id	sid	tid	token	lemma	pos
gs-1949	1	1	georgian	georgian	ADJ
gs-1949	1	2	scientists/ქართველი	scientists/ქართველი	NOUN
gs-1949	1	3	მეცნიერები	მეცნიერები	NOUN
gs-1949	1	4	ტ.	ტ.	VERB
gs-1949	1	5	5	5	NUM
gs-1949	1	6	n	n	PRON
gs-1949	1	7	2	2	NUM
gs-1949	1	8	,	,	PUNCT
gs-1949	1	9	2023	2023	NUM
gs-1949	1	10	21	21	NUM
gs-1949	1	11	georgian	georgian	PROPN
gs-1949	1	12	scientists	scientist	NOUN
gs-1949	1	13	ქართველი	ქართველი	ADJ
gs-1949	1	14	მეცნიერები	მეცნიერები	PROPN
gs-1949	1	15	vol	vol	NOUN
gs-1949	1	16	.	.	PUNCT
gs-1949	2	1	5	5	NUM
gs-1949	2	2	issue	issue	NOUN
gs-1949	2	3	3	3	NUM
gs-1949	2	4	,	,	PUNCT
gs-1949	2	5	2023	2023	NUM
gs-1949	2	6	https://doi.org/10.52340/gs.2023.05.03.03	https://doi.org/10.52340/gs.2023.05.03.03	AUX
gs-1949	2	7	on	on	ADP
gs-1949	2	8	the	the	DET
gs-1949	2	9	conditional	conditional	ADJ
gs-1949	2	10	distribution	distribution	NOUN
gs-1949	2	11	of	of	ADP
gs-1949	2	12	the	the	DET
gs-1949	2	13	sum	sum	NOUN
gs-1949	2	14	of	of	ADP
gs-1949	2	15	m	m	PROPN
gs-1949	2	16	−dependent	−dependent	NOUN
gs-1949	2	17	vectors	vector	NOUN
gs-1949	2	18	zurab	zurab	VERB
gs-1949	2	19	kvatadze	kvatadze	PROPN
gs-1949	2	20	*	*	PUNCT
gs-1949	2	21	,	,	PUNCT
gs-1949	2	22	beqnu	beqnu	NOUN
gs-1949	2	23	parjiani	parjiani	NOUN
gs-1949	2	24	*	*	PUNCT
gs-1949	2	25	*	*	PUNCT
gs-1949	2	26	and	and	CCONJ
gs-1949	2	27	tsiala	tsiala	NOUN
gs-1949	2	28	kvatadze	kvatadze	NOUN
gs-1949	2	29	*	*	PUNCT
gs-1949	3	1	*	*	PUNCT
gs-1949	3	2	*	*	PUNCT
gs-1949	3	3	*	*	PUNCT
gs-1949	3	4	professor	professor	NOUN
gs-1949	3	5	of	of	ADP
gs-1949	3	6	the	the	DET
gs-1949	3	7	department	department	NOUN
gs-1949	3	8	of	of	ADP
gs-1949	3	9	mathematics	mathematic	NOUN
gs-1949	3	10	of	of	ADP
gs-1949	3	11	georgian	georgian	PROPN
gs-1949	3	12	technical	technical	PROPN
gs-1949	3	13	university	university	PROPN
gs-1949	3	14	;	;	PUNCT
gs-1949	3	15	*	*	PUNCT
gs-1949	3	16	*	*	PUNCT
gs-1949	3	17	associate	associate	ADJ
gs-1949	3	18	professor	professor	NOUN
gs-1949	3	19	of	of	ADP
gs-1949	3	20	department	department	PROPN
gs-1949	3	21	of	of	ADP
gs-1949	3	22	mathematics	mathematic	NOUN
gs-1949	3	23	of	of	ADP
gs-1949	3	24	georgian	georgian	PROPN
gs-1949	3	25	technical	technical	PROPN
gs-1949	3	26	university	university	PROPN
gs-1949	3	27	;	;	PUNCT
gs-1949	3	28	*	*	PUNCT
gs-1949	3	29	invited	invite	VERB
gs-1949	3	30	lecturer	lecturer	NOUN
gs-1949	3	31	in	in	ADP
gs-1949	3	32	statistics	statistic	NOUN
gs-1949	3	33	,	,	PUNCT
gs-1949	3	34	international	international	ADJ
gs-1949	3	35	black	black	PROPN
gs-1949	3	36	sea	sea	PROPN
gs-1949	3	37	university	university	NOUN
gs-1949	3	38	abstract	abstract	NOUN
gs-1949	3	39	on	on	ADP
gs-1949	3	40	the	the	DET
gs-1949	3	41	probability	probability	NOUN
gs-1949	3	42	space	space	NOUN
gs-1949	3	43	(	(	PUNCT
gs-1949	3	44	,	,	PUNCT
gs-1949	3	45	,	,	PUNCT
gs-1949	3	46	)	)	PUNCT
gs-1949	3	47	f	f	NOUN
gs-1949	3	48	p	p	NOUN
gs-1949	3	49	is	be	AUX
gs-1949	3	50	considered	consider	VERB
gs-1949	3	51	a	a	DET
gs-1949	3	52	stationary	stationary	ADJ
gs-1949	3	53	(	(	PUNCT
gs-1949	3	54	in	in	ADP
gs-1949	3	55	the	the	DET
gs-1949	3	56	narrow	narrow	ADJ
gs-1949	3	57	sense	sense	NOUN
gs-1949	3	58	)	)	PUNCT
gs-1949	3	59	twocomponent	twocomponent	NOUN
gs-1949	3	60	sequence	sequence	NOUN
gs-1949	3	61			PROPN
gs-1949	3	62			PROPN
gs-1949	3	63	1	1	NUM
gs-1949	3	64	,	,	PUNCT
gs-1949	3	65	i	i	PRON
gs-1949	3	66	i	i	PRON
gs-1949	3	67	i	i	PRON
gs-1949	3	68	y	y	VERB
gs-1949	3	69			NUM
gs-1949	3	70	.	.	PUNCT
gs-1949	4	1	:	:	PUNCT
gs-1949	5	1	k	k	PROPN
gs-1949	5	2	iy	iy	PROPN
gs-1949	5	3	r	r	PROPN
gs-1949	5	4	is	be	AUX
gs-1949	5	5	conditionally	conditionally	ADV
gs-1949	5	6	m	m	VERB
gs-1949	5	7	−independent	−independent	ADJ
gs-1949	5	8	vectors	vector	NOUN
gs-1949	5	9	sequence	sequence	VERB
gs-1949	5	10	the	the	DET
gs-1949	5	11	decomposition	decomposition	NOUN
gs-1949	5	12			NOUN
gs-1949	5	13	1	1	NOUN
gs-1949	5	14	1	1	NUM
gs-1949	5	15	2	2	NUM
gs-1949	5	16	1	1	NUM
gs-1949	5	17	1	1	NUM
gs-1949	5	18	n	n	NUM
gs-1949	5	19	n	n	NOUN
gs-1949	5	20	i	i	PRON
gs-1949	5	21	n	n	CCONJ
gs-1949	5	22	n	n	NOUN
gs-1949	6	1	i	i	PRON
gs-1949	6	2	s	s	VERB
gs-1949	6	3	y	y	INTJ
gs-1949	6	4	ey	ey	PROPN
gs-1949	6	5	s	s	NOUN
gs-1949	6	6	s	s	X
gs-1949	6	7	n	n	CCONJ
gs-1949	7	1			NUM
gs-1949	7	2			PROPN
gs-1949	7	3			PROPN
gs-1949	7	4			PROPN
gs-1949	7	5			NOUN
gs-1949	7	6	is	be	AUX
gs-1949	7	7	applied	apply	VERB
gs-1949	7	8	,	,	PUNCT
gs-1949	7	9	where	where	SCONJ
gs-1949	7	10			NOUN
gs-1949	7	11	1	1	VERB
gs-1949	7	12	1	1	NUM
gs-1949	7	13	1	1	NUM
gs-1949	7	14	n	n	NUM
gs-1949	7	15	n	n	NOUN
gs-1949	8	1	i	i	PRON
gs-1949	8	2	i	i	PRON
gs-1949	9	1	i	i	PRON
gs-1949	10	1	i	i	PRON
gs-1949	10	2	s	s	AUX
gs-1949	10	3	y	y	PROPN
gs-1949	10	4	e	e	PROPN
gs-1949	10	5	y	y	PROPN
gs-1949	10	6	n	n	ADV
gs-1949	10	7			VERB
gs-1949	10	8			NUM
gs-1949	10	9			PROPN
gs-1949	10	10			PROPN
gs-1949	10	11			NOUN
gs-1949	10	12			NOUN
gs-1949	10	13	and	and	CCONJ
gs-1949	10	14			NOUN
gs-1949	10	15	2	2	ADJ
gs-1949	10	16	1	1	NUM
gs-1949	10	17	1	1	NUM
gs-1949	10	18	1	1	NUM
gs-1949	10	19	n	n	NUM
gs-1949	11	1	n	n	NOUN
gs-1949	12	1	i	i	PRON
gs-1949	13	1	i	i	PRON
gs-1949	14	1	i	i	PRON
gs-1949	14	2	s	s	VERB
gs-1949	14	3	e	e	X
gs-1949	14	4	y	y	PROPN
gs-1949	14	5	ey	ey	PRON
gs-1949	14	6	n	n	PRON
gs-1949	14	7			NOUN
gs-1949	14	8			NUM
gs-1949	14	9			PROPN
gs-1949	14	10			PROPN
gs-1949	14	11			NOUN
gs-1949	14	12			NOUN
gs-1949	14	13	.	.	PUNCT
gs-1949	15	1	is	be	AUX
gs-1949	15	2	proved	prove	VERB
gs-1949	15	3	that	that	SCONJ
gs-1949	15	4	if	if	SCONJ
gs-1949	15	5	2	2	NUM
gs-1949	15	6	(	(	PUNCT
gs-1949	15	7	)	)	PUNCT
gs-1949	15	8	(	(	PUNCT
gs-1949	15	9	)	)	PUNCT
gs-1949	15	10	ns	ns	NUM
gs-1949	15	11	n	n	PROPN
gs-1949	15	12	f	f	PROPN
gs-1949	15	13	q	q	X
gs-1949	15	14			NOUN
gs-1949	15	15			PROPN
gs-1949	15	16			NOUN
gs-1949	15	17			PROPN
gs-1949	15	18	and	and	CCONJ
gs-1949	15	19	(	(	PUNCT
gs-1949	15	20	)	)	PUNCT
gs-1949	15	21	q	q	PROPN
gs-1949	15	22			PROPN
gs-1949	15	23	is	be	AUX
gs-1949	15	24	nondegenerate	nondegenerate	ADJ
gs-1949	15	25	distribution	distribution	NOUN
gs-1949	15	26	,	,	PUNCT
gs-1949	15	27	then	then	ADV
gs-1949	15	28	for	for	ADP
gs-1949	15	29	each	each	PRON
gs-1949	15	30	,	,	PUNCT
gs-1949	15	31	kx	kx	PROPN
gs-1949	15	32	y	y	PROPN
gs-1949	15	33	r	r	PROPN
gs-1949	15	34			NOUN
gs-1949	16	1			PROPN
gs-1949	16	2	1	1	NUM
gs-1949	16	3	(	(	PUNCT
gs-1949	16	4	)	)	PUNCT
gs-1949	16	5	(	(	PUNCT
gs-1949	16	6	)	)	PUNCT
gs-1949	16	7	(	(	PUNCT
gs-1949	16	8	)	)	PUNCT
gs-1949	16	9	(	(	PUNCT
gs-1949	16	10	)	)	PUNCT
gs-1949	16	11	(	(	PUNCT
gs-1949	16	12	)	)	PUNCT
gs-1949	16	13	m	m	VERB
gs-1949	16	14	mn	mn	NOUN
gs-1949	16	15	n	n	ADV
gs-1949	16	16	r	r	NOUN
gs-1949	16	17	r	r	NOUN
gs-1949	16	18	ns	ns	NUM
gs-1949	16	19	p	p	NOUN
gs-1949	16	20	x	x	X
gs-1949	16	21	y	y	NOUN
gs-1949	16	22	f	f	NOUN
gs-1949	16	23	x	x	PUNCT
gs-1949	16	24	x	x	PUNCT
gs-1949	16	25	y	y	VERB
gs-1949	17	1	q	q	PROPN
gs-1949	17	2	y	y	PROPN
gs-1949	17	3	q	q	ADJ
gs-1949	17	4	y	y	PROPN
gs-1949	17	5			NOUN
gs-1949	17	6			NOUN
gs-1949	17	7			PROPN
gs-1949	17	8			VERB
gs-1949	17	9			NOUN
gs-1949	17	10			NOUN
gs-1949	17	11			PROPN
gs-1949	17	12			PUNCT
gs-1949	17	13			VERB
gs-1949	17	14			PROPN
gs-1949	17	15			PROPN
gs-1949	17	16	,	,	PUNCT
gs-1949	17	17	where	where	SCONJ
gs-1949	17	18			NOUN
gs-1949	17	19	(0	(0	NOUN
gs-1949	17	20	)	)	PUNCT
gs-1949	17	21	(	(	PUNCT
gs-1949	17	22	)	)	PUNCT
gs-1949	17	23	(	(	PUNCT
gs-1949	17	24	)	)	PUNCT
gs-1949	17	25	0	0	NUM
gs-1949	18	1	0	0	NUM
gs-1949	18	2	0	0	NUM
gs-1949	18	3	1	1	NUM
gs-1949	18	4	m	m	NOUN
gs-1949	18	5	t	t	NOUN
gs-1949	18	6	p	p	X
gs-1949	18	7	p	p	NOUN
gs-1949	18	8	m	m	NOUN
gs-1949	18	9	p	p	NOUN
gs-1949	18	10	r	r	NOUN
gs-1949	18	11	r	r	NOUN
gs-1949	18	12	r	r	NOUN
gs-1949	18	13	r	r	NOUN
gs-1949	18	14			NOUN
gs-1949	18	15			PROPN
gs-1949	18	16			PROPN
gs-1949	18	17			PROPN
gs-1949	18	18			PUNCT
gs-1949	18	19			VERB
gs-1949	18	20			X
gs-1949	18	21			NOUN
gs-1949	18	22	,	,	PUNCT
gs-1949	18	23			PROPN
gs-1949	18	24			SYM
gs-1949	18	25			NOUN
gs-1949	18	26	0	0	NOUN
gs-1949	18	27	1	1	NUM
gs-1949	18	28	1	1	NUM
gs-1949	18	29	1cov	1cov	NUM
gs-1949	18	30	,	,	PUNCT
gs-1949	18	31	p	p	X
gs-1949	18	32	p	p	X
gs-1949	18	33	nr	nr	PROPN
gs-1949	18	34	e	e	PROPN
gs-1949	18	35	y	y	PROPN
gs-1949	18	36	y	y	PROPN
gs-1949	18	37			PUNCT
gs-1949	18	38	,	,	PUNCT
gs-1949	19	1			PROPN
gs-1949	19	2	1	1	ADJ
gs-1949	19	3	1	1	NUM
gs-1949	19	4	2	2	NUM
gs-1949	19	5	,	,	PUNCT
gs-1949	19	6	,	,	PUNCT
gs-1949	19	7	...	...	PUNCT
gs-1949	19	8	,	,	PUNCT
gs-1949	19	9	n	n	CCONJ
gs-1949	19	10	n	n	PRON
gs-1949	19	11			NOUN
gs-1949	19	12			NOUN
gs-1949	19	13			PUNCT
gs-1949	19	14	is	be	AUX
gs-1949	19	15	fixed	fix	VERB
gs-1949	19	16	trajectory	trajectory	NOUN
gs-1949	19	17	of	of	ADP
gs-1949	19	18	control	control	NOUN
gs-1949	19	19	sequence	sequence	NOUN
gs-1949	19	20	.	.	PUNCT
gs-1949	20	1	when	when	SCONJ
gs-1949	20	2			PROPN
gs-1949	20	3			PROPN
gs-1949	20	4	1i	1i	NOUN
gs-1949	20	5	i	i	PRON
gs-1949	20	6			VERB
gs-1949	20	7			NUM
gs-1949	20	8	is	be	AUX
gs-1949	20	9	a	a	DET
gs-1949	20	10	finite	finite	ADJ
gs-1949	20	11	ergodic	ergodic	ADJ
gs-1949	20	12	markov	markov	NOUN
gs-1949	20	13	’s	’s	PART
gs-1949	20	14	chain	chain	NOUN
gs-1949	20	15	with	with	ADP
gs-1949	20	16	one	one	NUM
gs-1949	20	17	class	class	NOUN
gs-1949	20	18	of	of	ADP
gs-1949	20	19	ergodicity	ergodicity	NOUN
gs-1949	20	20	,	,	PUNCT
gs-1949	20	21	then	then	ADV
gs-1949	20	22	is	be	AUX
gs-1949	20	23	shownthat	shownthat	NOUN
gs-1949	20	24	(	(	PUNCT
gs-1949	20	25	)	)	PUNCT
gs-1949	20	26	(	(	PUNCT
gs-1949	20	27	)	)	PUNCT
gs-1949	20	28	tq	tq	ADV
gs-1949	20	29	r	r	NOUN
gs-1949	20	30			NOUN
gs-1949	20	31			VERB
gs-1949	20	32			NOUN
gs-1949	20	33			PROPN
gs-1949	20	34	,	,	PUNCT
gs-1949	20	35	where	where	SCONJ
gs-1949	20	36	t	t	PROPN
gs-1949	20	37	is	be	AUX
gs-1949	20	38	expressed	express	VERB
gs-1949	20	39	by	by	ADP
gs-1949	20	40	chain	chain	NOUN
gs-1949	20	41	parameters	parameter	NOUN
gs-1949	20	42	.	.	PUNCT
gs-1949	21	1	when	when	SCONJ
gs-1949	21	2	a	a	DET
gs-1949	21	3	chain	chain	NOUN
gs-1949	21	4	has	have	VERB
gs-1949	21	5	cyclic	cyclic	ADJ
gs-1949	21	6	subclasses	subclass	NOUN
gs-1949	21	7	,	,	PUNCT
gs-1949	21	8	the	the	DET
gs-1949	21	9	existence	existence	NOUN
gs-1949	21	10	of	of	ADP
gs-1949	21	11	the	the	DET
gs-1949	21	12	corresponding	corresponding	ADJ
gs-1949	21	13	limiting	limit	VERB
gs-1949	21	14	characteristics	characteristic	NOUN
gs-1949	21	15	is	be	AUX
gs-1949	21	16	understood	understand	VERB
gs-1949	21	17	in	in	ADP
gs-1949	21	18	the	the	DET
gs-1949	21	19	sense	sense	NOUN
gs-1949	21	20	of	of	ADP
gs-1949	21	21	cesaro	cesaro	NOUN
gs-1949	21	22	.	.	PUNCT
gs-1949	22	1	when	when	SCONJ
gs-1949	22	2	solving	solve	VERB
gs-1949	22	3	many	many	ADJ
gs-1949	22	4	practical	practical	ADJ
gs-1949	22	5	problems	problem	NOUN
gs-1949	22	6	,	,	PUNCT
gs-1949	22	7	the	the	DET
gs-1949	22	8	question	question	NOUN
gs-1949	22	9	arises	arise	VERB
gs-1949	22	10	of	of	ADP
gs-1949	22	11	constructing	construct	VERB
gs-1949	22	12	statistical	statistical	ADJ
gs-1949	22	13	estimates	estimate	NOUN
gs-1949	22	14	of	of	ADP
gs-1949	22	15	parameters	parameter	NOUN
gs-1949	22	16	by	by	ADP
gs-1949	22	17	dependent	dependent	ADJ
gs-1949	22	18	observations	observation	NOUN
gs-1949	22	19	.	.	PUNCT
gs-1949	23	1	for	for	ADP
gs-1949	23	2	example	example	NOUN
gs-1949	23	3	,	,	PUNCT
gs-1949	23	4	in	in	ADP
gs-1949	23	5	a	a	DET
gs-1949	23	6	study	study	NOUN
gs-1949	23	7	conducted	conduct	VERB
gs-1949	23	8	to	to	PART
gs-1949	23	9	determine	determine	VERB
gs-1949	23	10	the	the	DET
gs-1949	23	11	rating	rating	NOUN
gs-1949	23	12	model	model	NOUN
gs-1949	23	13	of	of	ADP
gs-1949	23	14	vocational	vocational	ADJ
gs-1949	23	15	colleges	college	NOUN
gs-1949	23	16	,	,	PUNCT
gs-1949	23	17	the	the	DET
gs-1949	23	18	data	datum	NOUN
gs-1949	23	19	obtained	obtain	VERB
gs-1949	23	20	from	from	ADP
gs-1949	23	21	a	a	DET
gs-1949	23	22	survey	survey	NOUN
gs-1949	23	23	of	of	ADP
gs-1949	23	24	students	student	NOUN
gs-1949	23	25	are	be	AUX
gs-1949	23	26	dependent	dependent	ADJ
gs-1949	23	27	on	on	ADP
gs-1949	23	28	each	each	DET
gs-1949	23	29	other	other	ADJ
gs-1949	23	30	,	,	PUNCT
gs-1949	23	31	due	due	ADP
gs-1949	23	32	to	to	ADP
gs-1949	23	33	the	the	DET
gs-1949	23	34	fact	fact	NOUN
gs-1949	23	35	that	that	SCONJ
gs-1949	23	36	they	they	PRON
gs-1949	23	37	are	be	AUX
gs-1949	23	38	obtained	obtain	VERB
gs-1949	23	39	from	from	ADP
gs-1949	23	40	the	the	DET
gs-1949	23	41	same	same	ADJ
gs-1949	23	42	social	social	ADJ
gs-1949	23	43	group	group	NOUN
gs-1949	23	44	.	.	PUNCT
gs-1949	24	1	(	(	PUNCT
gs-1949	24	2	r.	r.	PROPN
gs-1949	24	3	chartolani	chartolani	PROPN
gs-1949	24	4	,	,	PUNCT
gs-1949	24	5	n.	n.	PROPN
gs-1949	24	6	durglishvili	durglishvili	PROPN
gs-1949	24	7	,	,	PUNCT
gs-1949	24	8	z.	z.	PROPN
gs-1949	24	9	kvatadze	kvatadze	PROPN
gs-1949	24	10	.	.	PUNCT
gs-1949	25	1	optimization	optimization	NOUN
gs-1949	25	2	of	of	ADP
gs-1949	25	3	a	a	DET
gs-1949	25	4	state	state	NOUN
gs-1949	25	5	financing	financing	NOUN
gs-1949	25	6	model	model	NOUN
gs-1949	25	7	of	of	ADP
gs-1949	25	8	vocational	vocational	ADJ
gs-1949	25	9	colleges	college	NOUN
gs-1949	25	10	.	.	PUNCT
gs-1949	26	1	proc	proc	NOUN
gs-1949	26	2	.	.	PUNCT
gs-1949	27	1	a.	a.	PROPN
gs-1949	27	2	razmadze	razmadze	PROPN
gs-1949	27	3	math	math	PROPN
gs-1949	27	4	.	.	PUNCT
gs-1949	28	1	inst	inst	PROPN
gs-1949	28	2	.	.	PROPN
gs-1949	28	3	2015	2015	NUM
gs-1949	28	4	.	.	PUNCT
gs-1949	29	1	169.(2	169.(2	NUM
gs-1949	29	2	-	-	SYM
gs-1949	29	3	15	15	NUM
gs-1949	29	4	)	)	PUNCT
gs-1949	29	5	,	,	PUNCT
gs-1949	29	6	pp	pp	ADP
gs-1949	29	7	.	.	PUNCT
gs-1949	30	1	23	23	NUM
gs-1949	30	2	-	-	SYM
gs-1949	30	3	31	31	NUM
gs-1949	30	4	)	)	PUNCT
gs-1949	30	5	.	.	PUNCT
gs-1949	31	1	also	also	ADV
gs-1949	31	2	,	,	PUNCT
gs-1949	31	3	the	the	DET
gs-1949	31	4	dependence	dependence	NOUN
gs-1949	31	5	of	of	ADP
gs-1949	31	6	data	datum	NOUN
gs-1949	31	7	in	in	ADP
gs-1949	31	8	various	various	ADJ
gs-1949	31	9	studies	study	NOUN
gs-1949	31	10	of	of	ADP
gs-1949	31	11	the	the	DET
gs-1949	31	12	geophysical	geophysical	ADJ
gs-1949	31	13	direction	direction	NOUN
gs-1949	31	14	can	can	AUX
gs-1949	31	15	not	not	PART
gs-1949	31	16	be	be	AUX
gs-1949	31	17	neglected	neglect	VERB
gs-1949	31	18	.	.	PUNCT
gs-1949	32	1	for	for	ADP
gs-1949	32	2	example	example	NOUN
gs-1949	32	3	,	,	PUNCT
gs-1949	32	4	in	in	ADP
gs-1949	32	5	the	the	DET
gs-1949	32	6	preearthquake	preearthquake	NOUN
gs-1949	32	7	(	(	PUNCT
gs-1949	32	8	preparatory	preparatory	ADJ
gs-1949	32	9	)	)	PUNCT
gs-1949	32	10	period	period	NOUN
gs-1949	32	11	,	,	PUNCT
gs-1949	32	12	tectonic	tectonic	ADJ
gs-1949	32	13	processes	process	NOUN
gs-1949	32	14	in	in	ADP
gs-1949	32	15	rocks	rock	NOUN
gs-1949	32	16	develop	develop	VERB
gs-1949	32	17	continuously	continuously	ADV
gs-1949	32	18	in	in	ADP
gs-1949	32	19	time	time	NOUN
gs-1949	32	20	,	,	PUNCT
gs-1949	32	21	and	and	CCONJ
gs-1949	32	22	therefore	therefore	ADV
gs-1949	32	23	records	record	NOUN
gs-1949	32	24	of	of	ADP
gs-1949	32	25	any	any	DET
gs-1949	32	26	characteristic	characteristic	NOUN
gs-1949	32	27	taken	take	VERB
gs-1949	32	28	at	at	ADP
gs-1949	32	29	discrete	discrete	ADJ
gs-1949	32	30	points	point	NOUN
gs-1949	32	31	in	in	ADP
gs-1949	32	32	time	time	NOUN
gs-1949	32	33	depend	depend	VERB
gs-1949	32	34	on	on	ADP
gs-1949	32	35	each	each	DET
gs-1949	32	36	other	other	ADJ
gs-1949	32	37	as	as	SCONJ
gs-1949	32	38	georgian	georgian	PROPN
gs-1949	32	39	scientists/ქართველი	scientists/ქართველი	NOUN
gs-1949	32	40	მეცნიერები	მეცნიერები	NOUN
gs-1949	32	41	ტ.	ტ.	VERB
gs-1949	32	42	5	5	NUM
gs-1949	33	1	n	n	PRON
gs-1949	33	2	2	2	NUM
gs-1949	33	3	,	,	PUNCT
gs-1949	33	4	2023	2023	NUM
gs-1949	33	5	22	22	NUM
gs-1949	33	6	manifestations	manifestation	NOUN
gs-1949	33	7	of	of	ADP
gs-1949	33	8	one	one	NUM
gs-1949	33	9	whole	whole	NOUN
gs-1949	33	10	.	.	PUNCT
gs-1949	34	1	proceeding	proceed	VERB
gs-1949	34	2	from	from	ADP
gs-1949	34	3	similar	similar	ADJ
gs-1949	34	4	considerations	consideration	NOUN
gs-1949	34	5	,	,	PUNCT
gs-1949	34	6	when	when	SCONJ
gs-1949	34	7	determining	determine	VERB
gs-1949	34	8	the	the	DET
gs-1949	34	9	law	law	NOUN
gs-1949	34	10	of	of	ADP
gs-1949	34	11	distribution	distribution	NOUN
gs-1949	34	12	of	of	ADP
gs-1949	34	13	various	various	ADJ
gs-1949	34	14	populations	population	NOUN
gs-1949	34	15	,	,	PUNCT
gs-1949	34	16	density	density	NOUN
gs-1949	34	17	estimates	estimate	NOUN
gs-1949	34	18	are	be	AUX
gs-1949	34	19	constructed	construct	VERB
gs-1949	34	20	by	by	ADP
gs-1949	34	21	dependent	dependent	ADJ
gs-1949	34	22	observations	observation	NOUN
gs-1949	34	23	.	.	PUNCT
gs-1949	35	1	for	for	ADP
gs-1949	35	2	example	example	NOUN
gs-1949	35	3	,	,	PUNCT
gs-1949	35	4	nonparametric	nonparametric	ADJ
gs-1949	35	5	density	density	NOUN
gs-1949	35	6	estimates	estimate	NOUN
gs-1949	35	7	and	and	CCONJ
gs-1949	35	8	estimates	estimate	NOUN
gs-1949	35	9	of	of	ADP
gs-1949	35	10	regression	regression	NOUN
gs-1949	35	11	coefficients	coefficient	NOUN
gs-1949	35	12	are	be	AUX
gs-1949	35	13	known	know	VERB
gs-1949	35	14	,	,	PUNCT
gs-1949	35	15	built	build	VERB
gs-1949	35	16	by	by	ADP
gs-1949	35	17	observations	observation	NOUN
gs-1949	35	18	connected	connect	VERB
gs-1949	35	19	in	in	ADP
gs-1949	35	20	a	a	DET
gs-1949	35	21	markov	markov	NOUN
gs-1949	35	22	chain	chain	NOUN
gs-1949	35	23	(	(	PUNCT
gs-1949	35	24	yakowitz	yakowitz	PROPN
gs-1949	35	25	sidney	sidney	PROPN
gs-1949	35	26	(	(	PUNCT
gs-1949	35	27	1989	1989	NUM
gs-1949	35	28	)	)	PUNCT
gs-1949	35	29	nonparametric	nonparametric	NOUN
gs-1949	35	30	density	density	NOUN
gs-1949	35	31	and	and	CCONJ
gs-1949	35	32	regression	regression	NOUN
gs-1949	35	33	estimation	estimation	NOUN
gs-1949	35	34	for	for	ADP
gs-1949	35	35	markov	markov	NOUN
gs-1949	35	36	sequences	sequence	NOUN
gs-1949	35	37	without	without	ADP
gs-1949	35	38	mixing	mix	VERB
gs-1949	35	39	assumptions	assumption	NOUN
gs-1949	35	40	.	.	PUNCT
gs-1949	36	1	85721	85721	NUM
gs-1949	36	2	–	–	PUNCT
gs-1949	36	3	journal	journal	NOUN
gs-1949	36	4	of	of	ADP
gs-1949	36	5	multivariate	multivariate	NOUN
gs-1949	36	6	analysis	analysis	NOUN
gs-1949	36	7	,	,	PUNCT
gs-1949	36	8	30	30	NUM
gs-1949	36	9	:	:	SYM
gs-1949	36	10	124	124	NUM
gs-1949	36	11	-	-	SYM
gs-1949	36	12	136	136	NUM
gs-1949	36	13	.	.	PUNCT
gs-1949	37	1	arisona	arisona	PROPN
gs-1949	37	2	,	,	PUNCT
gs-1949	37	3	usa	usa	PROPN
gs-1949	37	4	)	)	PUNCT
gs-1949	37	5	.	.	PUNCT
gs-1949	38	1	conditionally	conditionally	ADV
gs-1949	38	2	independent	independent	ADJ
gs-1949	38	3	observations	observation	NOUN
gs-1949	38	4	and	and	CCONJ
gs-1949	38	5	observations	observation	NOUN
gs-1949	38	6	with	with	ADP
gs-1949	38	7	a	a	DET
gs-1949	38	8	chain	chain	NOUN
gs-1949	38	9	dependence	dependence	NOUN
gs-1949	38	10	are	be	AUX
gs-1949	38	11	also	also	ADV
gs-1949	38	12	considered	consider	VERB
gs-1949	38	13	.	.	PUNCT
gs-1949	39	1	the	the	DET
gs-1949	39	2	accuracies	accuracy	NOUN
gs-1949	39	3	of	of	ADP
gs-1949	39	4	density	density	NOUN
gs-1949	39	5	estimates	estimate	NOUN
gs-1949	39	6	constructed	construct	VERB
gs-1949	39	7	by	by	ADP
gs-1949	39	8	such	such	ADJ
gs-1949	39	9	observations	observation	NOUN
gs-1949	39	10	by	by	ADP
gs-1949	39	11	the	the	DET
gs-1949	39	12	2l	2l	NUM
gs-1949	39	13	metric	metric	ADJ
gs-1949	39	14	(	(	PUNCT
gs-1949	39	15	z	z	NOUN
gs-1949	39	16	,	,	PUNCT
gs-1949	39	17	kvatadze	kvatadze	PROPN
gs-1949	39	18	,	,	PUNCT
gs-1949	39	19	b.	b.	PROPN
gs-1949	39	20	phardjiani	phardjiani	PROPN
gs-1949	39	21	.	.	PUNCT
gs-1949	40	1	on	on	ADP
gs-1949	40	2	the	the	DET
gs-1949	40	3	exsactness	exsactness	NOUN
gs-1949	40	4	of	of	ADP
gs-1949	40	5	distribution	distribution	NOUN
gs-1949	40	6	density	density	NOUN
gs-1949	40	7	estimates	estimate	NOUN
gs-1949	40	8	constructed	construct	VERB
gs-1949	40	9	by	by	ADP
gs-1949	40	10	some	some	DET
gs-1949	40	11	class	class	NOUN
gs-1949	40	12	of	of	ADP
gs-1949	40	13	dependent	dependent	ADJ
gs-1949	40	14	observations	observation	NOUN
gs-1949	40	15	.	.	PUNCT
gs-1949	41	1	mathematics	mathematic	NOUN
gs-1949	41	2	and	and	CCONJ
gs-1949	41	3	statistics	statistic	NOUN
gs-1949	41	4	.	.	PUNCT
gs-1949	42	1	2019	2019	NUM
gs-1949	42	2	vol	vol	NOUN
gs-1949	42	3	.	.	PUNCT
gs-1949	43	1	7(4	7(4	NUM
gs-1949	43	2	)	)	PUNCT
gs-1949	43	3	,	,	PUNCT
gs-1949	43	4	pp	pp	PROPN
gs-1949	43	5	.	.	PUNCT
gs-1949	44	1	135	135	NUM
gs-1949	44	2	-	-	SYM
gs-1949	44	3	145	145	NUM
gs-1949	44	4	.	.	PUNCT
gs-1949	45	1	san	san	PROPN
gs-1949	45	2	jose	jose	PROPN
gs-1949	45	3	)	)	PUNCT
gs-1949	45	4	and	and	CCONJ
gs-1949	45	5	by	by	ADP
gs-1949	45	6	the	the	DET
gs-1949	45	7	1l	1l	NUM
gs-1949	45	8	metric	metric	NOUN
gs-1949	45	9	(	(	PUNCT
gs-1949	45	10	b.	b.	PROPN
gs-1949	45	11	parjiani	parjiani	PROPN
gs-1949	45	12	,	,	PUNCT
gs-1949	45	13	l.	l.	PROPN
gs-1949	45	14	labadze	labadze	PROPN
gs-1949	45	15	,	,	PUNCT
gs-1949	45	16	t.	t.	PROPN
gs-1949	45	17	kvatadze	kvatadze	PROPN
gs-1949	45	18	;	;	PUNCT
gs-1949	45	19	georgian	georgian	ADJ
gs-1949	45	20	scientists	scientist	NOUN
gs-1949	45	21	,	,	PUNCT
gs-1949	45	22	“	"	PUNCT
gs-1949	45	23	on	on	ADP
gs-1949	45	24	the	the	DET
gs-1949	45	25	accuracyby	accuracyby	NOUN
gs-1949	45	26	the	the	DET
gs-1949	45	27	metric	metric	ADJ
gs-1949	45	28	l1	l1	PROPN
gs-1949	45	29	of	of	ADP
gs-1949	45	30	the	the	DET
gs-1949	45	31	density	density	NOUN
gs-1949	45	32	estimation	estimation	NOUN
gs-1949	45	33	constructed	construct	VERB
gs-1949	45	34	by	by	ADP
gs-1949	45	35	dependent	dependent	ADJ
gs-1949	45	36	observations	observation	NOUN
gs-1949	45	37	”	"	PUNCT
gs-1949	45	38	vol	vol	NOUN
gs-1949	45	39	.	.	PROPN
gs-1949	46	1	5	5	NUM
gs-1949	46	2	.	.	X
gs-1949	46	3	issue	issue	NOUN
gs-1949	46	4	1	1	NUM
gs-1949	46	5	,	,	PUNCT
gs-1949	46	6	pp	pp	ADJ
gs-1949	46	7	.	.	PUNCT
gs-1949	47	1	308	308	NUM
gs-1949	47	2	-	-	SYM
gs-1949	47	3	321	321	NUM
gs-1949	47	4	,	,	PUNCT
gs-1949	47	5	2023	2023	NUM
gs-1949	47	6	)	)	PUNCT
gs-1949	47	7	are	be	AUX
gs-1949	47	8	known	know	VERB
gs-1949	47	9	.	.	PUNCT
gs-1949	48	1	to	to	PART
gs-1949	48	2	construct	construct	VERB
gs-1949	48	3	statistical	statistical	ADJ
gs-1949	48	4	estimates	estimate	NOUN
gs-1949	48	5	based	base	VERB
gs-1949	48	6	on	on	ADP
gs-1949	48	7	dependent	dependent	ADJ
gs-1949	48	8	observations	observation	NOUN
gs-1949	48	9	and	and	CCONJ
gs-1949	48	10	determine	determine	VERB
gs-1949	48	11	their	their	PRON
gs-1949	48	12	unbiasedness	unbiasedness	NOUN
gs-1949	48	13	,	,	PUNCT
gs-1949	48	14	it	it	PRON
gs-1949	48	15	is	be	AUX
gs-1949	48	16	necessary	necessary	ADJ
gs-1949	48	17	to	to	PART
gs-1949	48	18	know	know	VERB
gs-1949	48	19	the	the	DET
gs-1949	48	20	asymptotic	asymptotic	ADJ
gs-1949	48	21	distribution	distribution	NOUN
gs-1949	48	22	of	of	ADP
gs-1949	48	23	sums	sum	NOUN
gs-1949	48	24	of	of	ADP
gs-1949	48	25	dependent	dependent	ADJ
gs-1949	48	26	random	random	ADJ
gs-1949	48	27	variables	variable	NOUN
gs-1949	48	28	.	.	PUNCT
gs-1949	49	1	at	at	ADP
gs-1949	49	2	the	the	DET
gs-1949	49	3	present	present	ADJ
gs-1949	49	4	stage	stage	NOUN
gs-1949	49	5	,	,	PUNCT
gs-1949	49	6	the	the	DET
gs-1949	49	7	rich	rich	ADJ
gs-1949	49	8	theory	theory	NOUN
gs-1949	49	9	of	of	ADP
gs-1949	49	10	summation	summation	NOUN
gs-1949	49	11	of	of	ADP
gs-1949	49	12	independent	independent	ADJ
gs-1949	49	13	random	random	ADJ
gs-1949	49	14	variables	variable	NOUN
gs-1949	49	15	(	(	PUNCT
gs-1949	49	16	normal	normal	ADJ
gs-1949	49	17	approximation	approximation	NOUN
gs-1949	49	18	some	some	DET
gs-1949	49	19	recent	recent	ADJ
gs-1949	49	20	advances	advance	NOUN
gs-1949	49	21	.	.	PUNCT
gs-1949	50	1	sazonov	sazonov	PROPN
gs-1949	50	2	v.v	v.v	PROPN
gs-1949	50	3	.	.	PROPN
gs-1949	50	4	lecture	lecture	NOUN
gs-1949	50	5	notes	note	NOUN
gs-1949	50	6	in	in	ADP
gs-1949	50	7	math	math	NOUN
gs-1949	50	8	.	.	PUNCT
gs-1949	51	1	v.	v.	ADP
gs-1949	51	2	79	79	NUM
gs-1949	51	3	,	,	PUNCT
gs-1949	51	4	berlin	berlin	PROPN
gs-1949	51	5	,	,	PUNCT
gs-1949	51	6	ete	ete	PROPN
gs-1949	51	7	.	.	PROPN
gs-1949	51	8	,	,	PUNCT
gs-1949	51	9	:	:	PUNCT
gs-1949	51	10	springer	springer	NOUN
gs-1949	51	11	.	.	PUNCT
gs-1949	51	12	1981	1981	NUM
gs-1949	51	13	.	.	PUNCT
gs-1949	51	14	)	)	PUNCT
gs-1949	51	15	is	be	AUX
gs-1949	51	16	transferred	transfer	VERB
gs-1949	51	17	to	to	ADP
gs-1949	51	18	dependent	dependent	ADJ
gs-1949	51	19	random	random	ADJ
gs-1949	51	20	variables	variable	NOUN
gs-1949	51	21	.	.	PUNCT
gs-1949	52	1	in	in	ADP
gs-1949	52	2	many	many	ADJ
gs-1949	52	3	problems	problem	NOUN
gs-1949	52	4	,	,	PUNCT
gs-1949	52	5	markov	markov	NOUN
gs-1949	52	6	dependence	dependence	NOUN
gs-1949	52	7	is	be	AUX
gs-1949	52	8	used	use	VERB
gs-1949	52	9	,	,	PUNCT
gs-1949	52	10	which	which	PRON
gs-1949	52	11	is	be	AUX
gs-1949	52	12	one	one	NUM
gs-1949	52	13	of	of	ADP
gs-1949	52	14	the	the	DET
gs-1949	52	15	types	type	NOUN
gs-1949	52	16	of	of	ADP
gs-1949	52	17	weak	weak	ADJ
gs-1949	52	18	dependence	dependence	NOUN
gs-1949	52	19	.	.	PUNCT
gs-1949	53	1	questions	question	NOUN
gs-1949	53	2	of	of	ADP
gs-1949	53	3	the	the	DET
gs-1949	53	4	limiting	limit	VERB
gs-1949	53	5	asymptotic	asymptotic	ADJ
gs-1949	53	6	behavior	behavior	NOUN
gs-1949	53	7	of	of	ADP
gs-1949	53	8	sums	sum	NOUN
gs-1949	53	9	of	of	ADP
gs-1949	53	10	random	random	ADJ
gs-1949	53	11	variables	variable	NOUN
gs-1949	53	12	of	of	ADP
gs-1949	53	13	various	various	ADJ
gs-1949	53	14	types	type	NOUN
gs-1949	53	15	of	of	ADP
gs-1949	53	16	dependency	dependency	NOUN
gs-1949	53	17	(	(	PUNCT
gs-1949	53	18	weakly	weakly	ADV
gs-1949	53	19	dependent	dependent	ADJ
gs-1949	53	20	,	,	PUNCT
gs-1949	53	21	conditionally	conditionally	ADV
gs-1949	53	22	independent	independent	ADJ
gs-1949	53	23	,	,	PUNCT
gs-1949	53	24	connected	connect	VERB
gs-1949	53	25	in	in	ADP
gs-1949	53	26	a	a	DET
gs-1949	53	27	markov	markov	NOUN
gs-1949	53	28	chain	chain	NOUN
