-4323	195	17	pk	pk	NOUN
ejpam-4323	195	18	,	,	PUNCT
ejpam-4323	195	19	n	n	CCONJ
ejpam-4323	195	20	)	)	PUNCT
ejpam-4323	195	21	+	+	CCONJ
ejpam-4323	195	22	2	2	X
ejpam-4323	195	23	)	)	PUNCT
ejpam-4323	195	24	p3k	p3k	NOUN
ejpam-4323	195	25	,	,	PUNCT
ejpam-4323	195	26	n	n	PRON
ejpam-4323	195	27	≤	≤	PROPN
ejpam-4323	195	28	4qk	4qk	NOUN
ejpam-4323	195	29	,	,	PUNCT
ejpam-4323	195	30	n	n	PROPN
ejpam-4323	195	31	p3k	p3k	NOUN
ejpam-4323	195	32	,	,	PUNCT
ejpam-4323	195	33	n	n	NOUN
ejpam-4323	195	34	=	=	SYM
ejpam-4323	195	35	4on(1)(1	4on(1)(1	PROPN
ejpam-4323	195	36	+	+	CCONJ
ejpam-4323	195	37	on(1	on(1	NOUN
ejpam-4323	195	38	)	)	PUNCT
ejpam-4323	195	39	)	)	PUNCT
ejpam-4323	195	40	.	.	PUNCT
ejpam-4323	196	1	(	(	PUNCT
ejpam-4323	196	2	l4b	l4b	PROPN
ejpam-4323	196	3	)	)	PUNCT
ejpam-4323	196	4	hence	hence	ADV
ejpam-4323	196	5	b(n	b(n	PROPN
ejpam-4323	196	6	,	,	PUNCT
ejpam-4323	196	7	k	k	NOUN
ejpam-4323	196	8	)	)	PUNCT
ejpam-4323	196	9	≤	≤	NOUN
ejpam-4323	196	10	con(1)(1	con(1)(1	NOUN
ejpam-4323	196	11	+	+	CCONJ
ejpam-4323	196	12	on(1	on(1	NOUN
ejpam-4323	196	13	)	)	PUNCT
ejpam-4323	196	14	)	)	PUNCT
ejpam-4323	196	15	,	,	PUNCT
ejpam-4323	196	16	(	(	PUNCT
ejpam-4323	196	17	l4c	l4c	PROPN
ejpam-4323	196	18	)	)	PUNCT
ejpam-4323	196	19	for	for	ADP
ejpam-4323	196	20	some	some	DET
ejpam-4323	196	21	c	c	PROPN
ejpam-4323	196	22	>	>	X
ejpam-4323	196	23	0	0	PUNCT
ejpam-4323	197	1	by	by	ADP
ejpam-4323	197	2	(	(	PUNCT
ejpam-4323	197	3	l4a	l4a	PROPN
ejpam-4323	197	4	)	)	PUNCT
ejpam-4323	197	5	and	and	CCONJ
ejpam-4323	197	6	(	(	PUNCT
ejpam-4323	197	7	l4b	l4b	PROPN
ejpam-4323	197	8	)	)	PUNCT
ejpam-4323	197	9	.	.	PUNCT
ejpam-4323	198	1	ab	ab	PROPN
ejpam-4323	198	2	niang	niang	PROPN
ejpam-4323	198	3	et	et	PROPN
ejpam-4323	198	4	al	al	PROPN
ejpam-4323	198	5	.	.	PUNCT
ejpam-4323	198	6	/	/	SYM
ejpam-4323	198	7	eur	eur	PROPN
ejpam-4323	198	8	.	.	PUNCT
ejpam-4323	199	1	j.	j.	PROPN
ejpam-4323	199	2	pure	pure	PROPN
ejpam-4323	199	3	appl	appl	PROPN
ejpam-4323	199	4	.	.	PROPN
ejpam-4323	199	5	math	math	PROPN
ejpam-4323	199	6	,	,	PUNCT
ejpam-4323	199	7	15	15	NUM
ejpam-4323	199	8	(	(	PUNCT
ejpam-4323	199	9	2	2	NUM
ejpam-4323	199	10	)	)	PUNCT
ejpam-4323	199	11	(	(	PUNCT
ejpam-4323	199	12	2022	2022	NUM
ejpam-4323	199	13	)	)	PUNCT
ejpam-4323	199	14	,	,	PUNCT
ejpam-4323	199	15	511	511	NUM
ejpam-4323	199	16	-	-	SYM
ejpam-4323	199	17	527	527	NUM
ejpam-4323	199	18	525	525	NUM
ejpam-4323	199	19	finally	finally	ADV
ejpam-4323	199	20	,	,	PUNCT
ejpam-4323	199	21	by	by	ADP
ejpam-4323	199	22	putting	put	VERB
ejpam-4323	199	23	together	together	ADV
ejpam-4323	199	24	(	(	PUNCT
ejpam-4323	199	25	l1	l1	PROPN
ejpam-4323	199	26	)	)	PUNCT
ejpam-4323	199	27	,	,	PUNCT
ejpam-4323	199	28	(	(	PUNCT
ejpam-4323	199	29	l2	l2	NOUN
ejpam-4323	199	30	)	)	PUNCT
ejpam-4323	199	31	,	,	PUNCT
ejpam-4323	199	32	(	(	PUNCT
ejpam-4323	199	33	l3	l3	NOUN
ejpam-4323	199	34	)	)	PUNCT
ejpam-4323	199	35	and	and	CCONJ
ejpam-4323	199	36	(	(	PUNCT
ejpam-4323	199	37	l4c	l4c	PROPN
ejpam-4323	199	38	)	)	PUNCT
ejpam-4323	199	39	,	,	PUNCT
ejpam-4323	199	40	we	we	PRON
ejpam-4323	199	41	get	get	VERB
ejpam-4323	199	42	ln	ln	ADJ
ejpam-4323	199	43	,	,	PUNCT
ejpam-4323	199	44	p	p	X
ejpam-4323	199	45	(	(	PUNCT
ejpam-4323	199	46	ε	ε	PROPN
ejpam-4323	199	47	)	)	PUNCT
ejpam-4323	199	48	≤	≤	NOUN
ejpam-4323	199	49	on(1)(1	on(1)(1	ADP
ejpam-4323	199	50	+	+	NUM
ejpam-4323	199	51	on(1))(λ+	on(1))(λ+	NOUN
ejpam-4323	199	52	o(1	o(1	NOUN
ejpam-4323	199	53	)	)	PUNCT
ejpam-4323	199	54	)	)	PUNCT
ejpam-4323	199	55	{	{	PUNCT
ejpam-4323	200	1	1	1	NUM
ejpam-4323	200	2	+	+	NUM
ejpam-4323	200	3	2c(1	2c(1	NUM
ejpam-4323	200	4	+	+	CCONJ
ejpam-4323	200	5	on(1	on(1	NOUN
ejpam-4323	200	6	)	)	PUNCT
ejpam-4323	200	7	)	)	PUNCT
ejpam-4323	200	8	}	}	PUNCT
ejpam-4323	201	1	→	→	SYM
ejpam-4323	201	2	0	0	X
ejpam-4323	201	3	.	.	PUNCT
ejpam-4323	202	1	this	this	PRON
ejpam-4323	202	2	completes	complete	VERB
ejpam-4323	202	3	the	the	DET
ejpam-4323	202	4	proof	proof	NOUN
ejpam-4323	202	5	.	.	PUNCT
ejpam-4323	203	1	�	�	PROPN
ejpam-4323	203	2	a	a	DET
ejpam-4323	203	3	simple	simple	ADJ
ejpam-4323	203	4	application	application	NOUN
ejpam-4323	203	5	.	.	PUNCT
ejpam-4323	204	1	let	let	VERB
ejpam-4323	204	2	us	we	PRON
ejpam-4323	204	3	give	give	VERB
ejpam-4323	204	4	a	a	DET
ejpam-4323	204	5	simple	simple	ADJ
ejpam-4323	204	6	application	application	NOUN
ejpam-4323	204	7	to	to	ADP
ejpam-4323	204	8	a	a	DET
ejpam-4323	204	9	classical	classical	ADJ
ejpam-4323	204	10	example	example	NOUN
