id	sid	tid	token	lemma	pos
ejpam-5165	1	1	european	european	PROPN
ejpam-5165	1	2	journal	journal	PROPN
ejpam-5165	1	3	of	of	ADP
ejpam-5165	1	4	pure	pure	ADJ
ejpam-5165	1	5	and	and	CCONJ
ejpam-5165	1	6	applied	apply	VERB
ejpam-5165	1	7	mathematics	mathematic	NOUN
ejpam-5165	1	8	vol	vol	NOUN
ejpam-5165	1	9	.	.	PROPN
ejpam-5165	2	1	17	17	NUM
ejpam-5165	2	2	,	,	PUNCT
ejpam-5165	2	3	no	no	INTJ
ejpam-5165	2	4	.	.	NOUN
ejpam-5165	2	5	2	2	NUM
ejpam-5165	2	6	,	,	PUNCT
ejpam-5165	2	7	2024	2024	NUM
ejpam-5165	2	8	,	,	PUNCT
ejpam-5165	2	9	1183	1183	NUM
ejpam-5165	2	10	-	-	SYM
ejpam-5165	2	11	1196	1196	NUM
ejpam-5165	2	12	issn	issn	PROPN
ejpam-5165	2	13	1307	1307	NUM
ejpam-5165	2	14	-	-	SYM
ejpam-5165	2	15	5543	5543	NUM
ejpam-5165	2	16	–	–	PUNCT
ejpam-5165	3	1	ejpam.com	ejpam.com	X
ejpam-5165	3	2	published	publish	VERB
ejpam-5165	3	3	by	by	ADP
ejpam-5165	3	4	new	new	PROPN
ejpam-5165	3	5	york	york	PROPN
ejpam-5165	3	6	business	business	PROPN
ejpam-5165	3	7	global	global	PROPN
ejpam-5165	3	8	on	on	ADP
ejpam-5165	3	9	the	the	DET
ejpam-5165	3	10	mcshane	mcshane	PROPN
ejpam-5165	3	11	-	-	PUNCT
ejpam-5165	3	12	dunford	dunford	NOUN
ejpam-5165	3	13	-	-	PUNCT
ejpam-5165	3	14	stieltjes	stieltjes	NOUN
ejpam-5165	3	15	integral	integral	ADJ
ejpam-5165	3	16	and	and	CCONJ
ejpam-5165	3	17	mcshane	mcshane	PROPN
ejpam-5165	3	18	-	-	PUNCT
ejpam-5165	3	19	pettis	pettis	PROPN
ejpam-5165	3	20	-	-	PUNCT
ejpam-5165	3	21	stieltjes	stieltjes	NOUN
ejpam-5165	3	22	integral	integral	ADJ
ejpam-5165	3	23	develin	develin	PROPN
ejpam-5165	3	24	omayan1,∗	omayan1,∗	NOUN
ejpam-5165	3	25	,	,	PUNCT
ejpam-5165	3	26	greig	greig	PROPN
ejpam-5165	3	27	bates	bate	NOUN
ejpam-5165	3	28	flores2	flores2	PROPN
ejpam-5165	3	29	1,2	1,2	NUM
ejpam-5165	3	30	department	department	NOUN
ejpam-5165	3	31	of	of	ADP
ejpam-5165	3	32	mathematics	mathematic	NOUN
ejpam-5165	3	33	,	,	PUNCT
ejpam-5165	3	34	college	college	NOUN
ejpam-5165	3	35	of	of	ADP
ejpam-5165	3	36	arts	art	NOUN
ejpam-5165	3	37	and	and	CCONJ
ejpam-5165	3	38	sciences	science	NOUN
ejpam-5165	3	39	,	,	PUNCT
ejpam-5165	3	40	central	central	ADJ
ejpam-5165	3	41	mindanao	mindanao	PROPN
ejpam-5165	3	42	university	university	PROPN
ejpam-5165	3	43	,	,	PUNCT
ejpam-5165	3	44	philippines	philippine	NOUN
ejpam-5165	3	45	abstract	abstract	ADJ
ejpam-5165	3	46	.	.	PUNCT
ejpam-5165	4	1	this	this	DET
ejpam-5165	4	2	paper	paper	NOUN
ejpam-5165	4	3	combines	combine	VERB
ejpam-5165	4	4	the	the	DET
ejpam-5165	4	5	mcshane	mcshane	NOUN
ejpam-5165	4	6	-	-	PUNCT
ejpam-5165	4	7	stieltjes	stieltjes	NOUN
ejpam-5165	4	8	integral	integral	ADJ
ejpam-5165	4	9	and	and	CCONJ
ejpam-5165	4	10	pettis	pettis	NOUN
ejpam-5165	4	11	approaches	approach	NOUN
ejpam-5165	4	12	by	by	ADP
ejpam-5165	4	13	utilizing	utilize	VERB
ejpam-5165	4	14	pettis	pettis	NOUN
ejpam-5165	4	15	’	'	PUNCT
ejpam-5165	4	16	definition	definition	NOUN
ejpam-5165	4	17	,	,	PUNCT
ejpam-5165	4	18	which	which	PRON
ejpam-5165	4	19	coincides	coincide	VERB
ejpam-5165	4	20	with	with	ADP
ejpam-5165	4	21	the	the	DET
ejpam-5165	4	22	dunford	dunford	PROPN
ejpam-5165	4	23	integral	integral	ADJ
ejpam-5165	4	24	rather	rather	ADV
ejpam-5165	4	25	than	than	ADP
ejpam-5165	4	26	the	the	DET
ejpam-5165	4	27	version	version	NOUN
ejpam-5165	4	28	applicable	applicable	ADJ
ejpam-5165	4	29	to	to	ADP
ejpam-5165	4	30	weakly	weakly	ADJ
ejpam-5165	4	31	measurable	measurable	ADJ
ejpam-5165	4	32	functions	function	NOUN
ejpam-5165	4	33	with	with	ADP
ejpam-5165	4	34	lebesgue	lebesgue	PROPN
ejpam-5165	4	35	integrable	integrable	ADJ
ejpam-5165	4	36	images	image	NOUN
ejpam-5165	4	37	.	.	PUNCT
ejpam-5165	5	1	in	in	ADP
ejpam-5165	5	2	this	this	DET
ejpam-5165	5	3	way	way	NOUN
ejpam-5165	5	4	,	,	PUNCT
ejpam-5165	5	5	another	another	DET
ejpam-5165	5	6	integration	integration	NOUN
ejpam-5165	5	7	process	process	NOUN
ejpam-5165	5	8	without	without	ADP
ejpam-5165	5	9	measure	measure	NOUN
ejpam-5165	5	10	theoretic	theoretic	NOUN
ejpam-5165	5	11	standpoint	standpoint	NOUN
ejpam-5165	5	12	will	will	AUX
ejpam-5165	5	13	be	be	AUX
ejpam-5165	5	14	introduced	introduce	VERB
ejpam-5165	5	15	.	.	PUNCT
ejpam-5165	6	1	to	to	ADP
ejpam-5165	6	2	this	this	DET
ejpam-5165	6	3	end	end	NOUN
ejpam-5165	6	4	,	,	PUNCT
ejpam-5165	6	5	we	we	PRON
ejpam-5165	6	6	will	will	AUX
ejpam-5165	6	7	define	define	VERB
ejpam-5165	6	8	the	the	DET
ejpam-5165	6	9	mcshane	mcshane	PROPN
ejpam-5165	6	10	-	-	PUNCT
ejpam-5165	6	11	dunford	dunford	NOUN
ejpam-5165	6	12	-	-	PUNCT
ejpam-5165	6	13	stieltjes	stieltjes	NOUN
ejpam-5165	6	14	integral	integral	ADJ
ejpam-5165	6	15	and	and	CCONJ
ejpam-5165	6	16	mcshane	mcshane	PROPN
ejpam-5165	6	17	-	-	PUNCT
ejpam-5165	6	18	pettis	pettis	PROPN
ejpam-5165	6	19	-	-	PUNCT
ejpam-5165	6	20	stieltjes	stieltjes	NOUN
ejpam-5165	6	21	integral	integral	ADJ
ejpam-5165	6	22	in	in	ADP
ejpam-5165	6	23	banach	banach	NOUN
ejpam-5165	6	24	space	space	NOUN
ejpam-5165	6	25	and	and	CCONJ
ejpam-5165	6	26	provide	provide	VERB
ejpam-5165	6	27	its	its	PRON
ejpam-5165	6	28	simple	simple	ADJ
ejpam-5165	6	29	properties	property	NOUN
ejpam-5165	6	30	such	such	ADJ
ejpam-5165	6	31	as	as	ADP
ejpam-5165	6	32	the	the	DET
ejpam-5165	6	33	uniqueness	uniqueness	NOUN
ejpam-5165	6	34	,	,	PUNCT
ejpam-5165	6	35	linearity	linearity	NOUN
ejpam-5165	6	36	property	property	NOUN
ejpam-5165	6	37	of	of	ADP
ejpam-5165	6	38	both	both	PRON
ejpam-5165	6	39	the	the	DET
ejpam-5165	6	40	integrand	integrand	NOUN
ejpam-5165	6	41	and	and	CCONJ
ejpam-5165	6	42	integrator	integrator	NOUN
ejpam-5165	6	43	,	,	PUNCT
ejpam-5165	6	44	additivity	additivity	NOUN
ejpam-5165	6	45	and	and	CCONJ
ejpam-5165	6	46	formulate	formulate	VERB
ejpam-5165	6	47	the	the	DET
ejpam-5165	6	48	cauchy	cauchy	ADJ
ejpam-5165	6	49	criterion	criterion	NOUN
ejpam-5165	6	50	of	of	ADP
ejpam-5165	6	51	these	these	DET
ejpam-5165	6	52	integrals	integral	NOUN
ejpam-5165	6	53	.	.	PUNCT
ejpam-5165	7	1	in	in	ADP
ejpam-5165	7	2	addition	addition	NOUN
ejpam-5165	7	3	,	,	PUNCT
ejpam-5165	7	4	the	the	DET
ejpam-5165	7	5	existence	existence	NOUN
ejpam-5165	7	6	theorem	theorem	NOUN
ejpam-5165	7	7	of	of	ADP
ejpam-5165	7	8	mcshane	mcshane	PROPN
ejpam-5165	7	9	-	-	PUNCT
ejpam-5165	7	10	dunford	dunford	PROPN
ejpam-5165	7	11	stieltjes	stieltjes	PROPN
ejpam-5165	7	12	integral	integral	ADJ
ejpam-5165	7	13	will	will	AUX
ejpam-5165	7	14	also	also	ADV
ejpam-5165	7	15	be	be	AUX
ejpam-5165	7	16	presented	present	VERB
ejpam-5165	7	17	.	.	PUNCT
ejpam-5165	8	1	2020	2020	NUM
ejpam-5165	8	2	mathematics	mathematic	NOUN
ejpam-5165	8	3	subject	subject	NOUN
ejpam-5165	8	4	classifications	classification	NOUN
ejpam-5165	8	5	:	:	PUNCT
ejpam-5165	8	6	40a99	40a99	NUM
ejpam-5165	8	7	,	,	PUNCT
ejpam-5165	8	8	46bxx	46bxx	NOUN
ejpam-5165	8	9	,	,	PUNCT
ejpam-5165	8	10	49q15	49q15	NUM
ejpam-5165	8	11	,	,	PUNCT
ejpam-5165	8	12	26a42	26a42	NUM
ejpam-5165	8	13	,	,	PUNCT
ejpam-5165	8	14	26a45	26a45	NUM
ejpam-5165	8	15	key	key	ADJ
ejpam-5165	8	16	words	word	NOUN
ejpam-5165	8	17	and	and	CCONJ
ejpam-5165	8	18	phrases	phrase	NOUN
ejpam-5165	8	19	:	:	PUNCT
ejpam-5165	8	20	mcshane	mcshane	NOUN
ejpam-5165	8	21	-	-	PUNCT
ejpam-5165	8	22	stieltjes	stieltjes	PROPN
ejpam-5165	8	23	integral	integral	ADJ
ejpam-5165	8	24	,	,	PUNCT
ejpam-5165	8	25	mcshane	mcshane	PROPN
ejpam-5165	8	26	-	-	PUNCT
ejpam-5165	8	27	dunford	dunford	NOUN
ejpam-5165	8	28	-	-	PUNCT
ejpam-5165	8	29	stieltjes	stieltjes	NOUN
ejpam-5165	8	30	integral	integral	ADJ
ejpam-5165	8	31	,	,	PUNCT
ejpam-5165	8	32	mcshane	mcshane	PROPN
ejpam-5165	8	33	-	-	PUNCT
ejpam-5165	8	34	pettis	pettis	PROPN
ejpam-5165	8	35	-	-	PUNCT
ejpam-5165	8	36	stieltjes	stieltjes	NOUN
ejpam-5165	8	37	.	.	PUNCT
ejpam-5165	9	1	1	1	X
ejpam-5165	9	2	.	.	X
ejpam-5165	9	3	introduction	introduction	NOUN
ejpam-5165	9	4	the	the	DET
ejpam-5165	9	5	kurzweil	kurzweil	PROPN
ejpam-5165	9	6	-	-	PUNCT
ejpam-5165	9	7	henstock	henstock	PROPN
ejpam-5165	9	8	integral	integral	ADJ
ejpam-5165	9	9	,	,	PUNCT
ejpam-5165	9	10	also	also	ADV
ejpam-5165	9	11	known	know	VERB
ejpam-5165	9	12	as	as	ADP
ejpam-5165	9	13	the	the	DET
ejpam-5165	9	14	generalized	generalized	ADJ
ejpam-5165	9	15	riemann	riemann	PROPN
ejpam-5165	9	16	integral	integral	ADJ
ejpam-5165	9	17	,	,	PUNCT
ejpam-5165	9	18	in	in	ADP
ejpam-5165	9	19	most	most	ADJ
ejpam-5165	9	20	cases	case	NOUN
ejpam-5165	9	21	,	,	PUNCT
ejpam-5165	9	22	is	be	AUX
ejpam-5165	9	23	an	an	DET
ejpam-5165	9	24	expansion	expansion	NOUN
ejpam-5165	9	25	of	of	ADP
ejpam-5165	9	26	the	the	DET
ejpam-5165	9	27	lebesgue	lebesgue	NOUN
ejpam-5165	9	28	integral	integral	ADJ
ejpam-5165	9	29	in	in	ADP
ejpam-5165	9	30	the	the	DET
ejpam-5165	9	31	context	context	NOUN
ejpam-5165	9	32	of	of	ADP
ejpam-5165	9	33	riemann	riemann	PROPN
ejpam-5165	9	34	.	.	PUNCT
ejpam-5165	10	1	it	it	PRON
ejpam-5165	10	2	is	be	AUX
ejpam-5165	10	3	wellknown	wellknown	ADJ
ejpam-5165	10	4	that	that	SCONJ
ejpam-5165	10	5	english	english	PROPN
ejpam-5165	10	6	mathematician	mathematician	NOUN
ejpam-5165	10	7	ralph	ralph	PROPN
ejpam-5165	10	8	henstock	henstock	PROPN
ejpam-5165	10	9	and	and	CCONJ
ejpam-5165	10	10	czech	czech	PROPN
ejpam-5165	10	11	mathematician	mathematician	ADJ
ejpam-5165	10	12	jaroslav	jaroslav	PROPN
ejpam-5165	10	13	kurzweil	kurzweil	PROPN
ejpam-5165	10	14	provided	provide	VERB
ejpam-5165	10	15	a	a	DET
ejpam-5165	10	16	slight	slight	ADJ
ejpam-5165	10	17	but	but	CCONJ
ejpam-5165	10	18	clever	clever	ADJ
ejpam-5165	10	19	alteration	alteration	NOUN
ejpam-5165	10	20	to	to	ADP
ejpam-5165	10	21	the	the	DET
ejpam-5165	10	22	conventional	conventional	ADJ
ejpam-5165	10	23	riemann	riemann	PROPN
ejpam-5165	10	24	integral	integral	ADJ
ejpam-5165	10	25	to	to	PART
ejpam-5165	10	26	obtain	obtain	VERB
ejpam-5165	10	27	this	this	DET
ejpam-5165	10	28	definition	definition	NOUN
ejpam-5165	10	29	[	[	X
ejpam-5165	10	30	1	1	NUM
ejpam-5165	10	31	]	]	PUNCT
ejpam-5165	10	32	.	.	PUNCT
ejpam-5165	11	1	unlike	unlike	ADP
ejpam-5165	11	2	the	the	DET
ejpam-5165	11	3	lebesgue	lebesgue	NOUN
ejpam-5165	11	4	integral	integral	ADJ
ejpam-5165	11	5	,	,	PUNCT
ejpam-5165	11	6	which	which	PRON
ejpam-5165	11	7	requires	require	VERB
ejpam-5165	11	8	a	a	DET
ejpam-5165	11	9	foundation	foundation	NOUN
ejpam-5165	11	10	in	in	ADP
ejpam-5165	11	11	measure	measure	NOUN
ejpam-5165	11	12	theory	theory	NOUN
ejpam-5165	11	13	for	for	ADP
ejpam-5165	11	14	its	its	PRON
ejpam-5165	11	15	definition	definition	NOUN
ejpam-5165	11	16	making	make	VERB
ejpam-5165	11	17	it	it	PRON
ejpam-5165	11	18	a	a	DET
ejpam-5165	11	19	difficult	difficult	ADJ
ejpam-5165	11	20	one	one	NOUN
ejpam-5165	11	21	,	,	PUNCT
ejpam-5165	11	22	the	the	DET
ejpam-5165	11	23	kurzweil	kurzweil	PROPN
ejpam-5165	11	24	-	-	PUNCT
ejpam-5165	11	25	henstock	henstock	PROPN
ejpam-5165	11	26	integral	integral	ADJ
ejpam-5165	11	27	is	be	AUX
ejpam-5165	11	28	accessible	accessible	ADJ
ejpam-5165	11	29	through	through	ADP
ejpam-5165	11	30	a	a	DET
ejpam-5165	11	31	more	more	ADV
ejpam-5165	11	32	straightforward	straightforward	ADJ
ejpam-5165	11	33	gauge	gauge	NOUN
ejpam-5165	11	34	-	-	PUNCT
ejpam-5165	11	35	based	base	VERB
ejpam-5165	11	36	approach	approach	NOUN
ejpam-5165	11	37	.	.	PUNCT
ejpam-5165	12	1	now	now	ADV
ejpam-5165	12	2	,	,	PUNCT
ejpam-5165	12	3	for	for	ADP
ejpam-5165	12	4	real	real	ADV
ejpam-5165	12	5	-	-	PUNCT
ejpam-5165	12	6	valued	value	VERB
ejpam-5165	12	7	functions	function	NOUN
ejpam-5165	12	8	the	the	DET
ejpam-5165	12	9	generalization	generalization	NOUN
ejpam-5165	12	10	of	of	ADP
ejpam-5165	12	11	riemann	riemann	PROPN
ejpam-5165	12	12	integral	integral	ADJ
ejpam-5165	12	13	yields	yield	NOUN
ejpam-5165	12	14	to	to	ADP
ejpam-5165	12	15	an	an	DET
ejpam-5165	12	16	integral	integral	ADJ
ejpam-5165	12	17	referred	refer	VERB
ejpam-5165	12	18	to	to	ADP
ejpam-5165	12	19	as	as	SCONJ
ejpam-5165	12	20	the	the	DET
ejpam-5165	12	21	mcshane	mcshane	PROPN
ejpam-5165	12	22	integral	integral	ADJ
ejpam-5165	12	23	,	,	PUNCT
ejpam-5165	12	24	that	that	ADV
ejpam-5165	12	25	is	is	ADV
ejpam-5165	12	26	,	,	PUNCT
ejpam-5165	12	27	in	in	ADP
ejpam-5165	12	28	most	most	ADJ
ejpam-5165	12	29	cases	case	NOUN
ejpam-5165	12	30	,	,	PUNCT
ejpam-5165	12	31	equivalent	equivalent	ADJ
ejpam-5165	12	32	to	to	ADP
ejpam-5165	12	33	the	the	DET
ejpam-5165	12	34	lebesgue	lebesgue	NOUN
ejpam-5165	12	35	integral	integral	ADJ
ejpam-5165	12	36	[	[	X
ejpam-5165	12	37	4	4	NUM
ejpam-5165	12	38	]	]	PUNCT
ejpam-5165	12	39	.	.	PUNCT
ejpam-5165	13	1	meanwhile	meanwhile	ADV
ejpam-5165	13	2	,	,	PUNCT
ejpam-5165	13	3	in	in	ADP
ejpam-5165	13	4	the	the	DET
ejpam-5165	13	5	late	late	ADJ
ejpam-5165	13	6	1960	1960	NUM
ejpam-5165	13	7	’s	’s	NOUN
ejpam-5165	13	8	,	,	PUNCT
ejpam-5165	13	9	mcshane	mcshane	NOUN
ejpam-5165	14	1	[	[	X
ejpam-5165	14	2	9	9	NUM
ejpam-5165	14	3	]	]	PUNCT
ejpam-5165	14	4	proved	prove	VERB
ejpam-5165	14	5	that	that	SCONJ
ejpam-5165	14	6	the	the	DET
ejpam-5165	14	7	lebesgue	lebesgue	NOUN
ejpam-5165	14	8	integral	integral	NOUN
ejpam-5165	14	9	is	be	AUX
ejpam-5165	14	10	indeed	indeed	ADV
ejpam-5165	14	11	equivalent	equivalent	ADJ
ejpam-5165	14	12	to	to	ADP
ejpam-5165	14	13	a	a	DET
ejpam-5165	14	14	modified	modify	VERB
ejpam-5165	14	15	version	version	NOUN
ejpam-5165	14	16	of	of	ADP
ejpam-5165	14	17	the	the	DET
ejpam-5165	14	18	kurzweil	kurzweil	PROPN
ejpam-5165	14	19	-	-	PUNCT
ejpam-5165	14	20	henstock	henstock	NOUN
ejpam-5165	14	21	integral	integral	ADJ
ejpam-5165	14	22	[	[	X
ejpam-5165	14	23	6	6	NUM
ejpam-5165	14	24	]	]	PUNCT
ejpam-5165	14	25	.	.	PUNCT
ejpam-5165	15	1	note	note	VERB
ejpam-5165	15	2	that	that	SCONJ
ejpam-5165	15	3	the	the	DET
ejpam-5165	15	4	kurzweil	kurzweil	PROPN
ejpam-5165	15	5	-	-	PUNCT
ejpam-5165	15	6	henstock	henstock	PROPN
ejpam-5165	15	7	and	and	CCONJ
ejpam-5165	15	8	mcshane	mcshane	PROPN
ejpam-5165	15	9	integrals	integral	NOUN
ejpam-5165	15	10	differ	differ	VERB
ejpam-5165	15	11	in	in	ADP
ejpam-5165	15	12	how	how	SCONJ
ejpam-5165	15	13	the	the	DET
ejpam-5165	15	14	tagged	tag	VERB
ejpam-5165	15	15	intervals	interval	NOUN
ejpam-5165	15	16	∗corresponding	∗corresponde	VERB
ejpam-5165	15	17	author	author	NOUN
ejpam-5165	15	18	.	.	PUNCT
ejpam-5165	16	1	doi	doi	NOUN
ejpam-5165	16	2	:	:	PUNCT
ejpam-5165	16	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5165	https://doi.org/10.29020/nybg.ejpam.v17i2.5165	X
ejpam-5165	16	4	email	email	NOUN
ejpam-5165	16	5	addresses	address	VERB
ejpam-5165	16	6	:	:	PUNCT
ejpam-5165	16	7	develinomayan@gmail.com	develinomayan@gmail.com	X
ejpam-5165	16	8	(	(	PUNCT
ejpam-5165	16	9	d.	d.	PROPN
ejpam-5165	16	10	omayan	omayan	PROPN
ejpam-5165	16	11	)	)	PUNCT
ejpam-5165	16	12	,	,	PUNCT
ejpam-5165	16	13	f.greigbates.flores@cmu.edu.ph	f.greigbates.flores@cmu.edu.ph	PROPN
ejpam-5165	16	14	(	(	PUNCT
ejpam-5165	16	15	g.b	g.b	PROPN
ejpam-5165	16	16	.	.	PROPN
ejpam-5165	16	17	flores	flores	PROPN
ejpam-5165	16	18	)	)	PUNCT
ejpam-5165	16	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5165	16	20	1183	1183	NUM
ejpam-5165	16	21	©	©	ADP
ejpam-5165	16	22	2024	2024	NUM
ejpam-5165	16	23	ejpam	ejpam	NOUN
ejpam-5165	16	24	all	all	DET
ejpam-5165	16	25	rights	right	NOUN
ejpam-5165	16	26	reserved	reserve	VERB
ejpam-5165	16	27	.	.	PUNCT
ejpam-5165	17	1	d.	d.	PROPN
ejpam-5165	17	2	omayan	omayan	PROPN
ejpam-5165	17	3	,	,	PUNCT
ejpam-5165	17	4	g.b	g.b	PROPN
ejpam-5165	17	5	.	.	PROPN
ejpam-5165	17	6	flores	flores	PROPN
ejpam-5165	17	7	/	/	SYM
ejpam-5165	17	8	eur	eur	PROPN
ejpam-5165	17	9	.	.	PUNCT
ejpam-5165	18	1	j.	j.	PROPN
ejpam-5165	18	2	pure	pure	PROPN
ejpam-5165	18	3	appl	appl	PROPN
ejpam-5165	18	4	.	.	PROPN
ejpam-5165	18	5	math	math	PROPN
ejpam-5165	18	6	,	,	PUNCT
ejpam-5165	18	7	17	17	NUM
ejpam-5165	18	8	(	(	PUNCT
ejpam-5165	18	9	2	2	NUM
ejpam-5165	18	10	)	)	PUNCT
ejpam-5165	18	11	(	(	PUNCT
ejpam-5165	18	12	2024	2024	NUM
ejpam-5165	18	13	)	)	PUNCT
ejpam-5165	18	14	,	,	PUNCT
ejpam-5165	18	15	1183	1183	NUM
ejpam-5165	18	16	-	-	SYM
ejpam-5165	18	17	1196	1196	NUM
ejpam-5165	18	18	1184	1184	NUM
ejpam-5165	18	19	are	be	AUX
ejpam-5165	18	20	constructed	construct	VERB
ejpam-5165	18	21	.	.	PUNCT
ejpam-5165	19	1	in	in	ADP
ejpam-5165	19	2	the	the	DET
ejpam-5165	19	3	kurzweil	kurzweil	PROPN
ejpam-5165	19	4	-	-	PUNCT
ejpam-5165	19	5	henstock	henstock	PROPN
ejpam-5165	19	6	integral	integral	ADJ
ejpam-5165	19	7	,	,	PUNCT
ejpam-5165	19	8	the	the	DET
ejpam-5165	19	9	tags	tag	NOUN
ejpam-5165	19	10	must	must	AUX
ejpam-5165	19	11	be	be	AUX
ejpam-5165	19	12	within	within	ADP
ejpam-5165	19	13	the	the	DET
ejpam-5165	19	14	interval	interval	NOUN
ejpam-5165	19	15	while	while	SCONJ
