id	sid	tid	token	lemma	pos
gs-1575	1	1	georgian	georgian	ADJ
gs-1575	1	2	scientists/ქართველი	scientists/ქართველი	NOUN
gs-1575	1	3	მეცნიერები	მეცნიერები	NOUN
gs-1575	1	4	ტ.	ტ.	VERB
gs-1575	1	5	5	5	NUM
gs-1575	1	6	n	n	PRON
gs-1575	1	7	1	1	NUM
gs-1575	1	8	,	,	PUNCT
gs-1575	1	9	2023	2023	NUM
gs-1575	1	10	308	308	NUM
gs-1575	1	11	georgian	georgian	PROPN
gs-1575	1	12	scientists	scientist	NOUN
gs-1575	1	13	ქართველი	ქართველი	ADJ
gs-1575	1	14	მეცნიერები	მეცნიერები	PROPN
gs-1575	1	15	vol	vol	NOUN
gs-1575	1	16	.	.	PUNCT
gs-1575	2	1	5	5	NUM
gs-1575	2	2	issue	issue	NOUN
gs-1575	2	3	1	1	NUM
gs-1575	2	4	,	,	PUNCT
gs-1575	2	5	2023	2023	NUM
gs-1575	2	6	https://doi.org/10.52340/gs.2023.05.01.27	https://doi.org/10.52340/gs.2023.05.01.27	X
gs-1575	2	7	on	on	ADP
gs-1575	2	8	the	the	DET
gs-1575	2	9	accuracy	accuracy	NOUN
gs-1575	2	10	by	by	ADP
gs-1575	2	11	the	the	DET
gs-1575	2	12	metric	metric	ADJ
gs-1575	2	13	1l	1l	NUM
gs-1575	2	14	of	of	ADP
gs-1575	2	15	the	the	DET
gs-1575	2	16	density	density	NOUN
gs-1575	2	17	estimation	estimation	NOUN
gs-1575	2	18	constructed	construct	VERB
gs-1575	2	19	by	by	ADP
gs-1575	2	20	dependent	dependent	ADJ
gs-1575	2	21	observations	observation	NOUN
gs-1575	2	22	beqnu	beqnu	PROPN
gs-1575	2	23	parjiani1	parjiani1	PROPN
gs-1575	2	24	,	,	PUNCT
gs-1575	2	25	levan	levan	PROPN
gs-1575	2	26	labadze2	labadze2	PROPN
gs-1575	2	27	and	and	CCONJ
gs-1575	2	28	tsiala	tsiala	NOUN
gs-1575	2	29	kvatadze3	kvatadze3	NOUN
gs-1575	2	30	1associate	1associate	NUM
gs-1575	2	31	professor	professor	NOUN
gs-1575	2	32	of	of	ADP
gs-1575	2	33	department	department	PROPN
gs-1575	2	34	of	of	ADP
gs-1575	2	35	mathematics	mathematic	NOUN
gs-1575	2	36	of	of	ADP
gs-1575	2	37	georgian	georgian	PROPN
gs-1575	2	38	technical	technical	PROPN
gs-1575	2	39	university	university	PROPN
gs-1575	2	40	;	;	PUNCT
gs-1575	2	41	2invited	2invited	NUM
gs-1575	2	42	lecturer	lecturer	NOUN
gs-1575	2	43	of	of	ADP
gs-1575	2	44	economics	economic	NOUN
gs-1575	2	45	,	,	PUNCT
gs-1575	2	46	ilia	ilia	PROPN
gs-1575	2	47	state	state	PROPN
gs-1575	2	48	university	university	PROPN
gs-1575	2	49	;	;	PUNCT
gs-1575	2	50	3invited	3invited	NUM
gs-1575	2	51	lecturer	lecturer	NOUN
gs-1575	2	52	in	in	ADP
gs-1575	2	53	statistics	statistic	NOUN
gs-1575	2	54	,	,	PUNCT
gs-1575	2	55	international	international	ADJ
gs-1575	2	56	black	black	PROPN
gs-1575	2	57	sea	sea	PROPN
gs-1575	2	58	university	university	NOUN
gs-1575	2	59	abstract	abstract	NOUN
gs-1575	2	60	a	a	DET
gs-1575	2	61	narrowly	narrowly	ADV
gs-1575	2	62	stationary	stationary	ADJ
gs-1575	2	63	two	two	NUM
gs-1575	2	64	-	-	PUNCT
gs-1575	2	65	component	component	NOUN
gs-1575	2	66	sequence	sequence	NOUN
gs-1575	2	67			PROPN
gs-1575	2	68			PROPN
gs-1575	2	69	1	1	NUM
gs-1575	2	70	,	,	PUNCT
gs-1575	2	71	i	i	PRON
gs-1575	2	72	i	i	PRON
gs-1575	2	73	i	i	VERB
gs-1575	2	74	x	x	SYM
gs-1575	2	75			NUM
gs-1575	2	76			NOUN
gs-1575	2	77	is	be	AUX
gs-1575	2	78	considered	consider	VERB
gs-1575	2	79	on	on	ADP
gs-1575	2	80	the	the	DET
gs-1575	2	81	probability	probability	NOUN
gs-1575	2	82	space	space	NOUN
gs-1575	2	83			PROPN
gs-1575	2	84			PROPN
gs-1575	2	85	,	,	PUNCT
gs-1575	2	86	,	,	PUNCT
gs-1575	2	87	f	f	PROPN
gs-1575	2	88	p	p	NOUN
gs-1575	2	89	.	.	PUNCT
gs-1575	3	1	the	the	DET
gs-1575	3	2	control	control	NOUN
gs-1575	3	3	sequence	sequence	NOUN
gs-1575	3	4			PROPN
gs-1575	3	5			PROPN
gs-1575	3	6	1i	1i	NOUN
gs-1575	3	7	i	i	INTJ
gs-1575	3	8			NOUN
gs-1575	4	1	(	(	PUNCT
gs-1575	4	2	:	:	PUNCT
gs-1575	4	3	,	,	PUNCT
gs-1575	4	4	1,2,	1,2,	NUM
gs-1575	4	5	...	...	PUNCT
gs-1575	4	6	)i	)i	PUNCT
gs-1575	5	1	i	i	PROPN
gs-1575	5	2			NOUN
gs-1575	5	3	is	be	AUX
gs-1575	5	4	discrete	discrete	ADJ
gs-1575	5	5			X
gs-1575	5	6	1	1	NOUN
gs-1575	5	7	2	2	NUM
gs-1575	5	8	,	,	PUNCT
gs-1575	5	9	,	,	PUNCT
gs-1575	5	10	...	...	PUNCT
gs-1575	5	11	,	,	PUNCT
gs-1575	5	12	rb	rb	PROPN
gs-1575	5	13	b	b	PROPN
gs-1575	5	14	b	b	NOUN
gs-1575	5	15			PROPN
gs-1575	5	16	,	,	PUNCT
gs-1575	5	17	(	(	PUNCT
gs-1575	5	18	)	)	PUNCT
gs-1575	5	19	m	m	PROPN
gs-1575	5	20	mip	mip	PROPN
gs-1575	5	21	b	b	PROPN
gs-1575	5	22	p	p	PROPN
gs-1575	5	23			NOUN
gs-1575	5	24	,	,	PUNCT
gs-1575	6	1	1,m	1,m	PROPN
gs-1575	6	2	r	r	X
gs-1575	6	3	,	,	PUNCT
gs-1575	6	4	1,2,	1,2,	NUM
gs-1575	6	5	...	...	PUNCT
gs-1575	7	1	i	i	PRON
gs-1575	7	2			VERB
gs-1575	7	3	,	,	PUNCT
gs-1575	7	4	1	1	NUM
gs-1575	7	5	1	1	NUM
gs-1575	7	6	r	r	NOUN
gs-1575	7	7	m	m	VERB
gs-1575	7	8	m	m	VERB
gs-1575	7	9	p	p	ADJ
gs-1575	7	10			ADJ
gs-1575	7	11			X
gs-1575	7	12	.	.	PUNCT
gs-1575	8	1			PRON
gs-1575	8	2			PROPN
gs-1575	8	3	1i	1i	NOUN
gs-1575	9	1	i	i	NOUN
gs-1575	9	2	x	x	SYM
gs-1575	9	3			PROPN
gs-1575	9	4	(	(	PUNCT
gs-1575	9	5	:	:	PUNCT
gs-1575	9	6	,	,	PUNCT
gs-1575	9	7	1,2,	1,2,	NUM
gs-1575	9	8	...	...	PUNCT
gs-1575	9	9	)ix	)ix	PUNCT
gs-1575	10	1	r	r	PROPN
gs-1575	10	2	i	i	PROPN
gs-1575	10	3			PROPN
gs-1575	10	4	is	be	AUX
gs-1575	10	5	a	a	DET
gs-1575	10	6	conditionally	conditionally	ADV
gs-1575	10	7	independent	independent	ADJ
gs-1575	10	8	sequence	sequence	NOUN
gs-1575	10	9	,	,	PUNCT
gs-1575	10	10	those	those	DET
gs-1575	10	11	members	member	NOUN
gs-1575	10	12	represent	represent	VERB
gs-1575	10	13	observations	observation	NOUN
gs-1575	10	14	of	of	ADP
gs-1575	10	15	some	some	DET
gs-1575	10	16	random	random	ADJ
gs-1575	10	17	variable	variable	NOUN
gs-1575	10	18	x	x	X
gs-1575	10	19	.	.	PUNCT
gs-1575	11	1	the	the	DET
gs-1575	11	2	conditional	conditional	ADJ
gs-1575	11	3	distributions	distribution	NOUN
gs-1575	11	4	i	i	NOUN
gs-1575	11	5	mx	mx	VERB
gs-1575	11	6	b	b	PROPN
gs-1575	11	7	,	,	PUNCT
gs-1575	11	8	1,m	1,m	X
gs-1575	11	9	r	r	VERB
gs-1575	11	10	have	have	VERB
gs-1575	11	11	unknown	unknown	ADJ
gs-1575	11	12	densities	density	NOUN
gs-1575	11	13	(	(	PUNCT
gs-1575	11	14	)	)	PUNCT
gs-1575	11	15	mf	mf	NOUN
gs-1575	11	16	x	x	X
gs-1575	11	17	,	,	PUNCT
gs-1575	11	18	1,m	1,m	PROPN
gs-1575	11	19	r	r	NOUN
gs-1575	11	20	,	,	PUNCT
gs-1575	11	21	respectively	respectively	ADV
gs-1575	11	22	.	.	PUNCT
gs-1575	12	1	a	a	DET
gs-1575	12	2	core	core	NOUN
gs-1575	12	3	rosenblatt	rosenblatt	NOUN
gs-1575	12	4	-	-	PUNCT
gs-1575	12	5	parzen	parzen	NOUN
gs-1575	12	6	-	-	PUNCT
gs-1575	12	7	type	type	NOUN
gs-1575	12	8	estimate	estimate	NOUN
gs-1575	12	9	of	of	ADP
gs-1575	12	10	the	the	DET
gs-1575	12	11	density	density	NOUN
gs-1575	12	12	is	be	AUX
gs-1575	12	13	1	1	NUM
gs-1575	12	14	(	(	PUNCT
gs-1575	12	15	)	)	PUNCT
gs-1575	12	16	(	(	PUNCT
gs-1575	12	17	)	)	PUNCT
gs-1575	13	1	r	r	NOUN
gs-1575	13	2	m	m	VERB
gs-1575	13	3	m	m	VERB
gs-1575	13	4	m	m	VERB
gs-1575	13	5	f	f	NOUN
gs-1575	13	6	x	x	X
gs-1575	14	1	p	p	X
gs-1575	14	2	f	f	X
gs-1575	14	3	x	x	X
gs-1575	14	4			NUM
gs-1575	14	5			PROPN
gs-1575	14	6	constructed	construct	VERB
gs-1575	14	7	from	from	ADP
gs-1575	14	8	the	the	DET
gs-1575	14	9	dependent	dependent	ADJ
gs-1575	14	10	observations	observation	NOUN
gs-1575	14	11	.	.	PUNCT
gs-1575	15	1	the	the	DET
gs-1575	15	2	accuracy	accuracy	NOUN
gs-1575	15	3	of	of	ADP
gs-1575	15	4	this	this	DET
gs-1575	15	5	estimate	estimate	NOUN
gs-1575	15	6	is	be	AUX
gs-1575	15	7	determined	determine	VERB
gs-1575	15	8	by	by	ADP
gs-1575	15	9	the	the	DET
gs-1575	15	10	metric	metric	ADJ
gs-1575	15	11	1l	1l	NUM
gs-1575	15	12	.	.	PUNCT
gs-1575	16	1	a	a	DET
gs-1575	16	2	special	special	ADJ
gs-1575	16	3	case	case	NOUN
gs-1575	16	4	obtained	obtain	VERB
gs-1575	16	5	by	by	ADP
gs-1575	16	6	using	use	VERB
gs-1575	16	7	the	the	DET
gs-1575	16	8	bartlett	bartlett	PROPN
gs-1575	16	9	core	core	PROPN
gs-1575	16	10	and	and	CCONJ
gs-1575	16	11	taking	take	VERB
gs-1575	16	12	the	the	DET
gs-1575	16	13	smoothing	smooth	VERB
gs-1575	16	14	coefficient	coefficient	NOUN
gs-1575	16	15	as	as	SCONJ
gs-1575	16	16	a	a	DET
gs-1575	16	17	specific	specific	ADJ
gs-1575	16	18	sequence	sequence	NOUN
gs-1575	16	19	is	be	AUX
gs-1575	16	20	considered	consider	VERB
gs-1575	16	21	.	.	PUNCT
gs-1575	17	1	2010	2010	NUM
gs-1575	17	2	mathematics	mathematic	NOUN
gs-1575	17	3	subject	subject	NOUN
gs-1575	17	4	classification	classification	NOUN
gs-1575	17	5	.	.	PUNCT
gs-1575	18	1	62g05	62g05	ADJ
gs-1575	18	2	.	.	PUNCT
gs-1575	19	1	62g07	62g07	NUM
gs-1575	19	2	introduction	introduction	NOUN
gs-1575	19	3	during	during	ADP
gs-1575	19	4	statistical	statistical	ADJ
gs-1575	19	5	studies	study	NOUN
gs-1575	19	6	of	of	ADP
gs-1575	19	7	practical	practical	ADJ
gs-1575	19	8	tasks	task	NOUN
gs-1575	19	9	,	,	PUNCT
gs-1575	19	10	parametric	parametric	ADJ
gs-1575	19	11	and	and	CCONJ
gs-1575	19	12	non	non	ADJ
gs-1575	19	13	-	-	ADJ
gs-1575	19	14	parametric	parametric	ADJ
gs-1575	19	15	estimates	estimate	NOUN
gs-1575	19	16	are	be	AUX
gs-1575	19	17	obtained	obtain	VERB
gs-1575	19	18	.	.	PUNCT
gs-1575	20	1	one	one	NUM
gs-1575	20	2	important	important	ADJ
gs-1575	20	3	issue	issue	NOUN
gs-1575	20	4	is	be	AUX
gs-1575	20	5	the	the	DET
gs-1575	20	6	construction	construction	NOUN
gs-1575	20	7	of	of	ADP
gs-1575	20	8	an	an	DET
gs-1575	20	9	estimate	estimate	NOUN
gs-1575	20	10	of	of	ADP
gs-1575	20	11	the	the	DET
gs-1575	20	12	density	density	NOUN
gs-1575	20	13	of	of	ADP
gs-1575	20	14	the	the	DET
gs-1575	20	15	distribution	distribution	NOUN
gs-1575	20	16	.	.	PUNCT
gs-1575	21	1	until	until	SCONJ
gs-1575	21	2	recently	recently	ADV
gs-1575	21	3	,	,	PUNCT
gs-1575	21	4	estimates	estimate	NOUN
gs-1575	21	5	were	be	AUX
gs-1575	21	6	made	make	VERB
gs-1575	21	7	by	by	ADP
gs-1575	21	8	independent	independent	ADJ
gs-1575	21	9	observations	observation	NOUN
gs-1575	21	10	.	.	PUNCT
gs-1575	22	1	many	many	ADJ
gs-1575	22	2	problems	problem	NOUN
gs-1575	22	3	require	require	VERB
gs-1575	22	4	consideration	consideration	NOUN
gs-1575	22	5	of	of	ADP
gs-1575	22	6	dependent	dependent	ADJ
gs-1575	22	7	observations	observation	NOUN
gs-1575	22	8	.	.	PUNCT
gs-1575	23	1	long	long	ADJ
gs-1575	23	2	-	-	PUNCT
gs-1575	23	3	term	term	NOUN
gs-1575	23	4	financial	financial	ADJ
gs-1575	23	5	independence	independence	NOUN
gs-1575	23	6	studies	study	NOUN
gs-1575	23	7	of	of	ADP
gs-1575	23	8	investment	investment	NOUN
gs-1575	23	9	and	and	CCONJ
gs-1575	23	10	insurance	insurance	NOUN
gs-1575	23	11	companies	company	NOUN
gs-1575	23	12	are	be	AUX
gs-1575	23	13	constantly	constantly	ADV
gs-1575	23	14	conducted	conduct	VERB
gs-1575	23	15	in	in	ADP
gs-1575	23	16	the	the	DET
gs-1575	23	17	financial	financial	ADJ
gs-1575	23	18	market	market	NOUN
gs-1575	23	19	.	.	PUNCT
gs-1575	24	1	it	it	PRON
gs-1575	24	2	is	be	AUX
gs-1575	24	3	necessary	necessary	ADJ
gs-1575	24	4	to	to	PART
gs-1575	24	5	assess	assess	VERB
gs-1575	24	6	the	the	DET
gs-1575	24	7	risks	risk	NOUN
gs-1575	24	8	of	of	ADP
gs-1575	24	9	banking	banking	NOUN
gs-1575	24	10	investments	investment	NOUN
gs-1575	24	11	.	.	PUNCT
gs-1575	25	1	for	for	ADP
gs-1575	25	2	this	this	DET
gs-1575	25	3	purpose	purpose	NOUN
gs-1575	25	4	,	,	PUNCT
gs-1575	25	5	an	an	DET
gs-1575	25	6	analysis	analysis	NOUN
gs-1575	25	7	of	of	ADP
gs-1575	25	8	the	the	DET
gs-1575	25	9	flow	flow	NOUN
gs-1575	25	10	of	of	ADP
gs-1575	25	11	reinvestments	reinvestment	NOUN
gs-1575	25	12	is	be	AUX
gs-1575	25	13	carried	carry	VERB
gs-1575	25	14	out	out	ADP
gs-1575	25	15	,	,	PUNCT
gs-1575	25	16	and	and	CCONJ
gs-1575	25	17	the	the	DET
gs-1575	25	18	indicators	indicator	NOUN
gs-1575	25	19	of	of	ADP
gs-1575	25	20	the	the	DET
gs-1575	25	21	financial	financial	ADJ
gs-1575	25	22	stability	stability	NOUN
gs-1575	25	23	of	of	ADP
gs-1575	25	24	the	the	DET
gs-1575	25	25	companies	company	NOUN
gs-1575	25	26	are	be	AUX
gs-1575	25	27	evaluated	evaluate	VERB
gs-1575	25	28	.	.	PUNCT
gs-1575	26	1	georgian	georgian	ADJ
gs-1575	26	2	scientists/ქართველი	scientists/ქართველი	NOUN
gs-1575	26	3	მეცნიერები	მეცნიერები	NOUN
gs-1575	26	4	ტ.	ტ.	VERB
gs-1575	26	5	5	5	NUM
gs-1575	26	6	n	n	PRON
gs-1575	26	7	1	1	NUM
gs-1575	26	8	,	,	PUNCT
gs-1575	26	9	2023	2023	NUM
gs-1575	26	10	309	309	NUM
gs-1575	26	11	the	the	DET
gs-1575	26	12	listed	list	VERB
gs-1575	26	13	and	and	CCONJ
gs-1575	26	14	other	other	ADJ
gs-1575	26	15	tasks	task	NOUN
gs-1575	26	16	require	require	VERB
gs-1575	26	17	statistical	statistical	ADJ
gs-1575	26	18	analysis	analysis	NOUN
gs-1575	26	19	not	not	PART
gs-1575	26	20	only	only	ADV
gs-1575	26	21	with	with	ADP
gs-1575	26	22	independent	independent	ADJ
gs-1575	26	23	,	,	PUNCT
gs-1575	26	24	but	but	CCONJ
gs-1575	26	25	also	also	ADV
gs-1575	26	26	with	with	ADP
gs-1575	26	27	dependent	dependent	ADJ
gs-1575	26	28	data	datum	NOUN
gs-1575	26	29	.	.	PUNCT
gs-1575	27	1	research	research	NOUN
gs-1575	27	2	in	in	ADP
gs-1575	27	3	this	this	DET
gs-1575	27	4	direction	direction	NOUN
gs-1575	27	5	has	have	AUX
gs-1575	27	6	actually	actually	ADV
gs-1575	27	7	just	just	ADV
gs-1575	27	8	started	start	VERB
gs-1575	27	9	.	.	PUNCT
gs-1575	28	1	and	and	CCONJ
gs-1575	28	2	there	there	PRON
gs-1575	28	3	is	be	VERB
gs-1575	28	4	a	a	DET
gs-1575	28	5	rich	rich	ADJ
gs-1575	28	6	historical	historical	ADJ
gs-1575	28	7	experience	experience	NOUN
gs-1575	28	8	of	of	ADP
gs-1575	28	9	constructing	construct	VERB
gs-1575	28	10	non	non	ADJ
gs-1575	28	11	-	-	ADJ
gs-1575	28	12	parametric	parametric	ADJ
gs-1575	28	13	estimates	estimate	NOUN
gs-1575	28	14	of	of	ADP
gs-1575	28	15	density	density	NOUN
gs-1575	28	16	through	through	ADP
gs-1575	28	17	independent	independent	ADJ
gs-1575	28	18	observations	observation	NOUN
gs-1575	28	19	.	.	PUNCT
gs-1575	29	1	let	let	VERB
gs-1575	29	2	’s	’s	VERB
gs-1575	29	3	the	the	DET
gs-1575	29	4	quantities	quantity	NOUN
gs-1575	29	5	ix	ix	ADP
gs-1575	29	6	,	,	PUNCT
gs-1575	29	7	(	(	PUNCT
gs-1575	29	8	ix	ix	ADP
gs-1575	29	9	r	r	PROPN
gs-1575	29	10	)	)	PUNCT
gs-1575	29	11	,	,	PUNCT
gs-1575	29	12	i	i	PRON
gs-1575	29	13	=	=	SYM
gs-1575	29	14	1,2	1,2	NUM
gs-1575	29	15	...	...	PUNCT
gs-1575	29	16	represent	represent	VERB
gs-1575	29	17	independent	independent	ADJ
gs-1575	29	18	observations	observation	NOUN
gs-1575	29	19	of	of	ADP
gs-1575	29	20	a	a	DET
gs-1575	29	21	random	random	ADJ
gs-1575	29	22	variable	variable	NOUN
gs-1575	30	1	x	x	X
gs-1575	30	2	.	.	PUNCT
gs-1575	31	1	let	let	VERB
gs-1575	31	2	's	us	PRON
gs-1575	31	3	say	say	VERB
gs-1575	31	4	a	a	DET
gs-1575	31	5	quantity	quantity	NOUN
gs-1575	31	6	has	have	VERB
gs-1575	31	7	an	an	DET
gs-1575	31	8	unknown	unknown	ADJ
gs-1575	31	9	density	density	NOUN
gs-1575	31	10			NOUN
gs-1575	31	11	g	g	PROPN
gs-1575	31	12	x	x	X
gs-1575	31	13	.	.	PUNCT
gs-1575	32	1	in	in	ADP
gs-1575	32	2	m.	m.	PROPN
gs-1575	32	3	rosenblatt	rosenblatt	PROPN
gs-1575	32	4	and	and	CCONJ
gs-1575	32	5	e.	e.	PROPN
gs-1575	32	6	in	in	ADP
gs-1575	32	7	parzen	parzen	PROPN
gs-1575	32	8	's	's	PART
gs-1575	32	9	works	work	NOUN
gs-1575	32	10	(	(	PUNCT
gs-1575	32	11	see	see	VERB
gs-1575	32	12	[	[	X
gs-1575	32	13	1	1	NUM
gs-1575	32	14	]	]	PUNCT
gs-1575	32	15	,	,	PUNCT
gs-1575	32	16	[	[	X
gs-1575	32	17	2	2	NUM
gs-1575	32	18	]	]	NUM
gs-1575	32	19	)	)	PUNCT
gs-1575	32	20	,	,	PUNCT
gs-1575	32	21	the	the	DET
gs-1575	32	22	class	class	NOUN
gs-1575	32	23	of	of	ADP
gs-1575	32	24	core	core	NOUN
gs-1575	32	25	estimations	estimation	NOUN
gs-1575	32	26	is	be	AUX
gs-1575	32	27	considered	consider	VERB
gs-1575	32	28	as	as	ADP
gs-1575	32	29	a	a	DET
gs-1575	32	30	density	density	NOUN
gs-1575	32	31			NOUN
gs-1575	32	32	g	g	PUNCT
gs-1575	32	33	x	x	PUNCT
gs-1575	32	34	estimation	estimation	NOUN
gs-1575	32	35	.	.	PUNCT
gs-1575	33	1			NOUN
gs-1575	33	2			PUNCT
gs-1575	33	3			PROPN
gs-1575	34	1			NOUN
gs-1575	34	2			PROPN
gs-1575	34	3	1	1	NUM
gs-1575	34	4	ˆ	ˆ	NOUN
gs-1575	34	5	,	,	PUNCT
gs-1575	34	6	,	,	PUNCT
gs-1575	34	7	n	n	CCONJ
gs-1575	34	8	n	n	CCONJ
gs-1575	34	9	n	n	CCONJ
gs-1575	34	10	n	n	CCONJ
gs-1575	34	11	n	n	NOUN
gs-1575	35	1	i	i	PRON
gs-1575	35	2	i	i	PRON
gs-1575	35	3	a	a	DET
gs-1575	35	4	g	g	NOUN
gs-1575	35	5	x	x	PUNCT
gs-1575	35	6	a	a	PRON
gs-1575	35	7	k	k	PROPN
gs-1575	35	8	a	a	X
gs-1575	35	9	x	x	X
gs-1575	35	10	x	x	VERB
gs-1575	35	11	n	n	NOUN
gs-1575	35	12			NOUN
gs-1575	35	13			NUM
gs-1575	36	1			X
gs-1575	36	2	(	(	PUNCT
gs-1575	36	3	1	1	NUM
gs-1575	36	4	)	)	PUNCT
gs-1575	36	5	where	where	SCONJ
gs-1575	36	6			PROPN
gs-1575	36	7			PROPN
gs-1575	36	8	1n	1n	NUM
gs-1575	36	9	n	n	CCONJ
gs-1575	36	10	a	a	DET
gs-1575	36	11			NUM
gs-1575	36	12	is	be	AUX
gs-1575	36	13	a	a	DET
gs-1575	36	14	sequence	sequence	NOUN
gs-1575	36	15	of	of	ADP
gs-1575	36	16	positive	positive	ADJ
gs-1575	36	17	numbers	number	NOUN
gs-1575	36	18	such	such	ADJ
gs-1575	36	19	that	that	DET
gs-1575	36	20			NOUN
gs-1575	36	21	lim	lim	PRON
gs-1575	36	22	,	,	PUNCT
gs-1575	36	23	,	,	PUNCT
gs-1575	36	24	n	n	CCONJ
gs-1575	36	25	n	n	PROPN
gs-1575	36	26	n	n	ADV
gs-1575	36	27	a	a	DET
gs-1575	36	28	a	a	DET
gs-1575	36	29	o	o	NOUN
gs-1575	36	30	n	n	CCONJ
gs-1575	36	31			NOUN
gs-1575	36	32			NUM
gs-1575	36	33			VERB
gs-1575	36	34			PRON
gs-1575	36	35	(	(	PUNCT
gs-1575	36	36	2	2	NUM
gs-1575	36	37	)	)	PUNCT
gs-1575	36	38	and	and	CCONJ
gs-1575	36	39	the	the	DET
gs-1575	36	40	core	core	ADJ
gs-1575	36	41			PROPN
gs-1575	36	42	k	k	NUM
gs-1575	36	43	x	x	PUNCT
gs-1575	36	44	according	accord	VERB
gs-1575	36	45	to	to	ADP
gs-1575	36	46	lebesgue	lebesgue	NOUN
gs-1575	36	47	is	be	AUX
gs-1575	36	48	a	a	DET
gs-1575	36	49	integrated	integrate	VERB
gs-1575	36	50	certain	certain	ADJ
gs-1575	36	51	borel	borel	NOUN
gs-1575	36	52	function	function	NOUN
gs-1575	36	53	.	.	PUNCT
gs-1575	37	1	the	the	DET
gs-1575	37	2	accuracy	accuracy	NOUN
gs-1575	37	3	of	of	ADP
gs-1575	37	4	this	this	DET
gs-1575	37	5	type	type	NOUN
gs-1575	37	6	of	of	ADP
gs-1575	37	7	density	density	NOUN
gs-1575	37	8	2l	2l	NUM
gs-1575	37	9	approximation	approximation	NOUN
gs-1575	37	10	constructed	construct	VERB
gs-1575	37	11	by	by	ADP
gs-1575	37	12	independent	independent	ADJ
gs-1575	37	13	observations	observation	NOUN
gs-1575	37	14	(	(	PUNCT
gs-1575	37	15	[	[	X
gs-1575	37	16	1	1	NUM
gs-1575	37	17	]	]	PUNCT
gs-1575	37	18	,	,	PUNCT
gs-1575	37	19	[	[	X
gs-1575	37	20	3	3	NUM
gs-1575	37	21	]	]	PUNCT
gs-1575	37	22	,	,	PUNCT
gs-1575	37	23	[	[	X
gs-1575	37	24	4	4	NUM
gs-1575	37	25	]	]	PUNCT
gs-1575	37	26	)	)	PUNCT
gs-1575	37	27	and	and	CCONJ
gs-1575	37	28	metrics	metric	NOUN
gs-1575	37	29	(	(	PUNCT
gs-1575	37	30	[	[	X
gs-1575	37	31	5	5	NUM
gs-1575	37	32	]	]	PUNCT
gs-1575	37	33	)	)	PUNCT
gs-1575	37	34	has	have	AUX
gs-1575	37	35	been	be	AUX
gs-1575	37	36	determined	determine	VERB
gs-1575	37	37	under	under	ADP
gs-1575	37	38	different	different	ADJ
gs-1575	37	39	conditions	condition	NOUN
gs-1575	37	40	.	.	PUNCT
gs-1575	38	1	it	it	PRON
gs-1575	38	2	is	be	AUX
gs-1575	38	3	known	know	VERB
gs-1575	38	4	by	by	ADP
gs-1575	38	5	l.	l.	PROPN
gs-1575	38	6	devroye	devroye	PROPN
gs-1575	38	7	(	(	PUNCT
gs-1575	38	8	see	see	VERB
gs-1575	38	9	[	[	X
gs-1575	38	10	5	5	NUM
gs-1575	38	11	]	]	PUNCT
gs-1575	38	12	)	)	PUNCT
gs-1575	38	13	the	the	DET
gs-1575	38	14	accuracy	accuracy	NOUN
gs-1575	38	15	of	of	ADP
gs-1575	38	16	the	the	DET
gs-1575	38	17	metric	metric	ADJ
gs-1575	38	18	1l	1l	NUM
gs-1575	38	19	of	of	ADP
gs-1575	38	20	the	the	DET
gs-1575	38	21	estimate	estimate	NOUN
gs-1575	38	22	constructed	construct	VERB
gs-1575	38	23	by	by	ADP
gs-1575	38	24	independent	independent	ADJ
gs-1575	38	25	observations	observation	NOUN
gs-1575	38	26	of	of	ADP
gs-1575	38	27	the	the	DET
gs-1575	38	28	density	density	NOUN
gs-1575	38	29	.	.	PUNCT
gs-1575	39	1	let	let	VERB
gs-1575	39	2	's	us	PRON
gs-1575	39	3	state	state	NOUN
gs-1575	39	4	this	this	DET
gs-1575	39	5	result	result	NOUN
gs-1575	39	6	as	as	ADP
gs-1575	39	7	a	a	DET
gs-1575	39	8	lemma	lemma	PROPN
gs-1575	39	9	.	.	PUNCT
gs-1575	40	1	we	we	PRON
gs-1575	40	2	will	will	AUX
gs-1575	40	3	use	use	VERB
gs-1575	40	4	it	it	PRON
gs-1575	40	5	during	during	ADP
gs-1575	40	6	the	the	DET
gs-1575	40	7	proof	proof	NOUN
gs-1575	40	8	of	of	ADP
gs-1575	40	9	our	our	PRON
gs-1575	40	10	theorem	theorem	NOUN
gs-1575	40	11	.	.	PROPN
gs-1575	40	12	definition	definition	NOUN
gs-1575	40	13	1	1	NUM
gs-1575	40	14	(	(	PUNCT
gs-1575	40	15	see	see	VERB
gs-1575	40	16	[	[	X
gs-1575	40	17	5	5	NUM
gs-1575	40	18	]	]	PUNCT
gs-1575	40	19	)	)	PUNCT
gs-1575	40	20	.	.	PUNCT
gs-1575	41	1	let	let	VERB
gs-1575	41	2	us	we	PRON
gs-1575	41	3	denote	denote	VERB
gs-1575	41	4	by	by	ADP
gs-1575	41	5	f	f	PROPN
gs-1575	41	6	,	,	PUNCT
gs-1575	41	7	the	the	DET
gs-1575	41	8	set	set	NOUN
gs-1575	41	9	of	of	ADP
gs-1575	41	10	such	such	ADJ
gs-1575	41	11	functions	function	NOUN
gs-1575	41	12			NOUN
gs-1575	41	13	f	f	PUNCT
gs-1575	41	14	x	x	PUNCT
gs-1575	41	15	(	(	PUNCT
gs-1575	41	16	see	see	VERB
gs-1575	41	17	[	[	X
gs-1575	41	18	5	5	NUM
gs-1575	41	19	]	]	PUNCT
gs-1575	41	20	)	)	PUNCT
gs-1575	41	21	that	that	PRON
gs-1575	41	22	satisfy	satisfy	VERB
gs-1575	41	23	the	the	DET
gs-1575	41	24	conditions	condition	NOUN
gs-1575	41	25	:	:	PUNCT
gs-1575	41	26			NOUN
gs-1575	41	27	f	f	PROPN
gs-1575	41	28	x	x	PUNCT
gs-1575	41	29	is	be	AUX
gs-1575	41	30	absolutely	absolutely	ADV
gs-1575	41	31	continuous	continuous	ADJ
gs-1575	41	32	and	and	CCONJ
gs-1575	41	33	has	have	VERB
gs-1575	41	34	a	a	DET
gs-1575	41	35	derivative	derivative	NOUN
gs-1575	41	36	almost	almost	ADV
gs-1575	41	37	everywhere	everywhere	ADV
gs-1575	41	38	,	,	PUNCT
gs-1575	41	39	f	f	PROPN
gs-1575	42	1			ADV
gs-1575	42	2	,	,	PUNCT
gs-1575	43	1	f	f	PROPN
gs-1575	43	2			ADV
gs-1575	43	3	are	be	AUX
gs-1575	43	4	absolutely	absolutely	ADV
gs-1575	43	5	continuous	continuous	ADJ
gs-1575	43	6	and	and	CCONJ
gs-1575	43	7	has	have	VERB
gs-1575	43	8	a	a	DET
gs-1575	43	9	derivative	derivative	NOUN
gs-1575	43	10	almost	almost	ADV
gs-1575	43	11	everywhere	everywhere	ADV
gs-1575	43	12	,	,	PUNCT
gs-1575	43	13	f	f	PROPN
gs-1575	43	14			PROPN
gs-1575	43	15	,	,	PUNCT
gs-1575	43	16	f	f	PROPN
gs-1575	43	17			PROPN
gs-1575	43	18	are	be	AUX
gs-1575	43	19	bounded	bound	VERB
gs-1575	43	20	and	and	CCONJ
gs-1575	43	21	continuous	continuous	ADJ
gs-1575	43	22	.	.	PUNCT
gs-1575	44	1	definition	definition	NOUN
gs-1575	44	2	2	2	NUM
gs-1575	44	3	(	(	PUNCT
gs-1575	44	4	see	see	VERB
gs-1575	44	5	[	[	X
gs-1575	44	6	5	5	NUM
gs-1575	44	7	]	]	PUNCT
gs-1575	44	8	)	)	PUNCT
gs-1575	44	9	.	.	PUNCT
gs-1575	45	1	let	let	VERB
gs-1575	45	2	’s	’s	NOUN
gs-1575	45	3	denote	denote	VERB
gs-1575	45	4	by	by	ADP
gs-1575	45	5			PROPN
gs-1575	45	6	the	the	DET
gs-1575	45	7	set	set	NOUN
gs-1575	45	8	of	of	ADP
gs-1575	45	9	such	such	ADJ
gs-1575	45	10	functions	function	NOUN
gs-1575	45	11			PROPN
gs-1575	45	12	x	x	NOUN
gs-1575	45	13	(	(	PUNCT
gs-1575	45	14	see	see	VERB
gs-1575	45	15	[	[	X
gs-1575	45	16	5	5	NUM
gs-1575	45	17	]	]	PUNCT
gs-1575	45	18	)	)	PUNCT
gs-1575	45	19	that	that	PRON
gs-1575	45	20	satisfy	satisfy	VERB
gs-1575	45	21	the	the	DET
gs-1575	45	22	conditions	condition	NOUN
gs-1575	45	23	:	:	PUNCT
gs-1575	45	24			PROPN
gs-1575	45	25	x	x	PROPN
gs-1575	45	26	is	be	AUX
gs-1575	45	27	a	a	DET
gs-1575	45	28	density	density	NOUN
gs-1575	45	29	with	with	ADP
gs-1575	45	30	a	a	DET
gs-1575	45	31	compact	compact	ADJ
gs-1575	45	32	carrier	carrier	NOUN
gs-1575	45	33	having	have	VERB
gs-1575	45	34	derivatives	derivative	NOUN
gs-1575	45	35	up	up	ADP
gs-1575	45	36	to	to	ADP
gs-1575	45	37	the	the	DET
gs-1575	45	38	fourth	fourth	ADJ
gs-1575	45	39	order	order	NOUN
gs-1575	45	40	(	(	PUNCT
gs-1575	45	41	including	include	VERB
gs-1575	45	42	)	)	PUNCT
gs-1575	45	43	f	f	PRON
gs-1575	45	44			NOUN
gs-1575	45	45	,	,	PUNCT
gs-1575	45	46	f	f	PROPN
gs-1575	45	47	and	and	CCONJ
gs-1575	45	48			NOUN
gs-1575	45	49			SYM
gs-1575	45	50			PROPN
gs-1575	45	51	(1	(1	NOUN
gs-1575	45	52	)	)	PUNCT
gs-1575	45	53	a	a	DET
gs-1575	45	54	x	x	SYM
gs-1575	45	55	a	a	DET
gs-1575	45	56	x	x	X
gs-1575	45	57	a	a	NOUN
gs-1575	45	58			NOUN
gs-1575	45	59	definition	definition	NOUN
gs-1575	45	60	3	3	NUM
gs-1575	45	61	(	(	PUNCT
gs-1575	45	62	see	see	VERB
gs-1575	45	63	[	[	X
gs-1575	45	64	5	5	NUM
gs-1575	45	65	]	]	PUNCT
gs-1575	45	66	)	)	PUNCT
gs-1575	45	67	.	.	PUNCT
gs-1575	46	1	let	let	VERB
gs-1575	46	2	’s	’s	NOUN
gs-1575	46	3	denote	denote	VERB
gs-1575	46	4	by	by	ADP
gs-1575	46	5	k	k	PROPN
gs-1575	46	6	the	the	DET
gs-1575	46	7	class	class	NOUN
gs-1575	46	8	of	of	ADP
gs-1575	46	9	densities	density	NOUN
gs-1575	46	10	bounded	bound	VERB
gs-1575	46	11	on	on	ADP
gs-1575	46	12	r	r	NOUN
gs-1575	46	13	with	with	ADP
gs-1575	46	14	a	a	DET
gs-1575	46	15	compact	compact	ADJ
gs-1575	46	16	carrier	carrier	NOUN
gs-1575	46	17	on	on	ADP
gs-1575	46	18	(	(	PUNCT
gs-1575	46	19	see	see	VERB
gs-1575	46	20	[	[	X
gs-1575	46	21	5	5	NUM
gs-1575	46	22	]	]	NUM
gs-1575	46	23	)	)	PUNCT
gs-1575	46	24	,	,	PUNCT
gs-1575	46	25	for	for	ADP
gs-1575	46	26	that	that	PRON
gs-1575	46	27	(	(	PUNCT
gs-1575	46	28	)	)	PUNCT
gs-1575	46	29	(	(	PUNCT
gs-1575	46	30	)	)	PUNCT
gs-1575	46	31	k	k	X
gs-1575	46	32	x	x	X
gs-1575	46	33	k	k	PROPN
gs-1575	46	34	x	x	PROPN
gs-1575	46	35			PROPN
gs-1575	46	36	lemma	lemma	PROPN
gs-1575	46	37	(	(	PUNCT
gs-1575	46	38	see	see	VERB
gs-1575	46	39	[	[	X
gs-1575	46	40	5	5	NUM
gs-1575	46	41	]	]	PUNCT
gs-1575	46	42	)	)	PUNCT
gs-1575	46	43	let	let	VERB
gs-1575	46	44	’s	’s	VERB
gs-1575	46	45	the	the	DET
gs-1575	46	46	quantities	quantity	NOUN
gs-1575	46	47	ix	ix	ADV
gs-1575	46	48	,	,	PUNCT
gs-1575	46	49	ix	ix	ADP
gs-1575	46	50	r	r	PROPN
gs-1575	46	51	,	,	PUNCT
gs-1575	46	52	1,2,	1,2,	NUM
gs-1575	46	53	...	...	PUNCT
gs-1575	46	54	i	i	PRON
gs-1575	46	55			VERB
gs-1575	46	56	represent	represent	VERB
gs-1575	46	57	independent	independent	ADJ
gs-1575	46	58	observations	observation	NOUN
gs-1575	46	59	of	of	ADP
gs-1575	46	60	some	some	DET
gs-1575	46	61	random	random	ADJ
gs-1575	46	62	quantity	quantity	NOUN
gs-1575	46	63	x	x	PUNCT
gs-1575	46	64	having	have	VERB
gs-1575	46	65	an	an	DET
gs-1575	46	66	unknown	unknown	ADJ
gs-1575	46	67	density	density	NOUN
gs-1575	46	68			NOUN
gs-1575	46	69	g	g	PROPN
gs-1575	46	70	x	x	PUNCT
gs-1575	46	71	with	with	ADP
gs-1575	46	72	a	a	DET
gs-1575	46	73	compact	compact	ADJ
gs-1575	46	74	carrier	carrier	NOUN
gs-1575	46	75	.	.	PUNCT
gs-1575	47	1	let	let	VERB
gs-1575	47	2	's	us	PRON
gs-1575	47	3	say	say	VERB
gs-1575	47	4			PROPN
gs-1575	47	5	ˆ	ˆ	NOUN
gs-1575	47	6	,	,	PUNCT
gs-1575	47	7	n	n	NOUN
gs-1575	47	8	ng	ng	PROPN
gs-1575	47	9	x	x	X
gs-1575	47	10	a	a	PRON
gs-1575	47	11	is	be	AUX
gs-1575	47	12	determined	determine	VERB
gs-1575	47	13	by	by	ADP
gs-1575	47	14	the	the	DET
gs-1575	47	15	equality	equality	NOUN
gs-1575	47	16	(	(	PUNCT
gs-1575	47	17	1	1	NUM
gs-1575	47	18	)	)	PUNCT
gs-1575	47	19	,	,	PUNCT
gs-1575	47	20			PROPN
gs-1575	47	21	k	k	NUM
gs-1575	47	22	x	x	SYM
gs-1575	47	23	k	k	NOUN
gs-1575	47	24			NOUN
gs-1575	47	25	and	and	CCONJ
gs-1575	47	26	na	na	INTJ
gs-1575	47	27	is	be	AUX
gs-1575	47	28	a	a	DET
gs-1575	47	29	sequence	sequence	NOUN
gs-1575	47	30	(	(	PUNCT
gs-1575	47	31	2	2	NUM
gs-1575	47	32	)	)	PUNCT
gs-1575	47	33	,	,	PUNCT
gs-1575	47	34	then	then	ADV
gs-1575	47	35	for	for	ADP
gs-1575	47	36	the	the	DET
gs-1575	47	37	quantity	quantity	NOUN
gs-1575	47	38			PROPN
gs-1575	47	39	ˆ	ˆ	NOUN
gs-1575	47	40	(	(	PUNCT
gs-1575	47	41	)	)	PUNCT
gs-1575	47	42	,	,	PUNCT
gs-1575	47	43	(	(	PUNCT
gs-1575	47	44	)	)	PUNCT
gs-1575	47	45	n	n	CCONJ
gs-1575	47	46	n	n	PRON
gs-1575	47	47	nj	nj	PROPN
gs-1575	47	48	a	a	DET
gs-1575	47	49	g	g	NOUN
gs-1575	47	50	x	x	X
gs-1575	47	51	a	a	DET
gs-1575	47	52	g	g	NOUN
gs-1575	47	53	x	x	X
gs-1575	47	54	dx	dx	PROPN
gs-1575	47	55			VERB
gs-1575	47	56			NOUN
gs-1575	47	57			NOUN
gs-1575	47	58			PRON
gs-1575	47	59			NOUN
gs-1575	47	60	is	be	AUX
gs-1575	47	61	fair	fair	ADJ
gs-1575	47	62	the	the	DET
gs-1575	47	63	estimattion	estimattion	NOUN
gs-1575	47	64			NOUN
gs-1575	47	65			PROPN
gs-1575	48	1	2	2	NUM
gs-1575	48	2	0	0	NUM
gs-1575	48	3	2	2	NUM
gs-1575	48	4	1	1	NUM
gs-1575	48	5	(	(	PUNCT
gs-1575	48	6	)	)	PUNCT
gs-1575	48	7	(	(	PUNCT
gs-1575	48	8	)	)	PUNCT
gs-1575	48	9	sup	sup	NOUN
gs-1575	48	10	(	(	PUNCT
gs-1575	48	11	)	)	PUNCT
gs-1575	48	12	2	2	NUM
gs-1575	48	13	n	n	NUM
gs-1575	48	14	n	n	ADP
gs-1575	48	15	n	n	ADV
gs-1575	48	16	a	a	DET
gs-1575	48	17	an	an	DET
gs-1575	48	18	a	a	NOUN
gs-1575	48	19	a	a	DET
gs-1575	48	20	ej	ej	NOUN
gs-1575	49	1	a	a	DET
gs-1575	49	2	g	g	NOUN
gs-1575	49	3	x	x	X
gs-1575	49	4	dx	dx	PROPN
gs-1575	49	5	g	g	PROPN
gs-1575	49	6	x	x	X
gs-1575	49	7	dx	dx	PROPN
gs-1575	49	8	o	o	PROPN
gs-1575	49	9	n	n	CCONJ
gs-1575	49	10	a	a	DET
gs-1575	49	11	n	n	PRON
gs-1575	49	12			NOUN
gs-1575	49	13			NOUN
gs-1575	49	14			PUNCT
gs-1575	49	15			PROPN
gs-1575	49	16			PART
gs-1575	49	17			NOUN
gs-1575	49	18			PROPN
gs-1575	49	19			PROPN
gs-1575	49	20			PROPN
gs-1575	49	21			VERB
gs-1575	49	22			PROPN
gs-1575	49	23			PROPN
gs-1575	50	1			PROPN
gs-1575	50	2			NOUN
gs-1575	50	3			PUNCT
gs-1575	50	4			PUNCT
gs-1575	51	1			NOUN
gs-1575	51	2			NOUN
gs-1575	51	3			PROPN
gs-1575	51	4			PROPN
gs-1575	51	5	,	,	PUNCT
gs-1575	51	6	(	(	PUNCT
gs-1575	51	7	3	3	NUM
gs-1575	51	8	)	)	PUNCT
gs-1575	51	9	where	where	SCONJ