ejpam-4323	204	11	.	.	PUNCT
ejpam-4323	205	1	we	we	PRON
ejpam-4323	205	2	suppose	suppose	VERB
ejpam-4323	205	3	that	that	SCONJ
ejpam-4323	205	4	we	we	PRON
ejpam-4323	205	5	observe	observe	VERB
ejpam-4323	205	6	occurrences	occurrence	NOUN
ejpam-4323	205	7	of	of	ADP
ejpam-4323	205	8	landing	landing	NOUN
ejpam-4323	205	9	crashes	crash	NOUN
ejpam-4323	205	10	at	at	ADP
ejpam-4323	205	11	some	some	DET
ejpam-4323	205	12	airport	airport	NOUN
ejpam-4323	205	13	(	(	PUNCT
ejpam-4323	205	14	a	a	NOUN
ejpam-4323	205	15	)	)	PUNCT
ejpam-4323	205	16	over	over	ADP
ejpam-4323	205	17	a	a	DET
ejpam-4323	205	18	period	period	NOUN
ejpam-4323	205	19	t	t	X
ejpam-4323	205	20	>	>	X
ejpam-4323	205	21	0	0	X
ejpam-4323	205	22	.	.	PUNCT
ejpam-4323	206	1	we	we	PRON
ejpam-4323	206	2	know	know	VERB
ejpam-4323	206	3	that	that	SCONJ
ejpam-4323	206	4	those	those	DET
ejpam-4323	206	5	crashes	crash	NOUN
ejpam-4323	206	6	are	be	AUX
ejpam-4323	206	7	usually	usually	ADV
ejpam-4323	206	8	of	of	ADP
ejpam-4323	206	9	very	very	ADV
ejpam-4323	206	10	low	low	ADJ
ejpam-4323	206	11	probabilities	probability	NOUN
ejpam-4323	206	12	.	.	PUNCT
ejpam-4323	207	1	over	over	ADP
ejpam-4323	207	2	n	n	PRON
ejpam-4323	207	3	landings	landing	NOUN
ejpam-4323	207	4	,	,	PUNCT
ejpam-4323	207	5	we	we	PRON
ejpam-4323	207	6	denote	denote	VERB
ejpam-4323	207	7	xn	xn	PROPN
ejpam-4323	208	1	the	the	DET
ejpam-4323	208	2	number	number	NOUN
ejpam-4323	208	3	of	of	ADP
ejpam-4323	208	4	crashes	crash	NOUN
ejpam-4323	208	5	at	at	ADP
ejpam-4323	208	6	times	time	NOUN
ejpam-4323	208	7	k(n	k(n	PROPN
ejpam-4323	208	8	)	)	PUNCT
ejpam-4323	208	9	.	.	PUNCT
ejpam-4323	209	1	usually	usually	ADV
ejpam-4323	209	2	,	,	PUNCT
ejpam-4323	209	3	we	we	PRON
ejpam-4323	209	4	suppose	suppose	VERB
ejpam-4323	209	5	that	that	SCONJ
ejpam-4323	209	6	the	the	DET
ejpam-4323	209	7	data	datum	NOUN
ejpam-4323	209	8	(	(	PUNCT
ejpam-4323	209	9	of	of	ADP
ejpam-4323	209	10	landing	landing	NOUN
ejpam-4323	209	11	crashes	crash	NOUN
ejpam-4323	209	12	)	)	PUNCT
ejpam-4323	209	13	are	be	AUX
ejpam-4323	209	14	observations	observation	NOUN
ejpam-4323	209	15	of	of	ADP
ejpam-4323	209	16	iid	iid	VERB
ejpam-4323	209	17	bernoulli	bernoulli	NOUN
ejpam-4323	209	18	b(pn	b(pn	NOUN
ejpam-4323	209	19	)	)	PUNCT
ejpam-4323	209	20	and	and	CCONJ
ejpam-4323	209	21	then	then	ADV
ejpam-4323	209	22	,	,	PUNCT
ejpam-4323	209	23	the	the	DET
ejpam-4323	209	24	approximation	approximation	NOUN
ejpam-4323	209	25	xn	xn	PROPN
ejpam-4323	210	1	≈	≈	PROPN
ejpam-4323	210	2	z	z	NOUN
ejpam-4323	210	3	∼	∼	NOUN
ejpam-4323	210	4	p(λ	p(λ	NOUN
ejpam-4323	210	5	)	)	PUNCT
ejpam-4323	210	6	,	,	PUNCT
ejpam-4323	210	7	with	with	SCONJ
ejpam-4323	210	8	λ	λ	PROPN
ejpam-4323	210	9	=	=	NOUN
ejpam-4323	210	10	npn	npn	NOUN
ejpam-4323	210	11	can	can	AUX
ejpam-4323	210	12	be	be	AUX
ejpam-4323	210	13	used	use	VERB
ejpam-4323	210	14	.	.	PUNCT
ejpam-4323	211	1	that	that	DET
ejpam-4323	211	2	formula	formula	NOUN
ejpam-4323	211	3	was	be	AUX
ejpam-4323	211	4	systematically	systematically	ADV
ejpam-4323	211	5	used	use	VERB
ejpam-4323	211	6	with	with	ADP
ejpam-4323	211	7	limited	limited	ADJ
ejpam-4323	211	8	performance	performance	NOUN
ejpam-4323	211	9	of	of	ADP
ejpam-4323	211	10	computers	computer	NOUN
ejpam-4323	211	11	.	.	PUNCT
ejpam-4323	212	1	however	however	ADV
ejpam-4323	212	2	,	,	PUNCT
ejpam-4323	212	3	with	with	ADP
ejpam-4323	212	4	powerful	powerful	ADJ
ejpam-4323	212	5	computers	computer	NOUN
ejpam-4323	212	6	,	,	PUNCT
ejpam-4323	212	7	we	we	PRON
ejpam-4323	212	8	no	no	ADV
ejpam-4323	212	9	-	-	PUNCT
ejpam-4323	212	10	longer	long	ADJ
ejpam-4323	212	11	need	need	VERB
ejpam-4323	212	12	that	that	DET
ejpam-4323	212	13	approximation	approximation	NOUN
ejpam-4323	212	14	to	to	PART
ejpam-4323	212	15	compute	compute	VERB
ejpam-4323	212	16	the	the	DET
ejpam-4323	212	17	related	relate	VERB
ejpam-4323	212	18	p	p	NOUN
ejpam-4323	212	19	-	-	PUNCT
ejpam-4323	212	20	values	value	NOUN
ejpam-4323	212	21	p(xn	p(xn	PROPN
ejpam-4323	212	22	>	>	SYM
ejpam-4323	212	23	t	t	PROPN
ejpam-4323	212	24	)	)	PUNCT
ejpam-4323	212	25	of	of	ADP
ejpam-4323	212	26	the	the	DET
ejpam-4323	212	27	statistical	statistical	ADJ
ejpam-4323	212	28	tests	test	NOUN
ejpam-4323	212	29	since	since	SCONJ
ejpam-4323	212	30	we	we	PRON
ejpam-4323	212	31	know	know	VERB
ejpam-4323	212	32	the	the	DET
ejpam-4323	212	33	explicit	explicit	ADJ
ejpam-4323	212	34	form	form	NOUN
ejpam-4323	212	35	of	of	ADP
ejpam-4323	212	36	sn[x	sn[x	NOUN