ejpam-5165	19	16	for	for	SCONJ
ejpam-5165	19	17	the	the	DET
ejpam-5165	19	18	mcshane	mcshane	PROPN
ejpam-5165	19	19	integral	integral	ADJ
ejpam-5165	19	20	the	the	DET
ejpam-5165	19	21	tags	tag	NOUN
ejpam-5165	19	22	can	can	AUX
ejpam-5165	19	23	be	be	AUX
ejpam-5165	19	24	located	locate	VERB
ejpam-5165	19	25	outside	outside	ADP
ejpam-5165	19	26	the	the	DET
ejpam-5165	19	27	interval	interval	NOUN
ejpam-5165	19	28	.	.	PUNCT
ejpam-5165	20	1	on	on	ADP
ejpam-5165	20	2	the	the	DET
ejpam-5165	20	3	other	other	ADJ
ejpam-5165	20	4	hand	hand	NOUN
ejpam-5165	20	5	,	,	PUNCT
ejpam-5165	20	6	another	another	DET
ejpam-5165	20	7	integration	integration	NOUN
ejpam-5165	20	8	process	process	NOUN
ejpam-5165	20	9	called	call	VERB
ejpam-5165	20	10	pettis	pettis	PROPN
ejpam-5165	20	11	integral	integral	NOUN
ejpam-5165	20	12	was	be	AUX
ejpam-5165	20	13	discovered	discover	VERB
ejpam-5165	20	14	being	be	AUX
ejpam-5165	20	15	an	an	DET
ejpam-5165	20	16	extension	extension	NOUN
ejpam-5165	20	17	of	of	ADP
ejpam-5165	20	18	the	the	DET
ejpam-5165	20	19	lebesgue	lebesgue	NOUN
ejpam-5165	20	20	integral	integral	ADJ
ejpam-5165	20	21	to	to	ADP
ejpam-5165	20	22	a	a	DET
ejpam-5165	20	23	banach	banach	ADV
ejpam-5165	20	24	-	-	PUNCT
ejpam-5165	20	25	valued	value	VERB
ejpam-5165	20	26	functions	function	NOUN
ejpam-5165	20	27	on	on	ADP
ejpam-5165	20	28	a	a	DET
ejpam-5165	20	29	measure	measure	NOUN
ejpam-5165	20	30	space	space	NOUN
ejpam-5165	20	31	.	.	PUNCT
ejpam-5165	21	1	the	the	DET
ejpam-5165	21	2	pettis	pettis	PROPN
ejpam-5165	21	3	integral	integral	NOUN
ejpam-5165	21	4	has	have	VERB
ejpam-5165	21	5	two	two	NUM
ejpam-5165	21	6	definitions	definition	NOUN
ejpam-5165	21	7	:	:	PUNCT
ejpam-5165	21	8	one	one	NUM
ejpam-5165	21	9	for	for	ADP
ejpam-5165	21	10	dunford	dunford	PROPN
ejpam-5165	21	11	integrable	integrable	ADJ
ejpam-5165	21	12	functions	function	NOUN
ejpam-5165	21	13	,	,	PUNCT
ejpam-5165	21	14	where	where	SCONJ
ejpam-5165	21	15	the	the	DET
ejpam-5165	21	16	integral	integral	ADJ
ejpam-5165	21	17	coincides	coincide	NOUN
ejpam-5165	21	18	with	with	ADP
ejpam-5165	21	19	the	the	DET
ejpam-5165	21	20	dunford	dunford	PROPN
ejpam-5165	21	21	integral	integral	PROPN
ejpam-5165	21	22	;	;	PUNCT
ejpam-5165	21	23	the	the	DET
ejpam-5165	21	24	other	other	ADJ
ejpam-5165	21	25	for	for	ADP
ejpam-5165	21	26	weakly	weakly	ADJ
ejpam-5165	21	27	measurable	measurable	ADJ
ejpam-5165	21	28	functions	function	NOUN
ejpam-5165	21	29	with	with	ADP
ejpam-5165	21	30	lebesgue	lebesgue	PROPN
ejpam-5165	21	31	integrable	integrable	ADJ
ejpam-5165	21	32	images	image	NOUN
ejpam-5165	21	33	,	,	PUNCT
ejpam-5165	21	34	ensuring	ensure	VERB
ejpam-5165	21	35	the	the	DET
ejpam-5165	21	36	existence	existence	NOUN
ejpam-5165	21	37	of	of	ADP
ejpam-5165	21	38	an	an	DET
ejpam-5165	21	39	element	element	NOUN
ejpam-5165	21	40	satisfying	satisfy	VERB
ejpam-5165	21	41	a	a	DET
ejpam-5165	21	42	certain	certain	ADJ
ejpam-5165	21	43	condition	condition	NOUN
ejpam-5165	21	44	for	for	ADP
ejpam-5165	21	45	every	every	DET
ejpam-5165	21	46	measurable	measurable	NOUN
ejpam-5165	21	47	set	set	NOUN
ejpam-5165	21	48	[	[	X
ejpam-5165	21	49	10	10	NUM
ejpam-5165	21	50	]	]	PUNCT
ejpam-5165	21	51	.	.	PUNCT
ejpam-5165	22	1	it	it	PRON
ejpam-5165	22	2	is	be	AUX
ejpam-5165	22	3	also	also	ADV
ejpam-5165	22	4	important	important	ADJ
ejpam-5165	22	5	to	to	PART
ejpam-5165	22	6	note	note	VERB
ejpam-5165	22	7	that	that	SCONJ
ejpam-5165	22	8	the	the	DET
ejpam-5165	22	9	convergence	convergence	NOUN
ejpam-5165	22	10	theorems	theorem	VERB
ejpam-5165	22	11	of	of	ADP
ejpam-5165	22	12	the	the	DET
ejpam-5165	22	13	dunford	dunford	PROPN
ejpam-5165	22	14	integral	integral	PROPN
ejpam-5165	22	15	wherein	wherein	NOUN
ejpam-5165	22	16	in	in	ADP
ejpam-5165	22	17	a	a	DET
ejpam-5165	22	18	sequence	sequence	NOUN
ejpam-5165	22	19	of	of	ADP
ejpam-5165	22	20	dunford	dunford	PROPN
ejpam-5165	22	21	integrable	integrable	ADJ
ejpam-5165	22	22	function	function	NOUN
ejpam-5165	22	23	is	be	AUX
ejpam-5165	22	24	uniform	uniform	ADJ
ejpam-5165	22	25	convergent	convergent	NOUN
ejpam-5165	22	26	or	or	CCONJ
ejpam-5165	22	27	weakly	weakly	ADJ
ejpam-5165	22	28	convergent	convergent	NOUN
ejpam-5165	22	29	,	,	PUNCT
ejpam-5165	22	30	weakly	weakly	ADV
ejpam-5165	22	31	monotone	monotone	ADJ
ejpam-5165	22	32	and	and	CCONJ
ejpam-5165	22	33	its	its	PRON
ejpam-5165	22	34	limit	limit	NOUN
ejpam-5165	22	35	exists	exist	VERB
ejpam-5165	22	36	[	[	X
ejpam-5165	22	37	11	11	NUM
ejpam-5165	22	38	]	]	PUNCT
ejpam-5165	22	39	.	.	PUNCT
ejpam-5165	23	1	but	but	CCONJ
ejpam-5165	23	2	gouju	gouju	PROPN
ejpam-5165	23	3	and	and	CCONJ
ejpam-5165	23	4	schwabik	schwabik	PROPN
ejpam-5165	23	5	(	(	PUNCT
ejpam-5165	23	6	2002	2002	NUM
ejpam-5165	23	7	)	)	PUNCT
ejpam-5165	23	8	mentioned	mention	VERB
ejpam-5165	23	9	that	that	SCONJ
ejpam-5165	23	10	the	the	DET
ejpam-5165	23	11	relation	relation	NOUN
ejpam-5165	23	12	between	between	ADP
ejpam-5165	23	13	the	the	DET
ejpam-5165	23	14	pettis	pettis	PROPN
ejpam-5165	23	15	integral	integral	ADJ
ejpam-5165	23	16	and	and	CCONJ
ejpam-5165	23	17	the	the	DET
ejpam-5165	23	18	mcshane	mcshane	PROPN
ejpam-5165	23	19	integral	integral	ADJ
ejpam-5165	23	20	for	for	ADP
ejpam-5165	23	21	arbitrary	arbitrary	ADJ
ejpam-5165	23	22	spaces	space	NOUN
ejpam-5165	23	23	is	be	AUX
ejpam-5165	23	24	unknown	unknown	ADJ
ejpam-5165	23	25	[	[	X
ejpam-5165	23	26	5	5	NUM
ejpam-5165	23	27	]	]	PUNCT
ejpam-5165	23	28	.	.	PUNCT
ejpam-5165	24	1	meanwhile	meanwhile	ADV
ejpam-5165	24	2	,	,	PUNCT
ejpam-5165	24	3	benitez	benitez	PROPN
ejpam-5165	24	4	and	and	CCONJ
ejpam-5165	24	5	flores	flore	VERB
ejpam-5165	25	1	[	[	X
ejpam-5165	25	2	3	3	NUM
ejpam-5165	25	3	]	]	PUNCT
ejpam-5165	25	4	introduced	introduce	VERB
ejpam-5165	25	5	the	the	DET
ejpam-5165	25	6	mcshane	mcshane	NOUN
ejpam-5165	25	7	-	-	PUNCT
ejpam-5165	25	8	stieltjes	stieltjes	NOUN
ejpam-5165	25	9	integral	integral	ADJ
ejpam-5165	25	10	in	in	ADP
ejpam-5165	25	11	banach	banach	NOUN
ejpam-5165	25	12	space	space	NOUN
ejpam-5165	25	13	and	and	CCONJ
ejpam-5165	25	14	provided	provide	VERB
ejpam-5165	25	15	some	some	PRON
ejpam-5165	25	16	of	of	ADP
ejpam-5165	25	17	its	its	PRON
ejpam-5165	25	18	simple	simple	ADJ
ejpam-5165	25	19	properties	property	NOUN
ejpam-5165	25	20	.	.	PUNCT
ejpam-5165	26	1	furthermore	furthermore	ADV
ejpam-5165	26	2	,	,	PUNCT
ejpam-5165	26	3	the	the	DET
ejpam-5165	26	4	applicability	applicability	NOUN
ejpam-5165	26	5	of	of	ADP
ejpam-5165	26	6	this	this	DET
ejpam-5165	26	7	study	study	NOUN
ejpam-5165	26	8	spans	span	VERB
ejpam-5165	26	9	diverse	diverse	ADJ
ejpam-5165	26	10	areas	area	NOUN
ejpam-5165	26	11	,	,	PUNCT
ejpam-5165	26	12	including	include	VERB
ejpam-5165	26	13	the	the	DET
ejpam-5165	26	14	theory	theory	NOUN
ejpam-5165	26	15	of	of	ADP
ejpam-5165	26	16	curve	curve	NOUN
ejpam-5165	26	17	integrals	integral	NOUN
ejpam-5165	26	18	,	,	PUNCT
ejpam-5165	26	19	probability	probability	NOUN
ejpam-5165	26	20	,	,	PUNCT
ejpam-5165	26	21	hysteresis	hysteresis	NOUN
ejpam-5165	26	22	,	,	PUNCT
ejpam-5165	26	23	and	and	CCONJ
ejpam-5165	26	24	functional	functional	ADJ
ejpam-5165	26	25	-	-	PUNCT
ejpam-5165	26	26	differential	differential	ADJ
ejpam-5165	26	27	and	and	CCONJ
ejpam-5165	26	28	generalized	generalized	ADJ
ejpam-5165	26	29	differential	differential	ADJ
ejpam-5165	26	30	equations	equation	NOUN
ejpam-5165	26	31	.	.	PUNCT
ejpam-5165	27	1	2	2	X
ejpam-5165	27	2	.	.	X
ejpam-5165	27	3	preliminaries	preliminary	NOUN
ejpam-5165	27	4	this	this	DET
ejpam-5165	27	5	section	section	NOUN
ejpam-5165	27	6	will	will	AUX
ejpam-5165	27	7	be	be	AUX
ejpam-5165	27	8	discussing	discuss	VERB
ejpam-5165	27	9	essential	essential	ADJ
ejpam-5165	27	10	notions	notion	NOUN
ejpam-5165	27	11	that	that	PRON
ejpam-5165	27	12	are	be	AUX
ejpam-5165	27	13	necessary	necessary	ADJ
ejpam-5165	27	14	in	in	ADP
ejpam-5165	27	15	formulating	formulate	VERB
ejpam-5165	27	16	the	the	DET
ejpam-5165	27	17	mcshane	mcshane	PROPN
ejpam-5165	27	18	-	-	PUNCT
ejpam-5165	27	19	pettis	pettis	PROPN
ejpam-5165	27	20	-	-	PUNCT
ejpam-5165	27	21	stieltjes	stieltjes	NOUN
ejpam-5165	27	22	integral	integral	ADJ
ejpam-5165	27	23	in	in	ADP
ejpam-5165	27	24	a	a	DET
ejpam-5165	27	25	banach	banach	NOUN
ejpam-5165	27	26	space	space	NOUN
ejpam-5165	27	27	.	.	PUNCT
ejpam-5165	28	1	throughout	throughout	ADP
ejpam-5165	28	2	the	the	DET
ejpam-5165	28	3	paper	paper	NOUN
ejpam-5165	28	4	,	,	PUNCT
ejpam-5165	28	5	we	we	PRON
ejpam-5165	28	6	let	let	VERB
ejpam-5165	28	7	x	x	PART
ejpam-5165	28	8	to	to	PART
ejpam-5165	28	9	be	be	AUX
ejpam-5165	28	10	a	a	DET
ejpam-5165	28	11	banach	banach	NOUN
ejpam-5165	28	12	space	space	NOUN
ejpam-5165	28	13	,	,	PUNCT
ejpam-5165	28	14	rn	rn	PROPN
ejpam-5165	28	15	denotes	denote	VERB
ejpam-5165	28	16	the	the	DET
ejpam-5165	28	17	n	n	ADV
ejpam-5165	28	18	-	-	PUNCT
ejpam-5165	28	19	euclidean	euclidean	ADJ
ejpam-5165	28	20	space	space	NOUN
ejpam-5165	28	21	,	,	PUNCT
ejpam-5165	28	22	r+	r+	PRON
ejpam-5165	28	23	is	be	AUX
ejpam-5165	28	24	the	the	DET
ejpam-5165	28	25	set	set	NOUN
ejpam-5165	28	26	of	of	ADP
ejpam-5165	28	27	positive	positive	ADJ
ejpam-5165	28	28	real	real	ADJ
ejpam-5165	28	29	numbers	number	NOUN
ejpam-5165	28	30	,	,	PUNCT
ejpam-5165	29	1	[	[	X
ejpam-5165	29	2	a	a	X
ejpam-5165	29	3	,	,	PUNCT
ejpam-5165	29	4	b	b	NOUN
ejpam-5165	29	5	]	]	X
ejpam-5165	29	6	=	=	PUNCT
ejpam-5165	29	7	n∏	n∏	PROPN
ejpam-5165	29	8	i=1	i=1	X
ejpam-5165	30	1	[	[	X
ejpam-5165	30	2	ai	ai	NOUN
ejpam-5165	30	3	,	,	PUNCT
ejpam-5165	30	4	bi	bi	NOUN
ejpam-5165	30	5	]	]	X
ejpam-5165	30	6	,	,	PUNCT
ejpam-5165	30	7	where	where	SCONJ
ejpam-5165	30	8	−∞	−∞	ADP
ejpam-5165	30	9	<	<	X
ejpam-5165	30	10	ai	ai	VERB
ejpam-5165	30	11	<	<	X
ejpam-5165	30	12	bi	bi	NOUN
ejpam-5165	30	13	<	<	X
ejpam-5165	30	14	∞	∞	PROPN
ejpam-5165	30	15	for	for	ADP
ejpam-5165	30	16	i	i	PRON
ejpam-5165	30	17	=	=	NOUN
ejpam-5165	30	18	1	1	NUM
ejpam-5165	30	19	,	,	PUNCT
ejpam-5165	30	20	·	·	PUNCT
ejpam-5165	30	21	·	·	PUNCT
ejpam-5165	30	22	·	·	PUNCT
ejpam-5165	30	23	,	,	PUNCT
ejpam-5165	30	24	n	n	PART
ejpam-5165	30	25	to	to	PART
ejpam-5165	30	26	be	be	AUX
ejpam-5165	30	27	a	a	DET
ejpam-5165	30	28	compact	compact	ADJ
ejpam-5165	30	29	interval	interval	NOUN
ejpam-5165	30	30	in	in	ADP
ejpam-5165	30	31	rn	rn	PROPN
ejpam-5165	30	32	,	,	PUNCT
ejpam-5165	30	33	in([a	in([a	PROPN
ejpam-5165	30	34	,	,	PUNCT
ejpam-5165	30	35	b	b	NOUN
ejpam-5165	30	36	]	]	X
ejpam-5165	30	37	)	)	PUNCT
ejpam-5165	30	38	is	be	AUX
ejpam-5165	30	39	the	the	DET
ejpam-5165	30	40	collection	collection	NOUN
ejpam-5165	30	41	of	of	ADP
ejpam-5165	30	42	all	all	DET
ejpam-5165	30	43	compact	compact	ADJ
ejpam-5165	30	44	subintervals	subinterval	NOUN
ejpam-5165	30	45	of	of	ADP
ejpam-5165	30	46	[	[	X
ejpam-5165	30	47	a	a	X
ejpam-5165	30	48	,	,	PUNCT
ejpam-5165	30	49	b	b	NOUN
ejpam-5165	30	50	]	]	X
ejpam-5165	30	51	and	and	CCONJ
ejpam-5165	30	52	v	v	X
ejpam-5165	30	53	(	(	PUNCT
ejpam-5165	30	54	[	[	X
ejpam-5165	30	55	u	u	NOUN
ejpam-5165	30	56	,	,	PUNCT
ejpam-5165	30	57	v	v	NOUN
ejpam-5165	30	58	]	]	PUNCT
ejpam-5165	30	59	)	)	PUNCT
ejpam-5165	30	60	is	be	AUX
ejpam-5165	30	61	the	the	DET
ejpam-5165	30	62	collection	collection	NOUN
ejpam-5165	30	63	of	of	ADP
ejpam-5165	30	64	all	all	DET
ejpam-5165	30	65	vertices	vertex	NOUN
ejpam-5165	30	66	of	of	ADP
ejpam-5165	30	67	[	[	X
ejpam-5165	30	68	u	u	NOUN
ejpam-5165	30	69	,	,	PUNCT
ejpam-5165	30	70	v	v	NOUN
ejpam-5165	30	71	]	]	PUNCT
ejpam-5165	30	72	.	.	PUNCT
ejpam-5165	31	1	moreover	moreover	ADV
ejpam-5165	31	2	,	,	PUNCT
ejpam-5165	31	3	rn	rn	PROPN
ejpam-5165	31	4	is	be	AUX
ejpam-5165	31	5	equipped	equip	VERB
ejpam-5165	31	6	with	with	ADP
ejpam-5165	31	7	the	the	DET
ejpam-5165	31	8	maximum	maximum	ADJ
ejpam-5165	31	9	norm	norm	NOUN
ejpam-5165	31	10	∥·∥rn	∥·∥rn	PROPN
ejpam-5165	31	11	.	.	PUNCT
ejpam-5165	32	1	so	so	ADV
ejpam-5165	32	2	,	,	PUNCT
ejpam-5165	32	3	for	for	ADP
ejpam-5165	32	4	each	each	DET
ejpam-5165	32	5	x	x	PROPN
ejpam-5165	32	6	∈	∈	PROPN
ejpam-5165	32	7	rn	rn	PROPN
ejpam-5165	32	8	,	,	PUNCT
ejpam-5165	32	9	we	we	PRON
ejpam-5165	32	10	define	define	VERB
ejpam-5165	32	11	∥·∥	∥·∥	PROPN
ejpam-5165	32	12	the	the	DET
ejpam-5165	32	13	maximum	maximum	ADJ
ejpam-5165	32	14	norm	norm	NOUN
ejpam-5165	32	15	of	of	ADP
ejpam-5165	32	16	x	x	PUNCT
ejpam-5165	32	17	by	by	ADP
ejpam-5165	32	18	∥x∥rn	∥x∥rn	NOUN
ejpam-5165	32	19	=	=	SYM
ejpam-5165	32	20	max{|xi|	max{|xi|	NOUN
ejpam-5165	32	21	:	:	PUNCT
ejpam-5165	32	22	i	i	NOUN
ejpam-5165	32	23	=	=	NOUN
ejpam-5165	32	24	1	1	NUM
ejpam-5165	32	25	,	,	PUNCT
ejpam-5165	32	26	·	·	PUNCT
ejpam-5165	32	27	·	·	PUNCT
ejpam-5165	32	28	·	·	PUNCT
ejpam-5165	32	29	,	,	PUNCT
ejpam-5165	32	30	n	n	CCONJ
ejpam-5165	32	31	}	}	PUNCT
ejpam-5165	32	32	,	,	PUNCT
ejpam-5165	32	33	where	where	SCONJ
ejpam-5165	32	34	x	x	X
ejpam-5165	32	35	=	=	PRON
ejpam-5165	32	36	(	(	PUNCT
ejpam-5165	32	37	x1	x1	PROPN
ejpam-5165	32	38	,	,	PUNCT
ejpam-5165	32	39	·	·	PUNCT
ejpam-5165	32	40	·	·	PUNCT
ejpam-5165	32	41	·	·	PUNCT
ejpam-5165	32	42	,	,	PUNCT
ejpam-5165	32	43	xn	xn	X
ejpam-5165	32	44	)	)	PUNCT
ejpam-5165	32	45	and	and	CCONJ
ejpam-5165	32	46	given	give	VERB
ejpam-5165	32	47	r	r	PROPN
ejpam-5165	32	48	>	>	X
ejpam-5165	32	49	0	0	NUM
ejpam-5165	32	50	,	,	PUNCT
ejpam-5165	32	51	we	we	PRON
ejpam-5165	32	52	set	set	VERB
ejpam-5165	32	53	b(x	b(x	NOUN
ejpam-5165	32	54	,	,	PUNCT
ejpam-5165	32	55	r	r	NOUN
ejpam-5165	32	56	)	)	PUNCT
ejpam-5165	32	57	=	=	SYM
ejpam-5165	32	58	{	{	PUNCT
ejpam-5165	32	59	y	y	PROPN
ejpam-5165	32	60	∈	∈	PROPN
ejpam-5165	32	61	rn	rn	PROPN
ejpam-5165	32	62	:	:	PUNCT
ejpam-5165	33	1	∥x−	∥x−	PROPN
ejpam-5165	33	2	y∥rn	y∥rn	VERB
ejpam-5165	33	3	<	<	X
ejpam-5165	33	4	r	r	X
ejpam-5165	33	5	}	}	PUNCT
ejpam-5165	33	6	,	,	PUNCT
ejpam-5165	33	7	where	where	SCONJ
ejpam-5165	33	8	x−	x−	PROPN
ejpam-5165	33	9	y	y	PROPN
ejpam-5165	33	10	=	=	PRON
ejpam-5165	33	11	(	(	PUNCT
ejpam-5165	33	12	x1	x1	INTJ
ejpam-5165	33	13	−	−	PROPN
ejpam-5165	33	14	y2	y2	PROPN
ejpam-5165	33	15	,	,	PUNCT
ejpam-5165	33	16	x2	x2	PROPN
ejpam-5165	33	17	−	−	PROPN
ejpam-5165	33	18	y2	y2	PROPN
ejpam-5165	33	19	,	,	PUNCT
ejpam-5165	33	20	·	·	PUNCT
ejpam-5165	33	21	·	·	PUNCT
ejpam-5165	33	22	·	·	PUNCT
ejpam-5165	33	23	,	,	PUNCT
ejpam-5165	33	24	xn	xn	PROPN
ejpam-5165	34	1	−	−	PROPN
ejpam-5165	34	2	yn	yn	PROPN
ejpam-5165	34	3	)	)	PUNCT
ejpam-5165	34	4	.	.	PUNCT
ejpam-5165	35	1	definition	definition	NOUN
ejpam-5165	35	2	1	1	NUM
ejpam-5165	35	3	.	.	PUNCT
ejpam-5165	36	1	[	[	X
ejpam-5165	36	2	8	8	NUM
ejpam-5165	36	3	]	]	SYM
ejpam-5165	36	4	two	two	NUM
ejpam-5165	36	5	compact	compact	ADJ
ejpam-5165	36	6	intervals	interval	NOUN
ejpam-5165	36	7	[	[	X
ejpam-5165	36	8	q	q	X
ejpam-5165	36	9	,	,	PUNCT
ejpam-5165	36	10	r	r	NOUN
ejpam-5165	36	11	]	]	X
ejpam-5165	36	12	,	,	PUNCT
ejpam-5165	36	13	[	[	X
ejpam-5165	36	14	s	s	X
ejpam-5165	36	15	,	,	PUNCT
ejpam-5165	36	16	t	t	PROPN
ejpam-5165	36	17	]	]	X
ejpam-5165	36	18	∈	∈	PROPN
ejpam-5165	36	19	rn	rn	PROPN
ejpam-5165	36	20	are	be	AUX
ejpam-5165	36	21	said	say	VERB
ejpam-5165	36	22	to	to	PART
ejpam-5165	36	23	be	be	AUX
ejpam-5165	36	24	non	non	ADJ
ejpam-5165	36	25	-	-	ADJ
ejpam-5165	36	26	overlapping	overlapping	ADJ
ejpam-5165	36	27	if	if	SCONJ
ejpam-5165	36	28	n∏	n∏	PROPN
ejpam-5165	36	29	i=1	i=1	PROPN
ejpam-5165	36	30	(	(	PUNCT
ejpam-5165	36	31	qi	qi	PROPN
ejpam-5165	36	32	,	,	PUNCT
ejpam-5165	36	33	ri	ri	PROPN
ejpam-5165	36	34	)	)	PUNCT
ejpam-5165	36	35	⋂	⋂	PROPN
ejpam-5165	36	36	n∏	n∏	PROPN
ejpam-5165	36	37	i=1	i=1	PROPN
ejpam-5165	36	38	(	(	PUNCT
ejpam-5165	36	39	si	si	X
ejpam-5165	36	40	,	,	PUNCT
ejpam-5165	36	41	ti	ti	NOUN
ejpam-5165	36	42	)	)	PUNCT
ejpam-5165	36	43	=	=	NOUN
ejpam-5165	36	44	∅	∅	NOUN
ejpam-5165	36	45	,	,	PUNCT
ejpam-5165	36	46	where	where	SCONJ
ejpam-5165	36	47	q	q	NOUN
ejpam-5165	36	48	=	=	SYM
ejpam-5165	36	49	(	(	PUNCT
ejpam-5165	36	50	q1	q1	PROPN
ejpam-5165	36	51	,	,	PUNCT
ejpam-5165	36	52	q2	q2	NOUN
ejpam-5165	36	53	,	,	PUNCT
ejpam-5165	36	54	·	·	PUNCT
ejpam-5165	36	55	·	·	PUNCT
ejpam-5165	36	56	·	·	PUNCT
ejpam-5165	36	57	,	,	PUNCT
ejpam-5165	36	58	qn	qn	NOUN
ejpam-5165	36	59	)	)	PUNCT
ejpam-5165	36	60	,	,	PUNCT
ejpam-5165	36	61	r	r	NOUN
ejpam-5165	36	62	=	=	SYM
ejpam-5165	36	63	(	(	PUNCT
ejpam-5165	36	64	r1	r1	PROPN
ejpam-5165	36	65	,	,	PUNCT
ejpam-5165	36	66	r2	r2	PROPN
ejpam-5165	36	67	,	,	PUNCT
ejpam-5165	36	68	·	·	PUNCT
ejpam-5165	36	69	·	·	PUNCT
ejpam-5165	36	70	·	·	PUNCT
ejpam-5165	36	71	,	,	PUNCT
ejpam-5165	36	72	rn	rn	PROPN
ejpam-5165	36	73	)	)	PUNCT