gs-1575	51	10	2	2	NUM
gs-1575	51	11	(	(	PUNCT
gs-1575	51	12	)	)	PUNCT
gs-1575	51	13	k	k	NOUN
gs-1575	51	14	x	x	PUNCT
gs-1575	51	15	dx	dx	PROPN
gs-1575	51	16			VERB
gs-1575	51	17			VERB
gs-1575	52	1			NUM
gs-1575	52	2			NUM
gs-1575	52	3	,	,	PUNCT
gs-1575	52	4	2	2	NUM
gs-1575	52	5	(	(	PUNCT
gs-1575	52	6	)	)	PUNCT
gs-1575	52	7	x	x	SYM
gs-1575	52	8	k	k	NOUN
gs-1575	52	9	x	x	PUNCT
gs-1575	52	10	dx	dx	PROPN
gs-1575	52	11			VERB
gs-1575	52	12			VERB
gs-1575	52	13			NUM
gs-1575	52	14			X
gs-1575	52	15	,	,	PUNCT
gs-1575	52	16			ADJ
gs-1575	52	17			ADJ
gs-1575	52	18	,	,	PUNCT
gs-1575	52	19	and	and	CCONJ
gs-1575	52	20	the	the	DET
gs-1575	52	21	symbol	symbol	NOUN
gs-1575	52	22			PROPN
gs-1575	52	23	is	be	AUX
gs-1575	52	24	a	a	DET
gs-1575	52	25	composition	composition	NOUN
gs-1575	52	26	of	of	ADP
gs-1575	52	27	functions	function	NOUN
gs-1575	52	28	.	.	PUNCT
gs-1575	53	1	georgian	georgian	ADJ
gs-1575	53	2	scientists/ქართველი	scientists/ქართველი	PROPN
gs-1575	53	3	მეცნიერები	მეცნიერები	NOUN
gs-1575	53	4	ტ.	ტ.	VERB
gs-1575	53	5	5	5	NUM
gs-1575	53	6	n	n	PRON
gs-1575	53	7	1	1	NUM
gs-1575	53	8	,	,	PUNCT
gs-1575	53	9	2023	2023	NUM
gs-1575	53	10	310	310	NUM
gs-1575	53	11	if	if	SCONJ
gs-1575	53	12	at	at	ADP
gs-1575	53	13	the	the	DET
gs-1575	53	14	same	same	ADJ
gs-1575	53	15	time	time	NOUN
gs-1575	53	16	(	(	PUNCT
gs-1575	53	17	)	)	PUNCT
gs-1575	53	18	g	g	NOUN
gs-1575	53	19	x	x	SYM
gs-1575	53	20	f	f	NOUN
gs-1575	53	21	,	,	PUNCT
gs-1575	53	22	then	then	ADV
gs-1575	53	23	2	2	NUM
gs-1575	53	24	2	2	NUM
gs-1575	53	25	1	1	NUM
gs-1575	53	26	(	(	PUNCT
gs-1575	53	27	)	)	PUNCT
gs-1575	53	28	(	(	PUNCT
gs-1575	53	29	)	)	PUNCT
gs-1575	53	30	(	(	PUNCT
gs-1575	53	31	)	)	PUNCT
gs-1575	53	32	2	2	NUM
gs-1575	53	33	n	n	CCONJ
gs-1575	53	34	n	n	CCONJ
gs-1575	53	35	n	n	CCONJ
gs-1575	53	36	n	n	ADV
gs-1575	53	37	a	a	DET
gs-1575	53	38	a	a	DET
gs-1575	53	39	ej	ej	NOUN
gs-1575	53	40	a	a	DET
gs-1575	53	41	g	g	NOUN
gs-1575	53	42	x	x	X
gs-1575	53	43	dx	dx	PROPN
gs-1575	53	44	g	g	PROPN
gs-1575	53	45	x	x	X
gs-1575	53	46	dx	dx	PROPN
gs-1575	53	47	o	o	PROPN
gs-1575	53	48	n	n	CCONJ
gs-1575	53	49	a	a	DET
gs-1575	53	50	n	n	PRON
gs-1575	53	51			VERB
gs-1575	53	52			VERB
gs-1575	53	53			NOUN
gs-1575	53	54			NOUN
gs-1575	53	55			NUM
gs-1575	53	56			NOUN
gs-1575	53	57			PROPN
gs-1575	53	58			PROPN
gs-1575	53	59			ADV
gs-1575	53	60			VERB
gs-1575	53	61			PROPN
gs-1575	53	62			PROPN
gs-1575	54	1			PROPN
gs-1575	54	2			NOUN
gs-1575	54	3			PUNCT
gs-1575	54	4			PUNCT
gs-1575	55	1			NOUN
gs-1575	55	2			NOUN
gs-1575	55	3			PROPN
gs-1575	55	4	.	.	PUNCT
gs-1575	56	1	(	(	PUNCT
gs-1575	56	2	4	4	NUM
gs-1575	56	3	)	)	PUNCT
gs-1575	56	4	recently	recently	ADV
gs-1575	56	5	,	,	PUNCT
gs-1575	56	6	statistical	statistical	ADJ
gs-1575	56	7	analysis	analysis	NOUN
gs-1575	56	8	of	of	ADP
gs-1575	56	9	samples	sample	NOUN
gs-1575	56	10	consisting	consist	VERB
gs-1575	56	11	of	of	ADP
gs-1575	56	12	different	different	ADJ
gs-1575	56	13	types	type	NOUN
gs-1575	56	14	of	of	ADP
gs-1575	56	15	dependent	dependent	ADJ
gs-1575	56	16	observations	observation	NOUN
gs-1575	56	17	has	have	AUX
gs-1575	56	18	start	start	VERB
gs-1575	56	19	.	.	PUNCT
gs-1575	57	1	we	we	PRON
gs-1575	57	2	will	will	AUX
gs-1575	57	3	construct	construct	VERB
gs-1575	57	4	a	a	DET
gs-1575	57	5	core	core	NOUN
gs-1575	57	6	rosenblatt	rosenblatt	NOUN
gs-1575	57	7	-	-	PUNCT
gs-1575	57	8	parzen	parzen	NOUN
gs-1575	57	9	-	-	PUNCT
gs-1575	57	10	type	type	NOUN
gs-1575	57	11	estimation	estimation	NOUN
gs-1575	57	12	of	of	ADP
gs-1575	57	13	the	the	DET
gs-1575	57	14	density	density	NOUN
gs-1575	57	15	with	with	ADP
gs-1575	57	16	dependent	dependent	ADJ
gs-1575	57	17	observations	observation	NOUN
gs-1575	57	18	.	.	PUNCT
gs-1575	58	1	we	we	PRON
gs-1575	58	2	consider	consider	VERB
gs-1575	58	3	conditionally	conditionally	ADV
gs-1575	58	4	independent	independent	ADJ
gs-1575	58	5	observations	observation	NOUN
gs-1575	58	6	.	.	PUNCT
gs-1575	59	1	we	we	PRON
gs-1575	59	2	will	will	AUX
gs-1575	59	3	determine	determine	VERB
gs-1575	59	4	the	the	DET
gs-1575	59	5	accuracy	accuracy	NOUN
gs-1575	59	6	of	of	ADP
gs-1575	59	7	the	the	DET
gs-1575	59	8	built	build	VERB
gs-1575	59	9	estimate	estimate	NOUN
gs-1575	59	10	with	with	ADP
gs-1575	59	11	a	a	DET
gs-1575	59	12	metric	metric	ADJ
gs-1575	59	13	1l	1l	NUM
gs-1575	59	14	.	.	PUNCT
gs-1575	60	1	on	on	ADP
gs-1575	60	2	the	the	DET
gs-1575	60	3	probabilistic	probabilistic	ADJ
gs-1575	60	4	space	space	NOUN
gs-1575	60	5	(	(	PUNCT
gs-1575	60	6	ω	ω	PROPN
gs-1575	60	7	,	,	PUNCT
gs-1575	60	8	f	f	PROPN
gs-1575	60	9	,	,	PUNCT
gs-1575	60	10	p	p	X
gs-1575	60	11	)	)	PUNCT
gs-1575	60	12	let	let	VERB
gs-1575	60	13	us	we	PRON
gs-1575	60	14	consider	consider	VERB
gs-1575	60	15	the	the	DET
gs-1575	60	16	two	two	NUM
gs-1575	60	17	-	-	PUNCT
gs-1575	60	18	component	component	NOUN
gs-1575	60	19	stationary	stationary	NOUN
gs-1575	60	20	(	(	PUNCT
gs-1575	60	21	in	in	ADP
gs-1575	60	22	the	the	DET
gs-1575	60	23	narrow	narrow	ADJ
gs-1575	60	24	sense	sense	NOUN
gs-1575	60	25	)	)	PUNCT
gs-1575	60	26	sequence	sequence	NOUN
gs-1575	60	27	of	of	ADP
gs-1575	60	28	random	random	ADJ
gs-1575	60	29	variables	variable	NOUN
gs-1575	60	30			PROPN
gs-1575	60	31			PROPN
gs-1575	60	32	1	1	NUM
gs-1575	60	33	,	,	PUNCT
gs-1575	60	34	i	i	PRON
gs-1575	61	1	i	i	PRON
gs-1575	61	2	i	i	VERB
gs-1575	61	3	x	x	SYM
gs-1575	61	4			NUM
gs-1575	61	5			NOUN
gs-1575	61	6	(	(	PUNCT
gs-1575	61	7	5	5	NUM
gs-1575	61	8	)	)	PUNCT
gs-1575	61	9	where	where	SCONJ
gs-1575	61	10	,	,	PUNCT
gs-1575	61	11	:	:	PUNCT
gs-1575	61	12			INTJ
gs-1575	61	13	,	,	PUNCT
gs-1575	61	14	:	:	PUNCT
gs-1575	61	15	m	m	VERB
gs-1575	61	16	ix	ix	ADP
gs-1575	61	17	r	r	NOUN
gs-1575	61	18	and	and	CCONJ
gs-1575	61	19			NOUN
gs-1575	61	20	is	be	AUX
gs-1575	61	21	some	some	DET
gs-1575	61	22	space	space	NOUN
gs-1575	61	23	.	.	PUNCT
gs-1575	62	1	definition	definition	NOUN
gs-1575	62	2	4	4	NUM
gs-1575	62	3	.	.	PUNCT
gs-1575	63	1	the	the	DET
gs-1575	63	2	sequence	sequence	NOUN
gs-1575	63	3			PROPN
gs-1575	63	4			PROPN
gs-1575	63	5	1i	1i	NOUN
gs-1575	63	6	i	i	NOUN
gs-1575	63	7	x	x	X
gs-1575	63	8			NUM
gs-1575	63	9	in	in	ADP
gs-1575	63	10	(	(	PUNCT
gs-1575	63	11	5	5	NUM
gs-1575	63	12	)	)	PUNCT
gs-1575	63	13	is	be	AUX
gs-1575	63	14	called	call	VERB
gs-1575	63	15	a	a	DET
gs-1575	63	16	conditionally	conditionally	ADV
gs-1575	63	17	independent	independent	ADJ
gs-1575	63	18	sequence	sequence	NOUN
gs-1575	63	19	(	(	PUNCT
gs-1575	63	20	see	see	VERB
gs-1575	63	21	.	.	PUNCT
gs-1575	64	1	[	[	X
gs-1575	64	2	6],[7],[8	6],[7],[8	NOUN
gs-1575	64	3	]	]	X
gs-1575	64	4	)	)	PUNCT
gs-1575	64	5	controlled	control	VERB
gs-1575	64	6	by	by	ADP
gs-1575	64	7	the	the	DET
gs-1575	64	8	sequence	sequence	NOUN
gs-1575	64	9			PROPN
gs-1575	64	10			PROPN
gs-1575	64	11	1i	1i	NOUN
gs-1575	65	1	i	i	INTJ
gs-1575	65	2			NOUN
gs-1575	65	3	if	if	SCONJ
gs-1575	65	4	for	for	ADP
gs-1575	65	5	any	any	DET
gs-1575	65	6	natural	natural	ADJ
gs-1575	65	7	n	n	NOUN
gs-1575	65	8	and	and	CCONJ
gs-1575	65	9	the	the	DET
gs-1575	65	10	fixed	fix	VERB
gs-1575	65	11	trajectory	trajectory	NOUN
gs-1575	65	12			NOUN
gs-1575	65	13	1	1	VERB
gs-1575	65	14	1	1	NUM
gs-1575	65	15	2	2	NUM
gs-1575	65	16	,	,	PUNCT
gs-1575	65	17	,	,	PUNCT
gs-1575	65	18	...	...	PUNCT
gs-1575	65	19	,	,	PUNCT
gs-1575	65	20	n	n	DET
gs-1575	65	21	n	n	PROPN
gs-1575	65	22			NOUN
gs-1575	65	23			NOUN
gs-1575	65	24			VERB
gs-1575	65	25	the	the	DET
gs-1575	65	26	values	value	NOUN
gs-1575	65	27	1	1	NUM
gs-1575	65	28	2	2	NUM
gs-1575	65	29	,	,	PUNCT
gs-1575	65	30	,	,	PUNCT
gs-1575	65	31	...	...	PUNCT
gs-1575	65	32	,	,	PUNCT
gs-1575	65	33	nx	nx	X
gs-1575	65	34	x	x	PUNCT
gs-1575	65	35	x	x	VERB
gs-1575	65	36	become	become	VERB
gs-1575	65	37	independent	independent	ADJ
gs-1575	65	38	and	and	CCONJ
gs-1575	65	39	for	for	ADP
gs-1575	65	40	all	all	DET
gs-1575	65	41	natural	natural	ADJ
gs-1575	65	42	numbers	number	NOUN
gs-1575	65	43	i	i	PRON
gs-1575	65	44	,	,	PUNCT
gs-1575	65	45	l	l	NOUN
gs-1575	65	46	,	,	PUNCT
gs-1575	65	47	n	n	CCONJ
gs-1575	65	48	,	,	PUNCT
gs-1575	65	49	1	1	NUM
gs-1575	65	50	2	2	NUM
gs-1575	65	51	,	,	PUNCT
gs-1575	65	52	,	,	PUNCT
gs-1575	65	53	,	,	PUNCT
gs-1575	65	54	lj	lj	PROPN
gs-1575	65	55	j	j	PROPN
gs-1575	65	56	j	j	PROPN
gs-1575	65	57	,	,	PUNCT
gs-1575	65	58	2	2	PROPN
gs-1575	65	59	;	;	PUNCT
gs-1575	65	60	l	l	PROPN
gs-1575	65	61	n	n	NOUN
gs-1575	65	62			PROPN
gs-1575	66	1	i	i	PRON
gs-1575	66	2	n	n	NOUN
gs-1575	66	3	;	;	PUNCT
gs-1575	66	4	1	1	PROPN
gs-1575	66	5	21	21	NUM
gs-1575	66	6	...	...	PUNCT
gs-1575	67	1	lj	lj	PROPN
gs-1575	67	2	j	j	PROPN
gs-1575	68	1	j	j	PROPN
gs-1575	68	2	n	n	PROPN
gs-1575	68	3			PROPN
gs-1575	68	4			PROPN
gs-1575	68	5			PROPN
gs-1575	68	6			NOUN
gs-1575	68	7	the	the	DET
gs-1575	68	8	equalities	equality	NOUN
gs-1575	68	9			NOUN
gs-1575	68	10			PUNCT
gs-1575	68	11	1	1	NUM
gs-1575	68	12	1	1	NUM
gs-1575	68	13	1	1	NUM
gs-1575	68	14	2	2	NUM
gs-1575	68	15	21	21	NUM
gs-1575	68	16	2	2	NUM
gs-1575	68	17	1	1	NUM
gs-1575	68	18	,	,	PUNCT
gs-1575	68	19	,	,	PUNCT
gs-1575	68	20	,	,	PUNCT
gs-1575	68	21	...	...	PUNCT
gs-1575	68	22	,	,	PUNCT
gs-1575	68	23	,	,	PUNCT
gs-1575	68	24	j	j	PROPN
gs-1575	69	1	j	j	PROPN
gs-1575	69	2	j	j	PROPN
gs-1575	69	3	j	j	PROPN
gs-1575	69	4	j	j	PROPN
gs-1575	69	5	jj	jj	PROPN
gs-1575	69	6	j	j	PROPN
gs-1575	69	7	j	j	PROPN
gs-1575	69	8	n	n	CCONJ
gs-1575	69	9	l	l	NOUN
gs-1575	69	10	ll	ll	AUX
gs-1575	70	1	i	i	PRON
gs-1575	70	2	ii	ii	VERB
gs-1575	70	3	n	n	ADV
gs-1575	70	4	x	x	PUNCT
gs-1575	71	1	x	x	X
gs-1575	71	2	xx	xx	NUM
gs-1575	71	3	x	x	SYM
gs-1575	71	4	x	x	SYM
gs-1575	71	5	xx	xx	PRON
gs-1575	71	6			NOUN
gs-1575	71	7			NOUN
gs-1575	71	8			NOUN
gs-1575	71	9			NOUN
gs-1575	71	10			PROPN
gs-1575	71	11			PROPN
gs-1575	71	12			PROPN
gs-1575	71	13			PROPN
gs-1575	71	14			PROPN
gs-1575	71	15	are	be	AUX
gs-1575	71	16	fulfilled	fulfil	VERB
gs-1575	71	17	,	,	PUNCT
gs-1575	71	18	where	where	SCONJ
gs-1575	71	19	x	x	PUNCT
gs-1575	71	20	y	y	PROPN
gs-1575	71	21	is	be	AUX
gs-1575	71	22	the	the	DET
gs-1575	71	23	conditional	conditional	ADJ
gs-1575	71	24	distribution	distribution	NOUN
gs-1575	71	25	of	of	ADP
gs-1575	71	26	the	the	DET
gs-1575	71	27	value	value	NOUN
gs-1575	71	28	x	x	X
gs-1575	71	29	under	under	ADP
gs-1575	71	30	the	the	DET
gs-1575	71	31	condition	condition	NOUN
gs-1575	71	32	y	y	PROPN
gs-1575	71	33	.	.	PUNCT
gs-1575	72	1	the	the	DET
gs-1575	72	2	conditionally	conditionally	ADV
gs-1575	72	3	independent	independent	ADJ
gs-1575	72	4	sequence	sequence	NOUN
gs-1575	72	5			PROPN
gs-1575	72	6			PROPN
gs-1575	72	7	1i	1i	NOUN
gs-1575	72	8	i	i	NOUN
gs-1575	72	9	x	x	X
gs-1575	72	10			NUM
gs-1575	72	11	in	in	ADP
gs-1575	72	12	(	(	PUNCT
gs-1575	72	13	3	3	X
gs-1575	72	14	)	)	PUNCT
gs-1575	72	15	is	be	AUX
gs-1575	72	16	called	call	VERB
gs-1575	72	17	a	a	DET
gs-1575	72	18	sequence	sequence	NOUN
gs-1575	72	19	with	with	ADP
gs-1575	72	20	chain	chain	NOUN
gs-1575	72	21	dependence	dependence	NOUN
gs-1575	72	22	(	(	PUNCT
gs-1575	72	23	see	see	VERB
gs-1575	72	24	.	.	PUNCT
gs-1575	73	1	[	[	X
gs-1575	73	2	9],[10],[11	9],[10],[11	NUM
gs-1575	73	3	]	]	PUNCT
gs-1575	73	4	)	)	PUNCT
gs-1575	73	5	if	if	SCONJ
gs-1575	73	6			PROPN
gs-1575	73	7			PROPN
gs-1575	73	8	1i	1i	NOUN
gs-1575	73	9	i	i	PRON
gs-1575	73	10			VERB
gs-1575	73	11			NUM
gs-1575	73	12	is	be	AUX
gs-1575	73	13	a	a	DET
gs-1575	73	14	finite	finite	ADJ
gs-1575	73	15	markov	markov	NOUN
gs-1575	73	16	chain	chain	NOUN
gs-1575	73	17	with	with	ADP
gs-1575	73	18	discrete	discrete	ADJ
gs-1575	73	19	time	time	NOUN
gs-1575	73	20	.	.	PUNCT
gs-1575	74	1	we	we	PRON
gs-1575	74	2	are	be	AUX
gs-1575	74	3	considering	consider	VERB
gs-1575	74	4	the	the	DET
gs-1575	74	5	case	case	NOUN
gs-1575	74	6	,	,	PUNCT
gs-1575	74	7	when	when	SCONJ
gs-1575	74	8	the	the	DET
gs-1575	74	9	members	member	NOUN
gs-1575	74	10	of	of	ADP
gs-1575	74	11	sequence	sequence	NOUN
gs-1575	74	12	1	1	NUM
gs-1575	74	13	{	{	PUNCT
gs-1575	74	14	}	}	PUNCT
gs-1575	74	15	i	i	PRON
gs-1575	74	16	i	i	NOUN
gs-1575	74	17	are	be	AUX
gs-1575	74	18	independent	independent	ADJ
gs-1575	74	19	and	and	CCONJ
gs-1575	74	20	identically	identically	ADV
gs-1575	74	21	distributed	distribute	VERB
gs-1575	74	22	discrete	discrete	ADJ
gs-1575	74	23	random	random	ADJ
gs-1575	74	24	variables	variable	NOUN
gs-1575	74	25			PROPN
gs-1575	74	26	1	1	NOUN
gs-1575	74	27	2	2	NUM
gs-1575	74	28	,	,	PUNCT
gs-1575	74	29	,	,	PUNCT
gs-1575	74	30	...	...	PUNCT
gs-1575	74	31	,	,	PUNCT
gs-1575	74	32	rb	rb	PROPN
gs-1575	74	33	b	b	PROPN
gs-1575	74	34	b	b	NOUN
gs-1575	74	35			PROPN
gs-1575	74	36	;	;	PUNCT
gs-1575	74	37			NOUN
gs-1575	74	38	1	1	INTJ
gs-1575	75	1	i	i	PRON
gs-1575	75	2	ip	ip	VERB
gs-1575	75	3	b	b	NOUN
gs-1575	75	4	p	p	NOUN
gs-1575	76	1			NUM
gs-1575	76	2			PROPN
gs-1575	76	3	,	,	PUNCT
gs-1575	76	4	1,i	1,i	PROPN
gs-1575	76	5	r	r	NOUN
gs-1575	76	6	,	,	PUNCT
gs-1575	76	7	1	1	NUM
gs-1575	76	8	2	2	NUM
gs-1575	76	9	...	...	PUNCT
gs-1575	76	10	1rp	1rp	NOUN
gs-1575	76	11	p	p	VERB
gs-1575	76	12	p	p	NOUN
gs-1575	76	13			ADV
gs-1575	76	14			PROPN
gs-1575	76	15			PROPN
gs-1575	76	16	.	.	PUNCT
gs-1575	77	1	remark	remark	NOUN
gs-1575	77	2	:	:	PUNCT
gs-1575	77	3	if	if	SCONJ
gs-1575	77	4	the	the	DET
gs-1575	77	5	members	member	NOUN
gs-1575	77	6	of	of	ADP
gs-1575	77	7	a	a	DET
gs-1575	77	8	sequence	sequence	NOUN
gs-1575	77	9			PROPN
gs-1575	77	10			PROPN
gs-1575	77	11	1i	1i	NOUN
gs-1575	77	12	i	i	NOUN
gs-1575	77	13	x	x	SYM
gs-1575	77	14			NUM
gs-1575	77	15	represent	represent	VERB
gs-1575	77	16	elements	element	NOUN
gs-1575	77	17	of	of	ADP
gs-1575	77	18	a	a	DET
gs-1575	77	19	statistical	statistical	ADJ
gs-1575	77	20	sample	sample	NOUN
gs-1575	77	21	or	or	CCONJ
gs-1575	77	22	observation	observation	NOUN
gs-1575	77	23	,	,	PUNCT
gs-1575	77	24	they	they	PRON
gs-1575	77	25	are	be	AUX
gs-1575	77	26	called	call	VERB
gs-1575	77	27	conditionally	conditionally	ADV
gs-1575	77	28	independent	independent	ADJ
gs-1575	77	29	(	(	PUNCT
gs-1575	77	30	or	or	CCONJ
gs-1575	77	31	,	,	PUNCT
gs-1575	77	32	accordingly	accordingly	ADV
gs-1575	77	33	,	,	PUNCT
gs-1575	77	34	chain	chain	NOUN
gs-1575	77	35	dependent	dependent	ADJ
gs-1575	77	36	)	)	PUNCT
gs-1575	77	37	observations	observation	NOUN
gs-1575	77	38	.	.	PUNCT
gs-1575	78	1	to	to	PART
gs-1575	78	2	determine	determine	VERB
gs-1575	78	3	the	the	DET
gs-1575	78	4	accuracy	accuracy	NOUN
gs-1575	78	5	of	of	ADP
gs-1575	78	6	estimates	estimate	NOUN
gs-1575	78	7	constructed	construct	VERB
gs-1575	78	8	with	with	ADP
gs-1575	78	9	dependent	dependent	ADJ
gs-1575	78	10	observations	observation	NOUN
gs-1575	78	11	,	,	PUNCT
gs-1575	78	12	it	it	PRON
gs-1575	78	13	is	be	AUX
gs-1575	78	14	necessary	necessary	ADJ
gs-1575	78	15	to	to	PART
gs-1575	78	16	study	study	VERB
gs-1575	78	17	the	the	DET
gs-1575	78	18	asymptotics	asymptotic	NOUN
gs-1575	78	19	of	of	ADP
gs-1575	78	20	the	the	DET
gs-1575	78	21	sums	sum	NOUN
gs-1575	78	22	of	of	ADP
gs-1575	78	23	dependent	dependent	ADJ
gs-1575	78	24	random	random	ADJ
gs-1575	78	25	variables	variable	NOUN
gs-1575	78	26	.	.	PUNCT
gs-1575	79	1	in	in	ADP
gs-1575	79	2	this	this	DET
gs-1575	79	3	process	process	NOUN
gs-1575	79	4	,	,	PUNCT
gs-1575	79	5	the	the	DET
gs-1575	79	6	research	research	NOUN
gs-1575	79	7	methods	method	NOUN
gs-1575	79	8	of	of	ADP
gs-1575	79	9	distribution	distribution	NOUN
gs-1575	79	10	of	of	ADP
gs-1575	79	11	sums	sum	NOUN
gs-1575	79	12	of	of	ADP
gs-1575	79	13	independent	independent	ADJ
gs-1575	79	14	random	random	ADJ
gs-1575	79	15	variables	variable	NOUN
gs-1575	79	16	are	be	AUX
gs-1575	79	17	is	be	AUX
gs-1575	79	18	extended	extend	VERB
gs-1575	79	19	to	to	ADP
gs-1575	79	20	dependent	dependent	ADJ
gs-1575	79	21	random	random	ADJ
gs-1575	79	22	variables	variable	NOUN
gs-1575	79	23	.	.	PUNCT
gs-1575	80	1	markov	markov	NOUN
gs-1575	80	2	dependence	dependence	NOUN
gs-1575	80	3	is	be	AUX
gs-1575	80	4	considered	consider	VERB
gs-1575	80	5	in	in	ADP
gs-1575	80	6	many	many	ADJ
gs-1575	80	7	practical	practical	ADJ
gs-1575	80	8	and	and	CCONJ
gs-1575	80	9	theoretical	theoretical	ADJ
gs-1575	80	10	problems	problem	NOUN
gs-1575	80	11	.	.	PUNCT
gs-1575	81	1	it	it	PRON
gs-1575	81	2	is	be	AUX
gs-1575	81	3	one	one	NUM
gs-1575	81	4	of	of	ADP
gs-1575	81	5	the	the	DET
gs-1575	81	6	forms	form	NOUN
gs-1575	81	7	of	of	ADP
gs-1575	81	8	weak	weak	ADJ
gs-1575	81	9	dependence	dependence	NOUN
gs-1575	81	10	.	.	PUNCT
gs-1575	82	1	other	other	ADJ
gs-1575	82	2	forms	form	NOUN
gs-1575	82	3	of	of	ADP
gs-1575	82	4	weak	weak	ADJ
gs-1575	82	5	dependence	dependence	NOUN
gs-1575	82	6	are	be	AUX
gs-1575	82	7	also	also	ADV
gs-1575	82	8	known	know	VERB
gs-1575	82	9	.	.	PUNCT
gs-1575	83	1	in	in	ADP
gs-1575	83	2	the	the	DET
gs-1575	83	3	works	work	NOUN
gs-1575	83	4	[	[	X
gs-1575	83	5	6	6	NUM
gs-1575	83	6	]	]	PUNCT
gs-1575	83	7	and	and	CCONJ
gs-1575	83	8	[	[	X
gs-1575	83	9	9	9	NUM
gs-1575	83	10	]	]	PUNCT
gs-1575	83	11	are	be	AUX
gs-1575	83	12	considered	consider	VERB
gs-1575	83	13	limit	limit	NOUN
gs-1575	83	14	distributions	distribution	NOUN
gs-1575	83	15	of	of	ADP
gs-1575	83	16	sums	sum	NOUN
gs-1575	83	17	of	of	ADP
gs-1575	83	18	conditionally	conditionally	ADV
gs-1575	83	19	independent	independent	ADJ
gs-1575	83	20	random	random	ADJ
gs-1575	83	21	variables	variable	NOUN
gs-1575	83	22	and	and	CCONJ
gs-1575	83	23	limit	limit	VERB
gs-1575	83	24	theorems	theorem	NOUN
gs-1575	83	25	for	for	ADP
gs-1575	83	26	functions	function	NOUN
gs-1575	83	27	defined	define	VERB
gs-1575	83	28	on	on	ADP
gs-1575	83	29	the	the	DET
gs-1575	83	30	markov	markov	NOUN
gs-1575	83	31	chain	chain	NOUN
gs-1575	83	32	.	.	PUNCT
gs-1575	84	1	many	many	ADJ
gs-1575	84	2	authors	author	NOUN
gs-1575	84	3	consider	consider	VERB
gs-1575	84	4	sums	sum	NOUN
gs-1575	84	5	of	of	ADP
gs-1575	84	6	random	random	ADJ
gs-1575	84	7	variables	variable	NOUN
gs-1575	84	8	whose	whose	DET
gs-1575	84	9	joint	joint	ADJ
gs-1575	84	10	distribution	distribution	NOUN
gs-1575	84	11	is	be	AUX
gs-1575	84	12	determined	determine	VERB
gs-1575	84	13	by	by	ADP
gs-1575	84	14	some	some	DET
gs-1575	84	15	"	"	PUNCT
gs-1575	84	16	control	control	NOUN
gs-1575	84	17	"	"	PUNCT
gs-1575	84	18	sequence	sequence	NOUN
gs-1575	84	19	of	of	ADP
gs-1575	84	20	random	random	ADJ
gs-1575	84	21	elements	element	NOUN
gs-1575	84	22	.	.	PUNCT
gs-1575	85	1	i.	i.	PROPN
gs-1575	85	2	bokuchava	bokuchava	PROPN
gs-1575	85	3	,	,	PUNCT
gs-1575	85	4	z.	z.	PROPN
gs-1575	85	5	kvatadze	kvatadze	PROPN
gs-1575	85	6	and	and	CCONJ
gs-1575	85	7	t.	t.	PROPN
gs-1575	85	8	shervashidze	shervashidze	PROPN
gs-1575	85	9	established	establish	VERB
gs-1575	85	10	limit	limit	NOUN
gs-1575	85	11	distributions	distribution	NOUN
gs-1575	85	12	of	of	ADP
gs-1575	85	13	normed	normed	ADJ
gs-1575	85	14	sums	sum	NOUN
gs-1575	85	15	for	for	ADP
gs-1575	85	16	conditionally	conditionally	ADV
gs-1575	85	17	georgian	georgian	ADJ
gs-1575	85	18	scientists/ქართველი	scientists/ქართველი	NOUN
gs-1575	85	19	მეცნიერები	მეცნიერები	NOUN
gs-1575	85	20	ტ.	ტ.	VERB
gs-1575	85	21	5	5	NUM
gs-1575	85	22	n	n	PRON
gs-1575	85	23	1	1	NUM
gs-1575	85	24	,	,	PUNCT
gs-1575	85	25	2023	2023	NUM
gs-1575	85	26	311	311	NUM
gs-1575	85	27	independent	independent	ADJ
gs-1575	85	28	random	random	ADJ
gs-1575	85	29	variables	variable	NOUN
gs-1575	85	30	(	(	PUNCT
gs-1575	85	31	see	see	VERB
gs-1575	85	32	.	.	PUNCT
gs-1575	86	1	[	[	X
gs-1575	86	2	7	7	NUM
gs-1575	86	3	]	]	PUNCT
gs-1575	86	4	,	,	PUNCT
gs-1575	86	5	[	[	X
gs-1575	86	6	8	8	NUM
gs-1575	86	7	]	]	PUNCT
gs-1575	86	8	)	)	PUNCT
gs-1575	86	9	and	and	CCONJ
gs-1575	86	10	for	for	ADP
gs-1575	86	11	random	random	ADJ
gs-1575	86	12	variables	variable	NOUN
gs-1575	86	13	with	with	ADP
gs-1575	86	14	chain	chain	NOUN
gs-1575	86	15	dependence	dependence	NOUN
gs-1575	86	16	(	(	PUNCT
gs-1575	86	17	[	[	X
gs-1575	86	18	10	10	NUM
gs-1575	86	19	]	]	PUNCT
gs-1575	86	20	,	,	PUNCT
gs-1575	86	21	[	[	X
gs-1575	86	22	11	11	NUM
gs-1575	86	23	]	]	NUM
gs-1575	86	24	)	)	PUNCT
gs-1575	86	25	.	.	PUNCT
gs-1575	87	1	the	the	DET
gs-1575	87	2	study	study	NOUN
gs-1575	87	3	of	of	ADP
gs-1575	87	4	the	the	DET
gs-1575	87	5	asymptotic	asymptotic	ADJ
gs-1575	87	6	behavior	behavior	NOUN
gs-1575	87	7	of	of	ADP
gs-1575	87	8	the	the	DET
gs-1575	87	9	sums	sum	NOUN
gs-1575	87	10	of	of	ADP
gs-1575	87	11	dependent	dependent	ADJ
gs-1575	87	12	random	random	ADJ
gs-1575	87	13	variables	variable	NOUN
gs-1575	87	14	made	make	VERB
gs-1575	87	15	it	it	PRON
gs-1575	87	16	possible	possible	ADJ
gs-1575	87	17	to	to	PART
gs-1575	87	18	consider	consider	VERB
gs-1575	87	19	dependent	dependent	ADJ
gs-1575	87	20	observations	observation	NOUN
gs-1575	87	21	in	in	ADP
gs-1575	87	22	the	the	DET
gs-1575	87	23	theory	theory	NOUN
gs-1575	87	24	of	of	ADP
gs-1575	87	25	statistical	statistical	ADJ
gs-1575	87	26	estimates	estimate	NOUN
gs-1575	87	27	.	.	PUNCT
gs-1575	88	1	from	from	ADP
gs-1575	88	2	the	the	DET
gs-1575	88	3	second	second	ADJ
gs-1575	88	4	half	half	NOUN
gs-1575	88	5	of	of	ADP
gs-1575	88	6	the	the	DET
gs-1575	88	7	twentieth	twentieth	ADJ
gs-1575	88	8	century	century	NOUN
gs-1575	88	9	,	,	PUNCT
gs-1575	88	10	the	the	DET
gs-1575	88	11	construction	construction	NOUN
gs-1575	88	12	of	of	ADP
gs-1575	88	13	statistical	statistical	ADJ
gs-1575	88	14	estimates	estimate	NOUN
gs-1575	88	15	with	with	ADP
gs-1575	88	16	dependent	dependent	ADJ
gs-1575	88	17	observations	observation	NOUN
gs-1575	88	18	began	begin	VERB
gs-1575	88	19	.	.	PUNCT
gs-1575	89	1	in	in	ADP
gs-1575	89	2	this	this	DET
gs-1575	89	3	regard	regard	NOUN
gs-1575	89	4	,	,	PUNCT
gs-1575	89	5	the	the	DET
gs-1575	89	6	question	question	NOUN
gs-1575	89	7	of	of	ADP
gs-1575	89	8	constructing	construct	VERB
gs-1575	89	9	a	a	DET
gs-1575	89	10	non	non	ADJ
gs-1575	89	11	-	-	ADJ
gs-1575	89	12	parametric	parametric	ADJ
gs-1575	89	13	estimate	estimate	NOUN
gs-1575	89	14	of	of	ADP
gs-1575	89	15	the	the	DET
gs-1575	89	16	density	density	NOUN
gs-1575	89	17	on	on	ADP
gs-1575	89	18	the	the	DET
gs-1575	89	19	dependent	dependent	ADJ
gs-1575	89	20	observations	observation	NOUN
gs-1575	89	21	is	be	AUX
gs-1575	89	22	particularly	particularly	ADV
gs-1575	89	23	relevant	relevant	ADJ
gs-1575	89	24	.	.	PUNCT
gs-1575	90	1	in	in	ADP
gs-1575	90	2	the	the	DET
gs-1575	90	3	work	work	NOUN
gs-1575	90	4	of	of	ADP
gs-1575	90	5	yakowitz	yakowitz	PROPN
gs-1575	90	6	sidney	sidney	NOUN
gs-1575	90	7	[	[	X
gs-1575	90	8	12	12	NUM
gs-1575	90	9	]	]	PUNCT
gs-1575	90	10	,	,	PUNCT
gs-1575	90	11	estimates	estimate	NOUN
gs-1575	90	12	of	of	ADP
gs-1575	90	13	density	density	NOUN
gs-1575	90	14	and	and	CCONJ
gs-1575	90	15	regression	regression	NOUN
gs-1575	90	16	coefficients	coefficient	NOUN
gs-1575	90	17	are	be	AUX
gs-1575	90	18	constructed	construct	VERB
gs-1575	90	19	from	from	ADP
gs-1575	90	20	observations	observation	NOUN
gs-1575	90	21	bound	bind	VERB
gs-1575	90	22	in	in	ADP
gs-1575	90	23	a	a	DET
gs-1575	90	24	markov	markov	NOUN
gs-1575	90	25	chain	chain	NOUN
gs-1575	90	26	.	.	PUNCT
gs-1575	91	1	the	the	DET
gs-1575	91	2	accuracy	accuracy	NOUN
gs-1575	91	3	of	of	ADP
gs-1575	91	4	the	the	DET
gs-1575	91	5	density	density	NOUN
gs-1575	91	6	estimation	estimation	NOUN
gs-1575	91	7	constructed	construct	VERB
gs-1575	91	8	by	by	ADP
gs-1575	91	9	dependent	dependent	ADJ
gs-1575	91	10	observations	observation	NOUN
gs-1575	91	11	by	by	ADP
gs-1575	91	12	the	the	DET
gs-1575	91	13	metric	metric	ADJ
gs-1575	91	14	2l	2l	NOUN
gs-1575	91	15	is	be	AUX
gs-1575	91	16	known	know	VERB
gs-1575	91	17	(	(	PUNCT
gs-1575	91	18	see	see	VERB
gs-1575	91	19	[	[	X
gs-1575	91	20	13	13	NUM
gs-1575	91	21	]	]	NUM
gs-1575	91	22	)	)	PUNCT
gs-1575	91	23	.	.	PUNCT
gs-1575	92	1	in	in	ADP
gs-1575	92	2	the	the	DET
gs-1575	92	3	series	series	NOUN
gs-1575	92	4	of	of	ADP
gs-1575	92	5	works	work	NOUN
gs-1575	92	6	[	[	X
gs-1575	92	7	14	14	NUM
gs-1575	92	8	-	-	SYM
gs-1575	92	9	16	16	NUM
gs-1575	92	10	]	]	PUNCT
gs-1575	92	11	,	,	PUNCT
gs-1575	92	12	the	the	DET
gs-1575	92	13	rosenblatt	rosenblatt	NOUN
gs-1575	92	14	-	-	PUNCT
gs-1575	92	15	parzen	parzen	NOUN
gs-1575	92	16	-	-	PUNCT
gs-1575	92	17	type	type	NOUN
gs-1575	92	18	kernel	kernel	NOUN
gs-1575	92	19	estimates	estimate	NOUN
gs-1575	92	20	of	of	ADP
gs-1575	92	21	the	the	DET
gs-1575	92	22	density	density	NOUN
gs-1575	92	23	are	be	AUX
gs-1575	92	24	constructed	construct	VERB
gs-1575	92	25	with	with	ADP
gs-1575	92	26	chain	chain	NOUN
gs-1575	92	27	dependence	dependence	NOUN
gs-1575	92	28	observations	observation	NOUN
gs-1575	92	29	and	and	CCONJ
gs-1575	92	30	conditionally	conditionally	ADV
gs-1575	92	31	independent	independent	ADJ
gs-1575	92	32	observations	observation	NOUN
gs-1575	92	33	.	.	PUNCT
gs-1575	93	1	their	their	PRON
gs-1575	93	2	approximation	approximation	NOUN
gs-1575	93	3	accuracy	accuracy	NOUN
gs-1575	93	4	with	with	ADP
gs-1575	93	5	metrics	metric	NOUN
gs-1575	93	6	2l	2l	NOUN
gs-1575	93	7	and	and	CCONJ
gs-1575	93	8	1l	1l	NUM
gs-1575	93	9	is	be	AUX
gs-1575	93	10	considered	consider	VERB
gs-1575	93	11	.	.	PUNCT
gs-1575	94	1	z.	z.	PROPN
gs-1575	94	2	kvatadze	kvatadze	PROPN
gs-1575	94	3	and	and	CCONJ
gs-1575	94	4	b.	b.	PROPN
gs-1575	94	5	pharjiani	pharjiani	PROPN
gs-1575	94	6	's	's	PART
gs-1575	94	7	case	case	NOUN
gs-1575	94	8	2r	2r	NUM
gs-1575	94	9			NOUN
gs-1575	94	10	,	,	PUNCT
gs-1575	94	11	the	the	DET
gs-1575	94	12	accuracy	accuracy	NOUN
gs-1575	94	13	of	of	ADP
gs-1575	94	14	the	the	DET
gs-1575	94	15	estimations	estimation	NOUN
gs-1575	94	16	constructed	construct	VERB
gs-1575	94	17	with	with	ADP
gs-1575	94	18	both	both	DET
gs-1575	94	19	types	type	NOUN
gs-1575	94	20	of	of	ADP
gs-1575	94	21	dependent	dependent	ADJ
gs-1575	94	22	observations	observation	NOUN
gs-1575	94	23	was	be	AUX
gs-1575	94	24	determined	determine	VERB
gs-1575	94	25	by	by	ADP
gs-1575	94	26	metric	metric	ADJ
gs-1575	94	27	2l	2l	NOUN
gs-1575	94	28	(	(	PUNCT
gs-1575	94	29	see	see	VERB
gs-1575	94	30	[	[	X
gs-1575	94	31	14	14	NUM
gs-1575	94	32	]	]	SYM
gs-1575	94	33	)	)	PUNCT
gs-1575	94	34	.	.	PUNCT
gs-1575	95	1	in	in	ADP
gs-1575	95	2	general	general	ADJ
gs-1575	95	3	,	,	PUNCT
gs-1575	95	4	the	the	DET
gs-1575	95	5	estimate	estimate	NOUN
gs-1575	95	6	accuracy	accuracy	NOUN
gs-1575	95	7	constructed	construct	VERB
gs-1575	95	8	for	for	ADP
gs-1575	95	9	observations	observation	NOUN
gs-1575	95	10	with	with	ADP
gs-1575	95	11	chain	chain	NOUN
gs-1575	95	12	dependent	dependent	NOUN
gs-1575	95	13	is	be	AUX
gs-1575	95	14	established	establish	VERB
gs-1575	95	15	1l	1l	NUM
gs-1575	95	16	(	(	PUNCT
gs-1575	95	17	see	see	VERB
gs-1575	95	18	[	[	X
gs-1575	95	19	15	15	NUM
gs-1575	95	20	]	]	PUNCT
gs-1575	95	21	)	)	PUNCT
gs-1575	95	22	and	and	CCONJ
gs-1575	95	23	2l	2l	NUM
gs-1575	95	24	metrics	metric	NOUN
gs-1575	95	25	(	(	PUNCT
gs-1575	95	26	see	see	VERB
gs-1575	95	27	[	[	X
gs-1575	95	28	16	16	NUM
gs-1575	95	29	]	]	SYM
gs-1575	95	30	)	)	PUNCT
gs-1575	95	31	.	.	PUNCT
gs-1575	96	1	methodology	methodology	NOUN
gs-1575	96	2	during	during	ADP
gs-1575	96	3	the	the	DET
gs-1575	96	4	proof	proof	NOUN
gs-1575	96	5	of	of	ADP
gs-1575	96	6	the	the	DET
gs-1575	96	7	theorem	theorem	NOUN
gs-1575	96	8	is	be	AUX
gs-1575	96	9	applied	apply	VERB
gs-1575	96	10	the	the	DET
gs-1575	96	11	method	method	PROPN
gs-1575	96	12	i.	i.	PROPN
gs-1575	96	13	bokuchava	bokuchava	PROPN
gs-1575	96	14	,	,	PUNCT
gs-1575	96	15	t.	t.	PROPN
gs-1575	96	16	shervashidze	shervashidze	PROPN
gs-1575	96	17	and	and	CCONJ
gs-1575	96	18	z.	z.	PROPN
gs-1575	96	19	kvatadze	kvatadze	PROPN
gs-1575	96	20	presented	present	VERB
gs-1575	96	21	by	by	ADP
gs-1575	96	22	in	in	ADP
gs-1575	96	23	[	[	X
gs-1575	96	24	10	10	NUM
gs-1575	96	25	,	,	PUNCT
gs-1575	96	26	11	11	NUM
gs-1575	96	27	]	]	PUNCT
gs-1575	96	28	.	.	PUNCT
gs-1575	97	1	using	use	VERB
gs-1575	97	2	this	this	DET
gs-1575	97	3	method	method	NOUN
gs-1575	97	4	,	,	PUNCT
gs-1575	97	5	they	they	PRON
gs-1575	97	6	determined	determine	VERB
gs-1575	97	7	the	the	DET
gs-1575	97	8	limit	limit	NOUN
gs-1575	97	9	distributions	distribution	NOUN
gs-1575	97	10	of	of	ADP
gs-1575	97	11	the	the	DET
gs-1575	97	12	normed	normed	ADJ
gs-1575	97	13	sums	sum	NOUN
gs-1575	97	14	of	of	ADP
gs-1575	97	15	conditionally	conditionally	ADV
gs-1575	97	16	independent	independent	ADJ
gs-1575	97	17	sequences	sequence	NOUN
gs-1575	97	18	(	(	PUNCT
gs-1575	97	19	see	see	VERB
gs-1575	97	20	[	[	X
gs-1575	97	21	8	8	NUM
gs-1575	97	22	]	]	PUNCT
gs-1575	97	23	)	)	PUNCT
gs-1575	97	24	and	and	CCONJ
gs-1575	97	25	sequenge	sequenge	VERB
gs-1575	97	26	with	with	ADP
gs-1575	97	27	chain	chain	NOUN
gs-1575	97	28	dependence	dependence	NOUN
gs-1575	97	29	.	.	PUNCT
gs-1575	98	1	the	the	DET
gs-1575	98	2	asymptotics	asymptotic	NOUN
gs-1575	98	3	of	of	ADP
gs-1575	98	4	the	the	DET
gs-1575	98	5	conditional	conditional	ADJ
gs-1575	98	6	and	and	CCONJ