ejpam-4323	212	37	]	]	PUNCT
ejpam-4323	212	38	.	.	PUNCT
ejpam-4323	213	1	in	in	ADP
ejpam-4323	213	2	the	the	DET
ejpam-4323	213	3	software	software	NOUN
ejpam-4323	213	4	r	r	NOUN
ejpam-4323	213	5	,	,	PUNCT
ejpam-4323	213	6	the	the	DET
ejpam-4323	213	7	code	code	NOUN
ejpam-4323	213	8	1−	1−	NUM
ejpam-4323	214	1	pbiniom(t	pbiniom(t	NOUN
ejpam-4323	214	2	,	,	PUNCT
ejpam-4323	214	3	pn	pn	PROPN
ejpam-4323	214	4	)	)	PUNCT
ejpam-4323	214	5	gives	give	VERB
ejpam-4323	214	6	the	the	DET
ejpam-4323	214	7	desired	desire	VERB
ejpam-4323	214	8	values	value	NOUN
ejpam-4323	214	9	.	.	PUNCT
ejpam-4323	215	1	now	now	ADV
ejpam-4323	215	2	suppose	suppose	VERB
ejpam-4323	215	3	we	we	PRON
ejpam-4323	215	4	can	can	AUX
ejpam-4323	215	5	use	use	VERB
ejpam-4323	215	6	the	the	DET
ejpam-4323	215	7	independence	independence	NOUN
ejpam-4323	215	8	hypothesis	hypothesis	NOUN
ejpam-4323	215	9	only	only	ADV
ejpam-4323	215	10	and	and	CCONJ
ejpam-4323	215	11	not	not	PART
ejpam-4323	215	12	the	the	DET
ejpam-4323	215	13	stationary	stationary	ADJ
ejpam-4323	215	14	distribution	distribution	NOUN
ejpam-4323	215	15	.	.	PUNCT
ejpam-4323	216	1	hence	hence	ADV
ejpam-4323	216	2	the	the	DET
ejpam-4323	216	3	distribution	distribution	NOUN
ejpam-4323	216	4	of	of	ADP
ejpam-4323	216	5	xn	xn	PROPN
ejpam-4323	216	6	is	be	AUX
ejpam-4323	216	7	the	the	DET
ejpam-4323	216	8	convolution	convolution	NOUN
ejpam-4323	216	9	product	product	NOUN
ejpam-4323	216	10	of	of	ADP
ejpam-4323	216	11	bernoulli	bernoulli	NOUN
ejpam-4323	216	12	b(pk	b(pk	NOUN
ejpam-4323	216	13	,	,	PUNCT
ejpam-4323	216	14	n	n	CCONJ
ejpam-4323	216	15	)	)	PUNCT
ejpam-4323	216	16	distributions	distribution	NOUN
ejpam-4323	216	17	and	and	CCONJ
ejpam-4323	216	18	its	its	PRON
ejpam-4323	216	19	law	law	NOUN
ejpam-4323	216	20	is	be	AUX
ejpam-4323	216	21	not	not	PART
ejpam-4323	216	22	simple	simple	ADJ
ejpam-4323	216	23	.	.	PUNCT
ejpam-4323	217	1	so	so	ADV
ejpam-4323	217	2	,	,	PUNCT
ejpam-4323	217	3	the	the	DET
ejpam-4323	217	4	simplest	simple	ADJ
ejpam-4323	217	5	way	way	NOUN
ejpam-4323	217	6	to	to	PART
ejpam-4323	217	7	compute	compute	VERB
ejpam-4323	217	8	p(xn	p(xn	PROPN
ejpam-4323	217	9	>	>	SYM
ejpam-4323	217	10	t	t	PROPN
ejpam-4323	217	11	)	)	PUNCT
ejpam-4323	217	12	should	should	AUX
ejpam-4323	217	13	be	be	AUX
ejpam-4323	217	14	using	use	VERB
ejpam-4323	217	15	the	the	DET
ejpam-4323	217	16	approximation	approximation	NOUN
ejpam-4323	217	17	p(p(λ	p(p(λ	NOUN
ejpam-4323	217	18	)	)	PUNCT
ejpam-4323	217	19	>	>	X
ejpam-4323	218	1	t	t	PROPN
ejpam-4323	218	2	)	)	PUNCT
ejpam-4323	219	1	with	with	ADP
ejpam-4323	219	2	λ	λ	NOUN
ejpam-4323	219	3	=	=	NOUN
ejpam-4323	219	4	p1,n+	p1,n+	X
ejpam-4323	219	5	·	·	PUNCT
ejpam-4323	219	6	·	·	PUNCT
ejpam-4323	219	7	·	·	PUNCT
ejpam-4323	219	8	+	+	NOUN
ejpam-4323	219	9	pk(n),n	pk(n),n	X
ejpam-4323	219	10	.	.	PUNCT
ejpam-4323	220	1	so	so	ADV
ejpam-4323	220	2	it	it	PRON
ejpam-4323	220	3	is	be	AUX
ejpam-4323	220	4	better	well	ADJ
ejpam-4323	220	5	to	to	PART
ejpam-4323	220	6	use	use	VERB
ejpam-4323	220	7	the	the	DET
ejpam-4323	220	8	non	non	ADJ
ejpam-4323	220	9	-	-	ADJ
ejpam-4323	220	10	stationary	stationary	ADJ
ejpam-4323	220	11	scheme	scheme	NOUN
ejpam-4323	220	12	since	since	SCONJ
ejpam-4323	220	13	the	the	DET
ejpam-4323	220	14	stationary	stationary	ADJ
ejpam-4323	220	15	hypothesis	hypothesis	NOUN
ejpam-4323	220	16	is	be	AUX
ejpam-4323	220	17	usually	usually	ADV
ejpam-4323	220	18	a	a	DET
ejpam-4323	220	19	working	work	VERB
ejpam-4323	220	20	hypothesis	hypothesis	NOUN
ejpam-4323	220	21	,	,	PUNCT
ejpam-4323	220	22	not	not	PART
ejpam-4323	220	23	confirmed	confirm	VERB
ejpam-4323	220	24	,	,	PUNCT
ejpam-4323	220	25	and	and	CCONJ
ejpam-4323	220	26	pn	pn	PROPN
ejpam-4323	220	27	is	be	AUX
ejpam-4323	220	28	computed	compute	VERB
ejpam-4323	220	29	as	as	ADP
ejpam-4323	220	30	the	the	DET
ejpam-4323	220	31	average	average	ADJ
ejpam-4323	220	32	number	number	NOUN
ejpam-4323	220	33	of	of	ADP
ejpam-4323	220	34	crashes	crash	NOUN
ejpam-4323	220	35	.	.	PUNCT
ejpam-4323	221	1	these	these	DET
ejpam-4323	221	2	two	two	NUM
ejpam-4323	221	3	theorems	theorem	NOUN
ejpam-4323	221	4	actually	actually	ADV
ejpam-4323	221	5	are	be	AUX
ejpam-4323	221	6	still	still	ADV
ejpam-4323	221	7	particular	particular	ADJ
ejpam-4323	221	8	cases	case	NOUN
ejpam-4323	221	9	of	of	ADP
ejpam-4323	221	10	two	two	NUM
ejpam-4323	221	11	more	more	ADV
ejpam-4323	221	12	general	general	ADJ
ejpam-4323	221	13	results	result	NOUN