gs-1949	53	29	)	)	PUNCT
gs-1949	53	30	are	be	AUX
gs-1949	53	31	discussed	discuss	VERB
gs-1949	53	32	in	in	ADP
gs-1949	53	33	many	many	ADJ
gs-1949	53	34	papers	paper	NOUN
gs-1949	53	35	.	.	PUNCT
gs-1949	54	1	sums	sum	NOUN
gs-1949	54	2	of	of	ADP
gs-1949	54	3	such	such	ADJ
gs-1949	54	4	random	random	ADJ
gs-1949	54	5	variables	variable	NOUN
gs-1949	54	6	are	be	AUX
gs-1949	54	7	often	often	ADV
gs-1949	54	8	considered	consider	VERB
gs-1949	54	9	,	,	PUNCT
gs-1949	54	10	the	the	DET
gs-1949	54	11	joint	joint	ADJ
gs-1949	54	12	distribution	distribution	NOUN
gs-1949	54	13	of	of	ADP
gs-1949	54	14	which	which	PRON
gs-1949	54	15	is	be	AUX
gs-1949	54	16	determined	determine	VERB
gs-1949	54	17	by	by	ADP
gs-1949	54	18	some	some	DET
gs-1949	54	19	control	control	NOUN
gs-1949	54	20	sequence	sequence	NOUN
gs-1949	54	21	of	of	ADP
gs-1949	54	22	random	random	ADJ
gs-1949	54	23	elements	element	NOUN
gs-1949	54	24	.	.	PUNCT
gs-1949	55	1	conditionally	conditionally	ADV
gs-1949	55	2	independent	independent	ADJ
gs-1949	55	3	sequences	sequence	NOUN
gs-1949	55	4	(	(	PUNCT
gs-1949	55	5	bokuchava	bokuchava	PROPN
gs-1949	55	6	i.	i.	PROPN
gs-1949	55	7	v.	v.	PROPN
gs-1949	55	8	limit	limit	PROPN
gs-1949	55	9	theorems	theorem	VERB
gs-1949	55	10	for	for	ADP
gs-1949	55	11	conditionally	conditionally	ADV
gs-1949	55	12	independent	independent	ADJ
gs-1949	55	13	sequences	sequence	NOUN
gs-1949	55	14	.	.	PUNCT
gs-1949	56	1	(	(	PUNCT
gs-1949	56	2	in	in	ADP
gs-1949	56	3	russian	russian	PROPN
gs-1949	56	4	)	)	PUNCT
gs-1949	56	5	teor	teor	PROPN
gs-1949	56	6	.	.	PUNCT
gs-1949	56	7	verojatnost	verojatnost	PROPN
gs-1949	56	8	.	.	PUNCT
gs-1949	57	1	i	i	PRON
gs-1949	57	2	primenen	primenen	VERB
gs-1949	57	3	.	.	PUNCT
gs-1949	58	1	xxix	xxix	PROPN
gs-1949	58	2	.	.	PUNCT
gs-1949	59	1	(	(	PUNCT
gs-1949	59	2	1984	1984	NUM
gs-1949	59	3	)	)	PUNCT
gs-1949	59	4	.	.	PUNCT
gs-1949	60	1	№	№	ADP
gs-1949	60	2	1	1	NUM
gs-1949	60	3	,	,	PUNCT
gs-1949	60	4	p.	p.	NOUN
gs-1949	60	5	192	192	NUM
gs-1949	60	6	-	-	SYM
gs-1949	60	7	193	193	NUM
gs-1949	60	8	)	)	PUNCT
gs-1949	60	9	and	and	CCONJ
gs-1949	60	10	sequences	sequence	NOUN
gs-1949	60	11	with	with	ADP
gs-1949	60	12	chain	chain	NOUN
gs-1949	60	13	dependence	dependence	NOUN
gs-1949	60	14	are	be	AUX
gs-1949	60	15	considered	consider	VERB
gs-1949	60	16	.	.	PUNCT
gs-1949	61	1	for	for	ADP
gs-1949	61	2	example	example	NOUN
gs-1949	61	3	,	,	PUNCT
gs-1949	61	4	articles	article	NOUN
gs-1949	61	5	by	by	ADP
gs-1949	61	6	o'brien	o'brien	PROPN
gs-1949	61	7	(	(	PUNCT
gs-1949	61	8	o	o	NOUN
gs-1949	61	9	’	'	PUNCT
gs-1949	61	10	braien	braien	PROPN
gs-1949	61	11	g.l	g.l	PROPN
gs-1949	61	12	.	.	PROPN
gs-1949	61	13	limit	limit	PROPN
gs-1949	61	14	theorems	theorem	NOUN
gs-1949	61	15	for	for	ADP
gs-1949	61	16	sum	sum	NOUN
gs-1949	61	17	of	of	ADP
gs-1949	61	18	chain	chain	NOUN
gs-1949	61	19	dependent	dependent	ADJ
gs-1949	61	20	proccesses	proccesse	NOUN
gs-1949	61	21	.	.	PUNCT
gs-1949	62	1	u.	u.	PROPN
gs-1949	62	2	appl	appl	PROPN
gs-1949	62	3	.	.	PUNCT
gs-1949	63	1	probab	probab	PROPN
gs-1949	63	2	.	.	PROPN
gs-1949	63	3	,	,	PUNCT
gs-1949	63	4	1974	1974	NUM
gs-1949	63	5	,	,	PUNCT
gs-1949	63	6	11	11	NUM
gs-1949	63	7	,	,	PUNCT
gs-1949	63	8	582	582	NUM
gs-1949	63	9	-	-	SYM
gs-1949	63	10	587	587	NUM
gs-1949	63	11	)	)	PUNCT
gs-1949	63	12	,	,	PUNCT
gs-1949	63	13	y.	y.	PROPN
gs-1949	63	14	aleshkevichus	aleshkevichus	PROPN
gs-1949	63	15	(	(	PUNCT
gs-1949	63	16	g.	g.	PROPN
gs-1949	63	17	yu	yu	PROPN
gs-1949	63	18	.	.	PROPN
gs-1949	63	19	aleshkyavichus	aleshkyavichus	PROPN
gs-1949	63	20	,	,	PUNCT
gs-1949	63	21	on	on	ADP
gs-1949	63	22	the	the	DET
gs-1949	63	23	central	central	ADJ
gs-1949	63	24	limit	limit	NOUN
gs-1949	63	25	theorem	theorem	VERB
gs-1949	63	26	for	for	ADP
gs-1949	63	27	sums	sum	NOUN
gs-1949	63	28	of	of	ADP
gs-1949	63	29	random	random	ADJ
gs-1949	63	30	variables	variable	NOUN
gs-1949	63	31	given	give	VERB
gs-1949	63	32	on	on	ADP
gs-1949	63	33	a	a	DET
gs-1949	63	34	markov	markov	NOUN
gs-1949	63	35	chain	chain	NOUN
gs-1949	63	36	.	.	PUNCT
gs-1949	64	1	(	(	PUNCT
gs-1949	64	2	russian	russian	ADJ
gs-1949	64	3	)	)	PUNCT
gs-1949	64	4	lithuanian	lithuanian	PROPN
gs-1949	64	5	mathematical	mathematical	ADJ
gs-1949	64	6	collected	collect	VERB
gs-1949	64	7	works	work	NOUN
gs-1949	64	8	,	,	PUNCT
gs-1949	64	9	vilnius	vilnius	NOUN
gs-1949	64	10	6	6	NUM
gs-1949	64	11	(	(	PUNCT
gs-1949	64	12	1966	1966	NUM
gs-1949	64	13	)	)	PUNCT
gs-1949	64	14	,	,	PUNCT
gs-1949	64	15	№	№	NOUN
gs-1949	64	16	.	.	NOUN
gs-1949	64	17	1	1	NUM
gs-1949	64	18	,	,	PUNCT
gs-1949	64	19	15−22	15−22	NOUN
gs-1949	64	20	.	.	PUNCT
gs-1949	64	21	)	)	PUNCT
gs-1949	64	22	,	,	PUNCT
gs-1949	64	23	r.	r.	PROPN
gs-1949	64	24	chitashvili	chitashvili	PROPN
gs-1949	64	25	,	,	PUNCT
gs-1949	64	26	t.	t.	PROPN
gs-1949	64	27	shervashidze	shervashidze	PROPN
gs-1949	64	28	,	,	PUNCT
gs-1949	64	29	i.	i.	PROPN
gs-1949	64	30	bokuchava	bokuchava	PROPN
gs-1949	64	31	,	,	PUNCT
gs-1949	64	32	z.	z.	PROPN
gs-1949	64	33	kvatadze	kvatadze	PROPN
gs-1949	64	34	(	(	PUNCT
gs-1949	64	35	bokuchava	bokuchava	PROPN
gs-1949	64	36	i.	i.	PROPN
gs-1949	64	37	,	,	PUNCT
gs-1949	64	38	kvatadze	kvatadze	PROPN
gs-1949	64	39	z.	z.	PROPN
gs-1949	64	40	,	,	PUNCT
gs-1949	64	41	shervashidze	shervashidze	ADJ
gs-1949	64	42	t.	t.	PROPN
gs-1949	64	43	on	on	ADP
gs-1949	64	44	limit	limit	NOUN
gs-1949	64	45	theorem	theorem	VERB
gs-1949	64	46	for	for	ADP
gs-1949	64	47	random	random	ADJ
gs-1949	64	48	vectors	vector	NOUN
gs-1949	64	49	controlled	control	VERB
gs-1949	64	50	by	by	ADP
gs-1949	64	51	a	a	DET
gs-1949	64	52	marcov	marcov	NOUN
gs-1949	64	53	chain	chain	NOUN
gs-1949	64	54	.	.	PUNCT
gs-1949	65	1	prob	prob	PROPN
gs-1949	65	2	.	.	PROPN
gs-1949	66	1	theory	theory	NOUN
gs-1949	66	2	and	and	CCONJ
gs-1949	66	3	math	math	NOUN
gs-1949	66	4	.	.	PUNCT
gs-1949	67	1	stat	stat	PROPN
gs-1949	67	2	.	.	PUNCT
gs-1949	67	3	,	,	PUNCT
gs-1949	67	4	vol	vol	NOUN
gs-1949	67	5	.	.	PROPN
gs-1949	67	6	1	1	NUM
gs-1949	67	7	,	,	PUNCT
gs-1949	67	8	1986	1986	NUM
gs-1949	67	9	,	,	PUNCT
gs-1949	67	10	239	239	NUM
gs-1949	67	11	-	-	SYM
gs-1949	67	12	250	250	NUM
gs-1949	67	13	.	.	PUNCT
gs-1949	68	1	vnu	vnu	PROPN
gs-1949	68	2	science	science	PROPN
gs-1949	68	3	press	press	PROPN
gs-1949	68	4	,	,	PUNCT
gs-1949	68	5	utrecht	utrecht	PROPN
gs-1949	68	6	.	.	PUNCT
gs-1949	68	7	)	)	PUNCT
gs-1949	69	1	and	and	CCONJ
gs-1949	69	2	other	other	ADJ
gs-1949	69	3	authors	author	NOUN
gs-1949	69	4	deal	deal	VERB
gs-1949	69	5	with	with	ADP
gs-1949	69	6	these	these	DET
gs-1949	69	7	issues.in	issues.in	NOUN
gs-1949	69	8	this	this	DET
gs-1949	69	9	paper	paper	NOUN
gs-1949	69	10	,	,	PUNCT
gs-1949	69	11	we	we	PRON
gs-1949	69	12	discuss	discuss	VERB
gs-1949	69	13	the	the	DET
gs-1949	69	14	class	class	NOUN
gs-1949	69	15	of	of	ADP
gs-1949	69	16	sequences	sequence	NOUN
gs-1949	69	17	of	of	ADP
gs-1949	69	18	conditionally	conditionally	ADV
gs-1949	69	19	m	m	VERB
gs-1949	69	20	independent	independent	ADJ
gs-1949	69	21	vectors	vector	NOUN
gs-1949	69	22	and	and	CCONJ
gs-1949	69	23	the	the	DET
gs-1949	69	24	class	class	NOUN
gs-1949	69	25	of	of	ADP
gs-1949	69	26	sequences	sequence	NOUN
gs-1949	69	27	of	of	ADP
gs-1949	69	28	vectors	vector	NOUN
gs-1949	69	29	with	with	ADP
gs-1949	69	30	chain	chain	NOUN
gs-1949	69	31	m	m	PROPN
gs-1949	69	32	-dependence	-dependence	NOUN
gs-1949	69	33	.	.	PUNCT
gs-1949	70	1	(	(	PUNCT
gs-1949	70	2	kvatadze	kvatadze	PROPN
gs-1949	70	3	z.	z.	PROPN
gs-1949	70	4	,	,	PUNCT
gs-1949	70	5	shervashidzet	shervashidzet	PROPN
gs-1949	70	6	.	.	PUNCT
gs-1949	71	1	some	some	DET
gs-1949	71	2	limit	limit	NOUN
gs-1949	71	3	theorems	theorem	VERB
gs-1949	71	4	for	for	ADP
gs-1949	71	5	i.i.d	i.i.d	PROPN
gs-1949	71	6	.	.	PUNCT
gs-1949	72	1	and	and	CCONJ
gs-1949	72	2	conditionally	conditionally	ADV
gs-1949	72	3	independent	independent	ADJ
gs-1949	72	4	random	random	ADJ
gs-1949	72	5	variables	variable	NOUN
gs-1949	72	6	.	.	PUNCT
gs-1949	73	1	the	the	DET
gs-1949	73	2	second	second	ADJ
gs-1949	73	3	international	international	ADJ
gs-1949	73	4	conference	conference	NOUN
gs-1949	73	5	,	,	PUNCT
gs-1949	73	6	“	"	PUNCT
gs-1949	73	7	problems	problem	NOUN
gs-1949	73	8	of	of	ADP
gs-1949	73	9	cybernetics	cybernetic	NOUN
gs-1949	73	10	and	and	CCONJ
gs-1949	73	11	informatics	informatic	NOUN
gs-1949	73	12	”	"	PUNCT
gs-1949	73	13	.	.	PUNCT
gs-1949	74	1	september	september	PROPN
gs-1949	74	2	10	10	NUM
gs-1949	74	3	-	-	SYM
gs-1949	74	4	12	12	NUM
gs-1949	74	5	,	,	PUNCT
gs-1949	74	6	2008	2008	NUM
gs-1949	74	7	.	.	PUNCT
gs-1949	75	1	baku	baku	PROPN
gs-1949	75	2	.	.	PUNCT
gs-1949	75	3	azerbaijan	azerbaijan	PROPN
gs-1949	75	4	.	.	PROPN
gs-1949	75	5	section	section	NOUN
gs-1949	75	6	№	№	VERB
gs-1949	75	7	4	4	NUM
gs-1949	75	8	.	.	PUNCT
gs-1949	76	1	“	"	PUNCT
gs-1949	76	2	applied	apply	VERB
gs-1949	76	3	stochastic	stochastic	ADJ
gs-1949	76	4	analysis	analysis	NOUN
gs-1949	76	5	”	"	PUNCT
gs-1949	76	6	.	.	PUNCT
gs-1949	77	1	institute	institute	PROPN
gs-1949	77	2	of	of	ADP
gs-1949	77	3	information	information	NOUN
gs-1949	77	4	technologies	technology	NOUN
gs-1949	77	5	of	of	ADP
gs-1949	77	6	nasa	nasa	PROPN
gs-1949	77	7	.	.	PUNCT
gs-1949	78	1	printing	printing	NOUN
gs-1949	78	2	house	house	NOUN
gs-1949	78	3	of	of	ADP
gs-1949	78	4	“	"	PUNCT
gs-1949	78	5	information	information	NOUN
gs-1949	78	6	technology	technology	NOUN
gs-1949	78	7	”	"	PUNCT
gs-1949	78	8	baku	baku	PROPN
gs-1949	78	9	.	.	PROPN
gs-1949	78	10	2008	2008	NUM
gs-1949	78	11	.	.	PUNCT
gs-1949	79	1	vol	vol	NOUN
gs-1949	79	2	.	.	PUNCT
gs-1949	79	3	ii	ii	PROPN
gs-1949	79	4	,	,	PUNCT
gs-1949	79	5	217	217	NUM
gs-1949	79	6	-	-	SYM
gs-1949	79	7	219	219	NUM
gs-1949	79	8	)	)	PUNCT
gs-1949	79	9	.	.	PUNCT
gs-1949	80	1	in	in	ADP
gs-1949	80	2	the	the	DET
gs-1949	80	3	case	case	NOUN
gs-1949	80	4	of	of	ADP
gs-1949	80	5	a	a	DET
gs-1949	80	6	non	non	ADJ
gs-1949	80	7	-	-	ADJ
gs-1949	80	8	regular	regular	ADJ
gs-1949	80	9	ergodic	ergodic	ADJ
gs-1949	80	10	chain	chain	NOUN
gs-1949	80	11	,	,	PUNCT
gs-1949	80	12	the	the	DET
gs-1949	80	13	sequence	sequence	NOUN
gs-1949	80	14	of	of	ADP
gs-1949	80	15	functions	function	NOUN
gs-1949	80	16	is	be	AUX
gs-1949	80	17	defined	define	VERB
gs-1949	80	18	georgian	georgian	ADJ
gs-1949	80	19	scientists/ქართველი	scientists/ქართველი	NOUN
gs-1949	80	20	მეცნიერები	მეცნიერები	NOUN
gs-1949	80	21	ტ.	ტ.	VERB
gs-1949	80	22	5	5	NUM
gs-1949	80	23	n	n	DET
gs-1949	80	24	2	2	NUM
gs-1949	80	25	,	,	PUNCT
gs-1949	80	26	2023	2023	NUM
gs-1949	80	27	23	23	NUM
gs-1949	80	28	on	on	ADP
gs-1949	80	29	a	a	DET
gs-1949	80	30	sequence	sequence	NOUN
gs-1949	80	31	of	of	ADP
gs-1949	80	32	vectors	vector	NOUN
gs-1949	80	33	with	with	ADP
gs-1949	80	34	a	a	DET
gs-1949	80	35	chain	chain	NOUN
gs-1949	80	36	m	m	NOUN
gs-1949	80	37	-dependence	-dependence	NOUN
gs-1949	80	38	.	.	PUNCT
gs-1949	81	1	a	a	DET
gs-1949	81	2	representation	representation	NOUN
gs-1949	81	3	in	in	ADP
gs-1949	81	4	matrix	matrix	NOUN
gs-1949	81	5	form	form	NOUN
gs-1949	81	6	of	of	ADP
gs-1949	81	7	the	the	DET
gs-1949	81	8	limit	limit	NOUN
gs-1949	81	9	covariance	covariance	NOUN
gs-1949	81	10	matrix	matrix	NOUN
gs-1949	81	11	of	of	ADP
gs-1949	81	12	the	the	DET
gs-1949	81	13	normalized	normalize	VERB
gs-1949	81	14	sum	sum	NOUN
gs-1949	81	15	of	of	ADP
gs-1949	81	16	the	the	DET
gs-1949	81	17	sequence	sequence	NOUN
gs-1949	81	18	of	of	ADP
gs-1949	81	19	these	these	DET
gs-1949	81	20	functions	function	NOUN
gs-1949	81	21	is	be	AUX
gs-1949	81	22	obtained	obtain	VERB
gs-1949	81	23	.	.	PUNCT
gs-1949	82	1	the	the	DET
gs-1949	82	2	fundamental	fundamental	ADJ
gs-1949	82	3	matrix	matrix	NOUN
gs-1949	82	4	and	and	CCONJ
gs-1949	82	5	the	the	DET
gs-1949	82	6	corresponding	corresponding	ADJ
gs-1949	82	7	limiting	limit	VERB
gs-1949	82	8	characteristics	characteristic	NOUN
gs-1949	82	9	of	of	ADP
gs-1949	82	10	the	the	DET
gs-1949	82	11	markov	markov	NOUN
gs-1949	82	12	chain	chain	NOUN
gs-1949	82	13	in	in	ADP
gs-1949	82	14	the	the	DET
gs-1949	82	15	case	case	NOUN
gs-1949	82	16	of	of	ADP
gs-1949	82	17	cyclic	cyclic	ADJ
gs-1949	82	18	subclasses	subclass	NOUN
gs-1949	82	19	are	be	AUX
gs-1949	82	20	computed	compute	VERB
gs-1949	82	21	using	use	VERB
gs-1949	82	22	the	the	DET
gs-1949	82	23	cesaro	cesaro	ADJ
gs-1949	82	24	summation	summation	NOUN
gs-1949	82	25	.	.	PUNCT
gs-1949	83	1	the	the	DET
gs-1949	83	2	levy	levy	NOUN
gs-1949	83	3	-	-	PUNCT
gs-1949	83	4	prokhorov	prokhorov	NOUN
gs-1949	83	5	metric	metric	ADJ
gs-1949	83	6			NOUN
gs-1949	83	7			PROPN
gs-1949	83	8	,	,	PUNCT
gs-1949	83	9	sup	sup	NOUN
gs-1949	83	10	(	(	PUNCT
gs-1949	83	11	)	)	PUNCT
gs-1949	83	12	(	(	PUNCT
gs-1949	83	13	)	)	PUNCT
gs-1949	83	14	kx	kx	INTJ
gs-1949	84	1	r	r	NOUN
gs-1949	84	2	f	f	PROPN
gs-1949	85	1	g	g	PROPN
gs-1949	85	2	f	f	PROPN
gs-1949	85	3	x	x	SYM
gs-1949	85	4	g	g	PROPN
gs-1949	85	5	x	x	PROPN
gs-1949	85	6			PROPN
gs-1949	85	7			PROPN
gs-1949	85	8			PROPN
gs-1949	85	9	is	be	AUX
gs-1949	85	10	often	often	ADV
gs-1949	85	11	used	use	VERB
gs-1949	85	12	when	when	SCONJ
gs-1949	85	13	considering	consider	VERB
gs-1949	85	14	the	the	DET
gs-1949	85	15	convergence	convergence	NOUN
gs-1949	85	16	of	of	ADP
gs-1949	85	17	distributions	distribution	NOUN
gs-1949	85	18	on	on	ADP
gs-1949	85	19	the	the	DET
gs-1949	85	20	space	space	NOUN
gs-1949	85	21	of	of	ADP
gs-1949	85	22	distribution	distribution	NOUN
gs-1949	85	23	functions	function	NOUN
gs-1949	85	24	.	.	PUNCT
gs-1949	86	1	therefore	therefore	ADV
gs-1949	86	2	,	,	PUNCT
gs-1949	86	3	the	the	DET
gs-1949	86	4	question	question	NOUN
gs-1949	86	5	of	of	ADP
gs-1949	86	6	determining	determine	VERB
gs-1949	86	7	the	the	DET
gs-1949	86	8	limiting	limit	VERB
gs-1949	86	9	probability	probability	NOUN
gs-1949	86	10	of	of	ADP
gs-1949	86	11	the	the	DET
gs-1949	86	12	distribution	distribution	NOUN
gs-1949	86	13	of	of	ADP
gs-1949	86	14	the	the	DET
gs-1949	86	15	sum	sum	NOUN
gs-1949	86	16	of	of	ADP
gs-1949	86	17	functions	function	NOUN
gs-1949	86	18	falling	fall	VERB
gs-1949	86	19	into	into	ADP
gs-1949	86	20	a	a	DET
gs-1949	86	21	strip	strip	NOUN
gs-1949	86	22	consisting	consist	VERB
gs-1949	86	23	of	of	ADP
gs-1949	86	24	two	two	NUM
gs-1949	86	25	normal	normal	ADJ
gs-1949	86	26	shifted	shift	VERB
gs-1949	86	27	distributions	distribution	NOUN
gs-1949	86	28	is	be	AUX
gs-1949	86	29	of	of	ADP
gs-1949	86	30	natural	natural	ADJ
gs-1949	86	31	interest	interest	NOUN
gs-1949	86	32	.	.	PUNCT
gs-1949	87	1	the	the	DET
gs-1949	87	2	article	article	NOUN
gs-1949	87	3	discusses	discuss	VERB
gs-1949	87	4	the	the	DET
gs-1949	87	5	normalized	normalized	ADJ
gs-1949	87	6	sum	sum	NOUN
gs-1949	87	7	of	of	ADP
gs-1949	87	8	a	a	DET
gs-1949	87	9	sequence	sequence	NOUN
gs-1949	87	10	of	of	ADP
gs-1949	87	11	conditionally	conditionally	ADV
gs-1949	87	12	m	m	NUM
gs-1949	87	13	-dependent	-dependent	ADJ
gs-1949	87	14	vectors	vector	NOUN
gs-1949	87	15	.	.	PUNCT
gs-1949	88	1	the	the	DET
gs-1949	88	2	limiting	limit	VERB
gs-1949	88	3	probability	probability	NOUN
gs-1949	88	4	of	of	ADP
gs-1949	88	5	the	the	DET
gs-1949	88	6	conditional	conditional	ADJ
gs-1949	88	7	distribution	distribution	NOUN
gs-1949	88	8	of	of	ADP
gs-1949	88	9	this	this	DET
gs-1949	88	10	sum	sum	NOUN
gs-1949	88	11	falling	fall	VERB
gs-1949	88	12	into	into	ADP
gs-1949	88	13	the	the	DET
gs-1949	88	14	band	band	NOUN
gs-1949	88	15	consisting	consist	VERB
gs-1949	88	16	of	of	ADP
gs-1949	88	17	two	two	NUM
gs-1949	88	18	shifted	shift	VERB
gs-1949	88	19	normal	normal	ADJ
gs-1949	88	20	distributions	distribution	NOUN
gs-1949	88	21	is	be	AUX
gs-1949	88	22	determined	determine	VERB
gs-1949	88	23	.	.	PUNCT
gs-1949	89	1	the	the	DET
gs-1949	89	2	covariance	covariance	NOUN
gs-1949	89	3	matrix	matrix	NOUN
gs-1949	89	4	of	of	ADP
gs-1949	89	5	these	these	DET
gs-1949	89	6	distributions	distribution	NOUN
gs-1949	89	7	is	be	AUX
gs-1949	89	8	expressed	express	VERB
gs-1949	89	9	by	by	ADP
gs-1949	89	10	the	the	DET
gs-1949	89	11	markov	markov	NOUN
gs-1949	89	12	chain	chain	NOUN
gs-1949	89	13	parameters	parameter	NOUN
gs-1949	89	14	.	.	PUNCT
gs-1949	90	1	a	a	DET
gs-1949	90	2	similar	similar	ADJ
gs-1949	90	3	limiting	limiting	NOUN
gs-1949	90	4	probability	probability	NOUN
gs-1949	90	5	is	be	AUX
gs-1949	90	6	set	set	VERB
gs-1949	90	7	for	for	ADP
gs-1949	90	8	the	the	DET
gs-1949	90	9	normalized	normalize	VERB
gs-1949	90	10	sum	sum	NOUN
gs-1949	90	11	of	of	ADP
gs-1949	90	12	a	a	DET
gs-1949	90	13	sequence	sequence	NOUN
gs-1949	90	14	of	of	ADP
gs-1949	90	15	vectors	vector	NOUN
gs-1949	90	16	with	with	ADP
gs-1949	90	17	a	a	DET
gs-1949	90	18	chain	chain	NOUN
gs-1949	90	19	m	m	NOUN
gs-1949	90	20	-dependence	-dependence	NOUN
gs-1949	90	21	.	.	PUNCT
gs-1949	91	1	keywords	keyword	NOUN
gs-1949	91	2	:	:	PUNCT
gs-1949	91	3	conditionally	conditionally	ADV
gs-1949	91	4	m	m	VERB
gs-1949	91	5	−independent	−independent	ADJ
gs-1949	91	6	sequence	sequence	NOUN
gs-1949	91	7	,	,	PUNCT
gs-1949	91	8	conditional	conditional	ADJ
gs-1949	91	9	distribution	distribution	NOUN
gs-1949	91	10	,	,	PUNCT
gs-1949	91	11	markov	markov	NOUN
gs-1949	91	12	chain	chain	NOUN
gs-1949	91	13	,	,	PUNCT
gs-1949	91	14	m	m	VERB
gs-1949	91	15	-dependent	-dependent	ADJ
gs-1949	91	16	sequence	sequence	NOUN
gs-1949	91	17	controlled	control	VERB
gs-1949	91	18	by	by	ADP
gs-1949	91	19	the	the	DET
gs-1949	91	20	markov	markov	NOUN
gs-1949	91	21	chain	chain	NOUN
gs-1949	91	22	.	.	PUNCT
gs-1949	92	1	2010	2010	NUM
gs-1949	92	2	mathematics	mathematic	NOUN
gs-1949	92	3	subject	subject	NOUN
gs-1949	92	4	classification	classification	NOUN
gs-1949	92	5	.	.	PUNCT
gs-1949	93	1	60f05	60f05	NUM
gs-1949	93	2	.	.	PUNCT
gs-1949	94	1	60j10	60j10	NOUN
gs-1949	94	2	.	.	PUNCT
gs-1949	95	1	60j20	60j20	NUM
gs-1949	95	2	.	.	PUNCT
gs-1949	96	1	introduction	introduction	NOUN
gs-1949	96	2	when	when	SCONJ
gs-1949	96	3	solving	solve	VERB
gs-1949	96	4	practical	practical	ADJ
gs-1949	96	5	problems	problem	NOUN
gs-1949	96	6	,	,	PUNCT
gs-1949	96	7	it	it	PRON
gs-1949	96	8	is	be	AUX
gs-1949	96	9	often	often	ADV
gs-1949	96	10	necessary	necessary	ADJ
gs-1949	96	11	to	to	PART
gs-1949	96	12	build	build	VERB
gs-1949	96	13	statistical	statistical	ADJ
gs-1949	96	14	estimates	estimate	NOUN
gs-1949	96	15	based	base	VERB
gs-1949	96	16	on	on	ADP
gs-1949	96	17	dependent	dependent	ADJ
gs-1949	96	18	observations	observation	NOUN
gs-1949	96	19	.	.	PUNCT
gs-1949	97	1	for	for	ADP
gs-1949	97	2	example	example	NOUN
gs-1949	97	3	,	,	PUNCT
gs-1949	97	4	time	time	NOUN
gs-1949	97	5	series	series	PROPN
gs-1949	97	6	used	use	VERB
gs-1949	97	7	in	in	ADP
gs-1949	97	8	psychological	psychological	ADJ
gs-1949	97	9	research	research	NOUN
gs-1949	97	10	or	or	CCONJ
gs-1949	97	11	in	in	ADP
gs-1949	97	12	economic	economic	ADJ
gs-1949	97	13	parameter	parameter	NOUN
gs-1949	97	14	estimations	estimation	NOUN
gs-1949	97	15	,	,	PUNCT
gs-1949	97	16	in	in	ADP
gs-1949	97	17	most	most	ADJ
gs-1949	97	18	cases	case	NOUN
gs-1949	97	19	,	,	PUNCT
gs-1949	97	20	consist	consist	VERB
gs-1949	97	21	of	of	ADP
gs-1949	97	22	dependent	dependent	ADJ
gs-1949	97	23	data	datum	NOUN
gs-1949	97	24	.	.	PUNCT
gs-1949	98	1	determining	determine	VERB
gs-1949	98	2	the	the	DET
gs-1949	98	3	accuracy	accuracy	NOUN
gs-1949	98	4	and	and	CCONJ
gs-1949	98	5	unbiasedness	unbiasedness	NOUN
gs-1949	98	6	of	of	ADP
gs-1949	98	7	the	the	DET
gs-1949	98	8	constructed	construct	VERB
gs-1949	98	9	estimates	estimate	NOUN
gs-1949	98	10	is	be	AUX
gs-1949	98	11	related	relate	VERB
gs-1949	98	12	to	to	ADP
gs-1949	98	13	the	the	DET
gs-1949	98	14	knowledge	knowledge	NOUN
gs-1949	98	15	of	of	ADP
gs-1949	98	16	the	the	DET
gs-1949	98	17	asymptotic	asymptotic	ADJ
gs-1949	98	18	distribution	distribution	NOUN
gs-1949	98	19	of	of	ADP
gs-1949	98	20	the	the	DET
gs-1949	98	21	sums	sum	NOUN
gs-1949	98	22	of	of	ADP
gs-1949	98	23	dependent	dependent	ADJ
gs-1949	98	24	random	random	ADJ
gs-1949	98	25	variables	variable	NOUN
gs-1949	98	26	.	.	PUNCT
gs-1949	99	1	there	there	PRON
gs-1949	99	2	is	be	VERB
gs-1949	99	3	a	a	DET
gs-1949	99	4	spread	spread	NOUN
gs-1949	99	5	of	of	ADP
gs-1949	99	6	methods	method	NOUN
gs-1949	99	7	for	for	ADP
gs-1949	99	8	studying	study	VERB
gs-1949	99	9	the	the	DET
gs-1949	99	10	distribution	distribution	NOUN
gs-1949	99	11	of	of	ADP
gs-1949	99	12	sums	sum	NOUN
gs-1949	99	13	of	of	ADP
gs-1949	99	14	independent	independent	ADJ
gs-1949	99	15	random	random	ADJ
gs-1949	99	16	variables	variable	NOUN
gs-1949	99	17	(	(	PUNCT
gs-1949	99	18	[	[	X
gs-1949	99	19	1	1	NUM
gs-1949	99	20	]	]	PUNCT
gs-1949	99	21	)	)	PUNCT
gs-1949	99	22	over	over	ADP
gs-1949	99	23	dependent	dependent	ADJ
gs-1949	99	24	random	random	ADJ
gs-1949	99	25	variables	variable	NOUN
gs-1949	99	26	.	.	PUNCT
gs-1949	100	1	the	the	DET
gs-1949	100	2	markov	markov	NOUN
gs-1949	100	3	dependence	dependence	NOUN
gs-1949	100	4	,	,	PUNCT
gs-1949	100	5	which	which	PRON
gs-1949	100	6	is	be	AUX
gs-1949	100	7	one	one	NUM
gs-1949	100	8	of	of	ADP
gs-1949	100	9	the	the	DET
gs-1949	100	10	types	type	NOUN
gs-1949	100	11	of	of	ADP
gs-1949	100	12	weak	weak	ADJ
gs-1949	100	13	dependence	dependence	NOUN
gs-1949	100	14	,	,	PUNCT
gs-1949	100	15	naturally	naturally	ADV
gs-1949	100	16	enters	enter	VERB
gs-1949	100	17	this	this	DET
gs-1949	100	18	path	path	NOUN
gs-1949	100	19	.	.	PUNCT
gs-1949	101	1	limit	limit	VERB
gs-1949	101	2	theorems	theorem	NOUN
gs-1949	101	3	for	for	ADP
gs-1949	101	4	weakly	weakly	ADJ
gs-1949	101	5	dependent	dependent	ADJ
gs-1949	101	6	sequences	sequence	NOUN
gs-1949	101	7	are	be	AUX
gs-1949	101	8	expressed	express	VERB
gs-1949	101	9	in	in	ADP
gs-1949	101	10	terms	term	NOUN
gs-1949	101	11	of	of	ADP
gs-1949	101	12	sigma	sigma	PROPN
gs-1949	101	13	-	-	PUNCT
gs-1949	101	14	algebras	algebras	PROPN
gs-1949	101	15	generated	generate	VERB
gs-1949	101	16	by	by	ADP
gs-1949	101	17	asymptotically	asymptotically	ADV
gs-1949	101	18	separable	separable	ADJ
gs-1949	101	19	segments	segment	NOUN
gs-1949	101	20	of	of	ADP
gs-1949	101	21	the	the	DET
gs-1949	101	22	sequence	sequence	NOUN
gs-1949	101	23	.	.	PUNCT
gs-1949	102	1	an	an	DET
gs-1949	102	2	essential	essential	ADJ
gs-1949	102	3	role	role	NOUN
gs-1949	102	4	in	in	ADP
gs-1949	102	5	their	their	PRON
gs-1949	102	6	approval	approval	NOUN
gs-1949	102	7	is	be	AUX
gs-1949	102	8	played	play	VERB
gs-1949	102	9	by	by	ADP
gs-1949	102	10	bernstein	bernstein	PROPN
gs-1949	102	11	's	's	PART
gs-1949	102	12	"	"	PUNCT
gs-1949	102	13	sectioning	sectioning	NOUN
gs-1949	102	14	"	"	PUNCT
gs-1949	102	15	method	method	NOUN
gs-1949	102	16	,	,	PUNCT
gs-1949	102	17	which	which	PRON
gs-1949	102	18	uses	use	VERB
gs-1949	102	19	the	the	DET
gs-1949	102	20	effect	effect	NOUN
gs-1949	102	21	of	of	ADP
gs-1949	102	22	dependence	dependence	NOUN
gs-1949	102	23	weakening	weaken	VERB
gs-1949	102	24	with	with	ADP
gs-1949	102	25	increasing	increase	VERB
gs-1949	102	26	distance	distance	NOUN
gs-1949	102	27	between	between	ADP
gs-1949	102	28	segments	segment	NOUN
gs-1949	102	29	.	.	PUNCT
gs-1949	103	1	many	many	ADJ
gs-1949	103	2	authors	author	NOUN
gs-1949	103	3	study	study	VERB
gs-1949	103	4	sums	sum	NOUN
gs-1949	103	5	of	of	ADP
gs-1949	103	6	random	random	ADJ
gs-1949	103	7	variables	variable	NOUN
gs-1949	103	8	whose	whose	DET
gs-1949	103	9	distribution	distribution	NOUN
gs-1949	103	10	is	be	AUX
gs-1949	103	11	determined	determine	VERB
gs-1949	103	12	by	by	ADP
gs-1949	103	13	some	some	DET
gs-1949	103	14	"	"	PUNCT
gs-1949	103	15	control	control	NOUN
gs-1949	103	16	"	"	PUNCT
gs-1949	103	17	sequence	sequence	NOUN
gs-1949	103	18	of	of	ADP
gs-1949	103	19	random	random	ADJ
gs-1949	103	20	elements	element	NOUN
gs-1949	103	21	.	.	PUNCT
gs-1949	104	1	conditionally	conditionally	ADV
gs-1949	104	2	independent	independent	ADJ
gs-1949	104	3	sequences	sequence	NOUN
gs-1949	104	4	(	(	PUNCT
gs-1949	104	5	[	[	X
gs-1949	104	6	2],[3	2],[3	NUM
gs-1949	104	7	]	]	PUNCT
gs-1949	104	8	)	)	PUNCT
gs-1949	104	9	and	and	CCONJ
gs-1949	104	10	sequences	sequence	NOUN
gs-1949	104	11	with	with	ADP
gs-1949	104	12	chain	chain	NOUN
gs-1949	104	13	dependence	dependence	NOUN
gs-1949	104	14	(	(	PUNCT
gs-1949	104	15	[	[	X
gs-1949	104	16	4],[5	4],[5	NUM
gs-1949	104	17	]	]	PUNCT
gs-1949	104	18	)	)	PUNCT
gs-1949	104	19	are	be	AUX
gs-1949	104	20	considered	consider	VERB
gs-1949	104	21	.	.	PUNCT
gs-1949	105	1	in	in	ADP
gs-1949	105	2	this	this	DET
gs-1949	105	3	paper	paper	NOUN
gs-1949	105	4	,	,	PUNCT
gs-1949	105	5	we	we	PRON
gs-1949	105	6	consider	consider	VERB
gs-1949	105	7	a	a	DET
gs-1949	105	8	conditionally	conditionally	ADV
gs-1949	105	9	m	m	NOUN
gs-1949	105	10	-independent	-independent	ADJ
gs-1949	105	11	sequence	sequence	NOUN
gs-1949	105	12	of	of	ADP
gs-1949	105	13	vectors	vector	NOUN
gs-1949	105	14	and	and	CCONJ
gs-1949	105	15	a	a	DET
gs-1949	105	16	sequence	sequence	NOUN
gs-1949	105	17	of	of	ADP
gs-1949	105	18	vectors	vector	NOUN
gs-1949	105	19	with	with	ADP
gs-1949	105	20	a	a	DET
gs-1949	105	21	chain	chain	NOUN
gs-1949	105	22	m	m	NOUN
gs-1949	105	23	-dependence	-dependence	NOUN
gs-1949	105	24	.	.	PUNCT
gs-1949	106	1	let	let	VERB
gs-1949	106	2	's	us	PRON
gs-1949	106	3	calculate	calculate	VERB
gs-1949	106	4	the	the	DET
gs-1949	106	5	limiting	limit	VERB
gs-1949	106	6	probability	probability	NOUN
gs-1949	106	7	of	of	ADP
gs-1949	106	8	their	their	PRON
gs-1949	106	9	conditional	conditional	ADJ
gs-1949	106	10	distribution	distribution	NOUN
gs-1949	106	11	falling	fall	VERB
gs-1949	106	12	into	into	ADP
gs-1949	106	13	the	the	DET
gs-1949	106	14	band	band	NOUN
gs-1949	106	15	created	create	VERB
gs-1949	106	16	from	from	ADP
gs-1949	106	17	two	two	NUM
gs-1949	106	18	shifted	shift	VERB
gs-1949	106	19	normal	normal	ADJ
gs-1949	106	20	distributions	distribution	NOUN
gs-1949	106	21	.	.	PUNCT
gs-1949	107	1	georgian	georgian	ADJ
gs-1949	107	2	scientists/ქართველი	scientists/ქართველი	PROPN
gs-1949	107	3	მეცნიერები	მეცნიერები	NOUN