gs-1575	98	7	unconditional	unconditional	ADJ
gs-1575	98	8	distributions	distribution	NOUN
gs-1575	98	9	of	of	ADP
gs-1575	98	10	the	the	DET
gs-1575	98	11	geometric	geometric	ADJ
gs-1575	98	12	mean	mean	NOUN
gs-1575	98	13	of	of	ADP
gs-1575	98	14	conditionally	conditionally	ADV
gs-1575	98	15	independent	independent	ADJ
gs-1575	98	16	random	random	ADJ
gs-1575	98	17	variables	variable	NOUN
gs-1575	98	18	and	and	CCONJ
gs-1575	98	19	random	random	ADJ
gs-1575	98	20	variables	variable	NOUN
gs-1575	98	21	with	with	ADP
gs-1575	98	22	chain	chain	NOUN
gs-1575	98	23	dependence	dependence	NOUN
gs-1575	98	24	were	be	AUX
gs-1575	98	25	investigated	investigate	VERB
gs-1575	98	26	(	(	PUNCT
gs-1575	98	27	see	see	VERB
gs-1575	98	28	[	[	X
gs-1575	98	29	17	17	NUM
gs-1575	98	30	]	]	PUNCT
gs-1575	98	31	,	,	PUNCT
gs-1575	98	32	[	[	X
gs-1575	98	33	18	18	NUM
gs-1575	98	34	]	]	NUM
gs-1575	98	35	)	)	PUNCT
gs-1575	98	36	.	.	PUNCT
gs-1575	99	1	this	this	DET
gs-1575	99	2	method	method	NOUN
gs-1575	99	3	became	become	VERB
gs-1575	99	4	possible	possible	ADJ
gs-1575	99	5	to	to	PART
gs-1575	99	6	use	use	VERB
gs-1575	99	7	in	in	ADP
gs-1575	99	8	the	the	DET
gs-1575	99	9	theory	theory	NOUN
gs-1575	99	10	of	of	ADP
gs-1575	99	11	statistical	statistical	ADJ
gs-1575	99	12	estimations	estimation	NOUN
gs-1575	99	13	(	(	PUNCT
gs-1575	99	14	see	see	VERB
gs-1575	99	15	[	[	X
gs-1575	99	16	14	14	NUM
gs-1575	99	17	]	]	NUM
gs-1575	99	18	)	)	PUNCT
gs-1575	99	19	.	.	PUNCT
gs-1575	100	1	the	the	DET
gs-1575	100	2	method	method	NOUN
gs-1575	100	3	uses	use	VERB
gs-1575	100	4	the	the	DET
gs-1575	100	5	decomposition	decomposition	NOUN
gs-1575	100	6	of	of	ADP
gs-1575	100	7	the	the	DET
gs-1575	100	8	sum	sum	NOUN
gs-1575	100	9	to	to	PART
gs-1575	100	10	be	be	AUX
gs-1575	100	11	estimated	estimate	VERB
gs-1575	100	12	into	into	ADP
gs-1575	100	13	sums	sum	NOUN
gs-1575	100	14	corresponding	correspond	VERB
gs-1575	100	15	to	to	ADP
gs-1575	100	16	the	the	DET
gs-1575	100	17	values	value	NOUN
gs-1575	100	18	of	of	ADP
gs-1575	100	19	the	the	DET
gs-1575	100	20	control	control	NOUN
gs-1575	100	21	sequence	sequence	NOUN
gs-1575	100	22	.	.	PUNCT
gs-1575	101	1	on	on	ADP
gs-1575	101	2	the	the	DET
gs-1575	101	3	fixed	fix	VERB
gs-1575	101	4	trajectory	trajectory	NOUN
gs-1575	101	5			NOUN
gs-1575	101	6	1	1	VERB
gs-1575	101	7	1	1	NUM
gs-1575	101	8	2	2	NUM
gs-1575	101	9	,	,	PUNCT
gs-1575	101	10	,	,	PUNCT
gs-1575	101	11	...	...	PUNCT
gs-1575	101	12	,	,	PUNCT
gs-1575	101	13	n	n	DET
gs-1575	101	14	n	n	PROPN
gs-1575	101	15			NOUN
gs-1575	101	16			NOUN
gs-1575	101	17			NOUN
gs-1575	101	18	of	of	ADP
gs-1575	101	19	the	the	DET
gs-1575	101	20	control	control	NOUN
gs-1575	101	21	sequence	sequence	NOUN
gs-1575	101	22	(	(	PUNCT
gs-1575	101	23	5	5	NUM
gs-1575	101	24	)	)	PUNCT
gs-1575	101	25	,	,	PUNCT
gs-1575	101	26	the	the	DET
gs-1575	101	27	second	second	ADJ
gs-1575	101	28	components	component	NOUN
gs-1575	101	29	of	of	ADP
gs-1575	101	30	the	the	DET
gs-1575	101	31	sequence	sequence	NOUN
gs-1575	101	32	(	(	PUNCT
gs-1575	101	33	observations	observation	NOUN
gs-1575	101	34			PROPN
gs-1575	101	35			PROPN
gs-1575	101	36	1i	1i	NOUN
gs-1575	102	1	i	i	NOUN
gs-1575	102	2	x	x	SYM
gs-1575	102	3			NUM
gs-1575	102	4	)	)	PUNCT
gs-1575	102	5	become	become	VERB
gs-1575	102	6	independent	independent	ADJ
gs-1575	102	7	.	.	PUNCT
gs-1575	103	1	the	the	DET
gs-1575	103	2	sums	sum	NOUN
gs-1575	103	3	obtained	obtain	VERB
gs-1575	103	4	from	from	ADP
gs-1575	103	5	them	they	PRON
gs-1575	103	6	are	be	AUX
gs-1575	103	7	uncorrelated	uncorrelated	ADJ
gs-1575	103	8	and	and	CCONJ
gs-1575	103	9	consist	consist	VERB
gs-1575	103	10	of	of	ADP
gs-1575	103	11	independent	independent	ADJ
gs-1575	103	12	and	and	CCONJ
gs-1575	103	13	uniformly	uniformly	ADV
gs-1575	103	14	distributed	distribute	VERB
gs-1575	103	15	random	random	ADJ
gs-1575	103	16	variables	variable	NOUN
gs-1575	103	17	.	.	PUNCT
gs-1575	104	1	main	main	ADJ
gs-1575	104	2	results	result	NOUN
gs-1575	104	3	let	let	VERB
gs-1575	104	4	’s	’s	NOUN
gs-1575	104	5	consider	consider	VERB
gs-1575	104	6	the	the	DET
gs-1575	104	7	sequence	sequence	NOUN
gs-1575	104	8	(	(	PUNCT
gs-1575	104	9	5	5	NUM
gs-1575	104	10	)	)	PUNCT
gs-1575	104	11	.	.	PUNCT
gs-1575	105	1	i	i	NOUN
gs-1575	105	2	,	,	PUNCT
gs-1575	105	3	1	1	NUM
gs-1575	105	4	,	,	PUNCT
gs-1575	105	5	2,.i	2,.i	NUM
gs-1575	105	6			NUM
gs-1575	105	7	..	..	PUNCT
gs-1575	105	8	,	,	PUNCT
gs-1575	105	9	are	be	AUX
gs-1575	105	10	independent	independent	ADJ
gs-1575	105	11	and	and	CCONJ
gs-1575	105	12	identically	identically	ADV
gs-1575	105	13	distributed	distribute	VERB
gs-1575	105	14	discrete	discrete	ADJ
gs-1575	105	15	random	random	ADJ
gs-1575	105	16	variables	variable	NOUN
gs-1575	105	17	.	.	PUNCT
gs-1575	106	1	let	let	VERB
gs-1575	106	2	's	us	PRON
gs-1575	106	3	assume	assume	VERB
gs-1575	106	4	that	that	SCONJ
gs-1575	106	5			PROPN
gs-1575	106	6	1	1	NOUN
gs-1575	106	7	2	2	NUM
gs-1575	106	8	,	,	PUNCT
gs-1575	106	9	,	,	PUNCT
gs-1575	106	10	...	...	PUNCT
gs-1575	106	11	,	,	PUNCT
gs-1575	106	12	rb	rb	PROPN
gs-1575	106	13	b	b	PROPN
gs-1575	106	14	b	b	NOUN
gs-1575	106	15			PROPN
gs-1575	106	16	;	;	PUNCT
gs-1575	107	1			NOUN
gs-1575	107	2	1	1	INTJ
gs-1575	107	3	i	i	PRON
gs-1575	107	4	ip	ip	VERB
gs-1575	107	5	b	b	NOUN
gs-1575	108	1	p	p	NOUN
gs-1575	109	1			NUM
gs-1575	109	2			PROPN
gs-1575	109	3	,	,	PUNCT
gs-1575	109	4	1,i	1,i	PROPN
gs-1575	109	5	r	r	NOUN
gs-1575	109	6	,	,	PUNCT
gs-1575	109	7	1	1	NUM
gs-1575	109	8	2	2	NUM
gs-1575	109	9	...	...	PUNCT
gs-1575	109	10	1rp	1rp	NOUN
gs-1575	109	11	p	p	VERB
gs-1575	109	12	p	p	NOUN
gs-1575	109	13			ADV
gs-1575	109	14			PROPN
gs-1575	109	15			PROPN
gs-1575	109	16	.	.	PUNCT
gs-1575	110	1	let	let	VERB
gs-1575	110	2	us	we	PRON
gs-1575	110	3	fix	fix	VERB
gs-1575	110	4	the	the	DET
gs-1575	110	5	trajectory	trajectory	NOUN
gs-1575	110	6			NOUN
gs-1575	110	7	1	1	VERB
gs-1575	110	8	1	1	NUM
gs-1575	110	9	2	2	NUM
gs-1575	110	10	,	,	PUNCT
gs-1575	110	11	,	,	PUNCT
gs-1575	110	12	...	...	PUNCT
gs-1575	110	13	,	,	PUNCT
gs-1575	110	14	n	n	DET
gs-1575	110	15	n	n	PROPN
gs-1575	110	16			NOUN
gs-1575	110	17			NOUN
gs-1575	110	18			NOUN
gs-1575	110	19	of	of	ADP
gs-1575	110	20	the	the	DET
gs-1575	110	21	sequence	sequence	NOUN
gs-1575	110	22			PROPN
gs-1575	110	23			PROPN
gs-1575	110	24	1i	1i	NOUN
gs-1575	110	25	i	i	PRON
gs-1575	110	26			VERB
gs-1575	110	27			NUM
gs-1575	110	28	.	.	PUNCT
gs-1575	111	1	in	in	ADP
gs-1575	111	2	this	this	DET
gs-1575	111	3	case	case	NOUN
gs-1575	111	4	,	,	PUNCT
gs-1575	111	5	we	we	PRON
gs-1575	111	6	denote	denote	VERB
gs-1575	111	7	by	by	ADP
gs-1575	111	8	the	the	DET
gs-1575	111	9	values	value	NOUN
gs-1575	111	10			PROPN
gs-1575	111	11	1n	1n	PROPN
gs-1575	111	12	,	,	PUNCT
gs-1575	111	13			PROPN
gs-1575	111	14	2n	2n	PROPN
gs-1575	111	15	,	,	PUNCT
gs-1575	111	16	…	…	PUNCT
gs-1575	111	17	,	,	PUNCT
gs-1575	111	18			PROPN
gs-1575	111	19	n	n	PROPN
gs-1575	111	20	r	r	PROPN
gs-1575	111	21	,	,	PUNCT
gs-1575	111	22	the	the	DET
gs-1575	111	23	frequencies	frequency	NOUN
gs-1575	111	24	of	of	ADP
gs-1575	111	25	accepting	accept	VERB
gs-1575	111	26	the	the	DET
gs-1575	111	27	values	value	NOUN
gs-1575	111	28	1b	1b	NUM
gs-1575	111	29	,	,	PUNCT
gs-1575	111	30	2b	2b	NUM
gs-1575	111	31	,	,	PUNCT
gs-1575	111	32	...	...	PUNCT
gs-1575	111	33	,	,	PUNCT
gs-1575	111	34	rb	rb	X
gs-1575	111	35	(	(	PUNCT
gs-1575	111	36	respectively	respectively	ADV
gs-1575	111	37	)	)	PUNCT
gs-1575	111	38	by	by	ADP
gs-1575	111	39	the	the	DET
gs-1575	111	40	members	member	NOUN
gs-1575	111	41	1	1	NUM
gs-1575	111	42	,	,	PUNCT
gs-1575	111	43	2	2	PROPN
gs-1575	111	44	,	,	PUNCT
gs-1575	111	45	...	...	PUNCT
gs-1575	111	46	,	,	PUNCT
gs-1575	111	47	n	n	PROPN
gs-1575	111	48	of	of	ADP
gs-1575	111	49	the	the	DET
gs-1575	111	50	sequence	sequence	NOUN
gs-1575	111	51			PROPN
gs-1575	111	52			PROPN
gs-1575	111	53	1i	1i	NOUN
gs-1575	111	54	i	i	PRON
gs-1575	111	55			VERB
gs-1575	111	56			NUM
gs-1575	111	57	.	.	PUNCT
gs-1575	112	1			NOUN
gs-1575	113	1			PUNCT
gs-1575	113	2			NOUN
gs-1575	113	3			PUNCT
gs-1575	113	4	1	1	NUM
gs-1575	114	1	i	i	NOUN
gs-1575	114	2	k	k	PROPN
gs-1575	114	3	i	i	PRON
gs-1575	114	4	n	n	VERB
gs-1575	114	5	n	n	PROPN
gs-1575	114	6	b	b	PROPN
gs-1575	114	7	k	k	NOUN
gs-1575	115	1	i	i	PRON
gs-1575	115	2			VERB
gs-1575	115	3			NUM
gs-1575	115	4			PROPN
gs-1575	115	5			NOUN
gs-1575	115	6			INTJ
gs-1575	115	7	,	,	PUNCT
gs-1575	115	8	1,i	1,i	PROPN
gs-1575	115	9	r	r	NOUN
gs-1575	115	10	,	,	PUNCT
gs-1575	115	11	where	where	SCONJ
gs-1575	115	12			NOUN
gs-1575	115	13			PUNCT
gs-1575	115	14	i	i	PRON
gs-1575	115	15	is	be	AUX
gs-1575	115	16	the	the	DET
gs-1575	115	17	indicator	indicator	NOUN
gs-1575	115	18	function	function	NOUN
gs-1575	115	19	.	.	PUNCT
gs-1575	116	1	obviously	obviously	ADV
gs-1575	116	2	the	the	DET
gs-1575	116	3	equality	equality	NOUN
gs-1575	116	4	is	be	AUX
gs-1575	116	5	fair	fair	ADJ
gs-1575	116	6	georgian	georgian	ADJ
gs-1575	116	7	scientists/ქართველი	scientists/ქართველი	NOUN
gs-1575	116	8	მეცნიერები	მეცნიერები	NOUN
gs-1575	116	9	ტ.	ტ.	VERB
gs-1575	116	10	5	5	NUM
gs-1575	116	11	n	n	PRON
gs-1575	116	12	1	1	NUM
gs-1575	116	13	,	,	PUNCT
gs-1575	117	1	2023	2023	NUM
gs-1575	117	2	312	312	NUM
gs-1575	117	3			NOUN
gs-1575	117	4			SYM
gs-1575	117	5			NOUN
gs-1575	117	6			SYM
gs-1575	117	7			NOUN
gs-1575	117	8	1	1	ADJ
gs-1575	117	9	2	2	NUM
gs-1575	117	10	...	...	SYM
gs-1575	117	11	n	n	CCONJ
gs-1575	117	12	n	n	CCONJ
gs-1575	117	13	n	n	ADP
gs-1575	117	14	r	r	NOUN
gs-1575	117	15	n	n	PROPN
gs-1575	117	16			ADV
gs-1575	117	17			ADJ
gs-1575	117	18			NOUN
gs-1575	117	19			PROPN
gs-1575	117	20			PROPN
gs-1575	117	21	.	.	PUNCT
gs-1575	118	1	theorem	theorem	PROPN
gs-1575	118	2	.	.	PUNCT
gs-1575	119	1	let	let	VERB
gs-1575	119	2	’s	’s	NOUN
gs-1575	119	3	consider	consider	VERB
gs-1575	119	4	the	the	DET
gs-1575	119	5	sequence	sequence	NOUN
gs-1575	119	6	(	(	PUNCT
gs-1575	119	7	5	5	NUM
gs-1575	119	8	)	)	PUNCT
gs-1575	119	9	.	.	PUNCT
gs-1575	120	1	let	let	VERB
gs-1575	120	2	’s	’s	PRON
gs-1575	120	3	say	say	VERB
gs-1575	120	4	that	that	SCONJ
gs-1575	120	5	members	member	NOUN
gs-1575	120	6	of	of	ADP
gs-1575	120	7	the	the	DET
gs-1575	120	8	control	control	NOUN
gs-1575	120	9	sequence	sequence	NOUN
gs-1575	120	10			PROPN
gs-1575	120	11			PROPN
gs-1575	120	12	1i	1i	NOUN
gs-1575	120	13	i	i	PRON
gs-1575	120	14			VERB
gs-1575	120	15			NUM
gs-1575	120	16			PROPN
gs-1575	120	17			NOUN
gs-1575	120	18	1	1	NOUN
gs-1575	120	19	2	2	NUM
gs-1575	120	20	:	:	PUNCT
gs-1575	120	21	,	,	PUNCT
gs-1575	120	22	,	,	PUNCT
gs-1575	120	23	...	...	PUNCT
gs-1575	120	24	,	,	PUNCT
gs-1575	120	25	i	i	PRON
gs-1575	120	26	rb	rb	PROPN
gs-1575	120	27	b	b	PROPN
gs-1575	120	28	b	b	PROPN
gs-1575	120	29			PROPN
gs-1575	120	30	are	be	AUX
gs-1575	120	31	independent	independent	ADJ
gs-1575	120	32	,	,	PUNCT
gs-1575	120	33	identically	identically	ADV
gs-1575	120	34	distributed	distribute	VERB
gs-1575	120	35	,	,	PUNCT
gs-1575	120	36	discrete	discrete	ADJ
gs-1575	120	37	random	random	ADJ
gs-1575	120	38	variables	variable	NOUN
gs-1575	120	39			PROPN
gs-1575	120	40			NOUN
gs-1575	120	41	1	1	NOUN
gs-1575	120	42	2	2	NUM
gs-1575	120	43	,	,	PUNCT
gs-1575	120	44	,	,	PUNCT
gs-1575	120	45	...	...	PUNCT
gs-1575	120	46	,	,	PUNCT
gs-1575	120	47	rb	rb	PROPN
gs-1575	120	48	b	b	PROPN
gs-1575	120	49	b	b	NOUN
gs-1575	120	50			PROPN
gs-1575	120	51	,	,	PUNCT
gs-1575	121	1			PROPN
gs-1575	121	2	1	1	NOUN
gs-1575	121	3	k	k	PROPN
gs-1575	121	4	kp	kp	PROPN
gs-1575	121	5	b	b	PROPN
gs-1575	121	6	p	p	PROPN
gs-1575	121	7			NOUN
gs-1575	121	8	,	,	PUNCT
gs-1575	121	9	1,k	1,k	PROPN
gs-1575	121	10	r	r	VERB
gs-1575	121	11	,	,	PUNCT
gs-1575	121	12	1	1	NUM
gs-1575	121	13	2	2	NUM
gs-1575	121	14	...	...	PUNCT
gs-1575	121	15	1rp	1rp	NOUN
gs-1575	121	16	p	p	VERB
gs-1575	121	17	p	p	NOUN
gs-1575	121	18			ADV
gs-1575	121	19			PROPN
gs-1575	121	20			PROPN
gs-1575	121	21	.	.	PUNCT
gs-1575	122	1	let	let	VERB
gs-1575	122	2	us	we	PRON
gs-1575	122	3	say	say	VERB
gs-1575	122	4	that	that	SCONJ
gs-1575	122	5	the	the	DET
gs-1575	122	6	sequence	sequence	NOUN
gs-1575	122	7	of	of	ADP
gs-1575	122	8	positive	positive	ADJ
gs-1575	122	9	numbers	number	NOUN
gs-1575	122	10	na	na	PART
gs-1575	122	11	satisfies	satisfy	VERB
gs-1575	122	12	the	the	DET
gs-1575	122	13	conditions	condition	NOUN
gs-1575	122	14	(	(	PUNCT
gs-1575	122	15	2	2	NUM
gs-1575	122	16	)	)	PUNCT
gs-1575	122	17	.	.	PUNCT
gs-1575	123	1	let	let	VERB
gs-1575	123	2	's	us	PRON
gs-1575	123	3	say	say	VERB
gs-1575	123	4	that	that	SCONJ
gs-1575	123	5	for	for	ADP
gs-1575	123	6	each	each	DET
gs-1575	123	7	function	function	NOUN
gs-1575	123	8	1	1	NUM
gs-1575	123	9	:	:	PUNCT
gs-1575	123	10	,	,	PUNCT
gs-1575	123	11	r	r	NOUN
gs-1575	123	12			PROPN
gs-1575	123	13	for	for	ADP
gs-1575	123	14	that	that	DET
gs-1575	123	15			ADJ
gs-1575	123	16	ie	ie	NOUN
gs-1575	123	17			PUNCT
gs-1575	123	18			PROPN
gs-1575	123	19			VERB
gs-1575	123	20	when	when	SCONJ
gs-1575	123	21	noccurs	noccur	NOUN
gs-1575	123	22	the	the	DET
gs-1575	123	23	convergence	convergence	NOUN
gs-1575	123	24			NOUN
gs-1575	123	25	1	1	NOUN
gs-1575	123	26	(	(	PUNCT
gs-1575	123	27	)	)	PUNCT
gs-1575	123	28	1	1	NUM
gs-1575	123	29	1	1	NUM
gs-1575	123	30	n	n	ADP
gs-1575	123	31	ei	ei	X
gs-1575	123	32	jn	jn	X
gs-1575	123	33			X
gs-1575	124	1			X
gs-1575	124	2			PROPN
gs-1575	124	3			VERB
gs-1575	125	1			AUX
gs-1575	125	2			PROPN
gs-1575	125	3	a.	a.	PROPN
gs-1575	125	4	e.	e.	PROPN
gs-1575	125	5	(	(	PUNCT
gs-1575	125	6	6	6	X
gs-1575	125	7	)	)	PUNCT
gs-1575	125	8	let	let	VERB
gs-1575	125	9	’s	’s	NOUN
gs-1575	125	10	say	say	VERB
gs-1575	125	11	that	that	SCONJ
gs-1575	125	12	the	the	DET
gs-1575	125	13	members	member	NOUN
gs-1575	125	14	of	of	ADP
gs-1575	125	15	the	the	DET
gs-1575	125	16	sequence	sequence	NOUN
gs-1575	125	17			PROPN
gs-1575	125	18			PROPN
gs-1575	125	19	1i	1i	NOUN
gs-1575	126	1	i	i	NOUN
gs-1575	126	2	x	x	SYM
gs-1575	126	3			NUM
gs-1575	126	4	are	be	AUX
gs-1575	126	5	conditionally	conditionally	ADV
gs-1575	126	6	independent	independent	ADJ
gs-1575	126	7	observations	observation	NOUN
gs-1575	126	8	on	on	ADP
gs-1575	126	9	some	some	DET
gs-1575	126	10	random	random	ADJ
gs-1575	126	11	variable	variable	NOUN
gs-1575	126	12	x	x	X
gs-1575	126	13	and	and	CCONJ
gs-1575	126	14	the	the	DET
gs-1575	126	15	conditional	conditional	ADJ
gs-1575	126	16	distributions	distribution	NOUN
gs-1575	126	17	1	1	NUM
gs-1575	126	18	1	1	NUM
gs-1575	126	19	ix	ix	ADP
gs-1575	126	20	b	b	NOUN
gs-1575	126	21	,	,	PUNCT
gs-1575	126	22	1,i	1,i	PROPN
gs-1575	126	23	r	r	VERB
gs-1575	126	24	have	have	VERB
gs-1575	126	25	unknown	unknown	ADJ
gs-1575	126	26	densities	density	NOUN
gs-1575	126	27	(	(	PUNCT
gs-1575	126	28	)	)	PUNCT
gs-1575	126	29	if	if	SCONJ
gs-1575	126	30	x	x	PRON
gs-1575	126	31	,	,	PUNCT
gs-1575	126	32	1,i	1,i	NOUN
gs-1575	126	33	r	r	VERB
gs-1575	126	34	with	with	ADP
gs-1575	126	35	a	a	DET
gs-1575	126	36	compact	compact	ADJ
gs-1575	126	37	supports	support	NOUN
gs-1575	126	38	.	.	PUNCT
gs-1575	127	1	if	if	SCONJ
gs-1575	127	2	inequalities	inequality	NOUN
gs-1575	127	3			PROPN
gs-1575	127	4	n	n	PROPN
gs-1575	127	5	i	i	PRON
gs-1575	127	6	i	i	NOUN
gs-1575	127	7	c	c	NOUN
gs-1575	127	8	d	d	NOUN
gs-1575	127	9	n	n	NOUN
gs-1575	127	10	n	n	ADV
gs-1575	127	11			ADJ
gs-1575	127	12			NOUN
gs-1575	127	13			NUM
gs-1575	127	14			PROPN
gs-1575	128	1			ADJ
gs-1575	128	2			NOUN
gs-1575	128	3	,	,	PUNCT
gs-1575	128	4	1,i	1,i	PROPN
gs-1575	128	5	r	r	NOUN
gs-1575	128	6	,	,	PUNCT
gs-1575	128	7	(	(	PUNCT
gs-1575	128	8	7	7	X
gs-1575	128	9	)	)	PUNCT
gs-1575	128	10	are	be	AUX
gs-1575	128	11	fulfilled	fulfil	VERB
gs-1575	128	12	for	for	ADP
gs-1575	128	13	frequencies	frequency	NOUN
gs-1575	128	14			NOUN
gs-1575	128	15	n	n	PUNCT
gs-1575	128	16	i	i	PROPN
gs-1575	128	17	,	,	PUNCT
gs-1575	128	18	1,i	1,i	PROPN
gs-1575	128	19	r	r	NOUN
gs-1575	128	20	,	,	PUNCT
gs-1575	128	21	then	then	ADV
gs-1575	128	22	for	for	ADP
gs-1575	128	23	each	each	DET
gs-1575	128	24	natural	natural	ADJ
gs-1575	128	25	number	number	NOUN
gs-1575	128	26	n	n	NOUN
gs-1575	128	27	,	,	PUNCT
gs-1575	128	28	the	the	DET
gs-1575	128	29	density	density	NOUN
gs-1575	128	30	estimate	estimate	NOUN
gs-1575	128	31			NOUN
gs-1575	128	32			SYM
gs-1575	128	33			NOUN
gs-1575	128	34			NOUN
gs-1575	128	35	1	1	NUM
gs-1575	128	36	r	r	NOUN
gs-1575	129	1	i	i	PRON
gs-1575	130	1	i	i	PRON
gs-1575	131	1	i	i	PRON
gs-1575	131	2	f	f	VERB
gs-1575	132	1	x	x	X
gs-1575	132	2	p	p	X
gs-1575	132	3	f	f	X
gs-1575	132	4	x	x	X
gs-1575	132	5			NUM
gs-1575	132	6			PROPN
gs-1575	132	7	is	be	AUX
gs-1575	132	8	the	the	DET
gs-1575	132	9	sum	sum	NOUN
gs-1575	132	10			NOUN
gs-1575	132	11			PUNCT
gs-1575	132	12			NOUN
gs-1575	133	1			NOUN
gs-1575	134	1			PROPN
gs-1575	135	1	1	1	NUM
gs-1575	136	1	ˆ	ˆ	NOUN
gs-1575	136	2	,	,	PUNCT
gs-1575	136	3	n	n	CCONJ
gs-1575	136	4	n	n	CCONJ
gs-1575	136	5	n	n	CCONJ
gs-1575	136	6	n	n	CCONJ
gs-1575	136	7	n	n	NOUN
gs-1575	137	1	i	i	PRON
gs-1575	137	2	i	i	PRON
gs-1575	138	1	a	a	DET
gs-1575	138	2	f	f	X
gs-1575	138	3	x	x	X
gs-1575	139	1	a	a	PROPN
gs-1575	139	2	k	k	X
gs-1575	139	3	a	a	X
gs-1575	139	4	x	x	X
gs-1575	139	5	x	x	VERB
gs-1575	139	6	n	n	CCONJ
gs-1575	139	7			NOUN
gs-1575	139	8			NUM
gs-1575	140	1			NOUN
gs-1575	140	2	,	,	PUNCT
gs-1575	140	3	where	where	SCONJ
gs-1575	140	4			NOUN
gs-1575	140	5	k	k	VERB
gs-1575	140	6	x	x	SYM
gs-1575	141	1	k	k	NOUN
gs-1575	141	2			NOUN
gs-1575	141	3	,	,	PUNCT
gs-1575	141	4	and	and	CCONJ
gs-1575	141	5	for	for	ADP
gs-1575	141	6	the	the	DET
gs-1575	141	7	value	value	NOUN
gs-1575	141	8			PROPN
gs-1575	141	9	ˆ	ˆ	NOUN
gs-1575	141	10	(	(	PUNCT
gs-1575	141	11	)	)	PUNCT
gs-1575	141	12	(	(	PUNCT
gs-1575	141	13	,	,	PUNCT
gs-1575	141	14	)	)	PUNCT
gs-1575	141	15	n	n	CCONJ
gs-1575	141	16	n	n	PRON
gs-1575	141	17	nj	nj	PROPN
gs-1575	142	1	a	a	DET
gs-1575	142	2	f	f	X
gs-1575	142	3	x	x	X
gs-1575	142	4	a	a	DET
gs-1575	142	5	f	f	X
gs-1575	142	6	x	x	SYM
gs-1575	142	7	dx	dx	PROPN
gs-1575	142	8			VERB
gs-1575	142	9			VERB
gs-1575	142	10			NUM
gs-1575	142	11			NOUN
gs-1575	142	12	the	the	DET
gs-1575	142	13	estimate	estimate	NOUN
gs-1575	142	14	1	1	NUM
gs-1575	142	15	2	2	NUM
gs-1575	142	16	(	(	PUNCT
gs-1575	142	17	)	)	PUNCT
gs-1575	142	18	(	(	PUNCT
gs-1575	142	19	)	)	PUNCT
gs-1575	142	20	r	r	NOUN
gs-1575	142	21	n	n	NOUN
gs-1575	142	22	n	n	NOUN
gs-1575	143	1	i	i	PRON
gs-1575	143	2	i	i	PRON
gs-1575	143	3	i	i	PRON
gs-1575	143	4	a	a	PRON
gs-1575	143	5	ej	ej	PROPN
gs-1575	143	6	a	a	DET
gs-1575	143	7	p	p	X
gs-1575	143	8	f	f	X
gs-1575	143	9	x	x	SYM
gs-1575	143	10	dx	dx	PROPN
gs-1575	143	11	n	n	PART
gs-1575	143	12			VERB
gs-1575	143	13			NOUN
gs-1575	143	14			NOUN
gs-1575	143	15			NOUN
gs-1575	143	16			NOUN
gs-1575	143	17			NUM
gs-1575	143	18			ADJ
gs-1575	143	19			NOUN
gs-1575	143	20			PROPN
gs-1575	143	21	2	2	NUM
gs-1575	143	22	4	4	NUM
gs-1575	143	23	01	01	NUM
gs-1575	143	24	1	1	NUM
gs-1575	143	25	1	1	NUM
gs-1575	143	26	sup	sup	NOUN
gs-1575	143	27	(	(	PUNCT
gs-1575	143	28	)	)	PUNCT
gs-1575	143	29	2	2	NUM
gs-1575	143	30	r	r	NOUN
gs-1575	143	31	r	r	NOUN
gs-1575	143	32	n	n	NOUN
gs-1575	144	1	i	i	PRON
gs-1575	144	2	i	i	PRON
gs-1575	144	3	a	a	PRON
gs-1575	145	1	i	i	PRON
gs-1575	145	2	ai	ai	VERB
gs-1575	145	3	in	in	ADP
gs-1575	145	4	a	a	DET
gs-1575	145	5	p	p	X
gs-1575	145	6	f	f	X
gs-1575	145	7	x	x	X
gs-1575	145	8	dx	dx	PROPN
gs-1575	145	9	c	c	NOUN
gs-1575	145	10	o	o	PROPN
gs-1575	145	11	a	a	DET
gs-1575	145	12	nn	nn	INTJ
gs-1575	145	13			PROPN
gs-1575	145	14			PROPN
gs-1575	145	15			PROPN
gs-1575	145	16			PROPN
gs-1575	145	17			NOUN
gs-1575	145	18			NOUN
gs-1575	145	19			PROPN
gs-1575	145	20			PROPN
gs-1575	145	21			VERB
gs-1575	145	22			VERB
gs-1575	145	23			PROPN
gs-1575	145	24			PROPN
gs-1575	146	1			PROPN
gs-1575	146	2			PROPN
gs-1575	146	3			X
gs-1575	146	4			NUM
gs-1575	146	5	,	,	PUNCT
gs-1575	146	6	(	(	PUNCT
gs-1575	146	7	8)	8)	NUM
gs-1575	146	8	is	be	AUX
gs-1575	146	9	satisfied	satisfied	ADJ
gs-1575	146	10	,	,	PUNCT
gs-1575	146	11	where	where	SCONJ
gs-1575	146	12			NOUN
gs-1575	146	13	2k	2k	PUNCT
gs-1575	146	14	x	x	X
gs-1575	146	15	dx	dx	PROPN
gs-1575	146	16			VERB
gs-1575	146	17			VERB
gs-1575	146	18			NUM
gs-1575	146	19			NUM
gs-1575	146	20	,	,	PUNCT
gs-1575	146	21			PROPN
gs-1575	146	22	2x	2x	PUNCT
gs-1575	147	1	k	k	PUNCT
gs-1575	147	2	x	x	PUNCT
gs-1575	147	3	dx	dx	PROPN
gs-1575	147	4			VERB
gs-1575	147	5			VERB
gs-1575	147	6			NUM
gs-1575	147	7			X
gs-1575	147	8	,	,	PUNCT
gs-1575	147	9	a	a	DET
gs-1575	147	10			NOUN
gs-1575	147	11	.	.	PUNCT
gs-1575	148	1	if	if	SCONJ
gs-1575	148	2	also	also	ADV
gs-1575	148	3			VERB
gs-1575	148	4	if	if	NOUN
gs-1575	149	1	x	x	PUNCT
gs-1575	149	2	f	f	PROPN
gs-1575	149	3	,	,	PUNCT
gs-1575	149	4	1,i	1,i	PROPN
gs-1575	149	5	r	r	NOUN
gs-1575	149	6	,	,	PUNCT
gs-1575	149	7	then	then	ADV
gs-1575	149	8	2	2	NUM
gs-1575	149	9	4	4	NUM
gs-1575	149	10	1	1	NUM
gs-1575	149	11	1	1	NUM
gs-1575	149	12	1	1	NUM
gs-1575	149	13	2	2	NUM
gs-1575	149	14	1	1	NUM
gs-1575	149	15	(	(	PUNCT
gs-1575	149	16	)	)	PUNCT
gs-1575	149	17	(	(	PUNCT
gs-1575	149	18	)	)	PUNCT
gs-1575	149	19	(	(	PUNCT
gs-1575	149	20	)	)	PUNCT
gs-1575	149	21	2	2	NUM
gs-1575	150	1	r	r	NOUN
gs-1575	150	2	r	r	NOUN
gs-1575	150	3	r	r	NOUN
gs-1575	150	4	n	n	NOUN
gs-1575	150	5	n	n	NOUN
gs-1575	150	6	n	n	NOUN
gs-1575	151	1	i	i	PRON
gs-1575	152	1	i	i	PRON
gs-1575	153	1	i	i	PRON
gs-1575	154	1	i	i	PRON
gs-1575	155	1	i	i	PRON
gs-1575	156	1	i	i	PRON
gs-1575	157	1	i	i	PRON
gs-1575	157	2	in	in	ADP
gs-1575	157	3	a	a	DET
gs-1575	157	4	a	a	DET
gs-1575	157	5	ej	ej	NOUN
gs-1575	157	6	a	a	DET
gs-1575	157	7	p	p	X
gs-1575	158	1	f	f	X
gs-1575	158	2	x	x	X
gs-1575	158	3	dx	dx	PROPN
gs-1575	158	4	p	p	PROPN
gs-1575	158	5	f	f	PROPN
gs-1575	158	6	x	x	X
gs-1575	158	7	dx	dx	PROPN
gs-1575	158	8	c	c	NOUN
gs-1575	158	9	o	o	PROPN
gs-1575	158	10	n	n	CCONJ
gs-1575	158	11	a	a	DET
gs-1575	158	12	nn	nn	PROPN
gs-1575	158	13			PROPN
gs-1575	158	14			NOUN
gs-1575	158	15			ADJ
gs-1575	158	16			NOUN
gs-1575	158	17			VERB
gs-1575	158	18			NUM
gs-1575	158	19			PROPN
gs-1575	158	20			NOUN
gs-1575	158	21			VERB
gs-1575	158	22			NOUN
gs-1575	158	23			PROPN
gs-1575	158	24			PROPN
gs-1575	158	25			ADV
gs-1575	158	26			VERB
gs-1575	158	27			PUNCT
gs-1575	158	28			PROPN
gs-1575	159	1			PROPN
gs-1575	159	2			PROPN
gs-1575	159	3			PROPN
gs-1575	159	4			X
gs-1575	159	5			X
gs-1575	159	6			NUM
gs-1575	159	7			PUNCT
gs-1575	159	8	(	(	PUNCT
gs-1575	159	9	9	9	X
gs-1575	159	10	)	)	PUNCT
gs-1575	159	11	proof	proof	NOUN
gs-1575	159	12	.	.	PUNCT
gs-1575	160	1	of	of	ADP
gs-1575	160	2	theorem	theorem	PROPN
gs-1575	160	3	.	.	PUNCT
gs-1575	161	1	let	let	VERB
gs-1575	161	2	’s	’s	PRON
gs-1575	161	3	apply	apply	VERB
gs-1575	161	4	the	the	DET
gs-1575	161	5	method	method	NOUN
gs-1575	161	6	used	use	VERB
gs-1575	161	7	in	in	ADP
gs-1575	161	8	[	[	X
gs-1575	161	9	10	10	NUM
gs-1575	161	10	]	]	X
gs-1575	162	1	[	[	X
gs-1575	162	2	11	11	NUM
gs-1575	162	3	]	]	PUNCT
gs-1575	162	4	.	.	PUNCT
gs-1575	163	1	let	let	VERB
gs-1575	163	2	's	us	PRON
gs-1575	163	3	decompose	decompose	VERB
gs-1575	163	4	the	the	DET
gs-1575	163	5	sum	sum	NOUN
gs-1575	163	6			PROPN
gs-1575	163	7	ˆ	ˆ	NOUN
gs-1575	163	8	,	,	PUNCT
gs-1575	163	9	n	n	NOUN
gs-1575	163	10	nf	nf	NOUN
gs-1575	163	11	x	x	NOUN
gs-1575	163	12	a	a	PRON
gs-1575	163	13	into	into	ADP
gs-1575	163	14	r	r	NOUN
gs-1575	163	15	sums	sum	NOUN
gs-1575	163	16	.	.	PUNCT
gs-1575	164	1	let	let	VERB
gs-1575	164	2	's	us	PRON
gs-1575	164	3	fix	fix	VERB
gs-1575	164	4	the	the	DET
gs-1575	164	5	trajectory	trajectory	NOUN
gs-1575	164	6			NOUN
gs-1575	164	7	1	1	VERB
gs-1575	164	8	1	1	NUM
gs-1575	164	9	2	2	NUM
gs-1575	164	10	,	,	PUNCT
gs-1575	164	11	,	,	PUNCT
gs-1575	164	12	...	...	PUNCT
gs-1575	164	13	,	,	PUNCT
gs-1575	164	14	n	n	DET
gs-1575	164	15	n	n	PROPN
gs-1575	164	16			NOUN
gs-1575	164	17			NOUN
gs-1575	164	18			NOUN
gs-1575	164	19	.	.	PUNCT
gs-1575	165	1	for	for	ADP
gs-1575	165	2	each	each	DET
gs-1575	165	3	number	number	NOUN
gs-1575	165	4	i	i	PRON
gs-1575	165	5	(	(	PUNCT
gs-1575	165	6	1	1	NUM
gs-1575	165	7	i	i	PRON
gs-1575	165	8	r	r	VERB
gs-1575	165	9			NOUN
gs-1575	165	10	)	)	PUNCT
gs-1575	165	11	,	,	PUNCT
gs-1575	165	12	we	we	PRON
gs-1575	165	13	separately	separately	ADV
gs-1575	165	14	group	group	VERB
gs-1575	165	15	the	the	DET
gs-1575	165	16	terms	term	NOUN
gs-1575	165	17	of	of	ADP
gs-1575	165	18	those	those	DET
gs-1575	165	19	observations	observation	NOUN
gs-1575	165	20	1	1	NUM
gs-1575	165	21	2	2	NUM
gs-1575	165	22	,	,	PUNCT
gs-1575	165	23	,	,	PUNCT
gs-1575	165	24	...	...	PUNCT
gs-1575	165	25	,	,	PUNCT
gs-1575	165	26	nx	nx	X
gs-1575	165	27	x	x	X
gs-1575	165	28	x	x	X
gs-1575	165	29	out	out	ADP
gs-1575	165	30	of	of	ADP
gs-1575	165	31	the	the	DET
gs-1575	165	32	sum	sum	NOUN
gs-1575	165	33	of	of	ADP
gs-1575	165	34			PROPN
gs-1575	165	35	ˆ	ˆ	NOUN
gs-1575	165	36	,	,	PUNCT
gs-1575	165	37	n	n	NOUN
gs-1575	165	38	nf	nf	NOUN
gs-1575	165	39	x	x	NOUN
gs-1575	165	40	a	a	PRON
gs-1575	165	41	,	,	PUNCT
gs-1575	165	42	the	the	DET
gs-1575	165	43	corresponding	correspond	VERB
gs-1575	165	44	1	1	NUM
gs-1575	165	45	2	2	NUM
gs-1575	165	46	,	,	PUNCT
gs-1575	165	47	,	,	PUNCT
gs-1575	165	48	...	...	PUNCT
gs-1575	165	49	,	,	PUNCT
gs-1575	165	50	n	n	PRON
gs-1575	165	51			NOUN
gs-1575	165	52			AUX
gs-1575	165	53	control	control	VERB
gs-1575	165	54	random	random	ADJ
gs-1575	165	55	variables	variable	NOUN
gs-1575	165	56	of	of	ADP
gs-1575	165	57	which	which	PRON
gs-1575	165	58	took	take	VERB
gs-1575	165	59	the	the	DET
gs-1575	165	60	value	value	NOUN
gs-1575	165	61	9	9	NUM
gs-1575	165	62	.	.	PUNCT
gs-1575	166	1	let	let	VERB
gs-1575	166	2	's	us	PRON
gs-1575	166	3	renumber	renumber	VERB
gs-1575	166	4	the	the	DET
gs-1575	166	5	members	member	NOUN
gs-1575	166	6	of	of	ADP
gs-1575	166	7	each	each	DET
gs-1575	166	8	sum	sum	NOUN
gs-1575	166	9	.	.	PUNCT
gs-1575	166	10	0	0	PUNCT
gs-1575	167	1	(	(	PUNCT
gs-1575	167	2	)	)	PUNCT
gs-1575	167	3	0i	0i	NUM
gs-1575	168	1			NUM
gs-1575	168	2	,	,	PUNCT
gs-1575	168	3	1	1	NUM
gs-1575	168	4	(	(	PUNCT
gs-1575	168	5	)	)	PUNCT
gs-1575	168	6	min	min	NOUN
gs-1575	168	7	{	{	PUNCT
gs-1575	168	8	|	|	ADV
gs-1575	168	9	;	;	PUNCT
gs-1575	168	10	}	}	PUNCT
gs-1575	168	11	m	m	VERB
gs-1575	168	12	m	m	VERB
gs-1575	168	13	i	i	NOUN
gs-1575	168	14	ii	ii	PROPN
gs-1575	168	15	j	j	PROPN
gs-1575	168	16	j	j	PROPN
gs-1575	168	17	n	n	CCONJ
gs-1575	168	18	b	b	PROPN
gs-1575	168	19			PROPN
gs-1575	168	20			PROPN
gs-1575	168	21			PRON
gs-1575	168	22			NOUN
gs-1575	168	23			NOUN
gs-1575	168	24	;	;	PUNCT
gs-1575	168	25	1,i	1,i	NUM
gs-1575	168	26	r	r	NOUN
gs-1575	168	27	,	,	PUNCT
gs-1575	168	28	1	1	NUM
gs-1575	168	29	,	,	PUNCT
gs-1575	168	30	(	(	PUNCT
gs-1575	168	31	)	)	PUNCT
gs-1575	168	32	nm	nm	NOUN
gs-1575	168	33	i	i	INTJ
gs-1575	168	34	.	.	PUNCT
gs-1575	169	1	georgian	georgian	ADJ
gs-1575	169	2	scientists/ქართველი	scientists/ქართველი	PROPN
gs-1575	169	3	მეცნიერები	მეცნიერები	NOUN
gs-1575	169	4	ტ.	ტ.	VERB
gs-1575	169	5	5	5	NUM
gs-1575	169	6	n	n	PRON
gs-1575	169	7	1	1	NUM
gs-1575	169	8	,	,	PUNCT
gs-1575	169	9	2023	2023	NUM
gs-1575	169	10	313	313	NUM
gs-1575	169	11	it	it	PRON
gs-1575	169	12	turns	turn	VERB
gs-1575	169	13	out	out	ADP
gs-1575	169	14	r	r	NOUN
gs-1575	169	15	sequence	sequence	NOUN
gs-1575	169	16	of	of	ADP
gs-1575	169	17	indices	index	NOUN
gs-1575	169	18	1	1	NUM
gs-1575	169	19	2	2	NUM
gs-1575	169	20	(	(	PUNCT
gs-1575	169	21	)	)	PUNCT
gs-1575	169	22	(	(	PUNCT
gs-1575	169	23	)	)	PUNCT
gs-1575	169	24	,	,	PUNCT
gs-1575	169	25	(	(	PUNCT
gs-1575	169	26	)	)	PUNCT
gs-1575	169	27	,	,	PUNCT
gs-1575	169	28	...	...	PUNCT
gs-1575	169	29	,	,	PUNCT
gs-1575	169	30	(	(	PUNCT
gs-1575	169	31	)	)	PUNCT
gs-1575	170	1	n	n	X
gs-1575	170	2	ii	ii	NOUN
gs-1575	171	1	i	i	PRON
gs-1575	171	2	i	i	VERB
gs-1575	171	3			NOUN
gs-1575	171	4			NOUN
gs-1575	171	5	,	,	PUNCT
gs-1575	171	6	1,i	1,i	PROPN
gs-1575	171	7	r	r	X
gs-1575	171	8	.	.	PUNCT
gs-1575	172	1	the	the	DET
gs-1575	172	2	equalities	equality	NOUN
gs-1575	172	3	are	be	AUX
gs-1575	172	4	fulfilled	fulfil	VERB
gs-1575	172	5	for	for	ADP
gs-1575	172	6	them	they	PRON
gs-1575	172	7	(	(	PUNCT
gs-1575	172	8	)	)	PUNCT
gs-1575	172	9	,	,	PUNCT
gs-1575	172	10	1	1	NUM
gs-1575	172	11	,	,	PUNCT
gs-1575	172	12	,	,	PUNCT
gs-1575	172	13	1	1	NUM
gs-1575	172	14	,	,	PUNCT
gs-1575	172	15	(	(	PUNCT
gs-1575	172	16	)	)	PUNCT
gs-1575	172	17	m	m	VERB
gs-1575	172	18	i	i	INTJ
gs-1575	173	1	i	i	PRON
gs-1575	173	2	nb	nb	INTJ
gs-1575	174	1	i	i	PRON
gs-1575	175	1	r	r	NOUN
gs-1575	175	2	m	m	VERB
gs-1575	175	3	i	i	NOUN
gs-1575	175	4			ADJ
gs-1575	175	5			PROPN
gs-1575	175	6			INTJ
gs-1575	175	7	.	.	PUNCT
gs-1575	176	1	now	now	ADV
gs-1575	176	2	let	let	VERB
gs-1575	176	3	's	us	PRON
gs-1575	176	4	present	present	VERB
gs-1575	176	5	the	the	DET
gs-1575	176	6	sum	sum	NOUN
