id	sid	tid	token	lemma	pos
ijassa-1225	1	1	adv	adv	PROPN
ijassa-1225	1	2	syst	syst	PROPN
ijassa-1225	1	3	sci	sci	PROPN
ijassa-1225	1	4	appl	appl	PROPN
ijassa-1225	1	5	2022	2022	NUM
ijassa-1225	1	6	;	;	PUNCT
ijassa-1225	1	7	01:176–191	01:176–191	NUM
ijassa-1225	1	8	published	publish	VERB
ijassa-1225	1	9	online	online	ADV
ijassa-1225	1	10	at	at	ADP
ijassa-1225	1	11	https://ijassa.ipu.ru	https://ijassa.ipu.ru	ADV
ijassa-1225	1	12	.	.	PUNCT
ijassa-1225	2	1	on	on	ADP
ijassa-1225	2	2	order	order	NOUN
ijassa-1225	2	3	covering	cover	VERB
ijassa-1225	2	4	set	set	NOUN
ijassa-1225	2	5	-	-	PUNCT
ijassa-1225	2	6	valued	value	VERB
ijassa-1225	2	7	mappings	mapping	NOUN
ijassa-1225	2	8	and	and	CCONJ
ijassa-1225	2	9	their	their	PRON
ijassa-1225	2	10	applications	application	NOUN
ijassa-1225	2	11	to	to	ADP
ijassa-1225	2	12	the	the	DET
ijassa-1225	2	13	investigation	investigation	NOUN
ijassa-1225	2	14	of	of	ADP
ijassa-1225	2	15	implicit	implicit	ADJ
ijassa-1225	2	16	differential	differential	ADJ
ijassa-1225	2	17	inclusions	inclusion	NOUN
ijassa-1225	2	18	and	and	CCONJ
ijassa-1225	2	19	dynamic	dynamic	ADJ
ijassa-1225	2	20	models	model	NOUN
ijassa-1225	2	21	of	of	ADP
ijassa-1225	2	22	economic	economic	ADJ
ijassa-1225	2	23	processes	process	NOUN
ijassa-1225	2	24	evgenii	evgenii	ADJ
ijassa-1225	2	25	o.	o.	PROPN
ijassa-1225	2	26	burlakov1,2	burlakov1,2	PROPN
ijassa-1225	2	27	,	,	PUNCT
ijassa-1225	2	28	elena	elena	PROPN
ijassa-1225	2	29	a.	a.	PROPN
ijassa-1225	2	30	panasenko3,4	panasenko3,4	PROPN
ijassa-1225	2	31	,	,	PUNCT
ijassa-1225	2	32	irina	irina	PROPN
ijassa-1225	2	33	d.	d.	PROPN
ijassa-1225	2	34	serova1	serova1	PROPN
ijassa-1225	2	35	,	,	PUNCT
ijassa-1225	2	36	evgeny	evgeny	PROPN
ijassa-1225	2	37	s.	s.	PROPN
ijassa-1225	2	38	zhukovskiy2,3	zhukovskiy2,3	PROPN
ijassa-1225	2	39	*	*	PROPN
ijassa-1225	2	40	1university	1university	NUM
ijassa-1225	2	41	of	of	ADP
ijassa-1225	2	42	tyumen	tyuman	NOUN
ijassa-1225	2	43	,	,	PUNCT
ijassa-1225	2	44	tyumen	tyuman	NOUN
ijassa-1225	2	45	,	,	PUNCT
ijassa-1225	2	46	russia	russia	PROPN
ijassa-1225	2	47	2v.a	2v.a	NUM
ijassa-1225	2	48	.	.	PUNCT
ijassa-1225	3	1	trapeznikov	trapeznikov	PROPN
ijassa-1225	3	2	institute	institute	PROPN
ijassa-1225	3	3	of	of	ADP
ijassa-1225	3	4	control	control	PROPN
ijassa-1225	3	5	sciences	sciences	PROPN
ijassa-1225	3	6	,	,	PUNCT
ijassa-1225	3	7	russian	russian	ADJ
ijassa-1225	3	8	academy	academy	PROPN
ijassa-1225	3	9	of	of	ADP
ijassa-1225	3	10	sciences	sciences	PROPN
ijassa-1225	3	11	,	,	PUNCT
ijassa-1225	3	12	moscow	moscow	PROPN
ijassa-1225	3	13	,	,	PUNCT
ijassa-1225	3	14	russia	russia	PROPN
ijassa-1225	3	15	3derzhavin	3derzhavin	NUM
ijassa-1225	3	16	tambov	tambov	PROPN
ijassa-1225	3	17	state	state	PROPN
ijassa-1225	3	18	university	university	PROPN
ijassa-1225	3	19	,	,	PUNCT
ijassa-1225	3	20	tambov	tambov	PROPN
ijassa-1225	3	21	,	,	PUNCT
ijassa-1225	3	22	russia	russia	PROPN
ijassa-1225	3	23	4leonhard	4leonhard	PROPN
ijassa-1225	3	24	euler	euler	PROPN
ijassa-1225	3	25	international	international	PROPN
ijassa-1225	3	26	mathematical	mathematical	PROPN
ijassa-1225	3	27	institute	institute	PROPN
ijassa-1225	3	28	,	,	PUNCT
ijassa-1225	3	29	st	st	PROPN
ijassa-1225	3	30	.	.	PROPN
ijassa-1225	3	31	petersburg	petersburg	PROPN
ijassa-1225	3	32	,	,	PUNCT
ijassa-1225	3	33	russia	russia	PROPN
ijassa-1225	3	34	abstract	abstract	NOUN
ijassa-1225	3	35	:	:	PUNCT
ijassa-1225	3	36	the	the	DET
ijassa-1225	3	37	present	present	ADJ
ijassa-1225	3	38	work	work	NOUN
ijassa-1225	3	39	is	be	AUX
ijassa-1225	3	40	devoted	devote	VERB
ijassa-1225	3	41	to	to	ADP
ijassa-1225	3	42	investigation	investigation	NOUN
ijassa-1225	3	43	of	of	ADP
ijassa-1225	3	44	operator	operator	NOUN
ijassa-1225	3	45	inclusions	inclusion	NOUN
ijassa-1225	3	46	in	in	ADP
ijassa-1225	3	47	partially	partially	ADV
ijassa-1225	3	48	ordered	order	VERB
ijassa-1225	3	49	spaces	space	NOUN
ijassa-1225	3	50	and	and	CCONJ
ijassa-1225	3	51	application	application	NOUN
ijassa-1225	3	52	of	of	ADP
ijassa-1225	3	53	the	the	DET
ijassa-1225	3	54	obtained	obtain	VERB
ijassa-1225	3	55	results	result	NOUN
ijassa-1225	3	56	to	to	ADP
ijassa-1225	3	57	differential	differential	ADJ
ijassa-1225	3	58	inclusions	inclusion	NOUN
ijassa-1225	3	59	.	.	PUNCT
ijassa-1225	4	1	we	we	PRON
ijassa-1225	4	2	consider	consider	VERB
ijassa-1225	4	3	the	the	DET
ijassa-1225	4	4	inclusion	inclusion	NOUN
ijassa-1225	4	5	υ(x	υ(x	PROPN
ijassa-1225	4	6	,	,	PUNCT
ijassa-1225	4	7	x	x	NOUN
ijassa-1225	4	8	)	)	PUNCT
ijassa-1225	4	9	3	3	NUM
ijassa-1225	4	10	y	y	NOUN
ijassa-1225	4	11	with	with	ADP
ijassa-1225	4	12	respect	respect	NOUN
ijassa-1225	4	13	to	to	ADP
ijassa-1225	4	14	the	the	DET
ijassa-1225	4	15	unknown	unknown	ADJ
ijassa-1225	4	16	x	x	SYM
ijassa-1225	4	17	∈	∈	PROPN
ijassa-1225	4	18	x	x	NOUN
ijassa-1225	4	19	,	,	PUNCT
ijassa-1225	4	20	where	where	SCONJ
ijassa-1225	4	21	υ	υ	NOUN
ijassa-1225	4	22	:	:	PUNCT
ijassa-1225	4	23	x	x	X
ijassa-1225	4	24	×x	×x	VERB
ijassa-1225	4	25	⇒	⇒	X
ijassa-1225	4	26	y	y	PROPN
ijassa-1225	4	27	is	be	AUX
ijassa-1225	4	28	a	a	DET
ijassa-1225	4	29	setvalued	setvalue	VERB
ijassa-1225	4	30	mapping	mapping	NOUN
ijassa-1225	4	31	,	,	PUNCT
ijassa-1225	4	32	x	x	PUNCT
ijassa-1225	4	33	and	and	CCONJ
ijassa-1225	4	34	y	y	PROPN
ijassa-1225	4	35	are	be	AUX
ijassa-1225	4	36	partially	partially	ADV
ijassa-1225	4	37	ordered	order	VERB
ijassa-1225	4	38	spaces	space	NOUN
ijassa-1225	4	39	.	.	PUNCT
ijassa-1225	5	1	it	it	PRON
ijassa-1225	5	2	is	be	AUX
ijassa-1225	5	3	assumed	assume	VERB
ijassa-1225	5	4	that	that	SCONJ
ijassa-1225	5	5	the	the	DET
ijassa-1225	5	6	mapping	mapping	NOUN
ijassa-1225	5	7	υ	υ	NOUN
ijassa-1225	5	8	is	be	AUX
ijassa-1225	5	9	order	order	NOUN
ijassa-1225	5	10	covering	cover	VERB
ijassa-1225	5	11	with	with	ADP
ijassa-1225	5	12	respect	respect	NOUN
ijassa-1225	5	13	to	to	ADP
ijassa-1225	5	14	the	the	DET
ijassa-1225	5	15	first	first	ADJ
ijassa-1225	5	16	argument	argument	NOUN
ijassa-1225	5	17	and	and	CCONJ
ijassa-1225	5	18	antitone	antitone	VERB
ijassa-1225	5	19	with	with	ADP
ijassa-1225	5	20	respect	respect	NOUN
ijassa-1225	5	21	to	to	ADP
ijassa-1225	5	22	the	the	DET
ijassa-1225	5	23	second	second	ADJ
ijassa-1225	5	24	argument	argument	NOUN
ijassa-1225	5	25	.	.	PUNCT
ijassa-1225	6	1	we	we	PRON
ijassa-1225	6	2	prove	prove	VERB
ijassa-1225	6	3	that	that	SCONJ
ijassa-1225	6	4	for	for	ADP
ijassa-1225	6	5	any	any	DET
ijassa-1225	6	6	x0	x0	PROPN
ijassa-1225	6	7	∈	∈	PROPN
ijassa-1225	6	8	x	x	X
ijassa-1225	6	9	,	,	PUNCT
ijassa-1225	6	10	if	if	SCONJ
ijassa-1225	6	11	the	the	DET
ijassa-1225	6	12	set	set	VERB
ijassa-1225	6	13	g(x0	g(x0	NOUN
ijassa-1225	6	14	)	)	PUNCT
ijassa-1225	6	15	contains	contain	VERB
ijassa-1225	6	16	an	an	DET
ijassa-1225	6	17	element	element	NOUN
ijassa-1225	6	18	y0	y0	NOUN
ijassa-1225	6	19	such	such	ADJ
ijassa-1225	6	20	that	that	SCONJ
ijassa-1225	6	21	y	y	PROPN
ijassa-1225	6	22	�	�	PROPN
ijassa-1225	6	23	y0	y0	PROPN
ijassa-1225	6	24	,	,	PUNCT
ijassa-1225	6	25	then	then	ADV
ijassa-1225	6	26	there	there	PRON
ijassa-1225	6	27	exists	exist	VERB
ijassa-1225	6	28	a	a	DET
ijassa-1225	6	29	solution	solution	NOUN
ijassa-1225	6	30	to	to	ADP
ijassa-1225	6	31	the	the	DET
ijassa-1225	6	32	inclusion	inclusion	NOUN
ijassa-1225	6	33	under	under	ADP
ijassa-1225	6	34	consideration	consideration	NOUN
ijassa-1225	6	35	,	,	PUNCT
ijassa-1225	6	36	which	which	PRON
ijassa-1225	6	37	satisfies	satisfy	VERB
ijassa-1225	6	38	the	the	DET
ijassa-1225	6	39	inequality	inequality	NOUN
ijassa-1225	6	40	x	x	PUNCT
ijassa-1225	6	41	�	�	PROPN
ijassa-1225	6	42	x0	x0	PROPN
ijassa-1225	6	43	.	.	PUNCT
ijassa-1225	7	1	this	this	DET
ijassa-1225	7	2	statement	statement	NOUN
ijassa-1225	7	3	is	be	AUX
ijassa-1225	7	4	applied	apply	VERB
ijassa-1225	7	5	to	to	ADP
ijassa-1225	7	6	investigation	investigation	NOUN
ijassa-1225	7	7	of	of	ADP
ijassa-1225	7	8	a	a	DET
ijassa-1225	7	9	cauchi	cauchi	NOUN
ijassa-1225	7	10	problem	problem	NOUN
ijassa-1225	7	11	for	for	ADP
ijassa-1225	7	12	the	the	DET
ijassa-1225	7	13	differential	differential	ADJ
ijassa-1225	7	14	inclusion	inclusion	NOUN
ijassa-1225	7	15	f(t	f(t	NOUN
ijassa-1225	7	16	,	,	PUNCT
ijassa-1225	7	17	x	x	NOUN
ijassa-1225	7	18	,	,	PUNCT
ijassa-1225	7	19	ẋ	ẋ	PROPN
ijassa-1225	7	20	,	,	PUNCT
ijassa-1225	7	21	ẋ	ẋ	PROPN
ijassa-1225	7	22	)	)	PUNCT
ijassa-1225	7	23	3	3	NUM
ijassa-1225	7	24	0	0	NUM
ijassa-1225	7	25	with	with	ADP
ijassa-1225	7	26	a	a	DET
ijassa-1225	7	27	bound	bind	VERB
ijassa-1225	7	28	for	for	ADP
ijassa-1225	7	29	the	the	DET
ijassa-1225	7	30	derivative	derivative	NOUN
ijassa-1225	7	31	of	of	ADP
ijassa-1225	7	32	the	the	DET
ijassa-1225	7	33	unknown	unknown	ADJ
ijassa-1225	7	34	function	function	NOUN
ijassa-1225	7	35	ẋ(t	ẋ(t	SYM
ijassa-1225	7	36	)	)	PUNCT
ijassa-1225	7	37	∈	∈	PROPN
ijassa-1225	7	38	b(t	b(t	PROPN
ijassa-1225	7	39	)	)	PUNCT
ijassa-1225	8	1	(	(	PUNCT
ijassa-1225	8	2	here	here	ADV
ijassa-1225	8	3	f	f	X
ijassa-1225	8	4	:	:	PUNCT
ijassa-1225	9	1	[	[	X
ijassa-1225	9	2	a	a	X
ijassa-1225	9	3	,	,	PUNCT
ijassa-1225	9	4	b]×	b]×	NOUN
ijassa-1225	9	5	rn	rn	PROPN
ijassa-1225	9	6	×	×	PROPN
ijassa-1225	9	7	rn	rn	PROPN
ijassa-1225	9	8	×	×	PROPN
ijassa-1225	9	9	rn	rn	PROPN
ijassa-1225	9	10	⇒	⇒	PROPN
ijassa-1225	9	11	rm	rm	PROPN
ijassa-1225	9	12	,	,	PUNCT
ijassa-1225	9	13	b	b	NOUN
ijassa-1225	9	14	:	:	PUNCT
ijassa-1225	9	15	[	[	X
ijassa-1225	9	16	a	a	X
ijassa-1225	9	17	,	,	PUNCT
ijassa-1225	9	18	b	b	NOUN
ijassa-1225	9	19	]	]	X
ijassa-1225	9	20	⇒	⇒	PROPN
ijassa-1225	9	21	rn	rn	PROPN
ijassa-1225	9	22	)	)	PUNCT
ijassa-1225	9	23	.	.	PUNCT
ijassa-1225	10	1	we	we	PRON
ijassa-1225	10	2	obtain	obtain	VERB
ijassa-1225	10	3	conditions	condition	NOUN
ijassa-1225	10	4	of	of	ADP
ijassa-1225	10	5	solvability	solvability	NOUN
ijassa-1225	10	6	in	in	ADP
ijassa-1225	10	7	the	the	DET
ijassa-1225	10	8	space	space	NOUN
ijassa-1225	10	9	of	of	ADP
ijassa-1225	10	10	absolutely	absolutely	ADV
ijassa-1225	10	11	continuous	continuous	ADJ
ijassa-1225	10	12	functions	function	NOUN
ijassa-1225	10	13	,	,	PUNCT
ijassa-1225	10	14	conditions	condition	NOUN
ijassa-1225	10	15	of	of	ADP
ijassa-1225	10	16	existence	existence	NOUN
ijassa-1225	10	17	of	of	ADP
ijassa-1225	10	18	a	a	DET
ijassa-1225	10	19	solution	solution	NOUN
ijassa-1225	10	20	with	with	ADP
ijassa-1225	10	21	the	the	DET
ijassa-1225	10	22	least	least	ADJ
ijassa-1225	10	23	derivative	derivative	ADJ
ijassa-1225	10	24	,	,	PUNCT
ijassa-1225	10	25	and	and	CCONJ
ijassa-1225	10	26	derive	derive	VERB
ijassa-1225	10	27	the	the	DET
ijassa-1225	10	28	solutions	solution	NOUN
ijassa-1225	10	29	estimates	estimate	NOUN
ijassa-1225	10	30	.	.	PUNCT
ijassa-1225	11	1	the	the	DET
ijassa-1225	11	2	latter	latter	ADJ
ijassa-1225	11	3	results	result	NOUN
ijassa-1225	11	4	are	be	AUX
ijassa-1225	11	5	applied	apply	VERB
ijassa-1225	11	6	to	to	ADP
ijassa-1225	11	7	the	the	DET
ijassa-1225	11	8	analysis	analysis	NOUN
ijassa-1225	11	9	of	of	ADP
ijassa-1225	11	10	the	the	DET
ijassa-1225	11	11	dynamic	dynamic	ADJ
ijassa-1225	11	12	walrasian	walrasian	ADJ
ijassa-1225	11	13	-	-	PUNCT
ijassa-1225	11	14	evans	evans	PROPN
ijassa-1225	11	15	-	-	PUNCT
ijassa-1225	11	16	samuelson	samuelson	PROPN
ijassa-1225	11	17	model	model	NOUN
ijassa-1225	11	18	of	of	ADP
ijassa-1225	11	19	economic	economic	ADJ
ijassa-1225	11	20	processes	process	NOUN
ijassa-1225	11	21	,	,	PUNCT
ijassa-1225	11	22	which	which	PRON
ijassa-1225	11	23	can	can	AUX
ijassa-1225	11	24	be	be	AUX
ijassa-1225	11	25	reduced	reduce	VERB
ijassa-1225	11	26	to	to	ADP
ijassa-1225	11	27	a	a	DET
ijassa-1225	11	28	system	system	NOUN
ijassa-1225	11	29	of	of	ADP
ijassa-1225	11	30	implicit	implicit	ADJ
ijassa-1225	11	31	differential	differential	ADJ
ijassa-1225	11	32	inclusions	inclusion	NOUN
ijassa-1225	11	33	.	.	PUNCT
ijassa-1225	12	1	we	we	PRON
ijassa-1225	12	2	establish	establish	VERB
ijassa-1225	12	3	the	the	DET
ijassa-1225	12	4	existence	existence	NOUN
ijassa-1225	12	5	of	of	ADP
ijassa-1225	12	6	the	the	DET
ijassa-1225	12	7	equilibrium	equilibrium	NOUN
ijassa-1225	12	8	and	and	CCONJ
ijassa-1225	12	9	obtain	obtain	VERB
ijassa-1225	12	10	estimates	estimate	NOUN
ijassa-1225	12	11	of	of	ADP
ijassa-1225	12	12	the	the	DET
ijassa-1225	12	13	equilibrium	equilibrium	NOUN
ijassa-1225	12	14	prices	price	NOUN
ijassa-1225	12	15	.	.	PUNCT
ijassa-1225	13	1	keywords	keyword	NOUN
ijassa-1225	13	2	:	:	PUNCT
ijassa-1225	13	3	operator	operator	NOUN
ijassa-1225	13	4	inclusion	inclusion	NOUN
ijassa-1225	13	5	,	,	PUNCT
ijassa-1225	13	6	covering	cover	VERB
ijassa-1225	13	7	mapping	mapping	NOUN
ijassa-1225	13	8	of	of	ADP
ijassa-1225	13	9	partially	partially	ADV
ijassa-1225	13	10	ordered	order	VERB
ijassa-1225	13	11	spaces	space	NOUN
ijassa-1225	13	12	,	,	PUNCT
ijassa-1225	13	13	implicit	implicit	ADJ
ijassa-1225	13	14	differential	differential	ADJ
ijassa-1225	13	15	equation	equation	NOUN
ijassa-1225	13	16	,	,	PUNCT
ijassa-1225	13	17	supply	supply	NOUN
ijassa-1225	13	18	-	-	PUNCT
ijassa-1225	13	19	and	and	CCONJ
ijassa-1225	13	20	-	-	PUNCT
ijassa-1225	13	21	demand	demand	NOUN
ijassa-1225	13	22	model	model	NOUN
ijassa-1225	13	23	1	1	NUM
ijassa-1225	13	24	.	.	PUNCT
ijassa-1225	14	1	introduction	introduction	NOUN
ijassa-1225	14	2	the	the	DET
ijassa-1225	14	3	present	present	ADJ
ijassa-1225	14	4	work	work	NOUN
ijassa-1225	14	5	is	be	AUX
ijassa-1225	14	6	devoted	devote	VERB
ijassa-1225	14	7	to	to	ADP
ijassa-1225	14	8	the	the	DET
ijassa-1225	14	9	problem	problem	NOUN
ijassa-1225	14	10	of	of	ADP
ijassa-1225	14	11	solvability	solvability	NOUN
ijassa-1225	14	12	of	of	ADP
ijassa-1225	14	13	operator	operator	NOUN
ijassa-1225	14	14	inclusions	inclusion	NOUN
ijassa-1225	14	15	in	in	ADP
ijassa-1225	14	16	partially	partially	ADV
ijassa-1225	14	17	ordered	order	VERB
ijassa-1225	14	18	spaces	space	NOUN
ijassa-1225	14	19	.	.	PUNCT
ijassa-1225	15	1	the	the	DET
ijassa-1225	15	2	research	research	NOUN
ijassa-1225	15	3	uses	use	VERB
ijassa-1225	15	4	the	the	DET
ijassa-1225	15	5	notion	notion	NOUN
ijassa-1225	15	6	of	of	ADP
ijassa-1225	15	7	order	order	NOUN
ijassa-1225	15	8	covering	covering	NOUN
ijassa-1225	15	9	introduced	introduce	VERB
ijassa-1225	15	10	for	for	ADP
ijassa-1225	15	11	the	the	DET
ijassa-1225	15	12	“	"	PUNCT
ijassa-1225	15	13	standard	standard	ADJ
ijassa-1225	15	14	single	single	ADV
ijassa-1225	15	15	-	-	PUNCT
ijassa-1225	15	16	valued	value	VERB
ijassa-1225	15	17	”	"	PUNCT
ijassa-1225	15	18	mappings	mapping	NOUN
ijassa-1225	15	19	in	in	ADP
ijassa-1225	15	20	[	[	X
ijassa-1225	15	21	1	1	NUM
ijassa-1225	15	22	,	,	PUNCT
ijassa-1225	15	23	2	2	NUM
ijassa-1225	15	24	]	]	PUNCT
ijassa-1225	15	25	,	,	PUNCT
ijassa-1225	15	26	and	and	CCONJ
ijassa-1225	15	27	for	for	ADP
ijassa-1225	15	28	set	set	NOUN
ijassa-1225	15	29	-	-	PUNCT
ijassa-1225	15	30	valued	value	VERB
ijassa-1225	15	31	mappings	mapping	NOUN
ijassa-1225	15	32	in	in	ADP
ijassa-1225	15	33	[	[	X
ijassa-1225	15	34	3	3	NUM
ijassa-1225	15	35	,	,	PUNCT
ijassa-1225	15	36	4	4	NUM
ijassa-1225	15	37	]	]	PUNCT
ijassa-1225	15	38	.	.	PUNCT
ijassa-1225	16	1	for	for	ADP
ijassa-1225	16	2	a	a	DET
ijassa-1225	16	3	set	set	NOUN
ijassa-1225	16	4	-	-	PUNCT
ijassa-1225	16	5	valued	value	VERB
ijassa-1225	16	6	mapping	mapping	NOUN
ijassa-1225	16	7	g	g	ADP
ijassa-1225	16	8	acting	act	VERB
ijassa-1225	16	9	from	from	ADP
ijassa-1225	16	10	a	a	DET
ijassa-1225	16	11	partially	partially	ADV
ijassa-1225	16	12	ordered	order	VERB
ijassa-1225	16	13	space	space	NOUN
ijassa-1225	16	14	(	(	PUNCT
ijassa-1225	16	15	x	x	NOUN
ijassa-1225	16	16	,	,	PUNCT
ijassa-1225	16	17	�	�	PROPN
ijassa-1225	16	18	)	)	PUNCT
ijassa-1225	16	19	to	to	ADP
ijassa-1225	16	20	a	a	DET
ijassa-1225	16	21	partially	partially	ADV
ijassa-1225	16	22	ordered	order	VERB
ijassa-1225	16	23	space	space	NOUN
ijassa-1225	16	24	(	(	PUNCT
ijassa-1225	16	25	y	y	PROPN
ijassa-1225	16	26	,	,	PUNCT
ijassa-1225	16	27	�	�	PROPN
ijassa-1225	16	28	)	)	PUNCT
ijassa-1225	16	29	,	,	PUNCT
ijassa-1225	16	30	the	the	DET
ijassa-1225	16	31	property	property	NOUN
ijassa-1225	16	32	of	of	ADP
ijassa-1225	16	33	covering	covering	NOUN
ijassa-1225	16	34	means	mean	VERB
ijassa-1225	16	35	that	that	SCONJ
ijassa-1225	16	36	if	if	SCONJ
ijassa-1225	16	37	for	for	ADP
ijassa-1225	16	38	any	any	DET
ijassa-1225	16	39	u	u	NOUN
ijassa-1225	16	40	∈	∈	PROPN
ijassa-1225	16	41	x	x	X
ijassa-1225	16	42	and	and	CCONJ
ijassa-1225	16	43	y	y	PROPN
ijassa-1225	16	44	∈	∈	PROPN
ijassa-1225	16	45	y	y	PROPN
ijassa-1225	16	46	,	,	PUNCT
ijassa-1225	16	47	the	the	DET
ijassa-1225	16	48	set	set	NOUN
ijassa-1225	16	49	g(u	g(u	PROPN
ijassa-1225	16	50	)	)	PUNCT
ijassa-1225	16	51	contains	contain	VERB
ijassa-1225	16	52	an	an	DET
ijassa-1225	16	53	element	element	NOUN
ijassa-1225	16	54	v	v	ADP
ijassa-1225	16	55	such	such	ADJ
ijassa-1225	16	56	that	that	SCONJ
ijassa-1225	16	57	y	y	PROPN
ijassa-1225	16	58	�	�	PROPN
ijassa-1225	16	59	v	v	PROPN
ijassa-1225	16	60	,	,	PUNCT
ijassa-1225	16	61	then	then	ADV
ijassa-1225	16	62	there	there	PRON
ijassa-1225	16	63	exists	exist	VERB
ijassa-1225	16	64	a	a	DET
ijassa-1225	16	65	solution	solution	NOUN
ijassa-1225	16	66	x	x	PUNCT
ijassa-1225	16	67	of	of	ADP
ijassa-1225	16	68	the	the	DET
ijassa-1225	16	69	inclusion	inclusion	NOUN
ijassa-1225	16	70	g(x	g(x	NOUN
ijassa-1225	16	71	)	)	PUNCT
ijassa-1225	16	72	3	3	NUM
ijassa-1225	16	73	y	y	PROPN
ijassa-1225	16	74	,	,	PUNCT
ijassa-1225	16	75	which	which	PRON
ijassa-1225	16	76	satisfies	satisfy	VERB
ijassa-1225	16	77	the	the	DET
ijassa-1225	16	78	inequality	inequality	NOUN
ijassa-1225	16	79	x	x	X
ijassa-1225	16	80	�	�	PROPN
ijassa-1225	16	81	u.	u.	PROPN
ijassa-1225	16	82	in	in	ADP
ijassa-1225	16	83	the	the	DET
ijassa-1225	16	84	cited	cite	VERB
ijassa-1225	16	85	papers	paper	NOUN
ijassa-1225	16	86	,	,	PUNCT
ijassa-1225	16	87	the	the	DET
ijassa-1225	16	88	existence	existence	NOUN
ijassa-1225	16	89	of	of	ADP
ijassa-1225	16	90	a	a	DET
ijassa-1225	16	91	coincidence	coincidence	NOUN
ijassa-1225	16	92	point	point	NOUN
ijassa-1225	16	93	of	of	ADP
ijassa-1225	16	94	a	a	DET
ijassa-1225	16	95	covering	covering	NOUN
ijassa-1225	16	96	mapping	mapping	NOUN
ijassa-1225	16	97	and	and	CCONJ
ijassa-1225	16	98	an	an	DET
ijassa-1225	16	99	isotone	isotone	NOUN
ijassa-1225	16	100	mapping	mapping	NOUN
ijassa-1225	16	101	(	(	PUNCT
ijassa-1225	16	102	for	for	ADP
ijassa-1225	16	103	the	the	DET
ijassa-1225	16	104	cases	case	NOUN
ijassa-1225	16	105	of	of	ADP
ijassa-1225	16	106	singleand	singleand	NOUN
ijassa-1225	16	107	set	set	NOUN
ijassa-1225	16	108	-	-	PUNCT
ijassa-1225	16	109	valued	value	VERB
ijassa-1225	16	110	mappings	mapping	NOUN
ijassa-1225	16	111	)	)	PUNCT
ijassa-1225	16	112	is	be	AUX
ijassa-1225	16	113	demonstrated	demonstrate	VERB
ijassa-1225	16	114	.	.	PUNCT
ijassa-1225	17	1	in	in	ADP
ijassa-1225	17	2	the	the	DET
ijassa-1225	17	3	present	present	ADJ
ijassa-1225	17	4	work	work	NOUN
ijassa-1225	17	5	,	,	PUNCT
ijassa-1225	17	6	the	the	DET
ijassa-1225	17	7	stability	stability	NOUN
ijassa-1225	17	8	of	of	ADP
ijassa-1225	17	9	the	the	DET
ijassa-1225	17	10	solvability	solvability	NOUN
ijassa-1225	17	11	property	property	NOUN
ijassa-1225	17	12	of	of	ADP
ijassa-1225	17	13	inclusions	inclusion	NOUN
ijassa-1225	17	14	with	with	ADP
ijassa-1225	17	15	respect	respect	NOUN
ijassa-1225	17	16	to	to	PART
ijassa-1225	17	17	antitone	antitone	VERB
ijassa-1225	17	18	perturbations	perturbation	NOUN
ijassa-1225	17	19	is	be	AUX
ijassa-1225	17	20	investigated	investigate	VERB
ijassa-1225	17	21	.	.	PUNCT
ijassa-1225	18	1	this	this	DET
ijassa-1225	18	2	problem	problem	NOUN
ijassa-1225	18	3	is	be	AUX
ijassa-1225	18	4	formalised	formalise	VERB
ijassa-1225	18	5	in	in	ADP
ijassa-1225	18	6	terms	term	NOUN
ijassa-1225	18	7	of	of	ADP
ijassa-1225	18	8	the	the	DET
ijassa-1225	18	9	inclusion	inclusion	NOUN
ijassa-1225	18	10	∗corresponding	∗corresponde	VERB
ijassa-1225	18	11	author	author	NOUN
ijassa-1225	18	12	:	:	PUNCT
ijassa-1225	18	13	zukovskys@mail.ru	zukovskys@mail.ru	VERB
ijassa-1225	18	14	on	on	ADP
ijassa-1225	18	15	order	order	NOUN
ijassa-1225	18	16	covering	cover	VERB
ijassa-1225	18	17	set	set	NOUN
ijassa-1225	18	18	-	-	PUNCT
ijassa-1225	18	19	valued	value	VERB
ijassa-1225	18	20	mappings	mapping	NOUN
ijassa-1225	18	21	and	and	CCONJ
ijassa-1225	18	22	their	their	PRON
ijassa-1225	18	23	applications	application	NOUN
ijassa-1225	18	24	177	177	NUM
ijassa-1225	18	25	υ(x	υ(x	X
ijassa-1225	18	26	,	,	PUNCT
ijassa-1225	18	27	x	x	NOUN
ijassa-1225	18	28	)	)	PUNCT
ijassa-1225	18	29	3	3	NUM
ijassa-1225	18	30	y	y	NOUN
ijassa-1225	18	31	with	with	ADP
ijassa-1225	18	32	a	a	DET
ijassa-1225	18	33	set	set	NOUN
ijassa-1225	18	34	-	-	PUNCT
ijassa-1225	18	35	valued	value	VERB
ijassa-1225	18	36	mapping	mapping	NOUN
ijassa-1225	19	1	υ	υ	NOUN
ijassa-1225	19	2	:	:	PUNCT
ijassa-1225	19	3	x	x	X
ijassa-1225	19	4	×x	×x	VERB
ijassa-1225	19	5	⇒	⇒	NOUN
ijassa-1225	20	1	y	y	PROPN
ijassa-1225	21	1	that	that	PRON
ijassa-1225	21	2	is	be	AUX
ijassa-1225	21	3	order	order	NOUN
ijassa-1225	21	4	covering	cover	VERB
ijassa-1225	21	5	with	with	ADP
ijassa-1225	21	6	respect	respect	NOUN
ijassa-1225	21	7	to	to	ADP
ijassa-1225	21	8	the	the	DET
ijassa-1225	21	9	first	first	ADJ
ijassa-1225	21	10	argument	argument	NOUN
ijassa-1225	21	11	and	and	CCONJ
ijassa-1225	21	12	antitone	antitone	VERB
ijassa-1225	21	13	with	with	ADP
ijassa-1225	21	14	respect	respect	NOUN
ijassa-1225	21	15	to	to	ADP
ijassa-1225	21	16	the	the	DET
ijassa-1225	21	17	second	second	ADJ
ijassa-1225	21	18	argument	argument	NOUN
ijassa-1225	21	19	.	.	PUNCT
ijassa-1225	22	1	an	an	DET
ijassa-1225	22	2	analogous	analogous	ADJ
ijassa-1225	22	3	problem	problem	NOUN
ijassa-1225	22	4	for	for	ADP
ijassa-1225	22	5	“	"	PUNCT
ijassa-1225	22	6	standard	standard	ADJ
ijassa-1225	22	7	single	single	ADV
ijassa-1225	22	8	-	-	PUNCT
ijassa-1225	22	9	valued	value	VERB
ijassa-1225	22	10	”	"	PUNCT
ijassa-1225	22	11	mappings	mapping	NOUN
ijassa-1225	22	12	was	be	AUX
ijassa-1225	22	13	considered	consider	VERB
ijassa-1225	22	14	in	in	ADP
ijassa-1225	22	15	the	the	DET
ijassa-1225	22	16	papers	paper	NOUN
ijassa-1225	22	17	[	[	X
ijassa-1225	22	18	5–8	5–8	NOUN
ijassa-1225	22	19	]	]	PUNCT
ijassa-1225	22	20	.	.	PUNCT
ijassa-1225	23	1	based	base	VERB
ijassa-1225	23	2	on	on	ADP
ijassa-1225	23	3	the	the	DET
ijassa-1225	23	4	statements	statement	NOUN
ijassa-1225	23	5	on	on	ADP
ijassa-1225	23	6	antitone	antitone	NOUN
ijassa-1225	23	7	perturbations	perturbation	NOUN
ijassa-1225	23	8	proved	prove	VERB
ijassa-1225	23	9	in	in	ADP
ijassa-1225	23	10	these	these	DET
ijassa-1225	23	11	works	work	NOUN
ijassa-1225	23	12	,	,	PUNCT
ijassa-1225	23	13	comparison	comparison	NOUN
ijassa-1225	23	14	theorems	theorem	NOUN
ijassa-1225	23	15	(	(	PUNCT
ijassa-1225	23	16	of	of	ADP
ijassa-1225	23	17	the	the	DET
ijassa-1225	23	18	same	same	ADJ
ijassa-1225	23	19	type	type	NOUN
ijassa-1225	23	20	with	with	ADP
ijassa-1225	23	21	the	the	DET
ijassa-1225	23	22	well	well	ADV
ijassa-1225	23	23	-	-	PUNCT
ijassa-1225	23	24	known	know	VERB
ijassa-1225	23	25	chaplygin	chaplygin	NOUN
ijassa-1225	23	26	theorem	theorem	NOUN
ijassa-1225	23	27	[	[	X
ijassa-1225	23	28	9	9	NUM
ijassa-1225	23	29	]	]	PUNCT
ijassa-1225	23	30	on	on	ADP
ijassa-1225	23	31	differential	differential	ADJ
ijassa-1225	23	32	inequality	inequality	NOUN
ijassa-1225	23	33	)	)	PUNCT
ijassa-1225	23	34	for	for	ADP
ijassa-1225	23	35	the	the	DET
ijassa-1225	23	36	unresolved	unresolved	NOUN
ijassa-1225	23	37	with	with	ADP
ijassa-1225	23	38	respect	respect	NOUN
ijassa-1225	23	39	to	to	ADP
ijassa-1225	23	40	the	the	DET
ijassa-1225	23	41	derivative	derivative	ADJ
ijassa-1225	23	42	(	(	PUNCT
ijassa-1225	23	43	i.e.	i.e.	X
ijassa-1225	23	44	implicit	implicit	ADJ
ijassa-1225	23	45	)	)	PUNCT
ijassa-1225	23	46	differential	differential	ADJ
ijassa-1225	23	47	equations	equation	NOUN
ijassa-1225	23	48	were	be	AUX
ijassa-1225	23	49	obtained	obtain	VERB
ijassa-1225	23	50	(	(	PUNCT
ijassa-1225	23	51	see	see	VERB
ijassa-1225	23	52	[	[	X
ijassa-1225	23	53	5	5	NUM
ijassa-1225	23	54	,	,	PUNCT
ijassa-1225	23	55	10	10	NUM
ijassa-1225	23	56	]	]	NUM
ijassa-1225	23	57	)	)	PUNCT
ijassa-1225	23	58	.	.	PUNCT
ijassa-1225	24	1	the	the	DET
ijassa-1225	24	2	results	result	NOUN
ijassa-1225	24	3	on	on	ADP
ijassa-1225	24	4	antitone	antitone	ADJ
ijassa-1225	24	5	perturbations	perturbation	NOUN
ijassa-1225	24	6	of	of	ADP
ijassa-1225	24	7	order	order	NOUN
ijassa-1225	24	8	covering	cover	VERB
ijassa-1225	24	9	mappings	mapping	NOUN
ijassa-1225	24	10	presented	present	VERB
ijassa-1225	24	11	in	in	ADP
ijassa-1225	24	12	this	this	DET
ijassa-1225	24	13	article	article	NOUN
ijassa-1225	24	14	are	be	AUX
ijassa-1225	24	15	applied	apply	VERB
ijassa-1225	24	16	to	to	ADP
ijassa-1225	24	17	the	the	DET
ijassa-1225	24	18	investigation	investigation	NOUN
ijassa-1225	24	19	of	of	ADP
ijassa-1225	24	20	implicit	implicit	ADJ
ijassa-1225	24	21	differential	differential	ADJ
ijassa-1225	24	22	inclusions	inclusion	NOUN
ijassa-1225	24	23	.	.	PUNCT
ijassa-1225	25	1	conditions	condition	NOUN
ijassa-1225	25	2	of	of	ADP
ijassa-1225	25	3	existence	existence	NOUN
ijassa-1225	25	4	and	and	CCONJ
ijassa-1225	25	5	estimates	estimate	NOUN
ijassa-1225	25	6	of	of	ADP
ijassa-1225	25	7	solutions	solution	NOUN
ijassa-1225	25	8	of	of	ADP
ijassa-1225	25	9	a	a	DET
ijassa-1225	25	10	cauchi	cauchi	NOUN
ijassa-1225	25	11	problem	problem	NOUN
ijassa-1225	25	12	are	be	AUX
ijassa-1225	25	13	obtained	obtain	VERB
ijassa-1225	25	14	.	.	PUNCT
ijassa-1225	26	1	these	these	DET
ijassa-1225	26	2	results	result	NOUN
ijassa-1225	26	3	are	be	AUX
ijassa-1225	26	4	applied	apply	VERB
ijassa-1225	26	5	to	to	ADP
ijassa-1225	26	6	the	the	DET
ijassa-1225	26	7	analysis	analysis	NOUN
ijassa-1225	26	8	of	of	ADP
ijassa-1225	26	9	the	the	DET
ijassa-1225	26	10	dynamic	dynamic	ADJ
ijassa-1225	26	11	walrasian	walrasian	ADJ
ijassa-1225	26	12	-	-	PUNCT
ijassa-1225	26	13	evans	evans	PROPN
ijassa-1225	26	14	-	-	PUNCT
ijassa-1225	26	15	samuelson	samuelson	PROPN
ijassa-1225	26	16	supply	supply	PROPN
ijassa-1225	26	17	-	-	PUNCT
ijassa-1225	26	18	and	and	CCONJ
ijassa-1225	26	19	-	-	PUNCT
ijassa-1225	26	20	demand	demand	NOUN
ijassa-1225	26	21	model	model	NOUN
ijassa-1225	26	22	(	(	PUNCT
ijassa-1225	26	23	see	see	VERB
ijassa-1225	26	24	[	[	X
ijassa-1225	26	25	11–13	11–13	NUM
ijassa-1225	26	26	]	]	X
ijassa-1225	26	27	)	)	PUNCT
ijassa-1225	26	28	that	that	PRON
ijassa-1225	26	29	is	be	AUX
ijassa-1225	26	30	reduced	reduce	VERB
ijassa-1225	26	31	to	to	ADP
ijassa-1225	26	32	a	a	DET
ijassa-1225	26	33	system	system	NOUN
ijassa-1225	26	34	of	of	ADP
ijassa-1225	26	35	implicit	implicit	ADJ
ijassa-1225	26	36	differential	differential	ADJ
ijassa-1225	26	37	inclusions	inclusion	NOUN
ijassa-1225	26	38	.	.	PUNCT
ijassa-1225	27	1	the	the	DET
ijassa-1225	27	2	existence	existence	NOUN
ijassa-1225	27	3	of	of	ADP
ijassa-1225	27	4	the	the	DET
ijassa-1225	27	5	equilibrium	equilibrium	NOUN
ijassa-1225	27	6	state	state	NOUN
ijassa-1225	27	7	is	be	AUX
ijassa-1225	27	8	established	establish	VERB
ijassa-1225	27	9	and	and	CCONJ
ijassa-1225	27	10	the	the	DET
ijassa-1225	27	11	estimates	estimate	NOUN
ijassa-1225	27	12	of	of	ADP
ijassa-1225	27	13	the	the	DET
ijassa-1225	27	14	equilibrium	equilibrium	NOUN
ijassa-1225	27	15	prices	price	NOUN
ijassa-1225	27	16	are	be	AUX
ijassa-1225	27	17	obtained	obtain	VERB
ijassa-1225	27	18	.	.	PUNCT
ijassa-1225	28	1	these	these	DET
ijassa-1225	28	2	statements	statement	NOUN
ijassa-1225	28	3	extend	extend	VERB
ijassa-1225	28	4	the	the	DET
ijassa-1225	28	5	results	result	NOUN
ijassa-1225	28	6	on	on	ADP
ijassa-1225	28	7	the	the	DET
ijassa-1225	28	8	models	model	NOUN
ijassa-1225	28	9	of	of	ADP
ijassa-1225	28	10	economic	economic	ADJ
ijassa-1225	28	11	processes	process	NOUN
ijassa-1225	28	12	of	of	ADP
ijassa-1225	28	13	a.v	a.v	PROPN
ijassa-1225	28	14	.	.	PROPN
ijassa-1225	28	15	arutyunov	arutyunov	PROPN
ijassa-1225	28	16	,	,	PUNCT
ijassa-1225	28	17	n.g	n.g	PROPN
ijassa-1225	28	18	.	.	PROPN
ijassa-1225	28	19	pavlova	pavlova	PROPN
ijassa-1225	28	20	,	,	PUNCT
ijassa-1225	28	21	s.e	s.e	PROPN
ijassa-1225	28	22	.	.	PROPN
ijassa-1225	28	23	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	28	24	,	,	PUNCT
ijassa-1225	28	25	a.a	a.a	PROPN
ijassa-1225	28	26	.	.	PROPN
ijassa-1225	28	27	shananin	shananin	PROPN
ijassa-1225	28	28	(	(	PUNCT
ijassa-1225	28	29	see	see	VERB
ijassa-1225	28	30	[	[	X
ijassa-1225	28	31	14–17	14–17	NUM
ijassa-1225	28	32	]	]	PUNCT
ijassa-1225	28	33	)	)	PUNCT
ijassa-1225	28	34	which	which	PRON
ijassa-1225	28	35	employ	employ	VERB
ijassa-1225	28	36	single	single	ADJ
ijassa-1225	28	37	-	-	PUNCT
ijassa-1225	28	38	valued	value	VERB
ijassa-1225	28	39	functions	function	NOUN
ijassa-1225	28	40	of	of	ADP
ijassa-1225	28	41	supply	supply	NOUN
ijassa-1225	28	42	and	and	CCONJ
ijassa-1225	28	43	demand	demand	NOUN
ijassa-1225	28	44	.	.	PUNCT
ijassa-1225	29	1	the	the	DET
ijassa-1225	29	2	fundamental	fundamental	ADJ
ijassa-1225	29	3	mathematical	mathematical	ADJ
ijassa-1225	29	4	tools	tool	NOUN
ijassa-1225	29	5	for	for	ADP
ijassa-1225	29	6	these	these	DET
ijassa-1225	29	7	works	work	NOUN
ijassa-1225	29	8	were	be	AUX
ijassa-1225	29	9	represented	represent	VERB
ijassa-1225	29	10	by	by	ADP
ijassa-1225	29	11	the	the	DET
ijassa-1225	29	12	theorems	theorem	NOUN
ijassa-1225	29	13	of	of	ADP
ijassa-1225	29	14	the	the	DET
ijassa-1225	29	15	papers	paper	NOUN
ijassa-1225	29	16	[	[	X
ijassa-1225	29	17	18–21	18–21	NUM
ijassa-1225	29	18	]	]	X
ijassa-1225	29	19	on	on	ADP
ijassa-1225	29	20	coincidence	coincidence	NOUN
ijassa-1225	29	21	points	point	NOUN
ijassa-1225	29	22	of	of	ADP
ijassa-1225	29	23	single	single	ADV
ijassa-1225	29	24	-	-	PUNCT
ijassa-1225	29	25	valued	value	VERB
ijassa-1225	29	26	covering	cover	VERB
ijassa-1225	29	27	mapping	mapping	NOUN
ijassa-1225	29	28	of	of	ADP
ijassa-1225	29	29	metric	metric	ADJ
ijassa-1225	29	30	spaces	space	NOUN
ijassa-1225	29	31	.	.	PUNCT
ijassa-1225	30	1	2	2	X
ijassa-1225	30	2	.	.	X
ijassa-1225	30	3	a	a	DET
ijassa-1225	30	4	comparison	comparison	NOUN
ijassa-1225	30	5	theorem	theorem	VERB
ijassa-1225	30	6	for	for	ADP
ijassa-1225	30	7	operator	operator	NOUN
ijassa-1225	30	8	inclusions	inclusion	NOUN
ijassa-1225	30	9	in	in	ADP
ijassa-1225	30	10	partially	partially	ADV
ijassa-1225	30	11	ordered	order	VERB
ijassa-1225	30	12	spaces	space	NOUN
ijassa-1225	30	13	let	let	AUX
ijassa-1225	30	14	partially	partially	ADV
ijassa-1225	30	15	ordered	order	VERB
ijassa-1225	30	16	spaces	space	NOUN
ijassa-1225	30	17	(	(	PUNCT
ijassa-1225	30	18	x	x	NOUN
ijassa-1225	30	19	,	,	PUNCT
ijassa-1225	30	20	�	�	PROPN
ijassa-1225	30	21	)	)	PUNCT
ijassa-1225	30	22	,	,	PUNCT
ijassa-1225	30	23	(	(	PUNCT
ijassa-1225	30	24	y	y	NOUN
ijassa-1225	30	25	,	,	PUNCT
ijassa-1225	30	26	�	�	PROPN
ijassa-1225	30	27	)	)	PUNCT
ijassa-1225	30	28	be	be	AUX
ijassa-1225	30	29	given	give	VERB
ijassa-1225	30	30	.	.	PUNCT
ijassa-1225	31	1	for	for	ADP
ijassa-1225	31	2	any	any	DET
ijassa-1225	31	3	u	u	NOUN
ijassa-1225	31	4	,	,	PUNCT
ijassa-1225	31	5	v	v	NOUN
ijassa-1225	31	6	∈	∈	NOUN
ijassa-1225	31	7	x	x	SYM
ijassa-1225	31	8	andu	andu	NOUN
ijassa-1225	31	9	⊂	⊂	PROPN
ijassa-1225	31	10	x	x	X
ijassa-1225	31	11	,	,	PUNCT
ijassa-1225	31	12	we	we	PRON
ijassa-1225	31	13	denote	denote	VERB
ijassa-1225	31	14	[	[	X
ijassa-1225	31	15	u	u	NOUN
ijassa-1225	31	16	,	,	PUNCT
ijassa-1225	31	17	v]x	v]x	ADJ
ijassa-1225	31	18	.	.	PUNCT
ijassa-1225	32	1	=	=	PRON
ijassa-1225	32	2	{	{	PUNCT
ijassa-1225	32	3	x	x	PUNCT
ijassa-1225	32	4	∈	∈	PROPN
ijassa-1225	32	5	x	x	X
ijassa-1225	32	6	:	:	PUNCT
ijassa-1225	32	7	v	v	NUM
ijassa-1225	32	8	�	�	PROPN
ijassa-1225	32	9	x	x	SYM
ijassa-1225	32	10	�	�	PROPN
ijassa-1225	32	11	u	u	NOUN
ijassa-1225	32	12	}	}	PUNCT
ijassa-1225	32	13	,	,	PUNCT
ijassa-1225	32	14	ox(u	ox(u	X
ijassa-1225	32	15	)	)	PUNCT
ijassa-1225	32	16	.	.	PUNCT
ijassa-1225	33	1	=	=	PRON
ijassa-1225	33	2	{	{	PUNCT
ijassa-1225	33	3	x	x	PUNCT
ijassa-1225	33	4	∈	∈	NOUN
ijassa-1225	33	5	x	x	X
ijassa-1225	33	6	:	:	PUNCT
ijassa-1225	33	7	x	x	PUNCT
ijassa-1225	33	8	�	�	PROPN
ijassa-1225	33	9	u	u	NOUN
ijassa-1225	33	10	}	}	PUNCT
ijassa-1225	33	11	,	,	PUNCT
ijassa-1225	33	12	ox(u	ox(u	X
ijassa-1225	33	13	)	)	PUNCT
ijassa-1225	33	14	.	.	PUNCT
ijassa-1225	34	1	=	=	PUNCT
ijassa-1225	34	2	⋃	⋃	PROPN
ijassa-1225	34	3	∀u∈u	∀u∈u	PROPN
ijassa-1225	34	4	ox(u	ox(u	NOUN
ijassa-1225	34	5	)	)	PUNCT
ijassa-1225	34	6	.	.	PUNCT
ijassa-1225	35	1	consider	consider	VERB
ijassa-1225	35	2	a	a	DET
ijassa-1225	35	3	set	set	NOUN
ijassa-1225	35	4	-	-	PUNCT
ijassa-1225	35	5	valued	value	VERB
ijassa-1225	35	6	mappingg	mappingg	NOUN
ijassa-1225	35	7	:	:	PUNCT
ijassa-1225	35	8	x	x	SYM
ijassa-1225	35	9	⇒	⇒	PROPN
ijassa-1225	35	10	y	y	PROPN
ijassa-1225	35	11	,	,	PUNCT
ijassa-1225	35	12	i.e.	i.e.	X
ijassa-1225	35	13	a	a	DET
ijassa-1225	35	14	mapping	mapping	NOUN
ijassa-1225	35	15	that	that	PRON
ijassa-1225	35	16	puts	put	VERB
ijassa-1225	35	17	to	to	ADP
ijassa-1225	35	18	any	any	DET
ijassa-1225	35	19	element	element	NOUN
ijassa-1225	35	20	x	x	SYM
ijassa-1225	35	21	∈	∈	NOUN
ijassa-1225	35	22	x	x	X
ijassa-1225	35	23	into	into	ADP
ijassa-1225	35	24	the	the	DET
ijassa-1225	35	25	correspondence	correspondence	NOUN
ijassa-1225	35	26	a	a	DET
ijassa-1225	35	27	non	non	ADJ
ijassa-1225	35	28	-	-	ADJ
ijassa-1225	35	29	empty	empty	ADJ
ijassa-1225	35	30	set	set	VERB
ijassa-1225	35	31	g(x	g(x	NOUN
ijassa-1225	35	32	)	)	PUNCT
ijassa-1225	36	1	⊂	⊂	PROPN
ijassa-1225	36	2	y.	y.	PROPN
ijassa-1225	36	3	if	if	SCONJ
ijassa-1225	36	4	for	for	ADP
ijassa-1225	36	5	any	any	DET
ijassa-1225	36	6	x	x	SYM
ijassa-1225	36	7	∈	∈	PROPN
ijassa-1225	36	8	x	x	X
ijassa-1225	36	9	,	,	PUNCT
ijassa-1225	36	10	the	the	DET
ijassa-1225	36	11	set	set	ADJ
ijassa-1225	36	12	g(x	g(x	NOUN
ijassa-1225	36	13	)	)	PUNCT
ijassa-1225	36	14	contains	contain	VERB
ijassa-1225	36	15	only	only	ADV
ijassa-1225	36	16	one	one	NUM
ijassa-1225	36	17	element	element	NOUN
ijassa-1225	36	18	,	,	PUNCT
ijassa-1225	36	19	then	then	ADV
ijassa-1225	36	20	the	the	DET
ijassa-1225	36	21	mapping	mapping	NOUN
ijassa-1225	36	22	g	g	NOUN
ijassa-1225	36	23	becomes	become	VERB
ijassa-1225	36	24	a	a	DET
ijassa-1225	36	25	“	"	PUNCT
ijassa-1225	36	26	standard	standard	ADJ
ijassa-1225	36	27	single	single	ADV
ijassa-1225	36	28	-	-	PUNCT
ijassa-1225	36	29	valued	value	VERB
ijassa-1225	36	30	”	"	PUNCT
ijassa-1225	36	31	mapping	mapping	NOUN
ijassa-1225	36	32	(	(	PUNCT
ijassa-1225	36	33	we	we	PRON
ijassa-1225	36	34	conventionally	conventionally	ADV
ijassa-1225	36	35	denote	denote	VERB
ijassa-1225	36	36	such	such	DET
ijassa-1225	36	37	a	a	DET
ijassa-1225	36	38	mapping	mapping	NOUN
ijassa-1225	36	39	as	as	ADP
ijassa-1225	36	40	g	g	PROPN
ijassa-1225	36	41	:	:	PUNCT
ijassa-1225	36	42	x	x	PROPN
ijassa-1225	36	43	→	→	SYM
ijassa-1225	36	44	y	y	PROPN
ijassa-1225	36	45	)	)	PUNCT
ijassa-1225	36	46	.	.	PUNCT
ijassa-1225	37	1	thus	thus	ADV
ijassa-1225	37	2	,	,	PUNCT
ijassa-1225	37	3	set	set	NOUN
ijassa-1225	37	4	-	-	PUNCT
ijassa-1225	37	5	valued	value	VERB
ijassa-1225	37	6	mappings	mapping	NOUN
ijassa-1225	37	7	naturally	naturally	ADV
ijassa-1225	37	8	generalise	generalise	VERB
ijassa-1225	37	9	“	"	PUNCT
ijassa-1225	37	10	standard	standard	ADJ
ijassa-1225	37	11	”	"	PUNCT
ijassa-1225	37	12	mappings	mapping	NOUN
ijassa-1225	37	13	.	.	PUNCT
ijassa-1225	38	1	let	let	VERB
ijassa-1225	38	2	us	we	PRON
ijassa-1225	38	3	remind	remind	VERB
ijassa-1225	38	4	definitions	definition	NOUN
ijassa-1225	38	5	of	of	ADP
ijassa-1225	38	6	some	some	DET
ijassa-1225	38	7	properties	property	NOUN
ijassa-1225	38	8	of	of	ADP
ijassa-1225	38	9	set	set	NOUN
ijassa-1225	38	10	-	-	PUNCT
ijassa-1225	38	11	valued	value	VERB
ijassa-1225	38	12	mappings	mapping	NOUN
ijassa-1225	38	13	used	use	VERB
ijassa-1225	38	14	in	in	ADP
ijassa-1225	38	15	the	the	DET
ijassa-1225	38	16	present	present	ADJ
ijassa-1225	38	17	work	work	NOUN
ijassa-1225	38	18	.	.	PUNCT
ijassa-1225	39	1	definition	definition	NOUN
ijassa-1225	39	2	2.1	2.1	NUM
ijassa-1225	39	3	:	:	PUNCT
ijassa-1225	39	4	a	a	DET
ijassa-1225	39	5	mappingg	mappingg	NOUN
ijassa-1225	39	6	:	:	PUNCT
ijassa-1225	39	7	x	x	SYM
ijassa-1225	39	8	⇒	⇒	PROPN
ijassa-1225	39	9	y	y	PROPN
ijassa-1225	39	10	is	be	AUX
ijassa-1225	39	11	called	call	VERB
ijassa-1225	39	12	antitone	antitone	NOUN
ijassa-1225	39	13	(	(	PUNCT
ijassa-1225	39	14	isotone	isotone	NOUN
ijassa-1225	39	15	)	)	PUNCT
ijassa-1225	39	16	on	on	ADP
ijassa-1225	39	17	the	the	DET
ijassa-1225	39	18	set	set	NOUN
ijassa-1225	39	19	u	u	PROPN
ijassa-1225	39	20	⊂	⊂	PROPN
ijassa-1225	39	21	x	x	X
ijassa-1225	39	22	,	,	PUNCT
ijassa-1225	39	23	if	if	SCONJ
ijassa-1225	39	24	for	for	ADP
ijassa-1225	39	25	any	any	DET
ijassa-1225	39	26	x	x	NOUN
ijassa-1225	39	27	,	,	PUNCT
ijassa-1225	39	28	u	u	PROPN
ijassa-1225	39	29	∈	∈	PROPN
ijassa-1225	39	30	u	u	NOUN
ijassa-1225	39	31	such	such	ADJ
ijassa-1225	39	32	that	that	SCONJ
ijassa-1225	39	33	x	x	SYM
ijassa-1225	39	34	�	�	PROPN
ijassa-1225	39	35	u	u	PROPN
ijassa-1225	39	36	and	and	CCONJ
ijassa-1225	39	37	for	for	ADP
ijassa-1225	39	38	z	z	PROPN
ijassa-1225	39	39	∈	∈	PROPN
ijassa-1225	39	40	g(u	g(u	PROPN
ijassa-1225	39	41	)	)	PUNCT
ijassa-1225	39	42	,	,	PUNCT
ijassa-1225	39	43	there	there	PRON
ijassa-1225	39	44	exists	exist	VERB
ijassa-1225	39	45	y	y	PROPN
ijassa-1225	39	46	∈	∈	PROPN
ijassa-1225	39	47	g(x	g(x	PROPN
ijassa-1225	39	48	)	)	PUNCT
ijassa-1225	39	49	satisfying	satisfy	VERB
ijassa-1225	39	50	the	the	DET
ijassa-1225	39	51	inequality	inequality	NOUN
ijassa-1225	39	52	y	y	PROPN
ijassa-1225	39	53	�	�	PROPN
ijassa-1225	39	54	z	z	PROPN
ijassa-1225	39	55	(	(	PUNCT
ijassa-1225	39	56	y	y	PROPN
ijassa-1225	39	57	�	�	PROPN
ijassa-1225	39	58	z	z	PROPN
ijassa-1225	39	59	)	)	PUNCT
ijassa-1225	39	60	.	.	PUNCT
ijassa-1225	40	1	if	if	SCONJ
ijassa-1225	40	2	a	a	DET
ijassa-1225	40	3	mapping	mapping	NOUN
ijassa-1225	40	4	is	be	AUX
ijassa-1225	40	5	antitone	antitone	NOUN
ijassa-1225	40	6	(	(	PUNCT
ijassa-1225	40	7	isotone	isotone	NOUN
ijassa-1225	40	8	)	)	PUNCT
ijassa-1225	40	9	on	on	ADP
ijassa-1225	40	10	the	the	DET
ijassa-1225	40	11	whole	whole	ADJ
ijassa-1225	40	12	space	space	NOUN
ijassa-1225	40	13	x	x	X
ijassa-1225	40	14	,	,	PUNCT
ijassa-1225	40	15	it	it	PRON
ijassa-1225	40	16	is	be	AUX
ijassa-1225	40	17	called	call	VERB
ijassa-1225	40	18	antitone	antitone	NOUN
ijassa-1225	40	19	(	(	PUNCT
ijassa-1225	40	20	isotone	isotone	NOUN
ijassa-1225	40	21	)	)	PUNCT
ijassa-1225	40	22	.	.	PUNCT
ijassa-1225	41	1	the	the	DET
ijassa-1225	41	2	given	give	VERB
ijassa-1225	41	3	definition	definition	NOUN
ijassa-1225	41	4	of	of	ADP
ijassa-1225	41	5	the	the	DET
ijassa-1225	41	6	antitone	antitone	ADJ
ijassa-1225	41	7	property	property	NOUN
ijassa-1225	41	8	for	for	ADP
ijassa-1225	41	9	a	a	DET
ijassa-1225	41	10	mapping	mapping	NOUN
ijassa-1225	41	11	g	g	NOUN
ijassa-1225	41	12	:	:	PUNCT
ijassa-1225	41	13	x	x	X
ijassa-1225	41	14	→	→	SYM
ijassa-1225	41	15	y	y	PROPN
ijassa-1225	41	16	means	mean	VERB
ijassa-1225	41	17	that	that	SCONJ
ijassa-1225	41	18	∀x	∀x	NUM
ijassa-1225	41	19	,	,	PUNCT
ijassa-1225	41	20	u	u	PROPN
ijassa-1225	41	21	∈	∈	PROPN
ijassa-1225	41	22	u	u	NOUN
ijassa-1225	41	23	x	x	PROPN
ijassa-1225	41	24	�	�	PROPN
ijassa-1225	41	25	u	u	PROPN
ijassa-1225	41	26	⇒	⇒	VERB
ijassa-1225	41	27	g(x	g(x	PROPN
ijassa-1225	41	28	)	)	PUNCT
ijassa-1225	41	29	�	�	PROPN
ijassa-1225	41	30	g(u	g(u	PROPN
ijassa-1225	41	31	)	)	PUNCT
ijassa-1225	41	32	,	,	PUNCT
ijassa-1225	41	33	matches	match	VERB
ijassa-1225	41	34	the	the	DET
ijassa-1225	41	35	definition	definition	NOUN
ijassa-1225	41	36	of	of	ADP
ijassa-1225	41	37	the	the	DET
ijassa-1225	41	38	antitone	antitone	ADJ
ijassa-1225	41	39	property	property	NOUN
ijassa-1225	41	40	for	for	ADP
ijassa-1225	41	41	single	single	ADJ
ijassa-1225	41	42	-	-	PUNCT
ijassa-1225	41	43	valued	value	VERB
ijassa-1225	41	44	mappings	mapping	NOUN
ijassa-1225	41	45	.	.	PUNCT
ijassa-1225	42	1	the	the	DET
ijassa-1225	42	2	given	give	VERB
ijassa-1225	42	3	isotone	isotone	NOUN
ijassa-1225	42	4	property	property	NOUN
ijassa-1225	42	5	in	in	ADP
ijassa-1225	42	6	the	the	DET
ijassa-1225	42	7	case	case	NOUN
ijassa-1225	42	8	of	of	ADP
ijassa-1225	42	9	single	single	ADJ
ijassa-1225	42	10	-	-	PUNCT
ijassa-1225	42	11	valued	value	VERB
ijassa-1225	42	12	mappings	mapping	NOUN
ijassa-1225	42	13	also	also	ADV
ijassa-1225	42	14	matches	match	VERB
ijassa-1225	42	15	the	the	DET
ijassa-1225	42	16	“	"	PUNCT
ijassa-1225	42	17	classical	classical	ADJ
ijassa-1225	42	18	”	"	PUNCT
ijassa-1225	42	19	isotone	isotone	NOUN
ijassa-1225	42	20	property	property	NOUN
ijassa-1225	42	21	.	.	PUNCT
ijassa-1225	43	1	definition	definition	NOUN
ijassa-1225	43	2	2.2	2.2	NUM
ijassa-1225	43	3	:	:	PUNCT
ijassa-1225	43	4	a	a	DET
ijassa-1225	43	5	mapping	mapping	NOUN
ijassa-1225	43	6	g	g	NOUN
ijassa-1225	43	7	:	:	PUNCT
ijassa-1225	43	8	x	x	SYM
ijassa-1225	43	9	⇒	⇒	NOUN
ijassa-1225	43	10	y	y	PROPN
ijassa-1225	43	11	order	order	NOUN
ijassa-1225	43	12	covers	cover	VERB
ijassa-1225	43	13	the	the	DET
ijassa-1225	43	14	set	set	NOUN
ijassa-1225	43	15	v	v	ADP
ijassa-1225	43	16	⊂	⊂	PROPN
ijassa-1225	43	17	y	y	PROPN
ijassa-1225	43	18	if	if	SCONJ
ijassa-1225	43	19	∀u	∀u	NOUN
ijassa-1225	43	20	∈	∈	NOUN
ijassa-1225	43	21	x	x	SYM
ijassa-1225	43	22	oy	oy	X
ijassa-1225	43	23	(	(	PUNCT
ijassa-1225	43	24	g(u	g(u	PROPN
ijassa-1225	43	25	)	)	PUNCT
ijassa-1225	43	26	)	)	PUNCT
ijassa-1225	43	27	∩	∩	PROPN
ijassa-1225	43	28	v	v	ADP
ijassa-1225	43	29	⊂	⊂	PROPN
ijassa-1225	43	30	g	g	PROPN
ijassa-1225	43	31	(	(	PUNCT
ijassa-1225	43	32	ox(u	ox(u	X
ijassa-1225	43	33	)	)	PUNCT
ijassa-1225	43	34	)	)	PUNCT
ijassa-1225	43	35	.	.	PUNCT
ijassa-1225	44	1	(	(	PUNCT
ijassa-1225	44	2	2.1	2.1	NUM
ijassa-1225	44	3	)	)	PUNCT
ijassa-1225	44	4	the	the	DET
ijassa-1225	44	5	definition	definition	NOUN
ijassa-1225	44	6	of	of	ADP
ijassa-1225	44	7	order	order	NOUN
ijassa-1225	44	8	covering	cover	VERB
ijassa-1225	44	9	for	for	ADP
ijassa-1225	44	10	set	set	NOUN
ijassa-1225	44	11	-	-	PUNCT
ijassa-1225	44	12	valued	value	VERB
ijassa-1225	44	13	mappings	mapping	NOUN
ijassa-1225	44	14	was	be	AUX
ijassa-1225	44	15	introduced	introduce	VERB
ijassa-1225	44	16	in	in	ADP
ijassa-1225	44	17	[	[	X
ijassa-1225	44	18	3	3	NUM
ijassa-1225	44	19	,	,	PUNCT
ijassa-1225	44	20	4	4	NUM
ijassa-1225	44	21	]	]	PUNCT
ijassa-1225	44	22	for	for	ADP
ijassa-1225	44	23	the	the	DET
ijassa-1225	44	24	case	case	NOUN
ijassa-1225	44	25	v	v	ADP
ijassa-1225	44	26	=	=	SYM
ijassa-1225	44	27	y.	y.	NOUN
ijassa-1225	44	28	note	note	VERB
ijassa-1225	44	29	that	that	SCONJ
ijassa-1225	44	30	(	(	PUNCT
ijassa-1225	44	31	2.1	2.1	NUM
ijassa-1225	44	32	)	)	PUNCT
ijassa-1225	44	33	is	be	AUX
ijassa-1225	44	34	equivalent	equivalent	ADJ
ijassa-1225	44	35	to	to	ADP
ijassa-1225	44	36	the	the	DET
ijassa-1225	44	37	relation	relation	NOUN
ijassa-1225	44	38	(	(	PUNCT
ijassa-1225	45	1	∀u	∀u	NOUN
ijassa-1225	45	2	∈	∈	NOUN
ijassa-1225	45	3	x	x	SYM
ijassa-1225	45	4	∀v	∀v	PROPN
ijassa-1225	45	5	∈	∈	PROPN
ijassa-1225	45	6	g(u	g(u	PROPN
ijassa-1225	45	7	)	)	PUNCT
ijassa-1225	45	8	∀y	∀y	PROPN
ijassa-1225	45	9	∈	∈	NOUN
ijassa-1225	45	10	v	v	ADP
ijassa-1225	45	11	y	y	PROPN
ijassa-1225	45	12	�	�	PROPN
ijassa-1225	45	13	v	v	NOUN
ijassa-1225	45	14	)	)	PUNCT
ijassa-1225	45	15	⇒	⇒	NOUN
ijassa-1225	45	16	(	(	PUNCT
ijassa-1225	45	17	∃x	∃x	PROPN
ijassa-1225	45	18	∈	∈	PROPN
ijassa-1225	45	19	x	x	PUNCT
ijassa-1225	45	20	y	y	PROPN
ijassa-1225	45	21	∈	∈	PROPN
ijassa-1225	45	22	g(x	g(x	PROPN
ijassa-1225	45	23	)	)	PUNCT
ijassa-1225	45	24	and	and	CCONJ
ijassa-1225	45	25	x	x	PUNCT
ijassa-1225	45	26	�	�	PROPN
ijassa-1225	45	27	u	u	PROPN
ijassa-1225	45	28	)	)	PUNCT
ijassa-1225	45	29	.	.	PUNCT
ijassa-1225	46	1	copyright	copyright	NOUN
ijassa-1225	46	2	©	©	PROPN
ijassa-1225	46	3	2022	2022	NUM
ijassa-1225	46	4	assa	assa	NOUN
ijassa-1225	46	5	.	.	PUNCT
ijassa-1225	47	1	adv	adv	PROPN
ijassa-1225	47	2	syst	syst	PROPN
ijassa-1225	47	3	sci	sci	PROPN
ijassa-1225	47	4	appl	appl	PROPN
ijassa-1225	47	5	(	(	PUNCT
ijassa-1225	47	6	2022	2022	NUM
ijassa-1225	47	7	)	)	PUNCT
ijassa-1225	47	8	178	178	NUM
ijassa-1225	47	9	e.s	e.s	PROPN
ijassa-1225	47	10	.	.	PROPN
ijassa-1225	47	11	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	47	12	,	,	PUNCT
ijassa-1225	47	13	i.d	i.d	PROPN
ijassa-1225	47	14	.	.	PROPN
ijassa-1225	47	15	serova	serova	PROPN
ijassa-1225	47	16	,	,	PUNCT
ijassa-1225	47	17	e.a	e.a	PROPN
ijassa-1225	47	18	.	.	PROPN
ijassa-1225	47	19	panasenko	panasenko	PROPN
ijassa-1225	47	20	,	,	PUNCT
ijassa-1225	47	21	e.o	e.o	PROPN
ijassa-1225	47	22	.	.	PROPN
ijassa-1225	47	23	burlakov	burlakov	PROPN
ijassa-1225	48	1	moreover	moreover	ADV
ijassa-1225	48	2	,	,	PUNCT
ijassa-1225	48	3	if	if	SCONJ
ijassa-1225	48	4	v	v	NOUN
ijassa-1225	48	5	is	be	AUX
ijassa-1225	48	6	a	a	DET
ijassa-1225	48	7	one	one	NUM
ijassa-1225	48	8	-	-	PUNCT
ijassa-1225	48	9	element	element	NOUN
ijassa-1225	48	10	set	set	NOUN
ijassa-1225	48	11	,	,	PUNCT
ijassa-1225	48	12	i.e.	i.e.	X
ijassa-1225	48	13	v	v	NOUN
ijassa-1225	48	14	=	=	SYM
ijassa-1225	48	15	{	{	PUNCT
ijassa-1225	48	16	ŷ	ŷ	NUM
ijassa-1225	48	17	}	}	PUNCT
ijassa-1225	48	18	,	,	PUNCT
ijassa-1225	48	19	then	then	ADV
ijassa-1225	48	20	the	the	DET
ijassa-1225	48	21	relation	relation	NOUN
ijassa-1225	48	22	(	(	PUNCT
ijassa-1225	48	23	2.1	2.1	NUM
ijassa-1225	48	24	)	)	PUNCT
ijassa-1225	48	25	is	be	AUX
ijassa-1225	48	26	equivalent	equivalent	ADJ
ijassa-1225	48	27	to	to	ADP
ijassa-1225	48	28	the	the	DET
ijassa-1225	48	29	implication	implication	NOUN
ijassa-1225	48	30	∀u	∀u	NOUN
ijassa-1225	48	31	∈	∈	NOUN
ijassa-1225	48	32	x	x	SYM
ijassa-1225	48	33	ŷ	ŷ	NUM
ijassa-1225	48	34	∈	∈	PROPN
ijassa-1225	48	35	oy	oy	NOUN
ijassa-1225	48	36	(	(	PUNCT
ijassa-1225	48	37	g(u	g(u	PROPN
ijassa-1225	48	38	)	)	PUNCT
ijassa-1225	48	39	)	)	PUNCT
ijassa-1225	48	40	⇒	⇒	NOUN
ijassa-1225	48	41	ŷ	ŷ	NUM
ijassa-1225	49	1	∈	∈	PROPN
ijassa-1225	49	2	g	g	PROPN
ijassa-1225	49	3	(	(	PUNCT
ijassa-1225	49	4	ox(u	ox(u	PROPN
ijassa-1225	49	5	)	)	PUNCT
ijassa-1225	49	6	)	)	PUNCT
ijassa-1225	49	7	.	.	PUNCT
ijassa-1225	50	1	thus	thus	ADV
ijassa-1225	50	2	,	,	PUNCT
ijassa-1225	50	3	the	the	DET
ijassa-1225	50	4	property	property	NOUN
ijassa-1225	50	5	of	of	ADP
ijassa-1225	50	6	order	order	NOUN
ijassa-1225	50	7	covering	covering	NOUN
ijassa-1225	50	8	of	of	ADP
ijassa-1225	50	9	the	the	DET
ijassa-1225	50	10	set	set	NOUN
ijassa-1225	50	11	{	{	PUNCT
ijassa-1225	50	12	ŷ	ŷ	NUM
ijassa-1225	50	13	}	}	PUNCT
ijassa-1225	50	14	means	mean	VERB
ijassa-1225	50	15	that	that	SCONJ
ijassa-1225	50	16	for	for	ADP
ijassa-1225	50	17	any	any	DET
ijassa-1225	50	18	u	u	NOUN
ijassa-1225	50	19	∈	∈	PROPN
ijassa-1225	50	20	x	x	PUNCT
ijassa-1225	50	21	such	such	ADJ
ijassa-1225	50	22	that	that	SCONJ
ijassa-1225	50	23	the	the	DET
ijassa-1225	50	24	set	set	NOUN
ijassa-1225	50	25	g(u	g(u	PROPN
ijassa-1225	50	26	)	)	PUNCT
ijassa-1225	50	27	contains	contain	VERB
ijassa-1225	50	28	an	an	DET
ijassa-1225	50	29	element	element	NOUN
ijassa-1225	50	30	v	v	ADP
ijassa-1225	50	31	�	�	PROPN
ijassa-1225	50	32	ŷ	ŷ	NUM
ijassa-1225	50	33	,	,	PUNCT
ijassa-1225	50	34	the	the	DET
ijassa-1225	50	35	inclusion	inclusion	NOUN
ijassa-1225	50	36	ŷ	ŷ	NUM
ijassa-1225	50	37	∈	∈	PROPN
ijassa-1225	50	38	g(x	g(x	NOUN
ijassa-1225	50	39	)	)	PUNCT
ijassa-1225	50	40	(	(	PUNCT
ijassa-1225	50	41	2.2	2.2	NUM
ijassa-1225	50	42	)	)	PUNCT
ijassa-1225	50	43	has	have	VERB
ijassa-1225	50	44	a	a	DET
ijassa-1225	50	45	solution	solution	NOUN
ijassa-1225	50	46	x	x	X
ijassa-1225	50	47	∈	∈	NOUN
ijassa-1225	50	48	x	x	PUNCT
ijassa-1225	50	49	satisfying	satisfy	VERB
ijassa-1225	50	50	the	the	DET
ijassa-1225	50	51	inequality	inequality	NOUN
ijassa-1225	50	52	x	x	X
ijassa-1225	50	53	�	�	PROPN
ijassa-1225	50	54	u.	u.	PROPN
ijassa-1225	50	55	in	in	ADP
ijassa-1225	50	56	the	the	DET
ijassa-1225	50	57	same	same	ADJ
ijassa-1225	50	58	manner	manner	NOUN
ijassa-1225	50	59	,	,	PUNCT
ijassa-1225	50	60	a	a	DET
ijassa-1225	50	61	single	single	ADV
ijassa-1225	50	62	-	-	PUNCT
ijassa-1225	50	63	valued	value	VERB
ijassa-1225	50	64	mapping	mapping	NOUN
ijassa-1225	50	65	g	g	NOUN
ijassa-1225	50	66	:	:	PUNCT
ijassa-1225	50	67	x	x	X
ijassa-1225	50	68	→	→	SYM
ijassa-1225	50	69	y	y	NUM
ijassa-1225	50	70	order	order	NOUN
ijassa-1225	50	71	covers	cover	VERB
ijassa-1225	50	72	the	the	DET
ijassa-1225	50	73	set	set	NOUN
ijassa-1225	50	74	{	{	PUNCT
ijassa-1225	50	75	ŷ	ŷ	NUM
ijassa-1225	50	76	}	}	PUNCT
ijassa-1225	50	77	if	if	SCONJ
ijassa-1225	50	78	∀u	∀u	NOUN
ijassa-1225	50	79	∈	∈	NOUN
ijassa-1225	50	80	x	x	SYM
ijassa-1225	50	81	g(u	g(u	PROPN
ijassa-1225	50	82	)	)	PUNCT
ijassa-1225	50	83	�	�	PROPN
ijassa-1225	50	84	ŷ	ŷ	AUX
ijassa-1225	50	85	⇒	⇒	VERB
ijassa-1225	50	86	∃x	∃x	PROPN
ijassa-1225	50	87	∈	∈	PROPN
ijassa-1225	50	88	ox(u	ox(u	X
ijassa-1225	50	89	)	)	PUNCT
ijassa-1225	50	90	g(x	g(x	NOUN
ijassa-1225	50	91	)	)	PUNCT
ijassa-1225	51	1	=	=	SYM
ijassa-1225	51	2	ŷ.	ŷ.	NOUN
ijassa-1225	51	3	we	we	PRON
ijassa-1225	51	4	consider	consider	VERB
ijassa-1225	51	5	the	the	DET
ijassa-1225	51	6	problem	problem	NOUN
ijassa-1225	51	7	of	of	ADP
ijassa-1225	51	8	stability	stability	NOUN
ijassa-1225	51	9	of	of	ADP
ijassa-1225	51	10	the	the	DET
ijassa-1225	51	11	solvability	solvability	NOUN
ijassa-1225	51	12	property	property	NOUN
ijassa-1225	51	13	of	of	ADP
ijassa-1225	51	14	the	the	DET
ijassa-1225	51	15	inclusion	inclusion	NOUN
ijassa-1225	51	16	(	(	PUNCT
ijassa-1225	51	17	2.2	2.2	NUM
ijassa-1225	51	18	)	)	PUNCT
ijassa-1225	51	19	under	under	ADP
ijassa-1225	51	20	antitone	antitone	ADJ
ijassa-1225	51	21	perturbations	perturbation	NOUN
ijassa-1225	51	22	of	of	ADP
ijassa-1225	51	23	the	the	DET
ijassa-1225	51	24	order	order	NOUN
ijassa-1225	51	25	covering	cover	VERB
ijassa-1225	51	26	mapping	mapping	NOUN
ijassa-1225	51	27	.	.	PUNCT
ijassa-1225	52	1	let	let	VERB
ijassa-1225	52	2	a	a	DET
ijassa-1225	52	3	“	"	PUNCT
ijassa-1225	52	4	perturbed	perturb	VERB
ijassa-1225	52	5	”	"	PUNCT
ijassa-1225	52	6	mapping	mapping	NOUN
ijassa-1225	52	7	υ	υ	NOUN
ijassa-1225	52	8	:	:	PUNCT
ijassa-1225	52	9	x	x	X
ijassa-1225	52	10	×x	×x	VERB
ijassa-1225	52	11	⇒	⇒	NOUN
ijassa-1225	52	12	y	y	NOUN
ijassa-1225	52	13	that	that	DET
ijassa-1225	52	14	order	order	NOUN
ijassa-1225	52	15	covers	cover	VERB
ijassa-1225	52	16	the	the	DET
ijassa-1225	52	17	set	set	NOUN
ijassa-1225	52	18	{	{	PUNCT
ijassa-1225	52	19	ŷ	ŷ	NUM
ijassa-1225	52	20	}	}	PUNCT
ijassa-1225	52	21	with	with	ADP
ijassa-1225	52	22	respect	respect	NOUN
ijassa-1225	52	23	to	to	ADP
ijassa-1225	52	24	the	the	DET
ijassa-1225	52	25	first	first	ADJ
ijassa-1225	52	26	argument	argument	NOUN
ijassa-1225	52	27	and	and	CCONJ
ijassa-1225	52	28	antitone	antitone	VERB
ijassa-1225	52	29	with	with	ADP
ijassa-1225	52	30	respect	respect	NOUN
ijassa-1225	52	31	to	to	ADP
ijassa-1225	52	32	the	the	DET
ijassa-1225	52	33	second	second	ADJ
ijassa-1225	52	34	argument	argument	NOUN
ijassa-1225	52	35	be	be	AUX