gs-1949	107	4	ტ.	ტ.	VERB
gs-1949	107	5	5	5	NUM
gs-1949	107	6	n	n	PRON
gs-1949	107	7	2	2	NUM
gs-1949	107	8	,	,	PUNCT
gs-1949	107	9	2023	2023	NUM
gs-1949	107	10	24	24	NUM
gs-1949	107	11	on	on	ADP
gs-1949	107	12	the	the	DET
gs-1949	107	13	probability	probability	NOUN
gs-1949	107	14	space	space	NOUN
gs-1949	107	15	(	(	PUNCT
gs-1949	107	16	,	,	PUNCT
gs-1949	107	17	,	,	PUNCT
gs-1949	107	18	)	)	PUNCT
gs-1949	107	19	f	f	PROPN
gs-1949	107	20	p	p	NOUN
gs-1949	107	21	we	we	PRON
gs-1949	107	22	consider	consider	VERB
gs-1949	107	23	a	a	DET
gs-1949	107	24	two	two	NUM
gs-1949	107	25	-	-	PUNCT
gs-1949	107	26	component	component	NOUN
gs-1949	107	27	stationary	stationary	NOUN
gs-1949	107	28	(	(	PUNCT
gs-1949	107	29	in	in	ADP
gs-1949	107	30	the	the	DET
gs-1949	107	31	narrow	narrow	ADJ
gs-1949	107	32	sense	sense	NOUN
gs-1949	107	33	)	)	PUNCT
gs-1949	107	34	sequence	sequence	NOUN
gs-1949	107	35			PROPN
gs-1949	107	36			PROPN
gs-1949	107	37	1	1	NUM
gs-1949	107	38	,	,	PUNCT
gs-1949	107	39	i	i	PRON
gs-1949	107	40	i	i	PRON
gs-1949	107	41	i	i	PRON
gs-1949	107	42	y	y	VERB
gs-1949	107	43			NUM
gs-1949	107	44	(	(	PUNCT
gs-1949	107	45	1	1	NUM
gs-1949	107	46	)	)	PUNCT
gs-1949	107	47			NOUN
gs-1949	107	48			PROPN
gs-1949	107	49	1i	1i	NOUN
gs-1949	107	50	i	i	PRON
gs-1949	107	51			VERB
gs-1949	107	52			NUM
gs-1949	107	53	,	,	PUNCT
gs-1949	107	54			NOUN
gs-1949	107	55	:i	:i	ADJ
gs-1949	107	56			PROPN
gs-1949	107	57			NOUN
gs-1949	107	58	is	be	AUX
gs-1949	107	59	the	the	DET
gs-1949	107	60	control	control	NOUN
gs-1949	107	61	sequence	sequence	NOUN
gs-1949	107	62	.	.	PUNCT
gs-1949	108	1	assume	assume	VERB
gs-1949	108	2	that	that	SCONJ
gs-1949	108	3	the	the	DET
gs-1949	108	4	set	set	NOUN
gs-1949	108	5			NOUN
gs-1949	108	6	consists	consist	VERB
gs-1949	108	7	of	of	ADP
gs-1949	108	8	a	a	DET
gs-1949	108	9	finite	finite	ADJ
gs-1949	108	10	number	number	NOUN
gs-1949	108	11	of	of	ADP
gs-1949	108	12	finite	finite	ADJ
gs-1949	108	13	elements	element	NOUN
gs-1949	108	14	.	.	PUNCT
gs-1949	109	1			PRON
gs-1949	109	2			PROPN
gs-1949	109	3	1i	1i	NOUN
gs-1949	110	1	i	i	NOUN
gs-1949	110	2	y	y	PROPN
gs-1949	110	3			NUM
gs-1949	110	4	,	,	PUNCT
gs-1949	110	5			PROPN
gs-1949	110	6			PROPN
gs-1949	110	7	:	:	PUNCT
gs-1949	111	1	k	k	PROPN
gs-1949	111	2	iy	iy	PROPN
gs-1949	111	3	r	r	PROPN
gs-1949	111	4	is	be	AUX
gs-1949	111	5	a	a	DET
gs-1949	111	6	sequence	sequence	NOUN
gs-1949	111	7	of	of	ADP
gs-1949	111	8	conditionally	conditionally	ADV
gs-1949	111	9	m	m	VERB
gs-1949	111	10	−independent	−independent	ADJ
gs-1949	111	11	vectors	vector	NOUN
gs-1949	111	12	.	.	PUNCT
gs-1949	112	1	definition	definition	NOUN
gs-1949	112	2	.	.	PUNCT
gs-1949	113	1	(	(	PUNCT
gs-1949	113	2	see	see	VERB
gs-1949	113	3	.	.	PUNCT
gs-1949	114	1	[	[	X
gs-1949	114	2	6	6	NUM
gs-1949	114	3	]	]	PUNCT
gs-1949	114	4	)	)	PUNCT
gs-1949	114	5	the	the	DET
gs-1949	114	6	sequence	sequence	NOUN
gs-1949	114	7			PROPN
gs-1949	114	8			PROPN
gs-1949	114	9	1i	1i	NOUN
gs-1949	114	10	i	i	NOUN
gs-1949	114	11	y	y	PROPN
gs-1949	114	12			NUM
gs-1949	114	13	from	from	ADP
gs-1949	114	14	(	(	PUNCT
gs-1949	114	15	1	1	NUM
gs-1949	114	16	)	)	PUNCT
gs-1949	114	17	is	be	AUX
gs-1949	114	18	called	call	VERB
gs-1949	114	19	a	a	DET
gs-1949	114	20	conditionally	conditionally	ADV
gs-1949	114	21	m	m	NOUN
gs-1949	114	22	−independent	−independent	ADJ
gs-1949	114	23	sequence	sequence	NOUN
gs-1949	114	24	if	if	SCONJ
gs-1949	114	25	the	the	DET
gs-1949	114	26	vectors	vector	NOUN
gs-1949	114	27	1	1	NUM
gs-1949	114	28	2	2	NUM
gs-1949	114	29	,	,	PUNCT
gs-1949	114	30	,	,	PUNCT
gs-1949	114	31	,	,	PUNCT
gs-1949	114	32	ny	ny	PROPN
gs-1949	114	33	y	y	PROPN
gs-1949	114	34	y	y	PROPN
gs-1949	114	35	on	on	ADP
gs-1949	114	36	a	a	DET
gs-1949	114	37	fixed	fix	VERB
gs-1949	114	38	trajectory	trajectory	NOUN
gs-1949	114	39			NOUN
gs-1949	114	40	1	1	VERB
gs-1949	114	41	1	1	NUM
gs-1949	114	42	2	2	NUM
gs-1949	114	43	,	,	PUNCT
gs-1949	114	44	,	,	PUNCT
gs-1949	114	45	..	..	PUNCT
gs-1949	114	46	,	,	PUNCT
gs-1949	114	47	n	n	PRON
gs-1949	114	48	n	n	PRON
gs-1949	114	49			NOUN
gs-1949	114	50			NOUN
gs-1949	114	51			PUNCT
gs-1949	114	52	for	for	ADP
gs-1949	114	53	an	an	DET
gs-1949	114	54	arbitrary	arbitrary	ADJ
gs-1949	114	55	natural	natural	ADJ
gs-1949	114	56	number	number	NOUN
gs-1949	114	57	n	n	PRON
gs-1949	114	58	become	become	VERB
gs-1949	114	59	independent	independent	ADJ
gs-1949	114	60	when	when	SCONJ
gs-1949	114	61	thier	thier	PRON
gs-1949	114	62	index	index	NOUN
gs-1949	114	63	difference	difference	NOUN
gs-1949	114	64	exceeds	exceed	VERB
gs-1949	114	65	m	m	VERB
gs-1949	114	66	.	.	PUNCT
gs-1949	115	1	in	in	ADP
gs-1949	115	2	this	this	DET
gs-1949	115	3	case	case	NOUN
gs-1949	115	4	the	the	DET
gs-1949	115	5	distribution	distribution	NOUN
gs-1949	115	6	of	of	ADP
gs-1949	115	7	iy	iy	PROPN
gs-1949	115	8	is	be	AUX
gs-1949	115	9	depends	depend	VERB
gs-1949	115	10	only	only	ADV
gs-1949	115	11	on	on	ADP
gs-1949	115	12	i	i	PROPN
gs-1949	115	13	.	.	PUNCT
gs-1949	116	1	for	for	ADP
gs-1949	116	2	arbitrary	arbitrary	ADJ
gs-1949	116	3	natural	natural	ADJ
gs-1949	116	4	numbers	number	NOUN
gs-1949	116	5	i	i	PRON
gs-1949	116	6	,	,	PUNCT
gs-1949	116	7	l	l	NOUN
gs-1949	116	8	,	,	PUNCT
gs-1949	116	9	n	n	CCONJ
gs-1949	116	10	,	,	PUNCT
gs-1949	116	11	1	1	NUM
gs-1949	116	12	2	2	NUM
gs-1949	116	13	,	,	PUNCT
gs-1949	116	14	,	,	PUNCT
gs-1949	116	15	,	,	PUNCT
gs-1949	116	16	lj	lj	PROPN
gs-1949	116	17	j	j	PROPN
gs-1949	116	18	j	j	PROPN
gs-1949	116	19	,	,	PUNCT
gs-1949	116	20	(	(	PUNCT
gs-1949	116	21	2	2	NUM
gs-1949	116	22	l	l	NOUN
gs-1949	116	23	n	n	X
gs-1949	116	24			NOUN
gs-1949	116	25	;	;	PUNCT
gs-1949	116	26	i	i	PRON
gs-1949	116	27	n	n	X
gs-1949	116	28	;	;	PUNCT
gs-1949	116	29	1	1	NUM
gs-1949	116	30	21	21	NUM
gs-1949	116	31	...	...	PUNCT
gs-1949	117	1	lj	lj	PROPN
gs-1949	117	2	j	j	PROPN
gs-1949	117	3	j	j	PROPN
gs-1949	117	4	n	n	PROPN
gs-1949	117	5			PROPN
gs-1949	117	6			PROPN
gs-1949	117	7			PROPN
gs-1949	117	8			NOUN
gs-1949	117	9	)	)	PUNCT
gs-1949	118	1	the	the	DET
gs-1949	118	2	equations	equation	NOUN
gs-1949	118	3	are	be	AUX
gs-1949	118	4	fulfilled	fulfil	VERB
gs-1949	118	5	:	:	PUNCT
gs-1949	118	6			NOUN
gs-1949	118	7			SYM
gs-1949	118	8	1	1	NUM
gs-1949	118	9	1	1	NUM
gs-1949	118	10	1	1	NUM
gs-1949	118	11	2	2	NUM
gs-1949	118	12	22	22	NUM
gs-1949	118	13	,	,	PUNCT
gs-1949	118	14	,	,	PUNCT
gs-1949	118	15	,	,	PUNCT
gs-1949	118	16	...	...	PUNCT
gs-1949	118	17	,	,	PUNCT
gs-1949	119	1	j	j	PROPN
gs-1949	119	2	j	j	PROPN
gs-1949	119	3	j	j	PROPN
gs-1949	120	1	j	j	PROPN
gs-1949	120	2	j	j	PROPN
gs-1949	120	3	jj	jj	PROPN
gs-1949	120	4	j	j	PROPN
gs-1949	120	5	j	j	PROPN
gs-1949	120	6	n	n	CCONJ
gs-1949	120	7	l	l	NOUN
gs-1949	120	8	ll	ll	AUX
gs-1949	120	9	p	p	PROPN
gs-1949	120	10	qy	qy	PROPN
gs-1949	120	11	y	y	PROPN
gs-1949	120	12	yy	yy	PROPN
gs-1949	120	13	y	y	PROPN
gs-1949	120	14	y	y	PROPN
gs-1949	121	1	j	j	PROPN
gs-1949	122	1	j	j	PROPN
gs-1949	122	2	m	m	VERB
gs-1949	122	3			NOUN
gs-1949	122	4			NOUN
gs-1949	122	5			NOUN
gs-1949	122	6			PROPN
gs-1949	122	7			PROPN
gs-1949	122	8			PROPN
gs-1949	122	9			PROPN
gs-1949	122	10			VERB
gs-1949	122	11	tu	tu	PROPN
gs-1949	122	12	,	,	PUNCT
gs-1949	122	13			PROPN
gs-1949	122	14			PROPN
gs-1949	122	15	,	,	PUNCT
gs-1949	122	16	1,2,	1,2,	NUM
gs-1949	122	17	...	...	PUNCT
gs-1949	122	18	,p	,p	PUNCT
gs-1949	122	19	q	q	X
gs-1949	123	1	l	l	ADJ
gs-1949	123	2			NOUN
gs-1949	123	3	1	1	NUM
gs-1949	123	4	1	1	NUM
gs-1949	123	5	2	2	NUM
gs-1949	123	6	,	,	PUNCT
gs-1949	123	7	1	1	NUM
gs-1949	123	8	...	...	PUNCT
gs-1949	123	9	,	,	PUNCT
gs-1949	123	10	1	1	X
gs-1949	123	11	,	,	PUNCT
gs-1949	123	12	i	i	PRON
gs-1949	123	13	ii	ii	VERB
gs-1949	123	14	n	n	ADV
gs-1949	123	15	lyy	lyy	VERB
gs-1949	123	16	j	j	PROPN
gs-1949	124	1	j	j	PROPN
gs-1949	124	2	j	j	PROPN
gs-1949	124	3	n	n	CCONJ
gs-1949	124	4	i	i	PROPN
gs-1949	124	5	n	n	CCONJ
gs-1949	124	6			NOUN
gs-1949	124	7			PROPN
gs-1949	124	8			PROPN
gs-1949	124	9			PROPN
gs-1949	124	10			PROPN
gs-1949	124	11			PROPN
gs-1949	125	1			PROPN
gs-1949	126	1			INTJ
gs-1949	126	2	,	,	PUNCT
gs-1949	126	3	where	where	SCONJ
gs-1949	126	4	x	x	PRON
gs-1949	126	5	is	be	AUX
gs-1949	126	6	the	the	DET
gs-1949	126	7	distribution	distribution	NOUN
gs-1949	126	8	of	of	ADP
gs-1949	126	9	x	x	X
gs-1949	126	10	.	.	PUNCT
gs-1949	127	1	remark	remark	PROPN
gs-1949	127	2	:	:	PUNCT
gs-1949	127	3	if	if	SCONJ
gs-1949	127	4			PROPN
gs-1949	127	5			PROPN
gs-1949	127	6	1i	1i	NOUN
gs-1949	127	7	i	i	PRON
gs-1949	127	8			VERB
gs-1949	127	9			NUM
gs-1949	127	10	is	be	AUX
gs-1949	127	11	a	a	DET
gs-1949	127	12	markov	markov	NOUN
gs-1949	127	13	chain	chain	NOUN
gs-1949	127	14	with	with	ADP
gs-1949	127	15	discrete	discrete	ADJ
gs-1949	127	16	time	time	NOUN
gs-1949	127	17	,	,	PUNCT
gs-1949	127	18	then	then	ADV
gs-1949	127	19	the	the	DET
gs-1949	127	20	sequence	sequence	NOUN
gs-1949	127	21			PROPN
gs-1949	127	22			PROPN
gs-1949	127	23	1i	1i	NOUN
gs-1949	127	24	i	i	PRON
gs-1949	127	25	y	y	PROPN
gs-1949	127	26			PROPN
gs-1949	127	27	is	be	AUX
gs-1949	127	28	called	call	VERB
gs-1949	127	29	a	a	DET
gs-1949	127	30	conditionally	conditionally	ADV
gs-1949	127	31	m	m	NOUN
gs-1949	127	32	-dependent	-dependent	ADJ
gs-1949	127	33	sequence	sequence	NOUN
gs-1949	127	34	controlled	control	VERB
gs-1949	127	35	by	by	ADP
gs-1949	127	36	the	the	DET
gs-1949	127	37	markov	markov	NOUN
gs-1949	127	38	chain	chain	NOUN
gs-1949	127	39	(	(	PUNCT
gs-1949	127	40	sequence	sequence	NOUN
gs-1949	127	41	with	with	ADP
gs-1949	127	42	chain	chain	NOUN
gs-1949	127	43	m	m	VERB
gs-1949	127	44	-dependence	-dependence	NOUN
gs-1949	127	45	)	)	PUNCT
gs-1949	127	46	.	.	PUNCT
gs-1949	128	1	let	let	VERB
gs-1949	128	2	us	we	PRON
gs-1949	128	3	give	give	VERB
gs-1949	128	4	auxiliary	auxiliary	ADJ
gs-1949	128	5	lemmas	lemmas	PROPN
gs-1949	128	6	.	.	PUNCT
gs-1949	129	1	let	let	VERB
gs-1949	129	2	's	us	PRON
gs-1949	129	3	introduce	introduce	VERB
gs-1949	129	4	notations	notation	NOUN
gs-1949	129	5	:	:	PUNCT
gs-1949	129	6			NOUN
gs-1949	130	1			SYM
gs-1949	130	2	1	1	NUM
gs-1949	130	3	1	1	NUM
gs-1949	130	4	(	(	PUNCT
gs-1949	130	5	)	)	PUNCT
gs-1949	130	6	,	,	PUNCT
gs-1949	130	7	(	(	PUNCT
gs-1949	130	8	)	)	PUNCT
gs-1949	130	9	j	j	PROPN
gs-1949	131	1	j	j	PROPN
gs-1949	131	2	je	je	PROPN
gs-1949	131	3	y	y	PROPN
gs-1949	131	4	e	e	PROPN
gs-1949	131	5	ey	ey	PROPN
gs-1949	131	6			NOUN
gs-1949	131	7			VERB
gs-1949	131	8			NOUN
gs-1949	131	9			NOUN
gs-1949	131	10			PUNCT
gs-1949	131	11			NUM
gs-1949	131	12			NUM
gs-1949	131	13			NOUN
gs-1949	132	1			SYM
gs-1949	132	2			NOUN
gs-1949	132	3			SYM
gs-1949	132	4			NOUN
gs-1949	132	5			NOUN
gs-1949	132	6	1	1	PROPN
gs-1949	132	7	,	,	PUNCT
gs-1949	132	8	,	,	PUNCT
gs-1949	132	9	1	1	NUM
gs-1949	132	10	,	,	PUNCT
gs-1949	132	11	t	t	PROPN
gs-1949	132	12	j	j	PROPN
gs-1949	133	1	r	r	NOUN
gs-1949	133	2	j	j	PROPN
gs-1949	133	3	j	j	PROPN
gs-1949	133	4	r	r	NOUN
gs-1949	133	5	r	r	NOUN
gs-1949	133	6	nr	nr	PROPN
gs-1949	133	7	e	e	PROPN
gs-1949	133	8	y	y	PROPN
gs-1949	133	9	y	y	PROPN
gs-1949	133	10	j	j	PROPN
gs-1949	133	11	r	r	NOUN
gs-1949	133	12	n	n	PRON
gs-1949	133	13			NOUN
gs-1949	133	14			NOUN
gs-1949	133	15			NOUN
gs-1949	133	16			NOUN
gs-1949	133	17			NOUN
gs-1949	133	18			X
gs-1949	133	19			VERB
gs-1949	133	20			PROPN
gs-1949	133	21			PROPN
gs-1949	133	22			NOUN
gs-1949	133	23			PROPN
gs-1949	133	24			NOUN
gs-1949	133	25			PROPN
gs-1949	133	26			PROPN
gs-1949	133	27			PROPN
gs-1949	133	28			PUNCT
gs-1949	133	29			SYM
gs-1949	133	30			PROPN
gs-1949	133	31	(	(	PUNCT
gs-1949	133	32	)	)	PUNCT
gs-1949	133	33	(	(	PUNCT
gs-1949	133	34	)	)	PUNCT
gs-1949	133	35	0	0	NUM
gs-1949	133	36	1	1	NUM
gs-1949	133	37	1	1	NUM
gs-1949	133	38	0	0	NUM
gs-1949	133	39	1	1	NUM
gs-1949	133	40	1	1	NUM
gs-1949	133	41	,	,	PUNCT
gs-1949	133	42	,	,	PUNCT
gs-1949	133	43	,	,	PUNCT
gs-1949	133	44	,	,	PUNCT
gs-1949	133	45	0,	0,	NUM
gs-1949	133	46	...	...	PUNCT
gs-1949	133	47	,l	,l	X
gs-1949	134	1	l	l	NOUN
gs-1949	134	2	l	l	NOUN
gs-1949	134	3	lr	lr	X
gs-1949	134	4	er	er	INTJ
gs-1949	134	5	r	r	NOUN
gs-1949	134	6	er	er	INTJ
gs-1949	134	7	l	l	NOUN
gs-1949	134	8	m	m	DET
gs-1949	134	9			NOUN
gs-1949	134	10			PUNCT
gs-1949	134	11			NOUN
gs-1949	134	12			ADJ
gs-1949	134	13			PROPN
gs-1949	134	14			NUM
gs-1949	134	15			ADJ
gs-1949	134	16			NOUN
gs-1949	134	17			PROPN
gs-1949	134	18	(	(	PUNCT
gs-1949	134	19	)	)	PUNCT
gs-1949	134	20	(	(	PUNCT
gs-1949	134	21	0	0	NUM
gs-1949	134	22	)	)	PUNCT
gs-1949	134	23	(	(	PUNCT
gs-1949	134	24	)	)	PUNCT
gs-1949	134	25	(	(	PUNCT
gs-1949	134	26	)	)	PUNCT
gs-1949	134	27	0	0	NUM
gs-1949	134	28	0	0	NUM
gs-1949	134	29	0	0	NUM
gs-1949	134	30	0	0	NUM
gs-1949	134	31	1	1	NUM
gs-1949	134	32	,	,	PUNCT
gs-1949	134	33	m	m	VERB
gs-1949	134	34	m	m	VERB
gs-1949	134	35	t	t	NOUN
gs-1949	134	36	l	l	NOUN
gs-1949	134	37	l	l	X
gs-1949	134	38	l	l	X
gs-1949	134	39	m	m	VERB
gs-1949	134	40	l	l	NOUN
gs-1949	134	41	m	m	VERB
gs-1949	134	42	l	l	NOUN
gs-1949	134	43	r	r	NOUN
gs-1949	134	44	r	r	NOUN
gs-1949	134	45	r	r	NOUN
gs-1949	134	46	r	r	NOUN
gs-1949	134	47	r	r	NOUN
gs-1949	134	48			NOUN
gs-1949	134	49			PROPN
gs-1949	134	50			PROPN
gs-1949	134	51			NOUN
gs-1949	134	52			PROPN
gs-1949	134	53			PROPN
gs-1949	134	54			PUNCT
gs-1949	134	55			VERB
gs-1949	134	56			X
gs-1949	134	57			X
gs-1949	134	58			X
gs-1949	134	59	(	(	PUNCT
gs-1949	134	60	1	1	X
gs-1949	134	61	)	)	PUNCT
gs-1949	134	62	consider	consider	VERB
gs-1949	134	63	sum	sum	NOUN
gs-1949	134	64			ADJ
gs-1949	134	65			NOUN
gs-1949	134	66	1	1	NUM
gs-1949	134	67	1	1	NUM
gs-1949	134	68	n	n	NUM
gs-1949	134	69	n	n	NOUN
gs-1949	135	1	i	i	PRON
gs-1949	136	1	i	i	PRON
gs-1949	136	2	s	s	VERB
gs-1949	136	3	y	y	NOUN
gs-1949	136	4	n	n	PRON
gs-1949	136	5			NOUN
gs-1949	137	1			NUM
gs-1949	137	2			NUM
gs-1949	138	1			PROPN
gs-1949	138	2	.	.	PUNCT
gs-1949	139	1	let	let	VERB
gs-1949	139	2	us	we	PRON
gs-1949	139	3	use	use	VERB
gs-1949	139	4	the	the	DET
gs-1949	139	5	same	same	ADJ
gs-1949	139	6	method	method	NOUN
gs-1949	139	7	that	that	PRON
gs-1949	139	8	was	be	AUX
gs-1949	139	9	used	use	VERB
gs-1949	139	10	to	to	PART
gs-1949	139	11	determine	determine	VERB
gs-1949	139	12	the	the	DET
gs-1949	139	13	limit	limit	NOUN
gs-1949	139	14	distribution	distribution	NOUN
gs-1949	139	15	of	of	ADP
gs-1949	139	16	the	the	DET
gs-1949	139	17	sum	sum	NOUN
gs-1949	139	18	ns	n	VERB
gs-1949	139	19	by	by	ADP
gs-1949	139	20	fixing	fix	VERB
gs-1949	139	21	the	the	DET
gs-1949	139	22	trajectories	trajectory	NOUN
gs-1949	139	23	1n	1n	NUM
gs-1949	139	24	in	in	ADP
gs-1949	139	25	[	[	X
gs-1949	139	26	5	5	NUM
gs-1949	139	27	]	]	PUNCT
gs-1949	139	28	.	.	PUNCT
gs-1949	140	1	let	let	VERB
gs-1949	140	2	us	we	PRON
gs-1949	140	3	decompose	decompose	VERB
gs-1949	140	4	the	the	DET
gs-1949	140	5	sum	sum	NOUN
gs-1949	140	6	ns	ns	INTJ
gs-1949	140	7	on	on	ADP
gs-1949	140	8	a	a	DET
gs-1949	140	9	fixed	fix	VERB
gs-1949	140	10	trajectory	trajectory	NOUN
gs-1949	140	11	into	into	ADP
gs-1949	140	12	two	two	NUM
gs-1949	140	13	uncorrelated	uncorrelated	ADJ
gs-1949	140	14	and	and	CCONJ
gs-1949	140	15	asymptotically	asymptotically	ADV
gs-1949	140	16	independent	independent	ADJ
gs-1949	140	17	centered	center	VERB
gs-1949	140	18	sums	sum	NOUN
gs-1949	140	19	1	1	NUM
gs-1949	140	20	2n	2n	NUM
gs-1949	140	21	n	n	CCONJ
gs-1949	140	22	ns	ns	NUM
gs-1949	140	23	s	s	NOUN
gs-1949	140	24	s	s	NOUN
gs-1949	140	25			X
gs-1949	140	26	:	:	PUNCT
gs-1949	140	27			NOUN
gs-1949	140	28	1	1	VERB
gs-1949	140	29	1	1	NUM
gs-1949	140	30	1	1	NUM
gs-1949	140	31	n	n	NUM
gs-1949	140	32	n	n	PRON
gs-1949	140	33	j	j	PROPN
gs-1949	141	1	j	j	PROPN
gs-1949	142	1	j	j	PROPN
gs-1949	142	2	s	s	PROPN
gs-1949	142	3	y	y	PROPN
gs-1949	142	4	n	n	PRON
gs-1949	142	5			NOUN
gs-1949	142	6			NOUN
gs-1949	142	7			NUM
gs-1949	143	1			PROPN
gs-1949	143	2			NOUN
gs-1949	143	3			PROPN
gs-1949	143	4			VERB
gs-1949	143	5			X
gs-1949	143	6	,	,	PUNCT
gs-1949	143	7			NOUN
gs-1949	143	8	2	2	ADJ
gs-1949	143	9	1	1	NUM
gs-1949	143	10	1	1	NUM
gs-1949	143	11	n	n	NUM
gs-1949	143	12	n	n	DET
gs-1949	143	13	j	j	NOUN
gs-1949	144	1	i	i	PRON
gs-1949	144	2	s	s	VERB
gs-1949	144	3	n	n	PRON
gs-1949	144	4			NOUN
gs-1949	144	5			NOUN
gs-1949	144	6			NOUN
gs-1949	144	7			NOUN
gs-1949	145	1			PROPN
gs-1949	146	1			NOUN
gs-1949	146	2			PROPN
gs-1949	146	3			VERB
gs-1949	146	4			X
gs-1949	146	5	.	.	PUNCT
gs-1949	147	1	lemma	lemma	PROPN
gs-1949	147	2	1	1	NUM
gs-1949	147	3	.	.	PUNCT
gs-1949	148	1	(	(	PUNCT
gs-1949	148	2	see	see	VERB
gs-1949	148	3	[	[	X
gs-1949	148	4	5	5	NUM
gs-1949	148	5	]	]	PUNCT
gs-1949	148	6	)	)	PUNCT
gs-1949	148	7	suppose	suppose	VERB
gs-1949	148	8	that	that	SCONJ
gs-1949	148	9			PROPN
gs-1949	148	10			PROPN
gs-1949	148	11	1i	1i	NOUN
gs-1949	149	1	i	i	PRON
gs-1949	149	2	y	y	PROPN
gs-1949	149	3			NUM
gs-1949	149	4	is	be	AUX
gs-1949	149	5	a	a	DET
gs-1949	149	6	conditionally	conditionally	ADV
gs-1949	149	7	m	m	NOUN
gs-1949	149	8	−independent	−independent	ADJ
gs-1949	149	9	sequence	sequence	NOUN
gs-1949	149	10	in	in	ADP
gs-1949	149	11	model	model	NOUN
gs-1949	149	12	(	(	PUNCT
gs-1949	149	13	1	1	NUM
gs-1949	149	14	)	)	PUNCT
gs-1949	149	15	.	.	PUNCT
gs-1949	150	1	let	let	VERB
gs-1949	150	2	's	us	PRON
gs-1949	150	3	say	say	VERB
gs-1949	150	4	for	for	ADP
gs-1949	150	5	arbitrary	arbitrary	ADJ
gs-1949	150	6	function	function	NOUN
gs-1949	150	7	:	:	PUNCT
gs-1949	151	1	kr	kr	PROPN
gs-1949	151	2			NUM
gs-1949	151	3	when	when	SCONJ
gs-1949	151	4			NOUN
gs-1949	151	5	1pe	1pe	NOUN
gs-1949	151	6			NOUN
gs-1949	151	7			PROPN
gs-1949	151	8			VERB
gs-1949	151	9	(	(	PUNCT
gs-1949	151	10	1,p	1,p	PROPN
gs-1949	151	11	k	k	NOUN
gs-1949	151	12	,	,	PUNCT
gs-1949	151	13			PROPN
gs-1949	151	14			SYM
gs-1949	151	15			NOUN
gs-1949	151	16	1	1	NOUN
gs-1949	151	17	2	2	NUM
gs-1949	151	18	(	(	PUNCT
gs-1949	151	19	)	)	PUNCT
gs-1949	151	20	,	,	PUNCT
gs-1949	151	21	(	(	PUNCT
gs-1949	151	22	)	)	PUNCT
gs-1949	151	23	,	,	PUNCT
gs-1949	151	24	...	...	PUNCT
gs-1949	151	25	,	,	PUNCT
gs-1949	151	26	(	(	PUNCT
gs-1949	151	27	)	)	PUNCT
gs-1949	151	28	k	k	NOUN
gs-1949	152	1			NUM
gs-1949	152	2			NUM
gs-1949	152	3			PROPN
gs-1949	152	4			PROPN
gs-1949	152	5			PROPN
gs-1949	152	6			PROPN
gs-1949	152	7			PROPN
gs-1949	152	8			PROPN
gs-1949	152	9	)	)	PUNCT
gs-1949	152	10	almost	almost	ADV
gs-1949	152	11	everywhere	everywhere	ADV
gs-1949	152	12	an	an	DET
gs-1949	152	13	convergence	convergence	NOUN
gs-1949	152	14	is	be	AUX
gs-1949	152	15	executed	execute	VERB
gs-1949	152	16	georgian	georgian	ADJ
gs-1949	152	17	scientists/ქართველი	scientists/ქართველი	NOUN
gs-1949	152	18	მეცნიერები	მეცნიერები	NOUN
gs-1949	152	19	ტ.	ტ.	VERB
gs-1949	152	20	5	5	NUM
gs-1949	152	21	n	n	PRON
gs-1949	152	22	2	2	NUM
gs-1949	152	23	,	,	PUNCT
gs-1949	152	24	2023	2023	NUM
gs-1949	152	25	25	25	NUM
gs-1949	152	26			NOUN
gs-1949	152	27			SYM
gs-1949	152	28			NOUN
gs-1949	152	29	1	1	VERB
gs-1949	153	1	1	1	NUM
gs-1949	153	2	1	1	NUM
gs-1949	153	3	n	n	NUM
gs-1949	153	4	n	n	PRON
gs-1949	153	5	j	j	PROPN
gs-1949	153	6	j	j	PROPN
gs-1949	153	7	e	e	PROPN
gs-1949	153	8	n	n	CCONJ
gs-1949	153	9			VERB
gs-1949	153	10			VERB
gs-1949	153	11			PROPN
gs-1949	153	12			PROPN
gs-1949	153	13			NOUN
gs-1949	153	14			PROPN
gs-1949	153	15	a.	a.	PROPN
gs-1949	153	16	e.	e.	PROPN
gs-1949	153	17	(	(	PUNCT
gs-1949	153	18	2	2	X
gs-1949	153	19	)	)	PUNCT
gs-1949	153	20	let	let	VERB
gs-1949	153	21	's	us	PRON
gs-1949	153	22	say	say	VERB
gs-1949	153	23	(	(	PUNCT
gs-1949	153	24	)	)	PUNCT
gs-1949	153	25	msp	msp	PROPN
gs-1949	153	26	r	r	NOUN
gs-1949	153	27			PROPN
gs-1949	153	28			NOUN
gs-1949	153	29	(	(	PUNCT
gs-1949	153	30	3	3	NUM
gs-1949	153	31	)	)	PUNCT
gs-1949	153	32	then	then	ADV
gs-1949	153	33	,	,	PUNCT
gs-1949	153	34	for	for	ADP
gs-1949	153	35	n	n	PROPN
gs-1949	153	36	,	,	PUNCT
gs-1949	153	37	the	the	DET
gs-1949	153	38	following	follow	VERB
gs-1949	153	39	convergences	convergence	NOUN
gs-1949	153	40	are	be	AUX
gs-1949	153	41	fulfilled	fulfil	VERB
gs-1949	153	42	:	:	PUNCT
gs-1949	153	43	a	a	X
gs-1949	153	44	)	)	PUNCT
gs-1949	153	45	1	1	NUM
gs-1949	153	46	1	1	NUM
gs-1949	153	47	mn	mn	PROPN
gs-1949	153	48	n	n	PROPN
gs-1949	153	49	w	w	NOUN
gs-1949	153	50	rs	rs	NOUN
gs-1949	153	51			NOUN
gs-1949	153	52			PROPN
gs-1949	153	53	a.	a.	PROPN
gs-1949	153	54	e.	e.	PROPN
gs-1949	153	55	,	,	PUNCT
gs-1949	153	56	b	b	PROPN
gs-1949	153	57	)	)	PUNCT
gs-1949	153	58	1n	1n	NUM
gs-1949	153	59	m	m	VERB
gs-1949	153	60	w	w	PROPN
gs-1949	153	61	s	s	PROPN
gs-1949	153	62	r	r	NOUN
gs-1949	153	63	,	,	PUNCT
gs-1949	153	64	c	c	X
gs-1949	153	65	)	)	PUNCT
gs-1949	153	66	if	if	SCONJ
gs-1949	153	67	2n	2n	NUM
gs-1949	153	68	w	w	PROPN
gs-1949	153	69	s	s	X
gs-1949	153	70			NOUN
gs-1949	153	71	then	then	ADV
gs-1949	153	72	1n	1n	NUM
gs-1949	154	1	m	m	VERB
gs-1949	154	2	w	w	PROPN
gs-1949	154	3	s	s	PROPN
gs-1949	154	4	r	r	NOUN
gs-1949	154	5			PROPN
gs-1949	154	6	lemma	lemma	PROPN
gs-1949	154	7	2	2	X
gs-1949	154	8	.	.	PUNCT
gs-1949	155	1	(	(	PUNCT
gs-1949	155	2	see	see	VERB
gs-1949	155	3	.	.	PUNCT
gs-1949	156	1	[	[	X
gs-1949	156	2	7	7	NUM
gs-1949	156	3	]	]	PUNCT
gs-1949	156	4	)	)	PUNCT
gs-1949	156	5	let	let	VERB
gs-1949	156	6	’s	’s	PRON
gs-1949	156	7	say	say	VERB
gs-1949	156	8	:	:	PUNCT
gs-1949	156	9	g	g	PROPN
gs-1949	156	10	t	t	PROPN
gs-1949	156	11	t	t	PROPN
gs-1949	156	12			ADJ
gs-1949	156	13	is	be	AUX
gs-1949	156	14	a	a	DET
gs-1949	156	15	continuous	continuous	ADJ
gs-1949	156	16	mapping	mapping	NOUN
gs-1949	156	17	of	of	ADP
gs-1949	156	18	a	a	DET
gs-1949	156	19	t	t	NOUN
gs-1949	156	20	metric	metric	ADJ
gs-1949	156	21	space	space	NOUN
gs-1949	156	22	into	into	ADP
gs-1949	156	23	a	a	DET
gs-1949	156	24	t	t	NOUN
gs-1949	156	25			CCONJ
gs-1949	156	26	metric	metric	ADJ
gs-1949	156	27	space	space	NOUN
gs-1949	156	28	.	.	PUNCT
gs-1949	157	1	if	if	SCONJ
gs-1949	157	2	d	d	PROPN
gs-1949	157	3	nx	nx	X
gs-1949	158	1	x	x	PROPN
gs-1949	159	1	when	when	SCONJ
gs-1949	159	2	n	n	PROPN
gs-1949	159	3	then	then	ADV
gs-1949	159	4	(	(	PUNCT
gs-1949	159	5	)	)	PUNCT
gs-1949	159	6	(	(	PUNCT
gs-1949	159	7	)	)	PUNCT
gs-1949	159	8	d	d	X
gs-1949	159	9	ng	ng	PROPN
gs-1949	159	10	x	x	X
gs-1949	159	11	g	g	PROPN
gs-1949	159	12	x	x	PROPN
gs-1949	159	13	.	.	PUNCT
gs-1949	160	1	lemma	lemma	PROPN
gs-1949	161	1	3	3	X
gs-1949	161	2	.	.	PUNCT
gs-1949	161	3	(	(	PUNCT
gs-1949	161	4	see	see	VERB
gs-1949	161	5	.	.	PUNCT
gs-1949	162	1	[	[	X
gs-1949	162	2	7	7	NUM
gs-1949	162	3	]	]	PUNCT
gs-1949	162	4	)	)	PUNCT
gs-1949	162	5	assume	assume	VERB
gs-1949	162	6	that	that	SCONJ
gs-1949	162	7	,	,	PUNCT
gs-1949	162	8	nx	nx	INTJ
gs-1949	162	9	,	,	PUNCT
gs-1949	162	10	nz	nz	PROPN
gs-1949	162	11	and	and	CCONJ
gs-1949	162	12	x	x	PRON
gs-1949	162	13	are	be	AUX
gs-1949	162	14	random	random	ADJ
gs-1949	162	15	variables	variable	NOUN
gs-1949	162	16	with	with	ADP
gs-1949	162	17	values	value	NOUN
gs-1949	162	18	in	in	ADP
gs-1949	162	19	a	a	DET
gs-1949	162	20	separable	separable	ADJ
gs-1949	162	21	metric	metric	ADJ
gs-1949	162	22	space	space	NOUN
gs-1949	162	23	t	t	NOUN
gs-1949	162	24	.	.	PUNCT
gs-1949	163	1	let	let	VERB
gs-1949	163	2	's	us	PRON
gs-1949	163	3	say	say	VERB
gs-1949	163	4	when	when	SCONJ
gs-1949	163	5	n	n	ADJ
gs-1949	163	6	the	the	DET
gs-1949	163	7	limit	limit	NOUN
gs-1949	163	8	equalities	equalitie	VERB
gs-1949	163	9	d	d	NOUN
gs-1949	163	10	nx	nx	PROPN
gs-1949	163	11	x	x	PROPN
gs-1949	163	12	and	and	CCONJ
gs-1949	163	13			PROPN
gs-1949	163	14			PROPN
gs-1949	163	15	,	,	PUNCT
gs-1949	163	16	0n	0n	NOUN
gs-1949	163	17	nx	nx	PROPN
gs-1949	163	18	z	z	NUM
gs-1949	163	19			NOUN
gs-1949	163	20	are	be	AUX
gs-1949	163	21	satisfied	satisfied	ADJ
gs-1949	163	22	,	,	PUNCT
gs-1949	163	23	then	then	ADV
gs-1949	163	24	d	d	X
gs-1949	163	25	nz	nz	PROPN
gs-1949	163	26	x	x	PROPN
gs-1949	163	27	.	.	PUNCT
gs-1949	164	1	methodology	methodology	NOUN
gs-1949	164	2	when	when	SCONJ
gs-1949	164	3	proving	prove	VERB
gs-1949	164	4	the	the	DET
gs-1949	164	5	theorem	theorem	NOUN
gs-1949	164	6	,	,	PUNCT
gs-1949	164	7	we	we	PRON
gs-1949	164	8	use	use	VERB
gs-1949	164	9	the	the	DET
gs-1949	164	10	methods	method	NOUN
gs-1949	164	11	applicable	applicable	ADJ
gs-1949	164	12	in	in	ADP
gs-1949	164	13	article	article	NOUN
gs-1949	164	14	[	[	X
gs-1949	164	15	5	5	X
gs-1949	164	16	]	]	PUNCT
gs-1949	164	17	by	by	ADP
gs-1949	164	18	i.	i.	PROPN
gs-1949	164	19	bokuchava	bokuchava	PROPN
gs-1949	164	20	,	,	PUNCT
gs-1949	164	21	t.	t.	PROPN
gs-1949	164	22	shervashidze	shervashidze	PROPN
gs-1949	164	23	and	and	CCONJ
gs-1949	164	24	z.	z.	PROPN
gs-1949	164	25	kvatadze	kvatadze	PROPN
gs-1949	164	26	.	.	PUNCT
gs-1949	165	1	the	the	DET
gs-1949	165	2	sums	sum	NOUN
gs-1949	165	3	1ns	1ns	NOUN
gs-1949	165	4	and	and	CCONJ
gs-1949	165	5	2ns	2ns	NOUN
gs-1949	165	6	are	be	AUX
gs-1949	165	7	uncorrelated	uncorrelated	ADJ
gs-1949	165	8	and	and	CCONJ
gs-1949	165	9	asymptotically	asymptotically	ADV
gs-1949	165	10	independent	independent	ADJ
gs-1949	165	11	(	(	PUNCT
gs-1949	165	12	see	see	NOUN
gs-1949	165	13	.	.	PUNCT
gs-1949	166	1	[	[	X
gs-1949	166	2	5	5	NUM
gs-1949	166	3	]	]	PUNCT
gs-1949	166	4	)	)	PUNCT
gs-1949	166	5	.	.	PUNCT
gs-1949	167	1	for	for	ADP
gs-1949	167	2	calculated	calculate	VERB
gs-1949	167	3	expressions	expression	NOUN
gs-1949	167	4	in	in	ADP
gs-1949	167	5	inequalities	inequality	NOUN
gs-1949	167	6	,	,	PUNCT
gs-1949	167	7	we	we	PRON
gs-1949	167	8	use	use	VERB
gs-1949	167	9	the	the	DET
gs-1949	167	10	following	follow	VERB
gs-1949	167	11	representation	representation	NOUN
gs-1949	167	12			NOUN
gs-1949	167	13			SYM
gs-1949	167	14			NOUN
gs-1949	167	15			ADJ
gs-1949	167	16	1ne	1ne	NOUN
gs-1949	167	17	e	e	NOUN
gs-1949	167	18	e	e	NOUN
gs-1949	167	19			VERB
gs-1949	167	20			NOUN
gs-1949	167	21			PROPN
gs-1949	167	22	.	.	PUNCT
gs-1949	168	1	this	this	DET
gs-1949	168	2	representation	representation	NOUN
gs-1949	168	3	allows	allow	VERB
gs-1949	168	4	us	we	PRON