gs-1575	176	7			PROPN
gs-1575	176	8	ˆ	ˆ	NOUN
gs-1575	176	9	,	,	PUNCT
gs-1575	176	10	n	n	NOUN
gs-1575	176	11	nf	nf	NOUN
gs-1575	176	12	x	x	NOUN
gs-1575	176	13	a	a	PRON
gs-1575	176	14	as	as	ADP
gs-1575	176	15	following	follow	VERB
gs-1575	176	16	1	1	NUM
gs-1575	176	17	(	(	PUNCT
gs-1575	176	18	)	)	PUNCT
gs-1575	176	19	ˆ	ˆ	NOUN
gs-1575	176	20	ˆ	ˆ	PROPN
gs-1575	176	21	(	(	PUNCT
gs-1575	176	22	,	,	PUNCT
gs-1575	176	23	)	)	PUNCT
gs-1575	176	24	(	(	PUNCT
gs-1575	176	25	,	,	PUNCT
gs-1575	176	26	)	)	PUNCT
gs-1575	176	27	r	r	NOUN
gs-1575	176	28	n	n	CCONJ
gs-1575	176	29	n	n	CCONJ
gs-1575	176	30	n	n	NOUN
gs-1575	176	31	in	in	ADP
gs-1575	176	32	n	n	PRON
gs-1575	176	33	i	i	PRON
gs-1575	177	1	i	i	PRON
gs-1575	177	2	f	f	X
gs-1575	177	3	x	x	X
gs-1575	177	4	a	a	DET
gs-1575	177	5	f	f	X
gs-1575	177	6	x	x	X
gs-1575	177	7	a	a	DET
gs-1575	177	8	n	n	NOUN
gs-1575	177	9			PROPN
gs-1575	177	10			NOUN
gs-1575	177	11	,	,	PUNCT
gs-1575	177	12	where	where	SCONJ
gs-1575	177	13	(	(	PUNCT
gs-1575	177	14	)	)	PUNCT
gs-1575	177	15	(	(	PUNCT
gs-1575	177	16	)	)	PUNCT
gs-1575	177	17	1	1	NUM
gs-1575	177	18	ˆ	ˆ	NOUN
gs-1575	177	19	(	(	PUNCT
gs-1575	177	20	,	,	PUNCT
gs-1575	177	21	)	)	PUNCT
gs-1575	177	22	(	(	PUNCT
gs-1575	177	23	(	(	PUNCT
gs-1575	177	24	)	)	PUNCT
gs-1575	177	25	)	)	PUNCT
gs-1575	177	26	,	,	PUNCT
gs-1575	177	27	1	1	NUM
gs-1575	177	28	,	,	PUNCT
gs-1575	177	29	.	.	PUNCT
gs-1575	178	1	(	(	PUNCT
gs-1575	178	2	)	)	PUNCT
gs-1575	178	3	n	n	X
gs-1575	178	4	m	m	VERB
gs-1575	178	5	i	i	PRON
gs-1575	178	6	n	n	ADJ
gs-1575	178	7	in	in	ADP
gs-1575	178	8	n	n	PRON
gs-1575	179	1	n	n	NOUN
gs-1575	180	1	i	i	PRON
gs-1575	180	2	mn	mn	PROPN
gs-1575	180	3	a	a	DET
gs-1575	180	4	f	f	X
gs-1575	180	5	x	x	X
gs-1575	180	6	a	a	PROPN
gs-1575	180	7	k	k	X
gs-1575	181	1	a	a	X
gs-1575	181	2	x	x	X
gs-1575	181	3	x	x	X
gs-1575	181	4	i	i	NOUN
gs-1575	181	5	r	r	VERB
gs-1575	182	1	i	i	PRON
gs-1575	182	2			PROPN
gs-1575	182	3			NUM
gs-1575	182	4			PROPN
gs-1575	182	5			PROPN
gs-1575	182	6			ADJ
gs-1575	182	7			NOUN
gs-1575	182	8			INTJ
gs-1575	183	1	it	it	PRON
gs-1575	183	2	is	be	AUX
gs-1575	183	3	obvious	obvious	ADJ
gs-1575	183	4	that	that	SCONJ
gs-1575	183	5	if	if	SCONJ
gs-1575	183	6	(	(	PUNCT
gs-1575	183	7	)	)	PUNCT
gs-1575	183	8	0n	0n	NOUN
gs-1575	184	1	i	i	PRON
gs-1575	184	2			PROPN
gs-1575	184	3	,	,	PUNCT
gs-1575	184	4	then	then	ADV
gs-1575	184	5	the	the	DET
gs-1575	184	6	corresponding	corresponding	ADJ
gs-1575	184	7	sum	sum	NOUN
gs-1575	184	8	,	,	PUNCT
gs-1575	184	9	does	do	AUX
gs-1575	184	10	not	not	PART
gs-1575	184	11	exist	exist	VERB
gs-1575	184	12	.	.	PUNCT
gs-1575	185	1	let	let	VERB
gs-1575	185	2	us	we	PRON
gs-1575	185	3	show	show	VERB
gs-1575	185	4	that	that	PRON
gs-1575	185	5	are	be	AUX
gs-1575	185	6	finite	finite	ADJ
gs-1575	185	7	and	and	CCONJ
gs-1575	185	8	values	value	NOUN
gs-1575	185	9	.	.	PUNCT
gs-1575	186	1	let	let	VERB
gs-1575	186	2	's	us	PRON
gs-1575	186	3	represent	represent	VERB
gs-1575	186	4	the	the	DET
gs-1575	186	5	value	value	NOUN
gs-1575	186	6			PROPN
gs-1575	186	7	ˆ	ˆ	NOUN
gs-1575	186	8	,	,	PUNCT
gs-1575	186	9	n	n	NOUN
gs-1575	186	10	nef	nef	PROPN
gs-1575	186	11	x	x	X
gs-1575	186	12	a	a	PRON
gs-1575	186	13	as	as	ADP
gs-1575	186	14	a	a	DET
gs-1575	186	15	conditional	conditional	ADJ
gs-1575	186	16	mathematical	mathematical	ADJ
gs-1575	186	17	expectation	expectation	NOUN
gs-1575	186	18	on	on	ADP
gs-1575	186	19	the	the	DET
gs-1575	186	20	fixed	fix	VERB
gs-1575	186	21	trajectory	trajectory	NOUN
gs-1575	186	22	1n	1n	NUM
gs-1575	186	23			NOUN
gs-1575	187	1			SYM
gs-1575	187	2			NOUN
gs-1575	187	3			SYM
gs-1575	187	4			NOUN
gs-1575	187	5			SYM
gs-1575	187	6			NOUN
gs-1575	187	7	1	1	NOUN
gs-1575	187	8	1	1	NUM
gs-1575	187	9	1	1	NUM
gs-1575	187	10	ˆ	ˆ	NOUN
gs-1575	187	11	ˆ	ˆ	NOUN
gs-1575	187	12	ˆ	ˆ	ADJ
gs-1575	187	13	,	,	PUNCT
gs-1575	187	14	{	{	PUNCT
gs-1575	187	15	(	(	PUNCT
gs-1575	187	16	,	,	PUNCT
gs-1575	187	17	|	|	ADV
gs-1575	187	18	)	)	PUNCT
gs-1575	187	19	}	}	PUNCT
gs-1575	187	20	{	{	PUNCT
gs-1575	187	21	(	(	PUNCT
gs-1575	187	22	,	,	PUNCT
gs-1575	187	23	|	|	ADV
gs-1575	187	24	)	)	PUNCT
gs-1575	187	25	}	}	PUNCT
gs-1575	187	26	r	r	NOUN
gs-1575	187	27	n	n	CCONJ
gs-1575	187	28	n	n	CCONJ
gs-1575	187	29	n	n	CCONJ
gs-1575	187	30	n	n	CCONJ
gs-1575	187	31	n	n	CCONJ
gs-1575	187	32	n	n	NOUN
gs-1575	187	33	in	in	ADP
gs-1575	187	34	n	n	CCONJ
gs-1575	188	1	n	n	NOUN
gs-1575	189	1	i	i	PRON
gs-1575	189	2	i	i	PRON
gs-1575	189	3	ef	ef	VERB
gs-1575	189	4	x	x	PUNCT
gs-1575	189	5	a	a	DET
gs-1575	189	6	e	e	X
gs-1575	189	7	e	e	NOUN
gs-1575	189	8	f	f	X
gs-1575	189	9	x	x	X
gs-1575	189	10	a	a	DET
gs-1575	189	11	e	e	X
gs-1575	189	12	e	e	NOUN
gs-1575	189	13	f	f	X
gs-1575	189	14	x	x	PROPN
gs-1575	189	15	a	a	DET
gs-1575	189	16	n	n	CCONJ
gs-1575	189	17			ADJ
gs-1575	189	18			NOUN
gs-1575	189	19			NOUN
gs-1575	189	20			NUM
gs-1575	189	21			NUM
gs-1575	190	1			ADJ
gs-1575	190	2			X
gs-1575	190	3	.	.	PUNCT
gs-1575	191	1	let	let	VERB
gs-1575	191	2	us	we	PRON
gs-1575	191	3	take	take	VERB
gs-1575	191	4	into	into	ADP
gs-1575	191	5	account	account	NOUN
gs-1575	191	6	that	that	SCONJ
gs-1575	191	7	,	,	PUNCT
gs-1575	191	8	random	random	ADJ
gs-1575	191	9	variables	variable	NOUN
gs-1575	191	10	(	(	PUNCT
gs-1575	191	11	)	)	PUNCT
gs-1575	191	12	n	n	X
gs-1575	191	13	i	i	ADV
gs-1575	191	14	,	,	PUNCT
gs-1575	191	15	(	(	PUNCT
gs-1575	191	16	1,i	1,i	NOUN
gs-1575	191	17	r	r	NOUN
gs-1575	191	18	)	)	PUNCT
gs-1575	191	19	are	be	AUX
gs-1575	191	20	commensurate	commensurate	ADJ
gs-1575	191	21	with	with	ADP
gs-1575	191	22	respect	respect	NOUN
gs-1575	191	23	to	to	ADP
gs-1575	191	24	the	the	DET
gs-1575	191	25			PROPN
gs-1575	191	26	-algebra	-algebra	NOUN
gs-1575	191	27	induced	induce	VERB
gs-1575	191	28	by	by	ADP
gs-1575	191	29	the	the	DET
gs-1575	191	30	partitioning	partitioning	NOUN
gs-1575	191	31	of	of	ADP
gs-1575	191	32	the	the	DET
gs-1575	191	33	space	space	NOUN
gs-1575	191	34			PROPN
gs-1575	191	35	generated	generate	VERB
gs-1575	191	36	when	when	SCONJ
gs-1575	191	37	fixing	fix	VERB
gs-1575	191	38	the	the	DET
gs-1575	191	39	trajectory	trajectory	NOUN
gs-1575	191	40	1n	1n	PROPN
gs-1575	191	41	(	(	PUNCT
gs-1575	191	42	see	see	VERB
gs-1575	191	43	[	[	X
gs-1575	191	44	19	19	NUM
gs-1575	191	45	]	]	NUM
gs-1575	191	46	)	)	PUNCT
gs-1575	191	47	.	.	PUNCT
gs-1575	192	1	therefore	therefore	ADV
gs-1575	192	2	,	,	PUNCT
gs-1575	192	3	we	we	PRON
gs-1575	192	4	can	can	AUX
gs-1575	192	5	take	take	VERB
gs-1575	192	6	them	they	PRON
gs-1575	192	7	out	out	ADP
gs-1575	192	8	of	of	ADP
gs-1575	192	9	the	the	DET
gs-1575	192	10	determined	determine	VERB
gs-1575	192	11	by	by	ADP
gs-1575	192	12	condition	condition	NOUN
gs-1575	192	13	1n	1n	NUM
gs-1575	192	14	conditional	conditional	ADJ
gs-1575	192	15	mathematical	mathematical	ADJ
gs-1575	192	16	expectation	expectation	NOUN
gs-1575	192	17	sign	sign	NOUN
gs-1575	192	18	.	.	PUNCT
gs-1575	193	1	random	random	ADJ
gs-1575	193	2	variables	variable	NOUN
gs-1575	193	3	(	(	PUNCT
gs-1575	193	4	)	)	PUNCT
gs-1575	193	5	,	,	PUNCT
gs-1575	193	6	1	1	NUM
gs-1575	193	7	,	,	PUNCT
gs-1575	193	8	(	(	PUNCT
gs-1575	193	9	)	)	PUNCT
gs-1575	193	10	m	m	VERB
gs-1575	193	11	i	i	PRON
gs-1575	193	12	nx	nx	NOUN
gs-1575	193	13	m	m	VERB
gs-1575	193	14	i	i	PROPN
gs-1575	193	15			NOUN
gs-1575	193	16	are	be	AUX
gs-1575	193	17	independent	independent	ADJ
gs-1575	193	18	when	when	SCONJ
gs-1575	193	19	the	the	DET
gs-1575	193	20	trajectory	trajectory	NOUN
gs-1575	193	21	1n	1n	NUM
gs-1575	193	22	is	be	AUX
gs-1575	193	23	fixed	fix	VERB
gs-1575	193	24	.	.	PUNCT
gs-1575	194	1	they	they	PRON
gs-1575	194	2	have	have	VERB
gs-1575	194	3	the	the	DET
gs-1575	194	4	same	same	ADJ
gs-1575	194	5	conditional	conditional	ADJ
gs-1575	194	6	distribution	distribution	NOUN
gs-1575	194	7	1	1	NUM
gs-1575	194	8	1	1	NUM
gs-1575	194	9	ix	ix	ADP
gs-1575	194	10	b	b	NOUN
gs-1575	194	11	with	with	ADP
gs-1575	194	12	density	density	NOUN
gs-1575	194	13	(	(	PUNCT
gs-1575	194	14	)	)	PUNCT
gs-1575	194	15	if	if	SCONJ
gs-1575	194	16	x	x	X
gs-1575	194	17	.	.	PUNCT
gs-1575	195	1			NOUN
gs-1575	195	2			PUNCT
gs-1575	195	3			NOUN
gs-1575	195	4			PROPN
gs-1575	195	5	(	(	PUNCT
gs-1575	195	6	)	)	PUNCT
gs-1575	195	7	(	(	PUNCT
gs-1575	195	8	)	)	PUNCT
gs-1575	195	9	1	1	NUM
gs-1575	195	10	1	1	NUM
gs-1575	195	11	1	1	NUM
gs-1575	195	12	ˆ	ˆ	NOUN
gs-1575	195	13	,	,	PUNCT
gs-1575	195	14	{	{	PUNCT
gs-1575	195	15	(	(	PUNCT
gs-1575	195	16	(	(	PUNCT
gs-1575	195	17	(	(	PUNCT
gs-1575	195	18	)	)	PUNCT
gs-1575	195	19	)	)	PUNCT
gs-1575	195	20	|	|	ADV
gs-1575	195	21	)	)	PUNCT
gs-1575	195	22	}	}	PUNCT
gs-1575	195	23	(	(	PUNCT
gs-1575	195	24	)	)	PUNCT
gs-1575	195	25	n	n	CCONJ
gs-1575	195	26	m	m	VERB
gs-1575	195	27	ir	ir	PROPN
gs-1575	195	28	n	n	ADV
gs-1575	195	29	n	n	CCONJ
gs-1575	195	30	n	n	CCONJ
gs-1575	195	31	n	n	CCONJ
gs-1575	195	32	n	n	NOUN
gs-1575	195	33	i	i	PRON
gs-1575	195	34	n	n	CCONJ
gs-1575	196	1	i	i	PRON
gs-1575	196	2	mn	mn	INTJ
gs-1575	197	1	i	i	PRON
gs-1575	197	2	a	a	DET
gs-1575	197	3	ef	ef	X
gs-1575	197	4	x	x	PUNCT
gs-1575	197	5	a	a	DET
gs-1575	197	6	e	e	X
gs-1575	197	7	e	e	X
gs-1575	197	8	k	k	PROPN
gs-1575	197	9	a	a	X
gs-1575	197	10	x	x	X
gs-1575	197	11	x	x	SYM
gs-1575	197	12	n	n	NUM
gs-1575	197	13	i	i	NOUN
gs-1575	197	14			PROPN
gs-1575	197	15			PROPN
gs-1575	197	16			PROPN
gs-1575	197	17			X
gs-1575	197	18			X
gs-1575	197	19			X
gs-1575	197	20			NOUN
gs-1575	197	21			ADJ
gs-1575	197	22			NOUN
gs-1575	197	23			ADJ
gs-1575	197	24			NOUN
gs-1575	197	25			PROPN
gs-1575	197	26	1	1	NUM
gs-1575	197	27	(	(	PUNCT
gs-1575	197	28	)	)	PUNCT
gs-1575	197	29	1	1	NUM
gs-1575	197	30	1	1	NUM
gs-1575	197	31	1	1	NUM
gs-1575	197	32	(	(	PUNCT
gs-1575	197	33	)	)	PUNCT
gs-1575	197	34	{	{	PUNCT
gs-1575	197	35	(	(	PUNCT
gs-1575	197	36	(	(	PUNCT
gs-1575	197	37	)	)	PUNCT
gs-1575	197	38	(	(	PUNCT
gs-1575	197	39	(	(	PUNCT
gs-1575	197	40	)	)	PUNCT
gs-1575	197	41	)	)	PUNCT
gs-1575	197	42	|	|	ADV
gs-1575	197	43	)	)	PUNCT
gs-1575	197	44	}	}	PUNCT
gs-1575	197	45	(	(	PUNCT
gs-1575	197	46	(	(	PUNCT
gs-1575	197	47	)	)	PUNCT
gs-1575	197	48	)	)	PUNCT
gs-1575	197	49	(	(	PUNCT
gs-1575	197	50	)	)	PUNCT
gs-1575	197	51	(	(	PUNCT
gs-1575	197	52	)	)	PUNCT
gs-1575	197	53	(	(	PUNCT
gs-1575	197	54	)	)	PUNCT
gs-1575	197	55	r	r	NOUN
gs-1575	197	56	r	r	NOUN
gs-1575	197	57	n	n	CCONJ
gs-1575	197	58	n	n	CCONJ
gs-1575	197	59	n	n	CCONJ
gs-1575	197	60	n	n	CCONJ
gs-1575	197	61	n	n	NOUN
gs-1575	197	62	i	i	PRON
gs-1575	197	63	n	n	VERB
gs-1575	197	64	n	n	CCONJ
gs-1575	197	65	n	n	NOUN
gs-1575	197	66	i	i	PRON
gs-1575	197	67	i	i	PRON
gs-1575	197	68	in	in	ADP
gs-1575	197	69	i	i	PRON
gs-1575	197	70	a	a	PRON
gs-1575	197	71	i	i	NOUN
gs-1575	197	72	e	e	NOUN
gs-1575	197	73	e	e	NOUN
gs-1575	198	1	i	i	AUX
gs-1575	198	2	k	k	PROPN
gs-1575	198	3	a	a	X
gs-1575	198	4	x	x	X
gs-1575	198	5	x	x	X
gs-1575	198	6	a	a	DET
gs-1575	198	7	k	k	PROPN
gs-1575	198	8	a	a	X
gs-1575	198	9	x	x	SYM
gs-1575	198	10	u	u	NOUN
gs-1575	198	11	f	f	PROPN
gs-1575	198	12	u	u	PROPN
gs-1575	198	13	due	due	ADJ
gs-1575	198	14	n	n	NOUN
gs-1575	198	15	i	i	PRON
gs-1575	198	16	n	n	ADV
gs-1575	198	17			VERB
gs-1575	198	18			NUM
gs-1575	198	19			NUM
gs-1575	198	20			NOUN
gs-1575	199	1			NUM
gs-1575	199	2			NOUN
gs-1575	199	3			NUM
gs-1575	199	4			NOUN
gs-1575	199	5			X
gs-1575	199	6			PUNCT
gs-1575	199	7			ADJ
gs-1575	199	8			ADJ
gs-1575	199	9			NOUN
gs-1575	199	10			NOUN
gs-1575	199	11			NOUN
gs-1575	199	12	based	base	VERB
gs-1575	199	13	on	on	ADP
gs-1575	199	14	the	the	DET
gs-1575	199	15	condition	condition	NOUN
gs-1575	199	16	(	(	PUNCT
gs-1575	199	17	6	6	NUM
gs-1575	199	18	)	)	PUNCT
gs-1575	199	19	,	,	PUNCT
gs-1575	199	20	the	the	DET
gs-1575	199	21	equality	equality	NOUN
gs-1575	199	22			NOUN
gs-1575	199	23	n	n	PUNCT
gs-1575	199	24	i	i	PRON
gs-1575	200	1	i	i	VERB
gs-1575	201	1	e	e	VERB
gs-1575	202	1	p	p	NOUN
gs-1575	203	1	n	n	PRON
gs-1575	204	1			NOUN
gs-1575	205	1			NOUN
gs-1575	205	2	is	be	AUX
gs-1575	205	3	fulfilled	fulfil	VERB
gs-1575	205	4	.	.	PUNCT
gs-1575	206	1	let	let	VERB
gs-1575	206	2	's	us	PRON
gs-1575	206	3	take	take	VERB
gs-1575	206	4	into	into	ADP
gs-1575	206	5	account	account	NOUN
gs-1575	206	6	that	that	PRON
gs-1575	206	7	(	(	PUNCT
gs-1575	206	8	)	)	PUNCT
gs-1575	206	9	k	k	X
gs-1575	206	10	x	x	PUNCT
gs-1575	206	11	is	be	AUX
gs-1575	206	12	an	an	DET
gs-1575	206	13	even	even	ADJ
gs-1575	206	14	function	function	NOUN
gs-1575	206	15	and	and	CCONJ
gs-1575	206	16	transform	transform	VERB
gs-1575	206	17	the	the	DET
gs-1575	206	18	variable	variable	NOUN
gs-1575	206	19	(	(	PUNCT
gs-1575	206	20	)	)	PUNCT
gs-1575	206	21	na	na	PART
gs-1575	206	22	u	u	NOUN
gs-1575	206	23	x	x	NOUN
gs-1575	206	24	t	t	VERB
gs-1575	206	25			ADJ
gs-1575	206	26	under	under	ADP
gs-1575	206	27	the	the	DET
gs-1575	206	28	integral	integral	ADJ
gs-1575	206	29	sign	sign	NOUN
gs-1575	206	30	.	.	PUNCT
gs-1575	207	1	will	will	AUX
gs-1575	207	2	be	be	AUX
gs-1575	207	3	obtained	obtain	VERB
gs-1575	207	4	the	the	DET
gs-1575	207	5	equality	equality	NOUN
gs-1575	207	6			NOUN
gs-1575	207	7			PROPN
gs-1575	207	8	1	1	NUM
gs-1575	207	9	ˆ	ˆ	NOUN
gs-1575	207	10	,	,	PUNCT
gs-1575	207	11	(	(	PUNCT
gs-1575	207	12	)	)	PUNCT
gs-1575	207	13	(	(	PUNCT
gs-1575	207	14	)	)	PUNCT
gs-1575	207	15	r	r	NOUN
gs-1575	207	16	n	n	NOUN
gs-1575	207	17	n	n	NOUN
gs-1575	208	1	i	i	PRON
gs-1575	209	1	i	i	PRON
gs-1575	210	1	i	i	PRON
gs-1575	210	2	n	n	VERB
gs-1575	210	3	t	t	X
gs-1575	210	4	ef	ef	X
gs-1575	210	5	x	x	PUNCT
gs-1575	210	6	a	a	DET
gs-1575	210	7	p	p	X
gs-1575	210	8	k	k	PROPN
gs-1575	210	9	t	t	PROPN
gs-1575	210	10	f	f	X
gs-1575	211	1	x	x	X
gs-1575	211	2	dt	dt	X
gs-1575	211	3	a	a	DET
gs-1575	211	4			X
gs-1575	211	5			NOUN
gs-1575	211	6			NOUN
gs-1575	211	7			NUM
gs-1575	211	8			NOUN
gs-1575	211	9			PUNCT
gs-1575	211	10	.	.	PUNCT
gs-1575	212	1	(	(	PUNCT
gs-1575	212	2	)	)	PUNCT
gs-1575	212	3	k	k	X
gs-1575	212	4	x	x	PUNCT
gs-1575	212	5	is	be	AUX
gs-1575	212	6	a	a	DET
gs-1575	212	7	density	density	NOUN
gs-1575	212	8	and	and	CCONJ
gs-1575	212	9	(	(	PUNCT
gs-1575	212	10	)	)	PUNCT
gs-1575	212	11	if	if	SCONJ
gs-1575	212	12	x	x	PRON
gs-1575	212	13	is	be	AUX
gs-1575	212	14	a	a	DET
gs-1575	212	15	density	density	NOUN
gs-1575	212	16	bounded	bound	VERB
gs-1575	212	17	by	by	ADP
gs-1575	212	18	a	a	DET
gs-1575	212	19	finite	finite	NOUN
gs-1575	212	20	constant	constant	ADJ
gs-1575	212	21	.	.	PUNCT
gs-1575	213	1	therefore	therefore	ADV
gs-1575	213	2	,	,	PUNCT
gs-1575	213	3			PROPN
gs-1575	213	4	ˆ	ˆ	NOUN
gs-1575	213	5	,	,	PUNCT
gs-1575	213	6	n	n	NOUN
gs-1575	213	7	nef	nef	PROPN
gs-1575	213	8	x	x	X
gs-1575	213	9	a	a	PRON
gs-1575	213	10	is	be	AUX
gs-1575	213	11	a	a	DET
gs-1575	213	12	finite	finite	ADJ
gs-1575	213	13	quantity	quantity	NOUN
gs-1575	213	14	.	.	PUNCT
gs-1575	214	1	let	let	VERB
gs-1575	214	2	us	we	PRON
gs-1575	214	3	show	show	VERB
gs-1575	214	4	that	that	SCONJ
gs-1575	214	5	the	the	DET
gs-1575	214	6	quantity	quantity	NOUN
gs-1575	214	7			NOUN
gs-1575	214	8	ˆ	ˆ	NOUN
gs-1575	214	9	,	,	PUNCT
gs-1575	214	10	n	n	CCONJ
gs-1575	214	11	ndf	ndf	NOUN
gs-1575	214	12	x	x	X
gs-1575	214	13	a	a	PRON
gs-1575	214	14	is	be	AUX
gs-1575	214	15	finite	finite	ADJ
gs-1575	214	16	.	.	PUNCT
gs-1575	215	1			NOUN
gs-1575	215	2			SYM
gs-1575	215	3			NOUN
gs-1575	215	4			PUNCT
gs-1575	215	5			NOUN
gs-1575	215	6			NOUN
gs-1575	215	7	2	2	NUM
gs-1575	215	8	1	1	NUM
gs-1575	215	9	ˆ	ˆ	NOUN
gs-1575	215	10	ˆ	ˆ	NOUN
gs-1575	215	11	ˆ	ˆ	ADJ
gs-1575	215	12	,	,	PUNCT
gs-1575	215	13	{	{	PUNCT
gs-1575	215	14	(	(	PUNCT
gs-1575	215	15	[	[	PUNCT
gs-1575	215	16	,	,	PUNCT
gs-1575	215	17	,	,	PUNCT
gs-1575	215	18	]	]	PUNCT
gs-1575	215	19	|	|	ADV
gs-1575	215	20	)	)	PUNCT
gs-1575	215	21	}	}	PUNCT
gs-1575	215	22	n	n	CCONJ
gs-1575	215	23	n	n	CCONJ
gs-1575	215	24	n	n	CCONJ
gs-1575	215	25	n	n	CCONJ
gs-1575	215	26	n	n	CCONJ
gs-1575	215	27	n	n	ADV
gs-1575	215	28	ndf	ndf	NOUN
gs-1575	215	29	x	x	PUNCT
gs-1575	215	30	a	a	DET
gs-1575	215	31	e	e	X
gs-1575	215	32	e	e	NOUN
gs-1575	215	33	f	f	PROPN
gs-1575	215	34	x	x	PROPN
gs-1575	215	35	a	a	DET
gs-1575	215	36	ef	ef	X
gs-1575	215	37	x	x	PUNCT
gs-1575	215	38	a	a	VERB
gs-1575	215	39			PROPN
gs-1575	215	40			NOUN
gs-1575	215	41			NOUN
gs-1575	215	42	ˆ	ˆ	NOUN
gs-1575	215	43	,	,	PUNCT
gs-1575	215	44	in	in	ADP
gs-1575	215	45	nf	nf	NUM
gs-1575	215	46	x	x	DET
gs-1575	215	47	a	a	DET
gs-1575	215	48	1,i	1,i	PROPN
gs-1575	215	49	r	r	NOUN
gs-1575	215	50			PROPN
gs-1575	215	51	ˆ	ˆ	NOUN
gs-1575	215	52	,	,	PUNCT
gs-1575	215	53	n	n	NOUN
gs-1575	215	54	nef	nef	PROPN
gs-1575	215	55	x	x	PROPN
gs-1575	215	56	a	a	DET
gs-1575	215	57			NOUN
gs-1575	215	58	ˆ	ˆ	NOUN
gs-1575	215	59	,	,	PUNCT
gs-1575	215	60	n	n	CCONJ
gs-1575	215	61	ndf	ndf	NOUN
gs-1575	215	62	x	x	PUNCT
gs-1575	215	63	a	a	DET
gs-1575	215	64	georgian	georgian	ADJ
gs-1575	215	65	scientists/ქართველი	scientists/ქართველი	NOUN
gs-1575	215	66	მეცნიერები	მეცნიერები	NOUN
gs-1575	215	67	ტ.	ტ.	VERB
gs-1575	215	68	5	5	NUM
gs-1575	215	69	n	n	DET
gs-1575	215	70	1	1	NUM
gs-1575	215	71	,	,	PUNCT
gs-1575	215	72	2023	2023	NUM
gs-1575	215	73	314	314	NUM
gs-1575	215	74			NOUN
gs-1575	216	1			SYM
gs-1575	216	2			NOUN
gs-1575	216	3			SYM
gs-1575	216	4			NOUN
gs-1575	216	5			PUNCT
gs-1575	216	6			NOUN
gs-1575	216	7			NOUN
gs-1575	216	8	2	2	NUM
gs-1575	216	9	1	1	NUM
gs-1575	216	10	1	1	NUM
gs-1575	216	11	1	1	NUM
gs-1575	216	12	ˆ	ˆ	NOUN
gs-1575	216	13	ˆ	ˆ	ADJ
gs-1575	216	14	{	{	PUNCT
gs-1575	216	15	(	(	PUNCT
gs-1575	216	16	[	[	PUNCT
gs-1575	216	17	,	,	PUNCT
gs-1575	216	18	,	,	PUNCT
gs-1575	216	19	]	]	PUNCT
gs-1575	216	20	|	|	ADV
gs-1575	216	21	)	)	PUNCT
gs-1575	216	22	}	}	PUNCT
gs-1575	216	23	r	r	NOUN
gs-1575	216	24	r	r	NOUN
gs-1575	216	25	n	n	NOUN
gs-1575	216	26	n	n	NOUN
gs-1575	216	27	in	in	ADP
gs-1575	216	28	n	n	PROPN
gs-1575	216	29	in	in	ADP
gs-1575	216	30	n	n	CCONJ
gs-1575	216	31	n	n	NOUN
gs-1575	216	32	i	i	PRON
gs-1575	217	1	i	i	PRON
gs-1575	217	2	i	i	INTJ
gs-1575	218	1	i	i	VERB
gs-1575	218	2	e	e	VERB
gs-1575	219	1	e	e	NOUN
gs-1575	219	2	f	f	X
gs-1575	219	3	x	x	X
gs-1575	219	4	a	a	PRON
gs-1575	219	5	e	e	X
gs-1575	219	6	f	f	X
gs-1575	219	7	x	x	PROPN
gs-1575	219	8	a	a	DET
gs-1575	219	9	n	n	CCONJ
gs-1575	219	10	n	n	ADV
gs-1575	219	11			ADJ
gs-1575	219	12			ADJ
gs-1575	219	13			NOUN
gs-1575	220	1			NUM
gs-1575	220	2			NUM
gs-1575	220	3			PROPN
gs-1575	220	4			PROPN
gs-1575	220	5			X
gs-1575	220	6			X
gs-1575	220	7			NOUN
gs-1575	220	8			SYM
gs-1575	220	9			NOUN
gs-1575	220	10			PUNCT
gs-1575	220	11			NOUN
gs-1575	220	12			NOUN
gs-1575	220	13	2	2	NUM
gs-1575	220	14	1	1	NUM
gs-1575	220	15	1	1	NUM
gs-1575	220	16	ˆ	ˆ	NOUN
gs-1575	220	17	ˆ	ˆ	ADJ
gs-1575	220	18	{	{	PUNCT
gs-1575	220	19	(	(	PUNCT
gs-1575	220	20	[	[	PUNCT
gs-1575	220	21	(	(	PUNCT
gs-1575	220	22	,	,	PUNCT
gs-1575	220	23	,	,	PUNCT
gs-1575	220	24	]	]	PUNCT
gs-1575	220	25	|	|	ADV
gs-1575	220	26	)	)	PUNCT
gs-1575	220	27	}	}	PUNCT
gs-1575	220	28	r	r	NOUN
gs-1575	220	29	n	n	NOUN
gs-1575	220	30	in	in	ADP
gs-1575	220	31	n	n	PROPN
gs-1575	220	32	in	in	ADP
gs-1575	220	33	n	n	CCONJ
gs-1575	221	1	n	n	NOUN
gs-1575	222	1	i	i	PRON
gs-1575	222	2	i	i	INTJ
gs-1575	222	3	e	e	NOUN
gs-1575	222	4	e	e	NOUN
gs-1575	222	5	f	f	X
gs-1575	222	6	x	x	PROPN
gs-1575	222	7	a	a	DET
gs-1575	222	8	ef	ef	X
gs-1575	222	9	x	x	PUNCT
gs-1575	222	10	a	a	PRON
gs-1575	222	11	n	n	ADV
gs-1575	222	12			ADJ
gs-1575	222	13			NOUN
gs-1575	222	14			NUM
gs-1575	222	15			NOUN
gs-1575	223	1			PROPN
gs-1575	223	2	on	on	ADP
gs-1575	223	3	the	the	DET
gs-1575	223	4	fixed	fix	VERB
gs-1575	223	5	trajectory	trajectory	NOUN
gs-1575	223	6	1n	1n	PROPN
gs-1575	223	7	,	,	PUNCT
gs-1575	223	8	the	the	DET
gs-1575	223	9	quantities	quantity	NOUN
gs-1575	223	10			NOUN
gs-1575	223	11			PRON
gs-1575	224	1			PROPN
gs-1575	224	2	(	(	PUNCT
gs-1575	224	3	)	)	PUNCT
gs-1575	224	4	mn	mn	PROPN
gs-1575	224	5	ik	ik	PROPN
gs-1575	224	6	a	a	DET
gs-1575	224	7	x	x	SYM
gs-1575	224	8	x	x	PROPN
gs-1575	224	9			NOUN
gs-1575	224	10	,	,	PUNCT
gs-1575	224	11	1	1	NUM
gs-1575	224	12	,	,	PUNCT
gs-1575	224	13	(	(	PUNCT
gs-1575	224	14	)	)	PUNCT
gs-1575	224	15	nm	nm	NOUN
gs-1575	224	16	i	i	X
gs-1575	224	17	,	,	PUNCT
gs-1575	224	18	1,i	1,i	PROPN
gs-1575	224	19	r	r	VERB
gs-1575	224	20	and	and	CCONJ
gs-1575	224	21	accordingly	accordingly	ADV
gs-1575	224	22	,	,	PUNCT
gs-1575	224	23	the	the	DET
gs-1575	224	24	sums	sum	NOUN
gs-1575	224	25			PROPN
gs-1575	224	26	ˆ	ˆ	NOUN
gs-1575	224	27	,	,	PUNCT
gs-1575	224	28	in	in	ADP
gs-1575	224	29	nf	nf	NUM
gs-1575	224	30	x	x	SYM
gs-1575	224	31	a	a	PRON
gs-1575	224	32	,	,	PUNCT
gs-1575	224	33	1,i	1,i	NUM
gs-1575	224	34	r	r	NOUN
gs-1575	224	35	are	be	AUX
gs-1575	224	36	independent	independent	ADJ
gs-1575	224	37	.	.	PUNCT
gs-1575	225	1			NOUN
gs-1575	226	1			PUNCT
gs-1575	226	2			NOUN
gs-1575	226	3			SYM
gs-1575	226	4			NOUN
gs-1575	226	5			SYM
gs-1575	226	6			NOUN
gs-1575	226	7	2	2	ADJ
gs-1575	226	8	2	2	NUM
gs-1575	226	9	1	1	NUM
gs-1575	226	10	1	1	NUM
gs-1575	226	11	ˆ	ˆ	NOUN
gs-1575	226	12	ˆ	ˆ	NOUN
gs-1575	226	13	ˆ	ˆ	ADJ
gs-1575	226	14	,	,	PUNCT
gs-1575	226	15	{	{	PUNCT
gs-1575	226	16	(	(	PUNCT
gs-1575	226	17	(	(	PUNCT
gs-1575	226	18	)	)	PUNCT
gs-1575	226	19	[	[	PUNCT
gs-1575	226	20	,	,	PUNCT
gs-1575	226	21	,	,	PUNCT
gs-1575	226	22	]	]	PUNCT
gs-1575	226	23	|	|	CCONJ
gs-1575	226	24	)	)	PUNCT
gs-1575	226	25	r	r	NOUN
gs-1575	226	26	n	n	CCONJ
gs-1575	226	27	n	n	CCONJ
gs-1575	226	28	n	n	NOUN
gs-1575	226	29	in	in	ADP
gs-1575	226	30	n	n	PROPN
gs-1575	226	31	in	in	ADP
gs-1575	226	32	n	n	PRON
gs-1575	226	33	n	n	NOUN
gs-1575	227	1	i	i	PRON
gs-1575	227	2	i	i	PRON
gs-1575	227	3	df	df	VERB
gs-1575	227	4	x	x	X
gs-1575	227	5	a	a	DET
gs-1575	227	6	e	e	X
gs-1575	227	7	e	e	NOUN
gs-1575	227	8	f	f	PROPN
gs-1575	227	9	x	x	PROPN
gs-1575	227	10	a	a	DET
gs-1575	227	11	ef	ef	X
gs-1575	227	12	x	x	PUNCT
gs-1575	227	13	a	a	DET
gs-1575	227	14	n	n	PROPN
gs-1575	227	15			PROPN
gs-1575	227	16			NOUN
gs-1575	227	17			X
gs-1575	227	18			ADJ
gs-1575	227	19			NOUN
gs-1575	227	20			NOUN
gs-1575	227	21			SYM
gs-1575	227	22			NOUN
gs-1575	227	23			SYM
gs-1575	227	24			NOUN
gs-1575	227	25	2	2	ADJ
gs-1575	227	26	2	2	NUM
gs-1575	227	27	1	1	NUM
gs-1575	227	28	1	1	NUM
gs-1575	227	29	ˆ	ˆ	NOUN
gs-1575	227	30	ˆ	ˆ	ADJ
gs-1575	227	31	{	{	PUNCT
gs-1575	227	32	(	(	PUNCT
gs-1575	227	33	)	)	PUNCT
gs-1575	227	34	(	(	PUNCT
gs-1575	227	35	[	[	PUNCT
gs-1575	227	36	,	,	PUNCT
gs-1575	227	37	,	,	PUNCT
gs-1575	227	38	]	]	PUNCT
gs-1575	227	39	|	|	ADV
gs-1575	227	40	)	)	PUNCT
gs-1575	227	41	}	}	PUNCT
gs-1575	227	42	r	r	NOUN
gs-1575	227	43	n	n	NOUN
gs-1575	227	44	in	in	ADP
gs-1575	227	45	n	n	PROPN
gs-1575	227	46	in	in	ADP
gs-1575	227	47	n	n	CCONJ
gs-1575	227	48	n	n	NOUN
gs-1575	228	1	i	i	PRON
gs-1575	228	2	i	i	INTJ
gs-1575	228	3	e	e	NOUN
gs-1575	229	1	e	e	NOUN
gs-1575	229	2	f	f	X
gs-1575	229	3	x	x	PROPN
gs-1575	229	4	a	a	DET
gs-1575	229	5	ef	ef	X
gs-1575	229	6	x	x	PUNCT
gs-1575	229	7	a	a	DET
gs-1575	229	8	n	n	ADV
gs-1575	229	9			ADJ
gs-1575	229	10			NOUN
gs-1575	229	11			NUM
gs-1575	229	12			NUM
gs-1575	229	13			NOUN
gs-1575	229	14			PROPN
gs-1575	229	15			NOUN
gs-1575	229	16			SYM
gs-1575	229	17			NOUN
gs-1575	229	18			PUNCT
gs-1575	229	19			NOUN
gs-1575	229	20			NOUN
gs-1575	229	21			PUNCT
gs-1575	229	22			PROPN
gs-1575	229	23			NOUN
gs-1575	230	1			PUNCT
gs-1575	230	2			NOUN
gs-1575	230	3			PROPN
gs-1575	230	4	2	2	NUM
gs-1575	230	5	2	2	NUM
gs-1575	230	6	(	(	PUNCT
gs-1575	230	7	)	)	PUNCT
gs-1575	230	8	(	(	PUNCT
gs-1575	230	9	)	)	PUNCT
gs-1575	230	10	1	1	NUM
gs-1575	230	11	1	1	NUM
gs-1575	230	12	1	1	NUM
gs-1575	230	13	{	{	PUNCT
gs-1575	230	14	(	(	PUNCT
gs-1575	230	15	)	)	PUNCT
gs-1575	230	16	(	(	PUNCT
gs-1575	230	17	[	[	PUNCT
gs-1575	230	18	(	(	PUNCT
gs-1575	230	19	)	)	PUNCT
gs-1575	230	20	]	]	PUNCT
gs-1575	230	21	|	|	ADV
gs-1575	230	22	)	)	PUNCT
gs-1575	230	23	}	}	PUNCT
gs-1575	231	1	n	n	CCONJ
gs-1575	231	2	m	m	VERB
gs-1575	231	3	m	m	VERB
gs-1575	231	4	ir	ir	PROPN
gs-1575	231	5	n	n	ADV
gs-1575	231	6	n	n	CCONJ
gs-1575	231	7	n	n	NOUN
gs-1575	232	1	i	i	PRON
gs-1575	232	2	n	n	VERB
gs-1575	233	1	i	i	PRON
gs-1575	233	2	n	n	CCONJ
gs-1575	234	1	i	i	PRON
gs-1575	234	2	mn	mn	VERB
gs-1575	235	1	i	i	PRON
gs-1575	235	2	a	a	DET
gs-1575	235	3	e	e	X
gs-1575	235	4	e	e	X
gs-1575	235	5	k	k	PROPN
gs-1575	235	6	a	a	X
gs-1575	235	7	x	x	X
gs-1575	235	8	x	x	SYM
gs-1575	235	9	ek	ek	NOUN
gs-1575	235	10	a	a	PRON
gs-1575	235	11	x	x	SYM
gs-1575	235	12	x	x	SYM
gs-1575	235	13	n	n	NUM
gs-1575	235	14	i	i	NOUN
gs-1575	235	15			PROPN
gs-1575	235	16			PROPN
gs-1575	235	17			PROPN
gs-1575	235	18			PROPN
gs-1575	235	19			PROPN
gs-1575	235	20			X
gs-1575	235	21			X
gs-1575	235	22			ADJ
gs-1575	236	1			PROPN
gs-1575	236	2			NOUN
gs-1575	236	3			ADJ
gs-1575	236	4			NOUN
gs-1575	236	5			ADJ
gs-1575	236	6			NOUN
gs-1575	236	7			SYM
gs-1575	236	8			NOUN
gs-1575	236	9			PUNCT
gs-1575	236	10			NOUN
gs-1575	237	1			NOUN
gs-1575	238	1			PUNCT
gs-1575	238	2			NOUN
gs-1575	238	3			PUNCT
gs-1575	238	4			NOUN
gs-1575	238	5			NOUN
gs-1575	239	1	2	2	ADJ
gs-1575	239	2	2	2	NUM
gs-1575	239	3	2	2	NUM
gs-1575	239	4	(	(	PUNCT
gs-1575	239	5	)	)	PUNCT
gs-1575	239	6	(	(	PUNCT
gs-1575	239	7	)	)	PUNCT
gs-1575	239	8	1	1	NUM
gs-1575	239	9	1	1	NUM
gs-1575	239	10	1	1	NUM
gs-1575	239	11	{	{	PUNCT
gs-1575	239	12	(	(	PUNCT
gs-1575	239	13	)	)	PUNCT
gs-1575	239	14	(	(	PUNCT
gs-1575	239	15	)	)	PUNCT
gs-1575	239	16	(	(	PUNCT
gs-1575	239	17	[	[	PUNCT
gs-1575	239	18	]	]	X
gs-1575	239	19	|	|	ADV
gs-1575	239	20	)	)	PUNCT
gs-1575	239	21	}	}	PUNCT
gs-1575	239	22	n	n	CCONJ
gs-1575	239	23	m	m	VERB
gs-1575	239	24	m	m	VERB
gs-1575	239	25	ir	ir	PROPN
gs-1575	239	26	n	n	ADV
gs-1575	239	27	n	n	CCONJ
gs-1575	239	28	n	n	NOUN
gs-1575	239	29	i	i	PRON
gs-1575	239	30	n	n	VERB
gs-1575	239	31	i	i	PRON
gs-1575	239	32	n	n	VERB
gs-1575	239	33	m	m	VERB
gs-1575	239	34	jn	jn	VERB
gs-1575	239	35	i	i	PRON
gs-1575	239	36	a	a	DET
gs-1575	239	37	e	e	X
gs-1575	239	38	e	e	X
gs-1575	239	39	k	k	PROPN
gs-1575	239	40	a	a	X
gs-1575	239	41	x	x	X
gs-1575	239	42	x	x	SYM
gs-1575	239	43	ek	ek	NOUN
gs-1575	239	44	a	a	PRON
gs-1575	239	45	x	x	SYM
gs-1575	239	46	x	x	SYM
gs-1575	239	47	n	n	NUM
gs-1575	239	48	i	i	NOUN
gs-1575	239	49			PROPN
gs-1575	239	50			PROPN
gs-1575	239	51			PROPN
gs-1575	239	52			PROPN
gs-1575	239	53			PROPN
gs-1575	239	54			X
gs-1575	239	55			X
gs-1575	239	56			ADJ
gs-1575	239	57			PROPN
gs-1575	239	58			NOUN
gs-1575	239	59			ADJ
gs-1575	239	60			NOUN
gs-1575	239	61			ADJ
gs-1575	239	62			NOUN
gs-1575	239	63			PUNCT
gs-1575	239	64			NOUN
gs-1575	240	1			NOUN
gs-1575	240	2			PUNCT
gs-1575	240	3			PROPN
gs-1575	240	4			NOUN
gs-1575	241	1			PROPN
gs-1575	241	2	1	1	NUM
gs-1575	241	3	1	1	NUM
gs-1575	241	4	2	2	NUM
gs-1575	241	5	2	2	NUM
gs-1575	241	6	(	(	PUNCT
gs-1575	241	7	)	)	PUNCT
gs-1575	241	8	(	(	PUNCT
gs-1575	241	9	)	)	PUNCT
gs-1575	241	10	12	12	NUM
gs-1575	241	11	1	1	NUM
gs-1575	241	12	{	{	PUNCT
gs-1575	241	13	(	(	PUNCT
gs-1575	241	14	[	[	PUNCT
gs-1575	241	15	]	]	X
gs-1575	241	16	|	|	ADV
gs-1575	241	17	)	)	PUNCT
gs-1575	241	18	}	}	PUNCT
gs-1575	242	1	r	r	NOUN
gs-1575	242	2	n	n	NUM
gs-1575	242	3	n	n	CCONJ
gs-1575	242	4	n	n	NOUN
gs-1575	242	5	i	i	PRON
gs-1575	242	6	n	n	VERB
gs-1575	242	7	i	i	PRON
gs-1575	242	8	n	n	VERB
gs-1575	242	9	i	i	PRON
gs-1575	242	10	a	a	X
gs-1575	242	11	e	e	X
gs-1575	242	12	e	e	X
gs-1575	242	13	i	i	NOUN
gs-1575	242	14	e	e	PROPN
gs-1575	242	15	k	k	PROPN
gs-1575	242	16	a	a	X
gs-1575	242	17	x	x	X
gs-1575	242	18	x	x	SYM
gs-1575	242	19	ek	ek	NOUN
gs-1575	242	20	a	a	DET
gs-1575	242	21	x	x	NOUN
gs-1575	242	22	x	x	SYM
gs-1575	242	23	n	n	ADJ
gs-1575	242	24			PROPN
gs-1575	242	25			PROPN
gs-1575	242	26			PROPN
gs-1575	242	27			PROPN
gs-1575	242	28			PROPN
gs-1575	243	1			NOUN
gs-1575	243	2			VERB
gs-1575	243	3			NOUN
gs-1575	243	4			PROPN
gs-1575	243	5			PROPN
gs-1575	244	1			PROPN
gs-1575	244	2			PROPN
gs-1575	244	3			NOUN
gs-1575	245	1			PUNCT
gs-1575	245	2			NOUN
gs-1575	245	3	2	2	ADJ
gs-1575	245	4	2	2	NUM
gs-1575	245	5	1	1	NUM
gs-1575	245	6	[	[	PUNCT
gs-1575	245	7	(	(	PUNCT
gs-1575	245	8	)	)	PUNCT
gs-1575	245	9	]	]	PUNCT
gs-1575	245	10	(	(	PUNCT
gs-1575	245	11	)	)	PUNCT
gs-1575	245	12	(	(	PUNCT
gs-1575	245	13	)	)	PUNCT
gs-1575	245	14	r	r	NOUN
gs-1575	245	15	nn	nn	PROPN
gs-1575	245	16	n	n	CCONJ
gs-1575	245	17	n	n	NOUN
gs-1575	245	18	i	i	PRON
gs-1575	246	1	i	i	PRON
gs-1575	247	1	i	i	PRON
gs-1575	247	2	ia	ia	VERB
gs-1575	248	1	k	k	PROPN
gs-1575	248	2	a	a	X
gs-1575	248	3	x	x	X
gs-1575	248	4	u	u	X
gs-1575	248	5	k	k	PROPN
gs-1575	248	6	a	a	X
gs-1575	248	7	x	x	X
gs-1575	248	8	y	y	NOUN
gs-1575	248	9	f	f	PROPN
gs-1575	248	10	y	y	PROPN
gs-1575	248	11	dy	dy	PROPN
gs-1575	248	12	f	f	PROPN
gs-1575	248	13	u	u	PROPN
gs-1575	248	14	due	due	ADJ
gs-1575	248	15	n	n	CCONJ
gs-1575	248	16	n	n	PRON
gs-1575	248	17			VERB
gs-1575	248	18			VERB
gs-1575	248	19			NUM
gs-1575	248	20			NOUN