ijassa-1225	52	36	given	give	VERB
ijassa-1225	52	37	.	.	PUNCT
ijassa-1225	53	1	define	define	VERB
ijassa-1225	53	2	the	the	DET
ijassa-1225	53	3	mapping	mapping	NOUN
ijassa-1225	53	4	f	f	NOUN
ijassa-1225	53	5	:	:	PUNCT
ijassa-1225	53	6	x	x	SYM
ijassa-1225	53	7	⇒	⇒	NOUN
ijassa-1225	53	8	y	y	PROPN
ijassa-1225	53	9	by	by	ADP
ijassa-1225	53	10	the	the	DET
ijassa-1225	53	11	relation	relation	NOUN
ijassa-1225	53	12	∀x	∀x	PUNCT
ijassa-1225	53	13	∈	∈	PROPN
ijassa-1225	53	14	x	x	X
ijassa-1225	53	15	f	f	X
ijassa-1225	53	16	(	(	PUNCT
ijassa-1225	53	17	x	x	NOUN
ijassa-1225	53	18	)	)	PUNCT
ijassa-1225	53	19	=	=	SYM
ijassa-1225	53	20	υ(x	υ(x	PROPN
ijassa-1225	53	21	,	,	PUNCT
ijassa-1225	53	22	x	x	PRON
ijassa-1225	53	23	)	)	PUNCT
ijassa-1225	53	24	and	and	CCONJ
ijassa-1225	53	25	consider	consider	VERB
ijassa-1225	53	26	the	the	DET
ijassa-1225	53	27	inclusion	inclusion	NOUN
ijassa-1225	54	1	ŷ	ŷ	X
ijassa-1225	54	2	∈	∈	PROPN
ijassa-1225	55	1	f	f	X
ijassa-1225	55	2	(	(	PUNCT
ijassa-1225	55	3	x	x	X
ijassa-1225	55	4	)	)	PUNCT
ijassa-1225	55	5	(	(	PUNCT
ijassa-1225	55	6	2.3	2.3	NUM
ijassa-1225	55	7	)	)	PUNCT
ijassa-1225	55	8	(	(	PUNCT
ijassa-1225	55	9	with	with	ADP
ijassa-1225	55	10	respect	respect	NOUN
ijassa-1225	55	11	to	to	ADP
ijassa-1225	55	12	x	x	X
ijassa-1225	55	13	∈	∈	NOUN
ijassa-1225	55	14	x	x	NOUN
ijassa-1225	55	15	)	)	PUNCT
ijassa-1225	55	16	.	.	PUNCT
ijassa-1225	56	1	let	let	VERB
ijassa-1225	56	2	u	u	PRON
ijassa-1225	56	3	⊂	⊂	PROPN
ijassa-1225	56	4	x.	x.	NOUN
ijassa-1225	57	1	in	in	ADP
ijassa-1225	57	2	order	order	NOUN
ijassa-1225	57	3	to	to	PART
ijassa-1225	57	4	formulate	formulate	VERB
ijassa-1225	57	5	a	a	DET
ijassa-1225	57	6	theorem	theorem	NOUN
ijassa-1225	57	7	on	on	ADP
ijassa-1225	57	8	existence	existence	NOUN
ijassa-1225	57	9	of	of	ADP
ijassa-1225	57	10	solutions	solution	NOUN
ijassa-1225	57	11	to	to	ADP
ijassa-1225	57	12	(	(	PUNCT
ijassa-1225	57	13	2.3	2.3	NUM
ijassa-1225	57	14	)	)	PUNCT
ijassa-1225	57	15	,	,	PUNCT
ijassa-1225	57	16	we	we	PRON
ijassa-1225	57	17	define	define	VERB
ijassa-1225	57	18	the	the	DET
ijassa-1225	57	19	set	set	ADJ
ijassa-1225	57	20	s(υ	s(υ	PROPN
ijassa-1225	57	21	,	,	PUNCT
ijassa-1225	57	22	u	u	NOUN
ijassa-1225	57	23	,	,	PUNCT
ijassa-1225	57	24	ŷ	ŷ	NUM
ijassa-1225	57	25	)	)	PUNCT
ijassa-1225	57	26	of	of	ADP
ijassa-1225	57	27	all	all	DET
ijassa-1225	57	28	chains	chain	NOUN
ijassa-1225	57	29	s	s	PART
ijassa-1225	57	30	⊂	⊂	ADJ
ijassa-1225	57	31	u	u	NOUN
ijassa-1225	57	32	such	such	ADJ
ijassa-1225	57	33	that	that	SCONJ
ijassa-1225	57	34	the	the	DET
ijassa-1225	57	35	following	follow	VERB
ijassa-1225	57	36	relations	relation	NOUN
ijassa-1225	57	37	take	take	VERB
ijassa-1225	57	38	place	place	NOUN
ijassa-1225	57	39	:	:	PUNCT
ijassa-1225	57	40	∀x	∀x	X
ijassa-1225	57	41	∈	∈	PROPN
ijassa-1225	57	42	s	s	PART
ijassa-1225	57	43	∃y	∃y	PROPN
ijassa-1225	57	44	∈	∈	PROPN
ijassa-1225	57	45	υ(x	υ(x	PROPN
ijassa-1225	57	46	,	,	PUNCT
ijassa-1225	57	47	x	x	X
ijassa-1225	57	48	)	)	PUNCT
ijassa-1225	57	49	y	y	PROPN
ijassa-1225	57	50	�	�	PROPN
ijassa-1225	57	51	ŷ	ŷ	NUM
ijassa-1225	57	52	,	,	PUNCT
ijassa-1225	57	53	∀x	∀x	X
ijassa-1225	57	54	,	,	PUNCT
ijassa-1225	57	55	u	u	PROPN
ijassa-1225	57	56	∈	∈	PROPN
ijassa-1225	57	57	s	s	PART
ijassa-1225	57	58	x	x	NOUN
ijassa-1225	57	59	≺	≺	NOUN
ijassa-1225	57	60	u	u	PRON
ijassa-1225	57	61	⇒	⇒	VERB
ijassa-1225	57	62	∃ξ	∃ξ	PROPN
ijassa-1225	57	63	∈	∈	PROPN
ijassa-1225	58	1	[	[	X
ijassa-1225	58	2	x	x	X
ijassa-1225	58	3	,	,	PUNCT
ijassa-1225	58	4	u	u	NOUN
ijassa-1225	58	5	]	]	X
ijassa-1225	58	6	ŷ	ŷ	NUM
ijassa-1225	58	7	∈	∈	PROPN
ijassa-1225	58	8	υ(ξ	υ(ξ	PROPN
ijassa-1225	58	9	,	,	PUNCT
ijassa-1225	58	10	u	u	NOUN
ijassa-1225	58	11	)	)	PUNCT
ijassa-1225	58	12	.	.	PUNCT
ijassa-1225	59	1	(	(	PUNCT
ijassa-1225	59	2	2.4	2.4	NUM
ijassa-1225	59	3	)	)	PUNCT
ijassa-1225	59	4	theorem	theorem	VERB
ijassa-1225	59	5	2.1	2.1	NUM
ijassa-1225	59	6	:	:	PUNCT
ijassa-1225	59	7	let	let	VERB
ijassa-1225	59	8	there	there	PRON
ijassa-1225	59	9	exist	exist	VERB
ijassa-1225	59	10	u0	u0	ADJ
ijassa-1225	59	11	∈	∈	PROPN
ijassa-1225	59	12	x	x	X
ijassa-1225	59	13	and	and	CCONJ
ijassa-1225	59	14	y0	y0	PROPN
ijassa-1225	59	15	∈	∈	NOUN
ijassa-1225	59	16	y	y	NOUN
ijassa-1225	59	17	such	such	ADJ
ijassa-1225	59	18	that	that	SCONJ
ijassa-1225	59	19	y0	y0	PROPN
ijassa-1225	59	20	∈	∈	PROPN
ijassa-1225	59	21	υ(u0	υ(u0	NOUN
ijassa-1225	59	22	,	,	PUNCT
ijassa-1225	59	23	u0	u0	ADJ
ijassa-1225	59	24	)	)	PUNCT
ijassa-1225	59	25	,	,	PUNCT
ijassa-1225	59	26	y0	y0	PROPN
ijassa-1225	59	27	�	�	PROPN
ijassa-1225	59	28	ŷ	ŷ	NUM
ijassa-1225	59	29	,	,	PUNCT
ijassa-1225	59	30	(	(	PUNCT
ijassa-1225	59	31	2.5	2.5	NUM
ijassa-1225	59	32	)	)	PUNCT
ijassa-1225	59	33	and	and	CCONJ
ijassa-1225	59	34	the	the	DET
ijassa-1225	59	35	follwing	follwe	VERB
ijassa-1225	59	36	conditions	condition	NOUN
ijassa-1225	59	37	are	be	AUX
ijassa-1225	59	38	satisfied	satisfied	ADJ
ijassa-1225	59	39	:	:	PUNCT
ijassa-1225	59	40	(	(	PUNCT
ijassa-1225	59	41	a1	a1	NOUN
ijassa-1225	59	42	)	)	PUNCT
ijassa-1225	59	43	for	for	ADP
ijassa-1225	59	44	any	any	DET
ijassa-1225	59	45	x	x	SYM
ijassa-1225	59	46	∈	∈	PROPN
ijassa-1225	59	47	ox(u0	ox(u0	PROPN
ijassa-1225	59	48	)	)	PUNCT
ijassa-1225	59	49	,	,	PUNCT
ijassa-1225	59	50	the	the	DET
ijassa-1225	59	51	mapping	mapping	NOUN
ijassa-1225	59	52	υ	υ	NOUN
ijassa-1225	59	53	(	(	PUNCT
ijassa-1225	59	54	·	·	PUNCT
ijassa-1225	59	55	,	,	PUNCT
ijassa-1225	59	56	x	x	NOUN
ijassa-1225	59	57	)	)	PUNCT
ijassa-1225	59	58	:	:	PUNCT
ijassa-1225	59	59	x	x	SYM
ijassa-1225	59	60	⇒	⇒	NOUN
ijassa-1225	59	61	y	y	PROPN
ijassa-1225	59	62	order	order	NOUN
ijassa-1225	59	63	covers	cover	VERB
ijassa-1225	59	64	the	the	DET
ijassa-1225	59	65	set	set	NOUN
ijassa-1225	59	66	{	{	PUNCT
ijassa-1225	59	67	ŷ	ŷ	NUM
ijassa-1225	59	68	}	}	PUNCT
ijassa-1225	59	69	;	;	PUNCT
ijassa-1225	59	70	(	(	PUNCT
ijassa-1225	59	71	a2	a2	PROPN
ijassa-1225	59	72	)	)	PUNCT
ijassa-1225	59	73	for	for	ADP
ijassa-1225	59	74	any	any	DET
ijassa-1225	59	75	x	x	SYM
ijassa-1225	59	76	∈	∈	PROPN
ijassa-1225	59	77	ox(u0	ox(u0	PROPN
ijassa-1225	59	78	)	)	PUNCT
ijassa-1225	59	79	,	,	PUNCT
ijassa-1225	59	80	the	the	DET
ijassa-1225	59	81	mapping	mapping	NOUN
ijassa-1225	59	82	υ(x	υ(x	ADJ
ijassa-1225	59	83	,	,	PUNCT
ijassa-1225	59	84	·	·	PUNCT
ijassa-1225	59	85	)	)	PUNCT
ijassa-1225	59	86	:	:	PUNCT
ijassa-1225	60	1	x	x	SYM
ijassa-1225	60	2	⇒	⇒	PROPN
ijassa-1225	60	3	y	y	PROPN
ijassa-1225	60	4	is	be	AUX
ijassa-1225	60	5	antitone	antitone	ADJ
ijassa-1225	60	6	on	on	ADP
ijassa-1225	60	7	the	the	DET
ijassa-1225	60	8	set	set	NOUN
ijassa-1225	60	9	[	[	X
ijassa-1225	60	10	x	x	X
ijassa-1225	60	11	,	,	PUNCT
ijassa-1225	60	12	u0]x	u0]x	PRON
ijassa-1225	60	13	;	;	PUNCT
ijassa-1225	60	14	(	(	PUNCT
ijassa-1225	60	15	a3	a3	NOUN
ijassa-1225	60	16	)	)	PUNCT
ijassa-1225	60	17	any	any	DET
ijassa-1225	60	18	infinite	infinite	ADJ
ijassa-1225	60	19	chain	chain	NOUN
ijassa-1225	60	20	s	s	PART
ijassa-1225	60	21	∈	∈	NOUN
ijassa-1225	60	22	s	s	X
ijassa-1225	60	23	(	(	PUNCT
ijassa-1225	60	24	υ	υ	PROPN
ijassa-1225	60	25	,	,	PUNCT
ijassa-1225	60	26	ox(u0	ox(u0	PROPN
ijassa-1225	60	27	)	)	PUNCT
ijassa-1225	60	28	,	,	PUNCT
ijassa-1225	60	29	ŷ	ŷ	NUM
ijassa-1225	60	30	)	)	PUNCT
ijassa-1225	60	31	is	be	AUX
ijassa-1225	60	32	bounded	bound	VERB
ijassa-1225	60	33	from	from	ADP
ijassa-1225	60	34	below	below	ADV
ijassa-1225	60	35	,	,	PUNCT
ijassa-1225	60	36	and	and	CCONJ
ijassa-1225	60	37	for	for	ADP
ijassa-1225	60	38	some	some	DET
ijassa-1225	60	39	its	its	PRON
ijassa-1225	60	40	lower	low	ADJ
ijassa-1225	60	41	bound	bind	VERB
ijassa-1225	60	42	ω	ω	PROPN
ijassa-1225	60	43	∈	∈	PROPN
ijassa-1225	60	44	x	x	X
ijassa-1225	60	45	,	,	PUNCT
ijassa-1225	60	46	one	one	PRON
ijassa-1225	60	47	can	can	AUX
ijassa-1225	60	48	find	find	VERB
ijassa-1225	60	49	z	z	X
ijassa-1225	60	50	∈	∈	PROPN
ijassa-1225	60	51	υ(ω	υ(ω	PROPN
ijassa-1225	60	52	,	,	PUNCT
ijassa-1225	60	53	ω	ω	NOUN
ijassa-1225	60	54	)	)	PUNCT
ijassa-1225	60	55	satisfying	satisfy	VERB
ijassa-1225	60	56	the	the	DET
ijassa-1225	60	57	inequality	inequality	NOUN
ijassa-1225	61	1	z	z	PROPN
ijassa-1225	61	2	�	�	PROPN
ijassa-1225	61	3	ŷ.	ŷ.	PROPN
ijassa-1225	61	4	then	then	ADV
ijassa-1225	61	5	the	the	DET
ijassa-1225	61	6	inclusion	inclusion	NOUN
ijassa-1225	61	7	(	(	PUNCT
ijassa-1225	61	8	2.3	2.3	NUM
ijassa-1225	61	9	)	)	PUNCT
ijassa-1225	61	10	has	have	VERB
ijassa-1225	61	11	a	a	DET
ijassa-1225	61	12	solution	solution	NOUN
ijassa-1225	61	13	and	and	CCONJ
ijassa-1225	61	14	the	the	DET
ijassa-1225	61	15	set	set	NOUN
ijassa-1225	61	16	of	of	ADP
ijassa-1225	61	17	solutions	solution	NOUN
ijassa-1225	61	18	possesses	possess	VERB
ijassa-1225	61	19	a	a	DET
ijassa-1225	61	20	minimal	minimal	ADJ
ijassa-1225	61	21	element	element	NOUN
ijassa-1225	61	22	belonging	belong	VERB
ijassa-1225	61	23	to	to	ADP
ijassa-1225	61	24	the	the	DET
ijassa-1225	61	25	set	set	NOUN
ijassa-1225	61	26	ox(u0	ox(u0	NOUN
ijassa-1225	61	27	)	)	PUNCT
ijassa-1225	61	28	.	.	PUNCT
ijassa-1225	62	1	proof	proof	NOUN
ijassa-1225	62	2	we	we	PRON
ijassa-1225	62	3	introduce	introduce	VERB
ijassa-1225	62	4	the	the	DET
ijassa-1225	62	5	set	set	NOUN
ijassa-1225	62	6	u0	u0	NOUN
ijassa-1225	62	7	=	=	SYM
ijassa-1225	62	8	{	{	PUNCT
ijassa-1225	62	9	x	x	PROPN
ijassa-1225	62	10	∈	∈	PROPN
ijassa-1225	62	11	ox(u0	ox(u0	PROPN
ijassa-1225	62	12	)	)	PUNCT
ijassa-1225	62	13	:	:	PUNCT
ijassa-1225	63	1	∃y	∃y	PROPN
ijassa-1225	63	2	∈	∈	PROPN
ijassa-1225	63	3	f	f	PROPN
ijassa-1225	63	4	(	(	PUNCT
ijassa-1225	63	5	x	x	X
ijassa-1225	63	6	)	)	PUNCT
ijassa-1225	63	7	y	y	PROPN
ijassa-1225	63	8	�	�	PROPN
ijassa-1225	63	9	ŷ	ŷ	NUM
ijassa-1225	63	10	}	}	PUNCT
ijassa-1225	63	11	.	.	PUNCT
ijassa-1225	64	1	note	note	VERB
ijassa-1225	64	2	that	that	SCONJ
ijassa-1225	64	3	u0	u0	ADJ
ijassa-1225	64	4	6=	6=	PUNCT
ijassa-1225	64	5	∅	∅	NOUN
ijassa-1225	64	6	as	as	ADP
ijassa-1225	64	7	u0	u0	ADJ
ijassa-1225	64	8	∈	∈	PROPN
ijassa-1225	64	9	u0	u0	NOUN
ijassa-1225	64	10	.	.	PUNCT
ijassa-1225	65	1	we	we	PRON
ijassa-1225	65	2	define	define	VERB
ijassa-1225	65	3	binary	binary	ADJ
ijassa-1225	65	4	relations	relation	NOUN
ijassa-1225	65	5	�	�	PROPN
ijassa-1225	65	6	and	and	CCONJ
ijassa-1225	65	7	�	�	PROPN
ijassa-1225	65	8	on	on	ADP
ijassa-1225	65	9	u0	u0	ADJ
ijassa-1225	65	10	as	as	SCONJ
ijassa-1225	65	11	follows	follow	VERB
ijassa-1225	65	12	:	:	PUNCT
ijassa-1225	65	13	∀v	∀v	NOUN
ijassa-1225	65	14	,	,	PUNCT
ijassa-1225	65	15	u	u	PROPN
ijassa-1225	65	16	∈	∈	PROPN
ijassa-1225	65	17	u0	u0	NOUN
ijassa-1225	65	18	v	v	PROPN
ijassa-1225	65	19	�	�	PROPN
ijassa-1225	65	20	u	u	PROPN
ijassa-1225	65	21	⇔	⇔	X
ijassa-1225	65	22	(	(	PUNCT
ijassa-1225	65	23	v	v	NOUN
ijassa-1225	65	24	≺	≺	NOUN
ijassa-1225	65	25	u	u	NOUN
ijassa-1225	65	26	and	and	CCONJ
ijassa-1225	65	27	∃ξ	∃ξ	NOUN
ijassa-1225	65	28	∈	∈	PROPN
ijassa-1225	66	1	[	[	X
ijassa-1225	66	2	v	v	NOUN
ijassa-1225	66	3	,	,	PUNCT
ijassa-1225	66	4	u	u	NOUN
ijassa-1225	66	5	]	]	X
ijassa-1225	66	6	ŷ	ŷ	NUM
ijassa-1225	66	7	∈	∈	PROPN
ijassa-1225	66	8	υ(ξ	υ(ξ	PROPN
ijassa-1225	66	9	,	,	PUNCT
ijassa-1225	66	10	u	u	NOUN
ijassa-1225	66	11	)	)	PUNCT
ijassa-1225	66	12	)	)	PUNCT
ijassa-1225	66	13	,	,	PUNCT
ijassa-1225	66	14	∀v	∀v	PROPN
ijassa-1225	66	15	,	,	PUNCT
ijassa-1225	66	16	u	u	PROPN
ijassa-1225	66	17	∈	∈	PROPN
ijassa-1225	66	18	u0	u0	NOUN
ijassa-1225	66	19	v	v	PROPN
ijassa-1225	66	20	�	�	PROPN
ijassa-1225	66	21	u	u	PROPN
ijassa-1225	66	22	⇔	⇔	X
ijassa-1225	66	23	(	(	PUNCT
ijassa-1225	66	24	v	v	NOUN
ijassa-1225	66	25	=	=	SYM
ijassa-1225	66	26	u	u	NOUN
ijassa-1225	66	27	or	or	CCONJ
ijassa-1225	66	28	v	v	ADP
ijassa-1225	66	29	�	�	PROPN
ijassa-1225	66	30	u	u	PROPN
ijassa-1225	66	31	)	)	PUNCT
ijassa-1225	66	32	.	.	PUNCT
ijassa-1225	67	1	copyright	copyright	NOUN
ijassa-1225	67	2	©	©	PROPN
ijassa-1225	67	3	2022	2022	NUM
ijassa-1225	67	4	assa	assa	NOUN
ijassa-1225	67	5	.	.	PUNCT
ijassa-1225	68	1	adv	adv	PROPN
ijassa-1225	68	2	syst	syst	PROPN
ijassa-1225	68	3	sci	sci	PROPN
ijassa-1225	68	4	appl	appl	PROPN
ijassa-1225	68	5	(	(	PUNCT
ijassa-1225	68	6	2022	2022	NUM
ijassa-1225	68	7	)	)	PUNCT
ijassa-1225	68	8	on	on	ADP
ijassa-1225	68	9	order	order	NOUN
ijassa-1225	68	10	covering	cover	VERB
ijassa-1225	68	11	set	set	NOUN
ijassa-1225	68	12	-	-	PUNCT
ijassa-1225	68	13	valued	value	VERB
ijassa-1225	68	14	mappings	mapping	NOUN
ijassa-1225	68	15	and	and	CCONJ
ijassa-1225	68	16	their	their	PRON
ijassa-1225	68	17	applications	application	NOUN
ijassa-1225	68	18	179	179	NUM
ijassa-1225	68	19	let	let	VERB
ijassa-1225	68	20	us	we	PRON
ijassa-1225	68	21	demonstrate	demonstrate	VERB
ijassa-1225	68	22	that	that	SCONJ
ijassa-1225	68	23	�	�	PROPN
ijassa-1225	68	24	and	and	CCONJ
ijassa-1225	68	25	�	�	PROPN
ijassa-1225	68	26	are	be	AUX
ijassa-1225	68	27	strict	strict	ADJ
ijassa-1225	68	28	and	and	CCONJ
ijassa-1225	68	29	non	non	ADJ
ijassa-1225	68	30	-	-	ADJ
ijassa-1225	68	31	strict	strict	ADJ
ijassa-1225	68	32	order	order	NOUN
ijassa-1225	68	33	relations	relation	NOUN
ijassa-1225	68	34	,	,	PUNCT
ijassa-1225	68	35	respectively	respectively	ADV
ijassa-1225	68	36	.	.	PUNCT
ijassa-1225	69	1	as	as	SCONJ
ijassa-1225	69	2	the	the	DET
ijassa-1225	69	3	relation	relation	NOUN
ijassa-1225	69	4	≺	≺	NOUN
ijassa-1225	69	5	is	be	AUX
ijassa-1225	69	6	antisymmetric	antisymmetric	VERB
ijassa-1225	69	7	,	,	PUNCT
ijassa-1225	69	8	the	the	DET
ijassa-1225	69	9	relation	relation	NOUN
ijassa-1225	69	10	�	�	PROPN
ijassa-1225	69	11	is	be	AUX
ijassa-1225	69	12	antisymmetric	antisymmetric	ADJ
ijassa-1225	69	13	as	as	ADV
ijassa-1225	69	14	well	well	ADV
ijassa-1225	69	15	.	.	PUNCT
ijassa-1225	70	1	prove	prove	VERB
ijassa-1225	70	2	that	that	SCONJ
ijassa-1225	70	3	�	�	PROPN
ijassa-1225	70	4	is	be	AUX
ijassa-1225	70	5	transitive	transitive	ADJ
ijassa-1225	70	6	.	.	PUNCT
ijassa-1225	71	1	for	for	ADP
ijassa-1225	71	2	v	v	NOUN
ijassa-1225	71	3	,	,	PUNCT
ijassa-1225	71	4	w	w	PROPN
ijassa-1225	71	5	,	,	PUNCT
ijassa-1225	71	6	u	u	PROPN
ijassa-1225	71	7	∈	∈	PROPN
ijassa-1225	71	8	u0	u0	NOUN
ijassa-1225	71	9	such	such	ADJ
ijassa-1225	71	10	that	that	SCONJ
ijassa-1225	71	11	v	v	ADP
ijassa-1225	71	12	�	�	PROPN
ijassa-1225	71	13	w	w	PROPN
ijassa-1225	71	14	�	�	PROPN
ijassa-1225	71	15	u	u	PROPN
ijassa-1225	71	16	,	,	PUNCT
ijassa-1225	71	17	it	it	PRON
ijassa-1225	71	18	holds	hold	VERB
ijassa-1225	71	19	true	true	ADJ
ijassa-1225	71	20	that	that	SCONJ
ijassa-1225	71	21	v	v	ADP
ijassa-1225	71	22	≺	≺	NOUN
ijassa-1225	71	23	w	w	NOUN
ijassa-1225	71	24	≺	≺	NOUN
ijassa-1225	71	25	u	u	NOUN
ijassa-1225	71	26	and	and	CCONJ
ijassa-1225	71	27	∃ξ	∃ξ	NOUN
ijassa-1225	71	28	∈	∈	PROPN
ijassa-1225	71	29	[	[	X
ijassa-1225	71	30	w	w	NOUN
ijassa-1225	71	31	,	,	PUNCT
ijassa-1225	71	32	u	u	NOUN
ijassa-1225	71	33	]	]	X
ijassa-1225	71	34	⊂	⊂	PROPN
ijassa-1225	72	1	[	[	X
ijassa-1225	72	2	v	v	NOUN
ijassa-1225	72	3	,	,	PUNCT
ijassa-1225	72	4	u	u	NOUN
ijassa-1225	72	5	]	]	X
ijassa-1225	72	6	ŷ	ŷ	NUM
ijassa-1225	72	7	∈	∈	PROPN
ijassa-1225	72	8	υ(ξ	υ(ξ	PROPN
ijassa-1225	72	9	,	,	PUNCT
ijassa-1225	72	10	u	u	NOUN
ijassa-1225	72	11	)	)	PUNCT
ijassa-1225	72	12	.	.	PUNCT
ijassa-1225	73	1	(	(	PUNCT
ijassa-1225	73	2	2.6	2.6	NUM
ijassa-1225	73	3	)	)	PUNCT
ijassa-1225	73	4	thus	thus	ADV
ijassa-1225	73	5	,	,	PUNCT
ijassa-1225	73	6	we	we	PRON
ijassa-1225	73	7	have	have	VERB
ijassa-1225	73	8	v	v	ADP
ijassa-1225	73	9	�	�	PROPN
ijassa-1225	73	10	u	u	PROPN
ijassa-1225	73	11	,	,	PUNCT
ijassa-1225	73	12	,	,	PUNCT
ijassa-1225	73	13	which	which	PRON
ijassa-1225	73	14	means	mean	VERB
ijassa-1225	73	15	that	that	SCONJ
ijassa-1225	73	16	the	the	DET
ijassa-1225	73	17	relation	relation	NOUN
ijassa-1225	73	18	�	�	PROPN
ijassa-1225	73	19	is	be	AUX
ijassa-1225	73	20	transitive	transitive	ADJ
ijassa-1225	73	21	.	.	PUNCT
ijassa-1225	74	1	obviously	obviously	ADV
ijassa-1225	74	2	,	,	PUNCT
ijassa-1225	74	3	the	the	DET
ijassa-1225	74	4	relation	relation	NOUN
ijassa-1225	74	5	�	�	PROPN
ijassa-1225	74	6	is	be	AUX
ijassa-1225	74	7	also	also	ADV
ijassa-1225	74	8	antisymmetric	antisymmetric	ADJ
ijassa-1225	74	9	and	and	CCONJ
ijassa-1225	74	10	transitive	transitive	ADJ
ijassa-1225	74	11	,	,	PUNCT
ijassa-1225	74	12	and	and	CCONJ
ijassa-1225	74	13	,	,	PUNCT
ijassa-1225	74	14	moreover	moreover	ADV
ijassa-1225	74	15	,	,	PUNCT
ijassa-1225	74	16	reflexive	reflexive	ADJ
ijassa-1225	74	17	.	.	PUNCT
ijassa-1225	75	1	we	we	PRON
ijassa-1225	75	2	point	point	VERB
ijassa-1225	75	3	out	out	ADP
ijassa-1225	75	4	that	that	SCONJ
ijassa-1225	75	5	the	the	DET
ijassa-1225	75	6	relation	relation	NOUN
ijassa-1225	75	7	(	(	PUNCT
ijassa-1225	75	8	2.6	2.6	NUM
ijassa-1225	75	9	)	)	PUNCT
ijassa-1225	75	10	also	also	ADV
ijassa-1225	75	11	holds	hold	VERB
ijassa-1225	75	12	true	true	ADJ
ijassa-1225	75	13	for	for	ADP
ijassa-1225	75	14	v	v	NOUN
ijassa-1225	75	15	,	,	PUNCT
ijassa-1225	75	16	w	w	PROPN
ijassa-1225	75	17	,	,	PUNCT
ijassa-1225	75	18	u	u	PROPN
ijassa-1225	75	19	∈	∈	PROPN
ijassa-1225	75	20	u0	u0	NOUN
ijassa-1225	75	21	such	such	ADJ
ijassa-1225	75	22	that	that	SCONJ
ijassa-1225	75	23	v	v	NOUN
ijassa-1225	75	24	≺	≺	NOUN
ijassa-1225	75	25	w	w	PROPN
ijassa-1225	75	26	�	�	PROPN
ijassa-1225	75	27	u	u	PROPN
ijassa-1225	75	28	,	,	PUNCT
ijassa-1225	75	29	,	,	PUNCT
ijassa-1225	75	30	i.e.	i.e.	X
ijassa-1225	75	31	the	the	DET
ijassa-1225	75	32	relation	relation	NOUN
ijassa-1225	75	33	v	v	ADP
ijassa-1225	75	34	�	�	PROPN
ijassa-1225	75	35	u	u	NOUN
ijassa-1225	75	36	takes	take	VERB
ijassa-1225	75	37	place	place	NOUN
ijassa-1225	75	38	in	in	ADP
ijassa-1225	75	39	this	this	DET
ijassa-1225	75	40	case	case	NOUN
ijassa-1225	75	41	as	as	ADV
ijassa-1225	75	42	well	well	ADV
ijassa-1225	75	43	.	.	PUNCT
ijassa-1225	76	1	let	let	VERB
ijassa-1225	76	2	us	we	PRON
ijassa-1225	76	3	consider	consider	VERB
ijassa-1225	76	4	the	the	DET
ijassa-1225	76	5	partially	partially	ADV
ijassa-1225	76	6	ordered	order	VERB
ijassa-1225	76	7	set	set	NOUN
ijassa-1225	76	8	(	(	PUNCT
ijassa-1225	76	9	u0	u0	ADJ
ijassa-1225	76	10	,	,	PUNCT
ijassa-1225	76	11	�	�	PROPN
ijassa-1225	76	12	)	)	PUNCT
ijassa-1225	76	13	.	.	PUNCT
ijassa-1225	77	1	according	accord	VERB
ijassa-1225	77	2	to	to	ADP
ijassa-1225	77	3	the	the	DET
ijassa-1225	77	4	hausdorff	hausdorff	PROPN
ijassa-1225	77	5	maximal	maximal	ADJ
ijassa-1225	77	6	principle	principle	NOUN
ijassa-1225	77	7	(	(	PUNCT
ijassa-1225	77	8	see	see	VERB
ijassa-1225	77	9	e.g.	e.g.	ADV
ijassa-1225	77	10	[	[	X
ijassa-1225	77	11	22	22	NUM
ijassa-1225	77	12	,	,	PUNCT
ijassa-1225	77	13	chapter	chapter	NOUN
ijassa-1225	77	14	1	1	NUM
ijassa-1225	77	15	]	]	PUNCT
ijassa-1225	77	16	)	)	PUNCT
ijassa-1225	77	17	,	,	PUNCT
ijassa-1225	77	18	this	this	DET
ijassa-1225	77	19	set	set	NOUN
ijassa-1225	77	20	possesses	possess	VERB
ijassa-1225	77	21	a	a	DET
ijassa-1225	77	22	maximal	maximal	ADJ
ijassa-1225	77	23	chain	chain	NOUN
ijassa-1225	77	24	s	s	NOUN
ijassa-1225	77	25	that	that	PRON
ijassa-1225	77	26	contains	contain	VERB
ijassa-1225	77	27	u0	u0	ADJ
ijassa-1225	77	28	.	.	PUNCT
ijassa-1225	78	1	we	we	PRON
ijassa-1225	78	2	first	first	ADV
ijassa-1225	78	3	prove	prove	VERB
ijassa-1225	78	4	the	the	DET
ijassa-1225	78	5	theorem	theorem	ADJ
ijassa-1225	78	6	statement	statement	NOUN
ijassa-1225	78	7	in	in	ADP
ijassa-1225	78	8	the	the	DET
ijassa-1225	78	9	case	case	NOUN
ijassa-1225	78	10	when	when	SCONJ
ijassa-1225	78	11	the	the	DET
ijassa-1225	78	12	chain	chain	NOUN
ijassa-1225	78	13	s	s	PART
ijassa-1225	78	14	contains	contain	VERB
ijassa-1225	78	15	the	the	DET
ijassa-1225	78	16	least	least	ADJ
ijassa-1225	78	17	element	element	NOUN
ijassa-1225	78	18	ω	ω	PROPN
ijassa-1225	78	19	,	,	PUNCT
ijassa-1225	78	20	i.e.	i.e.	X
ijassa-1225	78	21	ω	ω	X
ijassa-1225	78	22	�	�	PROPN
ijassa-1225	78	23	x	x	PUNCT
ijassa-1225	78	24	for	for	ADP
ijassa-1225	78	25	any	any	DET
ijassa-1225	78	26	x	x	SYM
ijassa-1225	78	27	∈	∈	PROPN
ijassa-1225	78	28	s.	s.	PROPN
ijassa-1225	78	29	if	if	SCONJ
ijassa-1225	78	30	ω	ω	PROPN
ijassa-1225	78	31	is	be	AUX
ijassa-1225	78	32	not	not	PART
ijassa-1225	78	33	a	a	DET
ijassa-1225	78	34	solution	solution	NOUN
ijassa-1225	78	35	of	of	ADP
ijassa-1225	78	36	inclusion	inclusion	NOUN
ijassa-1225	78	37	(	(	PUNCT
ijassa-1225	78	38	2.3	2.3	NUM
ijassa-1225	78	39	)	)	PUNCT
ijassa-1225	78	40	,	,	PUNCT
ijassa-1225	78	41	then	then	ADV
ijassa-1225	78	42	for	for	ADP
ijassa-1225	78	43	some	some	DET
ijassa-1225	78	44	z	z	PROPN
ijassa-1225	78	45	∈	∈	PROPN
ijassa-1225	78	46	υ(ω	υ(ω	PROPN
ijassa-1225	78	47	,	,	PUNCT
ijassa-1225	78	48	ω	ω	NOUN
ijassa-1225	78	49	)	)	PUNCT
ijassa-1225	78	50	,	,	PUNCT
ijassa-1225	78	51	it	it	PRON
ijassa-1225	78	52	holds	hold	VERB
ijassa-1225	78	53	true	true	ADJ
ijassa-1225	78	54	that	that	SCONJ
ijassa-1225	78	55	z	z	PROPN
ijassa-1225	78	56	�	�	PROPN
ijassa-1225	78	57	ŷ	ŷ	PUNCT
ijassa-1225	78	58	and	and	CCONJ
ijassa-1225	78	59	,	,	PUNCT
ijassa-1225	78	60	hence	hence	ADV
ijassa-1225	78	61	,	,	PUNCT
ijassa-1225	78	62	by	by	ADP
ijassa-1225	78	63	the	the	DET
ijassa-1225	78	64	virtue	virtue	NOUN
ijassa-1225	78	65	of	of	ADP
ijassa-1225	78	66	the	the	DET
ijassa-1225	78	67	condition	condition	NOUN
ijassa-1225	78	68	(	(	PUNCT
ijassa-1225	78	69	a1	a1	NOUN
ijassa-1225	78	70	)	)	PUNCT
ijassa-1225	78	71	,	,	PUNCT
ijassa-1225	78	72	there	there	PRON
ijassa-1225	78	73	exists	exist	VERB
ijassa-1225	78	74	an	an	DET
ijassa-1225	78	75	element	element	NOUN
ijassa-1225	78	76	υ	υ	NOUN
ijassa-1225	78	77	∈	∈	PROPN
ijassa-1225	78	78	x	x	PUNCT
ijassa-1225	78	79	such	such	ADJ
ijassa-1225	79	1	that	that	DET
ijassa-1225	79	2	ŷ	ŷ	NUM
ijassa-1225	79	3	∈	∈	PROPN
ijassa-1225	79	4	υ(υ	υ(υ	PROPN
ijassa-1225	79	5	,	,	PUNCT
ijassa-1225	79	6	ω	ω	NOUN
ijassa-1225	79	7	)	)	PUNCT
ijassa-1225	79	8	and	and	CCONJ
ijassa-1225	79	9	υ	υ	PROPN
ijassa-1225	79	10	≺	≺	NOUN
ijassa-1225	79	11	ω	ω	NOUN
ijassa-1225	79	12	.	.	PUNCT
ijassa-1225	80	1	according	accord	VERB
ijassa-1225	80	2	to	to	ADP
ijassa-1225	80	3	(	(	PUNCT
ijassa-1225	80	4	a2	a2	PROPN
ijassa-1225	80	5	)	)	PUNCT
ijassa-1225	80	6	,	,	PUNCT
ijassa-1225	80	7	there	there	PRON
ijassa-1225	80	8	exists	exist	VERB
ijassa-1225	80	9	y	y	PROPN
ijassa-1225	80	10	∈	∈	PROPN
ijassa-1225	80	11	υ(υ	υ(υ	PROPN
ijassa-1225	80	12	,	,	PUNCT
ijassa-1225	80	13	υ	υ	NOUN
ijassa-1225	80	14	)	)	PUNCT
ijassa-1225	80	15	such	such	ADJ
ijassa-1225	80	16	that	that	SCONJ
ijassa-1225	80	17	y	y	PROPN
ijassa-1225	80	18	�	�	PROPN
ijassa-1225	80	19	ŷ.	ŷ.	AUX
ijassa-1225	81	1	so	so	ADV
ijassa-1225	81	2	,	,	PUNCT
ijassa-1225	81	3	υ	υ	PROPN
ijassa-1225	81	4	∈	∈	PROPN
ijassa-1225	81	5	u0	u0	NOUN
ijassa-1225	81	6	and	and	CCONJ
ijassa-1225	81	7	υ	υ	PRON
ijassa-1225	81	8	�	�	PROPN
ijassa-1225	81	9	ω	ω	PROPN
ijassa-1225	81	10	.	.	PUNCT
ijassa-1225	82	1	we	we	PRON
ijassa-1225	82	2	obtained	obtain	VERB
ijassa-1225	82	3	that	that	SCONJ
ijassa-1225	82	4	υ	υ	PROPN
ijassa-1225	82	5	�	�	PROPN
ijassa-1225	82	6	x	x	PUNCT
ijassa-1225	82	7	for	for	ADP
ijassa-1225	82	8	any	any	DET
ijassa-1225	82	9	x	x	SYM
ijassa-1225	82	10	∈	∈	PROPN
ijassa-1225	82	11	s	s	PART
ijassa-1225	82	12	which	which	PRON
ijassa-1225	82	13	contradicts	contradict	VERB
ijassa-1225	82	14	with	with	ADP
ijassa-1225	82	15	the	the	DET
ijassa-1225	82	16	maximality	maximality	NOUN
ijassa-1225	82	17	of	of	ADP
ijassa-1225	82	18	the	the	DET
ijassa-1225	82	19	chain	chain	NOUN
ijassa-1225	82	20	s.	s.	PROPN
ijassa-1225	82	21	thus	thus	ADV
ijassa-1225	82	22	,	,	PUNCT
ijassa-1225	82	23	ω	ω	PROPN
ijassa-1225	82	24	is	be	AUX
ijassa-1225	82	25	a	a	DET
ijassa-1225	82	26	solution	solution	NOUN
ijassa-1225	82	27	to	to	ADP
ijassa-1225	82	28	(	(	PUNCT
ijassa-1225	82	29	2.3	2.3	NUM
ijassa-1225	82	30	)	)	PUNCT
ijassa-1225	82	31	.	.	PUNCT
ijassa-1225	83	1	consider	consider	VERB
ijassa-1225	83	2	now	now	ADV
ijassa-1225	83	3	the	the	DET
ijassa-1225	83	4	case	case	NOUN
ijassa-1225	83	5	when	when	SCONJ
ijassa-1225	83	6	the	the	DET
ijassa-1225	83	7	chain	chain	NOUN
ijassa-1225	83	8	s	s	AUX
ijassa-1225	83	9	does	do	AUX
ijassa-1225	83	10	not	not	PART
ijassa-1225	83	11	possess	possess	VERB
ijassa-1225	83	12	the	the	DET
ijassa-1225	83	13	least	least	ADJ
ijassa-1225	83	14	element	element	NOUN
ijassa-1225	83	15	,	,	PUNCT
ijassa-1225	83	16	i.e.	i.e.	X
ijassa-1225	83	17	for	for	ADP
ijassa-1225	83	18	any	any	DET
ijassa-1225	83	19	x	x	SYM
ijassa-1225	83	20	∈	∈	PROPN
ijassa-1225	83	21	s	s	NOUN
ijassa-1225	83	22	,	,	PUNCT
ijassa-1225	83	23	there	there	PRON
ijassa-1225	83	24	exists	exist	VERB
ijassa-1225	83	25	u	u	PROPN
ijassa-1225	83	26	∈	∈	PROPN
ijassa-1225	83	27	s	s	PROPN
ijassa-1225	83	28	,	,	PUNCT
ijassa-1225	83	29	u	u	NOUN
ijassa-1225	83	30	�	�	PROPN
ijassa-1225	83	31	x.	x.	VERB
ijassa-1225	83	32	obviously	obviously	ADV
ijassa-1225	83	33	,	,	PUNCT
ijassa-1225	83	34	this	this	DET
ijassa-1225	83	35	chain	chain	NOUN
ijassa-1225	83	36	is	be	AUX
ijassa-1225	83	37	infinite	infinite	ADJ
ijassa-1225	83	38	.	.	PUNCT
ijassa-1225	84	1	note	note	VERB
ijassa-1225	84	2	that	that	SCONJ
ijassa-1225	84	3	s	s	VERB
ijassa-1225	84	4	is	be	AUX
ijassa-1225	84	5	a	a	DET
ijassa-1225	84	6	chain	chain	NOUN
ijassa-1225	84	7	with	with	ADP
ijassa-1225	84	8	respect	respect	NOUN
ijassa-1225	84	9	to	to	ADP
ijassa-1225	84	10	the	the	DET
ijassa-1225	84	11	initial	initial	ADJ
ijassa-1225	84	12	order	order	NOUN
ijassa-1225	84	13	�	�	PROPN
ijassa-1225	84	14	in	in	ADP
ijassa-1225	84	15	x	x	PUNCT
ijassa-1225	84	16	and	and	CCONJ
ijassa-1225	84	17	belongs	belong	VERB
ijassa-1225	84	18	to	to	ADP
ijassa-1225	84	19	s	s	PROPN
ijassa-1225	84	20	(	(	PUNCT
ijassa-1225	84	21	υ	υ	PROPN
ijassa-1225	84	22	,	,	PUNCT
ijassa-1225	84	23	ox(u0	ox(u0	PROPN
ijassa-1225	84	24	)	)	PUNCT
ijassa-1225	84	25	,	,	PUNCT
ijassa-1225	84	26	ŷ	ŷ	NUM
ijassa-1225	84	27	)	)	PUNCT
ijassa-1225	84	28	.	.	PUNCT
ijassa-1225	85	1	the	the	DET
ijassa-1225	85	2	assumption	assumption	NOUN
ijassa-1225	85	3	(	(	PUNCT
ijassa-1225	85	4	a3	a3	NOUN
ijassa-1225	85	5	)	)	PUNCT
ijassa-1225	85	6	implies	imply	VERB
ijassa-1225	85	7	that	that	SCONJ
ijassa-1225	85	8	this	this	DET
ijassa-1225	85	9	chain	chain	NOUN
ijassa-1225	85	10	has	have	VERB
ijassa-1225	85	11	a	a	DET
ijassa-1225	85	12	lower	low	ADJ
ijassa-1225	85	13	bound	bind	VERB
ijassa-1225	85	14	ω	ω	NOUN
ijassa-1225	85	15	(	(	PUNCT
ijassa-1225	85	16	with	with	ADP
ijassa-1225	85	17	respect	respect	NOUN
ijassa-1225	85	18	to	to	ADP
ijassa-1225	85	19	the	the	DET
ijassa-1225	85	20	initial	initial	ADJ
ijassa-1225	85	21	order	order	NOUN
ijassa-1225	85	22	�	�	NOUN
ijassa-1225	85	23	)	)	PUNCT
ijassa-1225	85	24	,	,	PUNCT
ijassa-1225	85	25	for	for	ADP
ijassa-1225	85	26	which	which	PRON
ijassa-1225	85	27	there	there	PRON
ijassa-1225	85	28	exists	exist	VERB
ijassa-1225	85	29	z	z	PROPN
ijassa-1225	85	30	∈	∈	PROPN
ijassa-1225	85	31	υ(ω	υ(ω	PROPN
ijassa-1225	85	32	,	,	PUNCT
ijassa-1225	85	33	ω	ω	NOUN
ijassa-1225	85	34	)	)	PUNCT
ijassa-1225	85	35	such	such	ADJ
ijassa-1225	85	36	that	that	SCONJ
ijassa-1225	85	37	z	z	PROPN
ijassa-1225	85	38	�	�	PROPN
ijassa-1225	85	39	ŷ	ŷ	NUM
ijassa-1225	85	40	,	,	PUNCT
ijassa-1225	85	41	i.e.	i.e.	X
ijassa-1225	85	42	ω	ω	NUM
ijassa-1225	85	43	∈	∈	PROPN
ijassa-1225	85	44	u0	u0	NOUN
ijassa-1225	85	45	and	and	CCONJ
ijassa-1225	85	46	ω	ω	PROPN
ijassa-1225	85	47	/∈	/∈	PUNCT
ijassa-1225	85	48	s.	s.	PROPN
ijassa-1225	85	49	for	for	ADP
ijassa-1225	85	50	any	any	DET
ijassa-1225	85	51	x	x	SYM
ijassa-1225	85	52	∈	∈	PROPN
ijassa-1225	85	53	s	s	NOUN
ijassa-1225	85	54	,	,	PUNCT
ijassa-1225	85	55	there	there	PRON
ijassa-1225	85	56	is	be	VERB
ijassa-1225	85	57	u	u	PROPN
ijassa-1225	85	58	∈	∈	PROPN
ijassa-1225	85	59	s	s	PROPN
ijassa-1225	85	60	,	,	PUNCT
ijassa-1225	85	61	u	u	NOUN
ijassa-1225	85	62	�	�	PROPN
ijassa-1225	85	63	x.	x.	PROPN
ijassa-1225	85	64	as	as	ADP
ijassa-1225	85	65	ω	ω	PROPN
ijassa-1225	85	66	≺	≺	NOUN
ijassa-1225	85	67	u	u	NOUN
ijassa-1225	85	68	,	,	PUNCT
ijassa-1225	85	69	we	we	PRON
ijassa-1225	85	70	get	get	VERB
ijassa-1225	85	71	ω	ω	NUM
ijassa-1225	85	72	�	�	PROPN
ijassa-1225	85	73	x.	x.	NOUN
ijassa-1225	85	74	the	the	DET
ijassa-1225	85	75	latter	latter	ADJ
ijassa-1225	85	76	contradicts	contradict	VERB
ijassa-1225	85	77	with	with	ADP
ijassa-1225	85	78	the	the	DET
ijassa-1225	85	79	maximality	maximality	NOUN
ijassa-1225	85	80	of	of	ADP
ijassa-1225	85	81	the	the	DET
ijassa-1225	85	82	chain	chain	NOUN
ijassa-1225	85	83	s	s	NOUN
ijassa-1225	85	84	,	,	PUNCT
ijassa-1225	85	85	so	so	ADV
ijassa-1225	85	86	the	the	DET
ijassa-1225	85	87	situation	situation	NOUN
ijassa-1225	85	88	where	where	SCONJ
ijassa-1225	85	89	the	the	DET
ijassa-1225	85	90	maximal	maximal	ADJ
ijassa-1225	85	91	chain	chain	NOUN
ijassa-1225	85	92	s	s	VERB
ijassa-1225	85	93	does	do	AUX
ijassa-1225	85	94	not	not	PART
ijassa-1225	85	95	possess	possess	VERB
ijassa-1225	85	96	the	the	DET
ijassa-1225	85	97	least	least	ADJ
ijassa-1225	85	98	element	element	NOUN
ijassa-1225	85	99	is	be	AUX
ijassa-1225	85	100	not	not	PART
ijassa-1225	85	101	possible	possible	ADJ
ijassa-1225	85	102	.	.	PUNCT
ijassa-1225	86	1	let	let	VERB
ijassa-1225	86	2	us	we	PRON
ijassa-1225	86	3	demonstrate	demonstrate	VERB
ijassa-1225	86	4	that	that	SCONJ
ijassa-1225	86	5	the	the	DET
ijassa-1225	86	6	obtained	obtain	VERB
ijassa-1225	86	7	element	element	NOUN
ijassa-1225	86	8	ω	ω	PROPN
ijassa-1225	86	9	∈	∈	PROPN
ijassa-1225	86	10	ox(u0	ox(u0	NOUN
ijassa-1225	86	11	)	)	PUNCT
ijassa-1225	86	12	is	be	AUX
ijassa-1225	86	13	minimal	minimal	ADJ
ijassa-1225	86	14	in	in	ADP
ijassa-1225	86	15	the	the	DET
ijassa-1225	86	16	set	set	NOUN
ijassa-1225	86	17	of	of	ADP
ijassa-1225	86	18	solutions	solution	NOUN
ijassa-1225	86	19	of	of	ADP
ijassa-1225	86	20	the	the	DET
ijassa-1225	86	21	inclusion	inclusion	NOUN
ijassa-1225	86	22	(	(	PUNCT
ijassa-1225	86	23	2.3	2.3	NUM
ijassa-1225	86	24	)	)	PUNCT
ijassa-1225	86	25	.	.	PUNCT
ijassa-1225	87	1	assume	assume	VERB
ijassa-1225	87	2	the	the	DET
ijassa-1225	87	3	contrary	contrary	NOUN
ijassa-1225	87	4	.	.	PUNCT
ijassa-1225	88	1	then	then	ADV
ijassa-1225	88	2	one	one	PRON
ijassa-1225	88	3	can	can	AUX
ijassa-1225	88	4	find	find	VERB
ijassa-1225	88	5	z	z	NOUN
ijassa-1225	88	6	≺	≺	NOUN
ijassa-1225	88	7	ω	ω	NOUN
ijassa-1225	88	8	such	such	ADJ
ijassa-1225	88	9	that	that	PRON
ijassa-1225	88	10	ŷ	ŷ	NUM
ijassa-1225	88	11	∈	∈	PROPN
ijassa-1225	88	12	υ(z	υ(z	PROPN
ijassa-1225	88	13	,	,	PUNCT
ijassa-1225	88	14	z	z	NOUN
ijassa-1225	88	15	)	)	PUNCT
ijassa-1225	88	16	.	.	PUNCT
ijassa-1225	89	1	hence	hence	ADV
ijassa-1225	89	2	,	,	PUNCT
ijassa-1225	89	3	z	z	PROPN
ijassa-1225	89	4	∈	∈	PROPN
ijassa-1225	89	5	u0	u0	NOUN
ijassa-1225	89	6	and	and	CCONJ
ijassa-1225	89	7	z	z	PROPN
ijassa-1225	89	8	�	�	PROPN
ijassa-1225	89	9	ω	ω	PROPN
ijassa-1225	89	10	.	.	PUNCT
ijassa-1225	90	1	however	however	ADV
ijassa-1225	90	2	,	,	PUNCT
ijassa-1225	90	3	this	this	DET
ijassa-1225	90	4	inequality	inequality	NOUN
ijassa-1225	90	5	is	be	AUX
ijassa-1225	90	6	not	not	PART
ijassa-1225	90	7	possible	possible	ADJ
ijassa-1225	90	8	by	by	ADP
ijassa-1225	90	9	the	the	DET
ijassa-1225	90	10	virtue	virtue	NOUN
ijassa-1225	90	11	of	of	ADP
ijassa-1225	90	12	the	the	DET
ijassa-1225	90	13	maximality	maximality	NOUN
ijassa-1225	90	14	of	of	ADP
ijassa-1225	90	15	the	the	DET
ijassa-1225	90	16	chain	chain	NOUN
ijassa-1225	90	17	s	s	NOUN
ijassa-1225	90	18	in	in	ADP
ijassa-1225	90	19	the	the	DET
ijassa-1225	90	20	space	space	NOUN
ijassa-1225	90	21	(	(	PUNCT
ijassa-1225	90	22	u0	u0	ADJ
ijassa-1225	90	23	,	,	PUNCT
ijassa-1225	90	24	�	�	PROPN
ijassa-1225	90	25	)	)	PUNCT
ijassa-1225	90	26	.	.	PUNCT
ijassa-1225	91	1	the	the	DET
ijassa-1225	91	2	theorem	theorem	ADJ
ijassa-1225	91	3	2.1	2.1	NUM
ijassa-1225	91	4	implies	imply	VERB
ijassa-1225	91	5	the	the	DET
ijassa-1225	91	6	theorem	theorem	NOUN
ijassa-1225	91	7	on	on	ADP
ijassa-1225	91	8	perturbations	perturbation	NOUN
ijassa-1225	91	9	of	of	ADP
ijassa-1225	91	10	an	an	DET
ijassa-1225	91	11	order	order	NOUN
ijassa-1225	91	12	covering	cover	VERB
ijassa-1225	91	13	single	single	ADV
ijassa-1225	91	14	-	-	PUNCT
ijassa-1225	91	15	valued	value	VERB
ijassa-1225	91	16	mapping	mapping	NOUN
ijassa-1225	91	17	υ	υ	NOUN
ijassa-1225	91	18	:	:	PUNCT
ijassa-1225	91	19	x	x	PROPN
ijassa-1225	91	20	×x	×x	ADP
ijassa-1225	91	21	→	→	PUNCT
ijassa-1225	91	22	y.	y.	NOUN
ijassa-1225	91	23	the	the	DET
ijassa-1225	91	24	corresponding	correspond	VERB
ijassa-1225	91	25	properties	property	NOUN
ijassa-1225	91	26	of	of	ADP
ijassa-1225	91	27	order	order	NOUN
ijassa-1225	91	28	covering	covering	NOUN
ijassa-1225	91	29	and	and	CCONJ
ijassa-1225	91	30	monotonicity	monotonicity	NOUN
ijassa-1225	91	31	of	of	ADP
ijassa-1225	91	32	a	a	DET
ijassa-1225	91	33	single	single	ADV
ijassa-1225	91	34	-	-	PUNCT
ijassa-1225	91	35	valued	value	VERB
ijassa-1225	91	36	mapping	mapping	NOUN
ijassa-1225	91	37	are	be	AUX
ijassa-1225	91	38	defined	define	VERB
ijassa-1225	91	39	above	above	ADV
ijassa-1225	91	40	,	,	PUNCT
ijassa-1225	91	41	and	and	CCONJ
ijassa-1225	91	42	the	the	DET
ijassa-1225	91	43	relations	relation	NOUN
ijassa-1225	91	44	(	(	PUNCT
ijassa-1225	91	45	2.4	2.4	NUM
ijassa-1225	91	46	)	)	PUNCT
ijassa-1225	91	47	can	can	AUX
ijassa-1225	91	48	be	be	AUX
ijassa-1225	91	49	written	write	VERB
ijassa-1225	91	50	as	as	ADP
ijassa-1225	91	51	:	:	PUNCT
ijassa-1225	91	52	∀x	∀x	NUM
ijassa-1225	91	53	∈	∈	PROPN
ijassa-1225	91	54	s	s	PART
ijassa-1225	91	55	υ(x	υ(x	X
ijassa-1225	91	56	,	,	PUNCT
ijassa-1225	91	57	x	x	X
ijassa-1225	91	58	)	)	PUNCT
ijassa-1225	91	59	�	�	PROPN
ijassa-1225	91	60	ŷ	ŷ	NUM
ijassa-1225	91	61	,	,	PUNCT
ijassa-1225	91	62	∀x	∀x	X
ijassa-1225	91	63	,	,	PUNCT
ijassa-1225	91	64	u	u	PROPN
ijassa-1225	91	65	∈	∈	PROPN
ijassa-1225	91	66	s	s	PART
ijassa-1225	91	67	x	x	NOUN
ijassa-1225	91	68	≺	≺	NOUN
ijassa-1225	91	69	u	u	PRON
ijassa-1225	91	70	⇒	⇒	VERB
ijassa-1225	91	71	∃ξ	∃ξ	PROPN
ijassa-1225	91	72	∈	∈	PROPN
ijassa-1225	92	1	[	[	X
ijassa-1225	92	2	x	x	X
ijassa-1225	92	3	,	,	PUNCT
ijassa-1225	92	4	u	u	NOUN
ijassa-1225	92	5	]	]	X
ijassa-1225	92	6	ŷ	ŷ	NUM
ijassa-1225	92	7	=	=	SYM
ijassa-1225	92	8	υ(ξ	υ(ξ	PROPN
ijassa-1225	92	9	,	,	PUNCT
ijassa-1225	92	10	u	u	NOUN
ijassa-1225	92	11	)	)	PUNCT
ijassa-1225	92	12	.	.	PUNCT
ijassa-1225	93	1	(	(	PUNCT
ijassa-1225	93	2	2.7	2.7	NUM
ijassa-1225	93	3	)	)	PUNCT
ijassa-1225	93	4	the	the	DET
ijassa-1225	93	5	statement	statement	NOUN
ijassa-1225	93	6	on	on	ADP
ijassa-1225	93	7	perturbations	perturbation	NOUN
ijassa-1225	93	8	of	of	ADP
ijassa-1225	93	9	order	order	NOUN
ijassa-1225	93	10	covering	cover	VERB
ijassa-1225	93	11	single	single	ADJ
ijassa-1225	93	12	-	-	PUNCT
ijassa-1225	93	13	valued	value	VERB
ijassa-1225	93	14	mappings	mapping	NOUN
ijassa-1225	93	15	is	be	AUX
ijassa-1225	93	16	analogous	analogous	ADJ
ijassa-1225	93	17	to	to	ADP
ijassa-1225	93	18	the	the	DET
ijassa-1225	93	19	results	result	NOUN
ijassa-1225	93	20	obtained	obtain	VERB
ijassa-1225	93	21	in	in	ADP
ijassa-1225	93	22	the	the	DET
ijassa-1225	93	23	papers	paper	NOUN
ijassa-1225	93	24	[	[	X
ijassa-1225	93	25	5	5	NUM
ijassa-1225	93	26	,	,	PUNCT
ijassa-1225	93	27	6	6	NUM
ijassa-1225	93	28	]	]	PUNCT
ijassa-1225	93	29	.	.	PUNCT
ijassa-1225	94	1	these	these	DET
ijassa-1225	94	2	works	work	NOUN
ijassa-1225	94	3	employed	employ	VERB
ijassa-1225	94	4	a	a	DET
ijassa-1225	94	5	less	less	ADV
ijassa-1225	94	6	restrictive	restrictive	ADJ
ijassa-1225	94	7	assumptions	assumption	NOUN
ijassa-1225	94	8	on	on	ADP
ijassa-1225	94	9	the	the	DET
ijassa-1225	94	10	chains	chain	NOUN
ijassa-1225	94	11	s	s	VERB
ijassa-1225	94	12	compared	compare	VERB
ijassa-1225	94	13	to	to	ADP
ijassa-1225	94	14	(	(	PUNCT
ijassa-1225	94	15	2.7	2.7	NUM
ijassa-1225	94	16	)	)	PUNCT
ijassa-1225	94	17	,	,	PUNCT
ijassa-1225	94	18	namely	namely	ADV
ijassa-1225	94	19	:	:	PUNCT
ijassa-1225	94	20	∀x	∀x	NUM
ijassa-1225	94	21	,	,	PUNCT
ijassa-1225	94	22	u	u	PROPN
ijassa-1225	94	23	∈	∈	PROPN
ijassa-1225	94	24	s	s	PART
ijassa-1225	94	25	x	x	NOUN
ijassa-1225	94	26	≺	≺	NOUN
ijassa-1225	94	27	u	u	NOUN
ijassa-1225	94	28	⇒	⇒	NOUN
ijassa-1225	94	29	ŷ	ŷ	X
ijassa-1225	94	30	�	�	PROPN
ijassa-1225	94	31	υ(ξ	υ(ξ	PROPN
ijassa-1225	94	32	,	,	PUNCT
ijassa-1225	94	33	u	u	NOUN
ijassa-1225	94	34	)	)	PUNCT
ijassa-1225	94	35	,	,	PUNCT
ijassa-1225	94	36	so	so	CCONJ
ijassa-1225	94	37	the	the	DET
ijassa-1225	94	38	condition	condition	NOUN
ijassa-1225	94	39	corresponding	correspond	VERB
ijassa-1225	94	40	to	to	ADP
ijassa-1225	94	41	(	(	PUNCT
ijassa-1225	94	42	a3	a3	PROPN
ijassa-1225	94	43	)	)	PUNCT
ijassa-1225	94	44	was	be	AUX
ijassa-1225	94	45	more	more	ADV
ijassa-1225	94	46	strict	strict	ADJ
ijassa-1225	94	47	.	.	PUNCT
ijassa-1225	95	1	3	3	X
ijassa-1225	95	2	.	.	X
ijassa-1225	95	3	conditions	condition	NOUN
ijassa-1225	95	4	of	of	ADP
ijassa-1225	95	5	order	order	NOUN
ijassa-1225	95	6	covering	cover	VERB
ijassa-1225	95	7	for	for	ADP
ijassa-1225	95	8	the	the	DET
ijassa-1225	95	9	nemytskii	nemytskii	ADJ
ijassa-1225	95	10	operator	operator	NOUN
ijassa-1225	95	11	in	in	ADP
ijassa-1225	95	12	the	the	DET
ijassa-1225	95	13	application	application	NOUN
ijassa-1225	95	14	of	of	ADP
ijassa-1225	95	15	theorem	theorem	ADJ
ijassa-1225	95	16	2.1	2.1	NUM
ijassa-1225	95	17	to	to	ADP
ijassa-1225	95	18	concrete	concrete	ADJ
ijassa-1225	95	19	functional	functional	ADJ
ijassa-1225	95	20	inclusions	inclusion	NOUN
ijassa-1225	95	21	,	,	PUNCT
ijassa-1225	95	22	the	the	DET
ijassa-1225	95	23	most	most	ADJ
ijassa-1225	95	24	of	of	ADP
ijassa-1225	95	25	the	the	DET
ijassa-1225	95	26	difficulties	difficulty	NOUN
ijassa-1225	95	27	connected	connect	VERB
ijassa-1225	95	28	with	with	ADP
ijassa-1225	95	29	the	the	DET
ijassa-1225	95	30	verification	verification	NOUN
ijassa-1225	95	31	of	of	ADP
ijassa-1225	95	32	the	the	DET
ijassa-1225	95	33	order	order	NOUN
ijassa-1225	95	34	covering	cover	VERB
ijassa-1225	95	35	property	property	NOUN
ijassa-1225	95	36	of	of	ADP
ijassa-1225	95	37	the	the	DET
ijassa-1225	95	38	corresponding	corresponding	ADJ
ijassa-1225	95	39	set	set	NOUN
ijassa-1225	95	40	-	-	PUNCT
ijassa-1225	95	41	valued	value	VERB
ijassa-1225	95	42	operators	operator	NOUN
ijassa-1225	95	43	,	,	PUNCT
ijassa-1225	95	44	primarily	primarily	ADV
ijassa-1225	95	45	the	the	DET
ijassa-1225	95	46	superposition	superposition	NOUN
ijassa-1225	95	47	operator	operator	NOUN
ijassa-1225	95	48	that	that	PRON
ijassa-1225	95	49	is	be	AUX
ijassa-1225	95	50	also	also	ADV
ijassa-1225	95	51	called	call	VERB
ijassa-1225	95	52	the	the	DET
ijassa-1225	95	53	nemytskii	nemytskii	ADJ
ijassa-1225	95	54	operator	operator	NOUN
ijassa-1225	95	55	.	.	PUNCT
ijassa-1225	96	1	here	here	ADV
ijassa-1225	96	2	we	we	PRON
ijassa-1225	96	3	demonstrate	demonstrate	VERB
ijassa-1225	96	4	that	that	SCONJ
ijassa-1225	96	5	the	the	DET
ijassa-1225	96	6	nemytskii	nemytskii	ADJ
ijassa-1225	96	7	operator	operator	NOUN
ijassa-1225	96	8	is	be	AUX
ijassa-1225	96	9	order	order	NOUN
ijassa-1225	96	10	covering	covering	NOUN
ijassa-1225	96	11	provided	provide	VERB
ijassa-1225	96	12	that	that	SCONJ
ijassa-1225	96	13	the	the	DET
ijassa-1225	96	14	corresponding	correspond	VERB
ijassa-1225	96	15	set	set	NOUN
ijassa-1225	96	16	-	-	PUNCT
ijassa-1225	96	17	valued	value	VERB
ijassa-1225	96	18	function	function	NOUN
ijassa-1225	96	19	possesses	possess	VERB
ijassa-1225	96	20	this	this	DET
ijassa-1225	96	21	property	property	NOUN
ijassa-1225	96	22	with	with	ADP
ijassa-1225	96	23	respect	respect	NOUN
ijassa-1225	96	24	to	to	ADP
ijassa-1225	96	25	the	the	DET
ijassa-1225	96	26	corresponding	correspond	VERB
ijassa-1225	96	27	argument	argument	NOUN
ijassa-1225	96	28	.	.	PUNCT
ijassa-1225	97	1	copyright	copyright	NOUN
ijassa-1225	97	2	©	©	PROPN
ijassa-1225	97	3	2022	2022	NUM
ijassa-1225	97	4	assa	assa	NOUN
ijassa-1225	97	5	.	.	PUNCT
ijassa-1225	98	1	adv	adv	PROPN
ijassa-1225	98	2	syst	syst	PROPN
ijassa-1225	98	3	sci	sci	PROPN
ijassa-1225	98	4	appl	appl	PROPN
ijassa-1225	98	5	(	(	PUNCT
ijassa-1225	98	6	2022	2022	NUM
ijassa-1225	98	7	)	)	PUNCT
ijassa-1225	98	8	180	180	NUM
ijassa-1225	98	9	e.s	e.s	PROPN
ijassa-1225	98	10	.	.	PROPN
ijassa-1225	98	11	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	98	12	,	,	PUNCT
ijassa-1225	98	13	i.d	i.d	PROPN
ijassa-1225	98	14	.	.	PROPN
ijassa-1225	98	15	serova	serova	PROPN
ijassa-1225	98	16	,	,	PUNCT
ijassa-1225	98	17	e.a	e.a	PROPN
ijassa-1225	98	18	.	.	PROPN
ijassa-1225	98	19	panasenko	panasenko	PROPN
ijassa-1225	98	20	,	,	PUNCT
ijassa-1225	98	21	e.o	e.o	PROPN
ijassa-1225	98	22	.	.	PROPN
ijassa-1225	98	23	burlakov	burlakov	PROPN
ijassa-1225	98	24	typically	typically	ADV
ijassa-1225	98	25	,	,	PUNCT
ijassa-1225	98	26	the	the	DET
ijassa-1225	98	27	verification	verification	NOUN
ijassa-1225	98	28	of	of	ADP
ijassa-1225	98	29	the	the	DET
ijassa-1225	98	30	order	order	NOUN
ijassa-1225	98	31	covering	cover	VERB
ijassa-1225	98	32	property	property	NOUN
ijassa-1225	98	33	for	for	ADP
ijassa-1225	98	34	functions	function	NOUN
ijassa-1225	98	35	does	do	AUX
ijassa-1225	98	36	not	not	PART
ijassa-1225	98	37	involve	involve	VERB
ijassa-1225	98	38	significant	significant	ADJ
ijassa-1225	98	39	difficulties	difficulty	NOUN
ijassa-1225	98	40	.	.	PUNCT
ijassa-1225	99	1	below	below	ADV
ijassa-1225	99	2	we	we	PRON
ijassa-1225	99	3	assume	assume	VERB
ijassa-1225	99	4	that	that	SCONJ
ijassa-1225	99	5	the	the	DET
ijassa-1225	99	6	space	space	NOUN
ijassa-1225	99	7	rn	rn	PROPN
ijassa-1225	99	8	is	be	AUX
ijassa-1225	99	9	equipped	equip	VERB
ijassa-1225	99	10	with	with	ADP
ijassa-1225	99	11	the	the	DET
ijassa-1225	99	12	natural	natural	ADJ
ijassa-1225	99	13	order	order	NOUN
ijassa-1225	99	14	,	,	PUNCT
ijassa-1225	99	15	i.e	i.e	X
ijassa-1225	99	16	for	for	ADP
ijassa-1225	99	17	x	x	SYM
ijassa-1225	99	18	=	=	SYM
ijassa-1225	99	19	(	(	PUNCT
ijassa-1225	99	20	x1	x1	PROPN
ijassa-1225	99	21	,	,	PUNCT
ijassa-1225	99	22	...	...	PUNCT
ijassa-1225	99	23	,	,	PUNCT
ijassa-1225	99	24	xn	xn	X
ijassa-1225	99	25	)	)	PUNCT
ijassa-1225	99	26	∈	∈	PROPN
ijassa-1225	99	27	rn	rn	PROPN
ijassa-1225	99	28	and	and	CCONJ
ijassa-1225	99	29	u	u	PROPN
ijassa-1225	99	30	=	=	PUNCT
ijassa-1225	99	31	(	(	PUNCT
ijassa-1225	99	32	u1	u1	PROPN
ijassa-1225	99	33	,	,	PUNCT
ijassa-1225	99	34	...	...	PUNCT
ijassa-1225	99	35	,	,	PUNCT
ijassa-1225	99	36	un	un	PROPN
ijassa-1225	99	37	)	)	PUNCT
ijassa-1225	99	38	∈	∈	PROPN
ijassa-1225	99	39	rn	rn	PROPN
ijassa-1225	99	40	,	,	PUNCT
ijassa-1225	99	41	we	we	PRON
ijassa-1225	99	42	have	have	VERB
ijassa-1225	99	43	x	x	NOUN
ijassa-1225	99	44	≤	≤	NUM
ijassa-1225	99	45	u	u	NOUN
ijassa-1225	99	46	if	if	SCONJ
ijassa-1225	99	47	xi	xi	PROPN
ijassa-1225	99	48	≤	≤	NUM
ijassa-1225	99	49	ui	ui	NOUN
ijassa-1225	99	50	for	for	ADP
ijassa-1225	99	51	all	all	DET
ijassa-1225	99	52	i	i	PRON
ijassa-1225	99	53	=	=	NOUN
ijassa-1225	99	54	1	1	NUM
ijassa-1225	99	55	,	,	PUNCT
ijassa-1225	99	56	n.	n.	NOUN
ijassa-1225	99	57	we	we	PRON
ijassa-1225	99	58	denote	denote	VERB
ijassa-1225	99	59	by	by	ADP
ijassa-1225	99	60	c(rn	c(rn	PROPN
ijassa-1225	99	61	)	)	PUNCT
ijassa-1225	99	62	and	and	CCONJ
ijassa-1225	99	63	k(rn	k(rn	NOUN
ijassa-1225	99	64	)	)	PUNCT
ijassa-1225	99	65	the	the	DET
ijassa-1225	99	66	sets	set	NOUN
ijassa-1225	99	67	of	of	ADP
ijassa-1225	99	68	all	all	DET
ijassa-1225	99	69	non	non	ADJ
ijassa-1225	99	70	-	-	ADJ
ijassa-1225	99	71	empty	empty	ADJ
ijassa-1225	99	72	closed	closed	ADJ
ijassa-1225	99	73	and	and	CCONJ
ijassa-1225	99	74	all	all	DET
ijassa-1225	99	75	non	non	ADJ
ijassa-1225	99	76	-	-	ADJ
ijassa-1225	99	77	empty	empty	ADJ
ijassa-1225	99	78	compact	compact	ADJ
ijassa-1225	99	79	subsets	subset	NOUN
ijassa-1225	99	80	of	of	ADP
ijassa-1225	99	81	the	the	DET
ijassa-1225	99	82	space	space	NOUN
ijassa-1225	99	83	rn	rn	PROPN
ijassa-1225	99	84	,	,	PUNCT
ijassa-1225	99	85	respectively	respectively	ADV
ijassa-1225	99	86	.	.	PUNCT
ijassa-1225	100	1	we	we	PRON
ijassa-1225	100	2	denote	denote	VERB
ijassa-1225	100	3	by	by	ADP
ijassa-1225	100	4	cc(rn	cc(rn	PROPN
ijassa-1225	100	5	)	)	PUNCT
ijassa-1225	100	6	and	and	CCONJ
ijassa-1225	100	7	kc(rn	kc(rn	PROPN
ijassa-1225	100	8	)	)	PUNCT
ijassa-1225	100	9	the	the	DET
ijassa-1225	100	10	sets	set	NOUN
ijassa-1225	100	11	of	of	ADP
ijassa-1225	100	12	all	all	PRON
ijassa-1225	100	13	non	non	ADJ
ijassa-1225	100	14	-	-	ADJ
ijassa-1225	100	15	empty	empty	ADJ
ijassa-1225	100	16	connected	connected	ADJ
ijassa-1225	100	17	closed	closed	ADJ
ijassa-1225	100	18	and	and	CCONJ
ijassa-1225	100	19	all	all	DET
ijassa-1225	100	20	non	non	ADJ
ijassa-1225	100	21	-	-	ADJ
ijassa-1225	100	22	empty	empty	ADJ
ijassa-1225	100	23	connected	connected	ADJ
ijassa-1225	100	24	compact	compact	ADJ
ijassa-1225	100	25	subsets	subset	NOUN
ijassa-1225	100	26	of	of	ADP
ijassa-1225	100	27	the	the	DET
ijassa-1225	100	28	space	space	NOUN
ijassa-1225	100	29	rn	rn	PROPN
ijassa-1225	100	30	,	,	PUNCT
ijassa-1225	100	31	respectively	respectively	ADV
ijassa-1225	100	32	.	.	PUNCT
ijassa-1225	101	1	let	let	VERB
ijassa-1225	101	2	a	a	DET
ijassa-1225	101	3	set	set	NOUN
ijassa-1225	101	4	-	-	PUNCT
ijassa-1225	101	5	valued	value	VERB
ijassa-1225	101	6	mapping	mapping	NOUN
ijassa-1225	101	7	b	b	NOUN
ijassa-1225	101	8	:	:	PUNCT
ijassa-1225	102	1	[	[	X
ijassa-1225	102	2	a	a	X
ijassa-1225	102	3	,	,	PUNCT
ijassa-1225	102	4	b	b	NOUN
ijassa-1225	102	5	]	]	X
ijassa-1225	102	6	⇒	⇒	PROPN
ijassa-1225	102	7	rn	rn	PROPN
ijassa-1225	102	8	having	have	VERB
ijassa-1225	102	9	closed	close	VERB
ijassa-1225	102	10	images	image	NOUN
ijassa-1225	102	11	b(t	b(t	NOUN
ijassa-1225	102	12	)	)	PUNCT
ijassa-1225	102	13	⊂	⊂	PROPN
ijassa-1225	102	14	rn	rn	PROPN
ijassa-1225	102	15	for	for	ADP
ijassa-1225	102	16	any	any	DET
ijassa-1225	102	17	t	t	NOUN
ijassa-1225	102	18	∈	∈	PROPN
ijassa-1225	102	19	[	[	X
ijassa-1225	102	20	a	a	X
ijassa-1225	102	21	,	,	PUNCT
ijassa-1225	102	22	b	b	AUX
ijassa-1225	102	23	]	]	PUNCT
ijassa-1225	102	24	be	be	AUX
ijassa-1225	102	25	given	give	VERB
ijassa-1225	102	26	.	.	PUNCT
ijassa-1225	103	1	we	we	PRON
ijassa-1225	103	2	denote	denote	VERB
ijassa-1225	103	3	such	such	DET
ijassa-1225	103	4	a	a	DET
ijassa-1225	103	5	mapping	mapping	NOUN
ijassa-1225	103	6	as	as	ADP
ijassa-1225	103	7	b	b	NOUN
ijassa-1225	103	8	:	:	PUNCT
ijassa-1225	103	9	[	[	X
ijassa-1225	103	10	a	a	PRON
ijassa-1225	103	11	,	,	PUNCT
ijassa-1225	103	12	b]→	b]→	NOUN
ijassa-1225	103	13	c(rn	c(rn	PROPN
ijassa-1225	103	14	)	)	PUNCT
ijassa-1225	103	15	.	.	PUNCT
ijassa-1225	104	1	let	let	VERB
ijassa-1225	104	2	this	this	DET
ijassa-1225	104	3	mapping	mapping	NOUN
ijassa-1225	104	4	be	be	AUX
ijassa-1225	104	5	measurable	measurable	ADJ
ijassa-1225	104	6	.	.	PUNCT
ijassa-1225	105	1	we	we	PRON
ijassa-1225	105	2	define	define	VERB
ijassa-1225	105	3	w	w	PROPN
ijassa-1225	105	4	(	(	PUNCT
ijassa-1225	105	5	b	b	NOUN
ijassa-1225	105	6	)	)	PUNCT
ijassa-1225	105	7	to	to	PART
ijassa-1225	105	8	be	be	AUX
ijassa-1225	105	9	the	the	DET
ijassa-1225	105	10	set	set	NOUN
ijassa-1225	105	11	of	of	ADP
ijassa-1225	105	12	all	all	DET
ijassa-1225	105	13	lebesgue	lebesgue	ADJ
ijassa-1225	105	14	measurable	measurable	ADJ
ijassa-1225	105	15	functions	function	NOUN
ijassa-1225	105	16	x	x	PUNCT
ijassa-1225	105	17	:	:	PUNCT
ijassa-1225	106	1	[	[	X
ijassa-1225	106	2	a	a	X
ijassa-1225	106	3	,	,	PUNCT
ijassa-1225	106	4	b]→	b]→	X
ijassa-1225	106	5	rn	rn	PROPN
ijassa-1225	106	6	such	such	ADJ
ijassa-1225	106	7	that	that	SCONJ
ijassa-1225	106	8	x(t	x(t	PROPN
ijassa-1225	106	9	)	)	PUNCT
ijassa-1225	106	10	∈	∈	PROPN
ijassa-1225	106	11	b(t	b(t	PROPN
ijassa-1225	106	12	)	)	PUNCT
ijassa-1225	106	13	for	for	ADP
ijassa-1225	106	14	almost	almost	ADV
ijassa-1225	106	15	all	all	PRON
ijassa-1225	106	16	t	t	NOUN
ijassa-1225	106	17	∈	∈	PRON
ijassa-1225	107	1	[	[	X
ijassa-1225	107	2	a	a	X
ijassa-1225	107	3	,	,	PUNCT
ijassa-1225	107	4	b	b	NOUN
ijassa-1225	107	5	]	]	X
ijassa-1225	107	6	.	.	PUNCT
ijassa-1225	108	1	thus	thus	ADV
ijassa-1225	108	2	,	,	PUNCT
ijassa-1225	108	3	the	the	DET
ijassa-1225	108	4	set	set	PROPN
ijassa-1225	108	5	w	w	PROPN
ijassa-1225	108	6	(	(	PUNCT
ijassa-1225	108	7	b	b	NOUN
ijassa-1225	108	8	)	)	PUNCT
ijassa-1225	108	9	is	be	AUX
ijassa-1225	108	10	the	the	DET
ijassa-1225	108	11	set	set	NOUN
ijassa-1225	108	12	of	of	ADP
ijassa-1225	108	13	all	all	DET
ijassa-1225	108	14	measurable	measurable	ADJ
ijassa-1225	108	15	selections	selection	NOUN
ijassa-1225	108	16	of	of	ADP
ijassa-1225	108	17	the	the	DET
ijassa-1225	108	18	set	set	NOUN
ijassa-1225	108	19	-	-	PUNCT
ijassa-1225	108	20	valued	value	VERB
ijassa-1225	108	21	mapping	mapping	NOUN
ijassa-1225	108	22	b.	b.	NOUN
ijassa-1225	109	1	we	we	PRON
ijassa-1225	109	2	endow	endow	VERB
ijassa-1225	109	3	the	the	DET
ijassa-1225	109	4	set	set	PROPN
ijassa-1225	109	5	w	w	PROPN
ijassa-1225	109	6	(	(	PUNCT
ijassa-1225	109	7	b	b	NOUN
ijassa-1225	109	8	)	)	PUNCT
ijassa-1225	109	9	with	with	ADP
ijassa-1225	109	10	an	an	DET
ijassa-1225	109	11	order	order	NOUN
ijassa-1225	109	12	by	by	ADP
ijassa-1225	109	13	assuming	assume	VERB
ijassa-1225	109	14	that	that	SCONJ
ijassa-1225	109	15	for	for	ADP
ijassa-1225	109	16	any	any	DET
ijassa-1225	109	17	two	two	NUM
ijassa-1225	109	18	its	its	PRON
ijassa-1225	109	19	elements	element	NOUN
ijassa-1225	109	20	x	x	X
ijassa-1225	109	21	,	,	PUNCT
ijassa-1225	109	22	u	u	NOUN
ijassa-1225	109	23	,	,	PUNCT
ijassa-1225	109	24	the	the	DET
ijassa-1225	109	25	inequality	inequality	NOUN
ijassa-1225	109	26	x	x	SYM
ijassa-1225	109	27	≤	≤	NUM
ijassa-1225	109	28	u	u	NOUN
ijassa-1225	109	29	holds	hold	VERB
ijassa-1225	109	30	true	true	ADJ
ijassa-1225	109	31	if	if	SCONJ
ijassa-1225	109	32	x(t	x(t	PROPN
ijassa-1225	109	33	)	)	PUNCT
ijassa-1225	109	34	≤	≤	NOUN
ijassa-1225	109	35	u(t	u(t	NOUN
ijassa-1225	109	36	)	)	PUNCT
ijassa-1225	109	37	for	for	ADP
ijassa-1225	109	38	almost	almost	ADV
ijassa-1225	109	39	all	all	PRON
ijassa-1225	109	40	t	t	NOUN
ijassa-1225	109	41	∈	∈	PRON
ijassa-1225	110	1	[	[	X
ijassa-1225	110	2	a	a	X
ijassa-1225	110	3	,	,	PUNCT
ijassa-1225	110	4	b	b	NOUN
ijassa-1225	110	5	]	]	X
ijassa-1225	110	6	.	.	PUNCT
ijassa-1225	111	1	in	in	ADP
ijassa-1225	111	2	the	the	DET
ijassa-1225	111	3	case	case	NOUN
ijassa-1225	111	4	b	b	PROPN
ijassa-1225	111	5	=	=	SYM
ijassa-1225	111	6	rn	rn	PROPN
ijassa-1225	111	7	,	,	PUNCT
ijassa-1225	111	8	this	this	DET
ijassa-1225	111	9	set	set	NOUN
ijassa-1225	111	10	of	of	ADP
ijassa-1225	111	11	all	all	DET
ijassa-1225	111	12	measurable	measurable	ADJ
ijassa-1225	111	13	functions	function	NOUN
ijassa-1225	111	14	x	x	SYM
ijassa-1225	111	15	∈	∈	NOUN
ijassa-1225	112	1	[	[	X
ijassa-1225	112	2	a	a	X
ijassa-1225	112	3	,	,	PUNCT
ijassa-1225	112	4	b]→	b]→	PROPN
ijassa-1225	112	5	rn	rn	PROPN
ijassa-1225	112	6	we	we	PRON
ijassa-1225	112	7	denote	denote	VERB
ijassa-1225	112	8	by	by	ADP
ijassa-1225	112	9	w	w	PROPN
ijassa-1225	112	10	n.	n.	PROPN
ijassa-1225	112	11	consider	consider	VERB
ijassa-1225	112	12	a	a	DET
ijassa-1225	112	13	set	set	NOUN
ijassa-1225	112	14	-	-	PUNCT
ijassa-1225	112	15	valued	value	VERB
ijassa-1225	112	16	mapping	mapping	NOUN
ijassa-1225	112	17	g	g	NOUN
ijassa-1225	112	18	:	:	PUNCT
ijassa-1225	112	19	[	[	X
ijassa-1225	112	20	a	a	X