gs-1949	168	5	to	to	PART
gs-1949	168	6	consider	consider	VERB
gs-1949	168	7	the	the	DET
gs-1949	168	8	terms	term	NOUN
gs-1949	168	9	of	of	ADP
gs-1949	168	10	these	these	DET
gs-1949	168	11	sums	sum	NOUN
gs-1949	168	12	on	on	ADP
gs-1949	168	13	a	a	DET
gs-1949	168	14	fixed	fix	VERB
gs-1949	168	15	trajectory	trajectory	NOUN
gs-1949	168	16	as	as	ADP
gs-1949	168	17	independent	independent	ADJ
gs-1949	168	18	quantities	quantity	NOUN
gs-1949	168	19	.	.	PUNCT
gs-1949	169	1	we	we	PRON
gs-1949	169	2	are	be	AUX
gs-1949	169	3	investigating	investigate	VERB
gs-1949	169	4	an	an	DET
gs-1949	169	5	ergodic	ergodic	ADJ
gs-1949	169	6	chain	chain	NOUN
gs-1949	169	7	that	that	PRON
gs-1949	169	8	is	be	AUX
gs-1949	169	9	not	not	PART
gs-1949	169	10	regular	regular	ADJ
gs-1949	169	11	.	.	PUNCT
gs-1949	170	1	since	since	SCONJ
gs-1949	170	2	there	there	PRON
gs-1949	170	3	are	be	VERB
gs-1949	170	4	cyclic	cyclic	ADJ
gs-1949	170	5	subclasses	subclass	NOUN
gs-1949	170	6	,	,	PUNCT
gs-1949	170	7	the	the	DET
gs-1949	170	8	existence	existence	NOUN
gs-1949	170	9	of	of	ADP
gs-1949	170	10	the	the	DET
gs-1949	170	11	fundamental	fundamental	ADJ
gs-1949	170	12	matrix	matrix	NOUN
gs-1949	170	13	of	of	ADP
gs-1949	170	14	a	a	DET
gs-1949	170	15	chain	chain	NOUN
gs-1949	170	16	is	be	AUX
gs-1949	170	17	understood	understand	VERB
gs-1949	170	18	in	in	ADP
gs-1949	170	19	the	the	DET
gs-1949	170	20	sense	sense	NOUN
gs-1949	170	21	of	of	ADP
gs-1949	170	22	cesaro	cesaro	NOUN
gs-1949	170	23	(	(	PUNCT
gs-1949	170	24	see.[8	see.[8	PROPN
gs-1949	170	25	]	]	NOUN
gs-1949	170	26	)	)	PUNCT
gs-1949	170	27	.	.	PUNCT
gs-1949	171	1	in	in	ADP
gs-1949	171	2	[	[	X
gs-1949	171	3	9	9	NUM
gs-1949	171	4	]	]	PUNCT
gs-1949	171	5	,	,	PUNCT
gs-1949	171	6	the	the	DET
gs-1949	171	7	representation	representation	NOUN
gs-1949	171	8	of	of	ADP
gs-1949	171	9	the	the	DET
gs-1949	171	10	covariance	covariance	NOUN
gs-1949	171	11	matrix	matrix	NOUN
gs-1949	171	12	of	of	ADP
gs-1949	171	13	the	the	DET
gs-1949	171	14	limit	limit	NOUN
gs-1949	171	15	distribution	distribution	NOUN
gs-1949	171	16	of	of	ADP
gs-1949	171	17	the	the	DET
gs-1949	171	18	normalized	normalize	VERB
gs-1949	171	19	sum	sum	NOUN
gs-1949	171	20	of	of	ADP
gs-1949	171	21	functions	function	NOUN
gs-1949	171	22	defined	define	VERB
gs-1949	171	23	on	on	ADP
gs-1949	171	24	a	a	DET
gs-1949	171	25	chain	chain	NOUN
gs-1949	171	26	was	be	AUX
gs-1949	171	27	obtained	obtain	VERB
gs-1949	171	28	using	use	VERB
gs-1949	171	29	the	the	DET
gs-1949	171	30	characteristics	characteristic	NOUN
gs-1949	171	31	of	of	ADP
gs-1949	171	32	the	the	DET
gs-1949	171	33	chain	chain	NOUN
gs-1949	171	34	.	.	PUNCT
gs-1949	172	1	main	main	ADJ
gs-1949	172	2	results	result	NOUN
gs-1949	172	3	theorem	theorem	VERB
gs-1949	172	4	1	1	NUM
gs-1949	172	5	.	.	PUNCT
gs-1949	172	6	suppose	suppose	VERB
gs-1949	172	7	that	that	SCONJ
gs-1949	172	8			PROPN
gs-1949	172	9			PROPN
gs-1949	172	10	1i	1i	NOUN
gs-1949	173	1	i	i	PRON
gs-1949	173	2	y	y	PROPN
gs-1949	173	3			NUM
gs-1949	173	4	is	be	AUX
gs-1949	173	5	a	a	DET
gs-1949	173	6	conditionally	conditionally	ADV
gs-1949	173	7	m	m	NOUN
gs-1949	173	8	−dependent	−dependent	NOUN
gs-1949	173	9	sequence	sequence	NOUN
gs-1949	173	10	in	in	ADP
gs-1949	173	11	model	model	NOUN
gs-1949	173	12	(	(	PUNCT
gs-1949	173	13	1	1	NUM
gs-1949	173	14	)	)	PUNCT
gs-1949	173	15	.	.	PUNCT
gs-1949	174	1	suppose	suppose	VERB
gs-1949	174	2	the	the	DET
gs-1949	174	3	control	control	NOUN
gs-1949	174	4	sequence	sequence	NOUN
gs-1949	174	5			PROPN
gs-1949	174	6			PROPN
gs-1949	174	7	1i	1i	NOUN
gs-1949	174	8	i	i	PRON
gs-1949	174	9			VERB
gs-1949	174	10			X
gs-1949	174	11	satisfies	satisfy	VERB
gs-1949	174	12	condition	condition	NOUN
gs-1949	174	13	(	(	PUNCT
gs-1949	174	14	2	2	NUM
gs-1949	174	15	)	)	PUNCT
gs-1949	174	16	and	and	CCONJ
gs-1949	174	17	inequality	inequality	NOUN
gs-1949	174	18	(	(	PUNCT
gs-1949	174	19	3	3	NUM
gs-1949	174	20	)	)	PUNCT
gs-1949	174	21	is	be	AUX
gs-1949	174	22	fulfilled	fulfil	VERB
gs-1949	174	23	.	.	PUNCT
gs-1949	175	1	then	then	ADV
gs-1949	175	2	the	the	DET
gs-1949	175	3	following	follow	VERB
gs-1949	175	4	propositions	proposition	NOUN
gs-1949	175	5	are	be	AUX
gs-1949	175	6	true	true	ADJ
gs-1949	175	7	:	:	PUNCT
gs-1949	175	8	a	a	X
gs-1949	175	9	)	)	PUNCT
gs-1949	175	10	let	let	VERB
gs-1949	175	11	’s	’s	PRON
gs-1949	175	12	say	say	VERB
gs-1949	175	13	2ns	2ns	NOUN
gs-1949	175	14	is	be	AUX
gs-1949	175	15	weakly	weakly	ADJ
gs-1949	175	16	converges	converge	NOUN
gs-1949	175	17	to	to	ADP
gs-1949	175	18	some	some	DET
gs-1949	175	19	non	non	ADJ
gs-1949	175	20	degenerate	degenerate	ADJ
gs-1949	175	21	distribution	distribution	NOUN
gs-1949	175	22	q	q	NOUN
gs-1949	175	23	with	with	ADP
gs-1949	175	24	distribution	distribution	NOUN
gs-1949	175	25	function	function	NOUN
gs-1949	175	26	(	(	PUNCT
gs-1949	175	27	)	)	PUNCT
gs-1949	175	28	q	q	PROPN
gs-1949	175	29			PROPN
gs-1949	175	30	,	,	PUNCT
gs-1949	175	31	then	then	ADV
gs-1949	175	32	for	for	ADP
gs-1949	175	33	arbitrary	arbitrary	ADJ
gs-1949	175	34	vectors	vector	NOUN
gs-1949	175	35	,	,	PUNCT
gs-1949	175	36	x	x	PROPN
gs-1949	175	37	y	y	PROPN
gs-1949	175	38	,	,	PUNCT
gs-1949	175	39			PROPN
gs-1949	175	40			PROPN
gs-1949	175	41	,	,	PUNCT
gs-1949	175	42	kx	kx	PROPN
gs-1949	175	43	y	y	PROPN
gs-1949	175	44	r	r	PROPN
gs-1949	175	45	when	when	SCONJ
gs-1949	175	46	n	n	PROPN
gs-1949	175	47	there	there	PRON
gs-1949	175	48	is	be	VERB
gs-1949	175	49	a	a	DET
gs-1949	175	50	convergence	convergence	NOUN
gs-1949	175	51			PRON
gs-1949	175	52			PROPN
gs-1949	175	53	1	1	NUM
gs-1949	175	54	p	p	NOUN
gs-1949	175	55	(	(	PUNCT
gs-1949	175	56	)	)	PUNCT
gs-1949	175	57	(	(	PUNCT
gs-1949	175	58	)	)	PUNCT
gs-1949	175	59	(	(	PUNCT
gs-1949	175	60	)	)	PUNCT
gs-1949	175	61	(	(	PUNCT
gs-1949	175	62	)	)	PUNCT
gs-1949	175	63	(	(	PUNCT
gs-1949	175	64	)	)	PUNCT
gs-1949	176	1	m	m	VERB
gs-1949	176	2	mn	mn	PROPN
gs-1949	176	3	n	n	ADV
gs-1949	176	4	r	r	NOUN
gs-1949	176	5	rs	rs	NOUN
gs-1949	177	1	x	x	VERB
gs-1949	177	2	y	y	NOUN
gs-1949	177	3	f	f	NOUN
gs-1949	177	4	x	x	PUNCT
gs-1949	178	1	x	x	PUNCT
gs-1949	178	2	y	y	VERB
gs-1949	178	3	q	q	PROPN
gs-1949	178	4	y	y	PROPN
gs-1949	178	5	q	q	ADJ
gs-1949	178	6	y	y	PROPN
gs-1949	178	7			NOUN
gs-1949	178	8			NOUN
gs-1949	178	9			VERB
gs-1949	178	10			NOUN
gs-1949	178	11			NOUN
gs-1949	178	12			NOUN
gs-1949	178	13			PUNCT
gs-1949	178	14			PUNCT
gs-1949	178	15			VERB
gs-1949	178	16			NOUN
gs-1949	178	17	(	(	PUNCT
gs-1949	178	18	4	4	NUM
gs-1949	178	19	)	)	PUNCT
gs-1949	178	20	b	b	NOUN
gs-1949	178	21	)	)	PUNCT
gs-1949	178	22	the	the	DET
gs-1949	178	23	opposite	opposite	NOUN
gs-1949	178	24	is	be	AUX
gs-1949	178	25	true	true	ADJ
gs-1949	178	26	,	,	PUNCT
gs-1949	178	27	if	if	SCONJ
gs-1949	178	28	(	(	PUNCT
gs-1949	178	29	4	4	X
gs-1949	178	30	)	)	PUNCT
gs-1949	178	31	is	be	AUX
gs-1949	178	32	true	true	ADJ
gs-1949	178	33	,	,	PUNCT
gs-1949	178	34	then	then	ADV
gs-1949	178	35	2n	2n	NUM
gs-1949	178	36	w	w	PROPN
gs-1949	178	37	s	s	X
gs-1949	178	38			ADJ
gs-1949	178	39	.	.	PUNCT
gs-1949	179	1	proof	proof	NOUN
gs-1949	179	2	.	.	PUNCT
gs-1949	180	1	let	let	VERB
gs-1949	180	2	's	us	PRON
gs-1949	180	3	use	use	VERB
gs-1949	180	4	the	the	DET
gs-1949	180	5	following	follow	VERB
gs-1949	180	6	representations	representation	NOUN
gs-1949	180	7	georgian	georgian	PROPN
gs-1949	180	8	scientists/ქართველი	scientists/ქართველი	NOUN
gs-1949	180	9	მეცნიერები	მეცნიერები	NOUN
gs-1949	180	10	ტ.	ტ.	VERB
gs-1949	180	11	5	5	NUM
gs-1949	180	12	n	n	DET
gs-1949	180	13	2	2	NUM
gs-1949	180	14	,	,	PUNCT
gs-1949	180	15	2023	2023	NUM
gs-1949	180	16	26	26	NUM
gs-1949	180	17			PROPN
gs-1949	180	18			PROPN
gs-1949	180	19			PROPN
gs-1949	180	20			PROPN
gs-1949	180	21	1	1	NUM
gs-1949	180	22	1	1	NUM
gs-1949	180	23	1	1	NUM
gs-1949	180	24	2p	2p	NUM
gs-1949	180	25	(	(	PUNCT
gs-1949	180	26	)	)	PUNCT
gs-1949	180	27	(	(	PUNCT
gs-1949	180	28	)	)	PUNCT
gs-1949	180	29	(	(	PUNCT
gs-1949	180	30	)	)	PUNCT
gs-1949	180	31	p	p	X
gs-1949	180	32	(	(	PUNCT
gs-1949	180	33	)	)	PUNCT
gs-1949	180	34	(	(	PUNCT
gs-1949	180	35	)	)	PUNCT
gs-1949	180	36	(	(	PUNCT
gs-1949	180	37	)	)	PUNCT
gs-1949	180	38	m	m	VERB
gs-1949	180	39	m	m	VERB
gs-1949	180	40	m	m	VERB
gs-1949	180	41	mn	mn	PROPN
gs-1949	180	42	n	n	PROPN
gs-1949	180	43	n	n	CCONJ
gs-1949	180	44	n	n	CCONJ
gs-1949	180	45	r	r	NOUN
gs-1949	180	46	r	r	NOUN
gs-1949	180	47	r	r	NOUN
gs-1949	180	48	n	n	NUM
gs-1949	180	49	rs	rs	NOUN
gs-1949	180	50	s	s	NOUN
gs-1949	180	51	x	x	X
gs-1949	180	52	y	y	NOUN
gs-1949	180	53	f	f	NOUN
gs-1949	181	1	x	x	PUNCT
gs-1949	181	2	x	x	PUNCT
gs-1949	181	3	y	y	NOUN
gs-1949	181	4	x	x	X
gs-1949	181	5	y	y	NOUN
gs-1949	181	6	f	f	PROPN
gs-1949	181	7	x	x	X
gs-1949	181	8	s	s	X
gs-1949	181	9	x	x	X
gs-1949	181	10	y	y	NOUN
gs-1949	181	11			NOUN
gs-1949	181	12			VERB
gs-1949	181	13			NOUN
gs-1949	181	14			VERB
gs-1949	181	15			NOUN
gs-1949	181	16			NOUN
gs-1949	181	17			NOUN
gs-1949	181	18			ADV
gs-1949	181	19			NUM
gs-1949	181	20			NUM
gs-1949	181	21			NOUN
gs-1949	181	22			NOUN
gs-1949	181	23			VERB
gs-1949	181	24			NOUN
gs-1949	181	25			NOUN
gs-1949	181	26			PUNCT
gs-1949	181	27	=	=	PUNCT
gs-1949	181	28			PROPN
gs-1949	181	29			PROPN
gs-1949	181	30			PROPN
gs-1949	181	31			PROPN
gs-1949	181	32	1	1	NUM
gs-1949	181	33	1	1	NUM
gs-1949	181	34	1	1	NUM
gs-1949	181	35	1	1	NUM
gs-1949	181	36	2	2	NUM
gs-1949	181	37	2p	2p	NUM
gs-1949	181	38	(	(	PUNCT
gs-1949	181	39	)	)	PUNCT
gs-1949	181	40	(	(	PUNCT
gs-1949	181	41	)	)	PUNCT
gs-1949	181	42	p	p	X
gs-1949	181	43	(	(	PUNCT
gs-1949	181	44	)	)	PUNCT
gs-1949	181	45	(	(	PUNCT
gs-1949	181	46	)	)	PUNCT
gs-1949	181	47	1	1	NUM
gs-1949	181	48	m	m	NOUN
gs-1949	181	49	mn	mn	PROPN
gs-1949	181	50	n	n	PROPN
gs-1949	181	51	n	n	CCONJ
gs-1949	181	52	n	n	CCONJ
gs-1949	181	53	n	n	ADP
gs-1949	181	54	r	r	NOUN
gs-1949	181	55	n	n	NUM
gs-1949	182	1	rs	rs	NOUN
gs-1949	182	2	s	s	PART
gs-1949	182	3	f	f	X
gs-1949	182	4	x	x	SYM
gs-1949	182	5	s	s	PROPN
gs-1949	182	6	x	x	X
gs-1949	182	7	y	y	NOUN
gs-1949	182	8	f	f	PROPN
gs-1949	182	9	x	x	X
gs-1949	182	10	s	s	X
gs-1949	182	11	x	x	X
gs-1949	182	12	y	y	NOUN
gs-1949	182	13			NOUN
gs-1949	182	14			VERB
gs-1949	182	15			NUM
gs-1949	182	16			NOUN
gs-1949	182	17			NOUN
gs-1949	182	18			NOUN
gs-1949	182	19			PUNCT
gs-1949	182	20			PROPN
gs-1949	182	21			PROPN
gs-1949	182	22			NUM
gs-1949	182	23			NOUN
gs-1949	182	24			PROPN
gs-1949	182	25			NOUN
gs-1949	182	26			PROPN
gs-1949	182	27			PROPN
gs-1949	182	28			PROPN
gs-1949	182	29			PROPN
gs-1949	182	30	p	p	PROPN
gs-1949	182	31	0	0	NUM
gs-1949	183	1	p	p	NOUN
gs-1949	183	2	0	0	NUM
gs-1949	183	3	1n	1n	NUM
gs-1949	183	4	nm	nm	PRON
gs-1949	183	5	l	l	NOUN
gs-1949	183	6			NOUN
gs-1949	183	7			PROPN
gs-1949	183	8			NUM
gs-1949	183	9			PROPN
gs-1949	183	10	(	(	PUNCT
gs-1949	183	11	5	5	NUM
gs-1949	183	12	)	)	PUNCT
gs-1949	183	13			NOUN
gs-1949	183	14			PROPN
gs-1949	183	15			PROPN
gs-1949	183	16			PROPN
gs-1949	183	17			NOUN
gs-1949	183	18	1	1	NOUN
gs-1949	183	19	1	1	NUM
gs-1949	183	20	2p	2p	NUM
gs-1949	183	21	(	(	PUNCT
gs-1949	183	22	)	)	PUNCT
gs-1949	183	23	(	(	PUNCT
gs-1949	183	24	)	)	PUNCT
gs-1949	183	25	(	(	PUNCT
gs-1949	183	26	)	)	PUNCT
gs-1949	184	1	p	p	NOUN
gs-1949	184	2	0	0	NUM
gs-1949	185	1	p	p	NOUN
gs-1949	185	2	0	0	NUM
gs-1949	185	3	1	1	NUM
gs-1949	185	4	m	m	NOUN
gs-1949	185	5	m	m	VERB
gs-1949	185	6	mr	mr	PROPN
gs-1949	185	7	r	r	PROPN
gs-1949	185	8	n	n	ADP
gs-1949	185	9	r	r	NOUN
gs-1949	185	10	n	n	NOUN
gs-1949	185	11	nx	nx	NOUN
gs-1949	185	12	y	y	PROPN
gs-1949	185	13	x	x	SYM
gs-1949	185	14	s	s	X
gs-1949	185	15	x	x	X
gs-1949	185	16	y	y	PROPN
gs-1949	185	17	m	m	PROPN
gs-1949	185	18	l	l	PROPN
gs-1949	185	19			PROPN
gs-1949	185	20			NOUN
gs-1949	185	21			NOUN
gs-1949	185	22			VERB
gs-1949	185	23			NOUN
gs-1949	185	24			NOUN
gs-1949	185	25			PUNCT
gs-1949	186	1			PROPN
gs-1949	186	2			PROPN
gs-1949	186	3			NOUN
gs-1949	186	4			NUM
gs-1949	186	5			PROPN
gs-1949	186	6	(	(	PUNCT
gs-1949	186	7	6	6	NUM
gs-1949	186	8	)	)	PUNCT
gs-1949	187	1	where	where	SCONJ
gs-1949	187	2	1	1	NUM
gs-1949	187	3	1	1	NUM
gs-1949	187	4	2	2	NUM
gs-1949	187	5	(	(	PUNCT
gs-1949	187	6	)	)	PUNCT
gs-1949	187	7	(	(	PUNCT
gs-1949	187	8	)	)	PUNCT
gs-1949	187	9	mn	mn	PROPN
gs-1949	187	10	n	n	PROPN
gs-1949	187	11	n	n	CCONJ
gs-1949	187	12	n	n	ADV
gs-1949	187	13	rs	rs	NOUN
gs-1949	187	14	m	m	NOUN
gs-1949	187	15	f	f	NOUN
gs-1949	187	16	x	x	SYM
gs-1949	187	17	s	s	X
gs-1949	187	18	x	x	X
gs-1949	187	19	y	y	PROPN
gs-1949	187	20			VERB
gs-1949	187	21			NUM
gs-1949	187	22			PROPN
gs-1949	187	23			NOUN
gs-1949	187	24			PUNCT
gs-1949	187	25	;	;	PUNCT
gs-1949	187	26	1	1	NUM
gs-1949	187	27	2	2	NUM
gs-1949	187	28	(	(	PUNCT
gs-1949	187	29	)	)	PUNCT
gs-1949	187	30	(	(	PUNCT
gs-1949	187	31	)	)	PUNCT
gs-1949	187	32	m	m	VERB
gs-1949	187	33	mn	mn	NOUN
gs-1949	187	34	r	r	PROPN
gs-1949	187	35	n	n	NOUN
gs-1949	187	36	rm	rm	NOUN
gs-1949	187	37	x	x	SYM
gs-1949	187	38	s	s	PROPN
gs-1949	187	39	x	x	X
gs-1949	187	40	y	y	NOUN
gs-1949	187	41			PROPN
gs-1949	187	42			NOUN
gs-1949	187	43			NOUN
gs-1949	187	44			PUNCT
gs-1949	187	45	;	;	PUNCT
gs-1949	187	46	1	1	NUM
gs-1949	187	47	1	1	NUM
gs-1949	187	48	2	2	NUM
gs-1949	187	49	(	(	PUNCT
gs-1949	187	50	)	)	PUNCT
gs-1949	187	51	(	(	PUNCT
gs-1949	187	52	)	)	PUNCT
gs-1949	187	53	mn	mn	PROPN
gs-1949	187	54	n	n	CCONJ
gs-1949	187	55	n	n	CCONJ
gs-1949	187	56	n	n	ADV
gs-1949	187	57	rs	rs	NOUN
gs-1949	187	58	l	l	NOUN
gs-1949	187	59	f	f	X
gs-1949	187	60	x	x	X
gs-1949	187	61	s	s	X
gs-1949	187	62	x	x	X
gs-1949	187	63	y	y	PROPN
gs-1949	187	64			VERB
gs-1949	187	65			PROPN
gs-1949	187	66			PROPN
gs-1949	187	67			VERB
gs-1949	187	68			NOUN
gs-1949	187	69	;	;	PUNCT
gs-1949	187	70			NOUN
gs-1949	187	71	1	1	NOUN
gs-1949	187	72	2	2	NUM
gs-1949	187	73	(	(	PUNCT
gs-1949	187	74	)	)	PUNCT
gs-1949	187	75	(	(	PUNCT
gs-1949	187	76	)	)	PUNCT
gs-1949	188	1	m	m	VERB
gs-1949	188	2	mn	mn	NOUN
gs-1949	188	3	r	r	NOUN
gs-1949	188	4	n	n	NOUN
gs-1949	188	5	rl	rl	VERB
gs-1949	188	6	x	x	SYM
gs-1949	188	7	s	s	NOUN
gs-1949	188	8	x	x	X
gs-1949	188	9	y	y	NOUN
gs-1949	188	10			PROPN
gs-1949	188	11			NOUN
gs-1949	188	12			VERB
gs-1949	188	13			NOUN
gs-1949	188	14	.	.	PUNCT
gs-1949	189	1	on	on	ADP
gs-1949	189	2	the	the	DET
gs-1949	189	3	space	space	NOUN
gs-1949	189	4	where	where	SCONJ
gs-1949	189	5	the	the	DET
gs-1949	189	6	sequence	sequence	NOUN
gs-1949	189	7	(	(	PUNCT
gs-1949	189	8	1	1	X
gs-1949	189	9	)	)	PUNCT
gs-1949	189	10	is	be	AUX
gs-1949	189	11	given	give	VERB
gs-1949	189	12	,	,	PUNCT
gs-1949	189	13	let	let	VERB
gs-1949	189	14	's	us	PRON
gs-1949	189	15	determine	determine	VERB
gs-1949	189	16	the	the	DET
gs-1949	189	17	random	random	ADJ
gs-1949	189	18	variable	variable	NOUN
gs-1949	189	19			PUNCT
gs-1949	189	20	with	with	ADP
gs-1949	189	21	distribution	distribution	NOUN
gs-1949	189	22	q	q	NOUN
gs-1949	189	23	.	.	PUNCT
gs-1949	190	1	due	due	ADJ
gs-1949	190	2	the	the	DET
gs-1949	190	3	continuity	continuity	NOUN
gs-1949	190	4	and	and	CCONJ
gs-1949	190	5	monotonicity	monotonicity	NOUN
gs-1949	190	6	of	of	ADP
gs-1949	190	7	the	the	DET
gs-1949	190	8	function	function	NOUN
gs-1949	190	9	(	(	PUNCT
gs-1949	190	10	)	)	PUNCT
gs-1949	190	11	mr	mr	VERB
gs-1949	190	12			PROPN
gs-1949	190	13			PROPN
gs-1949	190	14	2p	2p	NOUN
gs-1949	190	15	(	(	PUNCT
gs-1949	190	16	)	)	PUNCT
gs-1949	190	17	(	(	PUNCT
gs-1949	190	18	)	)	PUNCT
gs-1949	190	19	(	(	PUNCT
gs-1949	190	20	)	)	PUNCT
gs-1949	190	21	m	m	VERB
gs-1949	190	22	m	m	VERB
gs-1949	190	23	mr	mr	PROPN
gs-1949	190	24	r	r	PROPN
gs-1949	190	25	n	n	PRON
gs-1949	190	26	rx	rx	VERB
gs-1949	190	27	y	y	PROPN
gs-1949	190	28	x	x	X
gs-1949	190	29	s	s	AUX
gs-1949	190	30	x	x	X
gs-1949	190	31	y	y	ADJ
gs-1949	190	32			NOUN
gs-1949	190	33			NOUN
gs-1949	190	34			NOUN
gs-1949	190	35			VERB
gs-1949	190	36			NOUN
gs-1949	190	37			PROPN
gs-1949	190	38			ADV
gs-1949	190	39			PROPN
gs-1949	190	40			PROPN
gs-1949	190	41			PROPN
gs-1949	190	42			PROPN
gs-1949	190	43	2p	2p	NOUN
gs-1949	190	44	p	p	X
gs-1949	190	45	(	(	PUNCT
gs-1949	190	46	)	)	PUNCT
gs-1949	190	47	(	(	PUNCT
gs-1949	190	48	)	)	PUNCT
gs-1949	190	49	n	n	X
gs-1949	190	50	ny	ny	PROPN
gs-1949	190	51	s	s	PROPN
gs-1949	190	52	y	y	PROPN
gs-1949	190	53	y	y	PROPN
gs-1949	190	54	y	y	PROPN
gs-1949	190	55	q	q	PROPN
gs-1949	190	56	y	y	PROPN
gs-1949	190	57	q	q	PROPN
gs-1949	190	58	y	y	PROPN
gs-1949	190	59			NOUN
gs-1949	190	60			NOUN
gs-1949	190	61			NOUN
gs-1949	190	62			NOUN
gs-1949	190	63			PROPN
gs-1949	190	64			NOUN
gs-1949	190	65			NOUN
gs-1949	190	66			NUM
gs-1949	190	67			PROPN
gs-1949	190	68			PROPN
gs-1949	190	69	.	.	PUNCT
gs-1949	191	1	(	(	PUNCT
gs-1949	191	2	7	7	X
gs-1949	191	3	)	)	PUNCT
gs-1949	191	4	let	let	VERB
gs-1949	191	5	us	we	PRON
gs-1949	191	6	show	show	VERB
gs-1949	191	7	that	that	SCONJ
gs-1949	191	8	the	the	DET
gs-1949	191	9	quantities	quantity	NOUN
gs-1949	191	10	nm	nm	VERB
gs-1949	191	11	and	and	CCONJ
gs-1949	191	12	nl	nl	PROPN
gs-1949	191	13	have	have	VERB
gs-1949	191	14	the	the	DET
gs-1949	191	15	same	same	ADJ
gs-1949	191	16	limiting	limiting	NOUN
gs-1949	191	17	distributions	distribution	NOUN
gs-1949	191	18	as	as	ADP
gs-1949	191	19	the	the	DET
gs-1949	191	20	quantities	quantity	NOUN
gs-1949	191	21	1	1	NUM
gs-1949	191	22	nm	nm	NOUN
gs-1949	191	23	and	and	CCONJ
gs-1949	191	24	1	1	NUM
gs-1949	191	25	nl	nl	NOUN
gs-1949	191	26	(	(	PUNCT
gs-1949	191	27	respectively	respectively	ADV
gs-1949	191	28	)	)	PUNCT
gs-1949	191	29	.	.	PUNCT
gs-1949	192	1	(	(	PUNCT
gs-1949	192	2	)	)	PUNCT
gs-1949	192	3	mr	mr	PROPN
gs-1949	192	4	x	x	PROPN
gs-1949	192	5	t	t	NOUN
gs-1949	192	6			NOUN
gs-1949	192	7	is	be	AUX
gs-1949	192	8	continuous	continuous	ADJ
gs-1949	192	9	with	with	ADP
gs-1949	192	10	respect	respect	NOUN
gs-1949	192	11	to	to	ADP
gs-1949	192	12	t	t	NOUN
gs-1949	192	13	,	,	PUNCT
gs-1949	192	14	and	and	CCONJ
gs-1949	192	15	2n	2n	NUM
gs-1949	192	16	w	w	PROPN
gs-1949	192	17	s	s	PROPN
gs-1949	192	18			X
gs-1949	192	19	,	,	PUNCT
gs-1949	192	20	therefore	therefore	ADV
gs-1949	192	21	,	,	PUNCT
gs-1949	192	22	by	by	ADP
gs-1949	192	23	virtue	virtue	NOUN
gs-1949	192	24	of	of	ADP
gs-1949	192	25	lemma	lemma	PROPN
gs-1949	192	26	2	2	NUM
gs-1949	192	27	,	,	PUNCT
gs-1949	192	28	when	when	SCONJ
gs-1949	192	29	n	n	PROPN
gs-1949	192	30	,	,	PUNCT
gs-1949	192	31	the	the	DET
gs-1949	192	32	following	follow	VERB
gs-1949	192	33	convergences	convergence	NOUN
gs-1949	192	34	are	be	AUX
gs-1949	192	35	fulfilled	fulfil	VERB
gs-1949	192	36	1	1	NUM
gs-1949	192	37	2	2	NUM
gs-1949	192	38	(	(	PUNCT
gs-1949	192	39	)	)	PUNCT
gs-1949	192	40	(	(	PUNCT
gs-1949	192	41	)	)	PUNCT
gs-1949	192	42	(	(	PUNCT
gs-1949	192	43	)	)	PUNCT
gs-1949	192	44	(	(	PUNCT
gs-1949	192	45	)	)	PUNCT
gs-1949	192	46	m	m	VERB
gs-1949	192	47	m	m	VERB
gs-1949	192	48	m	m	VERB
gs-1949	192	49	m	m	PROPN
gs-1949	192	50	w	w	ADP
gs-1949	192	51	n	n	ADP
gs-1949	192	52	r	r	NOUN
gs-1949	192	53	n	n	NOUN
gs-1949	192	54	r	r	NOUN
gs-1949	192	55	r	r	NOUN
gs-1949	192	56	rm	rm	NOUN
gs-1949	192	57	x	x	X
gs-1949	192	58	s	s	PROPN
gs-1949	192	59	x	x	X
gs-1949	192	60	y	y	NOUN
gs-1949	192	61	x	x	PROPN
gs-1949	192	62	x	x	NOUN
gs-1949	192	63	y	y	NUM
gs-1949	192	64			PROPN
gs-1949	192	65			NOUN
gs-1949	192	66			NOUN
gs-1949	192	67			ADV
gs-1949	192	68			VERB
gs-1949	192	69			NOUN
gs-1949	192	70			NOUN
gs-1949	192	71			PUNCT
gs-1949	192	72	,	,	PUNCT
gs-1949	192	73	1	1	NUM
gs-1949	192	74	2	2	NUM
gs-1949	192	75	(	(	PUNCT
gs-1949	192	76	)	)	PUNCT
gs-1949	192	77	(	(	PUNCT
gs-1949	192	78	)	)	PUNCT
gs-1949	192	79	(	(	PUNCT
gs-1949	192	80	)	)	PUNCT
gs-1949	192	81	(	(	PUNCT
gs-1949	192	82	)	)	PUNCT
gs-1949	192	83	m	m	VERB
gs-1949	192	84	m	m	VERB
gs-1949	192	85	m	m	VERB
gs-1949	192	86	m	m	PROPN
gs-1949	192	87	w	w	ADP
gs-1949	192	88	n	n	ADP
gs-1949	192	89	r	r	NOUN
gs-1949	192	90	n	n	NOUN
gs-1949	192	91	r	r	NOUN
gs-1949	192	92	r	r	NOUN
gs-1949	192	93	rl	rl	NOUN
gs-1949	192	94	x	x	SYM
gs-1949	192	95	s	s	NOUN
gs-1949	192	96	x	x	X
gs-1949	192	97	y	y	NOUN
gs-1949	192	98	x	x	PROPN
gs-1949	192	99	x	x	NOUN
gs-1949	192	100	y	y	NUM
gs-1949	192	101			PROPN
gs-1949	192	102			NOUN
gs-1949	192	103			VERB
gs-1949	192	104			PROPN
gs-1949	192	105			ADP
gs-1949	192	106			NOUN
gs-1949	192	107			VERB
gs-1949	192	108			NOUN
gs-1949	192	109	.	.	PUNCT
gs-1949	193	1	let	let	VERB
gs-1949	193	2	us	we	PRON
gs-1949	193	3	introduce	introduce	VERB
gs-1949	193	4	the	the	DET
gs-1949	193	5	distance	distance	NOUN
gs-1949	193	6	between	between	ADP
gs-1949	193	7	the	the	DET
gs-1949	193	8	functions	function	NOUN
gs-1949	193	9	(	(	PUNCT
gs-1949	193	10	)	)	PUNCT
gs-1949	193	11	f	f	PROPN
gs-1949	193	12			NUM
gs-1949	193	13	and	and	CCONJ
gs-1949	193	14	(	(	PUNCT
gs-1949	193	15	)	)	PUNCT
gs-1949	193	16	g	g	PROPN
gs-1949	193	17			PROPN
gs-1949	193	18	as	as	ADP
gs-1949	193	19	following	follow	VERB
gs-1949	193	20	:	:	PUNCT
gs-1949	193	21			PROPN
gs-1949	193	22			PROPN
gs-1949	193	23	(	(	PUNCT
gs-1949	193	24	)	)	PUNCT
gs-1949	193	25	,	,	PUNCT
gs-1949	193	26	(	(	PUNCT
gs-1949	193	27	)	)	PUNCT
gs-1949	193	28	sup	sup	NOUN
gs-1949	193	29	(	(	PUNCT
gs-1949	193	30	)	)	PUNCT
gs-1949	193	31	(	(	PUNCT
gs-1949	193	32	)	)	PUNCT
gs-1949	194	1	kx	kx	INTJ
gs-1949	195	1	r	r	NOUN
gs-1949	195	2	f	f	PROPN
gs-1949	196	1	g	g	PROPN
gs-1949	196	2	f	f	PROPN
gs-1949	196	3	x	x	SYM
gs-1949	196	4	g	g	PROPN
gs-1949	196	5	x	x	PROPN
gs-1949	196	6			NOUN
gs-1949	196	7			NUM
gs-1949	196	8			NUM
gs-1949	196	9			NUM
gs-1949	196	10			NOUN
gs-1949	196	11	.	.	PUNCT
gs-1949	197	1	it	it	PRON
gs-1949	197	2	is	be	AUX
gs-1949	197	3	clear	clear	ADJ
gs-1949	197	4	that	that	SCONJ
gs-1949	197	5	on	on	ADP
gs-1949	197	6	a	a	DET
gs-1949	197	7	fixed	fix	VERB
gs-1949	197	8	trajectory	trajectory	NOUN
gs-1949	197	9			NOUN
gs-1949	197	10	1	1	VERB
gs-1949	197	11	1	1	NUM
gs-1949	197	12	2	2	NUM
gs-1949	197	13	,	,	PUNCT
gs-1949	197	14	,	,	PUNCT
gs-1949	197	15	..	..	PUNCT
gs-1949	197	16	,	,	PUNCT
gs-1949	197	17	n	n	PRON
gs-1949	197	18	n	n	PRON
gs-1949	197	19			NOUN
gs-1949	197	20			NOUN
gs-1949	197	21			PUNCT
gs-1949	197	22	,	,	PUNCT
gs-1949	197	23	the	the	DET
gs-1949	197	24	sum	sum	NOUN
gs-1949	197	25	2ns	2ns	NOUN
gs-1949	197	26	becomes	become	VERB
gs-1949	197	27	equal	equal	ADJ
gs-1949	197	28	to	to	ADP
gs-1949	197	29	some	some	DET
gs-1949	197	30	specific	specific	ADJ
gs-1949	197	31	(	(	PUNCT
gs-1949	197	32	trajectory	trajectory	NOUN
gs-1949	197	33	dependent	dependent	ADJ
gs-1949	197	34	)	)	PUNCT
gs-1949	197	35	number	number	NOUN
gs-1949	197	36	.	.	PUNCT
gs-1949	198	1	therefore	therefore	ADV
gs-1949	198	2	,	,	PUNCT
gs-1949	198	3	it	it	PRON
gs-1949	198	4	is	be	AUX
gs-1949	198	5	clear	clear	ADJ
gs-1949	198	6	that	that	SCONJ
gs-1949	198	7	the	the	DET
gs-1949	198	8	following	follow	VERB
gs-1949	198	9	equations	equation	NOUN
gs-1949	198	10	hold	hold	VERB
gs-1949	198	11			NOUN
gs-1949	198	12			SYM
gs-1949	198	13			NOUN
gs-1949	198	14	1	1	ADJ
gs-1949	198	15	1	1	NUM
gs-1949	198	16	,	,	PUNCT
gs-1949	198	17	,	,	PUNCT
gs-1949	198	18	n	n	CCONJ
gs-1949	198	19	n	n	CCONJ
gs-1949	198	20	n	n	ADV
gs-1949	198	21	nm	nm	ADV
gs-1949	198	22	m	m	VERB
gs-1949	198	23	l	l	NOUN
gs-1949	198	24	l	l	NOUN
gs-1949	198	25			NOUN
gs-1949	198	26			NUM
gs-1949	198	27	1	1	NUM
gs-1949	198	28	1	1	NUM
gs-1949	198	29	1	1	NUM
gs-1949	198	30	1	1	NUM
gs-1949	198	31	2	2	NUM
gs-1949	198	32	2sup	2sup	NUM
gs-1949	198	33	(	(	PUNCT
gs-1949	198	34	)	)	PUNCT
gs-1949	198	35	(	(	PUNCT
gs-1949	198	36	)	)	PUNCT
gs-1949	198	37	sup	sup	NOUN
gs-1949	198	38	(	(	PUNCT
gs-1949	198	39	)	)	PUNCT
gs-1949	198	40	(	(	PUNCT
gs-1949	198	41	)	)	PUNCT
gs-1949	198	42	m	m	VERB
gs-1949	198	43	mn	mn	PROPN
gs-1949	198	44	n	n	PROPN
gs-1949	198	45	n	n	CCONJ
gs-1949	198	46	n	n	CCONJ
gs-1949	198	47	n	n	ADP
gs-1949	198	48	r	r	NOUN
gs-1949	198	49	n	n	NUM
gs-1949	198	50	rs	rs	NOUN
gs-1949	198	51	s	s	PROPN
gs-1949	198	52	k	k	X
gs-1949	198	53	kx	kx	PROPN
gs-1949	199	1	r	r	NOUN
gs-1949	199	2	x	x	PUNCT
gs-1949	199	3	r	r	NOUN
gs-1949	199	4	f	f	X
gs-1949	199	5	x	x	SYM
gs-1949	199	6	s	s	PROPN
gs-1949	199	7	x	x	X
gs-1949	199	8	s	s	X
gs-1949	199	9	f	f	X
gs-1949	199	10	x	x	PUNCT
gs-1949	199	11	x	x	SYM
gs-1949	199	12			PRON
gs-1949	199	13			VERB
gs-1949	199	14			NOUN
gs-1949	199	15			NOUN
gs-1949	199	16			PROPN
gs-1949	199	17			PROPN
gs-1949	199	18			VERB
gs-1949	199	19			PROPN
gs-1949	199	20			PROPN
gs-1949	199	21			NOUN
gs-1949	199	22	.	.	PUNCT
gs-1949	200	1	by	by	ADP
gs-1949	200	2	virtue	virtue	NOUN
gs-1949	200	3	of	of	ADP
gs-1949	200	4	lemma	lemma	PROPN
gs-1949	200	5	1	1	NUM
gs-1949	200	6	,	,	PUNCT
gs-1949	200	7	when	when	SCONJ
gs-1949	200	8	n	n	PROPN
gs-1949	200	9	we	we	PRON
gs-1949	200	10	have	have	VERB
gs-1949	200	11	1	1	NUM
gs-1949	200	12	1	1	NUM
gs-1949	200	13	sup	sup	NOUN
gs-1949	200	14	(	(	PUNCT
gs-1949	200	15	)	)	PUNCT
gs-1949	200	16	(	(	PUNCT
gs-1949	200	17	)	)	PUNCT
gs-1949	200	18	0	0	NUM
gs-1949	201	1	mn	mn	PROPN
gs-1949	201	2	n	n	NUM
gs-1949	201	3	rs	rs	NOUN
gs-1949	202	1	kx	kx	INTJ
gs-1949	202	2	r	r	NOUN
gs-1949	202	3	f	f	PROPN
gs-1949	202	4	x	x	NOUN
gs-1949	202	5	x	x	SYM
gs-1949	202	6			VERB
gs-1949	202	7			NOUN
gs-1949	202	8			NOUN
gs-1949	202	9			NOUN
gs-1949	202	10	a.	a.	PROPN
gs-1949	202	11	e.	e.	PROPN
gs-1949	202	12	therefore	therefore	ADV
gs-1949	202	13			PROPN
gs-1949	202	14	1	1	PROPN
gs-1949	202	15	,	,	PUNCT
gs-1949	202	16	m	m	PROPN
gs-1949	202	17	0p	0p	NUM
gs-1949	202	18	n	n	PRON
gs-1949	202	19	nm	nm	PROPN
gs-1949	202	20			PROPN
gs-1949	202	21	,	,	PUNCT
gs-1949	202	22			PROPN
gs-1949	202	23	1	1	NOUN
gs-1949	202	24	,	,	PUNCT
gs-1949	202	25	0p	0p	PROPN
gs-1949	202	26	n	n	CCONJ
gs-1949	202	27	nl	nl	PROPN
gs-1949	202	28	l	l	NOUN
gs-1949	202	29			PROPN
gs-1949	202	30	.	.	PUNCT
gs-1949	203	1	by	by	ADP
gs-1949	203	2	virtue	virtue	NOUN
gs-1949	203	3	of	of	ADP
gs-1949	203	4	lemma	lemma	PROPN
gs-1949	203	5	3	3	NUM
gs-1949	203	6	,	,	PUNCT
gs-1949	203	7	we	we	PRON
gs-1949	203	8	will	will	AUX