gs-1575	248	21			NUM
gs-1575	249	1			NUM
gs-1575	249	2			PROPN
gs-1575	249	3			PROPN
gs-1575	249	4			PROPN
gs-1575	249	5			X
gs-1575	249	6			PUNCT
gs-1575	249	7			PROPN
gs-1575	249	8	apply	apply	VERB
gs-1575	249	9	equation	equation	NOUN
gs-1575	249	10			NOUN
gs-1575	249	11	n	n	PROPN
gs-1575	249	12	i	i	PRON
gs-1575	250	1	i	i	VERB
gs-1575	251	1	e	e	VERB
gs-1575	252	1	p	p	NOUN
gs-1575	253	1	n	n	CCONJ
gs-1575	254	1			NOUN
gs-1575	255	1			NUM
gs-1575	255	2	again	again	ADV
gs-1575	255	3	.	.	PUNCT
gs-1575	256	1	let	let	VERB
gs-1575	256	2	's	us	PRON
gs-1575	256	3	apply	apply	VERB
gs-1575	256	4	the	the	DET
gs-1575	256	5	same	same	ADJ
gs-1575	256	6	variable	variable	ADJ
gs-1575	256	7	transformation	transformation	NOUN
gs-1575	256	8	inside	inside	ADP
gs-1575	256	9	the	the	DET
gs-1575	256	10	integral	integral	ADJ
gs-1575	256	11	sign	sign	NOUN
gs-1575	256	12	as	as	SCONJ
gs-1575	256	13	when	when	SCONJ
gs-1575	256	14	considering	consider	VERB
gs-1575	256	15	the	the	DET
gs-1575	256	16	expression	expression	NOUN
gs-1575	256	17			NOUN
gs-1575	256	18	ˆ	ˆ	NOUN
gs-1575	256	19	,	,	PUNCT
gs-1575	256	20	n	n	NOUN
gs-1575	256	21	nef	nef	PROPN
gs-1575	256	22	x	x	X
gs-1575	256	23	a	a	PROPN
gs-1575	256	24	.	.	PUNCT
gs-1575	256	25	will	will	AUX
gs-1575	256	26	be	be	AUX
gs-1575	256	27	obtained	obtain	VERB
gs-1575	256	28	the	the	DET
gs-1575	256	29	equality	equality	NOUN
gs-1575	256	30			NOUN
gs-1575	256	31			PUNCT
gs-1575	256	32			NOUN
gs-1575	257	1			NOUN
gs-1575	258	1			PROPN
gs-1575	259	1	2	2	NUM
gs-1575	259	2	1	1	NUM
gs-1575	259	3	ˆ	ˆ	NOUN
gs-1575	259	4	,	,	PUNCT
gs-1575	259	5	[	[	PUNCT
gs-1575	259	6	(	(	PUNCT
gs-1575	259	7	)	)	PUNCT
gs-1575	259	8	(	(	PUNCT
gs-1575	259	9	)	)	PUNCT
gs-1575	259	10	]	]	PUNCT
gs-1575	259	11	(	(	PUNCT
gs-1575	259	12	)	)	PUNCT
gs-1575	259	13	r	r	NOUN
gs-1575	259	14	n	n	CCONJ
gs-1575	259	15	n	n	CCONJ
gs-1575	259	16	n	n	NOUN
gs-1575	259	17	i	i	PRON
gs-1575	260	1	n	n	VERB
gs-1575	260	2	i	i	PRON
gs-1575	261	1	i	i	PRON
gs-1575	261	2	i	i	VERB
gs-1575	261	3	n	n	VERB
gs-1575	261	4	a	a	DET
gs-1575	261	5	t	t	NOUN
gs-1575	261	6	df	df	NOUN
gs-1575	261	7	x	x	PUNCT
gs-1575	262	1	a	a	PRON
gs-1575	262	2	p	p	X
gs-1575	262	3	k	k	PROPN
gs-1575	262	4	t	t	PROPN
gs-1575	263	1	k	k	PROPN
gs-1575	263	2	a	a	X
gs-1575	263	3	x	x	X
gs-1575	263	4	y	y	NOUN
gs-1575	263	5	f	f	PROPN
gs-1575	263	6	y	y	PROPN
gs-1575	263	7	dy	dy	NOUN
gs-1575	263	8	f	f	PROPN
gs-1575	263	9	x	x	X
gs-1575	263	10	dt	dt	X
gs-1575	263	11	n	n	CCONJ
gs-1575	263	12	a	a	DET
gs-1575	263	13			NOUN
gs-1575	263	14			VERB
gs-1575	263	15			NUM
gs-1575	263	16			NOUN
gs-1575	263	17			NUM
gs-1575	263	18			NUM
gs-1575	263	19			PROPN
gs-1575	263	20			NOUN
gs-1575	263	21			NOUN
gs-1575	263	22			PUNCT
gs-1575	263	23			X
gs-1575	263	24	.	.	PUNCT
gs-1575	264	1	considering	consider	VERB
gs-1575	264	2	the	the	DET
gs-1575	264	3	properties	property	NOUN
gs-1575	264	4	of	of	ADP
gs-1575	264	5	(	(	PUNCT
gs-1575	264	6	)	)	PUNCT
gs-1575	264	7	k	k	NOUN
gs-1575	264	8	x	x	PUNCT
gs-1575	264	9	and	and	CCONJ
gs-1575	264	10	equalities	equality	NOUN
gs-1575	264	11	(	(	PUNCT
gs-1575	264	12	2	2	NUM
gs-1575	264	13	)	)	PUNCT
gs-1575	264	14	,	,	PUNCT
gs-1575	264	15	it	it	PRON
gs-1575	264	16	is	be	AUX
gs-1575	264	17	clear	clear	ADJ
gs-1575	264	18	that	that	SCONJ
gs-1575	264	19			NOUN
gs-1575	264	20	ˆ	ˆ	NOUN
gs-1575	264	21	,	,	PUNCT
gs-1575	264	22	n	n	CCONJ
gs-1575	264	23	ndf	ndf	NOUN
gs-1575	264	24	x	x	X
gs-1575	264	25	a	a	PRON
gs-1575	264	26	is	be	AUX
gs-1575	264	27	finite	finite	ADJ
gs-1575	264	28	.	.	PUNCT
gs-1575	265	1	let	let	VERB
gs-1575	265	2	's	us	PRON
gs-1575	265	3	estimate	estimate	VERB
gs-1575	265	4	(	(	PUNCT
gs-1575	265	5	)	)	PUNCT
gs-1575	265	6	nej	nej	NOUN
gs-1575	265	7	a	a	DET
gs-1575	265	8	.	.	NOUN
gs-1575	265	9	1	1	NUM
gs-1575	265	10	ˆ	ˆ	NOUN
gs-1575	265	11	(	(	PUNCT
gs-1575	265	12	)	)	PUNCT
gs-1575	265	13	[	[	PUNCT
gs-1575	265	14	(	(	PUNCT
gs-1575	265	15	(	(	PUNCT
gs-1575	265	16	,	,	PUNCT
gs-1575	265	17	)	)	PUNCT
gs-1575	265	18	(	(	PUNCT
gs-1575	265	19	)	)	PUNCT
gs-1575	265	20	|	|	ADV
gs-1575	265	21	)	)	PUNCT
gs-1575	265	22	]	]	PUNCT
gs-1575	265	23	n	n	CCONJ
gs-1575	265	24	n	n	PRON
gs-1575	265	25	n	n	ADV
gs-1575	265	26	nej	nej	VERB
gs-1575	265	27	a	a	DET
gs-1575	265	28	e	e	NOUN
gs-1575	265	29	e	e	X
gs-1575	265	30	f	f	X
gs-1575	265	31	x	x	PROPN
gs-1575	265	32	a	a	DET
gs-1575	265	33	f	f	X
gs-1575	265	34	x	x	SYM
gs-1575	265	35	dx	dx	PROPN
gs-1575	265	36			VERB
gs-1575	265	37			VERB
gs-1575	265	38			NUM
gs-1575	265	39			NOUN
gs-1575	265	40			PROPN
gs-1575	265	41			NOUN
gs-1575	265	42	1	1	NUM
gs-1575	265	43	1	1	NUM
gs-1575	265	44	1	1	NUM
gs-1575	265	45	(	(	PUNCT
gs-1575	265	46	)	)	PUNCT
gs-1575	265	47	ˆ	ˆ	NOUN
gs-1575	265	48	[	[	PUNCT
gs-1575	265	49	(	(	PUNCT
gs-1575	265	50	(	(	PUNCT
gs-1575	265	51	,	,	PUNCT
gs-1575	265	52	)	)	PUNCT
gs-1575	265	53	(	(	PUNCT
gs-1575	265	54	)	)	PUNCT
gs-1575	265	55	)	)	PUNCT
gs-1575	265	56	]	]	PUNCT
gs-1575	266	1	r	r	NOUN
gs-1575	266	2	r	r	NOUN
gs-1575	266	3	n	n	NOUN
gs-1575	266	4	in	in	ADP
gs-1575	266	5	n	n	PRON
gs-1575	266	6	i	i	PRON
gs-1575	266	7	i	i	PRON
gs-1575	266	8	n	n	VERB
gs-1575	267	1	i	i	PRON
gs-1575	267	2	i	i	PRON
gs-1575	268	1	i	i	INTJ
gs-1575	268	2	i	i	VERB
gs-1575	268	3	e	e	VERB
gs-1575	269	1	e	e	NOUN
gs-1575	269	2	f	f	X
gs-1575	269	3	x	x	PROPN
gs-1575	269	4	a	a	PRON
gs-1575	269	5	p	p	X
gs-1575	269	6	f	f	X
gs-1575	269	7	x	x	X
gs-1575	269	8	dx	dx	PROPN
gs-1575	269	9	a	a	DET
gs-1575	269	10	n	n	X
gs-1575	269	11			VERB
gs-1575	269	12			PROPN
gs-1575	269	13			NOUN
gs-1575	269	14			NOUN
gs-1575	269	15			VERB
gs-1575	269	16			CCONJ
gs-1575	269	17			NOUN
gs-1575	269	18			NOUN
gs-1575	269	19			NOUN
gs-1575	269	20	(	(	PUNCT
gs-1575	269	21	10	10	NUM
gs-1575	269	22	)	)	PUNCT
gs-1575	269	23	each	each	DET
gs-1575	269	24	summand	summand	PROPN
gs-1575	269	25	ia	ia	PROPN
gs-1575	269	26	is	be	AUX
gs-1575	269	27	estimated	estimate	VERB
gs-1575	269	28	in	in	ADP
gs-1575	269	29	the	the	DET
gs-1575	269	30	same	same	ADJ
gs-1575	269	31	way	way	NOUN
gs-1575	269	32	.	.	PUNCT
gs-1575	270	1	1	1	NUM
gs-1575	270	2	(	(	PUNCT
gs-1575	270	3	)	)	PUNCT
gs-1575	270	4	ˆ	ˆ	NOUN
gs-1575	270	5	[	[	PUNCT
gs-1575	270	6	(	(	PUNCT
gs-1575	270	7	(	(	PUNCT
gs-1575	270	8	,	,	PUNCT
gs-1575	270	9	)	)	PUNCT
gs-1575	270	10	(	(	PUNCT
gs-1575	270	11	)	)	PUNCT
gs-1575	270	12	)	)	PUNCT
gs-1575	271	1	]	]	PUNCT
gs-1575	271	2	n	n	X
gs-1575	271	3	i	i	PRON
gs-1575	271	4	in	in	ADP
gs-1575	271	5	n	n	CCONJ
gs-1575	271	6	i	i	PRON
gs-1575	271	7	i	i	PRON
gs-1575	271	8	n	n	VERB
gs-1575	271	9	i	i	PRON
gs-1575	271	10	a	a	X
gs-1575	271	11	e	e	X
gs-1575	271	12	e	e	X
gs-1575	271	13	f	f	X
gs-1575	271	14	x	x	PROPN
gs-1575	271	15	a	a	DET
gs-1575	271	16	p	p	X
gs-1575	271	17	f	f	X
gs-1575	271	18	x	x	SYM
gs-1575	271	19	dx	dx	PROPN
gs-1575	271	20	n	n	PRON
gs-1575	271	21			VERB
gs-1575	271	22			VERB
gs-1575	271	23			NUM
gs-1575	271	24			NOUN
gs-1575	271	25			NUM
gs-1575	271	26			ADJ
gs-1575	271	27			NOUN
gs-1575	271	28	1	1	NUM
gs-1575	271	29	1	1	NUM
gs-1575	271	30	(	(	PUNCT
gs-1575	271	31	)	)	PUNCT
gs-1575	271	32	(	(	PUNCT
gs-1575	271	33	)	)	PUNCT
gs-1575	271	34	(	(	PUNCT
gs-1575	271	35	)	)	PUNCT
gs-1575	271	36	ˆ	ˆ	X
gs-1575	271	37	[	[	PUNCT
gs-1575	271	38	(	(	PUNCT
gs-1575	271	39	(	(	PUNCT
gs-1575	271	40	,	,	PUNCT
gs-1575	271	41	)	)	PUNCT
gs-1575	271	42	(	(	PUNCT
gs-1575	271	43	)	)	PUNCT
gs-1575	271	44	)	)	PUNCT
gs-1575	271	45	]	]	PUNCT
gs-1575	272	1	[	[	PUNCT
gs-1575	272	2	(	(	PUNCT
gs-1575	272	3	(	(	PUNCT
gs-1575	272	4	)	)	PUNCT
gs-1575	272	5	(	(	PUNCT
gs-1575	272	6	)	)	PUNCT
gs-1575	272	7	)	)	PUNCT
gs-1575	272	8	]	]	PUNCT
gs-1575	272	9	n	n	CCONJ
gs-1575	272	10	n	n	PRON
gs-1575	272	11	n	n	NOUN
gs-1575	272	12	in	in	ADP
gs-1575	272	13	n	n	PRON
gs-1575	272	14	i	i	PRON
gs-1575	272	15	n	n	VERB
gs-1575	273	1	i	i	PRON
gs-1575	274	1	i	i	PRON
gs-1575	275	1	i	i	PRON
gs-1575	276	1	n	n	VERB
gs-1575	277	1	i	i	PRON
gs-1575	278	1	i	i	INTJ
gs-1575	278	2	i	i	VERB
gs-1575	278	3	e	e	VERB
gs-1575	279	1	e	e	NOUN
gs-1575	279	2	f	f	X
gs-1575	279	3	x	x	PROPN
gs-1575	279	4	a	a	DET
gs-1575	279	5	f	f	X
gs-1575	279	6	x	x	X
gs-1575	279	7	dx	dx	PROPN
gs-1575	279	8	e	e	PROPN
gs-1575	279	9	e	e	NOUN
gs-1575	279	10	f	f	PROPN
gs-1575	279	11	x	x	X
gs-1575	279	12	p	p	X
gs-1575	279	13	f	f	X
gs-1575	279	14	x	x	X
gs-1575	279	15	dx	dx	PROPN
gs-1575	279	16	n	n	CCONJ
gs-1575	279	17	n	n	CCONJ
gs-1575	279	18	n	n	CCONJ
gs-1575	279	19			ADV
gs-1575	279	20			ADJ
gs-1575	279	21			ADJ
gs-1575	279	22			NOUN
gs-1575	279	23			NOUN
gs-1575	279	24			VERB
gs-1575	279	25			VERB
gs-1575	279	26			NOUN
gs-1575	279	27			NOUN
gs-1575	279	28			NOUN
gs-1575	279	29			NOUN
gs-1575	279	30			VERB
gs-1575	279	31			NOUN
gs-1575	279	32			NUM
gs-1575	279	33			PUNCT
gs-1575	279	34	georgian	georgian	PROPN
gs-1575	279	35	scientists/ქართველი	scientists/ქართველი	PROPN
gs-1575	279	36	მეცნიერები	მეცნიერები	NOUN
gs-1575	279	37	ტ.	ტ.	VERB
gs-1575	279	38	5	5	NUM
gs-1575	279	39	n	n	PRON
gs-1575	279	40	1	1	NUM
gs-1575	279	41	,	,	PUNCT
gs-1575	279	42	2023	2023	NUM
gs-1575	279	43	315	315	NUM
gs-1575	279	44	1	1	NUM
gs-1575	279	45	1	1	NUM
gs-1575	279	46	1	1	NUM
gs-1575	279	47	2	2	NUM
gs-1575	279	48	(	(	PUNCT
gs-1575	279	49	)	)	PUNCT
gs-1575	279	50	(	(	PUNCT
gs-1575	279	51	)	)	PUNCT
gs-1575	279	52	ˆ	ˆ	X
gs-1575	279	53	{	{	PUNCT
gs-1575	279	54	[	[	PUNCT
gs-1575	279	55	(	(	PUNCT
gs-1575	279	56	,	,	PUNCT
gs-1575	279	57	)	)	PUNCT
gs-1575	279	58	(	(	PUNCT
gs-1575	279	59	)	)	PUNCT
gs-1575	279	60	]	]	PUNCT
gs-1575	279	61	}	}	PUNCT
gs-1575	279	62	{	{	PUNCT
gs-1575	279	63	[	[	PUNCT
gs-1575	279	64	(	(	PUNCT
gs-1575	279	65	)	)	PUNCT
gs-1575	279	66	]	]	X
gs-1575	279	67	}	}	PUNCT
gs-1575	279	68	n	n	CCONJ
gs-1575	279	69	n	n	NOUN
gs-1575	279	70	in	in	ADP
gs-1575	279	71	n	n	PRON
gs-1575	279	72	i	i	PRON
gs-1575	280	1	n	n	VERB
gs-1575	281	1	i	i	PRON
gs-1575	282	1	i	i	PRON
gs-1575	283	1	n	n	VERB
gs-1575	284	1	i	i	PRON
gs-1575	285	1	i	i	PRON
gs-1575	286	1	i	i	INTJ
gs-1575	286	2	i	i	VERB
gs-1575	286	3	e	e	VERB
gs-1575	287	1	e	e	NOUN
gs-1575	287	2	f	f	X
gs-1575	287	3	x	x	PROPN
gs-1575	287	4	a	a	DET
gs-1575	287	5	f	f	X
gs-1575	287	6	x	x	X
gs-1575	287	7	dx	dx	PROPN
gs-1575	287	8	e	e	PROPN
gs-1575	287	9	e	e	NOUN
gs-1575	287	10	p	p	X
gs-1575	287	11	f	f	PROPN
gs-1575	287	12	x	x	X
gs-1575	287	13	dx	dx	PROPN
gs-1575	287	14	a	a	DET
gs-1575	287	15	a	a	PROPN
gs-1575	287	16	n	n	CCONJ
gs-1575	287	17	n	n	ADV
gs-1575	287	18			ADJ
gs-1575	287	19			ADJ
gs-1575	287	20			NOUN
gs-1575	287	21			NOUN
gs-1575	287	22			VERB
gs-1575	287	23			VERB
gs-1575	287	24			NOUN
gs-1575	287	25			NOUN
gs-1575	287	26			NOUN
gs-1575	287	27			NOUN
gs-1575	287	28			VERB
gs-1575	287	29			PROPN
gs-1575	287	30			PROPN
gs-1575	287	31			NOUN
gs-1575	287	32			SYM
gs-1575	287	33			NOUN
gs-1575	287	34	ˆ	ˆ	NOUN
gs-1575	287	35	,	,	PUNCT
gs-1575	287	36	in	in	ADP
gs-1575	287	37	nf	nf	NUM
gs-1575	287	38	x	x	DET
gs-1575	287	39	a	a	PRON
gs-1575	287	40	is	be	AUX
gs-1575	287	41	a	a	DET
gs-1575	287	42	density	density	NOUN
gs-1575	287	43	estimate	estimate	NOUN
gs-1575	287	44	(	(	PUNCT
gs-1575	287	45	)	)	PUNCT
gs-1575	287	46	if	if	SCONJ
gs-1575	287	47	x	x	PRON
gs-1575	287	48	constructed	construct	VERB
gs-1575	287	49	from	from	ADP
gs-1575	287	50	independent	independent	ADJ
gs-1575	287	51	and	and	CCONJ
gs-1575	287	52	identically	identically	ADV
gs-1575	287	53	distributed	distribute	VERB
gs-1575	287	54	observations	observation	NOUN
gs-1575	287	55	on	on	ADP
gs-1575	287	56	a	a	DET
gs-1575	287	57	fixed	fix	VERB
gs-1575	287	58	trajectory	trajectory	NOUN
gs-1575	287	59	1n	1n	PROPN
gs-1575	287	60	.	.	PUNCT
gs-1575	288	1	to	to	PART
gs-1575	288	2	estimate	estimate	VERB
gs-1575	288	3	the	the	DET
gs-1575	288	4	quantity	quantity	NOUN
gs-1575	288	5	1	1	NUM
gs-1575	288	6	ˆ	ˆ	NOUN
gs-1575	288	7	[	[	PUNCT
gs-1575	288	8	(	(	PUNCT
gs-1575	288	9	,	,	PUNCT
gs-1575	288	10	)	)	PUNCT
gs-1575	288	11	(	(	PUNCT
gs-1575	288	12	)	)	PUNCT
gs-1575	288	13	]	]	PUNCT
gs-1575	288	14	}	}	PUNCT
gs-1575	288	15	in	in	ADP
gs-1575	288	16	n	n	PROPN
gs-1575	288	17	i	i	NOUN
gs-1575	288	18	ne	ne	PROPN
gs-1575	288	19	f	f	PROPN
gs-1575	288	20	x	x	X
gs-1575	288	21	a	a	DET
gs-1575	288	22	f	f	X
gs-1575	288	23	x	x	SYM
gs-1575	288	24	dx	dx	PROPN
gs-1575	288	25			NOUN
gs-1575	288	26			VERB
gs-1575	288	27			NOUN
gs-1575	288	28			NOUN
gs-1575	288	29	,	,	PUNCT
gs-1575	288	30	we	we	PRON
gs-1575	288	31	apply	apply	VERB
gs-1575	288	32	inequality	inequality	NOUN
gs-1575	288	33	(	(	PUNCT
gs-1575	288	34	3	3	NUM
gs-1575	288	35	)	)	PUNCT
gs-1575	288	36	.	.	PUNCT
gs-1575	289	1	1	1	NUM
gs-1575	289	2	1	1	NUM
gs-1575	289	3	(	(	PUNCT
gs-1575	289	4	)	)	PUNCT
gs-1575	289	5	ˆ	ˆ	NOUN
gs-1575	289	6	{	{	PUNCT
gs-1575	289	7	[	[	PUNCT
gs-1575	289	8	(	(	PUNCT
gs-1575	289	9	,	,	PUNCT
gs-1575	289	10	)	)	PUNCT
gs-1575	289	11	(	(	PUNCT
gs-1575	289	12	)	)	PUNCT
gs-1575	289	13	]	]	PUNCT
gs-1575	289	14	}	}	PUNCT
gs-1575	289	15	n	n	X
gs-1575	289	16	i	i	PRON
gs-1575	289	17	in	in	ADP
gs-1575	289	18	n	n	PROPN
gs-1575	289	19	i	i	PRON
gs-1575	289	20	n	n	VERB
gs-1575	289	21	i	i	PRON
gs-1575	289	22	a	a	X
gs-1575	289	23	e	e	X
gs-1575	289	24	e	e	X
gs-1575	289	25	f	f	X
gs-1575	289	26	x	x	PROPN
gs-1575	289	27	a	a	PRON
gs-1575	289	28	f	f	X
gs-1575	289	29	x	x	SYM
gs-1575	289	30	dx	dx	PROPN
gs-1575	289	31	n	n	CCONJ
gs-1575	289	32			ADJ
gs-1575	289	33			NOUN
gs-1575	289	34			VERB
gs-1575	289	35			VERB
gs-1575	289	36			NUM
gs-1575	289	37			NOUN
gs-1575	289	38			ADP
gs-1575	289	39			NOUN
gs-1575	289	40			PUNCT
gs-1575	289	41			NOUN
gs-1575	289	42			SYM
gs-1575	289	43			NOUN
gs-1575	289	44			PROPN
gs-1575	289	45	(	(	PUNCT
gs-1575	289	46	)	)	PUNCT
gs-1575	289	47	1	1	NUM
gs-1575	289	48	1	1	NUM
gs-1575	289	49	{	{	PUNCT
gs-1575	289	50	[	[	PUNCT
gs-1575	289	51	(	(	PUNCT
gs-1575	289	52	(	(	PUNCT
gs-1575	289	53	)	)	PUNCT
gs-1575	289	54	)	)	PUNCT
gs-1575	289	55	(	(	PUNCT
gs-1575	289	56	)	)	PUNCT
gs-1575	289	57	|	|	ADV
gs-1575	289	58	]	]	X
gs-1575	289	59	}	}	PUNCT
gs-1575	289	60	n	n	CCONJ
gs-1575	289	61	m	m	VERB
gs-1575	289	62	i	i	VERB
gs-1575	289	63	n	n	VERB
gs-1575	289	64	n	n	CCONJ
gs-1575	289	65	n	n	NOUN
gs-1575	290	1	i	i	PRON
gs-1575	290	2	i	i	PRON
gs-1575	290	3	n	n	VERB
gs-1575	290	4	mn	mn	NOUN
gs-1575	291	1	i	i	PRON
gs-1575	291	2	a	a	DET
gs-1575	291	3	e	e	X
gs-1575	291	4	e	e	X
gs-1575	291	5	k	k	PROPN
gs-1575	291	6	a	a	X
gs-1575	291	7	x	x	X
gs-1575	291	8	x	x	SYM
gs-1575	291	9	f	f	X
gs-1575	291	10	x	x	X
gs-1575	291	11	dx	dx	PROPN
gs-1575	292	1	n	n	INTJ
gs-1575	292	2	i	i	PRON
gs-1575	292	3			INTJ
gs-1575	292	4			NOUN
gs-1575	292	5			ADJ
gs-1575	292	6			CCONJ
gs-1575	292	7			ADJ
gs-1575	292	8			PROPN
gs-1575	292	9			NOUN
gs-1575	292	10			PROPN
gs-1575	292	11			PROPN
gs-1575	292	12			PROPN
gs-1575	292	13			ADP
gs-1575	292	14			NOUN
gs-1575	292	15			SYM
gs-1575	292	16			NOUN
gs-1575	292	17			SYM
gs-1575	292	18			NOUN
gs-1575	292	19			PROPN
gs-1575	292	20	2	2	NUM
gs-1575	292	21	0	0	NUM
gs-1575	292	22	2	2	NUM
gs-1575	292	23	1	1	NUM
gs-1575	292	24	{	{	PUNCT
gs-1575	292	25	[	[	PUNCT
gs-1575	292	26	(	(	PUNCT
gs-1575	292	27	)	)	PUNCT
gs-1575	292	28	sup	sup	NOUN
gs-1575	292	29	(	(	PUNCT
gs-1575	292	30	)	)	PUNCT
gs-1575	292	31	(	(	PUNCT
gs-1575	292	32	)	)	PUNCT
gs-1575	292	33	]	]	X
gs-1575	292	34	}	}	PUNCT
gs-1575	292	35	2	2	NUM
gs-1575	292	36	(	(	PUNCT
gs-1575	292	37	)	)	PUNCT
gs-1575	292	38	n	n	CCONJ
gs-1575	292	39	n	n	CCONJ
gs-1575	292	40	n	n	ADV
gs-1575	293	1	i	i	PRON
gs-1575	293	2	a	a	PRON
gs-1575	293	3	an	an	DET
gs-1575	293	4	n	n	NOUN
gs-1575	293	5	n	n	NOUN
gs-1575	294	1	i	i	PRON
gs-1575	294	2	a	a	PRON
gs-1575	294	3	a	a	DET
gs-1575	294	4	e	e	NOUN
gs-1575	294	5	f	f	X
gs-1575	294	6	x	x	X
gs-1575	294	7	dx	dx	PROPN
gs-1575	294	8	f	f	PROPN
gs-1575	294	9	x	x	X
gs-1575	294	10	dx	dx	PROPN
gs-1575	294	11	o	o	INTJ
gs-1575	295	1	n	n	CCONJ
gs-1575	295	2	i	i	PRON
gs-1575	296	1	a	a	PRON
gs-1575	296	2	i	i	PRON
gs-1575	296	3			ADJ
gs-1575	297	1			NOUN
gs-1575	297	2			NOUN
gs-1575	297	3			PROPN
gs-1575	297	4			ADJ
gs-1575	297	5			ADJ
gs-1575	297	6			ADJ
gs-1575	297	7			PROPN
gs-1575	297	8			VERB
gs-1575	297	9			ADJ
gs-1575	297	10			NOUN
gs-1575	297	11			PROPN
gs-1575	297	12			PUNCT
gs-1575	297	13			PROPN
gs-1575	297	14			PROPN
gs-1575	297	15			PUNCT
gs-1575	297	16	according	accord	VERB
gs-1575	297	17	to	to	ADP
gs-1575	297	18	the	the	DET
gs-1575	297	19	condition	condition	NOUN
gs-1575	297	20	of	of	ADP
gs-1575	297	21	theorem	theorem	NOUN
gs-1575	297	22	(	(	PUNCT
gs-1575	297	23	6	6	NUM
gs-1575	297	24	)	)	PUNCT
gs-1575	297	25	,	,	PUNCT
gs-1575	297	26	the	the	DET
gs-1575	297	27	equations	equation	NOUN
gs-1575	297	28	are	be	AUX
gs-1575	297	29	fulfilled	fulfil	VERB
gs-1575	297	30			NOUN
gs-1575	297	31	n	n	PROPN
gs-1575	298	1	i	i	PRON
gs-1575	298	2	i	i	VERB
gs-1575	298	3	e	e	VERB
gs-1575	298	4	p	p	NOUN
gs-1575	298	5	n	n	ADV
gs-1575	298	6			NOUN
gs-1575	299	1			INTJ
gs-1575	299	2	,	,	PUNCT
gs-1575	299	3			PROPN
gs-1575	299	4			PROPN
gs-1575	299	5	lim	lim	PROPN
gs-1575	299	6	n	n	CCONJ
gs-1575	299	7	i	i	PRON
gs-1575	299	8	n	n	VERB
gs-1575	300	1	i	i	PRON
gs-1575	300	2	p	p	NOUN
gs-1575	300	3	n	n	CCONJ
gs-1575	300	4			NOUN
gs-1575	300	5			NOUN
gs-1575	300	6			ADJ
gs-1575	300	7	.	.	PUNCT
gs-1575	301	1	therefore	therefore	ADV
gs-1575	301	2			NOUN
gs-1575	301	3			PROPN
gs-1575	301	4	~n	~n	NUM
gs-1575	301	5	ii	ii	NOUN
gs-1575	301	6	np	np	PROPN
gs-1575	301	7	and	and	CCONJ
gs-1575	301	8	accordingly	accordingly	ADV
gs-1575	301	9	we	we	PRON
gs-1575	301	10	have	have	VERB
gs-1575	301	11	equality	equality	NOUN
gs-1575	301	12	.	.	PUNCT
gs-1575	302	1			NOUN
gs-1575	302	2			PROPN
gs-1575	302	3	n	n	CCONJ
gs-1575	302	4	n	n	CCONJ
gs-1575	302	5	n	n	ADV
gs-1575	302	6	a	a	PRON
gs-1575	302	7	a	a	DET
gs-1575	302	8	o	o	NOUN
gs-1575	302	9	o	o	NOUN
gs-1575	303	1	i	i	PRON
gs-1575	303	2	n	n	VERB
gs-1575	303	3			NOUN
gs-1575	303	4			PROPN
gs-1575	303	5			NOUN
gs-1575	303	6			PROPN
gs-1575	303	7			PUNCT
gs-1575	304	1			PROPN
gs-1575	304	2			PROPN
gs-1575	304	3			NOUN
gs-1575	304	4			PROPN
gs-1575	305	1			ADJ
gs-1575	305	2			NOUN
gs-1575	305	3			NOUN
gs-1575	305	4	.	.	PUNCT
gs-1575	306	1	the	the	DET
gs-1575	306	2	following	follow	VERB
gs-1575	306	3	assessment	assessment	NOUN
gs-1575	306	4	of	of	ADP
gs-1575	306	5	the	the	DET
gs-1575	306	6	summand	summand	NOUN
gs-1575	306	7	1ia	1ia	NOUN
gs-1575	306	8	is	be	AUX
gs-1575	306	9	valid	valid	ADJ
gs-1575	306	10			NOUN
gs-1575	306	11			SYM
gs-1575	306	12			NOUN
gs-1575	306	13	1	1	VERB
gs-1575	306	14	2	2	NUM
gs-1575	306	15	0	0	NUM
gs-1575	306	16	2	2	NUM
gs-1575	306	17	(	(	PUNCT
gs-1575	306	18	)	)	PUNCT
gs-1575	306	19	1	1	NUM
gs-1575	306	20	(	(	PUNCT
gs-1575	306	21	)	)	PUNCT
gs-1575	306	22	(	(	PUNCT
gs-1575	306	23	)	)	PUNCT
gs-1575	306	24	{	{	PUNCT
gs-1575	306	25	}	}	PUNCT
gs-1575	306	26	sup	sup	NOUN
gs-1575	306	27	(	(	PUNCT
gs-1575	306	28	)	)	PUNCT
gs-1575	306	29	(	(	PUNCT
gs-1575	306	30	)	)	PUNCT
gs-1575	306	31	2	2	NUM
gs-1575	306	32	n	n	ADP
gs-1575	306	33	n	n	CCONJ
gs-1575	307	1	n	n	NOUN
gs-1575	308	1	i	i	PRON
gs-1575	308	2	i	i	PRON
gs-1575	308	3	a	a	PRON
gs-1575	308	4	an	an	DET
gs-1575	308	5	n	n	NOUN
gs-1575	309	1	i	i	PRON
gs-1575	309	2	a	a	X
gs-1575	309	3	i	i	PRON
gs-1575	310	1	a	a	DET
gs-1575	310	2	f	f	X
gs-1575	310	3	x	x	X
gs-1575	310	4	dxe	dxe	PROPN
gs-1575	310	5	f	f	PROPN
gs-1575	311	1	x	x	X
gs-1575	311	2	dxe	dxe	PROPN
gs-1575	311	3	n	n	INTJ
gs-1575	311	4	i	i	PRON
gs-1575	312	1	a	a	DET
gs-1575	312	2	n	n	CCONJ
gs-1575	312	3			NOUN
gs-1575	312	4			NOUN
gs-1575	312	5			NOUN
gs-1575	312	6			NOUN
gs-1575	312	7			PROPN
gs-1575	312	8			NOUN
gs-1575	312	9			ADJ
gs-1575	312	10			NOUN
gs-1575	312	11			VERB
gs-1575	312	12			ADJ
gs-1575	312	13			NOUN
gs-1575	312	14			PROPN
gs-1575	312	15			PUNCT
gs-1575	312	16			PROPN
gs-1575	312	17			NUM
gs-1575	312	18			PUNCT
gs-1575	312	19	(	(	PUNCT
gs-1575	312	20	)	)	PUNCT
gs-1575	312	21	2	2	NUM
gs-1575	312	22	(	(	PUNCT
gs-1575	312	23	)	)	PUNCT
gs-1575	312	24	(	(	PUNCT
gs-1575	312	25	)	)	PUNCT
gs-1575	312	26	(	(	PUNCT
gs-1575	312	27	)	)	PUNCT
gs-1575	312	28	n	n	CCONJ
gs-1575	312	29	n	n	CCONJ
gs-1575	312	30	n	n	CCONJ
gs-1575	312	31	n	n	NOUN
gs-1575	312	32	i	i	PRON
gs-1575	312	33	a	a	X
gs-1575	313	1	i	i	PRON
gs-1575	313	2	a	a	PRON
gs-1575	314	1	i	i	NOUN
gs-1575	314	2	o	o	X
gs-1575	314	3	e	e	NOUN
gs-1575	314	4	f	f	X
gs-1575	314	5	x	x	X
gs-1575	314	6	dxe	dxe	PROPN
gs-1575	314	7	n	n	CCONJ
gs-1575	314	8	n	n	CCONJ
gs-1575	314	9	n	n	CCONJ
gs-1575	314	10	n	n	CCONJ
gs-1575	314	11			NOUN
gs-1575	314	12			NOUN
gs-1575	314	13			ADJ
gs-1575	314	14			ADJ
gs-1575	314	15			NOUN
gs-1575	314	16			VERB
gs-1575	314	17			ADJ
gs-1575	314	18			NUM
gs-1575	314	19			SYM
gs-1575	314	20			NOUN
gs-1575	314	21			SYM
gs-1575	314	22	2	2	NUM
gs-1575	314	23	0	0	NUM
gs-1575	314	24	sup	sup	NOUN
gs-1575	314	25	(	(	PUNCT
gs-1575	314	26	)	)	PUNCT
gs-1575	314	27	(	(	PUNCT
gs-1575	314	28	)	)	PUNCT
gs-1575	314	29	2	2	X
gs-1575	315	1	i	i	PRON
gs-1575	315	2	n	n	VERB
gs-1575	315	3	a	a	PRON
gs-1575	315	4	i	i	PRON
gs-1575	315	5	an	an	DET
gs-1575	315	6	p	p	NOUN
gs-1575	315	7	a	a	DET
gs-1575	315	8	f	f	NOUN
gs-1575	315	9	x	x	X
gs-1575	315	10	dx	dx	PROPN
gs-1575	315	11	p	p	PROPN
gs-1575	315	12	o	o	PROPN
gs-1575	315	13	a	a	PRON
gs-1575	315	14	n	n	PRON
gs-1575	315	15			NOUN
gs-1575	315	16			PROPN
gs-1575	315	17			NOUN
gs-1575	315	18			VERB
gs-1575	315	19			NOUN
gs-1575	315	20			ADJ
gs-1575	315	21			PROPN
gs-1575	315	22			NUM
gs-1575	315	23	.	.	PUNCT
gs-1575	316	1	let	let	VERB
gs-1575	316	2	's	us	PRON
gs-1575	316	3	apply	apply	VERB
gs-1575	316	4	the	the	DET
gs-1575	316	5	inequality	inequality	NOUN
gs-1575	316	6	(	(	PUNCT
gs-1575	316	7	)	)	PUNCT
gs-1575	316	8	(	(	PUNCT
gs-1575	316	9	)	)	PUNCT
gs-1575	316	10	n	n	CCONJ
gs-1575	317	1	n	n	NOUN
gs-1575	318	1	i	i	PRON
gs-1575	319	1	i	i	INTJ
gs-1575	319	2	i	i	VERB
gs-1575	319	3	e	e	X
gs-1575	319	4	e	e	NOUN
gs-1575	319	5	p	p	PROPN
gs-1575	319	6	n	n	CCONJ
gs-1575	319	7	n	n	CCONJ
gs-1575	319	8			ADJ
gs-1575	319	9			ADJ
gs-1575	319	10			NOUN
gs-1575	319	11			NUM
gs-1575	319	12	.	.	PUNCT
gs-1575	320	1			NOUN
gs-1575	320	2	1	1	VERB
gs-1575	320	3	2	2	NUM
gs-1575	320	4	0	0	NUM
gs-1575	320	5	2	2	NUM
gs-1575	320	6	(	(	PUNCT
gs-1575	320	7	)	)	PUNCT
gs-1575	320	8	sup	sup	NOUN
gs-1575	320	9	(	(	PUNCT
gs-1575	320	10	)	)	PUNCT
gs-1575	320	11	(	(	PUNCT
gs-1575	320	12	)	)	PUNCT
gs-1575	320	13	2	2	NUM
gs-1575	320	14	n	n	NOUN
gs-1575	321	1	i	i	PRON
gs-1575	321	2	i	i	PRON
gs-1575	321	3	n	n	VERB
gs-1575	322	1	i	i	PRON
gs-1575	322	2	i	i	PRON
gs-1575	322	3	a	a	VERB
gs-1575	322	4	i	i	PRON
gs-1575	323	1	an	an	DET
gs-1575	323	2	a	a	DET
gs-1575	323	3	p	p	X
gs-1575	323	4	p	p	NOUN
gs-1575	323	5	a	a	DET
gs-1575	323	6	a	a	DET
gs-1575	323	7	f	f	NOUN
gs-1575	323	8	x	x	X
gs-1575	323	9	dx	dx	PROPN
gs-1575	323	10	f	f	PROPN
gs-1575	323	11	x	x	PROPN
gs-1575	323	12	dx	dx	PROPN
gs-1575	323	13	p	p	PROPN
gs-1575	323	14	o	o	PROPN
gs-1575	323	15	n	n	ADP
gs-1575	323	16	a	a	DET
gs-1575	323	17	n	n	DET
gs-1575	323	18			NOUN
gs-1575	323	19			NOUN
gs-1575	323	20			PROPN
gs-1575	323	21			NOUN
gs-1575	323	22			NOUN
gs-1575	323	23			VERB
gs-1575	323	24			ADJ
gs-1575	323	25			NOUN
gs-1575	323	26			PROPN
gs-1575	323	27			PUNCT
gs-1575	323	28			PROPN
gs-1575	323	29			NUM
gs-1575	323	30			PUNCT
gs-1575	323	31	.	.	PUNCT
gs-1575	324	1	we	we	PRON
gs-1575	324	2	take	take	VERB
gs-1575	324	3	the	the	DET
gs-1575	324	4	value	value	NOUN
gs-1575	324	5	(	(	PUNCT
gs-1575	324	6	)	)	PUNCT
gs-1575	324	7	(	(	PUNCT
gs-1575	324	8	)	)	PUNCT
gs-1575	324	9	n	n	CCONJ
gs-1575	325	1	i	i	PRON
gs-1575	326	1	i	i	PRON
gs-1575	326	2	p	p	VERB
gs-1575	326	3	n	n	PRON
gs-1575	326	4			ADJ
gs-1575	326	5			NOUN
gs-1575	326	6	out	out	ADP
gs-1575	326	7	of	of	ADP
gs-1575	326	8	the	the	DET
gs-1575	326	9	sign	sign	NOUN
gs-1575	326	10	of	of	ADP
gs-1575	326	11	the	the	DET
gs-1575	326	12	conditional	conditional	ADJ
gs-1575	326	13	expectation	expectation	NOUN
gs-1575	326	14	(	(	PUNCT
gs-1575	326	15	see	see	VERB
gs-1575	326	16	[	[	X
gs-1575	326	17	19	19	NUM
gs-1575	326	18	]	]	NUM
gs-1575	326	19	)	)	PUNCT
gs-1575	326	20	.	.	PUNCT
gs-1575	327	1	let	let	VERB
gs-1575	327	2	's	us	PRON
gs-1575	327	3	apply	apply	VERB
gs-1575	327	4	condition	condition	NOUN
gs-1575	327	5	(	(	PUNCT
gs-1575	327	6	6	6	NUM
gs-1575	327	7	)	)	PUNCT
gs-1575	327	8	and	and	CCONJ
gs-1575	327	9	inequality	inequality	NOUN
gs-1575	327	10	(	(	PUNCT
gs-1575	327	11	7	7	NUM
gs-1575	327	12	)	)	PUNCT
gs-1575	327	13	.	.	PUNCT
gs-1575	328	1	the	the	DET
gs-1575	328	2	following	follow	VERB
gs-1575	328	3	inequality	inequality	NOUN
gs-1575	328	4	will	will	AUX
gs-1575	328	5	be	be	AUX
gs-1575	328	6	obtained	obtain	VERB
gs-1575	328	7	2	2	NUM
gs-1575	328	8	2	2	NUM
gs-1575	328	9	1	1	NUM
gs-1575	328	10	(	(	PUNCT
gs-1575	328	11	)	)	PUNCT
gs-1575	328	12	(	(	PUNCT
gs-1575	328	13	)	)	PUNCT
gs-1575	328	14	(	(	PUNCT
gs-1575	328	15	)	)	PUNCT
gs-1575	328	16	[	[	PUNCT
gs-1575	328	17	(	(	PUNCT
gs-1575	328	18	(	(	PUNCT
gs-1575	328	19	)	)	PUNCT
gs-1575	328	20	|	|	ADV
gs-1575	328	21	)	)	PUNCT
gs-1575	328	22	]	]	PUNCT
gs-1575	329	1	(	(	PUNCT
gs-1575	329	2	)	)	PUNCT
gs-1575	329	3	n	n	CCONJ
gs-1575	329	4	n	n	NOUN
gs-1575	329	5	n	n	ADV
gs-1575	330	1	i	i	PRON
gs-1575	330	2	i	i	PRON
gs-1575	331	1	i	i	PRON
gs-1575	331	2	i	i	PRON
gs-1575	332	1	n	n	VERB
gs-1575	333	1	i	i	PRON
gs-1575	334	1	i	i	PRON
gs-1575	335	1	i	i	PRON
gs-1575	336	1	i	i	PRON
gs-1575	337	1	i	i	PRON
gs-1575	337	2	c	c	VERB
gs-1575	337	3	a	a	DET
gs-1575	337	4	e	e	NOUN
gs-1575	337	5	p	p	X
gs-1575	337	6	e	e	X
gs-1575	337	7	f	f	X
gs-1575	337	8	x	x	X
gs-1575	337	9	dx	dx	PROPN
gs-1575	337	10	e	e	NOUN
gs-1575	337	11	p	p	PROPN
gs-1575	337	12	e	e	PROPN
gs-1575	337	13	p	p	PROPN
gs-1575	337	14	n	n	CCONJ
gs-1575	337	15	n	n	CCONJ
gs-1575	337	16	n	n	CCONJ
gs-1575	337	17	n	n	CCONJ
gs-1575	337	18			ADV
gs-1575	337	19			ADJ
gs-1575	337	20			NOUN
gs-1575	337	21			NOUN
gs-1575	337	22			VERB
gs-1575	337	23			NUM
gs-1575	337	24			NUM
gs-1575	337	25			PROPN
gs-1575	337	26			PROPN
gs-1575	337	27			PROPN
gs-1575	337	28			NOUN
gs-1575	337	29			NOUN
gs-1575	337	30			NUM
gs-1575	337	31	.	.	PUNCT
gs-1575	338	1	finally	finally	ADV
gs-1575	338	2	,	,	PUNCT
gs-1575	338	3	the	the	DET
gs-1575	338	4	following	follow	VERB
gs-1575	338	5	estimation	estimation	NOUN
gs-1575	338	6	of	of	ADP
gs-1575	338	7	the	the	DET
gs-1575	338	8	summand	summand	PROPN
gs-1575	338	9	ia	ia	PROPN
gs-1575	338	10	will	will	AUX
gs-1575	338	11	be	be	AUX
gs-1575	338	12	obtained	obtain	VERB
gs-1575	338	13			NOUN
gs-1575	338	14			PROPN
gs-1575	338	15	2	2	NUM
gs-1575	338	16	4	4	NUM
gs-1575	338	17	0	0	NUM
gs-1575	338	18	2	2	NUM
gs-1575	338	19	(	(	PUNCT
gs-1575	338	20	)	)	PUNCT
gs-1575	338	21	sup	sup	NOUN
gs-1575	338	22	(	(	PUNCT
gs-1575	338	23	)	)	PUNCT
gs-1575	338	24	(	(	PUNCT
gs-1575	338	25	)	)	PUNCT
gs-1575	338	26	2	2	NUM
gs-1575	338	27	in	in	ADP
gs-1575	338	28	i	i	PRON
gs-1575	338	29	i	i	PRON
gs-1575	339	1	n	n	VERB
gs-1575	340	1	i	i	PRON
gs-1575	340	2	i	i	PRON
gs-1575	340	3	a	a	VERB
gs-1575	340	4	i	i	PRON
gs-1575	340	5	an	an	DET
gs-1575	340	6	ca	ca	NOUN
gs-1575	340	7	p	p	X
gs-1575	340	8	p	p	X
gs-1575	340	9	a	a	DET
gs-1575	340	10	a	a	DET
gs-1575	340	11	f	f	NOUN
gs-1575	340	12	x	x	X
gs-1575	340	13	dxe	dxe	PROPN
gs-1575	340	14	f	f	PROPN
gs-1575	341	1	x	x	X
gs-1575	341	2	dx	dx	PROPN
gs-1575	341	3	p	p	PROPN
gs-1575	341	4	o	o	PROPN
gs-1575	342	1	n	n	CCONJ
gs-1575	342	2	a	a	DET
gs-1575	342	3	n	n	CCONJ
gs-1575	342	4	n	n	PRON
gs-1575	342	5			NOUN
gs-1575	342	6			NOUN
gs-1575	342	7			PROPN
gs-1575	342	8			NOUN
gs-1575	342	9			NOUN
gs-1575	342	10			VERB
gs-1575	342	11			ADJ
gs-1575	342	12			VERB
gs-1575	342	13			PROPN
gs-1575	342	14			PUNCT
gs-1575	342	15			PROPN
gs-1575	342	16			X
gs-1575	342	17			NUM
gs-1575	342	18			PUNCT
gs-1575	342	19	.	.	PUNCT
gs-1575	343	1	we	we	PRON
gs-1575	343	2	apply	apply	VERB
gs-1575	343	3	this	this	DET
gs-1575	343	4	estimation	estimation	NOUN
gs-1575	343	5	in	in	ADP
gs-1575	343	6	inequality	inequality	NOUN
gs-1575	343	7	(	(	PUNCT
gs-1575	343	8	10	10	NUM
gs-1575	343	9	)	)	PUNCT
gs-1575	343	10	and	and	CCONJ
gs-1575	343	11	will	will	AUX
gs-1575	343	12	be	be	AUX
gs-1575	343	13	obtained	obtain	VERB
gs-1575	343	14	the	the	DET
gs-1575	343	15	estimation	estimation	NOUN
gs-1575	343	16	of	of	ADP
gs-1575	343	17	theorem	theorem	NOUN
gs-1575	343	18	(	(	PUNCT
gs-1575	343	19	8)	8)	NUM
gs-1575	343	20	.	.	PUNCT
gs-1575	344	1	georgian	georgian	ADJ
gs-1575	344	2	scientists/ქართველი	scientists/ქართველი	PROPN
gs-1575	344	3	მეცნიერები	მეცნიერები	NOUN
gs-1575	344	4	ტ.	ტ.	VERB
gs-1575	344	5	5	5	NUM
gs-1575	344	6	n	n	PRON
gs-1575	344	7	1	1	NUM
gs-1575	344	8	,	,	PUNCT
gs-1575	344	9	2023	2023	NUM
gs-1575	344	10	316	316	NUM
gs-1575	344	11	the	the	DET
gs-1575	344	12	estimation	estimation	NOUN
gs-1575	344	13	of	of	ADP
gs-1575	344	14	(	(	PUNCT
gs-1575	344	15	9	9	NUM