ijassa-1225	112	21	,	,	PUNCT
ijassa-1225	112	22	b]×	b]×	NOUN
ijassa-1225	112	23	rn	rn	PROPN
ijassa-1225	112	24	→	→	SYM
ijassa-1225	112	25	c(rm	c(rm	NOUN
ijassa-1225	112	26	)	)	PUNCT
ijassa-1225	112	27	.	.	PUNCT
ijassa-1225	113	1	assume	assume	VERB
ijassa-1225	113	2	that	that	SCONJ
ijassa-1225	113	3	it	it	PRON
ijassa-1225	113	4	satisfies	satisfy	VERB
ijassa-1225	113	5	the	the	DET
ijassa-1225	113	6	caratheodori	caratheodori	NOUN
ijassa-1225	113	7	conditions	condition	NOUN
ijassa-1225	113	8	(	(	PUNCT
ijassa-1225	113	9	i.e.	i.e.	X
ijassa-1225	113	10	it	it	PRON
ijassa-1225	113	11	is	be	AUX
ijassa-1225	113	12	measurable	measurable	ADJ
ijassa-1225	113	13	with	with	ADP
ijassa-1225	113	14	respect	respect	NOUN
ijassa-1225	113	15	to	to	ADP
ijassa-1225	113	16	the	the	DET
ijassa-1225	113	17	first	first	ADJ
ijassa-1225	113	18	argument	argument	NOUN
ijassa-1225	113	19	and	and	CCONJ
ijassa-1225	113	20	continuous	continuous	ADJ
ijassa-1225	113	21	in	in	ADP
ijassa-1225	113	22	the	the	DET
ijassa-1225	113	23	hausdorff	hausdorff	NOUN
ijassa-1225	113	24	metric	metric	NOUN
ijassa-1225	113	25	in	in	ADP
ijassa-1225	113	26	the	the	DET
ijassa-1225	113	27	second	second	ADJ
ijassa-1225	113	28	argument	argument	NOUN
ijassa-1225	113	29	)	)	PUNCT
ijassa-1225	113	30	.	.	PUNCT
ijassa-1225	114	1	these	these	DET
ijassa-1225	114	2	assumptions	assumption	NOUN
ijassa-1225	114	3	allow	allow	VERB
ijassa-1225	114	4	to	to	PART
ijassa-1225	114	5	define	define	VERB
ijassa-1225	114	6	the	the	DET
ijassa-1225	114	7	setvalued	setvalue	VERB
ijassa-1225	114	8	nemytskii	nemytskii	ADJ
ijassa-1225	114	9	operator	operator	NOUN
ijassa-1225	114	10	ng	ng	PROPN
ijassa-1225	114	11	:	:	PUNCT
ijassa-1225	114	12	w	w	NOUN
ijassa-1225	114	13	n	n	PRON
ijassa-1225	114	14	⇒	⇒	PROPN
ijassa-1225	114	15	wm	wm	PROPN
ijassa-1225	114	16	,	,	PUNCT
ijassa-1225	114	17	∀x	∀x	X
ijassa-1225	114	18	∈	∈	PROPN
ijassa-1225	114	19	w	w	NOUN
ijassa-1225	114	20	n	n	X
ijassa-1225	114	21	ng	ng	PROPN
ijassa-1225	114	22	x	x	SYM
ijassa-1225	115	1	=	=	PRON
ijassa-1225	115	2	{	{	PUNCT
ijassa-1225	115	3	y	y	PROPN
ijassa-1225	115	4	∈	∈	PROPN
ijassa-1225	115	5	wm	wm	PROPN
ijassa-1225	115	6	:	:	PUNCT
ijassa-1225	115	7	y(t	y(t	X
ijassa-1225	115	8	)	)	PUNCT
ijassa-1225	115	9	∈	∈	PROPN
ijassa-1225	115	10	g(t	g(t	PROPN
ijassa-1225	115	11	,	,	PUNCT
ijassa-1225	115	12	x(t	x(t	PROPN
ijassa-1225	115	13	)	)	PUNCT
ijassa-1225	115	14	)	)	PUNCT
ijassa-1225	115	15	for	for	ADP
ijassa-1225	115	16	almost	almost	ADV
ijassa-1225	115	17	all	all	PRON
ijassa-1225	115	18	t	t	NOUN
ijassa-1225	115	19	∈	∈	PRON
ijassa-1225	116	1	[	[	X
ijassa-1225	116	2	a	a	X
ijassa-1225	116	3	,	,	PUNCT
ijassa-1225	116	4	b	b	NOUN
ijassa-1225	116	5	]	]	PUNCT
ijassa-1225	116	6	}	}	PUNCT
ijassa-1225	116	7	.	.	PUNCT
ijassa-1225	117	1	we	we	PRON
ijassa-1225	117	2	denote	denote	VERB
ijassa-1225	117	3	∆	∆	PROPN
ijassa-1225	117	4	=	=	PRON
ijassa-1225	117	5	{	{	PUNCT
ijassa-1225	117	6	(	(	PUNCT
ijassa-1225	117	7	t	t	PROPN
ijassa-1225	117	8	,	,	PUNCT
ijassa-1225	117	9	x	x	NOUN
ijassa-1225	117	10	)	)	PUNCT
ijassa-1225	117	11	:	:	PUNCT
ijassa-1225	118	1	t	t	PROPN
ijassa-1225	118	2	∈	∈	PROPN
ijassa-1225	118	3	[	[	X
ijassa-1225	118	4	a	a	X
ijassa-1225	118	5	,	,	PUNCT
ijassa-1225	118	6	b	b	NOUN
ijassa-1225	118	7	]	]	X
ijassa-1225	118	8	,	,	PUNCT
ijassa-1225	118	9	x	x	SYM
ijassa-1225	118	10	∈	∈	PROPN
ijassa-1225	118	11	b(t	b(t	PROPN
ijassa-1225	118	12	)	)	PUNCT
ijassa-1225	118	13	}	}	PUNCT
ijassa-1225	118	14	and	and	CCONJ
ijassa-1225	118	15	define	define	VERB
ijassa-1225	118	16	g∆	g∆	NOUN
ijassa-1225	118	17	:	:	PUNCT
ijassa-1225	118	18	∆→	∆→	PROPN
ijassa-1225	118	19	c(rm	c(rm	NOUN
ijassa-1225	118	20	)	)	PUNCT
ijassa-1225	118	21	to	to	PART
ijassa-1225	118	22	be	be	AUX
ijassa-1225	118	23	the	the	DET
ijassa-1225	118	24	restriction	restriction	NOUN
ijassa-1225	118	25	of	of	ADP
ijassa-1225	118	26	the	the	DET
ijassa-1225	118	27	set	set	NOUN
ijassa-1225	118	28	-	-	PUNCT
ijassa-1225	118	29	valued	value	VERB
ijassa-1225	118	30	mapping	mapping	NOUN
ijassa-1225	118	31	g	g	NOUN
ijassa-1225	118	32	to	to	ADP
ijassa-1225	118	33	the	the	DET
ijassa-1225	118	34	set	set	NOUN
ijassa-1225	118	35	∆	∆	PROPN
ijassa-1225	118	36	,	,	PUNCT
ijassa-1225	118	37	and	and	CCONJ
ijassa-1225	118	38	by	by	ADP
ijassa-1225	118	39	ng∆	ng∆	PROPN
ijassa-1225	118	40	:	:	PUNCT
ijassa-1225	118	41	w	w	PROPN
ijassa-1225	118	42	(	(	PUNCT
ijassa-1225	118	43	b	b	NOUN
ijassa-1225	118	44	)	)	PUNCT
ijassa-1225	118	45	⇒	⇒	NOUN
ijassa-1225	118	46	wm	wm	PROPN
ijassa-1225	118	47	—	—	PUNCT
ijassa-1225	118	48	the	the	DET
ijassa-1225	118	49	restriction	restriction	NOUN
ijassa-1225	118	50	of	of	ADP
ijassa-1225	118	51	the	the	DET
ijassa-1225	118	52	operator	operator	NOUN
ijassa-1225	118	53	ng	ng	PROPN
ijassa-1225	118	54	to	to	ADP
ijassa-1225	118	55	w	w	PROPN
ijassa-1225	118	56	(	(	PUNCT
ijassa-1225	118	57	b	b	NOUN
ijassa-1225	118	58	)	)	PUNCT
ijassa-1225	118	59	.	.	PUNCT
ijassa-1225	119	1	the	the	DET
ijassa-1225	119	2	following	follow	VERB
ijassa-1225	119	3	statement	statement	NOUN
ijassa-1225	119	4	establishes	establish	VERB
ijassa-1225	119	5	connection	connection	NOUN
ijassa-1225	119	6	between	between	ADP
ijassa-1225	119	7	the	the	DET
ijassa-1225	119	8	property	property	NOUN
ijassa-1225	119	9	of	of	ADP
ijassa-1225	119	10	order	order	NOUN
ijassa-1225	119	11	covering	covering	NOUN
ijassa-1225	119	12	of	of	ADP
ijassa-1225	119	13	the	the	DET
ijassa-1225	119	14	set	set	NOUN
ijassa-1225	119	15	-	-	PUNCT
ijassa-1225	119	16	valued	value	VERB
ijassa-1225	119	17	mapping	mapping	NOUN
ijassa-1225	119	18	g∆	g∆	NOUN
ijassa-1225	119	19	with	with	ADP
ijassa-1225	119	20	respect	respect	NOUN
ijassa-1225	119	21	to	to	ADP
ijassa-1225	119	22	the	the	DET
ijassa-1225	119	23	second	second	ADJ
ijassa-1225	119	24	argument	argument	NOUN
ijassa-1225	119	25	and	and	CCONJ
ijassa-1225	119	26	the	the	DET
ijassa-1225	119	27	order	order	NOUN
ijassa-1225	119	28	covering	cover	VERB
ijassa-1225	119	29	property	property	NOUN
ijassa-1225	119	30	of	of	ADP
ijassa-1225	119	31	the	the	DET
ijassa-1225	119	32	corresponding	corresponding	ADJ
ijassa-1225	119	33	nemytskii	nemytskii	ADJ
ijassa-1225	119	34	operator	operator	NOUN
ijassa-1225	119	35	ng∆	ng∆	NOUN
ijassa-1225	119	36	.	.	PUNCT
ijassa-1225	120	1	let	let	VERB
ijassa-1225	120	2	a	a	DET
ijassa-1225	120	3	measurable	measurable	ADJ
ijassa-1225	120	4	function	function	NOUN
ijassa-1225	120	5	ŷ	ŷ	NUM
ijassa-1225	120	6	:	:	PUNCT
ijassa-1225	121	1	[	[	X
ijassa-1225	121	2	a	a	PRON
ijassa-1225	121	3	,	,	PUNCT
ijassa-1225	121	4	b]→	b]→	PROPN
ijassa-1225	121	5	rm	rm	PROPN
ijassa-1225	121	6	be	be	AUX
ijassa-1225	121	7	given	give	VERB
ijassa-1225	121	8	.	.	PUNCT
ijassa-1225	122	1	theorem	theorem	VERB
ijassa-1225	122	2	3.1	3.1	NUM
ijassa-1225	122	3	:	:	PUNCT
ijassa-1225	122	4	if	if	SCONJ
ijassa-1225	122	5	at	at	ADP
ijassa-1225	122	6	almost	almost	ADV
ijassa-1225	122	7	all	all	PRON
ijassa-1225	122	8	t	t	NOUN
ijassa-1225	122	9	∈	∈	PRON
ijassa-1225	122	10	[	[	X
ijassa-1225	122	11	a	a	X
ijassa-1225	122	12	,	,	PUNCT
ijassa-1225	122	13	b	b	NOUN
ijassa-1225	122	14	]	]	X
ijassa-1225	122	15	,	,	PUNCT
ijassa-1225	122	16	a	a	DET
ijassa-1225	122	17	set	set	NOUN
ijassa-1225	122	18	-	-	PUNCT
ijassa-1225	122	19	valued	value	VERB
ijassa-1225	122	20	mapping	mapping	NOUN
ijassa-1225	122	21	g∆(t	g∆(t	NOUN
ijassa-1225	122	22	,	,	PUNCT
ijassa-1225	122	23	·	·	PUNCT
ijassa-1225	122	24	)	)	PUNCT
ijassa-1225	122	25	:	:	PUNCT
ijassa-1225	122	26	b(t)→	b(t)→	ADP
ijassa-1225	122	27	c(rm	c(rm	NOUN
ijassa-1225	122	28	)	)	PUNCT
ijassa-1225	122	29	order	order	NOUN
ijassa-1225	122	30	covers	cover	VERB
ijassa-1225	122	31	the	the	DET
ijassa-1225	122	32	set	set	NOUN
ijassa-1225	122	33	{	{	PUNCT
ijassa-1225	122	34	ŷ(t	ŷ(t	NOUN
ijassa-1225	122	35	)	)	PUNCT
ijassa-1225	122	36	}	}	PUNCT
ijassa-1225	123	1	⊂	⊂	PROPN
ijassa-1225	123	2	rm	rm	PROPN
ijassa-1225	123	3	,	,	PUNCT
ijassa-1225	123	4	then	then	ADV
ijassa-1225	123	5	the	the	DET
ijassa-1225	123	6	operator	operator	NOUN
ijassa-1225	123	7	ng∆	ng∆	NOUN
ijassa-1225	123	8	:	:	PUNCT
ijassa-1225	123	9	w	w	PROPN
ijassa-1225	123	10	(	(	PUNCT
ijassa-1225	123	11	b	b	NOUN
ijassa-1225	123	12	)	)	PUNCT
ijassa-1225	123	13	⇒	⇒	NOUN
ijassa-1225	123	14	wm	wm	ADP
ijassa-1225	123	15	order	order	NOUN
ijassa-1225	123	16	covers	cover	VERB
ijassa-1225	123	17	the	the	DET
ijassa-1225	123	18	set	set	NOUN
ijassa-1225	123	19	{	{	PUNCT
ijassa-1225	123	20	ŷ	ŷ	NUM
ijassa-1225	123	21	}	}	PUNCT
ijassa-1225	123	22	⊂	⊂	PROPN
ijassa-1225	123	23	wm	wm	PROPN
ijassa-1225	123	24	.	.	PROPN
ijassa-1225	123	25	proof	proof	NOUN
ijassa-1225	123	26	let	let	VERB
ijassa-1225	123	27	the	the	DET
ijassa-1225	123	28	mapping	mapping	NOUN
ijassa-1225	123	29	g∆(t	g∆(t	NOUN
ijassa-1225	123	30	,	,	PUNCT
ijassa-1225	123	31	·	·	PUNCT
ijassa-1225	123	32	)	)	PUNCT
ijassa-1225	123	33	order	order	NOUN
ijassa-1225	123	34	cover	cover	VERB
ijassa-1225	123	35	the	the	DET
ijassa-1225	123	36	set	set	NOUN
ijassa-1225	123	37	{	{	PUNCT
ijassa-1225	123	38	ŷ(t	ŷ(t	NOUN
ijassa-1225	123	39	)	)	PUNCT
ijassa-1225	123	40	}	}	PUNCT
ijassa-1225	124	1	⊂	⊂	PROPN
ijassa-1225	124	2	rm	rm	PROPN
ijassa-1225	124	3	.	.	PROPN
ijassa-1225	124	4	assume	assume	VERB
ijassa-1225	124	5	that	that	SCONJ
ijassa-1225	124	6	for	for	ADP
ijassa-1225	124	7	some	some	DET
ijassa-1225	124	8	measurable	measurable	ADJ
ijassa-1225	124	9	function	function	NOUN
ijassa-1225	124	10	u	u	PROPN
ijassa-1225	124	11	∈	∈	PROPN
ijassa-1225	124	12	w	w	PROPN
ijassa-1225	124	13	(	(	PUNCT
ijassa-1225	124	14	b	b	NOUN
ijassa-1225	124	15	)	)	PUNCT
ijassa-1225	124	16	,	,	PUNCT
ijassa-1225	124	17	there	there	PRON
ijassa-1225	124	18	exists	exist	VERB
ijassa-1225	124	19	y	y	PROPN
ijassa-1225	124	20	∈	∈	PROPN
ijassa-1225	124	21	ng∆	ng∆	PROPN
ijassa-1225	124	22	u	u	NOUN
ijassa-1225	124	23	such	such	ADJ
ijassa-1225	124	24	that	that	SCONJ
ijassa-1225	124	25	y	y	PROPN
ijassa-1225	124	26	≥	≥	NOUN
ijassa-1225	124	27	ŷ.	ŷ.	NOUN
ijassa-1225	125	1	thus	thus	ADV
ijassa-1225	125	2	,	,	PUNCT
ijassa-1225	125	3	y(t	y(t	NOUN
ijassa-1225	125	4	)	)	PUNCT
ijassa-1225	125	5	∈	∈	PROPN
ijassa-1225	125	6	g∆	g∆	PROPN
ijassa-1225	125	7	(	(	PUNCT
ijassa-1225	125	8	t	t	PROPN
ijassa-1225	125	9	,	,	PUNCT
ijassa-1225	125	10	u(t	u(t	NOUN
ijassa-1225	125	11	)	)	PUNCT
ijassa-1225	125	12	)	)	PUNCT
ijassa-1225	125	13	and	and	CCONJ
ijassa-1225	125	14	y(t	y(t	NUM
ijassa-1225	125	15	)	)	PUNCT
ijassa-1225	125	16	≥	≥	NOUN
ijassa-1225	125	17	ŷ(t	ŷ(t	NOUN
ijassa-1225	125	18	)	)	PUNCT
ijassa-1225	125	19	for	for	ADP
ijassa-1225	125	20	almost	almost	ADV
ijassa-1225	125	21	all	all	PRON
ijassa-1225	125	22	t	t	NOUN
ijassa-1225	125	23	∈	∈	PRON
ijassa-1225	126	1	[	[	X
ijassa-1225	126	2	a	a	X
ijassa-1225	126	3	,	,	PUNCT
ijassa-1225	126	4	b	b	NOUN
ijassa-1225	126	5	]	]	X
ijassa-1225	126	6	.	.	PUNCT
ijassa-1225	127	1	we	we	PRON
ijassa-1225	127	2	define	define	VERB
ijassa-1225	127	3	the	the	DET
ijassa-1225	127	4	set	set	NOUN
ijassa-1225	127	5	-	-	PUNCT
ijassa-1225	127	6	valued	value	VERB
ijassa-1225	127	7	mappings	mapping	NOUN
ijassa-1225	127	8	o	o	NOUN
ijassa-1225	127	9	,	,	PUNCT
ijassa-1225	127	10	u	u	NOUN
ijassa-1225	127	11	:	:	PUNCT
ijassa-1225	128	1	[	[	X
ijassa-1225	128	2	a	a	X
ijassa-1225	128	3	,	,	PUNCT
ijassa-1225	128	4	b	b	NOUN
ijassa-1225	128	5	]	]	X
ijassa-1225	128	6	⇒	⇒	X
ijassa-1225	128	7	rn	rn	PROPN
ijassa-1225	128	8	by	by	ADP
ijassa-1225	128	9	the	the	DET
ijassa-1225	128	10	relations	relation	NOUN
ijassa-1225	128	11	:	:	PUNCT
ijassa-1225	128	12	o(t	o(t	NUM
ijassa-1225	128	13	)	)	PUNCT
ijassa-1225	128	14	.	.	PUNCT
ijassa-1225	129	1	=	=	NOUN
ijassa-1225	129	2	orn(u(t	orn(u(t	PROPN
ijassa-1225	129	3	)	)	PUNCT
ijassa-1225	129	4	)	)	PUNCT
ijassa-1225	129	5	,	,	PUNCT
ijassa-1225	129	6	u(t	u(t	NOUN
ijassa-1225	129	7	)	)	PUNCT
ijassa-1225	129	8	.	.	PUNCT
ijassa-1225	130	1	=	=	PUNCT
ijassa-1225	130	2	o(t	o(t	ADV
ijassa-1225	130	3	)	)	PUNCT
ijassa-1225	130	4	⋂	⋂	PROPN
ijassa-1225	130	5	b(t	b(t	NOUN
ijassa-1225	130	6	)	)	PUNCT
ijassa-1225	130	7	=	=	PRON
ijassa-1225	130	8	{	{	PUNCT
ijassa-1225	130	9	x	x	PUNCT
ijassa-1225	130	10	∈	∈	PROPN
ijassa-1225	130	11	b(t	b(t	PROPN
ijassa-1225	130	12	)	)	PUNCT
ijassa-1225	130	13	:	:	PUNCT
ijassa-1225	130	14	x	x	SYM
ijassa-1225	130	15	≤	≤	ADJ
ijassa-1225	130	16	u(t	u(t	NOUN
ijassa-1225	130	17	)	)	PUNCT
ijassa-1225	130	18	}	}	PUNCT
ijassa-1225	130	19	,	,	PUNCT
ijassa-1225	130	20	t	t	PROPN
ijassa-1225	130	21	∈	∈	PROPN
ijassa-1225	131	1	[	[	X
ijassa-1225	131	2	a	a	X
ijassa-1225	131	3	,	,	PUNCT
ijassa-1225	131	4	b	b	NOUN
ijassa-1225	131	5	]	]	X
ijassa-1225	131	6	.	.	PUNCT
ijassa-1225	132	1	for	for	ADP
ijassa-1225	132	2	almost	almost	ADV
ijassa-1225	132	3	all	all	PRON
ijassa-1225	132	4	t	t	NOUN
ijassa-1225	132	5	∈	∈	PRON
ijassa-1225	133	1	[	[	X
ijassa-1225	133	2	a	a	X
ijassa-1225	133	3	,	,	PUNCT
ijassa-1225	133	4	b	b	NOUN
ijassa-1225	133	5	]	]	X
ijassa-1225	133	6	,	,	PUNCT
ijassa-1225	133	7	the	the	DET
ijassa-1225	133	8	closedness	closedness	NOUN
ijassa-1225	133	9	of	of	ADP
ijassa-1225	133	10	the	the	DET
ijassa-1225	133	11	sets	set	NOUN
ijassa-1225	133	12	orn(u(t	orn(u(t	NOUN
ijassa-1225	133	13	)	)	PUNCT
ijassa-1225	133	14	)	)	PUNCT
ijassa-1225	133	15	and	and	CCONJ
ijassa-1225	133	16	b(t	b(t	NOUN
ijassa-1225	133	17	)	)	PUNCT
ijassa-1225	133	18	in	in	ADP
ijassa-1225	133	19	rnimplies	rnimplie	NOUN
ijassa-1225	133	20	the	the	DET
ijassa-1225	133	21	closedness	closedness	NOUN
ijassa-1225	133	22	of	of	ADP
ijassa-1225	133	23	the	the	DET
ijassa-1225	133	24	set	set	NOUN
ijassa-1225	133	25	u(t	u(t	NOUN
ijassa-1225	133	26	)	)	PUNCT
ijassa-1225	133	27	,	,	PUNCT
ijassa-1225	133	28	i.e.	i.e.	X
ijassa-1225	133	29	u	u	NOUN
ijassa-1225	133	30	:	:	PUNCT
ijassa-1225	133	31	[	[	X
ijassa-1225	133	32	a	a	PRON
ijassa-1225	133	33	,	,	PUNCT
ijassa-1225	133	34	b]→	b]→	NOUN
ijassa-1225	133	35	c(rn	c(rn	PROPN
ijassa-1225	133	36	)	)	PUNCT
ijassa-1225	133	37	.	.	PUNCT
ijassa-1225	134	1	the	the	DET
ijassa-1225	134	2	measurability	measurability	NOUN
ijassa-1225	134	3	of	of	ADP
ijassa-1225	134	4	o	o	PROPN
ijassa-1225	134	5	,	,	PUNCT
ijassa-1225	134	6	b	b	NOUN
ijassa-1225	134	7	:	:	PUNCT
ijassa-1225	134	8	[	[	X
ijassa-1225	134	9	a	a	PRON
ijassa-1225	134	10	,	,	PUNCT
ijassa-1225	134	11	b]→	b]→	ADJ
ijassa-1225	134	12	c(rn	c(rn	PROPN
ijassa-1225	134	13	)	)	PUNCT
ijassa-1225	134	14	guarantees	guarantee	VERB
ijassa-1225	134	15	the	the	DET
ijassa-1225	134	16	measurability	measurability	NOUN
ijassa-1225	134	17	of	of	ADP
ijassa-1225	134	18	the	the	DET
ijassa-1225	134	19	mapping	mapping	NOUN
ijassa-1225	134	20	u	u	NOUN
ijassa-1225	134	21	(	(	PUNCT
ijassa-1225	134	22	see	see	VERB
ijassa-1225	134	23	[	[	X
ijassa-1225	134	24	23	23	NUM
ijassa-1225	134	25	,	,	PUNCT
ijassa-1225	134	26	§	§	PROPN
ijassa-1225	134	27	1.5.1	1.5.1	NUM
ijassa-1225	134	28	,	,	PUNCT
ijassa-1225	134	29	§	§	PROPN
ijassa-1225	134	30	1.5.8	1.5.8	NUM
ijassa-1225	134	31	]	]	PUNCT
ijassa-1225	134	32	)	)	PUNCT
ijassa-1225	134	33	.	.	PUNCT
ijassa-1225	135	1	as	as	ADP
ijassa-1225	135	2	g∆(t	g∆(t	X
ijassa-1225	135	3	,	,	PUNCT
ijassa-1225	135	4	·	·	PUNCT
ijassa-1225	135	5	)	)	PUNCT
ijassa-1225	135	6	order	order	NOUN
ijassa-1225	135	7	covers	cover	VERB
ijassa-1225	135	8	the	the	DET
ijassa-1225	135	9	set	set	NOUN
ijassa-1225	135	10	{	{	PUNCT
ijassa-1225	135	11	ŷ(t	ŷ(t	NOUN
ijassa-1225	135	12	)	)	PUNCT
ijassa-1225	135	13	}	}	PUNCT
ijassa-1225	135	14	⊂	⊂	PROPN
ijassa-1225	135	15	rm	rm	PROPN
ijassa-1225	135	16	,	,	PUNCT
ijassa-1225	135	17	for	for	ADP
ijassa-1225	135	18	almost	almost	ADV
ijassa-1225	135	19	all	all	PRON
ijassa-1225	135	20	t	t	NOUN
ijassa-1225	135	21	∈	∈	PRON
ijassa-1225	136	1	[	[	X
ijassa-1225	136	2	a	a	X
ijassa-1225	136	3	,	,	PUNCT
ijassa-1225	136	4	b	b	NOUN
ijassa-1225	136	5	]	]	X
ijassa-1225	136	6	,	,	PUNCT
ijassa-1225	136	7	the	the	DET
ijassa-1225	136	8	inclusion	inclusion	NOUN
ijassa-1225	136	9	ŷ(t	ŷ(t	NOUN
ijassa-1225	136	10	)	)	PUNCT
ijassa-1225	136	11	∈	∈	PROPN
ijassa-1225	136	12	g∆	g∆	PROPN
ijassa-1225	136	13	(	(	PUNCT
ijassa-1225	136	14	t	t	PROPN
ijassa-1225	136	15	,	,	PUNCT
ijassa-1225	136	16	u(t	u(t	PROPN
ijassa-1225	136	17	)	)	PUNCT
ijassa-1225	136	18	)	)	PUNCT
ijassa-1225	136	19	takes	take	VERB
ijassa-1225	136	20	place	place	NOUN
ijassa-1225	136	21	for	for	ADP
ijassa-1225	136	22	almost	almost	ADV
ijassa-1225	136	23	all	all	PRON
ijassa-1225	136	24	t	t	NOUN
ijassa-1225	136	25	∈	∈	PRON
ijassa-1225	137	1	[	[	X
ijassa-1225	137	2	a	a	X
ijassa-1225	137	3	,	,	PUNCT
ijassa-1225	137	4	b	b	NOUN
ijassa-1225	137	5	]	]	X
ijassa-1225	137	6	.	.	PUNCT
ijassa-1225	138	1	therefore	therefore	ADV
ijassa-1225	138	2	,	,	PUNCT
ijassa-1225	138	3	according	accord	VERB
ijassa-1225	138	4	to	to	ADP
ijassa-1225	138	5	filippov	filippov	PROPN
ijassa-1225	138	6	’s	’s	PART
ijassa-1225	138	7	lemma	lemma	PROPN
ijassa-1225	138	8	on	on	ADP
ijassa-1225	138	9	implicit	implicit	ADJ
ijassa-1225	138	10	function	function	NOUN
ijassa-1225	138	11	(	(	PUNCT
ijassa-1225	138	12	see	see	VERB
ijassa-1225	138	13	[	[	X
ijassa-1225	138	14	23	23	NUM
ijassa-1225	138	15	,	,	PUNCT
ijassa-1225	138	16	§	§	PROPN
ijassa-1225	138	17	1.5.15	1.5.15	NUM
ijassa-1225	138	18	]	]	PUNCT
ijassa-1225	138	19	)	)	PUNCT
ijassa-1225	138	20	,	,	PUNCT
ijassa-1225	138	21	there	there	PRON
ijassa-1225	138	22	exists	exist	VERB
ijassa-1225	138	23	x̂	x̂	PUNCT
ijassa-1225	139	1	∈	∈	PROPN
ijassa-1225	139	2	w	w	ADP
ijassa-1225	139	3	n	n	PRON
ijassa-1225	139	4	such	such	ADJ
ijassa-1225	139	5	that	that	SCONJ
ijassa-1225	139	6	x̂(t	x̂(t	NOUN
ijassa-1225	139	7	)	)	PUNCT
ijassa-1225	139	8	∈	∈	PROPN
ijassa-1225	139	9	u(t	u(t	PROPN
ijassa-1225	139	10	)	)	PUNCT
ijassa-1225	139	11	and	and	CCONJ
ijassa-1225	139	12	ŷ(t	ŷ(t	NOUN
ijassa-1225	139	13	)	)	PUNCT
ijassa-1225	139	14	∈	∈	PROPN
ijassa-1225	139	15	g∆	g∆	PROPN
ijassa-1225	139	16	(	(	PUNCT
ijassa-1225	139	17	t	t	PROPN
ijassa-1225	139	18	,	,	PUNCT
ijassa-1225	139	19	x̂(t	x̂(t	NOUN
ijassa-1225	139	20	)	)	PUNCT
ijassa-1225	139	21	)	)	PUNCT
ijassa-1225	139	22	for	for	ADP
ijassa-1225	139	23	almost	almost	ADV
ijassa-1225	139	24	all	all	PRON
ijassa-1225	139	25	t	t	NOUN
ijassa-1225	139	26	∈	∈	PRON
ijassa-1225	140	1	[	[	X
ijassa-1225	140	2	a	a	X
ijassa-1225	140	3	,	,	PUNCT
ijassa-1225	140	4	b	b	NOUN
ijassa-1225	140	5	]	]	X
ijassa-1225	140	6	.	.	PUNCT
ijassa-1225	141	1	thus	thus	ADV
ijassa-1225	141	2	,	,	PUNCT
ijassa-1225	141	3	the	the	DET
ijassa-1225	141	4	relations	relation	NOUN
ijassa-1225	141	5	ŷ	ŷ	NUM
ijassa-1225	141	6	∈	∈	PROPN
ijassa-1225	141	7	ng∆	ng∆	PROPN
ijassa-1225	141	8	x̂	x̂	PROPN
ijassa-1225	141	9	and	and	CCONJ
ijassa-1225	141	10	x̂	x̂	NUM
ijassa-1225	141	11	≤	≤	NUM
ijassa-1225	141	12	u	u	NOUN
ijassa-1225	141	13	are	be	AUX
ijassa-1225	141	14	fulfilled	fulfil	VERB
ijassa-1225	141	15	,	,	PUNCT
ijassa-1225	141	16	i.e.	i.e.	X
ijassa-1225	141	17	the	the	DET
ijassa-1225	141	18	operator	operator	NOUN
ijassa-1225	141	19	ng∆	ng∆	ADJ
ijassa-1225	141	20	order	order	NOUN
ijassa-1225	141	21	covers	cover	VERB
ijassa-1225	141	22	the	the	DET
ijassa-1225	141	23	set	set	NOUN
ijassa-1225	141	24	{	{	PUNCT
ijassa-1225	141	25	ŷ	ŷ	NUM
ijassa-1225	141	26	}	}	PUNCT
ijassa-1225	141	27	⊂	⊂	PROPN
ijassa-1225	141	28	wm	wm	PROPN
ijassa-1225	141	29	.	.	PROPN
ijassa-1225	141	30	example	example	NOUN
ijassa-1225	141	31	2.1	2.1	NUM
ijassa-1225	141	32	:	:	PUNCT
ijassa-1225	141	33	let	let	VERB
ijassa-1225	141	34	ordinary	ordinary	ADJ
ijassa-1225	141	35	single	single	ADJ
ijassa-1225	141	36	-	-	PUNCT
ijassa-1225	141	37	valued	value	VERB
ijassa-1225	141	38	”	"	PUNCT
ijassa-1225	141	39	functions	function	NOUN
ijassa-1225	141	40	q0	q0	VERB
ijassa-1225	141	41	,	,	PUNCT
ijassa-1225	141	42	q1	q1	PROPN
ijassa-1225	141	43	:	:	PUNCT
ijassa-1225	142	1	[	[	X
ijassa-1225	142	2	a	a	PRON
ijassa-1225	142	3	,	,	PUNCT
ijassa-1225	142	4	b]→	b]→	ADJ
ijassa-1225	142	5	r	r	NOUN
ijassa-1225	142	6	be	be	AUX
ijassa-1225	142	7	given	give	VERB
ijassa-1225	142	8	.	.	PUNCT
ijassa-1225	143	1	consider	consider	VERB
ijassa-1225	143	2	the	the	DET
ijassa-1225	143	3	function	function	NOUN
ijassa-1225	143	4	copyright	copyright	NOUN
ijassa-1225	143	5	©	©	ADP
ijassa-1225	143	6	2022	2022	NUM
ijassa-1225	143	7	assa	assa	NOUN
ijassa-1225	143	8	.	.	PUNCT
ijassa-1225	144	1	adv	adv	PROPN
ijassa-1225	144	2	syst	syst	PROPN
ijassa-1225	144	3	sci	sci	PROPN
ijassa-1225	144	4	appl	appl	PROPN
ijassa-1225	144	5	(	(	PUNCT
ijassa-1225	144	6	2022	2022	NUM
ijassa-1225	144	7	)	)	PUNCT
ijassa-1225	144	8	on	on	ADP
ijassa-1225	144	9	order	order	NOUN
ijassa-1225	144	10	covering	cover	VERB
ijassa-1225	144	11	set	set	NOUN
ijassa-1225	144	12	-	-	PUNCT
ijassa-1225	144	13	valued	value	VERB
ijassa-1225	144	14	mappings	mapping	NOUN
ijassa-1225	144	15	and	and	CCONJ
ijassa-1225	144	16	their	their	PRON
ijassa-1225	144	17	applications	application	NOUN
ijassa-1225	144	18	181	181	NUM
ijassa-1225	144	19	g	g	NOUN
ijassa-1225	144	20	:	:	PUNCT
ijassa-1225	145	1	[	[	X
ijassa-1225	145	2	a	a	X
ijassa-1225	145	3	,	,	PUNCT
ijassa-1225	145	4	b]×	b]×	NOUN
ijassa-1225	145	5	r→	r→	PROPN
ijassa-1225	145	6	r	r	NOUN
ijassa-1225	145	7	defined	define	VERB
ijassa-1225	145	8	by	by	ADP
ijassa-1225	145	9	the	the	DET
ijassa-1225	145	10	formula	formula	NOUN
ijassa-1225	145	11	g(t	g(t	PROPN
ijassa-1225	145	12	,	,	PUNCT
ijassa-1225	145	13	x	x	NOUN
ijassa-1225	145	14	)	)	PUNCT
ijassa-1225	145	15	.	.	PUNCT
ijassa-1225	146	1	=	=	PUNCT
ijassa-1225	146	2	q0(t	q0(t	PROPN
ijassa-1225	146	3	)	)	PUNCT
ijassa-1225	146	4	+	+	NUM
ijassa-1225	146	5	2q1(t)x−	2q1(t)x−	NUM
ijassa-1225	146	6	x2	x2	NOUN
ijassa-1225	146	7	,	,	PUNCT
ijassa-1225	146	8	t	t	PROPN
ijassa-1225	146	9	∈	∈	PROPN
ijassa-1225	147	1	[	[	X
ijassa-1225	147	2	a	a	X
ijassa-1225	147	3	,	,	PUNCT
ijassa-1225	147	4	b	b	NOUN
ijassa-1225	147	5	]	]	X
ijassa-1225	147	6	,	,	PUNCT
ijassa-1225	147	7	x	x	PROPN
ijassa-1225	147	8	∈	∈	PROPN
ijassa-1225	147	9	r.	r.	PROPN
ijassa-1225	147	10	(	(	PUNCT
ijassa-1225	147	11	3.8	3.8	NUM
ijassa-1225	147	12	)	)	PUNCT
ijassa-1225	147	13	obviously	obviously	ADV
ijassa-1225	147	14	,	,	PUNCT
ijassa-1225	147	15	g	g	PROPN
ijassa-1225	147	16	satisfies	satisfy	VERB
ijassa-1225	147	17	the	the	DET
ijassa-1225	147	18	caratheodori	caratheodori	NOUN
ijassa-1225	147	19	conditions	condition	NOUN
ijassa-1225	147	20	.	.	PUNCT
ijassa-1225	148	1	let	let	VERB
ijassa-1225	148	2	r	r	PRON
ijassa-1225	148	3	>	>	X
ijassa-1225	148	4	0	0	NUM
ijassa-1225	148	5	,	,	PUNCT
ijassa-1225	148	6	b(t	b(t	NOUN
ijassa-1225	148	7	)	)	PUNCT
ijassa-1225	148	8	.	.	PUNCT
ijassa-1225	149	1	=	=	PUNCT
ijassa-1225	150	1	[	[	X
ijassa-1225	150	2	q1(t)−	q1(t)−	X
ijassa-1225	150	3	r	r	NOUN
ijassa-1225	150	4	,	,	PUNCT
ijassa-1225	150	5	q1(t	q1(t	NUM
ijassa-1225	150	6	)	)	PUNCT
ijassa-1225	151	1	+	+	CCONJ
ijassa-1225	151	2	r	r	X
ijassa-1225	151	3	]	]	X
ijassa-1225	151	4	and	and	CCONJ
ijassa-1225	151	5	∆	∆	X
ijassa-1225	151	6	=	=	PRON
ijassa-1225	151	7	{	{	PUNCT
ijassa-1225	151	8	(	(	PUNCT
ijassa-1225	151	9	t	t	PROPN
ijassa-1225	151	10	,	,	PUNCT
ijassa-1225	151	11	x	x	NOUN
ijassa-1225	151	12	)	)	PUNCT
ijassa-1225	151	13	:	:	PUNCT
ijassa-1225	151	14	t	t	PROPN
ijassa-1225	151	15	∈	∈	PROPN
ijassa-1225	152	1	[	[	X
ijassa-1225	152	2	a	a	X
ijassa-1225	152	3	,	,	PUNCT
ijassa-1225	152	4	b	b	NOUN
ijassa-1225	152	5	]	]	X
ijassa-1225	152	6	,	,	PUNCT
ijassa-1225	152	7	|x−	|x−	PROPN
ijassa-1225	152	8	q1(t)|	q1(t)|	NOUN
ijassa-1225	152	9	≤	≤	NUM
ijassa-1225	152	10	r	r	NOUN
ijassa-1225	152	11	}	}	PUNCT
ijassa-1225	152	12	,	,	PUNCT
ijassa-1225	152	13	respectively	respectively	ADV
ijassa-1225	152	14	.	.	PUNCT
ijassa-1225	153	1	the	the	DET
ijassa-1225	153	2	values	value	NOUN
ijassa-1225	153	3	of	of	ADP
ijassa-1225	153	4	g∆(t	g∆(t	NOUN
ijassa-1225	153	5	,	,	PUNCT
ijassa-1225	153	6	·	·	PUNCT
ijassa-1225	153	7	)	)	PUNCT
ijassa-1225	153	8	:	:	PUNCT
ijassa-1225	153	9	b(t)→	b(t)→	ADP
ijassa-1225	153	10	r	r	NOUN
ijassa-1225	153	11	constitute	constitute	VERB
ijassa-1225	153	12	the	the	DET
ijassa-1225	153	13	segment	segment	NOUN
ijassa-1225	153	14	[	[	PUNCT
ijassa-1225	153	15	q0(t	q0(t	PROPN
ijassa-1225	153	16	)	)	PUNCT
ijassa-1225	153	17	+	+	NUM
ijassa-1225	153	18	q2	q2	X
ijassa-1225	153	19	1(t)−	1(t)−	NUM
ijassa-1225	153	20	r2	r2	PROPN
ijassa-1225	153	21	,	,	PUNCT
ijassa-1225	153	22	q0(t	q0(t	PROPN
ijassa-1225	153	23	)	)	PUNCT
ijassa-1225	154	1	+	+	NUM
ijassa-1225	154	2	q2	q2	NOUN
ijassa-1225	154	3	1(t	1(t	NUM
ijassa-1225	154	4	)	)	PUNCT
ijassa-1225	154	5	]	]	PUNCT
ijassa-1225	154	6	.	.	PUNCT
ijassa-1225	155	1	if	if	SCONJ
ijassa-1225	155	2	for	for	ADP
ijassa-1225	155	3	the	the	DET
ijassa-1225	155	4	measurable	measurable	ADJ
ijassa-1225	155	5	function	function	NOUN
ijassa-1225	155	6	ŷ	ŷ	NUM
ijassa-1225	155	7	:	:	PUNCT
ijassa-1225	156	1	[	[	X
ijassa-1225	156	2	a	a	PRON
ijassa-1225	156	3	,	,	PUNCT
ijassa-1225	156	4	b]→	b]→	ADJ
ijassa-1225	156	5	r	r	NOUN
ijassa-1225	156	6	,	,	PUNCT
ijassa-1225	156	7	it	it	PRON
ijassa-1225	156	8	holds	hold	VERB
ijassa-1225	156	9	true	true	ADJ
ijassa-1225	156	10	that	that	SCONJ
ijassa-1225	156	11	ŷ(t	ŷ(t	PROPN
ijassa-1225	156	12	)	)	PUNCT
ijassa-1225	156	13	≥	≥	NOUN
ijassa-1225	156	14	q0(t	q0(t	PROPN
ijassa-1225	156	15	)	)	PUNCT
ijassa-1225	156	16	+	+	NUM
ijassa-1225	156	17	q2	q2	X
ijassa-1225	156	18	1(t)−	1(t)−	NUM
ijassa-1225	156	19	r2	r2	PROPN
ijassa-1225	156	20	,	,	PUNCT
ijassa-1225	156	21	(	(	PUNCT
ijassa-1225	156	22	3.9	3.9	NUM
ijassa-1225	156	23	)	)	PUNCT
ijassa-1225	156	24	then	then	ADV
ijassa-1225	156	25	g∆(t	g∆(t	NOUN
ijassa-1225	156	26	,	,	PUNCT
ijassa-1225	156	27	·	·	PUNCT
ijassa-1225	156	28	)	)	PUNCT
ijassa-1225	156	29	:	:	PUNCT
ijassa-1225	156	30	b(t)→	b(t)→	SCONJ
ijassa-1225	156	31	r	r	NOUN
ijassa-1225	156	32	order	order	NOUN
ijassa-1225	156	33	covers	cover	VERB
ijassa-1225	156	34	the	the	DET
ijassa-1225	156	35	set	set	NOUN
ijassa-1225	156	36	{	{	PUNCT
ijassa-1225	156	37	ŷ(t	ŷ(t	NOUN
ijassa-1225	156	38	)	)	PUNCT
ijassa-1225	156	39	}	}	PUNCT
ijassa-1225	157	1	⊂	⊂	PUNCT
ijassa-1225	157	2	r	r	NOUN
ijassa-1225	157	3	at	at	ADP
ijassa-1225	157	4	almost	almost	ADV
ijassa-1225	157	5	all	all	PRON
ijassa-1225	157	6	t	t	NOUN
ijassa-1225	157	7	∈	∈	PRON
ijassa-1225	158	1	[	[	X
ijassa-1225	158	2	a	a	X
ijassa-1225	158	3	,	,	PUNCT
ijassa-1225	158	4	b	b	NOUN
ijassa-1225	158	5	]	]	X
ijassa-1225	158	6	and	and	CCONJ
ijassa-1225	158	7	,	,	PUNCT
ijassa-1225	158	8	hence	hence	ADV
ijassa-1225	158	9	,	,	PUNCT
ijassa-1225	158	10	by	by	ADP
ijassa-1225	158	11	the	the	DET
ijassa-1225	158	12	virtue	virtue	NOUN
ijassa-1225	158	13	of	of	ADP
ijassa-1225	158	14	theorem	theorem	ADJ
ijassa-1225	158	15	3.1	3.1	NUM
ijassa-1225	158	16	,	,	PUNCT
ijassa-1225	158	17	the	the	DET
ijassa-1225	158	18	nemytskii	nemytskii	ADJ
ijassa-1225	158	19	operator	operator	NOUN
ijassa-1225	158	20	ng∆	ng∆	NOUN
ijassa-1225	158	21	:	:	PUNCT
ijassa-1225	158	22	w	w	PROPN
ijassa-1225	158	23	(	(	PUNCT
ijassa-1225	158	24	b	b	NOUN
ijassa-1225	158	25	)	)	PUNCT
ijassa-1225	158	26	⇒	⇒	NOUN
ijassa-1225	158	27	w	w	ADP
ijassa-1225	158	28	order	order	NOUN
ijassa-1225	158	29	covers	cover	VERB
ijassa-1225	158	30	the	the	DET
ijassa-1225	158	31	set	set	NOUN
ijassa-1225	158	32	{	{	PUNCT
ijassa-1225	158	33	ŷ	ŷ	NUM
ijassa-1225	158	34	}	}	PUNCT
ijassa-1225	158	35	⊂	⊂	PROPN
ijassa-1225	158	36	w.	w.	PROPN
ijassa-1225	158	37	in	in	ADP
ijassa-1225	158	38	the	the	DET
ijassa-1225	158	39	particular	particular	ADJ
ijassa-1225	158	40	case	case	NOUN
ijassa-1225	158	41	whenb(t	whenb(t	PROPN
ijassa-1225	158	42	)	)	PUNCT
ijassa-1225	158	43	≡	≡	PROPN
ijassa-1225	158	44	r	r	PROPN
ijassa-1225	158	45	,	,	PUNCT
ijassa-1225	158	46	the	the	DET
ijassa-1225	158	47	operatorng	operatorng	NOUN
ijassa-1225	158	48	:	:	PUNCT
ijassa-1225	158	49	w	w	NOUN
ijassa-1225	158	50	⇒	⇒	PROPN
ijassa-1225	158	51	w	w	NOUN
ijassa-1225	158	52	is	be	AUX
ijassa-1225	158	53	order	order	NOUN
ijassa-1225	158	54	covering	cover	VERB
ijassa-1225	158	55	(	(	PUNCT
ijassa-1225	158	56	i.e.	i.e.	X
ijassa-1225	158	57	order	order	NOUN
ijassa-1225	158	58	covers	cover	VERB
ijassa-1225	158	59	the	the	DET
ijassa-1225	158	60	whole	whole	ADJ
ijassa-1225	158	61	space	space	NOUN
ijassa-1225	158	62	w	w	PROPN
ijassa-1225	158	63	)	)	PUNCT
ijassa-1225	158	64	.	.	PUNCT
ijassa-1225	159	1	now	now	ADV
ijassa-1225	159	2	we	we	PRON
ijassa-1225	159	3	pick	pick	VERB
ijassa-1225	159	4	δ	δ	PROPN
ijassa-1225	159	5	>	>	X
ijassa-1225	159	6	0	0	PUNCT
ijassa-1225	159	7	and	and	CCONJ
ijassa-1225	159	8	define	define	VERB
ijassa-1225	159	9	two	two	NUM
ijassa-1225	159	10	set	set	NOUN
ijassa-1225	159	11	-	-	PUNCT
ijassa-1225	159	12	valued	value	VERB
ijassa-1225	159	13	mappings	mapping	NOUN
ijassa-1225	159	14	g+	g+	NOUN
ijassa-1225	159	15	,	,	PUNCT
ijassa-1225	159	16	g−	g−	ADJ
ijassa-1225	159	17	:	:	PUNCT
ijassa-1225	159	18	[	[	X
ijassa-1225	159	19	a	a	X
ijassa-1225	159	20	,	,	PUNCT
ijassa-1225	159	21	b]×	b]×	NOUN
ijassa-1225	159	22	r→	r→	PROPN
ijassa-1225	159	23	k(r	k(r	PROPN
ijassa-1225	159	24	)	)	PUNCT
ijassa-1225	159	25	by	by	ADP
ijassa-1225	159	26	the	the	DET
ijassa-1225	159	27	formulas	formula	NOUN
ijassa-1225	159	28	:	:	PUNCT
ijassa-1225	159	29	g+(t	g+(t	NOUN
ijassa-1225	159	30	,	,	PUNCT
ijassa-1225	159	31	x	x	NOUN
ijassa-1225	159	32	)	)	PUNCT
ijassa-1225	159	33	.	.	PUNCT
ijassa-1225	160	1	=	=	PUNCT
ijassa-1225	161	1	[	[	PUNCT
ijassa-1225	161	2	g(t	g(t	PROPN
ijassa-1225	161	3	,	,	PUNCT
ijassa-1225	161	4	x	x	X
ijassa-1225	161	5	)	)	PUNCT
ijassa-1225	161	6	,	,	PUNCT
ijassa-1225	161	7	g(t	g(t	PROPN
ijassa-1225	161	8	,	,	PUNCT
ijassa-1225	161	9	x)+δ	x)+δ	PROPN
ijassa-1225	161	10	]	]	PUNCT
ijassa-1225	161	11	,	,	PUNCT
ijassa-1225	161	12	g−(t	g−(t	PROPN
ijassa-1225	161	13	,	,	PUNCT
ijassa-1225	161	14	x	x	NOUN
ijassa-1225	161	15	)	)	PUNCT
ijassa-1225	161	16	.	.	PUNCT
ijassa-1225	162	1	=	=	PUNCT
ijassa-1225	163	1	[	[	PUNCT
ijassa-1225	163	2	g(t	g(t	PROPN
ijassa-1225	163	3	,	,	PUNCT
ijassa-1225	163	4	x)−δ	x)−δ	PROPN
ijassa-1225	163	5	,	,	PUNCT
ijassa-1225	163	6	g(t	g(t	PROPN
ijassa-1225	163	7	,	,	PUNCT
ijassa-1225	163	8	x	x	X
ijassa-1225	163	9	)	)	PUNCT
ijassa-1225	163	10	]	]	PUNCT
ijassa-1225	163	11	,	,	PUNCT
ijassa-1225	163	12	t	t	PROPN
ijassa-1225	163	13	∈	∈	PROPN
ijassa-1225	164	1	[	[	X
ijassa-1225	164	2	a	a	X
ijassa-1225	164	3	,	,	PUNCT
ijassa-1225	164	4	b	b	NOUN
ijassa-1225	164	5	]	]	X
ijassa-1225	164	6	,	,	PUNCT
ijassa-1225	164	7	x	x	PROPN
ijassa-1225	164	8	∈	∈	PROPN
ijassa-1225	164	9	r.	r.	PROPN
ijassa-1225	164	10	(	(	PUNCT
ijassa-1225	164	11	3.10	3.10	NUM
ijassa-1225	164	12	)	)	PUNCT
ijassa-1225	164	13	the	the	DET
ijassa-1225	164	14	images	image	NOUN
ijassa-1225	164	15	of	of	ADP
ijassa-1225	164	16	the	the	DET
ijassa-1225	164	17	set	set	NOUN
ijassa-1225	164	18	-	-	PUNCT
ijassa-1225	164	19	valued	value	VERB
ijassa-1225	164	20	functions	function	NOUN
ijassa-1225	164	21	g+	g+	NOUN
ijassa-1225	164	22	∆(t	∆(t	NOUN
ijassa-1225	164	23	,	,	PUNCT
ijassa-1225	164	24	·	·	PUNCT
ijassa-1225	164	25	)	)	PUNCT
ijassa-1225	164	26	:	:	PUNCT
ijassa-1225	164	27	b(t)→	b(t)→	ADP
ijassa-1225	164	28	k(r	k(r	PROPN
ijassa-1225	164	29	)	)	PUNCT
ijassa-1225	164	30	and	and	CCONJ
ijassa-1225	164	31	g−∆(t	g−∆(t	PROPN
ijassa-1225	164	32	,	,	PUNCT
ijassa-1225	164	33	·	·	PUNCT
ijassa-1225	164	34	)	)	PUNCT
ijassa-1225	164	35	:	:	PUNCT
ijassa-1225	165	1	b(t)→	b(t)→	ADP
ijassa-1225	165	2	k(r	k(r	NOUN
ijassa-1225	165	3	)	)	PUNCT
ijassa-1225	165	4	are	be	AUX
ijassa-1225	165	5	the	the	DET
ijassa-1225	165	6	sets	set	NOUN
ijassa-1225	165	7	[	[	PUNCT
ijassa-1225	165	8	q0(t	q0(t	PROPN
ijassa-1225	165	9	)	)	PUNCT
ijassa-1225	165	10	+	+	NUM
ijassa-1225	165	11	q2	q2	X
ijassa-1225	165	12	1(t)−	1(t)−	NUM
ijassa-1225	165	13	r2	r2	PROPN
ijassa-1225	165	14	,	,	PUNCT
ijassa-1225	165	15	q0(t	q0(t	PROPN
ijassa-1225	165	16	)	)	PUNCT
ijassa-1225	166	1	+	+	NUM
ijassa-1225	166	2	q2	q2	NOUN
ijassa-1225	166	3	1(t	1(t	NUM
ijassa-1225	166	4	)	)	PUNCT
ijassa-1225	167	1	+	+	CCONJ
ijassa-1225	167	2	δ	δ	X
ijassa-1225	167	3	]	]	PUNCT
ijassa-1225	167	4	,	,	PUNCT
ijassa-1225	167	5	and	and	CCONJ
ijassa-1225	167	6	[	[	PUNCT
ijassa-1225	167	7	q0(t	q0(t	PROPN
ijassa-1225	167	8	)	)	PUNCT
ijassa-1225	167	9	+	+	NUM
ijassa-1225	167	10	q2	q2	PROPN
ijassa-1225	167	11	1(t)−	1(t)−	PROPN
ijassa-1225	167	12	r2	r2	PROPN
ijassa-1225	167	13	−	−	PROPN
ijassa-1225	167	14	δ	δ	PROPN
ijassa-1225	167	15	,	,	PUNCT
ijassa-1225	167	16	q0(t	q0(t	PROPN
ijassa-1225	167	17	)	)	PUNCT
ijassa-1225	167	18	+	+	NUM
ijassa-1225	167	19	q2	q2	NOUN
ijassa-1225	167	20	1(t	1(t	NUM
ijassa-1225	167	21	)	)	PUNCT
ijassa-1225	167	22	]	]	PUNCT
ijassa-1225	167	23	,	,	PUNCT
ijassa-1225	167	24	respectively	respectively	ADV
ijassa-1225	167	25	.	.	PUNCT
ijassa-1225	168	1	using	use	VERB
ijassa-1225	168	2	theorem	theorem	ADJ
ijassa-1225	168	3	3.1	3.1	NUM
ijassa-1225	168	4	one	one	NOUN
ijassa-1225	168	5	can	can	AUX
ijassa-1225	168	6	easily	easily	ADV
ijassa-1225	168	7	demonstrate	demonstrate	VERB
ijassa-1225	168	8	that	that	SCONJ
ijassa-1225	168	9	if	if	SCONJ
ijassa-1225	168	10	the	the	DET
ijassa-1225	168	11	measurable	measurable	ADJ
ijassa-1225	168	12	function	function	NOUN
ijassa-1225	168	13	ŷ	ŷ	NUM
ijassa-1225	168	14	:	:	PUNCT
ijassa-1225	169	1	[	[	X
ijassa-1225	169	2	a	a	X
ijassa-1225	169	3	,	,	PUNCT
ijassa-1225	169	4	b]→	b]→	ADJ
ijassa-1225	169	5	r	r	NOUN
ijassa-1225	169	6	satisfies	satisfy	VERB
ijassa-1225	169	7	the	the	DET
ijassa-1225	169	8	inequality	inequality	NOUN
ijassa-1225	169	9	(	(	PUNCT
ijassa-1225	169	10	3.9	3.9	NUM
ijassa-1225	169	11	)	)	PUNCT
ijassa-1225	169	12	for	for	ADP
ijassa-1225	169	13	almost	almost	ADV
ijassa-1225	169	14	all	all	PRON
ijassa-1225	169	15	t	t	NOUN
ijassa-1225	169	16	∈	∈	PRON
ijassa-1225	170	1	[	[	X
ijassa-1225	170	2	a	a	X
ijassa-1225	170	3	,	,	PUNCT
ijassa-1225	170	4	b	b	NOUN
ijassa-1225	170	5	]	]	X
ijassa-1225	170	6	,	,	PUNCT
ijassa-1225	170	7	then	then	ADV
ijassa-1225	170	8	the	the	DET
ijassa-1225	170	9	operator	operator	NOUN
ijassa-1225	170	10	ng+	ng+	ADV
ijassa-1225	170	11	∆	∆	PROPN
ijassa-1225	171	1	:	:	PUNCT
ijassa-1225	171	2	w	w	X
ijassa-1225	171	3	(	(	PUNCT
ijassa-1225	171	4	b	b	NOUN
ijassa-1225	171	5	)	)	PUNCT
ijassa-1225	171	6	⇒	⇒	NOUN
ijassa-1225	171	7	c(w	c(w	PROPN
ijassa-1225	171	8	)	)	PUNCT
ijassa-1225	172	1	order	order	NOUN
ijassa-1225	172	2	covers	cover	VERB
ijassa-1225	172	3	the	the	DET
ijassa-1225	172	4	set	set	NOUN
ijassa-1225	172	5	{	{	PUNCT
ijassa-1225	172	6	ŷ(t	ŷ(t	NOUN
ijassa-1225	172	7	)	)	PUNCT
ijassa-1225	172	8	}	}	PUNCT
ijassa-1225	172	9	⊂	⊂	PROPN
ijassa-1225	172	10	r.	r.	PROPN
ijassa-1225	172	11	theorem	theorem	VERB
ijassa-1225	172	12	3.1	3.1	NUM
ijassa-1225	172	13	also	also	ADV
ijassa-1225	172	14	implies	imply	VERB
ijassa-1225	172	15	that	that	SCONJ
ijassa-1225	172	16	the	the	DET
ijassa-1225	172	17	operator	operator	NOUN
ijassa-1225	172	18	ng−	ng−	PROPN
ijassa-1225	172	19	∆	∆	PROPN
ijassa-1225	172	20	:	:	PUNCT
ijassa-1225	172	21	w	w	X
ijassa-1225	172	22	(	(	PUNCT
ijassa-1225	172	23	b	b	NOUN
ijassa-1225	172	24	)	)	PUNCT
ijassa-1225	172	25	⇒	⇒	NOUN
ijassa-1225	172	26	c(w	c(w	PROPN
ijassa-1225	172	27	)	)	PUNCT
ijassa-1225	172	28	order	order	NOUN
ijassa-1225	172	29	covers	cover	VERB
ijassa-1225	172	30	the	the	DET
ijassa-1225	172	31	set	set	NOUN
ijassa-1225	172	32	{	{	PUNCT
ijassa-1225	172	33	ŷ(t	ŷ(t	NOUN
ijassa-1225	172	34	)	)	PUNCT
ijassa-1225	172	35	}	}	PUNCT
ijassa-1225	173	1	⊂	⊂	PUNCT
ijassa-1225	173	2	r	r	NOUN
ijassa-1225	173	3	provided	provide	VERB
ijassa-1225	173	4	that	that	SCONJ
ijassa-1225	173	5	the	the	DET
ijassa-1225	173	6	inequality	inequality	NOUN
ijassa-1225	173	7	ŷ(t	ŷ(t	NOUN
ijassa-1225	173	8	)	)	PUNCT
ijassa-1225	173	9	≥	≥	NOUN
ijassa-1225	173	10	q0(t	q0(t	PROPN
ijassa-1225	173	11	)	)	PUNCT
ijassa-1225	173	12	+	+	NUM
ijassa-1225	173	13	q2	q2	PROPN
ijassa-1225	173	14	1(t)−	1(t)−	PROPN
ijassa-1225	173	15	r2	r2	PROPN
ijassa-1225	173	16	−	−	PROPN
ijassa-1225	173	17	δ	δ	PROPN
ijassa-1225	173	18	,	,	PUNCT
ijassa-1225	173	19	is	be	AUX
ijassa-1225	173	20	valid	valid	ADJ
ijassa-1225	173	21	almost	almost	ADV
ijassa-1225	173	22	everywhere	everywhere	ADV
ijassa-1225	173	23	on	on	ADP
ijassa-1225	173	24	[	[	X
ijassa-1225	173	25	a	a	X
ijassa-1225	173	26	,	,	PUNCT
ijassa-1225	173	27	b	b	NOUN
ijassa-1225	173	28	]	]	X
ijassa-1225	173	29	,	,	PUNCT
ijassa-1225	173	30	4	4	X
ijassa-1225	173	31	.	.	PUNCT
ijassa-1225	173	32	implicit	implicit	ADJ
ijassa-1225	173	33	differential	differential	ADJ
ijassa-1225	173	34	inclusion	inclusion	NOUN
ijassa-1225	173	35	in	in	ADP
ijassa-1225	173	36	this	this	DET
ijassa-1225	173	37	section	section	NOUN
ijassa-1225	173	38	,	,	PUNCT
ijassa-1225	173	39	based	base	VERB
ijassa-1225	173	40	on	on	ADP
ijassa-1225	173	41	theorems	theorem	NOUN
ijassa-1225	173	42	2.1	2.1	NUM
ijassa-1225	173	43	and	and	CCONJ
ijassa-1225	173	44	3.1	3.1	NUM
ijassa-1225	173	45	we	we	PRON
ijassa-1225	173	46	investigate	investigate	VERB
ijassa-1225	173	47	differential	differential	ADJ
ijassa-1225	173	48	inclusions	inclusion	NOUN
ijassa-1225	173	49	not	not	PART
ijassa-1225	173	50	resolved	resolve	VERB
ijassa-1225	173	51	with	with	ADP
ijassa-1225	173	52	respect	respect	NOUN
ijassa-1225	173	53	the	the	DET
ijassa-1225	173	54	derivative	derivative	NOUN
ijassa-1225	173	55	(	(	PUNCT
ijassa-1225	173	56	which	which	PRON
ijassa-1225	173	57	are	be	AUX
ijassa-1225	173	58	also	also	ADV
ijassa-1225	173	59	called	call	VERB
ijassa-1225	173	60	implicit	implicit	ADJ
ijassa-1225	173	61	differential	differential	ADJ
ijassa-1225	173	62	inclusions	inclusion	NOUN
ijassa-1225	173	63	)	)	PUNCT
ijassa-1225	173	64	.	.	PUNCT
ijassa-1225	174	1	let	let	VERB
ijassa-1225	174	2	a	a	DET
ijassa-1225	174	3	measurable	measurable	ADJ
ijassa-1225	174	4	set	set	NOUN
ijassa-1225	174	5	-	-	PUNCT
ijassa-1225	174	6	valued	value	VERB
ijassa-1225	174	7	mapping	mapping	NOUN
ijassa-1225	174	8	b	b	NOUN
ijassa-1225	174	9	:	:	PUNCT
ijassa-1225	175	1	[	[	X
ijassa-1225	175	2	a	a	PRON
ijassa-1225	175	3	,	,	PUNCT
ijassa-1225	175	4	b]→	b]→	X
ijassa-1225	175	5	c(rn	c(rn	PROPN
ijassa-1225	175	6	)	)	PUNCT
ijassa-1225	175	7	be	be	AUX
ijassa-1225	175	8	given	give	VERB
ijassa-1225	175	9	.	.	PUNCT
ijassa-1225	176	1	denote	denote	VERB
ijassa-1225	176	2	by	by	ADP
ijassa-1225	176	3	l(b	l(b	PROPN
ijassa-1225	176	4	)	)	PUNCT
ijassa-1225	176	5	the	the	DET
ijassa-1225	176	6	space	space	NOUN
ijassa-1225	176	7	of	of	ADP
ijassa-1225	176	8	all	all	DET
ijassa-1225	176	9	integrable	integrable	ADJ
ijassa-1225	176	10	selections	selection	NOUN
ijassa-1225	176	11	of	of	ADP
ijassa-1225	176	12	the	the	DET
ijassa-1225	176	13	set	set	NOUN
ijassa-1225	176	14	-	-	PUNCT
ijassa-1225	176	15	valued	value	VERB
ijassa-1225	176	16	mapping	mapping	NOUN
ijassa-1225	176	17	b	b	NOUN
ijassa-1225	176	18	and	and	CCONJ
ijassa-1225	176	19	denote	denote	VERB
ijassa-1225	176	20	by	by	ADP
ijassa-1225	176	21	ac(b	ac(b	NOUN
ijassa-1225	176	22	)	)	PUNCT
ijassa-1225	176	23	the	the	DET
ijassa-1225	176	24	space	space	NOUN
ijassa-1225	176	25	of	of	ADP
ijassa-1225	176	26	all	all	DET
ijassa-1225	176	27	absolutely	absolutely	ADV
ijassa-1225	176	28	continuous	continuous	ADJ
ijassa-1225	176	29	functions	function	NOUN
ijassa-1225	176	30	x	x	PUNCT
ijassa-1225	176	31	:	:	PUNCT
ijassa-1225	177	1	[	[	X
ijassa-1225	177	2	a	a	X
ijassa-1225	177	3	,	,	PUNCT
ijassa-1225	177	4	b]→	b]→	X
ijassa-1225	177	5	rn	rn	PROPN
ijassa-1225	177	6	such	such	ADJ
ijassa-1225	177	7	that	that	SCONJ
ijassa-1225	177	8	ẋ	ẋ	PROPN
ijassa-1225	177	9	∈	∈	PROPN
ijassa-1225	177	10	l(b	l(b	PROPN
ijassa-1225	177	11	)	)	PUNCT
ijassa-1225	177	12	.	.	PUNCT
ijassa-1225	178	1	in	in	ADP
ijassa-1225	178	2	the	the	DET
ijassa-1225	178	3	case	case	NOUN
ijassa-1225	178	4	b(t	b(t	NOUN
ijassa-1225	178	5	)	)	PUNCT
ijassa-1225	178	6	≡	≡	PROPN
ijassa-1225	178	7	rn	rn	PROPN
ijassa-1225	178	8	,	,	PUNCT
ijassa-1225	178	9	we	we	PRON
ijassa-1225	178	10	denote	denote	VERB
ijassa-1225	178	11	these	these	DET
ijassa-1225	178	12	spaces	space	NOUN
ijassa-1225	178	13	these	these	DET
ijassa-1225	178	14	spaces	space	NOUN
ijassa-1225	178	15	by	by	ADP
ijassa-1225	178	16	ln	ln	NOUN
ijassa-1225	178	17	and	and	CCONJ
ijassa-1225	178	18	acn	acn	PROPN
ijassa-1225	178	19	.	.	PUNCT
ijassa-1225	179	1	we	we	PRON
ijassa-1225	179	2	will	will	AUX
ijassa-1225	179	3	require	require	VERB
ijassa-1225	179	4	the	the	DET
ijassa-1225	179	5	fulfillment	fulfillment	NOUN
ijassa-1225	179	6	of	of	ADP
ijassa-1225	179	7	the	the	DET
ijassa-1225	179	8	following	follow	VERB
ijassa-1225	179	9	analogue	analogue	NOUN
ijassa-1225	179	10	of	of	ADP
ijassa-1225	179	11	the	the	DET
ijassa-1225	179	12	one	one	NUM
ijassa-1225	179	13	-	-	PUNCT
ijassa-1225	179	14	sided	side	VERB
ijassa-1225	179	15	continuity	continuity	NOUN
ijassa-1225	179	16	property	property	NOUN
ijassa-1225	179	17	known	know	VERB
ijassa-1225	179	18	for	for	ADP
ijassa-1225	179	19	“	"	PUNCT
ijassa-1225	179	20	ordinary	ordinary	ADJ
ijassa-1225	179	21	single	single	ADJ
ijassa-1225	179	22	-	-	PUNCT
ijassa-1225	179	23	valued	value	VERB
ijassa-1225	179	24	”	"	PUNCT
ijassa-1225	179	25	functions	function	NOUN
ijassa-1225	179	26	applicable	applicable	ADJ
ijassa-1225	179	27	to	to	ADP
ijassa-1225	179	28	a	a	DET
ijassa-1225	179	29	set	set	NOUN
ijassa-1225	179	30	-	-	PUNCT
ijassa-1225	179	31	valued	value	VERB
ijassa-1225	179	32	mapping	mapping	NOUN
ijassa-1225	179	33	g	g	NOUN
ijassa-1225	179	34	:	:	PUNCT
ijassa-1225	179	35	r→	r→	PROPN
ijassa-1225	179	36	k(rm	k(rm	PROPN
ijassa-1225	179	37	)	)	PUNCT
ijassa-1225	179	38	,	,	PUNCT
ijassa-1225	179	39	which	which	PRON
ijassa-1225	179	40	was	be	AUX
ijassa-1225	179	41	defined	define	VERB
ijassa-1225	179	42	in	in	ADP
ijassa-1225	179	43	[	[	X
ijassa-1225	179	44	24	24	NUM
ijassa-1225	179	45	]	]	PUNCT
ijassa-1225	179	46	.	.	PUNCT
ijassa-1225	180	1	such	such	ADJ
ijassa-1225	180	2	mapping	mapping	NOUN
ijassa-1225	180	3	is	be	AUX
ijassa-1225	180	4	called	call	VERB
ijassa-1225	180	5	right	right	ADV
ijassa-1225	180	6	continuous	continuous	ADJ
ijassa-1225	180	7	at	at	ADP
ijassa-1225	180	8	the	the	DET
ijassa-1225	180	9	point	point	NOUN
ijassa-1225	181	1	x0	x0	PROPN
ijassa-1225	181	2	∈	∈	PROPN
ijassa-1225	181	3	r	r	NOUN
ijassa-1225	181	4	if	if	SCONJ
ijassa-1225	181	5	for	for	ADP
ijassa-1225	181	6	any	any	DET
ijassa-1225	181	7	ε	ε	PROPN
ijassa-1225	181	8	>	>	X
ijassa-1225	181	9	0	0	PROPN
ijassa-1225	181	10	,	,	PUNCT
ijassa-1225	181	11	there	there	PRON
ijassa-1225	181	12	exists	exist	VERB
ijassa-1225	181	13	δ	δ	PROPN
ijassa-1225	181	14	>	>	X
ijassa-1225	181	15	0	0	NUM
ijassa-1225	182	1	such	such	ADJ
ijassa-1225	182	2	that	that	PRON
ijassa-1225	182	3	for	for	ADP
ijassa-1225	182	4	all	all	DET
ijassa-1225	182	5	x	x	SYM
ijassa-1225	182	6	∈	∈	PROPN
ijassa-1225	182	7	(	(	PUNCT
ijassa-1225	182	8	x0	x0	PROPN
ijassa-1225	182	9	,	,	PUNCT
ijassa-1225	182	10	x0	x0	PROPN
ijassa-1225	182	11	+	+	PROPN
ijassa-1225	182	12	δ	δ	PROPN
ijassa-1225	182	13	)	)	PUNCT
ijassa-1225	182	14	,	,	PUNCT
ijassa-1225	182	15	it	it	PRON
ijassa-1225	182	16	holds	hold	VERB
ijassa-1225	182	17	true	true	ADJ
ijassa-1225	182	18	that	that	SCONJ
ijassa-1225	182	19	hrm	hrm	PROPN
ijassa-1225	182	20	(	(	PUNCT
ijassa-1225	182	21	g(x0	g(x0	NOUN
ijassa-1225	182	22	)	)	PUNCT
ijassa-1225	182	23	,	,	PUNCT
ijassa-1225	182	24	g(x	g(x	NOUN
ijassa-1225	182	25	)	)	PUNCT
ijassa-1225	182	26	)	)	PUNCT
ijassa-1225	182	27	<	<	X
ijassa-1225	182	28	ε	ε	PROPN
ijassa-1225	182	29	(	(	PUNCT
ijassa-1225	182	30	hereinafter	hereinafter	VERB
ijassa-1225	182	31	the	the	DET
ijassa-1225	182	32	symbol	symbol	NOUN
ijassa-1225	182	33	hrm	hrm	PROPN
ijassa-1225	182	34	denotes	denote	VERB
ijassa-1225	182	35	the	the	DET
ijassa-1225	182	36	hausdorff	hausdorff	NOUN
ijassa-1225	182	37	distance	distance	NOUN
ijassa-1225	182	38	between	between	ADP
ijassa-1225	182	39	the	the	DET
ijassa-1225	182	40	sets	set	NOUN
ijassa-1225	182	41	in	in	ADP
ijassa-1225	182	42	the	the	DET
ijassa-1225	182	43	space	space	NOUN
ijassa-1225	182	44	rm	rm	PROPN
ijassa-1225	182	45	)	)	PUNCT
ijassa-1225	182	46	.	.	PUNCT
ijassa-1225	183	1	let	let	VERB
ijassa-1225	183	2	a	a	DET
ijassa-1225	183	3	set	set	NOUN
ijassa-1225	183	4	-	-	PUNCT
ijassa-1225	183	5	valued	value	VERB
ijassa-1225	183	6	function	function	NOUN
ijassa-1225	183	7	f	f	NOUN
ijassa-1225	183	8	:	:	PUNCT
ijassa-1225	184	1	[	[	X
ijassa-1225	184	2	a	a	X
ijassa-1225	184	3	,	,	PUNCT
ijassa-1225	184	4	b]×	b]×	NOUN
ijassa-1225	184	5	rn	rn	PROPN
ijassa-1225	184	6	×	×	PROPN
ijassa-1225	184	7	rn	rn	PROPN
ijassa-1225	184	8	×	×	PROPN
ijassa-1225	184	9	rn	rn	PROPN
ijassa-1225	184	10	→	→	SYM
ijassa-1225	184	11	k(rm	k(rm	PROPN
ijassa-1225	184	12	)	)	PUNCT
ijassa-1225	184	13	and	and	CCONJ
ijassa-1225	184	14	a	a	DET
ijassa-1225	184	15	vector	vector	NOUN
ijassa-1225	184	16	γ	γ	PROPN
ijassa-1225	184	17	∈	∈	PROPN
ijassa-1225	184	18	rn	rn	PROPN
ijassa-1225	184	19	be	be	AUX
ijassa-1225	184	20	given	give	VERB
ijassa-1225	184	21	.	.	PUNCT
ijassa-1225	185	1	we	we	PRON
ijassa-1225	185	2	assume	assume	VERB
ijassa-1225	185	3	that	that	SCONJ
ijassa-1225	185	4	for	for	ADP
ijassa-1225	185	5	any	any	DET
ijassa-1225	185	6	x	x	NOUN
ijassa-1225	185	7	,	,	PUNCT
ijassa-1225	185	8	v	v	NOUN
ijassa-1225	185	9	,	,	PUNCT
ijassa-1225	185	10	u	u	PROPN
ijassa-1225	185	11	∈	∈	PROPN
ijassa-1225	185	12	rn	rn	PROPN
ijassa-1225	185	13	,	,	PUNCT
ijassa-1225	185	14	the	the	DET
ijassa-1225	185	15	function	function	NOUN
ijassa-1225	185	16	f	f	X
ijassa-1225	185	17	(	(	PUNCT
ijassa-1225	185	18	·	·	PUNCT
ijassa-1225	185	19	,	,	PUNCT
ijassa-1225	185	20	x	x	NOUN
ijassa-1225	185	21	,	,	PUNCT
ijassa-1225	185	22	v	v	NOUN
ijassa-1225	185	23	,	,	PUNCT
ijassa-1225	185	24	u	u	NOUN
ijassa-1225	185	25	)	)	PUNCT
ijassa-1225	185	26	:	:	PUNCT
ijassa-1225	186	1	[	[	X
ijassa-1225	186	2	a	a	PRON
ijassa-1225	186	3	,	,	PUNCT
ijassa-1225	186	4	b]→	b]→	ADJ
ijassa-1225	186	5	k(rm	k(rm	NOUN
ijassa-1225	186	6	)	)	PUNCT
ijassa-1225	186	7	is	be	AUX
ijassa-1225	186	8	measurable	measurable	ADJ
ijassa-1225	186	9	;	;	PUNCT
ijassa-1225	186	10	for	for	ADP
ijassa-1225	186	11	almost	almost	ADV
ijassa-1225	186	12	all	all	PRON
ijassa-1225	186	13	t	t	NOUN
ijassa-1225	186	14	∈	∈	PRON
ijassa-1225	186	15	[	[	X
ijassa-1225	186	16	a	a	X
ijassa-1225	186	17	,	,	PUNCT
ijassa-1225	186	18	b	b	NOUN
ijassa-1225	186	19	]	]	X
ijassa-1225	186	20	and	and	CCONJ
ijassa-1225	186	21	all	all	DET
ijassa-1225	186	22	v	v	NOUN
ijassa-1225	186	23	,	,	PUNCT
ijassa-1225	186	24	u	u	PROPN
ijassa-1225	186	25	∈	∈	PROPN
ijassa-1225	186	26	rn	rn	PROPN
ijassa-1225	186	27	,	,	PUNCT
ijassa-1225	186	28	the	the	DET
ijassa-1225	186	29	function	function	NOUN
ijassa-1225	186	30	f(t	f(t	NOUN
ijassa-1225	186	31	,	,	PUNCT
ijassa-1225	186	32	·	·	PUNCT
ijassa-1225	186	33	,	,	PUNCT
ijassa-1225	186	34	v	v	NOUN
ijassa-1225	186	35	,	,	PUNCT
ijassa-1225	186	36	u	u	NOUN
ijassa-1225	186	37	)	)	PUNCT
ijassa-1225	186	38	:	:	PUNCT
ijassa-1225	186	39	rn	rn	PROPN
ijassa-1225	186	40	→	→	SYM
ijassa-1225	186	41	k(rm	k(rm	PROPN
ijassa-1225	186	42	)	)	PUNCT
ijassa-1225	186	43	is	be	AUX
ijassa-1225	186	44	right	right	ADV
ijassa-1225	186	45	continuous	continuous	ADJ
ijassa-1225	186	46	in	in	ADP
ijassa-1225	186	47	each	each	PRON
ijassa-1225	186	48	of	of	ADP
ijassa-1225	186	49	the	the	DET
ijassa-1225	186	50	arguments	argument	NOUN
ijassa-1225	186	51	x1	x1	NUM
ijassa-1225	186	52	,	,	PUNCT
ijassa-1225	186	53	.	.	PUNCT
ijassa-1225	186	54	.	.	PUNCT
ijassa-1225	187	1	.	.	PUNCT
ijassa-1225	188	1	,	,	PUNCT
ijassa-1225	188	2	xn	xn	PROPN
ijassa-1225	188	3	;	;	PUNCT
ijassa-1225	188	4	for	for	ADP
ijassa-1225	188	5	almost	almost	ADV
ijassa-1225	188	6	all	all	PRON
ijassa-1225	188	7	t	t	NOUN
ijassa-1225	188	8	∈	∈	PRON
ijassa-1225	189	1	[	[	X
ijassa-1225	189	2	a	a	X
ijassa-1225	189	3	,	,	PUNCT
ijassa-1225	189	4	b	b	NOUN
ijassa-1225	189	5	]	]	X
ijassa-1225	189	6	and	and	CCONJ
ijassa-1225	189	7	any	any	DET
ijassa-1225	189	8	x	x	NOUN
ijassa-1225	189	9	,	,	PUNCT
ijassa-1225	189	10	u	u	PROPN
ijassa-1225	189	11	∈	∈	PROPN
ijassa-1225	189	12	rn	rn	PROPN
ijassa-1225	189	13	,	,	PUNCT
ijassa-1225	189	14	the	the	DET
ijassa-1225	189	15	function	function	NOUN
ijassa-1225	189	16	f(t	f(t	NOUN
ijassa-1225	189	17	,	,	PUNCT
ijassa-1225	189	18	x	x	X
ijassa-1225	189	19	,	,	PUNCT
ijassa-1225	189	20	·	·	PUNCT
ijassa-1225	189	21	,	,	PUNCT
ijassa-1225	189	22	u	u	NOUN
ijassa-1225	189	23	)	)	PUNCT
ijassa-1225	189	24	:	:	PUNCT
ijassa-1225	189	25	rn	rn	PROPN
ijassa-1225	189	26	→	→	SYM
ijassa-1225	189	27	k(rm	k(rm	PROPN
ijassa-1225	189	28	)	)	PUNCT
ijassa-1225	189	29	is	be	AUX
ijassa-1225	189	30	right	right	ADV
ijassa-1225	189	31	continuous	continuous	ADJ
ijassa-1225	189	32	in	in	ADP
ijassa-1225	189	33	each	each	PRON
ijassa-1225	189	34	of	of	ADP
ijassa-1225	189	35	the	the	DET
ijassa-1225	189	36	copyright	copyright	NOUN
ijassa-1225	189	37	©	©	ADP
ijassa-1225	189	38	2022	2022	NUM
ijassa-1225	189	39	assa	assa	NOUN
ijassa-1225	189	40	.	.	PUNCT
ijassa-1225	190	1	adv	adv	PROPN
ijassa-1225	190	2	syst	syst	PROPN
ijassa-1225	190	3	sci	sci	PROPN
ijassa-1225	190	4	appl	appl	PROPN
ijassa-1225	190	5	(	(	PUNCT
ijassa-1225	190	6	2022	2022	NUM
ijassa-1225	190	7	)	)	PUNCT
ijassa-1225	190	8	182	182	NUM
ijassa-1225	190	9	e.s	e.s	PROPN
ijassa-1225	190	10	.	.	PROPN
ijassa-1225	190	11	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	190	12	,	,	PUNCT
ijassa-1225	190	13	i.d	i.d	PROPN
ijassa-1225	190	14	.	.	PROPN
ijassa-1225	190	15	serova	serova	PROPN
ijassa-1225	190	16	,	,	PUNCT
ijassa-1225	190	17	e.a	e.a	PROPN
ijassa-1225	190	18	.	.	PROPN
ijassa-1225	190	19	panasenko	panasenko	PROPN
ijassa-1225	190	20	,	,	PUNCT
ijassa-1225	190	21	e.o	e.o	PROPN
ijassa-1225	190	22	.	.	PROPN
ijassa-1225	190	23	burlakov	burlakov	PROPN
ijassa-1225	190	24	arguments	argument	NOUN
ijassa-1225	190	25	v1	v1	NOUN
ijassa-1225	190	26	,	,	PUNCT
ijassa-1225	190	27	.	.	PUNCT
ijassa-1225	190	28	.	.	PUNCT
ijassa-1225	190	29	.	.	PUNCT
ijassa-1225	191	1	,	,	PUNCT
ijassa-1225	191	2	vn	vn	X
ijassa-1225	191	3	;	;	PUNCT
ijassa-1225	191	4	for	for	ADP
ijassa-1225	191	5	almost	almost	ADV
ijassa-1225	191	6	all	all	PRON
ijassa-1225	191	7	t	t	NOUN
ijassa-1225	191	8	∈	∈	PRON
ijassa-1225	192	1	[	[	X
ijassa-1225	192	2	a	a	X
ijassa-1225	192	3	,	,	PUNCT
ijassa-1225	192	4	b	b	NOUN
ijassa-1225	192	5	]	]	X
ijassa-1225	192	6	and	and	CCONJ
ijassa-1225	192	7	any	any	DET
ijassa-1225	192	8	x	x	NOUN
ijassa-1225	192	9	,	,	PUNCT
ijassa-1225	192	10	v	v	PROPN
ijassa-1225	192	11	∈	∈	PROPN
ijassa-1225	192	12	rn	rn	PROPN
ijassa-1225	192	13	,	,	PUNCT
ijassa-1225	192	14	the	the	DET
ijassa-1225	192	15	function	function	NOUN
ijassa-1225	192	16	f(t	f(t	NOUN
ijassa-1225	192	17	,	,	PUNCT
ijassa-1225	192	18	x	x	NOUN
ijassa-1225	192	19	,	,	PUNCT
ijassa-1225	192	20	v	v	NOUN
ijassa-1225	192	21	,	,	PUNCT
ijassa-1225	192	22	·	·	PUNCT
ijassa-1225	192	23	)	)	PUNCT
ijassa-1225	192	24	:	:	PUNCT
ijassa-1225	193	1	rn	rn	PROPN
ijassa-1225	193	2	→	→	SYM
ijassa-1225	193	3	k(rm	k(rm	PROPN
ijassa-1225	193	4	)	)	PUNCT
ijassa-1225	193	5	is	be	AUX
ijassa-1225	193	6	continuous	continuous	ADJ
ijassa-1225	193	7	.	.	PUNCT