gs-1949	203	9	have	have	VERB
gs-1949	203	10	(	(	PUNCT
gs-1949	203	11	)	)	PUNCT
gs-1949	203	12	(	(	PUNCT
gs-1949	203	13	)	)	PUNCT
gs-1949	203	14	m	m	VERB
gs-1949	203	15	m	m	VERB
gs-1949	203	16	w	w	ADP
gs-1949	203	17	n	n	ADP
gs-1949	203	18	r	r	NOUN
gs-1949	203	19	rm	rm	NOUN
gs-1949	203	20	x	x	PUNCT
gs-1949	204	1	x	x	PUNCT
gs-1949	204	2	y	y	PROPN
gs-1949	204	3			NOUN
gs-1949	204	4			NOUN
gs-1949	204	5			PUNCT
gs-1949	204	6	,	,	PUNCT
gs-1949	204	7	georgian	georgian	ADJ
gs-1949	204	8	scientists/ქართველი	scientists/ქართველი	NOUN
gs-1949	204	9	მეცნიერები	მეცნიერები	NOUN
gs-1949	204	10	ტ.	ტ.	VERB
gs-1949	204	11	5	5	NUM
gs-1949	204	12	n	n	PRON
gs-1949	204	13	2	2	NUM
gs-1949	204	14	,	,	PUNCT
gs-1949	204	15	2023	2023	NUM
gs-1949	204	16	27	27	NUM
gs-1949	204	17	(	(	PUNCT
gs-1949	204	18	)	)	PUNCT
gs-1949	204	19	(	(	PUNCT
gs-1949	204	20	)	)	PUNCT
gs-1949	204	21	m	m	VERB
gs-1949	204	22	m	m	VERB
gs-1949	204	23	w	w	ADP
gs-1949	204	24	n	n	ADV
gs-1949	204	25	r	r	NOUN
gs-1949	204	26	rl	rl	NOUN
gs-1949	204	27	x	x	SYM
gs-1949	204	28	x	x	PUNCT
gs-1949	204	29	y	y	PROPN
gs-1949	204	30			NOUN
gs-1949	204	31			VERB
gs-1949	204	32			NOUN
gs-1949	204	33	.	.	PUNCT
gs-1949	205	1	we	we	PRON
gs-1949	205	2	have	have	AUX
gs-1949	205	3	obtained	obtain	VERB
gs-1949	205	4	that	that	SCONJ
gs-1949	205	5	the	the	DET
gs-1949	205	6	random	random	ADJ
gs-1949	205	7	vectors	vector	NOUN
gs-1949	205	8	nm	nm	VERB
gs-1949	205	9	and	and	CCONJ
gs-1949	205	10	nl	nl	PROPN
gs-1949	205	11	have	have	VERB
gs-1949	205	12	the	the	DET
gs-1949	205	13	same	same	ADJ
gs-1949	205	14	limiting	limiting	NOUN
gs-1949	205	15	distributions	distribution	NOUN
gs-1949	205	16	as	as	ADP
gs-1949	205	17	the	the	DET
gs-1949	205	18	vectors	vector	NOUN
gs-1949	205	19	1	1	NUM
gs-1949	205	20	nm	nm	NOUN
gs-1949	205	21	and	and	CCONJ
gs-1949	205	22	1	1	NUM
gs-1949	205	23	nl	nl	NOUN
gs-1949	205	24	.	.	PUNCT
gs-1949	206	1	according	accord	VERB
gs-1949	206	2	to	to	ADP
gs-1949	206	3	equalities	equality	NOUN
gs-1949	206	4	(	(	PUNCT
gs-1949	206	5	5	5	NUM
gs-1949	206	6	)	)	PUNCT
gs-1949	206	7	and	and	CCONJ
gs-1949	206	8	(	(	PUNCT
gs-1949	206	9	6	6	X
gs-1949	206	10	)	)	PUNCT
gs-1949	206	11	we	we	PRON
gs-1949	206	12	will	will	AUX
gs-1949	206	13	have	have	VERB
gs-1949	206	14			PROPN
gs-1949	206	15			PROPN
gs-1949	206	16			PROPN
gs-1949	206	17			PROPN
gs-1949	206	18			PROPN
gs-1949	206	19			NOUN
gs-1949	206	20			PROPN
gs-1949	206	21	1	1	NUM
gs-1949	206	22	lim	lim	PROPN
gs-1949	206	23	p	p	PROPN
gs-1949	206	24	(	(	PUNCT
gs-1949	206	25	)	)	PUNCT
gs-1949	206	26	(	(	PUNCT
gs-1949	206	27	)	)	PUNCT
gs-1949	206	28	(	(	PUNCT
gs-1949	206	29	)	)	PUNCT
gs-1949	206	30	lim	lim	PROPN
gs-1949	206	31	p	p	NOUN
gs-1949	206	32	0	0	PUNCT
gs-1949	207	1	+	+	NOUN
gs-1949	207	2	p	p	NOUN
gs-1949	207	3	0	0	NUM
gs-1949	207	4	1	1	NUM
gs-1949	207	5	m	m	NOUN
gs-1949	207	6	mn	mn	NOUN
gs-1949	207	7	n	n	ADV
gs-1949	207	8	r	r	NOUN
gs-1949	207	9	r	r	NOUN
gs-1949	207	10	n	n	CCONJ
gs-1949	207	11	nsn	nsn	PROPN
gs-1949	208	1	n	n	CCONJ
gs-1949	208	2	x	x	PROPN
gs-1949	208	3	y	y	NOUN
gs-1949	208	4	f	f	NOUN
gs-1949	208	5	x	x	PUNCT
gs-1949	208	6	x	x	PUNCT
gs-1949	208	7	y	y	PROPN
gs-1949	208	8	m	m	VERB
gs-1949	208	9	l	l	NOUN
gs-1949	208	10			NOUN
gs-1949	208	11			NOUN
gs-1949	208	12			NOUN
gs-1949	208	13			VERB
gs-1949	208	14			NOUN
gs-1949	208	15			NOUN
gs-1949	208	16			NOUN
gs-1949	208	17			VERB
gs-1949	208	18			NUM
gs-1949	208	19			PROPN
gs-1949	208	20			NUM
gs-1949	208	21			NOUN
gs-1949	208	22			NUM
gs-1949	208	23			PROPN
gs-1949	208	24			PROPN
gs-1949	208	25			PROPN
gs-1949	208	26			NOUN
gs-1949	209	1			PROPN
gs-1949	209	2			NOUN
gs-1949	209	3	1	1	NOUN
gs-1949	209	4	1	1	NUM
gs-1949	209	5	2lim	2lim	NUM
gs-1949	209	6	p	p	NOUN
gs-1949	209	7	0	0	PUNCT
gs-1949	210	1	+	+	NOUN
gs-1949	210	2	p	p	NOUN
gs-1949	210	3	0	0	NUM
gs-1949	210	4	1	1	NUM
gs-1949	210	5	lim	lim	NOUN
gs-1949	210	6	p	p	PROPN
gs-1949	210	7	(	(	PUNCT
gs-1949	210	8	)	)	PUNCT
gs-1949	210	9	(	(	PUNCT
gs-1949	210	10	)	)	PUNCT
gs-1949	210	11	(	(	PUNCT
gs-1949	210	12	)	)	PUNCT
gs-1949	210	13	m	m	VERB
gs-1949	210	14	m	m	VERB
gs-1949	210	15	mn	mn	PROPN
gs-1949	210	16	n	n	ADV
gs-1949	210	17	r	r	NOUN
gs-1949	210	18	r	r	NOUN
gs-1949	210	19	n	n	ADP
gs-1949	210	20	r	r	NOUN
gs-1949	210	21	n	n	NOUN
gs-1949	210	22	n	n	NOUN
gs-1949	210	23	m	m	VERB
gs-1949	210	24	l	l	NOUN
gs-1949	210	25	x	x	X
gs-1949	210	26	y	y	NOUN
gs-1949	210	27	x	x	X
gs-1949	210	28	s	s	NOUN
gs-1949	210	29	x	x	X
gs-1949	210	30	y	y	NOUN
gs-1949	210	31			NOUN
gs-1949	210	32			NOUN
gs-1949	210	33			PROPN
gs-1949	210	34			PROPN
gs-1949	210	35			NUM
gs-1949	210	36			VERB
gs-1949	210	37			PROPN
gs-1949	210	38			PROPN
gs-1949	210	39			NOUN
gs-1949	210	40			NOUN
gs-1949	210	41			NOUN
gs-1949	210	42			VERB
gs-1949	210	43			NOUN
gs-1949	210	44			PROPN
gs-1949	210	45			ADV
gs-1949	210	46			NUM
gs-1949	210	47	(	(	PUNCT
gs-1949	210	48	)	)	PUNCT
gs-1949	210	49	(	(	PUNCT
gs-1949	210	50	)	)	PUNCT
gs-1949	210	51	q	q	PROPN
gs-1949	210	52	y	y	PROPN
gs-1949	210	53	q	q	PROPN
gs-1949	210	54	y	y	PROPN
gs-1949	210	55			PROPN
gs-1949	210	56			VERB
gs-1949	210	57	the	the	DET
gs-1949	210	58	proof	proof	NOUN
gs-1949	210	59	of	of	ADP
gs-1949	210	60	point	point	NOUN
gs-1949	210	61	b	b	NOUN
gs-1949	210	62	)	)	PUNCT
gs-1949	210	63	is	be	AUX
gs-1949	210	64	obtained	obtain	VERB
gs-1949	210	65	from	from	ADP
gs-1949	210	66	the	the	DET
gs-1949	210	67	fact	fact	NOUN
gs-1949	210	68	that	that	SCONJ
gs-1949	210	69	the	the	DET
gs-1949	210	70	random	random	ADJ
gs-1949	210	71	vectors	vector	NOUN
gs-1949	210	72	nm	nm	VERB
gs-1949	210	73	and	and	CCONJ
gs-1949	210	74	nl	nl	PROPN
gs-1949	210	75	have	have	AUX
gs-1949	210	76	the	the	DET
gs-1949	210	77	same	same	ADJ
gs-1949	210	78	limiting	limiting	NOUN
gs-1949	210	79	distributions	distribution	NOUN
gs-1949	210	80	as	as	ADP
gs-1949	210	81	the	the	DET
gs-1949	210	82	vectors	vector	NOUN
gs-1949	210	83	1	1	NUM
gs-1949	210	84	nm	nm	NOUN
gs-1949	210	85	and	and	CCONJ
gs-1949	210	86	1	1	NUM
gs-1949	210	87	nl	nl	NOUN
gs-1949	210	88	respectively	respectively	ADV
gs-1949	210	89	.	.	PUNCT
gs-1949	211	1	according	accord	VERB
gs-1949	211	2	to	to	ADP
gs-1949	211	3	equalities	equality	NOUN
gs-1949	211	4	(	(	PUNCT
gs-1949	211	5	5	5	NUM
gs-1949	211	6	)	)	PUNCT
gs-1949	211	7	and	and	CCONJ
gs-1949	211	8	(	(	PUNCT
gs-1949	211	9	6	6	X
gs-1949	211	10	)	)	PUNCT
gs-1949	211	11	we	we	PRON
gs-1949	211	12	will	will	AUX
gs-1949	211	13	have	have	VERB
gs-1949	211	14			PROPN
gs-1949	212	1	2lim	2lim	PRON
gs-1949	212	2	p	p	NOUN
gs-1949	212	3	(	(	PUNCT
gs-1949	212	4	)	)	PUNCT
gs-1949	212	5	(	(	PUNCT
gs-1949	212	6	)	)	PUNCT
gs-1949	212	7	(	(	PUNCT
gs-1949	212	8	)	)	PUNCT
gs-1949	212	9	m	m	VERB
gs-1949	212	10	m	m	VERB
gs-1949	212	11	mr	mr	PROPN
gs-1949	212	12	r	r	PROPN
gs-1949	212	13	n	n	CCONJ
gs-1949	212	14	r	r	NOUN
gs-1949	212	15	n	n	NOUN
gs-1949	212	16	x	x	SYM
gs-1949	212	17	y	y	NOUN
gs-1949	212	18	x	x	X
gs-1949	212	19	s	s	NOUN
gs-1949	212	20	x	x	X
gs-1949	212	21	y	y	NOUN
gs-1949	212	22			NOUN
gs-1949	212	23			PROPN
gs-1949	212	24			VERB
gs-1949	212	25			NOUN
gs-1949	212	26			NOUN
gs-1949	212	27			VERB
gs-1949	212	28			NOUN
gs-1949	212	29			NOUN
gs-1949	212	30			PUNCT
gs-1949	212	31			PROPN
gs-1949	212	32			PROPN
gs-1949	212	33			PROPN
gs-1949	212	34			PROPN
gs-1949	212	35			NOUN
gs-1949	212	36			PROPN
gs-1949	212	37			PROPN
gs-1949	212	38			PROPN
gs-1949	212	39			PROPN
gs-1949	212	40			NOUN
gs-1949	212	41	1	1	VERB
gs-1949	212	42	1lim	1lim	NUM
gs-1949	212	43	p	p	NOUN
gs-1949	212	44	0	0	PUNCT
gs-1949	213	1	+	+	NOUN
gs-1949	213	2	p	p	NOUN
gs-1949	213	3	0	0	NUM
gs-1949	213	4	1	1	NUM
gs-1949	213	5	lim	lim	NOUN
gs-1949	213	6	p	p	NOUN
gs-1949	213	7	0	0	PUNCT
gs-1949	214	1	+	+	NOUN
gs-1949	214	2	p	p	NOUN
gs-1949	214	3	0	0	NUM
gs-1949	214	4	1n	1n	NUM
gs-1949	214	5	n	n	CCONJ
gs-1949	214	6	n	n	CCONJ
gs-1949	214	7	n	n	CCONJ
gs-1949	214	8	n	n	CCONJ
gs-1949	214	9	n	n	NOUN
gs-1949	214	10	m	m	PROPN
gs-1949	214	11	l	l	NOUN
gs-1949	214	12	m	m	VERB
gs-1949	214	13	l	l	NOUN
gs-1949	214	14			NOUN
gs-1949	214	15			NOUN
gs-1949	214	16			PROPN
gs-1949	214	17			PROPN
gs-1949	214	18			NUM
gs-1949	214	19			PROPN
gs-1949	214	20			PROPN
gs-1949	214	21			PROPN
gs-1949	214	22			NUM
gs-1949	214	23			NOUN
gs-1949	214	24			NUM
gs-1949	214	25			PROPN
gs-1949	214	26			PROPN
gs-1949	214	27	1	1	NUM
gs-1949	214	28	lim	lim	NOUN
gs-1949	214	29	p	p	PROPN
gs-1949	214	30	(	(	PUNCT
gs-1949	214	31	)	)	PUNCT
gs-1949	214	32	(	(	PUNCT
gs-1949	214	33	)	)	PUNCT
gs-1949	214	34	(	(	PUNCT
gs-1949	214	35	)	)	PUNCT
gs-1949	214	36	(	(	PUNCT
gs-1949	214	37	)	)	PUNCT
gs-1949	214	38	(	(	PUNCT
gs-1949	214	39	)	)	PUNCT
gs-1949	214	40	m	m	VERB
gs-1949	214	41	mn	mn	PROPN
gs-1949	214	42	n	n	PROPN
gs-1949	214	43	r	r	NOUN
gs-1949	214	44	rsn	rsn	NOUN
gs-1949	214	45	x	x	X
gs-1949	214	46	y	y	NOUN
gs-1949	214	47	f	f	PROPN
gs-1949	215	1	x	x	PUNCT
gs-1949	215	2	x	x	PUNCT
gs-1949	215	3	y	y	VERB
gs-1949	215	4	q	q	PROPN
gs-1949	215	5	y	y	PROPN
gs-1949	215	6	q	q	PROPN
gs-1949	215	7	y	y	PROPN
gs-1949	215	8			VERB
gs-1949	215	9			PROPN
gs-1949	215	10			PROPN
gs-1949	215	11			VERB
gs-1949	215	12			NOUN
gs-1949	215	13			NOUN
gs-1949	215	14			NOUN
gs-1949	215	15			PUNCT
gs-1949	215	16			PUNCT
gs-1949	215	17			VERB
gs-1949	215	18			NOUN
gs-1949	215	19	.	.	PUNCT
gs-1949	216	1	on	on	ADP
gs-1949	216	2	the	the	DET
gs-1949	216	3	other	other	ADJ
gs-1949	216	4	hand	hand	NOUN
gs-1949	216	5			PROPN
gs-1949	216	6			PROPN
gs-1949	216	7			PROPN
gs-1949	216	8	2	2	NOUN
gs-1949	216	9	2p	2p	NOUN
gs-1949	216	10	(	(	PUNCT
gs-1949	216	11	)	)	PUNCT
gs-1949	216	12	(	(	PUNCT
gs-1949	216	13	)	)	PUNCT
gs-1949	216	14	(	(	PUNCT
gs-1949	216	15	)	)	PUNCT
gs-1949	217	1	p	p	X
gs-1949	217	2	m	m	NOUN
gs-1949	217	3	m	m	VERB
gs-1949	217	4	mr	mr	PROPN
gs-1949	217	5	r	r	PROPN
gs-1949	217	6	n	n	NOUN
gs-1949	217	7	r	r	NOUN
gs-1949	217	8	nx	nx	NOUN
gs-1949	217	9	y	y	PROPN
gs-1949	217	10	x	x	X
gs-1949	217	11	s	s	X
gs-1949	217	12	x	x	X
gs-1949	217	13	y	y	PROPN
gs-1949	217	14	y	y	PROPN
gs-1949	217	15	s	s	PROPN
gs-1949	217	16	y	y	PROPN
gs-1949	217	17			NOUN
gs-1949	217	18			NOUN
gs-1949	217	19			NOUN
gs-1949	217	20			VERB
gs-1949	217	21			NOUN
gs-1949	217	22			NOUN
gs-1949	217	23			PUNCT
gs-1949	217	24			VERB
gs-1949	217	25			PROPN
gs-1949	217	26			NOUN
gs-1949	217	27			NOUN
gs-1949	217	28	from	from	ADP
gs-1949	217	29	this	this	PRON
gs-1949	217	30	we	we	PRON
gs-1949	217	31	will	will	AUX
gs-1949	217	32	obtain	obtain	VERB
gs-1949	217	33	b	b	NOUN
gs-1949	217	34	)	)	PUNCT
gs-1949	217	35	.	.	PUNCT
gs-1949	218	1	let	let	VERB
gs-1949	218	2	’s	’s	NOUN
gs-1949	218	3	suppose	suppose	VERB
gs-1949	218	4	that	that	SCONJ
gs-1949	218	5			PROPN
gs-1949	218	6			PROPN
gs-1949	218	7	1n	1n	NUM
gs-1949	218	8	n	n	PRON
gs-1949	218	9			NOUN
gs-1949	218	10			NUM
gs-1949	218	11	is	be	AUX
gs-1949	218	12	a	a	DET
gs-1949	218	13	finite	finite	ADJ
gs-1949	218	14	,	,	PUNCT
gs-1949	218	15	homogeneous	homogeneous	ADJ
gs-1949	218	16	,	,	PUNCT
gs-1949	218	17	stationary	stationary	ADJ
gs-1949	218	18	,	,	PUNCT
gs-1949	218	19	ergodic	ergodic	ADJ
gs-1949	218	20	markov	markov	NOUN
gs-1949	218	21	chain	chain	NOUN
gs-1949	218	22	with	with	ADP
gs-1949	218	23	one	one	NUM
gs-1949	218	24	class	class	NOUN
gs-1949	218	25	of	of	ADP
gs-1949	218	26	ergodicity	ergodicity	NOUN
gs-1949	218	27	,	,	PUNCT
gs-1949	218	28	which	which	PRON
gs-1949	218	29	may	may	AUX
gs-1949	218	30	contain	contain	VERB
gs-1949	218	31	cyclic	cyclic	ADJ
gs-1949	218	32	subclasses	subclass	NOUN
gs-1949	218	33	.	.	PUNCT
gs-1949	219	1	let	let	VERB
gs-1949	219	2	's	us	PRON
gs-1949	219	3	say	say	VERB
gs-1949	219	4	the	the	DET
gs-1949	219	5	set	set	NOUN
gs-1949	219	6	of	of	ADP
gs-1949	219	7	states	state	NOUN
gs-1949	219	8	of	of	ADP
gs-1949	219	9	the	the	DET
gs-1949	219	10	markov	markov	NOUN
gs-1949	219	11	chain	chain	NOUN
gs-1949	219	12	is	be	AUX
gs-1949	219	13			PROPN
gs-1949	219	14	1	1	NOUN
gs-1949	219	15	2	2	NUM
gs-1949	219	16	,	,	PUNCT
gs-1949	219	17	,	,	PUNCT
gs-1949	219	18	...	...	PUNCT
gs-1949	219	19	,	,	PUNCT
gs-1949	219	20	rb	rb	PROPN
gs-1949	219	21	b	b	PROPN
gs-1949	219	22	b	b	NOUN
gs-1949	219	23			PROPN
gs-1949	219	24	.	.	PUNCT
gs-1949	220	1	the	the	DET
gs-1949	220	2	limiting	limit	VERB
gs-1949	220	3	stationary	stationary	ADJ
gs-1949	220	4	distribution	distribution	NOUN
gs-1949	220	5	is	be	AUX
gs-1949	220	6	1	1	NUM
gs-1949	220	7	2	2	NUM
gs-1949	220	8	(	(	PUNCT
gs-1949	220	9	,	,	PUNCT
gs-1949	220	10	,	,	PUNCT
gs-1949	220	11	...	...	PUNCT
gs-1949	220	12	,	,	PUNCT
gs-1949	220	13	)	)	PUNCT
gs-1949	220	14	r	r	VERB
gs-1949	220	15			PROPN
gs-1949	220	16			PROPN
gs-1949	220	17			NOUN
gs-1949	220	18	.	.	PUNCT
gs-1949	221	1	consider	consider	VERB
gs-1949	221	2	a	a	DET
gs-1949	221	3	function	function	NOUN
gs-1949	221	4	:	:	PUNCT
gs-1949	221	5	kf	kf	PROPN
gs-1949	221	6	r	r	PROPN
gs-1949	221	7	defined	define	VERB
gs-1949	221	8	on	on	ADP
gs-1949	221	9	a	a	DET
gs-1949	221	10	chain	chain	NOUN
gs-1949	221	11	that	that	PRON
gs-1949	221	12	satisfies	satisfy	VERB
gs-1949	221	13	the	the	DET
gs-1949	221	14	conditions	condition	NOUN
gs-1949	221	15	of	of	ADP
gs-1949	221	16	lemma	lemma	PROPN
gs-1949	221	17	1	1	NUM
gs-1949	221	18	.	.	PUNCT
gs-1949	222	1	in	in	ADP
gs-1949	222	2	this	this	DET
gs-1949	222	3	case	case	NOUN
gs-1949	222	4	,	,	PUNCT
gs-1949	222	5	it	it	PRON
gs-1949	222	6	is	be	AUX
gs-1949	222	7	known	know	VERB
gs-1949	222	8	(	(	PUNCT
gs-1949	222	9	see	see	VERB
gs-1949	222	10	[	[	X
gs-1949	222	11	8	8	NUM
gs-1949	222	12	]	]	PUNCT
gs-1949	222	13	)	)	PUNCT
gs-1949	223	1	that	that	SCONJ
gs-1949	223	2	for	for	ADP
gs-1949	223	3	the	the	DET
gs-1949	223	4	sum	sum	NOUN
gs-1949	223	5	1	1	NUM
gs-1949	223	6	1	1	NUM
gs-1949	223	7	[	[	PUNCT
gs-1949	223	8	(	(	PUNCT
gs-1949	223	9	)	)	PUNCT
gs-1949	223	10	(	(	PUNCT
gs-1949	223	11	)	)	PUNCT
gs-1949	223	12	]	]	PUNCT
gs-1949	223	13	n	n	CCONJ
gs-1949	223	14	n	n	PRON
gs-1949	223	15	j	j	PROPN
gs-1949	223	16	j	j	PROPN
gs-1949	223	17	j	j	PROPN
gs-1949	223	18	u	u	X
gs-1949	223	19	f	f	PROPN
gs-1949	223	20	ef	ef	PROPN
gs-1949	223	21	n	n	PRON
gs-1949	223	22			NOUN
gs-1949	223	23			PUNCT
gs-1949	223	24			NUM
gs-1949	223	25			NOUN
gs-1949	223	26			PROPN
gs-1949	223	27	when	when	SCONJ
gs-1949	223	28	n	n	ADJ
gs-1949	223	29	thefollowing	thefollowing	NOUN
gs-1949	223	30	convergences	convergence	NOUN
gs-1949	223	31	take	take	VERB
gs-1949	223	32	place	place	NOUN
gs-1949	223	33			NOUN
gs-1949	223	34	cov	cov	NOUN
gs-1949	223	35	n	n	CCONJ
gs-1949	223	36	fu	fu	NOUN
gs-1949	223	37	t	t	X
gs-1949	223	38	,	,	PUNCT
gs-1949	223	39	n	n	PROPN
gs-1949	223	40	f	f	NOUN
gs-1949	223	41	w	w	NOUN
gs-1949	223	42	u	u	PROPN
gs-1949	223	43	t	t	NOUN
gs-1949	223	44	.	.	PUNCT
gs-1949	224	1	matrix	matrix	NOUN
gs-1949	224	2			NOUN
gs-1949	224	3			PROPN
gs-1949	224	4	,	,	PUNCT
gs-1949	224	5	,	,	PUNCT
gs-1949	224	6	1,i	1,i	PROPN
gs-1949	225	1	jf	jf	PROPN
gs-1949	225	2	f	f	PROPN
gs-1949	226	1	i	i	PRON
gs-1949	226	2	j	j	PROPN
gs-1949	227	1	k	k	PROPN
gs-1949	227	2	t	t	PROPN
gs-1949	227	3	t	t	PROPN
gs-1949	227	4			PRON
gs-1949	228	1			ADJ
gs-1949	228	2	elements	element	NOUN
gs-1949	228	3	are	be	AUX
gs-1949	228	4	expressed	express	VERB
gs-1949	228	5	by	by	ADP
gs-1949	228	6	markov	markov	NOUN
gs-1949	228	7	chain	chain	NOUN
gs-1949	228	8	parameters	parameter	NOUN
gs-1949	228	9	,	,	PUNCT
gs-1949	228	10	,	,	PUNCT
gs-1949	228	11	(	(	PUNCT
gs-1949	228	12	)	)	PUNCT
gs-1949	228	13	(	(	PUNCT
gs-1949	228	14	)	)	PUNCT
gs-1949	228	15	(	(	PUNCT
gs-1949	228	16	)	)	PUNCT
gs-1949	229	1	i	i	PRON
gs-1949	229	2	j	j	NOUN
gs-1949	230	1	r	r	NOUN
gs-1949	230	2	f	f	PROPN
gs-1949	231	1	i	i	PRON
gs-1949	231	2	jt	jt	PROPN
gs-1949	231	3	z	z	PROPN
gs-1949	232	1	z	z	PROPN
gs-1949	233	1	f	f	PROPN
gs-1949	234	1	f	f	PROPN
gs-1949	234	2			ADJ
gs-1949	234	3			PROPN
gs-1949	234	4			NOUN
gs-1949	234	5			X
gs-1949	234	6			PROPN
gs-1949	234	7			X
gs-1949	234	8			ADJ
gs-1949	234	9			X
gs-1949	234	10			PROPN
gs-1949	234	11			PROPN
gs-1949	234	12			PROPN
gs-1949	234	13			PROPN
gs-1949	234	14			PROPN
gs-1949	234	15			PROPN
gs-1949	234	16			NUM
gs-1949	234	17			NOUN
gs-1949	234	18			VERB
gs-1949	234	19			PUNCT
gs-1949	234	20			PROPN
gs-1949	234	21			PROPN
gs-1949	234	22	,	,	PUNCT
gs-1949	234	23	,	,	PUNCT
gs-1949	234	24	1,i	1,i	PROPN
gs-1949	234	25	j	j	PROPN
gs-1949	234	26	k	k	NOUN
gs-1949	234	27	.	.	PUNCT
gs-1949	235	1	(	(	PUNCT
gs-1949	235	2	8)	8)	NUM
gs-1949	235	3	where	where	SCONJ
gs-1949	235	4	z	z	NOUN
gs-1949	235	5	is	be	AUX
gs-1949	235	6	the	the	DET
gs-1949	235	7	fundamental	fundamental	ADJ
gs-1949	235	8	matrix	matrix	NOUN
gs-1949	235	9	of	of	ADP
gs-1949	235	10	the	the	DET
gs-1949	235	11	chain	chain	NOUN
gs-1949	235	12	1	1	NUM
gs-1949	235	13	,	,	PUNCT
gs-1949	235	14	1	1	NUM
gs-1949	235	15	,	,	PUNCT
gs-1949	235	16	1	1	NUM
gs-1949	235	17	[	[	PUNCT
gs-1949	235	18	(	(	PUNCT
gs-1949	235	19	)	)	PUNCT
gs-1949	235	20	]	]	PUNCT
gs-1949	235	21	(	(	PUNCT
gs-1949	235	22	)	)	PUNCT
gs-1949	235	23	j	j	PROPN
gs-1949	235	24	r	r	NOUN
gs-1949	235	25	j	j	PROPN
gs-1949	235	26	c	c	NOUN
gs-1949	235	27	z	z	NOUN
gs-1949	236	1	i	i	PRON
gs-1949	236	2	p	p	VERB
gs-1949	237	1	i	i	PRON
gs-1949	237	2	p	p	ADJ
gs-1949	237	3	z	z	NOUN
gs-1949	237	4			X
gs-1949	237	5			PROPN
gs-1949	237	6			VERB
gs-1949	237	7			PROPN
gs-1949	237	8			NUM
gs-1949	238	1			NUM
gs-1949	238	2			NOUN
gs-1949	238	3			NOUN
gs-1949	238	4			PROPN
gs-1949	238	5			PROPN
gs-1949	238	6			PROPN
gs-1949	238	7			PROPN
gs-1949	238	8			PROPN
gs-1949	238	9			PROPN
gs-1949	238	10			PUNCT
gs-1949	238	11			PROPN
gs-1949	238	12			PROPN
gs-1949	238	13			NOUN
gs-1949	238	14			X
gs-1949	238	15	,	,	PUNCT
gs-1949	238	16	,	,	PUNCT
gs-1949	238	17	1	1	NUM
gs-1949	238	18	,	,	PUNCT
gs-1949	238	19	,	,	PUNCT
gs-1949	238	20	,	,	PUNCT
gs-1949	238	21	,	,	PUNCT
gs-1949	238	22	1	1	NUM
gs-1949	238	23	,	,	PUNCT
gs-1949	238	24	r	r	NOUN
gs-1949	238	25	r	r	ADJ
gs-1949	238	26			ADJ
gs-1949	238	27			NOUN
gs-1949	239	1			PROPN
gs-1949	239	2			PROPN
gs-1949	239	3			PROPN
gs-1949	239	4			ADJ
gs-1949	239	5			NOUN
gs-1949	239	6			PROPN
gs-1949	239	7			NOUN
gs-1949	239	8			NOUN
gs-1949	239	9			PROPN
gs-1949	240	1			VERB
gs-1949	240	2			ADJ
gs-1949	240	3	,	,	PUNCT
gs-1949	240	4	georgian	georgian	ADJ
gs-1949	240	5	scientists/ქართველი	scientists/ქართველი	NOUN
gs-1949	240	6	მეცნიერები	მეცნიერები	NOUN
gs-1949	240	7	ტ.	ტ.	VERB
gs-1949	240	8	5	5	NUM
gs-1949	240	9	n	n	PRON
gs-1949	240	10	2	2	NUM
gs-1949	240	11	,	,	PUNCT
gs-1949	240	12	2023	2023	NUM
gs-1949	240	13	28	28	NUM
gs-1949	240	14	and	and	CCONJ
gs-1949	240	15	1	1	NUM
gs-1949	240	16	2	2	NUM
gs-1949	240	17	(	(	PUNCT
gs-1949	240	18	,	,	PUNCT
gs-1949	240	19	,	,	PUNCT
gs-1949	240	20	...	...	PUNCT
gs-1949	240	21	,	,	PUNCT
gs-1949	240	22	)	)	PUNCT
gs-1949	241	1	kf	kf	PROPN
gs-1949	241	2	f	f	PROPN
gs-1949	241	3	f	f	PROPN
gs-1949	241	4	f	f	PROPN
gs-1949	241	5	,	,	PUNCT
gs-1949	241	6	(	(	PUNCT
gs-1949	241	7	)	)	PUNCT
gs-1949	241	8	(	(	PUNCT
gs-1949	241	9	)	)	PUNCT
gs-1949	241	10	i	i	PRON
gs-1949	242	1	if	if	SCONJ
gs-1949	242	2	f	f	PROPN
gs-1949	242	3	b	b	VERB
gs-1949	242	4			PROPN
gs-1949	242	5	,	,	PUNCT
gs-1949	242	6	1,i	1,i	PROPN
gs-1949	242	7	k	k	NOUN
gs-1949	242	8	,	,	PUNCT
gs-1949	242	9	1	1	NUM
gs-1949	242	10	,	,	PUNCT
gs-1949	242	11	r	r	NOUN
gs-1949	242	12			NOUN
gs-1949	242	13	.	.	PUNCT
gs-1949	243	1	the	the	DET
gs-1949	243	2	symbol	symbol	NOUN
gs-1949	243	3			NOUN
gs-1949	243	4			PUNCT
gs-1949	243	5	c	c	PROPN
gs-1949	243	6			PROPN
gs-1949	243	7	stands	stand	VERB
gs-1949	243	8	for	for	ADP
gs-1949	243	9	convergence	convergence	NOUN
gs-1949	243	10	according	accord	VERB
gs-1949	243	11	to	to	ADP
gs-1949	243	12	cesaro	cesaro	NOUN
gs-1949	243	13	.	.	PUNCT
gs-1949	244	1	it	it	PRON
gs-1949	244	2	was	be	AUX
gs-1949	244	3	shown	show	VERB
gs-1949	244	4	in	in	ADP
gs-1949	244	5	[	[	X
gs-1949	244	6	8	8	NUM
gs-1949	244	7	]	]	PUNCT
gs-1949	244	8	that	that	SCONJ
gs-1949	244	9	when	when	SCONJ
gs-1949	244	10	the	the	DET
gs-1949	244	11	chain	chain	NOUN
gs-1949	244	12	is	be	AUX
gs-1949	244	13	irregular	irregular	ADJ
gs-1949	244	14	(	(	PUNCT
gs-1949	244	15	contains	contain	VERB
gs-1949	244	16	cyclic	cyclic	ADJ
gs-1949	244	17	subclasses	subclass	NOUN
gs-1949	244	18	)	)	PUNCT
gs-1949	244	19	,	,	PUNCT
gs-1949	244	20	then	then	ADV
gs-1949	244	21	both	both	DET
gs-1949	244	22	existence	existence	NOUN
gs-1949	244	23	z	z	NOUN
gs-1949	244	24	and	and	CCONJ
gs-1949	244	25	convergence	convergence	PROPN
gs-1949	244	26			PROPN
gs-1949	244	27	cov	cov	NOUN
gs-1949	244	28	n	n	CCONJ
gs-1949	244	29	fu	fu	NOUN
gs-1949	244	30	t	t	NOUN
gs-1949	244	31	are	be	AUX
gs-1949	244	32	understood	understand	VERB
gs-1949	244	33	in	in	ADP
gs-1949	244	34	the	the	DET
gs-1949	244	35	sense	sense	NOUN
gs-1949	244	36	of	of	ADP
gs-1949	244	37	cesaro	cesaro	NOUN
gs-1949	244	38	.	.	PUNCT
gs-1949	245	1	in	in	ADP
gs-1949	245	2	[	[	X
gs-1949	245	3	9	9	NUM
gs-1949	245	4	]	]	PUNCT
gs-1949	245	5	,	,	PUNCT
gs-1949	245	6	the	the	DET
gs-1949	245	7	representation	representation	NOUN
gs-1949	245	8	of	of	ADP
gs-1949	245	9	the	the	DET
gs-1949	245	10	matrix	matrix	NOUN
gs-1949	245	11	ft	ft	NOUN
gs-1949	245	12	is	be	AUX
gs-1949	245	13	accepted	accept	VERB
gs-1949	245	14	in	in	ADP
gs-1949	245	15	the	the	DET
gs-1949	245	16	matrix	matrix	NOUN
gs-1949	245	17	form	form	NOUN
gs-1949	245	18	[	[	PUNCT
gs-1949	245	19	(	(	PUNCT
gs-1949	245	20	)	)	PUNCT
gs-1949	246	1	]	]	X
gs-1949	246	2	t	t	X
gs-1949	246	3	t	t	X
gs-1949	246	4	f	f	PROPN
gs-1949	246	5	dg	dg	ADP
gs-1949	246	6	dg	dg	PROPN
gs-1949	246	7	dg	dg	PROPN
gs-1949	246	8	dgt	dgt	PROPN
gs-1949	246	9	f	f	PROPN
gs-1949	246	10	z	z	PROPN
gs-1949	246	11	z	z	PROPN
gs-1949	246	12	f	f	PROPN
gs-1949	247	1			ADP
gs-1949	247	2			PROPN
gs-1949	247	3			PROPN
gs-1949	247	4			PROPN
gs-1949	247	5			PROPN
gs-1949	247	6			PROPN
gs-1949	247	7	,	,	PUNCT
gs-1949	247	8	(	(	PUNCT
gs-1949	247	9	9	9	NUM
gs-1949	247	10	)	)	PUNCT
gs-1949	247	11	where	where	SCONJ
gs-1949	247	12	f	f	PROPN
gs-1949	247	13	is	be	AUX
gs-1949	247	14	the	the	DET
gs-1949	247	15	following	follow	VERB
gs-1949	247	16	matrix	matrix	NOUN
gs-1949	247	17	of	of	ADP
gs-1949	247	18	order	order	NOUN
gs-1949	247	19	k	k	X
gs-1949	247	20	r	r	PROPN
gs-1949	247	21	.	.	PUNCT
gs-1949	248	1	1	1	NUM
gs-1949	248	2	1	1	NUM
gs-1949	248	3	1	1	NUM
gs-1949	248	4	2	2	NUM
gs-1949	248	5	1	1	NUM
gs-1949	248	6	1	1	NUM
gs-1949	248	7	1	1	NUM
gs-1949	248	8	1	1	NUM
gs-1949	248	9	2	2	NUM
gs-1949	248	10	1	1	NUM
gs-1949	248	11	2	2	NUM
gs-1949	248	12	2	2	NUM
gs-1949	248	13	2	2	NUM
gs-1949	248	14	2	2	NUM
gs-1949	248	15	2	2	NUM
gs-1949	248	16	2	2	NUM
gs-1949	248	17	1	1	NUM
gs-1949	248	18	2	2	NUM
gs-1949	248	19	(	(	PUNCT
gs-1949	248	20	)	)	PUNCT
gs-1949	248	21	,	,	PUNCT
gs-1949	248	22	(	(	PUNCT
gs-1949	248	23	)	)	PUNCT
gs-1949	248	24	,	,	PUNCT
gs-1949	248	25	...	...	PUNCT
gs-1949	248	26	,	,	PUNCT
gs-1949	248	27	(	(	PUNCT
gs-1949	248	28	)	)	PUNCT
gs-1949	248	29	(	(	PUNCT
gs-1949	248	30	1	1	NUM
gs-1949	248	31	)	)	PUNCT
gs-1949	248	32	,	,	PUNCT
gs-1949	248	33	(	(	PUNCT
gs-1949	248	34	2	2	NUM
gs-1949	248	35	)	)	PUNCT
gs-1949	248	36	,	,	PUNCT
gs-1949	248	37	...	...	PUNCT
gs-1949	248	38	,	,	PUNCT
gs-1949	248	39	(	(	PUNCT
gs-1949	248	40	)	)	PUNCT
gs-1949	248	41	(	(	PUNCT
gs-1949	248	42	)	)	PUNCT
gs-1949	248	43	,	,	PUNCT
gs-1949	248	44	(	(	PUNCT
gs-1949	248	45	)	)	PUNCT
gs-1949	248	46	,	,	PUNCT
gs-1949	248	47	...	...	PUNCT
gs-1949	248	48	,	,	PUNCT
gs-1949	248	49	(	(	PUNCT
gs-1949	248	50	)	)	PUNCT
gs-1949	248	51	(	(	PUNCT
gs-1949	248	52	1	1	NUM
gs-1949	248	53	)	)	PUNCT
gs-1949	248	54	,	,	PUNCT
gs-1949	248	55	(	(	PUNCT
gs-1949	248	56	2	2	NUM
gs-1949	248	57	)	)	PUNCT
gs-1949	248	58	,	,	PUNCT
gs-1949	248	59	...	...	PUNCT
gs-1949	248	60	,	,	PUNCT
gs-1949	248	61	(	(	PUNCT
gs-1949	248	62	)	)	PUNCT
gs-1949	248	63	...................................	...................................	PUNCT
gs-1949	248	64	...............................	...............................	PUNCT
gs-1949	249	1	(	(	PUNCT
gs-1949	249	2	)	)	PUNCT
gs-1949	249	3	,	,	PUNCT
gs-1949	249	4	(	(	PUNCT
gs-1949	249	5	)	)	PUNCT
gs-1949	249	6	,	,	PUNCT
gs-1949	249	7	...	...	PUNCT
gs-1949	249	8	,	,	PUNCT
gs-1949	249	9	(	(	PUNCT
gs-1949	249	10	)	)	PUNCT
gs-1949	249	11	(	(	PUNCT
gs-1949	249	12	1	1	X
gs-1949	249	13	)	)	PUNCT
gs-1949	249	14	r	r	NOUN
gs-1949	249	15	r	r	NOUN
gs-1949	249	16	k	k	NOUN
gs-1949	250	1	k	k	PROPN
gs-1949	250	2	k	k	PROPN
gs-1949	251	1	r	r	NOUN
gs-1949	251	2	k	k	PROPN
gs-1949	252	1	f	f	PROPN
gs-1949	252	2	b	b	PROPN
gs-1949	252	3	f	f	PROPN
gs-1949	252	4	b	b	PROPN
gs-1949	252	5	f	f	PROPN
gs-1949	252	6	b	b	PROPN
gs-1949	252	7	f	f	X
gs-1949	253	1	f	f	X
gs-1949	253	2	f	f	PROPN
gs-1949	253	3	r	r	NOUN
gs-1949	253	4	f	f	PROPN
gs-1949	253	5	b	b	PROPN
gs-1949	253	6	f	f	PROPN
gs-1949	253	7	b	b	PROPN
gs-1949	253	8	f	f	PROPN
gs-1949	253	9	b	b	PROPN
gs-1949	253	10	f	f	X
gs-1949	254	1	f	f	X
gs-1949	254	2	f	f	PROPN
gs-1949	254	3	r	r	NOUN
gs-1949	255	1	f	f	PROPN
gs-1949	255	2	f	f	PROPN
gs-1949	255	3	b	b	PROPN
gs-1949	255	4	f	f	PROPN
gs-1949	255	5	b	b	PROPN
gs-1949	255	6	f	f	PROPN
gs-1949	255	7	b	b	PROPN
gs-1949	255	8	f	f	PROPN
gs-1949	255	9			NOUN
gs-1949	255	10			PROPN
gs-1949	255	11			PROPN
gs-1949	255	12			PROPN
gs-1949	256	1			PROPN
gs-1949	256	2			NOUN
gs-1949	257	1			PROPN
gs-1949	258	1			PROPN
gs-1949	259	1			INTJ
gs-1949	260	1			PROPN
gs-1949	260	2			PROPN
gs-1949	261	1			PROPN
gs-1949	261	2			NOUN
gs-1949	261	3	,	,	PUNCT
gs-1949	261	4	(	(	PUNCT
gs-1949	261	5	2	2	NUM
gs-1949	261	6	)	)	PUNCT
gs-1949	261	7	,	,	PUNCT
gs-1949	261	8	...	...	PUNCT
gs-1949	261	9	,	,	PUNCT
gs-1949	261	10	(	(	PUNCT
gs-1949	261	11	)	)	PUNCT
gs-1949	262	1	k	k	NOUN
gs-1949	262	2	kf	kf	PROPN
gs-1949	262	3	f	f	PROPN
gs-1949	262	4	r	r	NOUN
gs-1949	262	5			NOUN
gs-1949	262	6			PROPN
gs-1949	263	1			PROPN
gs-1949	264	1			PROPN
gs-1949	265	1			PROPN
gs-1949	266	1			INTJ