ejpam-5165	36	74	,	,	PUNCT
ejpam-5165	36	75	s	s	NOUN
ejpam-5165	36	76	=	=	PUNCT
ejpam-5165	36	77	(	(	PUNCT
ejpam-5165	36	78	s1	s1	PROPN
ejpam-5165	36	79	,	,	PUNCT
ejpam-5165	36	80	s2	s2	PROPN
ejpam-5165	36	81	,	,	PUNCT
ejpam-5165	36	82	·	·	PUNCT
ejpam-5165	36	83	·	·	PUNCT
ejpam-5165	36	84	·	·	PUNCT
ejpam-5165	36	85	,	,	PUNCT
ejpam-5165	36	86	sn	sn	PROPN
ejpam-5165	36	87	)	)	PUNCT
ejpam-5165	36	88	and	and	CCONJ
ejpam-5165	36	89	t	t	NOUN
ejpam-5165	36	90	=	=	SYM
ejpam-5165	36	91	(	(	PUNCT
ejpam-5165	36	92	t1	t1	NOUN
ejpam-5165	36	93	,	,	PUNCT
ejpam-5165	36	94	t2	t2	NOUN
ejpam-5165	36	95	,	,	PUNCT
ejpam-5165	36	96	·	·	PUNCT
ejpam-5165	36	97	·	·	PUNCT
ejpam-5165	36	98	·	·	PUNCT
ejpam-5165	36	99	,	,	PUNCT
ejpam-5165	36	100	tn	tn	PROPN
ejpam-5165	36	101	)	)	PUNCT
ejpam-5165	36	102	.	.	PUNCT
ejpam-5165	37	1	definition	definition	NOUN
ejpam-5165	37	2	2	2	NUM
ejpam-5165	37	3	.	.	PUNCT
ejpam-5165	38	1	[	[	X
ejpam-5165	38	2	8	8	NUM
ejpam-5165	38	3	]	]	PUNCT
ejpam-5165	38	4	a	a	DET
ejpam-5165	38	5	function	function	NOUN
ejpam-5165	38	6	δ	δ	NOUN
ejpam-5165	38	7	:	:	PUNCT
ejpam-5165	39	1	[	[	X
ejpam-5165	39	2	a	a	X
ejpam-5165	39	3	,	,	PUNCT
ejpam-5165	39	4	b	b	NOUN
ejpam-5165	39	5	]	]	PUNCT
ejpam-5165	39	6	→	→	PUNCT
ejpam-5165	39	7	r+	r+	PRON
ejpam-5165	39	8	is	be	AUX
ejpam-5165	39	9	called	call	VERB
ejpam-5165	39	10	a	a	DET
ejpam-5165	39	11	gauge	gauge	NOUN
ejpam-5165	39	12	on	on	ADP
ejpam-5165	39	13	[	[	X
ejpam-5165	39	14	a	a	X
ejpam-5165	39	15	,	,	PUNCT
ejpam-5165	39	16	b	b	NOUN
ejpam-5165	39	17	]	]	X
ejpam-5165	39	18	.	.	PUNCT
ejpam-5165	40	1	d.	d.	PROPN
ejpam-5165	40	2	omayan	omayan	PROPN
ejpam-5165	40	3	,	,	PUNCT
ejpam-5165	40	4	g.b	g.b	PROPN
ejpam-5165	40	5	.	.	PROPN
ejpam-5165	40	6	flores	flores	PROPN
ejpam-5165	40	7	/	/	SYM
ejpam-5165	40	8	eur	eur	PROPN
ejpam-5165	40	9	.	.	PUNCT
ejpam-5165	41	1	j.	j.	PROPN
ejpam-5165	41	2	pure	pure	PROPN
ejpam-5165	41	3	appl	appl	PROPN
ejpam-5165	41	4	.	.	PROPN
ejpam-5165	41	5	math	math	PROPN
ejpam-5165	41	6	,	,	PUNCT
ejpam-5165	41	7	17	17	NUM
ejpam-5165	41	8	(	(	PUNCT
ejpam-5165	41	9	2	2	NUM
ejpam-5165	41	10	)	)	PUNCT
ejpam-5165	41	11	(	(	PUNCT
ejpam-5165	41	12	2024	2024	NUM
ejpam-5165	41	13	)	)	PUNCT
ejpam-5165	41	14	,	,	PUNCT
ejpam-5165	41	15	1183	1183	NUM
ejpam-5165	41	16	-	-	SYM
ejpam-5165	41	17	1196	1196	NUM
ejpam-5165	41	18	1185	1185	NUM
ejpam-5165	41	19	definition	definition	NOUN
ejpam-5165	41	20	3	3	NUM
ejpam-5165	41	21	.	.	PUNCT
ejpam-5165	42	1	[	[	X
ejpam-5165	42	2	10	10	NUM
ejpam-5165	42	3	]	]	X
ejpam-5165	42	4	a	a	DET
ejpam-5165	42	5	pair	pair	NOUN
ejpam-5165	42	6	(	(	PUNCT
ejpam-5165	42	7	t	t	PROPN
ejpam-5165	42	8	,	,	PUNCT
ejpam-5165	42	9	[	[	X
ejpam-5165	42	10	u	u	NOUN
ejpam-5165	42	11	,	,	PUNCT
ejpam-5165	42	12	v	v	NOUN
ejpam-5165	42	13	]	]	X
ejpam-5165	42	14	)	)	PUNCT
ejpam-5165	42	15	of	of	ADP
ejpam-5165	42	16	a	a	DET
ejpam-5165	42	17	point	point	NOUN
ejpam-5165	42	18	t	t	PROPN
ejpam-5165	42	19	∈	∈	PROPN
ejpam-5165	42	20	rn	rn	PROPN
ejpam-5165	42	21	and	and	CCONJ
ejpam-5165	42	22	a	a	DET
ejpam-5165	42	23	compact	compact	ADJ
ejpam-5165	42	24	interval	interval	NOUN
ejpam-5165	42	25	[	[	X
ejpam-5165	42	26	u	u	NOUN
ejpam-5165	42	27	,	,	PUNCT
ejpam-5165	42	28	v	v	NOUN
ejpam-5165	42	29	]	]	PUNCT
ejpam-5165	42	30	of	of	ADP
ejpam-5165	42	31	rn	rn	PROPN
ejpam-5165	42	32	is	be	AUX
ejpam-5165	42	33	called	call	VERB
ejpam-5165	42	34	a	a	DET
ejpam-5165	42	35	tagged	tag	VERB
ejpam-5165	42	36	interval	interval	NOUN
ejpam-5165	42	37	.	.	PUNCT
ejpam-5165	43	1	here	here	ADV
ejpam-5165	43	2	,	,	PUNCT
ejpam-5165	43	3	t	t	PROPN
ejpam-5165	43	4	is	be	AUX
ejpam-5165	43	5	known	know	VERB
ejpam-5165	43	6	as	as	ADP
ejpam-5165	43	7	the	the	DET
ejpam-5165	43	8	tag	tag	NOUN
ejpam-5165	43	9	of	of	ADP
ejpam-5165	43	10	[	[	X
ejpam-5165	43	11	u	u	NOUN
ejpam-5165	43	12	,	,	PUNCT
ejpam-5165	43	13	v	v	NOUN
ejpam-5165	43	14	]	]	PUNCT
ejpam-5165	43	15	.	.	PUNCT
ejpam-5165	44	1	definition	definition	NOUN
ejpam-5165	44	2	4	4	NUM
ejpam-5165	44	3	.	.	PUNCT
ejpam-5165	45	1	[	[	X
ejpam-5165	45	2	10	10	NUM
ejpam-5165	45	3	]	]	PUNCT
ejpam-5165	45	4	a	a	DET
ejpam-5165	45	5	finite	finite	ADJ
ejpam-5165	45	6	collection	collection	NOUN
ejpam-5165	45	7	{	{	PUNCT
ejpam-5165	45	8	(	(	PUNCT
ejpam-5165	45	9	tk	tk	PROPN
ejpam-5165	45	10	,	,	PUNCT
ejpam-5165	45	11	[	[	X
ejpam-5165	45	12	uk	uk	NOUN
ejpam-5165	45	13	,	,	PUNCT
ejpam-5165	45	14	vk	vk	ADP
ejpam-5165	45	15	]	]	PUNCT
ejpam-5165	45	16	)	)	PUNCT
ejpam-5165	45	17	,	,	PUNCT
ejpam-5165	45	18	k	k	PROPN
ejpam-5165	45	19	=	=	SYM
ejpam-5165	45	20	1	1	NUM
ejpam-5165	45	21	,	,	PUNCT
ejpam-5165	45	22	2	2	NUM
ejpam-5165	45	23	,	,	PUNCT
ejpam-5165	45	24	·	·	PUNCT
ejpam-5165	45	25	·	·	PUNCT
ejpam-5165	45	26	·	·	PUNCT
ejpam-5165	45	27	,	,	PUNCT
ejpam-5165	45	28	p	p	X
ejpam-5165	45	29	}	}	PUNCT
ejpam-5165	45	30	of	of	ADP
ejpam-5165	45	31	pairwise	pairwise	NOUN
ejpam-5165	45	32	nonoverlapping	nonoverlappe	VERB
ejpam-5165	45	33	tagged	tag	VERB
ejpam-5165	45	34	intervals	interval	NOUN
ejpam-5165	45	35	is	be	AUX
ejpam-5165	45	36	called	call	VERB
ejpam-5165	45	37	an	an	DET
ejpam-5165	45	38	m	m	NOUN
ejpam-5165	45	39	-	-	NOUN
ejpam-5165	45	40	system	system	NOUN
ejpam-5165	45	41	in	in	ADP
ejpam-5165	45	42	[	[	X
ejpam-5165	45	43	a	a	DET
ejpam-5165	45	44	,	,	PUNCT
ejpam-5165	45	45	b	b	NOUN
ejpam-5165	45	46	]	]	X
ejpam-5165	45	47	if	if	SCONJ
ejpam-5165	45	48	[	[	X
ejpam-5165	45	49	uk	uk	PROPN
ejpam-5165	45	50	,	,	PUNCT
ejpam-5165	45	51	vk	vk	ADP
ejpam-5165	45	52	]	]	PUNCT
ejpam-5165	45	53	⊆	⊆	NUM
ejpam-5165	45	54	[	[	X
ejpam-5165	45	55	a	a	X
ejpam-5165	45	56	,	,	PUNCT
ejpam-5165	45	57	b	b	NOUN
ejpam-5165	45	58	]	]	X
ejpam-5165	45	59	for	for	ADP
ejpam-5165	45	60	k	k	PROPN
ejpam-5165	45	61	=	=	SYM
ejpam-5165	45	62	1	1	NUM
ejpam-5165	45	63	,	,	PUNCT
ejpam-5165	45	64	2	2	NUM
ejpam-5165	45	65	,	,	PUNCT
ejpam-5165	45	66	·	·	PUNCT
ejpam-5165	45	67	·	·	PUNCT
ejpam-5165	45	68	·	·	PUNCT
ejpam-5165	45	69	,	,	PUNCT
ejpam-5165	46	1	p.	p.	NOUN
ejpam-5165	46	2	definition	definition	NOUN
ejpam-5165	46	3	5	5	NUM
ejpam-5165	46	4	.	.	PUNCT
ejpam-5165	47	1	[	[	X
ejpam-5165	47	2	10	10	NUM
ejpam-5165	47	3	]	]	X
ejpam-5165	47	4	an	an	DET
ejpam-5165	47	5	m	m	NOUN
ejpam-5165	47	6	-system	-system	NOUN
ejpam-5165	47	7	{	{	PUNCT
ejpam-5165	47	8	(	(	PUNCT
ejpam-5165	47	9	tk	tk	PROPN
ejpam-5165	47	10	,	,	PUNCT
ejpam-5165	47	11	[	[	X
ejpam-5165	47	12	uk	uk	NOUN
ejpam-5165	47	13	,	,	PUNCT
ejpam-5165	47	14	vk	vk	ADP
ejpam-5165	47	15	]	]	PUNCT
ejpam-5165	47	16	)	)	PUNCT
ejpam-5165	47	17	,	,	PUNCT
ejpam-5165	47	18	k	k	PROPN
ejpam-5165	47	19	=	=	SYM
ejpam-5165	47	20	1	1	NUM
ejpam-5165	47	21	,	,	PUNCT
ejpam-5165	47	22	2	2	NUM
ejpam-5165	47	23	,	,	PUNCT
ejpam-5165	47	24	·	·	PUNCT
ejpam-5165	47	25	·	·	PUNCT
ejpam-5165	47	26	·	·	PUNCT
ejpam-5165	47	27	,	,	PUNCT
ejpam-5165	47	28	p	p	X
ejpam-5165	47	29	}	}	PUNCT
ejpam-5165	47	30	in	in	ADP
ejpam-5165	47	31	[	[	X
ejpam-5165	47	32	a	a	DET
ejpam-5165	47	33	,	,	PUNCT
ejpam-5165	47	34	b	b	NOUN
ejpam-5165	47	35	]	]	PUNCT
ejpam-5165	47	36	is	be	AUX
ejpam-5165	47	37	called	call	VERB
ejpam-5165	47	38	an	an	DET
ejpam-5165	47	39	m	m	NOUN
ejpam-5165	47	40	-	-	PUNCT
ejpam-5165	47	41	partition	partition	NOUN
ejpam-5165	47	42	of	of	ADP
ejpam-5165	47	43	the	the	DET
ejpam-5165	47	44	interval	interval	NOUN
ejpam-5165	47	45	if	if	SCONJ
ejpam-5165	47	46	p⋃	p⋃	PRON
ejpam-5165	47	47	k=1	k=1	PUNCT
ejpam-5165	48	1	[	[	X
ejpam-5165	48	2	uk	uk	PROPN
ejpam-5165	48	3	,	,	PUNCT
ejpam-5165	48	4	vk	vk	X
ejpam-5165	48	5	]	]	PUNCT
ejpam-5165	48	6	=	=	PUNCT
ejpam-5165	49	1	[	[	X
ejpam-5165	49	2	a	a	X
ejpam-5165	49	3	,	,	PUNCT
ejpam-5165	49	4	b	b	NOUN
ejpam-5165	49	5	]	]	PUNCT
ejpam-5165	49	6	.	.	PUNCT
ejpam-5165	50	1	definition	definition	NOUN
ejpam-5165	50	2	6	6	NUM
ejpam-5165	50	3	.	.	PUNCT
ejpam-5165	51	1	[	[	X
ejpam-5165	51	2	10	10	NUM
ejpam-5165	51	3	]	]	PUNCT
ejpam-5165	51	4	given	give	VERB
ejpam-5165	51	5	a	a	DET
ejpam-5165	51	6	gauge	gauge	NOUN
ejpam-5165	51	7	δ	δ	NOUN
ejpam-5165	51	8	defined	define	VERB
ejpam-5165	51	9	on	on	ADP
ejpam-5165	51	10	{	{	PUNCT
ejpam-5165	51	11	t1	t1	NOUN
ejpam-5165	51	12	,	,	PUNCT
ejpam-5165	51	13	·	·	PUNCT
ejpam-5165	51	14	·	·	PUNCT
ejpam-5165	51	15	·	·	PUNCT
ejpam-5165	51	16	,	,	PUNCT
ejpam-5165	51	17	tp	tp	PART
ejpam-5165	51	18	}	}	PUNCT
ejpam-5165	51	19	,	,	PUNCT
ejpam-5165	51	20	a	a	DET
ejpam-5165	51	21	tagged	tag	VERB
ejpam-5165	51	22	interval	interval	NOUN
ejpam-5165	51	23	(	(	PUNCT
ejpam-5165	51	24	t	t	PROPN
ejpam-5165	51	25	,	,	PUNCT
ejpam-5165	51	26	[	[	X
ejpam-5165	51	27	u	u	NOUN
ejpam-5165	51	28	,	,	PUNCT
ejpam-5165	51	29	v	v	NOUN
ejpam-5165	51	30	]	]	PUNCT
ejpam-5165	51	31	)	)	PUNCT
ejpam-5165	51	32	is	be	AUX
ejpam-5165	51	33	said	say	VERB
ejpam-5165	51	34	to	to	PART
ejpam-5165	51	35	be	be	AUX
ejpam-5165	51	36	δ	δ	NOUN
ejpam-5165	51	37	-	-	ADJ
ejpam-5165	51	38	fine	fine	ADJ
ejpam-5165	51	39	if	if	SCONJ
ejpam-5165	51	40	[	[	X
ejpam-5165	51	41	u	u	NOUN
ejpam-5165	51	42	,	,	PUNCT
ejpam-5165	51	43	v	v	NOUN
ejpam-5165	51	44	]	]	PUNCT
ejpam-5165	51	45	⊆	⊆	NUM
ejpam-5165	51	46	b(t	b(t	NOUN
ejpam-5165	51	47	,	,	PUNCT
ejpam-5165	51	48	δ(t	δ(t	PROPN
ejpam-5165	51	49	)	)	PUNCT
ejpam-5165	51	50	)	)	PUNCT
ejpam-5165	51	51	,	,	PUNCT
ejpam-5165	51	52	where	where	SCONJ
ejpam-5165	51	53	b(t	b(t	NOUN
ejpam-5165	51	54	,	,	PUNCT
ejpam-5165	51	55	δ(t	δ(t	PROPN
ejpam-5165	51	56	)	)	PUNCT
ejpam-5165	51	57	)	)	PUNCT
ejpam-5165	51	58	is	be	AUX
ejpam-5165	51	59	the	the	DET
ejpam-5165	51	60	open	open	ADJ
ejpam-5165	51	61	ball	ball	NOUN
ejpam-5165	51	62	in	in	ADP
ejpam-5165	51	63	rn	rn	PROPN
ejpam-5165	51	64	centered	center	VERB
ejpam-5165	51	65	at	at	ADP
ejpam-5165	51	66	t	t	PROPN
ejpam-5165	51	67	with	with	ADP
ejpam-5165	51	68	radius	radius	NOUN
ejpam-5165	51	69	δ(t	δ(t	PROPN
ejpam-5165	51	70	)	)	PUNCT
ejpam-5165	51	71	.	.	PUNCT
ejpam-5165	52	1	here	here	ADV
ejpam-5165	52	2	,	,	PUNCT
ejpam-5165	52	3	m	m	VERB
ejpam-5165	52	4	-systems	-system	NOUN
ejpam-5165	52	5	or	or	CCONJ
ejpam-5165	52	6	m	m	PROPN
ejpam-5165	52	7	-partitions	-partition	NOUN
ejpam-5165	52	8	are	be	AUX
ejpam-5165	52	9	called	call	VERB
ejpam-5165	52	10	δ	δ	NOUN
ejpam-5165	52	11	-	-	PUNCT
ejpam-5165	52	12	fine	fine	NOUN
ejpam-5165	52	13	if	if	SCONJ
ejpam-5165	52	14	all	all	DET
ejpam-5165	52	15	the	the	DET
ejpam-5165	52	16	tagged	tag	VERB
ejpam-5165	52	17	intervals	interval	NOUN
ejpam-5165	52	18	(	(	PUNCT
ejpam-5165	52	19	tk	tk	PROPN
ejpam-5165	52	20	,	,	PUNCT
ejpam-5165	52	21	[	[	X
ejpam-5165	52	22	uk	uk	NOUN
ejpam-5165	52	23	,	,	PUNCT
ejpam-5165	52	24	vk	vk	ADP
ejpam-5165	52	25	]	]	PUNCT
ejpam-5165	52	26	)	)	PUNCT
ejpam-5165	52	27	,	,	PUNCT
ejpam-5165	52	28	where	where	SCONJ
ejpam-5165	52	29	k	k	PROPN
ejpam-5165	52	30	=	=	SYM
ejpam-5165	52	31	1	1	NUM
ejpam-5165	52	32	,	,	PUNCT
ejpam-5165	52	33	2	2	NUM
ejpam-5165	52	34	,	,	PUNCT
ejpam-5165	52	35	·	·	PUNCT
ejpam-5165	52	36	·	·	PUNCT
ejpam-5165	52	37	·	·	PUNCT
ejpam-5165	52	38	,	,	PUNCT
ejpam-5165	52	39	p	p	X
ejpam-5165	52	40	,	,	PUNCT
ejpam-5165	52	41	are	be	AUX
ejpam-5165	52	42	δ	δ	NOUN
ejpam-5165	52	43	-	-	PUNCT
ejpam-5165	52	44	fine	fine	ADJ
ejpam-5165	52	45	with	with	ADP
ejpam-5165	52	46	respect	respect	NOUN
ejpam-5165	52	47	to	to	ADP
ejpam-5165	52	48	the	the	DET
ejpam-5165	52	49	gauge	gauge	NOUN
ejpam-5165	52	50	δ	δ	PROPN
ejpam-5165	52	51	.	.	PUNCT
ejpam-5165	53	1	for	for	ADP
ejpam-5165	53	2	simplicity	simplicity	NOUN
ejpam-5165	53	3	,	,	PUNCT
ejpam-5165	53	4	we	we	PRON
ejpam-5165	53	5	denote	denote	VERB
ejpam-5165	53	6	{	{	PUNCT
ejpam-5165	53	7	(	(	PUNCT
ejpam-5165	53	8	tk	tk	PROPN
ejpam-5165	53	9	,	,	PUNCT
ejpam-5165	53	10	[	[	X
ejpam-5165	53	11	uk	uk	NOUN
ejpam-5165	53	12	,	,	PUNCT
ejpam-5165	53	13	vk	vk	ADP
ejpam-5165	53	14	]	]	PUNCT
ejpam-5165	53	15	)	)	PUNCT
ejpam-5165	53	16	,	,	PUNCT
ejpam-5165	53	17	k	k	PROPN
ejpam-5165	54	1	=	=	SYM
ejpam-5165	54	2	1	1	NUM
ejpam-5165	54	3	,	,	PUNCT
ejpam-5165	54	4	2	2	NUM
ejpam-5165	54	5	,	,	PUNCT
ejpam-5165	54	6	·	·	PUNCT
ejpam-5165	54	7	·	·	PUNCT
ejpam-5165	54	8	·	·	PUNCT
ejpam-5165	54	9	,	,	PUNCT
ejpam-5165	54	10	p	p	X
ejpam-5165	54	11	}	}	PUNCT
ejpam-5165	54	12	by	by	ADP
ejpam-5165	54	13	{	{	PUNCT
ejpam-5165	54	14	(	(	PUNCT
ejpam-5165	54	15	t	t	PROPN
ejpam-5165	54	16	,	,	PUNCT
ejpam-5165	54	17	[	[	X
ejpam-5165	54	18	u	u	NOUN
ejpam-5165	54	19	,	,	PUNCT
ejpam-5165	54	20	v	v	NOUN
ejpam-5165	54	21	]	]	X
ejpam-5165	54	22	)	)	PUNCT
ejpam-5165	54	23	}	}	PUNCT
ejpam-5165	54	24	.	.	PUNCT
ejpam-5165	55	1	definition	definition	NOUN
ejpam-5165	55	2	7	7	NUM
ejpam-5165	55	3	.	.	PUNCT
ejpam-5165	56	1	[	[	X
ejpam-5165	56	2	12	12	NUM
ejpam-5165	56	3	]	]	PUNCT
ejpam-5165	56	4	let	let	VERB
ejpam-5165	56	5	δ	δ	PRON
ejpam-5165	56	6	be	be	AUX
ejpam-5165	56	7	a	a	DET
ejpam-5165	56	8	gauge	gauge	NOUN
ejpam-5165	56	9	defined	define	VERB
ejpam-5165	56	10	on	on	ADP
ejpam-5165	56	11	{	{	PUNCT
ejpam-5165	56	12	t	t	NOUN
ejpam-5165	56	13	}	}	PUNCT
ejpam-5165	56	14	.	.	PUNCT
ejpam-5165	57	1	an	an	DET
ejpam-5165	57	2	m	m	NOUN
ejpam-5165	57	3	-	-	NOUN
ejpam-5165	57	4	system	system	NOUN
ejpam-5165	57	5	p	p	NOUN
ejpam-5165	57	6	=	=	X
ejpam-5165	57	7	{	{	PUNCT
ejpam-5165	57	8	(	(	PUNCT
ejpam-5165	57	9	t	t	PROPN
ejpam-5165	57	10	,	,	PUNCT
ejpam-5165	57	11	[	[	X
ejpam-5165	57	12	u	u	NOUN
ejpam-5165	57	13	,	,	PUNCT
ejpam-5165	57	14	v	v	NOUN
ejpam-5165	57	15	]	]	PUNCT
ejpam-5165	57	16	)	)	PUNCT
ejpam-5165	57	17	}	}	PUNCT
ejpam-5165	57	18	is	be	AUX
ejpam-5165	57	19	said	say	VERB
ejpam-5165	57	20	to	to	PART
ejpam-5165	57	21	be	be	AUX
ejpam-5165	57	22	a	a	DET
ejpam-5165	57	23	δ	δ	NOUN
ejpam-5165	57	24	-	-	PUNCT
ejpam-5165	57	25	fine	fine	ADJ
ejpam-5165	57	26	division	division	NOUN
ejpam-5165	57	27	of	of	ADP
ejpam-5165	57	28	[	[	X
ejpam-5165	57	29	a	a	X
ejpam-5165	57	30	,	,	PUNCT
ejpam-5165	57	31	b	b	NOUN
ejpam-5165	57	32	]	]	X
ejpam-5165	57	33	if	if	SCONJ
ejpam-5165	57	34	t	t	PROPN
ejpam-5165	57	35	∈	∈	PROPN
ejpam-5165	57	36	[	[	X
ejpam-5165	57	37	u	u	NOUN
ejpam-5165	57	38	,	,	PUNCT
ejpam-5165	57	39	v	v	NOUN
ejpam-5165	57	40	]	]	PUNCT
ejpam-5165	57	41	⊆	⊆	NUM
ejpam-5165	57	42	b(t	b(t	NOUN
ejpam-5165	57	43	,	,	PUNCT
ejpam-5165	57	44	δ(t	δ(t	PROPN
ejpam-5165	57	45	)	)	PUNCT
ejpam-5165	57	46	)	)	PUNCT
ejpam-5165	57	47	.	.	PUNCT
ejpam-5165	58	1	lemma	lemma	PROPN
ejpam-5165	58	2	1	1	NUM
ejpam-5165	58	3	.	.	PUNCT
ejpam-5165	59	1	[	[	X
ejpam-5165	59	2	8	8	NUM
ejpam-5165	59	3	]	]	X
ejpam-5165	59	4	(	(	PUNCT
ejpam-5165	59	5	cousin	cousin	PROPN
ejpam-5165	59	6	’s	’s	PART
ejpam-5165	59	7	lemma	lemma	PROPN
ejpam-5165	59	8	)	)	PUNCT
ejpam-5165	59	9	if	if	SCONJ
ejpam-5165	59	10	δ	δ	PROPN
ejpam-5165	59	11	is	be	AUX
ejpam-5165	59	12	a	a	DET
ejpam-5165	59	13	gauge	gauge	NOUN
ejpam-5165	59	14	on	on	ADP
ejpam-5165	59	15	[	[	X
ejpam-5165	59	16	a	a	X
ejpam-5165	59	17	,	,	PUNCT
ejpam-5165	59	18	b	b	NOUN
ejpam-5165	59	19	]	]	X
ejpam-5165	59	20	,	,	PUNCT
ejpam-5165	59	21	then	then	ADV
ejpam-5165	59	22	there	there	PRON
ejpam-5165	59	23	exists	exist	VERB
ejpam-5165	59	24	a	a	DET
ejpam-5165	59	25	δ	δ	NOUN
ejpam-5165	59	26	-	-	PUNCT
ejpam-5165	59	27	fine	fine	ADJ
ejpam-5165	59	28	m	m	NOUN
ejpam-5165	59	29	-	-	NOUN
ejpam-5165	59	30	partition	partition	NOUN
ejpam-5165	59	31	of	of	ADP
ejpam-5165	59	32	[	[	X
ejpam-5165	59	33	a	a	X
ejpam-5165	59	34	,	,	PUNCT
ejpam-5165	59	35	b	b	NOUN
ejpam-5165	59	36	]	]	PUNCT
ejpam-5165	59	37	.	.	PUNCT
ejpam-5165	60	1	definition	definition	NOUN
ejpam-5165	60	2	8	8	NUM
ejpam-5165	60	3	.	.	PUNCT
ejpam-5165	61	1	[	[	X
ejpam-5165	61	2	8	8	NUM
ejpam-5165	61	3	]	]	PUNCT
ejpam-5165	61	4	let	let	VERB
ejpam-5165	61	5	g	g	NOUN
ejpam-5165	61	6	:	:	PUNCT
ejpam-5165	61	7	[	[	X
ejpam-5165	61	8	a	a	X
ejpam-5165	61	9	,	,	PUNCT
ejpam-5165	61	10	b	b	NOUN
ejpam-5165	61	11	]	]	X
ejpam-5165	61	12	→	→	PUNCT
ejpam-5165	61	13	r.	r.	X
ejpam-5165	61	14	the	the	DET
ejpam-5165	61	15	total	total	ADJ
ejpam-5165	61	16	variation	variation	NOUN
ejpam-5165	61	17	of	of	ADP
ejpam-5165	61	18	g	g	NOUN
ejpam-5165	61	19	over	over	ADP
ejpam-5165	61	20	[	[	X
ejpam-5165	61	21	a	a	DET
ejpam-5165	61	22	,	,	PUNCT
ejpam-5165	61	23	b	b	NOUN
ejpam-5165	61	24	]	]	PUNCT
ejpam-5165	61	25	is	be	AUX
ejpam-5165	61	26	given	give	VERB
ejpam-5165	61	27	by	by	ADP
ejpam-5165	61	28	v	v	NOUN
ejpam-5165	61	29	ar(g	ar(g	PROPN
ejpam-5165	61	30	,	,	PUNCT
ejpam-5165	62	1	[	[	X
ejpam-5165	62	2	a	a	X
ejpam-5165	62	3	,	,	PUNCT
ejpam-5165	62	4	b	b	NOUN
ejpam-5165	62	5	]	]	X
ejpam-5165	62	6	)	)	PUNCT
ejpam-5165	62	7	=	=	SYM
ejpam-5165	62	8	sup	sup	NOUN
ejpam-5165	62	9	{	{	PUNCT
ejpam-5165	62	10	∑	∑	PROPN
ejpam-5165	62	11	[	[	X