ijassa-1225	194	1	we	we	PRON
ijassa-1225	194	2	consider	consider	VERB
ijassa-1225	194	3	the	the	DET
ijassa-1225	194	4	differential	differential	ADJ
ijassa-1225	194	5	inclusion	inclusion	NOUN
ijassa-1225	194	6	f(t	f(t	NOUN
ijassa-1225	194	7	,	,	PUNCT
ijassa-1225	194	8	x	x	NOUN
ijassa-1225	194	9	,	,	PUNCT
ijassa-1225	194	10	ẋ	ẋ	PROPN
ijassa-1225	194	11	,	,	PUNCT
ijassa-1225	194	12	ẋ	ẋ	PROPN
ijassa-1225	194	13	)	)	PUNCT
ijassa-1225	194	14	3	3	NUM
ijassa-1225	194	15	0	0	NUM
ijassa-1225	194	16	,	,	PUNCT
ijassa-1225	194	17	t	t	PROPN
ijassa-1225	194	18	∈	∈	PROPN
ijassa-1225	195	1	[	[	X
ijassa-1225	195	2	a	a	X
ijassa-1225	195	3	,	,	PUNCT
ijassa-1225	195	4	b	b	NOUN
ijassa-1225	195	5	]	]	X
ijassa-1225	195	6	,	,	PUNCT
ijassa-1225	195	7	(	(	PUNCT
ijassa-1225	195	8	4.11	4.11	NUM
ijassa-1225	195	9	)	)	PUNCT
ijassa-1225	195	10	with	with	ADP
ijassa-1225	195	11	the	the	DET
ijassa-1225	195	12	following	follow	VERB
ijassa-1225	195	13	additional	additional	ADJ
ijassa-1225	195	14	restriction	restriction	NOUN
ijassa-1225	195	15	on	on	ADP
ijassa-1225	195	16	the	the	DET
ijassa-1225	195	17	derivative	derivative	NOUN
ijassa-1225	195	18	of	of	ADP
ijassa-1225	195	19	the	the	DET
ijassa-1225	195	20	unknown	unknown	ADJ
ijassa-1225	195	21	function	function	NOUN
ijassa-1225	195	22	:	:	PUNCT
ijassa-1225	195	23	ẋ(t	ẋ(t	X
ijassa-1225	195	24	)	)	PUNCT
ijassa-1225	195	25	∈	∈	PROPN
ijassa-1225	195	26	b(t	b(t	PROPN
ijassa-1225	195	27	)	)	PUNCT
ijassa-1225	195	28	,	,	PUNCT
ijassa-1225	195	29	t	t	PROPN
ijassa-1225	195	30	∈	∈	PROPN
ijassa-1225	196	1	[	[	X
ijassa-1225	196	2	a	a	X
ijassa-1225	196	3	,	,	PUNCT
ijassa-1225	196	4	b	b	NOUN
ijassa-1225	196	5	]	]	X
ijassa-1225	196	6	.	.	PUNCT
ijassa-1225	197	1	(	(	PUNCT
ijassa-1225	197	2	4.12	4.12	NUM
ijassa-1225	197	3	)	)	PUNCT
ijassa-1225	197	4	a	a	DET
ijassa-1225	197	5	solution	solution	NOUN
ijassa-1225	197	6	of	of	ADP
ijassa-1225	197	7	the	the	DET
ijassa-1225	197	8	system	system	NOUN
ijassa-1225	197	9	of	of	ADP
ijassa-1225	197	10	inclusions	inclusion	NOUN
ijassa-1225	197	11	(	(	PUNCT
ijassa-1225	197	12	4.11	4.11	NUM
ijassa-1225	197	13	)	)	PUNCT
ijassa-1225	197	14	,	,	PUNCT
ijassa-1225	197	15	(	(	PUNCT
ijassa-1225	197	16	4.12	4.12	NUM
ijassa-1225	197	17	)	)	PUNCT
ijassa-1225	197	18	is	be	AUX
ijassa-1225	197	19	understood	understand	VERB
ijassa-1225	197	20	to	to	PART
ijassa-1225	197	21	be	be	AUX
ijassa-1225	197	22	a	a	DET
ijassa-1225	197	23	function	function	NOUN
ijassa-1225	197	24	x	x	SYM
ijassa-1225	197	25	∈	∈	PROPN
ijassa-1225	197	26	ac(b	ac(b	NOUN
ijassa-1225	197	27	)	)	PUNCT
ijassa-1225	197	28	that	that	PRON
ijassa-1225	197	29	satisfies	satisfy	VERB
ijassa-1225	197	30	the	the	DET
ijassa-1225	197	31	inclusion	inclusion	NOUN
ijassa-1225	197	32	(	(	PUNCT
ijassa-1225	197	33	4.11	4.11	NUM
ijassa-1225	197	34	)	)	PUNCT
ijassa-1225	197	35	for	for	ADP
ijassa-1225	197	36	almost	almost	ADV
ijassa-1225	197	37	all	all	PRON
ijassa-1225	197	38	t	t	NOUN
ijassa-1225	197	39	∈	∈	PRON
ijassa-1225	198	1	[	[	X
ijassa-1225	198	2	a	a	X
ijassa-1225	198	3	,	,	PUNCT
ijassa-1225	198	4	b	b	NOUN
ijassa-1225	198	5	]	]	PUNCT
ijassa-1225	198	6	.	.	PUNCT
ijassa-1225	199	1	let	let	VERB
ijassa-1225	199	2	us	we	PRON
ijassa-1225	199	3	formulate	formulate	VERB
ijassa-1225	199	4	a	a	DET
ijassa-1225	199	5	statement	statement	NOUN
ijassa-1225	199	6	on	on	ADP
ijassa-1225	199	7	solvability	solvability	NOUN
ijassa-1225	199	8	and	and	CCONJ
ijassa-1225	199	9	estimates	estimate	NOUN
ijassa-1225	199	10	of	of	ADP
ijassa-1225	199	11	solutions	solution	NOUN
ijassa-1225	199	12	to	to	ADP
ijassa-1225	199	13	the	the	DET
ijassa-1225	199	14	cauchi	cauchi	PROPN
ijassa-1225	199	15	problem	problem	NOUN
ijassa-1225	199	16	for	for	ADP
ijassa-1225	199	17	the	the	DET
ijassa-1225	199	18	system	system	NOUN
ijassa-1225	199	19	(	(	PUNCT
ijassa-1225	199	20	4.11	4.11	NUM
ijassa-1225	199	21	)	)	PUNCT
ijassa-1225	199	22	,	,	PUNCT
ijassa-1225	199	23	(	(	PUNCT
ijassa-1225	199	24	4.12	4.12	NUM
ijassa-1225	199	25	)	)	PUNCT
ijassa-1225	199	26	with	with	ADP
ijassa-1225	199	27	the	the	DET
ijassa-1225	199	28	initial	initial	ADJ
ijassa-1225	199	29	condition	condition	NOUN
ijassa-1225	199	30	x(a	x(a	NOUN
ijassa-1225	199	31	)	)	PUNCT
ijassa-1225	199	32	=	=	SYM
ijassa-1225	199	33	γ	γ	X
ijassa-1225	199	34	.	.	PROPN
ijassa-1225	199	35	(	(	PUNCT
ijassa-1225	199	36	4.13	4.13	NUM
ijassa-1225	199	37	)	)	PUNCT
ijassa-1225	199	38	denote	denote	VERB
ijassa-1225	199	39	ω	ω	PROPN
ijassa-1225	199	40	=	=	SYM
ijassa-1225	199	41	{	{	PUNCT
ijassa-1225	199	42	(	(	PUNCT
ijassa-1225	199	43	t	t	PROPN
ijassa-1225	199	44	,	,	PUNCT
ijassa-1225	199	45	x	x	NOUN
ijassa-1225	199	46	,	,	PUNCT
ijassa-1225	199	47	v	v	NOUN
ijassa-1225	199	48	,	,	PUNCT
ijassa-1225	199	49	u	u	NOUN
ijassa-1225	199	50	)	)	PUNCT
ijassa-1225	199	51	:	:	PUNCT
ijassa-1225	200	1	t	t	PROPN
ijassa-1225	200	2	∈	∈	PROPN
ijassa-1225	200	3	[	[	X
ijassa-1225	200	4	a	a	X
ijassa-1225	200	5	,	,	PUNCT
ijassa-1225	200	6	b	b	NOUN
ijassa-1225	200	7	]	]	X
ijassa-1225	200	8	,	,	PUNCT
ijassa-1225	200	9	x	x	PROPN
ijassa-1225	200	10	∈	∈	PROPN
ijassa-1225	200	11	rn	rn	PROPN
ijassa-1225	200	12	,	,	PUNCT
ijassa-1225	200	13	v	v	PROPN
ijassa-1225	200	14	∈	∈	PROPN
ijassa-1225	200	15	b(t	b(t	NOUN
ijassa-1225	200	16	)	)	PUNCT
ijassa-1225	200	17	,	,	PUNCT
ijassa-1225	200	18	u	u	PROPN
ijassa-1225	200	19	∈	∈	PROPN
ijassa-1225	200	20	b(t	b(t	PROPN
ijassa-1225	200	21	)	)	PUNCT
ijassa-1225	200	22	}	}	PUNCT
ijassa-1225	200	23	and	and	CCONJ
ijassa-1225	200	24	define	define	VERB
ijassa-1225	200	25	fω	fω	X
ijassa-1225	200	26	:	:	PUNCT
ijassa-1225	200	27	ω→	ω→	NUM
ijassa-1225	200	28	c(rm	c(rm	NOUN
ijassa-1225	200	29	)	)	PUNCT
ijassa-1225	200	30	to	to	PART
ijassa-1225	200	31	be	be	AUX
ijassa-1225	200	32	the	the	DET
ijassa-1225	200	33	restriction	restriction	NOUN
ijassa-1225	200	34	of	of	ADP
ijassa-1225	200	35	the	the	DET
ijassa-1225	200	36	set	set	NOUN
ijassa-1225	200	37	-	-	PUNCT
ijassa-1225	200	38	valued	value	VERB
ijassa-1225	200	39	mapping	mapping	NOUN
ijassa-1225	200	40	f	f	NOUN
ijassa-1225	200	41	to	to	ADP
ijassa-1225	200	42	the	the	DET
ijassa-1225	200	43	set	set	PROPN
ijassa-1225	200	44	ω	ω	PROPN
ijassa-1225	200	45	.	.	PUNCT
ijassa-1225	200	46	theorem	theorem	VERB
ijassa-1225	200	47	4.1	4.1	NUM
ijassa-1225	200	48	:	:	PUNCT
ijassa-1225	200	49	let	let	VERB
ijassa-1225	200	50	a	a	DET
ijassa-1225	200	51	function	function	NOUN
ijassa-1225	200	52	v0	v0	NOUN
ijassa-1225	200	53	∈	∈	PROPN
ijassa-1225	200	54	ac(b	ac(b	NOUN
ijassa-1225	200	55	)	)	PUNCT
ijassa-1225	200	56	such	such	ADJ
ijassa-1225	200	57	that	that	DET
ijassa-1225	200	58	v0(a	v0(a	NUM
ijassa-1225	200	59	)	)	PUNCT
ijassa-1225	200	60	≥	≥	NOUN
ijassa-1225	200	61	γ	γ	PROPN
ijassa-1225	200	62	and	and	CCONJ
ijassa-1225	200	63	f	f	PROPN
ijassa-1225	200	64	(	(	PUNCT
ijassa-1225	200	65	t	t	PROPN
ijassa-1225	200	66	,	,	PUNCT
ijassa-1225	200	67	v0(t	v0(t	PROPN
ijassa-1225	200	68	)	)	PUNCT
ijassa-1225	200	69	,	,	PUNCT
ijassa-1225	200	70	v̇0(t	v̇0(t	PROPN
ijassa-1225	200	71	)	)	PUNCT
ijassa-1225	200	72	,	,	PUNCT
ijassa-1225	200	73	v̇0(t	v̇0(t	PROPN
ijassa-1225	200	74	)	)	PUNCT
ijassa-1225	200	75	)	)	PUNCT
ijassa-1225	200	76	∩	∩	PROPN
ijassa-1225	200	77	rn	rn	PROPN
ijassa-1225	200	78	+	+	PROPN
ijassa-1225	200	79	6=	6=	NOUN
ijassa-1225	200	80	∅	∅	NOUN
ijassa-1225	200	81	for	for	ADP
ijassa-1225	200	82	almost	almost	ADV
ijassa-1225	200	83	all	all	PRON
ijassa-1225	200	84	t	t	NOUN
ijassa-1225	200	85	∈	∈	PRON
ijassa-1225	201	1	[	[	X
ijassa-1225	201	2	a	a	X
ijassa-1225	201	3	,	,	PUNCT
ijassa-1225	201	4	b	b	NOUN
ijassa-1225	201	5	]	]	X
ijassa-1225	201	6	(	(	PUNCT
ijassa-1225	201	7	4.14	4.14	NUM
ijassa-1225	201	8	)	)	PUNCT
ijassa-1225	201	9	be	be	AUX
ijassa-1225	201	10	given	give	VERB
ijassa-1225	201	11	.	.	PUNCT
ijassa-1225	202	1	let	let	VERB
ijassa-1225	202	2	the	the	DET
ijassa-1225	202	3	set	set	NOUN
ijassa-1225	202	4	of	of	ADP
ijassa-1225	202	5	measurable	measurable	ADJ
ijassa-1225	202	6	selections	selection	NOUN
ijassa-1225	202	7	of	of	ADP
ijassa-1225	202	8	the	the	DET
ijassa-1225	202	9	set	set	NOUN
ijassa-1225	202	10	-	-	PUNCT
ijassa-1225	202	11	valued	value	VERB
ijassa-1225	202	12	mapping	mapping	NOUN
ijassa-1225	202	13	b	b	SYM
ijassa-1225	202	14	(	(	PUNCT
ijassa-1225	202	15	·	·	PUNCT
ijassa-1225	202	16	)	)	PUNCT
ijassa-1225	202	17	∩	∩	NOUN
ijassa-1225	202	18	orn	orn	X
ijassa-1225	202	19	(	(	PUNCT
ijassa-1225	202	20	v̇0	v̇0	PROPN
ijassa-1225	202	21	(	(	PUNCT
ijassa-1225	202	22	·	·	PUNCT
ijassa-1225	202	23	)	)	PUNCT
ijassa-1225	202	24	)	)	PUNCT
ijassa-1225	202	25	:	:	PUNCT
ijassa-1225	203	1	[	[	X
ijassa-1225	203	2	a	a	PRON
ijassa-1225	203	3	,	,	PUNCT
ijassa-1225	203	4	b]→	b]→	X
ijassa-1225	203	5	c(rn	c(rn	PROPN
ijassa-1225	203	6	)	)	PUNCT
ijassa-1225	203	7	be	be	AUX
ijassa-1225	203	8	integrally	integrally	ADV
ijassa-1225	203	9	bounded	bound	VERB
ijassa-1225	203	10	from	from	ADP
ijassa-1225	203	11	below	below	ADV
ijassa-1225	203	12	(	(	PUNCT
ijassa-1225	203	13	i.e.	i.e.	X
ijassa-1225	203	14	there	there	PRON
ijassa-1225	203	15	exists	exist	VERB
ijassa-1225	203	16	a	a	DET
ijassa-1225	203	17	number	number	NOUN
ijassa-1225	203	18	c	c	NOUN
ijassa-1225	203	19	such	such	ADJ
ijassa-1225	203	20	that	that	PRON
ijassa-1225	203	21	for	for	ADP
ijassa-1225	203	22	any	any	DET
ijassa-1225	203	23	measurable	measurable	ADJ
ijassa-1225	203	24	function	function	NOUN
ijassa-1225	203	25	u	u	PROPN
ijassa-1225	203	26	∈	∈	PROPN
ijassa-1225	203	27	w	w	PROPN
ijassa-1225	203	28	n	n	CCONJ
ijassa-1225	203	29	,	,	PUNCT
ijassa-1225	203	30	satisfying	satisfy	VERB
ijassa-1225	203	31	the	the	DET
ijassa-1225	203	32	relations	relation	NOUN
ijassa-1225	203	33	u(t	u(t	NOUN
ijassa-1225	203	34	)	)	PUNCT
ijassa-1225	203	35	∈	∈	PROPN
ijassa-1225	203	36	b(t	b(t	NOUN
ijassa-1225	203	37	)	)	PUNCT
ijassa-1225	203	38	and	and	CCONJ
ijassa-1225	203	39	u(t	u(t	NOUN
ijassa-1225	203	40	)	)	PUNCT
ijassa-1225	203	41	≤	≤	NOUN
ijassa-1225	203	42	v̇0(t	v̇0(t	PROPN
ijassa-1225	203	43	)	)	PUNCT
ijassa-1225	203	44	for	for	ADP
ijassa-1225	203	45	almost	almost	ADV
ijassa-1225	203	46	all	all	PRON
ijassa-1225	203	47	t	t	NOUN
ijassa-1225	203	48	∈	∈	PRON
ijassa-1225	204	1	[	[	X
ijassa-1225	204	2	a	a	X
ijassa-1225	204	3	,	,	PUNCT
ijassa-1225	204	4	b	b	NOUN
ijassa-1225	204	5	]	]	X
ijassa-1225	204	6	,	,	PUNCT
ijassa-1225	204	7	it	it	PRON
ijassa-1225	204	8	holds	hold	VERB
ijassa-1225	204	9	true	true	ADJ
ijassa-1225	204	10	that	that	SCONJ
ijassa-1225	204	11	∫	∫	PROPN
ijassa-1225	204	12	b	b	PROPN
ijassa-1225	204	13	a	a	DET
ijassa-1225	204	14	u(t)dt	u(t)dt	PROPN
ijassa-1225	204	15	≥	≥	NOUN
ijassa-1225	204	16	c	c	NOUN
ijassa-1225	204	17	)	)	PUNCT
ijassa-1225	204	18	and	and	CCONJ
ijassa-1225	204	19	the	the	DET
ijassa-1225	204	20	following	follow	VERB
ijassa-1225	204	21	conditions	condition	NOUN
ijassa-1225	204	22	are	be	AUX
ijassa-1225	204	23	fulfilled	fulfil	VERB
ijassa-1225	204	24	:	:	PUNCT
ijassa-1225	204	25	(	(	PUNCT
ijassa-1225	204	26	b1	b1	NOUN
ijassa-1225	204	27	)	)	PUNCT
ijassa-1225	204	28	for	for	ADP
ijassa-1225	204	29	almost	almost	ADV
ijassa-1225	204	30	all	all	PRON
ijassa-1225	204	31	t	t	NOUN
ijassa-1225	204	32	∈	∈	PRON
ijassa-1225	205	1	[	[	X
ijassa-1225	205	2	a	a	X
ijassa-1225	205	3	,	,	PUNCT
ijassa-1225	205	4	b	b	NOUN
ijassa-1225	205	5	]	]	X
ijassa-1225	205	6	,	,	PUNCT
ijassa-1225	205	7	any	any	DET
ijassa-1225	205	8	x	x	PROPN
ijassa-1225	205	9	∈	∈	PROPN
ijassa-1225	205	10	rn	rn	PROPN
ijassa-1225	205	11	and	and	CCONJ
ijassa-1225	205	12	v	v	ADP
ijassa-1225	205	13	∈	∈	PROPN
ijassa-1225	205	14	b(t	b(t	PROPN
ijassa-1225	205	15	)	)	PUNCT
ijassa-1225	205	16	,	,	PUNCT
ijassa-1225	206	1	the	the	DET
ijassa-1225	206	2	mapping	mapping	NOUN
ijassa-1225	206	3	fω(t	fω(t	VERB
ijassa-1225	206	4	,	,	PUNCT
ijassa-1225	206	5	x	x	NOUN
ijassa-1225	206	6	,	,	PUNCT
ijassa-1225	206	7	v	v	NOUN
ijassa-1225	206	8	,	,	PUNCT
ijassa-1225	206	9	·	·	PUNCT
ijassa-1225	206	10	)	)	PUNCT
ijassa-1225	206	11	:	:	PUNCT
ijassa-1225	206	12	b(t)→	b(t)→	ADV
ijassa-1225	206	13	k(rm	k(rm	NOUN
ijassa-1225	206	14	)	)	PUNCT
ijassa-1225	206	15	order	order	NOUN
ijassa-1225	206	16	covers	cover	VERB
ijassa-1225	206	17	the	the	DET
ijassa-1225	206	18	set	set	NOUN
ijassa-1225	206	19	{	{	PUNCT
ijassa-1225	206	20	0	0	NUM
ijassa-1225	206	21	}	}	PUNCT
ijassa-1225	206	22	⊂	⊂	PROPN
ijassa-1225	206	23	rm	rm	PROPN
ijassa-1225	206	24	;	;	PUNCT
ijassa-1225	206	25	(	(	PUNCT
ijassa-1225	206	26	b2	b2	NOUN
ijassa-1225	206	27	)	)	PUNCT
ijassa-1225	206	28	for	for	ADP
ijassa-1225	206	29	almost	almost	ADV
ijassa-1225	206	30	all	all	PRON
ijassa-1225	206	31	t	t	NOUN
ijassa-1225	206	32	∈	∈	PRON
ijassa-1225	207	1	[	[	X
ijassa-1225	207	2	a	a	X
ijassa-1225	207	3	,	,	PUNCT
ijassa-1225	207	4	b	b	NOUN
ijassa-1225	207	5	]	]	PUNCT
ijassa-1225	207	6	and	and	CCONJ
ijassa-1225	207	7	any	any	DET
ijassa-1225	207	8	u	u	PROPN
ijassa-1225	207	9	∈	∈	PROPN
ijassa-1225	207	10	b(t	b(t	PROPN
ijassa-1225	207	11	)	)	PUNCT
ijassa-1225	207	12	,	,	PUNCT
ijassa-1225	207	13	the	the	DET
ijassa-1225	207	14	mapping	mapping	NOUN
ijassa-1225	207	15	fω(t	fω(t	NOUN
ijassa-1225	207	16	,	,	PUNCT
ijassa-1225	207	17	·	·	PUNCT
ijassa-1225	207	18	,	,	PUNCT
ijassa-1225	207	19	·	·	PUNCT
ijassa-1225	207	20	,	,	PUNCT
ijassa-1225	207	21	u	u	NOUN
ijassa-1225	207	22	)	)	PUNCT
ijassa-1225	207	23	:	:	PUNCT
ijassa-1225	208	1	rn	rn	PROPN
ijassa-1225	208	2	×b(t)→	×b(t)→	PROPN
ijassa-1225	208	3	k(rm	k(rm	PROPN
ijassa-1225	208	4	)	)	PUNCT
ijassa-1225	208	5	is	be	AUX
ijassa-1225	208	6	antitone	antitone	ADJ
ijassa-1225	208	7	.	.	PUNCT
ijassa-1225	209	1	then	then	ADV
ijassa-1225	209	2	there	there	PRON
ijassa-1225	209	3	exists	exist	VERB
ijassa-1225	209	4	a	a	DET
ijassa-1225	209	5	solution	solution	NOUN
ijassa-1225	209	6	x	x	X
ijassa-1225	209	7	∈	∈	PROPN
ijassa-1225	209	8	ac(b	ac(b	NOUN
ijassa-1225	209	9	)	)	PUNCT
ijassa-1225	209	10	to	to	ADP
ijassa-1225	209	11	the	the	DET
ijassa-1225	209	12	problem	problem	NOUN
ijassa-1225	209	13	(	(	PUNCT
ijassa-1225	209	14	4.11	4.11	NUM
ijassa-1225	209	15	)	)	PUNCT
ijassa-1225	209	16	,	,	PUNCT
ijassa-1225	209	17	(	(	PUNCT
ijassa-1225	209	18	4.12	4.12	NUM
ijassa-1225	209	19	)	)	PUNCT
ijassa-1225	209	20	,	,	PUNCT
ijassa-1225	209	21	(	(	PUNCT
ijassa-1225	209	22	4.13	4.13	X
ijassa-1225	209	23	)	)	PUNCT
ijassa-1225	209	24	such	such	ADJ
ijassa-1225	209	25	that	that	DET
ijassa-1225	209	26	ẋ(t	ẋ(t	NOUN
ijassa-1225	209	27	)	)	PUNCT
ijassa-1225	209	28	≤	≤	NOUN
ijassa-1225	209	29	v̇0(t	v̇0(t	PROPN
ijassa-1225	209	30	)	)	PUNCT
ijassa-1225	209	31	for	for	ADP
ijassa-1225	209	32	almost	almost	ADV
ijassa-1225	209	33	all	all	PRON
ijassa-1225	209	34	t	t	NOUN
ijassa-1225	209	35	∈	∈	PRON
ijassa-1225	210	1	[	[	X
ijassa-1225	210	2	a	a	X
ijassa-1225	210	3	,	,	PUNCT
ijassa-1225	210	4	b	b	NOUN
ijassa-1225	210	5	]	]	PUNCT
ijassa-1225	210	6	.	.	PUNCT
ijassa-1225	211	1	proof	proof	NOUN
ijassa-1225	211	2	the	the	DET
ijassa-1225	211	3	problem	problem	NOUN
ijassa-1225	211	4	(	(	PUNCT
ijassa-1225	211	5	4.11	4.11	NUM
ijassa-1225	211	6	)	)	PUNCT
ijassa-1225	211	7	,	,	PUNCT
ijassa-1225	211	8	(	(	PUNCT
ijassa-1225	211	9	4.12	4.12	NUM
ijassa-1225	211	10	)	)	PUNCT
ijassa-1225	211	11	,	,	PUNCT
ijassa-1225	211	12	(	(	PUNCT
ijassa-1225	211	13	4.13	4.13	NUM
ijassa-1225	211	14	)	)	PUNCT
ijassa-1225	211	15	with	with	ADP
ijassa-1225	211	16	respect	respect	NOUN
ijassa-1225	211	17	to	to	ADP
ijassa-1225	211	18	the	the	DET
ijassa-1225	211	19	unknown	unknown	ADJ
ijassa-1225	211	20	function	function	NOUN
ijassa-1225	211	21	x	x	X
ijassa-1225	211	22	∈	∈	PROPN
ijassa-1225	211	23	ac(b	ac(b	NOUN
ijassa-1225	211	24	)	)	PUNCT
ijassa-1225	211	25	can	can	AUX
ijassa-1225	211	26	be	be	AUX
ijassa-1225	211	27	rewritten	rewrite	VERB
ijassa-1225	211	28	in	in	ADP
ijassa-1225	211	29	the	the	DET
ijassa-1225	211	30	form	form	NOUN
ijassa-1225	211	31	of	of	ADP
ijassa-1225	211	32	the	the	DET
ijassa-1225	211	33	following	follow	VERB
ijassa-1225	211	34	inclusion	inclusion	NOUN
ijassa-1225	211	35	fω	fω	X
ijassa-1225	211	36	(	(	PUNCT
ijassa-1225	211	37	t	t	PROPN
ijassa-1225	211	38	,	,	PUNCT
ijassa-1225	211	39	γ	γ	PROPN
ijassa-1225	211	40	+	+	PROPN
ijassa-1225	211	41	∫	∫	PROPN
ijassa-1225	211	42	t	t	PROPN
ijassa-1225	211	43	a	a	DET
ijassa-1225	211	44	u(s)ds	u(s)ds	PROPN
ijassa-1225	211	45	,	,	PUNCT
ijassa-1225	211	46	u(s	u(s	NUM
ijassa-1225	211	47	)	)	PUNCT
ijassa-1225	211	48	,	,	PUNCT
ijassa-1225	211	49	u(s	u(s	PROPN
ijassa-1225	211	50	)	)	PUNCT
ijassa-1225	211	51	)	)	PUNCT
ijassa-1225	211	52	3	3	NUM
ijassa-1225	211	53	0	0	NUM
ijassa-1225	211	54	,	,	PUNCT
ijassa-1225	211	55	t	t	PROPN
ijassa-1225	211	56	∈	∈	PROPN
ijassa-1225	212	1	[	[	X
ijassa-1225	212	2	a	a	X
ijassa-1225	212	3	,	,	PUNCT
ijassa-1225	212	4	b	b	NOUN
ijassa-1225	212	5	]	]	X
ijassa-1225	212	6	,	,	PUNCT
ijassa-1225	212	7	(	(	PUNCT
ijassa-1225	212	8	4.15	4.15	NUM
ijassa-1225	212	9	)	)	PUNCT
ijassa-1225	212	10	with	with	ADP
ijassa-1225	212	11	respect	respect	NOUN
ijassa-1225	212	12	to	to	ADP
ijassa-1225	212	13	the	the	DET
ijassa-1225	212	14	unknown	unknown	ADJ
ijassa-1225	212	15	function	function	NOUN
ijassa-1225	212	16	u	u	PROPN
ijassa-1225	212	17	=	=	PROPN
ijassa-1225	212	18	ẋ	ẋ	PROPN
ijassa-1225	212	19	∈	∈	PROPN
ijassa-1225	212	20	l(b	l(b	PROPN
ijassa-1225	212	21	)	)	PUNCT
ijassa-1225	212	22	.	.	PUNCT
ijassa-1225	213	1	let	let	VERB
ijassa-1225	213	2	us	we	PRON
ijassa-1225	213	3	demonstrate	demonstrate	VERB
ijassa-1225	213	4	that	that	SCONJ
ijassa-1225	213	5	the	the	DET
ijassa-1225	213	6	inclusion	inclusion	NOUN
ijassa-1225	213	7	(	(	PUNCT
ijassa-1225	213	8	4.15	4.15	NUM
ijassa-1225	213	9	)	)	PUNCT
ijassa-1225	213	10	can	can	AUX
ijassa-1225	213	11	be	be	AUX
ijassa-1225	213	12	represented	represent	VERB
ijassa-1225	213	13	in	in	ADP
ijassa-1225	213	14	the	the	DET
ijassa-1225	213	15	form	form	NOUN
ijassa-1225	213	16	of	of	ADP
ijassa-1225	213	17	the	the	DET
ijassa-1225	213	18	operator	operator	NOUN
ijassa-1225	213	19	inclusion	inclusion	NOUN
ijassa-1225	213	20	(	(	PUNCT
ijassa-1225	213	21	2.3	2.3	NUM
ijassa-1225	213	22	)	)	PUNCT
ijassa-1225	213	23	,	,	PUNCT
ijassa-1225	213	24	that	that	PRON
ijassa-1225	213	25	can	can	AUX
ijassa-1225	213	26	be	be	AUX
ijassa-1225	213	27	investigated	investigate	VERB
ijassa-1225	213	28	using	use	VERB
ijassa-1225	213	29	theorem	theorem	NOUN
ijassa-1225	213	30	2.1	2.1	NUM
ijassa-1225	213	31	.	.	PUNCT
ijassa-1225	214	1	according	accord	VERB
ijassa-1225	214	2	to	to	ADP
ijassa-1225	214	3	[	[	X
ijassa-1225	214	4	24	24	NUM
ijassa-1225	214	5	,	,	PUNCT
ijassa-1225	214	6	theorem	theorem	VERB
ijassa-1225	214	7	2.1	2.1	NUM
ijassa-1225	214	8	]	]	PUNCT
ijassa-1225	214	9	,	,	PUNCT
ijassa-1225	214	10	the	the	DET
ijassa-1225	214	11	assumptions	assumption	NOUN
ijassa-1225	214	12	made	make	VERB
ijassa-1225	214	13	for	for	ADP
ijassa-1225	214	14	the	the	DET
ijassa-1225	214	15	set	set	NOUN
ijassa-1225	214	16	-	-	PUNCT
ijassa-1225	214	17	valued	value	VERB
ijassa-1225	214	18	function	function	NOUN
ijassa-1225	214	19	f	f	PRON
ijassa-1225	214	20	provide	provide	VERB
ijassa-1225	214	21	its	its	PRON
ijassa-1225	214	22	superpositional	superpositional	ADJ
ijassa-1225	214	23	measurability	measurability	NOUN
ijassa-1225	214	24	,	,	PUNCT
ijassa-1225	214	25	hence	hence	ADV
ijassa-1225	214	26	,	,	PUNCT
ijassa-1225	214	27	for	for	ADP
ijassa-1225	214	28	any	any	DET
ijassa-1225	214	29	x	x	PROPN
ijassa-1225	214	30	∈	∈	PROPN
ijassa-1225	214	31	acn	acn	PROPN
ijassa-1225	214	32	,	,	PUNCT
ijassa-1225	214	33	the	the	DET
ijassa-1225	214	34	set	set	NOUN
ijassa-1225	214	35	-	-	PUNCT
ijassa-1225	214	36	valued	value	VERB
ijassa-1225	214	37	function	function	NOUN
ijassa-1225	214	38	f	f	PROPN
ijassa-1225	214	39	(	(	PUNCT
ijassa-1225	214	40	·	·	PUNCT
ijassa-1225	214	41	,	,	PUNCT
ijassa-1225	214	42	x	x	X
ijassa-1225	214	43	(	(	PUNCT
ijassa-1225	214	44	·	·	PUNCT
ijassa-1225	214	45	)	)	PUNCT
ijassa-1225	214	46	,	,	PUNCT
ijassa-1225	214	47	ẋ	ẋ	PROPN
ijassa-1225	214	48	(	(	PUNCT
ijassa-1225	214	49	·	·	PUNCT
ijassa-1225	214	50	)	)	PUNCT
ijassa-1225	214	51	,	,	PUNCT
ijassa-1225	214	52	ẋ	ẋ	PROPN
ijassa-1225	214	53	(	(	PUNCT
ijassa-1225	214	54	·	·	PUNCT
ijassa-1225	214	55	)	)	PUNCT
ijassa-1225	214	56	)	)	PUNCT
ijassa-1225	214	57	:	:	PUNCT
ijassa-1225	215	1	[	[	X
ijassa-1225	215	2	a	a	PRON
ijassa-1225	215	3	,	,	PUNCT
ijassa-1225	215	4	b]→	b]→	ADJ
ijassa-1225	215	5	k(rm	k(rm	NOUN
ijassa-1225	215	6	)	)	PUNCT
ijassa-1225	215	7	is	be	AUX
ijassa-1225	215	8	measurable	measurable	ADJ
ijassa-1225	215	9	.	.	PUNCT
ijassa-1225	216	1	superpositional	superpositional	ADJ
ijassa-1225	216	2	measurability	measurability	NOUN
ijassa-1225	216	3	of	of	ADP
ijassa-1225	216	4	f	f	PROPN
ijassa-1225	216	5	allows	allow	VERB
ijassa-1225	216	6	to	to	PART
ijassa-1225	216	7	define	define	VERB
ijassa-1225	216	8	the	the	DET
ijassa-1225	216	9	mapping	mapping	NOUN
ijassa-1225	216	10	υ	υ	NOUN
ijassa-1225	216	11	:	:	PUNCT
ijassa-1225	216	12	l(b)×	l(b)×	PROPN
ijassa-1225	216	13	l(b	l(b	PROPN
ijassa-1225	216	14	)	)	PUNCT
ijassa-1225	216	15	⇒	⇒	PROPN
ijassa-1225	216	16	wm	wm	PROPN
ijassa-1225	216	17	,	,	PUNCT
ijassa-1225	216	18	∀u	∀u	NOUN
ijassa-1225	216	19	,	,	PUNCT
ijassa-1225	216	20	v	v	PROPN
ijassa-1225	216	21	∈	∈	PROPN
ijassa-1225	216	22	l(b	l(b	PROPN
ijassa-1225	216	23	)	)	PUNCT
ijassa-1225	216	24	υ(u	υ(u	NUM
ijassa-1225	216	25	,	,	PUNCT
ijassa-1225	216	26	v	v	NOUN
ijassa-1225	216	27	)	)	PUNCT
ijassa-1225	216	28	.	.	PUNCT
ijassa-1225	217	1	=	=	PRON
ijassa-1225	217	2	fω	fω	PROPN
ijassa-1225	217	3	(	(	PUNCT
ijassa-1225	217	4	t	t	PROPN
ijassa-1225	217	5	,	,	PUNCT
ijassa-1225	217	6	γ	γ	PROPN
ijassa-1225	217	7	+	+	PROPN
ijassa-1225	217	8	∫	∫	PROPN
ijassa-1225	217	9	t	t	PROPN
ijassa-1225	218	1	a	a	PRON
ijassa-1225	218	2	v(s)ds	v(s)ds	PROPN
ijassa-1225	218	3	,	,	PUNCT
ijassa-1225	218	4	v(t	v(t	NOUN
ijassa-1225	218	5	)	)	PUNCT
ijassa-1225	218	6	,	,	PUNCT
ijassa-1225	218	7	u(t	u(t	NOUN
ijassa-1225	218	8	)	)	PUNCT
ijassa-1225	218	9	)	)	PUNCT
ijassa-1225	218	10	,	,	PUNCT
ijassa-1225	218	11	t	t	PROPN
ijassa-1225	218	12	∈	∈	PROPN
ijassa-1225	219	1	[	[	X
ijassa-1225	219	2	a	a	X
ijassa-1225	219	3	,	,	PUNCT
ijassa-1225	219	4	b	b	NOUN
ijassa-1225	219	5	]	]	X
ijassa-1225	219	6	,	,	PUNCT
ijassa-1225	219	7	(	(	PUNCT
ijassa-1225	219	8	4.16	4.16	NUM
ijassa-1225	219	9	)	)	PUNCT
ijassa-1225	219	10	copyright	copyright	NOUN
ijassa-1225	219	11	©	©	PROPN
ijassa-1225	219	12	2022	2022	NUM
ijassa-1225	219	13	assa	assa	NOUN
ijassa-1225	219	14	.	.	PUNCT
ijassa-1225	220	1	adv	adv	PROPN
ijassa-1225	220	2	syst	syst	PROPN
ijassa-1225	220	3	sci	sci	PROPN
ijassa-1225	220	4	appl	appl	PROPN
ijassa-1225	220	5	(	(	PUNCT
ijassa-1225	220	6	2022	2022	NUM
ijassa-1225	220	7	)	)	PUNCT
ijassa-1225	220	8	on	on	ADP
ijassa-1225	220	9	order	order	NOUN
ijassa-1225	220	10	covering	cover	VERB
ijassa-1225	220	11	set	set	NOUN
ijassa-1225	220	12	-	-	PUNCT
ijassa-1225	220	13	valued	value	VERB
ijassa-1225	220	14	mappings	mapping	NOUN
ijassa-1225	220	15	and	and	CCONJ
ijassa-1225	220	16	their	their	PRON
ijassa-1225	220	17	applications	application	NOUN
ijassa-1225	220	18	183	183	NUM
ijassa-1225	220	19	and	and	CCONJ
ijassa-1225	220	20	the	the	DET
ijassa-1225	220	21	corresponding	correspond	VERB
ijassa-1225	220	22	mapping	mapping	NOUN
ijassa-1225	220	23	f	f	X
ijassa-1225	220	24	:	:	PUNCT
ijassa-1225	220	25	l(b	l(b	PROPN
ijassa-1225	220	26	)	)	PUNCT
ijassa-1225	220	27	⇒	⇒	PROPN
ijassa-1225	220	28	wm	wm	PROPN
ijassa-1225	220	29	,	,	PUNCT
ijassa-1225	220	30	f	f	PROPN
ijassa-1225	220	31	(	(	PUNCT
ijassa-1225	220	32	u	u	NOUN
ijassa-1225	220	33	)	)	PUNCT
ijassa-1225	220	34	.	.	PUNCT
ijassa-1225	221	1	=	=	PUNCT
ijassa-1225	221	2	υ(u	υ(u	NUM
ijassa-1225	221	3	,	,	PUNCT
ijassa-1225	221	4	u	u	NOUN
ijassa-1225	221	5	)	)	PUNCT
ijassa-1225	221	6	.	.	PUNCT
ijassa-1225	222	1	let	let	VERB
ijassa-1225	222	2	us	we	PRON
ijassa-1225	222	3	verify	verify	VERB
ijassa-1225	222	4	the	the	DET
ijassa-1225	222	5	conditions	condition	NOUN
ijassa-1225	222	6	of	of	ADP
ijassa-1225	222	7	theorem	theorem	ADJ
ijassa-1225	222	8	2.1	2.1	NUM
ijassa-1225	222	9	(	(	PUNCT
ijassa-1225	222	10	where	where	SCONJ
ijassa-1225	222	11	we	we	PRON
ijassa-1225	222	12	put	put	VERB
ijassa-1225	222	13	ŷ	ŷ	X
ijassa-1225	222	14	=	=	SYM
ijassa-1225	222	15	0	0	SYM
ijassa-1225	222	16	∈	∈	PROPN
ijassa-1225	222	17	wm	wm	PROPN
ijassa-1225	222	18	)	)	PUNCT
ijassa-1225	222	19	for	for	ADP
ijassa-1225	222	20	these	these	DET
ijassa-1225	222	21	mappings	mapping	NOUN
ijassa-1225	222	22	.	.	PUNCT
ijassa-1225	223	1	first	first	ADV
ijassa-1225	223	2	of	of	ADP
ijassa-1225	223	3	all	all	PRON
ijassa-1225	223	4	,	,	PUNCT
ijassa-1225	223	5	there	there	PRON
ijassa-1225	223	6	exists	exist	VERB
ijassa-1225	223	7	a	a	DET
ijassa-1225	223	8	measurable	measurable	ADJ
ijassa-1225	223	9	function	function	NOUN
ijassa-1225	223	10	y	y	PROPN
ijassa-1225	223	11	∈	∈	PROPN
ijassa-1225	223	12	wm	wm	X
ijassa-1225	223	13	satisfying	satisfy	VERB
ijassa-1225	223	14	the	the	DET
ijassa-1225	223	15	relations	relation	NOUN
ijassa-1225	223	16	y(t	y(t	NUM
ijassa-1225	223	17	)	)	PUNCT
ijassa-1225	224	1	∈	∈	PROPN
ijassa-1225	224	2	f	f	X
ijassa-1225	224	3	(	(	PUNCT
ijassa-1225	224	4	t	t	PROPN
ijassa-1225	224	5	,	,	PUNCT
ijassa-1225	224	6	v0(a	v0(a	PROPN
ijassa-1225	224	7	)	)	PUNCT
ijassa-1225	224	8	+	+	NUM
ijassa-1225	224	9	∫	∫	PROPN
ijassa-1225	224	10	t	t	PROPN
ijassa-1225	224	11	a	a	DET
ijassa-1225	224	12	v̇0(s)ds	v̇0(s)ds	NOUN
ijassa-1225	224	13	,	,	PUNCT
ijassa-1225	224	14	v̇0(t	v̇0(t	PROPN
ijassa-1225	224	15	)	)	PUNCT
ijassa-1225	224	16	,	,	PUNCT
ijassa-1225	224	17	v̇0(t	v̇0(t	PROPN
ijassa-1225	224	18	)	)	PUNCT
ijassa-1225	224	19	)	)	PUNCT
ijassa-1225	225	1	=	=	SYM
ijassa-1225	225	2	fω	fω	PROPN
ijassa-1225	225	3	(	(	PUNCT
ijassa-1225	225	4	t	t	PROPN
ijassa-1225	225	5	,	,	PUNCT
ijassa-1225	225	6	v0(a	v0(a	PROPN
ijassa-1225	225	7	)	)	PUNCT
ijassa-1225	225	8	+	+	NUM
ijassa-1225	225	9	∫	∫	PROPN
ijassa-1225	225	10	t	t	PROPN
ijassa-1225	225	11	a	a	DET
ijassa-1225	225	12	v̇0(s)ds	v̇0(s)ds	NOUN
ijassa-1225	225	13	,	,	PUNCT
ijassa-1225	225	14	v̇0(t	v̇0(t	PROPN
ijassa-1225	225	15	)	)	PUNCT
ijassa-1225	225	16	,	,	PUNCT
ijassa-1225	225	17	v̇0(t	v̇0(t	PROPN
ijassa-1225	225	18	)	)	PUNCT
ijassa-1225	225	19	)	)	PUNCT
ijassa-1225	225	20	,	,	PUNCT
ijassa-1225	225	21	y(t	y(t	NUM
ijassa-1225	225	22	)	)	PUNCT
ijassa-1225	225	23	≥	≥	NOUN
ijassa-1225	225	24	0	0	NUM
ijassa-1225	225	25	for	for	ADP
ijassa-1225	225	26	almost	almost	ADV
ijassa-1225	225	27	all	all	PRON
ijassa-1225	225	28	t	t	NOUN
ijassa-1225	225	29	∈	∈	PRON
ijassa-1225	226	1	[	[	X
ijassa-1225	226	2	a	a	X
ijassa-1225	226	3	,	,	PUNCT
ijassa-1225	226	4	b	b	NOUN
ijassa-1225	226	5	]	]	X
ijassa-1225	226	6	.	.	PUNCT
ijassa-1225	227	1	these	these	DET
ijassa-1225	227	2	relations	relation	NOUN
ijassa-1225	227	3	,	,	PUNCT
ijassa-1225	227	4	according	accord	VERB
ijassa-1225	227	5	to	to	ADP
ijassa-1225	227	6	(	(	PUNCT
ijassa-1225	227	7	b2	b2	NOUN
ijassa-1225	227	8	)	)	PUNCT
ijassa-1225	227	9	,	,	PUNCT
ijassa-1225	227	10	imply	imply	VERB
ijassa-1225	227	11	the	the	DET
ijassa-1225	227	12	existence	existence	NOUN
ijassa-1225	227	13	of	of	ADP
ijassa-1225	227	14	a	a	DET
ijassa-1225	227	15	measurable	measurable	ADJ
ijassa-1225	227	16	function	function	NOUN
ijassa-1225	227	17	y0	y0	PROPN
ijassa-1225	227	18	∈	∈	PROPN
ijassa-1225	227	19	wm	wm	ADP
ijassa-1225	227	20	such	such	ADJ
ijassa-1225	227	21	that	that	PRON
ijassa-1225	227	22	y0(t	y0(t	NOUN
ijassa-1225	227	23	)	)	PUNCT
ijassa-1225	227	24	∈	∈	PROPN
ijassa-1225	227	25	fω	fω	PROPN
ijassa-1225	227	26	(	(	PUNCT
ijassa-1225	227	27	t	t	PROPN
ijassa-1225	227	28	,	,	PUNCT
ijassa-1225	227	29	γ	γ	PROPN
ijassa-1225	227	30	+	+	PROPN
ijassa-1225	227	31	∫	∫	PROPN
ijassa-1225	227	32	t	t	PROPN
ijassa-1225	227	33	a	a	DET
ijassa-1225	227	34	v̇0(s)ds	v̇0(s)ds	NOUN
ijassa-1225	227	35	,	,	PUNCT
ijassa-1225	227	36	v̇0(t	v̇0(t	PROPN
ijassa-1225	227	37	)	)	PUNCT
ijassa-1225	227	38	,	,	PUNCT
ijassa-1225	227	39	v̇0(t	v̇0(t	PROPN
ijassa-1225	227	40	)	)	PUNCT
ijassa-1225	227	41	)	)	PUNCT
ijassa-1225	227	42	,	,	PUNCT
ijassa-1225	227	43	y0(t	y0(t	X
ijassa-1225	227	44	)	)	PUNCT
ijassa-1225	227	45	≥	≥	NOUN
ijassa-1225	227	46	y(t	y(t	PROPN
ijassa-1225	227	47	)	)	PUNCT
ijassa-1225	227	48	≥	≥	NOUN
ijassa-1225	227	49	0	0	NUM
ijassa-1225	227	50	for	for	ADP
ijassa-1225	227	51	almost	almost	ADV
ijassa-1225	227	52	all	all	PRON
ijassa-1225	227	53	t	t	NOUN
ijassa-1225	227	54	∈	∈	PRON
ijassa-1225	227	55	[	[	X
ijassa-1225	227	56	a	a	X
ijassa-1225	227	57	,	,	PUNCT
ijassa-1225	227	58	b	b	NOUN
ijassa-1225	227	59	]	]	X
ijassa-1225	227	60	.	.	PUNCT
ijassa-1225	228	1	thus	thus	ADV
ijassa-1225	228	2	,	,	PUNCT
ijassa-1225	228	3	for	for	ADP
ijassa-1225	228	4	the	the	DET
ijassa-1225	228	5	mapping	mapping	NOUN
ijassa-1225	228	6	υ	υ	NOUN
ijassa-1225	228	7	defined	define	VERB
ijassa-1225	228	8	by	by	ADP
ijassa-1225	228	9	(	(	PUNCT
ijassa-1225	228	10	4.16	4.16	NUM
ijassa-1225	228	11	)	)	PUNCT
ijassa-1225	228	12	,	,	PUNCT
ijassa-1225	228	13	we	we	PRON
ijassa-1225	228	14	have	have	AUX
ijassa-1225	228	15	υ(v̇0	υ(v̇0	VERB
ijassa-1225	228	16	,	,	PUNCT
ijassa-1225	228	17	v̇0	v̇0	NOUN
ijassa-1225	228	18	)	)	PUNCT
ijassa-1225	228	19	3	3	NUM
ijassa-1225	228	20	y0	y0	NOUN
ijassa-1225	228	21	,	,	PUNCT
ijassa-1225	228	22	y0	y0	PROPN
ijassa-1225	228	23	≥	≥	NOUN
ijassa-1225	228	24	0	0	NUM
ijassa-1225	228	25	,	,	PUNCT
ijassa-1225	228	26	i.e.	i.e.	X
ijassa-1225	228	27	the	the	DET
ijassa-1225	228	28	relations	relation	NOUN
ijassa-1225	228	29	(	(	PUNCT
ijassa-1225	228	30	2.5	2.5	NUM
ijassa-1225	228	31	)	)	PUNCT
ijassa-1225	228	32	where	where	SCONJ
ijassa-1225	228	33	u0	u0	ADJ
ijassa-1225	228	34	=	=	PROPN
ijassa-1225	228	35	v̇0	v̇0	PROPN
ijassa-1225	228	36	∈	∈	PROPN
ijassa-1225	228	37	l(b	l(b	PROPN
ijassa-1225	228	38	)	)	PUNCT
ijassa-1225	228	39	are	be	AUX
ijassa-1225	228	40	fulfilled	fulfil	VERB
ijassa-1225	228	41	.	.	PUNCT
ijassa-1225	229	1	secondly	secondly	ADV
ijassa-1225	229	2	,	,	PUNCT
ijassa-1225	229	3	for	for	ADP
ijassa-1225	229	4	any	any	DET
ijassa-1225	229	5	v	v	NUM
ijassa-1225	229	6	∈	∈	PROPN
ijassa-1225	229	7	l(b	l(b	PROPN
ijassa-1225	229	8	)	)	PUNCT
ijassa-1225	229	9	,	,	PUNCT
ijassa-1225	229	10	the	the	DET
ijassa-1225	229	11	mapping	mapping	NOUN
ijassa-1225	229	12	υ	υ	NOUN
ijassa-1225	229	13	(	(	PUNCT
ijassa-1225	229	14	·	·	PUNCT
ijassa-1225	229	15	,	,	PUNCT
ijassa-1225	229	16	v	v	NOUN
ijassa-1225	229	17	)	)	PUNCT
ijassa-1225	229	18	:	:	PUNCT
ijassa-1225	229	19	l(b	l(b	PROPN
ijassa-1225	229	20	)	)	PUNCT
ijassa-1225	229	21	⇒	⇒	PROPN
ijassa-1225	229	22	wm	wm	PROPN
ijassa-1225	229	23	is	be	AUX
ijassa-1225	229	24	the	the	DET
ijassa-1225	229	25	nemytskii	nemytskii	ADJ
ijassa-1225	229	26	operator	operator	NOUN
ijassa-1225	229	27	generated	generate	VERB
ijassa-1225	229	28	by	by	ADP
ijassa-1225	229	29	the	the	DET
ijassa-1225	229	30	restriction	restriction	NOUN
ijassa-1225	229	31	g∆	g∆	NOUN
ijassa-1225	229	32	to	to	ADP
ijassa-1225	229	33	the	the	DET
ijassa-1225	229	34	set	set	NOUN
ijassa-1225	229	35	∆	∆	X
ijassa-1225	229	36	=	=	PRON
ijassa-1225	229	37	{	{	PUNCT
ijassa-1225	229	38	(	(	PUNCT
ijassa-1225	229	39	t	t	PROPN
ijassa-1225	229	40	,	,	PUNCT
ijassa-1225	229	41	u	u	NOUN
ijassa-1225	229	42	)	)	PUNCT
ijassa-1225	229	43	:	:	PUNCT
ijassa-1225	229	44	t	t	PROPN
ijassa-1225	229	45	∈	∈	PROPN
ijassa-1225	230	1	[	[	X
ijassa-1225	230	2	a	a	X
ijassa-1225	230	3	,	,	PUNCT
ijassa-1225	230	4	b	b	NOUN
ijassa-1225	230	5	]	]	X
ijassa-1225	230	6	,	,	PUNCT
ijassa-1225	230	7	u	u	PROPN
ijassa-1225	230	8	∈	∈	PROPN
ijassa-1225	230	9	b(t	b(t	PROPN
ijassa-1225	230	10	)	)	PUNCT
ijassa-1225	230	11	}	}	PUNCT
ijassa-1225	230	12	of	of	ADP
ijassa-1225	230	13	the	the	DET
ijassa-1225	230	14	function	function	NOUN
ijassa-1225	230	15	g	g	NOUN
ijassa-1225	230	16	:	:	PUNCT
ijassa-1225	230	17	[	[	X
ijassa-1225	230	18	a	a	X
ijassa-1225	230	19	,	,	PUNCT
ijassa-1225	230	20	b]×	b]×	NOUN
ijassa-1225	230	21	rn	rn	PROPN
ijassa-1225	230	22	→	→	SYM
ijassa-1225	230	23	k(rm	k(rm	PROPN
ijassa-1225	230	24	)	)	PUNCT
ijassa-1225	230	25	,	,	PUNCT
ijassa-1225	230	26	g(t	g(t	PROPN
ijassa-1225	230	27	,	,	PUNCT
ijassa-1225	230	28	u	u	NOUN
ijassa-1225	230	29	)	)	PUNCT
ijassa-1225	230	30	.	.	PUNCT
ijassa-1225	231	1	=	=	PRON
ijassa-1225	231	2	fω	fω	PROPN
ijassa-1225	231	3	(	(	PUNCT
ijassa-1225	231	4	t	t	PROPN
ijassa-1225	231	5	,	,	PUNCT
ijassa-1225	231	6	γ	γ	PROPN
ijassa-1225	231	7	+	+	PROPN
ijassa-1225	231	8	∫	∫	PROPN
ijassa-1225	231	9	t	t	PROPN
ijassa-1225	231	10	a	a	DET
ijassa-1225	231	11	v(s)ds	v(s)ds	PROPN
ijassa-1225	231	12	,	,	PUNCT
ijassa-1225	231	13	v(t	v(t	NOUN
ijassa-1225	231	14	)	)	PUNCT
ijassa-1225	231	15	,	,	PUNCT
ijassa-1225	231	16	u	u	NOUN
ijassa-1225	231	17	)	)	PUNCT
ijassa-1225	231	18	for	for	ADP
ijassa-1225	231	19	almost	almost	ADV
ijassa-1225	231	20	all	all	PRON
ijassa-1225	231	21	t	t	NOUN
ijassa-1225	231	22	∈	∈	PRON
ijassa-1225	232	1	[	[	X
ijassa-1225	232	2	a	a	X
ijassa-1225	232	3	,	,	PUNCT
ijassa-1225	232	4	b	b	NOUN
ijassa-1225	232	5	]	]	PUNCT
ijassa-1225	232	6	and	and	CCONJ
ijassa-1225	232	7	any	any	DET
ijassa-1225	232	8	u	u	PROPN
ijassa-1225	232	9	∈	∈	PROPN
ijassa-1225	232	10	rn	rn	PROPN
ijassa-1225	232	11	.	.	PUNCT
ijassa-1225	233	1	the	the	DET
ijassa-1225	233	2	assumption	assumption	NOUN
ijassa-1225	233	3	(	(	PUNCT
ijassa-1225	233	4	b1	b1	NOUN
ijassa-1225	233	5	)	)	PUNCT
ijassa-1225	233	6	implies	imply	VERB
ijassa-1225	233	7	that	that	SCONJ
ijassa-1225	233	8	for	for	ADP
ijassa-1225	233	9	almost	almost	ADV
ijassa-1225	233	10	all	all	PRON
ijassa-1225	233	11	t	t	NOUN
ijassa-1225	233	12	∈	∈	PRON
ijassa-1225	234	1	[	[	X
ijassa-1225	234	2	a	a	X
ijassa-1225	234	3	,	,	PUNCT
ijassa-1225	234	4	b	b	NOUN
ijassa-1225	234	5	]	]	X
ijassa-1225	234	6	,	,	PUNCT
ijassa-1225	234	7	the	the	DET
ijassa-1225	234	8	function	function	NOUN
ijassa-1225	234	9	g∆(t	g∆(t	NOUN
ijassa-1225	234	10	,	,	PUNCT
ijassa-1225	234	11	·	·	PUNCT
ijassa-1225	234	12	)	)	PUNCT
ijassa-1225	234	13	:	:	PUNCT
ijassa-1225	234	14	b(t)→	b(t)→	ADV
ijassa-1225	234	15	k(rm	k(rm	NOUN
ijassa-1225	234	16	)	)	PUNCT
ijassa-1225	234	17	order	order	NOUN
ijassa-1225	234	18	covers	cover	VERB
ijassa-1225	234	19	the	the	DET
ijassa-1225	234	20	set	set	NOUN
ijassa-1225	234	21	{	{	PUNCT
ijassa-1225	234	22	0	0	NUM
ijassa-1225	234	23	}	}	PUNCT
ijassa-1225	234	24	∈	∈	PROPN
ijassa-1225	234	25	rm	rm	NOUN
ijassa-1225	234	26	.	.	PUNCT
ijassa-1225	235	1	according	accord	VERB
ijassa-1225	235	2	to	to	ADP
ijassa-1225	235	3	theorem	theorem	ADJ
ijassa-1225	235	4	3.1	3.1	NUM
ijassa-1225	235	5	,	,	PUNCT
ijassa-1225	235	6	for	for	ADP
ijassa-1225	235	7	any	any	DET
ijassa-1225	235	8	v	v	NUM
ijassa-1225	235	9	∈	∈	PROPN
ijassa-1225	235	10	l(b	l(b	PROPN
ijassa-1225	235	11	)	)	PUNCT
ijassa-1225	235	12	,	,	PUNCT
ijassa-1225	235	13	the	the	DET
ijassa-1225	235	14	mapping	mapping	NOUN
ijassa-1225	235	15	υ	υ	NOUN
ijassa-1225	235	16	(	(	PUNCT
ijassa-1225	235	17	·	·	PUNCT
ijassa-1225	235	18	,	,	PUNCT
ijassa-1225	235	19	v	v	NOUN
ijassa-1225	235	20	)	)	PUNCT
ijassa-1225	235	21	order	order	NOUN
ijassa-1225	235	22	covers	cover	VERB
ijassa-1225	235	23	the	the	DET
ijassa-1225	235	24	set	set	NOUN
ijassa-1225	235	25	{	{	PUNCT
ijassa-1225	235	26	0	0	NUM
ijassa-1225	235	27	}	}	PUNCT
ijassa-1225	235	28	∈	∈	PROPN
ijassa-1225	235	29	wm	wm	PROPN
ijassa-1225	235	30	.	.	PUNCT
ijassa-1225	236	1	thus	thus	ADV
ijassa-1225	236	2	,	,	PUNCT
ijassa-1225	236	3	the	the	DET
ijassa-1225	236	4	condition	condition	NOUN
ijassa-1225	236	5	(	(	PUNCT
ijassa-1225	236	6	a1	a1	PROPN
ijassa-1225	236	7	)	)	PUNCT
ijassa-1225	236	8	of	of	ADP
ijassa-1225	236	9	theorem	theorem	ADJ
ijassa-1225	236	10	2.1	2.1	NUM
ijassa-1225	236	11	is	be	AUX
ijassa-1225	236	12	satisfied	satisfied	ADJ
ijassa-1225	236	13	.	.	PUNCT
ijassa-1225	237	1	next	next	ADV
ijassa-1225	237	2	,	,	PUNCT
ijassa-1225	237	3	due	due	ADP
ijassa-1225	237	4	to	to	ADP
ijassa-1225	237	5	the	the	DET
ijassa-1225	237	6	assumption	assumption	NOUN
ijassa-1225	237	7	(	(	PUNCT
ijassa-1225	237	8	b2	b2	NOUN
ijassa-1225	237	9	)	)	PUNCT
ijassa-1225	237	10	,	,	PUNCT
ijassa-1225	237	11	for	for	ADP
ijassa-1225	237	12	any	any	DET
ijassa-1225	237	13	u	u	PROPN
ijassa-1225	237	14	∈	∈	PROPN
ijassa-1225	237	15	l(b	l(b	PROPN
ijassa-1225	237	16	)	)	PUNCT
ijassa-1225	237	17	,	,	PUNCT
ijassa-1225	237	18	the	the	DET
ijassa-1225	237	19	mapping	mapping	NOUN
ijassa-1225	237	20	υ(u	υ(u	PROPN
ijassa-1225	237	21	,	,	PUNCT
ijassa-1225	237	22	·	·	PUNCT
ijassa-1225	237	23	)	)	PUNCT
ijassa-1225	237	24	:	:	PUNCT
ijassa-1225	237	25	l(b	l(b	PROPN
ijassa-1225	237	26	)	)	PUNCT
ijassa-1225	237	27	⇒	⇒	PROPN
ijassa-1225	237	28	wm	wm	PROPN
ijassa-1225	237	29	is	be	AUX
ijassa-1225	237	30	antitone	antitone	ADJ
ijassa-1225	237	31	,	,	PUNCT
ijassa-1225	237	32	so	so	CCONJ
ijassa-1225	237	33	the	the	DET
ijassa-1225	237	34	condition	condition	NOUN
ijassa-1225	237	35	(	(	PUNCT
ijassa-1225	237	36	a2	a2	PROPN
ijassa-1225	237	37	)	)	PUNCT
ijassa-1225	237	38	of	of	ADP
ijassa-1225	237	39	theorem	theorem	ADJ
ijassa-1225	237	40	2.1	2.1	NUM
ijassa-1225	237	41	is	be	AUX
ijassa-1225	237	42	fulfilled	fulfil	VERB
ijassa-1225	237	43	as	as	ADV
ijassa-1225	237	44	well	well	ADV
ijassa-1225	237	45	.	.	PUNCT
ijassa-1225	238	1	in	in	ADP
ijassa-1225	238	2	order	order	NOUN
ijassa-1225	238	3	to	to	PART
ijassa-1225	238	4	verify	verify	VERB
ijassa-1225	238	5	the	the	DET
ijassa-1225	238	6	assumption	assumption	NOUN
ijassa-1225	238	7	(	(	PUNCT
ijassa-1225	238	8	a1	a1	NOUN
ijassa-1225	238	9	)	)	PUNCT
ijassa-1225	238	10	of	of	ADP
ijassa-1225	238	11	theorem	theorem	NOUN
ijassa-1225	238	12	2.1	2.1	NUM
ijassa-1225	238	13	,	,	PUNCT
ijassa-1225	238	14	we	we	PRON
ijassa-1225	238	15	consider	consider	VERB
ijassa-1225	238	16	an	an	DET
ijassa-1225	238	17	arbitrary	arbitrary	ADJ
ijassa-1225	238	18	chain	chain	NOUN
ijassa-1225	238	19	s	s	PART
ijassa-1225	238	20	∈	∈	NOUN
ijassa-1225	238	21	s	s	X
ijassa-1225	238	22	(	(	PUNCT
ijassa-1225	238	23	υ	υ	PROPN
ijassa-1225	238	24	,	,	PUNCT
ijassa-1225	238	25	ol(b)(v̇0	ol(b)(v̇0	NUM
ijassa-1225	238	26	)	)	PUNCT
ijassa-1225	238	27	,	,	PUNCT
ijassa-1225	238	28	0	0	NUM
ijassa-1225	238	29	)	)	PUNCT
ijassa-1225	238	30	and	and	CCONJ
ijassa-1225	238	31	demonstrate	demonstrate	VERB
ijassa-1225	238	32	that	that	SCONJ
ijassa-1225	238	33	it	it	PRON
ijassa-1225	238	34	possesses	possess	VERB
ijassa-1225	238	35	an	an	DET
ijassa-1225	238	36	infimum	infimum	ADJ
ijassa-1225	238	37	u	u	NOUN
ijassa-1225	238	38	.	.	PUNCT
ijassa-1225	239	1	=	=	PROPN
ijassa-1225	239	2	inf	inf	PROPN
ijassa-1225	239	3	s	s	PART
ijassa-1225	239	4	and	and	CCONJ
ijassa-1225	239	5	,	,	PUNCT
ijassa-1225	239	6	moreover	moreover	ADV
ijassa-1225	239	7	,	,	PUNCT
ijassa-1225	239	8	there	there	PRON
ijassa-1225	239	9	exists	exist	VERB
ijassa-1225	239	10	a	a	DET
ijassa-1225	239	11	decreasing	decrease	VERB
ijassa-1225	239	12	sequence	sequence	NOUN
ijassa-1225	239	13	{	{	PUNCT
ijassa-1225	239	14	un	un	PROPN
ijassa-1225	239	15	}	}	PUNCT
ijassa-1225	239	16	⊂	⊂	PRON
ijassa-1225	239	17	s	s	AUX
ijassa-1225	239	18	having	have	VERB
ijassa-1225	239	19	the	the	DET
ijassa-1225	239	20	same	same	ADJ
ijassa-1225	239	21	lower	lower	ADV
ijassa-1225	239	22	bound	bind	VERB
ijassa-1225	239	23	inf{un	inf{un	NOUN
ijassa-1225	239	24	}	}	PUNCT
ijassa-1225	239	25	=	=	SYM
ijassa-1225	239	26	inf	inf	NOUN
ijassa-1225	239	27	s	s	PART
ijassa-1225	239	28	=	=	NOUN
ijassa-1225	239	29	u.	u.	NOUN
ijassa-1225	239	30	for	for	ADP
ijassa-1225	239	31	any	any	DET
ijassa-1225	239	32	u	u	PROPN
ijassa-1225	239	33	∈	∈	PROPN
ijassa-1225	239	34	s	s	PART
ijassa-1225	239	35	,	,	PUNCT
ijassa-1225	239	36	we	we	PRON
ijassa-1225	239	37	define	define	VERB
ijassa-1225	239	38	the	the	DET
ijassa-1225	239	39	number	number	NOUN
ijassa-1225	239	40	lu	lu	NOUN
ijassa-1225	239	41	.	.	PUNCT
ijassa-1225	240	1	=	=	PRON
ijassa-1225	240	2	∫	∫	PROPN
ijassa-1225	240	3	a	a	DET
ijassa-1225	240	4	0	0	NUM
ijassa-1225	240	5	u(s)ds	u(s)ds	PROPN
ijassa-1225	240	6	.	.	PUNCT
ijassa-1225	241	1	the	the	DET
ijassa-1225	241	2	set	set	NOUN
ijassa-1225	241	3	ls	ls	ADJ
ijassa-1225	241	4	.	.	PUNCT
ijassa-1225	242	1	=	=	PRON
ijassa-1225	242	2	{	{	PUNCT
ijassa-1225	242	3	lu	lu	PROPN
ijassa-1225	242	4	,	,	PUNCT
ijassa-1225	242	5	u	u	PROPN
ijassa-1225	242	6	∈	∈	PROPN
ijassa-1225	242	7	s	s	PART
ijassa-1225	242	8	}	}	PUNCT
ijassa-1225	242	9	is	be	AUX
ijassa-1225	242	10	a	a	DET
ijassa-1225	242	11	chain	chain	NOUN
ijassa-1225	242	12	in	in	ADP
ijassa-1225	242	13	r	r	NOUN
ijassa-1225	242	14	,	,	PUNCT
ijassa-1225	242	15	which	which	PRON
ijassa-1225	242	16	is	be	AUX
ijassa-1225	242	17	bounded	bound	VERB
ijassa-1225	242	18	from	from	ADP
ijassa-1225	242	19	below	below	ADP
ijassa-1225	242	20	due	due	ADP
ijassa-1225	242	21	to	to	ADP
ijassa-1225	242	22	the	the	DET
ijassa-1225	242	23	integral	integral	ADJ
ijassa-1225	242	24	boundedness	boundedness	NOUN
ijassa-1225	242	25	of	of	ADP
ijassa-1225	242	26	the	the	DET
ijassa-1225	242	27	set	set	NOUN
ijassa-1225	242	28	of	of	ADP
ijassa-1225	242	29	measurable	measurable	ADJ
ijassa-1225	242	30	selections	selection	NOUN
ijassa-1225	242	31	of	of	ADP
ijassa-1225	242	32	the	the	DET
ijassa-1225	242	33	set	set	NOUN
ijassa-1225	242	34	-	-	PUNCT
ijassa-1225	242	35	valued	value	VERB
ijassa-1225	242	36	mapping	mapping	NOUN
ijassa-1225	242	37	b	b	SYM
ijassa-1225	242	38	(	(	PUNCT
ijassa-1225	242	39	·	·	PUNCT
ijassa-1225	242	40	)	)	PUNCT
ijassa-1225	242	41	∩	∩	NOUN
ijassa-1225	242	42	orn	orn	X
ijassa-1225	242	43	(	(	PUNCT
ijassa-1225	242	44	v̇0	v̇0	PROPN
ijassa-1225	242	45	(	(	PUNCT
ijassa-1225	242	46	·	·	PUNCT
ijassa-1225	242	47	)	)	PUNCT
ijassa-1225	242	48	)	)	PUNCT
ijassa-1225	242	49	:	:	PUNCT
ijassa-1225	243	1	[	[	X
ijassa-1225	243	2	a	a	DET
ijassa-1225	243	3	,	,	PUNCT
ijassa-1225	243	4	b]→	b]→	X
ijassa-1225	243	5	c(rn	c(rn	PROPN
ijassa-1225	243	6	)	)	PUNCT
ijassa-1225	243	7	from	from	ADP
ijassa-1225	243	8	below	below	ADV
ijassa-1225	243	9	.	.	PUNCT
ijassa-1225	244	1	thus	thus	ADV
ijassa-1225	244	2	,	,	PUNCT
ijassa-1225	244	3	there	there	PRON
ijassa-1225	244	4	exists	exist	VERB
ijassa-1225	244	5	λ	λ	X
ijassa-1225	244	6	.	.	PUNCT
ijassa-1225	245	1	=	=	PROPN
ijassa-1225	245	2	inf	inf	PROPN
ijassa-1225	245	3	ls	ls	PROPN
ijassa-1225	245	4	,	,	PUNCT
ijassa-1225	245	5	and	and	CCONJ
ijassa-1225	245	6	,	,	PUNCT
ijassa-1225	245	7	hence	hence	ADV
ijassa-1225	245	8	,	,	PUNCT
ijassa-1225	245	9	exists	exist	VERB
ijassa-1225	245	10	a	a	DET
ijassa-1225	245	11	decreasing	decrease	VERB
ijassa-1225	245	12	sequence	sequence	NOUN
ijassa-1225	245	13	{	{	PUNCT
ijassa-1225	245	14	un	un	PROPN
ijassa-1225	245	15	}	}	PUNCT
ijassa-1225	245	16	⊂	⊂	PRON
ijassa-1225	245	17	s	s	VERB
ijassa-1225	245	18	such	such	ADJ
ijassa-1225	245	19	that	that	SCONJ
ijassa-1225	245	20	limn→∞	limn→∞	PROPN
ijassa-1225	245	21	lun	lun	NOUN
ijassa-1225	245	22	=	=	SYM
ijassa-1225	245	23	λ	λ	PROPN
ijassa-1225	245	24	.	.	PROPN
ijassa-1225	246	1	in	in	ADP
ijassa-1225	246	2	the	the	DET
ijassa-1225	246	3	space	space	NOUN
ijassa-1225	246	4	l	l	NOUN
ijassa-1225	246	5	,	,	PUNCT
ijassa-1225	246	6	any	any	DET
ijassa-1225	246	7	decreasing	decrease	VERB
ijassa-1225	246	8	norm	norm	NOUN
ijassa-1225	246	9	bounded	bound	VERB
ijassa-1225	246	10	sequence	sequence	NOUN
ijassa-1225	246	11	has	have	VERB
ijassa-1225	246	12	an	an	DET
ijassa-1225	246	13	infimum	infimum	ADJ
ijassa-1225	246	14	(	(	PUNCT
ijassa-1225	246	15	see	see	VERB
ijassa-1225	246	16	e.g.	e.g.	ADV
ijassa-1225	246	17	[	[	X
ijassa-1225	246	18	25	25	NUM
ijassa-1225	246	19	,	,	PUNCT
ijassa-1225	246	20	p.	p.	NOUN
ijassa-1225	246	21	257	257	NUM
ijassa-1225	246	22	]	]	NOUN
ijassa-1225	246	23	)	)	PUNCT
ijassa-1225	246	24	,	,	PUNCT
ijassa-1225	246	25	so	so	CCONJ
ijassa-1225	246	26	there	there	PRON
ijassa-1225	246	27	exists	exist	VERB
ijassa-1225	246	28	u	u	NOUN
ijassa-1225	246	29	=	=	NOUN
ijassa-1225	246	30	inf{un	inf{un	NOUN
ijassa-1225	246	31	}	}	PUNCT
ijassa-1225	246	32	,	,	PUNCT
ijassa-1225	246	33	and	and	CCONJ
ijassa-1225	246	34	,	,	PUNCT
ijassa-1225	246	35	moreover	moreover	ADV
ijassa-1225	246	36	,	,	PUNCT
ijassa-1225	246	37	for	for	ADP
ijassa-1225	246	38	almost	almost	ADV
ijassa-1225	246	39	all	all	PRON
ijassa-1225	246	40	t	t	NOUN
ijassa-1225	246	41	∈	∈	PRON
ijassa-1225	247	1	[	[	X
ijassa-1225	247	2	a	a	X
ijassa-1225	247	3	,	,	PUNCT
ijassa-1225	247	4	b	b	NOUN
ijassa-1225	247	5	]	]	X
ijassa-1225	247	6	,	,	PUNCT
ijassa-1225	247	7	it	it	PRON
ijassa-1225	247	8	holds	hold	VERB
ijassa-1225	247	9	true	true	ADJ
ijassa-1225	247	10	that	that	SCONJ
ijassa-1225	247	11	u(t	u(t	NOUN
ijassa-1225	247	12	)	)	PUNCT
ijassa-1225	247	13	=	=	SYM
ijassa-1225	247	14	inf{un(t	inf{un(t	NOUN
ijassa-1225	247	15	)	)	PUNCT
ijassa-1225	247	16	}	}	PUNCT
ijassa-1225	247	17	=	=	SYM
ijassa-1225	247	18	limn→∞	limn→∞	NOUN
ijassa-1225	247	19	un(t	un(t	NUM
ijassa-1225	247	20	)	)	PUNCT
ijassa-1225	247	21	.	.	PUNCT
ijassa-1225	248	1	therefore	therefore	ADV
ijassa-1225	248	2	,	,	PUNCT
ijassa-1225	248	3	for	for	ADP
ijassa-1225	248	4	almost	almost	ADV
ijassa-1225	248	5	all	all	PRON
ijassa-1225	248	6	t	t	NOUN
ijassa-1225	248	7	∈	∈	PRON
ijassa-1225	249	1	[	[	X
ijassa-1225	249	2	a	a	X
ijassa-1225	249	3	,	,	PUNCT
ijassa-1225	249	4	b	b	NOUN
ijassa-1225	249	5	]	]	X
ijassa-1225	249	6	,	,	PUNCT
ijassa-1225	249	7	due	due	ADP
ijassa-1225	249	8	to	to	ADP
ijassa-1225	249	9	closedness	closedness	NOUN
ijassa-1225	249	10	of	of	ADP
ijassa-1225	249	11	the	the	DET
ijassa-1225	249	12	set	set	NOUN
ijassa-1225	249	13	b(t	b(t	PROPN
ijassa-1225	249	14	)	)	PUNCT
ijassa-1225	249	15	⊂	⊂	PROPN
ijassa-1225	249	16	rn	rn	PROPN
ijassa-1225	249	17	,	,	PUNCT
ijassa-1225	249	18	the	the	DET
ijassa-1225	249	19	inclusion	inclusion	NOUN
ijassa-1225	249	20	u(t	u(t	NOUN
ijassa-1225	249	21	)	)	PUNCT
ijassa-1225	249	22	∈	∈	PROPN
ijassa-1225	249	23	b(t	b(t	NOUN
ijassa-1225	249	24	)	)	PUNCT
ijassa-1225	249	25	takes	take	VERB
ijassa-1225	249	26	place	place	NOUN
ijassa-1225	249	27	,	,	PUNCT
ijassa-1225	249	28	so	so	CCONJ
ijassa-1225	249	29	u	u	PROPN
ijassa-1225	249	30	∈	∈	PROPN
ijassa-1225	249	31	l(b	l(b	PROPN
ijassa-1225	249	32	)	)	PUNCT
ijassa-1225	249	33	.	.	PUNCT
ijassa-1225	250	1	let	let	VERB
ijassa-1225	250	2	us	we	PRON
ijassa-1225	250	3	now	now	ADV
ijassa-1225	250	4	demonstrate	demonstrate	VERB
ijassa-1225	250	5	that	that	DET
ijassa-1225	250	6	inf	inf	NOUN
ijassa-1225	250	7	s	s	PART
ijassa-1225	250	8	=	=	NOUN
ijassa-1225	250	9	u.	u.	NOUN
ijassa-1225	250	10	for	for	ADP
ijassa-1225	250	11	any	any	DET
ijassa-1225	250	12	u	u	PROPN
ijassa-1225	250	13	∈	∈	PROPN
ijassa-1225	250	14	s	s	PART
ijassa-1225	250	15	,	,	PUNCT
ijassa-1225	250	16	it	it	PRON
ijassa-1225	250	17	holds	hold	VERB
ijassa-1225	250	18	true	true	ADJ
ijassa-1225	250	19	that	that	SCONJ
ijassa-1225	250	20	lu	lu	PROPN
ijassa-1225	250	21	>	>	X
ijassa-1225	250	22	λ	λ	PROPN
ijassa-1225	250	23	,	,	PUNCT
ijassa-1225	250	24	so	so	ADV
ijassa-1225	250	25	for	for	ADP
ijassa-1225	250	26	some	some	DET
ijassa-1225	250	27	number	number	NOUN
ijassa-1225	250	28	n	n	CCONJ
ijassa-1225	250	29	,	,	PUNCT
ijassa-1225	250	30	we	we	PRON
ijassa-1225	250	31	get	get	VERB
ijassa-1225	250	32	lu	lu	PROPN
ijassa-1225	250	33	>	>	X
ijassa-1225	250	34	lun	lun	PROPN
ijassa-1225	250	35	,	,	PUNCT
ijassa-1225	250	36	hence	hence	ADV
ijassa-1225	250	37	u	u	X
ijassa-1225	250	38	>	>	X
ijassa-1225	250	39	un	un	PROPN
ijassa-1225	250	40	>	>	X
ijassa-1225	250	41	u.	u.	PROPN
ijassa-1225	251	1	thus	thus	ADV
ijassa-1225	251	2	,	,	PUNCT
ijassa-1225	251	3	u	u	NOUN
ijassa-1225	251	4	is	be	AUX
ijassa-1225	251	5	a	a	DET
ijassa-1225	251	6	lower	low	ADJ
ijassa-1225	251	7	bound	bind	VERB
ijassa-1225	251	8	of	of	ADP
ijassa-1225	251	9	s	s	NOUN
ijassa-1225	251	10	,	,	PUNCT
ijassa-1225	251	11	and	and	CCONJ
ijassa-1225	251	12	any	any	DET
ijassa-1225	251	13	function	function	NOUN
ijassa-1225	251	14	that	that	PRON
ijassa-1225	251	15	is	be	AUX
ijassa-1225	251	16	greater	great	ADJ
ijassa-1225	251	17	than	than	ADP
ijassa-1225	251	18	u	u	NOUN
ijassa-1225	251	19	,	,	PUNCT
ijassa-1225	251	20	is	be	AUX
ijassa-1225	251	21	not	not	PART
ijassa-1225	251	22	a	a	DET
ijassa-1225	251	23	lower	low	ADJ
ijassa-1225	251	24	bound	bind	VERB
ijassa-1225	251	25	of	of	ADP
ijassa-1225	251	26	the	the	DET
ijassa-1225	251	27	sequence	sequence	NOUN
ijassa-1225	251	28	{	{	PUNCT
ijassa-1225	251	29	un	un	PROPN
ijassa-1225	251	30	}	}	PUNCT
ijassa-1225	251	31	and	and	CCONJ
ijassa-1225	251	32	moreover	moreover	ADV
ijassa-1225	251	33	,	,	PUNCT
ijassa-1225	251	34	not	not	PART
ijassa-1225	251	35	a	a	DET
ijassa-1225	251	36	lower	lower	ADV
ijassa-1225	251	37	bound	bind	VERB
ijassa-1225	251	38	of	of	ADP
ijassa-1225	251	39	the	the	DET
ijassa-1225	251	40	chain	chain	NOUN
ijassa-1225	251	41	s.	s.	PROPN
ijassa-1225	252	1	so	so	ADV
ijassa-1225	252	2	,	,	PUNCT
ijassa-1225	252	3	u	u	PROPN
ijassa-1225	252	4	=	=	PROPN
ijassa-1225	252	5	inf	inf	PROPN
ijassa-1225	252	6	s	s	NOUN
ijassa-1225	252	7	and	and	CCONJ
ijassa-1225	252	8	u(t	u(t	NOUN
ijassa-1225	252	9	)	)	PUNCT
ijassa-1225	252	10	=	=	SYM
ijassa-1225	252	11	inf{un(t	inf{un(t	NOUN
ijassa-1225	252	12	)	)	PUNCT
ijassa-1225	252	13	}	}	PUNCT
ijassa-1225	252	14	=	=	SYM
ijassa-1225	252	15	limn→∞	limn→∞	NOUN
ijassa-1225	252	16	un(t	un(t	X
ijassa-1225	252	17	)	)	PUNCT
ijassa-1225	252	18	for	for	ADP
ijassa-1225	252	19	almost	almost	ADV
ijassa-1225	252	20	all	all	PRON
ijassa-1225	252	21	t	t	NOUN
ijassa-1225	252	22	∈	∈	PRON
ijassa-1225	253	1	[	[	X
ijassa-1225	253	2	a	a	X
ijassa-1225	253	3	,	,	PUNCT
ijassa-1225	253	4	b	b	NOUN
ijassa-1225	253	5	]	]	X
ijassa-1225	253	6	.	.	PUNCT
ijassa-1225	254	1	it	it	PRON
ijassa-1225	254	2	remains	remain	VERB
ijassa-1225	254	3	now	now	ADV
ijassa-1225	254	4	to	to	PART
ijassa-1225	254	5	prove	prove	VERB
ijassa-1225	254	6	the	the	DET
ijassa-1225	254	7	existence	existence	NOUN
ijassa-1225	254	8	of	of	ADP
ijassa-1225	254	9	a	a	DET
ijassa-1225	254	10	non	non	ADJ
ijassa-1225	254	11	-	-	ADJ
ijassa-1225	254	12	negative	negative	ADJ
ijassa-1225	254	13	measurable	measurable	ADJ
ijassa-1225	254	14	selection	selection	NOUN
ijassa-1225	254	15	of	of	ADP
ijassa-1225	254	16	the	the	DET
ijassa-1225	254	17	setvalued	setvalued	ADJ
ijassa-1225	254	18	mapping	mapping	NOUN
ijassa-1225	254	19	υ(u	υ(u	PROPN
ijassa-1225	254	20	,	,	PUNCT
ijassa-1225	254	21	u	u	NOUN
ijassa-1225	254	22	)	)	PUNCT
ijassa-1225	254	23	:	:	PUNCT
ijassa-1225	255	1	[	[	X
ijassa-1225	255	2	a	a	PRON
ijassa-1225	255	3	,	,	PUNCT
ijassa-1225	255	4	b]→	b]→	ADJ
ijassa-1225	255	5	k(rm	k(rm	NOUN
ijassa-1225	255	6	)	)	PUNCT
ijassa-1225	255	7	to	to	PART
ijassa-1225	255	8	verify	verify	VERB
ijassa-1225	255	9	the	the	DET
ijassa-1225	255	10	condition	condition	NOUN
ijassa-1225	255	11	(	(	PUNCT
ijassa-1225	255	12	a3	a3	NOUN
ijassa-1225	255	13	)	)	PUNCT
ijassa-1225	255	14	.	.	PUNCT
ijassa-1225	256	1	by	by	ADP
ijassa-1225	256	2	the	the	DET
ijassa-1225	256	3	definition	definition	NOUN
ijassa-1225	256	4	of	of	ADP
ijassa-1225	256	5	the	the	DET
ijassa-1225	256	6	chain	chain	NOUN
ijassa-1225	256	7	s	s	PROPN