gs-1949	267	1			PROPN
gs-1949	268	1			INTJ
gs-1949	269	1			PROPN
gs-1949	269	2			PROPN
gs-1949	270	1			PROPN
gs-1949	270	2			NOUN
gs-1949	270	3	,	,	PUNCT
gs-1949	270	4	1	1	NUM
gs-1949	270	5	2	2	NUM
gs-1949	270	6	1	1	NUM
gs-1949	270	7	2	2	NUM
gs-1949	270	8	1	1	NUM
gs-1949	270	9	2	2	NUM
gs-1949	270	10	,	,	PUNCT
gs-1949	270	11	,	,	PUNCT
gs-1949	270	12	...	...	PUNCT
gs-1949	270	13	,	,	PUNCT
gs-1949	270	14	,	,	PUNCT
gs-1949	270	15	,	,	PUNCT
gs-1949	270	16	...	...	PUNCT
gs-1949	270	17	,	,	PUNCT
gs-1949	270	18	lim	lim	PROPN
gs-1949	270	19	(	(	PUNCT
gs-1949	270	20	)	)	PUNCT
gs-1949	270	21	...............	...............	PUNCT
gs-1949	270	22	,	,	PUNCT
gs-1949	270	23	,	,	PUNCT
gs-1949	270	24	...	...	PUNCT
gs-1949	270	25	,	,	PUNCT
gs-1949	270	26	r	r	NOUN
gs-1949	270	27	rn	rn	PROPN
gs-1949	270	28	c	c	PROPN
gs-1949	270	29	n	n	ADP
gs-1949	270	30	r	r	NOUN
gs-1949	270	31	p	p	X
gs-1949	270	32			PROPN
gs-1949	270	33			PROPN
gs-1949	270	34			PROPN
gs-1949	270	35			PROPN
gs-1949	270	36			PROPN
gs-1949	270	37			PROPN
gs-1949	270	38			PROPN
gs-1949	270	39			PROPN
gs-1949	270	40			ADJ
gs-1949	270	41			NOUN
gs-1949	271	1			NOUN
gs-1949	271	2			PROPN
gs-1949	271	3			PROPN
gs-1949	271	4			PROPN
gs-1949	272	1			PROPN
gs-1949	272	2			NOUN
gs-1949	273	1			PROPN
gs-1949	273	2			PROPN
gs-1949	274	1			PROPN
gs-1949	275	1			INTJ
gs-1949	276	1			PROPN
gs-1949	276	2			PROPN
gs-1949	277	1			PROPN
gs-1949	277	2			NOUN
gs-1949	277	3	.	.	PUNCT
gs-1949	278	1	let	let	VERB
gs-1949	278	2	's	us	PRON
gs-1949	278	3	use	use	VERB
gs-1949	278	4	this	this	DET
gs-1949	278	5	fact	fact	NOUN
gs-1949	278	6	.	.	PUNCT
gs-1949	279	1	consider	consider	VERB
gs-1949	279	2	,	,	PUNCT
gs-1949	279	3	as	as	ADP
gs-1949	279	4	a	a	DET
gs-1949	279	5	function	function	NOUN
gs-1949	279	6	:	:	PUNCT
gs-1949	279	7	kf	kf	PROPN
gs-1949	280	1	r	r	PROPN
gs-1949	280	2	,	,	PUNCT
gs-1949	280	3	the	the	DET
gs-1949	280	4	function	function	NOUN
gs-1949	280	5	:	:	PUNCT
gs-1949	280	6	kr	kr	ADJ
gs-1949	280	7			INTJ
gs-1949	280	8	.	.	PUNCT
gs-1949	281	1			NOUN
gs-1949	282	1			PUNCT
gs-1949	282	2			NOUN
gs-1949	282	3			SYM
gs-1949	282	4			NOUN
gs-1949	282	5			SYM
gs-1949	282	6			NOUN
gs-1949	282	7	1	1	NOUN
gs-1949	282	8	2	2	NUM
gs-1949	282	9	(	(	PUNCT
gs-1949	282	10	)	)	PUNCT
gs-1949	282	11	,	,	PUNCT
gs-1949	282	12	(	(	PUNCT
gs-1949	282	13	)	)	PUNCT
gs-1949	282	14	,	,	PUNCT
gs-1949	282	15	...	...	PUNCT
gs-1949	282	16	,	,	PUNCT
gs-1949	282	17	(	(	PUNCT
gs-1949	282	18	)	)	PUNCT
gs-1949	282	19	j	j	PROPN
gs-1949	283	1	j	j	PROPN
gs-1949	283	2	j	j	PROPN
gs-1949	284	1	j	j	PROPN
gs-1949	284	2	j	j	PROPN
gs-1949	284	3	j	j	PROPN
gs-1949	284	4	k	k	PROPN
gs-1949	284	5	jf	jf	PROPN
gs-1949	284	6	e	e	NOUN
gs-1949	284	7	y	y	NUM
gs-1949	284	8			NOUN
gs-1949	284	9			NOUN
gs-1949	284	10			VERB
gs-1949	284	11			NOUN
gs-1949	284	12			NOUN
gs-1949	284	13			NOUN
gs-1949	284	14			NOUN
gs-1949	284	15			NOUN
gs-1949	284	16			PUNCT
gs-1949	284	17			ADV
gs-1949	284	18			NOUN
gs-1949	284	19	,	,	PUNCT
gs-1949	284	20	(	(	PUNCT
gs-1949	284	21	)	)	PUNCT
gs-1949	284	22	(	(	PUNCT
gs-1949	284	23	)	)	PUNCT
gs-1949	284	24	(	(	PUNCT
gs-1949	284	25	)	)	PUNCT
gs-1949	284	26	p	p	X
gs-1949	285	1	p	p	X
gs-1949	285	2	j	j	PROPN
gs-1949	285	3	p	p	X
gs-1949	285	4	j	j	PROPN
gs-1949	285	5	j	j	PROPN
gs-1949	285	6	jf	jf	PROPN
gs-1949	285	7	e	e	NOUN
gs-1949	285	8	y	y	NUM
gs-1949	285	9			NOUN
gs-1949	285	10			NOUN
gs-1949	285	11			PUNCT
gs-1949	285	12			NOUN
gs-1949	285	13	,	,	PUNCT
gs-1949	285	14	1,p	1,p	PROPN
gs-1949	285	15	k	k	NOUN
gs-1949	285	16	,	,	PUNCT
gs-1949	285	17			PROPN
gs-1949	285	18	1	1	ADJ
gs-1949	285	19	2	2	NUM
gs-1949	285	20	,	,	PUNCT
gs-1949	285	21	,	,	PUNCT
gs-1949	285	22	...	...	PUNCT
gs-1949	285	23	,	,	PUNCT
gs-1949	286	1	k	k	PROPN
gs-1949	286	2	j	j	PROPN
gs-1949	286	3	j	j	PROPN
gs-1949	286	4	j	j	PROPN
gs-1949	286	5	jy	jy	PROPN
gs-1949	286	6	y	y	PROPN
gs-1949	286	7	y	y	PROPN
gs-1949	286	8	y	y	PROPN
gs-1949	286	9	,	,	PUNCT
gs-1949	286	10			PROPN
gs-1949	286	11			SYM
gs-1949	286	12			NOUN
gs-1949	286	13			PUNCT
gs-1949	286	14			NOUN
gs-1949	287	1	j	j	INTJ
gs-1949	287	2	jf	jf	PROPN
gs-1949	287	3	e	e	PROPN
gs-1949	287	4	y	y	PROPN
gs-1949	287	5			NOUN
gs-1949	287	6			X
gs-1949	287	7			PUNCT
gs-1949	287	8			NOUN
gs-1949	287	9			NOUN
gs-1949	287	10			NOUN
gs-1949	287	11	,	,	PUNCT
gs-1949	287	12	1	1	NUM
gs-1949	287	13	,	,	PUNCT
gs-1949	287	14	r	r	NOUN
gs-1949	287	15			NOUN
gs-1949	287	16	,	,	PUNCT
gs-1949	287	17	(	(	PUNCT
gs-1949	287	18	)	)	PUNCT
gs-1949	287	19	(	(	PUNCT
gs-1949	287	20	)	)	PUNCT
gs-1949	287	21	(	(	PUNCT
gs-1949	287	22	)	)	PUNCT
gs-1949	287	23	p	p	X
gs-1949	288	1	p	p	X
gs-1949	288	2	p	p	X
gs-1949	288	3	j	j	PROPN
gs-1949	288	4	jf	jf	PROPN
gs-1949	288	5	e	e	PROPN
gs-1949	288	6	y	y	PROPN
gs-1949	288	7			NOUN
gs-1949	288	8			X
gs-1949	288	9			PUNCT
gs-1949	288	10			NOUN
gs-1949	288	11			NOUN
gs-1949	288	12			NOUN
gs-1949	288	13	,	,	PUNCT
gs-1949	288	14	1,p	1,p	PROPN
gs-1949	288	15	k	k	NOUN
gs-1949	288	16	,	,	PUNCT
gs-1949	288	17	1	1	NUM
gs-1949	288	18	,	,	PUNCT
gs-1949	288	19	r	r	NOUN
gs-1949	288	20			NOUN
gs-1949	288	21	.	.	PUNCT
gs-1949	289	1	it	it	PRON
gs-1949	289	2	is	be	AUX
gs-1949	289	3	clear	clear	ADJ
gs-1949	289	4	that	that	SCONJ
gs-1949	289	5			NOUN
gs-1949	289	6			NOUN
gs-1949	289	7			PROPN
gs-1949	289	8			PROPN
gs-1949	289	9			NOUN
gs-1949	289	10			PROPN
gs-1949	289	11			NOUN
gs-1949	289	12			PROPN
gs-1949	289	13	1	1	NUM
gs-1949	289	14	r	r	NOUN
gs-1949	289	15	j	j	PROPN
gs-1949	289	16	j	j	PROPN
gs-1949	289	17	je	je	X
gs-1949	289	18	e	e	PROPN
gs-1949	289	19	e	e	PROPN
gs-1949	289	20	y	y	PROPN
gs-1949	289	21			NOUN
gs-1949	289	22			X
gs-1949	289	23			NOUN
gs-1949	289	24			NOUN
gs-1949	289	25			NOUN
gs-1949	289	26			NOUN
gs-1949	289	27			ADJ
gs-1949	289	28			NOUN
gs-1949	289	29			X
gs-1949	289	30			NOUN
gs-1949	289	31			NUM
gs-1949	290	1			NUM
gs-1949	290	2			PROPN
gs-1949	290	3	.	.	PUNCT
gs-1949	291	1	accordingly	accordingly	ADV
gs-1949	291	2	,	,	PUNCT
gs-1949	291	3	as	as	ADP
gs-1949	291	4	a	a	DET
gs-1949	291	5	the	the	DET
gs-1949	291	6	sum	sum	NOUN
gs-1949	291	7	nu	nu	NOUN
gs-1949	291	8	will	will	AUX
gs-1949	291	9	be	be	AUX
gs-1949	291	10	considered	consider	VERB
gs-1949	291	11	the	the	DET
gs-1949	291	12	sum	sum	NOUN
gs-1949	291	13	2	2	NUM
gs-1949	291	14	1	1	NUM
gs-1949	291	15	1	1	NUM
gs-1949	291	16	(	(	PUNCT
gs-1949	291	17	)	)	PUNCT
gs-1949	291	18	n	n	CCONJ
gs-1949	291	19	n	n	PRON
gs-1949	291	20	j	j	PROPN
gs-1949	291	21	j	j	PROPN
gs-1949	291	22	s	s	PART
gs-1949	291	23	n	n	PRON
gs-1949	291	24			NOUN
gs-1949	291	25			NOUN
gs-1949	291	26			NOUN
gs-1949	291	27			NOUN
gs-1949	291	28			PROPN
gs-1949	292	1			PROPN
gs-1949	292	2			NOUN
gs-1949	292	3			NOUN
gs-1949	292	4	.	.	PUNCT
gs-1949	293	1	we	we	PRON
gs-1949	293	2	will	will	AUX
gs-1949	293	3	have	have	VERB
gs-1949	293	4	the	the	DET
gs-1949	293	5	representation	representation	NOUN
gs-1949	293	6	obtained	obtain	VERB
gs-1949	293	7	from	from	ADP
gs-1949	293	8	(	(	PUNCT
gs-1949	293	9	9	9	NUM
gs-1949	293	10	)	)	PUNCT
gs-1949	293	11	[	[	PUNCT
gs-1949	293	12	(	(	PUNCT
gs-1949	293	13	)	)	PUNCT
gs-1949	293	14	]	]	PUNCT
gs-1949	293	15	t	t	X
gs-1949	293	16	t	t	NOUN
gs-1949	293	17	dg	dg	PROPN
gs-1949	293	18	dg	dg	PROPN
gs-1949	293	19	dg	dg	PROPN
gs-1949	293	20	dgt	dgt	PROPN
gs-1949	293	21	z	z	PROPN
gs-1949	293	22	z	z	NUM
gs-1949	293	23			NOUN
gs-1949	293	24			NOUN
gs-1949	294	1			PROPN
gs-1949	294	2			PROPN
gs-1949	294	3			PROPN
gs-1949	294	4			PROPN
gs-1949	294	5			PROPN
gs-1949	294	6			PROPN
gs-1949	294	7			PROPN
gs-1949	294	8			PROPN
gs-1949	294	9	,	,	PUNCT
gs-1949	294	10	(	(	PUNCT
gs-1949	294	11	10	10	NUM
gs-1949	294	12	)	)	PUNCT
gs-1949	294	13	georgian	georgian	ADJ
gs-1949	294	14	scientists/ქართველი	scientists/ქართველი	NOUN
gs-1949	294	15	მეცნიერები	მეცნიერები	NOUN
gs-1949	294	16	ტ.	ტ.	VERB
gs-1949	294	17	5	5	NUM
gs-1949	294	18	n	n	PRON
gs-1949	294	19	2	2	NUM
gs-1949	294	20	,	,	PUNCT
gs-1949	294	21	2023	2023	NUM
gs-1949	294	22	29	29	NUM
gs-1949	294	23	where	where	SCONJ
gs-1949	294	24	1	1	NUM
gs-1949	294	25	1	1	NUM
gs-1949	294	26	1	1	NUM
gs-1949	294	27	2	2	NUM
gs-1949	294	28	1	1	NUM
gs-1949	294	29	1	1	NUM
gs-1949	294	30	1	1	NUM
gs-1949	294	31	1	1	NUM
gs-1949	294	32	2	2	NUM
gs-1949	294	33	1	1	NUM
gs-1949	294	34	2	2	NUM
gs-1949	294	35	2	2	NUM
gs-1949	294	36	2	2	NUM
gs-1949	294	37	2	2	NUM
gs-1949	294	38	2	2	NUM
gs-1949	294	39	2	2	NUM
gs-1949	294	40	1	1	NUM
gs-1949	294	41	2	2	NUM
gs-1949	294	42	(	(	PUNCT
gs-1949	294	43	)	)	PUNCT
gs-1949	294	44	,	,	PUNCT
gs-1949	294	45	(	(	PUNCT
gs-1949	294	46	)	)	PUNCT
gs-1949	294	47	,	,	PUNCT
gs-1949	294	48	...	...	PUNCT
gs-1949	294	49	,	,	PUNCT
gs-1949	294	50	(	(	PUNCT
gs-1949	294	51	)	)	PUNCT
gs-1949	294	52	(	(	PUNCT
gs-1949	294	53	1	1	NUM
gs-1949	294	54	)	)	PUNCT
gs-1949	294	55	,	,	PUNCT
gs-1949	294	56	(	(	PUNCT
gs-1949	294	57	2	2	NUM
gs-1949	294	58	)	)	PUNCT
gs-1949	294	59	,	,	PUNCT
gs-1949	294	60	...	...	PUNCT
gs-1949	294	61	,	,	PUNCT
gs-1949	294	62	(	(	PUNCT
gs-1949	294	63	)	)	PUNCT
gs-1949	294	64	(	(	PUNCT
gs-1949	294	65	)	)	PUNCT
gs-1949	294	66	,	,	PUNCT
gs-1949	294	67	(	(	PUNCT
gs-1949	294	68	)	)	PUNCT
gs-1949	294	69	,	,	PUNCT
gs-1949	294	70	...	...	PUNCT
gs-1949	294	71	,	,	PUNCT
gs-1949	294	72	(	(	PUNCT
gs-1949	294	73	)	)	PUNCT
gs-1949	294	74	(	(	PUNCT
gs-1949	294	75	1	1	NUM
gs-1949	294	76	)	)	PUNCT
gs-1949	294	77	,	,	PUNCT
gs-1949	294	78	(	(	PUNCT
gs-1949	294	79	2	2	NUM
gs-1949	294	80	)	)	PUNCT
gs-1949	294	81	,	,	PUNCT
gs-1949	294	82	...	...	PUNCT
gs-1949	294	83	,	,	PUNCT
gs-1949	294	84	(	(	PUNCT
gs-1949	294	85	)	)	PUNCT
gs-1949	294	86	...................................	...................................	PUNCT
gs-1949	294	87	...............................	...............................	PUNCT
gs-1949	295	1	(	(	PUNCT
gs-1949	295	2	)	)	PUNCT
gs-1949	295	3	,	,	PUNCT
gs-1949	295	4	(	(	PUNCT
gs-1949	295	5	)	)	PUNCT
gs-1949	295	6	,	,	PUNCT
gs-1949	295	7	...	...	PUNCT
gs-1949	295	8	,	,	PUNCT
gs-1949	295	9	(	(	PUNCT
gs-1949	295	10	)	)	PUNCT
gs-1949	295	11	(	(	PUNCT
gs-1949	295	12	1	1	X
gs-1949	295	13	)	)	PUNCT
gs-1949	295	14	r	r	NOUN
gs-1949	295	15	r	r	NOUN
gs-1949	295	16	k	k	NOUN
gs-1949	295	17	k	k	PROPN
gs-1949	295	18	k	k	PROPN
gs-1949	295	19	r	r	NOUN
gs-1949	295	20	k	k	PROPN
gs-1949	295	21	b	b	PROPN
gs-1949	295	22	b	b	PROPN
gs-1949	295	23	b	b	PROPN
gs-1949	295	24	r	r	NOUN
gs-1949	295	25	b	b	PROPN
gs-1949	295	26	b	b	PROPN
gs-1949	295	27	b	b	PROPN
gs-1949	295	28	r	r	NOUN
gs-1949	295	29	b	b	PROPN
gs-1949	295	30	b	b	PROPN
gs-1949	295	31	b	b	NOUN
gs-1949	295	32			NOUN
gs-1949	295	33			NOUN
gs-1949	295	34			NOUN
gs-1949	295	35			NOUN
gs-1949	295	36			NOUN
gs-1949	295	37			NOUN
gs-1949	295	38			NOUN
gs-1949	295	39			NOUN
gs-1949	295	40			NOUN
gs-1949	295	41			NOUN
gs-1949	295	42			NOUN
gs-1949	295	43			NOUN
gs-1949	295	44			NOUN
gs-1949	295	45			NOUN
gs-1949	295	46			NOUN
gs-1949	295	47			NOUN
gs-1949	295	48			NOUN
gs-1949	295	49			NOUN
gs-1949	296	1			PROPN
gs-1949	296	2			PROPN
gs-1949	296	3			PROPN
gs-1949	297	1			PROPN
gs-1949	297	2			NOUN
gs-1949	298	1			PROPN
gs-1949	298	2			PROPN
gs-1949	299	1			PROPN
gs-1949	300	1			PROPN
gs-1949	300	2			PROPN
gs-1949	301	1			PROPN
gs-1949	301	2			NOUN
gs-1949	301	3	,	,	PUNCT
gs-1949	301	4	(	(	PUNCT
gs-1949	301	5	2	2	NUM
gs-1949	301	6	)	)	PUNCT
gs-1949	301	7	,	,	PUNCT
gs-1949	301	8	...	...	PUNCT
gs-1949	301	9	,	,	PUNCT
gs-1949	301	10	(	(	PUNCT
gs-1949	301	11	)	)	PUNCT
gs-1949	301	12	k	k	PROPN
gs-1949	301	13	k	k	PROPN
gs-1949	301	14	r	r	NUM
gs-1949	301	15			NOUN
gs-1949	301	16			NOUN
gs-1949	301	17			PROPN
gs-1949	301	18			PROPN
gs-1949	302	1			PROPN
gs-1949	303	1			PROPN
gs-1949	304	1			INTJ
gs-1949	305	1			PROPN
gs-1949	306	1			INTJ
gs-1949	307	1			PROPN
gs-1949	307	2			PROPN
gs-1949	308	1			PROPN
gs-1949	308	2			NOUN
gs-1949	308	3	,	,	PUNCT
gs-1949	308	4	accordingly	accordingly	ADV
gs-1949	308	5			NOUN
gs-1949	308	6			PROPN
gs-1949	308	7	,	,	PUNCT
gs-1949	308	8	,	,	PUNCT
gs-1949	309	1	1,i	1,i	PROPN
gs-1949	309	2	j	j	NOUN
gs-1949	310	1	i	i	PRON
gs-1949	310	2	j	j	PROPN
gs-1949	311	1	k	k	PROPN
gs-1949	311	2	t	t	PROPN
gs-1949	311	3	t	t	NUM
gs-1949	311	4			NOUN
gs-1949	312	1			NOUN
gs-1949	312	2			NOUN
gs-1949	312	3	,	,	PUNCT
gs-1949	312	4	where	where	SCONJ
gs-1949	312	5	,	,	PUNCT
gs-1949	312	6	,	,	PUNCT
gs-1949	312	7	(	(	PUNCT
gs-1949	312	8	)	)	PUNCT
gs-1949	312	9	(	(	PUNCT
gs-1949	312	10	)	)	PUNCT
gs-1949	312	11	(	(	PUNCT
gs-1949	312	12	)	)	PUNCT
gs-1949	313	1	i	i	PRON
gs-1949	313	2	j	j	NOUN
gs-1949	314	1	r	r	NOUN
gs-1949	314	2	i	i	PRON
gs-1949	314	3	jt	jt	PROPN
gs-1949	314	4	z	z	PROPN
gs-1949	314	5	z	z	PROPN
gs-1949	314	6			PROPN
gs-1949	314	7			ADJ
gs-1949	314	8			NOUN
gs-1949	314	9			NOUN
gs-1949	314	10			X
gs-1949	314	11			PROPN
gs-1949	314	12			X
gs-1949	314	13			ADJ
gs-1949	314	14			X
gs-1949	314	15			PROPN
gs-1949	314	16			PROPN
gs-1949	314	17			PROPN
gs-1949	314	18			PROPN
gs-1949	314	19			PROPN
gs-1949	314	20			NOUN
gs-1949	314	21			NUM
gs-1949	314	22			NOUN
gs-1949	314	23			NOUN
gs-1949	314	24			NOUN
gs-1949	314	25			NOUN
gs-1949	314	26			PUNCT
gs-1949	314	27			PROPN
gs-1949	314	28			PROPN
gs-1949	314	29	,	,	PUNCT
gs-1949	314	30	,	,	PUNCT
gs-1949	314	31	1,i	1,i	PROPN
gs-1949	314	32	j	j	PROPN
gs-1949	314	33	k	k	NOUN
gs-1949	314	34	.	.	PUNCT
gs-1949	315	1	(	(	PUNCT
gs-1949	315	2	11	11	NUM
gs-1949	315	3	)	)	PUNCT
gs-1949	315	4	and	and	CCONJ
gs-1949	315	5			PROPN
gs-1949	315	6	is	be	AUX
gs-1949	315	7	the	the	DET
gs-1949	315	8	kronecker	kronecker	NOUN
gs-1949	315	9	symbol	symbol	NOUN
gs-1949	315	10	.	.	PUNCT
gs-1949	316	1	theorem	theorem	NOUN
gs-1949	316	2	2	2	NUM
gs-1949	316	3	.	.	PUNCT
gs-1949	316	4	suppose	suppose	VERB
gs-1949	316	5	that	that	SCONJ
gs-1949	316	6			PROPN
gs-1949	316	7			PROPN
gs-1949	316	8	1i	1i	NOUN
gs-1949	317	1	i	i	PRON
gs-1949	317	2	y	y	PROPN
gs-1949	317	3			NUM
gs-1949	317	4	is	be	AUX
gs-1949	317	5	a	a	DET
gs-1949	317	6	sequence	sequence	NOUN
gs-1949	317	7	with	with	ADP
gs-1949	317	8	a	a	DET
gs-1949	317	9	chain	chain	NOUN
gs-1949	317	10	m	m	VERB
gs-1949	317	11	-dependence	-dependence	NOUN
gs-1949	317	12	in	in	ADP
gs-1949	317	13	model	model	NOUN
gs-1949	317	14	(	(	PUNCT
gs-1949	317	15	1	1	NUM
gs-1949	317	16	)	)	PUNCT
gs-1949	317	17	.	.	PUNCT
gs-1949	318	1	suppose	suppose	VERB
gs-1949	318	2	the	the	DET
gs-1949	318	3	control	control	NOUN
gs-1949	318	4	sequence	sequence	NOUN
gs-1949	318	5			PROPN
gs-1949	318	6			PROPN
gs-1949	318	7	1i	1i	NOUN
gs-1949	318	8	i	i	PRON
gs-1949	318	9			VERB
gs-1949	318	10			X
gs-1949	318	11	satisfies	satisfy	VERB
gs-1949	318	12	condition	condition	NOUN
gs-1949	318	13	(	(	PUNCT
gs-1949	318	14	2	2	NUM
gs-1949	318	15	)	)	PUNCT
gs-1949	318	16	and	and	CCONJ
gs-1949	318	17	inequality	inequality	NOUN
gs-1949	318	18	(	(	PUNCT
gs-1949	318	19	3	3	NUM
gs-1949	318	20	)	)	PUNCT
gs-1949	318	21	is	be	AUX
gs-1949	318	22	fulfilled	fulfil	VERB
gs-1949	318	23	.	.	PUNCT
gs-1949	319	1	suppose	suppose	VERB
gs-1949	319	2			PRON
gs-1949	319	3			PROPN
gs-1949	319	4	1n	1n	NUM
gs-1949	319	5	n	n	PRON
gs-1949	319	6			NOUN
gs-1949	319	7			NUM
gs-1949	319	8	is	be	AUX
gs-1949	319	9	a	a	DET
gs-1949	319	10	finite	finite	ADJ
gs-1949	319	11	,	,	PUNCT
gs-1949	319	12	homogeneous	homogeneous	ADJ
gs-1949	319	13	,	,	PUNCT
gs-1949	319	14	stationary	stationary	ADJ
gs-1949	319	15	,	,	PUNCT
gs-1949	319	16	ergodic	ergodic	ADJ
gs-1949	319	17	markov	markov	NOUN
gs-1949	319	18	chain	chain	NOUN
gs-1949	319	19	with	with	ADP
gs-1949	319	20	one	one	NUM
gs-1949	319	21	ergodicity	ergodicity	NOUN
gs-1949	319	22	class	class	NOUN
gs-1949	319	23	,	,	PUNCT
gs-1949	319	24	which	which	PRON
gs-1949	319	25	may	may	AUX
gs-1949	319	26	contain	contain	VERB
gs-1949	319	27	cyclic	cyclic	ADJ
gs-1949	319	28	subclasses	subclass	NOUN
gs-1949	319	29	.	.	PUNCT
gs-1949	320	1	let	let	VERB
gs-1949	320	2	's	us	PRON
gs-1949	320	3	say	say	VERB
gs-1949	320	4	the	the	DET
gs-1949	320	5	set	set	NOUN
gs-1949	320	6	of	of	ADP
gs-1949	320	7	states	state	NOUN
gs-1949	320	8	of	of	ADP
gs-1949	320	9	the	the	DET
gs-1949	320	10	markov	markov	NOUN
gs-1949	320	11	chain	chain	NOUN
gs-1949	320	12	is	be	AUX
gs-1949	320	13			PROPN
gs-1949	320	14	1	1	NOUN
gs-1949	320	15	2	2	NUM
gs-1949	320	16	,	,	PUNCT
gs-1949	320	17	,	,	PUNCT
gs-1949	320	18	...	...	PUNCT
gs-1949	320	19	,	,	PUNCT
gs-1949	320	20	rb	rb	PROPN
gs-1949	320	21	b	b	PROPN
gs-1949	320	22	b	b	NOUN
gs-1949	320	23			PROPN
gs-1949	320	24	.	.	PUNCT
gs-1949	321	1	the	the	DET
gs-1949	321	2	limiting	limit	VERB
gs-1949	321	3	stationary	stationary	ADJ
gs-1949	321	4	distribution	distribution	NOUN
gs-1949	321	5	is	be	AUX
gs-1949	321	6	1	1	NUM
gs-1949	321	7	2	2	NUM
gs-1949	321	8	(	(	PUNCT
gs-1949	321	9	,	,	PUNCT
gs-1949	321	10	,	,	PUNCT
gs-1949	321	11	...	...	PUNCT
gs-1949	321	12	,	,	PUNCT
gs-1949	321	13	)	)	PUNCT
gs-1949	321	14	r	r	VERB
gs-1949	321	15			PROPN
gs-1949	321	16			PROPN
gs-1949	321	17			NOUN
gs-1949	321	18	.	.	PUNCT
gs-1949	322	1	then	then	ADV
gs-1949	322	2	in	in	ADP
gs-1949	322	3	the	the	DET
gs-1949	322	4	above	above	ADJ
gs-1949	322	5	notation	notation	NOUN
gs-1949	322	6	for	for	ADP
gs-1949	322	7	any	any	DET
gs-1949	322	8	vectors	vector	NOUN
gs-1949	322	9			PROPN
gs-1949	322	10			PROPN
gs-1949	322	11	,	,	PUNCT
gs-1949	322	12	kx	kx	PROPN
gs-1949	322	13	y	y	PROPN
gs-1949	322	14	r	r	PROPN
gs-1949	322	15	when	when	SCONJ
gs-1949	322	16	n	n	PROPN
gs-1949	322	17	occurs	occur	VERB
gs-1949	322	18	the	the	DET
gs-1949	322	19	convergence	convergence	NOUN
gs-1949	322	20	,	,	PUNCT
gs-1949	322	21	x	x	VERB
gs-1949	322	22	y	y	PROPN
gs-1949	322	23			PROPN
gs-1949	322	24			PROPN
gs-1949	322	25	1	1	NUM
gs-1949	322	26	p	p	NOUN
gs-1949	322	27	(	(	PUNCT
gs-1949	322	28	)	)	PUNCT
gs-1949	322	29	(	(	PUNCT
gs-1949	322	30	)	)	PUNCT
gs-1949	322	31	(	(	PUNCT
gs-1949	322	32	)	)	PUNCT
gs-1949	322	33	(	(	PUNCT
gs-1949	322	34	)	)	PUNCT
gs-1949	322	35	(	(	PUNCT
gs-1949	322	36	)	)	PUNCT
gs-1949	323	1	m	m	VERB
gs-1949	323	2	mn	mn	NOUN
gs-1949	324	1	n	n	ADV
gs-1949	324	2	r	r	NOUN
gs-1949	324	3	r	r	NOUN
gs-1949	324	4	t	t	NOUN
gs-1949	324	5	ts	ts	X
gs-1949	324	6	x	x	PUNCT
gs-1949	324	7	y	y	NOUN
gs-1949	324	8	f	f	NOUN
gs-1949	324	9	x	x	PUNCT
gs-1949	324	10	x	x	VERB
gs-1949	324	11	y	y	VERB
gs-1949	324	12	y	y	PROPN
gs-1949	324	13	y	y	PROPN
gs-1949	324	14			NOUN
gs-1949	324	15			PROPN
gs-1949	324	16			PROPN
gs-1949	324	17			VERB
gs-1949	324	18			NOUN
gs-1949	324	19			NOUN
gs-1949	324	20			NOUN
gs-1949	324	21			ADJ
gs-1949	324	22			X
gs-1949	324	23			NOUN
gs-1949	324	24			NOUN
gs-1949	324	25	(	(	PUNCT
gs-1949	324	26	12	12	NUM
gs-1949	324	27	)	)	PUNCT
gs-1949	324	28	proof	proof	NOUN
gs-1949	324	29	.	.	PUNCT
gs-1949	325	1	the	the	DET
gs-1949	325	2	proof	proof	NOUN
gs-1949	325	3	of	of	ADP
gs-1949	325	4	the	the	DET
gs-1949	325	5	theorem	theorem	NOUN
gs-1949	325	6	is	be	AUX
gs-1949	325	7	carried	carry	VERB
gs-1949	325	8	out	out	ADP
gs-1949	325	9	similarly	similarly	ADV
gs-1949	325	10	to	to	AUX
gs-1949	325	11	theorem	theorem	NOUN
gs-1949	325	12	1	1	NUM
gs-1949	325	13	.	.	PUNCT
gs-1949	326	1	it	it	PRON
gs-1949	326	2	is	be	AUX
gs-1949	326	3	only	only	ADV
gs-1949	326	4	necessary	necessary	ADJ
gs-1949	326	5	to	to	PART
gs-1949	326	6	take	take	VERB
gs-1949	326	7	into	into	ADP
gs-1949	326	8	account	account	NOUN
gs-1949	326	9	that	that	SCONJ
gs-1949	326	10	the	the	DET
gs-1949	326	11	conditions	condition	NOUN
gs-1949	326	12	of	of	ADP
gs-1949	326	13	theorem	theorem	ADJ
gs-1949	326	14	2	2	NUM
gs-1949	326	15	include	include	VERB
gs-1949	326	16	the	the	DET
gs-1949	326	17	conditions	condition	NOUN
gs-1949	326	18	of	of	ADP
gs-1949	326	19	theorem	theorem	NOUN
gs-1949	326	20	1	1	NUM
gs-1949	326	21	.	.	PUNCT
gs-1949	327	1	at	at	ADP
gs-1949	327	2	the	the	DET
gs-1949	327	3	moment	moment	NOUN
gs-1949	327	4	,	,	PUNCT
gs-1949	327	5	it	it	PRON
gs-1949	327	6	is	be	AUX
gs-1949	327	7	known	know	VERB
gs-1949	327	8	that	that	SCONJ
gs-1949	327	9	the	the	DET
gs-1949	327	10	limit	limit	NOUN
gs-1949	327	11	distribution	distribution	NOUN
gs-1949	327	12	of	of	ADP
gs-1949	327	13	the	the	DET
gs-1949	327	14	sum	sum	NOUN
gs-1949	327	15	2ns	2ns	NOUN
gs-1949	327	16	is	be	AUX
gs-1949	327	17	expressed	express	VERB
gs-1949	327	18	by	by	ADP
gs-1949	327	19	the	the	DET
gs-1949	327	20	parameters	parameter	NOUN
gs-1949	327	21	of	of	ADP
gs-1949	327	22	the	the	DET
gs-1949	327	23	markov	markov	NOUN
gs-1949	327	24	chain	chain	NOUN
gs-1949	327	25	.	.	PUNCT
gs-1949	328	1	in	in	ADP
gs-1949	328	2	particular	particular	ADJ
gs-1949	328	3	,	,	PUNCT
gs-1949	328	4	its	its	PRON
gs-1949	328	5	limiting	limit	VERB
gs-1949	328	6	covariance	covariance	NOUN
gs-1949	328	7	matrix	matrix	NOUN
gs-1949	328	8	is	be	AUX
gs-1949	328	9	established	establish	VERB
gs-1949	328	10	.	.	PUNCT
gs-1949	329	1	it	it	PRON
gs-1949	329	2	can	can	AUX
gs-1949	329	3	be	be	AUX
gs-1949	329	4	seen	see	VERB
gs-1949	329	5	from	from	ADP
gs-1949	329	6	(	(	PUNCT
gs-1949	329	7	10	10	NUM
gs-1949	329	8	)	)	PUNCT
gs-1949	329	9	that	that	SCONJ
gs-1949	329	10	at	at	ADP
gs-1949	329	11	n	n	CCONJ
gs-1949	329	12			NOUN
gs-1949	329	13	2n	2n	NUM
gs-1949	329	14	w	w	PROPN
gs-1949	329	15	s	s	PROPN
gs-1949	329	16	t	t	PROPN
gs-1949	329	17			INTJ
gs-1949	329	18	.	.	PUNCT
gs-1949	330	1	this	this	PRON
gs-1949	330	2	means	mean	VERB
gs-1949	330	3	that	that	SCONJ
gs-1949	330	4	instead	instead	ADV
gs-1949	330	5	of	of	ADP
gs-1949	330	6	a	a	DET
gs-1949	330	7	distribution	distribution	NOUN
gs-1949	330	8	of	of	ADP
gs-1949	330	9	(	(	PUNCT
gs-1949	330	10	)	)	PUNCT
gs-1949	330	11	q	q	PROPN
gs-1949	330	12			PROPN
gs-1949	330	13	,	,	PUNCT
gs-1949	330	14	we	we	PRON
gs-1949	330	15	can	can	AUX
gs-1949	330	16	consider	consider	VERB
gs-1949	330	17	a	a	DET
gs-1949	330	18	distribution	distribution	NOUN
gs-1949	330	19	of	of	ADP
gs-1949	330	20	(	(	PUNCT
gs-1949	330	21	)	)	PUNCT
gs-1949	330	22	t	t	PROPN
gs-1949	330	23			PROPN
gs-1949	330	24			PROPN
gs-1949	330	25	.	.	PUNCT
gs-1949	331	1	the	the	DET
gs-1949	331	2	form	form	NOUN
gs-1949	331	3	of	of	ADP
gs-1949	331	4	the	the	DET
gs-1949	331	5	matrix	matrix	NOUN
gs-1949	331	6	t	t	PROPN
gs-1949	331	7	in	in	ADP
gs-1949	331	8	the	the	DET
gs-1949	331	9	presence	presence	NOUN
gs-1949	331	10	of	of	ADP
gs-1949	331	11	cyclic	cyclic	ADJ
gs-1949	331	12	subclasses	subclass	NOUN
gs-1949	331	13	is	be	AUX
gs-1949	331	14	obtained	obtain	VERB
gs-1949	331	15	with	with	ADP
gs-1949	331	16	the	the	DET
gs-1949	331	17	help	help	NOUN
gs-1949	331	18	of	of	ADP
gs-1949	331	19	cesaro	cesaro	ADJ
gs-1949	331	20	convergence	convergence	NOUN
gs-1949	331	21	.	.	PUNCT
gs-1949	332	1	discussion	discussion	NOUN
gs-1949	332	2	in	in	ADP
gs-1949	332	3	the	the	DET
gs-1949	332	4	particular	particular	ADJ
gs-1949	332	5	case	case	NOUN
gs-1949	332	6	when	when	SCONJ
gs-1949	332	7	the	the	DET
gs-1949	332	8	markov	markov	NOUN
gs-1949	332	9	chain	chain	NOUN
gs-1949	332	10	is	be	AUX
gs-1949	332	11	regular	regular	ADJ
gs-1949	332	12	(	(	PUNCT
gs-1949	332	13	does	do	AUX
gs-1949	332	14	not	not	PART
gs-1949	332	15	contain	contain	VERB
gs-1949	332	16	cyclic	cyclic	ADJ
gs-1949	332	17	subclasses	subclass	NOUN
gs-1949	332	18	)	)	PUNCT
gs-1949	332	19	and	and	CCONJ
gs-1949	332	20			PROPN
gs-1949	332	21			PROPN
gs-1949	332	22	1n	1n	NUM
gs-1949	332	23	n	n	CCONJ
gs-1949	332	24	y	y	PROPN
gs-1949	332	25			NUM
gs-1949	332	26	are	be	AUX
gs-1949	332	27	one	one	NUM
gs-1949	332	28	-	-	PUNCT
gs-1949	332	29	dimensional	dimensional	ADJ
gs-1949	332	30	(	(	PUNCT
gs-1949	332	31	1k	1k	NUM
gs-1949	332	32			NOUN
gs-1949	332	33	)	)	PUNCT
gs-1949	332	34	discrete	discrete	VERB
gs-1949	332	35	random	random	ADJ
gs-1949	332	36	variables	variable	NOUN
gs-1949	332	37	,	,	PUNCT
gs-1949	332	38	then	then	ADV
gs-1949	332	39	an	an	DET
gs-1949	332	40	analogue	analogue	NOUN
gs-1949	332	41	of	of	ADP
gs-1949	332	42	(	(	PUNCT
gs-1949	332	43	11	11	NUM
gs-1949	332	44	)	)	PUNCT
gs-1949	332	45	was	be	AUX
gs-1949	332	46	obtained	obtain	VERB
gs-1949	332	47	in	in	ADP
gs-1949	332	48	[	[	X
gs-1949	332	49	10	10	NUM
gs-1949	332	50	]	]	PUNCT
gs-1949	332	51	.	.	PUNCT
gs-1949	333	1	from	from	ADP
gs-1949	333	2	here	here	ADV
gs-1949	333	3	we	we	PRON
gs-1949	333	4	can	can	AUX
gs-1949	333	5	obtain	obtain	VERB
gs-1949	333	6	(	(	PUNCT
gs-1949	333	7	11	11	NUM
gs-1949	333	8	)	)	PUNCT
gs-1949	333	9	by	by	ADP
gs-1949	333	10	the	the	DET
gs-1949	333	11	cramer	cramer	NOUN
gs-1949	333	12	-	-	PUNCT
gs-1949	333	13	wold	wold	ADJ
gs-1949	333	14	method	method	NOUN
gs-1949	333	15	.	.	PUNCT
gs-1949	334	1	however	however	ADV
gs-1949	334	2	,	,	PUNCT
gs-1949	334	3	this	this	PRON
gs-1949	334	4	does	do	AUX
gs-1949	334	5	not	not	PART
gs-1949	334	6	give	give	VERB
gs-1949	334	7	us	we	PRON
gs-1949	334	8	the	the	DET
gs-1949	334	9	matrix	matrix	NOUN
gs-1949	334	10	representation	representation	NOUN
gs-1949	334	11	(	(	PUNCT
gs-1949	334	12	10	10	NUM
gs-1949	334	13	)	)	PUNCT
gs-1949	334	14	.	.	PUNCT
gs-1949	335	1	in	in	ADP
gs-1949	335	2	[	[	X
gs-1949	335	3	8	8	NUM
gs-1949	335	4	]	]	PUNCT
gs-1949	335	5	,	,	PUNCT
gs-1949	335	6	the	the	DET
gs-1949	335	7	case	case	NOUN
gs-1949	335	8	1k	1k	PRON
gs-1949	335	9			PRON
gs-1949	335	10	was	be	AUX
gs-1949	335	11	considered	consider	VERB
gs-1949	335	12	,	,	PUNCT
gs-1949	335	13	when	when	SCONJ
gs-1949	335	14	the	the	DET
gs-1949	335	15	markov	markov	NOUN
gs-1949	335	16	chain	chain	NOUN
gs-1949	335	17	already	already	ADV
gs-1949	335	18	contains	contain	VERB
gs-1949	335	19	cyclic	cyclic	ADJ
gs-1949	335	20	subclasses	subclass	NOUN
gs-1949	335	21	.	.	PUNCT
gs-1949	336	1	in	in	ADP
gs-1949	336	2	[	[	X
gs-1949	336	3	9	9	NUM
gs-1949	336	4	]	]	PUNCT
gs-1949	336	5	,	,	PUNCT
gs-1949	336	6	a	a	DET
gs-1949	336	7	matrix	matrix	NOUN
gs-1949	336	8	georgian	georgian	ADJ
gs-1949	336	9	scientists/ქართველი	scientists/ქართველი	NOUN
gs-1949	336	10	მეცნიერები	მეცნიერები	NOUN
gs-1949	336	11	ტ.	ტ.	VERB
gs-1949	336	12	5	5	NUM
gs-1949	336	13	n	n	PRON