ejpam-5165	62	12	u	u	NOUN
ejpam-5165	62	13	,	,	PUNCT
ejpam-5165	62	14	v]∈d	v]∈d	PROPN
ejpam-5165	62	15	|∆g([u	|∆g([u	PROPN
ejpam-5165	62	16	,	,	PUNCT
ejpam-5165	62	17	v])|	v])|	NOUN
ejpam-5165	62	18	:	:	PUNCT
ejpam-5165	62	19	d	d	X
ejpam-5165	62	20	is	be	AUX
ejpam-5165	62	21	a	a	DET
ejpam-5165	62	22	partition	partition	NOUN
ejpam-5165	62	23	of	of	ADP
ejpam-5165	62	24	[	[	X
ejpam-5165	62	25	a	a	X
ejpam-5165	62	26	,	,	PUNCT
ejpam-5165	62	27	b	b	NOUN
ejpam-5165	62	28	]	]	X
ejpam-5165	62	29	}	}	PUNCT
ejpam-5165	62	30	where	where	SCONJ
ejpam-5165	62	31	∆g([u	∆g([u	NOUN
ejpam-5165	62	32	,	,	PUNCT
ejpam-5165	62	33	v	v	NOUN
ejpam-5165	62	34	]	]	X
ejpam-5165	62	35	)	)	PUNCT
ejpam-5165	62	36	=	=	PUNCT
ejpam-5165	63	1	∑	∑	X
ejpam-5165	63	2	t∈v	t∈v	X
ejpam-5165	63	3	(	(	PUNCT
ejpam-5165	63	4	[	[	X
ejpam-5165	63	5	u	u	NOUN
ejpam-5165	63	6	,	,	PUNCT
ejpam-5165	63	7	v	v	NOUN
ejpam-5165	63	8	]	]	X
ejpam-5165	63	9	)	)	PUNCT
ejpam-5165	63	10	(	(	PUNCT
ejpam-5165	63	11	g(t	g(t	PROPN
ejpam-5165	63	12	)	)	PUNCT
ejpam-5165	63	13	n∏	n∏	PROPN
ejpam-5165	64	1	k=1	k=1	X
ejpam-5165	64	2	(	(	PUNCT
ejpam-5165	64	3	−1)χ{uk}(tk	−1)χ{uk}(tk	NOUN
ejpam-5165	64	4	)	)	PUNCT
ejpam-5165	64	5	)	)	PUNCT
ejpam-5165	65	1	(	(	PUNCT
ejpam-5165	65	2	⋆	⋆	NOUN
ejpam-5165	65	3	)	)	PUNCT
ejpam-5165	65	4	and	and	CCONJ
ejpam-5165	65	5	[	[	X
ejpam-5165	65	6	u	u	NOUN
ejpam-5165	65	7	,	,	PUNCT
ejpam-5165	65	8	v	v	NOUN
ejpam-5165	65	9	]	]	X
ejpam-5165	65	10	∈	∈	NOUN
ejpam-5165	65	11	in	in	ADP
ejpam-5165	65	12	(	(	PUNCT
ejpam-5165	65	13	[	[	X
ejpam-5165	65	14	a	a	X
ejpam-5165	65	15	,	,	PUNCT
ejpam-5165	65	16	b	b	NOUN
ejpam-5165	65	17	]	]	PUNCT
ejpam-5165	65	18	)	)	PUNCT
ejpam-5165	65	19	.	.	PUNCT
ejpam-5165	66	1	definition	definition	NOUN
ejpam-5165	66	2	9	9	NUM
ejpam-5165	66	3	.	.	PUNCT
ejpam-5165	67	1	[	[	X
ejpam-5165	67	2	8	8	X
ejpam-5165	67	3	]	]	X
ejpam-5165	67	4	a	a	DET
ejpam-5165	67	5	function	function	NOUN
ejpam-5165	67	6	g	g	NOUN
ejpam-5165	67	7	:	:	PUNCT
ejpam-5165	68	1	[	[	X
ejpam-5165	68	2	a	a	X
ejpam-5165	68	3	,	,	PUNCT
ejpam-5165	68	4	b	b	NOUN
ejpam-5165	68	5	]	]	X
ejpam-5165	68	6	→	→	PUNCT
ejpam-5165	68	7	r	r	NOUN
ejpam-5165	68	8	is	be	AUX
ejpam-5165	68	9	said	say	VERB
ejpam-5165	68	10	to	to	PART
ejpam-5165	68	11	be	be	AUX
ejpam-5165	68	12	of	of	ADP
ejpam-5165	68	13	bounded	bounded	ADJ
ejpam-5165	68	14	variation	variation	NOUN
ejpam-5165	68	15	on	on	ADP
ejpam-5165	68	16	[	[	X
ejpam-5165	68	17	a	a	X
ejpam-5165	68	18	,	,	PUNCT
ejpam-5165	68	19	b	b	NOUN
ejpam-5165	68	20	]	]	X
ejpam-5165	68	21	if	if	SCONJ
ejpam-5165	68	22	v	v	NOUN
ejpam-5165	68	23	ar(g	ar(g	PROPN
ejpam-5165	68	24	,	,	PUNCT
ejpam-5165	68	25	[	[	X
ejpam-5165	68	26	a	a	X
ejpam-5165	68	27	,	,	PUNCT
ejpam-5165	68	28	b	b	NOUN
ejpam-5165	68	29	]	]	X
ejpam-5165	68	30	)	)	PUNCT
ejpam-5165	68	31	is	be	AUX
ejpam-5165	68	32	finite	finite	ADJ
ejpam-5165	68	33	.	.	PUNCT
ejpam-5165	69	1	definition	definition	NOUN
ejpam-5165	69	2	10	10	NUM
ejpam-5165	69	3	.	.	PUNCT
ejpam-5165	70	1	[	[	X
ejpam-5165	70	2	2	2	X
ejpam-5165	70	3	]	]	PUNCT
ejpam-5165	70	4	let	let	VERB
ejpam-5165	70	5	f	f	PRON
ejpam-5165	70	6	be	be	AUX
ejpam-5165	70	7	banach	banach	ADV
ejpam-5165	70	8	-	-	PUNCT
ejpam-5165	70	9	valued	value	VERB
ejpam-5165	70	10	function	function	NOUN
ejpam-5165	70	11	defined	define	VERB
ejpam-5165	70	12	on	on	ADP
ejpam-5165	70	13	[	[	X
ejpam-5165	70	14	a	a	X
ejpam-5165	70	15	,	,	PUNCT
ejpam-5165	70	16	b	b	NOUN
ejpam-5165	70	17	]	]	PUNCT
ejpam-5165	70	18	and	and	CCONJ
ejpam-5165	70	19	g	g	PROPN
ejpam-5165	70	20	be	be	AUX
ejpam-5165	70	21	a	a	DET
ejpam-5165	70	22	realvalued	realvalue	VERB
ejpam-5165	70	23	function	function	NOUN
ejpam-5165	70	24	defined	define	VERB
ejpam-5165	70	25	[	[	PUNCT
ejpam-5165	70	26	a	a	PRON
ejpam-5165	70	27	,	,	PUNCT
ejpam-5165	70	28	b	b	NOUN
ejpam-5165	70	29	]	]	X
ejpam-5165	70	30	.	.	PUNCT
ejpam-5165	71	1	a	a	DET
ejpam-5165	71	2	function	function	NOUN
ejpam-5165	71	3	f	f	PROPN
ejpam-5165	71	4	is	be	AUX
ejpam-5165	71	5	said	say	VERB
ejpam-5165	71	6	to	to	PART
ejpam-5165	71	7	be	be	AUX
ejpam-5165	71	8	mcshane	mcshane	NOUN
ejpam-5165	71	9	-	-	PUNCT
ejpam-5165	71	10	stieltjes	stieltjes	NOUN
ejpam-5165	71	11	integrable	integrable	ADJ
ejpam-5165	71	12	,	,	PUNCT
ejpam-5165	71	13	or	or	CCONJ
ejpam-5165	71	14	simply	simply	ADV
ejpam-5165	71	15	ms	ms	PROPN
ejpam-5165	71	16	-	-	PUNCT
ejpam-5165	71	17	integrable	integrable	ADJ
ejpam-5165	71	18	,	,	PUNCT
ejpam-5165	71	19	with	with	ADP
ejpam-5165	71	20	respect	respect	NOUN
ejpam-5165	71	21	to	to	ADP
ejpam-5165	71	22	g	g	NOUN
ejpam-5165	71	23	on	on	ADP
ejpam-5165	71	24	[	[	X
ejpam-5165	71	25	a	a	X
ejpam-5165	71	26	,	,	PUNCT
ejpam-5165	71	27	b	b	NOUN
ejpam-5165	71	28	]	]	X
ejpam-5165	71	29	if	if	SCONJ
ejpam-5165	71	30	there	there	PRON
ejpam-5165	71	31	exists	exist	VERB
ejpam-5165	71	32	j	j	PROPN
ejpam-5165	71	33	∈	∈	PROPN
ejpam-5165	71	34	x	x	PUNCT
ejpam-5165	71	35	with	with	ADP
ejpam-5165	71	36	the	the	DET
ejpam-5165	71	37	following	follow	VERB
ejpam-5165	71	38	property	property	NOUN
ejpam-5165	71	39	:	:	PUNCT
ejpam-5165	71	40	for	for	ADP
ejpam-5165	71	41	each	each	DET
ejpam-5165	71	42	ε	ε	PROPN
ejpam-5165	71	43	>	>	X
ejpam-5165	71	44	0	0	PUNCT
ejpam-5165	72	1	there	there	PRON
ejpam-5165	72	2	is	be	VERB
ejpam-5165	72	3	a	a	DET
ejpam-5165	72	4	gauge	gauge	NOUN
ejpam-5165	72	5	δ	δ	NOUN
ejpam-5165	72	6	such	such	ADJ
ejpam-5165	72	7	that	that	PRON
ejpam-5165	72	8	for	for	ADP
ejpam-5165	72	9	every	every	DET
ejpam-5165	72	10	δ	δ	PROPN
ejpam-5165	72	11	-	-	PUNCT
ejpam-5165	72	12	fine	fine	ADJ
ejpam-5165	72	13	m	m	NOUN
ejpam-5165	72	14	-	-	NOUN
ejpam-5165	72	15	partition	partition	NOUN
ejpam-5165	72	16	p	p	NOUN
ejpam-5165	72	17	=	=	X
ejpam-5165	72	18	{	{	PUNCT
ejpam-5165	72	19	(	(	PUNCT
ejpam-5165	72	20	t	t	PROPN
ejpam-5165	72	21	,	,	PUNCT
ejpam-5165	72	22	[	[	X
ejpam-5165	72	23	u	u	NOUN
ejpam-5165	72	24	,	,	PUNCT
ejpam-5165	72	25	v	v	NOUN
ejpam-5165	72	26	]	]	X
ejpam-5165	72	27	)	)	PUNCT
ejpam-5165	72	28	}	}	PUNCT
ejpam-5165	72	29	of	of	ADP
ejpam-5165	72	30	[	[	X
ejpam-5165	72	31	a	a	X
ejpam-5165	72	32	,	,	PUNCT
ejpam-5165	72	33	b	b	NOUN
ejpam-5165	72	34	]	]	X
ejpam-5165	72	35	the	the	DET
ejpam-5165	72	36	inequality∥∥∥∥∥∥	inequality∥∥∥∥∥∥	PROPN
ejpam-5165	72	37	∑	∑	PUNCT
ejpam-5165	72	38	(	(	PUNCT
ejpam-5165	72	39	t,[u	t,[u	ADJ
ejpam-5165	72	40	,	,	PUNCT
ejpam-5165	72	41	v])∈p	v])∈p	PROPN
ejpam-5165	72	42	f(t)∆g([u	f(t)∆g([u	PROPN
ejpam-5165	72	43	,	,	PUNCT
ejpam-5165	72	44	v])−	v])−	PROPN
ejpam-5165	72	45	j	j	PROPN
ejpam-5165	72	46	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-5165	73	1	x	x	X
ejpam-5165	73	2	<	<	X
ejpam-5165	73	3	ε	ε	PROPN
ejpam-5165	73	4	d.	d.	PROPN
ejpam-5165	73	5	omayan	omayan	PROPN
ejpam-5165	73	6	,	,	PUNCT
ejpam-5165	73	7	g.b	g.b	PROPN
ejpam-5165	73	8	.	.	PROPN
ejpam-5165	73	9	flores	flores	PROPN
ejpam-5165	73	10	/	/	SYM
ejpam-5165	73	11	eur	eur	PROPN
ejpam-5165	73	12	.	.	PUNCT
ejpam-5165	74	1	j.	j.	PROPN
ejpam-5165	74	2	pure	pure	PROPN
ejpam-5165	74	3	appl	appl	PROPN
ejpam-5165	74	4	.	.	PROPN
ejpam-5165	74	5	math	math	PROPN
ejpam-5165	74	6	,	,	PUNCT
ejpam-5165	74	7	17	17	NUM
ejpam-5165	74	8	(	(	PUNCT
ejpam-5165	74	9	2	2	NUM
ejpam-5165	74	10	)	)	PUNCT
ejpam-5165	74	11	(	(	PUNCT
ejpam-5165	74	12	2024	2024	NUM
ejpam-5165	74	13	)	)	PUNCT
ejpam-5165	74	14	,	,	PUNCT
ejpam-5165	74	15	1183	1183	NUM
ejpam-5165	74	16	-	-	SYM
ejpam-5165	74	17	1196	1196	NUM
ejpam-5165	74	18	1186	1186	NUM
ejpam-5165	74	19	holds	hold	NOUN
ejpam-5165	74	20	.	.	PUNCT
ejpam-5165	75	1	in	in	ADP
ejpam-5165	75	2	this	this	DET
ejpam-5165	75	3	case	case	NOUN
ejpam-5165	75	4	,	,	PUNCT
ejpam-5165	75	5	the	the	DET
ejpam-5165	75	6	mcshane	mcshane	NOUN
ejpam-5165	75	7	-	-	PUNCT
ejpam-5165	75	8	stieltjes	stieltjes	PROPN
ejpam-5165	75	9	integral	integral	ADJ
ejpam-5165	75	10	is	be	AUX
ejpam-5165	75	11	j	j	PROPN
ejpam-5165	75	12	=	=	SYM
ejpam-5165	75	13	(	(	PUNCT
ejpam-5165	75	14	ms	ms	PROPN
ejpam-5165	75	15	)	)	PUNCT
ejpam-5165	75	16	∫	∫	PROPN
ejpam-5165	76	1	[	[	X
ejpam-5165	76	2	a	a	X
ejpam-5165	76	3	,	,	PUNCT
ejpam-5165	76	4	b	b	NOUN
ejpam-5165	76	5	]	]	X
ejpam-5165	76	6	fdg	fdg	PROPN
ejpam-5165	76	7	.	.	PROPN
ejpam-5165	77	1	for	for	ADP
ejpam-5165	77	2	brevity	brevity	NOUN
ejpam-5165	77	3	,	,	PUNCT
ejpam-5165	77	4	denote	denote	VERB
ejpam-5165	77	5	s(f	s(f	PROPN
ejpam-5165	77	6	,	,	PUNCT
ejpam-5165	77	7	g	g	NOUN
ejpam-5165	77	8	,	,	PUNCT
ejpam-5165	77	9	p	p	NOUN
ejpam-5165	77	10	)	)	PUNCT
ejpam-5165	78	1	=	=	SYM
ejpam-5165	78	2	∑	∑	PUNCT
ejpam-5165	78	3	(	(	PUNCT
ejpam-5165	78	4	t,[u	t,[u	ADJ
ejpam-5165	78	5	,	,	PUNCT
ejpam-5165	78	6	v])∈p	v])∈p	PROPN
ejpam-5165	78	7	f(t)∆g([u	f(t)∆g([u	PROPN
ejpam-5165	78	8	,	,	PUNCT
ejpam-5165	78	9	v	v	NOUN
ejpam-5165	78	10	]	]	PUNCT
ejpam-5165	78	11	)	)	PUNCT
ejpam-5165	78	12	and	and	CCONJ
ejpam-5165	78	13	ms([a	ms([a	PROPN
ejpam-5165	78	14	,	,	PUNCT
ejpam-5165	78	15	b	b	NOUN
ejpam-5165	78	16	]	]	X
ejpam-5165	78	17	,	,	PUNCT
ejpam-5165	78	18	g	g	NOUN
ejpam-5165	78	19	)	)	PUNCT
ejpam-5165	78	20	be	be	VERB
ejpam-5165	78	21	the	the	DET
ejpam-5165	78	22	collection	collection	NOUN
ejpam-5165	78	23	of	of	ADP
ejpam-5165	78	24	msintegrable	msintegrable	ADJ
ejpam-5165	78	25	function	function	NOUN
ejpam-5165	78	26	with	with	ADP
ejpam-5165	78	27	respect	respect	NOUN
ejpam-5165	78	28	to	to	ADP
ejpam-5165	78	29	g	g	NOUN
ejpam-5165	78	30	on	on	ADP
ejpam-5165	78	31	[	[	X
ejpam-5165	78	32	a	a	X
ejpam-5165	78	33	,	,	PUNCT
ejpam-5165	78	34	b	b	NOUN
ejpam-5165	78	35	]	]	PUNCT
ejpam-5165	78	36	.	.	PUNCT
ejpam-5165	79	1	definition	definition	NOUN
ejpam-5165	79	2	11	11	NUM
ejpam-5165	79	3	.	.	PUNCT
ejpam-5165	80	1	[	[	X
ejpam-5165	80	2	3	3	X
ejpam-5165	80	3	]	]	PUNCT
ejpam-5165	80	4	let	let	VERB
ejpam-5165	80	5	f	f	NOUN
ejpam-5165	80	6	:	:	PUNCT
ejpam-5165	81	1	[	[	X
ejpam-5165	81	2	a	a	X
ejpam-5165	81	3	,	,	PUNCT
ejpam-5165	81	4	b	b	NOUN
ejpam-5165	81	5	]	]	X
ejpam-5165	81	6	→	→	SYM
ejpam-5165	81	7	x	x	X
ejpam-5165	81	8	and	and	CCONJ
ejpam-5165	81	9	g	g	NOUN
ejpam-5165	81	10	:	:	PUNCT
ejpam-5165	82	1	[	[	X
ejpam-5165	82	2	a	a	X
ejpam-5165	82	3	,	,	PUNCT
ejpam-5165	82	4	b	b	NOUN
ejpam-5165	82	5	]	]	X
ejpam-5165	82	6	→	→	PUNCT
ejpam-5165	82	7	r	r	NOUN
ejpam-5165	82	8	be	be	AUX
ejpam-5165	82	9	a	a	DET
ejpam-5165	82	10	function	function	NOUN
ejpam-5165	82	11	.	.	PUNCT
ejpam-5165	83	1	we	we	PRON
ejpam-5165	83	2	say	say	VERB
ejpam-5165	83	3	that	that	SCONJ
ejpam-5165	83	4	f	f	PROPN
ejpam-5165	83	5	is	be	AUX
ejpam-5165	83	6	pul	pul	NOUN
ejpam-5165	83	7	-	-	PUNCT
ejpam-5165	83	8	stieltjes	stieltjes	NOUN
ejpam-5165	83	9	integrable	integrable	ADJ
ejpam-5165	83	10	to	to	ADP
ejpam-5165	83	11	a	a	DET
ejpam-5165	83	12	∈	∈	NOUN
ejpam-5165	83	13	x	x	PUNCT
ejpam-5165	83	14	with	with	ADP
ejpam-5165	83	15	respect	respect	NOUN
ejpam-5165	83	16	to	to	ADP
ejpam-5165	83	17	g	g	NOUN
ejpam-5165	83	18	on	on	ADP
ejpam-5165	83	19	[	[	X
ejpam-5165	83	20	a	a	X
ejpam-5165	83	21	,	,	PUNCT
ejpam-5165	83	22	b	b	NOUN
ejpam-5165	83	23	]	]	X
ejpam-5165	83	24	if	if	SCONJ
ejpam-5165	83	25	for	for	ADP
ejpam-5165	83	26	every	every	DET
ejpam-5165	83	27	ε	ε	PROPN
ejpam-5165	83	28	>	>	X
ejpam-5165	83	29	0	0	PROPN
ejpam-5165	83	30	,	,	PUNCT
ejpam-5165	83	31	there	there	PRON
ejpam-5165	83	32	exists	exist	VERB
ejpam-5165	83	33	a	a	DET
ejpam-5165	83	34	gauge	gauge	NOUN
ejpam-5165	83	35	δ	δ	NOUN
ejpam-5165	83	36	on	on	ADP
ejpam-5165	83	37	[	[	X
ejpam-5165	83	38	a	a	DET
ejpam-5165	83	39	,	,	PUNCT
ejpam-5165	83	40	b	b	NOUN
ejpam-5165	83	41	]	]	X
ejpam-5165	83	42	such	such	ADJ
ejpam-5165	83	43	that	that	PRON
ejpam-5165	83	44	for	for	ADP
ejpam-5165	83	45	every	every	DET
ejpam-5165	83	46	δ	δ	PROPN
ejpam-5165	83	47	-	-	PUNCT
ejpam-5165	83	48	fine	fine	ADJ
ejpam-5165	83	49	division	division	NOUN
ejpam-5165	83	50	d	d	NOUN
ejpam-5165	83	51	of	of	ADP
ejpam-5165	83	52	[	[	X
ejpam-5165	83	53	a	a	X
ejpam-5165	83	54	,	,	PUNCT
ejpam-5165	83	55	b	b	NOUN
ejpam-5165	83	56	]	]	X
ejpam-5165	83	57	,	,	PUNCT
ejpam-5165	83	58	we	we	PRON
ejpam-5165	83	59	have	have	VERB
ejpam-5165	83	60	∥s(f	∥s(f	ADJ
ejpam-5165	83	61	,	,	PUNCT
ejpam-5165	83	62	g	g	PROPN
ejpam-5165	83	63	,	,	PUNCT
ejpam-5165	84	1	d)−a)∥	d)−a)∥	PROPN
ejpam-5165	84	2	<	<	X
ejpam-5165	84	3	ε	ε	PROPN
ejpam-5165	84	4	.	.	PUNCT
ejpam-5165	85	1	in	in	ADP
ejpam-5165	85	2	this	this	DET
ejpam-5165	85	3	case	case	NOUN
ejpam-5165	85	4	,	,	PUNCT
ejpam-5165	85	5	a	a	PRON
ejpam-5165	85	6	is	be	AUX
ejpam-5165	85	7	the	the	DET
ejpam-5165	85	8	pul	pul	NOUN
ejpam-5165	85	9	-	-	PUNCT
ejpam-5165	85	10	stieltjes	stieltjes	NOUN
ejpam-5165	85	11	integral	integral	ADJ
ejpam-5165	85	12	of	of	ADP
ejpam-5165	85	13	f	f	PROPN
ejpam-5165	85	14	with	with	ADP
ejpam-5165	85	15	respect	respect	NOUN
ejpam-5165	85	16	to	to	ADP
ejpam-5165	85	17	g	g	NOUN
ejpam-5165	86	1	and	and	CCONJ
ejpam-5165	86	2	we	we	PRON
ejpam-5165	86	3	write	write	VERB
ejpam-5165	86	4	a	a	DET
ejpam-5165	86	5	=	=	X
ejpam-5165	86	6	(	(	PUNCT
ejpam-5165	86	7	p	p	NOUN
ejpam-5165	86	8	)	)	PUNCT
ejpam-5165	86	9	∫	∫	PROPN
ejpam-5165	87	1	[	[	X
ejpam-5165	87	2	a	a	X
ejpam-5165	87	3	,	,	PUNCT
ejpam-5165	87	4	b	b	NOUN
ejpam-5165	87	5	]	]	X
ejpam-5165	87	6	fdg	fdg	PROPN
ejpam-5165	87	7	.	.	PROPN
ejpam-5165	87	8	theorem	theorem	NOUN
ejpam-5165	87	9	1	1	NUM
ejpam-5165	87	10	.	.	PUNCT
ejpam-5165	88	1	[	[	X
ejpam-5165	88	2	2	2	X
ejpam-5165	88	3	]	]	PUNCT
ejpam-5165	88	4	a	a	DET
ejpam-5165	88	5	function	function	NOUN
ejpam-5165	88	6	f	f	NOUN
ejpam-5165	88	7	:	:	PUNCT
ejpam-5165	89	1	[	[	X
ejpam-5165	89	2	a	a	X
ejpam-5165	89	3	,	,	PUNCT
ejpam-5165	89	4	b	b	NOUN
ejpam-5165	89	5	]	]	X
ejpam-5165	89	6	→	→	PUNCT
ejpam-5165	89	7	x	x	X
ejpam-5165	89	8	is	be	AUX
ejpam-5165	89	9	pul	pul	NOUN
ejpam-5165	89	10	-	-	PUNCT
ejpam-5165	89	11	stieltjes	stieltjes	NOUN
ejpam-5165	89	12	integrable	integrable	ADJ
ejpam-5165	89	13	with	with	ADP
ejpam-5165	89	14	respect	respect	NOUN
ejpam-5165	89	15	to	to	ADP
ejpam-5165	89	16	g	g	NOUN
ejpam-5165	89	17	:	:	PUNCT
ejpam-5165	90	1	[	[	X
ejpam-5165	90	2	a	a	X
ejpam-5165	90	3	,	,	PUNCT
ejpam-5165	90	4	b	b	NOUN
ejpam-5165	90	5	]	]	X
ejpam-5165	90	6	→	→	SYM
ejpam-5165	90	7	r	r	NOUN
ejpam-5165	90	8	if	if	SCONJ
ejpam-5165	90	9	and	and	CCONJ
ejpam-5165	90	10	only	only	ADV
ejpam-5165	90	11	if	if	SCONJ
ejpam-5165	90	12	f	f	PROPN
ejpam-5165	90	13	is	be	AUX
ejpam-5165	90	14	mcshane	mcshane	NOUN
ejpam-5165	90	15	-	-	PUNCT
ejpam-5165	90	16	stieltjes	stieltjes	NOUN
ejpam-5165	90	17	integrable	integrable	ADJ
ejpam-5165	90	18	with	with	ADP
ejpam-5165	90	19	respect	respect	NOUN
ejpam-5165	90	20	to	to	ADP
ejpam-5165	90	21	g	g	NOUN
ejpam-5165	90	22	on	on	ADP
ejpam-5165	90	23	[	[	X
ejpam-5165	90	24	a	a	X
ejpam-5165	90	25	,	,	PUNCT
ejpam-5165	90	26	b	b	NOUN
ejpam-5165	90	27	]	]	X
ejpam-5165	90	28	.	.	PUNCT
ejpam-5165	91	1	moreover	moreover	ADV
ejpam-5165	91	2	,	,	PUNCT
ejpam-5165	91	3	(	(	PUNCT
ejpam-5165	91	4	p	p	NOUN
ejpam-5165	91	5	)	)	PUNCT
ejpam-5165	91	6	∫	∫	PROPN
ejpam-5165	92	1	[	[	X
ejpam-5165	92	2	a	a	X
ejpam-5165	92	3	,	,	PUNCT
ejpam-5165	92	4	b	b	NOUN
ejpam-5165	92	5	]	]	X
ejpam-5165	92	6	fdg	fdg	PROPN
ejpam-5165	92	7	=	=	X
ejpam-5165	92	8	(	(	PUNCT
ejpam-5165	92	9	ms	ms	PROPN
ejpam-5165	92	10	)	)	PUNCT
ejpam-5165	92	11	∫	∫	PROPN
ejpam-5165	93	1	[	[	X
ejpam-5165	93	2	a	a	X
ejpam-5165	93	3	,	,	PUNCT
ejpam-5165	93	4	b	b	NOUN
ejpam-5165	93	5	]	]	X
ejpam-5165	93	6	fdg	fdg	PROPN
ejpam-5165	93	7	.	.	PUNCT
ejpam-5165	93	8	definition	definition	NOUN
ejpam-5165	93	9	12	12	NUM
ejpam-5165	93	10	.	.	PUNCT
ejpam-5165	94	1	[	[	X
ejpam-5165	94	2	10	10	NUM
ejpam-5165	94	3	]	]	X
ejpam-5165	94	4	if	if	SCONJ
ejpam-5165	94	5	f	f	X
ejpam-5165	94	6	:	:	PUNCT
ejpam-5165	95	1	[	[	X
ejpam-5165	95	2	a	a	X
ejpam-5165	95	3	,	,	PUNCT
ejpam-5165	95	4	b	b	NOUN
ejpam-5165	95	5	]	]	X
ejpam-5165	95	6	→	→	PUNCT
ejpam-5165	95	7	x	x	X
ejpam-5165	95	8	is	be	AUX
ejpam-5165	95	9	weakly	weakly	ADV
ejpam-5165	95	10	measurable	measurable	ADJ
ejpam-5165	95	11	such	such	ADJ
ejpam-5165	95	12	that	that	SCONJ
ejpam-5165	95	13	the	the	DET
ejpam-5165	95	14	function	function	NOUN
ejpam-5165	95	15	x∗(f	x∗(f	PROPN
ejpam-5165	95	16	)	)	PUNCT
ejpam-5165	95	17	:	:	PUNCT
ejpam-5165	96	1	[	[	X
ejpam-5165	96	2	a	a	X
ejpam-5165	96	3	,	,	PUNCT
ejpam-5165	96	4	b	b	NOUN
ejpam-5165	96	5	]	]	X
ejpam-5165	96	6	→	→	PUNCT
ejpam-5165	96	7	r	r	NOUN
ejpam-5165	96	8	is	be	AUX
ejpam-5165	96	9	mcshane	mcshane	NOUN
ejpam-5165	96	10	integrable	integrable	ADJ
ejpam-5165	96	11	for	for	ADP
ejpam-5165	96	12	each	each	DET
ejpam-5165	96	13	x∗	x∗	PROPN
ejpam-5165	96	14	∈	∈	PROPN