ijassa-1225	256	8	,	,	PUNCT
ijassa-1225	256	9	for	for	ADP
ijassa-1225	256	10	any	any	DET
ijassa-1225	256	11	natural	natural	ADJ
ijassa-1225	256	12	n	n	CCONJ
ijassa-1225	256	13	,	,	PUNCT
ijassa-1225	256	14	there	there	PRON
ijassa-1225	256	15	exists	exist	VERB
ijassa-1225	256	16	a	a	DET
ijassa-1225	256	17	measurable	measurable	ADJ
ijassa-1225	256	18	function	function	NOUN
ijassa-1225	256	19	yn	yn	PROPN
ijassa-1225	256	20	∈	∈	PROPN
ijassa-1225	256	21	wm	wm	PROPN
ijassa-1225	256	22	such	such	ADJ
ijassa-1225	256	23	that	that	SCONJ
ijassa-1225	256	24	yn	yn	PROPN
ijassa-1225	256	25	∈	∈	PROPN
ijassa-1225	256	26	υ(un	υ(un	PROPN
ijassa-1225	256	27	,	,	PUNCT
ijassa-1225	256	28	un	un	PROPN
ijassa-1225	256	29	)	)	PUNCT
ijassa-1225	256	30	and	and	CCONJ
ijassa-1225	256	31	yn	yn	PRON
ijassa-1225	256	32	≥	≥	NOUN
ijassa-1225	256	33	0.as	0.as	NOUN
ijassa-1225	257	1	the	the	DET
ijassa-1225	257	2	mapping	mapping	NOUN
ijassa-1225	257	3	υ(un	υ(un	PROPN
ijassa-1225	257	4	,	,	PUNCT
ijassa-1225	257	5	·	·	PUNCT
ijassa-1225	257	6	)	)	PUNCT
ijassa-1225	257	7	is	be	AUX
ijassa-1225	257	8	antitone	antitone	ADJ
ijassa-1225	257	9	,	,	PUNCT
ijassa-1225	257	10	there	there	PRON
ijassa-1225	257	11	exists	exist	VERB
ijassa-1225	257	12	a	a	DET
ijassa-1225	257	13	measurable	measurable	ADJ
ijassa-1225	257	14	function	function	NOUN
ijassa-1225	257	15	ζn	ζn	ADP
ijassa-1225	257	16	∈	∈	PROPN
ijassa-1225	257	17	wm	wm	PROPN
ijassa-1225	257	18	such	such	ADJ
ijassa-1225	257	19	that	that	SCONJ
ijassa-1225	257	20	ζn	ζn	PRON
ijassa-1225	257	21	∈	∈	PROPN
ijassa-1225	257	22	υ(un	υ(un	PROPN
ijassa-1225	257	23	,	,	PUNCT
ijassa-1225	257	24	u	u	NOUN
ijassa-1225	257	25	)	)	PUNCT
ijassa-1225	257	26	and	and	CCONJ
ijassa-1225	257	27	ζn	ζn	DET
ijassa-1225	257	28	≥	≥	NOUN
ijassa-1225	257	29	0	0	NUM
ijassa-1225	257	30	.	.	PUNCT
ijassa-1225	258	1	the	the	DET
ijassa-1225	258	2	mapping	mapping	NOUN
ijassa-1225	258	3	υ	υ	PROPN
ijassa-1225	258	4	(	(	PUNCT
ijassa-1225	258	5	·	·	PUNCT
ijassa-1225	258	6	,	,	PUNCT
ijassa-1225	258	7	u	u	NOUN
ijassa-1225	258	8	)	)	PUNCT
ijassa-1225	258	9	:	:	PUNCT
ijassa-1225	258	10	l(b	l(b	PROPN
ijassa-1225	258	11	)	)	PUNCT
ijassa-1225	258	12	⇒	⇒	PROPN
ijassa-1225	258	13	wm	wm	PROPN
ijassa-1225	258	14	is	be	AUX
ijassa-1225	258	15	the	the	DET
ijassa-1225	258	16	restriction	restriction	NOUN
ijassa-1225	258	17	to	to	ADP
ijassa-1225	258	18	l(b	l(b	PROPN
ijassa-1225	258	19	)	)	PUNCT
ijassa-1225	258	20	of	of	ADP
ijassa-1225	258	21	the	the	DET
ijassa-1225	258	22	nemytskii	nemytskii	ADJ
ijassa-1225	258	23	operator	operator	NOUN
ijassa-1225	258	24	generated	generate	VERB
ijassa-1225	258	25	by	by	ADP
ijassa-1225	258	26	the	the	DET
ijassa-1225	258	27	function	function	NOUN
ijassa-1225	258	28	g	g	NOUN
ijassa-1225	258	29	:	:	PUNCT
ijassa-1225	258	30	[	[	X
ijassa-1225	258	31	a	a	X
ijassa-1225	258	32	,	,	PUNCT
ijassa-1225	258	33	b]×	b]×	NOUN
ijassa-1225	258	34	rn	rn	PROPN
ijassa-1225	258	35	→	→	SYM
ijassa-1225	258	36	k(rm	k(rm	PROPN
ijassa-1225	258	37	)	)	PUNCT
ijassa-1225	258	38	,	,	PUNCT
ijassa-1225	258	39	g(t	g(t	PROPN
ijassa-1225	258	40	,	,	PUNCT
ijassa-1225	258	41	u	u	NOUN
ijassa-1225	258	42	)	)	PUNCT
ijassa-1225	258	43	.	.	PUNCT
ijassa-1225	259	1	=	=	PUNCT
ijassa-1225	259	2	f	f	PROPN
ijassa-1225	259	3	(	(	PUNCT
ijassa-1225	259	4	t	t	PROPN
ijassa-1225	259	5	,	,	PUNCT
ijassa-1225	259	6	γ	γ	PROPN
ijassa-1225	259	7	+	+	PROPN
ijassa-1225	259	8	∫	∫	PROPN
ijassa-1225	259	9	t	t	PROPN
ijassa-1225	259	10	a	a	DET
ijassa-1225	259	11	u(s)ds	u(s)ds	PROPN
ijassa-1225	259	12	,	,	PUNCT
ijassa-1225	259	13	u(t	u(t	NOUN
ijassa-1225	259	14	)	)	PUNCT
ijassa-1225	259	15	,	,	PUNCT
ijassa-1225	259	16	u	u	NOUN
ijassa-1225	259	17	)	)	PUNCT
ijassa-1225	259	18	for	for	ADP
ijassa-1225	259	19	almost	almost	ADV
ijassa-1225	259	20	all	all	PRON
ijassa-1225	259	21	t	t	NOUN
ijassa-1225	259	22	∈	∈	PRON
ijassa-1225	260	1	[	[	X
ijassa-1225	260	2	a	a	X
ijassa-1225	260	3	,	,	PUNCT
ijassa-1225	260	4	b	b	NOUN
ijassa-1225	260	5	]	]	PUNCT
ijassa-1225	260	6	and	and	CCONJ
ijassa-1225	260	7	any	any	DET
ijassa-1225	260	8	u	u	PROPN
ijassa-1225	260	9	∈	∈	PROPN
ijassa-1225	260	10	rn	rn	PROPN
ijassa-1225	260	11	,	,	PUNCT
ijassa-1225	260	12	copyright	copyright	NOUN
ijassa-1225	260	13	©	©	PROPN
ijassa-1225	260	14	2022	2022	NUM
ijassa-1225	260	15	assa	assa	NOUN
ijassa-1225	260	16	.	.	PUNCT
ijassa-1225	261	1	adv	adv	PROPN
ijassa-1225	261	2	syst	syst	PROPN
ijassa-1225	261	3	sci	sci	PROPN
ijassa-1225	261	4	appl	appl	PROPN
ijassa-1225	261	5	(	(	PUNCT
ijassa-1225	261	6	2022	2022	NUM
ijassa-1225	261	7	)	)	PUNCT
ijassa-1225	261	8	184	184	NUM
ijassa-1225	261	9	e.s	e.s	PROPN
ijassa-1225	261	10	.	.	PROPN
ijassa-1225	261	11	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	261	12	,	,	PUNCT
ijassa-1225	261	13	i.d	i.d	PROPN
ijassa-1225	261	14	.	.	PROPN
ijassa-1225	261	15	serova	serova	PROPN
ijassa-1225	261	16	,	,	PUNCT
ijassa-1225	261	17	e.a	e.a	PROPN
ijassa-1225	261	18	.	.	PROPN
ijassa-1225	261	19	panasenko	panasenko	PROPN
ijassa-1225	261	20	,	,	PUNCT
ijassa-1225	261	21	e.o	e.o	PROPN
ijassa-1225	261	22	.	.	PROPN
ijassa-1225	261	23	burlakov	burlakov	PROPN
ijassa-1225	261	24	that	that	PRON
ijassa-1225	261	25	satisfies	satisfy	VERB
ijassa-1225	261	26	the	the	DET
ijassa-1225	261	27	caratheodori	caratheodori	NOUN
ijassa-1225	261	28	conditions	condition	NOUN
ijassa-1225	261	29	.	.	PUNCT
ijassa-1225	262	1	therefore	therefore	ADV
ijassa-1225	262	2	hrm	hrm	PROPN
ijassa-1225	262	3	(	(	PUNCT
ijassa-1225	262	4	g(t	g(t	PROPN
ijassa-1225	262	5	,	,	PUNCT
ijassa-1225	262	6	un(t	un(t	NUM
ijassa-1225	262	7	)	)	PUNCT
ijassa-1225	262	8	)	)	PUNCT
ijassa-1225	262	9	,	,	PUNCT
ijassa-1225	262	10	g(t	g(t	PROPN
ijassa-1225	262	11	,	,	PUNCT
ijassa-1225	262	12	u(t	u(t	NOUN
ijassa-1225	262	13	)	)	PUNCT
ijassa-1225	262	14	)	)	PUNCT
ijassa-1225	262	15	)	)	PUNCT
ijassa-1225	263	1	→	→	SYM
ijassa-1225	263	2	0	0	X
ijassa-1225	263	3	.	.	PUNCT
ijassa-1225	264	1	(	(	PUNCT
ijassa-1225	264	2	4.17	4.17	NUM
ijassa-1225	264	3	)	)	PUNCT
ijassa-1225	264	4	for	for	ADP
ijassa-1225	264	5	almost	almost	ADV
ijassa-1225	264	6	all	all	PRON
ijassa-1225	264	7	t	t	NOUN
ijassa-1225	264	8	∈	∈	PRON
ijassa-1225	265	1	[	[	X
ijassa-1225	265	2	a	a	X
ijassa-1225	265	3	,	,	PUNCT
ijassa-1225	265	4	b	b	NOUN
ijassa-1225	265	5	]	]	X
ijassa-1225	265	6	,	,	PUNCT
ijassa-1225	265	7	it	it	PRON
ijassa-1225	265	8	holds	hold	VERB
ijassa-1225	265	9	true	true	ADJ
ijassa-1225	265	10	that	that	SCONJ
ijassa-1225	265	11	g(t	g(t	PROPN
ijassa-1225	265	12	,	,	PUNCT
ijassa-1225	265	13	un(t	un(t	NUM
ijassa-1225	265	14	)	)	PUNCT
ijassa-1225	265	15	)	)	PUNCT
ijassa-1225	265	16	∩	∩	PROPN
ijassa-1225	265	17	rm	rm	PROPN
ijassa-1225	265	18	+	+	CCONJ
ijassa-1225	265	19	6=	6=	PROPN
ijassa-1225	265	20	∅	∅	NOUN
ijassa-1225	265	21	(	(	PUNCT
ijassa-1225	265	22	as	as	ADP
ijassa-1225	265	23	ζn(t	ζn(t	NOUN
ijassa-1225	265	24	)	)	PUNCT
ijassa-1225	265	25	∈	∈	PROPN
ijassa-1225	265	26	g(t	g(t	PROPN
ijassa-1225	265	27	,	,	PUNCT
ijassa-1225	265	28	un(t	un(t	NUM
ijassa-1225	265	29	)	)	PUNCT
ijassa-1225	265	30	)	)	PUNCT
ijassa-1225	265	31	)	)	PUNCT
ijassa-1225	265	32	.	.	PUNCT
ijassa-1225	266	1	assume	assume	VERB
ijassa-1225	266	2	that	that	SCONJ
ijassa-1225	266	3	the	the	DET
ijassa-1225	266	4	set	set	NOUN
ijassa-1225	266	5	-	-	PUNCT
ijassa-1225	266	6	valued	value	VERB
ijassa-1225	266	7	mapping	mapping	NOUN
ijassa-1225	266	8	g	g	NOUN
ijassa-1225	266	9	(	(	PUNCT
ijassa-1225	266	10	·	·	PUNCT
ijassa-1225	266	11	,	,	PUNCT
ijassa-1225	266	12	u	u	NOUN
ijassa-1225	266	13	(	(	PUNCT
ijassa-1225	266	14	·	·	PUNCT
ijassa-1225	266	15	)	)	PUNCT
ijassa-1225	266	16	)	)	PUNCT
ijassa-1225	266	17	does	do	AUX
ijassa-1225	266	18	not	not	PART
ijassa-1225	266	19	possess	possess	VERB
ijassa-1225	266	20	non	non	ADJ
ijassa-1225	266	21	-	-	ADJ
ijassa-1225	266	22	negative	negative	ADJ
ijassa-1225	266	23	selections	selection	NOUN
ijassa-1225	266	24	.	.	PUNCT
ijassa-1225	267	1	then	then	ADV
ijassa-1225	267	2	for	for	ADP
ijassa-1225	267	3	some	some	DET
ijassa-1225	267	4	set	set	NOUN
ijassa-1225	267	5	t	t	PROPN
ijassa-1225	267	6	⊂	⊂	PROPN
ijassa-1225	268	1	[	[	X
ijassa-1225	268	2	a	a	X
ijassa-1225	268	3	,	,	PUNCT
ijassa-1225	268	4	b	b	NOUN
ijassa-1225	268	5	]	]	PUNCT
ijassa-1225	268	6	of	of	ADP
ijassa-1225	268	7	a	a	DET
ijassa-1225	268	8	positive	positive	ADJ
ijassa-1225	268	9	measure	measure	NOUN
ijassa-1225	268	10	,	,	PUNCT
ijassa-1225	268	11	it	it	PRON
ijassa-1225	268	12	holds	hold	VERB
ijassa-1225	268	13	true	true	ADJ
ijassa-1225	268	14	that	that	SCONJ
ijassa-1225	268	15	g(t	g(t	PROPN
ijassa-1225	268	16	,	,	PUNCT
ijassa-1225	268	17	u(t	u(t	NOUN
ijassa-1225	268	18	)	)	PUNCT
ijassa-1225	268	19	)	)	PUNCT
ijassa-1225	268	20	∩	∩	PROPN
ijassa-1225	268	21	rm	rm	NOUN
ijassa-1225	268	22	+	+	CCONJ
ijassa-1225	268	23	=	=	X
ijassa-1225	268	24	∅.	∅.	NOUN
ijassa-1225	268	25	in	in	ADP
ijassa-1225	268	26	this	this	DET
ijassa-1225	268	27	case	case	NOUN
ijassa-1225	268	28	,	,	PUNCT
ijassa-1225	268	29	for	for	ADP
ijassa-1225	268	30	t	t	PROPN
ijassa-1225	268	31	∈	∈	PROPN
ijassa-1225	268	32	t	t	NOUN
ijassa-1225	268	33	there	there	PRON
ijassa-1225	268	34	is	be	VERB
ijassa-1225	268	35	ε	ε	PROPN
ijassa-1225	268	36	>	>	X
ijassa-1225	268	37	0	0	NUM
ijassa-1225	268	38	such	such	ADJ
ijassa-1225	268	39	that	that	SCONJ
ijassa-1225	268	40	the	the	DET
ijassa-1225	268	41	ε	ε	PROPN
ijassa-1225	268	42	-	-	PUNCT
ijassa-1225	268	43	neighborhood	neighborhood	NOUN
ijassa-1225	268	44	of	of	ADP
ijassa-1225	268	45	the	the	DET
ijassa-1225	268	46	set	set	PROPN
ijassa-1225	268	47	g(t	g(t	PROPN
ijassa-1225	268	48	,	,	PUNCT
ijassa-1225	268	49	u(t	u(t	NOUN
ijassa-1225	268	50	)	)	PUNCT
ijassa-1225	268	51	)	)	PUNCT
ijassa-1225	268	52	does	do	AUX
ijassa-1225	268	53	not	not	PART
ijassa-1225	268	54	have	have	VERB
ijassa-1225	268	55	intersections	intersection	NOUN
ijassa-1225	268	56	with	with	ADP
ijassa-1225	268	57	the	the	DET
ijassa-1225	268	58	cone	cone	NOUN
ijassa-1225	268	59	rm	rm	NOUN
ijassa-1225	268	60	+	+	X
ijassa-1225	268	61	.	.	PUNCT
ijassa-1225	269	1	the	the	DET
ijassa-1225	269	2	latter	latter	ADJ
ijassa-1225	269	3	implies	imply	VERB
ijassa-1225	269	4	that	that	SCONJ
ijassa-1225	269	5	hrm	hrm	PROPN
ijassa-1225	269	6	(	(	PUNCT
ijassa-1225	269	7	g(t	g(t	PROPN
ijassa-1225	269	8	,	,	PUNCT
ijassa-1225	269	9	un(t	un(t	NUM
ijassa-1225	269	10	)	)	PUNCT
ijassa-1225	269	11	)	)	PUNCT
ijassa-1225	269	12	,	,	PUNCT
ijassa-1225	269	13	g(t	g(t	PROPN
ijassa-1225	269	14	,	,	PUNCT
ijassa-1225	269	15	u(t	u(t	NOUN
ijassa-1225	269	16	)	)	PUNCT
ijassa-1225	269	17	)	)	PUNCT
ijassa-1225	269	18	)	)	PUNCT
ijassa-1225	269	19	>	>	PUNCT
ijassa-1225	270	1	ε	ε	PROPN
ijassa-1225	270	2	for	for	ADP
ijassa-1225	270	3	any	any	DET
ijassa-1225	270	4	n	n	CCONJ
ijassa-1225	270	5	,	,	PUNCT
ijassa-1225	270	6	which	which	PRON
ijassa-1225	270	7	contradicts	contradict	VERB
ijassa-1225	270	8	with	with	ADP
ijassa-1225	270	9	the	the	DET
ijassa-1225	270	10	convergence	convergence	NOUN
ijassa-1225	270	11	(	(	PUNCT
ijassa-1225	270	12	4.17	4.17	NUM
ijassa-1225	270	13	)	)	PUNCT
ijassa-1225	270	14	.	.	PUNCT
ijassa-1225	271	1	thus	thus	ADV
ijassa-1225	271	2	,	,	PUNCT
ijassa-1225	271	3	the	the	DET
ijassa-1225	271	4	condition	condition	NOUN
ijassa-1225	271	5	(	(	PUNCT
ijassa-1225	271	6	a3	a3	NOUN
ijassa-1225	271	7	)	)	PUNCT
ijassa-1225	271	8	is	be	AUX
ijassa-1225	271	9	also	also	ADV
ijassa-1225	271	10	fulfilled	fulfil	VERB
ijassa-1225	271	11	.	.	PUNCT
ijassa-1225	272	1	theorem	theorem	VERB
ijassa-1225	272	2	2.1	2.1	NUM
ijassa-1225	272	3	implies	imply	VERB
ijassa-1225	272	4	the	the	DET
ijassa-1225	272	5	existence	existence	NOUN
ijassa-1225	272	6	of	of	ADP
ijassa-1225	272	7	a	a	DET
ijassa-1225	272	8	solution	solution	NOUN
ijassa-1225	272	9	u	u	PROPN
ijassa-1225	272	10	∈	∈	PROPN
ijassa-1225	272	11	l(b	l(b	PROPN
ijassa-1225	272	12	)	)	PUNCT
ijassa-1225	272	13	of	of	ADP
ijassa-1225	272	14	the	the	DET
ijassa-1225	272	15	inclusion	inclusion	NOUN
ijassa-1225	272	16	(	(	PUNCT
ijassa-1225	272	17	4.15	4.15	NUM
ijassa-1225	272	18	)	)	PUNCT
ijassa-1225	272	19	and	and	CCONJ
ijassa-1225	272	20	,	,	PUNCT
ijassa-1225	272	21	hence	hence	ADV
ijassa-1225	272	22	,	,	PUNCT
ijassa-1225	272	23	the	the	DET
ijassa-1225	272	24	existence	existence	NOUN
ijassa-1225	272	25	of	of	ADP
ijassa-1225	272	26	a	a	DET
ijassa-1225	272	27	solution	solution	NOUN
ijassa-1225	272	28	x	x	X
ijassa-1225	272	29	∈	∈	PROPN
ijassa-1225	272	30	ac(b	ac(b	NOUN
ijassa-1225	272	31	)	)	PUNCT
ijassa-1225	272	32	of	of	ADP
ijassa-1225	272	33	the	the	DET
ijassa-1225	272	34	problem	problem	NOUN
ijassa-1225	272	35	(	(	PUNCT
ijassa-1225	272	36	4.11	4.11	NUM
ijassa-1225	272	37	)	)	PUNCT
ijassa-1225	272	38	,	,	PUNCT
ijassa-1225	272	39	(	(	PUNCT
ijassa-1225	272	40	4.12	4.12	NUM
ijassa-1225	272	41	)	)	PUNCT
ijassa-1225	272	42	,	,	PUNCT
ijassa-1225	272	43	(	(	PUNCT
ijassa-1225	272	44	4.13	4.13	NUM
ijassa-1225	272	45	)	)	PUNCT
ijassa-1225	272	46	(	(	PUNCT
ijassa-1225	272	47	which	which	PRON
ijassa-1225	272	48	is	be	AUX
ijassa-1225	272	49	defined	define	VERB
ijassa-1225	272	50	by	by	ADP
ijassa-1225	272	51	the	the	DET
ijassa-1225	272	52	formula	formula	NOUN
ijassa-1225	272	53	x	x	PUNCT
ijassa-1225	272	54	=	=	SYM
ijassa-1225	272	55	γ	γ	X
ijassa-1225	272	56	+	+	PROPN
ijassa-1225	272	57	∫	∫	PROPN
ijassa-1225	272	58	t	t	PROPN
ijassa-1225	272	59	a	a	DET
ijassa-1225	272	60	u(s)ds	u(s)ds	PROPN
ijassa-1225	272	61	)	)	PUNCT
ijassa-1225	272	62	.	.	PUNCT
ijassa-1225	273	1	let	let	VERB
ijassa-1225	273	2	us	we	PRON
ijassa-1225	273	3	now	now	ADV
ijassa-1225	273	4	illustrate	illustrate	VERB
ijassa-1225	273	5	applications	application	NOUN
ijassa-1225	273	6	of	of	ADP
ijassa-1225	273	7	theorem	theorem	ADJ
ijassa-1225	273	8	4.1	4.1	NUM
ijassa-1225	273	9	to	to	ADP
ijassa-1225	273	10	investigation	investigation	NOUN
ijassa-1225	273	11	of	of	ADP
ijassa-1225	273	12	concrete	concrete	ADJ
ijassa-1225	273	13	differential	differential	ADJ
ijassa-1225	273	14	equations	equation	NOUN
ijassa-1225	273	15	and	and	CCONJ
ijassa-1225	273	16	inclusions	inclusion	NOUN
ijassa-1225	273	17	.	.	PUNCT
ijassa-1225	274	1	example	example	NOUN
ijassa-1225	274	2	3.1	3.1	NUM
ijassa-1225	274	3	:	:	PUNCT
ijassa-1225	274	4	we	we	PRON
ijassa-1225	274	5	denote	denote	VERB
ijassa-1225	274	6	by	by	ADP
ijassa-1225	274	7	χ	χ	PRON
ijassa-1225	274	8	the	the	DET
ijassa-1225	274	9	heaviside	heaviside	ADJ
ijassa-1225	274	10	function	function	NOUN
ijassa-1225	274	11	,	,	PUNCT
ijassa-1225	274	12	i.e.	i.e.	X
ijassa-1225	274	13	χ(x	χ(x	X
ijassa-1225	274	14	)	)	PUNCT
ijassa-1225	274	15	=	=	PUNCT
ijassa-1225	275	1	1	1	NUM
ijassa-1225	275	2	for	for	ADP
ijassa-1225	275	3	x	x	X
ijassa-1225	275	4	≥	≥	NOUN
ijassa-1225	275	5	0	0	NUM
ijassa-1225	275	6	and	and	CCONJ
ijassa-1225	275	7	χ(x	χ(x	PROPN
ijassa-1225	275	8	)	)	PUNCT
ijassa-1225	276	1	=	=	SYM
ijassa-1225	276	2	0	0	NUM
ijassa-1225	277	1	for	for	SCONJ
ijassa-1225	277	2	x	x	PUNCT
ijassa-1225	277	3	<	<	X
ijassa-1225	277	4	0	0	X
ijassa-1225	277	5	.	.	PUNCT
ijassa-1225	277	6	let	let	VERB
ijassa-1225	277	7	a	a	DET
ijassa-1225	277	8	measurable	measurable	ADJ
ijassa-1225	277	9	function	function	NOUN
ijassa-1225	277	10	q0	q0	NOUN
ijassa-1225	277	11	:	:	PUNCT
ijassa-1225	278	1	[	[	X
ijassa-1225	278	2	a	a	PRON
ijassa-1225	278	3	,	,	PUNCT
ijassa-1225	278	4	b]→	b]→	ADJ
ijassa-1225	278	5	r	r	NOUN
ijassa-1225	278	6	,	,	PUNCT
ijassa-1225	278	7	a	a	DET
ijassa-1225	278	8	measurable	measurable	ADJ
ijassa-1225	278	9	integrable	integrable	ADJ
ijassa-1225	278	10	function	function	NOUN
ijassa-1225	278	11	q1	q1	PROPN
ijassa-1225	278	12	:	:	PUNCT
ijassa-1225	278	13	[	[	X
ijassa-1225	278	14	a	a	PRON
ijassa-1225	278	15	,	,	PUNCT
ijassa-1225	278	16	b]→	b]→	ADJ
ijassa-1225	278	17	r	r	NOUN
ijassa-1225	278	18	,	,	PUNCT
ijassa-1225	278	19	and	and	CCONJ
ijassa-1225	278	20	a	a	DET
ijassa-1225	278	21	positive	positive	ADJ
ijassa-1225	278	22	number	number	NOUN
ijassa-1225	278	23	r	r	NOUN
ijassa-1225	278	24	be	be	AUX
ijassa-1225	278	25	given	give	VERB
ijassa-1225	278	26	.	.	PUNCT
ijassa-1225	279	1	we	we	PRON
ijassa-1225	279	2	consider	consider	VERB
ijassa-1225	279	3	the	the	DET
ijassa-1225	279	4	differential	differential	ADJ
ijassa-1225	279	5	equation	equation	NOUN
ijassa-1225	279	6	ẋ2	ẋ2	PROPN
ijassa-1225	279	7	−	−	PROPN
ijassa-1225	280	1	2q1(t)ẋ+	2q1(t)ẋ+	NUM
ijassa-1225	281	1	χ(x)−	χ(x)−	PROPN
ijassa-1225	281	2	q0(t	q0(t	PROPN
ijassa-1225	281	3	)	)	PUNCT
ijassa-1225	281	4	=	=	SYM
ijassa-1225	281	5	0	0	NUM
ijassa-1225	281	6	,	,	PUNCT
ijassa-1225	281	7	t	t	PROPN
ijassa-1225	281	8	∈	∈	PROPN
ijassa-1225	282	1	[	[	X
ijassa-1225	282	2	a	a	X
ijassa-1225	282	3	,	,	PUNCT
ijassa-1225	282	4	b	b	NOUN
ijassa-1225	282	5	]	]	X
ijassa-1225	282	6	,	,	PUNCT
ijassa-1225	282	7	(	(	PUNCT
ijassa-1225	282	8	4.18	4.18	NUM
ijassa-1225	282	9	)	)	PUNCT
ijassa-1225	282	10	together	together	ADV
ijassa-1225	282	11	with	with	ADP
ijassa-1225	282	12	the	the	DET
ijassa-1225	282	13	additional	additional	ADJ
ijassa-1225	282	14	condition	condition	NOUN
ijassa-1225	282	15	ẋ	ẋ	PROPN
ijassa-1225	282	16	∈	∈	PROPN
ijassa-1225	282	17	b(t	b(t	PROPN
ijassa-1225	282	18	)	)	PUNCT
ijassa-1225	282	19	.	.	PUNCT
ijassa-1225	283	1	=	=	PUNCT
ijassa-1225	284	1	[	[	X
ijassa-1225	284	2	q1(t)−	q1(t)−	X
ijassa-1225	284	3	r	r	NOUN
ijassa-1225	284	4	,	,	PUNCT
ijassa-1225	284	5	q1(t	q1(t	NUM
ijassa-1225	284	6	)	)	PUNCT
ijassa-1225	285	1	+	+	CCONJ
ijassa-1225	285	2	r	r	X
ijassa-1225	285	3	]	]	X
ijassa-1225	285	4	,	,	PUNCT
ijassa-1225	285	5	t	t	PROPN
ijassa-1225	285	6	∈	∈	PROPN
ijassa-1225	286	1	[	[	X
ijassa-1225	286	2	a	a	X
ijassa-1225	286	3	,	,	PUNCT
ijassa-1225	286	4	b	b	NOUN
ijassa-1225	286	5	]	]	X
ijassa-1225	286	6	.	.	PUNCT
ijassa-1225	287	1	(	(	PUNCT
ijassa-1225	287	2	4.19	4.19	NUM
ijassa-1225	287	3	)	)	PUNCT
ijassa-1225	287	4	let	let	VERB
ijassa-1225	287	5	us	we	PRON
ijassa-1225	287	6	demonstrate	demonstrate	VERB
ijassa-1225	287	7	that	that	SCONJ
ijassa-1225	287	8	if	if	SCONJ
ijassa-1225	287	9	the	the	DET
ijassa-1225	287	10	inequalities	inequality	NOUN
ijassa-1225	287	11	−	−	PROPN
ijassa-1225	287	12	1	1	NUM
ijassa-1225	287	13	≤	≤	NUM
ijassa-1225	287	14	q0(t	q0(t	PROPN
ijassa-1225	287	15	)	)	PUNCT
ijassa-1225	287	16	+	+	NUM
ijassa-1225	287	17	q2	q2	NOUN
ijassa-1225	287	18	1(t	1(t	NUM
ijassa-1225	287	19	)	)	PUNCT
ijassa-1225	287	20	≤	≤	NUM
ijassa-1225	287	21	r2	r2	NOUN
ijassa-1225	287	22	,	,	PUNCT
ijassa-1225	287	23	t	t	PROPN
ijassa-1225	287	24	∈	∈	PROPN
ijassa-1225	287	25	[	[	X
ijassa-1225	287	26	a	a	X
ijassa-1225	287	27	,	,	PUNCT
ijassa-1225	287	28	b	b	NOUN
ijassa-1225	287	29	]	]	X
ijassa-1225	287	30	,	,	PUNCT
ijassa-1225	287	31	(	(	PUNCT
ijassa-1225	287	32	4.20	4.20	NUM
ijassa-1225	287	33	)	)	PUNCT
ijassa-1225	287	34	are	be	AUX
ijassa-1225	287	35	fulfilled	fulfil	VERB
ijassa-1225	287	36	,	,	PUNCT
ijassa-1225	287	37	the	the	DET
ijassa-1225	287	38	cauchi	cauchi	PROPN
ijassa-1225	287	39	problem	problem	NOUN
ijassa-1225	287	40	for	for	ADP
ijassa-1225	287	41	the	the	DET
ijassa-1225	287	42	system	system	NOUN
ijassa-1225	287	43	(	(	PUNCT
ijassa-1225	287	44	4.18	4.18	NUM
ijassa-1225	287	45	)	)	PUNCT
ijassa-1225	287	46	,	,	PUNCT
ijassa-1225	287	47	(	(	PUNCT
ijassa-1225	287	48	4.19	4.19	NUM
ijassa-1225	287	49	)	)	PUNCT
ijassa-1225	287	50	with	with	ADP
ijassa-1225	287	51	the	the	DET
ijassa-1225	287	52	initial	initial	ADJ
ijassa-1225	287	53	condition	condition	NOUN
ijassa-1225	287	54	(	(	PUNCT
ijassa-1225	287	55	4.13	4.13	NUM
ijassa-1225	287	56	)	)	PUNCT
ijassa-1225	287	57	for	for	ADP
ijassa-1225	287	58	any	any	DET
ijassa-1225	287	59	γ	γ	NOUN
ijassa-1225	287	60	has	have	VERB
ijassa-1225	287	61	a	a	DET
ijassa-1225	287	62	solution	solution	NOUN
ijassa-1225	287	63	x	x	X
ijassa-1225	287	64	∈	∈	PROPN
ijassa-1225	287	65	ac(b	ac(b	NOUN
ijassa-1225	287	66	)	)	PUNCT
ijassa-1225	287	67	such	such	ADJ
ijassa-1225	287	68	that	that	SCONJ
ijassa-1225	287	69	ẋ(t	ẋ(t	NOUN
ijassa-1225	287	70	)	)	PUNCT
ijassa-1225	287	71	≤	≤	NOUN
ijassa-1225	288	1	q1(t	q1(t	X
ijassa-1225	288	2	)	)	PUNCT
ijassa-1225	288	3	,	,	PUNCT
ijassa-1225	288	4	t	t	PROPN
ijassa-1225	288	5	∈	∈	PROPN
ijassa-1225	289	1	[	[	X
ijassa-1225	289	2	a	a	X
ijassa-1225	289	3	,	,	PUNCT
ijassa-1225	289	4	b	b	NOUN
ijassa-1225	289	5	]	]	X
ijassa-1225	289	6	.	.	PUNCT
ijassa-1225	290	1	we	we	PRON
ijassa-1225	290	2	treat	treat	VERB
ijassa-1225	290	3	the	the	DET
ijassa-1225	290	4	equation	equation	NOUN
ijassa-1225	290	5	(	(	PUNCT
ijassa-1225	290	6	4.18	4.18	NUM
ijassa-1225	290	7	)	)	PUNCT
ijassa-1225	290	8	as	as	ADP
ijassa-1225	290	9	the	the	DET
ijassa-1225	290	10	inclusion	inclusion	NOUN
ijassa-1225	290	11	(	(	PUNCT
ijassa-1225	290	12	4.11	4.11	NUM
ijassa-1225	290	13	)	)	PUNCT
ijassa-1225	290	14	with	with	ADP
ijassa-1225	290	15	the	the	DET
ijassa-1225	290	16	single	single	ADV
ijassa-1225	290	17	-	-	PUNCT
ijassa-1225	290	18	valued	value	VERB
ijassa-1225	290	19	mapping	mapping	NOUN
ijassa-1225	290	20	f	f	X
ijassa-1225	290	21	:	:	PUNCT
ijassa-1225	291	1	[	[	X
ijassa-1225	291	2	a	a	X
ijassa-1225	291	3	,	,	PUNCT
ijassa-1225	291	4	b]×	b]×	NOUN
ijassa-1225	291	5	r×	r×	NOUN
ijassa-1225	291	6	r→	r→	PROPN
ijassa-1225	291	7	r	r	NOUN
ijassa-1225	291	8	defined	define	VERB
ijassa-1225	291	9	by	by	ADP
ijassa-1225	291	10	the	the	DET
ijassa-1225	291	11	relation	relation	NOUN
ijassa-1225	291	12	f(t	f(t	PROPN
ijassa-1225	291	13	,	,	PUNCT
ijassa-1225	291	14	x	x	NOUN
ijassa-1225	291	15	,	,	PUNCT
ijassa-1225	291	16	u	u	NOUN
ijassa-1225	291	17	)	)	PUNCT
ijassa-1225	291	18	=	=	SYM
ijassa-1225	291	19	g(t	g(t	PROPN
ijassa-1225	291	20	,	,	PUNCT
ijassa-1225	291	21	u)−	u)−	PROPN
ijassa-1225	291	22	χ(x	χ(x	PROPN
ijassa-1225	291	23	)	)	PUNCT
ijassa-1225	291	24	,	,	PUNCT
ijassa-1225	291	25	t	t	PROPN
ijassa-1225	291	26	∈	∈	PROPN
ijassa-1225	292	1	[	[	X
ijassa-1225	292	2	a	a	X
ijassa-1225	292	3	,	,	PUNCT
ijassa-1225	292	4	b	b	NOUN
ijassa-1225	292	5	]	]	X
ijassa-1225	292	6	,	,	PUNCT
ijassa-1225	292	7	x	x	X
ijassa-1225	292	8	,	,	PUNCT
ijassa-1225	292	9	u	u	PROPN
ijassa-1225	292	10	∈	∈	PROPN
ijassa-1225	292	11	r	r	NOUN
ijassa-1225	292	12	,	,	PUNCT
ijassa-1225	292	13	where	where	SCONJ
ijassa-1225	292	14	g	g	PROPN
ijassa-1225	292	15	is	be	AUX
ijassa-1225	292	16	given	give	VERB
ijassa-1225	292	17	in	in	ADP
ijassa-1225	292	18	the	the	DET
ijassa-1225	292	19	example	example	NOUN
ijassa-1225	292	20	2.1	2.1	NUM
ijassa-1225	292	21	by	by	ADP
ijassa-1225	292	22	the	the	DET
ijassa-1225	292	23	formula	formula	NOUN
ijassa-1225	292	24	(	(	PUNCT
ijassa-1225	292	25	3.8	3.8	NUM
ijassa-1225	292	26	)	)	PUNCT
ijassa-1225	292	27	.	.	PUNCT
ijassa-1225	293	1	obviously	obviously	ADV
ijassa-1225	293	2	,	,	PUNCT
ijassa-1225	293	3	for	for	ADP
ijassa-1225	293	4	all	all	DET
ijassa-1225	293	5	x	x	NOUN
ijassa-1225	293	6	,	,	PUNCT
ijassa-1225	293	7	u	u	NOUN
ijassa-1225	293	8	,	,	PUNCT
ijassa-1225	293	9	the	the	DET
ijassa-1225	293	10	function	function	NOUN
ijassa-1225	293	11	f	f	X
ijassa-1225	293	12	(	(	PUNCT
ijassa-1225	293	13	·	·	PUNCT
ijassa-1225	293	14	,	,	PUNCT
ijassa-1225	293	15	x	x	NOUN
ijassa-1225	293	16	,	,	PUNCT
ijassa-1225	293	17	u	u	NOUN
ijassa-1225	293	18	)	)	PUNCT
ijassa-1225	293	19	is	be	AUX
ijassa-1225	293	20	measurable	measurable	ADJ
ijassa-1225	293	21	,	,	PUNCT
ijassa-1225	293	22	for	for	ADP
ijassa-1225	293	23	almost	almost	ADV
ijassa-1225	293	24	all	all	PRON
ijassa-1225	293	25	t	t	NOUN
ijassa-1225	293	26	and	and	CCONJ
ijassa-1225	293	27	any	any	DET
ijassa-1225	293	28	u	u	NOUN
ijassa-1225	293	29	,	,	PUNCT
ijassa-1225	293	30	the	the	DET
ijassa-1225	293	31	function	function	NOUN
ijassa-1225	293	32	f(t	f(t	NOUN
ijassa-1225	293	33	,	,	PUNCT
ijassa-1225	293	34	·	·	PUNCT
ijassa-1225	293	35	,	,	PUNCT
ijassa-1225	293	36	u	u	NOUN
ijassa-1225	293	37	)	)	PUNCT
ijassa-1225	293	38	decreases	decrease	NOUN
ijassa-1225	293	39	(	(	PUNCT
ijassa-1225	293	40	i.e.	i.e.	X
ijassa-1225	293	41	the	the	DET
ijassa-1225	293	42	condition	condition	NOUN
ijassa-1225	293	43	(	(	PUNCT
ijassa-1225	293	44	b2	b2	NOUN
ijassa-1225	293	45	)	)	PUNCT
ijassa-1225	293	46	of	of	ADP
ijassa-1225	293	47	theorem	theorem	ADJ
ijassa-1225	293	48	4.1	4.1	NUM
ijassa-1225	293	49	is	be	AUX
ijassa-1225	293	50	fulfilled	fulfil	VERB
ijassa-1225	293	51	)	)	PUNCT
ijassa-1225	293	52	and	and	CCONJ
ijassa-1225	293	53	right	right	ADV
ijassa-1225	293	54	continuous	continuous	ADJ
ijassa-1225	293	55	,	,	PUNCT
ijassa-1225	293	56	and	and	CCONJ
ijassa-1225	293	57	for	for	ADP
ijassa-1225	293	58	almost	almost	ADV
ijassa-1225	293	59	all	all	PRON
ijassa-1225	293	60	t	t	NOUN
ijassa-1225	293	61	and	and	CCONJ
ijassa-1225	293	62	any	any	DET
ijassa-1225	293	63	x	x	NOUN
ijassa-1225	293	64	,	,	PUNCT
ijassa-1225	293	65	the	the	DET
ijassa-1225	293	66	function	function	NOUN
ijassa-1225	293	67	f(t	f(t	NOUN
ijassa-1225	293	68	,	,	PUNCT
ijassa-1225	293	69	x	x	X
ijassa-1225	293	70	,	,	PUNCT
ijassa-1225	293	71	·	·	PUNCT
ijassa-1225	293	72	)	)	PUNCT
ijassa-1225	293	73	is	be	AUX
ijassa-1225	293	74	continuous	continuous	ADJ
ijassa-1225	293	75	.	.	PUNCT
ijassa-1225	294	1	as	as	SCONJ
ijassa-1225	294	2	it	it	PRON
ijassa-1225	294	3	was	be	AUX
ijassa-1225	294	4	demonstrated	demonstrate	VERB
ijassa-1225	294	5	in	in	ADP
ijassa-1225	294	6	example	example	NOUN
ijassa-1225	294	7	2.1	2.1	NUM
ijassa-1225	294	8	,	,	PUNCT
ijassa-1225	294	9	the	the	DET
ijassa-1225	294	10	inequality	inequality	NOUN
ijassa-1225	294	11	q0(t	q0(t	PROPN
ijassa-1225	294	12	)	)	PUNCT
ijassa-1225	294	13	+	+	NUM
ijassa-1225	294	14	q2	q2	NOUN
ijassa-1225	294	15	1(t	1(t	NUM
ijassa-1225	294	16	)	)	PUNCT
ijassa-1225	294	17	≤	≤	NUM
ijassa-1225	294	18	r2	r2	NOUN
ijassa-1225	294	19	implies	imply	VERB
ijassa-1225	294	20	the	the	DET
ijassa-1225	294	21	condition	condition	NOUN
ijassa-1225	294	22	(	(	PUNCT
ijassa-1225	294	23	b1	b1	NOUN
ijassa-1225	294	24	)	)	PUNCT
ijassa-1225	294	25	of	of	ADP
ijassa-1225	294	26	theorem	theorem	NOUN
ijassa-1225	294	27	4.1	4.1	NUM
ijassa-1225	294	28	.	.	PUNCT
ijassa-1225	295	1	if	if	SCONJ
ijassa-1225	295	2	one	one	PRON
ijassa-1225	295	3	takes	take	VERB
ijassa-1225	295	4	v0(t	v0(t	NOUN
ijassa-1225	295	5	)	)	PUNCT
ijassa-1225	295	6	=	=	SYM
ijassa-1225	295	7	γ	γ	PROPN
ijassa-1225	295	8	+	+	NOUN
ijassa-1225	295	9	∫	∫	PROPN
ijassa-1225	295	10	b	b	PROPN
ijassa-1225	295	11	a	a	DET
ijassa-1225	295	12	p(s)ds	p(s)ds	NOUN
ijassa-1225	295	13	,	,	PUNCT
ijassa-1225	295	14	t	t	PROPN
ijassa-1225	295	15	∈	∈	PROPN
ijassa-1225	296	1	[	[	X
ijassa-1225	296	2	a	a	X
ijassa-1225	296	3	,	,	PUNCT
ijassa-1225	296	4	b	b	NOUN
ijassa-1225	296	5	]	]	X
ijassa-1225	296	6	,	,	PUNCT
ijassa-1225	296	7	the	the	DET
ijassa-1225	296	8	relations	relation	NOUN
ijassa-1225	296	9	f	f	PROPN
ijassa-1225	296	10	(	(	PUNCT
ijassa-1225	296	11	t	t	PROPN
ijassa-1225	296	12	,	,	PUNCT
ijassa-1225	296	13	v0(t	v0(t	PROPN
ijassa-1225	296	14	)	)	PUNCT
ijassa-1225	296	15	,	,	PUNCT
ijassa-1225	296	16	v̇0(t	v̇0(t	PROPN
ijassa-1225	296	17	)	)	PUNCT
ijassa-1225	296	18	)	)	PUNCT
ijassa-1225	297	1	=	=	SYM
ijassa-1225	297	2	−v̇2	−v̇2	PUNCT
ijassa-1225	297	3	0(t	0(t	NUM
ijassa-1225	297	4	)	)	PUNCT
ijassa-1225	297	5	+	+	CCONJ
ijassa-1225	297	6	2q1(t)v̇0(t)−	2q1(t)v̇0(t)−	NUM
ijassa-1225	297	7	χ(vo(t	χ(vo(t	NUM
ijassa-1225	297	8	)	)	PUNCT
ijassa-1225	297	9	)	)	PUNCT
ijassa-1225	298	1	+	+	CCONJ
ijassa-1225	299	1	q0(t	q0(t	PROPN
ijassa-1225	299	2	)	)	PUNCT
ijassa-1225	299	3	≥	≥	PROPN
ijassa-1225	299	4	q2	q2	NOUN
ijassa-1225	299	5	1(t)−	1(t)−	PROPN
ijassa-1225	299	6	1	1	NUM
ijassa-1225	299	7	+	+	NUM
ijassa-1225	299	8	q0(t	q0(t	PROPN
ijassa-1225	299	9	)	)	PUNCT
ijassa-1225	299	10	≥	≥	NOUN
ijassa-1225	299	11	0	0	NUM
ijassa-1225	299	12	take	take	VERB
ijassa-1225	299	13	place	place	NOUN
ijassa-1225	299	14	for	for	ADP
ijassa-1225	299	15	all	all	DET
ijassa-1225	299	16	t	t	NOUN
ijassa-1225	299	17	∈	∈	PROPN
ijassa-1225	300	1	[	[	X
ijassa-1225	300	2	a	a	X
ijassa-1225	300	3	,	,	PUNCT
ijassa-1225	300	4	b	b	NOUN
ijassa-1225	300	5	]	]	X
ijassa-1225	300	6	.	.	PUNCT
ijassa-1225	301	1	thus	thus	ADV
ijassa-1225	301	2	,	,	PUNCT
ijassa-1225	301	3	the	the	DET
ijassa-1225	301	4	condition	condition	NOUN
ijassa-1225	301	5	(	(	PUNCT
ijassa-1225	301	6	4.14	4.14	NUM
ijassa-1225	301	7	)	)	PUNCT
ijassa-1225	301	8	is	be	AUX
ijassa-1225	301	9	also	also	ADV
ijassa-1225	301	10	satisfied	satisfied	ADJ
ijassa-1225	301	11	,	,	PUNCT
ijassa-1225	301	12	and	and	CCONJ
ijassa-1225	301	13	,	,	PUNCT
ijassa-1225	301	14	according	accord	VERB
ijassa-1225	301	15	to	to	ADP
ijassa-1225	301	16	theorem	theorem	NOUN
ijassa-1225	301	17	4.1	4.1	NUM
ijassa-1225	301	18	,	,	PUNCT
ijassa-1225	301	19	the	the	DET
ijassa-1225	301	20	problem	problem	NOUN
ijassa-1225	301	21	(	(	PUNCT
ijassa-1225	301	22	4.18	4.18	NUM
ijassa-1225	301	23	)	)	PUNCT
ijassa-1225	301	24	,	,	PUNCT
ijassa-1225	301	25	(	(	PUNCT
ijassa-1225	301	26	4.19	4.19	NUM
ijassa-1225	301	27	)	)	PUNCT
ijassa-1225	301	28	,	,	PUNCT
ijassa-1225	301	29	(	(	PUNCT
ijassa-1225	301	30	4.13	4.13	NUM
ijassa-1225	301	31	)	)	PUNCT
ijassa-1225	301	32	has	have	VERB
ijassa-1225	301	33	a	a	DET
ijassa-1225	301	34	solution	solution	NOUN
ijassa-1225	301	35	x	x	X
ijassa-1225	301	36	∈	∈	PROPN
ijassa-1225	301	37	ac(b	ac(b	NOUN
ijassa-1225	301	38	)	)	PUNCT
ijassa-1225	301	39	satisfying	satisfy	VERB
ijassa-1225	301	40	the	the	DET
ijassa-1225	301	41	estimate	estimate	NOUN
ijassa-1225	301	42	ẋ(t	ẋ(t	NOUN
ijassa-1225	301	43	)	)	PUNCT
ijassa-1225	301	44	≤	≤	NOUN
ijassa-1225	301	45	q1(t	q1(t	X
ijassa-1225	301	46	)	)	PUNCT
ijassa-1225	301	47	,	,	PUNCT
ijassa-1225	301	48	t	t	PROPN
ijassa-1225	301	49	∈	∈	PROPN
ijassa-1225	302	1	[	[	X
ijassa-1225	302	2	a	a	X
ijassa-1225	302	3	,	,	PUNCT
ijassa-1225	302	4	b	b	NOUN
ijassa-1225	302	5	]	]	PUNCT
ijassa-1225	302	6	.	.	PUNCT
ijassa-1225	303	1	consider	consider	VERB
ijassa-1225	303	2	now	now	ADV
ijassa-1225	303	3	the	the	DET
ijassa-1225	303	4	following	follow	VERB
ijassa-1225	303	5	differential	differential	ADJ
ijassa-1225	303	6	inclusion	inclusion	NOUN
ijassa-1225	303	7	g+(t	g+(t	PROPN
ijassa-1225	303	8	,	,	PUNCT
ijassa-1225	303	9	ẋ)−	ẋ)−	PROPN
ijassa-1225	303	10	χ(x	χ(x	PROPN
ijassa-1225	303	11	)	)	PUNCT
ijassa-1225	303	12	3	3	NUM
ijassa-1225	303	13	0	0	NUM
ijassa-1225	303	14	,	,	PUNCT
ijassa-1225	303	15	t	t	PROPN
ijassa-1225	303	16	∈	∈	PROPN
ijassa-1225	304	1	[	[	X
ijassa-1225	304	2	a	a	X
ijassa-1225	304	3	,	,	PUNCT
ijassa-1225	304	4	b	b	NOUN
ijassa-1225	304	5	]	]	X
ijassa-1225	304	6	,	,	PUNCT
ijassa-1225	304	7	(	(	PUNCT
ijassa-1225	304	8	4.21	4.21	NUM
ijassa-1225	304	9	)	)	PUNCT
ijassa-1225	304	10	copyright	copyright	NOUN
ijassa-1225	304	11	©	©	ADP
ijassa-1225	304	12	2022	2022	NUM
ijassa-1225	304	13	assa	assa	NOUN
ijassa-1225	304	14	.	.	PUNCT
ijassa-1225	305	1	adv	adv	PROPN
ijassa-1225	305	2	syst	syst	PROPN
ijassa-1225	305	3	sci	sci	PROPN
ijassa-1225	305	4	appl	appl	PROPN
ijassa-1225	305	5	(	(	PUNCT
ijassa-1225	305	6	2022	2022	NUM
ijassa-1225	305	7	)	)	PUNCT
ijassa-1225	305	8	on	on	ADP
ijassa-1225	305	9	order	order	NOUN
ijassa-1225	305	10	covering	cover	VERB
ijassa-1225	305	11	set	set	NOUN
ijassa-1225	305	12	-	-	PUNCT
ijassa-1225	305	13	valued	value	VERB
ijassa-1225	305	14	mappings	mapping	NOUN
ijassa-1225	305	15	and	and	CCONJ
ijassa-1225	305	16	their	their	PRON
ijassa-1225	305	17	applications	application	NOUN
ijassa-1225	305	18	185	185	NUM
ijassa-1225	305	19	where	where	SCONJ
ijassa-1225	305	20	the	the	DET
ijassa-1225	305	21	set	set	NOUN
ijassa-1225	305	22	-	-	PUNCT
ijassa-1225	305	23	valued	value	VERB
ijassa-1225	305	24	mapping	mapping	NOUN
ijassa-1225	305	25	g+	g+	NOUN
ijassa-1225	305	26	:	:	PUNCT
ijassa-1225	306	1	[	[	X
ijassa-1225	306	2	a	a	X
ijassa-1225	306	3	,	,	PUNCT
ijassa-1225	306	4	b]×	b]×	NOUN
ijassa-1225	306	5	r→	r→	PROPN
ijassa-1225	306	6	k(r	k(r	PROPN
ijassa-1225	306	7	)	)	PUNCT
ijassa-1225	306	8	is	be	AUX
ijassa-1225	306	9	given	give	VERB
ijassa-1225	306	10	by	by	ADP
ijassa-1225	306	11	the	the	DET
ijassa-1225	306	12	first	first	ADJ
ijassa-1225	306	13	formula	formula	NOUN
ijassa-1225	306	14	in	in	ADP
ijassa-1225	306	15	(	(	PUNCT
ijassa-1225	306	16	3.10	3.10	NUM
ijassa-1225	306	17	)	)	PUNCT
ijassa-1225	306	18	(	(	PUNCT
ijassa-1225	306	19	see	see	VERB
ijassa-1225	306	20	example	example	NOUN
ijassa-1225	306	21	2.1	2.1	NUM
ijassa-1225	306	22	)	)	PUNCT
ijassa-1225	306	23	.	.	PUNCT
ijassa-1225	307	1	in	in	ADP
ijassa-1225	307	2	the	the	DET
ijassa-1225	307	3	investigation	investigation	NOUN
ijassa-1225	307	4	of	of	ADP
ijassa-1225	307	5	this	this	DET
ijassa-1225	307	6	inclusion	inclusion	NOUN
ijassa-1225	307	7	,	,	PUNCT
ijassa-1225	307	8	one	one	PRON
ijassa-1225	307	9	can	can	AUX
ijassa-1225	307	10	also	also	ADV
ijassa-1225	307	11	make	make	VERB
ijassa-1225	307	12	use	use	NOUN
ijassa-1225	307	13	of	of	ADP
ijassa-1225	307	14	theorem	theorem	NOUN
ijassa-1225	307	15	4.1	4.1	NUM
ijassa-1225	307	16	.	.	PUNCT
ijassa-1225	308	1	in	in	ADP
ijassa-1225	308	2	order	order	NOUN
ijassa-1225	308	3	to	to	PART
ijassa-1225	308	4	do	do	AUX
ijassa-1225	308	5	this	this	PRON
ijassa-1225	308	6	,	,	PUNCT
ijassa-1225	308	7	one	one	PRON
ijassa-1225	308	8	should	should	AUX
ijassa-1225	308	9	use	use	VERB
ijassa-1225	308	10	the	the	DET
ijassa-1225	308	11	condition	condition	NOUN
ijassa-1225	308	12	that	that	PRON
ijassa-1225	308	13	guarantees	guarantee	VERB
ijassa-1225	308	14	that	that	SCONJ
ijassa-1225	308	15	the	the	DET
ijassa-1225	308	16	mapping	mapping	NOUN
ijassa-1225	308	17	g+(t	g+(t	PROPN
ijassa-1225	308	18	,	,	PUNCT
ijassa-1225	308	19	·	·	PUNCT
ijassa-1225	308	20	)	)	PUNCT
ijassa-1225	308	21	order	order	NOUN
ijassa-1225	308	22	covers	cover	VERB
ijassa-1225	308	23	the	the	DET
ijassa-1225	308	24	set	set	NOUN
ijassa-1225	308	25	{	{	PUNCT
ijassa-1225	308	26	0	0	NUM
ijassa-1225	308	27	}	}	PUNCT
ijassa-1225	308	28	⊂	⊂	PROPN
ijassa-1225	308	29	r	r	NOUN
ijassa-1225	308	30	,	,	PUNCT
ijassa-1225	308	31	which	which	PRON
ijassa-1225	308	32	was	be	AUX
ijassa-1225	308	33	derived	derive	VERB
ijassa-1225	308	34	in	in	ADP
ijassa-1225	308	35	example	example	NOUN
ijassa-1225	308	36	2.1	2.1	NUM
ijassa-1225	308	37	.	.	PUNCT
ijassa-1225	309	1	one	one	NOUN
ijassa-1225	309	2	thus	thus	ADV
ijassa-1225	309	3	concludes	conclude	VERB
ijassa-1225	309	4	that	that	SCONJ
ijassa-1225	309	5	if	if	SCONJ
ijassa-1225	309	6	the	the	DET
ijassa-1225	309	7	inequalities	inequality	NOUN
ijassa-1225	309	8	−	−	PROPN
ijassa-1225	309	9	1−	1−	NUM
ijassa-1225	309	10	δ	δ	PROPN
ijassa-1225	309	11	≤	≤	PROPN
ijassa-1225	309	12	q0(t	q0(t	PROPN
ijassa-1225	309	13	)	)	PUNCT
ijassa-1225	309	14	+	+	NUM
ijassa-1225	309	15	q2	q2	NOUN
ijassa-1225	309	16	1(t	1(t	NUM
ijassa-1225	309	17	)	)	PUNCT
ijassa-1225	309	18	≤	≤	NUM
ijassa-1225	309	19	r2	r2	NOUN
ijassa-1225	309	20	,	,	PUNCT
ijassa-1225	309	21	t	t	PROPN
ijassa-1225	309	22	∈	∈	PROPN
ijassa-1225	309	23	[	[	X
ijassa-1225	309	24	a	a	X
ijassa-1225	309	25	,	,	PUNCT
ijassa-1225	309	26	b	b	NOUN
ijassa-1225	309	27	]	]	X
ijassa-1225	309	28	,	,	PUNCT
ijassa-1225	309	29	(	(	PUNCT
ijassa-1225	309	30	4.22	4.22	NUM
ijassa-1225	309	31	)	)	PUNCT
ijassa-1225	309	32	are	be	AUX
ijassa-1225	309	33	satisfied	satisfied	ADJ
ijassa-1225	309	34	,	,	PUNCT
ijassa-1225	309	35	the	the	DET
ijassa-1225	309	36	problem	problem	NOUN
ijassa-1225	309	37	(	(	PUNCT
ijassa-1225	309	38	4.21	4.21	NUM
ijassa-1225	309	39	)	)	PUNCT
ijassa-1225	309	40	,	,	PUNCT
ijassa-1225	309	41	(	(	PUNCT
ijassa-1225	309	42	4.19	4.19	NUM
ijassa-1225	309	43	)	)	PUNCT
ijassa-1225	309	44	,	,	PUNCT
ijassa-1225	309	45	(	(	PUNCT
ijassa-1225	309	46	4.13	4.13	X
ijassa-1225	309	47	)	)	PUNCT
ijassa-1225	309	48	possesses	possess	VERB
ijassa-1225	309	49	a	a	DET
ijassa-1225	309	50	solution	solution	NOUN
ijassa-1225	309	51	for	for	ADP
ijassa-1225	309	52	any	any	DET
ijassa-1225	309	53	γ	γ	NOUN
ijassa-1225	309	54	.	.	PUNCT
ijassa-1225	309	55	finally	finally	ADV
ijassa-1225	309	56	,	,	PUNCT
ijassa-1225	309	57	we	we	PRON
ijassa-1225	309	58	consider	consider	VERB
ijassa-1225	309	59	the	the	DET
ijassa-1225	309	60	differential	differential	ADJ
ijassa-1225	309	61	inclusion	inclusion	NOUN
ijassa-1225	309	62	g−(t	g−(t	PROPN
ijassa-1225	309	63	,	,	PUNCT
ijassa-1225	309	64	ẋ)−	ẋ)−	PROPN
ijassa-1225	309	65	χ(x	χ(x	PROPN
ijassa-1225	309	66	)	)	PUNCT
ijassa-1225	309	67	3	3	NUM
ijassa-1225	309	68	0	0	NUM
ijassa-1225	309	69	,	,	PUNCT
ijassa-1225	309	70	t	t	PROPN
ijassa-1225	309	71	∈	∈	PROPN
ijassa-1225	310	1	[	[	X
ijassa-1225	310	2	a	a	X
ijassa-1225	310	3	,	,	PUNCT
ijassa-1225	310	4	b	b	NOUN
ijassa-1225	310	5	]	]	X
ijassa-1225	310	6	,	,	PUNCT
ijassa-1225	310	7	(	(	PUNCT
ijassa-1225	310	8	4.23	4.23	NUM
ijassa-1225	310	9	)	)	PUNCT
ijassa-1225	310	10	with	with	ADP
ijassa-1225	310	11	the	the	DET
ijassa-1225	310	12	set	set	NOUN
ijassa-1225	310	13	-	-	PUNCT
ijassa-1225	310	14	valued	value	VERB
ijassa-1225	310	15	function	function	NOUN
ijassa-1225	310	16	g−	g−	ADJ
ijassa-1225	310	17	:	:	PUNCT
ijassa-1225	310	18	[	[	X
ijassa-1225	310	19	a	a	X
ijassa-1225	310	20	,	,	PUNCT
ijassa-1225	310	21	b]×	b]×	NOUN
ijassa-1225	310	22	r→	r→	PROPN
ijassa-1225	310	23	k(r	k(r	NOUN
ijassa-1225	310	24	)	)	PUNCT
ijassa-1225	310	25	given	give	VERB
ijassa-1225	310	26	by	by	ADP
ijassa-1225	310	27	the	the	DET
ijassa-1225	310	28	second	second	ADJ
ijassa-1225	310	29	formula	formula	NOUN
ijassa-1225	310	30	in	in	ADP
ijassa-1225	310	31	(	(	PUNCT
ijassa-1225	310	32	3.10	3.10	NUM
ijassa-1225	310	33	)	)	PUNCT
ijassa-1225	310	34	.	.	PUNCT
ijassa-1225	311	1	for	for	ADP
ijassa-1225	311	2	this	this	DET
ijassa-1225	311	3	inclusion	inclusion	NOUN
ijassa-1225	311	4	,	,	PUNCT
ijassa-1225	311	5	we	we	PRON
ijassa-1225	311	6	analogously	analogously	ADV
ijassa-1225	311	7	find	find	VERB
ijassa-1225	311	8	that	that	SCONJ
ijassa-1225	311	9	the	the	DET
ijassa-1225	311	10	validity	validity	NOUN
ijassa-1225	311	11	of	of	ADP
ijassa-1225	311	12	the	the	DET
ijassa-1225	311	13	inequalities	inequality	NOUN
ijassa-1225	311	14	−	−	PROPN
ijassa-1225	311	15	1	1	NUM
ijassa-1225	311	16	≤	≤	NUM
ijassa-1225	311	17	q0(t	q0(t	PROPN
ijassa-1225	311	18	)	)	PUNCT
ijassa-1225	311	19	+	+	NUM
ijassa-1225	311	20	q2	q2	NOUN
ijassa-1225	311	21	1(t	1(t	NUM
ijassa-1225	311	22	)	)	PUNCT
ijassa-1225	311	23	≤	≤	NUM
ijassa-1225	311	24	r2	r2	NOUN
ijassa-1225	311	25	+	+	CCONJ
ijassa-1225	311	26	δ	δ	PROPN
ijassa-1225	311	27	,	,	PUNCT
ijassa-1225	311	28	t	t	PROPN
ijassa-1225	311	29	∈	∈	PROPN
ijassa-1225	312	1	[	[	X
ijassa-1225	312	2	a	a	X
ijassa-1225	312	3	,	,	PUNCT
ijassa-1225	312	4	b	b	NOUN
ijassa-1225	312	5	]	]	X
ijassa-1225	312	6	,	,	PUNCT
ijassa-1225	312	7	(	(	PUNCT
ijassa-1225	312	8	4.24	4.24	NUM
ijassa-1225	312	9	)	)	PUNCT
ijassa-1225	312	10	guarantees	guarantee	VERB
ijassa-1225	312	11	the	the	DET
ijassa-1225	312	12	solvability	solvability	NOUN
ijassa-1225	312	13	of	of	ADP
ijassa-1225	312	14	the	the	DET
ijassa-1225	312	15	problem	problem	NOUN
ijassa-1225	312	16	(	(	PUNCT
ijassa-1225	312	17	4.23	4.23	NUM
ijassa-1225	312	18	)	)	PUNCT
ijassa-1225	312	19	,	,	PUNCT
ijassa-1225	312	20	(	(	PUNCT
ijassa-1225	312	21	4.19	4.19	NUM
ijassa-1225	312	22	)	)	PUNCT
ijassa-1225	312	23	,	,	PUNCT
ijassa-1225	312	24	(	(	PUNCT
ijassa-1225	312	25	4.13	4.13	NUM
ijassa-1225	312	26	)	)	PUNCT
ijassa-1225	312	27	for	for	SCONJ
ijassa-1225	312	28	any	any	DET
ijassa-1225	312	29	γ	γ	NOUN
ijassa-1225	312	30	.	.	PUNCT
ijassa-1225	312	31	consider	consider	VERB
ijassa-1225	312	32	a	a	DET
ijassa-1225	312	33	particular	particular	ADJ
ijassa-1225	312	34	case	case	NOUN
ijassa-1225	312	35	of	of	ADP
ijassa-1225	312	36	the	the	DET
ijassa-1225	312	37	inclusion	inclusion	NOUN
ijassa-1225	312	38	(	(	PUNCT
ijassa-1225	312	39	4.11	4.11	NUM
ijassa-1225	312	40	)	)	PUNCT
ijassa-1225	312	41	,	,	PUNCT
ijassa-1225	312	42	which	which	PRON
ijassa-1225	312	43	allows	allow	VERB
ijassa-1225	312	44	to	to	PART
ijassa-1225	312	45	obtain	obtain	VERB
ijassa-1225	312	46	the	the	DET
ijassa-1225	312	47	existence	existence	NOUN
ijassa-1225	312	48	of	of	ADP
ijassa-1225	312	49	a	a	DET
ijassa-1225	312	50	lower	low	ADJ
ijassa-1225	312	51	solution	solution	NOUN
ijassa-1225	312	52	to	to	ADP
ijassa-1225	312	53	the	the	DET
ijassa-1225	312	54	corresponding	correspond	VERB
ijassa-1225	312	55	cauchi	cauchi	PROPN
ijassa-1225	312	56	problem	problem	NOUN
ijassa-1225	312	57	.	.	PUNCT
ijassa-1225	313	1	let	let	VERB
ijassa-1225	313	2	m	m	VERB
ijassa-1225	313	3	=	=	SYM
ijassa-1225	313	4	n	n	PROPN
ijassa-1225	313	5	and	and	CCONJ
ijassa-1225	313	6	the	the	DET
ijassa-1225	313	7	components	component	NOUN
ijassa-1225	313	8	of	of	ADP
ijassa-1225	313	9	f	f	PROPN
ijassa-1225	313	10	be	be	AUX
ijassa-1225	313	11	given	give	VERB
ijassa-1225	313	12	by	by	ADP
ijassa-1225	313	13	the	the	DET
ijassa-1225	313	14	functions	function	NOUN
ijassa-1225	313	15	fi	fi	NOUN
ijassa-1225	313	16	:	:	PUNCT
ijassa-1225	314	1	[	[	X
ijassa-1225	314	2	a	a	X
ijassa-1225	314	3	,	,	PUNCT
ijassa-1225	314	4	b]×	b]×	NOUN
ijassa-1225	314	5	rn	rn	PROPN
ijassa-1225	314	6	×	×	PROPN
ijassa-1225	314	7	rn	rn	PROPN
ijassa-1225	314	8	×	×	PROPN
ijassa-1225	314	9	r→	r→	PROPN
ijassa-1225	314	10	kc(r	kc(r	NOUN
ijassa-1225	314	11	)	)	PUNCT
ijassa-1225	314	12	,	,	PUNCT
ijassa-1225	314	13	i	i	PRON
ijassa-1225	314	14	=	=	NOUN
ijassa-1225	314	15	1	1	NUM
ijassa-1225	314	16	,	,	PUNCT
ijassa-1225	314	17	n	n	CCONJ
ijassa-1225	314	18	(	(	PUNCT
ijassa-1225	314	19	having	have	VERB
ijassa-1225	314	20	compact	compact	ADJ
ijassa-1225	314	21	and	and	CCONJ
ijassa-1225	314	22	connected	connected	ADJ
ijassa-1225	314	23	values	value	NOUN
ijassa-1225	314	24	,	,	PUNCT
ijassa-1225	314	25	i.e.	i.e.	X
ijassa-1225	314	26	the	the	DET
ijassa-1225	314	27	real	real	ADJ
ijassa-1225	314	28	line	line	NOUN
ijassa-1225	314	29	segments	segment	NOUN
ijassa-1225	314	30	)	)	PUNCT
ijassa-1225	314	31	.	.	PUNCT
ijassa-1225	315	1	let	let	VERB
ijassa-1225	315	2	us	we	PRON
ijassa-1225	315	3	assume	assume	VERB
ijassa-1225	315	4	that	that	SCONJ
ijassa-1225	315	5	for	for	ADP
ijassa-1225	315	6	any	any	DET
ijassa-1225	315	7	x	x	NOUN
ijassa-1225	315	8	,	,	PUNCT
ijassa-1225	315	9	v	v	PROPN
ijassa-1225	315	10	∈	∈	PROPN
ijassa-1225	315	11	rn	rn	PROPN
ijassa-1225	315	12	,	,	PUNCT
ijassa-1225	315	13	z	z	PROPN
ijassa-1225	315	14	∈	∈	PROPN
ijassa-1225	315	15	r	r	NOUN
ijassa-1225	315	16	,	,	PUNCT
ijassa-1225	315	17	the	the	DET
ijassa-1225	315	18	function	function	NOUN
ijassa-1225	315	19	fi	fi	NOUN
ijassa-1225	315	20	(	(	PUNCT
ijassa-1225	315	21	·	·	PUNCT
ijassa-1225	315	22	,	,	PUNCT
ijassa-1225	315	23	x	x	NOUN
ijassa-1225	315	24	,	,	PUNCT
ijassa-1225	315	25	v	v	NOUN
ijassa-1225	315	26	,	,	PUNCT
ijassa-1225	315	27	z	z	NOUN
ijassa-1225	315	28	)	)	PUNCT
ijassa-1225	315	29	:	:	PUNCT
ijassa-1225	316	1	[	[	X
ijassa-1225	316	2	a	a	DET
ijassa-1225	316	3	,	,	PUNCT
ijassa-1225	316	4	b]→	b]→	NOUN
ijassa-1225	316	5	kc(r	kc(r	X
ijassa-1225	316	6	)	)	PUNCT
ijassa-1225	316	7	is	be	AUX
ijassa-1225	316	8	measurable	measurable	ADJ
ijassa-1225	316	9	;	;	PUNCT
ijassa-1225	316	10	for	for	ADP
ijassa-1225	316	11	almost	almost	ADV
ijassa-1225	316	12	all	all	PRON
ijassa-1225	316	13	t	t	NOUN
ijassa-1225	316	14	∈	∈	PRON
ijassa-1225	316	15	[	[	X
ijassa-1225	316	16	a	a	X
ijassa-1225	316	17	,	,	PUNCT
ijassa-1225	316	18	b	b	NOUN
ijassa-1225	316	19	]	]	X
ijassa-1225	316	20	,	,	PUNCT
ijassa-1225	316	21	any	any	DET
ijassa-1225	316	22	v	v	ADP
ijassa-1225	316	23	∈	∈	PROPN
ijassa-1225	316	24	rn	rn	PROPN
ijassa-1225	316	25	and	and	CCONJ
ijassa-1225	316	26	z	z	NOUN
ijassa-1225	316	27	∈	∈	PROPN
ijassa-1225	316	28	r	r	NOUN
ijassa-1225	316	29	,	,	PUNCT
ijassa-1225	316	30	the	the	DET
ijassa-1225	316	31	function	function	NOUN
ijassa-1225	316	32	fi(t	fi(t	NOUN
ijassa-1225	316	33	,	,	PUNCT
ijassa-1225	316	34	·	·	PUNCT
ijassa-1225	316	35	,	,	PUNCT
ijassa-1225	316	36	v	v	NOUN
ijassa-1225	316	37	,	,	PUNCT
ijassa-1225	316	38	z	z	NOUN
ijassa-1225	316	39	)	)	PUNCT
ijassa-1225	316	40	:	:	PUNCT
ijassa-1225	316	41	rn	rn	PROPN
ijassa-1225	316	42	→	→	SYM
ijassa-1225	316	43	kc(r	kc(r	CCONJ
ijassa-1225	316	44	)	)	PUNCT
ijassa-1225	316	45	is	be	AUX
ijassa-1225	316	46	right	right	ADV
ijassa-1225	316	47	continuous	continuous	ADJ
ijassa-1225	316	48	in	in	ADP
ijassa-1225	316	49	each	each	PRON
ijassa-1225	316	50	of	of	ADP
ijassa-1225	316	51	the	the	DET
ijassa-1225	316	52	arguments	argument	NOUN
ijassa-1225	316	53	x1	x1	NUM
ijassa-1225	316	54	,	,	PUNCT
ijassa-1225	316	55	.	.	PUNCT
ijassa-1225	316	56	.	.	PUNCT
ijassa-1225	317	1	.	.	PUNCT
ijassa-1225	318	1	,	,	PUNCT
ijassa-1225	318	2	xn	xn	PROPN
ijassa-1225	318	3	;	;	PUNCT
ijassa-1225	318	4	for	for	ADP
ijassa-1225	318	5	almost	almost	ADV
ijassa-1225	318	6	all	all	PRON
ijassa-1225	318	7	t	t	NOUN
ijassa-1225	318	8	∈	∈	PRON
ijassa-1225	319	1	[	[	X
ijassa-1225	319	2	a	a	X
ijassa-1225	319	3	,	,	PUNCT
ijassa-1225	319	4	b	b	NOUN
ijassa-1225	319	5	]	]	X
ijassa-1225	319	6	,	,	PUNCT
ijassa-1225	319	7	any	any	DET
ijassa-1225	319	8	x	x	PROPN
ijassa-1225	319	9	∈	∈	PROPN
ijassa-1225	319	10	rn	rn	PROPN
ijassa-1225	319	11	and	and	CCONJ
ijassa-1225	319	12	z	z	NOUN
ijassa-1225	319	13	∈	∈	PROPN
ijassa-1225	319	14	r	r	NOUN
ijassa-1225	319	15	,	,	PUNCT
ijassa-1225	319	16	the	the	DET
ijassa-1225	319	17	function	function	NOUN
ijassa-1225	319	18	fi(t	fi(t	NOUN
ijassa-1225	319	19	,	,	PUNCT
ijassa-1225	319	20	x	x	X
ijassa-1225	319	21	,	,	PUNCT
ijassa-1225	319	22	·	·	PUNCT
ijassa-1225	319	23	,	,	PUNCT
ijassa-1225	319	24	z	z	NOUN
ijassa-1225	319	25	)	)	PUNCT
ijassa-1225	319	26	:	:	PUNCT
ijassa-1225	319	27	rn	rn	PROPN
ijassa-1225	319	28	→	→	SYM
ijassa-1225	319	29	kc(r	kc(r	CCONJ
ijassa-1225	319	30	)	)	PUNCT
ijassa-1225	319	31	is	be	AUX
ijassa-1225	319	32	right	right	ADV
ijassa-1225	319	33	continuous	continuous	ADJ
ijassa-1225	319	34	in	in	ADP
ijassa-1225	319	35	each	each	PRON
ijassa-1225	319	36	of	of	ADP
ijassa-1225	319	37	the	the	DET
ijassa-1225	319	38	arguments	argument	NOUN
ijassa-1225	319	39	v1	v1	NOUN
ijassa-1225	319	40	,	,	PUNCT
ijassa-1225	319	41	.	.	PUNCT
ijassa-1225	319	42	.	.	PUNCT
ijassa-1225	320	1	.	.	PUNCT
ijassa-1225	321	1	,	,	PUNCT
ijassa-1225	321	2	vn	vn	X
ijassa-1225	321	3	;	;	PUNCT
ijassa-1225	321	4	for	for	ADP
ijassa-1225	321	5	almost	almost	ADV
ijassa-1225	321	6	all	all	PRON
ijassa-1225	321	7	t	t	NOUN
ijassa-1225	321	8	∈	∈	PRON
ijassa-1225	322	1	[	[	X
ijassa-1225	322	2	a	a	X
ijassa-1225	322	3	,	,	PUNCT
ijassa-1225	322	4	b	b	NOUN
ijassa-1225	322	5	]	]	X
ijassa-1225	322	6	and	and	CCONJ
ijassa-1225	322	7	any	any	DET
ijassa-1225	322	8	x	x	NOUN
ijassa-1225	322	9	,	,	PUNCT
ijassa-1225	322	10	v	v	PROPN
ijassa-1225	322	11	∈	∈	PROPN
ijassa-1225	322	12	rn	rn	PROPN
ijassa-1225	322	13	,	,	PUNCT
ijassa-1225	322	14	the	the	DET
ijassa-1225	322	15	function	function	NOUN
ijassa-1225	322	16	fi(t	fi(t	NOUN
ijassa-1225	322	17	,	,	PUNCT
ijassa-1225	322	18	x	x	NOUN
ijassa-1225	322	19	,	,	PUNCT
ijassa-1225	322	20	v	v	NOUN
ijassa-1225	322	21	,	,	PUNCT
ijassa-1225	322	22	·	·	PUNCT
ijassa-1225	322	23	)	)	PUNCT
ijassa-1225	322	24	:	:	PUNCT
ijassa-1225	323	1	r→	r→	PROPN
ijassa-1225	323	2	kc(r	kc(r	VERB
ijassa-1225	323	3	)	)	PUNCT
ijassa-1225	323	4	is	be	AUX
ijassa-1225	323	5	continuous	continuous	ADJ
ijassa-1225	323	6	.	.	PUNCT
ijassa-1225	324	1	we	we	PRON
ijassa-1225	324	2	investigate	investigate	VERB
ijassa-1225	324	3	the	the	DET
ijassa-1225	324	4	following	follow	VERB
ijassa-1225	324	5	system	system	NOUN
ijassa-1225	324	6	:	:	PUNCT
ijassa-1225	324	7	fi(t	fi(t	NUM
ijassa-1225	324	8	,	,	PUNCT
ijassa-1225	324	9	x	x	X
ijassa-1225	324	10	,	,	PUNCT
ijassa-1225	324	11	ẋ	ẋ	PROPN
ijassa-1225	324	12	,	,	PUNCT
ijassa-1225	324	13	ẋi	ẋi	PROPN
ijassa-1225	324	14	)	)	PUNCT
ijassa-1225	324	15	3	3	NUM
ijassa-1225	324	16	0	0	NUM
ijassa-1225	324	17	,	,	PUNCT
ijassa-1225	324	18	t	t	PROPN
ijassa-1225	324	19	∈	∈	PROPN
ijassa-1225	325	1	[	[	X
ijassa-1225	325	2	a	a	X
ijassa-1225	325	3	,	,	PUNCT
ijassa-1225	325	4	b	b	NOUN
ijassa-1225	325	5	]	]	X
ijassa-1225	325	6	,	,	PUNCT
ijassa-1225	325	7	i	i	PRON
ijassa-1225	325	8	=	=	NOUN
ijassa-1225	325	9	1	1	NUM
ijassa-1225	325	10	,	,	PUNCT
ijassa-1225	325	11	n.	n.	NOUN
ijassa-1225	325	12	(	(	PUNCT
ijassa-1225	325	13	4.25	4.25	NUM
ijassa-1225	325	14	)	)	PUNCT
ijassa-1225	325	15	theorem	theorem	VERB
ijassa-1225	325	16	4.2	4.2	NUM
ijassa-1225	325	17	:	:	PUNCT
ijassa-1225	325	18	let	let	VERB
ijassa-1225	325	19	functions	function	NOUN
ijassa-1225	325	20	u0	u0	VERB
ijassa-1225	325	21	,	,	PUNCT
ijassa-1225	325	22	v0	v0	PROPN
ijassa-1225	325	23	∈	∈	PROPN
ijassa-1225	325	24	acn	acn	PROPN
ijassa-1225	325	25	such	such	ADJ
ijassa-1225	325	26	that	that	PRON
ijassa-1225	325	27	u0(a	u0(a	PROPN
ijassa-1225	325	28	)	)	PUNCT
ijassa-1225	325	29	≤	≤	NUM
ijassa-1225	325	30	γ	γ	X
ijassa-1225	325	31	≤	≤	NOUN
ijassa-1225	325	32	v0(a	v0(a	NUM
ijassa-1225	325	33	)	)	PUNCT
ijassa-1225	325	34	,	,	PUNCT
ijassa-1225	325	35	−fi	−fi	PROPN
ijassa-1225	325	36	(	(	PUNCT
ijassa-1225	325	37	t	t	PROPN
ijassa-1225	325	38	,	,	PUNCT
ijassa-1225	325	39	u0(t	u0(t	PROPN
ijassa-1225	325	40	)	)	PUNCT
ijassa-1225	325	41	,	,	PUNCT
ijassa-1225	325	42	u̇0(t	u̇0(t	NOUN
ijassa-1225	325	43	)	)	PUNCT
ijassa-1225	325	44	,	,	PUNCT
ijassa-1225	325	45	u̇0i(t	u̇0i(t	NOUN
ijassa-1225	325	46	)	)	PUNCT
ijassa-1225	325	47	)	)	PUNCT
ijassa-1225	326	1	∩	∩	NOUN
ijassa-1225	326	2	r+	r+	VERB
ijassa-1225	326	3	6=	6=	ADP
ijassa-1225	326	4	∅	∅	NOUN
ijassa-1225	326	5	for	for	ADP
ijassa-1225	326	6	almost	almost	ADV
ijassa-1225	326	7	all	all	PRON
ijassa-1225	326	8	t	t	NOUN
ijassa-1225	326	9	∈	∈	PRON
ijassa-1225	327	1	[	[	X
ijassa-1225	327	2	a	a	X
ijassa-1225	327	3	,	,	PUNCT
ijassa-1225	327	4	b	b	NOUN
ijassa-1225	327	5	]	]	X
ijassa-1225	327	6	,	,	PUNCT
ijassa-1225	327	7	i	i	PRON
ijassa-1225	327	8	=	=	NOUN
ijassa-1225	327	9	1	1	NUM
ijassa-1225	327	10	,	,	PUNCT
ijassa-1225	327	11	n	n	CCONJ
ijassa-1225	327	12	,	,	PUNCT
ijassa-1225	327	13	fi	fi	X
ijassa-1225	327	14	(	(	PUNCT
ijassa-1225	327	15	t	t	PROPN
ijassa-1225	327	16	,	,	PUNCT
ijassa-1225	327	17	v0(t	v0(t	PROPN
ijassa-1225	327	18	)	)	PUNCT
ijassa-1225	327	19	,	,	PUNCT
ijassa-1225	327	20	v̇0(t	v̇0(t	PROPN
ijassa-1225	327	21	)	)	PUNCT
ijassa-1225	327	22	,	,	PUNCT
ijassa-1225	327	23	v̇0i(t	v̇0i(t	NOUN
ijassa-1225	327	24	)	)	PUNCT
ijassa-1225	327	25	)	)	PUNCT
ijassa-1225	328	1	∩	∩	NOUN
ijassa-1225	328	2	r+	r+	VERB
ijassa-1225	328	3	6=	6=	ADP
ijassa-1225	328	4	∅	∅	NOUN
ijassa-1225	328	5	for	for	ADP
ijassa-1225	328	6	almost	almost	ADV
ijassa-1225	328	7	all	all	PRON
ijassa-1225	328	8	t	t	NOUN
ijassa-1225	328	9	∈	∈	PRON
ijassa-1225	329	1	[	[	X
ijassa-1225	329	2	a	a	X
ijassa-1225	329	3	,	,	PUNCT
ijassa-1225	329	4	b	b	NOUN
ijassa-1225	329	5	]	]	X
ijassa-1225	329	6	,	,	PUNCT
ijassa-1225	329	7	i	i	PRON
ijassa-1225	329	8	=	=	NOUN
ijassa-1225	329	9	1	1	NUM
ijassa-1225	329	10	,	,	PUNCT
ijassa-1225	329	11	n	n	CCONJ
ijassa-1225	329	12	,	,	PUNCT
ijassa-1225	329	13	be	be	AUX
ijassa-1225	329	14	given	give	VERB
ijassa-1225	329	15	.	.	PUNCT
ijassa-1225	330	1	define	define	VERB
ijassa-1225	330	2	a	a	DET
ijassa-1225	330	3	set	set	NOUN
ijassa-1225	330	4	-	-	PUNCT
ijassa-1225	330	5	valued	value	VERB