ejpam-4323	221	14	.	.	PUNCT
ejpam-4323	222	1	theorem	theorem	NOUN
ejpam-4323	222	2	3	3	X
ejpam-4323	222	3	.	.	PUNCT
ejpam-4323	223	1	let	let	VERB
ejpam-4323	223	2	x	x	PUNCT
ejpam-4323	223	3	=	=	PRON
ejpam-4323	223	4	{	{	PUNCT
ejpam-4323	223	5	{	{	PUNCT
ejpam-4323	223	6	xk	xk	PROPN
ejpam-4323	223	7	,	,	PUNCT
ejpam-4323	223	8	n	n	CCONJ
ejpam-4323	223	9	,	,	PUNCT
ejpam-4323	223	10	1	1	NUM
ejpam-4323	223	11	≤	≤	NUM
ejpam-4323	223	12	k	k	X
ejpam-4323	223	13	≤	≤	PROPN
ejpam-4323	224	1	kn	kn	NOUN
ejpam-4323	224	2	=	=	PUNCT
ejpam-4323	224	3	k(n	k(n	PROPN
ejpam-4323	224	4	)	)	PUNCT
ejpam-4323	224	5	}	}	PUNCT
ejpam-4323	224	6	,	,	PUNCT
ejpam-4323	224	7	n	n	X
ejpam-4323	224	8	≥	≥	NOUN
ejpam-4323	224	9	1	1	NUM
ejpam-4323	224	10	}	}	PUNCT
ejpam-4323	224	11	,	,	PUNCT
ejpam-4323	224	12	be	be	AUX
ejpam-4323	224	13	an	an	DET
ejpam-4323	224	14	array	array	NOUN
ejpam-4323	224	15	of	of	ADP
ejpam-4323	224	16	by	by	ADP
ejpam-4323	224	17	-	-	PUNCT
ejpam-4323	224	18	row	row	NOUN
ejpam-4323	224	19	-	-	PUNCT
ejpam-4323	224	20	independent	independent	ADJ
ejpam-4323	224	21	bernoulli	bernoulli	PROPN
ejpam-4323	224	22	random	random	ADJ
ejpam-4323	224	23	variables	variable	NOUN
ejpam-4323	224	24	,	,	PUNCT
ejpam-4323	224	25	that	that	PRON
ejpam-4323	224	26	is	be	AUX
ejpam-4323	224	27	:	:	PUNCT
ejpam-4323	224	28	(	(	PUNCT
ejpam-4323	224	29	gp1	gp1	NOUN
ejpam-4323	224	30	)	)	PUNCT
ejpam-4323	224	31	∀n	∀n	PUNCT
ejpam-4323	224	32	≥	≥	NOUN
ejpam-4323	224	33	1	1	NUM
ejpam-4323	224	34	,	,	PUNCT
ejpam-4323	224	35	∀1	∀1	VERB
ejpam-4323	224	36	≤	≤	PUNCT
ejpam-4323	224	37	k	k	X
ejpam-4323	224	38	≤	≤	X
ejpam-4323	224	39	k(n	k(n	PROPN
ejpam-4323	224	40	)	)	PUNCT
ejpam-4323	224	41	,	,	PUNCT
ejpam-4323	224	42	xk	xk	PROPN
ejpam-4323	224	43	,	,	PUNCT
ejpam-4323	224	44	n	n	PRON
ejpam-4323	224	45	∼	∼	NOUN
ejpam-4323	224	46	b(pk	b(pk	NOUN
ejpam-4323	224	47	,	,	PUNCT
ejpam-4323	224	48	n	n	CCONJ
ejpam-4323	224	49	)	)	PUNCT
ejpam-4323	224	50	,	,	PUNCT
ejpam-4323	224	51	with	with	ADP
ejpam-4323	224	52	0	0	NUM
ejpam-4323	224	53	<	<	X
ejpam-4323	224	54	pk	pk	NOUN
ejpam-4323	224	55	,	,	PUNCT
ejpam-4323	224	56	n	n	CCONJ
ejpam-4323	224	57	<	<	X
ejpam-4323	224	58	1	1	NUM
ejpam-4323	224	59	and	and	CCONJ
ejpam-4323	224	60	:	:	PUNCT
ejpam-4323	224	61	(	(	PUNCT
ejpam-4323	224	62	gp2	gp2	PROPN
ejpam-4323	224	63	)	)	PUNCT
ejpam-4323	224	64	sup1≤k≤k(n	sup1≤k≤k(n	PROPN
ejpam-4323	224	65	)	)	PUNCT
ejpam-4323	224	66	pk	pk	NOUN
ejpam-4323	224	67	,	,	PUNCT
ejpam-4323	224	68	n(1−	n(1−	ADJ
ejpam-4323	224	69	pk	pk	NOUN
ejpam-4323	224	70	,	,	PUNCT
ejpam-4323	224	71	n	n	CCONJ
ejpam-4323	224	72	)	)	PUNCT
ejpam-4323	224	73	→	→	X
ejpam-4323	224	74	0	0	NUM
ejpam-4323	224	75	;	;	PUNCT
ejpam-4323	224	76	(	(	PUNCT
ejpam-4323	224	77	gp3	gp3	PROPN
ejpam-4323	224	78	)	)	PUNCT
ejpam-4323	224	79	∑	∑	ADP
ejpam-4323	224	80	1≤k≤k(n	1≤k≤k(n	NUM
ejpam-4323	224	81	)	)	PUNCT
ejpam-4323	224	82	pk	pk	NOUN
ejpam-4323	224	83	,	,	PUNCT
ejpam-4323	224	84	n(1−	n(1−	ADJ
ejpam-4323	224	85	pk	pk	NOUN
ejpam-4323	224	86	,	,	PUNCT
ejpam-4323	224	87	n	n	CCONJ
ejpam-4323	224	88	)	)	PUNCT
ejpam-4323	224	89	→	→	SYM
ejpam-4323	224	90	λ	λ	NOUN
ejpam-4323	224	91	∈]0	∈]0	X
ejpam-4323	224	92	,	,	PUNCT
ejpam-4323	224	93	+	+	NOUN
ejpam-4323	224	94	∞	∞	PROPN
ejpam-4323	224	95	[	[	PUNCT
ejpam-4323	224	96	and	and	CCONJ
ejpam-4323	224	97	∑	∑	NOUN
ejpam-4323	224	98	1≤k≤k(n	1≤k≤k(n	NUM
ejpam-4323	224	99	)	)	PUNCT
ejpam-4323	224	100	pk	pk	NOUN
ejpam-4323	224	101	,	,	PUNCT
ejpam-4323	224	102	n	n	PROPN
ejpam-4323	224	103	→	→	SYM
ejpam-4323	224	104	λ	λ	PROPN
ejpam-4323	224	105	;	;	PUNCT
ejpam-4323	224	106	ab	ab	PROPN
ejpam-4323	224	107	niang	niang	PROPN
ejpam-4323	224	108	et	et	PROPN
ejpam-4323	224	109	al	al	PROPN
ejpam-4323	224	110	.	.	PUNCT
ejpam-4323	224	111	/	/	SYM
ejpam-4323	224	112	eur	eur	PROPN
ejpam-4323	224	113	.	.	PUNCT
ejpam-4323	225	1	j.	j.	PROPN
ejpam-4323	225	2	pure	pure	PROPN
ejpam-4323	225	3	appl	appl	PROPN
ejpam-4323	225	4	.	.	PROPN
ejpam-4323	225	5	math	math	PROPN
ejpam-4323	225	6	,	,	PUNCT
ejpam-4323	225	7	15	15	NUM
ejpam-4323	225	8	(	(	PUNCT
ejpam-4323	225	9	2	2	NUM
ejpam-4323	225	10	)	)	PUNCT
ejpam-4323	225	11	(	(	PUNCT
ejpam-4323	225	12	2022	2022	NUM
ejpam-4323	225	13	)	)	PUNCT
ejpam-4323	225	14	,	,	PUNCT
ejpam-4323	225	15	511	511	NUM
ejpam-4323	225	16	-	-	SYM
ejpam-4323	225	17	527	527	NUM
ejpam-4323	225	18	526	526	NUM
ejpam-4323	225	19	(	(	PUNCT
ejpam-4323	225	20	gp4	gp4	PROPN
ejpam-4323	225	21	)	)	PUNCT
ejpam-4323	225	22	for	for	ADP