gs-1575	344	16	)	)	PUNCT
gs-1575	344	17	is	be	AUX
gs-1575	344	18	obtained	obtain	VERB
gs-1575	344	19	directly	directly	ADV
gs-1575	344	20	from	from	ADP
gs-1575	344	21	(	(	PUNCT
gs-1575	344	22	8)	8)	NUM
gs-1575	344	23	.	.	PUNCT
gs-1575	345	1	let	let	VERB
gs-1575	345	2	's	us	PRON
gs-1575	345	3	apply	apply	VERB
gs-1575	345	4	the	the	DET
gs-1575	345	5	following	follow	VERB
gs-1575	345	6	fact	fact	NOUN
gs-1575	345	7	shown	show	VERB
gs-1575	345	8	in	in	ADP
gs-1575	345	9	[	[	X
gs-1575	345	10	5	5	NUM
gs-1575	345	11	]	]	PUNCT
gs-1575	345	12	while	while	SCONJ
gs-1575	345	13	proving	prove	VERB
gs-1575	345	14	the	the	DET
gs-1575	345	15	inequality	inequality	NOUN
gs-1575	345	16	of	of	ADP
gs-1575	345	17	lemma	lemma	PROPN
gs-1575	345	18	(	(	PUNCT
gs-1575	345	19	4	4	NUM
gs-1575	345	20	)	)	PUNCT
gs-1575	345	21	.	.	PUNCT
gs-1575	346	1	for	for	ADP
gs-1575	346	2			NOUN
gs-1575	346	3	g	g	PROPN
gs-1575	346	4	x	x	SYM
gs-1575	346	5	f	f	NOUN
gs-1575	346	6	class	class	NOUN
gs-1575	346	7	functions	function	NOUN
gs-1575	346	8	,	,	PUNCT
gs-1575	346	9	the	the	DET
gs-1575	346	10	expression	expression	NOUN
gs-1575	346	11			NOUN
gs-1575	346	12			PROPN
gs-1575	346	13	0	0	NUM
gs-1575	346	14	sup	sup	NOUN
gs-1575	346	15	(	(	PUNCT
gs-1575	346	16	)	)	PUNCT
gs-1575	346	17	a	a	DET
gs-1575	346	18	a	a	DET
gs-1575	346	19	g	g	NOUN
gs-1575	346	20	x	x	X
gs-1575	346	21	dx	dx	PROPN
gs-1575	346	22			VERB
gs-1575	346	23			PRON
gs-1575	346	24			VERB
gs-1575	346	25			ADV
gs-1575	346	26			ADJ
gs-1575	346	27	does	do	AUX
gs-1575	346	28	not	not	PART
gs-1575	346	29	depend	depend	VERB
gs-1575	346	30	on	on	ADP
gs-1575	346	31	the	the	DET
gs-1575	346	32	selection	selection	NOUN
gs-1575	346	33	of	of	ADP
gs-1575	346	34	the	the	DET
gs-1575	346	35	function	function	NOUN
gs-1575	346	36			PROPN
gs-1575	346	37	x	x	ADJ
gs-1575	346	38			PROPN
gs-1575	346	39	,	,	PUNCT
gs-1575	346	40	and	and	CCONJ
gs-1575	346	41	the	the	DET
gs-1575	346	42	equality	equality	NOUN
gs-1575	346	43	is	be	AUX
gs-1575	346	44	shown	show	VERB
gs-1575	346	45			NOUN
gs-1575	346	46			PROPN
gs-1575	346	47	0	0	NUM
gs-1575	346	48	sup	sup	NOUN
gs-1575	346	49	(	(	PUNCT
gs-1575	346	50	)	)	PUNCT
gs-1575	346	51	(	(	PUNCT
gs-1575	346	52	)	)	PUNCT
gs-1575	346	53	a	a	DET
gs-1575	346	54	a	a	DET
gs-1575	346	55	g	g	NOUN
gs-1575	346	56	x	x	X
gs-1575	346	57	dx	dx	PROPN
gs-1575	346	58	g	g	PROPN
gs-1575	346	59	x	x	PUNCT
gs-1575	346	60	dx	dx	PROPN
gs-1575	346	61			PROPN
gs-1575	346	62			VERB
gs-1575	346	63			PRON
gs-1575	346	64			VERB
gs-1575	346	65			NOUN
gs-1575	347	1			X
gs-1575	347	2			PROPN
gs-1575	347	3			PROPN
gs-1575	347	4			NOUN
gs-1575	347	5	corollary	corollary	NOUN
gs-1575	347	6	1	1	NUM
gs-1575	347	7	.	.	PUNCT
gs-1575	348	1	if	if	SCONJ
gs-1575	348	2	under	under	ADP
gs-1575	348	3	the	the	DET
gs-1575	348	4	conditions	condition	NOUN
gs-1575	348	5			PROPN
gs-1575	348	6	k	k	VERB
gs-1575	348	7	x	x	PUNCT
gs-1575	348	8	of	of	ADP
gs-1575	348	9	theorem	theorem	NOUN
gs-1575	348	10	is	be	AUX
gs-1575	348	11	bartlett	bartlett	PROPN
gs-1575	348	12	's	's	PART
gs-1575	348	13	core	core	NOUN
gs-1575	348	14	then	then	ADV
gs-1575	348	15	for	for	ADP
gs-1575	348	16	each	each	DET
gs-1575	348	17	natural	natural	ADJ
gs-1575	348	18	number	number	NOUN
gs-1575	348	19	n	n	PART
gs-1575	348	20	is	be	AUX
gs-1575	348	21	the	the	DET
gs-1575	348	22	estimation	estimation	NOUN
gs-1575	348	23	of	of	ADP
gs-1575	348	24	the	the	DET
gs-1575	348	25	density	density	NOUN
gs-1575	348	26			NOUN
gs-1575	348	27			SYM
gs-1575	348	28			NOUN
gs-1575	349	1			NOUN
gs-1575	349	2	1	1	NUM
gs-1575	349	3	r	r	NOUN
gs-1575	350	1	i	i	PRON
gs-1575	350	2	i	i	PRON
gs-1575	351	1	i	i	PRON
gs-1575	351	2	f	f	VERB
gs-1575	352	1	x	x	X
gs-1575	352	2	p	p	X
gs-1575	352	3	f	f	X
gs-1575	352	4	x	x	X
gs-1575	352	5			NUM
gs-1575	352	6			PROPN
gs-1575	352	7	is	be	AUX
gs-1575	352	8	presented	present	VERB
gs-1575	352	9	by	by	ADP
gs-1575	352	10	sum	sum	NOUN
gs-1575	352	11			NOUN
gs-1575	352	12			PROPN
gs-1575	352	13	2	2	NUM
gs-1575	352	14	1	1	NUM
gs-1575	352	15	[	[	PUNCT
gs-1575	352	16	]	]	X
gs-1575	352	17	1	1	NUM
gs-1575	352	18	3	3	NUM
gs-1575	352	19	,	,	PUNCT
gs-1575	352	20	(	(	PUNCT
gs-1575	352	21	1	1	NUM
gs-1575	352	22	[	[	PUNCT
gs-1575	352	23	(	(	PUNCT
gs-1575	352	24	)	)	PUNCT
gs-1575	352	25	]	]	PUNCT
gs-1575	352	26	)	)	PUNCT
gs-1575	352	27	4	4	NUM
gs-1575	353	1	i	i	PRON
gs-1575	353	2	n	n	VERB
gs-1575	353	3	n	n	CCONJ
gs-1575	353	4	n	n	CCONJ
gs-1575	353	5	n	n	CCONJ
gs-1575	353	6	n	n	CCONJ
gs-1575	353	7	n	n	NOUN
gs-1575	353	8	i	i	NOUN
gs-1575	353	9	x	x	PUNCT
gs-1575	353	10	x	x	VERB
gs-1575	353	11	i	i	PRON
gs-1575	353	12	a	a	PRON
gs-1575	353	13	a	a	DET
gs-1575	353	14	f	f	X
gs-1575	353	15	x	x	X
gs-1575	353	16	a	a	DET
gs-1575	353	17	a	a	PRON
gs-1575	353	18	x	x	SYM
gs-1575	353	19	x	x	SYM
gs-1575	353	20	n	n	PRON
gs-1575	353	21			VERB
gs-1575	353	22			NUM
gs-1575	353	23			NUM
gs-1575	353	24			PROPN
gs-1575	353	25			PROPN
gs-1575	353	26			NOUN
gs-1575	353	27			ADV
gs-1575	353	28	and	and	CCONJ
gs-1575	353	29	for	for	ADP
gs-1575	353	30	quantity	quantity	NOUN
gs-1575	353	31			NOUN
gs-1575	353	32			PROPN
gs-1575	353	33	(	(	PUNCT
gs-1575	353	34	)	)	PUNCT
gs-1575	353	35	(	(	PUNCT
gs-1575	353	36	,	,	PUNCT
gs-1575	353	37	)	)	PUNCT
gs-1575	353	38	n	n	CCONJ
gs-1575	353	39	n	n	PRON
gs-1575	353	40	nj	nj	PROPN
gs-1575	354	1	a	a	DET
gs-1575	354	2	f	f	X
gs-1575	354	3	x	x	X
gs-1575	354	4	a	a	DET
gs-1575	354	5	f	f	X
gs-1575	354	6	x	x	SYM
gs-1575	354	7	dx	dx	PROPN
gs-1575	354	8			VERB
gs-1575	354	9			VERB
gs-1575	354	10			NUM
gs-1575	354	11			NOUN
gs-1575	354	12	,	,	PUNCT
gs-1575	354	13	we	we	PRON
gs-1575	354	14	have	have	VERB
gs-1575	354	15	the	the	DET
gs-1575	354	16	estimate	estimate	NOUN
gs-1575	354	17	1	1	NUM
gs-1575	354	18	3	3	NUM
gs-1575	354	19	2	2	NUM
gs-1575	354	20	(	(	PUNCT
gs-1575	354	21	)	)	PUNCT
gs-1575	354	22	(	(	PUNCT
gs-1575	354	23	)	)	PUNCT
gs-1575	354	24	5	5	NUM
gs-1575	354	25	r	r	NOUN
gs-1575	354	26	n	n	NOUN
gs-1575	354	27	n	n	NOUN
gs-1575	355	1	i	i	PRON
gs-1575	355	2	i	i	PRON
gs-1575	355	3	i	i	PRON
gs-1575	355	4	a	a	PRON
gs-1575	355	5	ej	ej	PROPN
gs-1575	355	6	a	a	DET
gs-1575	355	7	p	p	X
gs-1575	355	8	f	f	X
gs-1575	355	9	x	x	SYM
gs-1575	355	10	dx	dx	PROPN
gs-1575	355	11	n	n	PROPN
gs-1575	355	12			PROPN
gs-1575	355	13			VERB
gs-1575	355	14			NOUN
gs-1575	355	15			NOUN
gs-1575	355	16			NOUN
gs-1575	355	17			NOUN
gs-1575	355	18			PUNCT
gs-1575	355	19			PROPN
gs-1575	355	20			SYM
gs-1575	355	21	2	2	NUM
gs-1575	355	22	4	4	NUM
gs-1575	355	23	01	01	NUM
gs-1575	355	24	1	1	NUM
gs-1575	355	25	0,1	0,1	NUM
gs-1575	355	26	1	1	NUM
gs-1575	355	27	sup	sup	NOUN
gs-1575	355	28	(	(	PUNCT
gs-1575	355	29	)	)	PUNCT
gs-1575	355	30	(	(	PUNCT
gs-1575	355	31	)	)	PUNCT
gs-1575	355	32	r	r	NOUN
gs-1575	355	33	r	r	NOUN
gs-1575	355	34	n	n	NOUN
gs-1575	356	1	i	i	PRON
gs-1575	356	2	i	i	PRON
gs-1575	356	3	a	a	PRON
gs-1575	357	1	i	i	PRON
gs-1575	357	2	ai	ai	VERB
gs-1575	357	3	in	in	ADP
gs-1575	357	4	a	a	DET
gs-1575	357	5	p	p	X
gs-1575	357	6	f	f	X
gs-1575	357	7	x	x	X
gs-1575	357	8	dx	dx	PROPN
gs-1575	357	9	c	c	NOUN
gs-1575	357	10	o	o	PROPN
gs-1575	357	11	a	a	DET
gs-1575	357	12	nn	nn	X
gs-1575	357	13			PROPN
gs-1575	357	14			PROPN
gs-1575	357	15			PROPN
gs-1575	357	16			NOUN
gs-1575	357	17			VERB
gs-1575	357	18			PROPN
gs-1575	357	19			ADV
gs-1575	357	20			NOUN
gs-1575	357	21			NOUN
gs-1575	357	22	.	.	PUNCT
gs-1575	358	1	(	(	PUNCT
gs-1575	358	2	11	11	NUM
gs-1575	358	3	)	)	PUNCT
gs-1575	358	4	if	if	SCONJ
gs-1575	358	5	also	also	ADV
gs-1575	358	6			VERB
gs-1575	358	7	if	if	NOUN
gs-1575	358	8	x	x	PUNCT
gs-1575	358	9	f	f	PROPN
gs-1575	358	10	,	,	PUNCT
gs-1575	358	11	1,i	1,i	PROPN
gs-1575	358	12	r	r	NOUN
gs-1575	358	13	,	,	PUNCT
gs-1575	358	14	then	then	ADV
gs-1575	358	15	the	the	DET
gs-1575	358	16	inequality	inequality	NOUN
gs-1575	358	17	is	be	AUX
gs-1575	358	18	fulfilled	fulfil	VERB
gs-1575	358	19	2	2	NUM
gs-1575	358	20	4	4	NUM
gs-1575	358	21	1	1	NUM
gs-1575	358	22	1	1	NUM
gs-1575	358	23	1	1	NUM
gs-1575	358	24	3	3	NUM
gs-1575	358	25	2	2	NUM
gs-1575	358	26	0,1	0,1	NUM
gs-1575	358	27	1	1	NUM
gs-1575	358	28	(	(	PUNCT
gs-1575	358	29	)	)	PUNCT
gs-1575	358	30	(	(	PUNCT
gs-1575	358	31	)	)	PUNCT
gs-1575	358	32	(	(	PUNCT
gs-1575	358	33	)	)	PUNCT
gs-1575	358	34	(	(	PUNCT
gs-1575	358	35	)	)	PUNCT
gs-1575	358	36	5	5	NUM
gs-1575	358	37	r	r	NOUN
gs-1575	358	38	r	r	NOUN
gs-1575	358	39	r	r	NOUN
gs-1575	358	40	n	n	NOUN
gs-1575	358	41	n	n	NOUN
gs-1575	358	42	n	n	NOUN
gs-1575	359	1	i	i	PRON
gs-1575	360	1	i	i	PRON
gs-1575	361	1	i	i	PRON
gs-1575	362	1	i	i	PRON
gs-1575	363	1	i	i	PRON
gs-1575	364	1	i	i	PRON
gs-1575	365	1	i	i	PRON
gs-1575	365	2	in	in	ADP
gs-1575	365	3	a	a	DET
gs-1575	365	4	a	a	DET
gs-1575	365	5	ej	ej	NOUN
gs-1575	365	6	a	a	DET
gs-1575	365	7	p	p	X
gs-1575	366	1	f	f	X
gs-1575	366	2	x	x	X
gs-1575	366	3	dx	dx	PROPN
gs-1575	366	4	p	p	PROPN
gs-1575	366	5	f	f	PROPN
gs-1575	366	6	x	x	X
gs-1575	366	7	dx	dx	PROPN
gs-1575	366	8	c	c	NOUN
gs-1575	366	9	o	o	PROPN
gs-1575	366	10	n	n	CCONJ
gs-1575	366	11	a	a	DET
gs-1575	366	12	nn	nn	PROPN
gs-1575	366	13			PROPN
gs-1575	366	14			VERB
gs-1575	366	15			NUM
gs-1575	366	16			PROPN
gs-1575	366	17			NOUN
gs-1575	366	18			VERB
gs-1575	366	19			PROPN
gs-1575	366	20			ADV
gs-1575	366	21			PUNCT
gs-1575	366	22			X
gs-1575	366	23			X
gs-1575	366	24			NUM
gs-1575	366	25			PUNCT
gs-1575	366	26	.	.	PUNCT
gs-1575	367	1	(	(	PUNCT
gs-1575	367	2	12	12	NUM
gs-1575	367	3	)	)	PUNCT
gs-1575	367	4	proof	proof	NOUN
gs-1575	367	5	.	.	PUNCT
gs-1575	368	1	it	it	PRON
gs-1575	368	2	is	be	AUX
gs-1575	368	3	clear	clear	ADJ
gs-1575	368	4	that	that	SCONJ
gs-1575	368	5			NOUN
gs-1575	368	6			SYM
gs-1575	368	7			NOUN
gs-1575	368	8	k	k	NUM
gs-1575	368	9	x	x	SYM
gs-1575	369	1	k	k	PROPN
gs-1575	369	2	x	x	PROPN
gs-1575	369	3			PROPN
gs-1575	369	4	,	,	PUNCT
gs-1575	369	5			PROPN
gs-1575	369	6			PROPN
gs-1575	369	7	3	3	NUM
gs-1575	369	8	4	4	NUM
gs-1575	369	9	k	k	NOUN
gs-1575	369	10	x	x	SYM
gs-1575	369	11			NOUN
gs-1575	369	12	and	and	CCONJ
gs-1575	369	13			PROPN
gs-1575	369	14	k	k	VERB
gs-1575	369	15	x	x	PUNCT
gs-1575	369	16	have	have	VERB
gs-1575	369	17	a	a	DET
gs-1575	369	18	compact	compact	ADJ
gs-1575	369	19	support	support	NOUN
gs-1575	369	20	.	.	PUNCT
gs-1575	370	1	therefore	therefore	ADV
gs-1575	370	2	,	,	PUNCT
gs-1575	370	3	it	it	PRON
gs-1575	370	4	satisfies	satisfy	VERB
gs-1575	370	5	the	the	DET
gs-1575	370	6	conditions	condition	NOUN
gs-1575	370	7	of	of	ADP
gs-1575	370	8	the	the	DET
gs-1575	370	9	theorem	theorem	NOUN
gs-1575	370	10	.	.	PUNCT
gs-1575	371	1	the	the	DET
gs-1575	371	2	inequalities	inequality	NOUN
gs-1575	371	3	(	(	PUNCT
gs-1575	371	4	11	11	NUM
gs-1575	371	5	)	)	PUNCT
gs-1575	371	6	and	and	CCONJ
gs-1575	371	7	(	(	PUNCT
gs-1575	371	8	12	12	NUM
gs-1575	371	9	)	)	PUNCT
gs-1575	371	10	are	be	AUX
gs-1575	371	11	obtained	obtain	VERB
gs-1575	371	12	from	from	ADP
gs-1575	371	13	(	(	PUNCT
gs-1575	371	14	8)	8)	NUM
gs-1575	371	15	and	and	CCONJ
gs-1575	371	16	(	(	PUNCT
gs-1575	371	17	9	9	NUM
gs-1575	371	18	)	)	PUNCT
gs-1575	371	19	if	if	SCONJ
gs-1575	371	20	we	we	PRON
gs-1575	371	21	calculate	calculate	VERB
gs-1575	371	22			X
gs-1575	371	23	and	and	CCONJ
gs-1575	371	24			VERB
gs-1575	371	25	the	the	DET
gs-1575	371	26	quantities	quantity	NOUN
gs-1575	371	27			NOUN
gs-1575	372	1			SYM
gs-1575	372	2	1	1	NUM
gs-1575	372	3	2	2	NUM
gs-1575	372	4	2	2	NUM
gs-1575	372	5	2	2	NUM
gs-1575	372	6	1	1	NUM
gs-1575	372	7	3	3	NUM
gs-1575	372	8	3	3	NUM
gs-1575	372	9	(	(	PUNCT
gs-1575	372	10	1	1	NUM
gs-1575	372	11	)	)	PUNCT
gs-1575	372	12	4	4	NUM
gs-1575	372	13	5	5	NUM
gs-1575	372	14	k	k	NOUN
gs-1575	372	15	x	x	SYM
gs-1575	372	16	dx	dx	PROPN
gs-1575	372	17	x	x	PUNCT
gs-1575	372	18	dx	dx	PROPN
gs-1575	372	19			VERB
gs-1575	372	20			NUM
gs-1575	372	21			NOUN
gs-1575	372	22			PROPN
gs-1575	372	23			PROPN
gs-1575	372	24			NOUN
gs-1575	372	25			PROPN
gs-1575	372	26			X
gs-1575	372	27			PROPN
gs-1575	372	28			SYM
gs-1575	372	29	1	1	NUM
gs-1575	372	30	2	2	NUM
gs-1575	372	31	2	2	NUM
gs-1575	372	32	4	4	NUM
gs-1575	372	33	1	1	NUM
gs-1575	372	34	3	3	NUM
gs-1575	372	35	1	1	NUM
gs-1575	372	36	(	(	PUNCT
gs-1575	372	37	)	)	PUNCT
gs-1575	372	38	4	4	NUM
gs-1575	372	39	5	5	NUM
gs-1575	372	40	x	x	SYM
gs-1575	372	41	k	k	NOUN
gs-1575	372	42	x	x	X
gs-1575	372	43	dx	dx	PROPN
gs-1575	372	44	x	x	SYM
gs-1575	372	45	x	x	SYM
gs-1575	372	46	dx	dx	NOUN
gs-1575	372	47			VERB
gs-1575	372	48			VERB
gs-1575	372	49			NOUN
gs-1575	372	50			PROPN
gs-1575	372	51			PROPN
gs-1575	372	52			NOUN
gs-1575	372	53			PROPN
gs-1575	372	54			X
gs-1575	372	55	.	.	PUNCT
gs-1575	373	1	corollary	corollary	ADJ
gs-1575	373	2	2	2	NUM
gs-1575	373	3	.	.	PUNCT
gs-1575	374	1	if	if	SCONJ
gs-1575	374	2	we	we	PRON
gs-1575	374	3	apply	apply	VERB
gs-1575	374	4	the	the	DET
gs-1575	374	5	sequence	sequence	NOUN
gs-1575	374	6	na	na	INTJ
gs-1575	374	7	n	n	NOUN
gs-1575	374	8	under	under	ADP
gs-1575	374	9	the	the	DET
gs-1575	374	10	conditions	condition	NOUN
gs-1575	374	11	of	of	ADP
gs-1575	374	12	corollary	corollary	ADJ
gs-1575	374	13	1	1	NUM
gs-1575	374	14	,	,	PUNCT
gs-1575	374	15	we	we	PRON
gs-1575	374	16	obtain	obtain	VERB
gs-1575	374	17	the	the	DET
gs-1575	374	18	estimation	estimation	NOUN
gs-1575	374	19	of	of	ADP
gs-1575	374	20	density	density	NOUN
gs-1575	374	21			NOUN
gs-1575	374	22			PUNCT
gs-1575	374	23			NOUN
gs-1575	374	24			NOUN
gs-1575	374	25	1	1	NUM
gs-1575	374	26	r	r	NOUN
gs-1575	375	1	i	i	PRON
gs-1575	376	1	i	i	PRON
gs-1575	377	1	i	i	PRON
gs-1575	377	2	f	f	VERB
gs-1575	378	1	x	x	X
gs-1575	378	2	p	p	X
gs-1575	378	3	f	f	X
gs-1575	378	4	x	x	X
gs-1575	378	5			NUM
gs-1575	378	6			PROPN
gs-1575	378	7			NOUN
gs-1575	378	8			SYM
gs-1575	378	9			NOUN
gs-1575	378	10			PROPN
gs-1575	378	11	2	2	NUM
gs-1575	378	12	[	[	PUNCT
gs-1575	378	13	1	1	NUM
gs-1575	378	14	]	]	SYM
gs-1575	378	15	3	3	NUM
gs-1575	378	16	(	(	PUNCT
gs-1575	378	17	1	1	NUM
gs-1575	378	18	)	)	SYM
gs-1575	378	19	4	4	NUM
gs-1575	378	20	x	x	SYM
gs-1575	378	21	k	k	NOUN
gs-1575	378	22	x	x	PUNCT
gs-1575	378	23	k	k	NOUN
gs-1575	378	24	x	x	PUNCT
gs-1575	378	25	x	x	SYM
gs-1575	378	26			NUM
gs-1575	378	27			NUM
gs-1575	378	28			PROPN
gs-1575	378	29			PROPN
gs-1575	378	30			ADP
gs-1575	378	31	georgian	georgian	ADJ
gs-1575	378	32	scientists/ქართველი	scientists/ქართველი	NOUN
gs-1575	378	33	მეცნიერები	მეცნიერები	NOUN
gs-1575	378	34	ტ.	ტ.	VERB
gs-1575	378	35	5	5	NUM
gs-1575	378	36	n	n	PRON
gs-1575	378	37	1	1	NUM
gs-1575	378	38	,	,	PUNCT
gs-1575	378	39	2023	2023	NUM
gs-1575	378	40	317	317	NUM
gs-1575	378	41			NOUN
gs-1575	378	42			PROPN
gs-1575	378	43	2	2	NUM
gs-1575	378	44	1	1	NUM
gs-1575	378	45	[	[	PUNCT
gs-1575	378	46	]	]	X
gs-1575	378	47	1	1	NUM
gs-1575	378	48	3	3	NUM
gs-1575	378	49	,	,	PUNCT
gs-1575	378	50	(	(	PUNCT
gs-1575	378	51	1	1	NUM
gs-1575	378	52	[	[	PUNCT
gs-1575	378	53	(	(	PUNCT
gs-1575	378	54	)	)	PUNCT
gs-1575	378	55	]	]	PUNCT
gs-1575	378	56	)	)	PUNCT
gs-1575	378	57	4	4	NUM
gs-1575	379	1	i	i	PRON
gs-1575	379	2	n	n	VERB
gs-1575	379	3	n	n	CCONJ
gs-1575	379	4	n	n	NOUN
gs-1575	379	5	i	i	NOUN
gs-1575	379	6	x	x	PUNCT
gs-1575	379	7	x	x	VERB
gs-1575	379	8	i	i	PRON
gs-1575	379	9	n	n	VERB
gs-1575	379	10	f	f	NOUN
gs-1575	379	11	x	x	X
gs-1575	379	12	a	a	DET
gs-1575	379	13	n	n	NOUN
gs-1575	379	14	x	x	SYM
gs-1575	379	15	x	x	SYM
gs-1575	379	16	n	n	PRON
gs-1575	379	17			VERB
gs-1575	379	18			NUM
gs-1575	379	19			NUM
gs-1575	379	20			PROPN
gs-1575	379	21			PROPN
gs-1575	379	22			NOUN
gs-1575	379	23			NOUN
gs-1575	379	24	.	.	PUNCT
gs-1575	380	1	the	the	DET
gs-1575	380	2	estimations	estimation	NOUN
gs-1575	380	3	are	be	AUX
gs-1575	380	4	obtained	obtain	VERB
gs-1575	380	5	from	from	ADP
gs-1575	380	6	inequalities	inequality	NOUN
gs-1575	380	7	(	(	PUNCT
gs-1575	380	8	11	11	NUM
gs-1575	380	9	)	)	PUNCT
gs-1575	380	10	and	and	CCONJ
gs-1575	380	11	(	(	PUNCT
gs-1575	380	12	12	12	NUM
gs-1575	380	13	)	)	PUNCT
gs-1575	380	14	4	4	NUM
gs-1575	380	15	1	1	NUM
gs-1575	380	16	1	1	NUM
gs-1575	380	17	6	6	NUM
gs-1575	380	18	(	(	PUNCT
gs-1575	380	19	)	)	PUNCT
gs-1575	380	20	(	(	PUNCT
gs-1575	380	21	)	)	PUNCT
gs-1575	380	22	5	5	NUM
gs-1575	380	23	r	r	NOUN
gs-1575	380	24	n	n	NOUN
gs-1575	381	1	i	i	PRON
gs-1575	382	1	i	i	PRON
gs-1575	383	1	i	i	PRON
gs-1575	383	2	ej	ej	VERB
gs-1575	383	3	a	a	DET
gs-1575	383	4	p	p	X
gs-1575	383	5	f	f	X
gs-1575	383	6	x	x	SYM
gs-1575	383	7	dx	dx	PROPN
gs-1575	383	8	n	n	PROPN
gs-1575	383	9			PROPN
gs-1575	383	10			VERB
gs-1575	383	11			NOUN
gs-1575	383	12			NOUN
gs-1575	383	13			NOUN
gs-1575	383	14			NOUN
gs-1575	383	15			PUNCT
gs-1575	383	16			PROPN
gs-1575	384	1			PROPN
gs-1575	384	2	4	4	NUM
gs-1575	384	3	4	4	NUM
gs-1575	384	4	01	01	NUM
gs-1575	384	5	1	1	NUM
gs-1575	384	6	0,1	0,1	NUM
gs-1575	384	7	1	1	NUM
gs-1575	384	8	1	1	NUM
gs-1575	384	9	sup	sup	NOUN
gs-1575	384	10	(	(	PUNCT
gs-1575	384	11	)	)	PUNCT
gs-1575	384	12	(	(	PUNCT
gs-1575	384	13	)	)	PUNCT
gs-1575	384	14	r	r	NOUN
gs-1575	384	15	r	r	NOUN
gs-1575	385	1	i	i	PRON
gs-1575	385	2	i	i	PRON
gs-1575	385	3	a	a	INTJ
gs-1575	386	1	i	i	PRON
gs-1575	386	2	ai	ai	VERB
gs-1575	386	3	i	i	PRON
gs-1575	386	4	p	p	NOUN
gs-1575	386	5	f	f	PROPN
gs-1575	387	1	x	x	X
gs-1575	388	1	dx	dx	PROPN
gs-1575	388	2	c	c	NOUN
gs-1575	388	3	o	o	PROPN
gs-1575	388	4	n	n	CCONJ
gs-1575	388	5	n	n	CCONJ
gs-1575	388	6	n	n	CCONJ
gs-1575	388	7			PROPN
gs-1575	388	8			PROPN
gs-1575	388	9			PROPN
gs-1575	388	10			NOUN
gs-1575	388	11			VERB
gs-1575	388	12			PROPN
gs-1575	388	13			ADV
gs-1575	388	14			VERB
gs-1575	388	15			NUM
gs-1575	388	16	4	4	NUM
gs-1575	388	17	4	4	NUM
gs-1575	388	18	4	4	NUM
gs-1575	388	19	1	1	NUM
gs-1575	388	20	1	1	NUM
gs-1575	388	21	1	1	NUM
gs-1575	388	22	1	1	NUM
gs-1575	388	23	6	6	NUM
gs-1575	388	24	0,1	0,1	NUM
gs-1575	388	25	1	1	NUM
gs-1575	388	26	1	1	NUM
gs-1575	388	27	(	(	PUNCT
gs-1575	388	28	)	)	PUNCT
gs-1575	388	29	(	(	PUNCT
gs-1575	388	30	)	)	PUNCT
gs-1575	388	31	(	(	PUNCT
gs-1575	388	32	)	)	PUNCT
gs-1575	388	33	(	(	PUNCT
gs-1575	388	34	)	)	PUNCT
gs-1575	388	35	5	5	NUM
gs-1575	388	36	r	r	NOUN
gs-1575	388	37	r	r	NOUN
gs-1575	388	38	r	r	NOUN
gs-1575	388	39	n	n	NOUN
gs-1575	389	1	i	i	PRON
gs-1575	389	2	i	i	PRON
gs-1575	390	1	i	i	PRON
gs-1575	390	2	i	i	PRON
gs-1575	391	1	i	i	PRON
gs-1575	391	2	i	i	PRON
gs-1575	392	1	i	i	PRON
gs-1575	392	2	i	i	PRON
gs-1575	392	3	ej	ej	VERB
gs-1575	392	4	a	a	DET
gs-1575	392	5	p	p	X
gs-1575	392	6	f	f	X
gs-1575	393	1	x	x	X
gs-1575	393	2	dx	dx	PROPN
gs-1575	394	1	p	p	PROPN
gs-1575	394	2	f	f	PROPN
gs-1575	395	1	x	x	X
gs-1575	395	2	dx	dx	PROPN
gs-1575	396	1	c	c	PROPN
gs-1575	396	2	o	o	X
gs-1575	396	3	nn	nn	X
gs-1575	396	4	n	n	CCONJ
gs-1575	396	5	n	n	VERB
gs-1575	396	6			NOUN
gs-1575	396	7			VERB
gs-1575	396	8			NUM
gs-1575	396	9			PROPN
gs-1575	396	10			NOUN
gs-1575	396	11			VERB
gs-1575	396	12			PROPN
gs-1575	396	13			ADV
gs-1575	396	14			PUNCT
gs-1575	396	15			X
gs-1575	396	16			X
gs-1575	396	17			NUM
gs-1575	396	18			NOUN
gs-1575	396	19	discussion	discussion	NOUN
gs-1575	396	20	let	let	VERB
gs-1575	396	21	's	us	PRON
gs-1575	396	22	note	note	VERB
gs-1575	396	23	that	that	SCONJ
gs-1575	396	24	when	when	SCONJ
gs-1575	396	25	proving	prove	VERB
gs-1575	396	26	the	the	DET
gs-1575	396	27	theorem	theorem	NOUN
gs-1575	396	28	,	,	PUNCT
gs-1575	396	29	the	the	DET
gs-1575	396	30	trajectory	trajectory	NOUN
gs-1575	396	31	of	of	ADP
gs-1575	396	32	the	the	DET
gs-1575	396	33	control	control	NOUN
gs-1575	396	34	sequence	sequence	NOUN
gs-1575	396	35			NOUN
gs-1575	396	36	1	1	VERB
gs-1575	396	37	1	1	NUM
gs-1575	396	38	2	2	NUM
gs-1575	396	39	,	,	PUNCT
gs-1575	396	40	,	,	PUNCT
gs-1575	396	41	..	..	PUNCT
gs-1575	396	42	,	,	PUNCT
gs-1575	396	43	n	n	PRON
gs-1575	396	44	n	n	PRON
gs-1575	396	45			NOUN
gs-1575	396	46			NOUN
gs-1575	396	47			PUNCT
gs-1575	396	48	is	be	AUX
gs-1575	396	49	fixed	fix	VERB
gs-1575	396	50	and	and	CCONJ
gs-1575	396	51	the	the	DET
gs-1575	396	52	quantity	quantity	NOUN
gs-1575	396	53	(	(	PUNCT
gs-1575	396	54	)	)	PUNCT
gs-1575	396	55	nej	nej	NOUN
gs-1575	396	56	a	a	PRON
gs-1575	396	57	is	be	AUX
gs-1575	396	58	presented	present	VERB
gs-1575	396	59	as	as	ADP
gs-1575	396	60			PROPN
gs-1575	396	61	1	1	PROPN
gs-1575	396	62	(	(	PUNCT
gs-1575	396	63	)	)	PUNCT
gs-1575	396	64	(	(	PUNCT
gs-1575	396	65	(	(	PUNCT
gs-1575	396	66	)	)	PUNCT
gs-1575	396	67	)	)	PUNCT
gs-1575	396	68	n	n	CCONJ
gs-1575	396	69	n	n	ADV
gs-1575	396	70	nej	nej	VERB
gs-1575	396	71	a	a	DET
gs-1575	396	72	e	e	NOUN
gs-1575	396	73	e	e	X
gs-1575	396	74	j	j	PROPN
gs-1575	396	75	a	a	PRON
gs-1575	396	76			PUNCT
gs-1575	396	77	.	.	PUNCT
gs-1575	397	1	this	this	DET
gs-1575	397	2	method	method	NOUN
gs-1575	397	3	makes	make	VERB
gs-1575	397	4	it	it	PRON
gs-1575	397	5	possible	possible	ADJ
gs-1575	397	6	to	to	PART
gs-1575	397	7	use	use	VERB
gs-1575	397	8	the	the	DET
gs-1575	397	9	independence	independence	NOUN
gs-1575	397	10	of	of	ADP
gs-1575	397	11	observations	observation	NOUN
gs-1575	397	12	1	1	NUM
gs-1575	397	13	2	2	NUM
gs-1575	397	14	,	,	PUNCT
gs-1575	397	15	,	,	PUNCT
gs-1575	397	16	...	...	PUNCT
gs-1575	397	17	,	,	PUNCT
gs-1575	397	18	nx	nx	X
gs-1575	397	19	x	x	X
gs-1575	397	20	x	x	NOUN
gs-1575	397	21	on	on	ADP
gs-1575	397	22	a	a	DET
gs-1575	397	23	fixed	fix	VERB
gs-1575	397	24	trajectory	trajectory	NOUN
gs-1575	397	25	.	.	PUNCT
gs-1575	398	1	at	at	ADP
gs-1575	398	2	this	this	DET
gs-1575	398	3	time	time	NOUN
gs-1575	398	4	,	,	PUNCT
gs-1575	398	5	it	it	PRON
gs-1575	398	6	becomes	become	VERB
gs-1575	398	7	possible	possible	ADJ
gs-1575	398	8	to	to	PART
gs-1575	398	9	expand	expand	VERB
gs-1575	398	10	the	the	DET
gs-1575	398	11	estimated	estimate	VERB
gs-1575	398	12	sum	sum	NOUN
gs-1575	398	13	by	by	ADP
gs-1575	398	14	the	the	DET
gs-1575	398	15	method	method	NOUN
gs-1575	398	16	presented	present	VERB
gs-1575	398	17	in	in	ADP
gs-1575	398	18	[	[	X
gs-1575	398	19	11	11	NUM
gs-1575	398	20	]	]	PUNCT
gs-1575	398	21	and	and	CCONJ
gs-1575	398	22	[	[	X
gs-1575	398	23	15	15	NUM
gs-1575	398	24	]	]	PUNCT
gs-1575	398	25	.	.	PUNCT
gs-1575	399	1	grouping	group	VERB
gs-1575	399	2	of	of	ADP
gs-1575	399	3	identically	identically	ADV
gs-1575	399	4	distributed	distribute	VERB
gs-1575	399	5	values	value	NOUN
gs-1575	399	6	into	into	ADP
gs-1575	399	7	one	one	NUM
gs-1575	399	8	sum	sum	NOUN
gs-1575	399	9	according	accord	VERB
gs-1575	399	10	to	to	ADP
gs-1575	399	11	the	the	DET
gs-1575	399	12	values	value	NOUN
gs-1575	399	13	of	of	ADP
gs-1575	399	14	the	the	DET
gs-1575	399	15	control	control	NOUN
gs-1575	399	16	sequence	sequence	NOUN
gs-1575	399	17	is	be	AUX
gs-1575	399	18	used	use	VERB
gs-1575	399	19	.	.	PUNCT
gs-1575	400	1	each	each	DET
gs-1575	400	2	sum	sum	NOUN
gs-1575	400	3	is	be	AUX
gs-1575	400	4	then	then	ADV
gs-1575	400	5	represented	represent	VERB
gs-1575	400	6	as	as	ADP
gs-1575	400	7	two	two	NUM
gs-1575	400	8	sums	sum	NOUN
gs-1575	400	9	of	of	ADP
gs-1575	400	10	centered	center	VERB
gs-1575	400	11	quantities	quantity	NOUN
gs-1575	400	12	.	.	PUNCT
gs-1575	401	1	estimations	estimation	NOUN
gs-1575	401	2	for	for	ADP
gs-1575	401	3	one	one	NUM
gs-1575	401	4	of	of	ADP
gs-1575	401	5	them	they	PRON
gs-1575	401	6	are	be	AUX
gs-1575	401	7	written	write	VERB
gs-1575	401	8	down	down	ADP
gs-1575	401	9	using	use	VERB
gs-1575	401	10	the	the	DET
gs-1575	401	11	methods	method	NOUN
gs-1575	401	12	used	use	VERB
gs-1575	401	13	in	in	ADP
gs-1575	401	14	[	[	X
gs-1575	401	15	10	10	NUM
gs-1575	401	16	]	]	PUNCT
gs-1575	401	17	and	and	CCONJ
gs-1575	401	18	[	[	X
gs-1575	401	19	11	11	NUM
gs-1575	401	20	]	]	PUNCT
gs-1575	401	21	.	.	PUNCT
gs-1575	402	1	the	the	DET
gs-1575	402	2	sums	sum	NOUN
gs-1575	402	3	of	of	ADP
gs-1575	402	4	the	the	DET
gs-1575	402	5	second	second	ADJ
gs-1575	402	6	type	type	NOUN
gs-1575	402	7	are	be	AUX
gs-1575	402	8	evaluated	evaluate	VERB
gs-1575	402	9	by	by	ADP
gs-1575	402	10	the	the	DET
gs-1575	402	11	classical	classical	ADJ
gs-1575	402	12	results	result	NOUN
gs-1575	402	13	obtained	obtain	VERB
gs-1575	402	14	in	in	ADP
gs-1575	402	15	{	{	PUNCT
gs-1575	402	16	5	5	NUM
gs-1575	402	17	}	}	PUNCT
gs-1575	402	18	.	.	PUNCT
gs-1575	403	1	the	the	DET
gs-1575	403	2	measurability	measurability	NOUN
gs-1575	403	3	of	of	ADP
gs-1575	403	4	the	the	DET
gs-1575	403	5	quantities	quantity	NOUN
gs-1575	403	6			NOUN
gs-1575	403	7	n	n	PUNCT
gs-1575	403	8	i	i	ADJ
gs-1575	403	9	and	and	CCONJ
gs-1575	403	10	their	their	PRON
gs-1575	403	11	compositions	composition	NOUN
gs-1575	403	12	with	with	ADP
gs-1575	403	13	continuous	continuous	ADJ
gs-1575	403	14	functions	function	NOUN
gs-1575	403	15	(	(	PUNCT
gs-1575	403	16	see	see	VERB
gs-1575	403	17	[	[	X
gs-1575	403	18	19	19	NUM
gs-1575	403	19	]	]	PUNCT
gs-1575	403	20	)	)	PUNCT
gs-1575	403	21	with	with	ADP
gs-1575	403	22	respect	respect	NOUN
gs-1575	403	23	to	to	ADP
gs-1575	403	24	the	the	DET
gs-1575	403	25	sigma	sigma	PROPN
gs-1575	403	26	algebra	algebra	PROPN
gs-1575	403	27	generated	generate	VERB
gs-1575	403	28	by	by	ADP
gs-1575	403	29	the	the	DET
gs-1575	403	30	division	division	NOUN
gs-1575	403	31	of	of	ADP
gs-1575	403	32	the	the	DET
gs-1575	403	33	probability	probability	NOUN
gs-1575	403	34	space	space	NOUN
gs-1575	403	35	is	be	AUX
gs-1575	403	36	used	use	VERB
gs-1575	403	37	when	when	SCONJ
gs-1575	403	38	fixing	fix	VERB
gs-1575	403	39	the	the	DET
gs-1575	403	40	trajectory	trajectory	NOUN
gs-1575	403	41	1n	1n	PROPN
gs-1575	403	42	.	.	PUNCT
gs-1575	404	1	conclusion	conclusion	NOUN
gs-1575	404	2	.	.	PUNCT
gs-1575	405	1	with	with	ADP
gs-1575	405	2	the	the	DET
gs-1575	405	3	method	method	NOUN
gs-1575	405	4	used	use	VERB
gs-1575	405	5	in	in	ADP
gs-1575	405	6	the	the	DET
gs-1575	405	7	paper	paper	NOUN
gs-1575	405	8	,	,	PUNCT
gs-1575	405	9	it	it	PRON
gs-1575	405	10	is	be	AUX
gs-1575	405	11	possible	possible	ADJ
gs-1575	405	12	to	to	PART
gs-1575	405	13	determine	determine	VERB
gs-1575	405	14	the	the	DET
gs-1575	405	15	exact	exact	ADJ
gs-1575	405	16	upper	upper	ADJ
gs-1575	405	17	boundaries	boundary	NOUN
gs-1575	405	18	of	of	ADP
gs-1575	405	19	the	the	DET
gs-1575	405	20	obtained	obtain	VERB
gs-1575	405	21	estimates	estimate	NOUN
gs-1575	405	22	.	.	PUNCT
gs-1575	406	1	the	the	DET
gs-1575	406	2	method	method	NOUN
gs-1575	406	3	gives	give	VERB
gs-1575	406	4	the	the	DET
gs-1575	406	5	possibility	possibility	NOUN
gs-1575	406	6	to	to	PART
gs-1575	406	7	be	be	AUX
gs-1575	406	8	used	use	VERB
gs-1575	406	9	in	in	ADP
gs-1575	406	10	determining	determine	VERB
gs-1575	406	11	the	the	DET
gs-1575	406	12	accuracy	accuracy	NOUN
gs-1575	406	13	of	of	ADP
gs-1575	406	14	other	other	ADJ
gs-1575	406	15	(	(	PUNCT
gs-1575	406	16	including	include	VERB
gs-1575	406	17	non	non	ADJ
gs-1575	406	18	-	-	ADJ
gs-1575	406	19	parametric	parametric	ADJ
gs-1575	406	20	)	)	PUNCT
gs-1575	406	21	estimates	estimate	NOUN
gs-1575	406	22	.	.	PUNCT
gs-1575	407	1	we	we	PRON
gs-1575	407	2	would	would	AUX
gs-1575	407	3	like	like	VERB
gs-1575	407	4	to	to	PART
gs-1575	407	5	be	be	AUX
gs-1575	407	6	thankful	thankful	ADJ
gs-1575	407	7	to	to	ADP
gs-1575	407	8	our	our	PRON
gs-1575	407	9	colleague	colleague	NOUN
gs-1575	407	10	prof	prof	PROPN
gs-1575	407	11	.	.	PUNCT
gs-1575	408	1	tengiz	tengiz	PROPN
gs-1575	408	2	shervashidze	shervashidze	PROPN
gs-1575	408	3	and	and	CCONJ
gs-1575	408	4	will	will	AUX
gs-1575	408	5	honor	honor	VERB
gs-1575	408	6	his	his	PRON
gs-1575	408	7	bright	bright	ADJ
gs-1575	408	8	memory	memory	NOUN
gs-1575	408	9	.	.	PUNCT
gs-1575	409	1	references	reference	NOUN
gs-1575	409	2	1	1	NUM
gs-1575	409	3	.	.	PUNCT
gs-1575	409	4	m.	m.	NOUN
gs-1575	409	5	rosenblatt	rosenblatt	PROPN
gs-1575	409	6	(	(	PUNCT
gs-1575	409	7	1956	1956	NUM
gs-1575	409	8	)	)	PUNCT
gs-1575	409	9	,	,	PUNCT
gs-1575	409	10	remarks	remark	VERB
gs-1575	409	11	on	on	ADP
gs-1575	409	12	some	some	DET
gs-1575	409	13	nonparametric	nonparametric	ADJ
gs-1575	409	14	estimates	estimate	NOUN
gs-1575	409	15	of	of	ADP
gs-1575	409	16	a	a	DET
gs-1575	409	17	density	density	NOUN
gs-1575	409	18	function	function	NOUN
gs-1575	409	19	.	.	PUNCT
gs-1575	410	1	ann	ann	PROPN
gs-1575	410	2	.	.	PUNCT
gs-1575	410	3	math	math	PROPN
gs-1575	410	4	.	.	PUNCT
gs-1575	411	1	statist	statist	NOUN
gs-1575	411	2	.	.	PUNCT
gs-1575	412	1	27	27	NUM
gs-1575	412	2	,	,	PUNCT
gs-1575	412	3	chicago	chicago	PROPN
gs-1575	412	4	,	,	PUNCT
gs-1575	412	5	832	832	NUM
gs-1575	412	6	-	-	SYM
gs-1575	412	7	837	837	NUM
gs-1575	412	8	.	.	PUNCT
gs-1575	413	1	2	2	X
gs-1575	413	2	.	.	X
gs-1575	413	3	e.	e.	PROPN
gs-1575	413	4	parzen	parzen	PROPN
gs-1575	413	5	(	(	PUNCT
gs-1575	413	6	1962	1962	NUM
gs-1575	413	7	)	)	PUNCT
gs-1575	413	8	,	,	PUNCT
gs-1575	413	9	on	on	ADP
gs-1575	413	10	estimation	estimation	NOUN
gs-1575	413	11	of	of	ADP
gs-1575	413	12	a	a	DET
gs-1575	413	13	probability	probability	NOUN
gs-1575	413	14	density	density	NOUN
gs-1575	413	15	function	function	NOUN