ijassa-1225	330	6	mapping	mapping	NOUN
ijassa-1225	330	7	b	b	NOUN
ijassa-1225	330	8	:	:	PUNCT
ijassa-1225	331	1	[	[	X
ijassa-1225	331	2	a	a	PRON
ijassa-1225	331	3	,	,	PUNCT
ijassa-1225	331	4	b]→	b]→	ADJ
ijassa-1225	331	5	cc(rn	cc(rn	PROPN
ijassa-1225	331	6	)	)	PUNCT
ijassa-1225	331	7	as	as	SCONJ
ijassa-1225	331	8	follows	follow	VERB
ijassa-1225	331	9	:	:	PUNCT
ijassa-1225	331	10	b(t	b(t	NOUN
ijassa-1225	331	11	)	)	PUNCT
ijassa-1225	331	12	.	.	PUNCT
ijassa-1225	332	1	=	=	PUNCT
ijassa-1225	332	2	[	[	PUNCT
ijassa-1225	332	3	v̇0(t	v̇0(t	PROPN
ijassa-1225	332	4	)	)	PUNCT
ijassa-1225	332	5	,	,	PUNCT
ijassa-1225	332	6	u̇0(t	u̇0(t	NOUN
ijassa-1225	332	7	)	)	PUNCT
ijassa-1225	332	8	]	]	PUNCT
ijassa-1225	332	9	rn	rn	PROPN
ijassa-1225	332	10	,	,	PUNCT
ijassa-1225	332	11	t	t	PROPN
ijassa-1225	332	12	∈	∈	PROPN
ijassa-1225	333	1	[	[	X
ijassa-1225	333	2	a	a	X
ijassa-1225	333	3	,	,	PUNCT
ijassa-1225	333	4	b	b	NOUN
ijassa-1225	333	5	]	]	X
ijassa-1225	333	6	.	.	PUNCT
ijassa-1225	334	1	(	(	PUNCT
ijassa-1225	334	2	4.26	4.26	NUM
ijassa-1225	334	3	)	)	PUNCT
ijassa-1225	334	4	assume	assume	VERB
ijassa-1225	334	5	that	that	SCONJ
ijassa-1225	334	6	for	for	ADP
ijassa-1225	334	7	any	any	DET
ijassa-1225	334	8	i	i	NOUN
ijassa-1225	334	9	=	=	NOUN
ijassa-1225	334	10	1	1	NUM
ijassa-1225	334	11	,	,	PUNCT
ijassa-1225	334	12	n	n	CCONJ
ijassa-1225	334	13	,	,	PUNCT
ijassa-1225	334	14	for	for	ADP
ijassa-1225	334	15	almost	almost	ADV
ijassa-1225	334	16	all	all	PRON
ijassa-1225	334	17	t	t	NOUN
ijassa-1225	334	18	∈	∈	PRON
ijassa-1225	334	19	[	[	X
ijassa-1225	334	20	a	a	X
ijassa-1225	334	21	,	,	PUNCT
ijassa-1225	334	22	b	b	NOUN
ijassa-1225	334	23	]	]	X
ijassa-1225	334	24	and	and	CCONJ
ijassa-1225	334	25	all	all	DET
ijassa-1225	334	26	u	u	PROPN
ijassa-1225	334	27	∈	∈	PROPN
ijassa-1225	334	28	b(t	b(t	PROPN
ijassa-1225	334	29	)	)	PUNCT
ijassa-1225	334	30	,	,	PUNCT
ijassa-1225	334	31	the	the	DET
ijassa-1225	334	32	mapping	mapping	NOUN
ijassa-1225	334	33	fi(t	fi(t	NOUN
ijassa-1225	334	34	,	,	PUNCT
ijassa-1225	334	35	·	·	PUNCT
ijassa-1225	334	36	,	,	PUNCT
ijassa-1225	334	37	·	·	PUNCT
ijassa-1225	334	38	,	,	PUNCT
ijassa-1225	334	39	u	u	NOUN
ijassa-1225	334	40	)	)	PUNCT
ijassa-1225	334	41	:	:	PUNCT
ijassa-1225	334	42	rn	rn	PROPN
ijassa-1225	334	43	×	×	PROPN
ijassa-1225	334	44	rn	rn	PROPN
ijassa-1225	334	45	→	→	SYM
ijassa-1225	334	46	kc(r	kc(r	PRON
ijassa-1225	334	47	)	)	PUNCT
ijassa-1225	334	48	is	be	AUX
ijassa-1225	334	49	antitone	antitone	ADJ
ijassa-1225	334	50	on	on	ADP
ijassa-1225	334	51	the	the	DET
ijassa-1225	334	52	set	set	PROPN
ijassa-1225	334	53	rn	rn	PROPN
ijassa-1225	334	54	×b(t	×b(t	PROPN
ijassa-1225	334	55	)	)	PUNCT
ijassa-1225	334	56	.	.	PUNCT
ijassa-1225	335	1	then	then	ADV
ijassa-1225	335	2	there	there	PRON
ijassa-1225	335	3	exists	exist	VERB
ijassa-1225	335	4	a	a	DET
ijassa-1225	335	5	solution	solution	NOUN
ijassa-1225	335	6	x	x	X
ijassa-1225	335	7	∈	∈	PROPN
ijassa-1225	335	8	ac(b	ac(b	NOUN
ijassa-1225	335	9	)	)	PUNCT
ijassa-1225	335	10	to	to	ADP
ijassa-1225	335	11	the	the	DET
ijassa-1225	335	12	problem	problem	NOUN
ijassa-1225	335	13	(	(	PUNCT
ijassa-1225	335	14	4.25	4.25	NUM
ijassa-1225	335	15	)	)	PUNCT
ijassa-1225	335	16	,	,	PUNCT
ijassa-1225	335	17	(	(	PUNCT
ijassa-1225	335	18	4.12	4.12	NUM
ijassa-1225	335	19	)	)	PUNCT
ijassa-1225	335	20	,	,	PUNCT
ijassa-1225	335	21	(	(	PUNCT
ijassa-1225	335	22	4.13	4.13	NUM
ijassa-1225	335	23	)	)	PUNCT
ijassa-1225	335	24	.	.	PUNCT
ijassa-1225	336	1	moreover	moreover	ADV
ijassa-1225	336	2	,	,	PUNCT
ijassa-1225	336	3	the	the	DET
ijassa-1225	336	4	set	set	NOUN
ijassa-1225	336	5	of	of	ADP
ijassa-1225	336	6	solutions	solution	NOUN
ijassa-1225	336	7	to	to	ADP
ijassa-1225	336	8	the	the	DET
ijassa-1225	336	9	problem	problem	NOUN
ijassa-1225	336	10	(	(	PUNCT
ijassa-1225	336	11	4.25	4.25	NUM
ijassa-1225	336	12	)	)	PUNCT
ijassa-1225	336	13	,	,	PUNCT
ijassa-1225	336	14	(	(	PUNCT
ijassa-1225	336	15	4.12	4.12	NUM
ijassa-1225	336	16	)	)	PUNCT
ijassa-1225	336	17	,	,	PUNCT
ijassa-1225	336	18	(	(	PUNCT
ijassa-1225	336	19	4.13	4.13	NUM
ijassa-1225	336	20	)	)	PUNCT
ijassa-1225	336	21	contains	contain	VERB
ijassa-1225	336	22	a	a	DET
ijassa-1225	336	23	solution	solution	NOUN
ijassa-1225	336	24	with	with	ADP
ijassa-1225	336	25	the	the	DET
ijassa-1225	336	26	least	least	ADJ
ijassa-1225	336	27	derivative	derivative	ADJ
ijassa-1225	336	28	.	.	PUNCT
ijassa-1225	337	1	remark	remark	VERB
ijassa-1225	337	2	4.1	4.1	NUM
ijassa-1225	337	3	:	:	PUNCT
ijassa-1225	337	4	by	by	ADP
ijassa-1225	337	5	the	the	DET
ijassa-1225	337	6	virtue	virtue	NOUN
ijassa-1225	337	7	of	of	ADP
ijassa-1225	337	8	the	the	DET
ijassa-1225	337	9	definition	definition	NOUN
ijassa-1225	337	10	of	of	ADP
ijassa-1225	337	11	the	the	DET
ijassa-1225	337	12	mapping	mapping	NOUN
ijassa-1225	337	13	b	b	NOUN
ijassa-1225	337	14	by	by	ADP
ijassa-1225	337	15	(	(	PUNCT
ijassa-1225	337	16	4.26	4.26	NUM
ijassa-1225	337	17	)	)	PUNCT
ijassa-1225	337	18	,	,	PUNCT
ijassa-1225	337	19	the	the	DET
ijassa-1225	337	20	fact	fact	NOUN
ijassa-1225	337	21	that	that	SCONJ
ijassa-1225	337	22	a	a	DET
ijassa-1225	337	23	solution	solution	NOUN
ijassa-1225	337	24	x	x	PUNCT
ijassa-1225	337	25	belongs	belong	VERB
ijassa-1225	337	26	to	to	ADP
ijassa-1225	337	27	ac(b	ac(b	PROPN
ijassa-1225	337	28	)	)	PUNCT
ijassa-1225	337	29	means	mean	VERB
ijassa-1225	337	30	that	that	SCONJ
ijassa-1225	337	31	this	this	DET
ijassa-1225	337	32	absolutely	absolutely	ADV
ijassa-1225	337	33	continuous	continuous	ADJ
ijassa-1225	337	34	function	function	NOUN
ijassa-1225	337	35	satisfies	satisfy	VERB
ijassa-1225	337	36	the	the	DET
ijassa-1225	337	37	inequalities	inequality	NOUN
ijassa-1225	337	38	u̇0(t	u̇0(t	NOUN
ijassa-1225	337	39	)	)	PUNCT
ijassa-1225	337	40	≤	≤	NOUN
ijassa-1225	337	41	ẋ(t	ẋ(t	NOUN
ijassa-1225	337	42	)	)	PUNCT
ijassa-1225	337	43	≤	≤	NOUN
ijassa-1225	337	44	v̇0(t	v̇0(t	PROPN
ijassa-1225	337	45	)	)	PUNCT
ijassa-1225	337	46	for	for	ADP
ijassa-1225	337	47	almost	almost	ADV
ijassa-1225	337	48	all	all	PRON
ijassa-1225	337	49	t	t	NOUN
ijassa-1225	337	50	∈	∈	PRON
ijassa-1225	338	1	[	[	X
ijassa-1225	338	2	a	a	X
ijassa-1225	338	3	,	,	PUNCT
ijassa-1225	338	4	b	b	NOUN
ijassa-1225	338	5	]	]	PUNCT
ijassa-1225	338	6	.	.	PUNCT
ijassa-1225	339	1	proof	proof	NOUN
ijassa-1225	339	2	we	we	PRON
ijassa-1225	339	3	will	will	AUX
ijassa-1225	339	4	denote	denote	VERB
ijassa-1225	339	5	the	the	DET
ijassa-1225	339	6	restrictions	restriction	NOUN
ijassa-1225	339	7	of	of	ADP
ijassa-1225	339	8	mappings	mapping	NOUN
ijassa-1225	339	9	by	by	ADP
ijassa-1225	339	10	the	the	DET
ijassa-1225	339	11	same	same	ADJ
ijassa-1225	339	12	symbols	symbol	NOUN
ijassa-1225	339	13	as	as	ADP
ijassa-1225	339	14	the	the	DET
ijassa-1225	339	15	initial	initial	ADJ
ijassa-1225	339	16	mappings	mapping	NOUN
ijassa-1225	339	17	copyright	copyright	NOUN
ijassa-1225	339	18	©	©	ADP
ijassa-1225	339	19	2022	2022	NUM
ijassa-1225	339	20	assa	assa	NOUN
ijassa-1225	339	21	.	.	PUNCT
ijassa-1225	340	1	adv	adv	PROPN
ijassa-1225	340	2	syst	syst	PROPN
ijassa-1225	340	3	sci	sci	PROPN
ijassa-1225	340	4	appl	appl	PROPN
ijassa-1225	340	5	(	(	PUNCT
ijassa-1225	340	6	2022	2022	NUM
ijassa-1225	340	7	)	)	PUNCT
ijassa-1225	340	8	186	186	NUM
ijassa-1225	340	9	e.s	e.s	PROPN
ijassa-1225	340	10	.	.	PROPN
ijassa-1225	340	11	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	340	12	,	,	PUNCT
ijassa-1225	340	13	i.d	i.d	PROPN
ijassa-1225	340	14	.	.	PROPN
ijassa-1225	340	15	serova	serova	PROPN
ijassa-1225	340	16	,	,	PUNCT
ijassa-1225	340	17	e.a	e.a	PROPN
ijassa-1225	340	18	.	.	PROPN
ijassa-1225	340	19	panasenko	panasenko	PROPN
ijassa-1225	340	20	,	,	PUNCT
ijassa-1225	340	21	e.o	e.o	PROPN
ijassa-1225	340	22	.	.	PROPN
ijassa-1225	340	23	burlakov	burlakov	PROPN
ijassa-1225	340	24	provided	provide	VERB
ijassa-1225	340	25	that	that	PRON
ijassa-1225	340	26	leads	lead	VERB
ijassa-1225	340	27	to	to	ADP
ijassa-1225	340	28	no	no	DET
ijassa-1225	340	29	ambiguity	ambiguity	NOUN
ijassa-1225	340	30	.	.	PUNCT
ijassa-1225	341	1	we	we	PRON
ijassa-1225	341	2	denote	denote	VERB
ijassa-1225	341	3	the	the	DET
ijassa-1225	341	4	components	component	NOUN
ijassa-1225	341	5	of	of	ADP
ijassa-1225	341	6	the	the	DET
ijassa-1225	341	7	set	set	NOUN
ijassa-1225	341	8	-	-	PUNCT
ijassa-1225	341	9	valued	value	VERB
ijassa-1225	341	10	mappingb	mappingb	NOUN
ijassa-1225	341	11	:	:	PUNCT
ijassa-1225	342	1	[	[	X
ijassa-1225	342	2	a	a	PRON
ijassa-1225	342	3	,	,	PUNCT
ijassa-1225	342	4	b]→	b]→	ADJ
ijassa-1225	342	5	cc(rn	cc(rn	PROPN
ijassa-1225	342	6	)	)	PUNCT
ijassa-1225	342	7	as	as	ADP
ijassa-1225	342	8	bi	bi	NOUN
ijassa-1225	342	9	:	:	PUNCT
ijassa-1225	343	1	[	[	X
ijassa-1225	343	2	a	a	PRON
ijassa-1225	343	3	,	,	PUNCT
ijassa-1225	343	4	b]→	b]→	ADJ
ijassa-1225	343	5	cc(r	cc(r	NOUN
ijassa-1225	343	6	)	)	PUNCT
ijassa-1225	343	7	,	,	PUNCT
ijassa-1225	343	8	i.e.	i.e.	X
ijassa-1225	343	9	bi(t	bi(t	NOUN
ijassa-1225	343	10	)	)	PUNCT
ijassa-1225	343	11	.	.	PUNCT
ijassa-1225	344	1	=	=	PUNCT
ijassa-1225	345	1	[	[	PUNCT
ijassa-1225	345	2	v̇0i(t	v̇0i(t	NOUN
ijassa-1225	345	3	)	)	PUNCT
ijassa-1225	345	4	,	,	PUNCT
ijassa-1225	345	5	u̇0i(t	u̇0i(t	NOUN
ijassa-1225	345	6	)	)	PUNCT
ijassa-1225	345	7	]	]	PUNCT
ijassa-1225	345	8	,	,	PUNCT
ijassa-1225	345	9	t	t	PROPN
ijassa-1225	345	10	∈	∈	PROPN
ijassa-1225	346	1	[	[	X
ijassa-1225	346	2	a	a	X
ijassa-1225	346	3	,	,	PUNCT
ijassa-1225	346	4	b	b	NOUN
ijassa-1225	346	5	]	]	X
ijassa-1225	346	6	.	.	PUNCT
ijassa-1225	347	1	we	we	PRON
ijassa-1225	347	2	define	define	VERB
ijassa-1225	347	3	the	the	DET
ijassa-1225	347	4	set	set	NOUN
ijassa-1225	347	5	ti	ti	PROPN
ijassa-1225	347	6	⊂	⊂	PROPN
ijassa-1225	348	1	[	[	X
ijassa-1225	348	2	a	a	X
ijassa-1225	348	3	,	,	PUNCT
ijassa-1225	348	4	b	b	NOUN
ijassa-1225	348	5	]	]	PUNCT
ijassa-1225	348	6	of	of	ADP
ijassa-1225	348	7	such	such	ADJ
ijassa-1225	348	8	t	t	PROPN
ijassa-1225	348	9	∈	∈	PROPN
ijassa-1225	349	1	[	[	X
ijassa-1225	349	2	a	a	X
ijassa-1225	349	3	,	,	PUNCT
ijassa-1225	349	4	b	b	NOUN
ijassa-1225	349	5	]	]	X
ijassa-1225	349	6	that	that	SCONJ
ijassa-1225	349	7	for	for	ADP
ijassa-1225	349	8	all	all	DET
ijassa-1225	349	9	x	x	PROPN
ijassa-1225	349	10	∈	∈	PROPN
ijassa-1225	349	11	rn	rn	PROPN
ijassa-1225	349	12	,	,	PUNCT
ijassa-1225	349	13	v	v	PROPN
ijassa-1225	349	14	∈	∈	PROPN
ijassa-1225	349	15	b(t	b(t	NOUN
ijassa-1225	349	16	)	)	PUNCT
ijassa-1225	349	17	,	,	PUNCT
ijassa-1225	349	18	the	the	DET
ijassa-1225	349	19	mapping	mapping	NOUN
ijassa-1225	349	20	fi(t	fi(t	NOUN
ijassa-1225	349	21	,	,	PUNCT
ijassa-1225	349	22	x	x	NOUN
ijassa-1225	349	23	,	,	PUNCT
ijassa-1225	349	24	v	v	NOUN
ijassa-1225	349	25	,	,	PUNCT
ijassa-1225	349	26	·	·	PUNCT
ijassa-1225	349	27	)	)	PUNCT
ijassa-1225	349	28	:	:	PUNCT
ijassa-1225	349	29	bi(t)→	bi(t)→	NOUN
ijassa-1225	349	30	kc(r	kc(r	PRON
ijassa-1225	349	31	)	)	PUNCT
ijassa-1225	349	32	is	be	AUX
ijassa-1225	349	33	continuous	continuous	ADJ
ijassa-1225	349	34	,	,	PUNCT
ijassa-1225	349	35	and−∞	and−∞	PROPN
ijassa-1225	349	36	<	<	X
ijassa-1225	349	37	v̇0(t	v̇0(t	PROPN
ijassa-1225	349	38	)	)	PUNCT
ijassa-1225	349	39	,	,	PUNCT
ijassa-1225	349	40	u̇0(t	u̇0(t	NOUN
ijassa-1225	349	41	)	)	PUNCT
ijassa-1225	349	42	<	<	X
ijassa-1225	350	1	+	+	PUNCT
ijassa-1225	350	2	∞.	∞.	PROPN
ijassa-1225	350	3	the	the	DET
ijassa-1225	350	4	lebesgue	lebesgue	ADJ
ijassa-1225	350	5	measure	measure	NOUN
ijassa-1225	350	6	of	of	ADP
ijassa-1225	350	7	this	this	DET
ijassa-1225	350	8	set	set	NOUN
ijassa-1225	350	9	equals	equal	VERB
ijassa-1225	350	10	to	to	ADP
ijassa-1225	350	11	b−	b−	PROPN
ijassa-1225	350	12	a	a	NOUN
ijassa-1225	350	13	,	,	PUNCT
ijassa-1225	350	14	and	and	CCONJ
ijassa-1225	350	15	for	for	ADP
ijassa-1225	350	16	all	all	DET
ijassa-1225	350	17	t	t	NOUN
ijassa-1225	350	18	∈	∈	PRON
ijassa-1225	350	19	ti	ti	NOUN
ijassa-1225	350	20	,	,	PUNCT
ijassa-1225	350	21	the	the	DET
ijassa-1225	350	22	set	set	NOUN
ijassa-1225	350	23	bi(t	bi(t	NOUN
ijassa-1225	350	24	)	)	PUNCT
ijassa-1225	350	25	is	be	AUX
ijassa-1225	350	26	a	a	DET
ijassa-1225	350	27	segment	segment	NOUN
ijassa-1225	350	28	of	of	ADP
ijassa-1225	350	29	the	the	DET
ijassa-1225	350	30	real	real	ADJ
ijassa-1225	350	31	line	line	NOUN
ijassa-1225	350	32	.	.	PUNCT
ijassa-1225	351	1	let	let	VERB
ijassa-1225	351	2	us	we	PRON
ijassa-1225	351	3	verify	verify	VERB
ijassa-1225	351	4	the	the	DET
ijassa-1225	351	5	condition	condition	NOUN
ijassa-1225	351	6	(	(	PUNCT
ijassa-1225	351	7	b1	b1	NOUN
ijassa-1225	351	8	)	)	PUNCT
ijassa-1225	351	9	of	of	ADP
ijassa-1225	351	10	theorem	theorem	NOUN
ijassa-1225	351	11	4.1	4.1	NUM
ijassa-1225	351	12	.	.	PUNCT
ijassa-1225	352	1	let	let	VERB
ijassa-1225	352	2	for	for	ADP
ijassa-1225	352	3	any	any	DET
ijassa-1225	352	4	i	i	NOUN
ijassa-1225	352	5	=	=	NOUN
ijassa-1225	352	6	1	1	NUM
ijassa-1225	352	7	,	,	PUNCT
ijassa-1225	352	8	n	n	CCONJ
ijassa-1225	352	9	,	,	PUNCT
ijassa-1225	352	10	for	for	ADP
ijassa-1225	352	11	some	some	DET
ijassa-1225	352	12	t	t	NOUN
ijassa-1225	352	13	∈	∈	NOUN
ijassa-1225	352	14	ti	ti	NOUN
ijassa-1225	352	15	,	,	PUNCT
ijassa-1225	352	16	there	there	PRON
ijassa-1225	352	17	exist	exist	VERB
ijassa-1225	352	18	x	x	SYM
ijassa-1225	352	19	∈	∈	PROPN
ijassa-1225	352	20	rn	rn	PROPN
ijassa-1225	352	21	,	,	PUNCT
ijassa-1225	352	22	v	v	PROPN
ijassa-1225	352	23	∈	∈	PROPN
ijassa-1225	352	24	b(t	b(t	NOUN
ijassa-1225	352	25	)	)	PUNCT
ijassa-1225	352	26	such	such	ADJ
ijassa-1225	352	27	that	that	SCONJ
ijassa-1225	352	28	the	the	DET
ijassa-1225	352	29	mapping	mapping	NOUN
ijassa-1225	352	30	fi(t	fi(t	NOUN
ijassa-1225	352	31	,	,	PUNCT
ijassa-1225	352	32	x	x	NOUN
ijassa-1225	352	33	,	,	PUNCT
ijassa-1225	352	34	v	v	NOUN
ijassa-1225	352	35	,	,	PUNCT
ijassa-1225	352	36	·	·	PUNCT
ijassa-1225	352	37	)	)	PUNCT
ijassa-1225	352	38	:	:	PUNCT
ijassa-1225	352	39	bi(t)→	bi(t)→	NOUN
ijassa-1225	352	40	kc(r	kc(r	VERB
ijassa-1225	352	41	)	)	PUNCT
ijassa-1225	352	42	does	do	AUX
ijassa-1225	352	43	not	not	PART
ijassa-1225	352	44	order	order	VERB
ijassa-1225	352	45	cover	cover	VERB
ijassa-1225	352	46	the	the	DET
ijassa-1225	352	47	set	set	NOUN
ijassa-1225	352	48	{	{	PUNCT
ijassa-1225	352	49	0	0	NUM
ijassa-1225	352	50	}	}	PUNCT
ijassa-1225	352	51	⊂	⊂	PROPN
ijassa-1225	352	52	r.	r.	PROPN
ijassa-1225	352	53	then	then	ADV
ijassa-1225	352	54	there	there	PRON
ijassa-1225	352	55	exists	exist	VERB
ijassa-1225	352	56	z0	z0	PROPN
ijassa-1225	352	57	∈	∈	PROPN
ijassa-1225	352	58	r	r	NOUN
ijassa-1225	352	59	such	such	ADJ
ijassa-1225	352	60	that	that	SCONJ
ijassa-1225	352	61	the	the	DET
ijassa-1225	352	62	set	set	NOUN
ijassa-1225	352	63	fi(t	fi(t	NOUN
ijassa-1225	352	64	,	,	PUNCT
ijassa-1225	352	65	x	x	NOUN
ijassa-1225	352	66	,	,	PUNCT
ijassa-1225	352	67	v	v	NOUN
ijassa-1225	352	68	,	,	PUNCT
ijassa-1225	352	69	z0	z0	PROPN
ijassa-1225	352	70	)	)	PUNCT
ijassa-1225	352	71	contains	contain	VERB
ijassa-1225	352	72	some	some	DET
ijassa-1225	352	73	positive	positive	ADJ
ijassa-1225	352	74	number	number	NOUN
ijassa-1225	352	75	,	,	PUNCT
ijassa-1225	352	76	and	and	CCONJ
ijassa-1225	352	77	for	for	ADP
ijassa-1225	352	78	any	any	DET
ijassa-1225	352	79	z	z	NOUN
ijassa-1225	352	80	∈	∈	PROPN
ijassa-1225	353	1	[	[	X
ijassa-1225	353	2	v̇0i(t	v̇0i(t	NOUN
ijassa-1225	353	3	)	)	PUNCT
ijassa-1225	353	4	,	,	PUNCT
ijassa-1225	353	5	z0	z0	PROPN
ijassa-1225	353	6	]	]	PUNCT
ijassa-1225	353	7	,	,	PUNCT
ijassa-1225	353	8	zero	zero	NUM
ijassa-1225	353	9	does	do	AUX
ijassa-1225	353	10	not	not	PART
ijassa-1225	353	11	belong	belong	VERB
ijassa-1225	353	12	to	to	ADP
ijassa-1225	353	13	the	the	DET
ijassa-1225	353	14	set	set	NOUN
ijassa-1225	353	15	fi(t	fi(t	NOUN
ijassa-1225	353	16	,	,	PUNCT
ijassa-1225	353	17	x	x	NOUN
ijassa-1225	353	18	,	,	PUNCT
ijassa-1225	353	19	v	v	NOUN
ijassa-1225	353	20	,	,	PUNCT
ijassa-1225	353	21	z	z	NOUN
ijassa-1225	353	22	)	)	PUNCT
ijassa-1225	353	23	.	.	PUNCT
ijassa-1225	354	1	let	let	VERB
ijassa-1225	354	2	us	we	PRON
ijassa-1225	354	3	demonstrate	demonstrate	VERB
ijassa-1225	354	4	that	that	SCONJ
ijassa-1225	354	5	there	there	PRON
ijassa-1225	354	6	exists	exist	VERB
ijassa-1225	354	7	δ	δ	PROPN
ijassa-1225	354	8	>	>	X
ijassa-1225	354	9	0	0	NUM
ijassa-1225	354	10	such	such	ADJ
ijassa-1225	354	11	that	that	PRON
ijassa-1225	354	12	for	for	ADP
ijassa-1225	354	13	any	any	DET
ijassa-1225	354	14	z	z	NOUN
ijassa-1225	354	15	∈	∈	PROPN
ijassa-1225	355	1	[	[	X
ijassa-1225	355	2	v̇0i(t	v̇0i(t	NOUN
ijassa-1225	355	3	)	)	PUNCT
ijassa-1225	355	4	,	,	PUNCT
ijassa-1225	355	5	z0	z0	PROPN
ijassa-1225	355	6	]	]	PUNCT
ijassa-1225	355	7	,	,	PUNCT
ijassa-1225	355	8	it	it	PRON
ijassa-1225	355	9	holds	hold	VERB
ijassa-1225	355	10	true	true	ADJ
ijassa-1225	355	11	that	that	SCONJ
ijassa-1225	355	12	fi(t	fi(t	NOUN
ijassa-1225	355	13	,	,	PUNCT
ijassa-1225	355	14	x	x	NOUN
ijassa-1225	355	15	,	,	PUNCT
ijassa-1225	355	16	v	v	NOUN
ijassa-1225	355	17	,	,	PUNCT
ijassa-1225	355	18	z	z	NOUN
ijassa-1225	355	19	)	)	PUNCT
ijassa-1225	355	20	∩	∩	NOUN
ijassa-1225	355	21	(	(	PUNCT
ijassa-1225	355	22	−δ	−δ	ADJ
ijassa-1225	355	23	,	,	PUNCT
ijassa-1225	355	24	δ	δ	X
ijassa-1225	355	25	)	)	PUNCT
ijassa-1225	355	26	=	=	PUNCT
ijassa-1225	355	27	∅.	∅.	X
ijassa-1225	355	28	(	(	PUNCT
ijassa-1225	355	29	4.27	4.27	NUM
ijassa-1225	355	30	)	)	PUNCT
ijassa-1225	355	31	otherwise	otherwise	ADV
ijassa-1225	355	32	,	,	PUNCT
ijassa-1225	355	33	there	there	PRON
ijassa-1225	355	34	exists	exist	VERB
ijassa-1225	355	35	a	a	DET
ijassa-1225	355	36	sequence	sequence	NOUN
ijassa-1225	355	37	{	{	PUNCT
ijassa-1225	355	38	zk}∞k=1	zk}∞k=1	X
ijassa-1225	355	39	⊂	⊂	X
ijassa-1225	356	1	[	[	X
ijassa-1225	356	2	v̇0i(t	v̇0i(t	NOUN
ijassa-1225	356	3	)	)	PUNCT
ijassa-1225	356	4	,	,	PUNCT
ijassa-1225	356	5	z0	z0	PROPN
ijassa-1225	356	6	]	]	X
ijassa-1225	356	7	whose	whose	DET
ijassa-1225	356	8	elements	element	NOUN
ijassa-1225	356	9	satisfy	satisfy	VERB
ijassa-1225	356	10	the	the	DET
ijassa-1225	356	11	inequality	inequality	NOUN
ijassa-1225	356	12	|zk|	|zk|	NOUN
ijassa-1225	356	13	<	<	X
ijassa-1225	356	14	2−k	2−k	NUM
ijassa-1225	356	15	.	.	PUNCT
ijassa-1225	357	1	this	this	DET
ijassa-1225	357	2	sequence	sequence	NOUN
ijassa-1225	357	3	is	be	AUX
ijassa-1225	357	4	compact	compact	ADJ
ijassa-1225	357	5	,	,	PUNCT
ijassa-1225	357	6	so	so	CCONJ
ijassa-1225	357	7	it	it	PRON
ijassa-1225	357	8	contains	contain	VERB
ijassa-1225	357	9	a	a	DET
ijassa-1225	357	10	subsequence	subsequence	NOUN
ijassa-1225	357	11	converging	converge	VERB
ijassa-1225	357	12	to	to	ADP
ijassa-1225	357	13	some	some	DET
ijassa-1225	357	14	z	z	NOUN
ijassa-1225	357	15	∈	∈	PROPN
ijassa-1225	358	1	[	[	X
ijassa-1225	358	2	v̇0i(t	v̇0i(t	NOUN
ijassa-1225	358	3	)	)	PUNCT
ijassa-1225	358	4	,	,	PUNCT
ijassa-1225	358	5	z0	z0	PROPN
ijassa-1225	358	6	]	]	PUNCT
ijassa-1225	358	7	.	.	PUNCT
ijassa-1225	359	1	due	due	ADP
ijassa-1225	359	2	to	to	ADP
ijassa-1225	359	3	continuity	continuity	NOUN
ijassa-1225	359	4	of	of	ADP
ijassa-1225	359	5	the	the	DET
ijassa-1225	359	6	mapping	mapping	NOUN
ijassa-1225	359	7	fi(t	fi(t	NOUN
ijassa-1225	359	8	,	,	PUNCT
ijassa-1225	359	9	x	x	NOUN
ijassa-1225	359	10	,	,	PUNCT
ijassa-1225	359	11	v	v	NOUN
ijassa-1225	359	12	,	,	PUNCT
ijassa-1225	359	13	·	·	PUNCT
ijassa-1225	359	14	)	)	PUNCT
ijassa-1225	359	15	at	at	ADP
ijassa-1225	359	16	z	z	PROPN
ijassa-1225	359	17	,	,	PUNCT
ijassa-1225	359	18	the	the	DET
ijassa-1225	359	19	inclusion	inclusion	NOUN
ijassa-1225	359	20	0	0	NUM
ijassa-1225	359	21	∈	∈	PROPN
ijassa-1225	359	22	fi(t	fi(t	NOUN
ijassa-1225	359	23	,	,	PUNCT
ijassa-1225	359	24	x	x	NOUN
ijassa-1225	359	25	,	,	PUNCT
ijassa-1225	359	26	v	v	NOUN
ijassa-1225	359	27	,	,	PUNCT
ijassa-1225	359	28	z	z	NOUN
ijassa-1225	359	29	)	)	PUNCT
ijassa-1225	359	30	holds	hold	VERB
ijassa-1225	359	31	true	true	ADJ
ijassa-1225	359	32	,	,	PUNCT
ijassa-1225	359	33	which	which	PRON
ijassa-1225	359	34	contradicts	contradict	VERB
ijassa-1225	359	35	with	with	ADP
ijassa-1225	359	36	the	the	DET
ijassa-1225	359	37	assumptions	assumption	NOUN
ijassa-1225	359	38	made	make	VERB
ijassa-1225	359	39	.	.	PUNCT
ijassa-1225	360	1	the	the	DET
ijassa-1225	360	2	relation	relation	NOUN
ijassa-1225	360	3	(	(	PUNCT
ijassa-1225	360	4	4.27	4.27	NUM
ijassa-1225	360	5	)	)	PUNCT
ijassa-1225	360	6	,	,	PUNCT
ijassa-1225	360	7	due	due	ADP
ijassa-1225	360	8	to	to	ADP
ijassa-1225	360	9	the	the	DET
ijassa-1225	360	10	connectedness	connectedness	NOUN
ijassa-1225	360	11	of	of	ADP
ijassa-1225	360	12	the	the	DET
ijassa-1225	360	13	values	value	NOUN
ijassa-1225	360	14	fi(t	fi(t	NOUN
ijassa-1225	360	15	,	,	PUNCT
ijassa-1225	360	16	x	x	NOUN
ijassa-1225	360	17	,	,	PUNCT
ijassa-1225	360	18	v	v	NOUN
ijassa-1225	360	19	,	,	PUNCT
ijassa-1225	360	20	z	z	NOUN
ijassa-1225	360	21	)	)	PUNCT
ijassa-1225	360	22	,	,	PUNCT
ijassa-1225	360	23	implies	imply	VERB
ijassa-1225	360	24	that	that	SCONJ
ijassa-1225	360	25	the	the	DET
ijassa-1225	360	26	segment	segment	NOUN
ijassa-1225	360	27	u	u	NOUN
ijassa-1225	360	28	.	.	PUNCT
ijassa-1225	361	1	=	=	PUNCT
ijassa-1225	362	1	[	[	X
ijassa-1225	362	2	v̇0i(t	v̇0i(t	NOUN
ijassa-1225	362	3	)	)	PUNCT
ijassa-1225	362	4	,	,	PUNCT
ijassa-1225	362	5	z0	z0	PROPN
ijassa-1225	362	6	]	]	PUNCT
ijassa-1225	362	7	is	be	AUX
ijassa-1225	362	8	a	a	DET
ijassa-1225	362	9	union	union	NOUN
ijassa-1225	362	10	of	of	ADP
ijassa-1225	362	11	the	the	DET
ijassa-1225	362	12	following	follow	VERB
ijassa-1225	362	13	two	two	NUM
ijassa-1225	362	14	sets	set	NOUN
ijassa-1225	362	15	:	:	PUNCT
ijassa-1225	362	16	u+	u+	NUM
ijassa-1225	362	17	.	.	PUNCT
ijassa-1225	363	1	=	=	PRON
ijassa-1225	363	2	{	{	PUNCT
ijassa-1225	363	3	z	z	NOUN
ijassa-1225	363	4	∈	∈	PROPN
ijassa-1225	363	5	u	u	NOUN
ijassa-1225	363	6	:	:	PUNCT
ijassa-1225	363	7	fi(t	fi(t	NOUN
ijassa-1225	363	8	,	,	PUNCT
ijassa-1225	363	9	x	x	NOUN
ijassa-1225	363	10	,	,	PUNCT
ijassa-1225	363	11	v	v	NOUN
ijassa-1225	363	12	,	,	PUNCT
ijassa-1225	363	13	z	z	NOUN
ijassa-1225	363	14	)	)	PUNCT
ijassa-1225	363	15	⊂	⊂	PROPN
ijassa-1225	364	1	[	[	X
ijassa-1225	364	2	δ,+∞	δ,+∞	NOUN
ijassa-1225	364	3	)	)	PUNCT
ijassa-1225	364	4	}	}	PUNCT
ijassa-1225	364	5	,	,	PUNCT
ijassa-1225	364	6	u−	u−	PROPN
ijassa-1225	364	7	.	.	PUNCT
ijassa-1225	365	1	=	=	PRON
ijassa-1225	365	2	{	{	PUNCT
ijassa-1225	365	3	z	z	NOUN
ijassa-1225	365	4	∈	∈	PROPN
ijassa-1225	365	5	u	u	NOUN
ijassa-1225	365	6	:	:	PUNCT
ijassa-1225	365	7	fi(t	fi(t	NOUN
ijassa-1225	365	8	,	,	PUNCT
ijassa-1225	365	9	x	x	NOUN
ijassa-1225	365	10	,	,	PUNCT
ijassa-1225	365	11	v	v	NOUN
ijassa-1225	365	12	,	,	PUNCT
ijassa-1225	365	13	z	z	NOUN
ijassa-1225	365	14	)	)	PUNCT
ijassa-1225	365	15	⊂	⊂	PROPN
ijassa-1225	365	16	(	(	PUNCT
ijassa-1225	365	17	−∞	−∞	PROPN
ijassa-1225	365	18	,	,	PUNCT
ijassa-1225	365	19	δ	δ	PROPN
ijassa-1225	365	20	]	]	PUNCT
ijassa-1225	365	21	}	}	PUNCT
ijassa-1225	365	22	.	.	PUNCT
ijassa-1225	366	1	both	both	PRON
ijassa-1225	366	2	these	these	DET
ijassa-1225	366	3	sets	set	NOUN
ijassa-1225	366	4	should	should	AUX
ijassa-1225	366	5	be	be	AUX
ijassa-1225	366	6	closed	close	VERB
ijassa-1225	366	7	as	as	ADP
ijassa-1225	366	8	the	the	DET
ijassa-1225	366	9	mapping	mapping	NOUN
ijassa-1225	366	10	fi(t	fi(t	NOUN
ijassa-1225	366	11	,	,	PUNCT
ijassa-1225	366	12	x	x	NOUN
ijassa-1225	366	13	,	,	PUNCT
ijassa-1225	366	14	v	v	NOUN
ijassa-1225	366	15	,	,	PUNCT
ijassa-1225	366	16	·	·	PUNCT
ijassa-1225	366	17	)	)	PUNCT
ijassa-1225	366	18	is	be	AUX
ijassa-1225	366	19	continuous	continuous	ADJ
ijassa-1225	366	20	.	.	PUNCT
ijassa-1225	367	1	however	however	ADV
ijassa-1225	367	2	,	,	PUNCT
ijassa-1225	367	3	this	this	PRON
ijassa-1225	367	4	is	be	AUX
ijassa-1225	367	5	not	not	PART
ijassa-1225	367	6	possible	possible	ADJ
ijassa-1225	367	7	by	by	ADP
ijassa-1225	367	8	the	the	DET
ijassa-1225	367	9	virtue	virtue	NOUN
ijassa-1225	367	10	of	of	ADP
ijassa-1225	367	11	the	the	DET
ijassa-1225	367	12	connectedness	connectedness	NOUN
ijassa-1225	367	13	of	of	ADP
ijassa-1225	367	14	the	the	DET
ijassa-1225	367	15	segment	segment	NOUN
ijassa-1225	367	16	u.	u.	PROPN
ijassa-1225	367	17	thus	thus	ADV
ijassa-1225	367	18	,	,	PUNCT
ijassa-1225	367	19	it	it	PRON
ijassa-1225	367	20	is	be	AUX
ijassa-1225	367	21	proved	prove	VERB
ijassa-1225	367	22	that	that	SCONJ
ijassa-1225	367	23	for	for	ADP
ijassa-1225	367	24	any	any	DET
ijassa-1225	367	25	t	t	NOUN
ijassa-1225	367	26	∈	∈	PROPN
ijassa-1225	367	27	ti	ti	NOUN
ijassa-1225	367	28	,	,	PUNCT
ijassa-1225	367	29	for	for	ADP
ijassa-1225	367	30	all	all	DET
ijassa-1225	367	31	x	x	SYM
ijassa-1225	367	32	∈	∈	PROPN
ijassa-1225	367	33	rn	rn	PROPN
ijassa-1225	367	34	and	and	CCONJ
ijassa-1225	367	35	v	v	ADP
ijassa-1225	367	36	∈	∈	PROPN
ijassa-1225	367	37	b(t	b(t	PROPN
ijassa-1225	367	38	)	)	PUNCT
ijassa-1225	367	39	,	,	PUNCT
ijassa-1225	367	40	the	the	DET
ijassa-1225	367	41	mapping	mapping	NOUN
ijassa-1225	367	42	fi(t	fi(t	NOUN
ijassa-1225	367	43	,	,	PUNCT
ijassa-1225	367	44	x	x	NOUN
ijassa-1225	367	45	,	,	PUNCT
ijassa-1225	367	46	v	v	NOUN
ijassa-1225	367	47	,	,	PUNCT
ijassa-1225	367	48	·	·	PUNCT
ijassa-1225	367	49	)	)	PUNCT
ijassa-1225	367	50	:	:	PUNCT
ijassa-1225	367	51	bi(t)→	bi(t)→	NOUN
ijassa-1225	367	52	kc(r	kc(r	PUNCT
ijassa-1225	367	53	)	)	PUNCT
ijassa-1225	367	54	order	order	NOUN
ijassa-1225	367	55	covers	cover	VERB
ijassa-1225	367	56	the	the	DET
ijassa-1225	367	57	set	set	NOUN
ijassa-1225	367	58	{	{	PUNCT
ijassa-1225	367	59	0	0	NUM
ijassa-1225	367	60	}	}	PUNCT
ijassa-1225	367	61	⊂	⊂	PROPN
ijassa-1225	367	62	r.	r.	PROPN
ijassa-1225	367	63	considering	consider	VERB
ijassa-1225	367	64	the	the	DET
ijassa-1225	367	65	fact	fact	NOUN
ijassa-1225	367	66	that	that	SCONJ
ijassa-1225	367	67	the	the	DET
ijassa-1225	367	68	lebesgue	lebesgue	ADJ
ijassa-1225	367	69	measure	measure	NOUN
ijassa-1225	367	70	of	of	ADP
ijassa-1225	367	71	the	the	DET
ijassa-1225	367	72	set	set	NOUN
ijassa-1225	367	73	ti	ti	NOUN
ijassa-1225	367	74	equals	equal	VERB
ijassa-1225	367	75	to	to	ADP
ijassa-1225	367	76	b−	b−	PROPN
ijassa-1225	367	77	a	a	NOUN
ijassa-1225	367	78	,	,	PUNCT
ijassa-1225	367	79	the	the	DET
ijassa-1225	367	80	condition	condition	NOUN
ijassa-1225	367	81	(	(	PUNCT
ijassa-1225	367	82	b1	b1	NOUN
ijassa-1225	367	83	)	)	PUNCT
ijassa-1225	367	84	is	be	AUX
ijassa-1225	367	85	satisfied	satisfied	ADJ
ijassa-1225	367	86	.	.	PUNCT
ijassa-1225	368	1	the	the	DET
ijassa-1225	368	2	validity	validity	NOUN
ijassa-1225	368	3	of	of	ADP
ijassa-1225	368	4	the	the	DET
ijassa-1225	368	5	rest	rest	NOUN
ijassa-1225	368	6	of	of	ADP
ijassa-1225	368	7	the	the	DET
ijassa-1225	368	8	conditions	condition	NOUN
ijassa-1225	368	9	of	of	ADP
ijassa-1225	368	10	theorem	theorem	NOUN
ijassa-1225	368	11	4.1	4.1	NUM
ijassa-1225	368	12	under	under	ADP
ijassa-1225	368	13	the	the	DET
ijassa-1225	368	14	assumptions	assumption	NOUN
ijassa-1225	368	15	of	of	ADP
ijassa-1225	368	16	the	the	DET
ijassa-1225	368	17	statement	statement	NOUN
ijassa-1225	368	18	being	be	AUX
ijassa-1225	368	19	proved	prove	VERB
ijassa-1225	368	20	is	be	AUX
ijassa-1225	368	21	obvious	obvious	ADJ
ijassa-1225	368	22	.	.	PUNCT
ijassa-1225	369	1	thus	thus	ADV
ijassa-1225	369	2	,	,	PUNCT
ijassa-1225	369	3	there	there	PRON
ijassa-1225	369	4	exists	exist	VERB
ijassa-1225	369	5	a	a	DET
ijassa-1225	369	6	solution	solution	NOUN
ijassa-1225	369	7	x	x	X
ijassa-1225	369	8	∈	∈	PROPN
ijassa-1225	369	9	ac(b	ac(b	NOUN
ijassa-1225	369	10	)	)	PUNCT
ijassa-1225	369	11	of	of	ADP
ijassa-1225	369	12	the	the	DET
ijassa-1225	369	13	problem	problem	NOUN
ijassa-1225	369	14	(	(	PUNCT
ijassa-1225	369	15	4.25	4.25	NUM
ijassa-1225	369	16	)	)	PUNCT
ijassa-1225	369	17	,	,	PUNCT
ijassa-1225	369	18	(	(	PUNCT
ijassa-1225	369	19	4.12	4.12	NUM
ijassa-1225	369	20	)	)	PUNCT
ijassa-1225	369	21	,	,	PUNCT
ijassa-1225	369	22	(	(	PUNCT
ijassa-1225	369	23	4.13	4.13	NUM
ijassa-1225	369	24	)	)	PUNCT
ijassa-1225	369	25	.	.	PUNCT
ijassa-1225	370	1	we	we	PRON
ijassa-1225	370	2	now	now	ADV
ijassa-1225	370	3	prove	prove	VERB
ijassa-1225	370	4	the	the	DET
ijassa-1225	370	5	existence	existence	NOUN
ijassa-1225	370	6	of	of	ADP
ijassa-1225	370	7	a	a	DET
ijassa-1225	370	8	solution	solution	NOUN
ijassa-1225	370	9	with	with	ADP
ijassa-1225	370	10	the	the	DET
ijassa-1225	370	11	least	least	ADJ
ijassa-1225	370	12	derivative	derivative	NOUN
ijassa-1225	370	13	.	.	PUNCT
ijassa-1225	371	1	let	let	VERB
ijassa-1225	371	2	us	we	PRON
ijassa-1225	371	3	remind	remind	VERB
ijassa-1225	371	4	the	the	DET
ijassa-1225	371	5	reader	reader	NOUN
ijassa-1225	371	6	(	(	PUNCT
ijassa-1225	371	7	see	see	VERB
ijassa-1225	371	8	the	the	DET
ijassa-1225	371	9	proof	proof	NOUN
ijassa-1225	371	10	of	of	ADP
ijassa-1225	371	11	theorem	theorem	NOUN
ijassa-1225	371	12	4.1	4.1	NUM
ijassa-1225	371	13	)	)	PUNCT
ijassa-1225	371	14	that	that	SCONJ
ijassa-1225	371	15	the	the	DET
ijassa-1225	371	16	derivatives	derivative	NOUN
ijassa-1225	371	17	of	of	ADP
ijassa-1225	371	18	the	the	DET
ijassa-1225	371	19	solutions	solution	NOUN
ijassa-1225	371	20	of	of	ADP
ijassa-1225	371	21	the	the	DET
ijassa-1225	371	22	problem	problem	NOUN
ijassa-1225	371	23	(	(	PUNCT
ijassa-1225	371	24	4.25	4.25	NUM
ijassa-1225	371	25	)	)	PUNCT
ijassa-1225	371	26	,	,	PUNCT
ijassa-1225	371	27	(	(	PUNCT
ijassa-1225	371	28	4.12	4.12	NUM
ijassa-1225	371	29	)	)	PUNCT
ijassa-1225	371	30	,	,	PUNCT
ijassa-1225	371	31	(	(	PUNCT
ijassa-1225	371	32	4.13	4.13	NUM
ijassa-1225	371	33	)	)	PUNCT
ijassa-1225	371	34	are	be	AUX
ijassa-1225	371	35	the	the	DET
ijassa-1225	371	36	solutions	solution	NOUN
ijassa-1225	371	37	of	of	ADP
ijassa-1225	371	38	the	the	DET
ijassa-1225	371	39	following	follow	VERB
ijassa-1225	371	40	system	system	NOUN
ijassa-1225	371	41	of	of	ADP
ijassa-1225	371	42	inclusions	inclusion	NOUN
ijassa-1225	371	43	fi	fi	NOUN
ijassa-1225	371	44	(	(	PUNCT
ijassa-1225	371	45	t	t	PROPN
ijassa-1225	371	46	,	,	PUNCT
ijassa-1225	371	47	γ	γ	PROPN
ijassa-1225	371	48	+	+	PROPN
ijassa-1225	371	49	∫	∫	PROPN
ijassa-1225	371	50	t	t	PROPN
ijassa-1225	371	51	a	a	DET
ijassa-1225	371	52	u(s)ds	u(s)ds	PROPN
ijassa-1225	371	53	,	,	PUNCT
ijassa-1225	371	54	u(t	u(t	NOUN
ijassa-1225	371	55	)	)	PUNCT
ijassa-1225	371	56	,	,	PUNCT
ijassa-1225	371	57	ui(t	ui(t	NOUN
ijassa-1225	371	58	)	)	PUNCT
ijassa-1225	371	59	)	)	PUNCT
ijassa-1225	371	60	3	3	NUM
ijassa-1225	371	61	0	0	NUM
ijassa-1225	371	62	,	,	PUNCT
ijassa-1225	371	63	t	t	PROPN
ijassa-1225	371	64	∈	∈	PROPN
ijassa-1225	372	1	[	[	X
ijassa-1225	372	2	a	a	X
ijassa-1225	372	3	,	,	PUNCT
ijassa-1225	372	4	b	b	NOUN
ijassa-1225	372	5	]	]	X
ijassa-1225	372	6	,	,	PUNCT
ijassa-1225	372	7	i	i	PRON
ijassa-1225	372	8	=	=	NOUN
ijassa-1225	372	9	1	1	NUM
ijassa-1225	372	10	,	,	PUNCT
ijassa-1225	372	11	n.	n.	NOUN
ijassa-1225	372	12	(	(	PUNCT
ijassa-1225	372	13	4.28	4.28	NUM
ijassa-1225	372	14	)	)	PUNCT
ijassa-1225	373	1	thus	thus	ADV
ijassa-1225	373	2	,	,	PUNCT
ijassa-1225	373	3	it	it	PRON
ijassa-1225	373	4	remains	remain	VERB
ijassa-1225	373	5	to	to	PART
ijassa-1225	373	6	prove	prove	VERB
ijassa-1225	373	7	that	that	SCONJ
ijassa-1225	373	8	the	the	DET
ijassa-1225	373	9	set	set	NOUN
ijassa-1225	373	10	of	of	ADP
ijassa-1225	373	11	solutions	solution	NOUN
ijassa-1225	373	12	of	of	ADP
ijassa-1225	373	13	the	the	DET
ijassa-1225	373	14	system	system	NOUN
ijassa-1225	373	15	(	(	PUNCT
ijassa-1225	373	16	4.28	4.28	NUM
ijassa-1225	373	17	)	)	PUNCT
ijassa-1225	373	18	possesses	possess	VERB
ijassa-1225	373	19	the	the	DET
ijassa-1225	373	20	least	least	ADJ
ijassa-1225	373	21	element	element	NOUN
ijassa-1225	373	22	.	.	PUNCT
ijassa-1225	374	1	denote	denote	VERB
ijassa-1225	374	2	by	by	ADP
ijassa-1225	374	3	r	r	NOUN
ijassa-1225	374	4	the	the	DET
ijassa-1225	374	5	set	set	NOUN
ijassa-1225	374	6	(	(	PUNCT
ijassa-1225	374	7	in	in	ADP
ijassa-1225	374	8	the	the	DET
ijassa-1225	374	9	space	space	NOUN
ijassa-1225	374	10	l(b	l(b	PROPN
ijassa-1225	374	11	)	)	PUNCT
ijassa-1225	374	12	)	)	PUNCT
ijassa-1225	374	13	of	of	ADP
ijassa-1225	374	14	solutions	solution	NOUN
ijassa-1225	374	15	of	of	ADP
ijassa-1225	374	16	the	the	DET
ijassa-1225	374	17	system	system	NOUN
ijassa-1225	374	18	(	(	PUNCT
ijassa-1225	374	19	4.28	4.28	NUM
ijassa-1225	374	20	)	)	PUNCT
ijassa-1225	374	21	.	.	PUNCT
ijassa-1225	375	1	according	accord	VERB
ijassa-1225	375	2	to	to	ADP
ijassa-1225	375	3	theorem	theorem	ADJ
ijassa-1225	375	4	2.1	2.1	NUM
ijassa-1225	375	5	,	,	PUNCT
ijassa-1225	375	6	the	the	DET
ijassa-1225	375	7	set	set	NOUN
ijassa-1225	375	8	r	r	NOUN
ijassa-1225	375	9	possesses	possess	VERB
ijassa-1225	375	10	a	a	DET
ijassa-1225	375	11	minimal	minimal	ADJ
ijassa-1225	375	12	element	element	NOUN
ijassa-1225	375	13	û	û	NUM
ijassa-1225	375	14	∈	∈	PROPN
ijassa-1225	375	15	l(b	l(b	PROPN
ijassa-1225	375	16	)	)	PUNCT
ijassa-1225	375	17	.	.	PUNCT
ijassa-1225	376	1	assume	assume	VERB
ijassa-1225	376	2	that	that	SCONJ
ijassa-1225	376	3	this	this	DET
ijassa-1225	376	4	element	element	NOUN
ijassa-1225	376	5	is	be	AUX
ijassa-1225	376	6	not	not	PART
ijassa-1225	376	7	the	the	DET
ijassa-1225	376	8	least	least	ADJ
ijassa-1225	376	9	in	in	ADP
ijassa-1225	376	10	r.	r.	PROPN
ijassa-1225	376	11	then	then	ADV
ijassa-1225	376	12	there	there	PRON
ijassa-1225	376	13	exists	exist	VERB
ijassa-1225	376	14	a	a	DET
ijassa-1225	376	15	solution	solution	NOUN
ijassa-1225	376	16	z	z	NOUN
ijassa-1225	376	17	∈	∈	NOUN
ijassa-1225	376	18	r	r	NOUN
ijassa-1225	376	19	of	of	ADP
ijassa-1225	376	20	(	(	PUNCT
ijassa-1225	376	21	4.28	4.28	NUM
ijassa-1225	376	22	)	)	PUNCT
ijassa-1225	376	23	such	such	ADJ
ijassa-1225	376	24	that	that	SCONJ
ijassa-1225	376	25	z	z	PROPN
ijassa-1225	376	26	�	�	PROPN
ijassa-1225	376	27	û.	û.	PROPN
ijassa-1225	376	28	for	for	ADP
ijassa-1225	376	29	each	each	DET
ijassa-1225	376	30	i	i	NOUN
ijassa-1225	376	31	=	=	NOUN
ijassa-1225	376	32	1	1	NUM
ijassa-1225	376	33	,	,	PUNCT
ijassa-1225	376	34	n	n	CCONJ
ijassa-1225	376	35	,	,	PUNCT
ijassa-1225	376	36	we	we	PRON
ijassa-1225	376	37	define	define	VERB
ijassa-1225	376	38	the	the	DET
ijassa-1225	376	39	sets	set	NOUN
ijassa-1225	376	40	ei+	ei+	NOUN
ijassa-1225	377	1	=	=	PRON
ijassa-1225	377	2	{	{	PUNCT
ijassa-1225	377	3	t	t	PROPN
ijassa-1225	377	4	∈	∈	PROPN
ijassa-1225	378	1	[	[	X
ijassa-1225	378	2	0	0	NUM
ijassa-1225	378	3	,	,	PUNCT
ijassa-1225	378	4	1	1	NUM
ijassa-1225	378	5	]	]	PUNCT
ijassa-1225	378	6	:	:	PUNCT
ijassa-1225	378	7	ûi(t	ûi(t	NUM
ijassa-1225	378	8	)	)	PUNCT
ijassa-1225	378	9	≤	≤	NOUN
ijassa-1225	378	10	zi(t	zi(t	NOUN
ijassa-1225	378	11	)	)	PUNCT
ijassa-1225	378	12	}	}	PUNCT
ijassa-1225	378	13	,	,	PUNCT
ijassa-1225	378	14	ei−	ei−	ADJ
ijassa-1225	378	15	=	=	SYM
ijassa-1225	378	16	{	{	PUNCT
ijassa-1225	378	17	t	t	PROPN
ijassa-1225	378	18	∈	∈	PROPN
ijassa-1225	379	1	[	[	X
ijassa-1225	379	2	0	0	NUM
ijassa-1225	379	3	,	,	PUNCT
ijassa-1225	379	4	1	1	NUM
ijassa-1225	379	5	]	]	PUNCT
ijassa-1225	379	6	:	:	PUNCT
ijassa-1225	379	7	ûi(t	ûi(t	NUM
ijassa-1225	379	8	)	)	PUNCT
ijassa-1225	379	9	>	>	X
ijassa-1225	379	10	zi(t	zi(t	NOUN
ijassa-1225	379	11	)	)	PUNCT
ijassa-1225	379	12	}	}	PUNCT
ijassa-1225	379	13	.	.	PUNCT
ijassa-1225	380	1	define	define	VERB
ijassa-1225	380	2	a	a	DET
ijassa-1225	380	3	measurable	measurable	ADJ
ijassa-1225	380	4	function	function	NOUN
ijassa-1225	380	5	ẑ	ẑ	NUM
ijassa-1225	380	6	with	with	ADP
ijassa-1225	380	7	the	the	DET
ijassa-1225	380	8	components	component	NOUN
ijassa-1225	380	9	equal	equal	ADJ
ijassa-1225	380	10	to	to	ADP
ijassa-1225	380	11	ẑi(t	ẑi(t	NOUN
ijassa-1225	380	12	)	)	PUNCT
ijassa-1225	380	13	=	=	SYM
ijassa-1225	380	14	min	min	NOUN
ijassa-1225	380	15	{	{	PUNCT
ijassa-1225	380	16	zi(t	zi(t	NUM
ijassa-1225	380	17	)	)	PUNCT
ijassa-1225	380	18	,	,	PUNCT
ijassa-1225	380	19	ûi(t	ûi(t	NUM
ijassa-1225	380	20	)	)	PUNCT
ijassa-1225	380	21	}	}	PUNCT
ijassa-1225	380	22	=	=	SYM
ijassa-1225	380	23	{	{	PUNCT
ijassa-1225	380	24	ûi(t	ûi(t	NOUN
ijassa-1225	380	25	)	)	PUNCT
ijassa-1225	380	26	for	for	ADP
ijassa-1225	380	27	t	t	PROPN
ijassa-1225	380	28	∈	∈	PROPN
ijassa-1225	380	29	ei+	ei+	NOUN
ijassa-1225	380	30	,	,	PUNCT
ijassa-1225	380	31	zi(t	zi(t	NOUN
ijassa-1225	380	32	)	)	PUNCT
ijassa-1225	380	33	for	for	ADP
ijassa-1225	380	34	t	t	PROPN
ijassa-1225	380	35	∈	∈	PROPN
ijassa-1225	380	36	ei−	ei−	VERB
ijassa-1225	380	37	,	,	PUNCT
ijassa-1225	380	38	i	i	PRON
ijassa-1225	380	39	=	=	NOUN
ijassa-1225	380	40	1	1	NUM
ijassa-1225	380	41	,	,	PUNCT
ijassa-1225	380	42	n.	n.	NOUN
ijassa-1225	380	43	thus	thus	ADV
ijassa-1225	380	44	,	,	PUNCT
ijassa-1225	380	45	the	the	DET
ijassa-1225	380	46	inequality	inequality	NOUN
ijassa-1225	380	47	ẑ	ẑ	PROPN
ijassa-1225	380	48	<	<	X
ijassa-1225	380	49	û	û	X
ijassa-1225	380	50	is	be	AUX
ijassa-1225	380	51	fulfilled	fulfil	VERB
ijassa-1225	380	52	.	.	PUNCT
ijassa-1225	381	1	hence	hence	ADV
ijassa-1225	381	2	,	,	PUNCT
ijassa-1225	381	3	for	for	ADP
ijassa-1225	381	4	almost	almost	ADV
ijassa-1225	381	5	all	all	PRON
ijassa-1225	381	6	t	t	PROPN
ijassa-1225	381	7	∈	∈	PROPN
ijassa-1225	381	8	ei+	ei+	NOUN
ijassa-1225	381	9	,	,	PUNCT
ijassa-1225	381	10	the	the	DET
ijassa-1225	381	11	inclusion	inclusion	NOUN
ijassa-1225	381	12	0	0	NUM
ijassa-1225	381	13	∈	∈	PROPN
ijassa-1225	381	14	fi	fi	NOUN
ijassa-1225	381	15	(	(	PUNCT
ijassa-1225	381	16	t	t	PROPN
ijassa-1225	381	17	,	,	PUNCT
ijassa-1225	381	18	γ	γ	PROPN
ijassa-1225	381	19	+	+	PROPN
ijassa-1225	381	20	∫	∫	PROPN
ijassa-1225	381	21	t	t	PROPN
ijassa-1225	381	22	a	a	DET
ijassa-1225	381	23	û(s)ds	û(s)ds	NOUN
ijassa-1225	381	24	,	,	PUNCT
ijassa-1225	381	25	û(t	û(t	NOUN
ijassa-1225	381	26	)	)	PUNCT
ijassa-1225	381	27	,	,	PUNCT
ijassa-1225	381	28	ûi(t	ûi(t	NUM
ijassa-1225	381	29	)	)	PUNCT
ijassa-1225	381	30	)	)	PUNCT
ijassa-1225	381	31	,	,	PUNCT
ijassa-1225	381	32	i	i	PRON
ijassa-1225	381	33	=	=	NOUN
ijassa-1225	381	34	1	1	NUM
ijassa-1225	381	35	,	,	PUNCT
ijassa-1225	381	36	n	n	CCONJ
ijassa-1225	381	37	,	,	PUNCT
ijassa-1225	381	38	copyright	copyright	NOUN
ijassa-1225	381	39	©	©	PROPN
ijassa-1225	381	40	2022	2022	NUM
ijassa-1225	381	41	assa	assa	NOUN
ijassa-1225	381	42	.	.	PUNCT
ijassa-1225	382	1	adv	adv	PROPN
ijassa-1225	382	2	syst	syst	PROPN
ijassa-1225	382	3	sci	sci	PROPN
ijassa-1225	382	4	appl	appl	PROPN
ijassa-1225	382	5	(	(	PUNCT
ijassa-1225	382	6	2022	2022	NUM
ijassa-1225	382	7	)	)	PUNCT
ijassa-1225	382	8	on	on	ADP
ijassa-1225	382	9	order	order	NOUN
ijassa-1225	382	10	covering	cover	VERB
ijassa-1225	382	11	set	set	NOUN
ijassa-1225	382	12	-	-	PUNCT
ijassa-1225	382	13	valued	value	VERB
ijassa-1225	382	14	mappings	mapping	NOUN
ijassa-1225	382	15	and	and	CCONJ
ijassa-1225	382	16	their	their	PRON
ijassa-1225	382	17	applications	application	NOUN
ijassa-1225	382	18	187	187	NUM
ijassa-1225	382	19	due	due	ADP
ijassa-1225	382	20	to	to	ADP
ijassa-1225	382	21	antitonicity	antitonicity	NOUN
ijassa-1225	382	22	of	of	ADP
ijassa-1225	382	23	the	the	DET
ijassa-1225	382	24	mapping	mapping	NOUN
ijassa-1225	382	25	fi(t	fi(t	NOUN
ijassa-1225	382	26	,	,	PUNCT
ijassa-1225	382	27	·	·	PUNCT
ijassa-1225	382	28	,	,	PUNCT
ijassa-1225	382	29	·	·	PUNCT
ijassa-1225	382	30	,	,	PUNCT
ijassa-1225	382	31	u	u	NOUN
ijassa-1225	382	32	)	)	PUNCT
ijassa-1225	382	33	on	on	ADP
ijassa-1225	382	34	rn	rn	PROPN
ijassa-1225	382	35	×b(t	×b(t	PROPN
ijassa-1225	382	36	)	)	PUNCT
ijassa-1225	382	37	,	,	PUNCT
ijassa-1225	382	38	implies	imply	VERB
ijassa-1225	382	39	that	that	SCONJ
ijassa-1225	382	40	for	for	ADP
ijassa-1225	382	41	any	any	DET
ijassa-1225	382	42	i	i	NOUN
ijassa-1225	382	43	=	=	NOUN
ijassa-1225	382	44	1	1	NUM
ijassa-1225	382	45	,	,	PUNCT
ijassa-1225	382	46	n	n	CCONJ
ijassa-1225	382	47	,	,	PUNCT
ijassa-1225	382	48	the	the	DET
ijassa-1225	382	49	set	set	ADJ
ijassa-1225	382	50	fi	fi	NOUN
ijassa-1225	382	51	(	(	PUNCT
ijassa-1225	382	52	t	t	PROPN
ijassa-1225	382	53	,	,	PUNCT
ijassa-1225	382	54	γ	γ	PROPN
ijassa-1225	382	55	+	+	PROPN
ijassa-1225	382	56	∫	∫	PROPN
ijassa-1225	382	57	t	t	PROPN
ijassa-1225	382	58	a	a	DET
ijassa-1225	382	59	ẑ(s)ds	ẑ(s)ds	PROPN
ijassa-1225	382	60	,	,	PUNCT
ijassa-1225	382	61	ẑ(t	ẑ(t	NUM
ijassa-1225	382	62	)	)	PUNCT
ijassa-1225	382	63	,	,	PUNCT
ijassa-1225	382	64	ẑi(t	ẑi(t	PROPN
ijassa-1225	382	65	)	)	PUNCT
ijassa-1225	382	66	)	)	PUNCT
ijassa-1225	383	1	=	=	PUNCT
ijassa-1225	383	2	fi	fi	NOUN
ijassa-1225	383	3	(	(	PUNCT
ijassa-1225	383	4	t	t	PROPN
ijassa-1225	383	5	,	,	PUNCT
ijassa-1225	383	6	γ	γ	PROPN
ijassa-1225	383	7	+	+	PROPN
ijassa-1225	383	8	∫	∫	PROPN
ijassa-1225	383	9	t	t	PROPN
ijassa-1225	383	10	a	a	DET
ijassa-1225	383	11	ẑ(s)ds	ẑ(s)ds	PROPN
ijassa-1225	383	12	,	,	PUNCT
ijassa-1225	383	13	ẑ(t	ẑ(t	NUM
ijassa-1225	383	14	)	)	PUNCT
ijassa-1225	383	15	,	,	PUNCT
ijassa-1225	383	16	ûi(t	ûi(t	NUM
ijassa-1225	383	17	)	)	PUNCT
ijassa-1225	383	18	)	)	PUNCT
ijassa-1225	383	19	contains	contain	VERB
ijassa-1225	383	20	a	a	DET
ijassa-1225	383	21	non	non	ADJ
ijassa-1225	383	22	-	-	ADJ
ijassa-1225	383	23	negative	negative	ADJ
ijassa-1225	383	24	number	number	NOUN
ijassa-1225	383	25	.	.	PUNCT
ijassa-1225	384	1	analogously	analogously	ADV
ijassa-1225	384	2	,	,	PUNCT
ijassa-1225	384	3	for	for	ADP
ijassa-1225	384	4	any	any	DET
ijassa-1225	384	5	i	i	NOUN
ijassa-1225	384	6	=	=	NOUN
ijassa-1225	384	7	1	1	NUM
ijassa-1225	384	8	,	,	PUNCT
ijassa-1225	384	9	n	n	CCONJ
ijassa-1225	384	10	,	,	PUNCT
ijassa-1225	384	11	we	we	PRON
ijassa-1225	384	12	get	get	VERB
ijassa-1225	384	13	that	that	PRON
ijassa-1225	384	14	for	for	ADP
ijassa-1225	384	15	almost	almost	ADV
ijassa-1225	384	16	all	all	PRON
ijassa-1225	384	17	t	t	NOUN
ijassa-1225	384	18	∈	∈	PRON
ijassa-1225	384	19	ei−	ei−	AUX
ijassa-1225	384	20	,	,	PUNCT
ijassa-1225	384	21	some	some	DET
ijassa-1225	384	22	non	non	ADJ
ijassa-1225	384	23	-	-	ADJ
ijassa-1225	384	24	negative	negative	ADJ
ijassa-1225	384	25	number	number	NOUN
ijassa-1225	384	26	belongs	belong	VERB
ijassa-1225	384	27	to	to	ADP
ijassa-1225	384	28	the	the	DET
ijassa-1225	384	29	set	set	VERB
ijassa-1225	384	30	fi	fi	NOUN
ijassa-1225	384	31	(	(	PUNCT
ijassa-1225	384	32	t	t	PROPN
ijassa-1225	384	33	,	,	PUNCT
ijassa-1225	384	34	γ	γ	PROPN
ijassa-1225	384	35	+	+	PROPN
ijassa-1225	384	36	∫	∫	PROPN
ijassa-1225	384	37	t	t	PROPN
ijassa-1225	384	38	a	a	DET
ijassa-1225	384	39	ẑ(s)ds	ẑ(s)ds	PROPN
ijassa-1225	384	40	,	,	PUNCT
ijassa-1225	384	41	ẑ(t	ẑ(t	NUM
ijassa-1225	384	42	)	)	PUNCT
ijassa-1225	384	43	,	,	PUNCT
ijassa-1225	384	44	ẑi(t	ẑi(t	PROPN
ijassa-1225	384	45	)	)	PUNCT
ijassa-1225	384	46	)	)	PUNCT
ijassa-1225	384	47	.	.	PUNCT
ijassa-1225	385	1	by	by	ADP
ijassa-1225	385	2	theorem	theorem	NOUN
ijassa-1225	385	3	2.1	2.1	NUM
ijassa-1225	385	4	,	,	PUNCT
ijassa-1225	385	5	there	there	PRON
ijassa-1225	385	6	exists	exist	VERB
ijassa-1225	385	7	a	a	DET
ijassa-1225	385	8	solution	solution	NOUN
ijassa-1225	385	9	ξ	ξ	X
ijassa-1225	385	10	∈	∈	NOUN
ijassa-1225	385	11	r	r	NOUN
ijassa-1225	385	12	of	of	ADP
ijassa-1225	385	13	the	the	DET
ijassa-1225	385	14	system	system	NOUN
ijassa-1225	385	15	(	(	PUNCT
ijassa-1225	385	16	4.28	4.28	NUM
ijassa-1225	385	17	)	)	PUNCT
ijassa-1225	385	18	such	such	ADJ
ijassa-1225	385	19	that	that	SCONJ
ijassa-1225	385	20	ξ	ξ	PROPN
ijassa-1225	385	21	≤	≤	ADV
ijassa-1225	385	22	ẑ	ẑ	X
ijassa-1225	385	23	<	<	X
ijassa-1225	385	24	û.	û.	PROPN
ijassa-1225	385	25	the	the	DET
ijassa-1225	385	26	latter	latter	ADJ
ijassa-1225	385	27	,	,	PUNCT
ijassa-1225	385	28	however	however	ADV
ijassa-1225	385	29	,	,	PUNCT
ijassa-1225	385	30	contradicts	contradict	VERB
ijassa-1225	385	31	with	with	ADP
ijassa-1225	385	32	the	the	DET
ijassa-1225	385	33	minimality	minimality	NOUN
ijassa-1225	385	34	of	of	ADP
ijassa-1225	385	35	û	û	NUM
ijassa-1225	385	36	inr	inr	PROPN
ijassa-1225	385	37	.	.	PUNCT
ijassa-1225	386	1	finally	finally	ADV
ijassa-1225	386	2	,	,	PUNCT
ijassa-1225	386	3	we	we	PRON
ijassa-1225	386	4	note	note	VERB
ijassa-1225	386	5	that	that	SCONJ
ijassa-1225	386	6	the	the	DET
ijassa-1225	386	7	equation	equation	NOUN
ijassa-1225	386	8	(	(	PUNCT
ijassa-1225	386	9	4.18	4.18	NUM
ijassa-1225	386	10	)	)	PUNCT
ijassa-1225	386	11	considered	consider	VERB
ijassa-1225	386	12	in	in	ADP
ijassa-1225	386	13	example	example	NOUN
ijassa-1225	386	14	3.1	3.1	NUM
ijassa-1225	386	15	under	under	ADP
ijassa-1225	386	16	the	the	DET
ijassa-1225	386	17	restriction	restriction	NOUN
ijassa-1225	386	18	(	(	PUNCT
ijassa-1225	386	19	4.20	4.20	NUM
ijassa-1225	386	20	)	)	PUNCT
ijassa-1225	386	21	satisfies	satisfie	NOUN
ijassa-1225	386	22	not	not	PART
ijassa-1225	386	23	only	only	ADV
ijassa-1225	386	24	the	the	DET
ijassa-1225	386	25	assumptions	assumption	NOUN
ijassa-1225	386	26	of	of	ADP
ijassa-1225	386	27	theorem	theorem	NOUN
ijassa-1225	386	28	4.1	4.1	NUM
ijassa-1225	386	29	,	,	PUNCT
ijassa-1225	386	30	but	but	CCONJ
ijassa-1225	386	31	also	also	ADV
ijassa-1225	386	32	the	the	DET
ijassa-1225	386	33	assumptions	assumption	NOUN
ijassa-1225	386	34	of	of	ADP
ijassa-1225	386	35	theorem	theorem	ADJ
ijassa-1225	386	36	4.2	4.2	NUM
ijassa-1225	386	37	if	if	SCONJ
ijassa-1225	386	38	one	one	PRON
ijassa-1225	386	39	takes	take	VERB
ijassa-1225	386	40	v0(t	v0(t	NOUN
ijassa-1225	386	41	)	)	PUNCT
ijassa-1225	386	42	=	=	SYM
ijassa-1225	387	1	γ	γ	PROPN
ijassa-1225	387	2	+	+	NOUN
ijassa-1225	387	3	∫	∫	PROPN
ijassa-1225	387	4	b	b	PROPN
ijassa-1225	387	5	a	a	DET
ijassa-1225	387	6	q1(s)ds	q1(s)ds	NOUN
ijassa-1225	387	7	,	,	PUNCT
ijassa-1225	387	8	u0(t	u0(t	ADJ
ijassa-1225	387	9	)	)	PUNCT
ijassa-1225	387	10	=	=	SYM
ijassa-1225	387	11	γ	γ	X
ijassa-1225	387	12	+	+	NOUN
ijassa-1225	387	13	∫	∫	PROPN
ijassa-1225	387	14	b	b	PROPN
ijassa-1225	387	15	a	a	DET
ijassa-1225	387	16	(	(	PUNCT
ijassa-1225	387	17	q1(s)−	q1(s)−	ADP
ijassa-1225	387	18	r	r	NOUN
ijassa-1225	387	19	)	)	PUNCT
ijassa-1225	387	20	ds	ds	PROPN
ijassa-1225	387	21	,	,	PUNCT
ijassa-1225	387	22	t	t	PROPN
ijassa-1225	387	23	∈	∈	PROPN
ijassa-1225	388	1	[	[	X
ijassa-1225	388	2	a	a	X
ijassa-1225	388	3	,	,	PUNCT
ijassa-1225	388	4	b	b	NOUN
ijassa-1225	388	5	]	]	X
ijassa-1225	388	6	.	.	PUNCT
ijassa-1225	389	1	therefore	therefore	ADV
ijassa-1225	389	2	,	,	PUNCT
ijassa-1225	389	3	the	the	DET
ijassa-1225	389	4	set	set	NOUN
ijassa-1225	389	5	of	of	ADP
ijassa-1225	389	6	solutions	solution	NOUN
ijassa-1225	389	7	of	of	ADP
ijassa-1225	389	8	the	the	DET
ijassa-1225	389	9	problem	problem	NOUN
ijassa-1225	389	10	(	(	PUNCT
ijassa-1225	389	11	4.18	4.18	NUM
ijassa-1225	389	12	)	)	PUNCT
ijassa-1225	389	13	,	,	PUNCT
ijassa-1225	389	14	(	(	PUNCT
ijassa-1225	389	15	4.19	4.19	NUM
ijassa-1225	389	16	)	)	PUNCT
ijassa-1225	389	17	,	,	PUNCT
ijassa-1225	389	18	(	(	PUNCT
ijassa-1225	389	19	4.13	4.13	X
ijassa-1225	389	20	)	)	PUNCT
ijassa-1225	389	21	such	such	ADJ
ijassa-1225	389	22	that	that	SCONJ
ijassa-1225	389	23	q1(t)−	q1(t)−	PROPN
ijassa-1225	389	24	r	r	NOUN
ijassa-1225	389	25	≤	≤	NUM
ijassa-1225	389	26	ẋ(t	ẋ(t	NOUN
ijassa-1225	389	27	)	)	PUNCT
ijassa-1225	389	28	≤	≤	NOUN
ijassa-1225	389	29	q1(t	q1(t	X
ijassa-1225	389	30	)	)	PUNCT
ijassa-1225	389	31	,	,	PUNCT
ijassa-1225	389	32	t	t	PROPN
ijassa-1225	389	33	∈	∈	PROPN
ijassa-1225	390	1	[	[	X
ijassa-1225	390	2	a	a	X
ijassa-1225	390	3	,	,	PUNCT
ijassa-1225	390	4	b	b	NOUN
ijassa-1225	390	5	]	]	X
ijassa-1225	390	6	,	,	PUNCT
ijassa-1225	390	7	(	(	PUNCT
ijassa-1225	390	8	4.29	4.29	NUM
ijassa-1225	390	9	)	)	PUNCT
ijassa-1225	390	10	contains	contain	VERB
ijassa-1225	390	11	a	a	DET
ijassa-1225	390	12	solution	solution	NOUN
ijassa-1225	390	13	with	with	ADP
ijassa-1225	390	14	the	the	DET
ijassa-1225	390	15	least	least	ADJ
ijassa-1225	390	16	derivative	derivative	NOUN
ijassa-1225	390	17	.	.	PUNCT
ijassa-1225	391	1	analogously	analogously	ADV
ijassa-1225	391	2	,	,	PUNCT
ijassa-1225	391	3	for	for	ADP
ijassa-1225	391	4	the	the	DET
ijassa-1225	391	5	system	system	NOUN
ijassa-1225	391	6	of	of	ADP
ijassa-1225	391	7	inclusions	inclusion	NOUN
ijassa-1225	391	8	(	(	PUNCT
ijassa-1225	391	9	4.21	4.21	NUM
ijassa-1225	391	10	)	)	PUNCT
ijassa-1225	391	11	,	,	PUNCT
ijassa-1225	391	12	(	(	PUNCT
ijassa-1225	391	13	4.19	4.19	NUM
ijassa-1225	391	14	)	)	PUNCT
ijassa-1225	391	15	with	with	ADP
ijassa-1225	391	16	the	the	DET
ijassa-1225	391	17	initial	initial	ADJ
ijassa-1225	391	18	condition	condition	NOUN
ijassa-1225	391	19	(	(	PUNCT
ijassa-1225	391	20	4.13	4.13	NUM
ijassa-1225	391	21	)	)	PUNCT
ijassa-1225	391	22	,	,	PUNCT
ijassa-1225	391	23	which	which	PRON
ijassa-1225	391	24	was	be	AUX
ijassa-1225	391	25	considered	consider	VERB
ijassa-1225	391	26	in	in	ADP
ijassa-1225	391	27	example	example	NOUN
ijassa-1225	391	28	3.1	3.1	NUM
ijassa-1225	391	29	,	,	PUNCT
ijassa-1225	391	30	if	if	SCONJ
ijassa-1225	391	31	the	the	DET
ijassa-1225	391	32	relations	relation	NOUN
ijassa-1225	391	33	(	(	PUNCT
ijassa-1225	391	34	4.22	4.22	NUM
ijassa-1225	391	35	)	)	PUNCT
ijassa-1225	391	36	take	take	VERB
ijassa-1225	391	37	place	place	NOUN
ijassa-1225	391	38	,	,	PUNCT
ijassa-1225	391	39	the	the	DET
ijassa-1225	391	40	set	set	NOUN
ijassa-1225	391	41	of	of	ADP
ijassa-1225	391	42	solutions	solution	NOUN
ijassa-1225	391	43	that	that	PRON
ijassa-1225	391	44	satisfy	satisfy	VERB
ijassa-1225	391	45	the	the	DET
ijassa-1225	391	46	inequalities	inequality	NOUN
ijassa-1225	391	47	(	(	PUNCT
ijassa-1225	391	48	4.29	4.29	NUM
ijassa-1225	391	49	)	)	PUNCT
ijassa-1225	391	50	contains	contain	VERB
ijassa-1225	391	51	a	a	DET
ijassa-1225	391	52	solution	solution	NOUN
ijassa-1225	391	53	with	with	ADP
ijassa-1225	391	54	the	the	DET
ijassa-1225	391	55	least	least	ADJ
ijassa-1225	391	56	derivative	derivative	NOUN
ijassa-1225	391	57	.	.	PUNCT
ijassa-1225	392	1	the	the	DET
ijassa-1225	392	2	same	same	ADJ
ijassa-1225	392	3	statement	statement	NOUN
ijassa-1225	392	4	is	be	AUX
ijassa-1225	392	5	valid	valid	ADJ
ijassa-1225	392	6	for	for	ADP
ijassa-1225	392	7	the	the	DET
ijassa-1225	392	8	cauchi	cauchi	PROPN
ijassa-1225	392	9	problem	problem	NOUN
ijassa-1225	392	10	(	(	PUNCT
ijassa-1225	392	11	4.23	4.23	NUM
ijassa-1225	392	12	)	)	PUNCT
ijassa-1225	392	13	,	,	PUNCT
ijassa-1225	392	14	(	(	PUNCT
ijassa-1225	392	15	4.19	4.19	NUM
ijassa-1225	392	16	)	)	PUNCT
ijassa-1225	392	17	,	,	PUNCT
ijassa-1225	392	18	(	(	PUNCT
ijassa-1225	392	19	4.13	4.13	NUM
ijassa-1225	392	20	)	)	PUNCT
ijassa-1225	392	21	.	.	PUNCT
ijassa-1225	393	1	namely	namely	ADV
ijassa-1225	393	2	,	,	PUNCT
ijassa-1225	393	3	if	if	SCONJ
ijassa-1225	393	4	the	the	DET
ijassa-1225	393	5	condition	condition	NOUN
ijassa-1225	393	6	(	(	PUNCT
ijassa-1225	393	7	4.24	4.24	NUM
ijassa-1225	393	8	)	)	PUNCT
ijassa-1225	393	9	takes	take	VERB
ijassa-1225	393	10	place	place	NOUN
ijassa-1225	393	11	,	,	PUNCT
ijassa-1225	393	12	the	the	DET
ijassa-1225	393	13	set	set	NOUN
ijassa-1225	393	14	of	of	ADP
ijassa-1225	393	15	solutions	solution	NOUN
ijassa-1225	393	16	satisfying	satisfy	VERB
ijassa-1225	393	17	the	the	DET
ijassa-1225	393	18	inequalities	inequality	NOUN
ijassa-1225	393	19	(	(	PUNCT
ijassa-1225	393	20	4.29	4.29	NUM
ijassa-1225	393	21	)	)	PUNCT
ijassa-1225	393	22	possesses	possess	VERB
ijassa-1225	393	23	a	a	DET
ijassa-1225	393	24	solution	solution	NOUN
ijassa-1225	393	25	with	with	ADP
ijassa-1225	393	26	the	the	DET
ijassa-1225	393	27	least	least	ADJ