gs-1949	336	14	2	2	NUM
gs-1949	336	15	,	,	PUNCT
gs-1949	336	16	2023	2023	NUM
gs-1949	336	17	30	30	NUM
gs-1949	336	18	representation	representation	NOUN
gs-1949	336	19	(	(	PUNCT
gs-1949	336	20	9	9	NUM
gs-1949	336	21	)	)	PUNCT
gs-1949	336	22	was	be	AUX
gs-1949	336	23	obtained	obtain	VERB
gs-1949	336	24	in	in	ADP
gs-1949	336	25	the	the	DET
gs-1949	336	26	general	general	ADJ
gs-1949	336	27	case	case	NOUN
gs-1949	336	28	when	when	SCONJ
gs-1949	336	29	1k	1k	PROPN
gs-1949	336	30			PROPN
gs-1949	336	31	and	and	CCONJ
gs-1949	336	32	the	the	DET
gs-1949	336	33	chain	chain	NOUN
gs-1949	336	34	has	have	VERB
gs-1949	336	35	cyclic	cyclic	ADJ
gs-1949	336	36	subclasses	subclass	NOUN
gs-1949	336	37	.	.	PUNCT
gs-1949	337	1	in	in	ADP
gs-1949	337	2	this	this	DET
gs-1949	337	3	case	case	NOUN
gs-1949	337	4	,	,	PUNCT
gs-1949	337	5	as	as	SCONJ
gs-1949	337	6	in	in	ADP
gs-1949	337	7	[	[	X
gs-1949	337	8	8	8	NUM
gs-1949	337	9	]	]	PUNCT
gs-1949	337	10	,	,	PUNCT
gs-1949	337	11	the	the	DET
gs-1949	337	12	result	result	NOUN
gs-1949	337	13	is	be	AUX
gs-1949	337	14	obtained	obtain	VERB
gs-1949	337	15	using	use	VERB
gs-1949	337	16	cesàro	cesàro	PROPN
gs-1949	337	17	convergence	convergence	NOUN
gs-1949	337	18	.	.	PUNCT
gs-1949	338	1	an	an	DET
gs-1949	338	2	analog	analog	NOUN
gs-1949	338	3	of	of	ADP
gs-1949	338	4	theorem	theorem	NOUN
gs-1949	338	5	2	2	NUM
gs-1949	338	6	was	be	AUX
gs-1949	338	7	obtained	obtain	VERB
gs-1949	338	8	in	in	ADP
gs-1949	338	9	[	[	X
gs-1949	338	10	11	11	NUM
gs-1949	338	11	]	]	PUNCT
gs-1949	338	12	for	for	ADP
gs-1949	338	13	one	one	NUM
gs-1949	338	14	-	-	PUNCT
gs-1949	338	15	dimensional	dimensional	ADJ
gs-1949	338	16	integer	integer	NOUN
gs-1949	338	17	random	random	ADJ
gs-1949	338	18	variables	variable	NOUN
gs-1949	338	19	connected	connect	VERB
gs-1949	338	20	by	by	ADP
gs-1949	338	21	a	a	DET
gs-1949	338	22	regular	regular	ADJ
gs-1949	338	23	markov	markov	NOUN
gs-1949	338	24	chain	chain	NOUN
gs-1949	338	25	.	.	PUNCT
gs-1949	339	1	this	this	DET
gs-1949	339	2	result	result	NOUN
gs-1949	339	3	was	be	AUX
gs-1949	339	4	generalized	generalize	VERB
gs-1949	339	5	in	in	ADP
gs-1949	339	6	[	[	X
gs-1949	339	7	12	12	NUM
gs-1949	339	8	]	]	PUNCT
gs-1949	339	9	by	by	ADP
gs-1949	339	10	partially	partially	ADV
gs-1949	339	11	removing	remove	VERB
gs-1949	339	12	the	the	DET
gs-1949	339	13	restriction	restriction	NOUN
gs-1949	339	14	on	on	ADP
gs-1949	339	15	random	random	ADJ
gs-1949	339	16	variables	variable	NOUN
gs-1949	339	17	.	.	PUNCT
gs-1949	340	1	conditionally	conditionally	ADV
gs-1949	340	2	m	m	VERB
gs-1949	340	3	-independent	-independent	ADJ
gs-1949	340	4	and	and	CCONJ
gs-1949	340	5	chain	chain	NOUN
gs-1949	340	6	m	m	VERB
gs-1949	340	7	-dependent	-dependent	ADJ
gs-1949	340	8	one	one	NUM
gs-1949	340	9	-	-	PUNCT
gs-1949	340	10	dimensional	dimensional	ADJ
gs-1949	340	11	random	random	ADJ
gs-1949	340	12	variables	variable	NOUN
gs-1949	340	13	are	be	AUX
gs-1949	340	14	discussed	discuss	VERB
gs-1949	340	15	in	in	ADP
gs-1949	340	16	[	[	X
gs-1949	340	17	12	12	NUM
gs-1949	340	18	]	]	PUNCT
gs-1949	340	19	.	.	PUNCT
gs-1949	341	1	the	the	DET
gs-1949	341	2	case	case	NOUN
gs-1949	341	3	when	when	SCONJ
gs-1949	341	4	the	the	DET
gs-1949	341	5	chain	chain	NOUN
gs-1949	341	6	has	have	VERB
gs-1949	341	7	no	no	DET
gs-1949	341	8	cyclic	cyclic	ADJ
gs-1949	341	9	subclasses	subclass	NOUN
gs-1949	341	10	is	be	AUX
gs-1949	341	11	considered	consider	VERB
gs-1949	341	12	.	.	PUNCT
gs-1949	342	1	analogues	analogue	NOUN
gs-1949	342	2	(	(	PUNCT
gs-1949	342	3	4	4	NUM
gs-1949	342	4	)	)	PUNCT
gs-1949	342	5	and	and	CCONJ
gs-1949	342	6	(	(	PUNCT
gs-1949	342	7	12	12	NUM
gs-1949	342	8	)	)	PUNCT
gs-1949	342	9	are	be	AUX
gs-1949	342	10	obtained	obtain	VERB
gs-1949	342	11	for	for	ADP
gs-1949	342	12	this	this	DET
gs-1949	342	13	particular	particular	ADJ
gs-1949	342	14	case	case	NOUN
gs-1949	342	15	.	.	PUNCT
gs-1949	343	1	conclusion	conclusion	NOUN
gs-1949	343	2	.	.	PUNCT
gs-1949	344	1	in	in	ADP
gs-1949	344	2	the	the	DET
gs-1949	344	3	work	work	NOUN
gs-1949	344	4	,	,	PUNCT
gs-1949	344	5	we	we	PRON
gs-1949	344	6	have	have	AUX
gs-1949	344	7	established	establish	VERB
gs-1949	344	8	the	the	DET
gs-1949	344	9	probability	probability	NOUN
gs-1949	344	10	of	of	ADP
gs-1949	344	11	the	the	DET
gs-1949	344	12	conditional	conditional	ADJ
gs-1949	344	13	distributions	distribution	NOUN
gs-1949	344	14	of	of	ADP
gs-1949	344	15	partial	partial	ADJ
gs-1949	344	16	sums	sum	NOUN
gs-1949	344	17	of	of	ADP
gs-1949	344	18	a	a	DET
gs-1949	344	19	sequence	sequence	NOUN
gs-1949	344	20	of	of	ADP
gs-1949	344	21	conditionally	conditionally	ADV
gs-1949	344	22	m	m	NOUN
gs-1949	344	23	-	-	NOUN
gs-1949	344	24	independent	independent	ADJ
gs-1949	344	25	of	of	ADP
gs-1949	344	26	random	random	ADJ
gs-1949	344	27	vectors	vector	NOUN
gs-1949	344	28	falling	fall	VERB
gs-1949	344	29	into	into	ADP
gs-1949	344	30	a	a	DET
gs-1949	344	31	strip	strip	NOUN
gs-1949	344	32	consisting	consist	VERB
gs-1949	344	33	of	of	ADP
gs-1949	344	34	two	two	NUM
gs-1949	344	35	shifted	shift	VERB
gs-1949	344	36	normal	normal	ADJ
gs-1949	344	37	distributions	distribution	NOUN
gs-1949	344	38	.	.	PUNCT
gs-1949	345	1	from	from	ADP
gs-1949	345	2	this	this	DET
gs-1949	345	3	theorem	theorem	NOUN
gs-1949	345	4	,	,	PUNCT
gs-1949	345	5	a	a	DET
gs-1949	345	6	similar	similar	ADJ
gs-1949	345	7	result	result	NOUN
gs-1949	345	8	is	be	AUX
gs-1949	345	9	obtained	obtain	VERB
gs-1949	345	10	for	for	ADP
gs-1949	345	11	sequences	sequence	NOUN
gs-1949	345	12	of	of	ADP
gs-1949	345	13	random	random	ADJ
gs-1949	345	14	vectors	vector	NOUN
gs-1949	345	15	with	with	ADP
gs-1949	345	16	a	a	DET
gs-1949	345	17	chain	chain	NOUN
gs-1949	345	18	m	m	NOUN
gs-1949	345	19	−dependence	−dependence	NOUN
gs-1949	345	20	.	.	PUNCT
gs-1949	346	1	this	this	DET
gs-1949	346	2	latter	latter	ADJ
gs-1949	346	3	is	be	AUX
gs-1949	346	4	a	a	DET
gs-1949	346	5	generalization	generalization	NOUN
gs-1949	346	6	of	of	ADP
gs-1949	346	7	the	the	DET
gs-1949	346	8	result	result	NOUN
gs-1949	346	9	obtained	obtain	VERB
gs-1949	346	10	by	by	ADP
gs-1949	346	11	z.	z.	PROPN
gs-1949	346	12	bezhaeva	bezhaeva	VERB
gs-1949	346	13	[	[	X
gs-1949	346	14	11	11	NUM
gs-1949	346	15	]	]	PUNCT
gs-1949	346	16	to	to	ADP
gs-1949	346	17	the	the	DET
gs-1949	346	18	multidimensional	multidimensional	ADJ
gs-1949	346	19	case	case	NOUN
gs-1949	346	20	,	,	PUNCT
gs-1949	346	21	when	when	SCONJ
gs-1949	346	22	the	the	DET
gs-1949	346	23	chain	chain	NOUN
gs-1949	346	24	is	be	AUX
gs-1949	346	25	not	not	PART
gs-1949	346	26	regular	regular	ADJ
gs-1949	346	27	and	and	CCONJ
gs-1949	346	28	has	have	VERB
gs-1949	346	29	cyclic	cyclic	ADJ
gs-1949	346	30	subclasses	subclass	NOUN
gs-1949	346	31	.	.	PUNCT
gs-1949	347	1	a	a	DET
gs-1949	347	2	matrix	matrix	NOUN
gs-1949	347	3	representation	representation	NOUN
gs-1949	347	4	of	of	ADP
gs-1949	347	5	the	the	DET
gs-1949	347	6	covariance	covariance	NOUN
gs-1949	347	7	matrix	matrix	NOUN
gs-1949	347	8	of	of	ADP
gs-1949	347	9	this	this	PRON
gs-1949	347	10	shifted	shift	VERB
gs-1949	347	11	normal	normal	ADJ
gs-1949	347	12	distribution	distribution	NOUN
gs-1949	347	13	with	with	ADP
gs-1949	347	14	characteristics	characteristic	NOUN
gs-1949	347	15	of	of	ADP
gs-1949	347	16	a	a	DET
gs-1949	347	17	markov	markov	NOUN
gs-1949	347	18	chain	chain	NOUN
gs-1949	347	19	is	be	AUX
gs-1949	347	20	given	give	VERB
gs-1949	347	21	.	.	PUNCT
gs-1949	348	1	these	these	DET
gs-1949	348	2	characteristics	characteristic	NOUN
gs-1949	348	3	are	be	AUX
gs-1949	348	4	established	establish	VERB
gs-1949	348	5	in	in	ADP
gs-1949	348	6	the	the	DET
gs-1949	348	7	sense	sense	NOUN
gs-1949	348	8	of	of	ADP
gs-1949	348	9	convergence	convergence	NOUN
gs-1949	348	10	and	and	CCONJ
gs-1949	348	11	summation	summation	NOUN
gs-1949	348	12	according	accord	VERB
gs-1949	348	13	to	to	ADP
gs-1949	348	14	cesàro	cesàro	PROPN
gs-1949	348	15	.	.	PUNCT
gs-1949	349	1	references	reference	NOUN
gs-1949	349	2	1	1	NUM
gs-1949	349	3	.	.	X
gs-1949	349	4	normal	normal	ADJ
gs-1949	349	5	approximation	approximation	NOUN
gs-1949	349	6	some	some	DET
gs-1949	349	7	recent	recent	ADJ
gs-1949	349	8	advances	advance	NOUN
gs-1949	349	9	.	.	PUNCT
gs-1949	350	1	sazonov	sazonov	PROPN
gs-1949	350	2	v.	v.	CCONJ
gs-1949	350	3	v.	v.	ADP
gs-1949	350	4	lecture	lecture	NOUN
gs-1949	350	5	notes	note	NOUN
gs-1949	350	6	in	in	ADP
gs-1949	350	7	math	math	NOUN
gs-1949	350	8	.	.	PUNCT
gs-1949	351	1	v.	v.	ADP
gs-1949	351	2	79	79	NUM
gs-1949	351	3	,	,	PUNCT
gs-1949	351	4	berlin	berlin	PROPN
gs-1949	351	5	,	,	PUNCT
gs-1949	351	6	ete	ete	NOUN
gs-1949	351	7	.	.	PUNCT
gs-1949	351	8	,:springer	,:springer	PROPN
gs-1949	351	9	.	.	PUNCT
gs-1949	352	1	1981	1981	NUM
gs-1949	352	2	.	.	PUNCT
gs-1949	353	1	https://www.amazon.com/normal-approximation-advances-lecturemathematics/dp/3540108637	https://www.amazon.com/normal-approximation-advances-lecturemathematics/dp/3540108637	NOUN
gs-1949	353	2	2	2	NUM
gs-1949	353	3	.	.	PUNCT
gs-1949	353	4	bokuchava	bokuchava	PROPN
gs-1949	353	5	i.	i.	PROPN
gs-1949	354	1	v.	v.	PROPN
gs-1949	355	1	limit	limit	PROPN
gs-1949	355	2	theorems	theorem	VERB
gs-1949	355	3	for	for	ADP
gs-1949	355	4	conditionally	conditionally	ADV
gs-1949	355	5	independent	independent	ADJ
gs-1949	355	6	sequences	sequence	NOUN
gs-1949	355	7	.	.	PUNCT
gs-1949	356	1	(	(	PUNCT
gs-1949	356	2	in	in	ADP
gs-1949	356	3	russian	russian	PROPN
gs-1949	356	4	)	)	PUNCT
gs-1949	356	5	teor	teor	PROPN
gs-1949	356	6	.	.	PUNCT
gs-1949	356	7	verojatnost	verojatnost	PROPN
gs-1949	356	8	.	.	PUNCT
gs-1949	357	1	i	i	PRON
gs-1949	357	2	primenen	primenen	VERB
gs-1949	357	3	.	.	PUNCT
gs-1949	358	1	xxix	xxix	PROPN
gs-1949	358	2	.	.	PUNCT
gs-1949	359	1	(	(	PUNCT
gs-1949	359	2	1984	1984	NUM
gs-1949	359	3	)	)	PUNCT
gs-1949	359	4	.	.	PUNCT
gs-1949	360	1	№	№	ADP
gs-1949	360	2	1	1	NUM
gs-1949	360	3	,	,	PUNCT
gs-1949	360	4	p.	p.	NOUN
gs-1949	360	5	192	192	NUM
gs-1949	360	6	-	-	SYM
gs-1949	360	7	193	193	NUM
gs-1949	360	8	.	.	PUNCT
gs-1949	361	1	https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=tvp&paperid=1992&option	https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=tvp&paperid=1992&option	NOUN
gs-1949	361	2	_	_	NOUN
gs-1949	361	3	lang	lang	PROPN
gs-1949	361	4	=	=	NOUN
gs-1949	361	5	rus	rus	NOUN
gs-1949	361	6	3	3	NUM
gs-1949	361	7	.	.	PUNCT
gs-1949	361	8	kvatadze	kvatadze	PROPN
gs-1949	361	9	z.	z.	PROPN
gs-1949	361	10	,	,	PUNCT
gs-1949	361	11	shervashidze	shervashidze	ADJ
gs-1949	361	12	t.	t.	PROPN
gs-1949	361	13	some	some	DET
gs-1949	361	14	limit	limit	NOUN
gs-1949	361	15	theorems	theorem	VERB
gs-1949	361	16	for	for	ADP
gs-1949	361	17	i.i.d	i.i.d	PROPN
gs-1949	361	18	.	.	PUNCT
gs-1949	361	19	and	and	CCONJ
gs-1949	361	20	conditionally	conditionally	ADV
gs-1949	361	21	independent	independent	ADJ
gs-1949	361	22	random	random	ADJ
gs-1949	361	23	variables	variable	NOUN
gs-1949	361	24	.	.	PUNCT
gs-1949	362	1	the	the	DET
gs-1949	362	2	second	second	ADJ
gs-1949	362	3	international	international	ADJ
gs-1949	362	4	conference	conference	NOUN
gs-1949	362	5	,	,	PUNCT
gs-1949	362	6	“	"	PUNCT
gs-1949	362	7	problems	problem	NOUN
gs-1949	362	8	of	of	ADP
gs-1949	362	9	cybernetics	cybernetic	NOUN
gs-1949	362	10	and	and	CCONJ
gs-1949	362	11	informatics	informatic	NOUN
gs-1949	362	12	”	"	PUNCT
gs-1949	362	13	.	.	PUNCT
gs-1949	363	1	september	september	PROPN
gs-1949	363	2	10	10	NUM
gs-1949	363	3	-	-	SYM
gs-1949	363	4	12	12	NUM
gs-1949	363	5	,	,	PUNCT
gs-1949	363	6	2008	2008	NUM
gs-1949	363	7	.	.	PUNCT
gs-1949	364	1	baku	baku	PROPN
gs-1949	364	2	.	.	PUNCT
gs-1949	364	3	azerbaijan	azerbaijan	PROPN
gs-1949	364	4	.	.	PROPN
gs-1949	364	5	section	section	NOUN
gs-1949	364	6	№	№	VERB
gs-1949	364	7	4	4	NUM
gs-1949	364	8	.	.	PUNCT
gs-1949	365	1	“	"	PUNCT
gs-1949	365	2	applied	apply	VERB
gs-1949	365	3	stochastic	stochastic	ADJ
gs-1949	365	4	analysis	analysis	NOUN
gs-1949	365	5	”	"	PUNCT
gs-1949	365	6	.	.	PUNCT
gs-1949	366	1	www.pci2008.science.az/4/12.pdf	www.pci2008.science.az/4/12.pdf	ADJ
gs-1949	366	2	.	.	PUNCT
gs-1949	366	3	azerbaijan	azerbaijan	PROPN
gs-1949	366	4	national	national	PROPN
gs-1949	366	5	academy	academy	PROPN
gs-1949	366	6	of	of	ADP
gs-1949	366	7	sciences	sciences	PROPN
gs-1949	366	8	.	.	PUNCT
gs-1949	367	1	institute	institute	PROPN
gs-1949	367	2	of	of	ADP
gs-1949	367	3	information	information	NOUN
gs-1949	367	4	technologies	technology	NOUN
gs-1949	367	5	of	of	ADP
gs-1949	367	6	nasa	nasa	PROPN
gs-1949	367	7	.	.	PUNCT
gs-1949	368	1	printing	printing	NOUN
gs-1949	368	2	house	house	NOUN
gs-1949	368	3	of	of	ADP
gs-1949	368	4	“	"	PUNCT
gs-1949	368	5	information	information	NOUN
gs-1949	368	6	technology	technology	NOUN
gs-1949	368	7	”	"	PUNCT
gs-1949	368	8	baku	baku	PROPN
gs-1949	368	9	.	.	PROPN
gs-1949	368	10	2008	2008	NUM
gs-1949	368	11	.	.	PUNCT
gs-1949	369	1	vol	vol	NOUN
gs-1949	369	2	.	.	PUNCT
gs-1949	369	3	ii	ii	PROPN
gs-1949	369	4	,	,	PUNCT
gs-1949	369	5	217	217	NUM
gs-1949	369	6	-	-	SYM
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gs-1949	376	7	,	,	PUNCT
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gs-1949	376	13	.	.	PUNCT
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gs-1949	377	6	.	.	PUNCT
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gs-1949	379	1	kvatadze	kvatadze	PROPN
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gs-1949	379	20	.	.	PUNCT
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gs-1949	380	2	of	of	ADP
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gs-1949	380	6	of	of	ADP
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gs-1949	380	26	(	(	PUNCT
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gs-1949	381	2	.	.	PROPN
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gs-1949	381	4	-	-	SYM
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gs-1949	381	7	,	,	PUNCT
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gs-1949	381	9	;	;	PUNCT
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gs-1949	381	13	.	.	PUNCT
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gs-1949	382	2	.	.	PUNCT
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gs-1949	383	2	-	-	SYM
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gs-1949	383	4	.	.	PUNCT
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gs-1949	384	2	;	;	PUNCT
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gs-1949	384	4	.	.	X
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gs-1949	384	11	(	(	PUNCT
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gs-1949	384	15	.	.	PUNCT
gs-1949	385	1	moscow	moscow	PROPN
gs-1949	385	2	.	.	PUNCT
gs-1949	386	1	“	"	PUNCT
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gs-1949	386	3	”	"	PUNCT
gs-1949	386	4	,	,	PUNCT
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gs-1949	386	6	.	.	PUNCT
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gs-1949	387	2	;	;	PUNCT
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gs-1949	387	4	.	.	PUNCT
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gs-1949	387	6	g.	g.	PROPN
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gs-1949	387	8	,	,	PUNCT
gs-1949	387	9	j.	j.	PROPN
gs-1949	387	10	l.	l.	PROPN
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gs-1949	388	7	.	.	PUNCT
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gs-1949	389	6	;	;	PUNCT
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gs-1949	389	8	,	,	PUNCT
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gs-1949	389	14	.	.	PUNCT
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gs-1949	390	3	,	,	PUNCT
gs-1949	390	4	kvatadze	kvatadze	PROPN
gs-1949	390	5	ts	ts	NOUN
gs-1949	390	6	.	.	PUNCT
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gs-1949	391	4	a	a	DET
gs-1949	391	5	sequence	sequence	NOUN
gs-1949	391	6	of	of	ADP
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gs-1949	391	9	on	on	ADP
gs-1949	391	10	a	a	DET
gs-1949	391	11	markov	markov	NOUN
gs-1949	391	12	chain	chain	NOUN
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gs-1949	392	1	proceedings	proceeding	NOUN
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gs-1949	393	2	.	.	PROPN
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gs-1949	393	4	.	.	PUNCT
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gs-1949	394	2	.	.	PUNCT
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gs-1949	395	5	-	-	SYM
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gs-1949	395	7	.	.	PUNCT
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gs-1949	396	2	;	;	PUNCT
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gs-1949	396	4	.	.	PUNCT
gs-1949	397	1	doob	doob	PROPN
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gs-1949	397	5	.	.	PUNCT
gs-1949	398	1	(	(	PUNCT
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gs-1949	398	5	.	.	PUNCT
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gs-1949	399	4	“	"	PUNCT
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gs-1949	399	6	”	"	PUNCT
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gs-1949	400	3	;	;	PUNCT
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gs-1949	400	5	.	.	X
gs-1949	401	1	bežaeva	bežaeva	PROPN
gs-1949	401	2	z.	z.	PROPN
gs-1949	401	3	i.	i.	PROPN
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gs-1949	401	6	for	for	ADP
gs-1949	401	7	conditional	conditional	ADJ
gs-1949	401	8	markov	markov	NOUN
gs-1949	401	9	chains	chain	NOUN
gs-1949	401	10	(	(	PUNCT
gs-1949	401	11	in	in	ADP
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gs-1949	402	4	.	.	PUNCT
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gs-1949	403	3	.	.	PUNCT
gs-1949	403	4	,	,	PUNCT
gs-1949	403	5	1971	1971	NUM
gs-1949	403	6	,	,	PUNCT
gs-1949	403	7	v.	v.	ADP
gs-1949	403	8	xvi	xvi	NOUN
gs-1949	403	9	,	,	PUNCT
gs-1949	403	10	№	№	NOUN
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gs-1949	403	12	,	,	PUNCT
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gs-1949	404	1	https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=tvp&paperid=2257&option	https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=tvp&paperid=2257&option	PROPN
gs-1949	404	2	_	_	PROPN
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gs-1949	405	4	;	;	PUNCT
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gs-1949	405	6	.	.	PUNCT
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gs-1949	406	6	,	,	PUNCT
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gs-1949	406	9	theorems	theorem	NOUN
gs-1949	406	10	for	for	ADP
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gs-1949	406	16	by	by	ADP
gs-1949	406	17	a	a	DET
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gs-1949	406	19	markov	markov	NOUN
gs-1949	406	20	chain	chain	NOUN
gs-1949	406	21	.	.	PUNCT
gs-1949	407	1	probability	probability	NOUN
gs-1949	407	2	theory	theory	NOUN
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gs-1949	407	5	ststistics	ststistic	NOUN
gs-1949	407	6	(	(	PUNCT
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gs-1949	408	3	-	-	PUNCT
gs-1949	408	4	ussr	ussr	ADJ
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gs-1949	408	6	on	on	ADP
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gs-1949	408	8	theory	theory	NOUN
gs-1949	408	9	.	.	PUNCT
gs-1949	409	1	kyoto	kyoto	PROPN
gs-1949	409	2	.	.	PUNCT
gs-1949	410	1	july	july	PROPN
gs-1949	410	2	8	8	NUM
gs-1949	410	3	-	-	SYM
gs-1949	410	4	14	14	NUM
gs-1949	410	5	1986	1986	NUM
gs-1949	410	6	)	)	PUNCT
gs-1949	410	7	.	.	PUNCT
gs-1949	411	1	lecture	lecture	NOUN
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gs-1949	411	5	.	.	PUNCT
gs-1949	412	1	vol	vol	NOUN
gs-1949	412	2	.	.	PROPN
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gs-1949	412	4	,	,	PUNCT
gs-1949	412	5	p.	p.	NOUN
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gs-1949	412	7	-	-	SYM
gs-1949	412	8	259	259	NUM
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gs-1949	412	10	-	-	PUNCT
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gs-1949	412	12	,	,	PUNCT
gs-1949	412	13	berlin	berlin	PROPN
gs-1949	412	14	.	.	PUNCT
gs-1949	413	1	etc	etc	X
gs-1949	413	2	.	.	X
gs-1949	413	3	,	,	PUNCT
gs-1949	413	4	1987	1987	NUM
gs-1949	413	5	.	.	PUNCT
gs-1949	414	1	doi	doi	X
gs-1949	414	2	·	·	PUNCT
gs-1949	414	3	https://doi.org/10.1007/bfb0078480	https://doi.org/10.1007/bfb0078480	PROPN
gs-1949	414	4	http://www.viam.science.tsu.ge/enl_ses/vol35/vol35.html	http://www.viam.science.tsu.ge/enl_ses/vol35/vol35.html	PROPN
gs-1949	414	5	http://bibliofilspb.ru/item.php?id=15498739	http://bibliofilspb.ru/item.php?id=15498739	PROPN
gs-1949	414	6	https://www.math.pku.edu.cn/teachers/yaoy/fall2011/kemeny-snell1976.pdf	https://www.math.pku.edu.cn/teachers/yaoy/fall2011/kemeny-snell1976.pdf	PROPN
gs-1949	414	7	https://rmi.tsu.ge/transactions/trmi-volumes/174-2/v174(2)-8.pdf	https://rmi.tsu.ge/transactions/trmi-volumes/174-2/v174(2)-8.pdf	PROPN
gs-1949	414	8	https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=tvp&paperid=2257&option_lang=eng	https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=tvp&paperid=2257&option_lang=eng	PROPN
gs-1949	414	9	https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=tvp&paperid=2257&option_lang=eng	https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=tvp&paperid=2257&option_lang=eng	PROPN
gs-1949	414	10	https://doi.org/10.1007/bfb0078480	https://doi.org/10.1007/bfb0078480	PROPN
gs-1949	414	11	georgian	georgian	PROPN
gs-1949	414	12	scientists/ქართველი	scientists/ქართველი	NOUN
gs-1949	414	13	მეცნიერები	მეცნიერები	NOUN
gs-1949	414	14	ტ.	ტ.	VERB
gs-1949	414	15	5	5	NUM
gs-1949	414	16	n	n	PRON
gs-1949	414	17	2	2	NUM
gs-1949	414	18	,	,	PUNCT
gs-1949	414	19	2023	2023	NUM
gs-1949	414	20	32	32	NUM
gs-1949	414	21	m	m	NOUN
gs-1949	414	22	დამოკიდებულ	დამოკიდებულ	PROPN
gs-1949	414	23	ვექტორთა	ვექტორთა	PROPN
gs-1949	414	24	ჯამის	ჯამის	PROPN
gs-1949	414	25	პირობითი	პირობითი	PROPN
gs-1949	414	26	განაწილების	განაწილების	PROPN
gs-1949	414	27	შესახებ	შესახებ	VERB
gs-1949	414	28	ზურაბ	ზურაბ	PROPN
gs-1949	414	29	ქვათაძე	ქვათაძე	PROPN
gs-1949	414	30	*	*	NOUN
gs-1949	414	31	,	,	PUNCT
gs-1949	414	32	ბექნუ	ბექნუ	ADJ
gs-1949	414	33	ფარჯიანი	ფარჯიანი	NOUN
gs-1949	414	34	*	*	PUNCT
gs-1949	414	35	*	*	PROPN
gs-1949	414	36	,	,	PUNCT
gs-1949	414	37	ციალა	ციალა	PROPN
gs-1949	414	38	ქვათაძე	ქვათაძე	NOUN
gs-1949	414	39	*	*	PROPN
gs-1949	414	40	*	*	PUNCT
gs-1949	414	41	*	*	PUNCT
gs-1949	414	42	*	*	PUNCT
gs-1949	415	1	სტუ-ს	სტუ-ს	ADV
gs-1949	415	2	მათემატიკის	მათემატიკის	NOUN
gs-1949	415	3	დეპარტამენტი.	დეპარტამენტი.	NOUN
gs-1949	415	4	პროფესორი	პროფესორი	PROPN
gs-1949	415	5	,	,	PUNCT
gs-1949	415	6	*	*	PUNCT
gs-1949	415	7	*	*	PUNCT
gs-1949	415	8	სტუ-ს	სტუ-ს	ADV
gs-1949	415	9	მათემატიკის	მათემატიკის	NOUN
gs-1949	415	10	დეპარტამენტი.	დეპარტამენტი.	ADJ
gs-1949	415	11	ასოცირებული	ასოცირებული	PROPN
gs-1949	415	12	პროფესორი	პროფესორი	NOUN
gs-1949	415	13	,	,	PUNCT
gs-1949	415	14	*	*	PUNCT
gs-1949	415	15	*	*	PUNCT
gs-1949	415	16	*	*	PUNCT
gs-1949	415	17	სტატისტიკის	სტატისტიკის	PROPN
gs-1949	415	18	ლექტორი	ლექტორი	PROPN
gs-1949	415	19	,	,	PUNCT
gs-1949	415	20	შავი	შავი	PROPN
gs-1949	415	21	სღვის	სღვის	PROPN
gs-1949	415	22	საერთაშორისო	საერთაშორისო	PROPN
gs-1949	415	23	უნივერსიტეტი	უნივერსიტეტი	NOUN
gs-1949	415	24	,	,	PUNCT
gs-1949	415	25	აბსტრაქტი	აბსტრაქტი	NOUN
gs-1949	415	26	მრავალი	მრავალი	ADJ
gs-1949	415	27	პრაქტიკული	პრაქტიკული	PROPN
gs-1949	415	28	ამოცანის	ამოცანის	PROPN
gs-1949	415	29	გადაჭრის	გადაჭრის	PROPN
gs-1949	415	30	დროს	დროს	PROPN
gs-1949	415	31	დგება	დგება	PROPN
gs-1949	415	32	დამოკიდებული	დამოკიდებული	PROPN
gs-1949	415	33	დაკვირვებებით	დაკვირვებებით	PROPN
gs-1949	415	34	პარამეტრების	პარამეტრების	PROPN
gs-1949	415	35	სტატისტიკური	სტატისტიკური	PROPN
gs-1949	415	36	შეფასებების	შეფასებების	PROPN
gs-1949	415	37	აგების	აგების	PROPN
gs-1949	415	38	საკითხი.	საკითხი.	PROPN
gs-1949	415	39	მაგალითად	მაგალითად	PROPN
gs-1949	415	40	პროფესიული	პროფესიული	VERB
gs-1949	415	41	კოლეჯების	კოლეჯების	PROPN
gs-1949	415	42	რანჟირების	რანჟირების	PROPN
gs-1949	415	43	მოდელის	მოდელის	PROPN
gs-1949	416	1	დასადგენად	დასადგენად	PROPN
gs-1949	416	2	ჩატარებულ	ჩატარებულ	PROPN
gs-1949	416	3	კვლევაში	კვლევაში	PROPN
gs-1949	416	4	სტუდენტების	სტუდენტების	PROPN
gs-1949	416	5	გამოკითხვით	გამოკითხვით	PROPN
gs-1949	416	6	მიღებული	მიღებული	PROPN
gs-1949	416	7	მონაცემები	მონაცემები	NOUN
gs-1949	416	8	დამოკიდებულია	დამოკიდებულია	VERB
gs-1949	416	9	ერთმანეთზე	ერთმანეთზე	ADJ
gs-1949	416	10	,	,	PUNCT
gs-1949	416	11	გამომდინარე	გამომდინარე	PROPN
gs-1949	416	12	იქედან	იქედან	PROPN
gs-1949	416	13	,	,	PUNCT
gs-1949	416	14	რომ	რომ	PROPN
gs-1949	416	15	ისინი	ისინი	NOUN
gs-1949	416	16	მიღებულია	მიღებულია	ADJ
gs-1949	416	17	ერთი	ერთი	ADJ
gs-1949	416	18	სოციუმის	სოციუმის	PROPN
gs-1949	416	19	ჯგუფიდან	ჯგუფიდან	PROPN
gs-1949	416	20	(	(	PUNCT
gs-1949	416	21	r.	r.	PROPN
gs-1949	416	22	chartolani	chartolani	PROPN
gs-1949	416	23	,	,	PUNCT
gs-1949	416	24	n.	n.	PROPN
gs-1949	416	25	durglishvili	durglishvili	PROPN
gs-1949	416	26	,	,	PUNCT
gs-1949	416	27	z.	z.	PROPN
gs-1949	416	28	kvatadze	kvatadze	PROPN
gs-1949	416	29	.	.	PUNCT
gs-1949	417	1	optimization	optimization	NOUN
gs-1949	417	2	of	of	ADP
gs-1949	417	3	a	a	DET
gs-1949	417	4	state	state	NOUN
gs-1949	417	5	financing	financing	NOUN
gs-1949	417	6	model	model	NOUN
gs-1949	417	7	of	of	ADP
gs-1949	417	8	vocational	vocational	ADJ
gs-1949	417	9	colleges	college	NOUN
gs-1949	417	10	.	.	PUNCT
gs-1949	418	1	proc	proc	NOUN
gs-1949	418	2	.	.	PUNCT
gs-1949	419	1	a.	a.	PROPN
gs-1949	419	2	razmadze	razmadze	PROPN
gs-1949	419	3	math	math	PROPN
gs-1949	419	4	.	.	PUNCT
gs-1949	420	1	inst	inst	PROPN
gs-1949	420	2	.	.	PROPN
gs-1949	420	3	2015	2015	NUM
gs-1949	420	4	.	.	PUNCT
gs-1949	421	1	169.(2	169.(2	NUM
gs-1949	421	2	-	-	SYM