ejpam-4323	225	23	0	0	NUM
ejpam-4323	225	24	<	<	X
ejpam-4323	225	25	ε	ε	X
ejpam-4323	225	26	<	<	X
ejpam-4323	225	27	1	1	NUM
ejpam-4323	225	28	,	,	PUNCT
ejpam-4323	225	29	n	n	PRON
ejpam-4323	225	30	≥	≥	NOUN
ejpam-4323	225	31	1	1	NUM
ejpam-4323	225	32	,	,	PUNCT
ejpam-4323	225	33	1	1	NUM
ejpam-4323	225	34	≤	≤	NUM
ejpam-4323	225	35	k	k	X
ejpam-4323	225	36	≤	≤	X
ejpam-4323	225	37	k(n	k(n	X
ejpam-4323	225	38	)	)	PUNCT
ejpam-4323	225	39	,	,	PUNCT
ejpam-4323	225	40	and	and	CCONJ
ejpam-4323	225	41	for	for	ADP
ejpam-4323	225	42	b(ε	b(ε	PROPN
ejpam-4323	225	43	,	,	PUNCT
ejpam-4323	225	44	k	k	NOUN
ejpam-4323	225	45	,	,	PUNCT
ejpam-4323	225	46	n	n	CCONJ
ejpam-4323	225	47	)	)	PUNCT
ejpam-4323	225	48	=	=	PUNCT
ejpam-4323	226	1	1∑	1∑	NUM
ejpam-4323	226	2	j=0	j=0	PROPN
ejpam-4323	226	3	1(∣∣∣∣j−qk	1(∣∣∣∣j−qk	PROPN
ejpam-4323	226	4	,	,	PUNCT
ejpam-4323	226	5	n−1	n−1	PROPN
ejpam-4323	226	6	∣∣∣∣≥ε	∣∣∣∣≥ε	NOUN
ejpam-4323	226	7	)	)	PUNCT
ejpam-4323	226	8	(	(	PUNCT
ejpam-4323	226	9	j	j	PROPN
ejpam-4323	226	10	−	−	PROPN
ejpam-4323	226	11	pk	pk	PROPN
ejpam-4323	226	12	,	,	PUNCT
ejpam-4323	226	13	n	n	NOUN
ejpam-4323	226	14	)	)	PUNCT
ejpam-4323	226	15	2	2	NUM
ejpam-4323	226	16	pjk	pjk	NOUN
ejpam-4323	226	17	,	,	PUNCT
ejpam-4323	226	18	nq	nq	PROPN
ejpam-4323	226	19	1−j	1−j	NUM
ejpam-4323	226	20	k	k	NOUN
ejpam-4323	226	21	,	,	PUNCT
ejpam-4323	226	22	n	n	CCONJ
ejpam-4323	226	23	,	,	PUNCT
ejpam-4323	226	24	we	we	PRON
ejpam-4323	226	25	have	have	VERB
ejpam-4323	226	26	b(ε	b(ε	NOUN
ejpam-4323	226	27	,	,	PUNCT
ejpam-4323	226	28	n	n	CCONJ
ejpam-4323	226	29	)	)	PUNCT
ejpam-4323	226	30	=	=	PUNCT
ejpam-4323	227	1	k(n)∑	k(n)∑	NOUN
ejpam-4323	227	2	k=1	k=1	X
ejpam-4323	227	3	b(ε	b(ε	PROPN
ejpam-4323	227	4	,	,	PUNCT
ejpam-4323	227	5	k	k	NOUN
ejpam-4323	227	6	,	,	PUNCT
ejpam-4323	227	7	n	n	CCONJ
ejpam-4323	227	8	)	)	PUNCT
ejpam-4323	227	9	→	→	SYM
ejpam-4323	227	10	0	0	X
ejpam-4323	227	11	.	.	PUNCT
ejpam-4323	228	1	then	then	ADV
ejpam-4323	228	2	we	we	PRON
ejpam-4323	228	3	have	have	AUX
ejpam-4323	228	4	sn[x	sn[x	VERB
ejpam-4323	228	5	]	]	PUNCT
ejpam-4323	228	6	p(λ	p(λ	NOUN
ejpam-4323	228	7	)	)	PUNCT
ejpam-4323	228	8	.	.	PUNCT
ejpam-4323	229	1	theorem	theorem	ADJ
ejpam-4323	229	2	4	4	NUM
ejpam-4323	229	3	.	.	PUNCT
ejpam-4323	230	1	let	let	VERB
ejpam-4323	230	2	x	x	PUNCT
ejpam-4323	230	3	=	=	PRON
ejpam-4323	230	4	{	{	PUNCT
ejpam-4323	230	5	{	{	PUNCT
ejpam-4323	230	6	xk	xk	PROPN
ejpam-4323	230	7	,	,	PUNCT
ejpam-4323	230	8	n	n	CCONJ
ejpam-4323	230	9	,	,	PUNCT
ejpam-4323	230	10	1	1	NUM
ejpam-4323	230	11	≤	≤	NUM
ejpam-4323	230	12	k	k	X
ejpam-4323	230	13	≤	≤	PROPN
ejpam-4323	231	1	kn	kn	NOUN
ejpam-4323	231	2	=	=	PUNCT
ejpam-4323	231	3	k(n	k(n	PROPN
ejpam-4323	231	4	)	)	PUNCT
ejpam-4323	231	5	}	}	PUNCT
ejpam-4323	231	6	,	,	PUNCT
ejpam-4323	231	7	n	n	X
ejpam-4323	231	8	≥	≥	NOUN
ejpam-4323	231	9	1	1	NUM
ejpam-4323	231	10	}	}	PUNCT
ejpam-4323	231	11	,	,	PUNCT
ejpam-4323	231	12	be	be	AUX
ejpam-4323	231	13	an	an	DET
ejpam-4323	231	14	array	array	NOUN
ejpam-4323	231	15	of	of	ADP
ejpam-4323	231	16	by	by	ADP
ejpam-4323	231	17	-	-	PUNCT
ejpam-4323	231	18	row	row	NOUN
ejpam-4323	231	19	-	-	PUNCT
ejpam-4323	231	20	independent	independent	ADJ
ejpam-4323	231	21	corrected	correct	VERB
ejpam-4323	231	22	geometric	geometric	ADJ
ejpam-4323	231	23	random	random	ADJ
ejpam-4323	231	24	variables	variable	NOUN
ejpam-4323	231	25	,	,	PUNCT
ejpam-4323	231	26	that	that	PRON
ejpam-4323	231	27	is	be	AUX
ejpam-4323	231	28	:	:	PUNCT
ejpam-4323	231	29	(	(	PUNCT
ejpam-4323	231	30	gn1	gn1	NOUN
ejpam-4323	231	31	)	)	PUNCT
ejpam-4323	231	32	∀n	∀n	PUNCT
ejpam-4323	231	33	≥	≥	NOUN
ejpam-4323	231	34	1	1	NUM
ejpam-4323	231	35	,	,	PUNCT
ejpam-4323	231	36	∀1	∀1	VERB
ejpam-4323	231	37	≤	≤	PUNCT
ejpam-4323	231	38	k	k	X
ejpam-4323	231	39	≤	≤	X
ejpam-4323	231	40	k(n	k(n	PROPN
ejpam-4323	231	41	)	)	PUNCT
ejpam-4323	231	42	,	,	PUNCT
ejpam-4323	231	43	xk	xk	PROPN
ejpam-4323	231	44	,	,	PUNCT
ejpam-4323	231	45	n	n	PRON
ejpam-4323	231	46	∼	∼	NOUN
ejpam-4323	231	47	g∗(pk	g∗(pk	NOUN
ejpam-4323	231	48	,	,	PUNCT
ejpam-4323	231	49	n	n	CCONJ
ejpam-4323	231	50	)	)	PUNCT
ejpam-4323	231	51	,	,	PUNCT
ejpam-4323	231	52	with	with	ADP
ejpam-4323	231	53	0	0	NUM
ejpam-4323	231	54	<	<	X
ejpam-4323	231	55	pk	pk	NOUN
ejpam-4323	231	56	,	,	PUNCT
ejpam-4323	231	57	n	n	NOUN
ejpam-4323	231	58	=	=	SYM
ejpam-4323	231	59	1−	1−	NUM
ejpam-4323	231	60	qk	qk	NOUN
ejpam-4323	231	61	,	,	PUNCT
ejpam-4323	231	62	n	n	CCONJ
ejpam-4323	231	63	<	<	X