ijassa-1225	393	28	derivative	derivative	ADJ
ijassa-1225	393	29	.	.	PUNCT
ijassa-1225	394	1	5	5	X
ijassa-1225	394	2	.	.	X
ijassa-1225	394	3	existence	existence	NOUN
ijassa-1225	394	4	and	and	CCONJ
ijassa-1225	394	5	estimates	estimate	NOUN
ijassa-1225	394	6	of	of	ADP
ijassa-1225	394	7	equilibrium	equilibrium	NOUN
ijassa-1225	394	8	prices	price	NOUN
ijassa-1225	394	9	in	in	ADP
ijassa-1225	394	10	dynamical	dynamical	ADJ
ijassa-1225	394	11	continuous	continuous	ADJ
ijassa-1225	394	12	supply	supply	NOUN
ijassa-1225	394	13	-	-	PUNCT
ijassa-1225	394	14	and	and	CCONJ
ijassa-1225	394	15	-	-	PUNCT
ijassa-1225	394	16	demand	demand	NOUN
ijassa-1225	394	17	models	model	NOUN
ijassa-1225	394	18	in	in	ADP
ijassa-1225	394	19	this	this	DET
ijassa-1225	394	20	section	section	NOUN
ijassa-1225	394	21	,	,	PUNCT
ijassa-1225	394	22	theorems	theorem	VERB
ijassa-1225	394	23	4.1	4.1	NUM
ijassa-1225	394	24	and	and	CCONJ
ijassa-1225	394	25	4.2	4.2	NUM
ijassa-1225	394	26	are	be	AUX
ijassa-1225	394	27	applied	apply	VERB
ijassa-1225	394	28	to	to	ADP
ijassa-1225	394	29	investigation	investigation	NOUN
ijassa-1225	394	30	of	of	ADP
ijassa-1225	394	31	equilibrium	equilibrium	NOUN
ijassa-1225	394	32	in	in	ADP
ijassa-1225	394	33	dynamical	dynamical	ADJ
ijassa-1225	394	34	supply	supply	NOUN
ijassa-1225	394	35	-	-	PUNCT
ijassa-1225	394	36	and	and	CCONJ
ijassa-1225	394	37	-	-	PUNCT
ijassa-1225	394	38	demand	demand	NOUN
ijassa-1225	394	39	models	model	NOUN
ijassa-1225	394	40	.	.	PUNCT
ijassa-1225	395	1	the	the	DET
ijassa-1225	395	2	model	model	NOUN
ijassa-1225	395	3	of	of	ADP
ijassa-1225	395	4	economic	economic	ADJ
ijassa-1225	395	5	processes	process	NOUN
ijassa-1225	395	6	we	we	PRON
ijassa-1225	395	7	consider	consider	VERB
ijassa-1225	395	8	has	have	VERB
ijassa-1225	395	9	its	its	PRON
ijassa-1225	395	10	roots	root	NOUN
ijassa-1225	395	11	in	in	ADP
ijassa-1225	395	12	the	the	DET
ijassa-1225	395	13	classical	classical	ADJ
ijassa-1225	395	14	works	work	NOUN
ijassa-1225	395	15	of	of	ADP
ijassa-1225	395	16	g.c	g.c	PROPN
ijassa-1225	395	17	.	.	PROPN
ijassa-1225	395	18	evans	evans	PROPN
ijassa-1225	396	1	[	[	X
ijassa-1225	396	2	11	11	NUM
ijassa-1225	396	3	]	]	PUNCT
ijassa-1225	396	4	,	,	PUNCT
ijassa-1225	396	5	p.a	p.a	PROPN
ijassa-1225	396	6	.	.	PUNCT
ijassa-1225	396	7	samuelson	samuelson	PROPN
ijassa-1225	397	1	[	[	X
ijassa-1225	397	2	12	12	NUM
ijassa-1225	397	3	]	]	PUNCT
ijassa-1225	397	4	,	,	PUNCT
ijassa-1225	397	5	and	and	CCONJ
ijassa-1225	397	6	r.	r.	PROPN
ijassa-1225	397	7	allen	allen	PROPN
ijassa-1225	398	1	[	[	X
ijassa-1225	398	2	13	13	NUM
ijassa-1225	398	3	]	]	PUNCT
ijassa-1225	398	4	.	.	PUNCT
ijassa-1225	399	1	a	a	DET
ijassa-1225	399	2	considerable	considerable	ADJ
ijassa-1225	399	3	advance	advance	NOUN
ijassa-1225	399	4	in	in	ADP
ijassa-1225	399	5	the	the	DET
ijassa-1225	399	6	investigation	investigation	NOUN
ijassa-1225	399	7	of	of	ADP
ijassa-1225	399	8	models	model	NOUN
ijassa-1225	399	9	describing	describe	VERB
ijassa-1225	399	10	equilibrium	equilibrium	NOUN
ijassa-1225	399	11	processes	process	NOUN
ijassa-1225	399	12	in	in	ADP
ijassa-1225	399	13	market	market	NOUN
ijassa-1225	399	14	models	model	NOUN
ijassa-1225	399	15	were	be	AUX
ijassa-1225	399	16	the	the	DET
ijassa-1225	399	17	results	result	NOUN
ijassa-1225	399	18	of	of	ADP
ijassa-1225	399	19	a.v	a.v	PROPN
ijassa-1225	399	20	.	.	PROPN
ijassa-1225	399	21	arutyunov	arutyunov	PROPN
ijassa-1225	399	22	,	,	PUNCT
ijassa-1225	399	23	n.g	n.g	PROPN
ijassa-1225	399	24	.	.	PROPN
ijassa-1225	399	25	pavlova	pavlova	PROPN
ijassa-1225	399	26	,	,	PUNCT
ijassa-1225	399	27	s.e	s.e	PROPN
ijassa-1225	399	28	.	.	PROPN
ijassa-1225	399	29	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	399	30	,	,	PUNCT
ijassa-1225	399	31	a.a	a.a	PROPN
ijassa-1225	399	32	.	.	PROPN
ijassa-1225	399	33	shananin	shananin	PROPN
ijassa-1225	399	34	(	(	PUNCT
ijassa-1225	399	35	see	see	VERB
ijassa-1225	399	36	[	[	X
ijassa-1225	399	37	14–17	14–17	NUM
ijassa-1225	399	38	]	]	PUNCT
ijassa-1225	399	39	)	)	PUNCT
ijassa-1225	399	40	obtained	obtain	VERB
ijassa-1225	399	41	using	use	VERB
ijassa-1225	399	42	the	the	DET
ijassa-1225	399	43	results	result	NOUN
ijassa-1225	399	44	on	on	ADP
ijassa-1225	399	45	covering	cover	VERB
ijassa-1225	399	46	mappings	mapping	NOUN
ijassa-1225	399	47	of	of	ADP
ijassa-1225	399	48	metric	metric	ADJ
ijassa-1225	399	49	spaces	space	NOUN
ijassa-1225	399	50	.	.	PUNCT
ijassa-1225	400	1	in	in	ADP
ijassa-1225	400	2	particular	particular	ADJ
ijassa-1225	400	3	,	,	PUNCT
ijassa-1225	400	4	in	in	ADP
ijassa-1225	400	5	[	[	X
ijassa-1225	400	6	17	17	NUM
ijassa-1225	400	7	]	]	PUNCT
ijassa-1225	400	8	the	the	DET
ijassa-1225	400	9	authors	author	NOUN
ijassa-1225	400	10	managed	manage	VERB
ijassa-1225	400	11	to	to	PART
ijassa-1225	400	12	investigate	investigate	VERB
ijassa-1225	400	13	the	the	DET
ijassa-1225	400	14	models	model	NOUN
ijassa-1225	400	15	with	with	ADP
ijassa-1225	400	16	the	the	DET
ijassa-1225	400	17	mappings	mapping	NOUN
ijassa-1225	400	18	of	of	ADP
ijassa-1225	400	19	supply	supply	NOUN
ijassa-1225	400	20	and	and	CCONJ
ijassa-1225	400	21	demand	demand	NOUN
ijassa-1225	400	22	that	that	PRON
ijassa-1225	400	23	are	be	AUX
ijassa-1225	400	24	dependent	dependent	ADJ
ijassa-1225	400	25	not	not	PART
ijassa-1225	400	26	only	only	ADV
ijassa-1225	400	27	on	on	ADP
ijassa-1225	400	28	the	the	DET
ijassa-1225	400	29	market	market	NOUN
ijassa-1225	400	30	prices	price	NOUN
ijassa-1225	400	31	,	,	PUNCT
ijassa-1225	400	32	but	but	CCONJ
ijassa-1225	400	33	also	also	ADV
ijassa-1225	400	34	on	on	ADP
ijassa-1225	400	35	the	the	PRON
ijassa-1225	400	36	the	the	DET
ijassa-1225	400	37	prices	price	NOUN
ijassa-1225	400	38	change	change	VERB
ijassa-1225	400	39	rates	rate	NOUN
ijassa-1225	400	40	.	.	PUNCT
ijassa-1225	401	1	in	in	ADP
ijassa-1225	401	2	this	this	DET
ijassa-1225	401	3	section	section	NOUN
ijassa-1225	401	4	,	,	PUNCT
ijassa-1225	401	5	the	the	DET
ijassa-1225	401	6	models	model	NOUN
ijassa-1225	401	7	under	under	ADP
ijassa-1225	401	8	consideration	consideration	NOUN
ijassa-1225	401	9	contain	contain	VERB
ijassa-1225	401	10	set	set	NOUN
ijassa-1225	401	11	-	-	PUNCT
ijassa-1225	401	12	valued	value	VERB
ijassa-1225	401	13	mappings	mapping	NOUN
ijassa-1225	401	14	of	of	ADP
ijassa-1225	401	15	supply	supply	NOUN
ijassa-1225	401	16	and	and	CCONJ
ijassa-1225	401	17	demand	demand	NOUN
ijassa-1225	401	18	.	.	PUNCT
ijassa-1225	402	1	such	such	ADJ
ijassa-1225	402	2	generalisation	generalisation	NOUN
ijassa-1225	402	3	is	be	AUX
ijassa-1225	402	4	natural	natural	ADJ
ijassa-1225	402	5	as	as	SCONJ
ijassa-1225	402	6	the	the	DET
ijassa-1225	402	7	values	value	NOUN
ijassa-1225	402	8	of	of	ADP
ijassa-1225	402	9	these	these	DET
ijassa-1225	402	10	mappings	mapping	NOUN
ijassa-1225	402	11	are	be	AUX
ijassa-1225	402	12	defined	define	VERB
ijassa-1225	402	13	in	in	ADP
ijassa-1225	402	14	the	the	DET
ijassa-1225	402	15	economic	economic	ADJ
ijassa-1225	402	16	problems	problem	NOUN
ijassa-1225	402	17	as	as	ADP
ijassa-1225	402	18	the	the	DET
ijassa-1225	402	19	set	set	NOUN
ijassa-1225	402	20	of	of	ADP
ijassa-1225	402	21	solutions	solution	NOUN
ijassa-1225	402	22	of	of	ADP
ijassa-1225	402	23	constraint	constraint	NOUN
ijassa-1225	402	24	minimisation	minimisation	NOUN
ijassa-1225	402	25	problems	problem	NOUN
ijassa-1225	402	26	(	(	PUNCT
ijassa-1225	402	27	see	see	VERB
ijassa-1225	402	28	e.g.	e.g.	ADV
ijassa-1225	402	29	[	[	X
ijassa-1225	402	30	23	23	NUM
ijassa-1225	402	31	,	,	PUNCT
ijassa-1225	402	32	§	§	PROPN
ijassa-1225	402	33	4.2.2	4.2.2	NUM
ijassa-1225	402	34	]	]	NOUN
ijassa-1225	402	35	)	)	PUNCT
ijassa-1225	402	36	.	.	PUNCT
ijassa-1225	403	1	in	in	ADP
ijassa-1225	403	2	the	the	DET
ijassa-1225	403	3	present	present	ADJ
ijassa-1225	403	4	research	research	NOUN
ijassa-1225	403	5	,	,	PUNCT
ijassa-1225	403	6	in	in	ADP
ijassa-1225	403	7	contrast	contrast	NOUN
ijassa-1225	403	8	to	to	ADP
ijassa-1225	403	9	the	the	DET
ijassa-1225	403	10	cited	cite	VERB
ijassa-1225	403	11	works	work	NOUN
ijassa-1225	403	12	that	that	DET
ijassa-1225	403	13	base	base	NOUN
ijassa-1225	403	14	on	on	ADP
ijassa-1225	403	15	the	the	DET
ijassa-1225	403	16	results	result	NOUN
ijassa-1225	403	17	on	on	ADP
ijassa-1225	403	18	mappings	mapping	NOUN
ijassa-1225	403	19	of	of	ADP
ijassa-1225	403	20	metric	metric	ADJ
ijassa-1225	403	21	spaces	space	NOUN
ijassa-1225	403	22	,	,	PUNCT
ijassa-1225	403	23	methods	method	NOUN
ijassa-1225	403	24	of	of	ADP
ijassa-1225	403	25	analysis	analysis	NOUN
ijassa-1225	403	26	of	of	ADP
ijassa-1225	403	27	mappings	mapping	NOUN
ijassa-1225	403	28	of	of	ADP
ijassa-1225	403	29	partially	partially	ADV
ijassa-1225	403	30	ordered	order	VERB
ijassa-1225	403	31	spaces	space	NOUN
ijassa-1225	403	32	are	be	AUX
ijassa-1225	403	33	employed	employ	VERB
ijassa-1225	403	34	.	.	PUNCT
ijassa-1225	404	1	let	let	VERB
ijassa-1225	404	2	us	we	PRON
ijassa-1225	404	3	formulate	formulate	VERB
ijassa-1225	404	4	the	the	DET
ijassa-1225	404	5	problem	problem	NOUN
ijassa-1225	404	6	.	.	PUNCT
ijassa-1225	405	1	let	let	VERB
ijassa-1225	405	2	us	we	PRON
ijassa-1225	405	3	have	have	VERB
ijassa-1225	405	4	n	n	DET
ijassa-1225	405	5	types	type	NOUN
ijassa-1225	405	6	of	of	ADP
ijassa-1225	405	7	goods	good	NOUN
ijassa-1225	405	8	,	,	PUNCT
ijassa-1225	406	1	whose	whose	DET
ijassa-1225	406	2	prices	price	NOUN
ijassa-1225	406	3	at	at	ADP
ijassa-1225	406	4	any	any	DET
ijassa-1225	406	5	time	time	NOUN
ijassa-1225	406	6	t	t	X
ijassa-1225	406	7	∈	∈	PROPN
ijassa-1225	407	1	[	[	X
ijassa-1225	407	2	a	a	X
ijassa-1225	407	3	,	,	PUNCT
ijassa-1225	407	4	b	b	NOUN
ijassa-1225	407	5	]	]	X
ijassa-1225	407	6	we	we	PRON
ijassa-1225	407	7	denote	denote	VERB
ijassa-1225	407	8	by	by	ADP
ijassa-1225	407	9	pi(t	pi(t	NOUN
ijassa-1225	407	10	)	)	PUNCT
ijassa-1225	407	11	,	,	PUNCT
ijassa-1225	407	12	i	i	PRON
ijassa-1225	407	13	=	=	NOUN
ijassa-1225	407	14	1	1	NUM
ijassa-1225	407	15	,	,	PUNCT
ijassa-1225	407	16	n.	n.	NOUN
ijassa-1225	407	17	let	let	VERB
ijassa-1225	407	18	these	these	DET
ijassa-1225	407	19	prices	price	NOUN
ijassa-1225	407	20	be	be	AUX
ijassa-1225	407	21	known	know	VERB
ijassa-1225	407	22	at	at	ADP
ijassa-1225	407	23	the	the	DET
ijassa-1225	407	24	initial	initial	ADJ
ijassa-1225	407	25	moment	moment	NOUN
ijassa-1225	407	26	of	of	ADP
ijassa-1225	407	27	time	time	NOUN
ijassa-1225	407	28	pi(a	pi(a	PUNCT
ijassa-1225	407	29	)	)	PUNCT
ijassa-1225	407	30	=	=	SYM
ijassa-1225	407	31	γi	γi	NOUN
ijassa-1225	407	32	,	,	PUNCT
ijassa-1225	407	33	i	i	NOUN
ijassa-1225	407	34	=	=	NOUN
ijassa-1225	407	35	1	1	NUM
ijassa-1225	407	36	,	,	PUNCT
ijassa-1225	407	37	n.	n.	NOUN
ijassa-1225	407	38	(	(	PUNCT
ijassa-1225	407	39	5.30	5.30	NUM
ijassa-1225	407	40	)	)	PUNCT
ijassa-1225	407	41	copyright	copyright	NOUN
ijassa-1225	407	42	©	©	PROPN
ijassa-1225	407	43	2022	2022	NUM
ijassa-1225	407	44	assa	assa	NOUN
ijassa-1225	407	45	.	.	PUNCT
ijassa-1225	408	1	adv	adv	PROPN
ijassa-1225	408	2	syst	syst	PROPN
ijassa-1225	408	3	sci	sci	PROPN
ijassa-1225	408	4	appl	appl	PROPN
ijassa-1225	408	5	(	(	PUNCT
ijassa-1225	408	6	2022	2022	NUM
ijassa-1225	408	7	)	)	PUNCT
ijassa-1225	408	8	188	188	NUM
ijassa-1225	408	9	e.s	e.s	PROPN
ijassa-1225	408	10	.	.	PROPN
ijassa-1225	408	11	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	408	12	,	,	PUNCT
ijassa-1225	408	13	i.d	i.d	PROPN
ijassa-1225	408	14	.	.	PROPN
ijassa-1225	408	15	serova	serova	PROPN
ijassa-1225	408	16	,	,	PUNCT
ijassa-1225	408	17	e.a	e.a	PROPN
ijassa-1225	408	18	.	.	PROPN
ijassa-1225	408	19	panasenko	panasenko	PROPN
ijassa-1225	408	20	,	,	PUNCT
ijassa-1225	408	21	e.o	e.o	PROPN
ijassa-1225	408	22	.	.	PROPN
ijassa-1225	408	23	burlakov	burlakov	PROPN
ijassa-1225	408	24	we	we	PRON
ijassa-1225	408	25	define	define	VERB
ijassa-1225	408	26	the	the	DET
ijassa-1225	408	27	vector	vector	NOUN
ijassa-1225	408	28	p(t	p(t	NOUN
ijassa-1225	408	29	)	)	PUNCT
ijassa-1225	408	30	=	=	PRON
ijassa-1225	408	31	(	(	PUNCT
ijassa-1225	408	32	p1(t	p1(t	PROPN
ijassa-1225	408	33	)	)	PUNCT
ijassa-1225	408	34	,	,	PUNCT
ijassa-1225	408	35	.	.	PUNCT
ijassa-1225	408	36	.	.	PUNCT
ijassa-1225	408	37	.	.	PUNCT
ijassa-1225	409	1	,	,	PUNCT
ijassa-1225	409	2	pn(t	pn(t	NUM
ijassa-1225	409	3	)	)	PUNCT
ijassa-1225	409	4	)	)	PUNCT
ijassa-1225	410	1	∈	∈	PROPN
ijassa-1225	410	2	rn	rn	PROPN
ijassa-1225	410	3	+	+	X
ijassa-1225	410	4	of	of	ADP
ijassa-1225	410	5	prices	price	NOUN
ijassa-1225	410	6	.	.	PUNCT
ijassa-1225	411	1	assume	assume	VERB
ijassa-1225	411	2	that	that	SCONJ
ijassa-1225	411	3	there	there	PRON
ijassa-1225	411	4	are	be	VERB
ijassa-1225	411	5	some	some	DET
ijassa-1225	411	6	restrictions	restriction	NOUN
ijassa-1225	411	7	on	on	ADP
ijassa-1225	411	8	the	the	DET
ijassa-1225	411	9	change	change	NOUN
ijassa-1225	411	10	rates	rate	NOUN
ijassa-1225	411	11	of	of	ADP
ijassa-1225	411	12	the	the	DET
ijassa-1225	411	13	prices	price	NOUN
ijassa-1225	411	14	,	,	PUNCT
ijassa-1225	411	15	i.e.	i.e.	X
ijassa-1225	411	16	there	there	PRON
ijassa-1225	411	17	is	be	VERB
ijassa-1225	411	18	a	a	DET
ijassa-1225	411	19	measurable	measurable	ADJ
ijassa-1225	411	20	set	set	NOUN
ijassa-1225	411	21	-	-	PUNCT
ijassa-1225	411	22	valued	value	VERB
ijassa-1225	411	23	mapping	mapping	NOUN
ijassa-1225	411	24	b	b	NOUN
ijassa-1225	411	25	:	:	PUNCT
ijassa-1225	412	1	[	[	X
ijassa-1225	412	2	a	a	DET
ijassa-1225	412	3	,	,	PUNCT
ijassa-1225	412	4	b]→	b]→	NOUN
ijassa-1225	412	5	k(rn	k(rn	NOUN
ijassa-1225	412	6	)	)	PUNCT
ijassa-1225	412	7	and	and	CCONJ
ijassa-1225	412	8	the	the	DET
ijassa-1225	412	9	inclusion	inclusion	NOUN
ijassa-1225	412	10	ṗ(t	ṗ(t	NOUN
ijassa-1225	412	11	)	)	PUNCT
ijassa-1225	412	12	=	=	SYM
ijassa-1225	412	13	(	(	PUNCT
ijassa-1225	412	14	ṗ1(t	ṗ1(t	PROPN
ijassa-1225	412	15	)	)	PUNCT
ijassa-1225	412	16	,	,	PUNCT
ijassa-1225	412	17	.	.	PUNCT
ijassa-1225	412	18	.	.	PUNCT
ijassa-1225	412	19	.	.	PUNCT
ijassa-1225	412	20	,	,	PUNCT
ijassa-1225	412	21	ṗn(t	ṗn(t	NOUN
ijassa-1225	412	22	)	)	PUNCT
ijassa-1225	412	23	)	)	PUNCT
ijassa-1225	412	24	∈	∈	PROPN
ijassa-1225	412	25	b(t	b(t	PROPN
ijassa-1225	412	26	)	)	PUNCT
ijassa-1225	412	27	for	for	ADP
ijassa-1225	412	28	almost	almost	ADV
ijassa-1225	412	29	all	all	PRON
ijassa-1225	412	30	t	t	NOUN
ijassa-1225	412	31	∈	∈	PRON
ijassa-1225	413	1	[	[	X
ijassa-1225	413	2	a	a	X
ijassa-1225	413	3	,	,	PUNCT
ijassa-1225	413	4	b	b	NOUN
ijassa-1225	413	5	]	]	X
ijassa-1225	413	6	(	(	PUNCT
ijassa-1225	413	7	5.31	5.31	NUM
ijassa-1225	413	8	)	)	PUNCT
ijassa-1225	413	9	takes	take	VERB
ijassa-1225	413	10	place	place	NOUN
ijassa-1225	413	11	.	.	PUNCT
ijassa-1225	414	1	next	next	ADV
ijassa-1225	414	2	,	,	PUNCT
ijassa-1225	414	3	let	let	VERB
ijassa-1225	415	1	the	the	DET
ijassa-1225	415	2	set	set	NOUN
ijassa-1225	415	3	-	-	PUNCT
ijassa-1225	415	4	valued	value	VERB
ijassa-1225	415	5	mappings	mapping	NOUN
ijassa-1225	415	6	d	d	NOUN
ijassa-1225	415	7	:	:	PUNCT
ijassa-1225	416	1	[	[	X
ijassa-1225	416	2	a	a	X
ijassa-1225	416	3	,	,	PUNCT
ijassa-1225	416	4	b]×	b]×	NOUN
ijassa-1225	416	5	rn	rn	NOUN
ijassa-1225	416	6	+	+	CCONJ
ijassa-1225	416	7	×	×	PROPN
ijassa-1225	416	8	rn	rn	PROPN
ijassa-1225	416	9	×	×	PROPN
ijassa-1225	416	10	rn	rn	PROPN
ijassa-1225	416	11	→	→	SYM
ijassa-1225	416	12	k(rn	k(rn	PROPN
ijassa-1225	416	13	+	+	PUNCT
ijassa-1225	416	14	)	)	PUNCT
ijassa-1225	416	15	and	and	CCONJ
ijassa-1225	416	16	s	s	VERB
ijassa-1225	416	17	:	:	PUNCT
ijassa-1225	416	18	[	[	X
ijassa-1225	416	19	a	a	X
ijassa-1225	416	20	,	,	PUNCT
ijassa-1225	416	21	b]×	b]×	NOUN
ijassa-1225	416	22	rn	rn	NOUN
ijassa-1225	417	1	+	+	CCONJ
ijassa-1225	417	2	×	×	PROPN
ijassa-1225	417	3	rn	rn	PROPN
ijassa-1225	417	4	→	→	SYM
ijassa-1225	417	5	k(rn	k(rn	PROPN
ijassa-1225	417	6	+	+	PUNCT
ijassa-1225	417	7	)	)	PUNCT
ijassa-1225	417	8	be	be	AUX
ijassa-1225	417	9	given	give	VERB
ijassa-1225	417	10	.	.	PUNCT
ijassa-1225	418	1	we	we	PRON
ijassa-1225	418	2	assume	assume	VERB
ijassa-1225	418	3	that	that	SCONJ
ijassa-1225	418	4	for	for	ADP
ijassa-1225	418	5	any	any	DET
ijassa-1225	418	6	x	x	SYM
ijassa-1225	418	7	∈	∈	PROPN
ijassa-1225	418	8	rn	rn	PROPN
ijassa-1225	418	9	+	+	PROPN
ijassa-1225	418	10	and	and	CCONJ
ijassa-1225	418	11	any	any	DET
ijassa-1225	418	12	v	v	NOUN
ijassa-1225	418	13	,	,	PUNCT
ijassa-1225	418	14	u	u	PROPN
ijassa-1225	418	15	∈	∈	PROPN
ijassa-1225	418	16	rn	rn	PROPN
ijassa-1225	418	17	,	,	PUNCT
ijassa-1225	418	18	the	the	DET
ijassa-1225	418	19	functions	function	NOUN
ijassa-1225	418	20	d	d	X
ijassa-1225	418	21	(	(	PUNCT
ijassa-1225	418	22	·	·	PUNCT
ijassa-1225	418	23	,	,	PUNCT
ijassa-1225	418	24	x	x	NOUN
ijassa-1225	418	25	,	,	PUNCT
ijassa-1225	418	26	v	v	NOUN
ijassa-1225	418	27	,	,	PUNCT
ijassa-1225	418	28	u	u	NOUN
ijassa-1225	418	29	)	)	PUNCT
ijassa-1225	418	30	,	,	PUNCT
ijassa-1225	418	31	s	s	X
ijassa-1225	418	32	(	(	PUNCT
ijassa-1225	418	33	·	·	PUNCT
ijassa-1225	418	34	,	,	PUNCT
ijassa-1225	418	35	x	x	NOUN
ijassa-1225	418	36	,	,	PUNCT
ijassa-1225	418	37	v	v	NOUN
ijassa-1225	418	38	)	)	PUNCT
ijassa-1225	418	39	:	:	PUNCT
ijassa-1225	419	1	[	[	X
ijassa-1225	419	2	a	a	X
ijassa-1225	419	3	,	,	PUNCT
ijassa-1225	419	4	b]→	b]→	ADJ
ijassa-1225	419	5	k(rn	k(rn	PROPN
ijassa-1225	419	6	+	+	PUNCT
ijassa-1225	419	7	)	)	PUNCT
ijassa-1225	419	8	are	be	AUX
ijassa-1225	419	9	measurable	measurable	ADJ
ijassa-1225	419	10	;	;	PUNCT
ijassa-1225	419	11	for	for	ADP
ijassa-1225	419	12	almost	almost	ADV
ijassa-1225	419	13	all	all	PRON
ijassa-1225	419	14	t	t	NOUN
ijassa-1225	419	15	∈	∈	PRON
ijassa-1225	420	1	[	[	X
ijassa-1225	420	2	a	a	X
ijassa-1225	420	3	,	,	PUNCT
ijassa-1225	420	4	b	b	NOUN
ijassa-1225	420	5	]	]	PUNCT
ijassa-1225	420	6	and	and	CCONJ
ijassa-1225	420	7	any	any	DET
ijassa-1225	420	8	v	v	NOUN
ijassa-1225	420	9	,	,	PUNCT
ijassa-1225	420	10	u	u	PROPN
ijassa-1225	420	11	∈	∈	PROPN
ijassa-1225	420	12	rn	rn	PROPN
ijassa-1225	420	13	,	,	PUNCT
ijassa-1225	420	14	the	the	DET
ijassa-1225	420	15	functions	function	NOUN
ijassa-1225	420	16	d(t	d(t	PROPN
ijassa-1225	420	17	,	,	PUNCT
ijassa-1225	420	18	·	·	PUNCT
ijassa-1225	420	19	,	,	PUNCT
ijassa-1225	420	20	v	v	NOUN
ijassa-1225	420	21	,	,	PUNCT
ijassa-1225	420	22	u	u	NOUN
ijassa-1225	420	23	)	)	PUNCT
ijassa-1225	420	24	,	,	PUNCT
ijassa-1225	420	25	s(t	s(t	PROPN
ijassa-1225	420	26	,	,	PUNCT
ijassa-1225	420	27	·	·	PUNCT
ijassa-1225	420	28	,	,	PUNCT
ijassa-1225	420	29	v	v	NOUN
ijassa-1225	420	30	)	)	PUNCT
ijassa-1225	420	31	:	:	PUNCT
ijassa-1225	420	32	rn	rn	PROPN
ijassa-1225	421	1	+	+	PROPN
ijassa-1225	421	2	→	→	SYM
ijassa-1225	421	3	k(rn	k(rn	PRON
ijassa-1225	421	4	+	+	NOUN
ijassa-1225	421	5	)	)	PUNCT
ijassa-1225	421	6	are	be	AUX
ijassa-1225	421	7	right	right	ADV
ijassa-1225	421	8	continuous	continuous	ADJ
ijassa-1225	421	9	in	in	ADP
ijassa-1225	421	10	each	each	PRON
ijassa-1225	421	11	of	of	ADP
ijassa-1225	421	12	the	the	DET
ijassa-1225	421	13	arguments	argument	NOUN
ijassa-1225	421	14	x1	x1	NUM
ijassa-1225	421	15	,	,	PUNCT
ijassa-1225	421	16	.	.	PUNCT
ijassa-1225	421	17	.	.	PUNCT
ijassa-1225	422	1	.	.	PUNCT
ijassa-1225	423	1	,	,	PUNCT
ijassa-1225	423	2	xn	xn	PROPN
ijassa-1225	423	3	;	;	PUNCT
ijassa-1225	423	4	for	for	ADP
ijassa-1225	423	5	almost	almost	ADV
ijassa-1225	423	6	all	all	PRON
ijassa-1225	423	7	t	t	NOUN
ijassa-1225	423	8	∈	∈	PRON
ijassa-1225	424	1	[	[	X
ijassa-1225	424	2	a	a	X
ijassa-1225	424	3	,	,	PUNCT
ijassa-1225	424	4	b	b	NOUN
ijassa-1225	424	5	]	]	PUNCT
ijassa-1225	424	6	and	and	CCONJ
ijassa-1225	424	7	any	any	DET
ijassa-1225	424	8	x	x	SYM
ijassa-1225	424	9	∈	∈	PROPN
ijassa-1225	424	10	rn	rn	PROPN
ijassa-1225	425	1	+	+	PROPN
ijassa-1225	425	2	,	,	PUNCT
ijassa-1225	425	3	u	u	PROPN
ijassa-1225	425	4	∈	∈	PROPN
ijassa-1225	425	5	rn	rn	PROPN
ijassa-1225	425	6	,	,	PUNCT
ijassa-1225	425	7	the	the	DET
ijassa-1225	425	8	functionsd(t	functionsd(t	PROPN
ijassa-1225	425	9	,	,	PUNCT
ijassa-1225	425	10	x	x	NOUN
ijassa-1225	425	11	,	,	PUNCT
ijassa-1225	425	12	·	·	PUNCT
ijassa-1225	425	13	,	,	PUNCT
ijassa-1225	425	14	u	u	NOUN
ijassa-1225	425	15	)	)	PUNCT
ijassa-1225	425	16	,	,	PUNCT
ijassa-1225	425	17	s(t	s(t	PROPN
ijassa-1225	425	18	,	,	PUNCT
ijassa-1225	425	19	x	x	X
ijassa-1225	425	20	,	,	PUNCT
ijassa-1225	425	21	·	·	PUNCT
ijassa-1225	425	22	)	)	PUNCT
ijassa-1225	425	23	:	:	PUNCT
ijassa-1225	425	24	rn	rn	PROPN
ijassa-1225	425	25	→	→	SYM
ijassa-1225	425	26	k(rn	k(rn	PROPN
ijassa-1225	425	27	+	+	PUNCT
ijassa-1225	425	28	)	)	PUNCT
ijassa-1225	425	29	are	be	AUX
ijassa-1225	425	30	right	right	ADV
ijassa-1225	425	31	continuous	continuous	ADJ
ijassa-1225	425	32	in	in	ADP
ijassa-1225	425	33	each	each	PRON
ijassa-1225	425	34	of	of	ADP
ijassa-1225	425	35	the	the	DET
ijassa-1225	425	36	arguments	argument	NOUN
ijassa-1225	425	37	v1	v1	NOUN
ijassa-1225	425	38	,	,	PUNCT
ijassa-1225	425	39	.	.	PUNCT
ijassa-1225	425	40	.	.	PUNCT
ijassa-1225	426	1	.	.	PUNCT
ijassa-1225	427	1	,	,	PUNCT
ijassa-1225	427	2	vn	vn	X
ijassa-1225	427	3	;	;	PUNCT
ijassa-1225	427	4	for	for	ADP
ijassa-1225	427	5	almost	almost	ADV
ijassa-1225	427	6	all	all	PRON
ijassa-1225	427	7	t	t	NOUN
ijassa-1225	427	8	∈	∈	PRON
ijassa-1225	428	1	[	[	X
ijassa-1225	428	2	a	a	X
ijassa-1225	428	3	,	,	PUNCT
ijassa-1225	428	4	b	b	NOUN
ijassa-1225	428	5	]	]	PUNCT
ijassa-1225	428	6	and	and	CCONJ
ijassa-1225	428	7	any	any	DET
ijassa-1225	428	8	x	x	SYM
ijassa-1225	428	9	∈	∈	PROPN
ijassa-1225	428	10	rn	rn	PROPN
ijassa-1225	429	1	+	+	PROPN
ijassa-1225	429	2	,	,	PUNCT
ijassa-1225	429	3	v	v	PROPN
ijassa-1225	429	4	∈	∈	PROPN
ijassa-1225	429	5	rn	rn	PROPN
ijassa-1225	429	6	,	,	PUNCT
ijassa-1225	429	7	the	the	DET
ijassa-1225	429	8	function	function	NOUN
ijassa-1225	429	9	d(t	d(t	PROPN
ijassa-1225	429	10	,	,	PUNCT
ijassa-1225	429	11	x	x	NOUN
ijassa-1225	429	12	,	,	PUNCT
ijassa-1225	429	13	v	v	NOUN
ijassa-1225	429	14	,	,	PUNCT
ijassa-1225	429	15	·	·	PUNCT
ijassa-1225	429	16	)	)	PUNCT
ijassa-1225	429	17	:	:	PUNCT
ijassa-1225	429	18	rn	rn	PROPN
ijassa-1225	429	19	→	→	SYM
ijassa-1225	429	20	k(rn	k(rn	PROPN
ijassa-1225	429	21	+	+	PUNCT
ijassa-1225	429	22	)	)	PUNCT
ijassa-1225	429	23	is	be	AUX
ijassa-1225	429	24	continuous	continuous	ADJ
ijassa-1225	429	25	.	.	PUNCT
ijassa-1225	430	1	we	we	PRON
ijassa-1225	430	2	assume	assume	VERB
ijassa-1225	430	3	that	that	SCONJ
ijassa-1225	430	4	the	the	DET
ijassa-1225	430	5	aggregate	aggregate	ADJ
ijassa-1225	430	6	consumer	consumer	NOUN
ijassa-1225	430	7	demand	demand	NOUN
ijassa-1225	430	8	at	at	ADP
ijassa-1225	430	9	time	time	NOUN
ijassa-1225	430	10	t	t	PROPN
ijassa-1225	430	11	is	be	AUX
ijassa-1225	430	12	defined	define	VERB
ijassa-1225	430	13	by	by	ADP
ijassa-1225	430	14	the	the	DET
ijassa-1225	430	15	formula	formula	NOUN
ijassa-1225	431	1	d	d	X
ijassa-1225	431	2	(	(	PUNCT
ijassa-1225	431	3	t	t	PROPN
ijassa-1225	431	4	,	,	PUNCT
ijassa-1225	431	5	p(t	p(t	NOUN
ijassa-1225	431	6	)	)	PUNCT
ijassa-1225	431	7	,	,	PUNCT
ijassa-1225	431	8	ṗ(t	ṗ(t	NOUN
ijassa-1225	431	9	)	)	PUNCT
ijassa-1225	431	10	,	,	PUNCT
ijassa-1225	431	11	ṗ(t	ṗ(t	NOUN
ijassa-1225	431	12	)	)	PUNCT
ijassa-1225	431	13	)	)	PUNCT
ijassa-1225	431	14	and	and	CCONJ
ijassa-1225	431	15	aggregate	aggregate	ADJ
ijassa-1225	431	16	manufacturer	manufacturer	NOUN
ijassa-1225	431	17	’s	’s	PART
ijassa-1225	431	18	supply	supply	NOUN
ijassa-1225	431	19	—	—	PUNCT
ijassa-1225	431	20	by	by	ADP
ijassa-1225	431	21	the	the	DET
ijassa-1225	431	22	formula	formula	NOUN
ijassa-1225	431	23	s	s	X
ijassa-1225	431	24	(	(	PUNCT
ijassa-1225	431	25	t	t	PROPN
ijassa-1225	431	26	,	,	PUNCT
ijassa-1225	431	27	p(t	p(t	NOUN
ijassa-1225	431	28	)	)	PUNCT
ijassa-1225	431	29	,	,	PUNCT
ijassa-1225	431	30	ṗ(t	ṗ(t	NOUN
ijassa-1225	431	31	)	)	PUNCT
ijassa-1225	431	32	)	)	PUNCT
ijassa-1225	431	33	.	.	PUNCT
ijassa-1225	432	1	for	for	ADP
ijassa-1225	432	2	the	the	DET
ijassa-1225	432	3	defined	define	VERB
ijassa-1225	432	4	above	above	ADP
ijassa-1225	432	5	set	set	NOUN
ijassa-1225	432	6	-	-	PUNCT
ijassa-1225	432	7	valued	value	VERB
ijassa-1225	432	8	mappings	mapping	NOUN
ijassa-1225	432	9	of	of	ADP
ijassa-1225	432	10	supply	supply	NOUN
ijassa-1225	432	11	and	and	CCONJ
ijassa-1225	432	12	demand	demand	NOUN
ijassa-1225	432	13	,	,	PUNCT
ijassa-1225	432	14	we	we	PRON
ijassa-1225	432	15	consider	consider	VERB
ijassa-1225	432	16	the	the	DET
ijassa-1225	432	17	problem	problem	NOUN
ijassa-1225	432	18	of	of	ADP
ijassa-1225	432	19	existence	existence	NOUN
ijassa-1225	432	20	of	of	ADP
ijassa-1225	432	21	an	an	DET
ijassa-1225	432	22	equilibrium	equilibrium	NOUN
ijassa-1225	432	23	—	—	PUNCT
ijassa-1225	432	24	a	a	DET
ijassa-1225	432	25	solution	solution	NOUN
ijassa-1225	432	26	p	p	X
ijassa-1225	432	27	∈	∈	PROPN
ijassa-1225	432	28	ac(b	ac(b	NOUN
ijassa-1225	432	29	)	)	PUNCT
ijassa-1225	432	30	(	(	PUNCT
ijassa-1225	432	31	i.e.	i.e.	X
ijassa-1225	432	32	absolutely	absolutely	ADV
ijassa-1225	432	33	continuous	continuous	ADJ
ijassa-1225	432	34	function	function	NOUN
ijassa-1225	432	35	,	,	PUNCT
ijassa-1225	432	36	whose	whose	DET
ijassa-1225	432	37	derivative	derivative	ADJ
ijassa-1225	432	38	satisfies	satisfie	NOUN
ijassa-1225	432	39	the	the	DET
ijassa-1225	432	40	restriction	restriction	NOUN
ijassa-1225	432	41	(	(	PUNCT
ijassa-1225	432	42	5.31	5.31	NUM
ijassa-1225	432	43	)	)	PUNCT
ijassa-1225	432	44	)	)	PUNCT
ijassa-1225	432	45	of	of	ADP
ijassa-1225	432	46	the	the	DET
ijassa-1225	432	47	inclusion	inclusion	NOUN
ijassa-1225	432	48	d	d	X
ijassa-1225	432	49	(	(	PUNCT
ijassa-1225	432	50	t	t	PROPN
ijassa-1225	432	51	,	,	PUNCT
ijassa-1225	432	52	p(t	p(t	NOUN
ijassa-1225	432	53	)	)	PUNCT
ijassa-1225	432	54	,	,	PUNCT
ijassa-1225	432	55	ṗ(t	ṗ(t	NOUN
ijassa-1225	432	56	)	)	PUNCT
ijassa-1225	432	57	,	,	PUNCT
ijassa-1225	432	58	ṗ(t	ṗ(t	NOUN
ijassa-1225	432	59	)	)	PUNCT
ijassa-1225	432	60	)	)	PUNCT
ijassa-1225	433	1	−	−	PROPN
ijassa-1225	433	2	s	s	X
ijassa-1225	433	3	(	(	PUNCT
ijassa-1225	433	4	t	t	PROPN
ijassa-1225	433	5	,	,	PUNCT
ijassa-1225	433	6	p(t	p(t	NOUN
ijassa-1225	433	7	)	)	PUNCT
ijassa-1225	433	8	,	,	PUNCT
ijassa-1225	433	9	ṗ(t	ṗ(t	NOUN
ijassa-1225	433	10	)	)	PUNCT
ijassa-1225	433	11	)	)	PUNCT
ijassa-1225	433	12	3	3	NUM
ijassa-1225	433	13	0	0	NUM
ijassa-1225	433	14	,	,	PUNCT
ijassa-1225	433	15	(	(	PUNCT
ijassa-1225	433	16	5.32	5.32	NUM
ijassa-1225	433	17	)	)	PUNCT
ijassa-1225	433	18	with	with	ADP
ijassa-1225	433	19	the	the	DET
ijassa-1225	433	20	initial	initial	ADJ
ijassa-1225	433	21	condition	condition	NOUN
ijassa-1225	433	22	(	(	PUNCT
ijassa-1225	433	23	5.30	5.30	NUM
ijassa-1225	433	24	)	)	PUNCT
ijassa-1225	433	25	.	.	PUNCT
ijassa-1225	434	1	here	here	ADV
ijassa-1225	434	2	the	the	DET
ijassa-1225	434	3	difference	difference	NOUN
ijassa-1225	435	1	d	d	INTJ
ijassa-1225	435	2	−	−	NOUN
ijassa-1225	435	3	s	s	NOUN
ijassa-1225	435	4	of	of	ADP
ijassa-1225	435	5	sets	set	NOUN
ijassa-1225	435	6	in	in	ADP
ijassa-1225	435	7	the	the	DET
ijassa-1225	435	8	space	space	NOUN
ijassa-1225	435	9	rn	rn	PROPN
ijassa-1225	435	10	is	be	AUX
ijassa-1225	435	11	the	the	DET
ijassa-1225	435	12	set	set	NOUN
ijassa-1225	435	13	of	of	ADP
ijassa-1225	435	14	all	all	DET
ijassa-1225	435	15	vectors	vector	NOUN
ijassa-1225	435	16	x−	x−	PROPN
ijassa-1225	435	17	y	y	PROPN
ijassa-1225	435	18	,	,	PUNCT
ijassa-1225	435	19	where	where	SCONJ
ijassa-1225	435	20	x	x	SYM
ijassa-1225	435	21	∈	∈	PROPN
ijassa-1225	435	22	d	d	NOUN
ijassa-1225	435	23	,	,	PUNCT
ijassa-1225	435	24	y	y	PROPN
ijassa-1225	435	25	∈	∈	PROPN
ijassa-1225	435	26	s.	s.	PROPN
ijassa-1225	435	27	we	we	PRON
ijassa-1225	435	28	will	will	AUX
ijassa-1225	435	29	denote	denote	VERB
ijassa-1225	435	30	the	the	DET
ijassa-1225	435	31	restrictions	restriction	NOUN
ijassa-1225	435	32	of	of	ADP
ijassa-1225	435	33	mappings	mapping	NOUN
ijassa-1225	435	34	by	by	ADP
ijassa-1225	435	35	the	the	DET
ijassa-1225	435	36	same	same	ADJ
ijassa-1225	435	37	symbols	symbol	NOUN
ijassa-1225	435	38	as	as	ADP
ijassa-1225	435	39	the	the	DET
ijassa-1225	435	40	initial	initial	ADJ
ijassa-1225	435	41	mappings	mapping	NOUN
ijassa-1225	435	42	indicating	indicate	VERB
ijassa-1225	435	43	their	their	PRON
ijassa-1225	435	44	domains	domain	NOUN
ijassa-1225	435	45	and	and	CCONJ
ijassa-1225	435	46	ranges	range	NOUN
ijassa-1225	435	47	.	.	PUNCT
ijassa-1225	436	1	applying	apply	VERB
ijassa-1225	436	2	theorem	theorem	NOUN
ijassa-1225	436	3	4.1	4.1	NUM
ijassa-1225	436	4	to	to	ADP
ijassa-1225	436	5	the	the	DET
ijassa-1225	436	6	mapping	mapping	NOUN
ijassa-1225	436	7	f	f	NOUN
ijassa-1225	436	8	:	:	PUNCT
ijassa-1225	437	1	[	[	X
ijassa-1225	437	2	a	a	X
ijassa-1225	437	3	,	,	PUNCT
ijassa-1225	437	4	b]×	b]×	NOUN
ijassa-1225	437	5	rn	rn	NOUN
ijassa-1225	437	6	+	+	CCONJ
ijassa-1225	437	7	×	×	PROPN
ijassa-1225	437	8	rn	rn	PROPN
ijassa-1225	437	9	×	×	PROPN
ijassa-1225	437	10	rn	rn	PROPN
ijassa-1225	437	11	→	→	SYM
ijassa-1225	437	12	k(rn	k(rn	PROPN
ijassa-1225	437	13	+	+	NOUN
ijassa-1225	437	14	)	)	PUNCT
ijassa-1225	437	15	defined	define	VERB
ijassa-1225	437	16	by	by	ADP
ijassa-1225	437	17	the	the	DET
ijassa-1225	437	18	relation	relation	NOUN
ijassa-1225	437	19	f(t	f(t	PROPN
ijassa-1225	437	20	,	,	PUNCT
ijassa-1225	437	21	x	x	NOUN
ijassa-1225	437	22	,	,	PUNCT
ijassa-1225	437	23	v	v	NOUN
ijassa-1225	437	24	,	,	PUNCT
ijassa-1225	437	25	u	u	NOUN
ijassa-1225	437	26	)	)	PUNCT
ijassa-1225	437	27	.	.	PUNCT
ijassa-1225	438	1	=	=	PUNCT
ijassa-1225	438	2	d(t	d(t	PROPN
ijassa-1225	438	3	,	,	PUNCT
ijassa-1225	438	4	x	x	NOUN
ijassa-1225	438	5	,	,	PUNCT
ijassa-1225	438	6	v	v	NOUN
ijassa-1225	438	7	,	,	PUNCT
ijassa-1225	438	8	u)−	u)−	PROPN
ijassa-1225	438	9	s(t	s(t	PROPN
ijassa-1225	438	10	,	,	PUNCT
ijassa-1225	438	11	x	x	NOUN
ijassa-1225	438	12	,	,	PUNCT
ijassa-1225	438	13	v	v	NOUN
ijassa-1225	438	14	)	)	PUNCT
ijassa-1225	438	15	for	for	ADP
ijassa-1225	438	16	almost	almost	ADV
ijassa-1225	438	17	all	all	PRON
ijassa-1225	438	18	t	t	NOUN
ijassa-1225	438	19	∈	∈	PRON
ijassa-1225	439	1	[	[	X
ijassa-1225	439	2	a	a	X
ijassa-1225	439	3	,	,	PUNCT
ijassa-1225	439	4	b	b	NOUN
ijassa-1225	439	5	]	]	PUNCT
ijassa-1225	439	6	and	and	CCONJ
ijassa-1225	439	7	any	any	DET
ijassa-1225	439	8	x	x	SYM
ijassa-1225	439	9	∈	∈	PROPN
ijassa-1225	439	10	rn	rn	PROPN
ijassa-1225	440	1	+	+	PROPN
ijassa-1225	440	2	,	,	PUNCT
ijassa-1225	440	3	v	v	NOUN
ijassa-1225	440	4	,	,	PUNCT
ijassa-1225	440	5	u	u	PROPN
ijassa-1225	440	6	∈	∈	PROPN
ijassa-1225	440	7	rn	rn	PROPN
ijassa-1225	441	1	+	+	PROPN
ijassa-1225	441	2	,	,	PUNCT
ijassa-1225	441	3	we	we	PRON
ijassa-1225	441	4	get	get	VERB
ijassa-1225	441	5	the	the	DET
ijassa-1225	441	6	following	follow	VERB
ijassa-1225	441	7	statement	statement	NOUN
ijassa-1225	441	8	.	.	PUNCT
ijassa-1225	442	1	corollary	corollary	ADJ
ijassa-1225	442	2	5.1	5.1	NUM
ijassa-1225	442	3	:	:	PUNCT
ijassa-1225	442	4	let	let	VERB
ijassa-1225	442	5	a	a	DET
ijassa-1225	442	6	non	non	ADJ
ijassa-1225	442	7	-	-	ADJ
ijassa-1225	442	8	negative	negative	ADJ
ijassa-1225	442	9	function	function	NOUN
ijassa-1225	442	10	p	p	PROPN
ijassa-1225	442	11	∈	∈	PROPN
ijassa-1225	442	12	ac(b	ac(b	NOUN
ijassa-1225	442	13	)	)	PUNCT
ijassa-1225	442	14	such	such	ADJ
ijassa-1225	442	15	that	that	DET
ijassa-1225	442	16	p(a	p(a	PROPN
ijassa-1225	442	17	)	)	PUNCT
ijassa-1225	442	18	≥	≥	PROPN
ijassa-1225	442	19	γ	γ	PROPN
ijassa-1225	442	20	and	and	CCONJ
ijassa-1225	442	21	(	(	PUNCT
ijassa-1225	442	22	d	d	PROPN
ijassa-1225	442	23	(	(	PUNCT
ijassa-1225	442	24	t	t	PROPN
ijassa-1225	442	25	,	,	PUNCT
ijassa-1225	442	26	p(t	p(t	NOUN
ijassa-1225	442	27	)	)	PUNCT
ijassa-1225	442	28	,	,	PUNCT
ijassa-1225	442	29	ṗ(t	ṗ(t	NOUN
ijassa-1225	442	30	)	)	PUNCT
ijassa-1225	442	31	,	,	PUNCT
ijassa-1225	442	32	ṗ(t	ṗ(t	NOUN
ijassa-1225	442	33	)	)	PUNCT
ijassa-1225	442	34	)	)	PUNCT
ijassa-1225	443	1	−	−	PROPN
ijassa-1225	443	2	s	s	X
ijassa-1225	443	3	(	(	PUNCT
ijassa-1225	443	4	t	t	PROPN
ijassa-1225	443	5	,	,	PUNCT
ijassa-1225	443	6	p(t	p(t	NOUN
ijassa-1225	443	7	)	)	PUNCT
ijassa-1225	443	8	,	,	PUNCT
ijassa-1225	443	9	ṗ(t	ṗ(t	NOUN
ijassa-1225	443	10	)	)	PUNCT
ijassa-1225	443	11	)	)	PUNCT
ijassa-1225	443	12	)	)	PUNCT
ijassa-1225	443	13	∩	∩	PROPN
ijassa-1225	443	14	rn	rn	PROPN
ijassa-1225	443	15	+	+	PROPN
ijassa-1225	443	16	6=	6=	NOUN
ijassa-1225	443	17	∅	∅	NOUN
ijassa-1225	443	18	for	for	ADP
ijassa-1225	443	19	almost	almost	ADV
ijassa-1225	443	20	all	all	PRON
ijassa-1225	443	21	t	t	NOUN
ijassa-1225	443	22	∈	∈	PRON
ijassa-1225	444	1	[	[	X
ijassa-1225	444	2	a	a	X
ijassa-1225	444	3	,	,	PUNCT
ijassa-1225	444	4	b	b	NOUN
ijassa-1225	444	5	]	]	X
ijassa-1225	444	6	,	,	PUNCT
ijassa-1225	444	7	be	be	AUX
ijassa-1225	444	8	given	give	VERB
ijassa-1225	444	9	.	.	PUNCT
ijassa-1225	445	1	let	let	VERB
ijassa-1225	445	2	the	the	DET
ijassa-1225	445	3	set	set	NOUN
ijassa-1225	445	4	of	of	ADP
ijassa-1225	445	5	measurable	measurable	ADJ
ijassa-1225	445	6	selections	selection	NOUN
ijassa-1225	445	7	of	of	ADP
ijassa-1225	445	8	the	the	DET
ijassa-1225	445	9	set	set	NOUN
ijassa-1225	445	10	-	-	PUNCT
ijassa-1225	445	11	valued	value	VERB
ijassa-1225	445	12	mapping	mapping	NOUN
ijassa-1225	445	13	b	b	SYM
ijassa-1225	445	14	(	(	PUNCT
ijassa-1225	445	15	·	·	PUNCT
ijassa-1225	445	16	)	)	PUNCT
ijassa-1225	445	17	∩	∩	NOUN
ijassa-1225	445	18	orn	orn	X
ijassa-1225	445	19	(	(	PUNCT
ijassa-1225	445	20	p	p	X
ijassa-1225	445	21	(	(	PUNCT
ijassa-1225	445	22	·	·	PUNCT
ijassa-1225	445	23	)	)	PUNCT
ijassa-1225	445	24	)	)	PUNCT
ijassa-1225	445	25	:	:	PUNCT
ijassa-1225	446	1	[	[	X
ijassa-1225	446	2	a	a	PRON
ijassa-1225	446	3	,	,	PUNCT
ijassa-1225	446	4	b]→	b]→	X
ijassa-1225	446	5	c(rn	c(rn	PROPN
ijassa-1225	446	6	)	)	PUNCT
ijassa-1225	446	7	be	be	AUX
ijassa-1225	446	8	integrally	integrally	ADV
ijassa-1225	446	9	bounded	bound	VERB
ijassa-1225	446	10	from	from	ADP
ijassa-1225	446	11	below	below	ADV
ijassa-1225	446	12	(	(	PUNCT
ijassa-1225	446	13	i.e.	i.e.	X
ijassa-1225	446	14	there	there	PRON
ijassa-1225	446	15	exists	exist	VERB
ijassa-1225	446	16	a	a	DET
ijassa-1225	446	17	number	number	NOUN
ijassa-1225	446	18	c	c	NOUN
ijassa-1225	446	19	such	such	ADJ
ijassa-1225	446	20	that	that	PRON
ijassa-1225	446	21	for	for	ADP
ijassa-1225	446	22	any	any	DET
ijassa-1225	446	23	measurable	measurable	ADJ
ijassa-1225	446	24	function	function	NOUN
ijassa-1225	446	25	u	u	PROPN
ijassa-1225	446	26	∈	∈	PROPN
ijassa-1225	446	27	w	w	PROPN
ijassa-1225	446	28	n	n	CCONJ
ijassa-1225	446	29	,	,	PUNCT
ijassa-1225	446	30	satisfying	satisfy	VERB
ijassa-1225	446	31	the	the	DET
ijassa-1225	446	32	relations	relation	NOUN
ijassa-1225	446	33	u(t	u(t	NOUN
ijassa-1225	446	34	)	)	PUNCT
ijassa-1225	446	35	∈	∈	PROPN
ijassa-1225	446	36	b(t	b(t	NOUN
ijassa-1225	446	37	)	)	PUNCT
ijassa-1225	446	38	and	and	CCONJ
ijassa-1225	446	39	u(t	u(t	NOUN
ijassa-1225	446	40	)	)	PUNCT
ijassa-1225	446	41	≤	≤	PUNCT
ijassa-1225	447	1	ṗ(t	ṗ(t	NOUN
ijassa-1225	447	2	)	)	PUNCT
ijassa-1225	447	3	for	for	ADP
ijassa-1225	447	4	almost	almost	ADV
ijassa-1225	447	5	all	all	PRON
ijassa-1225	447	6	t	t	NOUN
ijassa-1225	447	7	∈	∈	PRON
ijassa-1225	448	1	[	[	X
ijassa-1225	448	2	a	a	X
ijassa-1225	448	3	,	,	PUNCT
ijassa-1225	448	4	b	b	NOUN
ijassa-1225	448	5	]	]	X
ijassa-1225	448	6	,	,	PUNCT
ijassa-1225	448	7	it	it	PRON
ijassa-1225	448	8	holds	hold	VERB
ijassa-1225	448	9	true	true	ADJ
ijassa-1225	448	10	that	that	SCONJ
ijassa-1225	448	11	∫	∫	PROPN
ijassa-1225	448	12	b	b	PROPN
ijassa-1225	448	13	a	a	DET
ijassa-1225	448	14	u(t)dt	u(t)dt	PROPN
ijassa-1225	448	15	≥	≥	NOUN
ijassa-1225	448	16	c	c	NOUN
ijassa-1225	448	17	)	)	PUNCT
ijassa-1225	448	18	and	and	CCONJ
ijassa-1225	448	19	the	the	DET
ijassa-1225	448	20	following	follow	VERB
ijassa-1225	448	21	conditions	condition	NOUN
ijassa-1225	448	22	take	take	VERB
ijassa-1225	448	23	place	place	NOUN
ijassa-1225	448	24	:	:	PUNCT
ijassa-1225	448	25	(	(	PUNCT
ijassa-1225	448	26	c1	c1	NOUN
ijassa-1225	448	27	)	)	PUNCT
ijassa-1225	448	28	for	for	ADP
ijassa-1225	448	29	almost	almost	ADV
ijassa-1225	448	30	all	all	PRON
ijassa-1225	448	31	t	t	NOUN
ijassa-1225	448	32	∈	∈	PRON
ijassa-1225	449	1	[	[	X
ijassa-1225	449	2	a	a	X
ijassa-1225	449	3	,	,	PUNCT
ijassa-1225	449	4	b	b	NOUN
ijassa-1225	449	5	]	]	X
ijassa-1225	449	6	,	,	PUNCT
ijassa-1225	449	7	any	any	DET
ijassa-1225	449	8	x	x	PROPN
ijassa-1225	449	9	∈	∈	PROPN
ijassa-1225	449	10	rn	rn	PROPN
ijassa-1225	449	11	+	+	NOUN
ijassa-1225	449	12	and	and	CCONJ
ijassa-1225	449	13	v	v	ADP
ijassa-1225	449	14	∈	∈	PROPN
ijassa-1225	449	15	b(t	b(t	PROPN
ijassa-1225	449	16	)	)	PUNCT
ijassa-1225	449	17	,	,	PUNCT
ijassa-1225	449	18	the	the	DET
ijassa-1225	449	19	mapping	mapping	NOUN
ijassa-1225	449	20	d(t	d(t	PROPN
ijassa-1225	449	21	,	,	PUNCT
ijassa-1225	449	22	x	x	NOUN
ijassa-1225	449	23	,	,	PUNCT
ijassa-1225	449	24	v	v	NOUN
ijassa-1225	449	25	,	,	PUNCT
ijassa-1225	449	26	·	·	PUNCT
ijassa-1225	449	27	)	)	PUNCT
ijassa-1225	449	28	:	:	PUNCT
ijassa-1225	450	1	b(t)→	b(t)→	SCONJ
ijassa-1225	450	2	k(rn	k(rn	X
ijassa-1225	450	3	+	+	NOUN
ijassa-1225	450	4	)	)	PUNCT
ijassa-1225	450	5	order	order	NOUN
ijassa-1225	450	6	covers	cover	VERB
ijassa-1225	450	7	the	the	DET
ijassa-1225	450	8	set	set	NOUN
ijassa-1225	450	9	{	{	PUNCT
ijassa-1225	450	10	0	0	NUM
ijassa-1225	450	11	}	}	PUNCT
ijassa-1225	450	12	⊂	⊂	PROPN
ijassa-1225	450	13	rn	rn	PROPN
ijassa-1225	450	14	;	;	PUNCT
ijassa-1225	450	15	(	(	PUNCT
ijassa-1225	450	16	c2	c2	PROPN
ijassa-1225	450	17	)	)	PUNCT
ijassa-1225	450	18	for	for	ADP
ijassa-1225	450	19	almost	almost	ADV
ijassa-1225	450	20	all	all	PRON
ijassa-1225	450	21	t	t	NOUN
ijassa-1225	450	22	∈	∈	PRON
ijassa-1225	451	1	[	[	X
ijassa-1225	451	2	a	a	X
ijassa-1225	451	3	,	,	PUNCT
ijassa-1225	451	4	b	b	NOUN
ijassa-1225	451	5	]	]	PUNCT
ijassa-1225	451	6	and	and	CCONJ
ijassa-1225	451	7	any	any	DET
ijassa-1225	451	8	u	u	PROPN
ijassa-1225	451	9	∈	∈	PROPN
ijassa-1225	451	10	b(t	b(t	PROPN
ijassa-1225	451	11	)	)	PUNCT
ijassa-1225	451	12	,	,	PUNCT
ijassa-1225	451	13	the	the	DET
ijassa-1225	451	14	mapping	mapping	NOUN
ijassa-1225	451	15	d(t	d(t	PROPN
ijassa-1225	451	16	,	,	PUNCT
ijassa-1225	451	17	·	·	PUNCT
ijassa-1225	451	18	,	,	PUNCT
ijassa-1225	451	19	·	·	PUNCT
ijassa-1225	451	20	,	,	PUNCT
ijassa-1225	451	21	u	u	NOUN
ijassa-1225	451	22	)	)	PUNCT
ijassa-1225	451	23	:	:	PUNCT
ijassa-1225	451	24	rn	rn	PROPN
ijassa-1225	451	25	+	+	CCONJ
ijassa-1225	451	26	×b(t)→	×b(t)→	PROPN
ijassa-1225	451	27	k(rn	k(rn	PROPN
ijassa-1225	451	28	+	+	PUNCT
ijassa-1225	451	29	)	)	PUNCT
ijassa-1225	451	30	is	be	AUX
ijassa-1225	451	31	antitone	antitone	ADJ
ijassa-1225	451	32	,	,	PUNCT
ijassa-1225	451	33	and	and	CCONJ
ijassa-1225	451	34	the	the	DET
ijassa-1225	451	35	mapping	mapping	NOUN
ijassa-1225	451	36	s(t	s(t	PROPN
ijassa-1225	451	37	,	,	PUNCT
ijassa-1225	451	38	·	·	PUNCT
ijassa-1225	451	39	,	,	PUNCT
ijassa-1225	451	40	·	·	PUNCT
ijassa-1225	451	41	)	)	PUNCT
ijassa-1225	451	42	:	:	PUNCT
ijassa-1225	452	1	rn	rn	PROPN
ijassa-1225	452	2	+	+	PROPN
ijassa-1225	452	3	→	→	SYM
ijassa-1225	452	4	k(rn	k(rn	PRON
ijassa-1225	452	5	+	+	NOUN
ijassa-1225	452	6	)	)	PUNCT
ijassa-1225	452	7	is	be	AUX
ijassa-1225	452	8	isotone	isotone	VERB
ijassa-1225	452	9	.	.	PUNCT
ijassa-1225	453	1	then	then	ADV
ijassa-1225	453	2	there	there	PRON
ijassa-1225	453	3	exists	exist	VERB
ijassa-1225	453	4	a	a	DET
ijassa-1225	453	5	solution	solution	NOUN
ijassa-1225	453	6	p	p	X
ijassa-1225	453	7	∈	∈	PROPN
ijassa-1225	453	8	ac(b	ac(b	NOUN
ijassa-1225	453	9	)	)	PUNCT
ijassa-1225	453	10	of	of	ADP
ijassa-1225	453	11	the	the	DET
ijassa-1225	453	12	problem	problem	NOUN
ijassa-1225	453	13	(	(	PUNCT
ijassa-1225	453	14	5.32	5.32	NUM
ijassa-1225	453	15	)	)	PUNCT
ijassa-1225	453	16	,	,	PUNCT
ijassa-1225	453	17	(	(	PUNCT
ijassa-1225	453	18	5.31	5.31	NUM
ijassa-1225	453	19	)	)	PUNCT
ijassa-1225	453	20	,	,	PUNCT
ijassa-1225	453	21	(	(	PUNCT
ijassa-1225	453	22	5.30	5.30	NUM
ijassa-1225	453	23	)	)	PUNCT
ijassa-1225	453	24	such	such	ADJ
ijassa-1225	453	25	that	that	SCONJ
ijassa-1225	453	26	ṗ(t	ṗ(t	NOUN
ijassa-1225	453	27	)	)	PUNCT
ijassa-1225	453	28	≤	≤	NOUN
ijassa-1225	453	29	ṗ(t	ṗ(t	NOUN
ijassa-1225	453	30	)	)	PUNCT
ijassa-1225	453	31	for	for	ADP
ijassa-1225	453	32	almost	almost	ADV
ijassa-1225	453	33	all	all	PRON
ijassa-1225	453	34	t	t	NOUN
ijassa-1225	453	35	∈	∈	PRON
ijassa-1225	454	1	[	[	X
ijassa-1225	454	2	a	a	X
ijassa-1225	454	3	,	,	PUNCT
ijassa-1225	454	4	b	b	NOUN
ijassa-1225	454	5	]	]	X
ijassa-1225	454	6	.	.	PUNCT
ijassa-1225	455	1	(	(	PUNCT
ijassa-1225	455	2	5.33	5.33	NUM
ijassa-1225	455	3	)	)	PUNCT
ijassa-1225	455	4	copyright	copyright	NOUN
ijassa-1225	455	5	©	©	PROPN
ijassa-1225	455	6	2022	2022	NUM
ijassa-1225	455	7	assa	assa	NOUN
ijassa-1225	455	8	.	.	PUNCT
ijassa-1225	456	1	adv	adv	PROPN
ijassa-1225	456	2	syst	syst	PROPN
ijassa-1225	456	3	sci	sci	PROPN
ijassa-1225	456	4	appl	appl	PROPN
ijassa-1225	456	5	(	(	PUNCT
ijassa-1225	456	6	2022	2022	NUM
ijassa-1225	456	7	)	)	PUNCT
ijassa-1225	456	8	on	on	ADP
ijassa-1225	456	9	order	order	NOUN
ijassa-1225	456	10	covering	cover	VERB
ijassa-1225	456	11	set	set	NOUN
ijassa-1225	456	12	-	-	PUNCT
ijassa-1225	456	13	valued	value	VERB
ijassa-1225	456	14	mappings	mapping	NOUN
ijassa-1225	456	15	and	and	CCONJ
ijassa-1225	456	16	their	their	PRON
ijassa-1225	456	17	applications	application	NOUN
ijassa-1225	456	18	189	189	NUM
ijassa-1225	456	19	note	note	NOUN
ijassa-1225	456	20	that	that	SCONJ
ijassa-1225	456	21	the	the	DET
ijassa-1225	456	22	assumptions	assumption	NOUN
ijassa-1225	456	23	(	(	PUNCT
ijassa-1225	456	24	c2	c2	PROPN
ijassa-1225	456	25	)	)	PUNCT
ijassa-1225	456	26	have	have	VERB
ijassa-1225	456	27	natural	natural	ADJ
ijassa-1225	456	28	economic	economic	ADJ
ijassa-1225	456	29	sense	sense	NOUN
ijassa-1225	456	30	:	:	PUNCT
ijassa-1225	456	31	a	a	DET
ijassa-1225	456	32	decrease	decrease	NOUN
ijassa-1225	456	33	of	of	ADP
ijassa-1225	456	34	the	the	DET
ijassa-1225	456	35	prices	price	NOUN
ijassa-1225	456	36	and	and	CCONJ
ijassa-1225	456	37	the	the	DET
ijassa-1225	456	38	growth	growth	NOUN
ijassa-1225	456	39	rates	rate	NOUN
ijassa-1225	456	40	of	of	ADP
ijassa-1225	456	41	prices	price	NOUN
ijassa-1225	456	42	result	result	VERB
ijassa-1225	456	43	in	in	ADP
ijassa-1225	456	44	an	an	DET
ijassa-1225	456	45	increase	increase	NOUN
ijassa-1225	456	46	of	of	ADP
ijassa-1225	456	47	the	the	DET
ijassa-1225	456	48	demand	demand	NOUN
ijassa-1225	456	49	and	and	CCONJ
ijassa-1225	456	50	a	a	DET
ijassa-1225	456	51	decrease	decrease	NOUN
ijassa-1225	456	52	of	of	ADP
ijassa-1225	456	53	supply	supply	NOUN
ijassa-1225	456	54	.	.	PUNCT
ijassa-1225	457	1	the	the	DET
ijassa-1225	457	2	main	main	ADJ
ijassa-1225	457	3	distinctions	distinction	NOUN
ijassa-1225	457	4	of	of	ADP
ijassa-1225	457	5	corollary	corollary	ADJ
ijassa-1225	457	6	5.1	5.1	NUM
ijassa-1225	457	7	from	from	ADP
ijassa-1225	457	8	the	the	DET
ijassa-1225	457	9	results	result	NOUN
ijassa-1225	457	10	of	of	ADP
ijassa-1225	457	11	[	[	X
ijassa-1225	457	12	14–17	14–17	NUM
ijassa-1225	457	13	]	]	PUNCT
ijassa-1225	457	14	are	be	AUX
ijassa-1225	457	15	:	:	PUNCT
ijassa-1225	457	16	set	set	NOUN
ijassa-1225	457	17	-	-	PUNCT
ijassa-1225	457	18	valued	value	VERB
ijassa-1225	457	19	mappings	mapping	NOUN
ijassa-1225	457	20	of	of	ADP
ijassa-1225	457	21	supply	supply	NOUN
ijassa-1225	457	22	and	and	CCONJ
ijassa-1225	457	23	demand	demand	NOUN
ijassa-1225	457	24	,	,	PUNCT
ijassa-1225	457	25	omission	omission	NOUN
ijassa-1225	457	26	of	of	ADP
ijassa-1225	457	27	the	the	DET
ijassa-1225	457	28	additional	additional	ADJ
ijassa-1225	457	29	condition	condition	NOUN
ijassa-1225	457	30	of	of	ADP
ijassa-1225	457	31	essentially	essentially	ADV
ijassa-1225	457	32	boundedness	boundedness	NOUN
ijassa-1225	457	33	of	of	ADP
ijassa-1225	457	34	the	the	DET
ijassa-1225	457	35	derivative	derivative	ADJ
ijassa-1225	457	36	ṗ	ṗ	NOUN
ijassa-1225	457	37	of	of	ADP
ijassa-1225	457	38	the	the	DET
ijassa-1225	457	39	prices	price	NOUN
ijassa-1225	457	40	function	function	VERB
ijassa-1225	457	41	,	,	PUNCT
ijassa-1225	457	42	and	and	CCONJ
ijassa-1225	457	43	the	the	DET
ijassa-1225	457	44	estimate	estimate	NOUN
ijassa-1225	457	45	of	of	ADP
ijassa-1225	457	46	the	the	DET
ijassa-1225	457	47	equilibrium	equilibrium	NOUN
ijassa-1225	457	48	price	price	NOUN
ijassa-1225	457	49	derivative	derivative	NOUN
ijassa-1225	457	50	of	of	ADP
ijassa-1225	457	51	the	the	DET
ijassa-1225	457	52	form	form	NOUN
ijassa-1225	457	53	(	(	PUNCT
ijassa-1225	457	54	5.33	5.33	NUM
ijassa-1225	457	55	)	)	PUNCT
ijassa-1225	457	56	.	.	PUNCT
ijassa-1225	458	1	corollary	corollary	ADJ
ijassa-1225	458	2	5.1	5.1	NUM
ijassa-1225	458	3	has	have	VERB
ijassa-1225	458	4	the	the	DET
ijassa-1225	458	5	type	type	NOUN
ijassa-1225	458	6	of	of	ADP
ijassa-1225	458	7	the	the	DET
ijassa-1225	458	8	chaplygin	chaplygin	ADJ
ijassa-1225	458	9	comparison	comparison	NOUN
ijassa-1225	458	10	theorem	theorem	VERB
ijassa-1225	458	11	for	for	ADP
ijassa-1225	458	12	the	the	DET
ijassa-1225	458	13	differential	differential	ADJ
ijassa-1225	458	14	inclusion	inclusion	NOUN
ijassa-1225	458	15	modelling	model	VERB
ijassa-1225	458	16	the	the	DET
ijassa-1225	458	17	economic	economic	ADJ
ijassa-1225	458	18	processes	process	NOUN
ijassa-1225	458	19	under	under	ADP
ijassa-1225	458	20	consideration	consideration	NOUN
ijassa-1225	458	21	.	.	PUNCT
ijassa-1225	459	1	finally	finally	ADV
ijassa-1225	459	2	,	,	PUNCT
ijassa-1225	459	3	let	let	VERB
ijassa-1225	459	4	us	we	PRON
ijassa-1225	459	5	formulate	formulate	VERB
ijassa-1225	459	6	a	a	DET
ijassa-1225	459	7	statement	statement	NOUN
ijassa-1225	459	8	allowing	allow	VERB
ijassa-1225	459	9	to	to	PART
ijassa-1225	459	10	obtain	obtain	VERB
ijassa-1225	459	11	two	two	NUM
ijassa-1225	459	12	-	-	PUNCT
ijassa-1225	459	13	sided	sided	ADJ
ijassa-1225	459	14	estimates	estimate	NOUN
ijassa-1225	459	15	of	of	ADP
ijassa-1225	459	16	the	the	DET
ijassa-1225	459	17	equilibrium	equilibrium	NOUN
ijassa-1225	459	18	prices	price	NOUN
ijassa-1225	459	19	and	and	CCONJ
ijassa-1225	459	20	guarantee	guarantee	VERB
ijassa-1225	459	21	the	the	DET
ijassa-1225	459	22	existence	existence	NOUN
ijassa-1225	459	23	of	of	ADP
ijassa-1225	459	24	the	the	DET
ijassa-1225	459	25	equilibrium	equilibrium	NOUN
ijassa-1225	459	26	price	price	NOUN
ijassa-1225	459	27	having	have	VERB
ijassa-1225	459	28	the	the	DET
ijassa-1225	459	29	least	least	ADJ
ijassa-1225	459	30	rate	rate	NOUN
ijassa-1225	459	31	of	of	ADP
ijassa-1225	459	32	change	change	NOUN
ijassa-1225	459	33	.	.	PUNCT
ijassa-1225	460	1	let	let	VERB
ijassa-1225	460	2	the	the	DET
ijassa-1225	460	3	componentsdi	componentsdi	NOUN
ijassa-1225	460	4	,	,	PUNCT
ijassa-1225	460	5	si	si	PROPN
ijassa-1225	460	6	of	of	ADP
ijassa-1225	460	7	the	the	DET
ijassa-1225	460	8	mappingsd	mappingsd	PROPN
ijassa-1225	460	9	,	,	PUNCT
ijassa-1225	460	10	s	s	PART
ijassa-1225	460	11	be	be	AUX
ijassa-1225	460	12	the	the	DET
ijassa-1225	460	13	functionsdi	functionsdi	NOUN
ijassa-1225	460	14	:	:	PUNCT
ijassa-1225	461	1	[	[	X
ijassa-1225	461	2	a	a	X
ijassa-1225	461	3	,	,	PUNCT
ijassa-1225	461	4	b]×	b]×	NOUN
ijassa-1225	461	5	rn	rn	NOUN
ijassa-1225	461	6	+	+	CCONJ
ijassa-1225	461	7	×	×	PROPN
ijassa-1225	461	8	rn	rn	PROPN
ijassa-1225	461	9	×	×	PROPN
ijassa-1225	461	10	r→	r→	PROPN
ijassa-1225	461	11	kc(r	kc(r	NOUN
ijassa-1225	461	12	)	)	PUNCT
ijassa-1225	461	13	,	,	PUNCT
ijassa-1225	461	14	si	si	X
ijassa-1225	461	15	:	:	PUNCT
ijassa-1225	461	16	[	[	X
ijassa-1225	461	17	a	a	X
ijassa-1225	461	18	,	,	PUNCT
ijassa-1225	461	19	b]×	b]×	NOUN
ijassa-1225	461	20	rn	rn	NOUN
ijassa-1225	462	1	+	+	CCONJ
ijassa-1225	462	2	×	×	PROPN
ijassa-1225	462	3	rn	rn	PROPN
ijassa-1225	462	4	→	→	SYM
ijassa-1225	462	5	kc(r	kc(r	NOUN
ijassa-1225	462	6	)	)	PUNCT
ijassa-1225	462	7	,	,	PUNCT
ijassa-1225	462	8	i	i	PRON
ijassa-1225	462	9	=	=	NOUN
ijassa-1225	462	10	1	1	NUM
ijassa-1225	462	11	,	,	PUNCT
ijassa-1225	462	12	n	n	CCONJ
ijassa-1225	462	13	(	(	PUNCT
ijassa-1225	462	14	having	have	VERB
ijassa-1225	462	15	compact	compact	ADJ
ijassa-1225	462	16	connected	connected	ADJ
ijassa-1225	462	17	values	value	NOUN
ijassa-1225	462	18	)	)	PUNCT
ijassa-1225	462	19	.	.	PUNCT
ijassa-1225	463	1	we	we	PRON
ijassa-1225	463	2	assume	assume	VERB
ijassa-1225	463	3	that	that	SCONJ
ijassa-1225	463	4	for	for	ADP
ijassa-1225	463	5	any	any	DET
ijassa-1225	463	6	x	x	SYM
ijassa-1225	463	7	∈	∈	PROPN
ijassa-1225	463	8	rn	rn	PROPN
ijassa-1225	463	9	+	+	PROPN
ijassa-1225	463	10	,	,	PUNCT
ijassa-1225	463	11	v	v	PROPN
ijassa-1225	463	12	∈	∈	PROPN
ijassa-1225	463	13	rn	rn	PROPN
ijassa-1225	463	14	,	,	PUNCT
ijassa-1225	463	15	z	z	PROPN
ijassa-1225	463	16	∈	∈	PROPN
ijassa-1225	463	17	r	r	NOUN
ijassa-1225	463	18	,	,	PUNCT
ijassa-1225	463	19	the	the	DET
ijassa-1225	463	20	functionsdi	functionsdi	NOUN
ijassa-1225	463	21	(	(	PUNCT
ijassa-1225	463	22	·	·	PUNCT
ijassa-1225	463	23	,	,	PUNCT
ijassa-1225	463	24	x	x	NOUN
ijassa-1225	463	25	,	,	PUNCT
ijassa-1225	463	26	v	v	NOUN
ijassa-1225	463	27	,	,	PUNCT
ijassa-1225	463	28	z	z	NOUN
ijassa-1225	463	29	)	)	PUNCT
ijassa-1225	463	30	:	:	PUNCT
ijassa-1225	464	1	[	[	X
ijassa-1225	464	2	a	a	DET
ijassa-1225	464	3	,	,	PUNCT
ijassa-1225	464	4	b]→	b]→	NOUN
ijassa-1225	464	5	kc(r	kc(r	NOUN
ijassa-1225	464	6	)	)	PUNCT
ijassa-1225	464	7	,	,	PUNCT
ijassa-1225	464	8	si	si	X
ijassa-1225	464	9	(	(	PUNCT
ijassa-1225	464	10	·	·	PUNCT
ijassa-1225	464	11	,	,	PUNCT
ijassa-1225	464	12	x	x	NOUN
ijassa-1225	464	13	,	,	PUNCT
ijassa-1225	464	14	v	v	NOUN
ijassa-1225	464	15	)	)	PUNCT
ijassa-1225	464	16	:	:	PUNCT
ijassa-1225	465	1	[	[	X
ijassa-1225	465	2	a	a	DET
ijassa-1225	465	3	,	,	PUNCT
ijassa-1225	465	4	b]→	b]→	NOUN
ijassa-1225	465	5	kc(r	kc(r	VERB
ijassa-1225	465	6	)	)	PUNCT
ijassa-1225	465	7	are	be	AUX
ijassa-1225	465	8	measurable	measurable	ADJ
ijassa-1225	465	9	;	;	PUNCT
ijassa-1225	465	10	for	for	ADP
ijassa-1225	465	11	almost	almost	ADV
ijassa-1225	465	12	all	all	PRON
ijassa-1225	465	13	t	t	NOUN
ijassa-1225	465	14	∈	∈	PRON
ijassa-1225	466	1	[	[	X
ijassa-1225	466	2	a	a	X
ijassa-1225	466	3	,	,	PUNCT
ijassa-1225	466	4	b	b	NOUN
ijassa-1225	466	5	]	]	X
ijassa-1225	466	6	,	,	PUNCT
ijassa-1225	466	7	any	any	DET
ijassa-1225	466	8	v	v	ADP
ijassa-1225	466	9	∈	∈	PROPN
ijassa-1225	466	10	rn	rn	PROPN
ijassa-1225	466	11	and	and	CCONJ
ijassa-1225	466	12	z	z	NOUN
ijassa-1225	466	13	∈	∈	PROPN
ijassa-1225	466	14	r	r	NOUN
ijassa-1225	466	15	,	,	PUNCT
ijassa-1225	466	16	the	the	DET
ijassa-1225	466	17	functions	function	NOUN
ijassa-1225	466	18	di(t	di(t	ADV
ijassa-1225	466	19	,	,	PUNCT
ijassa-1225	466	20	·	·	PUNCT
ijassa-1225	466	21	,	,	PUNCT
ijassa-1225	466	22	v	v	NOUN
ijassa-1225	466	23	,	,	PUNCT
ijassa-1225	466	24	z	z	NOUN
ijassa-1225	466	25	)	)	PUNCT
ijassa-1225	466	26	:	:	PUNCT
ijassa-1225	467	1	rn	rn	PROPN
ijassa-1225	467	2	+	+	CCONJ
ijassa-1225	467	3	→	→	SYM
ijassa-1225	467	4	kc(r	kc(r	NOUN
ijassa-1225	467	5	)	)	PUNCT
ijassa-1225	467	6	,	,	PUNCT
ijassa-1225	467	7	si(t	si(t	X
ijassa-1225	467	8	,	,	PUNCT
ijassa-1225	467	9	·	·	PUNCT
ijassa-1225	467	10	,	,	PUNCT
ijassa-1225	467	11	v	v	NOUN
ijassa-1225	467	12	)	)	PUNCT
ijassa-1225	467	13	:	:	PUNCT
ijassa-1225	468	1	rn	rn	PROPN