ejpam-5165	96	15	x∗	x∗	PROPN
ejpam-5165	96	16	then	then	ADV
ejpam-5165	96	17	f	f	PROPN
ejpam-5165	96	18	is	be	AUX
ejpam-5165	96	19	called	call	VERB
ejpam-5165	96	20	dunford	dunford	PROPN
ejpam-5165	96	21	integrable	integrable	PROPN
ejpam-5165	96	22	.	.	PUNCT
ejpam-5165	97	1	the	the	DET
ejpam-5165	97	2	dunford	dunford	PROPN
ejpam-5165	97	3	integral	integral	ADJ
ejpam-5165	97	4	(	(	PUNCT
ejpam-5165	97	5	d	d	NOUN
ejpam-5165	97	6	)	)	PUNCT
ejpam-5165	97	7	∫	∫	PROPN
ejpam-5165	97	8	e	e	PROPN
ejpam-5165	97	9	f	f	PROPN
ejpam-5165	97	10	of	of	ADP
ejpam-5165	97	11	f	f	PROPN
ejpam-5165	97	12	over	over	ADP
ejpam-5165	97	13	a	a	DET
ejpam-5165	97	14	measurable	measurable	ADJ
ejpam-5165	97	15	set	set	NOUN
ejpam-5165	97	16	e	e	NOUN
ejpam-5165	97	17	⊆	⊆	NUM
ejpam-5165	97	18	[	[	X
ejpam-5165	97	19	a	a	X
ejpam-5165	97	20	,	,	PUNCT
ejpam-5165	97	21	b	b	NOUN
ejpam-5165	97	22	]	]	PUNCT
ejpam-5165	97	23	is	be	AUX
ejpam-5165	97	24	defined	define	VERB
ejpam-5165	97	25	by	by	ADP
ejpam-5165	97	26	the	the	DET
ejpam-5165	97	27	element	element	NOUN
ejpam-5165	97	28	x∗∗e	x∗∗e	PROPN
ejpam-5165	97	29	∈	∈	PROPN
ejpam-5165	97	30	x∗∗	x∗∗	PROPN
ejpam-5165	97	31	,	,	PUNCT
ejpam-5165	97	32	that	that	ADV
ejpam-5165	97	33	is	is	ADV
ejpam-5165	97	34	,	,	PUNCT
ejpam-5165	97	35	(	(	PUNCT
ejpam-5165	97	36	d	d	X
ejpam-5165	97	37	)	)	PUNCT
ejpam-5165	97	38	∫	∫	PROPN
ejpam-5165	97	39	e	e	PROPN
ejpam-5165	97	40	f	f	PROPN
ejpam-5165	97	41	=	=	SYM
ejpam-5165	97	42	x∗∗e	x∗∗e	PROPN
ejpam-5165	97	43	∈	∈	PROPN
ejpam-5165	97	44	x∗∗	x∗∗	PROPN
ejpam-5165	97	45	,	,	PUNCT
ejpam-5165	97	46	where	where	SCONJ
ejpam-5165	97	47	x∗∗e	x∗∗e	PROPN
ejpam-5165	97	48	(	(	PUNCT
ejpam-5165	97	49	x∗	x∗	PROPN
ejpam-5165	97	50	)	)	PUNCT
ejpam-5165	98	1	=	=	PUNCT
ejpam-5165	98	2	(	(	PUNCT
ejpam-5165	98	3	d	d	X
ejpam-5165	98	4	)	)	PUNCT
ejpam-5165	98	5	∫	∫	PROPN
ejpam-5165	98	6	e	e	PROPN
ejpam-5165	98	7	x∗(f	x∗(f	PROPN
ejpam-5165	98	8	)	)	PUNCT
ejpam-5165	98	9	for	for	ADP
ejpam-5165	98	10	all	all	DET
ejpam-5165	98	11	x∗	x∗	PROPN
ejpam-5165	98	12	∈	∈	PROPN
ejpam-5165	98	13	x∗.	x∗.	VERB
ejpam-5165	99	1	here	here	ADV
ejpam-5165	99	2	,	,	PUNCT
ejpam-5165	99	3	denote	denote	VERB
ejpam-5165	99	4	by	by	ADP
ejpam-5165	99	5	d[a	d[a	PROPN
ejpam-5165	99	6	,	,	PUNCT
ejpam-5165	99	7	b	b	AUX
ejpam-5165	99	8	]	]	X
ejpam-5165	99	9	the	the	DET
ejpam-5165	99	10	set	set	NOUN
ejpam-5165	99	11	of	of	ADP
ejpam-5165	99	12	all	all	DET
ejpam-5165	99	13	dunford	dunford	PROPN
ejpam-5165	99	14	integrable	integrable	ADJ
ejpam-5165	99	15	functions	function	NOUN
ejpam-5165	99	16	on	on	ADP
ejpam-5165	99	17	[	[	X
ejpam-5165	99	18	a	a	X
ejpam-5165	99	19	,	,	PUNCT
ejpam-5165	99	20	b	b	NOUN
ejpam-5165	99	21	]	]	PUNCT
ejpam-5165	99	22	.	.	PUNCT
ejpam-5165	100	1	definition	definition	NOUN
ejpam-5165	100	2	13	13	NUM
ejpam-5165	100	3	.	.	PUNCT
ejpam-5165	101	1	[	[	X
ejpam-5165	101	2	10	10	NUM
ejpam-5165	101	3	]	]	X
ejpam-5165	101	4	if	if	SCONJ
ejpam-5165	101	5	f	f	X
ejpam-5165	101	6	:	:	PUNCT
ejpam-5165	102	1	[	[	X
ejpam-5165	102	2	a	a	X
ejpam-5165	102	3	,	,	PUNCT
ejpam-5165	102	4	b	b	NOUN
ejpam-5165	102	5	]	]	X
ejpam-5165	102	6	→	→	PUNCT
ejpam-5165	102	7	x	x	X
ejpam-5165	102	8	is	be	AUX
ejpam-5165	102	9	dunford	dunford	PROPN
ejpam-5165	102	10	integrable	integrable	ADJ
ejpam-5165	102	11	where	where	SCONJ
ejpam-5165	102	12	(	(	PUNCT
ejpam-5165	102	13	d	d	NOUN
ejpam-5165	102	14	)	)	PUNCT
ejpam-5165	102	15	∫	∫	PROPN
ejpam-5165	102	16	e	e	X
ejpam-5165	102	17	(	(	PUNCT
ejpam-5165	102	18	f	f	X
ejpam-5165	102	19	)	)	PUNCT
ejpam-5165	102	20	in	in	ADP
ejpam-5165	102	21	x	x	X
ejpam-5165	102	22	(	(	PUNCT
ejpam-5165	102	23	or	or	CCONJ
ejpam-5165	102	24	more	more	ADV
ejpam-5165	102	25	precisely	precisely	ADV
ejpam-5165	102	26	(	(	PUNCT
ejpam-5165	102	27	d	d	NOUN
ejpam-5165	102	28	)	)	PUNCT
ejpam-5165	102	29	∫	∫	PROPN
ejpam-5165	102	30	e	e	PROPN
ejpam-5165	102	31	f	f	PROPN
ejpam-5165	102	32	∈	∈	PROPN
ejpam-5165	102	33	e(x	e(x	NUM
ejpam-5165	102	34	)	)	PUNCT
ejpam-5165	102	35	⊆	⊆	NUM
ejpam-5165	102	36	x∗∗	x∗∗	NOUN
ejpam-5165	102	37	,	,	PUNCT
ejpam-5165	102	38	where	where	SCONJ
ejpam-5165	102	39	e	e	NOUN
ejpam-5165	102	40	is	be	AUX
ejpam-5165	102	41	the	the	DET
ejpam-5165	102	42	canonical	canonical	ADJ
ejpam-5165	102	43	embedding	embedding	NOUN
ejpam-5165	102	44	of	of	ADP
ejpam-5165	102	45	x	x	PUNCT
ejpam-5165	102	46	into	into	ADP
ejpam-5165	102	47	x∗∗	x∗∗	NOUN
ejpam-5165	102	48	)	)	PUNCT
ejpam-5165	102	49	for	for	ADP
ejpam-5165	102	50	every	every	DET
ejpam-5165	102	51	measurable	measurable	NOUN
ejpam-5165	102	52	e	e	NOUN
ejpam-5165	102	53	⊆	⊆	NUM
ejpam-5165	102	54	[	[	X
ejpam-5165	102	55	a	a	X
ejpam-5165	102	56	,	,	PUNCT
ejpam-5165	102	57	b	b	NOUN
ejpam-5165	102	58	]	]	X
ejpam-5165	102	59	,	,	PUNCT
ejpam-5165	102	60	then	then	ADV
ejpam-5165	102	61	f	f	PROPN
ejpam-5165	102	62	is	be	AUX
ejpam-5165	102	63	called	call	VERB
ejpam-5165	102	64	pettis	pettis	PROPN
ejpam-5165	102	65	integrable	integrable	ADJ
ejpam-5165	102	66	and	and	CCONJ
ejpam-5165	102	67	(	(	PUNCT
ejpam-5165	102	68	p	p	NOUN
ejpam-5165	102	69	)	)	PUNCT
ejpam-5165	102	70	∫	∫	PROPN
ejpam-5165	103	1	e	e	X
ejpam-5165	103	2	f	f	PROPN
ejpam-5165	103	3	=	=	SYM
ejpam-5165	103	4	(	(	PUNCT
ejpam-5165	103	5	d	d	NOUN
ejpam-5165	103	6	)	)	PUNCT
ejpam-5165	103	7	∫	∫	PROPN
ejpam-5165	104	1	e	e	X
ejpam-5165	104	2	f	f	PROPN
ejpam-5165	104	3	is	be	AUX
ejpam-5165	104	4	called	call	VERB
ejpam-5165	104	5	the	the	DET
ejpam-5165	104	6	pettis	pettis	NOUN
ejpam-5165	104	7	integral	integral	NOUN
ejpam-5165	104	8	of	of	ADP
ejpam-5165	104	9	f	f	PROPN
ejpam-5165	104	10	over	over	ADP
ejpam-5165	104	11	the	the	DET
ejpam-5165	104	12	set	set	NOUN
ejpam-5165	104	13	e.	e.	PROPN
ejpam-5165	104	14	definition	definition	NOUN
ejpam-5165	104	15	14	14	NUM
ejpam-5165	104	16	.	.	PUNCT
ejpam-5165	105	1	[	[	X
ejpam-5165	105	2	7	7	X
ejpam-5165	105	3	]	]	X
ejpam-5165	105	4	a	a	DET
ejpam-5165	105	5	linear	linear	ADJ
ejpam-5165	105	6	functional	functional	ADJ
ejpam-5165	105	7	f	f	PROPN
ejpam-5165	105	8	is	be	AUX
ejpam-5165	105	9	a	a	DET
ejpam-5165	105	10	linear	linear	ADJ
ejpam-5165	105	11	operator	operator	NOUN
ejpam-5165	105	12	with	with	ADP
ejpam-5165	105	13	domain	domain	NOUN
ejpam-5165	105	14	in	in	ADP
ejpam-5165	105	15	a	a	DET
ejpam-5165	105	16	vector	vector	NOUN
ejpam-5165	105	17	space	space	NOUN
ejpam-5165	105	18	x	x	PUNCT
ejpam-5165	105	19	and	and	CCONJ
ejpam-5165	105	20	range	range	VERB
ejpam-5165	105	21	in	in	ADP
ejpam-5165	105	22	the	the	DET
ejpam-5165	105	23	scalar	scalar	ADJ
ejpam-5165	105	24	field	field	NOUN
ejpam-5165	105	25	k	k	PROPN
ejpam-5165	105	26	of	of	ADP
ejpam-5165	105	27	x	x	PRON
ejpam-5165	105	28	,	,	PUNCT
ejpam-5165	105	29	that	that	ADV
ejpam-5165	105	30	is	is	ADV
ejpam-5165	105	31	,	,	PUNCT
ejpam-5165	105	32	f	f	X
ejpam-5165	105	33	:	:	PUNCT
ejpam-5165	105	34	x	x	X
ejpam-5165	105	35	→	→	SYM
ejpam-5165	105	36	k	k	NOUN
ejpam-5165	105	37	,	,	PUNCT
ejpam-5165	105	38	where	where	SCONJ
ejpam-5165	105	39	k	k	PROPN
ejpam-5165	105	40	=	=	SYM
ejpam-5165	105	41	r	r	NOUN
ejpam-5165	105	42	or	or	CCONJ
ejpam-5165	105	43	k	k	NOUN
ejpam-5165	105	44	=	=	PROPN
ejpam-5165	105	45	c.	c.	PROPN
ejpam-5165	105	46	d.	d.	PROPN
ejpam-5165	105	47	omayan	omayan	PROPN
ejpam-5165	105	48	,	,	PUNCT
ejpam-5165	105	49	g.b	g.b	PROPN
ejpam-5165	105	50	.	.	PROPN
ejpam-5165	105	51	flores	flores	PROPN
ejpam-5165	105	52	/	/	SYM
ejpam-5165	105	53	eur	eur	PROPN
ejpam-5165	105	54	.	.	PUNCT
ejpam-5165	106	1	j.	j.	PROPN
ejpam-5165	106	2	pure	pure	PROPN
ejpam-5165	106	3	appl	appl	PROPN
ejpam-5165	106	4	.	.	PROPN
ejpam-5165	106	5	math	math	PROPN
ejpam-5165	106	6	,	,	PUNCT
ejpam-5165	106	7	17	17	NUM
ejpam-5165	106	8	(	(	PUNCT
ejpam-5165	106	9	2	2	NUM
ejpam-5165	106	10	)	)	PUNCT
ejpam-5165	106	11	(	(	PUNCT
ejpam-5165	106	12	2024	2024	NUM
ejpam-5165	106	13	)	)	PUNCT
ejpam-5165	106	14	,	,	PUNCT
ejpam-5165	106	15	1183	1183	NUM
ejpam-5165	106	16	-	-	SYM
ejpam-5165	106	17	1196	1196	NUM
ejpam-5165	106	18	1187	1187	NUM
ejpam-5165	106	19	definition	definition	NOUN
ejpam-5165	106	20	15	15	NUM
ejpam-5165	106	21	.	.	PUNCT
ejpam-5165	107	1	[	[	X
ejpam-5165	107	2	2	2	X
ejpam-5165	107	3	]	]	PUNCT
ejpam-5165	107	4	let	let	VERB
ejpam-5165	107	5	f	f	NOUN
ejpam-5165	107	6	:	:	PUNCT
ejpam-5165	108	1	[	[	X
ejpam-5165	108	2	a	a	X
ejpam-5165	108	3	,	,	PUNCT
ejpam-5165	108	4	b	b	NOUN
ejpam-5165	108	5	]	]	X
ejpam-5165	108	6	→	→	PUNCT
ejpam-5165	108	7	x	x	X
ejpam-5165	108	8	be	be	AUX
ejpam-5165	108	9	any	any	DET
ejpam-5165	108	10	banach	banach	ADV
ejpam-5165	108	11	-	-	PUNCT
ejpam-5165	108	12	valued	value	VERB
ejpam-5165	108	13	function	function	NOUN
ejpam-5165	108	14	.	.	PUNCT
ejpam-5165	109	1	we	we	PRON
ejpam-5165	109	2	say	say	VERB
ejpam-5165	109	3	that	that	SCONJ
ejpam-5165	109	4	f	f	PROPN
ejpam-5165	109	5	is	be	AUX
ejpam-5165	109	6	continuous	continuous	ADJ
ejpam-5165	109	7	at	at	ADP
ejpam-5165	109	8	a	a	DET
ejpam-5165	109	9	point	point	NOUN
ejpam-5165	109	10	y	y	PROPN
ejpam-5165	109	11	∈	∈	PROPN
ejpam-5165	110	1	[	[	X
ejpam-5165	110	2	a	a	X
ejpam-5165	110	3	,	,	PUNCT
ejpam-5165	110	4	b	b	NOUN
ejpam-5165	110	5	]	]	X
ejpam-5165	110	6	if	if	SCONJ
ejpam-5165	110	7	for	for	ADP
ejpam-5165	110	8	every	every	DET
ejpam-5165	110	9	ε	ε	PROPN
ejpam-5165	110	10	>	>	X
ejpam-5165	110	11	0	0	PROPN
ejpam-5165	110	12	,	,	PUNCT
ejpam-5165	110	13	there	there	PRON
ejpam-5165	110	14	exists	exist	VERB
ejpam-5165	110	15	a	a	DET
ejpam-5165	110	16	δ	δ	PROPN
ejpam-5165	110	17	>	>	X
ejpam-5165	110	18	0	0	NUM
ejpam-5165	111	1	such	such	ADJ
ejpam-5165	111	2	that	that	PRON
ejpam-5165	111	3	for	for	ADP
ejpam-5165	111	4	every	every	DET
ejpam-5165	111	5	x	x	SYM
ejpam-5165	111	6	∈	∈	PROPN
ejpam-5165	111	7	[	[	X
ejpam-5165	111	8	a	a	X
ejpam-5165	111	9	,	,	PUNCT
ejpam-5165	111	10	b	b	NOUN
ejpam-5165	111	11	]	]	X
ejpam-5165	111	12	with	with	ADP
ejpam-5165	111	13	∥x−	∥x−	PROPN
ejpam-5165	111	14	y∥rn	y∥rn	PROPN
ejpam-5165	111	15	<	<	X
ejpam-5165	111	16	δ	δ	PROPN
ejpam-5165	111	17	,	,	PUNCT
ejpam-5165	111	18	we	we	PRON
ejpam-5165	111	19	have	have	VERB
ejpam-5165	111	20	|f(x)−	|f(x)−	NOUN
ejpam-5165	111	21	f(y)|	f(y)|	PROPN
ejpam-5165	111	22	<	<	X
ejpam-5165	111	23	ε	ε	PROPN
ejpam-5165	111	24	.	.	PUNCT
ejpam-5165	111	25	definition	definition	NOUN
ejpam-5165	111	26	16	16	NUM
ejpam-5165	111	27	.	.	PUNCT
ejpam-5165	112	1	[	[	X
ejpam-5165	112	2	7	7	X
ejpam-5165	112	3	]	]	X
ejpam-5165	112	4	let	let	VERB
ejpam-5165	112	5	x	x	PRON
ejpam-5165	112	6	be	be	AUX
ejpam-5165	112	7	a	a	DET
ejpam-5165	112	8	vector	vector	NOUN
ejpam-5165	112	9	space	space	NOUN
ejpam-5165	112	10	and	and	CCONJ
ejpam-5165	112	11	x	x	PUNCT
ejpam-5165	112	12	∈	∈	NOUN
ejpam-5165	112	13	x.	x.	NOUN
ejpam-5165	112	14	define	define	VERB
ejpam-5165	112	15	x∗	x∗	PROPN
ejpam-5165	113	1	=	=	PRON
ejpam-5165	113	2	{	{	PUNCT
ejpam-5165	113	3	f	f	X
ejpam-5165	113	4	:	:	PUNCT
ejpam-5165	113	5	x	x	X
ejpam-5165	113	6	→	→	SYM
ejpam-5165	113	7	k	k	X
ejpam-5165	113	8	|f	|f	PROPN
ejpam-5165	113	9	is	be	AUX
ejpam-5165	113	10	a	a	DET
ejpam-5165	113	11	linear	linear	ADJ
ejpam-5165	113	12	functional	functional	NOUN
ejpam-5165	113	13	}	}	PUNCT
ejpam-5165	113	14	and	and	CCONJ
ejpam-5165	113	15	the	the	DET
ejpam-5165	113	16	following	follow	VERB
ejpam-5165	113	17	operations	operation	NOUN
ejpam-5165	113	18	in	in	ADP
ejpam-5165	113	19	x∗	x∗	PROPN
ejpam-5165	113	20	:	:	PUNCT
ejpam-5165	113	21	(	(	PUNCT
ejpam-5165	113	22	i	i	NOUN
ejpam-5165	113	23	)	)	PUNCT
ejpam-5165	113	24	(	(	PUNCT
ejpam-5165	113	25	f1	f1	NOUN
ejpam-5165	113	26	+	+	CCONJ
ejpam-5165	113	27	f2)(x	f2)(x	PROPN
ejpam-5165	113	28	)	)	PUNCT
ejpam-5165	113	29	=	=	SYM
ejpam-5165	113	30	f1(x	f1(x	NOUN
ejpam-5165	113	31	)	)	PUNCT
ejpam-5165	113	32	+	+	NOUN
ejpam-5165	113	33	f2(x	f2(x	NOUN
ejpam-5165	113	34	)	)	PUNCT
ejpam-5165	113	35	;	;	PUNCT
ejpam-5165	113	36	and	and	CCONJ
ejpam-5165	113	37	(	(	PUNCT
ejpam-5165	113	38	ii	ii	NOUN
ejpam-5165	113	39	)	)	PUNCT
ejpam-5165	113	40	(	(	PUNCT
ejpam-5165	113	41	αf)(x	αf)(x	PROPN
ejpam-5165	113	42	)	)	PUNCT
ejpam-5165	113	43	=	=	SYM
ejpam-5165	113	44	α(f(x	α(f(x	PROPN
ejpam-5165	113	45	)	)	PUNCT
ejpam-5165	113	46	)	)	PUNCT
ejpam-5165	113	47	.	.	PUNCT
ejpam-5165	114	1	then	then	ADV
ejpam-5165	114	2	(	(	PUNCT
ejpam-5165	114	3	x∗,+	x∗,+	NUM
ejpam-5165	114	4	,	,	PUNCT
ejpam-5165	114	5	·	·	PUNCT
ejpam-5165	114	6	)	)	PUNCT
ejpam-5165	114	7	is	be	AUX
ejpam-5165	114	8	a	a	DET
ejpam-5165	114	9	vector	vector	NOUN
ejpam-5165	114	10	space	space	NOUN
ejpam-5165	114	11	called	call	VERB
ejpam-5165	114	12	the	the	DET
ejpam-5165	114	13	algebraic	algebraic	ADJ
ejpam-5165	114	14	dual	dual	ADJ
ejpam-5165	114	15	space	space	NOUN
ejpam-5165	114	16	.	.	PUNCT
ejpam-5165	115	1	definition	definition	NOUN
ejpam-5165	115	2	17	17	NUM
ejpam-5165	115	3	.	.	PUNCT
ejpam-5165	116	1	[	[	X
ejpam-5165	116	2	7	7	X
ejpam-5165	116	3	]	]	X
ejpam-5165	116	4	let	let	VERB
ejpam-5165	116	5	x	x	PRON
ejpam-5165	116	6	be	be	AUX
ejpam-5165	116	7	a	a	DET
ejpam-5165	116	8	vector	vector	NOUN
ejpam-5165	116	9	space	space	NOUN
ejpam-5165	116	10	and	and	CCONJ
ejpam-5165	116	11	fix	fix	NOUN
ejpam-5165	116	12	x	x	SYM
ejpam-5165	116	13	∈	∈	NOUN
ejpam-5165	116	14	x.	x.	NOUN
ejpam-5165	116	15	define	define	VERB
ejpam-5165	116	16	x∗∗	x∗∗	NOUN
ejpam-5165	117	1	=	=	PRON
ejpam-5165	117	2	{	{	PUNCT
ejpam-5165	117	3	g	g	NOUN
ejpam-5165	117	4	:	:	PUNCT
ejpam-5165	117	5	x∗	x∗	PROPN
ejpam-5165	117	6	→	→	SYM
ejpam-5165	117	7	k	k	PROPN
ejpam-5165	117	8	|g(f	|g(f	PROPN
ejpam-5165	117	9	)	)	PUNCT
ejpam-5165	117	10	=	=	SYM
ejpam-5165	117	11	gx(f	gx(f	NOUN
ejpam-5165	117	12	)	)	PUNCT
ejpam-5165	117	13	=	=	SYM
ejpam-5165	117	14	f(x	f(x	PROPN
ejpam-5165	117	15	)	)	PUNCT
ejpam-5165	117	16	∀	∀	X
ejpam-5165	118	1	f	f	NOUN
ejpam-5165	118	2	∈	∈	PROPN
ejpam-5165	118	3	x∗	x∗	PROPN
ejpam-5165	118	4	is	be	AUX
ejpam-5165	118	5	a	a	DET
ejpam-5165	118	6	linear	linear	ADJ
ejpam-5165	118	7	functional	functional	NOUN
ejpam-5165	118	8	}	}	PUNCT
ejpam-5165	118	9	and	and	CCONJ
ejpam-5165	118	10	the	the	DET
ejpam-5165	118	11	following	follow	VERB
ejpam-5165	118	12	operations	operation	NOUN
ejpam-5165	118	13	in	in	ADP
ejpam-5165	118	14	x∗∗	x∗∗	PROPN
ejpam-5165	118	15	:	:	PUNCT
ejpam-5165	118	16	(	(	PUNCT
ejpam-5165	118	17	i	i	NOUN
ejpam-5165	118	18	)	)	PUNCT
ejpam-5165	118	19	(	(	PUNCT
ejpam-5165	118	20	g1	g1	PROPN
ejpam-5165	118	21	+	+	CCONJ
ejpam-5165	118	22	g2)(f	g2)(f	PROPN
ejpam-5165	118	23	)	)	PUNCT
ejpam-5165	118	24	=	=	SYM
ejpam-5165	118	25	g1(f	g1(f	X
ejpam-5165	118	26	)	)	PUNCT
ejpam-5165	118	27	+	+	CCONJ
ejpam-5165	118	28	g2(f	g2(f	X
ejpam-5165	118	29	)	)	PUNCT
ejpam-5165	118	30	;	;	PUNCT
ejpam-5165	118	31	and	and	CCONJ
ejpam-5165	118	32	(	(	PUNCT
ejpam-5165	118	33	ii	ii	NOUN
ejpam-5165	118	34	)	)	PUNCT
ejpam-5165	118	35	(	(	PUNCT
ejpam-5165	118	36	αg)(f	αg)(f	PROPN
ejpam-5165	118	37	)	)	PUNCT
ejpam-5165	118	38	=	=	SYM
ejpam-5165	118	39	α(g(f	α(g(f	NOUN
ejpam-5165	118	40	)	)	PUNCT
ejpam-5165	118	41	)	)	PUNCT
ejpam-5165	118	42	.	.	PUNCT
ejpam-5165	119	1	then	then	ADV
ejpam-5165	119	2	(	(	PUNCT
ejpam-5165	119	3	x∗∗,+	x∗∗,+	X
ejpam-5165	119	4	,	,	PUNCT
ejpam-5165	119	5	·	·	PUNCT
ejpam-5165	119	6	)	)	PUNCT
ejpam-5165	119	7	is	be	AUX
ejpam-5165	119	8	a	a	DET
ejpam-5165	119	9	vector	vector	NOUN
ejpam-5165	119	10	space	space	NOUN
ejpam-5165	119	11	called	call	VERB
ejpam-5165	119	12	the	the	DET
ejpam-5165	119	13	second	second	ADJ
ejpam-5165	119	14	algebraic	algebraic	ADJ
ejpam-5165	119	15	dual	dual	ADJ
ejpam-5165	119	16	space	space	NOUN
ejpam-5165	119	17	.	.	PUNCT
ejpam-5165	120	1	3	3	X
ejpam-5165	120	2	.	.	X
ejpam-5165	120	3	mcshane	mcshane	PROPN
ejpam-5165	120	4	-	-	PUNCT
ejpam-5165	120	5	dunford	dunford	PROPN
ejpam-5165	120	6	-	-	PUNCT
ejpam-5165	120	7	stieltjes	stieltjes	NOUN
ejpam-5165	120	8	integral	integral	ADJ
ejpam-5165	120	9	and	and	CCONJ
ejpam-5165	120	10	mcshane	mcshane	PROPN
ejpam-5165	120	11	-	-	PUNCT
ejpam-5165	120	12	pettis	pettis	PROPN
ejpam-5165	120	13	-	-	PUNCT
ejpam-5165	120	14	stieltjes	stieltjes	NOUN
ejpam-5165	120	15	integral	integral	ADJ
ejpam-5165	120	16	in	in	ADP
ejpam-5165	120	17	banach	banach	NOUN
ejpam-5165	120	18	space	space	NOUN
ejpam-5165	120	19	before	before	ADP
ejpam-5165	120	20	going	go	VERB
ejpam-5165	120	21	through	through	ADP
ejpam-5165	120	22	the	the	DET
ejpam-5165	120	23	paper	paper	NOUN
ejpam-5165	120	24	an	an	DET
ejpam-5165	120	25	important	important	ADJ
ejpam-5165	120	26	proposition	proposition	NOUN
ejpam-5165	120	27	is	be	AUX
ejpam-5165	120	28	provided	provide	VERB
ejpam-5165	120	29	.	.	PUNCT
ejpam-5165	121	1	proposition	proposition	NOUN