ejpam-4323	231	64	1	1	NUM
ejpam-4323	231	65	and	and	CCONJ
ejpam-4323	231	66	:	:	PUNCT
ejpam-4323	231	67	(	(	PUNCT
ejpam-4323	231	68	gn2	gn2	NOUN
ejpam-4323	231	69	)	)	PUNCT
ejpam-4323	231	70	sup1≤k≤k(n)(qk	sup1≤k≤k(n)(qk	NOUN
ejpam-4323	231	71	,	,	PUNCT
ejpam-4323	231	72	n	n	CCONJ
ejpam-4323	231	73	/	/	SYM
ejpam-4323	231	74	p	p	PROPN
ejpam-4323	231	75	2	2	NUM
ejpam-4323	231	76	k	k	NOUN
ejpam-4323	231	77	,	,	PUNCT
ejpam-4323	231	78	n	n	CCONJ
ejpam-4323	231	79	)	)	PUNCT
ejpam-4323	231	80	→	→	X
ejpam-4323	231	81	0	0	NUM
ejpam-4323	231	82	;	;	PUNCT
ejpam-4323	231	83	(	(	PUNCT
ejpam-4323	231	84	gn3	gn3	NOUN
ejpam-4323	231	85	)	)	PUNCT
ejpam-4323	231	86	for	for	ADP
ejpam-4323	231	87	h	h	PROPN
ejpam-4323	231	88	∈	∈	PROPN
ejpam-4323	231	89	{	{	PUNCT
ejpam-4323	231	90	1	1	NUM
ejpam-4323	231	91	,	,	PUNCT
ejpam-4323	231	92	2	2	NUM
ejpam-4323	231	93	}	}	PUNCT
ejpam-4323	231	94	,	,	PUNCT
ejpam-4323	231	95	∑	∑	PROPN
ejpam-4323	231	96	1≤k≤k(n)(qk	1≤k≤k(n)(qk	NUM
ejpam-4323	231	97	,	,	PUNCT
ejpam-4323	231	98	n	n	CCONJ
ejpam-4323	231	99	/	/	SYM
ejpam-4323	231	100	p	p	NOUN
ejpam-4323	231	101	h	h	NOUN
ejpam-4323	231	102	k	k	NOUN
ejpam-4323	231	103	,	,	PUNCT
ejpam-4323	231	104	n	n	CCONJ
ejpam-4323	231	105	)	)	PUNCT
ejpam-4323	231	106	→	→	SYM
ejpam-4323	231	107	λ	λ	NOUN
ejpam-4323	231	108	∈]0	∈]0	X
ejpam-4323	231	109	,	,	PUNCT
ejpam-4323	231	110	+	+	NOUN
ejpam-4323	231	111	∞	∞	PROPN
ejpam-4323	231	112	[	[	X
ejpam-4323	231	113	.	.	PUNCT
ejpam-4323	232	1	(	(	PUNCT
ejpam-4323	232	2	gn4	gn4	NOUN
ejpam-4323	232	3	)	)	PUNCT
ejpam-4323	232	4	for	for	ADP
ejpam-4323	232	5	0	0	NUM
ejpam-4323	232	6	<	<	X
ejpam-4323	232	7	ε	ε	X
ejpam-4323	232	8	<	<	X
ejpam-4323	232	9	1	1	NUM
ejpam-4323	232	10	,	,	PUNCT
ejpam-4323	232	11	n	n	PRON
ejpam-4323	232	12	≥	≥	NOUN
ejpam-4323	232	13	1	1	NUM
ejpam-4323	232	14	,	,	PUNCT
ejpam-4323	232	15	0	0	NUM
ejpam-4323	232	16	≤	≤	NUM
ejpam-4323	232	17	k	k	X
ejpam-4323	232	18	≤	≤	X
ejpam-4323	232	19	k(n	k(n	X
ejpam-4323	232	20	)	)	PUNCT
ejpam-4323	232	21	,	,	PUNCT
ejpam-4323	232	22	and	and	CCONJ
ejpam-4323	232	23	for	for	ADP
ejpam-4323	232	24	b(ε	b(ε	PROPN
ejpam-4323	232	25	,	,	PUNCT
ejpam-4323	232	26	k	k	NOUN
ejpam-4323	232	27	,	,	PUNCT
ejpam-4323	232	28	n	n	CCONJ
ejpam-4323	232	29	)	)	PUNCT
ejpam-4323	232	30	=	=	PUNCT
ejpam-4323	233	1	+	+	ADP
ejpam-4323	233	2	∞∑	∞∑	NUM
ejpam-4323	233	3	j=0	j=0	PROPN
ejpam-4323	233	4	1(∣∣∣∣j−	1(∣∣∣∣j−	PROPN
ejpam-4323	233	5	qk	qk	PROPN
ejpam-4323	233	6	,	,	PUNCT
ejpam-4323	233	7	n	n	PRON
ejpam-4323	233	8	pk	pk	NOUN
ejpam-4323	233	9	,	,	PUNCT
ejpam-4323	233	10	n	n	NOUN
ejpam-4323	233	11	−1	−1	NOUN
ejpam-4323	233	12	∣∣∣∣≥ε	∣∣∣∣≥ε	NOUN
ejpam-4323	233	13	)	)	PUNCT
ejpam-4323	233	14	(	(	PUNCT
ejpam-4323	233	15	j	j	PROPN
ejpam-4323	233	16	−	−	PROPN
ejpam-4323	233	17	qk	qk	PROPN
ejpam-4323	233	18	,	,	PUNCT
ejpam-4323	233	19	n	n	PRON
ejpam-4323	233	20	pk	pk	NOUN
ejpam-4323	233	21	,	,	PUNCT
ejpam-4323	233	22	n	n	NOUN
ejpam-4323	233	23	)	)	PUNCT
ejpam-4323	233	24	2	2	NUM
ejpam-4323	233	25	pk	pk	NOUN
ejpam-4323	233	26	,	,	PUNCT
ejpam-4323	233	27	nq	nq	PROPN
ejpam-4323	233	28	j	j	PROPN
ejpam-4323	233	29	k	k	PROPN
ejpam-4323	233	30	,	,	PUNCT
ejpam-4323	233	31	n	n	CCONJ
ejpam-4323	233	32	,	,	PUNCT
ejpam-4323	233	33	we	we	PRON
ejpam-4323	233	34	have	have	VERB
ejpam-4323	233	35	b(ε	b(ε	NOUN
ejpam-4323	233	36	,	,	PUNCT
ejpam-4323	233	37	n	n	CCONJ
ejpam-4323	233	38	)	)	PUNCT
ejpam-4323	233	39	=	=	PUNCT
ejpam-4323	234	1	k(n)∑	k(n)∑	NOUN
ejpam-4323	234	2	k=1	k=1	X
ejpam-4323	234	3	b(ε	b(ε	PROPN
ejpam-4323	234	4	,	,	PUNCT
ejpam-4323	234	5	k	k	NOUN
ejpam-4323	234	6	,	,	PUNCT
ejpam-4323	234	7	n	n	CCONJ
ejpam-4323	234	8	)	)	PUNCT
ejpam-4323	234	9	→	→	SYM
ejpam-4323	234	10	0	0	X
ejpam-4323	234	11	.	.	PUNCT
ejpam-4323	235	1	then	then	ADV
ejpam-4323	235	2	we	we	PRON
ejpam-4323	235	3	have	have	AUX
ejpam-4323	235	4	sn[x	sn[x	VERB
ejpam-4323	235	5	]	]	PUNCT
ejpam-4323	235	6	p(λ	p(λ	NOUN
ejpam-4323	235	7	)	)	PUNCT
ejpam-4323	235	8	.	.	PUNCT
ejpam-4323	236	1	references	reference	NOUN
ejpam-4323	236	2	527	527	NUM
ejpam-4323	236	3	proofs	proof	NOUN
ejpam-4323	236	4	of	of	ADP
ejpam-4323	236	5	theorems	theorem	NOUN
ejpam-4323	236	6	3	3	NUM
ejpam-4323	236	7	and	and	CCONJ
ejpam-4323	236	8	4	4	NUM
ejpam-4323	236	9	.	.	X
ejpam-4323	237	1	in	in	ADP
ejpam-4323	237	2	the	the	DET
ejpam-4323	237	3	proofs	proof	NOUN
ejpam-4323	237	4	of	of	ADP
ejpam-4323	237	5	theorems	theorem	NOUN
ejpam-4323	237	6	1	1	NUM
ejpam-4323	237	7	and	and	CCONJ