ijassa-1225	468	2	+	+	CCONJ
ijassa-1225	468	3	→	→	NOUN
ijassa-1225	468	4	kc(r	kc(r	PRON
ijassa-1225	468	5	)	)	PUNCT
ijassa-1225	468	6	are	be	AUX
ijassa-1225	468	7	right	right	ADV
ijassa-1225	468	8	continuous	continuous	ADJ
ijassa-1225	468	9	in	in	ADP
ijassa-1225	468	10	each	each	PRON
ijassa-1225	468	11	of	of	ADP
ijassa-1225	468	12	the	the	DET
ijassa-1225	468	13	arguments	argument	NOUN
ijassa-1225	468	14	x1	x1	NUM
ijassa-1225	468	15	,	,	PUNCT
ijassa-1225	468	16	.	.	PUNCT
ijassa-1225	468	17	.	.	PUNCT
ijassa-1225	469	1	.	.	PUNCT
ijassa-1225	470	1	,	,	PUNCT
ijassa-1225	470	2	xn	xn	PROPN
ijassa-1225	470	3	;	;	PUNCT
ijassa-1225	470	4	for	for	ADP
ijassa-1225	470	5	almost	almost	ADV
ijassa-1225	470	6	all	all	PRON
ijassa-1225	470	7	t	t	NOUN
ijassa-1225	470	8	∈	∈	PRON
ijassa-1225	471	1	[	[	X
ijassa-1225	471	2	a	a	X
ijassa-1225	471	3	,	,	PUNCT
ijassa-1225	471	4	b	b	NOUN
ijassa-1225	471	5	]	]	X
ijassa-1225	471	6	,	,	PUNCT
ijassa-1225	471	7	any	any	DET
ijassa-1225	471	8	x	x	PROPN
ijassa-1225	471	9	∈	∈	PROPN
ijassa-1225	471	10	rn	rn	PROPN
ijassa-1225	471	11	+	+	PROPN
ijassa-1225	471	12	and	and	CCONJ
ijassa-1225	471	13	z	z	NOUN
ijassa-1225	471	14	∈	∈	PROPN
ijassa-1225	471	15	r	r	NOUN
ijassa-1225	471	16	,	,	PUNCT
ijassa-1225	471	17	the	the	DET
ijassa-1225	471	18	functions	function	NOUN
ijassa-1225	471	19	di(t	di(t	PART
ijassa-1225	471	20	,	,	PUNCT
ijassa-1225	471	21	x	x	X
ijassa-1225	471	22	,	,	PUNCT
ijassa-1225	471	23	·	·	PUNCT
ijassa-1225	471	24	,	,	PUNCT
ijassa-1225	471	25	z	z	NOUN
ijassa-1225	471	26	)	)	PUNCT
ijassa-1225	471	27	:	:	PUNCT
ijassa-1225	471	28	rn	rn	PROPN
ijassa-1225	471	29	→	→	SYM
ijassa-1225	471	30	kc(r	kc(r	NOUN
ijassa-1225	471	31	)	)	PUNCT
ijassa-1225	471	32	,	,	PUNCT
ijassa-1225	471	33	si(t	si(t	X
ijassa-1225	471	34	,	,	PUNCT
ijassa-1225	471	35	x	x	X
ijassa-1225	471	36	,	,	PUNCT
ijassa-1225	471	37	·	·	PUNCT
ijassa-1225	471	38	)	)	PUNCT
ijassa-1225	471	39	:	:	PUNCT
ijassa-1225	471	40	rn	rn	PROPN
ijassa-1225	471	41	→	→	SYM
ijassa-1225	471	42	kc(r	kc(r	CCONJ
ijassa-1225	471	43	)	)	PUNCT
ijassa-1225	471	44	are	be	AUX
ijassa-1225	471	45	right	right	ADV
ijassa-1225	471	46	continuous	continuous	ADJ
ijassa-1225	471	47	in	in	ADP
ijassa-1225	471	48	each	each	PRON
ijassa-1225	471	49	of	of	ADP
ijassa-1225	471	50	the	the	DET
ijassa-1225	471	51	arguments	argument	NOUN
ijassa-1225	471	52	v1	v1	NOUN
ijassa-1225	471	53	,	,	PUNCT
ijassa-1225	471	54	.	.	PUNCT
ijassa-1225	471	55	.	.	PUNCT
ijassa-1225	472	1	.	.	PUNCT
ijassa-1225	473	1	,	,	PUNCT
ijassa-1225	473	2	vn	vn	X
ijassa-1225	473	3	;	;	PUNCT
ijassa-1225	473	4	for	for	ADP
ijassa-1225	473	5	almost	almost	ADV
ijassa-1225	473	6	all	all	PRON
ijassa-1225	473	7	t	t	NOUN
ijassa-1225	473	8	∈	∈	PRON
ijassa-1225	474	1	[	[	X
ijassa-1225	474	2	a	a	X
ijassa-1225	474	3	,	,	PUNCT
ijassa-1225	474	4	b	b	NOUN
ijassa-1225	474	5	]	]	PUNCT
ijassa-1225	474	6	and	and	CCONJ
ijassa-1225	474	7	any	any	DET
ijassa-1225	474	8	x	x	SYM
ijassa-1225	474	9	∈	∈	PROPN
ijassa-1225	474	10	rn	rn	PROPN
ijassa-1225	475	1	+	+	PROPN
ijassa-1225	475	2	,	,	PUNCT
ijassa-1225	475	3	v	v	PROPN
ijassa-1225	475	4	∈	∈	PROPN
ijassa-1225	475	5	rn	rn	PROPN
ijassa-1225	475	6	,	,	PUNCT
ijassa-1225	475	7	the	the	DET
ijassa-1225	475	8	function	function	NOUN
ijassa-1225	475	9	di(t	di(t	NOUN
ijassa-1225	475	10	,	,	PUNCT
ijassa-1225	475	11	x	x	NOUN
ijassa-1225	475	12	,	,	PUNCT
ijassa-1225	475	13	v	v	NOUN
ijassa-1225	475	14	,	,	PUNCT
ijassa-1225	475	15	·	·	PUNCT
ijassa-1225	475	16	)	)	PUNCT
ijassa-1225	475	17	:	:	PUNCT
ijassa-1225	476	1	r→	r→	PROPN
ijassa-1225	476	2	kc(r	kc(r	VERB
ijassa-1225	476	3	)	)	PUNCT
ijassa-1225	476	4	is	be	AUX
ijassa-1225	476	5	continuous	continuous	ADJ
ijassa-1225	476	6	.	.	PUNCT
ijassa-1225	477	1	consider	consider	VERB
ijassa-1225	477	2	a	a	DET
ijassa-1225	477	3	particular	particular	ADJ
ijassa-1225	477	4	case	case	NOUN
ijassa-1225	477	5	of	of	ADP
ijassa-1225	477	6	the	the	DET
ijassa-1225	477	7	inclusion	inclusion	NOUN
ijassa-1225	477	8	(	(	PUNCT
ijassa-1225	477	9	5.32	5.32	NUM
ijassa-1225	477	10	)	)	PUNCT
ijassa-1225	477	11	—	—	PUNCT
ijassa-1225	477	12	the	the	DET
ijassa-1225	477	13	system	system	NOUN
ijassa-1225	477	14	di(t	di(t	VERB
ijassa-1225	477	15	,	,	PUNCT
ijassa-1225	477	16	x	x	X
ijassa-1225	477	17	,	,	PUNCT
ijassa-1225	477	18	ẋ	ẋ	PROPN
ijassa-1225	477	19	,	,	PUNCT
ijassa-1225	477	20	ẋi)−	ẋi)−	ADP
ijassa-1225	477	21	si(t	si(t	NOUN
ijassa-1225	477	22	,	,	PUNCT
ijassa-1225	477	23	x	x	X
ijassa-1225	477	24	,	,	PUNCT
ijassa-1225	477	25	ẋ	ẋ	PROPN
ijassa-1225	477	26	)	)	PUNCT
ijassa-1225	477	27	3	3	NUM
ijassa-1225	477	28	0	0	NUM
ijassa-1225	477	29	,	,	PUNCT
ijassa-1225	477	30	t	t	PROPN
ijassa-1225	477	31	∈	∈	PROPN
ijassa-1225	478	1	[	[	X
ijassa-1225	478	2	a	a	X
ijassa-1225	478	3	,	,	PUNCT
ijassa-1225	478	4	b	b	NOUN
ijassa-1225	478	5	]	]	X
ijassa-1225	478	6	,	,	PUNCT
ijassa-1225	478	7	i	i	PRON
ijassa-1225	478	8	=	=	NOUN
ijassa-1225	478	9	1	1	NUM
ijassa-1225	478	10	,	,	PUNCT
ijassa-1225	478	11	n.	n.	NOUN
ijassa-1225	478	12	(	(	PUNCT
ijassa-1225	478	13	5.34	5.34	NUM
ijassa-1225	478	14	)	)	PUNCT
ijassa-1225	478	15	theorem	theorem	VERB
ijassa-1225	478	16	4.2	4.2	NUM
ijassa-1225	478	17	implies	imply	VERB
ijassa-1225	478	18	the	the	DET
ijassa-1225	478	19	following	follow	VERB
ijassa-1225	478	20	statement	statement	NOUN
ijassa-1225	478	21	.	.	PUNCT
ijassa-1225	479	1	corollary	corollary	ADJ
ijassa-1225	479	2	5.2	5.2	NUM
ijassa-1225	479	3	:	:	PUNCT
ijassa-1225	479	4	let	let	VERB
ijassa-1225	479	5	functions	function	NOUN
ijassa-1225	479	6	u0	u0	VERB
ijassa-1225	479	7	,	,	PUNCT
ijassa-1225	479	8	v0	v0	PROPN
ijassa-1225	479	9	∈	∈	PROPN
ijassa-1225	479	10	acn	acn	PROPN
ijassa-1225	479	11	such	such	ADJ
ijassa-1225	479	12	that	that	PRON
ijassa-1225	479	13	u0(a	u0(a	PROPN
ijassa-1225	479	14	)	)	PUNCT
ijassa-1225	479	15	≤	≤	NUM
ijassa-1225	479	16	γ	γ	X
ijassa-1225	479	17	≤	≤	NOUN
ijassa-1225	479	18	v0(a	v0(a	NUM
ijassa-1225	479	19	)	)	PUNCT
ijassa-1225	479	20	,	,	PUNCT
ijassa-1225	479	21	(	(	PUNCT
ijassa-1225	479	22	si	si	X
ijassa-1225	479	23	(	(	PUNCT
ijassa-1225	479	24	t	t	PROPN
ijassa-1225	479	25	,	,	PUNCT
ijassa-1225	479	26	u0(t	u0(t	PROPN
ijassa-1225	479	27	)	)	PUNCT
ijassa-1225	479	28	,	,	PUNCT
ijassa-1225	479	29	u̇0(t	u̇0(t	NOUN
ijassa-1225	479	30	)	)	PUNCT
ijassa-1225	479	31	)	)	PUNCT
ijassa-1225	479	32	−di	−di	PROPN
ijassa-1225	479	33	(	(	PUNCT
ijassa-1225	479	34	t	t	PROPN
ijassa-1225	479	35	,	,	PUNCT
ijassa-1225	479	36	u0(t	u0(t	PROPN
ijassa-1225	479	37	)	)	PUNCT
ijassa-1225	479	38	,	,	PUNCT
ijassa-1225	479	39	u̇0(t	u̇0(t	NOUN
ijassa-1225	479	40	)	)	PUNCT
ijassa-1225	479	41	,	,	PUNCT
ijassa-1225	479	42	u̇0i(t	u̇0i(t	NOUN
ijassa-1225	479	43	)	)	PUNCT
ijassa-1225	479	44	)	)	PUNCT
ijassa-1225	479	45	)	)	PUNCT
ijassa-1225	480	1	∩	∩	NOUN
ijassa-1225	480	2	r+	r+	VERB
ijassa-1225	480	3	6=∅	6=∅	NUM
ijassa-1225	480	4	for	for	ADP
ijassa-1225	480	5	almost	almost	ADV
ijassa-1225	480	6	all	all	PRON
ijassa-1225	480	7	t	t	NOUN
ijassa-1225	480	8	∈	∈	PRON
ijassa-1225	481	1	[	[	X
ijassa-1225	481	2	a	a	X
ijassa-1225	481	3	,	,	PUNCT
ijassa-1225	481	4	b	b	NOUN
ijassa-1225	481	5	]	]	X
ijassa-1225	481	6	,	,	PUNCT
ijassa-1225	481	7	i	i	PRON
ijassa-1225	481	8	=	=	NOUN
ijassa-1225	481	9	1	1	NUM
ijassa-1225	481	10	,	,	PUNCT
ijassa-1225	481	11	n	n	CCONJ
ijassa-1225	481	12	,	,	PUNCT
ijassa-1225	481	13	(	(	PUNCT
ijassa-1225	481	14	di	di	X
ijassa-1225	481	15	(	(	PUNCT
ijassa-1225	481	16	t	t	PROPN
ijassa-1225	481	17	,	,	PUNCT
ijassa-1225	481	18	v0(t	v0(t	PROPN
ijassa-1225	481	19	)	)	PUNCT
ijassa-1225	481	20	,	,	PUNCT
ijassa-1225	481	21	v̇0(t	v̇0(t	PROPN
ijassa-1225	481	22	)	)	PUNCT
ijassa-1225	481	23	,	,	PUNCT
ijassa-1225	481	24	v̇0i(t	v̇0i(t	NOUN
ijassa-1225	481	25	)	)	PUNCT
ijassa-1225	481	26	)	)	PUNCT
ijassa-1225	482	1	−	−	PROPN
ijassa-1225	482	2	si	si	INTJ
ijassa-1225	482	3	(	(	PUNCT
ijassa-1225	482	4	t	t	PROPN
ijassa-1225	482	5	,	,	PUNCT
ijassa-1225	482	6	v0(t	v0(t	PROPN
ijassa-1225	482	7	)	)	PUNCT
ijassa-1225	482	8	,	,	PUNCT
ijassa-1225	482	9	v̇0(t	v̇0(t	PROPN
ijassa-1225	482	10	)	)	PUNCT
ijassa-1225	482	11	)	)	PUNCT
ijassa-1225	482	12	)	)	PUNCT
ijassa-1225	483	1	∩	∩	NOUN
ijassa-1225	483	2	r+	r+	VERB
ijassa-1225	483	3	6=	6=	ADP
ijassa-1225	483	4	∅	∅	NOUN
ijassa-1225	483	5	for	for	ADP
ijassa-1225	483	6	almost	almost	ADV
ijassa-1225	483	7	all	all	PRON
ijassa-1225	483	8	t	t	NOUN
ijassa-1225	483	9	∈	∈	PRON
ijassa-1225	484	1	[	[	X
ijassa-1225	484	2	a	a	X
ijassa-1225	484	3	,	,	PUNCT
ijassa-1225	484	4	b	b	NOUN
ijassa-1225	484	5	]	]	X
ijassa-1225	484	6	,	,	PUNCT
ijassa-1225	484	7	i	i	PRON
ijassa-1225	484	8	=	=	NOUN
ijassa-1225	484	9	1	1	NUM
ijassa-1225	484	10	,	,	PUNCT
ijassa-1225	484	11	n	n	CCONJ
ijassa-1225	484	12	,	,	PUNCT
ijassa-1225	484	13	be	be	AUX
ijassa-1225	484	14	given	give	VERB
ijassa-1225	484	15	.	.	PUNCT
ijassa-1225	485	1	define	define	VERB
ijassa-1225	485	2	a	a	DET
ijassa-1225	485	3	set	set	NOUN
ijassa-1225	485	4	-	-	PUNCT
ijassa-1225	485	5	valued	value	VERB
ijassa-1225	485	6	mapping	mapping	NOUN
ijassa-1225	485	7	b	b	NOUN
ijassa-1225	485	8	:	:	PUNCT
ijassa-1225	486	1	[	[	X
ijassa-1225	486	2	a	a	PRON
ijassa-1225	486	3	,	,	PUNCT
ijassa-1225	486	4	b]→	b]→	ADJ
ijassa-1225	486	5	cc(rn	cc(rn	PROPN
ijassa-1225	486	6	)	)	PUNCT
ijassa-1225	486	7	by	by	ADP
ijassa-1225	486	8	the	the	DET
ijassa-1225	486	9	relation	relation	NOUN
ijassa-1225	486	10	(	(	PUNCT
ijassa-1225	486	11	4.26	4.26	NUM
ijassa-1225	486	12	)	)	PUNCT
ijassa-1225	486	13	.	.	PUNCT
ijassa-1225	487	1	assume	assume	VERB
ijassa-1225	487	2	that	that	SCONJ
ijassa-1225	487	3	for	for	ADP
ijassa-1225	487	4	any	any	DET
ijassa-1225	487	5	i	i	NOUN
ijassa-1225	487	6	=	=	NOUN
ijassa-1225	487	7	1	1	NUM
ijassa-1225	487	8	,	,	PUNCT
ijassa-1225	487	9	n	n	CCONJ
ijassa-1225	487	10	,	,	PUNCT
ijassa-1225	487	11	for	for	ADP
ijassa-1225	487	12	almost	almost	ADV
ijassa-1225	487	13	all	all	PRON
ijassa-1225	487	14	t	t	NOUN
ijassa-1225	487	15	∈	∈	PRON
ijassa-1225	488	1	[	[	X
ijassa-1225	488	2	a	a	X
ijassa-1225	488	3	,	,	PUNCT
ijassa-1225	488	4	b	b	NOUN
ijassa-1225	488	5	]	]	X
ijassa-1225	488	6	and	and	CCONJ
ijassa-1225	488	7	all	all	DET
ijassa-1225	488	8	u	u	PROPN
ijassa-1225	488	9	∈	∈	PROPN
ijassa-1225	488	10	b(t	b(t	PROPN
ijassa-1225	488	11	)	)	PUNCT
ijassa-1225	488	12	,	,	PUNCT
ijassa-1225	488	13	the	the	DET
ijassa-1225	488	14	mapping	mapping	NOUN
ijassa-1225	488	15	di(t	di(t	PART
ijassa-1225	488	16	,	,	PUNCT
ijassa-1225	488	17	·	·	PUNCT
ijassa-1225	488	18	,	,	PUNCT
ijassa-1225	488	19	·	·	PUNCT
ijassa-1225	488	20	,	,	PUNCT
ijassa-1225	488	21	u	u	NOUN
ijassa-1225	488	22	)	)	PUNCT
ijassa-1225	488	23	:	:	PUNCT
ijassa-1225	489	1	rn	rn	PROPN
ijassa-1225	489	2	+	+	CCONJ
ijassa-1225	489	3	×	×	PROPN
ijassa-1225	489	4	rn	rn	PROPN
ijassa-1225	489	5	→	→	SYM
ijassa-1225	489	6	kc(r	kc(r	PRON
ijassa-1225	489	7	)	)	PUNCT
ijassa-1225	489	8	is	be	AUX
ijassa-1225	489	9	antitone	antitone	ADJ
ijassa-1225	489	10	on	on	ADP
ijassa-1225	489	11	the	the	DET
ijassa-1225	489	12	set	set	PROPN
ijassa-1225	489	13	rn	rn	PROPN
ijassa-1225	489	14	×b(t	×b(t	PROPN
ijassa-1225	489	15	)	)	PUNCT
ijassa-1225	489	16	and	and	CCONJ
ijassa-1225	489	17	the	the	DET
ijassa-1225	489	18	mapping	mapping	NOUN
ijassa-1225	489	19	si(t	si(t	NOUN
ijassa-1225	489	20	,	,	PUNCT
ijassa-1225	489	21	·	·	PUNCT
ijassa-1225	489	22	,	,	PUNCT
ijassa-1225	489	23	·	·	PUNCT
ijassa-1225	489	24	)	)	PUNCT
ijassa-1225	489	25	:	:	PUNCT
ijassa-1225	490	1	rn	rn	PROPN
ijassa-1225	490	2	+	+	CCONJ
ijassa-1225	490	3	×	×	PROPN
ijassa-1225	490	4	rn	rn	PROPN
ijassa-1225	490	5	→	→	SYM
ijassa-1225	490	6	kc(r	kc(r	CCONJ
ijassa-1225	490	7	)	)	PUNCT
ijassa-1225	490	8	is	be	AUX
ijassa-1225	490	9	isotone	isotone	VERB
ijassa-1225	490	10	on	on	ADP
ijassa-1225	490	11	the	the	DET
ijassa-1225	490	12	set	set	PROPN
ijassa-1225	490	13	rn	rn	PROPN
ijassa-1225	490	14	×b(t	×b(t	PROPN
ijassa-1225	490	15	)	)	PUNCT
ijassa-1225	490	16	.	.	PUNCT
ijassa-1225	491	1	then	then	ADV
ijassa-1225	491	2	there	there	PRON
ijassa-1225	491	3	exists	exist	VERB
ijassa-1225	491	4	a	a	DET
ijassa-1225	491	5	solution	solution	NOUN
ijassa-1225	491	6	p	p	X
ijassa-1225	491	7	∈	∈	PROPN
ijassa-1225	491	8	ac(b	ac(b	NOUN
ijassa-1225	491	9	)	)	PUNCT
ijassa-1225	491	10	of	of	ADP
ijassa-1225	491	11	the	the	DET
ijassa-1225	491	12	problem	problem	NOUN
ijassa-1225	491	13	(	(	PUNCT
ijassa-1225	491	14	5.34	5.34	NUM
ijassa-1225	491	15	)	)	PUNCT
ijassa-1225	491	16	,	,	PUNCT
ijassa-1225	491	17	(	(	PUNCT
ijassa-1225	491	18	5.31	5.31	NUM
ijassa-1225	491	19	)	)	PUNCT
ijassa-1225	491	20	,	,	PUNCT
ijassa-1225	491	21	(	(	PUNCT
ijassa-1225	491	22	5.30	5.30	NUM
ijassa-1225	491	23	)	)	PUNCT
ijassa-1225	491	24	.	.	PUNCT
ijassa-1225	492	1	moreover	moreover	ADV
ijassa-1225	492	2	,	,	PUNCT
ijassa-1225	492	3	the	the	DET
ijassa-1225	492	4	set	set	NOUN
ijassa-1225	492	5	of	of	ADP
ijassa-1225	492	6	solutions	solution	NOUN
ijassa-1225	492	7	of	of	ADP
ijassa-1225	492	8	the	the	DET
ijassa-1225	492	9	problem	problem	NOUN
ijassa-1225	492	10	(	(	PUNCT
ijassa-1225	492	11	5.34	5.34	NUM
ijassa-1225	492	12	)	)	PUNCT
ijassa-1225	492	13	,	,	PUNCT
ijassa-1225	492	14	(	(	PUNCT
ijassa-1225	492	15	5.31	5.31	NUM
ijassa-1225	492	16	)	)	PUNCT
ijassa-1225	492	17	,	,	PUNCT
ijassa-1225	492	18	(	(	PUNCT
ijassa-1225	492	19	5.30	5.30	NUM
ijassa-1225	492	20	)	)	PUNCT
ijassa-1225	492	21	contains	contain	VERB
ijassa-1225	492	22	a	a	DET
ijassa-1225	492	23	solution	solution	NOUN
ijassa-1225	492	24	with	with	ADP
ijassa-1225	492	25	the	the	DET
ijassa-1225	492	26	least	least	ADJ
ijassa-1225	492	27	derivative	derivative	ADJ
ijassa-1225	492	28	.	.	PUNCT
ijassa-1225	493	1	acknowledgements	acknowledgement	NOUN
ijassa-1225	493	2	the	the	DET
ijassa-1225	493	3	reported	report	VERB
ijassa-1225	493	4	study	study	NOUN
ijassa-1225	493	5	was	be	AUX
ijassa-1225	493	6	funded	fund	VERB
ijassa-1225	493	7	by	by	ADP
ijassa-1225	493	8	rfbr	rfbr	NOUN
ijassa-1225	493	9	,	,	PUNCT
ijassa-1225	493	10	project	project	NOUN
ijassa-1225	493	11	number	number	NOUN
ijassa-1225	493	12	20	20	NUM
ijassa-1225	493	13	-	-	PUNCT
ijassa-1225	493	14	04	04	NUM
ijassa-1225	493	15	-	-	PUNCT
ijassa-1225	493	16	60524	60524	NUM
ijassa-1225	493	17	.	.	PUNCT
ijassa-1225	494	1	the	the	DET
ijassa-1225	494	2	results	result	NOUN
ijassa-1225	494	3	in	in	ADP
ijassa-1225	494	4	section	section	NOUN
ijassa-1225	494	5	4	4	NUM
ijassa-1225	494	6	were	be	AUX
ijassa-1225	494	7	obtained	obtain	VERB
ijassa-1225	494	8	with	with	ADP
ijassa-1225	494	9	the	the	DET
ijassa-1225	494	10	support	support	NOUN
ijassa-1225	494	11	of	of	ADP
ijassa-1225	494	12	ministry	ministry	PROPN
ijassa-1225	494	13	of	of	ADP
ijassa-1225	494	14	science	science	PROPN
ijassa-1225	494	15	and	and	CCONJ
ijassa-1225	494	16	higher	high	ADJ
ijassa-1225	494	17	education	education	NOUN
ijassa-1225	494	18	of	of	ADP
ijassa-1225	494	19	the	the	DET
ijassa-1225	494	20	russian	russian	PROPN
ijassa-1225	494	21	federation	federation	PROPN
ijassa-1225	494	22	(	(	PUNCT
ijassa-1225	494	23	agreement	agreement	NOUN
ijassa-1225	494	24	no	no	INTJ
ijassa-1225	494	25	.	.	PUNCT
ijassa-1225	494	26	075	075	NUM
ijassa-1225	495	1	-	-	PUNCT
ijassa-1225	495	2	15	15	NUM
ijassa-1225	495	3	-	-	PUNCT
ijassa-1225	495	4	2019	2019	NUM
ijassa-1225	495	5	-	-	PUNCT
ijassa-1225	495	6	1619	1619	NUM
ijassa-1225	495	7	)	)	PUNCT
ijassa-1225	496	1	.	.	PUNCT
ijassa-1225	497	1	the	the	DET
ijassa-1225	497	2	results	result	NOUN
ijassa-1225	497	3	in	in	ADP
ijassa-1225	497	4	sections	section	NOUN
ijassa-1225	497	5	2	2	NUM
ijassa-1225	497	6	and	and	CCONJ
ijassa-1225	497	7	3	3	NUM
ijassa-1225	497	8	were	be	AUX
ijassa-1225	497	9	obtained	obtain	VERB
ijassa-1225	497	10	with	with	ADP
ijassa-1225	497	11	the	the	DET
ijassa-1225	497	12	support	support	NOUN
ijassa-1225	497	13	of	of	ADP
ijassa-1225	497	14	the	the	DET
ijassa-1225	497	15	russian	russian	PROPN
ijassa-1225	497	16	science	science	PROPN
ijassa-1225	497	17	foundation	foundation	PROPN
ijassa-1225	497	18	(	(	PUNCT
ijassa-1225	497	19	grant	grant	VERB
ijassa-1225	497	20	no	no	INTJ
ijassa-1225	497	21	.	.	NOUN
ijassa-1225	497	22	20	20	NUM
ijassa-1225	497	23	-	-	SYM
ijassa-1225	497	24	11	11	NUM
ijassa-1225	497	25	-	-	SYM
ijassa-1225	497	26	20131	20131	NUM
ijassa-1225	497	27	)	)	PUNCT
ijassa-1225	497	28	in	in	ADP
ijassa-1225	497	29	v.a	v.a	PROPN
ijassa-1225	497	30	.	.	PROPN
ijassa-1225	497	31	trapeznikov	trapeznikov	PROPN
ijassa-1225	497	32	institute	institute	PROPN
ijassa-1225	497	33	of	of	ADP
ijassa-1225	497	34	control	control	PROPN
ijassa-1225	497	35	sciences	sciences	PROPN
ijassa-1225	497	36	of	of	ADP
ijassa-1225	497	37	ras	ras	PROPN
ijassa-1225	497	38	.	.	PROPN
ijassa-1225	497	39	references	reference	NOUN
ijassa-1225	497	40	1	1	NUM
ijassa-1225	498	1	.	.	PUNCT
ijassa-1225	498	2	arutyunov	arutyunov	PROPN
ijassa-1225	498	3	,	,	PUNCT
ijassa-1225	498	4	a.v	a.v	PROPN
ijassa-1225	498	5	.	.	PROPN
ijassa-1225	498	6	,	,	PUNCT
ijassa-1225	498	7	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	498	8	,	,	PUNCT
ijassa-1225	498	9	e.s	e.s	PROPN
ijassa-1225	498	10	.	.	PROPN
ijassa-1225	498	11	&	&	CCONJ
ijassa-1225	498	12	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	498	13	,	,	PUNCT
ijassa-1225	498	14	s.e	s.e	PROPN
ijassa-1225	498	15	.	.	PROPN
ijassa-1225	498	16	(	(	PUNCT
ijassa-1225	498	17	2013	2013	NUM
ijassa-1225	498	18	)	)	PUNCT
ijassa-1225	498	19	on	on	ADP
ijassa-1225	498	20	coincidence	coincidence	NOUN
ijassa-1225	498	21	points	point	NOUN
ijassa-1225	498	22	of	of	ADP
ijassa-1225	498	23	mappings	mapping	NOUN
ijassa-1225	498	24	in	in	ADP
ijassa-1225	498	25	partially	partially	ADV
ijassa-1225	498	26	ordered	order	VERB
ijassa-1225	498	27	spaces	space	NOUN
ijassa-1225	498	28	,	,	PUNCT
ijassa-1225	498	29	dokl	dokl	NOUN
ijassa-1225	498	30	.	.	PUNCT
ijassa-1225	499	1	math	math	PROPN
ijassa-1225	499	2	.	.	PUNCT
ijassa-1225	499	3	,	,	PUNCT
ijassa-1225	499	4	88(3	88(3	NUM
ijassa-1225	499	5	)	)	PUNCT
ijassa-1225	499	6	,	,	PUNCT
ijassa-1225	499	7	710–713	710–713	NUM
ijassa-1225	499	8	.	.	PUNCT
ijassa-1225	500	1	copyright	copyright	NOUN
ijassa-1225	500	2	©	©	PROPN
ijassa-1225	500	3	2022	2022	NUM
ijassa-1225	500	4	assa	assa	NOUN
ijassa-1225	500	5	.	.	PUNCT
ijassa-1225	501	1	adv	adv	PROPN
ijassa-1225	501	2	syst	syst	PROPN
ijassa-1225	501	3	sci	sci	PROPN
ijassa-1225	501	4	appl	appl	PROPN
ijassa-1225	501	5	(	(	PUNCT
ijassa-1225	501	6	2022	2022	NUM
ijassa-1225	501	7	)	)	PUNCT
ijassa-1225	501	8	190	190	NUM
ijassa-1225	501	9	e.s	e.s	PROPN
ijassa-1225	501	10	.	.	PROPN
ijassa-1225	501	11	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	501	12	,	,	PUNCT
ijassa-1225	501	13	i.d	i.d	PROPN
ijassa-1225	501	14	.	.	PROPN
ijassa-1225	501	15	serova	serova	PROPN
ijassa-1225	501	16	,	,	PUNCT
ijassa-1225	501	17	e.a	e.a	PROPN
ijassa-1225	501	18	.	.	PROPN
ijassa-1225	501	19	panasenko	panasenko	PROPN
ijassa-1225	501	20	,	,	PUNCT
ijassa-1225	501	21	e.o	e.o	PROPN
ijassa-1225	501	22	.	.	PROPN
ijassa-1225	501	23	burlakov	burlakov	PROPN
ijassa-1225	501	24	2	2	X
ijassa-1225	501	25	.	.	X
ijassa-1225	501	26	arutyunov	arutyunov	PROPN
ijassa-1225	501	27	,	,	PUNCT
ijassa-1225	501	28	a.v	a.v	PROPN
ijassa-1225	501	29	.	.	PROPN
ijassa-1225	501	30	,	,	PUNCT
ijassa-1225	501	31	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	501	32	,	,	PUNCT
ijassa-1225	501	33	e.s	e.s	PROPN
ijassa-1225	501	34	.	.	PROPN
ijassa-1225	501	35	&	&	CCONJ
ijassa-1225	501	36	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	501	37	,	,	PUNCT
ijassa-1225	501	38	s.e	s.e	PROPN
ijassa-1225	501	39	.	.	PROPN
ijassa-1225	501	40	(	(	PUNCT
ijassa-1225	501	41	2015	2015	NUM
ijassa-1225	501	42	)	)	PUNCT
ijassa-1225	501	43	coincidence	coincidence	NOUN
ijassa-1225	501	44	points	point	VERB
ijassa-1225	501	45	principle	principle	NOUN
ijassa-1225	501	46	for	for	ADP
ijassa-1225	501	47	mappings	mapping	NOUN
ijassa-1225	501	48	in	in	ADP
ijassa-1225	501	49	partially	partially	ADV
ijassa-1225	501	50	ordered	order	VERB
ijassa-1225	501	51	spaces	space	NOUN
ijassa-1225	501	52	,	,	PUNCT
ijassa-1225	501	53	topol	topol	PROPN
ijassa-1225	501	54	.	.	PUNCT
ijassa-1225	502	1	appl	appl	PROPN
ijassa-1225	502	2	.	.	PROPN
ijassa-1225	502	3	,	,	PUNCT
ijassa-1225	502	4	179(1	179(1	NUM
ijassa-1225	502	5	)	)	PUNCT
ijassa-1225	502	6	,	,	PUNCT
ijassa-1225	502	7	13–33	13–33	NUM
ijassa-1225	502	8	.	.	PUNCT
ijassa-1225	503	1	3	3	X
ijassa-1225	503	2	.	.	X
ijassa-1225	503	3	arutyunov	arutyunov	PROPN
ijassa-1225	503	4	,	,	PUNCT
ijassa-1225	503	5	a.v	a.v	PROPN
ijassa-1225	503	6	.	.	PROPN
ijassa-1225	503	7	,	,	PUNCT
ijassa-1225	503	8	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	503	9	,	,	PUNCT
ijassa-1225	503	10	e.s	e.s	PROPN
ijassa-1225	503	11	.	.	PROPN
ijassa-1225	503	12	&	&	CCONJ
ijassa-1225	503	13	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	503	14	,	,	PUNCT
ijassa-1225	503	15	s.e	s.e	PROPN
ijassa-1225	503	16	.	.	PROPN
ijassa-1225	503	17	(	(	PUNCT
ijassa-1225	503	18	2013	2013	NUM
ijassa-1225	503	19	)	)	PUNCT
ijassa-1225	503	20	on	on	ADP
ijassa-1225	503	21	coincidence	coincidence	NOUN
ijassa-1225	503	22	points	point	NOUN
ijassa-1225	503	23	of	of	ADP
ijassa-1225	503	24	mappings	mapping	NOUN
ijassa-1225	503	25	in	in	ADP
ijassa-1225	503	26	partially	partially	ADV
ijassa-1225	503	27	ordered	order	VERB
ijassa-1225	503	28	spaces	space	NOUN
ijassa-1225	503	29	,	,	PUNCT
ijassa-1225	503	30	dokl	dokl	NOUN
ijassa-1225	503	31	.	.	PUNCT
ijassa-1225	504	1	math	math	PROPN
ijassa-1225	504	2	.	.	PUNCT
ijassa-1225	504	3	,	,	PUNCT
ijassa-1225	504	4	88(3	88(3	NUM
ijassa-1225	504	5	)	)	PUNCT
ijassa-1225	504	6	,	,	PUNCT
ijassa-1225	504	7	727–729	727–729	NUM
ijassa-1225	504	8	.	.	PUNCT
ijassa-1225	505	1	4	4	X
ijassa-1225	505	2	.	.	X
ijassa-1225	505	3	arutyunov	arutyunov	PROPN
ijassa-1225	505	4	,	,	PUNCT
ijassa-1225	505	5	a.v	a.v	PROPN
ijassa-1225	505	6	.	.	PROPN
ijassa-1225	505	7	,	,	PUNCT
ijassa-1225	505	8	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	505	9	,	,	PUNCT
ijassa-1225	505	10	e.s	e.s	PROPN
ijassa-1225	505	11	.	.	PROPN
ijassa-1225	505	12	&	&	CCONJ
ijassa-1225	505	13	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	505	14	,	,	PUNCT
ijassa-1225	505	15	s.e	s.e	PROPN
ijassa-1225	505	16	.	.	PROPN
ijassa-1225	505	17	(	(	PUNCT
ijassa-1225	505	18	2016	2016	NUM
ijassa-1225	505	19	)	)	PUNCT
ijassa-1225	505	20	coincidence	coincidence	NOUN
ijassa-1225	505	21	points	point	VERB
ijassa-1225	505	22	principle	principle	NOUN
ijassa-1225	505	23	for	for	ADP
ijassa-1225	505	24	set	set	NOUN
ijassa-1225	505	25	-	-	PUNCT
ijassa-1225	505	26	valued	value	VERB
ijassa-1225	505	27	mappings	mapping	NOUN
ijassa-1225	505	28	in	in	ADP
ijassa-1225	505	29	partially	partially	ADV
ijassa-1225	505	30	ordered	order	VERB
ijassa-1225	505	31	spaces	space	NOUN
ijassa-1225	505	32	,	,	PUNCT
ijassa-1225	505	33	topol	topol	PROPN
ijassa-1225	505	34	.	.	PUNCT
ijassa-1225	506	1	appl	appl	PROPN
ijassa-1225	506	2	.	.	PROPN
ijassa-1225	506	3	,	,	PUNCT
ijassa-1225	506	4	201	201	NUM
ijassa-1225	506	5	,	,	PUNCT
ijassa-1225	506	6	330	330	NUM
ijassa-1225	506	7	–	–	PUNCT
ijassa-1225	506	8	343	343	NUM
ijassa-1225	506	9	.	.	NOUN
ijassa-1225	507	1	5	5	NUM
ijassa-1225	507	2	.	.	X
ijassa-1225	507	3	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	507	4	,	,	PUNCT
ijassa-1225	507	5	e.s	e.s	PROPN
ijassa-1225	507	6	.	.	PROPN
ijassa-1225	507	7	(	(	PUNCT
ijassa-1225	507	8	2016	2016	NUM
ijassa-1225	507	9	)	)	PUNCT
ijassa-1225	507	10	on	on	ADP
ijassa-1225	507	11	ordered	order	VERB
ijassa-1225	507	12	-	-	PUNCT
ijassa-1225	507	13	covering	cover	VERB
ijassa-1225	507	14	mappings	mapping	NOUN
ijassa-1225	507	15	and	and	CCONJ
ijassa-1225	507	16	implicit	implicit	ADJ
ijassa-1225	507	17	differential	differential	ADJ
ijassa-1225	507	18	inequalities	inequality	NOUN
ijassa-1225	507	19	,	,	PUNCT
ijassa-1225	507	20	differ	differ	VERB
ijassa-1225	507	21	.	.	PUNCT
ijassa-1225	508	1	equ	equ	PROPN
ijassa-1225	508	2	.	.	PROPN
ijassa-1225	508	3	,	,	PUNCT
ijassa-1225	508	4	52(12	52(12	NUM
ijassa-1225	508	5	)	)	PUNCT
ijassa-1225	508	6	,	,	PUNCT
ijassa-1225	508	7	1539–1556	1539–1556	NUM
ijassa-1225	508	8	.	.	PUNCT
ijassa-1225	509	1	6	6	NUM
ijassa-1225	509	2	.	.	X
ijassa-1225	509	3	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	509	4	,	,	PUNCT
ijassa-1225	509	5	e.s	e.s	PROPN
ijassa-1225	509	6	.	.	PROPN
ijassa-1225	509	7	(	(	PUNCT
ijassa-1225	509	8	2019	2019	NUM
ijassa-1225	509	9	)	)	PUNCT
ijassa-1225	509	10	on	on	ADP
ijassa-1225	509	11	order	order	NOUN
ijassa-1225	509	12	covering	cover	VERB
ijassa-1225	509	13	maps	map	NOUN
ijassa-1225	509	14	in	in	ADP
ijassa-1225	509	15	ordered	order	VERB
ijassa-1225	509	16	spaces	space	NOUN
ijassa-1225	509	17	and	and	CCONJ
ijassa-1225	509	18	chaplygin	chaplygin	ADJ
ijassa-1225	509	19	-	-	PUNCT
ijassa-1225	509	20	type	type	NOUN
ijassa-1225	509	21	inequalities	inequality	NOUN
ijassa-1225	509	22	,	,	PUNCT
ijassa-1225	509	23	st	st	PROPN
ijassa-1225	509	24	.	.	PROPN
ijassa-1225	509	25	petersburg	petersburg	PROPN
ijassa-1225	509	26	math	math	PROPN
ijassa-1225	509	27	.	.	PUNCT
ijassa-1225	510	1	j.	j.	PROPN
ijassa-1225	510	2	,	,	PUNCT
ijassa-1225	510	3	30(1	30(1	NUM
ijassa-1225	510	4	)	)	PUNCT
ijassa-1225	510	5	,	,	PUNCT
ijassa-1225	510	6	73–94	73–94	NUM
ijassa-1225	510	7	.	.	PUNCT
ijassa-1225	510	8	7	7	NUM
ijassa-1225	510	9	.	.	X
ijassa-1225	510	10	benarab	benarab	NOUN
ijassa-1225	510	11	,	,	PUNCT
ijassa-1225	510	12	s.	s.	PROPN
ijassa-1225	510	13	&	&	CCONJ
ijassa-1225	510	14	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	510	15	,	,	PUNCT
ijassa-1225	510	16	e.s	e.s	PROPN
ijassa-1225	510	17	.	.	PROPN
ijassa-1225	510	18	(	(	PUNCT
ijassa-1225	510	19	2020	2020	NUM
ijassa-1225	510	20	)	)	PUNCT
ijassa-1225	510	21	coincidence	coincidence	NOUN
ijassa-1225	510	22	points	point	NOUN
ijassa-1225	510	23	of	of	ADP
ijassa-1225	510	24	two	two	NUM
ijassa-1225	510	25	mappings	mapping	NOUN
ijassa-1225	510	26	acting	act	VERB
ijassa-1225	510	27	from	from	ADP
ijassa-1225	510	28	a	a	DET
ijassa-1225	510	29	partially	partially	ADV
ijassa-1225	510	30	ordered	order	VERB
ijassa-1225	510	31	space	space	NOUN
ijassa-1225	510	32	to	to	ADP
ijassa-1225	510	33	an	an	DET
ijassa-1225	510	34	arbitrary	arbitrary	ADJ
ijassa-1225	510	35	set	set	NOUN
ijassa-1225	510	36	,	,	PUNCT
ijassa-1225	510	37	russ	russ	PROPN
ijassa-1225	510	38	.	.	PROPN
ijassa-1225	510	39	math	math	PROPN
ijassa-1225	510	40	.	.	PUNCT
ijassa-1225	511	1	,	,	PUNCT
ijassa-1225	511	2	64(5	64(5	PROPN
ijassa-1225	511	3	)	)	PUNCT
ijassa-1225	511	4	,	,	PUNCT
ijassa-1225	511	5	8–16	8–16	PROPN
ijassa-1225	511	6	.	.	PROPN
ijassa-1225	512	1	8	8	NUM
ijassa-1225	512	2	.	.	X
ijassa-1225	513	1	zhukovskaya	zhukovskaya	PROPN
ijassa-1225	513	2	,	,	PUNCT
ijassa-1225	513	3	t.v	t.v	PROPN
ijassa-1225	513	4	.	.	PROPN
ijassa-1225	513	5	,	,	PUNCT
ijassa-1225	513	6	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	513	7	,	,	PUNCT
ijassa-1225	513	8	e.s	e.s	PROPN
ijassa-1225	513	9	.	.	PROPN
ijassa-1225	513	10	&	&	CCONJ
ijassa-1225	513	11	serova	serova	PROPN
ijassa-1225	513	12	,	,	PUNCT
ijassa-1225	513	13	i.d	i.d	PROPN
ijassa-1225	513	14	.	.	PROPN
ijassa-1225	513	15	(	(	PUNCT
ijassa-1225	513	16	2020	2020	NUM
ijassa-1225	513	17	)	)	PUNCT
ijassa-1225	513	18	some	some	DET
ijassa-1225	513	19	questions	question	NOUN
ijassa-1225	513	20	of	of	ADP
ijassa-1225	513	21	the	the	DET
ijassa-1225	513	22	analysis	analysis	NOUN
ijassa-1225	513	23	of	of	ADP
ijassa-1225	513	24	mappings	mapping	NOUN
ijassa-1225	513	25	of	of	ADP
ijassa-1225	513	26	metric	metric	ADJ
ijassa-1225	513	27	and	and	CCONJ
ijassa-1225	513	28	partially	partially	ADV
ijassa-1225	513	29	ordered	order	VERB
ijassa-1225	513	30	spaces	space	NOUN
ijassa-1225	513	31	,	,	PUNCT
ijassa-1225	513	32	russian	russian	ADJ
ijassa-1225	513	33	universities	university	NOUN
ijassa-1225	513	34	reports	report	VERB
ijassa-1225	513	35	.	.	PUNCT
ijassa-1225	514	1	mathematics	mathematic	NOUN
ijassa-1225	514	2	,	,	PUNCT
ijassa-1225	514	3	25(132	25(132	NOUN
ijassa-1225	514	4	)	)	PUNCT
ijassa-1225	514	5	,	,	PUNCT
ijassa-1225	514	6	345–358	345–358	NUM
ijassa-1225	514	7	.	.	PUNCT
ijassa-1225	514	8	9	9	NUM
ijassa-1225	514	9	.	.	X
ijassa-1225	514	10	chaplygin	chaplygin	PROPN
ijassa-1225	514	11	,	,	PUNCT
ijassa-1225	514	12	s.a	s.a	PROPN
ijassa-1225	514	13	.	.	PROPN
ijassa-1225	514	14	(	(	PUNCT
ijassa-1225	514	15	1948	1948	NUM
ijassa-1225	514	16	)	)	PUNCT
ijassa-1225	514	17	osnovaniya	osnovaniya	PROPN
ijassa-1225	514	18	novogo	novogo	NOUN
ijassa-1225	514	19	spospba	spospba	VERB
ijassa-1225	514	20	priblizhennogo	priblizhennogo	PROPN
ijassa-1225	514	21	integrirovaniya	integrirovaniya	PROPN
ijassa-1225	514	22	differentsialnykh	differentsialnykh	VERB
ijassa-1225	514	23	uravneniy	uravneniy	ADJ
ijassa-1225	514	24	.	.	PUNCT
ijassa-1225	515	1	in	in	ADP
ijassa-1225	515	2	sobranie	sobranie	PROPN
ijassa-1225	515	3	sochineniy	sochineniy	PROPN
ijassa-1225	516	1	[	[	X
ijassa-1225	516	2	the	the	DET
ijassa-1225	516	3	foundations	foundation	NOUN
ijassa-1225	516	4	of	of	ADP
ijassa-1225	516	5	a	a	DET
ijassa-1225	516	6	novel	novel	ADJ
ijassa-1225	516	7	approach	approach	NOUN
ijassa-1225	516	8	to	to	ADP
ijassa-1225	516	9	approximate	approximate	ADJ
ijassa-1225	516	10	integration	integration	NOUN
ijassa-1225	516	11	of	of	ADP
ijassa-1225	516	12	differential	differential	ADJ
ijassa-1225	516	13	equations	equation	NOUN
ijassa-1225	516	14	.	.	PUNCT
ijassa-1225	517	1	in	in	ADP
ijassa-1225	517	2	collection	collection	NOUN
ijassa-1225	517	3	of	of	ADP
ijassa-1225	517	4	works	work	NOUN
ijassa-1225	517	5	]	]	PUNCT
ijassa-1225	517	6	(	(	PUNCT
ijassa-1225	517	7	pp	pp	ADP
ijassa-1225	517	8	.	.	PUNCT
ijassa-1225	518	1	348–368	348–368	NUM
ijassa-1225	518	2	)	)	PUNCT
ijassa-1225	518	3	moscow	moscow	PROPN
ijassa-1225	518	4	,	,	PUNCT
ijassa-1225	518	5	russia	russia	PROPN
ijassa-1225	518	6	:	:	PUNCT
ijassa-1225	518	7	gostekhizdat	gostekhizdat	NOUN
ijassa-1225	518	8	,	,	PUNCT
ijassa-1225	518	9	[	[	X
ijassa-1225	518	10	in	in	ADP
ijassa-1225	518	11	russian	russian	PROPN
ijassa-1225	518	12	]	]	PUNCT
ijassa-1225	518	13	.	.	PUNCT
ijassa-1225	519	1	10	10	NUM
ijassa-1225	519	2	.	.	X
ijassa-1225	519	3	benarab	benarab	NOUN
ijassa-1225	519	4	,	,	PUNCT
ijassa-1225	519	5	s.	s.	PROPN
ijassa-1225	519	6	,	,	PUNCT
ijassa-1225	519	7	zhukovskaya	zhukovskaya	PROPN
ijassa-1225	519	8	,	,	PUNCT
ijassa-1225	519	9	z.t	z.t	PROPN
ijassa-1225	519	10	.	.	PROPN
ijassa-1225	519	11	,	,	PUNCT
ijassa-1225	519	12	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	519	13	,	,	PUNCT
ijassa-1225	519	14	e.s	e.s	PROPN
ijassa-1225	519	15	.	.	PROPN
ijassa-1225	519	16	&	&	CCONJ
ijassa-1225	519	17	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	519	18	,	,	PUNCT
ijassa-1225	519	19	s.e	s.e	PROPN
ijassa-1225	519	20	.	.	PROPN
ijassa-1225	519	21	(	(	PUNCT
ijassa-1225	519	22	2020	2020	NUM
ijassa-1225	519	23	)	)	PUNCT
ijassa-1225	519	24	functional	functional	ADJ
ijassa-1225	519	25	and	and	CCONJ
ijassa-1225	519	26	differential	differential	ADJ
ijassa-1225	519	27	inequalities	inequality	NOUN
ijassa-1225	519	28	and	and	CCONJ
ijassa-1225	519	29	their	their	PRON
ijassa-1225	519	30	applications	application	NOUN
ijassa-1225	519	31	to	to	PART
ijassa-1225	519	32	control	control	VERB
ijassa-1225	519	33	problems	problem	NOUN
ijassa-1225	519	34	,	,	PUNCT
ijassa-1225	519	35	differ	differ	VERB
ijassa-1225	519	36	.	.	PUNCT
ijassa-1225	520	1	equ	equ	PROPN
ijassa-1225	520	2	.	.	PROPN
ijassa-1225	520	3	,	,	PUNCT
ijassa-1225	520	4	56(11	56(11	NUM
ijassa-1225	520	5	)	)	PUNCT
ijassa-1225	520	6	,	,	PUNCT
ijassa-1225	520	7	1440–1451	1440–1451	NUM
ijassa-1225	520	8	.	.	PUNCT
ijassa-1225	521	1	11	11	NUM
ijassa-1225	521	2	.	.	PUNCT
ijassa-1225	522	1	evans	evans	PROPN
ijassa-1225	522	2	,	,	PUNCT
ijassa-1225	522	3	g.c	g.c	PROPN
ijassa-1225	522	4	.	.	PROPN
ijassa-1225	522	5	(	(	PUNCT
ijassa-1225	522	6	1930	1930	NUM
ijassa-1225	522	7	)	)	PUNCT
ijassa-1225	522	8	mathematical	mathematical	ADJ
ijassa-1225	522	9	introduction	introduction	NOUN
ijassa-1225	522	10	to	to	ADP
ijassa-1225	522	11	economics	economic	NOUN
ijassa-1225	522	12	.	.	PUNCT
ijassa-1225	523	1	new	new	PROPN
ijassa-1225	523	2	york	york	PROPN
ijassa-1225	523	3	,	,	PUNCT
ijassa-1225	523	4	ny	ny	PROPN
ijassa-1225	523	5	:	:	PUNCT
ijassa-1225	523	6	mcgrawhill	mcgrawhill	ADJ
ijassa-1225	523	7	education	education	NOUN
ijassa-1225	523	8	.	.	PUNCT
ijassa-1225	524	1	12	12	NUM
ijassa-1225	524	2	.	.	PUNCT
ijassa-1225	525	1	samuelson	samuelson	PROPN
ijassa-1225	525	2	,	,	PUNCT
ijassa-1225	525	3	p.a	p.a	PROPN
ijassa-1225	525	4	.	.	PROPN
ijassa-1225	525	5	&	&	CCONJ
ijassa-1225	525	6	nordhaus	nordhaus	PROPN
ijassa-1225	525	7	,	,	PUNCT
ijassa-1225	525	8	w.d	w.d	PROPN
ijassa-1225	525	9	.	.	PROPN
ijassa-1225	525	10	(	(	PUNCT
ijassa-1225	525	11	2010	2010	NUM
ijassa-1225	525	12	)	)	PUNCT
ijassa-1225	525	13	economics	economic	NOUN
ijassa-1225	525	14	.	.	PUNCT
ijassa-1225	526	1	new	new	PROPN
ijassa-1225	526	2	york	york	PROPN
ijassa-1225	526	3	,	,	PUNCT
ijassa-1225	526	4	ny	ny	PROPN
ijassa-1225	526	5	:	:	PUNCT
ijassa-1225	526	6	mcgraw	mcgraw	PROPN
ijassa-1225	526	7	-	-	PUNCT
ijassa-1225	526	8	hill	hill	NOUN
ijassa-1225	526	9	education	education	NOUN
ijassa-1225	526	10	.	.	PUNCT
ijassa-1225	527	1	13	13	NUM
ijassa-1225	527	2	.	.	X
ijassa-1225	527	3	allen	allen	PROPN
ijassa-1225	527	4	,	,	PUNCT
ijassa-1225	527	5	r.	r.	PROPN
ijassa-1225	527	6	(	(	PUNCT
ijassa-1225	527	7	1960	1960	NUM
ijassa-1225	527	8	)	)	PUNCT
ijassa-1225	527	9	mathematical	mathematical	ADJ
ijassa-1225	527	10	economics	economic	NOUN
ijassa-1225	527	11	.	.	PUNCT
ijassa-1225	528	1	london	london	PROPN
ijassa-1225	528	2	,	,	PUNCT
ijassa-1225	528	3	uk	uk	PROPN
ijassa-1225	528	4	:	:	PUNCT
ijassa-1225	528	5	macmillan	macmillan	PROPN
ijassa-1225	528	6	and	and	CCONJ
ijassa-1225	528	7	co	co	NOUN
ijassa-1225	528	8	ltd	ltd	PROPN
ijassa-1225	528	9	.	.	PROPN
ijassa-1225	528	10	14	14	NUM
ijassa-1225	528	11	.	.	PUNCT
ijassa-1225	529	1	arutyunov	arutyunov	PROPN
ijassa-1225	529	2	,	,	PUNCT
ijassa-1225	529	3	a.v	a.v	PROPN
ijassa-1225	529	4	.	.	PROPN
ijassa-1225	529	5	,	,	PUNCT
ijassa-1225	529	6	zhukovskiy	zhukovskiy	PROPN
ijassa-1225	529	7	,	,	PUNCT
ijassa-1225	529	8	s.e	s.e	PROPN
ijassa-1225	529	9	.	.	PROPN
ijassa-1225	529	10	&	&	CCONJ
ijassa-1225	529	11	pavlova	pavlova	PROPN
ijassa-1225	529	12	,	,	PUNCT
ijassa-1225	529	13	n.g	n.g	PROPN
ijassa-1225	529	14	.	.	PROPN
ijassa-1225	529	15	(	(	PUNCT
ijassa-1225	529	16	2013	2013	NUM
ijassa-1225	529	17	)	)	PUNCT
ijassa-1225	529	18	equilibrium	equilibrium	NOUN
ijassa-1225	529	19	price	price	NOUN
ijassa-1225	529	20	as	as	ADP
ijassa-1225	529	21	a	a	DET
ijassa-1225	529	22	coincidence	coincidence	NOUN
ijassa-1225	529	23	point	point	NOUN
ijassa-1225	529	24	of	of	ADP
ijassa-1225	529	25	two	two	NUM
ijassa-1225	529	26	mappings	mapping	NOUN
ijassa-1225	529	27	,	,	PUNCT
ijassa-1225	529	28	comput	comput	NOUN
ijassa-1225	529	29	.	.	PUNCT
ijassa-1225	530	1	math	math	NOUN
ijassa-1225	530	2	.	.	PUNCT
ijassa-1225	531	1	math	math	NOUN
ijassa-1225	531	2	.	.	PUNCT
ijassa-1225	532	1	phys	phy	NOUN
ijassa-1225	532	2	.	.	PUNCT
ijassa-1225	532	3	,	,	PUNCT
ijassa-1225	532	4	53(2	53(2	NUM
ijassa-1225	532	5	)	)	PUNCT
ijassa-1225	532	6	,	,	PUNCT
ijassa-1225	532	7	158–169	158–169	NUM
ijassa-1225	532	8	15	15	NUM
ijassa-1225	532	9	.	.	PUNCT
ijassa-1225	533	1	arutyunov	arutyunov	PROPN
ijassa-1225	533	2	,	,	PUNCT
ijassa-1225	533	3	a.v	a.v	PROPN
ijassa-1225	533	4	.	.	PROPN
ijassa-1225	533	5	,	,	PUNCT
ijassa-1225	533	6	pavlova	pavlova	PROPN
ijassa-1225	533	7	,	,	PUNCT
ijassa-1225	533	8	n.g	n.g	PROPN
ijassa-1225	533	9	.	.	PROPN
ijassa-1225	533	10	&	&	CCONJ
ijassa-1225	533	11	shananin	shananin	PROPN
ijassa-1225	533	12	,	,	PUNCT
ijassa-1225	533	13	a.a	a.a	PROPN
ijassa-1225	533	14	.	.	PROPN
ijassa-1225	533	15	(	(	PUNCT
ijassa-1225	533	16	2016	2016	NUM
ijassa-1225	533	17	)	)	PUNCT
ijassa-1225	533	18	equilibrium	equilibrium	NOUN
ijassa-1225	533	19	prices	price	NOUN
ijassa-1225	533	20	in	in	ADP
ijassa-1225	533	21	an	an	DET
ijassa-1225	533	22	economic	economic	ADJ
ijassa-1225	533	23	equilibrium	equilibrium	NOUN
ijassa-1225	533	24	model	model	NOUN
ijassa-1225	533	25	,	,	PUNCT
ijassa-1225	533	26	mathemathical	mathemathical	ADJ
ijassa-1225	533	27	modelling	modelling	NOUN
ijassa-1225	533	28	,	,	PUNCT
ijassa-1225	533	29	28(3	28(3	NUM
ijassa-1225	533	30	)	)	PUNCT
ijassa-1225	533	31	,	,	PUNCT
ijassa-1225	533	32	3–22	3–22	PROPN
ijassa-1225	533	33	.	.	PUNCT
ijassa-1225	534	1	16	16	NUM
ijassa-1225	534	2	.	.	PUNCT
ijassa-1225	535	1	belyakova	belyakova	PROPN
ijassa-1225	535	2	,	,	PUNCT
ijassa-1225	535	3	e.s	e.s	PROPN
ijassa-1225	535	4	.	.	PROPN
ijassa-1225	535	5	&	&	CCONJ
ijassa-1225	535	6	pavlova	pavlova	PROPN
ijassa-1225	535	7	,	,	PUNCT
ijassa-1225	535	8	n.g	n.g	PROPN
ijassa-1225	535	9	.	.	PROPN
ijassa-1225	535	10	(	(	PUNCT
ijassa-1225	535	11	2016	2016	NUM
ijassa-1225	535	12	)	)	PUNCT
ijassa-1225	535	13	equilibrium	equilibrium	NOUN
ijassa-1225	535	14	prices	price	NOUN
ijassa-1225	535	15	in	in	ADP
ijassa-1225	535	16	economic	economic	ADJ
ijassa-1225	535	17	equilibrium	equilibrium	NOUN
ijassa-1225	535	18	models	model	NOUN
ijassa-1225	535	19	with	with	ADP
ijassa-1225	535	20	transaction	transaction	NOUN
ijassa-1225	535	21	costs	cost	NOUN
ijassa-1225	535	22	,	,	PUNCT
ijassa-1225	535	23	tambov	tambov	PROPN
ijassa-1225	535	24	university	university	NOUN
ijassa-1225	535	25	reports	report	VERB
ijassa-1225	535	26	.	.	PUNCT
ijassa-1225	536	1	series	series	NOUN
ijassa-1225	536	2	:	:	PUNCT
ijassa-1225	536	3	natural	natural	ADJ
ijassa-1225	536	4	and	and	CCONJ
ijassa-1225	536	5	technical	technical	ADJ
ijassa-1225	536	6	sciences	science	NOUN
ijassa-1225	536	7	,	,	PUNCT
ijassa-1225	536	8	21(1	21(1	NUM
ijassa-1225	536	9	)	)	PUNCT
ijassa-1225	536	10	,	,	PUNCT
ijassa-1225	536	11	9–16	9–16	PROPN
ijassa-1225	536	12	.	.	PUNCT
ijassa-1225	537	1	17	17	NUM
ijassa-1225	537	2	.	.	PUNCT
ijassa-1225	538	1	pavlova	pavlova	PROPN
ijassa-1225	538	2	,	,	PUNCT
ijassa-1225	538	3	n.g	n.g	PROPN
ijassa-1225	538	4	.	.	PROPN
ijassa-1225	538	5	(	(	PUNCT
ijassa-1225	538	6	2017	2017	NUM
ijassa-1225	538	7	)	)	PUNCT
ijassa-1225	538	8	on	on	ADP
ijassa-1225	538	9	the	the	DET
ijassa-1225	538	10	application	application	NOUN
ijassa-1225	538	11	of	of	ADP
ijassa-1225	538	12	the	the	DET
ijassa-1225	538	13	results	result	NOUN
ijassa-1225	538	14	of	of	ADP
ijassa-1225	538	15	covering	cover	VERB
ijassa-1225	538	16	mappings	mapping	NOUN
ijassa-1225	538	17	theory	theory	NOUN
ijassa-1225	538	18	for	for	ADP
ijassa-1225	538	19	the	the	DET
ijassa-1225	538	20	study	study	NOUN
ijassa-1225	538	21	of	of	ADP
ijassa-1225	538	22	dynamical	dynamical	ADJ
ijassa-1225	538	23	models	model	NOUN
ijassa-1225	538	24	of	of	ADP
ijassa-1225	538	25	economic	economic	ADJ
ijassa-1225	538	26	processes	process	NOUN
ijassa-1225	538	27	,	,	PUNCT
ijassa-1225	538	28	tambov	tambov	PROPN
ijassa-1225	538	29	university	university	NOUN
ijassa-1225	538	30	reports	report	VERB
ijassa-1225	538	31	.	.	PUNCT
ijassa-1225	539	1	series	series	NOUN
ijassa-1225	539	2	:	:	PUNCT
ijassa-1225	539	3	natural	natural	ADJ
ijassa-1225	539	4	and	and	CCONJ
ijassa-1225	539	5	technical	technical	ADJ
ijassa-1225	539	6	sciences	science	NOUN
ijassa-1225	539	7	,	,	PUNCT
ijassa-1225	539	8	22(6	22(6	NUM
ijassa-1225	539	9	)	)	PUNCT
ijassa-1225	539	10	,	,	PUNCT
ijassa-1225	539	11	1304–1308	1304–1308	NUM
ijassa-1225	539	12	18	18	NUM
ijassa-1225	539	13	.	.	PUNCT
ijassa-1225	540	1	arutyunov	arutyunov	PROPN
ijassa-1225	540	2	,	,	PUNCT
ijassa-1225	540	3	a.v	a.v	PROPN
ijassa-1225	540	4	.	.	PROPN
ijassa-1225	540	5	(	(	PUNCT
ijassa-1225	540	6	2007	2007	NUM
ijassa-1225	540	7	)	)	PUNCT
ijassa-1225	540	8	covering	cover	VERB
ijassa-1225	540	9	mappings	mapping	NOUN
ijassa-1225	540	10	in	in	ADP
ijassa-1225	540	11	metric	metric	ADJ
ijassa-1225	540	12	spaces	space	NOUN
ijassa-1225	540	13	and	and	CCONJ
ijassa-1225	540	14	fixed	fix	VERB
ijassa-1225	540	15	points	point	NOUN
ijassa-1225	540	16	,	,	PUNCT
ijassa-1225	540	17	dokl	dokl	NOUN
ijassa-1225	540	18	.	.	PUNCT
ijassa-1225	541	1	math	math	PROPN
ijassa-1225	541	2	.	.	PUNCT
ijassa-1225	541	3	,	,	PUNCT
ijassa-1225	541	4	416(2	416(2	NUM
ijassa-1225	541	5	)	)	PUNCT
ijassa-1225	541	6	,	,	PUNCT
ijassa-1225	542	1	665–668	665–668	NUM
ijassa-1225	542	2	.	.	PROPN
ijassa-1225	542	3	19	19	NUM
ijassa-1225	542	4	.	.	X
ijassa-1225	542	5	arutyunov	arutyunov	PROPN
ijassa-1225	542	6	,	,	PUNCT
ijassa-1225	542	7	a.v	a.v	PROPN
ijassa-1225	542	8	.	.	PROPN
ijassa-1225	542	9	(	(	PUNCT
ijassa-1225	542	10	2014	2014	NUM
ijassa-1225	542	11	)	)	PUNCT
ijassa-1225	542	12	coincidence	coincidence	NOUN
ijassa-1225	542	13	points	point	NOUN
ijassa-1225	542	14	of	of	ADP
ijassa-1225	542	15	two	two	NUM
ijassa-1225	542	16	maps	map	NOUN
ijassa-1225	542	17	,	,	PUNCT
ijassa-1225	542	18	funct	funct	NOUN
ijassa-1225	542	19	.	.	PUNCT
ijassa-1225	543	1	anal	anal	PROPN
ijassa-1225	543	2	.	.	PUNCT
ijassa-1225	544	1	appl	appl	PROPN
ijassa-1225	544	2	.	.	PROPN
ijassa-1225	544	3	,	,	PUNCT
ijassa-1225	544	4	48(1	48(1	NOUN
ijassa-1225	544	5	)	)	PUNCT
ijassa-1225	544	6	,	,	PUNCT
ijassa-1225	544	7	72–75	72–75	PROPN
ijassa-1225	544	8	.	.	NOUN
ijassa-1225	544	9	20	20	NUM
ijassa-1225	544	10	.	.	PUNCT
ijassa-1225	545	1	arutyunov	arutyunov	PROPN
ijassa-1225	545	2	,	,	PUNCT
ijassa-1225	545	3	a.v	a.v	PROPN
ijassa-1225	545	4	.	.	PROPN
ijassa-1225	545	5	(	(	PUNCT
ijassa-1225	545	6	2009	2009	NUM
ijassa-1225	545	7	)	)	PUNCT
ijassa-1225	545	8	stability	stability	NOUN
ijassa-1225	545	9	of	of	ADP
ijassa-1225	545	10	coincidence	coincidence	NOUN
ijassa-1225	545	11	points	point	NOUN
ijassa-1225	545	12	and	and	CCONJ
ijassa-1225	545	13	properties	property	NOUN
ijassa-1225	545	14	of	of	ADP
ijassa-1225	545	15	covering	cover	VERB
ijassa-1225	545	16	mappings	mapping	NOUN
ijassa-1225	545	17	,	,	PUNCT
ijassa-1225	545	18	math	math	NOUN
ijassa-1225	545	19	.	.	PUNCT
ijassa-1225	546	1	notes	note	NOUN
ijassa-1225	546	2	,	,	PUNCT
ijassa-1225	546	3	86(2	86(2	NOUN
ijassa-1225	546	4	)	)	PUNCT
ijassa-1225	546	5	,	,	PUNCT
ijassa-1225	546	6	153–158	153–158	NUM
ijassa-1225	546	7	.	.	PUNCT
ijassa-1225	547	1	21	21	NUM
ijassa-1225	547	2	.	.	PUNCT
ijassa-1225	548	1	arutyunov	arutyunov	PROPN
ijassa-1225	548	2	,	,	PUNCT
ijassa-1225	548	3	a.	a.	NOUN
ijassa-1225	548	4	,	,	PUNCT
ijassa-1225	548	5	avakov	avakov	PROPN
ijassa-1225	548	6	,	,	PUNCT
ijassa-1225	548	7	e.	e.	PROPN
ijassa-1225	548	8	,	,	PUNCT
ijassa-1225	548	9	gel‘man	gel‘man	PROPN
ijassa-1225	548	10	,	,	PUNCT
ijassa-1225	548	11	b.	b.	PROPN
ijassa-1225	548	12	,	,	PUNCT
ijassa-1225	548	13	dmitruk	dmitruk	PROPN
ijassa-1225	548	14	,	,	PUNCT
ijassa-1225	548	15	a.	a.	PROPN
ijassa-1225	548	16	&	&	CCONJ
ijassa-1225	548	17	obukhovskii	obukhovskii	PROPN
ijassa-1225	548	18	,	,	PUNCT
ijassa-1225	548	19	v.	v.	CCONJ
ijassa-1225	548	20	(	(	PUNCT
ijassa-1225	548	21	2009	2009	NUM
ijassa-1225	548	22	)	)	PUNCT
ijassa-1225	548	23	locally	locally	ADV
ijassa-1225	548	24	covering	cover	VERB
ijassa-1225	548	25	maps	map	NOUN
ijassa-1225	548	26	in	in	ADP
ijassa-1225	548	27	metric	metric	ADJ
ijassa-1225	548	28	spaces	space	NOUN
ijassa-1225	548	29	and	and	CCONJ
ijassa-1225	548	30	coincidence	coincidence	NOUN
ijassa-1225	548	31	points	point	NOUN
ijassa-1225	548	32	,	,	PUNCT
ijassa-1225	548	33	j.	j.	PROPN
ijassa-1225	548	34	fixed	fix	VERB
ijassa-1225	548	35	points	point	NOUN
ijassa-1225	548	36	theory	theory	NOUN
ijassa-1225	548	37	and	and	CCONJ
ijassa-1225	548	38	appl	appl	NOUN
ijassa-1225	548	39	.	.	PUNCT
ijassa-1225	548	40	5(1	5(1	NUM
ijassa-1225	548	41	)	)	PUNCT
ijassa-1225	548	42	,	,	PUNCT
ijassa-1225	548	43	105–127	105–127	NUM
ijassa-1225	548	44	.	.	PUNCT
ijassa-1225	548	45	22	22	NUM
ijassa-1225	548	46	.	.	PUNCT
ijassa-1225	549	1	kolmogorov	kolmogorov	PROPN
ijassa-1225	549	2	,	,	PUNCT
ijassa-1225	549	3	a.n	a.n	PROPN
ijassa-1225	549	4	.	.	PROPN
ijassa-1225	549	5	&	&	CCONJ
ijassa-1225	549	6	fomin	fomin	PROPN
ijassa-1225	549	7	,	,	PUNCT
ijassa-1225	549	8	s.v	s.v	PROPN
ijassa-1225	549	9	.	.	PROPN
ijassa-1225	549	10	(	(	PUNCT
ijassa-1225	549	11	1963	1963	NUM
ijassa-1225	549	12	)	)	PUNCT
ijassa-1225	549	13	elements	element	NOUN
ijassa-1225	549	14	of	of	ADP
ijassa-1225	549	15	the	the	DET
ijassa-1225	549	16	theory	theory	NOUN
ijassa-1225	549	17	of	of	ADP
ijassa-1225	549	18	functions	function	NOUN
ijassa-1225	549	19	and	and	CCONJ
ijassa-1225	549	20	functional	functional	ADJ
ijassa-1225	549	21	analysis	analysis	NOUN
ijassa-1225	549	22	.	.	PUNCT
ijassa-1225	550	1	new	new	PROPN
ijassa-1225	550	2	york	york	PROPN
ijassa-1225	550	3	,	,	PUNCT
ijassa-1225	550	4	ny	ny	PROPN
ijassa-1225	550	5	:	:	PUNCT
ijassa-1225	550	6	graylock	graylock	PROPN
ijassa-1225	550	7	press	press	PROPN
ijassa-1225	550	8	.	.	PUNCT
ijassa-1225	551	1	albany	albany	PROPN
ijassa-1225	551	2	.	.	PUNCT
ijassa-1225	552	1	23	23	NUM
ijassa-1225	552	2	.	.	PUNCT
ijassa-1225	553	1	borisovich	borisovich	NOUN
ijassa-1225	553	2	,	,	PUNCT
ijassa-1225	553	3	yu.g	yu.g	PROPN
ijassa-1225	553	4	.	.	PROPN
ijassa-1225	553	5	,	,	PUNCT
ijassa-1225	553	6	gelman	gelman	PROPN
ijassa-1225	553	7	,	,	PUNCT
ijassa-1225	553	8	b.d	b.d	PROPN
ijassa-1225	553	9	.	.	PROPN
ijassa-1225	553	10	,	,	PUNCT
ijassa-1225	553	11	myshkis	myshkis	PROPN
ijassa-1225	553	12	,	,	PUNCT
ijassa-1225	553	13	a.d	a.d	PROPN
ijassa-1225	553	14	.	.	PROPN
ijassa-1225	553	15	&	&	CCONJ
ijassa-1225	553	16	obukhovskii	obukhovskii	PROPN
ijassa-1225	553	17	,	,	PUNCT
ijassa-1225	553	18	v.v	v.v	PROPN
ijassa-1225	553	19	.	.	PROPN
ijassa-1225	553	20	(	(	PUNCT
ijassa-1225	553	21	2011	2011	NUM
ijassa-1225	553	22	)	)	PUNCT
ijassa-1225	553	23	introduction	introduction	NOUN
ijassa-1225	553	24	to	to	ADP
ijassa-1225	553	25	the	the	DET
ijassa-1225	553	26	theory	theory	NOUN
ijassa-1225	553	27	of	of	ADP
ijassa-1225	553	28	multi	multi	ADJ
ijassa-1225	553	29	-	-	ADJ
ijassa-1225	553	30	valued	value	VERB
ijassa-1225	553	31	mappings	mapping	NOUN
ijassa-1225	553	32	and	and	CCONJ
ijassa-1225	553	33	differential	differential	ADJ
ijassa-1225	553	34	inclusions	inclusion	NOUN
ijassa-1225	553	35	.	.	PUNCT
ijassa-1225	554	1	moscow	moscow	PROPN
ijassa-1225	554	2	,	,	PUNCT
ijassa-1225	554	3	russia	russia	PROPN
ijassa-1225	554	4	:	:	PUNCT
ijassa-1225	554	5	librokom	librokom	VERB
ijassa-1225	554	6	.	.	PUNCT
ijassa-1225	555	1	copyright	copyright	NOUN
ijassa-1225	555	2	©	©	ADP
ijassa-1225	555	3	2022	2022	NUM
ijassa-1225	555	4	assa	assa	NOUN
ijassa-1225	555	5	.	.	PUNCT
ijassa-1225	556	1	adv	adv	PROPN
ijassa-1225	556	2	syst	syst	PROPN
ijassa-1225	556	3	sci	sci	PROPN
ijassa-1225	556	4	appl	appl	PROPN
ijassa-1225	556	5	(	(	PUNCT
ijassa-1225	556	6	2022	2022	NUM
ijassa-1225	556	7	)	)	PUNCT
ijassa-1225	556	8	on	on	ADP
ijassa-1225	556	9	order	order	NOUN
ijassa-1225	556	10	covering	cover	VERB
ijassa-1225	556	11	set	set	NOUN
ijassa-1225	556	12	-	-	PUNCT
ijassa-1225	556	13	valued	value	VERB
ijassa-1225	556	14	mappings	mapping	NOUN
ijassa-1225	556	15	and	and	CCONJ
ijassa-1225	556	16	their	their	PRON
ijassa-1225	556	17	applications	application	NOUN
ijassa-1225	556	18	191	191	NUM
ijassa-1225	556	19	24	24	NUM
ijassa-1225	556	20	.	.	PUNCT
ijassa-1225	557	1	serova	serova	PROPN
ijassa-1225	557	2	,	,	PUNCT
ijassa-1225	557	3	i.d	i.d	PROPN
ijassa-1225	557	4	.	.	PROPN
ijassa-1225	557	5	(	(	PUNCT
ijassa-1225	557	6	2021	2021	NUM
ijassa-1225	557	7	)	)	PUNCT
ijassa-1225	557	8	superpositional	superpositional	ADJ
ijassa-1225	557	9	measurability	measurability	NOUN
ijassa-1225	557	10	of	of	ADP
ijassa-1225	557	11	a	a	DET
ijassa-1225	557	12	multivalued	multivalue	VERB
ijassa-1225	557	13	function	function	NOUN
ijassa-1225	557	14	under	under	ADP
ijassa-1225	557	15	generalized	generalized	ADJ
ijassa-1225	557	16	caratheodory	caratheodory	ADJ
ijassa-1225	557	17	conditions	condition	NOUN
ijassa-1225	557	18	,	,	PUNCT
ijassa-1225	557	19	russian	russian	ADJ
ijassa-1225	557	20	universities	university	NOUN
ijassa-1225	557	21	reports	report	VERB
ijassa-1225	557	22	.	.	PUNCT
ijassa-1225	558	1	mathematics	mathematic	NOUN
ijassa-1225	558	2	,	,	PUNCT
ijassa-1225	558	3	26(135	26(135	NOUN
ijassa-1225	558	4	)	)	PUNCT
ijassa-1225	558	5	,	,	PUNCT
ijassa-1225	558	6	305–314	305–314	NUM
ijassa-1225	558	7	.	.	PUNCT
ijassa-1225	559	1	25	25	NUM
ijassa-1225	559	2	.	.	PUNCT
ijassa-1225	560	1	krasnoselskii	krasnoselskii	PROPN
ijassa-1225	560	2	,	,	PUNCT
ijassa-1225	560	3	m.a	m.a	PROPN
ijassa-1225	560	4	.	.	PROPN
ijassa-1225	560	5	&	&	CCONJ
ijassa-1225	560	6	zabreiko	zabreiko	PROPN
ijassa-1225	560	7	,	,	PUNCT
ijassa-1225	560	8	p.p	p.p	PROPN
ijassa-1225	560	9	.	.	PROPN
ijassa-1225	560	10	(	(	PUNCT
ijassa-1225	560	11	1984	1984	NUM
ijassa-1225	560	12	)	)	PUNCT
ijassa-1225	560	13	geometrical	geometrical	ADJ
ijassa-1225	560	14	methods	method	NOUN
ijassa-1225	560	15	of	of	ADP
ijassa-1225	560	16	nonlinear	nonlinear	ADJ
ijassa-1225	560	17	analysis	analysis	NOUN
ijassa-1225	560	18	.	.	PUNCT
ijassa-1225	561	1	berlin	berlin	PROPN
ijassa-1225	561	2	,	,	PUNCT
ijassa-1225	561	3	germany	germany	PROPN
ijassa-1225	561	4	:	:	PUNCT
ijassa-1225	561	5	springer	springer	NOUN
ijassa-1225	561	6	.	.	PUNCT
ijassa-1225	562	1	copyright	copyright	NOUN
ijassa-1225	562	2	©	©	ADP
ijassa-1225	562	3	2022	2022	NUM
ijassa-1225	562	4	assa	assa	NOUN
ijassa-1225	562	5	.	.	PUNCT
ijassa-1225	563	1	adv	adv	PROPN
ijassa-1225	563	2	syst	syst	PROPN
ijassa-1225	563	3	sci	sci	PROPN
ijassa-1225	563	4	appl	appl	PROPN
ijassa-1225	563	5	(	(	PUNCT
ijassa-1225	563	6	2022	2022	NUM
ijassa-1225	563	7	)	)	PUNCT
ijassa-1225	563	8	introduction	introduction	NOUN
ijassa-1225	563	9	a	a	DET
ijassa-1225	563	10	comparison	comparison	NOUN
ijassa-1225	563	11	theorem	theorem	VERB
ijassa-1225	563	12	for	for	ADP
ijassa-1225	563	13	operator	operator	NOUN
ijassa-1225	563	14	inclusions	inclusion	NOUN
ijassa-1225	563	15	in	in	ADP
ijassa-1225	563	16	partially	partially	ADV
ijassa-1225	563	17	ordered	order	VERB
ijassa-1225	563	18	spaces	space	NOUN
ijassa-1225	563	19	conditions	condition	NOUN
ijassa-1225	563	20	of	of	ADP
ijassa-1225	563	21	order	order	NOUN
ijassa-1225	563	22	covering	cover	VERB
ijassa-1225	563	23	for	for	ADP
ijassa-1225	563	24	the	the	DET
ijassa-1225	563	25	nemytskii	nemytskii	ADJ
ijassa-1225	563	26	operator	operator	NOUN
ijassa-1225	563	27	implicit	implicit	ADJ
ijassa-1225	563	28	differential	differential	ADJ
ijassa-1225	563	29	inclusion	inclusion	NOUN
ijassa-1225	563	30	existence	existence	NOUN
ijassa-1225	563	31	and	and	CCONJ
ijassa-1225	563	32	estimates	estimate	NOUN
ijassa-1225	563	33	of	of	ADP
ijassa-1225	563	34	equilibrium	equilibrium	NOUN
ijassa-1225	563	35	prices	price	NOUN
ijassa-1225	563	36	in	in	ADP
ijassa-1225	563	37	dynamical	dynamical	ADJ
ijassa-1225	563	38	continuous	continuous	ADJ
ijassa-1225	563	39	supply	supply	NOUN
ijassa-1225	563	40	-	-	PUNCT
ijassa-1225	563	41	and	and	CCONJ
ijassa-1225	563	42	-	-	PUNCT
ijassa-1225	563	43	demand	demand	NOUN
ijassa-1225	563	44	models	model	NOUN