ejpam-5165	121	2	1	1	NUM
ejpam-5165	121	3	.	.	PUNCT
ejpam-5165	122	1	let	let	VERB
ejpam-5165	122	2	f	f	NOUN
ejpam-5165	122	3	:	:	PUNCT
ejpam-5165	123	1	[	[	X
ejpam-5165	123	2	a	a	X
ejpam-5165	123	3	,	,	PUNCT
ejpam-5165	123	4	b	b	NOUN
ejpam-5165	123	5	]	]	X
ejpam-5165	123	6	→	→	SYM
ejpam-5165	123	7	x	x	X
ejpam-5165	123	8	and	and	CCONJ
ejpam-5165	123	9	g	g	NOUN
ejpam-5165	123	10	:	:	PUNCT
ejpam-5165	124	1	[	[	X
ejpam-5165	124	2	a	a	X
ejpam-5165	124	3	,	,	PUNCT
ejpam-5165	124	4	b	b	NOUN
ejpam-5165	124	5	]	]	X
ejpam-5165	124	6	→	→	PUNCT
ejpam-5165	124	7	r	r	NOUN
ejpam-5165	124	8	be	be	NOUN
ejpam-5165	124	9	functions	function	NOUN
ejpam-5165	124	10	.	.	PUNCT
ejpam-5165	125	1	if	if	SCONJ
ejpam-5165	125	2	f	f	PROPN
ejpam-5165	125	3	is	be	AUX
ejpam-5165	125	4	mcshanestieltjes	mcshanestieltjes	NOUN
ejpam-5165	125	5	integrable	integrable	ADJ
ejpam-5165	125	6	with	with	ADP
ejpam-5165	125	7	(	(	PUNCT
ejpam-5165	125	8	ms	ms	PROPN
ejpam-5165	125	9	)	)	PUNCT
ejpam-5165	125	10	∫	∫	PROPN
ejpam-5165	126	1	[	[	X
ejpam-5165	126	2	a	a	X
ejpam-5165	126	3	,	,	PUNCT
ejpam-5165	126	4	b	b	NOUN
ejpam-5165	126	5	]	]	X
ejpam-5165	126	6	f	f	X
ejpam-5165	126	7	dg	dg	PROPN
ejpam-5165	126	8	∈	∈	PROPN
ejpam-5165	126	9	x	x	PUNCT
ejpam-5165	126	10	with	with	ADP
ejpam-5165	126	11	respect	respect	NOUN
ejpam-5165	126	12	to	to	ADP
ejpam-5165	126	13	g	g	NOUN
ejpam-5165	126	14	on	on	ADP
ejpam-5165	126	15	[	[	X
ejpam-5165	126	16	a	a	X
ejpam-5165	126	17	,	,	PUNCT
ejpam-5165	126	18	b	b	NOUN
ejpam-5165	126	19	]	]	X
ejpam-5165	126	20	.	.	PUNCT
ejpam-5165	127	1	then	then	ADV
ejpam-5165	127	2	for	for	ADP
ejpam-5165	127	3	all	all	DET
ejpam-5165	127	4	x∗	x∗	PROPN
ejpam-5165	127	5	∈	∈	PROPN
ejpam-5165	127	6	x∗	x∗	VERB
ejpam-5165	127	7	the	the	DET
ejpam-5165	127	8	real	real	ADJ
ejpam-5165	127	9	function	function	NOUN
ejpam-5165	127	10	x∗(f	x∗(f	PROPN
ejpam-5165	127	11	)	)	PUNCT
ejpam-5165	127	12	:	:	PUNCT
ejpam-5165	128	1	[	[	X
ejpam-5165	128	2	a	a	X
ejpam-5165	128	3	,	,	PUNCT
ejpam-5165	128	4	b	b	NOUN
ejpam-5165	128	5	]	]	X
ejpam-5165	128	6	→	→	PUNCT
ejpam-5165	128	7	r	r	NOUN
ejpam-5165	128	8	is	be	AUX
ejpam-5165	128	9	mcshane	mcshane	NOUN
ejpam-5165	128	10	-	-	PUNCT
ejpam-5165	128	11	stieltjes	stieltjes	NOUN
ejpam-5165	128	12	integrable	integrable	ADJ
ejpam-5165	128	13	and	and	CCONJ
ejpam-5165	128	14	(	(	PUNCT
ejpam-5165	128	15	ms	ms	PROPN
ejpam-5165	128	16	)	)	PUNCT
ejpam-5165	128	17	∫	∫	PROPN
ejpam-5165	129	1	[	[	X
ejpam-5165	129	2	a	a	X
ejpam-5165	129	3	,	,	PUNCT
ejpam-5165	129	4	b	b	NOUN
ejpam-5165	129	5	]	]	X
ejpam-5165	129	6	x∗(f)dg	x∗(f)dg	X
ejpam-5165	129	7	=	=	PUNCT
ejpam-5165	129	8	x∗	x∗	PROPN
ejpam-5165	129	9	(	(	PUNCT
ejpam-5165	129	10	(	(	PUNCT
ejpam-5165	129	11	ms	ms	PROPN
ejpam-5165	129	12	)	)	PUNCT
ejpam-5165	129	13	∫	∫	PROPN
ejpam-5165	130	1	[	[	X
ejpam-5165	130	2	a	a	X
ejpam-5165	130	3	,	,	PUNCT
ejpam-5165	130	4	b	b	NOUN
ejpam-5165	130	5	]	]	X
ejpam-5165	130	6	fdg	fdg	PROPN
ejpam-5165	130	7	)	)	PUNCT
ejpam-5165	130	8	.	.	PUNCT
ejpam-5165	131	1	proof	proof	NOUN
ejpam-5165	131	2	.	.	PUNCT
ejpam-5165	132	1	suppose	suppose	VERB
ejpam-5165	132	2	that	that	SCONJ
ejpam-5165	132	3	f	f	PROPN
ejpam-5165	132	4	is	be	AUX
ejpam-5165	132	5	ms	ms	NOUN
ejpam-5165	132	6	-	-	PUNCT
ejpam-5165	132	7	integrable	integrable	ADJ
ejpam-5165	132	8	to	to	ADP
ejpam-5165	132	9	a	a	DET
ejpam-5165	132	10	=	=	SYM
ejpam-5165	132	11	(	(	PUNCT
ejpam-5165	132	12	ms	ms	PROPN
ejpam-5165	132	13	)	)	PUNCT
ejpam-5165	132	14	∫	∫	PROPN
ejpam-5165	133	1	[	[	X
ejpam-5165	133	2	a	a	X
ejpam-5165	133	3	,	,	PUNCT
ejpam-5165	133	4	b	b	NOUN
ejpam-5165	133	5	]	]	X
ejpam-5165	133	6	f	f	X
ejpam-5165	133	7	dg	dg	VERB
ejpam-5165	133	8	with	with	ADP
ejpam-5165	133	9	respect	respect	NOUN
ejpam-5165	133	10	to	to	ADP
ejpam-5165	133	11	g	g	NOUN
ejpam-5165	133	12	on	on	ADP
ejpam-5165	133	13	[	[	X
ejpam-5165	133	14	a	a	X
ejpam-5165	133	15	,	,	PUNCT
ejpam-5165	133	16	b	b	NOUN
ejpam-5165	133	17	]	]	PUNCT
ejpam-5165	133	18	.	.	PUNCT
ejpam-5165	134	1	let	let	VERB
ejpam-5165	134	2	x∗	x∗	PROPN
ejpam-5165	134	3	∈	∈	PROPN
ejpam-5165	134	4	x∗	x∗	PROPN
ejpam-5165	134	5	and	and	CCONJ
ejpam-5165	134	6	let	let	VERB
ejpam-5165	134	7	ε	ε	PROPN
ejpam-5165	134	8	>	>	X
ejpam-5165	134	9	0	0	PROPN
ejpam-5165	134	10	.	.	PUNCT
ejpam-5165	135	1	then	then	ADV
ejpam-5165	135	2	there	there	PRON
ejpam-5165	135	3	exists	exist	VERB
ejpam-5165	135	4	a	a	DET
ejpam-5165	135	5	gauge	gauge	NOUN
ejpam-5165	135	6	δ	δ	NOUN
ejpam-5165	135	7	such	such	ADJ
ejpam-5165	135	8	that∥∥∥∥∥∥	that∥∥∥∥∥∥	PROPN
ejpam-5165	135	9	∑	∑	PUNCT
ejpam-5165	135	10	(	(	PUNCT
ejpam-5165	135	11	t,[u	t,[u	ADJ
ejpam-5165	135	12	,	,	PUNCT
ejpam-5165	135	13	v])∈p	v])∈p	PROPN
ejpam-5165	135	14	f(t)∆g([u	f(t)∆g([u	PROPN
ejpam-5165	135	15	,	,	PUNCT
ejpam-5165	135	16	v])−a	v])−a	PROPN
ejpam-5165	135	17	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-5165	136	1	x	x	X
ejpam-5165	136	2	<	<	X
ejpam-5165	136	3	ε	ε	X
ejpam-5165	136	4	∥x∗∥x∗	∥x∗∥x∗	VERB
ejpam-5165	136	5	+	+	CCONJ
ejpam-5165	136	6	1	1	NUM
ejpam-5165	136	7	·	·	PUNCT
ejpam-5165	136	8	for	for	ADP
ejpam-5165	136	9	every	every	DET
ejpam-5165	136	10	δ	δ	PROPN
ejpam-5165	136	11	-	-	PUNCT
ejpam-5165	136	12	fine	fine	ADJ
ejpam-5165	136	13	m	m	PROPN
ejpam-5165	136	14	-partition	-partition	NOUN
ejpam-5165	136	15	p	p	NOUN
ejpam-5165	136	16	=	=	X
ejpam-5165	136	17	{	{	PUNCT
ejpam-5165	136	18	(	(	PUNCT
ejpam-5165	136	19	t	t	PROPN
ejpam-5165	136	20	,	,	PUNCT
ejpam-5165	136	21	[	[	X
ejpam-5165	136	22	u	u	NOUN
ejpam-5165	136	23	,	,	PUNCT
ejpam-5165	136	24	v	v	NOUN
ejpam-5165	136	25	]	]	X
ejpam-5165	136	26	)	)	PUNCT
ejpam-5165	136	27	}	}	PUNCT
ejpam-5165	136	28	of	of	ADP
ejpam-5165	136	29	[	[	X
ejpam-5165	136	30	a	a	X
ejpam-5165	136	31	,	,	PUNCT
ejpam-5165	136	32	b	b	NOUN
ejpam-5165	136	33	]	]	PUNCT
ejpam-5165	136	34	.	.	PUNCT
ejpam-5165	137	1	observe	observe	VERB
ejpam-5165	137	2	that∥∥∥∥∥∥	that∥∥∥∥∥∥	PROPN
ejpam-5165	137	3	∑	∑	PROPN
ejpam-5165	137	4	(	(	PUNCT
ejpam-5165	137	5	t,[u	t,[u	ADJ
ejpam-5165	137	6	,	,	PUNCT
ejpam-5165	137	7	v])∈p	v])∈p	NOUN
ejpam-5165	137	8	(	(	PUNCT
ejpam-5165	137	9	x∗f)(t)∆g([u	x∗f)(t)∆g([u	PROPN
ejpam-5165	137	10	,	,	PUNCT
ejpam-5165	137	11	v])−	v])−	NOUN
ejpam-5165	137	12	x∗	x∗	PROPN
ejpam-5165	137	13	(	(	PUNCT
ejpam-5165	137	14	(	(	PUNCT
ejpam-5165	137	15	ms	ms	PROPN
ejpam-5165	137	16	)	)	PUNCT
ejpam-5165	137	17	∫	∫	PROPN
ejpam-5165	138	1	[	[	X
ejpam-5165	138	2	a	a	X
ejpam-5165	138	3	,	,	PUNCT
ejpam-5165	138	4	b	b	NOUN
ejpam-5165	138	5	]	]	X
ejpam-5165	138	6	f	f	X
ejpam-5165	138	7	dg	dg	PROPN
ejpam-5165	138	8	)	)	PUNCT
ejpam-5165	138	9	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-5165	139	1	x∗	x∗	PROPN
ejpam-5165	139	2	d.	d.	PROPN
ejpam-5165	139	3	omayan	omayan	PROPN
ejpam-5165	139	4	,	,	PUNCT
ejpam-5165	139	5	g.b	g.b	PROPN
ejpam-5165	139	6	.	.	PROPN
ejpam-5165	139	7	flores	flores	PROPN
ejpam-5165	139	8	/	/	SYM
ejpam-5165	139	9	eur	eur	PROPN
ejpam-5165	139	10	.	.	PUNCT
ejpam-5165	140	1	j.	j.	PROPN
ejpam-5165	140	2	pure	pure	PROPN
ejpam-5165	140	3	appl	appl	PROPN
ejpam-5165	140	4	.	.	PROPN
ejpam-5165	140	5	math	math	PROPN
ejpam-5165	140	6	,	,	PUNCT
ejpam-5165	140	7	17	17	NUM
ejpam-5165	140	8	(	(	PUNCT
ejpam-5165	140	9	2	2	NUM
ejpam-5165	140	10	)	)	PUNCT
ejpam-5165	140	11	(	(	PUNCT
ejpam-5165	140	12	2024	2024	NUM
ejpam-5165	140	13	)	)	PUNCT
ejpam-5165	140	14	,	,	PUNCT
ejpam-5165	140	15	1183	1183	NUM
ejpam-5165	140	16	-	-	SYM
ejpam-5165	140	17	1196	1196	NUM
ejpam-5165	140	18	1188	1188	NUM
ejpam-5165	140	19	=	=	SYM
ejpam-5165	141	1	∥∥∥∥∥∥x∗	∥∥∥∥∥∥x∗	PROPN
ejpam-5165	141	2	(	(	PUNCT
ejpam-5165	141	3	∑	∑	PROPN
ejpam-5165	141	4	(	(	PUNCT
ejpam-5165	141	5	t,[u	t,[u	ADJ
ejpam-5165	141	6	,	,	PUNCT
ejpam-5165	141	7	v])∈p	v])∈p	PROPN
ejpam-5165	141	8	f(t)∆g([u	f(t)∆g([u	PROPN
ejpam-5165	141	9	,	,	PUNCT
ejpam-5165	141	10	v	v	NOUN
ejpam-5165	141	11	]	]	X
ejpam-5165	141	12	)	)	PUNCT
ejpam-5165	141	13	)	)	PUNCT
ejpam-5165	142	1	−	−	PROPN
ejpam-5165	142	2	x∗	x∗	PROPN
ejpam-5165	142	3	(	(	PUNCT
ejpam-5165	142	4	(	(	PUNCT
ejpam-5165	142	5	ms	ms	PROPN
ejpam-5165	142	6	)	)	PUNCT
ejpam-5165	142	7	∫	∫	PROPN
ejpam-5165	143	1	[	[	X
ejpam-5165	143	2	a	a	X
ejpam-5165	143	3	,	,	PUNCT
ejpam-5165	143	4	b	b	NOUN
ejpam-5165	143	5	]	]	X
ejpam-5165	143	6	f	f	X
ejpam-5165	143	7	dg	dg	PROPN
ejpam-5165	143	8	)	)	PUNCT
ejpam-5165	143	9	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-5165	144	1	x∗	x∗	PROPN
ejpam-5165	145	1	=	=	SYM
ejpam-5165	145	2	∥∥∥∥∥∥x∗	∥∥∥∥∥∥x∗	PROPN
ejpam-5165	145	3	(	(	PUNCT
ejpam-5165	145	4	∑	∑	PROPN
ejpam-5165	145	5	(	(	PUNCT
ejpam-5165	145	6	t,[u	t,[u	ADJ
ejpam-5165	145	7	,	,	PUNCT
ejpam-5165	145	8	v])∈p	v])∈p	PROPN
ejpam-5165	145	9	f(t)∆g([u	f(t)∆g([u	PROPN
ejpam-5165	145	10	,	,	PUNCT
ejpam-5165	145	11	v])−	v])−	NOUN
ejpam-5165	145	12	(	(	PUNCT
ejpam-5165	145	13	ms	ms	PROPN
ejpam-5165	145	14	)	)	PUNCT
ejpam-5165	145	15	∫	∫	PROPN
ejpam-5165	146	1	[	[	X
ejpam-5165	146	2	a	a	X
ejpam-5165	146	3	,	,	PUNCT
ejpam-5165	146	4	b	b	NOUN
ejpam-5165	146	5	]	]	X
ejpam-5165	146	6	f	f	X
ejpam-5165	146	7	dg	dg	PROPN
ejpam-5165	146	8	)	)	PUNCT
ejpam-5165	146	9	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-5165	147	1	x∗	x∗	PROPN
ejpam-5165	147	2	≤	≤	PROPN
ejpam-5165	148	1	∥x∗∥x∗	∥x∗∥x∗	PROPN
ejpam-5165	148	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-5165	149	1	∑	∑	PUNCT
ejpam-5165	149	2	(	(	PUNCT
ejpam-5165	149	3	t,[u	t,[u	ADJ
ejpam-5165	149	4	,	,	PUNCT
ejpam-5165	149	5	v])∈p	v])∈p	PROPN
ejpam-5165	149	6	f(t)∆g([u	f(t)∆g([u	PROPN
ejpam-5165	149	7	,	,	PUNCT
ejpam-5165	149	8	v])−	v])−	NOUN
ejpam-5165	149	9	(	(	PUNCT
ejpam-5165	149	10	ms	ms	PROPN
ejpam-5165	149	11	)	)	PUNCT
ejpam-5165	149	12	∫	∫	PROPN
ejpam-5165	150	1	[	[	X
ejpam-5165	150	2	a	a	X
ejpam-5165	150	3	,	,	PUNCT
ejpam-5165	150	4	b	b	NOUN
ejpam-5165	150	5	]	]	X
ejpam-5165	150	6	f	f	X
ejpam-5165	150	7	dg	dg	PROPN
ejpam-5165	150	8	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-5165	151	1	x∗	x∗	PROPN
ejpam-5165	151	2	<	<	X
ejpam-5165	152	1	∥x∗∥x∗	∥x∗∥x∗	PROPN
ejpam-5165	152	2	ε	ε	PROPN
ejpam-5165	153	1	∥x∗∥x∗	∥x∗∥x∗	PROPN
ejpam-5165	153	2	+	+	CCONJ
ejpam-5165	153	3	1	1	NUM
ejpam-5165	153	4	=	=	SYM
ejpam-5165	153	5	ε	ε	PROPN
ejpam-5165	153	6	.	.	PUNCT
ejpam-5165	154	1	since	since	SCONJ
ejpam-5165	154	2	ε	ε	PROPN
ejpam-5165	154	3	is	be	AUX
ejpam-5165	154	4	arbitrarily	arbitrarily	ADV
ejpam-5165	154	5	chosen	choose	VERB
ejpam-5165	154	6	,	,	PUNCT
ejpam-5165	154	7	we	we	PRON
ejpam-5165	154	8	have	have	VERB
ejpam-5165	154	9	(	(	PUNCT
ejpam-5165	154	10	ms	ms	NOUN
ejpam-5165	154	11	)	)	PUNCT
ejpam-5165	154	12	∫	∫	PROPN
ejpam-5165	155	1	[	[	X
ejpam-5165	155	2	a	a	X
ejpam-5165	155	3	,	,	PUNCT
ejpam-5165	155	4	b	b	NOUN
ejpam-5165	155	5	]	]	X
ejpam-5165	155	6	x∗(f)dg	x∗(f)dg	X
ejpam-5165	155	7	=	=	PUNCT
ejpam-5165	155	8	x∗	x∗	PROPN
ejpam-5165	155	9	(	(	PUNCT
ejpam-5165	155	10	(	(	PUNCT
ejpam-5165	155	11	ms	ms	PROPN
ejpam-5165	155	12	)	)	PUNCT
ejpam-5165	155	13	∫	∫	PROPN
ejpam-5165	156	1	[	[	X
ejpam-5165	156	2	a	a	X
ejpam-5165	156	3	,	,	PUNCT
ejpam-5165	156	4	b	b	NOUN
ejpam-5165	156	5	]	]	X
ejpam-5165	156	6	fdg	fdg	PROPN
ejpam-5165	156	7	)	)	PUNCT
ejpam-5165	156	8	;	;	PUNCT
ejpam-5165	156	9	which	which	PRON
ejpam-5165	156	10	means	mean	VERB
ejpam-5165	156	11	that	that	SCONJ
ejpam-5165	156	12	x∗(f	x∗(f	PROPN
ejpam-5165	156	13	)	)	PUNCT
ejpam-5165	156	14	is	be	AUX
ejpam-5165	156	15	ms	ms	NOUN
ejpam-5165	156	16	-	-	PUNCT
ejpam-5165	156	17	integrable	integrable	ADJ
ejpam-5165	156	18	with	with	ADP
ejpam-5165	156	19	respect	respect	NOUN
ejpam-5165	156	20	to	to	ADP
ejpam-5165	156	21	g	g	NOUN
ejpam-5165	156	22	on	on	ADP
ejpam-5165	156	23	[	[	X
ejpam-5165	156	24	a	a	X
ejpam-5165	156	25	,	,	PUNCT
ejpam-5165	156	26	b	b	NOUN
ejpam-5165	156	27	]	]	X
ejpam-5165	156	28	integrable	integrable	ADJ
ejpam-5165	156	29	for	for	ADP
ejpam-5165	156	30	all	all	DET
ejpam-5165	156	31	x∗	x∗	PROPN
ejpam-5165	156	32	∈	∈	PROPN
ejpam-5165	156	33	x∗.	x∗.	PUNCT
ejpam-5165	157	1	□	□	PUNCT
ejpam-5165	157	2	in	in	ADP
ejpam-5165	157	3	this	this	DET
ejpam-5165	157	4	part	part	NOUN
ejpam-5165	157	5	,	,	PUNCT
ejpam-5165	157	6	the	the	DET
ejpam-5165	157	7	mcshane	mcshane	PROPN
ejpam-5165	157	8	-	-	PUNCT
ejpam-5165	157	9	dunford	dunford	NOUN
ejpam-5165	157	10	-	-	PUNCT
ejpam-5165	157	11	stieltjes	stieltjes	NOUN
ejpam-5165	157	12	integral	integral	NOUN
ejpam-5165	157	13	is	be	AUX
ejpam-5165	157	14	established	establish	VERB
ejpam-5165	157	15	as	as	SCONJ
ejpam-5165	157	16	it	it	PRON
ejpam-5165	157	17	is	be	AUX
ejpam-5165	157	18	a	a	DET
ejpam-5165	157	19	necessary	necessary	ADJ
ejpam-5165	157	20	concept	concept	NOUN
ejpam-5165	157	21	in	in	ADP
ejpam-5165	157	22	introducing	introduce	VERB
ejpam-5165	157	23	the	the	DET
ejpam-5165	157	24	mcshane	mcshane	PROPN
ejpam-5165	157	25	-	-	PUNCT
ejpam-5165	157	26	pettis	pettis	PROPN
ejpam-5165	157	27	-	-	PUNCT
ejpam-5165	157	28	stieltjes	stieltjes	NOUN
ejpam-5165	157	29	integral	integral	ADJ
ejpam-5165	157	30	.	.	PUNCT
ejpam-5165	158	1	definition	definition	NOUN
ejpam-5165	158	2	18	18	NUM
ejpam-5165	158	3	.	.	PUNCT
ejpam-5165	159	1	let	let	VERB
ejpam-5165	159	2	f	f	NOUN
ejpam-5165	159	3	:	:	PUNCT
ejpam-5165	160	1	[	[	X
ejpam-5165	160	2	a	a	X
ejpam-5165	160	3	,	,	PUNCT
ejpam-5165	160	4	b	b	NOUN
ejpam-5165	160	5	]	]	X
ejpam-5165	160	6	→	→	SYM
ejpam-5165	160	7	x	x	X
ejpam-5165	160	8	and	and	CCONJ
ejpam-5165	160	9	g	g	NOUN
ejpam-5165	160	10	:	:	PUNCT
ejpam-5165	161	1	[	[	X
ejpam-5165	161	2	a	a	X
ejpam-5165	161	3	,	,	PUNCT
ejpam-5165	161	4	b	b	NOUN
ejpam-5165	161	5	]	]	X
ejpam-5165	161	6	→	→	PUNCT
ejpam-5165	161	7	r	r	NOUN
ejpam-5165	161	8	be	be	NOUN
ejpam-5165	161	9	functions	function	NOUN
ejpam-5165	161	10	.	.	PUNCT
ejpam-5165	162	1	if	if	SCONJ
ejpam-5165	162	2	the	the	DET
ejpam-5165	162	3	function	function	NOUN
ejpam-5165	162	4	x∗(f	x∗(f	PROPN
ejpam-5165	162	5	)	)	PUNCT
ejpam-5165	162	6	:	:	PUNCT
ejpam-5165	163	1	[	[	X
ejpam-5165	163	2	a	a	X
ejpam-5165	163	3	,	,	PUNCT
ejpam-5165	163	4	b	b	NOUN
ejpam-5165	163	5	]	]	X
ejpam-5165	163	6	→	→	PUNCT
ejpam-5165	163	7	r	r	NOUN
ejpam-5165	163	8	is	be	AUX
ejpam-5165	163	9	mcshane	mcshane	NOUN
ejpam-5165	163	10	-	-	PUNCT
ejpam-5165	163	11	stieltjes	stieltjes	NOUN
ejpam-5165	163	12	integrable	integrable	ADJ
ejpam-5165	163	13	for	for	ADP
ejpam-5165	163	14	all	all	DET
ejpam-5165	163	15	x∗	x∗	PROPN
ejpam-5165	163	16	∈	∈	PROPN
ejpam-5165	163	17	x∗	x∗	PROPN
ejpam-5165	163	18	with	with	ADP
ejpam-5165	163	19	respect	respect	NOUN
ejpam-5165	163	20	to	to	ADP
ejpam-5165	163	21	g	g	NOUN
ejpam-5165	163	22	on	on	ADP
ejpam-5165	163	23	[	[	X
ejpam-5165	163	24	a	a	X
ejpam-5165	163	25	,	,	PUNCT
ejpam-5165	163	26	b	b	NOUN
ejpam-5165	163	27	]	]	PUNCT
ejpam-5165	163	28	and	and	CCONJ
ejpam-5165	163	29	if	if	SCONJ
ejpam-5165	163	30	for	for	ADP
ejpam-5165	163	31	every	every	DET
ejpam-5165	163	32	interval	interval	NOUN
ejpam-5165	163	33	j	j	PROPN
ejpam-5165	163	34	⊆	⊆	NUM
ejpam-5165	163	35	[	[	X
ejpam-5165	163	36	a	a	X
ejpam-5165	163	37	,	,	PUNCT
ejpam-5165	163	38	b	b	NOUN
ejpam-5165	163	39	]	]	X
ejpam-5165	163	40	,	,	PUNCT
ejpam-5165	163	41	there	there	PRON
ejpam-5165	163	42	exists	exist	VERB
ejpam-5165	163	43	an	an	DET
ejpam-5165	163	44	element	element	NOUN
ejpam-5165	163	45	x∗∗j	x∗∗j	PROPN
ejpam-5165	163	46	∈	∈	PROPN
ejpam-5165	163	47	x∗∗	x∗∗	NOUN
ejpam-5165	164	1	such	such	ADJ
ejpam-5165	164	2	that	that	SCONJ
ejpam-5165	164	3	x∗∗j	x∗∗j	PROPN
ejpam-5165	164	4	(	(	PUNCT
ejpam-5165	164	5	x∗	x∗	PROPN
ejpam-5165	164	6	)	)	PUNCT
ejpam-5165	164	7	=	=	SYM
ejpam-5165	164	8	(	(	PUNCT
ejpam-5165	164	9	ms	ms	PROPN
ejpam-5165	164	10	)	)	PUNCT
ejpam-5165	164	11	∫	∫	PROPN
ejpam-5165	164	12	j	j	PROPN
ejpam-5165	164	13	x∗(f	x∗(f	PROPN
ejpam-5165	164	14	)	)	PUNCT
ejpam-5165	164	15	dg	dg	VERB
ejpam-5165	164	16	for	for	ADP
ejpam-5165	164	17	all	all	DET
ejpam-5165	164	18	x∗	x∗	PROPN
ejpam-5165	164	19	∈	∈	PROPN
ejpam-5165	164	20	x∗	x∗	PROPN
ejpam-5165	164	21	,	,	PUNCT
ejpam-5165	164	22	then	then	ADV
ejpam-5165	164	23	f	f	PROPN
ejpam-5165	164	24	is	be	AUX
ejpam-5165	164	25	called	call	VERB
ejpam-5165	164	26	mcshane	mcshane	NOUN
ejpam-5165	164	27	-	-	PUNCT
ejpam-5165	164	28	dunfordstieltjes	dunfordstieltjes	PROPN
ejpam-5165	164	29	integrable	integrable	ADJ
ejpam-5165	164	30	(	(	PUNCT
ejpam-5165	164	31	or	or	CCONJ
ejpam-5165	164	32	simply	simply	ADV
ejpam-5165	164	33	mds	mds	NOUN
ejpam-5165	164	34	-	-	PUNCT
ejpam-5165	164	35	integrable	integrable	ADJ
ejpam-5165	164	36	)	)	PUNCT
ejpam-5165	164	37	with	with	ADP