ejpam-4323	237	8	2	2	NUM
ejpam-4323	237	9	,	,	PUNCT
ejpam-4323	237	10	the	the	DET
ejpam-4323	237	11	uan	uan	PROPN
ejpam-4323	237	12	,	,	PUNCT
ejpam-4323	237	13	the	the	DET
ejpam-4323	237	14	cvh	cvh	NOUN
ejpam-4323	237	15	,	,	PUNCT
ejpam-4323	237	16	the	the	DET
ejpam-4323	237	17	poisson	poisson	NOUN
ejpam-4323	237	18	lynderberg	lynderberg	PROPN
ejpam-4323	237	19	condition	condition	NOUN
ejpam-4323	237	20	and	and	CCONJ
ejpam-4323	237	21	the	the	DET
ejpam-4323	237	22	convergence	convergence	NOUN
ejpam-4323	237	23	of	of	ADP
ejpam-4323	237	24	esn[x	esn[x	ADJ
ejpam-4323	237	25	]	]	PUNCT
ejpam-4323	237	26	are	be	AUX
ejpam-4323	237	27	the	the	DET
ejpam-4323	237	28	general	general	ADJ
ejpam-4323	237	29	conditions	condition	NOUN
ejpam-4323	237	30	for	for	ADP
ejpam-4323	237	31	sn[x	sn[x	VERB
ejpam-4323	237	32	]	]	X
ejpam-4323	237	33	p(λ	p(λ	NOUN
ejpam-4323	237	34	)	)	PUNCT
ejpam-4323	237	35	.	.	PUNCT
ejpam-4323	238	1	in	in	ADP
ejpam-4323	238	2	theorems	theorem	NOUN
ejpam-4323	238	3	3	3	NUM
ejpam-4323	238	4	and	and	CCONJ
ejpam-4323	238	5	4	4	NUM
ejpam-4323	238	6	,	,	PUNCT
ejpam-4323	238	7	uniform	uniform	ADJ
ejpam-4323	238	8	convergence	convergence	NOUN
ejpam-4323	238	9	simplifies	simplify	VERB
ejpam-4323	238	10	these	these	DET
ejpam-4323	238	11	conditions	condition	NOUN
ejpam-4323	238	12	,	,	PUNCT
ejpam-4323	238	13	making	make	VERB
ejpam-4323	238	14	the	the	DET
ejpam-4323	238	15	proofs	proof	NOUN
ejpam-4323	238	16	lighter	lighter	ADV
ejpam-4323	238	17	.	.	PUNCT
ejpam-4323	239	1	�	�	PROPN
ejpam-4323	239	2	4	4	NUM
ejpam-4323	239	3	.	.	PUNCT
ejpam-4323	240	1	concluding	conclude	VERB
ejpam-4323	240	2	remarks	remark	VERB
ejpam-4323	240	3	the	the	DET
ejpam-4323	240	4	extensions	extension	NOUN
ejpam-4323	240	5	we	we	PRON
ejpam-4323	240	6	provide	provide	VERB
ejpam-4323	240	7	are	be	AUX
ejpam-4323	240	8	the	the	DET
ejpam-4323	240	9	first	first	ADJ
ejpam-4323	240	10	general	general	ADJ
ejpam-4323	240	11	results	result	NOUN
ejpam-4323	240	12	.	.	PUNCT
ejpam-4323	241	1	the	the	DET
ejpam-4323	241	2	central	central	ADJ
ejpam-4323	241	3	limit	limit	NOUN
ejpam-4323	241	4	theorem	theorem	ADJ
ejpam-4323	241	5	frame	frame	NOUN
ejpam-4323	241	6	seems	seem	VERB
ejpam-4323	241	7	to	to	PART
ejpam-4323	241	8	be	be	AUX
ejpam-4323	241	9	the	the	DET
ejpam-4323	241	10	appropriate	appropriate	ADJ
ejpam-4323	241	11	way	way	NOUN
ejpam-4323	241	12	to	to	PART
ejpam-4323	241	13	get	get	VERB
ejpam-4323	241	14	more	more	ADJ
ejpam-4323	241	15	general	general	ADJ
ejpam-4323	241	16	extensions	extension	NOUN
ejpam-4323	241	17	.	.	PUNCT
ejpam-4323	242	1	theorems	theorem	NOUN
ejpam-4323	242	2	1	1	NUM
ejpam-4323	242	3	and	and	CCONJ
ejpam-4323	242	4	2	2	NUM
ejpam-4323	242	5	can	can	AUX
ejpam-4323	242	6	be	be	AUX
ejpam-4323	242	7	done	do	VERB
ejpam-4323	242	8	by	by	ADP
ejpam-4323	242	9	direct	direct	ADJ
ejpam-4323	242	10	methods	method	NOUN
ejpam-4323	242	11	.	.	PUNCT
ejpam-4323	243	1	however	however	ADV
ejpam-4323	243	2	,	,	PUNCT
ejpam-4323	243	3	general	general	ADJ
ejpam-4323	243	4	forms	form	NOUN
ejpam-4323	243	5	in	in	ADP
ejpam-4323	243	6	theorems	theorem	NOUN
ejpam-4323	243	7	3	3	NUM
ejpam-4323	243	8	and	and	CCONJ
ejpam-4323	243	9	4	4	NUM
ejpam-4323	243	10	could	could	AUX
ejpam-4323	243	11	hardly	hardly	ADV
ejpam-4323	243	12	be	be	AUX
ejpam-4323	243	13	obtained	obtain	VERB
ejpam-4323	243	14	in	in	ADP
ejpam-4323	243	15	direct	direct	ADJ
ejpam-4323	243	16	methods	method	NOUN
ejpam-4323	243	17	.	.	PUNCT
ejpam-4323	244	1	they	they	PRON
ejpam-4323	244	2	are	be	AUX
ejpam-4323	244	3	products	product	NOUN
ejpam-4323	244	4	of	of	ADP
ejpam-4323	244	5	the	the	DET
ejpam-4323	244	6	clt	clt	NOUN
ejpam-4323	244	7	frame	frame	NOUN
ejpam-4323	244	8	.	.	PUNCT
ejpam-4323	245	1	references	reference	NOUN
ejpam-4323	245	2	[	[	X
ejpam-4323	245	3	1	1	NUM
ejpam-4323	245	4	]	]	PUNCT
ejpam-4323	245	5	w	w	NOUN
ejpam-4323	245	6	feller	feller	NOUN
ejpam-4323	245	7	.	.	PUNCT
ejpam-4323	246	1	an	an	DET
ejpam-4323	246	2	introduction	introduction	NOUN
ejpam-4323	246	3	to	to	ADP
ejpam-4323	246	4	probability	probability	NOUN
ejpam-4323	246	5	theory	theory	NOUN
ejpam-4323	246	6	and	and	CCONJ
ejpam-4323	246	7	its	its	PRON
ejpam-4323	246	8	applications	application	NOUN
ejpam-4323	246	9	.	.	PUNCT
ejpam-4323	247	1	volume	volume	NOUN
ejpam-4323	247	2	i.	i.	PROPN
ejpam-4323	247	3	third	third	PROPN
ejpam-4323	247	4	editions	edition	NOUN
ejpam-4323	247	5	.	.	PUNCT
ejpam-4323	248	1	john	john	PROPN