gs-1575	413	16	and	and	CCONJ
gs-1575	413	17	mode	mode	NOUN
gs-1575	413	18	.	.	PUNCT
gs-1575	414	1	ann	ann	PROPN
gs-1575	414	2	.	.	PUNCT
gs-1575	414	3	math	math	PROPN
gs-1575	414	4	.	.	PUNCT
gs-1575	415	1	statist.33	statist.33	PROPN
gs-1575	415	2	,	,	PUNCT
gs-1575	415	3	stanford	stanford	PROPN
gs-1575	415	4	,	,	PUNCT
gs-1575	415	5	usa	usa	PROPN
gs-1575	415	6	,	,	PUNCT
gs-1575	415	7	1065	1065	NUM
gs-1575	415	8	-	-	SYM
gs-1575	415	9	1076	1076	NUM
gs-1575	415	10	.	.	PUNCT
gs-1575	416	1	3	3	X
gs-1575	416	2	.	.	X
gs-1575	416	3	g.	g.	PROPN
gs-1575	416	4	s.	s.	PROPN
gs-1575	416	5	watson	watson	PROPN
gs-1575	416	6	,	,	PUNCT
gs-1575	416	7	m.r	m.r	PROPN
gs-1575	416	8	.	.	PROPN
gs-1575	416	9	leadbetter	leadbetter	PROPN
gs-1575	416	10	(	(	PUNCT
gs-1575	416	11	1963	1963	NUM
gs-1575	416	12	)	)	PUNCT
gs-1575	416	13	on	on	ADP
gs-1575	416	14	the	the	DET
gs-1575	416	15	estimation	estimation	NOUN
gs-1575	416	16	of	of	ADP
gs-1575	416	17	the	the	DET
gs-1575	416	18	probability	probability	NOUN
gs-1575	416	19	density	density	NOUN
gs-1575	416	20	.	.	PUNCT
gs-1575	417	1	ann	ann	PROPN
gs-1575	417	2	.	.	PUNCT
gs-1575	417	3	math	math	PROPN
gs-1575	417	4	.	.	PUNCT
gs-1575	418	1	statist	statist	PROPN
gs-1575	418	2	.	.	PUNCT
gs-1575	419	1	34	34	NUM
gs-1575	419	2	,	,	PUNCT
gs-1575	419	3	toronto	toronto	PROPN
gs-1575	419	4	,	,	PUNCT
gs-1575	419	5	:	:	PUNCT
gs-1575	419	6	480	480	NUM
gs-1575	419	7	-	-	SYM
gs-1575	419	8	491	491	NUM
gs-1575	419	9	.	.	PUNCT
gs-1575	420	1	4	4	X
gs-1575	420	2	.	.	X
gs-1575	420	3	e.	e.	PROPN
gs-1575	420	4	a.	a.	PROPN
gs-1575	420	5	nadaraya	nadaraya	PROPN
gs-1575	420	6	(	(	PUNCT
gs-1575	420	7	1983	1983	NUM
gs-1575	420	8	)	)	PUNCT
gs-1575	420	9	,	,	PUNCT
gs-1575	420	10	nonparametric	nonparametric	NOUN
gs-1575	420	11	estimation	estimation	NOUN
gs-1575	420	12	of	of	ADP
gs-1575	420	13	the	the	DET
gs-1575	420	14	probability	probability	NOUN
gs-1575	420	15	density	density	NOUN
gs-1575	420	16	and	and	CCONJ
gs-1575	420	17	regression	regression	NOUN
gs-1575	420	18	curve	curve	NOUN
gs-1575	420	19	.	.	PUNCT
gs-1575	421	1	(	(	PUNCT
gs-1575	421	2	in	in	ADP
gs-1575	421	3	russian	russian	PROPN
gs-1575	421	4	)	)	PUNCT
gs-1575	421	5	tbilisi	tbilisi	PROPN
gs-1575	421	6	state	state	PROPN
gs-1575	421	7	univ	univ	PROPN
gs-1575	421	8	.	.	PUNCT
gs-1575	422	1	press	press	PROPN
gs-1575	422	2	,	,	PUNCT
gs-1575	422	3	1983	1983	NUM
gs-1575	422	4	.	.	PUNCT
gs-1575	423	1	georgian	georgian	ADJ
gs-1575	423	2	scientists/ქართველი	scientists/ქართველი	PROPN
gs-1575	423	3	მეცნიერები	მეცნიერები	NOUN
gs-1575	423	4	ტ.	ტ.	VERB
gs-1575	423	5	5	5	NUM
gs-1575	423	6	n	n	PRON
gs-1575	423	7	1	1	NUM
gs-1575	423	8	,	,	PUNCT
gs-1575	423	9	2023	2023	NUM
gs-1575	423	10	318	318	NUM
gs-1575	423	11	5	5	NUM
gs-1575	423	12	.	.	PUNCT
gs-1575	424	1	devroye	devroye	PROPN
gs-1575	424	2	l.	l.	PROPN
gs-1575	424	3	,	,	PUNCT
gs-1575	424	4	györfi	györfi	PROPN
gs-1575	424	5	l.	l.	PROPN
gs-1575	424	6	nonparametric	nonparametric	PROPN
gs-1575	424	7	density	density	PROPN
gs-1575	424	8	estimation	estimation	PROPN
gs-1575	424	9	:	:	PUNCT
gs-1575	424	10	the	the	DET
gs-1575	424	11	1l	1l	NUM
gs-1575	424	12	view	view	NOUN
gs-1575	424	13	.	.	PUNCT
gs-1575	425	1	wiley	wiley	PROPN
gs-1575	425	2	series	series	PROPN
gs-1575	425	3	in	in	ADP
gs-1575	425	4	probability	probability	NOUN
gs-1575	425	5	and	and	CCONJ
gs-1575	425	6	mathematical	mathematical	ADJ
gs-1575	425	7	statistics	statistic	NOUN
gs-1575	425	8	,	,	PUNCT
gs-1575	425	9	canada	canada	PROPN
gs-1575	425	10	:	:	PUNCT
gs-1575	425	11	john	john	PROPN
gs-1575	425	12	wiley	wiley	PROPN
gs-1575	425	13	&	&	CCONJ
gs-1575	425	14	sons	son	NOUN
gs-1575	425	15	;	;	PUNCT
gs-1575	425	16	1985	1985	NUM
gs-1575	425	17	.	.	PUNCT
gs-1575	426	1	p.	p.	NOUN
gs-1575	426	2	367	367	NUM
gs-1575	426	3	.	.	PUNCT
gs-1575	427	1	6	6	NUM
gs-1575	427	2	.	.	PUNCT
gs-1575	427	3	r.	r.	PROPN
gs-1575	427	4	z.	z.	PROPN
gs-1575	427	5	khasminski	khasminski	PROPN
gs-1575	427	6	,	,	PUNCT
gs-1575	427	7	on	on	ADP
gs-1575	427	8	limiting	limit	VERB
gs-1575	427	9	distributions	distribution	NOUN
gs-1575	427	10	for	for	ADP
gs-1575	427	11	sums	sum	NOUN
gs-1575	427	12	of	of	ADP
gs-1575	427	13	conditionally	conditionally	ADV
gs-1575	427	14	independent	independent	ADJ
gs-1575	427	15	random	random	ADJ
gs-1575	427	16	variables	variable	NOUN
gs-1575	427	17	.	.	PUNCT
gs-1575	428	1	(	(	PUNCT
gs-1575	428	2	russian	russian	ADJ
gs-1575	428	3	)	)	PUNCT
gs-1575	428	4	teor	teor	PROPN
gs-1575	428	5	.	.	PUNCT
gs-1575	428	6	verojatnosti	verojatnosti	PROPN
gs-1575	428	7	.	.	PUNCT
gs-1575	429	1	i	i	PRON
gs-1575	429	2	primenen	primenen	VERB
gs-1575	429	3	.	.	PUNCT
gs-1575	430	1	6	6	NUM
gs-1575	430	2	.	.	X
gs-1575	430	3	(	(	PUNCT
gs-1575	430	4	1961	1961	NUM
gs-1575	430	5	)	)	PUNCT
gs-1575	430	6	.	.	PUNCT
gs-1575	431	1	№	№	VERB
gs-1575	431	2	1,.119	1,.119	NUM
gs-1575	431	3	-	-	SYM
gs-1575	431	4	125	125	NUM
gs-1575	431	5	.	.	PUNCT
gs-1575	432	1	7	7	X
gs-1575	432	2	.	.	PUNCT
gs-1575	432	3	g.	g.	PROPN
gs-1575	432	4	l.	l.	PROPN
gs-1575	432	5	o'brien	o'brien	PROPN
gs-1575	432	6	,	,	PUNCT
gs-1575	432	7	limit	limit	VERB
gs-1575	432	8	theorems	theorem	NOUN
gs-1575	432	9	for	for	ADP
gs-1575	432	10	sums	sum	NOUN
gs-1575	432	11	of	of	ADP
gs-1575	432	12	chain	chain	NOUN
gs-1575	432	13	-	-	PUNCT
gs-1575	432	14	dependent	dependent	ADJ
gs-1575	432	15	processes	process	NOUN
gs-1575	432	16	.	.	PUNCT
gs-1575	433	1	j.	j.	PROPN
gs-1575	433	2	appl	appl	PROPN
gs-1575	433	3	.	.	PROPN
gs-1575	434	1	probability	probability	NOUN
gs-1575	434	2	11	11	NUM
gs-1575	434	3	(	(	PUNCT
gs-1575	434	4	1974	1974	NUM
gs-1575	434	5	)	)	PUNCT
gs-1575	434	6	,	,	PUNCT
gs-1575	434	7	582	582	NUM
gs-1575	434	8	-	-	SYM
gs-1575	434	9	587	587	NUM
gs-1575	434	10	.	.	PUNCT
gs-1575	435	1	8	8	NUM
gs-1575	435	2	.	.	PUNCT
gs-1575	435	3	bokuchava	bokuchava	PROPN
gs-1575	435	4	i.	i.	PROPN
gs-1575	435	5	v.	v.	PROPN
gs-1575	435	6	(	(	PUNCT
gs-1575	435	7	1984	1984	NUM
gs-1575	435	8	)	)	PUNCT
gs-1575	435	9	limit	limit	NOUN
gs-1575	435	10	theorems	theorem	NOUN
gs-1575	435	11	for	for	ADP
gs-1575	435	12	conditionally	conditionally	ADV
gs-1575	435	13	independent	independent	ADJ
gs-1575	435	14	sequences	sequence	NOUN
gs-1575	435	15	.	.	PUNCT
gs-1575	435	16	.	.	PUNCT
gs-1575	436	1	(	(	PUNCT
gs-1575	436	2	in	in	ADP
gs-1575	436	3	russian	russian	PROPN
gs-1575	436	4	)	)	PUNCT
gs-1575	436	5	teor	teor	PROPN
gs-1575	436	6	.	.	PUNCT
gs-1575	436	7	verojatnost	verojatnost	PROPN
gs-1575	436	8	.	.	PUNCT
gs-1575	437	1	i	i	PRON
gs-1575	437	2	primenen.-mathnet.ru	primenen.-mathnet.ru	X
gs-1575	437	3	xxix	xxix	PROPN
gs-1575	437	4	.	.	PUNCT
gs-1575	438	1	(	(	PUNCT
gs-1575	438	2	1984	1984	NUM
gs-1575	438	3	)	)	PUNCT
gs-1575	438	4	.	.	PUNCT
gs-1575	439	1	№	№	ADP
gs-1575	439	2	1	1	NUM
gs-1575	439	3	,	,	PUNCT
gs-1575	439	4	.	.	PUNCT
gs-1575	440	1	p.	p.	NOUN
gs-1575	440	2	192	192	NUM
gs-1575	440	3	-	-	SYM
gs-1575	440	4	193.1984	193.1984	NUM
gs-1575	440	5	.	.	NOUN
gs-1575	440	6	theory	theory	NOUN
gs-1575	440	7	of	of	ADP
gs-1575	440	8	probability	probability	NOUN
gs-1575	440	9	and	and	CCONJ
gs-1575	440	10	its	its	PRON
gs-1575	440	11	applications	application	NOUN
gs-1575	440	12	,	,	PUNCT
gs-1575	440	13	1985	1985	NUM
gs-1575	440	14	,	,	PUNCT
gs-1575	440	15	29:1	29:1	NUM
gs-1575	440	16	,	,	PUNCT
gs-1575	440	17	190	190	NUM
gs-1575	440	18	-	-	SYM
gs-1575	440	19	196	196	NUM
gs-1575	440	20	9	9	NUM
gs-1575	440	21	.	.	PUNCT
gs-1575	441	1	kvatadze	kvatadze	PROPN
gs-1575	441	2	z.	z.	PROPN
gs-1575	441	3	,	,	PUNCT
gs-1575	441	4	shervashidze	shervashidze	ADJ
gs-1575	441	5	t.	t.	PROPN
gs-1575	441	6	(	(	PUNCT
gs-1575	441	7	2008	2008	NUM
gs-1575	441	8	)	)	PUNCT
gs-1575	441	9	some	some	DET
gs-1575	441	10	limit	limit	VERB
gs-1575	441	11	theorems	theorem	VERB
gs-1575	441	12	for	for	ADP
gs-1575	441	13	i.i.d	i.i.d	PROPN
gs-1575	441	14	.	.	PUNCT
gs-1575	441	15	and	and	CCONJ
gs-1575	441	16	conditionally	conditionally	ADV
gs-1575	441	17	independent	independent	ADJ
gs-1575	441	18	random	random	ADJ
gs-1575	441	19	variables	variable	NOUN
gs-1575	441	20	.	.	PUNCT
gs-1575	442	1	the	the	DET
gs-1575	442	2	second	second	ADJ
gs-1575	442	3	international	international	ADJ
gs-1575	442	4	conference	conference	NOUN
gs-1575	442	5	,	,	PUNCT
gs-1575	442	6	“	"	PUNCT
gs-1575	442	7	problems	problem	NOUN
gs-1575	442	8	of	of	ADP
gs-1575	442	9	cybernetics	cybernetic	NOUN
gs-1575	442	10	and	and	CCONJ
gs-1575	442	11	informatics	informatic	NOUN
gs-1575	442	12	“	"	PUNCT
gs-1575	442	13	.	.	PUNCT
gs-1575	443	1	september	september	PROPN
gs-1575	443	2	10	10	NUM
gs-1575	443	3	-	-	SYM
gs-1575	443	4	12	12	NUM
gs-1575	443	5	,	,	PUNCT
gs-1575	443	6	2008	2008	NUM
gs-1575	443	7	.	.	PUNCT
gs-1575	444	1	baku	baku	PROPN
gs-1575	444	2	,	,	PUNCT
gs-1575	444	3	azerbaijan	azerbaijan	PROPN
gs-1575	444	4	.	.	PROPN
gs-1575	444	5	section	section	NOUN
gs-1575	444	6	#	#	SYM
gs-1575	444	7	4	4	NUM
gs-1575	444	8	.	.	PUNCT
gs-1575	445	1	“	"	PUNCT
gs-1575	445	2	applied	apply	VERB
gs-1575	445	3	stochastic	stochastic	ADJ
gs-1575	445	4	analysis	analysis	NOUN
gs-1575	445	5	”	"	PUNCT
gs-1575	445	6	www.pci2008.science.az/4/12.pdf	www.pci2008.science.az/4/12.pdf	ADJ
gs-1575	445	7	.	.	PUNCT
gs-1575	446	1	azerbaijan	azerbaijan	PROPN
gs-1575	446	2	national	national	PROPN
gs-1575	446	3	academy	academy	PROPN
gs-1575	446	4	of	of	ADP
gs-1575	446	5	sciences	sciences	PROPN
gs-1575	446	6	.	.	PUNCT
gs-1575	447	1	institute	institute	PROPN
gs-1575	447	2	of	of	ADP
gs-1575	447	3	information	information	NOUN
gs-1575	447	4	technology	technology	NOUN
gs-1575	447	5	.	.	PUNCT
gs-1575	448	1	printing	print	VERB
gs-1575	448	2	house	house	NOUN
gs-1575	448	3	of	of	ADP
gs-1575	448	4	“	"	PUNCT
gs-1575	448	5	information	information	NOUN
gs-1575	448	6	technology	technology	NOUN
gs-1575	448	7	”	"	PUNCT
gs-1575	448	8	baku	baku	PROPN
gs-1575	448	9	.	.	PROPN
gs-1575	448	10	2008	2008	NUM
gs-1575	448	11	.	.	PUNCT
gs-1575	449	1	vol	vol	NOUN
gs-1575	449	2	.	.	PUNCT
gs-1575	449	3	ii	ii	PROPN
gs-1575	449	4	.	.	PUNCT
gs-1575	450	1	pp.217	pp.217	PROPN
gs-1575	450	2	-	-	SYM
gs-1575	450	3	219	219	NUM
gs-1575	450	4	.	.	PUNCT
gs-1575	451	1	10	10	NUM
gs-1575	451	2	.	.	PUNCT
gs-1575	452	1	i.	i.	PROPN
gs-1575	452	2	v.	v.	PROPN
gs-1575	452	3	bokuchava	bokuchava	PROPN
gs-1575	452	4	,	,	PUNCT
gs-1575	452	5	z.	z.	PROPN
gs-1575	452	6	kvatadze	kvatadze	PROPN
gs-1575	452	7	,	,	PUNCT
gs-1575	452	8	t.	t.	PROPN
gs-1575	452	9	shervashidze	shervashidze	PROPN
gs-1575	452	10	,	,	PUNCT
gs-1575	452	11	on	on	ADP
gs-1575	452	12	limit	limit	NOUN
gs-1575	452	13	theorems	theorem	NOUN
gs-1575	452	14	for	for	ADP
gs-1575	452	15	random	random	ADJ
gs-1575	452	16	vectors	vector	NOUN
gs-1575	452	17	controlled	control	VERB
gs-1575	452	18	by	by	ADP
gs-1575	452	19	a	a	DET
gs-1575	452	20	markov	markov	NOUN
gs-1575	452	21	chain	chain	NOUN
gs-1575	452	22	.	.	PUNCT
gs-1575	453	1	probability	probability	NOUN
gs-1575	453	2	theory	theory	NOUN
gs-1575	453	3	and	and	CCONJ
gs-1575	453	4	mathematical	mathematical	ADJ
gs-1575	453	5	statistics	statistic	NOUN
gs-1575	453	6	,	,	PUNCT
gs-1575	453	7	vol	vol	NOUN
gs-1575	453	8	.	.	PUNCT
gs-1575	454	1	i	i	PRON
gs-1575	454	2	(	(	PUNCT
gs-1575	454	3	vilnius	vilnius	PROPN
gs-1575	454	4	,	,	PUNCT
gs-1575	454	5	1985	1985	NUM
gs-1575	454	6	)	)	PUNCT
gs-1575	454	7	,	,	PUNCT
gs-1575	454	8	231	231	NUM
gs-1575	454	9	-	-	SYM
gs-1575	454	10	250	250	NUM
gs-1575	454	11	,	,	PUNCT
gs-1575	454	12	vnu	vnu	PROPN
gs-1575	454	13	sci	sci	PROPN
gs-1575	454	14	.	.	PUNCT
gs-1575	455	1	press	press	PROPN
gs-1575	455	2	,	,	PUNCT
gs-1575	455	3	utrecht	utrecht	PROPN
gs-1575	455	4	,	,	PUNCT
gs-1575	455	5	1987	1987	NUM
gs-1575	455	6	.	.	PUNCT
gs-1575	456	1	11	11	NUM
gs-1575	456	2	.	.	PUNCT
gs-1575	457	1	kvatadze	kvatadze	PROPN
gs-1575	457	2	z.	z.	PROPN
gs-1575	457	3	,	,	PUNCT
gs-1575	457	4	shervashidze	shervashidze	ADJ
gs-1575	457	5	t.	t.	PROPN
gs-1575	457	6	(	(	PUNCT
gs-1575	457	7	1987	1987	NUM
gs-1575	457	8	)	)	PUNCT
gs-1575	457	9	on	on	ADP
gs-1575	457	10	limit	limit	NOUN
gs-1575	457	11	theorems	theorem	NOUN
gs-1575	457	12	for	for	ADP
gs-1575	457	13	conditionally	conditionally	ADV
gs-1575	457	14	independent	independent	ADJ
gs-1575	457	15	random	random	ADJ
gs-1575	457	16	variable	variable	NOUN
gs-1575	457	17	controlled	control	VERB
gs-1575	457	18	by	by	ADP
gs-1575	457	19	a	a	DET
gs-1575	457	20	finite	finite	ADJ
gs-1575	457	21	markov	markov	NOUN
gs-1575	457	22	chain	chain	NOUN
gs-1575	457	23	.	.	PUNCT
gs-1575	458	1	probability	probability	NOUN
gs-1575	458	2	theory	theory	NOUN
gs-1575	458	3	and	and	CCONJ
gs-1575	458	4	mathematical	mathematical	ADJ
gs-1575	458	5	statistics	statistic	NOUN
gs-1575	458	6	.	.	PUNCT
gs-1575	459	1	(	(	PUNCT
gs-1575	459	2	proc	proc	NOUN
gs-1575	459	3	.	.	PUNCT
gs-1575	460	1	5th	5th	ADJ
gs-1575	460	2	japan	japan	PROPN
gs-1575	460	3	-	-	PUNCT
gs-1575	460	4	ussr	ussr	ADJ
gs-1575	460	5	symposium	symposium	NOUN
gs-1575	460	6	on	on	ADP
gs-1575	460	7	probability	probability	NOUN
gs-1575	460	8	theory	theory	NOUN
gs-1575	460	9	.	.	PUNCT
gs-1575	461	1	kyoto	kyoto	PROPN
gs-1575	461	2	.	.	PUNCT
gs-1575	461	3	1986	1986	NUM
gs-1575	461	4	)	)	PUNCT
gs-1575	461	5	.	.	PUNCT
gs-1575	462	1	lecture	lecture	NOUN
gs-1575	462	2	notes	note	NOUN
gs-1575	462	3	in	in	ADP
gs-1575	462	4	mathematics	mathematic	NOUN
gs-1575	462	5	,	,	PUNCT
gs-1575	462	6	1299	1299	NUM
gs-1575	462	7	:	:	PUNCT
gs-1575	463	1	250	250	NUM
gs-1575	463	2	-	-	SYM
gs-1575	463	3	259	259	NUM
gs-1575	463	4	.	.	PUNCT
gs-1575	463	5	springer	springer	NOUN
gs-1575	463	6	-	-	PUNCT
gs-1575	463	7	verlag	verlag	PROPN
gs-1575	463	8	.	.	PUNCT
gs-1575	464	1	berlin	berlin	PROPN
gs-1575	464	2	(	(	PUNCT
gs-1575	464	3	germany	germany	PROPN
gs-1575	464	4	)	)	PUNCT
gs-1575	464	5	.	.	PUNCT
gs-1575	465	1	12	12	NUM
gs-1575	465	2	.	.	PUNCT
gs-1575	465	3	yakowitz	yakowitz	PROPN
gs-1575	465	4	sidney	sidney	PROPN
gs-1575	465	5	(	(	PUNCT
gs-1575	465	6	1989	1989	NUM
gs-1575	465	7	)	)	PUNCT
gs-1575	465	8	nonparametric	nonparametric	NOUN
gs-1575	465	9	density	density	NOUN
gs-1575	465	10	and	and	CCONJ
gs-1575	465	11	regression	regression	NOUN
gs-1575	465	12	estimation	estimation	NOUN
gs-1575	465	13	for	for	ADP
gs-1575	465	14	markov	markov	NOUN
gs-1575	465	15	sequences	sequence	NOUN
gs-1575	465	16	without	without	ADP
gs-1575	465	17	mixing	mix	VERB
gs-1575	465	18	assumptions	assumption	NOUN
gs-1575	465	19	.	.	PUNCT
gs-1575	466	1	85721	85721	NUM
gs-1575	466	2	–	–	PUNCT
gs-1575	466	3	journal	journal	NOUN
gs-1575	466	4	of	of	ADP
gs-1575	466	5	multivariate	multivariate	NOUN
gs-1575	466	6	analysis	analysis	NOUN
gs-1575	466	7	,	,	PUNCT
gs-1575	466	8	30	30	NUM
gs-1575	466	9	:	:	SYM
gs-1575	466	10	124	124	NUM
gs-1575	466	11	-	-	SYM
gs-1575	466	12	136	136	NUM
gs-1575	466	13	.	.	PUNCT
gs-1575	467	1	arisona	arisona	PROPN
gs-1575	467	2	,	,	PUNCT
gs-1575	467	3	usa	usa	PROPN
gs-1575	467	4	.	.	PROPN
gs-1575	467	5	13	13	NUM
gs-1575	467	6	.	.	PUNCT
gs-1575	468	1	j.	j.	PROPN
gs-1575	468	2	meloche	meloche	PROPN
gs-1575	468	3	.	.	PUNCT
gs-1575	469	1	asymptotic	asymptotic	ADJ
gs-1575	469	2	behavior	behavior	NOUN
gs-1575	469	3	of	of	ADP
gs-1575	469	4	the	the	DET
gs-1575	469	5	mean	mean	NOUN
gs-1575	469	6	integrated	integrate	VERB
gs-1575	469	7	squared	square	VERB
gs-1575	469	8	error	error	NOUN
gs-1575	469	9	of	of	ADP
gs-1575	469	10	kernel	kernel	NOUN
gs-1575	469	11	density	density	NOUN
gs-1575	469	12	estimators	estimator	NOUN
gs-1575	469	13	for	for	ADP
gs-1575	469	14	dependent	dependent	ADJ
gs-1575	469	15	observations	observation	NOUN
gs-1575	469	16	.	.	PUNCT
gs-1575	470	1	canadian	canadian	ADJ
gs-1575	470	2	journal	journal	PROPN
gs-1575	470	3	of	of	ADP
gs-1575	470	4	statistics	statistic	NOUN
gs-1575	470	5	.	.	PUNCT
gs-1575	471	1	2009	2009	NUM
gs-1575	471	2	.	.	PUNCT
gs-1575	471	3	,	,	PUNCT
gs-1575	471	4	18	18	NUM
gs-1575	471	5	(	(	PUNCT
gs-1575	471	6	3	3	NUM
gs-1575	471	7	):	):	PUNCT
gs-1575	471	8	p.	p.	NOUN
gs-1575	471	9	205211	205211	NUM
gs-1575	471	10	.	.	PUNCT
gs-1575	472	1	14	14	NUM
gs-1575	472	2	.	.	X
gs-1575	473	1	z	z	X
gs-1575	473	2	,	,	PUNCT
gs-1575	473	3	kvatadze	kvatadze	PROPN
gs-1575	473	4	,	,	PUNCT
gs-1575	473	5	b.	b.	PROPN
gs-1575	473	6	phardjiani	phardjiani	PROPN
gs-1575	473	7	.	.	PUNCT
gs-1575	474	1	on	on	ADP
gs-1575	474	2	the	the	DET
gs-1575	474	3	exsactness	exsactness	NOUN
gs-1575	474	4	of	of	ADP
gs-1575	474	5	distribution	distribution	NOUN
gs-1575	474	6	density	density	NOUN
gs-1575	474	7	estimates	estimate	NOUN
gs-1575	474	8	constructed	construct	VERB
gs-1575	474	9	by	by	ADP
gs-1575	474	10	some	some	DET
gs-1575	474	11	class	class	NOUN
gs-1575	474	12	of	of	ADP
gs-1575	474	13	dependent	dependent	ADJ
gs-1575	474	14	observations	observation	NOUN
gs-1575	474	15	.	.	PUNCT
gs-1575	475	1	mathematics	mathematic	NOUN
gs-1575	475	2	and	and	CCONJ
gs-1575	475	3	statistics	statistic	NOUN
gs-1575	475	4	.	.	PUNCT
gs-1575	476	1	2019	2019	NUM
gs-1575	476	2	vol	vol	NOUN
gs-1575	476	3	.	.	PUNCT
gs-1575	477	1	7(4	7(4	NUM
gs-1575	477	2	)	)	PUNCT
gs-1575	477	3	,	,	PUNCT
gs-1575	477	4	pp	pp	PROPN
gs-1575	477	5	.	.	PUNCT
gs-1575	478	1	135	135	NUM
gs-1575	478	2	-	-	SYM
gs-1575	478	3	145	145	NUM
gs-1575	478	4	.	.	PUNCT
gs-1575	479	1	san	san	PROPN
gs-1575	479	2	jose	jose	PROPN
gs-1575	479	3	.	.	PUNCT
gs-1575	480	1	15	15	NUM
gs-1575	480	2	.	.	PUNCT
gs-1575	481	1	kvatadze	kvatadze	PROPN
gs-1575	481	2	z.	z.	PROPN
gs-1575	481	3	,	,	PUNCT
gs-1575	481	4	pharjiani	pharjiani	PROPN
gs-1575	481	5	b.	b.	PROPN
gs-1575	481	6	,	,	PUNCT
gs-1575	481	7	construction	construction	NOUN
gs-1575	481	8	of	of	ADP
gs-1575	481	9	a	a	DET
gs-1575	481	10	kernel	kernel	PROPN
gs-1575	481	11	density	density	NOUN
gs-1575	481	12	estimator	estimator	NOUN
gs-1575	481	13	of	of	ADP
gs-1575	481	14	rosenblatt	rosenblatt	PROPN
gs-1575	481	15	-	-	PUNCT
gs-1575	481	16	parzen	parzen	NOUN
gs-1575	481	17	type	type	NOUN
gs-1575	481	18	by	by	ADP
gs-1575	481	19	conditionally	conditionally	ADV
gs-1575	481	20	independent	independent	ADJ
gs-1575	481	21	observations	observation	NOUN
gs-1575	481	22	.	.	PUNCT
gs-1575	482	1	proceedings	proceeding	NOUN
gs-1575	482	2	of	of	ADP
gs-1575	482	3	a.	a.	NOUN
gs-1575	482	4	razmadze	razmadze	PROPN
gs-1575	482	5	mathematical	mathematical	PROPN
gs-1575	482	6	institute	institute	PROPN
gs-1575	482	7	.	.	PUNCT
gs-1575	483	1	vol	vol	NOUN
gs-1575	483	2	.	.	PUNCT
gs-1575	484	1	173	173	NUM
gs-1575	484	2	.	.	X
gs-1575	485	1	2019	2019	NUM
gs-1575	485	2	.	.	PUNCT
gs-1575	486	1	issue	issue	NOUN
gs-1575	486	2	3	3	NUM
gs-1575	486	3	,	,	PUNCT
gs-1575	486	4	93	93	NUM
gs-1575	486	5	-	-	SYM
gs-1575	486	6	102	102	NUM
gs-1575	486	7	.	.	PUNCT
gs-1575	487	1	16	16	NUM
gs-1575	487	2	.	.	PUNCT
gs-1575	488	1	pharjiani	pharjiani	PROPN
gs-1575	488	2	b.	b.	PROPN
gs-1575	488	3	,	,	PUNCT
gs-1575	488	4	kvatadze	kvatadze	PROPN
gs-1575	488	5	ts	ts	PROPN
gs-1575	488	6	.	.	PROPN
gs-1575	488	7	,	,	PUNCT
gs-1575	488	8	kvatadze	kvatadze	PROPN
gs-1575	488	9	z.	z.	PROPN
gs-1575	488	10	,	,	PUNCT
gs-1575	488	11	on	on	ADP
gs-1575	488	12	an	an	DET
gs-1575	488	13	application	application	NOUN
gs-1575	488	14	of	of	ADP
gs-1575	488	15	density	density	NOUN
gs-1575	488	16	estimation	estimation	NOUN
gs-1575	488	17	constructed	construct	VERB
gs-1575	488	18	by	by	ADP
gs-1575	488	19	means	mean	NOUN
gs-1575	488	20	of	of	ADP
gs-1575	488	21	chain	chain	NOUN
gs-1575	488	22	dependent	dependent	ADJ
gs-1575	488	23	samples	sample	NOUN
gs-1575	488	24	.	.	PUNCT
gs-1575	489	1	report	report	NOUN
gs-1575	489	2	of	of	ADP
gs-1575	489	3	xxxiv	xxxiv	PROPN
gs-1575	489	4	enlarged	enlarged	ADJ
gs-1575	489	5	session	session	NOUN
gs-1575	489	6	of	of	ADP
gs-1575	489	7	the	the	DET
gs-1575	489	8	seminar	seminar	NOUN
gs-1575	489	9	of	of	ADP
gs-1575	489	10	i.	i.	PROPN
gs-1575	489	11	vekua	vekua	PROPN
gs-1575	489	12	institute	institute	PROPN
gs-1575	489	13	of	of	ADP
gs-1575	489	14	applied	apply	VERB
gs-1575	489	15	mathematics	mathematics	PROPN
gs-1575	489	16	(	(	PUNCT
gs-1575	489	17	viam	viam	PROPN
gs-1575	489	18	)	)	PUNCT
gs-1575	489	19	,	,	PUNCT
gs-1575	489	20	of	of	ADP
gs-1575	489	21	ivane	ivane	NOUN
gs-1575	489	22	javakhisvili	javakhisvili	PROPN
gs-1575	489	23	tbilisi	tbilisi	PROPN
gs-1575	489	24	state	state	PROPN
gs-1575	489	25	university	university	PROPN
gs-1575	489	26	(	(	PUNCT
gs-1575	489	27	tsu	tsu	PROPN
gs-1575	489	28	)	)	PUNCT
gs-1575	489	29	.	.	PUNCT
gs-1575	490	1	sept	sept	PROPN
gs-1575	490	2	.	.	PROPN
gs-1575	491	1	16	16	NUM
gs-1575	491	2	-	-	SYM
gs-1575	491	3	19	19	NUM
gs-1575	491	4	.	.	PUNCT
gs-1575	492	1	2020	2020	NUM
gs-1575	492	2	;	;	PUNCT
gs-1575	493	1	volume	volume	NOUN
gs-1575	493	2	,	,	PUNCT
gs-1575	493	3	34	34	NUM
gs-1575	493	4	.	.	PUNCT
gs-1575	494	1	pp	pp	ADJ
gs-1575	494	2	.	.	PUNCT
gs-1575	495	1	69	69	NUM
gs-1575	495	2	-	-	SYM
gs-1575	495	3	72	72	NUM
gs-1575	495	4	.	.	PUNCT
gs-1575	496	1	17	17	NUM
gs-1575	496	2	.	.	PUNCT
gs-1575	497	1	kvatadze	kvatadze	PROPN
gs-1575	497	2	z.	z.	PROPN
gs-1575	497	3	,	,	PUNCT
gs-1575	497	4	shervashidze	shervashidze	PROPN
gs-1575	497	5	t.	t.	PROPN
gs-1575	497	6	,	,	PUNCT
gs-1575	497	7	some	some	DET
gs-1575	497	8	limit	limit	NOUN
gs-1575	497	9	theorems	theorem	VERB
gs-1575	497	10	for	for	ADP
gs-1575	497	11	iid	iid	NOUN
gs-1575	497	12	and	and	CCONJ
gs-1575	497	13	conditionally	conditionally	ADV
gs-1575	497	14	independent	independent	ADJ
gs-1575	497	15	random	random	ADJ
gs-1575	497	16	variables	variable	NOUN
gs-1575	497	17	.	.	PUNCT
gs-1575	498	1	the	the	DET
gs-1575	498	2	second	second	ADJ
gs-1575	498	3	international	international	ADJ
gs-1575	498	4	conference	conference	NOUN
gs-1575	498	5	,	,	PUNCT
gs-1575	498	6	“	"	PUNCT
gs-1575	498	7	problems	problem	NOUN
gs-1575	498	8	of	of	ADP
gs-1575	498	9	cybernetics	cybernetic	NOUN
gs-1575	498	10	and	and	CCONJ
gs-1575	498	11	georgian	georgian	ADJ
gs-1575	498	12	scientists/ქართველი	scientists/ქართველი	NOUN
gs-1575	498	13	მეცნიერები	მეცნიერები	NOUN
gs-1575	498	14	ტ.	ტ.	VERB
gs-1575	498	15	5	5	NUM
gs-1575	498	16	n	n	PRON
gs-1575	498	17	1	1	NUM
gs-1575	498	18	,	,	PUNCT
gs-1575	498	19	2023	2023	NUM
gs-1575	498	20	319	319	NUM
gs-1575	498	21	informatics	informatic	NOUN
gs-1575	498	22	”	"	PUNCT
gs-1575	498	23	.	.	PUNCT
gs-1575	499	1	september	september	PROPN
gs-1575	499	2	10	10	NUM
gs-1575	499	3	-	-	SYM
gs-1575	499	4	12	12	NUM
gs-1575	499	5	,	,	PUNCT
gs-1575	499	6	2008	2008	NUM
gs-1575	499	7	.	.	PUNCT
gs-1575	500	1	baku	baku	PROPN
gs-1575	500	2	.	.	PROPN
gs-1575	500	3	azerbaijan	azerbaijan	PROPN
gs-1575	500	4	section	section	PROPN
gs-1575	500	5	n	n	PROPN
gs-1575	500	6	4	4	NUM
gs-1575	500	7	.	.	PUNCT
gs-1575	501	1	“	"	PUNCT
gs-1575	501	2	applied	apply	VERB
gs-1575	501	3	stochastic	stochastic	ADJ
gs-1575	501	4	analysis	analysis	NOUN
gs-1575	501	5	”	"	PUNCT
gs-1575	501	6	.	.	PUNCT
gs-1575	502	1	science	science	PROPN
gs-1575	502	2	14/12.pdf	14/12.pdf	PROPN
gs-1575	502	3	.	.	PUNCT
gs-1575	502	4	azerbaijan	azerbaijan	PROPN
gs-1575	502	5	national	national	PROPN
gs-1575	502	6	academy	academy	PROPN
gs-1575	502	7	of	of	ADP
gs-1575	502	8	sciences	sciences	PROPN
gs-1575	502	9	.	.	PUNCT
gs-1575	503	1	institute	institute	PROPN
gs-1575	503	2	of	of	ADP
gs-1575	503	3	information	information	NOUN
gs-1575	503	4	technology	technology	NOUN
gs-1575	503	5	.	.	PUNCT
gs-1575	504	1	printing	print	VERB
gs-1575	504	2	house	house	NOUN
gs-1575	504	3	of	of	ADP
gs-1575	504	4	“	"	PUNCT
gs-1575	504	5	information	information	NOUN
gs-1575	504	6	technology	technology	NOUN
gs-1575	504	7	”	"	PUNCT
gs-1575	504	8	baku	baku	PROPN
gs-1575	504	9	.	.	PROPN
gs-1575	504	10	2008	2008	NUM
gs-1575	504	11	.	.	PUNCT
gs-1575	505	1	vol	vol	NOUN
gs-1575	505	2	.	.	PUNCT
gs-1575	505	3	ii	ii	PROPN
gs-1575	505	4	,	,	PUNCT
gs-1575	505	5	217	217	NUM
gs-1575	505	6	-	-	SYM
gs-1575	505	7	219	219	NUM
gs-1575	505	8	.	.	PUNCT
gs-1575	505	9	18	18	NUM
gs-1575	505	10	.	.	PUNCT
gs-1575	506	1	kvatadze	kvatadze	PROPN
gs-1575	506	2	z.	z.	PROPN
gs-1575	506	3	,	,	PUNCT
gs-1575	506	4	shervashidze	shervashidze	ADJ
gs-1575	506	5	t.	t.	PROPN
gs-1575	506	6	on	on	ADP
gs-1575	506	7	some	some	DET
gs-1575	506	8	limit	limit	NOUN
gs-1575	506	9	theorems	theorem	NOUN
gs-1575	506	10	for	for	ADP
gs-1575	506	11	sums	sum	NOUN
gs-1575	506	12	and	and	CCONJ
gs-1575	506	13	products	product	NOUN
gs-1575	506	14	of	of	ADP
gs-1575	506	15	random	random	ADJ
gs-1575	506	16	variables	variable	NOUN
gs-1575	506	17	.	.	PUNCT
gs-1575	507	1	proceedings	proceeding	NOUN
gs-1575	507	2	of	of	ADP
gs-1575	507	3	a.	a.	NOUN
gs-1575	507	4	razmadze	razmadze	PROPN
gs-1575	507	5	mathematical	mathematical	PROPN
gs-1575	507	6	institute	institute	PROPN
gs-1575	507	7	.	.	PUNCT
gs-1575	508	1	vol	vol	NOUN
gs-1575	508	2	.	.	PROPN
gs-1575	509	1	150	150	NUM
gs-1575	509	2	.	.	X
gs-1575	510	1	2009	2009	NUM
gs-1575	510	2	.	.	PUNCT
gs-1575	511	1	99	99	NUM
gs-1575	511	2	-	-	SYM
gs-1575	511	3	104	104	NUM
gs-1575	511	4	.	.	PUNCT
gs-1575	512	1	19	19	NUM
gs-1575	512	2	.	.	PUNCT
gs-1575	513	1	kvatadze	kvatadze	PROPN
gs-1575	513	2	z.	z.	PROPN
gs-1575	513	3	,	,	PUNCT
gs-1575	513	4	kvatadze	kvatadze	PROPN
gs-1575	513	5	ts	ts	NOUN
gs-1575	513	6	.	.	PUNCT
gs-1575	514	1	limiting	limit	VERB
gs-1575	514	2	distribution	distribution	NOUN
gs-1575	514	3	of	of	ADP
gs-1575	514	4	a	a	DET
gs-1575	514	5	sequence	sequence	NOUN
gs-1575	514	6	of	of	ADP
gs-1575	514	7	functions	function	NOUN
gs-1575	514	8	defined	define	VERB
gs-1575	514	9	on	on	ADP
gs-1575	514	10	a	a	DET
gs-1575	514	11	markov	markov	NOUN
gs-1575	514	12	chain	chain	NOUN
gs-1575	514	13	.	.	PUNCT
gs-1575	515	1	proceedings	proceeding	NOUN
gs-1575	515	2	of	of	ADP
gs-1575	515	3	a.	a.	NOUN
gs-1575	515	4	razmadze	razmadze	PROPN
gs-1575	515	5	mathematical	mathematical	PROPN
gs-1575	515	6	institute	institute	PROPN
gs-1575	515	7	.	.	PUNCT
gs-1575	516	1	vol	vol	NOUN
gs-1575	516	2	.	.	PROPN
gs-1575	516	3	174	174	NUM
gs-1575	516	4	.	.	PUNCT
gs-1575	517	1	2020	2020	NUM
gs-1575	517	2	.	.	PUNCT
gs-1575	518	1	issue	issue	NOUN
gs-1575	518	2	2	2	NUM
gs-1575	518	3	,	,	PUNCT
gs-1575	518	4	199	199	NUM
gs-1575	518	5	-	-	SYM
gs-1575	518	6	205	205	NUM
gs-1575	518	7	.	.	PUNCT
gs-1575	519	1	სიმკვრივის	სიმკვრივის	NOUN
gs-1575	519	2	დამოკიდებული	დამოკიდებული	PROPN
gs-1575	519	3	დაკვირვებებით	დაკვირვებებით	PROPN
gs-1575	519	4	აგებული	აგებული	PROPN
gs-1575	519	5	შეფასების	შეფასების	PROPN
gs-1575	519	6	𝑳𝟏	𝑳𝟏	VERB
gs-1575	519	7	მეტრიკით	მეტრიკით	PROPN
gs-1575	519	8	სიზუსტის	სიზუსტის	PROPN
gs-1575	519	9	შესახებ	შესახებ	VERB
gs-1575	519	10	ბექნუ	ბექნუ	NOUN
gs-1575	519	11	ფარჯიანი	ფარჯიანი	NOUN
gs-1575	519	12	,	,	PUNCT
gs-1575	519	13	ლევან	ლევან	ADJ
gs-1575	519	14	ლაბაძე	ლაბაძე	NOUN
gs-1575	519	15	,	,	PUNCT
gs-1575	519	16	ციალა	ციალა	PROPN
gs-1575	519	17	ქვათაძე	ქვათაძე	VERB
gs-1575	519	18	რეზიუმე	რეზიუმე	PROPN
gs-1575	519	19	თანამედროვე	თანამედროვე	PROPN
gs-1575	519	20	სტატისტიკურ	სტატისტიკურ	PROPN
gs-1575	519	21	კვლევებში	კვლევებში	PROPN
gs-1575	519	22	მრავალი	მრავალი	ADJ
gs-1575	519	23	ამოცანის	ამოცანის	NOUN
gs-1575	519	24	გადაჭრა	გადაჭრა	NOUN
gs-1575	519	25	,	,	PUNCT
gs-1575	519	26	(	(	PUNCT
gs-1575	519	27	როგორებიცაა	როგორებიცაა	ADJ
gs-1575	519	28	მაგალითად	მაგალითად	NOUN
gs-1575	519	29	საინვესტიციო	საინვესტიციო	NOUN
gs-1575	519	30	და	და	PROPN
gs-1575	519	31	სადაზღვევო	სადაზღვევო	PROPN
gs-1575	519	32	კომპანიების	კომპანიების	ADJ
gs-1575	519	33	ფინანსური	ფინანსური	ADJ
gs-1575	519	34	დამოუკიდებლობის	დამოუკიდებლობის	NOUN
gs-1575	519	35	კვლევები	კვლევები	NOUN
gs-1575	519	36	,	,	PUNCT
gs-1575	519	37	საბანკო	საბანკო	PROPN
gs-1575	519	38	ინვესტიციების	ინვესტიციების	PROPN
gs-1575	519	39	რისკების	რისკების	PROPN
gs-1575	519	40	შეფასება	შეფასება	PROPN
gs-1575	519	41	,	,	PUNCT
gs-1575	519	42	კომპანიების	კომპანიების	ADJ
gs-1575	519	43	ფინანსური	ფინანსური	ADJ
gs-1575	519	44	სტაბილურობის	სტაბილურობის	PROPN
gs-1575	519	45	ინდიკატორების	ინდიკატორების	ADJ
gs-1575	519	46	შეფასება	შეფასება	ADJ
gs-1575	519	47	და	და	PROPN
gs-1575	519	48	ა.	ა.	PROPN
gs-1575	519	49	შ.	შ.	PROPN
gs-1575	519	50	)	)	PUNCT
gs-1575	519	51	მოითხოვს	მოითხოვს	PROPN
gs-1575	519	52	დამოკიდებული	დამოკიდებული	PROPN
gs-1575	519	53	დაკვირვებების	დაკვირვებების	ADJ
gs-1575	519	54	განხილვას.	განხილვას.	NOUN
gs-1575	519	55	დამოკიდებული	დამოკიდებული	PROPN
gs-1575	519	56	მონაცემებით	მონაცემებით	PROPN
gs-1575	519	57	შეფასებების	შეფასებების	PROPN
gs-1575	519	58	აგება	აგება	PROPN
gs-1575	519	59	ემყარება	ემყარება	PROPN
gs-1575	519	60	დამოუკიდებელი	დამოუკიდებელი	NOUN
gs-1575	519	61	მონაცემებით	მონაცემებით	PROPN
gs-1575	519	62	შეფასებათა	შეფასებათა	VERB
gs-1575	520	1	აგების	აგების	ADV
gs-1575	520	2	მდიდარ	მდიდარ	X
gs-1575	520	3	ისტორიულ	ისტორიულ	ADJ
gs-1575	520	4	გამოცდილებას.	გამოცდილებას.	NOUN
gs-1575	520	5	აგებული	აგებული	PROPN
gs-1575	520	6	შეფასებების	შეფასებების	PROPN
gs-1575	520	7	სიზუსტის	სიზუსტის	PROPN