ejpam-5165	164	38	respect	respect	NOUN
ejpam-5165	164	39	to	to	ADP
ejpam-5165	164	40	g	g	NOUN
ejpam-5165	164	41	on	on	ADP
ejpam-5165	164	42	[	[	X
ejpam-5165	164	43	a	a	X
ejpam-5165	164	44	,	,	PUNCT
ejpam-5165	164	45	b	b	NOUN
ejpam-5165	164	46	]	]	X
ejpam-5165	164	47	.	.	PUNCT
ejpam-5165	165	1	for	for	ADP
ejpam-5165	165	2	an	an	DET
ejpam-5165	165	3	interval	interval	NOUN
ejpam-5165	165	4	j	j	PROPN
ejpam-5165	165	5	⊆	⊆	NUM
ejpam-5165	165	6	[	[	X
ejpam-5165	165	7	a	a	X
ejpam-5165	165	8	,	,	PUNCT
ejpam-5165	165	9	b	b	NOUN
ejpam-5165	165	10	]	]	X
ejpam-5165	165	11	,	,	PUNCT
ejpam-5165	165	12	we	we	PRON
ejpam-5165	165	13	write	write	VERB
ejpam-5165	165	14	the	the	DET
ejpam-5165	165	15	mds	mds	NOUN
ejpam-5165	165	16	integral	integral	ADJ
ejpam-5165	165	17	of	of	ADP
ejpam-5165	165	18	f	f	PROPN
ejpam-5165	165	19	with	with	ADP
ejpam-5165	165	20	respect	respect	NOUN
ejpam-5165	165	21	to	to	ADP
ejpam-5165	165	22	g	g	NOUN
ejpam-5165	165	23	on	on	ADP
ejpam-5165	165	24	[	[	X
ejpam-5165	165	25	a	a	X
ejpam-5165	165	26	,	,	PUNCT
ejpam-5165	165	27	b	b	NOUN
ejpam-5165	165	28	]	]	PUNCT
ejpam-5165	165	29	by	by	ADP
ejpam-5165	165	30	(	(	PUNCT
ejpam-5165	165	31	mds	mds	PROPN
ejpam-5165	165	32	)	)	PUNCT
ejpam-5165	165	33	∫	∫	PROPN
ejpam-5165	166	1	j	j	PROPN
ejpam-5165	166	2	f	f	PROPN
ejpam-5165	166	3	dg	dg	PROPN
ejpam-5165	166	4	=	=	SYM
ejpam-5165	166	5	x∗∗j	x∗∗j	PROPN
ejpam-5165	166	6	∈	∈	PROPN
ejpam-5165	166	7	x∗∗.	x∗∗.	X
ejpam-5165	166	8	denote	denote	NOUN
ejpam-5165	166	9	by	by	ADP
ejpam-5165	166	10	mds([a	mds([a	NOUN
ejpam-5165	166	11	,	,	PUNCT
ejpam-5165	166	12	b	b	NOUN
ejpam-5165	166	13	]	]	X
ejpam-5165	166	14	,	,	PUNCT
ejpam-5165	166	15	g	g	NOUN
ejpam-5165	166	16	)	)	PUNCT
ejpam-5165	166	17	the	the	DET
ejpam-5165	166	18	set	set	NOUN
ejpam-5165	166	19	of	of	ADP
ejpam-5165	166	20	all	all	DET
ejpam-5165	166	21	mcshane	mcshane	PROPN
ejpam-5165	166	22	-	-	PUNCT
ejpam-5165	166	23	dunford	dunford	NOUN
ejpam-5165	166	24	-	-	PUNCT
ejpam-5165	166	25	stieltjes	stieltjes	PROPN
ejpam-5165	166	26	integrable	integrable	ADJ
ejpam-5165	166	27	functions	function	NOUN
ejpam-5165	166	28	f	f	NOUN
ejpam-5165	167	1	:	:	PUNCT
ejpam-5165	168	1	[	[	X
ejpam-5165	168	2	a	a	X
ejpam-5165	168	3	,	,	PUNCT
ejpam-5165	168	4	b	b	NOUN
ejpam-5165	168	5	]	]	X
ejpam-5165	168	6	→	→	PUNCT
ejpam-5165	168	7	x	x	SYM
ejpam-5165	168	8	with	with	ADP
ejpam-5165	168	9	respect	respect	NOUN
ejpam-5165	168	10	to	to	ADP
ejpam-5165	168	11	g	g	NOUN
ejpam-5165	168	12	on	on	ADP
ejpam-5165	168	13	[	[	X
ejpam-5165	168	14	a	a	X
ejpam-5165	168	15	,	,	PUNCT
ejpam-5165	168	16	b	b	NOUN
ejpam-5165	168	17	]	]	PUNCT
ejpam-5165	168	18	.	.	PUNCT
ejpam-5165	169	1	theorem	theorem	NOUN
ejpam-5165	169	2	2	2	NUM
ejpam-5165	169	3	.	.	X
ejpam-5165	170	1	there	there	PRON
ejpam-5165	170	2	is	be	VERB
ejpam-5165	170	3	at	at	ADP
ejpam-5165	170	4	most	most	ADV
ejpam-5165	170	5	one	one	NUM
ejpam-5165	170	6	value	value	NOUN
ejpam-5165	170	7	satisfying	satisfy	VERB
ejpam-5165	170	8	definition	definition	NOUN
ejpam-5165	170	9	18	18	NUM
ejpam-5165	170	10	.	.	PUNCT
ejpam-5165	170	11	proof	proof	NOUN
ejpam-5165	170	12	.	.	PUNCT
ejpam-5165	171	1	assume	assume	VERB
ejpam-5165	171	2	that	that	SCONJ
ejpam-5165	171	3	f	f	PROPN
ejpam-5165	171	4	is	be	AUX
ejpam-5165	171	5	mds	mds	NOUN
ejpam-5165	171	6	-	-	PUNCT
ejpam-5165	171	7	integrable	integrable	ADJ
ejpam-5165	171	8	with	with	ADP
ejpam-5165	171	9	respect	respect	NOUN
ejpam-5165	171	10	to	to	ADP
ejpam-5165	171	11	g	g	NOUN
ejpam-5165	171	12	on	on	ADP
ejpam-5165	171	13	[	[	X
ejpam-5165	171	14	a	a	X
ejpam-5165	171	15	,	,	PUNCT
ejpam-5165	171	16	b	b	NOUN
ejpam-5165	171	17	]	]	PUNCT
ejpam-5165	171	18	.	.	PUNCT
ejpam-5165	172	1	by	by	ADP
ejpam-5165	172	2	definition	definition	NOUN
ejpam-5165	172	3	18	18	NUM
ejpam-5165	172	4	,	,	PUNCT
ejpam-5165	172	5	x∗(f	x∗(f	PROPN
ejpam-5165	172	6	)	)	PUNCT
ejpam-5165	172	7	is	be	AUX
ejpam-5165	172	8	msintegrable	msintegrable	ADJ
ejpam-5165	172	9	with	with	ADP
ejpam-5165	172	10	respect	respect	NOUN
ejpam-5165	172	11	to	to	ADP
ejpam-5165	172	12	g	g	NOUN
ejpam-5165	172	13	on	on	ADP
ejpam-5165	172	14	[	[	X
ejpam-5165	172	15	a	a	X
ejpam-5165	172	16	,	,	PUNCT
ejpam-5165	172	17	b	b	NOUN
ejpam-5165	172	18	]	]	X
ejpam-5165	172	19	for	for	ADP
ejpam-5165	172	20	all	all	DET
ejpam-5165	172	21	x∗	x∗	PROPN
ejpam-5165	172	22	∈	∈	PROPN
ejpam-5165	172	23	x∗.	x∗.	PROPN
ejpam-5165	173	1	for	for	ADP
ejpam-5165	173	2	each	each	DET
ejpam-5165	173	3	interval	interval	NOUN
ejpam-5165	173	4	j	j	PROPN
ejpam-5165	173	5	⊆	⊆	NUM
ejpam-5165	173	6	[	[	X
ejpam-5165	173	7	a	a	X
ejpam-5165	173	8	,	,	PUNCT
ejpam-5165	173	9	b	b	NOUN
ejpam-5165	173	10	]	]	X
ejpam-5165	173	11	,	,	PUNCT
ejpam-5165	173	12	there	there	PRON
ejpam-5165	173	13	is	be	VERB
ejpam-5165	173	14	an	an	DET
ejpam-5165	173	15	element	element	NOUN
ejpam-5165	173	16	x∗∗j	x∗∗j	PROPN
ejpam-5165	173	17	∈	∈	PROPN
ejpam-5165	173	18	x∗∗	x∗∗	NOUN
ejpam-5165	173	19	such	such	ADJ
ejpam-5165	173	20	that	that	SCONJ
ejpam-5165	173	21	x∗∗j	x∗∗j	PROPN
ejpam-5165	173	22	(	(	PUNCT
ejpam-5165	173	23	x∗	x∗	PROPN
ejpam-5165	173	24	)	)	PUNCT
ejpam-5165	173	25	=	=	SYM
ejpam-5165	174	1	(	(	PUNCT
ejpam-5165	174	2	ms	ms	PROPN
ejpam-5165	174	3	)	)	PUNCT
ejpam-5165	174	4	∫	∫	PROPN
ejpam-5165	174	5	j	j	PROPN
ejpam-5165	174	6	x∗(f	x∗(f	PROPN
ejpam-5165	174	7	)	)	PUNCT
ejpam-5165	174	8	dg	dg	PART
ejpam-5165	174	9	∀x∗	∀x∗	NOUN
ejpam-5165	174	10	∈	∈	PROPN
ejpam-5165	174	11	x∗.	x∗.	PUNCT
ejpam-5165	175	1	now	now	ADV
ejpam-5165	175	2	,	,	PUNCT
ejpam-5165	175	3	for	for	ADP
ejpam-5165	175	4	an	an	DET
ejpam-5165	175	5	interval	interval	NOUN
ejpam-5165	175	6	j	j	PROPN
ejpam-5165	175	7	⊆	⊆	NUM
ejpam-5165	175	8	[	[	X
ejpam-5165	175	9	a	a	X
ejpam-5165	175	10	,	,	PUNCT
ejpam-5165	175	11	b	b	NOUN
ejpam-5165	175	12	]	]	PUNCT
ejpam-5165	175	13	.	.	PUNCT
ejpam-5165	175	14	suppose	suppose	VERB
ejpam-5165	175	15	that	that	SCONJ
ejpam-5165	175	16	x∗∗j	x∗∗j	PROPN
ejpam-5165	175	17	,	,	PUNCT
ejpam-5165	175	18	y∗∗j	y∗∗j	PROPN
ejpam-5165	175	19	∈	∈	PROPN
ejpam-5165	175	20	x∗∗	x∗∗	PROPN
ejpam-5165	175	21	are	be	AUX
ejpam-5165	175	22	the	the	DET
ejpam-5165	175	23	values	value	NOUN
ejpam-5165	175	24	of	of	ADP
ejpam-5165	175	25	mds	mds	PROPN
ejpam-5165	175	26	integral	integral	ADJ
ejpam-5165	175	27	of	of	ADP
ejpam-5165	175	28	f	f	PROPN
ejpam-5165	175	29	with	with	ADP
ejpam-5165	175	30	respect	respect	NOUN
ejpam-5165	175	31	to	to	ADP
ejpam-5165	175	32	g	g	NOUN
ejpam-5165	175	33	on	on	ADP
ejpam-5165	175	34	[	[	X
ejpam-5165	175	35	a	a	X
ejpam-5165	175	36	,	,	PUNCT
ejpam-5165	175	37	b	b	NOUN
ejpam-5165	175	38	]	]	PUNCT
ejpam-5165	175	39	.	.	PUNCT
ejpam-5165	176	1	let	let	VERB
ejpam-5165	176	2	x∗	x∗	PROPN
ejpam-5165	176	3	∈	∈	PROPN
ejpam-5165	176	4	x∗.	x∗.	PROPN
ejpam-5165	177	1	then	then	ADV
ejpam-5165	177	2	x∗(f	x∗(f	PROPN
ejpam-5165	177	3	)	)	PUNCT
ejpam-5165	177	4	is	be	AUX
ejpam-5165	177	5	mcshane	mcshane	NOUN
ejpam-5165	177	6	-	-	PUNCT
ejpam-5165	177	7	stieltjes	stieltjes	NOUN
ejpam-5165	177	8	integrable	integrable	ADJ
ejpam-5165	177	9	with	with	ADP
ejpam-5165	177	10	respect	respect	NOUN
ejpam-5165	177	11	to	to	ADP
ejpam-5165	177	12	g	g	NOUN
ejpam-5165	177	13	on	on	ADP
ejpam-5165	177	14	[	[	X
ejpam-5165	177	15	a	a	X
ejpam-5165	177	16	,	,	PUNCT
ejpam-5165	177	17	b	b	NOUN
ejpam-5165	177	18	]	]	PUNCT
ejpam-5165	177	19	.	.	PUNCT
ejpam-5165	178	1	but	but	CCONJ
ejpam-5165	178	2	x∗∗j	x∗∗j	PROPN
ejpam-5165	178	3	(	(	PUNCT
ejpam-5165	178	4	x∗	x∗	PROPN
ejpam-5165	178	5	)	)	PUNCT
ejpam-5165	178	6	=	=	SYM
ejpam-5165	179	1	(	(	PUNCT
ejpam-5165	179	2	ms	ms	PROPN
ejpam-5165	179	3	)	)	PUNCT
ejpam-5165	179	4	∫	∫	PROPN
ejpam-5165	179	5	j	j	PROPN
ejpam-5165	179	6	x∗(f	x∗(f	PROPN
ejpam-5165	179	7	)	)	PUNCT
ejpam-5165	179	8	dg	dg	PART
ejpam-5165	179	9	=	=	SYM
ejpam-5165	179	10	y∗∗j	y∗∗j	X
ejpam-5165	179	11	(	(	PUNCT
ejpam-5165	179	12	x∗	x∗	PROPN
ejpam-5165	179	13	)	)	PUNCT
ejpam-5165	179	14	.	.	PUNCT
ejpam-5165	180	1	d.	d.	PROPN
ejpam-5165	180	2	omayan	omayan	PROPN
ejpam-5165	180	3	,	,	PUNCT
ejpam-5165	180	4	g.b	g.b	PROPN
ejpam-5165	180	5	.	.	PROPN
ejpam-5165	180	6	flores	flores	PROPN
ejpam-5165	180	7	/	/	SYM
ejpam-5165	180	8	eur	eur	PROPN
ejpam-5165	180	9	.	.	PUNCT
ejpam-5165	181	1	j.	j.	PROPN
ejpam-5165	181	2	pure	pure	PROPN
ejpam-5165	181	3	appl	appl	PROPN
ejpam-5165	181	4	.	.	PROPN
ejpam-5165	181	5	math	math	PROPN
ejpam-5165	181	6	,	,	PUNCT
ejpam-5165	181	7	17	17	NUM
ejpam-5165	181	8	(	(	PUNCT
ejpam-5165	181	9	2	2	NUM
ejpam-5165	181	10	)	)	PUNCT
ejpam-5165	181	11	(	(	PUNCT
ejpam-5165	181	12	2024	2024	NUM
ejpam-5165	181	13	)	)	PUNCT
ejpam-5165	181	14	,	,	PUNCT
ejpam-5165	181	15	1183	1183	NUM
ejpam-5165	181	16	-	-	SYM
ejpam-5165	181	17	1196	1196	NUM
ejpam-5165	181	18	1189	1189	NUM
ejpam-5165	181	19	hence	hence	ADV
ejpam-5165	181	20	,	,	PUNCT
ejpam-5165	181	21	x∗∗j	x∗∗j	PROPN
ejpam-5165	181	22	=	=	SYM
ejpam-5165	181	23	(	(	PUNCT
ejpam-5165	181	24	mds	mds	PROPN
ejpam-5165	181	25	)	)	PUNCT
ejpam-5165	181	26	∫	∫	PROPN
ejpam-5165	182	1	j	j	PROPN
ejpam-5165	182	2	f	f	PROPN
ejpam-5165	182	3	dg	dg	PROPN
ejpam-5165	183	1	=	=	X
ejpam-5165	183	2	y∗∗j	y∗∗j	PROPN
ejpam-5165	183	3	.	.	PUNCT
ejpam-5165	184	1	this	this	PRON
ejpam-5165	184	2	means	mean	VERB
ejpam-5165	184	3	that	that	SCONJ
ejpam-5165	184	4	x∗∗j	x∗∗j	PROPN
ejpam-5165	184	5	=	=	PUNCT
ejpam-5165	184	6	y∗∗j	y∗∗j	NOUN
ejpam-5165	184	7	.	.	PUNCT
ejpam-5165	185	1	thus	thus	ADV
ejpam-5165	185	2	,	,	PUNCT
ejpam-5165	185	3	(	(	PUNCT
ejpam-5165	185	4	mds	mds	PROPN
ejpam-5165	185	5	)	)	PUNCT
ejpam-5165	185	6	∫	∫	PROPN
ejpam-5165	186	1	j	j	PROPN
ejpam-5165	186	2	f	f	PROPN
ejpam-5165	186	3	dg	dg	PROPN
ejpam-5165	186	4	is	be	AUX
ejpam-5165	186	5	unique	unique	ADJ
ejpam-5165	186	6	.	.	PUNCT
ejpam-5165	187	1	□	□	PUNCT
ejpam-5165	187	2	theorem	theorem	ADJ
ejpam-5165	187	3	3	3	NUM
ejpam-5165	187	4	.	.	PUNCT
ejpam-5165	187	5	(	(	PUNCT
ejpam-5165	187	6	linearity	linearity	NOUN
ejpam-5165	187	7	of	of	ADP
ejpam-5165	187	8	mds	mds	NOUN
ejpam-5165	187	9	-	-	PUNCT
ejpam-5165	187	10	integral	integral	ADJ
ejpam-5165	187	11	over	over	ADP
ejpam-5165	187	12	the	the	DET
ejpam-5165	187	13	integrand	integrand	NOUN
ejpam-5165	187	14	)	)	PUNCT
ejpam-5165	187	15	let	let	VERB
ejpam-5165	187	16	f1	f1	NOUN
ejpam-5165	187	17	,	,	PUNCT
ejpam-5165	187	18	f2	f2	PROPN
ejpam-5165	187	19	:	:	PUNCT
ejpam-5165	187	20	[	[	X
ejpam-5165	187	21	a	a	X
ejpam-5165	187	22	,	,	PUNCT
ejpam-5165	187	23	b	b	NOUN
ejpam-5165	187	24	]	]	X
ejpam-5165	187	25	→	→	SYM
ejpam-5165	187	26	x	x	X
ejpam-5165	187	27	and	and	CCONJ
ejpam-5165	187	28	g	g	NOUN
ejpam-5165	187	29	:	:	PUNCT
ejpam-5165	188	1	[	[	X
ejpam-5165	188	2	a	a	X
ejpam-5165	188	3	,	,	PUNCT
ejpam-5165	188	4	b	b	NOUN
ejpam-5165	188	5	]	]	X
ejpam-5165	188	6	→	→	PUNCT
ejpam-5165	188	7	r	r	NOUN
ejpam-5165	188	8	be	be	NOUN
ejpam-5165	188	9	functions	function	NOUN
ejpam-5165	188	10	.	.	PUNCT
ejpam-5165	189	1	if	if	SCONJ
ejpam-5165	189	2	f1	f1	PROPN
ejpam-5165	189	3	,	,	PUNCT
ejpam-5165	189	4	f2	f2	PROPN
ejpam-5165	189	5	∈	∈	PROPN
ejpam-5165	189	6	mds([a	mds([a	NOUN
ejpam-5165	189	7	,	,	PUNCT
ejpam-5165	189	8	b	b	NOUN
ejpam-5165	189	9	]	]	X
ejpam-5165	189	10	,	,	PUNCT
ejpam-5165	189	11	g	g	NOUN
ejpam-5165	189	12	)	)	PUNCT
ejpam-5165	189	13	,	,	PUNCT
ejpam-5165	189	14	then	then	ADV
ejpam-5165	189	15	for	for	ADP
ejpam-5165	189	16	every	every	DET
ejpam-5165	189	17	α	α	NOUN
ejpam-5165	189	18	,	,	PUNCT
ejpam-5165	189	19	β	β	X
ejpam-5165	189	20	∈	∈	NOUN
ejpam-5165	189	21	r	r	NOUN
ejpam-5165	189	22	,	,	PUNCT
ejpam-5165	189	23	αf1	αf1	X
ejpam-5165	189	24	+	+	CCONJ
ejpam-5165	189	25	βf2	βf2	PROPN
ejpam-5165	189	26	∈	∈	PROPN
ejpam-5165	189	27	mds([a	mds([a	NOUN
ejpam-5165	189	28	,	,	PUNCT
ejpam-5165	189	29	b	b	NOUN
ejpam-5165	189	30	]	]	X
ejpam-5165	189	31	,	,	PUNCT
ejpam-5165	189	32	g	g	NOUN
ejpam-5165	189	33	)	)	PUNCT
ejpam-5165	189	34	and	and	CCONJ
ejpam-5165	189	35	for	for	ADP
ejpam-5165	189	36	all	all	DET
ejpam-5165	189	37	j	j	NOUN
ejpam-5165	189	38	⊆	⊆	NUM
ejpam-5165	189	39	[	[	X
ejpam-5165	189	40	a	a	X
ejpam-5165	189	41	,	,	PUNCT
ejpam-5165	189	42	b	b	NOUN
ejpam-5165	189	43	]	]	X
ejpam-5165	189	44	(	(	PUNCT
ejpam-5165	189	45	mds	mds	PROPN
ejpam-5165	189	46	)	)	PUNCT
ejpam-5165	189	47	∫	∫	PROPN
ejpam-5165	190	1	j	j	PROPN
ejpam-5165	190	2	(	(	PUNCT
ejpam-5165	190	3	αf1	αf1	X
ejpam-5165	190	4	+	+	CCONJ
ejpam-5165	190	5	βf2	βf2	X
ejpam-5165	190	6	)	)	PUNCT
ejpam-5165	190	7	dg	dg	PROPN
ejpam-5165	190	8	=	=	SYM
ejpam-5165	190	9	α	α	PROPN
ejpam-5165	190	10	·	·	PUNCT
ejpam-5165	190	11	(	(	PUNCT
ejpam-5165	190	12	mds	mds	PROPN
ejpam-5165	190	13	)	)	PUNCT
ejpam-5165	190	14	∫	∫	PROPN
ejpam-5165	191	1	j	j	PROPN
ejpam-5165	191	2	f1	f1	PROPN
ejpam-5165	191	3	dg	dg	VERB
ejpam-5165	191	4	+	+	X
ejpam-5165	191	5	β	β	X
ejpam-5165	191	6	·	·	PUNCT
ejpam-5165	191	7	(	(	PUNCT
ejpam-5165	191	8	mds	mds	PROPN
ejpam-5165	191	9	)	)	PUNCT
ejpam-5165	191	10	∫	∫	PROPN
ejpam-5165	192	1	j	j	PROPN
ejpam-5165	192	2	f2	f2	PROPN
ejpam-5165	192	3	dg	dg	VERB
ejpam-5165	192	4	.	.	PUNCT
ejpam-5165	193	1	proof	proof	NOUN
ejpam-5165	193	2	.	.	PUNCT
ejpam-5165	194	1	fix	fix	VERB
ejpam-5165	194	2	x∗	x∗	PROPN
ejpam-5165	194	3	∈	∈	PROPN
ejpam-5165	195	1	x∗.	x∗.	PROPN
ejpam-5165	195	2	assume	assume	VERB
ejpam-5165	195	3	that	that	SCONJ
ejpam-5165	195	4	f1	f1	NOUN
ejpam-5165	195	5	,	,	PUNCT
ejpam-5165	195	6	f2	f2	PROPN
ejpam-5165	195	7	is	be	AUX
ejpam-5165	195	8	mds	mds	NOUN
ejpam-5165	195	9	-	-	PUNCT
ejpam-5165	195	10	integrable	integrable	ADJ
ejpam-5165	195	11	with	with	ADP
ejpam-5165	195	12	respect	respect	NOUN
ejpam-5165	195	13	to	to	ADP
ejpam-5165	195	14	g	g	NOUN
ejpam-5165	195	15	on	on	ADP
ejpam-5165	195	16	[	[	X
ejpam-5165	195	17	a	a	X
ejpam-5165	195	18	,	,	PUNCT
ejpam-5165	195	19	b	b	NOUN
ejpam-5165	195	20	]	]	X
ejpam-5165	195	21	.	.	PUNCT
ejpam-5165	196	1	then	then	ADV
ejpam-5165	196	2	x∗(f1	x∗(f1	PROPN
ejpam-5165	196	3	)	)	PUNCT
ejpam-5165	196	4	and	and	CCONJ
ejpam-5165	196	5	x∗(f2	x∗(f2	PROPN
ejpam-5165	196	6	)	)	PUNCT
ejpam-5165	196	7	is	be	AUX
ejpam-5165	196	8	ms	ms	PROPN
ejpam-5165	196	9	-	-	PUNCT
ejpam-5165	196	10	integrable	integrable	ADJ
ejpam-5165	196	11	.	.	PUNCT
ejpam-5165	197	1	this	this	PRON
ejpam-5165	197	2	further	further	ADJ
ejpam-5165	197	3	means	mean	VERB
ejpam-5165	197	4	that	that	SCONJ
ejpam-5165	197	5	x∗(f1	x∗(f1	PROPN
ejpam-5165	197	6	)	)	PUNCT
ejpam-5165	197	7	+	+	CCONJ
ejpam-5165	198	1	x∗(f2	x∗(f2	PROPN
ejpam-5165	198	2	)	)	PUNCT
ejpam-5165	198	3	is	be	AUX
ejpam-5165	198	4	ms	ms	PROPN
ejpam-5165	198	5	-	-	PUNCT
ejpam-5165	198	6	integrable	integrable	ADJ
ejpam-5165	198	7	.	.	PUNCT
ejpam-5165	199	1	now	now	ADV
ejpam-5165	199	2	,	,	PUNCT
ejpam-5165	199	3	let	let	VERB
ejpam-5165	199	4	α	α	PRON
ejpam-5165	199	5	,	,	PUNCT
ejpam-5165	199	6	β	β	PROPN
ejpam-5165	199	7	∈	∈	PROPN
ejpam-5165	199	8	r.	r.	PROPN
ejpam-5165	199	9	notice	notice	VERB
ejpam-5165	199	10	that	that	SCONJ
ejpam-5165	199	11	x∗(αf1	x∗(αf1	PROPN
ejpam-5165	199	12	+	+	CCONJ
ejpam-5165	199	13	βf2	βf2	PROPN
ejpam-5165	199	14	)	)	PUNCT
ejpam-5165	200	1	=	=	SYM
ejpam-5165	200	2	x∗(αf1	x∗(αf1	X
ejpam-5165	200	3	)	)	PUNCT
ejpam-5165	201	1	+	+	CCONJ
ejpam-5165	201	2	x∗(βf2	x∗(βf2	PROPN
ejpam-5165	201	3	)	)	PUNCT
ejpam-5165	202	1	=	=	SYM
ejpam-5165	202	2	α	α	X
ejpam-5165	202	3	·	·	PUNCT
ejpam-5165	202	4	x∗(f1	x∗(f1	PROPN
ejpam-5165	202	5	)	)	PUNCT
ejpam-5165	203	1	+	+	CCONJ
ejpam-5165	203	2	β	β	X
ejpam-5165	203	3	·	·	PUNCT
ejpam-5165	203	4	x∗(f2	x∗(f2	PROPN
ejpam-5165	203	5	)	)	PUNCT
ejpam-5165	203	6	.	.	PUNCT
ejpam-5165	204	1	and	and	CCONJ
ejpam-5165	204	2	so	so	ADV
ejpam-5165	204	3	,	,	PUNCT
ejpam-5165	204	4	α	α	PROPN
ejpam-5165	204	5	·	·	PUNCT
ejpam-5165	204	6	x∗(f1	x∗(f1	PROPN
ejpam-5165	204	7	)	)	PUNCT
ejpam-5165	205	1	+	+	CCONJ
ejpam-5165	205	2	β	β	X
ejpam-5165	205	3	·	·	PUNCT
ejpam-5165	205	4	x∗(f2	x∗(f2	PROPN
ejpam-5165	205	5	)	)	PUNCT
ejpam-5165	205	6	is	be	AUX
ejpam-5165	205	7	also	also	ADV
ejpam-5165	205	8	ms	ms	ADJ
ejpam-5165	205	9	-	-	PUNCT
ejpam-5165	205	10	integrable	integrable	ADJ
ejpam-5165	205	11	with	with	ADP
ejpam-5165	205	12	respect	respect	NOUN
ejpam-5165	205	13	to	to	ADP
ejpam-5165	205	14	g	g	NOUN
ejpam-5165	205	15	on	on	ADP
ejpam-5165	205	16	[	[	X
ejpam-5165	205	17	a	a	X
ejpam-5165	205	18	,	,	PUNCT
ejpam-5165	205	19	b	b	NOUN
ejpam-5165	205	20	]	]	PUNCT
ejpam-5165	205	21	.	.	PUNCT
ejpam-5165	206	1	by	by	ADP
ejpam-5165	206	2	the	the	DET
ejpam-5165	206	3	linearity	linearity	NOUN
ejpam-5165	206	4	property	property	NOUN
ejpam-5165	206	5	of	of	ADP
ejpam-5165	206	6	the	the	DET
ejpam-5165	206	7	ms	ms	NOUN