ejpam-4323	248	2	wiley	wiley	PROPN
ejpam-4323	248	3	&	&	CCONJ
ejpam-4323	248	4	sons	sons	PROPN
ejpam-4323	248	5	inc	inc	PROPN
ejpam-4323	248	6	,	,	PUNCT
ejpam-4323	248	7	new	new	PROPN
ejpam-4323	248	8	-	-	PUNCT
ejpam-4323	248	9	york	york	NOUN
ejpam-4323	248	10	,	,	PUNCT
ejpam-4323	248	11	1968	1968	NUM
ejpam-4323	248	12	.	.	PUNCT
ejpam-4323	249	1	[	[	X
ejpam-4323	249	2	2	2	NUM
ejpam-4323	249	3	]	]	PUNCT
ejpam-4323	249	4	w	w	NOUN
ejpam-4323	249	5	feller	feller	NOUN
ejpam-4323	249	6	.	.	PUNCT
ejpam-4323	250	1	an	an	DET
ejpam-4323	250	2	introduction	introduction	NOUN
ejpam-4323	250	3	to	to	ADP
ejpam-4323	250	4	probability	probability	NOUN
ejpam-4323	250	5	theory	theory	NOUN
ejpam-4323	250	6	and	and	CCONJ
ejpam-4323	250	7	its	its	PRON
ejpam-4323	250	8	applications	application	NOUN
ejpam-4323	250	9	.	.	PUNCT
ejpam-4323	251	1	volume	volume	NOUN
ejpam-4323	251	2	ii	ii	PROPN
ejpam-4323	251	3	.	.	PUNCT
ejpam-4323	252	1	third	third	ADJ
ejpam-4323	252	2	editions	edition	NOUN
ejpam-4323	252	3	.	.	PUNCT
ejpam-4323	253	1	john	john	PROPN
ejpam-4323	253	2	wiley	wiley	PROPN
ejpam-4323	253	3	&	&	CCONJ
ejpam-4323	253	4	sons	sons	PROPN
ejpam-4323	253	5	inc	inc	PROPN
ejpam-4323	253	6	,	,	PUNCT
ejpam-4323	253	7	new	new	PROPN
ejpam-4323	253	8	-	-	PUNCT
ejpam-4323	253	9	york	york	NOUN
ejpam-4323	253	10	,	,	PUNCT
ejpam-4323	253	11	1968	1968	NUM
ejpam-4323	253	12	.	.	PUNCT
ejpam-4323	254	1	[	[	X
ejpam-4323	254	2	3	3	X
ejpam-4323	254	3	]	]	PUNCT
ejpam-4323	254	4	a	a	DET
ejpam-4323	254	5	gut	gut	NOUN
ejpam-4323	254	6	.	.	PUNCT
ejpam-4323	255	1	probability	probability	NOUN
ejpam-4323	255	2	:	:	PUNCT
ejpam-4323	255	3	a	a	DET
ejpam-4323	255	4	graduate	graduate	ADJ
ejpam-4323	255	5	course	course	NOUN
ejpam-4323	255	6	.	.	PUNCT
ejpam-4323	256	1	springer	springer	NOUN
ejpam-4323	256	2	science+business	science+business	PROPN
ejpam-4323	256	3	media	medium	NOUN
ejpam-4323	256	4	,	,	PUNCT
ejpam-4323	256	5	inc	inc	PROPN
ejpam-4323	256	6	,	,	PUNCT
ejpam-4323	256	7	singapore	singapore	PROPN
ejpam-4323	256	8	,	,	PUNCT
ejpam-4323	256	9	2005	2005	NUM
ejpam-4323	256	10	.	.	PUNCT
ejpam-4323	257	1	[	[	X
ejpam-4323	257	2	4	4	X
ejpam-4323	257	3	]	]	X
ejpam-4323	257	4	gs	gs	PROPN
ejpam-4323	257	5	lo	lo	PROPN
ejpam-4323	257	6	.	.	PROPN
ejpam-4323	258	1	mathematical	mathematical	ADJ
ejpam-4323	258	2	foundations	foundation	NOUN
ejpam-4323	258	3	of	of	ADP
ejpam-4323	258	4	probability	probability	NOUN
ejpam-4323	258	5	theory	theory	NOUN
ejpam-4323	258	6	.	.	PUNCT
ejpam-4323	259	1	spas	spas	PROPN
ejpam-4323	259	2	books	books	PROPN
ejpam-4323	259	3	series	series	PROPN
ejpam-4323	259	4	.	.	PUNCT
ejpam-4323	259	5	,	,	PUNCT
ejpam-4323	259	6	calgary	calgary	PROPN
ejpam-4323	259	7	,	,	PUNCT
ejpam-4323	259	8	2018	2018	NUM
ejpam-4323	259	9	.	.	PUNCT
ejpam-4323	260	1	[	[	X
ejpam-4323	260	2	5	5	X
ejpam-4323	260	3	]	]	PUNCT
ejpam-4323	260	4	gs	gs	PROPN
ejpam-4323	260	5	lo	lo	PROPN
ejpam-4323	260	6	,	,	PUNCT
ejpam-4323	260	7	ta	ta	ADP
ejpam-4323	260	8	kpanzou	kpanzou	PROPN
ejpam-4323	260	9	,	,	PUNCT
ejpam-4323	260	10	m	m	AUX
ejpam-4323	260	11	ngom	ngom	ADJ
ejpam-4323	260	12	,	,	PUNCT
ejpam-4323	260	13	and	and	CCONJ
ejpam-4323	261	1	ab	ab	PROPN
ejpam-4323	261	2	niang	niang	PROPN
ejpam-4323	261	3	.	.	PUNCT
ejpam-4323	262	1	weak	weak	ADJ
ejpam-4323	262	2	convergence	convergence	NOUN
ejpam-4323	262	3	(	(	PUNCT
ejpam-4323	262	4	ia	ia	PROPN
ejpam-4323	262	5	):	):	PUNCT
ejpam-4323	262	6	sequences	sequence	NOUN
ejpam-4323	262	7	of	of	ADP
ejpam-4323	262	8	random	random	ADJ
ejpam-4323	262	9	vectors	vector	NOUN
ejpam-4323	262	10	.	.	PUNCT
ejpam-4323	263	1	spas	spas	PROPN
ejpam-4323	263	2	books	books	PROPN
ejpam-4323	263	3	series	series	PROPN
ejpam-4323	263	4	.	.	PUNCT
ejpam-4323	263	5	,	,	PUNCT
ejpam-4323	263	6	calgary	calgary	PROPN
ejpam-4323	263	7	,	,	PUNCT
ejpam-4323	263	8	2021	2021	NUM
ejpam-4323	263	9	.	.	PUNCT
ejpam-4323	264	1	[	[	X
ejpam-4323	264	2	6	6	NUM
ejpam-4323	264	3	]	]	PUNCT
ejpam-4323	264	4	m	m	NOUN
ejpam-4323	264	5	loève	loève	NOUN
ejpam-4323	264	6	.	.	PUNCT
ejpam-4323	265	1	probability	probability	NOUN
ejpam-4323	265	2	theory	theory	PROPN
ejpam-4323	265	3	i.	i.	PROPN
ejpam-4323	265	4	springer	springer	PROPN
ejpam-4323	265	5	-	-	PUNCT
ejpam-4323	265	6	verlag	verlag	PROPN
ejpam-4323	265	7	.	.	PUNCT
ejpam-4323	266	1	,	,	PUNCT
ejpam-4323	266	2	new	new	PROPN
ejpam-4323	266	3	-	-	PUNCT
ejpam-4323	266	4	york	york	NOUN
ejpam-4323	266	5	,	,	PUNCT
ejpam-4323	266	6	1977	1977	NUM
ejpam-4323	266	7	.	.	PUNCT