gs-1575	520	8	დადგენისთვის	დადგენისთვის	PROPN
gs-1575	520	9	საჭიროა	საჭიროა	PROPN
gs-1575	520	10	დამოკიდებული	დამოკიდებული	PROPN
gs-1575	520	11	შემთხვევითი	შემთხვევითი	NOUN
gs-1575	520	12	სიდიდეების	სიდიდეების	VERB
gs-1575	520	13	ჯამების	ჯამების	VERB
gs-1575	520	14	ასიმპტოტიკის	ასიმპტოტიკის	ADJ
gs-1575	520	15	შესწავლა.	შესწავლა.	PROPN
gs-1575	520	16	ამ	ამ	ADP
gs-1575	520	17	პროცესში	პროცესში	NOUN
gs-1575	520	18	ხდება	ხდება	NOUN
gs-1575	520	19	დამოუკიდებელ	დამოუკიდებელ	NOUN
gs-1575	520	20	შემთხვევით	შემთხვევით	NOUN
gs-1575	520	21	სიდიდეთა	სიდიდეთა	ADV
gs-1575	520	22	ჯამების	ჯამების	VERB
gs-1575	520	23	განაწილების	განაწილების	PROPN
gs-1575	520	24	კვლევის	კვლევის	PROPN
gs-1575	520	25	მეთოდების	მეთოდების	PROPN
gs-1575	520	26	დამოკიდებულ	დამოკიდებულ	PROPN
gs-1575	520	27	შემთხვევით	შემთხვევით	PROPN
gs-1575	520	28	სიდიდეებზე	სიდიდეებზე	PROPN
gs-1575	520	29	გავრცობა.	გავრცობა.	PROPN
gs-1575	520	30	განიხილება	განიხილება	PROPN
gs-1575	520	31	მარკოვული	მარკოვული	PROPN
gs-1575	520	32	დამოკიდებულება.	დამოკიდებულება.	PROPN
gs-1575	520	33	ის	ის	NOUN
gs-1575	520	34	სუსტად	სუსტად	NOUN
gs-1575	520	35	დამოკიდებულების	დამოკიდებულების	ADJ
gs-1575	520	36	ერთ-ერთი	ერთ-ერთი	NOUN
gs-1575	520	37	სახეა.	სახეა.	VERB
gs-1575	520	38	მრავალი	მრავალი	ADJ
gs-1575	520	39	ავტორი	ავტორი	PROPN
gs-1575	520	40	იხილავს	იხილავს	PROPN
gs-1575	520	41	ისეთ	ისეთ	NOUN
gs-1575	520	42	შემთხვევით	შემთხვევით	PROPN
gs-1575	520	43	სიდიდეთა	სიდიდეთა	ADV
gs-1575	520	44	ჯამებს	ჯამებს	ADV
gs-1575	520	45	,	,	PUNCT
gs-1575	520	46	რომელთა	რომელთა	PROPN
gs-1575	520	47	ერთობლივი	ერთობლივი	PROPN
gs-1575	520	48	განაწილება	განაწილება	PROPN
gs-1575	520	49	განისაზღვრება	განისაზღვრება	PROPN
gs-1575	520	50	შემთხვევით	შემთხვევით	PROPN
gs-1575	520	51	ელემენტთა	ელემენტთა	PROPN
gs-1575	520	52	რაიმე	რაიმე	PROPN
gs-1575	520	53	„	„	PUNCT
gs-1575	520	54	მმართველი	მმართველი	ADJ
gs-1575	520	55	“	"	PUNCT
gs-1575	520	56	მიმდევრობით.	მიმდევრობით.	ADJ
gs-1575	520	57	ი.	ი.	ADJ
gs-1575	520	58	ბოკუჩავამ	ბოკუჩავამ	ADJ
gs-1575	520	59	,	,	PUNCT
gs-1575	520	60	თ.	თ.	ADJ
gs-1575	520	61	შერვაშიძემ	შერვაშიძემ	PROPN
gs-1575	520	62	და	და	PROPN
gs-1575	520	63	ზ.	ზ.	PROPN
gs-1575	520	64	ქვათაძემ	ქვათაძემ	ADJ
gs-1575	520	65	დაადგინეს	დაადგინეს	NOUN
gs-1575	520	66	პირობითად	პირობითად	VERB
gs-1575	520	67	დამოუკიდებელი	დამოუკიდებელი	NOUN
gs-1575	520	68	(	(	PUNCT
gs-1575	520	69	bokuchava	bokuchava	PROPN
gs-1575	520	70	i.	i.	PROPN
gs-1575	520	71	v.	v.	PROPN
gs-1575	520	72	(	(	PUNCT
gs-1575	520	73	1984	1984	NUM
gs-1575	520	74	)	)	PUNCT
gs-1575	520	75	limit	limit	NOUN
gs-1575	520	76	theorems	theorem	NOUN
gs-1575	520	77	for	for	ADP
gs-1575	520	78	conditionally	conditionally	ADV
gs-1575	520	79	independent	independent	ADJ
gs-1575	520	80	sequences	sequence	NOUN
gs-1575	520	81	.	.	PUNCT
gs-1575	521	1	(	(	PUNCT
gs-1575	521	2	in	in	ADP
gs-1575	521	3	russian	russian	PROPN
gs-1575	521	4	)	)	PUNCT
gs-1575	521	5	teor	teor	PROPN
gs-1575	521	6	.	.	PUNCT
gs-1575	521	7	verojatnost	verojatnost	PROPN
gs-1575	521	8	.	.	PUNCT
gs-1575	522	1	i	i	PRON
gs-1575	522	2	primenen.-mathnet.ru	primenen.-mathnet.ru	X
gs-1575	522	3	xxix	xxix	PROPN
gs-1575	522	4	.	.	PUNCT
gs-1575	523	1	(	(	PUNCT
gs-1575	523	2	1984	1984	NUM
gs-1575	523	3	)	)	PUNCT
gs-1575	523	4	.	.	PUNCT
gs-1575	524	1	№	№	ADP
gs-1575	524	2	1	1	NUM
gs-1575	524	3	,	,	PUNCT
gs-1575	524	4	pp	pp	ADJ
gs-1575	524	5	.	.	PUNCT
gs-1575	525	1	192	192	NUM
gs-1575	525	2	-	-	SYM
gs-1575	525	3	193.1984	193.1984	NUM
gs-1575	525	4	.	.	NOUN
gs-1575	525	5	theory	theory	NOUN
gs-1575	525	6	of	of	ADP
gs-1575	525	7	probability	probability	NOUN
gs-1575	525	8	and	and	CCONJ
gs-1575	525	9	its	its	PRON
gs-1575	525	10	applications	application	NOUN
gs-1575	525	11	,	,	PUNCT
gs-1575	525	12	1985	1985	NUM
gs-1575	525	13	,	,	PUNCT
gs-1575	525	14	29:1	29:1	NUM
gs-1575	525	15	,	,	PUNCT
gs-1575	525	16	190	190	NUM
gs-1575	525	17	-	-	SYM
gs-1575	525	18	196	196	NUM
gs-1575	525	19	;	;	PUNCT
gs-1575	525	20	kvatadze	kvatadze	PROPN
gs-1575	525	21	z.	z.	PROPN
gs-1575	525	22	,	,	PUNCT
gs-1575	525	23	shervashidze	shervashidze	ADJ
gs-1575	525	24	t.	t.	PROPN
gs-1575	525	25	(	(	PUNCT
gs-1575	525	26	2008	2008	NUM
gs-1575	525	27	)	)	PUNCT
gs-1575	525	28	some	some	DET
gs-1575	525	29	limit	limit	VERB
gs-1575	525	30	theorems	theorem	VERB
gs-1575	525	31	for	for	ADP
gs-1575	525	32	i.i.d	i.i.d	PROPN
gs-1575	525	33	.	.	PUNCT
gs-1575	526	1	and	and	CCONJ
gs-1575	526	2	conditionally	conditionally	ADV
gs-1575	526	3	independent	independent	ADJ
gs-1575	526	4	random	random	ADJ
gs-1575	526	5	variables	variable	NOUN
gs-1575	526	6	.	.	PUNCT
gs-1575	527	1	the	the	DET
gs-1575	527	2	second	second	ADJ
gs-1575	527	3	international	international	ADJ
gs-1575	527	4	conference	conference	NOUN
gs-1575	527	5	,	,	PUNCT
gs-1575	527	6	“	"	PUNCT
gs-1575	527	7	problems	problem	NOUN
gs-1575	527	8	of	of	ADP
gs-1575	527	9	cybernetics	cybernetic	NOUN
gs-1575	527	10	and	and	CCONJ
gs-1575	527	11	informatics	informatic	NOUN
gs-1575	527	12	“	"	PUNCT
gs-1575	527	13	.	.	PUNCT
gs-1575	528	1	september	september	PROPN
gs-1575	528	2	10	10	NUM
gs-1575	528	3	-	-	SYM
gs-1575	528	4	12	12	NUM
gs-1575	528	5	,	,	PUNCT
gs-1575	528	6	2008	2008	NUM
gs-1575	528	7	.	.	PUNCT
gs-1575	529	1	baku	baku	PROPN
gs-1575	529	2	,	,	PUNCT
gs-1575	529	3	azerbaijan	azerbaijan	PROPN
gs-1575	529	4	.	.	PUNCT
gs-1575	530	1	“	"	PUNCT
gs-1575	530	2	applied	apply	VERB
gs-1575	530	3	stochastic	stochastic	ADJ
gs-1575	530	4	analysis	analysis	NOUN
gs-1575	530	5	”	"	PUNCT
gs-1575	530	6	www.pci2008.science.az/4/12.pdf	www.pci2008.science.az/4/12.pdf	ADJ
gs-1575	530	7	.	.	PUNCT
gs-1575	531	1	azerbaijan	azerbaijan	PROPN
gs-1575	531	2	national	national	PROPN
gs-1575	531	3	academy	academy	PROPN
gs-1575	531	4	of	of	ADP
gs-1575	531	5	sciences	sciences	PROPN
gs-1575	531	6	.	.	PUNCT
gs-1575	532	1	institute	institute	PROPN
gs-1575	532	2	of	of	ADP
gs-1575	532	3	information	information	NOUN
gs-1575	532	4	technology	technology	NOUN
gs-1575	532	5	.	.	PUNCT
gs-1575	533	1	printing	print	VERB
gs-1575	533	2	house	house	NOUN
gs-1575	533	3	of	of	ADP
gs-1575	533	4	“	"	PUNCT
gs-1575	533	5	information	information	NOUN
gs-1575	533	6	technology	technology	NOUN
gs-1575	533	7	”	"	PUNCT
gs-1575	533	8	baku	baku	PROPN
gs-1575	533	9	.	.	PROPN
gs-1575	533	10	2008	2008	NUM
gs-1575	533	11	.	.	PUNCT
gs-1575	534	1	vol	vol	NOUN
gs-1575	534	2	.	.	PUNCT
gs-1575	534	3	ii	ii	PROPN
gs-1575	534	4	.	.	PUNCT
gs-1575	535	1	pp	pp	ADJ
gs-1575	535	2	.	.	PUNCT
gs-1575	536	1	217	217	NUM
gs-1575	536	2	-	-	SYM
gs-1575	536	3	219	219	NUM
gs-1575	536	4	)	)	PUNCT
gs-1575	536	5	და	და	NOUN
gs-1575	536	6	ჯაჭვურად	ჯაჭვურად	NOUN
gs-1575	536	7	დამოკიდებული	დამოკიდებული	VERB
gs-1575	536	8	georgian	georgian	ADJ
gs-1575	536	9	scientists/ქართველი	scientists/ქართველი	NOUN
gs-1575	536	10	მეცნიერები	მეცნიერები	NOUN
gs-1575	536	11	ტ.	ტ.	VERB
gs-1575	536	12	5	5	NUM
gs-1575	536	13	n	n	PRON
gs-1575	536	14	1	1	NUM
gs-1575	536	15	,	,	PUNCT
gs-1575	536	16	2023	2023	NUM
gs-1575	536	17	320	320	NUM
gs-1575	536	18	(	(	PUNCT
gs-1575	536	19	i.	i.	PROPN
gs-1575	536	20	v.	v.	PROPN
gs-1575	536	21	bokuchava	bokuchava	PROPN
gs-1575	536	22	,	,	PUNCT
gs-1575	536	23	z.	z.	PROPN
gs-1575	536	24	kvatadze	kvatadze	PROPN
gs-1575	536	25	,	,	PUNCT
gs-1575	536	26	t.	t.	PROPN
gs-1575	536	27	shervashidze	shervashidze	PROPN
gs-1575	536	28	,	,	PUNCT
gs-1575	536	29	on	on	ADP
gs-1575	536	30	limit	limit	NOUN
gs-1575	536	31	theorems	theorem	NOUN
gs-1575	536	32	for	for	ADP
gs-1575	536	33	random	random	ADJ
gs-1575	536	34	vectors	vector	NOUN
gs-1575	536	35	controlled	control	VERB
gs-1575	536	36	by	by	ADP
gs-1575	536	37	a	a	DET
gs-1575	536	38	markov	markov	NOUN
gs-1575	536	39	chain	chain	NOUN
gs-1575	536	40	.	.	PUNCT
gs-1575	537	1	probability	probability	NOUN
gs-1575	537	2	theory	theory	NOUN
gs-1575	537	3	and	and	CCONJ
gs-1575	537	4	mathematical	mathematical	ADJ
gs-1575	537	5	statistics	statistic	NOUN
gs-1575	537	6	,	,	PUNCT
gs-1575	537	7	vol	vol	NOUN
gs-1575	537	8	.	.	PUNCT
gs-1575	538	1	i	i	PRON
gs-1575	538	2	(	(	PUNCT
gs-1575	538	3	vilnius	vilnius	PROPN
gs-1575	538	4	,	,	PUNCT
gs-1575	538	5	1985	1985	NUM
gs-1575	538	6	)	)	PUNCT
gs-1575	538	7	,	,	PUNCT
gs-1575	538	8	231	231	NUM
gs-1575	538	9	-	-	SYM
gs-1575	538	10	250	250	NUM
gs-1575	538	11	,	,	PUNCT
gs-1575	538	12	vnu	vnu	PROPN
gs-1575	538	13	sci	sci	PROPN
gs-1575	538	14	.	.	PUNCT
gs-1575	539	1	press	press	PROPN
gs-1575	539	2	,	,	PUNCT
gs-1575	539	3	utrecht	utrecht	PROPN
gs-1575	539	4	,	,	PUNCT
gs-1575	539	5	1987	1987	NUM
gs-1575	539	6	;	;	PUNCT
gs-1575	539	7	kvatadze	kvatadze	PROPN
gs-1575	539	8	z.	z.	PROPN
gs-1575	539	9	,	,	PUNCT
gs-1575	539	10	shervashidze	shervashidze	ADJ
gs-1575	539	11	t.	t.	PROPN
gs-1575	539	12	(	(	PUNCT
gs-1575	539	13	1987	1987	NUM
gs-1575	539	14	)	)	PUNCT
gs-1575	539	15	on	on	ADP
gs-1575	539	16	limit	limit	NOUN
gs-1575	539	17	theorems	theorem	NOUN
gs-1575	539	18	for	for	ADP
gs-1575	539	19	conditionally	conditionally	ADV
gs-1575	539	20	independent	independent	ADJ
gs-1575	539	21	random	random	ADJ
gs-1575	539	22	variable	variable	NOUN
gs-1575	539	23	controlled	control	VERB
gs-1575	539	24	by	by	ADP
gs-1575	539	25	a	a	DET
gs-1575	539	26	finite	finite	ADJ
gs-1575	539	27	markov	markov	NOUN
gs-1575	539	28	chain	chain	NOUN
gs-1575	539	29	.	.	PUNCT
gs-1575	540	1	probability	probability	NOUN
gs-1575	540	2	theory	theory	NOUN
gs-1575	540	3	and	and	CCONJ
gs-1575	540	4	mathematical	mathematical	ADJ
gs-1575	540	5	statistics	statistic	NOUN
gs-1575	540	6	.	.	PUNCT
gs-1575	541	1	(	(	PUNCT
gs-1575	541	2	proc	proc	NOUN
gs-1575	541	3	.	.	PUNCT
gs-1575	542	1	5th	5th	ADJ
gs-1575	542	2	japan	japan	PROPN
gs-1575	542	3	-	-	PUNCT
gs-1575	542	4	ussr	ussr	ADJ
gs-1575	542	5	symposium	symposium	NOUN
gs-1575	542	6	on	on	ADP
gs-1575	542	7	probability	probability	NOUN
gs-1575	542	8	theory	theory	NOUN
gs-1575	542	9	.	.	PUNCT
gs-1575	543	1	kyoto	kyoto	PROPN
gs-1575	543	2	.	.	PUNCT
gs-1575	543	3	1986	1986	NUM
gs-1575	543	4	)	)	PUNCT
gs-1575	543	5	.	.	PUNCT
gs-1575	544	1	lecture	lecture	NOUN
gs-1575	544	2	notes	note	NOUN
gs-1575	544	3	in	in	ADP
gs-1575	544	4	mathematics	mathematic	NOUN
gs-1575	544	5	,	,	PUNCT
gs-1575	544	6	1299	1299	NUM
gs-1575	544	7	:	:	PUNCT
gs-1575	545	1	250	250	NUM
gs-1575	545	2	-	-	SYM
gs-1575	545	3	259	259	NUM
gs-1575	545	4	.	.	PUNCT
gs-1575	545	5	springer	springer	NOUN
gs-1575	545	6	-	-	PUNCT
gs-1575	545	7	verlag	verlag	PROPN
gs-1575	545	8	.	.	PUNCT
gs-1575	546	1	berlin	berlin	PROPN
gs-1575	546	2	(	(	PUNCT
gs-1575	546	3	germany	germany	PROPN
gs-1575	546	4	)	)	PUNCT
gs-1575	546	5	)	)	PUNCT
gs-1575	546	6	შემთხვევითი	შემთხვევითი	NOUN
gs-1575	546	7	სიდიდეების	სიდიდეების	VERB
gs-1575	546	8	ნორმირებული	ნორმირებული	PROPN
gs-1575	546	9	ჯამების	ჯამების	PROPN
gs-1575	547	1	ზღვარითი	ზღვარითი	NOUN
gs-1575	547	2	განაწილებები.	განაწილებები.	VERB
gs-1575	547	3	არაპარამეტრულ	არაპარამეტრულ	PROPN
gs-1575	547	4	შეფასებათა	შეფასებათა	VERB
gs-1575	547	5	თეორიაში	თეორიაში	PROPN
gs-1575	547	6	მნიშვნელოვანი	მნიშვნელოვანი	PROPN
gs-1575	547	7	ადგილი	ადგილი	NOUN
gs-1575	547	8	ეთმობა	ეთმობა	NOUN
gs-1575	547	9	განაწილების	განაწილების	NOUN
gs-1575	547	10	უცნობი	უცნობი	NOUN
gs-1575	547	11	სიმკვრივის	სიმკვრივის	NOUN
gs-1575	547	12	შეფასებას.	შეფასებას.	NOUN
gs-1575	548	1	მ.	მ.	PROPN
gs-1575	548	2	როზენბლატის	როზენბლატის	PROPN
gs-1575	548	3	და	და	PROPN
gs-1575	548	4	ე.	ე.	PROPN
gs-1575	548	5	პარზენის	პარზენის	PROPN
gs-1575	548	6	ნაშრომებში	ნაშრომებში	PROPN
gs-1575	548	7	(	(	PUNCT
gs-1575	548	8	m.	m.	NOUN
gs-1575	548	9	rosenblatt	rosenblatt	PROPN
gs-1575	548	10	(	(	PUNCT
gs-1575	548	11	1956	1956	NUM
gs-1575	548	12	)	)	PUNCT
gs-1575	548	13	,	,	PUNCT
gs-1575	548	14	remarks	remark	VERB
gs-1575	548	15	on	on	ADP
gs-1575	548	16	some	some	DET
gs-1575	548	17	nonparametric	nonparametric	ADJ
gs-1575	548	18	estimates	estimate	NOUN
gs-1575	548	19	of	of	ADP
gs-1575	548	20	a	a	DET
gs-1575	548	21	density	density	NOUN
gs-1575	548	22	function	function	NOUN
gs-1575	548	23	.	.	PUNCT
gs-1575	549	1	ann	ann	PROPN
gs-1575	549	2	.	.	PUNCT
gs-1575	549	3	math	math	PROPN
gs-1575	549	4	.	.	PUNCT
gs-1575	550	1	statist	statist	NOUN
gs-1575	550	2	.	.	PUNCT
gs-1575	551	1	27	27	NUM
gs-1575	551	2	,	,	PUNCT
gs-1575	551	3	chicago	chicago	PROPN
gs-1575	551	4	,	,	PUNCT
gs-1575	551	5	832	832	NUM
gs-1575	551	6	-	-	SYM
gs-1575	551	7	837	837	NUM
gs-1575	551	8	,	,	PUNCT
gs-1575	551	9	e.	e.	PROPN
gs-1575	551	10	parzen	parzen	PROPN
gs-1575	551	11	(	(	PUNCT
gs-1575	551	12	1962	1962	NUM
gs-1575	551	13	)	)	PUNCT
gs-1575	551	14	,	,	PUNCT
gs-1575	551	15	on	on	ADP
gs-1575	551	16	estimation	estimation	NOUN
gs-1575	551	17	of	of	ADP
gs-1575	551	18	a	a	DET
gs-1575	551	19	probability	probability	NOUN
gs-1575	551	20	density	density	NOUN
gs-1575	551	21	function	function	NOUN
gs-1575	551	22	and	and	CCONJ
gs-1575	551	23	mode	mode	NOUN
gs-1575	551	24	.	.	PUNCT
gs-1575	552	1	ann	ann	PROPN
gs-1575	552	2	.	.	PUNCT
gs-1575	552	3	math	math	PROPN
gs-1575	552	4	.	.	PUNCT
gs-1575	553	1	statist.33	statist.33	PROPN
gs-1575	553	2	,	,	PUNCT
gs-1575	553	3	stanford	stanford	PROPN
gs-1575	553	4	,	,	PUNCT
gs-1575	553	5	usa	usa	PROPN
gs-1575	553	6	,	,	PUNCT
gs-1575	553	7	1065	1065	NUM
gs-1575	553	8	-	-	SYM
gs-1575	553	9	1076	1076	NUM
gs-1575	553	10	)	)	PUNCT
gs-1575	553	11	განხილულია	განხილულია	VERB
gs-1575	553	12	დამოუკიდებელი	დამოუკიდებელი	NOUN
gs-1575	553	13	დაკვირვებებით	დაკვირვებებით	PROPN
gs-1575	553	14	აგებული	აგებული	PROPN
gs-1575	553	15	სიმკვრივის	სიმკვრივის	NOUN
gs-1575	553	16	გულოვანი	გულოვანი	NOUN
gs-1575	553	17	შეფასებების	შეფასებების	PROPN
gs-1575	553	18	კლასი.	კლასი.	PROPN
gs-1575	553	19	ცნობილია	ცნობილია	VERB
gs-1575	553	20	ამ	ამ	PROPN
gs-1575	553	21	შეფასებების	შეფასებების	PROPN
gs-1575	553	22	სიზუსტე	სიზუსტე	PROPN
gs-1575	553	23	2l	2l	NUM
gs-1575	553	24	(	(	PUNCT
gs-1575	553	25	e.	e.	PROPN
gs-1575	553	26	a.	a.	PROPN
gs-1575	553	27	nadaraya	nadaraya	PROPN
gs-1575	553	28	(	(	PUNCT
gs-1575	553	29	1983	1983	NUM
gs-1575	553	30	)	)	PUNCT
gs-1575	553	31	,	,	PUNCT
gs-1575	553	32	nonparametric	nonparametric	NOUN
gs-1575	553	33	estimation	estimation	NOUN
gs-1575	553	34	of	of	ADP
gs-1575	553	35	the	the	DET
gs-1575	553	36	probability	probability	NOUN
gs-1575	553	37	density	density	NOUN
gs-1575	553	38	and	and	CCONJ
gs-1575	553	39	regression	regression	NOUN
gs-1575	553	40	curve	curve	NOUN
gs-1575	553	41	.	.	PUNCT
gs-1575	554	1	(	(	PUNCT
gs-1575	554	2	in	in	ADP
gs-1575	554	3	russian	russian	PROPN
gs-1575	554	4	)	)	PUNCT
gs-1575	554	5	tbilisi	tbilisi	PROPN
gs-1575	554	6	state	state	PROPN
gs-1575	554	7	univ	univ	PROPN
gs-1575	554	8	.	.	PUNCT
gs-1575	555	1	press	press	PROPN
gs-1575	555	2	,	,	PUNCT
gs-1575	555	3	1983	1983	NUM
gs-1575	555	4	)	)	PUNCT
gs-1575	555	5	და	და	NOUN
gs-1575	555	6	1l	1l	NUM
gs-1575	555	7	(	(	PUNCT
gs-1575	555	8	devroye	devroye	PROPN
gs-1575	555	9	l.	l.	PROPN
gs-1575	555	10	,	,	PUNCT
gs-1575	555	11	györfi	györfi	PROPN
gs-1575	555	12	l.	l.	PROPN
gs-1575	555	13	nonparametric	nonparametric	PROPN
gs-1575	555	14	density	density	PROPN
gs-1575	555	15	estimation	estimation	PROPN
gs-1575	555	16	:	:	PUNCT
gs-1575	555	17	the	the	DET
gs-1575	555	18	1l	1l	NUM
gs-1575	555	19	view	view	NOUN
gs-1575	555	20	.	.	PUNCT
gs-1575	556	1	wiley	wiley	PROPN
gs-1575	556	2	series	series	PROPN
gs-1575	556	3	in	in	ADP
gs-1575	556	4	probability	probability	NOUN
gs-1575	556	5	and	and	CCONJ
gs-1575	556	6	mathematical	mathematical	ADJ
gs-1575	556	7	statistics	statistic	NOUN
gs-1575	556	8	,	,	PUNCT
gs-1575	556	9	canada	canada	PROPN
gs-1575	556	10	:	:	PUNCT
gs-1575	556	11	john	john	PROPN
gs-1575	556	12	wiley	wiley	PROPN
gs-1575	556	13	&	&	CCONJ
gs-1575	556	14	sons	son	NOUN
gs-1575	556	15	;	;	PUNCT
gs-1575	556	16	1985	1985	NUM
gs-1575	556	17	.	.	PUNCT
gs-1575	557	1	p.	p.	NOUN
gs-1575	557	2	367	367	NUM
gs-1575	557	3	)	)	PUNCT
gs-1575	557	4	მეტრიკებით.	მეტრიკებით.	PROPN
gs-1575	557	5	დამოკიდებულ	დამოკიდებულ	PROPN
gs-1575	557	6	შემთხვევით	შემთხვევით	PROPN
gs-1575	557	7	სიდიდეთა	სიდიდეთა	ADV
gs-1575	557	8	ჯამების	ჯამების	VERB
gs-1575	557	9	ასიმპტოტური	ასიმპტოტური	PROPN
gs-1575	557	10	ყოფაქცევის	ყოფაქცევის	PROPN
gs-1575	557	11	შესწავლამ	შესწავლამ	PROPN
gs-1575	557	12	შესაძლებელი	შესაძლებელი	PROPN
gs-1575	557	13	გახადა	გახადა	PROPN
gs-1575	557	14	სტატისტიკურ	სტატისტიკურ	PROPN
gs-1575	557	15	შეფასებათა	შეფასებათა	PROPN
gs-1575	557	16	თეორიაში	თეორიაში	PROPN
gs-1575	557	17	დამოკიდებული	დამოკიდებული	PROPN
gs-1575	557	18	დაკვირვებების	დაკვირვებების	ADV
gs-1575	557	19	განხილვა.	განხილვა.	VERB
gs-1575	557	20	ცნობილია	ცნობილია	VERB
gs-1575	557	21	სიმკვრივის	სიმკვრივის	PROPN
gs-1575	557	22	არაპარამეტრული	არაპარამეტრული	PROPN
gs-1575	557	23	შეფასება	შეფასება	PROPN
gs-1575	557	24	და	და	PROPN
gs-1575	557	25	რეგრესიის	რეგრესიის	PROPN
gs-1575	557	26	კოეფიციენტების	კოეფიციენტების	PROPN
gs-1575	557	27	შეფასებები	შეფასებები	VERB
gs-1575	557	28	მარკოვის	მარკოვის	NOUN
gs-1575	557	29	ჯაჭვად	ჯაჭვად	ADJ
gs-1575	557	30	შეკრული	შეკრული	NOUN
gs-1575	557	31	დაკვირვებებით	დაკვირვებებით	PROPN
gs-1575	557	32	(	(	PUNCT
gs-1575	557	33	yakowitz	yakowitz	PROPN
gs-1575	557	34	sidney	sidney	PROPN
gs-1575	557	35	(	(	PUNCT
gs-1575	557	36	1989	1989	NUM
gs-1575	557	37	)	)	PUNCT
gs-1575	557	38	nonparametric	nonparametric	NOUN
gs-1575	557	39	density	density	NOUN
gs-1575	557	40	and	and	CCONJ
gs-1575	557	41	regression	regression	NOUN
gs-1575	557	42	estimation	estimation	NOUN
gs-1575	557	43	for	for	ADP
gs-1575	557	44	markov	markov	NOUN
gs-1575	557	45	sequences	sequence	NOUN
gs-1575	557	46	without	without	ADP
gs-1575	557	47	mixing	mix	VERB
gs-1575	557	48	assumptions	assumption	NOUN
gs-1575	557	49	.	.	PUNCT
gs-1575	558	1	85721	85721	NUM
gs-1575	558	2	–	–	PUNCT
gs-1575	558	3	journal	journal	NOUN
gs-1575	558	4	of	of	ADP
gs-1575	558	5	multivariate	multivariate	NOUN
gs-1575	558	6	analysis	analysis	NOUN
gs-1575	558	7	,	,	PUNCT
gs-1575	558	8	30	30	NUM
gs-1575	558	9	:	:	SYM
gs-1575	558	10	124	124	NUM
gs-1575	558	11	-	-	SYM
gs-1575	558	12	136	136	NUM
gs-1575	558	13	.	.	PUNCT
gs-1575	559	1	arisona	arisona	PROPN
gs-1575	559	2	,	,	PUNCT
gs-1575	559	3	usa	usa	PROPN
gs-1575	559	4	)	)	PUNCT
gs-1575	559	5	.	.	PUNCT
gs-1575	560	1	ასევე	ასევე	PROPN
gs-1575	560	2	დადგენილია	დადგენილია	VERB
gs-1575	560	3	დამოკიდებული	დამოკიდებული	PROPN
gs-1575	560	4	დაკვირვებებით	დაკვირვებებით	PROPN
gs-1575	560	5	აგებული	აგებული	PROPN
gs-1575	560	6	სიმკვრივის	სიმკვრივის	PROPN
gs-1575	560	7	შეფასების	შეფასების	PROPN
gs-1575	560	8	სიზუსტე	სიზუსტე	PROPN
gs-1575	560	9	2l	2l	NUM
gs-1575	560	10	მეტრიკით	მეტრიკით	NOUN
gs-1575	560	11	(	(	PUNCT
gs-1575	560	12	j.	j.	PROPN
gs-1575	560	13	meloche	meloche	PROPN
gs-1575	560	14	.	.	PUNCT
gs-1575	561	1	asymptotic	asymptotic	ADJ
gs-1575	561	2	behavior	behavior	NOUN
gs-1575	561	3	of	of	ADP
gs-1575	561	4	the	the	DET
gs-1575	561	5	mean	mean	NOUN
gs-1575	561	6	integrated	integrate	VERB
gs-1575	561	7	squared	square	VERB
gs-1575	561	8	error	error	NOUN
gs-1575	561	9	of	of	ADP
gs-1575	561	10	kernel	kernel	NOUN
gs-1575	561	11	density	density	NOUN
gs-1575	561	12	estimators	estimator	NOUN
gs-1575	561	13	for	for	ADP
gs-1575	561	14	dependent	dependent	ADJ
gs-1575	561	15	observations	observation	NOUN
gs-1575	561	16	.	.	PUNCT
gs-1575	562	1	canadian	canadian	ADJ
gs-1575	562	2	journal	journal	PROPN
gs-1575	562	3	of	of	ADP
gs-1575	562	4	statistics	statistic	NOUN
gs-1575	562	5	.	.	PUNCT
gs-1575	563	1	2009	2009	NUM
gs-1575	563	2	.	.	PUNCT
gs-1575	563	3	,	,	PUNCT
gs-1575	563	4	18	18	NUM
gs-1575	563	5	(	(	PUNCT
gs-1575	563	6	3	3	NUM
gs-1575	563	7	):	):	PUNCT
gs-1575	563	8	p.	p.	NOUN
gs-1575	563	9	205	205	NUM
gs-1575	563	10	-	-	SYM
gs-1575	563	11	211	211	NUM
gs-1575	563	12	)	)	PUNCT
gs-1575	563	13	.	.	PUNCT
gs-1575	564	1	ზ.	ზ.	NOUN
gs-1575	564	2	ქვათაძის	ქვათაძის	ADP
gs-1575	564	3	და	და	NOUN
gs-1575	564	4	ბ.	ბ.	NOUN
gs-1575	564	5	ფარჯიანის	ფარჯიანის	PROPN
gs-1575	564	6	მიერ	მიერ	PROPN
gs-1575	564	7	აგებულია	აგებულია	PROPN
gs-1575	564	8	სიმკვრივის	სიმკვრივის	NOUN
gs-1575	564	9	გულოვანი	გულოვანი	NOUN
gs-1575	564	10	შეფასება	შეფასება	PROPN
gs-1575	564	11	პირობითად	პირობითად	VERB
gs-1575	564	12	დამოუკიდებელი	დამოუკიდებელი	NOUN
gs-1575	564	13	და	და	NOUN
gs-1575	564	14	ჯაჭვურად	ჯაჭვურად	NOUN
gs-1575	564	15	დამოკიდებული	დამოკიდებული	NOUN
gs-1575	564	16	დაკვირვებებით	დაკვირვებებით	PROPN
gs-1575	564	17	და	და	PROPN
gs-1575	564	18	დადგენილია	დადგენილია	VERB
gs-1575	564	19	მათი	მათი	PROPN
gs-1575	564	20	სიზუსტე	სიზუსტე	NOUN
gs-1575	564	21	2l	2l	PROPN
gs-1575	564	22	მეტრიკით	მეტრიკით	NOUN
gs-1575	564	23	იმ	იმ	PROPN
gs-1575	564	24	კერძო	კერძო	PROPN
gs-1575	564	25	შემთხვევაში	შემთხვევაში	PROPN
gs-1575	564	26	,	,	PUNCT
gs-1575	564	27	როდესაც	როდესაც	ADJ
gs-1575	564	28	მმართველი	მმართველი	VERB
gs-1575	564	29	მიმდევრობა	მიმდევრობა	PROPN
gs-1575	564	30	იღებს	იღებს	ADV
gs-1575	565	1	ორ	ორ	PROPN
gs-1575	565	2	მნიშვნელობას	მნიშვნელობას	NOUN
gs-1575	565	3	(	(	PUNCT
gs-1575	565	4	2r	2r	NUM
gs-1575	565	5			NOUN
gs-1575	565	6	)	)	PUNCT
gs-1575	565	7	(	(	PUNCT
gs-1575	565	8	z	z	X
gs-1575	565	9	,	,	PUNCT
gs-1575	565	10	kvatadze	kvatadze	PROPN
gs-1575	565	11	,	,	PUNCT
gs-1575	565	12	b.	b.	PROPN
gs-1575	565	13	phardjiani	phardjiani	PROPN
gs-1575	565	14	.	.	PUNCT
gs-1575	566	1	on	on	ADP
gs-1575	566	2	the	the	DET
gs-1575	566	3	exsactness	exsactness	NOUN
gs-1575	566	4	of	of	ADP
gs-1575	566	5	distribution	distribution	NOUN
gs-1575	566	6	density	density	NOUN
gs-1575	566	7	estimates	estimate	NOUN
gs-1575	566	8	constructed	construct	VERB
gs-1575	566	9	by	by	ADP
gs-1575	566	10	some	some	DET
gs-1575	566	11	class	class	NOUN
gs-1575	566	12	of	of	ADP
gs-1575	566	13	dependent	dependent	ADJ
gs-1575	566	14	observations	observation	NOUN
gs-1575	566	15	.	.	PUNCT
gs-1575	567	1	mathematics	mathematic	NOUN
gs-1575	567	2	and	and	CCONJ
gs-1575	567	3	statistics	statistic	NOUN
gs-1575	567	4	.	.	PUNCT
gs-1575	568	1	2019	2019	NUM
gs-1575	568	2	vol	vol	NOUN
gs-1575	568	3	.	.	PUNCT
gs-1575	569	1	7(4	7(4	NUM
gs-1575	569	2	)	)	PUNCT
gs-1575	569	3	,	,	PUNCT
gs-1575	569	4	pp	pp	PROPN
gs-1575	569	5	.	.	PUNCT
gs-1575	570	1	135	135	NUM
gs-1575	570	2	-	-	SYM
gs-1575	570	3	145	145	NUM
gs-1575	570	4	.	.	PUNCT
gs-1575	571	1	san	san	PROPN
gs-1575	571	2	jose	jose	PROPN
gs-1575	571	3	)	)	PUNCT
gs-1575	571	4	.	.	PUNCT
gs-1575	572	1	ასევე	ასევე	PROPN
gs-1575	572	2	მიღებულია	მიღებულია	ADJ
gs-1575	572	3	ჯაჭვურად	ჯაჭვურად	PROPN
gs-1575	572	4	დამოკიდებული	დამოკიდებული	PROPN
gs-1575	572	5	შეფასებებით	შეფასებებით	PROPN
gs-1575	572	6	აგებული	აგებული	PROPN
gs-1575	572	7	გულოვანი	გულოვანი	NOUN
gs-1575	572	8	შეფასების	შეფასების	VERB
gs-1575	572	9	სიზუსტე	სიზუსტე	PROPN
gs-1575	572	10	2l	2l	NUM
gs-1575	572	11	მეტრიკით	მეტრიკით	NOUN
gs-1575	572	12	2r	2r	NUM
gs-1575	573	1			PROPN
gs-1575	573	2	შემთხვევაშიც.	შემთხვევაშიც.	PROPN
gs-1575	573	3	წინამდებარე	წინამდებარე	PROPN
gs-1575	573	4	ნაშრომში	ნაშრომში	VERB
gs-1575	573	5	პირობითად	პირობითად	VERB
gs-1575	573	6	დამოუკიდებელი	დამოუკიდებელი	NOUN
gs-1575	573	7	დაკვირვებებით	დაკვირვებებით	PROPN
gs-1575	573	8	აგებულია	აგებულია	PROPN
gs-1575	573	9	სიმკვრივის	სიმკვრივის	PROPN
gs-1575	573	10	როზენბლატ−პარზენის	როზენბლატ−პარზენის	PUNCT
gs-1575	573	11	ტიპის	ტიპის	NOUN
gs-1575	573	12	გულოვანი	გულოვანი	NOUN
gs-1575	573	13	შეფასება.	შეფასება.	PROPN
gs-1575	573	14	გამოყენებულია	გამოყენებულია	ADJ
gs-1575	573	15	ი.	ი.	ADJ
gs-1575	573	16	ბოკუჩავას	ბოკუჩავას	NOUN
gs-1575	573	17	,	,	PUNCT
gs-1575	573	18	თ.	თ.	NOUN
gs-1575	573	19	შერვაშიძის	შერვაშიძის	X
gs-1575	573	20	და	და	PROPN
gs-1575	573	21	ზ.	ზ.	PROPN
gs-1575	573	22	ქვათაძის	ქვათაძის	ADP
gs-1575	573	23	მიღებული	მიღებული	PROPN
gs-1575	573	24	შედეგები	შედეგები	PROPN
gs-1575	573	25	პირობითად	პირობითად	PROPN
gs-1575	573	26	დამოუკიდებელ	დამოუკიდებელ	NOUN
gs-1575	573	27	შემთხვევით	შემთხვევით	NOUN
gs-1575	573	28	სიდიდეთა	სიდიდეთა	ADV
gs-1575	573	29	ჯამების	ჯამების	VERB
gs-1575	573	30	ზღვარითი	ზღვარითი	NOUN
gs-1575	573	31	georgian	georgian	ADJ
gs-1575	573	32	scientists/ქართველი	scientists/ქართველი	PROPN
gs-1575	573	33	მეცნიერები	მეცნიერები	NOUN
gs-1575	573	34	ტ.	ტ.	VERB
gs-1575	573	35	5	5	NUM
gs-1575	573	36	n	n	PRON
gs-1575	573	37	1	1	NUM
gs-1575	573	38	,	,	PUNCT
gs-1575	573	39	2023	2023	NUM
gs-1575	573	40	321	321	NUM
gs-1575	573	41	განაწილების	განაწილების	NOUN
gs-1575	573	42	შესახებ	შესახებ	VERB
gs-1575	573	43	და	და	PROPN
gs-1575	573	44	დადგენილია	დადგენილია	VERB
gs-1575	573	45	აგებული	აგებული	PROPN
gs-1575	573	46	შეფასების	შეფასების	PROPN
gs-1575	573	47	სიზუსტე	სიზუსტე	PROPN
gs-1575	573	48	1l	1l	NUM
gs-1575	573	49	მეტრიკით.	მეტრიკით.	PROPN
gs-1575	573	50	თეორემის	თეორემის	PROPN
gs-1575	573	51	დამტკიცების	დამტკიცების	PROPN
gs-1575	573	52	დროს	დროს	PROPN
gs-1575	573	53	გამოიყენება	გამოიყენება	PROPN
gs-1575	573	54	თ.	თ.	PROPN
gs-1575	573	55	შერვაშიძის	შერვაშიძის	PROPN
gs-1575	573	56	და	და	PROPN
gs-1575	573	57	ზ.	ზ.	PROPN
gs-1575	573	58	ქვათაძის	ქვათაძის	ADP
gs-1575	573	59	მიერ	მიერ	PROPN
gs-1575	573	60	განხილული	განხილული	PROPN
gs-1575	573	61	მეთოდი.	მეთოდი.	ADJ
gs-1575	573	62	დაფიქსირებულ	დაფიქსირებულ	ADJ
gs-1575	573	63			NOUN
gs-1575	573	64	1	1	VERB
gs-1575	573	65	1	1	NUM
gs-1575	573	66	2	2	NUM
gs-1575	573	67	,	,	PUNCT
gs-1575	573	68	,	,	PUNCT
gs-1575	573	69	...	...	PUNCT
gs-1575	573	70	,	,	PUNCT
gs-1575	573	71	n	n	DET
gs-1575	573	72	n	n	PROPN
gs-1575	573	73			NOUN
gs-1575	573	74			SYM
gs-1575	573	75			PUNCT
gs-1575	573	76	ტრაექტორიაზე	ტრაექტორიაზე	NOUN
gs-1575	573	77	ხდება	ხდება	VERB
gs-1575	573	78	შესაფასებელი	შესაფასებელი	NOUN
gs-1575	573	79	ჯამის	ჯამის	PROPN
gs-1575	573	80	დაშლა	დაშლა	NOUN
gs-1575	573	81	მმართველი	მმართველი	NOUN
gs-1575	573	82	მიმდევრობის	მიმდევრობის	PROPN
gs-1575	573	83	მდგომარეობების	მდგომარეობების	ADJ
gs-1575	573	84	შესაბამის	შესაბამის	NOUN
gs-1575	573	85	ჯამებად.	ჯამებად.	NOUN
gs-1575	573	86	ეს	ეს	PROPN
gs-1575	573	87	ჯამები	ჯამები	VERB
gs-1575	573	88	არაკორელირებულებია.	არაკორელირებულებია.	VERB
gs-1575	573	89	დაფიქსირებულ	დაფიქსირებულ	PROPN
gs-1575	573	90	ტრაექტორიაზე	ტრაექტორიაზე	NOUN
gs-1575	573	91	თითოეული	თითოეული	PROPN
gs-1575	573	92	ჯამის	ჯამის	PROPN
gs-1575	573	93	შემადგენელი	შემადგენელი	PROPN
gs-1575	573	94	შესაკრებები	შესაკრებები	NOUN
gs-1575	573	95	დამოუკიდებლებია.	დამოუკიდებლებია.	NOUN
gs-1575	573	96	გამოყენებულია	გამოყენებულია	VERB
gs-1575	573	97	ჯაჭვის	ჯაჭვის	NOUN
gs-1575	573	98	მდგომარეობებზე	მდგომარეობებზე	NOUN
gs-1575	573	99	განსაზღვრული	განსაზღვრული	NOUN
gs-1575	573	100	(	(	PUNCT
gs-1575	573	101	)	)	PUNCT
gs-1575	573	102	n	n	X
gs-1575	573	103	i	i	PROPN
gs-1575	573	104	(	(	PUNCT
gs-1575	573	105	1	1	NUM
gs-1575	573	106	,	,	PUNCT
gs-1575	573	107	i	i	PRON
gs-1575	573	108	s	s	ADJ
gs-1575	573	109	)	)	PUNCT
gs-1575	574	1	ფუნქციების	ფუნქციების	ADJ
gs-1575	574	2	ზომადობა	ზომადობა	NOUN
gs-1575	574	3	(	(	PUNCT
gs-1575	574	4	kvatadze	kvatadze	PROPN
gs-1575	574	5	z.	z.	PROPN
gs-1575	574	6	,	,	PUNCT
gs-1575	574	7	kvatadze	kvatadze	PROPN
gs-1575	574	8	ts	ts	NOUN
gs-1575	574	9	.	.	PUNCT
gs-1575	575	1	limiting	limit	VERB
gs-1575	575	2	distribution	distribution	NOUN
gs-1575	575	3	of	of	ADP
gs-1575	575	4	a	a	DET
gs-1575	575	5	sequence	sequence	NOUN
gs-1575	575	6	of	of	ADP
gs-1575	575	7	functions	function	NOUN
gs-1575	575	8	defined	define	VERB
gs-1575	575	9	on	on	ADP
gs-1575	575	10	a	a	DET
gs-1575	575	11	markov	markov	NOUN
gs-1575	575	12	chain	chain	NOUN
gs-1575	575	13	.	.	PUNCT
gs-1575	576	1	proceedings	proceeding	NOUN
gs-1575	576	2	of	of	ADP
gs-1575	576	3	a.	a.	NOUN
gs-1575	576	4	razmadze	razmadze	PROPN
gs-1575	576	5	mathematical	mathematical	PROPN
gs-1575	576	6	institute	institute	PROPN
gs-1575	576	7	.	.	PUNCT
gs-1575	577	1	vol	vol	NOUN
gs-1575	577	2	.	.	PROPN
gs-1575	577	3	174	174	NUM
gs-1575	577	4	.	.	PUNCT
gs-1575	578	1	2020	2020	NUM
gs-1575	578	2	.	.	PUNCT
gs-1575	579	1	issue	issue	NOUN
gs-1575	579	2	2	2	NUM
gs-1575	579	3	,	,	PUNCT
gs-1575	579	4	199	199	NUM
gs-1575	579	5	-	-	SYM
gs-1575	579	6	205	205	NUM
gs-1575	579	7	)	)	PUNCT
gs-1575	580	1	1n	1n	NOUN
gs-1575	580	2	ტრაექტორიის	ტრაექტორიის	NOUN
gs-1575	580	3	დაფიქსირებით	დაფიქსირებით	NOUN
gs-1575	580	4	მიღებული	მიღებული	VERB
gs-1575	581	1	ალბათური	ალბათური	PROPN
gs-1575	581	2	სივრცის	სივრცის	PROPN
gs-1575	581	3	დაყოფით	დაყოფით	PROPN
gs-1575	581	4	ინდუცირებული	ინდუცირებული	PROPN
gs-1575	581	5			PROPN
gs-1575	581	6	ალგებრის	ალგებრის	NOUN
gs-1575	581	7	მიმართ.	მიმართ.	NOUN
gs-1575	581	8	გამოყენებული	გამოყენებული	PROPN
gs-1575	581	9	მეთოდი	მეთოდი	PROPN
gs-1575	581	10	შესაძლებლობას	შესაძლებლობას	PROPN
gs-1575	581	11	იძლევა	იძლევა	NOUN
gs-1575	581	12	მიღებულ	მიღებულ	PROPN
gs-1575	581	13	იქნას	იქნას	NOUN
gs-1575	581	14	დამოკიდებული	დამოკიდებული	VERB
gs-1575	581	15	დაკვირვებებით	დაკვირვებებით	PROPN
gs-1575	581	16	აგებული	აგებული	PROPN
gs-1575	581	17	სხვა	სხვა	PROPN
gs-1575	581	18	ტიპის	ტიპის	PROPN
gs-1575	581	19	შეფასების	შეფასების	PROPN
gs-1575	581	20	სიზუსტე.	სიზუსტე.	ADJ