gs-1949	421	3	15	15	NUM
gs-1949	421	4	)	)	PUNCT
gs-1949	421	5	,	,	PUNCT
gs-1949	421	6	pp	pp	ADP
gs-1949	421	7	.	.	PUNCT
gs-1949	422	1	23	23	NUM
gs-1949	422	2	-	-	SYM
gs-1949	422	3	31	31	NUM
gs-1949	422	4	)	)	PUNCT
gs-1949	422	5	.	.	PUNCT
gs-1949	423	1	ასევე	ასევე	PROPN
gs-1949	423	2	ვერ	ვერ	PROPN
gs-1949	423	3	უგულვებელვყოფთ	უგულვებელვყოფთ	NOUN
gs-1949	423	4	მონაცემთა	მონაცემთა	VERB
gs-1949	423	5	დამოკიდებულებას	დამოკიდებულებას	PROPN
gs-1949	423	6	გეოფიზიკური	გეოფიზიკური	PROPN
gs-1949	423	7	მიმართულების	მიმართულების	PROPN
gs-1949	423	8	სხვადასხვა	სხვადასხვა	PROPN
gs-1949	423	9	კვლევების	კვლევების	PROPN
gs-1949	423	10	დროსაც.	დროსაც.	PROPN
gs-1949	423	11	მაგალითად	მაგალითად	PROPN
gs-1949	423	12	მიწისძვრის	მიწისძვრის	PROPN
gs-1949	423	13	წინა	წინა	ADJ
gs-1949	423	14	(	(	PUNCT
gs-1949	423	15	მოსამზადებელ	მოსამზადებელ	NOUN
gs-1949	423	16	)	)	PUNCT
gs-1949	423	17	პერიოდში	პერიოდში	PROPN
gs-1949	423	18	ქანებში	ქანებში	VERB
gs-1949	423	19	მიმდინარე	მიმდინარე	NOUN
gs-1949	423	20	ტექტონიკური	ტექტონიკური	CCONJ
gs-1949	423	21	პროცესები	პროცესები	NOUN
gs-1949	423	22	დროში	დროში	PROPN
gs-1949	423	23	უწყვეტად	უწყვეტად	PROPN
gs-1949	423	24	ვითარდება	ვითარდება	PROPN
gs-1949	423	25	და	და	PROPN
gs-1949	423	26	შესაბამისად	შესაბამისად	PROPN
gs-1949	423	27	დისკრეტულ	დისკრეტულ	PROPN
gs-1949	423	28	მომენტებში	მომენტებში	PROPN
gs-1949	423	29	აღებული	აღებული	PROPN
gs-1949	423	30	ნებისმიერი	ნებისმიერი	NOUN
gs-1949	423	31	მახასიათებლის	მახასიათებლის	NOUN
gs-1949	423	32	ჩანაწერები	ჩანაწერები	NOUN
gs-1949	423	33	როგორც	როგორც	PROPN
gs-1949	423	34	ერთი	ერთი	NOUN
gs-1949	423	35	მთლიანის	მთლიანის	PROPN
gs-1949	423	36	გამოვლინებები	გამოვლინებები	NOUN
gs-1949	423	37	დამოკიდებულია	დამოკიდებულია	VERB
gs-1949	423	38	ერთმანეთზე.	ერთმანეთზე.	NOUN
gs-1949	423	39	ანალოგიური	ანალოგიური	PROPN
gs-1949	423	40	მოსაზრებებიდან	მოსაზრებებიდან	VERB
gs-1949	423	41	გამომდინარე	გამომდინარე	PROPN
gs-1949	423	42	სხვადასხვა	სხვადასხვა	PROPN
gs-1949	423	43	პოპულაციების	პოპულაციების	AUX
gs-1949	423	44	განაწილების	განაწილების	VERB
gs-1949	423	45	კანონის	კანონის	NOUN
gs-1949	423	46	დადგენის	დადგენის	PROPN
gs-1949	423	47	დროს	დროს	VERB
gs-1949	423	48	ხდება	ხდება	NOUN
gs-1949	423	49	სიმკვრივის	სიმკვრივის	NOUN
gs-1949	423	50	შეფასების	შეფასების	NOUN
gs-1949	423	51	აგება	აგება	PROPN
gs-1949	423	52	დამოკიდებული	დამოკიდებული	PROPN
gs-1949	423	53	დაკვირვებებით.	დაკვირვებებით.	NOUN
gs-1949	423	54	მაგალითად	მაგალითად	NOUN
gs-1949	423	55	ცნობილია	ცნობილია	VERB
gs-1949	423	56	სიმკვრივის	სიმკვრივის	NOUN
gs-1949	423	57	არაპარამეტრული	არაპარამეტრული	NOUN
gs-1949	423	58	შეფასებები	შეფასებები	VERB
gs-1949	423	59	და	და	NOUN
gs-1949	423	60	რეგრესიის	რეგრესიის	PROPN
gs-1949	423	61	კოეფიციენტების	კოეფიციენტების	NOUN
gs-1949	423	62	შეფასებები	შეფასებები	VERB
gs-1949	423	63	რომლებიც	რომლებიც	VERB
gs-1949	423	64	აგებულია	აგებულია	VERB
gs-1949	423	65	მარკოვის	მარკოვის	PROPN
gs-1949	423	66	ჯაჭვად	ჯაჭვად	ADJ
gs-1949	423	67	შეკრული	შეკრული	NOUN
gs-1949	423	68	დაკვირვებებით	დაკვირვებებით	PROPN
gs-1949	423	69	(	(	PUNCT
gs-1949	423	70	yakowitz	yakowitz	PROPN
gs-1949	423	71	sidney	sidney	PROPN
gs-1949	423	72	(	(	PUNCT
gs-1949	423	73	1989	1989	NUM
gs-1949	423	74	)	)	PUNCT
gs-1949	423	75	nonparametric	nonparametric	NOUN
gs-1949	423	76	density	density	NOUN
gs-1949	423	77	and	and	CCONJ
gs-1949	423	78	regression	regression	NOUN
gs-1949	423	79	estimation	estimation	NOUN
gs-1949	423	80	for	for	ADP
gs-1949	423	81	markov	markov	NOUN
gs-1949	423	82	sequences	sequence	NOUN
gs-1949	423	83	without	without	ADP
gs-1949	423	84	mixing	mix	VERB
gs-1949	423	85	assumptions	assumption	NOUN
gs-1949	423	86	.	.	PUNCT
gs-1949	424	1	85721	85721	NUM
gs-1949	424	2	–	–	PUNCT
gs-1949	424	3	journal	journal	NOUN
gs-1949	424	4	of	of	ADP
gs-1949	424	5	multivariate	multivariate	NOUN
gs-1949	424	6	analysis	analysis	NOUN
gs-1949	424	7	,	,	PUNCT
gs-1949	424	8	30	30	NUM
gs-1949	424	9	:	:	SYM
gs-1949	424	10	124	124	NUM
gs-1949	424	11	-	-	SYM
gs-1949	424	12	136	136	NUM
gs-1949	424	13	.	.	PUNCT
gs-1949	425	1	arisona	arisona	PROPN
gs-1949	425	2	,	,	PUNCT
gs-1949	425	3	usa	usa	PROPN
gs-1949	425	4	)	)	PUNCT
gs-1949	425	5	.	.	PUNCT
gs-1949	426	1	ასევე	ასევე	PROPN
gs-1949	426	2	განიხილება	განიხილება	PROPN
gs-1949	426	3	პირობითად	პირობითად	VERB
gs-1949	426	4	დამოუკიდებელი	დამოუკიდებელი	ADJ
gs-1949	426	5	და	და	NOUN
gs-1949	426	6	ჯაჭვურად	ჯაჭვურად	NOUN
gs-1949	426	7	დამოკიდებული	დამოკიდებული	PROPN
gs-1949	426	8	დაკვირვებები.	დაკვირვებები.	ADV
gs-1949	426	9	ცნობილია	ცნობილია	ADJ
gs-1949	426	10	მათი	მათი	PROPN
gs-1949	426	11	საშუალებით	საშუალებით	PROPN
gs-1949	426	12	აგებული	აგებული	PROPN
gs-1949	426	13	სიმკვრივის	სიმკვრივის	NOUN
gs-1949	426	14	გულოვანი	გულოვანი	NOUN
gs-1949	426	15	შეფასებები	შეფასებები	VERB
gs-1949	426	16	და	და	NOUN
gs-1949	426	17	მათი	მათი	NOUN
gs-1949	426	18	სიზუსტე	სიზუსტე	NOUN
gs-1949	426	19	2l	2l	PROPN
gs-1949	426	20	მეტრიკით	მეტრიკით	NOUN
gs-1949	426	21	(	(	PUNCT
gs-1949	426	22	z	z	NOUN
gs-1949	426	23	,	,	PUNCT
gs-1949	426	24	kvatadze	kvatadze	PROPN
gs-1949	426	25	,	,	PUNCT
gs-1949	426	26	b.	b.	PROPN
gs-1949	426	27	phardjiani	phardjiani	PROPN
gs-1949	426	28	.	.	PUNCT
gs-1949	427	1	on	on	ADP
gs-1949	427	2	the	the	DET
gs-1949	427	3	exsactness	exsactness	NOUN
gs-1949	427	4	of	of	ADP
gs-1949	427	5	distribution	distribution	NOUN
gs-1949	427	6	density	density	NOUN
gs-1949	427	7	estimates	estimate	NOUN
gs-1949	427	8	constructed	construct	VERB
gs-1949	427	9	by	by	ADP
gs-1949	427	10	some	some	DET
gs-1949	427	11	class	class	NOUN
gs-1949	427	12	of	of	ADP
gs-1949	427	13	dependent	dependent	ADJ
gs-1949	427	14	observations	observation	NOUN
gs-1949	427	15	.	.	PUNCT
gs-1949	428	1	mathematics	mathematic	NOUN
gs-1949	428	2	and	and	CCONJ
gs-1949	428	3	statistics	statistic	NOUN
gs-1949	428	4	.	.	PUNCT
gs-1949	429	1	2019	2019	NUM
gs-1949	429	2	vol	vol	NOUN
gs-1949	429	3	.	.	PUNCT
gs-1949	430	1	7(4	7(4	NUM
gs-1949	430	2	)	)	PUNCT
gs-1949	430	3	,	,	PUNCT
gs-1949	430	4	pp	pp	PROPN
gs-1949	430	5	.	.	PUNCT
gs-1949	431	1	135	135	NUM
gs-1949	431	2	-	-	SYM
gs-1949	431	3	145	145	NUM
gs-1949	431	4	.	.	PUNCT
gs-1949	432	1	san	san	PROPN
gs-1949	432	2	jose	jose	PROPN
gs-1949	432	3	)	)	PUNCT
gs-1949	432	4	და	და	PROPN
gs-1949	432	5	1l	1l	NUM
gs-1949	432	6	მეტრიკით	მეტრიკით	NOUN
gs-1949	432	7	(	(	PUNCT
gs-1949	432	8	b.	b.	PROPN
gs-1949	432	9	parjiani	parjiani	PROPN
gs-1949	432	10	,	,	PUNCT
gs-1949	432	11	l.	l.	PROPN
gs-1949	432	12	labadze	labadze	PROPN
gs-1949	432	13	,	,	PUNCT
gs-1949	432	14	t.	t.	PROPN
gs-1949	432	15	kvatadze	kvatadze	PROPN
gs-1949	432	16	;	;	PUNCT
gs-1949	432	17	georgian	georgian	ADJ
gs-1949	432	18	scientists	scientist	NOUN
gs-1949	432	19	,	,	PUNCT
gs-1949	432	20	“	"	PUNCT
gs-1949	432	21	on	on	ADP
gs-1949	432	22	the	the	DET
gs-1949	432	23	accuracyby	accuracyby	NOUN
gs-1949	432	24	the	the	DET
gs-1949	432	25	metric	metric	ADJ
gs-1949	432	26	l1	l1	PROPN
gs-1949	432	27	of	of	ADP
gs-1949	432	28	the	the	DET
gs-1949	432	29	density	density	NOUN
gs-1949	432	30	estimation	estimation	NOUN
gs-1949	432	31	constructed	construct	VERB
gs-1949	432	32	by	by	ADP
gs-1949	432	33	dependent	dependent	ADJ
gs-1949	432	34	observations	observation	NOUN
gs-1949	432	35	”	"	PUNCT
gs-1949	432	36	vol	vol	NOUN
gs-1949	432	37	.	.	PROPN
gs-1949	433	1	5	5	NUM
gs-1949	433	2	.	.	X
gs-1949	433	3	issue	issue	NOUN
gs-1949	433	4	1	1	NUM
gs-1949	433	5	,	,	PUNCT
gs-1949	433	6	pp	pp	ADJ
gs-1949	433	7	.	.	PUNCT
gs-1949	434	1	308	308	NUM
gs-1949	434	2	-	-	SYM
gs-1949	434	3	321	321	NUM
gs-1949	434	4	,	,	PUNCT
gs-1949	434	5	2023	2023	NUM
gs-1949	434	6	)	)	PUNCT
gs-1949	434	7	.	.	PUNCT
gs-1949	435	1	დამოკიდებული	დამოკიდებული	PROPN
gs-1949	435	2	დაკვირვებებით	დაკვირვებებით	PROPN
gs-1949	435	3	სტატისტიკური	სტატისტიკური	PROPN
gs-1949	435	4	შეფასებების	შეფასებების	PROPN
gs-1949	435	5	ასაგებად	ასაგებად	PROPN
gs-1949	435	6	და	და	PROPN
gs-1949	435	7	მათი	მათი	PROPN
gs-1949	435	8	ძალმოსილობის	ძალმოსილობის	ADJ
gs-1949	435	9	დასადგენად	დასადგენად	NOUN
gs-1949	435	10	საჭიროა	საჭიროა	NOUN
gs-1949	435	11	დამოკიდებელი	დამოკიდებელი	PROPN
gs-1949	435	12	შემთხვევითი	შემთხვევითი	NOUN
gs-1949	435	13	სიდიდეების	სიდიდეების	VERB
gs-1949	435	14	ჯამების	ჯამების	ADV
gs-1949	435	15	განაწილების	განაწილების	VERB
gs-1949	435	16	ასიმპტოტიკის	ასიმპტოტიკის	ADJ
gs-1949	435	17	ცოდნა.	ცოდნა.	ADJ
gs-1949	435	18	თანამედროვე	თანამედროვე	PROPN
gs-1949	435	19	ეტაპზე	ეტაპზე	PROPN
gs-1949	435	20	ხდება	ხდება	PROPN
gs-1949	435	21	დამოუკიდებელ	დამოუკიდებელ	NOUN
gs-1949	435	22	შემთხვევით	შემთხვევით	NOUN
gs-1949	435	23	სიდიდეთა	სიდიდეთა	ADV
gs-1949	435	24	შეკრების	შეკრების	PROPN
gs-1949	435	25	მდიდარი	მდიდარი	PROPN
gs-1949	435	26	თეორიის	თეორიის	PROPN
gs-1949	435	27	(	(	PUNCT
gs-1949	435	28	normal	normal	ADJ
gs-1949	435	29	approximation	approximation	NOUN
gs-1949	435	30	some	some	DET
gs-1949	435	31	recent	recent	ADJ
gs-1949	435	32	advances	advance	NOUN
gs-1949	435	33	.	.	PUNCT
gs-1949	436	1	sazonov	sazonov	PROPN
gs-1949	436	2	v.	v.	CCONJ
gs-1949	436	3	v.	v.	ADP
gs-1949	436	4	lecture	lecture	NOUN
gs-1949	436	5	notes	note	NOUN
gs-1949	436	6	in	in	ADP
gs-1949	436	7	math	math	NOUN
gs-1949	436	8	.	.	PUNCT
gs-1949	437	1	v.	v.	ADP
gs-1949	437	2	79	79	NUM
gs-1949	437	3	,	,	PUNCT
gs-1949	437	4	berlin	berlin	PROPN
gs-1949	437	5	,	,	PUNCT
gs-1949	437	6	ete	ete	PROPN
gs-1949	437	7	.	.	PROPN
gs-1949	437	8	,	,	PUNCT
gs-1949	437	9	:	:	PUNCT
gs-1949	437	10	springer	springer	NOUN
gs-1949	437	11	.	.	PUNCT
gs-1949	438	1	1981	1981	NUM
gs-1949	438	2	.	.	PUNCT
gs-1949	438	3	)	)	PUNCT
gs-1949	439	1	გადატანა	გადატანა	VERB
gs-1949	439	2	დამოკიდებულ	დამოკიდებულ	PROPN
gs-1949	439	3	შემთხვევით	შემთხვევით	PROPN
gs-1949	439	4	სიდიდეებზე.	სიდიდეებზე.	VERB
gs-1949	439	5	მრავალ	მრავალ	PROPN
gs-1949	439	6	ამოცანაში	ამოცანაში	PROPN
gs-1949	439	7	გამოიყენება	გამოიყენება	PROPN
gs-1949	439	8	მარკოვული	მარკოვული	PROPN
gs-1949	439	9	დამოკიდებულება	დამოკიდებულება	PROPN
gs-1949	439	10	,	,	PUNCT
gs-1949	439	11	რომელიც	რომელიც	ADJ
gs-1949	439	12	სუსტად	სუსტად	NOUN
gs-1949	439	13	დამოკიდებულების	დამოკიდებულების	ADJ
gs-1949	439	14	ერთ-ერთი	ერთ-ერთი	NOUN
gs-1949	439	15	სახეა.	სახეა.	VERB
gs-1949	439	16	სხვადასხვა	სხვადასხვა	ADJ
gs-1949	439	17	ტიპის	ტიპის	NOUN
gs-1949	439	18	დამოკიდებულების	დამოკიდებულების	NOUN
gs-1949	439	19	(	(	PUNCT
gs-1949	439	20	სუსტად	სუსტად	ADJ
gs-1949	439	21	დამოკიდებული	დამოკიდებული	PROPN
gs-1949	439	22	,	,	PUNCT
gs-1949	439	23	პირობითად	პირობითად	NOUN
gs-1949	439	24	დამოუკიდებული	დამოუკიდებული	NOUN
gs-1949	439	25	,	,	PUNCT
gs-1949	439	26	georgian	georgian	ADJ
gs-1949	439	27	scientists/ქართველი	scientists/ქართველი	NOUN
gs-1949	439	28	მეცნიერები	მეცნიერები	NOUN
gs-1949	439	29	ტ.	ტ.	VERB
gs-1949	439	30	5	5	NUM
gs-1949	439	31	n	n	PRON
gs-1949	439	32	2	2	NUM
gs-1949	439	33	,	,	PUNCT
gs-1949	439	34	2023	2023	NUM
gs-1949	439	35	33	33	NUM
gs-1949	439	36	მარკოვის	მარკოვის	NOUN
gs-1949	439	37	ჯაჭვად	ჯაჭვად	ADJ
gs-1949	439	38	შეკრული	შეკრული	NOUN
gs-1949	439	39	)	)	PUNCT
gs-1949	439	40	შემთხვევითი	შემთხვევითი	NOUN
gs-1949	439	41	სიდიდეების	სიდიდეების	VERB
gs-1949	439	42	ჯამების	ჯამების	PROPN
gs-1949	439	43	ზღვარითი	ზღვარითი	NOUN
gs-1949	439	44	ასიმპტოტიკის	ასიმპტოტიკის	PROPN
gs-1949	439	45	საკითხები	საკითხები	PROPN
gs-1949	439	46	მრავალ	მრავალ	NOUN
gs-1949	439	47	ნაშრომშია	ნაშრომშია	PROPN
gs-1949	439	48	გადმოცემული.	გადმოცემული.	PROPN
gs-1949	439	49	ხშირად	ხშირად	VERB
gs-1949	439	50	განიხილება	განიხილება	ADJ
gs-1949	439	51	ისეთ	ისეთ	NOUN
gs-1949	439	52	შემთხვევით	შემთხვევით	PROPN
gs-1949	439	53	სიდიდეთა	სიდიდეთა	ADV
gs-1949	439	54	ჯამები	ჯამები	NOUN
gs-1949	439	55	,	,	PUNCT
gs-1949	439	56	რომელთა	რომელთა	PROPN
gs-1949	439	57	ერთობლივი	ერთობლივი	PROPN
gs-1949	439	58	განაწილება	განაწილება	PROPN
gs-1949	439	59	განისაზღვრება	განისაზღვრება	PROPN
gs-1949	439	60	შემთხვევით	შემთხვევით	PROPN
gs-1949	439	61	ელემენტთა	ელემენტთა	PROPN
gs-1949	439	62	რაიმე	რაიმე	PROPN
gs-1949	439	63	მმართველი	მმართველი	PROPN
gs-1949	439	64	მიმდევრობით.	მიმდევრობით.	PROPN
gs-1949	439	65	განიხილება	განიხილება	PROPN
gs-1949	439	66	პირობითად	პირობითად	PROPN
gs-1949	439	67	დამოუკიდებელი	დამოუკიდებელი	PROPN
gs-1949	439	68	(	(	PUNCT
gs-1949	439	69	bokuchava	bokuchava	PROPN
gs-1949	439	70	i.	i.	PROPN
gs-1949	439	71	v.	v.	PROPN
gs-1949	439	72	limit	limit	PROPN
gs-1949	439	73	theorems	theorem	VERB
gs-1949	439	74	for	for	ADP
gs-1949	439	75	conditionally	conditionally	ADV
gs-1949	439	76	independent	independent	ADJ
gs-1949	439	77	sequences	sequence	NOUN
gs-1949	439	78	.	.	PUNCT
gs-1949	440	1	(	(	PUNCT
gs-1949	440	2	in	in	ADP
gs-1949	440	3	russian	russian	PROPN
gs-1949	440	4	)	)	PUNCT
gs-1949	440	5	teor	teor	PROPN
gs-1949	440	6	.	.	PUNCT
gs-1949	440	7	verojatnost	verojatnost	PROPN
gs-1949	440	8	.	.	PUNCT
gs-1949	441	1	i	i	PRON
gs-1949	441	2	primenen	primenen	VERB
gs-1949	441	3	.	.	PUNCT
gs-1949	442	1	xxix	xxix	PROPN
gs-1949	442	2	.	.	PUNCT
gs-1949	443	1	(	(	PUNCT
gs-1949	443	2	1984	1984	NUM
gs-1949	443	3	)	)	PUNCT
gs-1949	443	4	.	.	PUNCT
gs-1949	444	1	№	№	ADP
gs-1949	444	2	1	1	NUM
gs-1949	444	3	,	,	PUNCT
gs-1949	444	4	p.	p.	NOUN
gs-1949	444	5	192	192	NUM
gs-1949	444	6	-	-	SYM
gs-1949	444	7	193	193	NUM
gs-1949	444	8	)	)	PUNCT
gs-1949	444	9	და	და	NOUN
gs-1949	444	10	ჯაჭვურად	ჯაჭვურად	NOUN
gs-1949	444	11	დამოკიდებული	დამოკიდებული	PROPN
gs-1949	444	12	მიმდევრობები.	მიმდევრობები.	NOUN
gs-1949	444	13	ამ	ამ	VERB
gs-1949	444	14	საკითხებს	საკითხებს	PROPN
gs-1949	444	15	ეხება	ეხება	PROPN
gs-1949	444	16	მაგალითად	მაგალითად	PROPN
gs-1949	444	17	გ.	გ.	PROPN
gs-1949	444	18	ობრაინის	ობრაინის	PROPN
gs-1949	444	19	(	(	PUNCT
gs-1949	444	20	o	o	NOUN
gs-1949	444	21	’	'	PUNCT
gs-1949	444	22	braien	braien	PROPN
gs-1949	444	23	g.l	g.l	PROPN
gs-1949	444	24	.	.	PROPN
gs-1949	444	25	limit	limit	PROPN
gs-1949	444	26	theorems	theorem	NOUN
gs-1949	444	27	for	for	ADP
gs-1949	444	28	sum	sum	NOUN
gs-1949	444	29	of	of	ADP
gs-1949	444	30	chain	chain	NOUN
gs-1949	444	31	dependent	dependent	ADJ
gs-1949	444	32	proccesses	proccesse	NOUN
gs-1949	444	33	.	.	PUNCT
gs-1949	445	1	u.	u.	PROPN
gs-1949	445	2	appl	appl	PROPN
gs-1949	445	3	.	.	PUNCT
gs-1949	446	1	probab	probab	PROPN
gs-1949	446	2	.	.	PROPN
gs-1949	446	3	,	,	PUNCT
gs-1949	446	4	1974	1974	NUM
gs-1949	446	5	,	,	PUNCT
gs-1949	446	6	11	11	NUM
gs-1949	446	7	,	,	PUNCT
gs-1949	446	8	582	582	NUM
gs-1949	446	9	-	-	SYM
gs-1949	446	10	587	587	NUM
gs-1949	446	11	)	)	PUNCT
gs-1949	446	12	;	;	PUNCT
gs-1949	446	13	ი.	ი.	ADJ
gs-1949	446	14	ალეშკიავიჩუსის	ალეშკიავიჩუსის	NOUN
gs-1949	446	15	(	(	PUNCT
gs-1949	446	16	g.	g.	PROPN
gs-1949	446	17	yu	yu	PROPN
gs-1949	446	18	.	.	PROPN
gs-1949	446	19	aleshkyavichus	aleshkyavichus	PROPN
gs-1949	446	20	,	,	PUNCT
gs-1949	446	21	on	on	ADP
gs-1949	446	22	the	the	DET
gs-1949	446	23	central	central	ADJ
gs-1949	446	24	limit	limit	NOUN
gs-1949	446	25	theorem	theorem	VERB
gs-1949	446	26	for	for	ADP
gs-1949	446	27	sums	sum	NOUN
gs-1949	446	28	of	of	ADP
gs-1949	446	29	random	random	ADJ
gs-1949	446	30	variables	variable	NOUN
gs-1949	446	31	given	give	VERB
gs-1949	446	32	on	on	ADP
gs-1949	446	33	a	a	DET
gs-1949	446	34	markov	markov	NOUN
gs-1949	446	35	chain	chain	NOUN
gs-1949	446	36	.	.	PUNCT
gs-1949	447	1	(	(	PUNCT
gs-1949	447	2	russian	russian	ADJ
gs-1949	447	3	)	)	PUNCT
gs-1949	447	4	lithuanian	lithuanian	PROPN
gs-1949	447	5	mathematical	mathematical	ADJ
gs-1949	447	6	collected	collect	VERB
gs-1949	447	7	works	work	NOUN
gs-1949	447	8	,	,	PUNCT
gs-1949	447	9	vilnius	vilnius	NOUN
gs-1949	447	10	6	6	NUM
gs-1949	447	11	(	(	PUNCT
gs-1949	447	12	1966	1966	NUM
gs-1949	447	13	)	)	PUNCT
gs-1949	447	14	,	,	PUNCT
gs-1949	447	15	№	№	NOUN
gs-1949	447	16	.	.	NOUN
gs-1949	447	17	1	1	NUM
gs-1949	447	18	,	,	PUNCT
gs-1949	447	19	15−22	15−22	NOUN
gs-1949	447	20	.	.	PUNCT
gs-1949	447	21	)	)	PUNCT
gs-1949	447	22	;	;	PUNCT
gs-1949	447	23	რ.	რ.	PROPN
gs-1949	447	24	ჩიტაშვილის	ჩიტაშვილის	PROPN
gs-1949	447	25	,	,	PUNCT
gs-1949	447	26	თ.	თ.	PROPN
gs-1949	447	27	შერვაშიძის	შერვაშიძის	NOUN
gs-1949	447	28	,	,	PUNCT
gs-1949	447	29	ი.	ი.	ADJ
gs-1949	447	30	ბოკუჩავას	ბოკუჩავას	NOUN
gs-1949	447	31	,	,	PUNCT
gs-1949	447	32	ზ.	ზ.	NOUN
gs-1949	447	33	ქვათაძის	ქვათაძის	NOUN
gs-1949	447	34	(	(	PUNCT
gs-1949	447	35	bokuchava	bokuchava	PROPN
gs-1949	447	36	i.	i.	PROPN
gs-1949	447	37	,	,	PUNCT
gs-1949	447	38	kvatadze	kvatadze	PROPN
gs-1949	447	39	z.	z.	PROPN
gs-1949	447	40	,	,	PUNCT
gs-1949	447	41	shervashidze	shervashidze	ADJ
gs-1949	447	42	t.	t.	PROPN
gs-1949	447	43	on	on	ADP
gs-1949	447	44	limit	limit	NOUN
gs-1949	447	45	theorem	theorem	VERB
gs-1949	447	46	for	for	ADP
gs-1949	447	47	random	random	ADJ
gs-1949	447	48	vectors	vector	NOUN
gs-1949	447	49	controlled	control	VERB
gs-1949	447	50	by	by	ADP
gs-1949	447	51	a	a	DET
gs-1949	447	52	marcov	marcov	NOUN
gs-1949	447	53	chain	chain	NOUN
gs-1949	447	54	.	.	PUNCT
gs-1949	448	1	prob	prob	PROPN
gs-1949	448	2	.	.	PROPN
gs-1949	449	1	theory	theory	NOUN
gs-1949	449	2	and	and	CCONJ
gs-1949	449	3	math	math	NOUN
gs-1949	449	4	.	.	PUNCT
gs-1949	450	1	stat	stat	PROPN
gs-1949	450	2	.	.	PUNCT
gs-1949	450	3	,	,	PUNCT
gs-1949	450	4	vol	vol	NOUN
gs-1949	450	5	.	.	PROPN
gs-1949	450	6	1	1	NUM
gs-1949	450	7	,	,	PUNCT
gs-1949	450	8	1986	1986	NUM
gs-1949	450	9	,	,	PUNCT
gs-1949	450	10	239	239	NUM
gs-1949	450	11	-	-	SYM
gs-1949	450	12	250	250	NUM
gs-1949	450	13	.	.	PUNCT
gs-1949	451	1	vnu	vnu	PROPN
gs-1949	451	2	science	science	PROPN
gs-1949	451	3	press	press	PROPN
gs-1949	451	4	,	,	PUNCT
gs-1949	451	5	utrecht	utrecht	PROPN
gs-1949	451	6	.	.	PUNCT
gs-1949	451	7	)	)	PUNCT
gs-1949	452	1	და	და	NOUN
gs-1949	452	2	სხვათა	სხვათა	NOUN
gs-1949	452	3	ნაშრომები.	ნაშრომები.	ADJ
gs-1949	452	4	წინამდებარე	წინამდებარე	NOUN
gs-1949	452	5	ნაშრომში	ნაშრომში	VERB
gs-1949	452	6	განხილულია	განხილულია	VERB
gs-1949	452	7	პირობითად	პირობითად	NOUN
gs-1949	452	8	m	m	VERB
gs-1949	452	9	−დამოუკიდებულ	−დამოუკიდებულ	NOUN
gs-1949	452	10	ვექტორთა	ვექტორთა	PROPN
gs-1949	452	11	მიმდევრობების	მიმდევრობების	PROPN
gs-1949	452	12	კლასი	კლასი	VERB
gs-1949	452	13	და	და	PROPN
gs-1949	452	14	ჯაჭვურად	ჯაჭვურად	NOUN
gs-1949	452	15	m	m	VERB
gs-1949	452	16	−დამოკიდებულ	−დამოკიდებულ	ADP
gs-1949	452	17	ვექტორთა	ვექტორთა	PROPN
gs-1949	452	18	მიმდევრობების	მიმდევრობების	PROPN
gs-1949	452	19	კლასი	კლასი	PROPN
gs-1949	452	20	(	(	PUNCT
gs-1949	452	21	kvatadze	kvatadze	PROPN
gs-1949	452	22	z.	z.	PROPN
gs-1949	452	23	,	,	PUNCT
gs-1949	452	24	shervashidzet	shervashidzet	PROPN
gs-1949	452	25	.	.	PUNCT
gs-1949	453	1	some	some	DET
gs-1949	453	2	limit	limit	NOUN
gs-1949	453	3	theorems	theorem	VERB
gs-1949	453	4	for	for	ADP
gs-1949	453	5	i.i.d	i.i.d	PROPN
gs-1949	453	6	.	.	PUNCT
gs-1949	454	1	and	and	CCONJ
gs-1949	454	2	conditionally	conditionally	ADV
gs-1949	454	3	independent	independent	ADJ
gs-1949	454	4	random	random	ADJ
gs-1949	454	5	variables	variable	NOUN
gs-1949	454	6	.	.	PUNCT
gs-1949	455	1	the	the	DET
gs-1949	455	2	second	second	ADJ
gs-1949	455	3	international	international	ADJ
gs-1949	455	4	conference	conference	NOUN
gs-1949	455	5	,	,	PUNCT
gs-1949	455	6	“	"	PUNCT
gs-1949	455	7	problems	problem	NOUN
gs-1949	455	8	of	of	ADP
gs-1949	455	9	cybernetics	cybernetic	NOUN
gs-1949	455	10	and	and	CCONJ
gs-1949	455	11	informatics	informatic	NOUN
gs-1949	455	12	”	"	PUNCT
gs-1949	455	13	.	.	PUNCT
gs-1949	456	1	september	september	PROPN
gs-1949	456	2	10	10	NUM
gs-1949	456	3	-	-	SYM
gs-1949	456	4	12	12	NUM
gs-1949	456	5	,	,	PUNCT
gs-1949	456	6	2008	2008	NUM
gs-1949	456	7	.	.	PUNCT
gs-1949	457	1	baku	baku	PROPN
gs-1949	457	2	.	.	PUNCT
gs-1949	457	3	azerbaijan	azerbaijan	PROPN
gs-1949	457	4	.	.	PROPN
gs-1949	457	5	section	section	NOUN
gs-1949	457	6	№	№	VERB
gs-1949	457	7	4	4	NUM
gs-1949	457	8	.	.	PUNCT
gs-1949	458	1	“	"	PUNCT
gs-1949	458	2	applied	apply	VERB
gs-1949	458	3	stochastic	stochastic	ADJ
gs-1949	458	4	analysis	analysis	NOUN
gs-1949	458	5	”	"	PUNCT
gs-1949	458	6	.	.	PUNCT
gs-1949	459	1	institute	institute	PROPN
gs-1949	459	2	of	of	ADP
gs-1949	459	3	information	information	NOUN
gs-1949	459	4	technologies	technology	NOUN
gs-1949	459	5	of	of	ADP
gs-1949	459	6	nasa	nasa	PROPN
gs-1949	459	7	.	.	PUNCT
gs-1949	460	1	printing	printing	NOUN
gs-1949	460	2	house	house	NOUN
gs-1949	460	3	of	of	ADP
gs-1949	460	4	“	"	PUNCT
gs-1949	460	5	information	information	NOUN
gs-1949	460	6	technology	technology	NOUN
gs-1949	460	7	”	"	PUNCT
gs-1949	460	8	baku	baku	PROPN
gs-1949	460	9	.	.	PROPN
gs-1949	460	10	2008	2008	NUM
gs-1949	460	11	.	.	PUNCT
gs-1949	461	1	vol	vol	NOUN
gs-1949	461	2	.	.	PUNCT
gs-1949	461	3	ii	ii	PROPN
gs-1949	461	4	,	,	PUNCT
gs-1949	461	5	217	217	NUM
gs-1949	461	6	-	-	SYM
gs-1949	461	7	219	219	NUM
gs-1949	461	8	)	)	PUNCT
gs-1949	461	9	.	.	PUNCT
gs-1949	462	1	დადგენილია	დადგენილია	VERB
gs-1949	462	2	მათი	მათი	PROPN
gs-1949	462	3	ნორმირებული	ნორმირებული	PROPN
gs-1949	462	4	ჯამის	ჯამის	PROPN
gs-1949	462	5	ზღვარითი	ზღვარითი	NOUN
gs-1949	462	6	განაწილება.	განაწილება.	PROPN
gs-1949	462	7	არარეგულარული	არარეგულარული	PROPN
gs-1949	463	1	ერგოდული	ერგოდული	PROPN
gs-1949	463	2	ჯაჭვის	ჯაჭვის	NOUN
gs-1949	463	3	შემთხვევაში	შემთხვევაში	PROPN
gs-1949	463	4	ჯაჭვურად	ჯაჭვურად	NOUN
gs-1949	463	5	m	m	VERB
gs-1949	463	6	−დამოკიდებულ	−დამოკიდებულ	SCONJ
gs-1949	463	7	ვექტორთა	ვექტორთა	PROPN
gs-1949	463	8	მიმდევრობაზე	მიმდევრობაზე	PROPN
gs-1949	463	9	განსაზღვრულია	განსაზღვრულია	VERB
gs-1949	463	10	ფუნქციათა	ფუნქციათა	PROPN
gs-1949	463	11	მიმდევრობა.	მიმდევრობა.	PROPN
gs-1949	464	1	მიღებულია	მიღებულია	PROPN
gs-1949	464	2	ამ	ამ	ADP
gs-1949	464	3	ფუნქციათა	ფუნქციათა	NOUN
gs-1949	464	4	მიმდევრობის	მიმდევრობის	PROPN
gs-1949	464	5	ნორმირებული	ნორმირებული	PROPN
gs-1949	464	6	ჯამის	ჯამის	PROPN
gs-1949	464	7	ზღვარითი	ზღვარითი	NOUN
gs-1949	465	1	კოვარიაციის	კოვარიაციის	PROPN
gs-1949	465	2	მატრიცის	მატრიცის	PROPN
gs-1949	465	3	წარმოდგენა	წარმოდგენა	PROPN
gs-1949	465	4	მატრიცული	მატრიცული	PROPN
gs-1949	465	5	სახით.	სახით.	PROPN
gs-1949	465	6	ჯაჭვის	ჯაჭვის	NOUN
gs-1949	465	7	შესაბამისი	შესაბამისი	PROPN
gs-1949	465	8	ფუნდამენტური	ფუნდამენტური	PROPN
gs-1949	465	9	მატრიცა	მატრიცა	VERB
gs-1949	465	10	და	და	PROPN
gs-1949	465	11	ზღვარითი	ზღვარითი	NOUN
gs-1949	465	12	მახასიათებლები	მახასიათებლები	PROPN
gs-1949	465	13	ციკლური	ციკლური	PROPN
gs-1949	465	14	ქვეკლასების	ქვეკლასების	NOUN
gs-1949	465	15	არსებობის	არსებობის	PROPN
gs-1949	465	16	შემთხვევაში	შემთხვევაში	PROPN
gs-1949	465	17	გამოთვლილია	გამოთვლილია	VERB
gs-1949	465	18	ჩეზაროს	ჩეზაროს	NOUN
gs-1949	465	19	აზრით	აზრით	NOUN
gs-1949	465	20	კრებადობის	კრებადობის	NOUN
gs-1949	465	21	გამოყენებით.	გამოყენებით.	PROPN
gs-1949	465	22	განაწილების	განაწილების	VERB
gs-1949	465	23	ფუნქციათა	ფუნქციათა	PROPN
gs-1949	465	24	სივრცეზე	სივრცეზე	PROPN
gs-1949	465	25	განაწილებების	განაწილებების	PROPN
gs-1949	465	26	კრებადობის	კრებადობის	NOUN
gs-1949	465	27	განხილვის	განხილვის	NOUN
gs-1949	465	28	დროს	დროს	NOUN
gs-1949	465	29	ხშირად	ხშირად	VERB
gs-1949	465	30	გამოიყენება	გამოიყენება	ADJ
gs-1949	465	31	ლევი-პროხოროვის	ლევი-პროხოროვის	NOUN
gs-1949	465	32	მეტრიკა	მეტრიკა	ADV
gs-1949	465	33			NOUN
gs-1949	465	34			PROPN
gs-1949	465	35	,	,	PUNCT
gs-1949	465	36	sup	sup	NOUN
gs-1949	465	37	(	(	PUNCT
gs-1949	465	38	)	)	PUNCT
gs-1949	465	39	(	(	PUNCT
gs-1949	465	40	)	)	PUNCT
gs-1949	465	41	kx	kx	INTJ
gs-1949	466	1	r	r	NOUN
gs-1949	467	1	f	f	PROPN
gs-1949	468	1	g	g	PROPN
gs-1949	469	1	f	f	PROPN
gs-1949	470	1	x	x	SYM
gs-1949	470	2	g	g	PROPN
gs-1949	470	3	x	x	PROPN
gs-1949	470	4			PROPN
gs-1949	470	5			PROPN
gs-1949	470	6			PROPN
gs-1949	470	7	.	.	PUNCT
gs-1949	471	1	ამიტომ	ამიტომ	PROPN
gs-1949	471	2	ბუნებრივია	ბუნებრივია	PROPN
gs-1949	471	3	საინტერესოა	საინტერესოა	PROPN
gs-1949	471	4	საკითხი	საკითხი	PROPN
gs-1949	471	5	ფუნქციათა	ფუნქციათა	PROPN
gs-1949	471	6	ჯამის	ჯამის	PROPN
gs-1949	471	7	განაწილების	განაწილების	PROPN
gs-1949	471	8	ორი	ორი	PROPN
gs-1949	471	9	ნორმალური	ნორმალური	PROPN
gs-1949	471	10	წანაცვლებული	წანაცვლებული	PROPN
gs-1949	471	11	განაწილებისგან	განაწილებისგან	NOUN
gs-1949	471	12	შედგენილ	შედგენილ	VERB
gs-1949	471	13	ზოლში	ზოლში	PROPN
gs-1949	471	14	მოხვედრის	მოხვედრის	NOUN
gs-1949	471	15	ზღვარითი	ზღვარითი	NOUN
gs-1949	471	16	ალბათობის	ალბათობის	VERB
gs-1949	471	17	დადგენის	დადგენის	PROPN
gs-1949	471	18	შესახებ.	შესახებ.	NOUN
gs-1949	471	19	ნაშრომში	ნაშრომში	VERB
gs-1949	471	20	განხილულია	განხილულია	VERB
gs-1949	471	21	პირობითად	პირობითად	NOUN
gs-1949	471	22	m	m	VERB
gs-1949	471	23	−დამოკიდებულ	−დამოკიდებულ	ADP
gs-1949	471	24	ვექტორთა	ვექტორთა	PROPN
gs-1949	471	25	მიმდევრობის	მიმდევრობის	PROPN
gs-1949	471	26	ნორმირებული	ნორმირებული	PROPN
gs-1949	471	27	ჯამი.	ჯამი.	PROPN
gs-1949	471	28	დადგენილია	დადგენილია	VERB
gs-1949	471	29	ამ	ამ	ADP
gs-1949	471	30	ჯამის	ჯამის	PROPN
gs-1949	471	31	პირობითი	პირობითი	NOUN
gs-1949	471	32	განაწილების	განაწილების	VERB
gs-1949	471	33	ორი	ორი	PROPN
gs-1949	471	34	წანაცვლებული	წანაცვლებული	PROPN
gs-1949	471	35	ნორმალური	ნორმალური	NOUN
gs-1949	471	36	განაწილებისგან	განაწილებისგან	NOUN
gs-1949	471	37	შედგენილ	შედგენილ	VERB
gs-1949	471	38	ზოლში	ზოლში	PROPN
gs-1949	471	39	მოხვედრის	მოხვედრის	NOUN
gs-1949	471	40	ზღვარითი	ზღვარითი	NOUN
gs-1949	471	41	ალბათობა.	ალბათობა.	VERB
gs-1949	471	42	ამ	ამ	AUX
gs-1949	471	43	განაწილებების	განაწილებების	ADJ
gs-1949	471	44	კოვარიაციის	კოვარიაციის	PROPN
gs-1949	471	45	მატრიცა	მატრიცა	NOUN
gs-1949	471	46	გამოსახულია	გამოსახულია	VERB
gs-1949	471	47	ჯაჭვის	ჯაჭვის	NOUN
gs-1949	471	48	პარამეტრების	პარამეტრების	ADJ
gs-1949	471	49	საშუალებით.	საშუალებით.	PROPN
gs-1949	471	50	დადგენილია	დადგენილია	VERB
gs-1949	471	51	ასეთივე	ასეთივე	ADJ
gs-1949	471	52	ზღვარითი	ზღვარითი	NOUN
gs-1949	471	53	ალბათობა	ალბათობა	VERB
gs-1949	471	54	ჯაჭვურად	ჯაჭვურად	NOUN
gs-1949	471	55	m	m	VERB
gs-1949	471	56	−დამოკიდებულ	−დამოკიდებულ	ADP
gs-1949	471	57	ვექტორთა	ვექტორთა	PROPN
gs-1949	471	58	მიმდევრობის	მიმდევრობის	PROPN
gs-1949	471	59	ნორმირებული	ნორმირებული	PROPN
gs-1949	471	60	ჯამისთვის.	ჯამისთვის.	VERB