ejpam-5165	206	8	-	-	ADJ
ejpam-5165	206	9	integral	integral	ADJ
ejpam-5165	206	10	and	and	CCONJ
ejpam-5165	206	11	for	for	ADP
ejpam-5165	206	12	an	an	DET
ejpam-5165	206	13	interval	interval	NOUN
ejpam-5165	206	14	j	j	PROPN
ejpam-5165	206	15	⊆	⊆	NUM
ejpam-5165	206	16	[	[	X
ejpam-5165	206	17	a	a	X
ejpam-5165	206	18	,	,	PUNCT
ejpam-5165	206	19	b	b	NOUN
ejpam-5165	206	20	]	]	X
ejpam-5165	206	21	,	,	PUNCT
ejpam-5165	206	22	(	(	PUNCT
ejpam-5165	206	23	ms	ms	PROPN
ejpam-5165	206	24	)	)	PUNCT
ejpam-5165	206	25	∫	∫	PROPN
ejpam-5165	206	26	j	j	PROPN
ejpam-5165	207	1	[	[	X
ejpam-5165	207	2	α	α	X
ejpam-5165	207	3	·	·	PUNCT
ejpam-5165	207	4	x∗(f1	x∗(f1	PROPN
ejpam-5165	207	5	)	)	PUNCT
ejpam-5165	208	1	+	+	CCONJ
ejpam-5165	208	2	β	β	X
ejpam-5165	208	3	·	·	PUNCT
ejpam-5165	208	4	x∗(f2	x∗(f2	PROPN
ejpam-5165	208	5	)	)	PUNCT
ejpam-5165	208	6	]	]	PUNCT
ejpam-5165	209	1	dg	dg	X
ejpam-5165	209	2	=	=	SYM
ejpam-5165	209	3	α	α	PROPN
ejpam-5165	209	4	·	·	PUNCT
ejpam-5165	209	5	(	(	PUNCT
ejpam-5165	209	6	ms	ms	PROPN
ejpam-5165	209	7	)	)	PUNCT
ejpam-5165	209	8	∫	∫	PROPN
ejpam-5165	210	1	j	j	PROPN
ejpam-5165	210	2	x∗(f1)dg	x∗(f1)dg	PROPN
ejpam-5165	211	1	+	+	CCONJ
ejpam-5165	211	2	β	β	X
ejpam-5165	211	3	·	·	PUNCT
ejpam-5165	211	4	(	(	PUNCT
ejpam-5165	211	5	ms	ms	PROPN
ejpam-5165	211	6	)	)	PUNCT
ejpam-5165	211	7	∫	∫	PROPN
ejpam-5165	211	8	j	j	PROPN
ejpam-5165	211	9	x∗(f2)dg	x∗(f2)dg	PROPN
ejpam-5165	211	10	.	.	PUNCT
ejpam-5165	212	1	fix	fix	VERB
ejpam-5165	212	2	an	an	DET
ejpam-5165	212	3	interval	interval	NOUN
ejpam-5165	212	4	j	j	NOUN
ejpam-5165	213	1	⊆	⊆	NUM
ejpam-5165	213	2	[	[	X
ejpam-5165	213	3	a	a	X
ejpam-5165	213	4	,	,	PUNCT
ejpam-5165	213	5	b	b	NOUN
ejpam-5165	213	6	]	]	X
ejpam-5165	213	7	.	.	PUNCT
ejpam-5165	214	1	since	since	SCONJ
ejpam-5165	214	2	f1	f1	NOUN
ejpam-5165	214	3	,	,	PUNCT
ejpam-5165	214	4	f2	f2	PROPN
ejpam-5165	214	5	∈	∈	PROPN
ejpam-5165	214	6	mds([a	mds([a	NOUN
ejpam-5165	214	7	,	,	PUNCT
ejpam-5165	214	8	b	b	NOUN
ejpam-5165	214	9	]	]	X
ejpam-5165	214	10	,	,	PUNCT
ejpam-5165	214	11	g	g	NOUN
ejpam-5165	214	12	)	)	PUNCT
ejpam-5165	214	13	,	,	PUNCT
ejpam-5165	214	14	it	it	PRON
ejpam-5165	214	15	follows	follow	VERB
ejpam-5165	214	16	that	that	SCONJ
ejpam-5165	214	17	we	we	PRON
ejpam-5165	214	18	can	can	AUX
ejpam-5165	214	19	pick	pick	VERB
ejpam-5165	214	20	operators	operator	NOUN
ejpam-5165	214	21	x∗∗j	x∗∗j	PROPN
ejpam-5165	214	22	,	,	PUNCT
ejpam-5165	215	1	y∗∗j	y∗∗j	PROPN
ejpam-5165	215	2	∈	∈	PROPN
ejpam-5165	215	3	x∗∗	x∗∗	NOUN
ejpam-5165	215	4	such	such	ADJ
ejpam-5165	215	5	that	that	SCONJ
ejpam-5165	215	6	x∗∗j	x∗∗j	PROPN
ejpam-5165	215	7	(	(	PUNCT
ejpam-5165	215	8	x∗	x∗	PROPN
ejpam-5165	215	9	)	)	PUNCT
ejpam-5165	215	10	=	=	SYM
ejpam-5165	215	11	(	(	PUNCT
ejpam-5165	215	12	ms	ms	PROPN
ejpam-5165	215	13	)	)	PUNCT
ejpam-5165	215	14	∫	∫	PROPN
ejpam-5165	215	15	j	j	PROPN
ejpam-5165	215	16	x∗(f1	x∗(f1	PROPN
ejpam-5165	215	17	)	)	PUNCT
ejpam-5165	215	18	dg	dg	NOUN
ejpam-5165	215	19	and	and	CCONJ
ejpam-5165	215	20	y∗∗j	y∗∗j	PROPN
ejpam-5165	215	21	(	(	PUNCT
ejpam-5165	215	22	x∗	x∗	PROPN
ejpam-5165	215	23	)	)	PUNCT
ejpam-5165	216	1	=	=	PUNCT
ejpam-5165	216	2	(	(	PUNCT
ejpam-5165	216	3	ms	ms	PROPN
ejpam-5165	216	4	)	)	PUNCT
ejpam-5165	216	5	∫	∫	PROPN
ejpam-5165	216	6	j	j	PROPN
ejpam-5165	216	7	x∗(f2	x∗(f2	PROPN
ejpam-5165	216	8	)	)	PUNCT
ejpam-5165	216	9	dg	dg	VERB
ejpam-5165	216	10	∀x∗	∀x∗	NOUN
ejpam-5165	216	11	∈	∈	PROPN
ejpam-5165	216	12	x∗.	x∗.	PUNCT
ejpam-5165	217	1	now	now	ADV
ejpam-5165	217	2	,	,	PUNCT
ejpam-5165	217	3	αx∗∗j	αx∗∗j	NUM
ejpam-5165	217	4	+	+	CCONJ
ejpam-5165	217	5	βy∗∗j	βy∗∗j	NUM
ejpam-5165	217	6	∈	∈	NOUN
ejpam-5165	217	7	x∗∗.	x∗∗.	X
ejpam-5165	217	8	take	take	VERB
ejpam-5165	217	9	w∗∗	w∗∗	PROPN
ejpam-5165	217	10	j	j	NOUN
ejpam-5165	217	11	=	=	SYM
ejpam-5165	217	12	αx∗∗j	αx∗∗j	PROPN
ejpam-5165	217	13	+	+	X
ejpam-5165	217	14	βy∗∗j	βy∗∗j	NUM
ejpam-5165	217	15	.	.	PUNCT
ejpam-5165	218	1	fix	fix	VERB
ejpam-5165	218	2	x∗	x∗	PROPN
ejpam-5165	218	3	∈	∈	PROPN
ejpam-5165	219	1	x∗.	x∗.	PROPN
ejpam-5165	220	1	then	then	ADV
ejpam-5165	220	2	w∗∗	w∗∗	PRON
ejpam-5165	220	3	j	j	PROPN
ejpam-5165	220	4	(	(	PUNCT
ejpam-5165	220	5	x∗	x∗	PROPN
ejpam-5165	220	6	)	)	PUNCT
ejpam-5165	220	7	=	=	SYM
ejpam-5165	220	8	(	(	PUNCT
ejpam-5165	220	9	αx∗∗j	αx∗∗j	NOUN
ejpam-5165	220	10	+	+	X
ejpam-5165	220	11	βy∗∗j	βy∗∗j	NUM
ejpam-5165	220	12	)	)	PUNCT
ejpam-5165	220	13	(	(	PUNCT
ejpam-5165	220	14	x∗	x∗	X
ejpam-5165	220	15	)	)	PUNCT
ejpam-5165	220	16	=	=	SYM
ejpam-5165	220	17	αx∗∗j	αx∗∗j	NOUN
ejpam-5165	220	18	(	(	PUNCT
ejpam-5165	220	19	x∗	x∗	PROPN
ejpam-5165	220	20	)	)	PUNCT
ejpam-5165	221	1	+	+	CCONJ
ejpam-5165	221	2	βy∗∗j	βy∗∗j	NUM
ejpam-5165	221	3	(	(	PUNCT
ejpam-5165	221	4	x∗	x∗	X
ejpam-5165	221	5	)	)	PUNCT
ejpam-5165	221	6	=	=	SYM
ejpam-5165	221	7	α(ms	α(ms	NUM
ejpam-5165	221	8	)	)	PUNCT
ejpam-5165	221	9	∫	∫	PROPN
ejpam-5165	221	10	j	j	PROPN
ejpam-5165	221	11	x∗(f1	x∗(f1	PROPN
ejpam-5165	221	12	)	)	PUNCT
ejpam-5165	221	13	dg	dg	PROPN
ejpam-5165	221	14	+	+	CCONJ
ejpam-5165	221	15	β(ms	β(ms	NUM
ejpam-5165	221	16	)	)	PUNCT
ejpam-5165	221	17	∫	∫	PROPN
ejpam-5165	221	18	j	j	PROPN
ejpam-5165	221	19	x∗(f2	x∗(f2	PROPN
ejpam-5165	221	20	)	)	PUNCT
ejpam-5165	221	21	dg	dg	PROPN
ejpam-5165	222	1	=	=	SYM
ejpam-5165	222	2	(	(	PUNCT
ejpam-5165	222	3	ms	ms	PROPN
ejpam-5165	222	4	)	)	PUNCT
ejpam-5165	222	5	∫	∫	PROPN
ejpam-5165	222	6	j	j	PROPN
ejpam-5165	222	7	α	α	PROPN
ejpam-5165	222	8	·	·	PUNCT
ejpam-5165	222	9	x∗(f1	x∗(f1	PROPN
ejpam-5165	222	10	)	)	PUNCT
ejpam-5165	222	11	dg	dg	PROPN
ejpam-5165	223	1	+	+	CCONJ
ejpam-5165	223	2	(	(	PUNCT
ejpam-5165	223	3	ms	ms	PROPN
ejpam-5165	223	4	)	)	PUNCT
ejpam-5165	223	5	∫	∫	PROPN
ejpam-5165	223	6	j	j	PROPN
ejpam-5165	223	7	β	β	X
ejpam-5165	223	8	·	·	PUNCT
ejpam-5165	223	9	x∗(f2	x∗(f2	PROPN
ejpam-5165	223	10	)	)	PUNCT
ejpam-5165	223	11	dg	dg	PROPN
ejpam-5165	224	1	=	=	SYM
ejpam-5165	224	2	(	(	PUNCT
ejpam-5165	224	3	ms	ms	PROPN
ejpam-5165	224	4	)	)	PUNCT
ejpam-5165	224	5	∫	∫	PROPN
ejpam-5165	224	6	j	j	PROPN
ejpam-5165	225	1	[	[	X
ejpam-5165	225	2	α	α	X
ejpam-5165	225	3	·	·	PUNCT
ejpam-5165	225	4	x∗(f1	x∗(f1	PROPN
ejpam-5165	225	5	)	)	PUNCT
ejpam-5165	226	1	+	+	CCONJ
ejpam-5165	226	2	β	β	X
ejpam-5165	226	3	·	·	PUNCT
ejpam-5165	226	4	x∗(f2	x∗(f2	PROPN
ejpam-5165	226	5	)	)	PUNCT
ejpam-5165	226	6	]	]	PUNCT
ejpam-5165	227	1	dg	dg	PROPN
ejpam-5165	227	2	=	=	SYM
ejpam-5165	227	3	(	(	PUNCT
ejpam-5165	227	4	ms	ms	PROPN
ejpam-5165	227	5	)	)	PUNCT
ejpam-5165	227	6	∫	∫	PROPN
ejpam-5165	227	7	j	j	PROPN
ejpam-5165	227	8	x∗(αf1	x∗(αf1	PROPN
ejpam-5165	228	1	+	+	CCONJ
ejpam-5165	228	2	βf2	βf2	PROPN
ejpam-5165	228	3	)	)	PUNCT
ejpam-5165	228	4	dg	dg	PROPN
ejpam-5165	228	5	.	.	PUNCT
ejpam-5165	229	1	consequently	consequently	ADV
ejpam-5165	229	2	,	,	PUNCT
ejpam-5165	229	3	αf1	αf1	ADJ
ejpam-5165	229	4	+	+	CCONJ
ejpam-5165	229	5	βf2	βf2	PROPN
ejpam-5165	229	6	is	be	AUX
ejpam-5165	229	7	mds	mds	NOUN
ejpam-5165	229	8	-	-	PUNCT
ejpam-5165	229	9	integrable	integrable	ADJ
ejpam-5165	229	10	with	with	ADP
ejpam-5165	229	11	respect	respect	NOUN
ejpam-5165	229	12	to	to	ADP
ejpam-5165	229	13	g	g	NOUN
ejpam-5165	229	14	on	on	ADP
ejpam-5165	229	15	[	[	X
ejpam-5165	229	16	a	a	X
ejpam-5165	229	17	,	,	PUNCT
ejpam-5165	229	18	b	b	NOUN
ejpam-5165	229	19	]	]	X
ejpam-5165	229	20	.	.	PUNCT
ejpam-5165	230	1	therefore	therefore	ADV
ejpam-5165	230	2	,	,	PUNCT
ejpam-5165	230	3	(	(	PUNCT
ejpam-5165	230	4	mds	mds	PROPN
ejpam-5165	230	5	)	)	PUNCT
ejpam-5165	230	6	∫	∫	PROPN
ejpam-5165	231	1	j	j	PROPN
ejpam-5165	231	2	(	(	PUNCT
ejpam-5165	231	3	αf1	αf1	X
ejpam-5165	231	4	+	+	CCONJ
ejpam-5165	231	5	βf2	βf2	X
ejpam-5165	231	6	)	)	PUNCT
ejpam-5165	231	7	dg	dg	PROPN
ejpam-5165	231	8	=	=	PUNCT
ejpam-5165	232	1	w∗∗	w∗∗	X
ejpam-5165	232	2	j	j	PROPN
ejpam-5165	232	3	=	=	SYM
ejpam-5165	232	4	αx∗∗j	αx∗∗j	PROPN
ejpam-5165	232	5	+	+	CCONJ
ejpam-5165	232	6	βy∗∗j	βy∗∗j	NUM
ejpam-5165	232	7	=	=	SYM
ejpam-5165	232	8	α	α	X
ejpam-5165	232	9	·	·	PUNCT
ejpam-5165	232	10	(	(	PUNCT
ejpam-5165	232	11	mds	mds	PROPN
ejpam-5165	232	12	)	)	PUNCT
ejpam-5165	232	13	∫	∫	PROPN
ejpam-5165	232	14	j	j	PROPN
ejpam-5165	232	15	f1	f1	PROPN
ejpam-5165	232	16	dg	dg	VERB
ejpam-5165	232	17	+	+	X
ejpam-5165	232	18	β	β	X
ejpam-5165	232	19	·	·	PUNCT
ejpam-5165	232	20	(	(	PUNCT
ejpam-5165	232	21	mds	mds	PROPN
ejpam-5165	232	22	)	)	PUNCT
ejpam-5165	232	23	∫	∫	PROPN
ejpam-5165	233	1	j	j	PROPN
ejpam-5165	233	2	f2	f2	PROPN
ejpam-5165	233	3	dg	dg	PROPN
ejpam-5165	233	4	.	.	PUNCT
ejpam-5165	234	1	□	□	PUNCT
ejpam-5165	234	2	d.	d.	PROPN
ejpam-5165	234	3	omayan	omayan	NOUN
ejpam-5165	234	4	,	,	PUNCT
ejpam-5165	234	5	g.b	g.b	PROPN
ejpam-5165	234	6	.	.	PROPN
ejpam-5165	234	7	flores	flores	PROPN
ejpam-5165	234	8	/	/	SYM
ejpam-5165	234	9	eur	eur	PROPN
ejpam-5165	234	10	.	.	PUNCT
ejpam-5165	235	1	j.	j.	PROPN
ejpam-5165	235	2	pure	pure	PROPN
ejpam-5165	235	3	appl	appl	PROPN
ejpam-5165	235	4	.	.	PROPN
ejpam-5165	235	5	math	math	PROPN
ejpam-5165	235	6	,	,	PUNCT
ejpam-5165	235	7	17	17	NUM
ejpam-5165	235	8	(	(	PUNCT
ejpam-5165	235	9	2	2	NUM
ejpam-5165	235	10	)	)	PUNCT
ejpam-5165	235	11	(	(	PUNCT
ejpam-5165	235	12	2024	2024	NUM
ejpam-5165	235	13	)	)	PUNCT
ejpam-5165	235	14	,	,	PUNCT
ejpam-5165	235	15	1183	1183	NUM
ejpam-5165	235	16	-	-	SYM
ejpam-5165	235	17	1196	1196	NUM
ejpam-5165	235	18	1190	1190	NUM
ejpam-5165	235	19	theorem	theorem	NOUN
ejpam-5165	235	20	4	4	NUM
ejpam-5165	235	21	.	.	PUNCT
ejpam-5165	236	1	(	(	PUNCT
ejpam-5165	236	2	linearity	linearity	NOUN
ejpam-5165	236	3	of	of	ADP
ejpam-5165	236	4	mds	mds	NOUN
ejpam-5165	236	5	-	-	PUNCT
ejpam-5165	236	6	integral	integral	ADJ
ejpam-5165	236	7	over	over	ADP
ejpam-5165	236	8	the	the	DET
ejpam-5165	236	9	integrator	integrator	NOUN
ejpam-5165	236	10	)	)	PUNCT
ejpam-5165	236	11	let	let	VERB
ejpam-5165	236	12	f	f	NOUN
ejpam-5165	236	13	:	:	PUNCT
ejpam-5165	237	1	[	[	X
ejpam-5165	237	2	a	a	X
ejpam-5165	237	3	,	,	PUNCT
ejpam-5165	237	4	b	b	NOUN
ejpam-5165	237	5	]	]	X
ejpam-5165	237	6	→	→	SYM
ejpam-5165	237	7	x	x	X
ejpam-5165	237	8	and	and	CCONJ
ejpam-5165	237	9	g1	g1	PROPN
ejpam-5165	237	10	,	,	PUNCT
ejpam-5165	237	11	g2	g2	PROPN
ejpam-5165	237	12	:	:	PUNCT
ejpam-5165	238	1	[	[	X
ejpam-5165	238	2	a	a	X
ejpam-5165	238	3	,	,	PUNCT
ejpam-5165	238	4	b	b	NOUN
ejpam-5165	238	5	]	]	X
ejpam-5165	238	6	→	→	PUNCT
ejpam-5165	238	7	r	r	NOUN
ejpam-5165	238	8	be	be	NOUN
ejpam-5165	238	9	functions	function	NOUN
ejpam-5165	238	10	.	.	PUNCT
ejpam-5165	239	1	if	if	SCONJ
ejpam-5165	239	2	f	f	PROPN
ejpam-5165	239	3	is	be	AUX
ejpam-5165	239	4	mds	mds	NOUN
ejpam-5165	239	5	-	-	PUNCT
ejpam-5165	239	6	integrable	integrable	ADJ
ejpam-5165	239	7	with	with	ADP
ejpam-5165	239	8	respect	respect	NOUN
ejpam-5165	239	9	to	to	ADP
ejpam-5165	239	10	g1	g1	VERB
ejpam-5165	239	11	and	and	CCONJ
ejpam-5165	239	12	g2	g2	PROPN
ejpam-5165	239	13	on	on	ADP
ejpam-5165	239	14	[	[	X
ejpam-5165	239	15	a	a	DET
ejpam-5165	239	16	,	,	PUNCT
ejpam-5165	239	17	b	b	NOUN
ejpam-5165	239	18	]	]	PUNCT
ejpam-5165	239	19	,	,	PUNCT
ejpam-5165	239	20	then	then	ADV
ejpam-5165	239	21	f	f	PROPN
ejpam-5165	239	22	∈	∈	PROPN
ejpam-5165	239	23	mds([a	mds([a	NOUN
ejpam-5165	239	24	,	,	PUNCT
ejpam-5165	239	25	b	b	NOUN
ejpam-5165	239	26	]	]	X
ejpam-5165	239	27	,	,	PUNCT
ejpam-5165	239	28	αg1	αg1	X
ejpam-5165	239	29	+	+	X
ejpam-5165	239	30	βg2	βg2	X
ejpam-5165	239	31	)	)	PUNCT
ejpam-5165	239	32	and	and	CCONJ
ejpam-5165	239	33	for	for	ADP
ejpam-5165	239	34	every	every	DET
ejpam-5165	239	35	j	j	PROPN
ejpam-5165	239	36	⊆	⊆	NUM
ejpam-5165	239	37	[	[	X
ejpam-5165	239	38	a	a	X
ejpam-5165	239	39	,	,	PUNCT
ejpam-5165	239	40	b	b	NOUN
ejpam-5165	239	41	]	]	X
ejpam-5165	239	42	(	(	PUNCT
ejpam-5165	239	43	mds	mds	PROPN
ejpam-5165	239	44	)	)	PUNCT
ejpam-5165	240	1	∫	∫	PROPN
ejpam-5165	241	1	j	j	PROPN
ejpam-5165	241	2	f	f	PROPN
ejpam-5165	241	3	d[αg1	d[αg1	PROPN
ejpam-5165	242	1	+	+	CCONJ
ejpam-5165	242	2	βg2	βg2	X
ejpam-5165	242	3	]	]	X
ejpam-5165	242	4	=	=	SYM
ejpam-5165	242	5	α	α	X
ejpam-5165	242	6	·	·	PUNCT
ejpam-5165	242	7	(	(	PUNCT
ejpam-5165	242	8	mds	mds	PROPN
ejpam-5165	242	9	)	)	PUNCT
ejpam-5165	242	10	∫	∫	PROPN
ejpam-5165	243	1	j	j	PROPN
ejpam-5165	243	2	f	f	PROPN
ejpam-5165	243	3	dg1	dg1	PROPN
ejpam-5165	244	1	+	+	X
ejpam-5165	244	2	β	β	X
ejpam-5165	244	3	·	·	PUNCT
ejpam-5165	244	4	(	(	PUNCT
ejpam-5165	244	5	mds	mds	PROPN
ejpam-5165	244	6	)	)	PUNCT
ejpam-5165	244	7	∫	∫	PROPN
ejpam-5165	245	1	j	j	PROPN
ejpam-5165	245	2	f	f	PROPN
ejpam-5165	245	3	dg2	dg2	PROPN
ejpam-5165	245	4	.	.	PROPN
ejpam-5165	245	5	proof	proof	NOUN
ejpam-5165	245	6	.	.	PUNCT
ejpam-5165	246	1	fix	fix	VERB
ejpam-5165	246	2	x∗	x∗	PROPN
ejpam-5165	246	3	∈	∈	PROPN
ejpam-5165	246	4	x∗.	x∗.	PROPN
ejpam-5165	246	5	assume	assume	VERB
ejpam-5165	246	6	that	that	SCONJ
ejpam-5165	246	7	f	f	PROPN
ejpam-5165	246	8	is	be	AUX
ejpam-5165	246	9	mcshane	mcshane	PROPN
ejpam-5165	246	10	-	-	PUNCT
ejpam-5165	246	11	dunford	dunford	NOUN
ejpam-5165	246	12	-	-	PUNCT
ejpam-5165	246	13	stieltjes	stieltjes	NOUN
ejpam-5165	246	14	integrable	integrable	ADJ
ejpam-5165	246	15	with	with	ADP
ejpam-5165	246	16	respect	respect	NOUN
ejpam-5165	246	17	to	to	ADP
ejpam-5165	246	18	g1	g1	VERB
ejpam-5165	246	19	and	and	CCONJ
ejpam-5165	246	20	g2	g2	PROPN
ejpam-5165	246	21	on	on	ADP
ejpam-5165	246	22	[	[	X
ejpam-5165	246	23	a	a	X
ejpam-5165	246	24	,	,	PUNCT
ejpam-5165	246	25	b	b	NOUN
ejpam-5165	246	26	]	]	X
ejpam-5165	246	27	.	.	PUNCT
ejpam-5165	247	1	then	then	ADV
ejpam-5165	247	2	x∗(f	x∗(f	PROPN
ejpam-5165	247	3	)	)	PUNCT
ejpam-5165	247	4	is	be	AUX
ejpam-5165	247	5	ms	ms	NOUN
ejpam-5165	247	6	-	-	PUNCT
ejpam-5165	247	7	integrable	integrable	ADJ
ejpam-5165	247	8	with	with	ADP
ejpam-5165	247	9	respect	respect	NOUN
ejpam-5165	247	10	to	to	ADP
ejpam-5165	247	11	g1	g1	VERB
ejpam-5165	247	12	and	and	CCONJ
ejpam-5165	247	13	g2	g2	PROPN
ejpam-5165	247	14	on	on	ADP
ejpam-5165	247	15	[	[	X
ejpam-5165	247	16	a	a	X
ejpam-5165	247	17	,	,	PUNCT
ejpam-5165	247	18	b	b	NOUN
ejpam-5165	247	19	]	]	PUNCT
ejpam-5165	247	20	.	.	PUNCT
ejpam-5165	248	1	utilizing	utilize	VERB
ejpam-5165	248	2	the	the	DET
ejpam-5165	248	3	linearity	linearity	NOUN
ejpam-5165	248	4	property	property	NOUN
ejpam-5165	248	5	of	of	ADP
ejpam-5165	248	6	ms	ms	NOUN
ejpam-5165	248	7	-	-	ADJ
ejpam-5165	248	8	integral	integral	ADJ
ejpam-5165	248	9	over	over	ADP
ejpam-5165	248	10	an	an	DET
ejpam-5165	248	11	integrator	integrator	NOUN
ejpam-5165	248	12	and	and	CCONJ
ejpam-5165	248	13	for	for	ADP
ejpam-5165	248	14	an	an	DET
ejpam-5165	248	15	interval	interval	NOUN
ejpam-5165	248	16	j	j	PROPN
ejpam-5165	248	17	⊆	⊆	NUM
ejpam-5165	248	18	[	[	X
ejpam-5165	248	19	a	a	X
ejpam-5165	248	20	,	,	PUNCT
ejpam-5165	248	21	b	b	NOUN
ejpam-5165	248	22	]	]	X
ejpam-5165	248	23	,	,	PUNCT
ejpam-5165	248	24	(	(	PUNCT
ejpam-5165	248	25	ms	ms	PROPN
ejpam-5165	248	26	)	)	PUNCT
ejpam-5165	248	27	∫	∫	PROPN
ejpam-5165	249	1	[	[	X
ejpam-5165	249	2	a	a	X
ejpam-5165	249	3	,	,	PUNCT
ejpam-5165	249	4	b	b	NOUN
ejpam-5165	249	5	]	]	X
ejpam-5165	249	6	x∗(f)d[αg1	x∗(f)d[αg1	PROPN
ejpam-5165	250	1	+	+	NUM
ejpam-5165	250	2	βg2	βg2	X
ejpam-5165	250	3	]	]	X
ejpam-5165	250	4	=	=	SYM
ejpam-5165	250	5	α(ms	α(ms	NUM
ejpam-5165	250	6	)	)	PUNCT
ejpam-5165	250	7	∫	∫	NOUN
ejpam-5165	251	1	[	[	X
ejpam-5165	251	2	a	a	X
ejpam-5165	251	3	,	,	PUNCT
ejpam-5165	251	4	b	b	NOUN
ejpam-5165	251	5	]	]	X
ejpam-5165	251	6	x∗(f)dg1	x∗(f)dg1	PUNCT
ejpam-5165	252	1	+	+	CCONJ
ejpam-5165	252	2	β(ms	β(ms	NUM
ejpam-5165	252	3	)	)	PUNCT
ejpam-5165	252	4	∫	∫	PROPN
ejpam-5165	253	1	[	[	X
ejpam-5165	253	2	a	a	X
ejpam-5165	253	3	,	,	PUNCT
ejpam-5165	253	4	b	b	NOUN
ejpam-5165	253	5	]	]	X
ejpam-5165	253	6	x∗(f)dg2	x∗(f)dg2	PROPN
ejpam-5165	253	7	.	.	PUNCT
ejpam-5165	254	1	let	let	VERB
ejpam-5165	254	2	an	an	DET
ejpam-5165	254	3	interval	interval	NOUN
ejpam-5165	254	4	j	j	NOUN
ejpam-5165	254	5	⊆	⊆	NUM
ejpam-5165	254	6	[	[	X
ejpam-5165	254	7	a	a	X
ejpam-5165	254	8	,	,	PUNCT
ejpam-5165	254	9	b	b	NOUN
ejpam-5165	254	10	]	]	X
ejpam-5165	254	11	.	.	PUNCT
ejpam-5165	255	1	since	since	SCONJ
ejpam-5165	255	2	f	f	PROPN
ejpam-5165	255	3	is	be	AUX
ejpam-5165	255	4	mds	mds	NOUN
ejpam-5165	255	5	-	-	PUNCT
ejpam-5165	255	6	integrable	integrable	ADJ
ejpam-5165	255	7	with	with	ADP
ejpam-5165	255	8	respect	respect	NOUN
ejpam-5165	255	9	to	to	ADP
ejpam-5165	255	10	g1	g1	VERB
ejpam-5165	255	11	and	and	CCONJ
ejpam-5165	255	12	g2	g2	PROPN
ejpam-5165	255	13	on	on	ADP
ejpam-5165	255	14	[	[	X
ejpam-5165	255	15	a	a	DET
ejpam-5165	255	16	,	,	PUNCT
ejpam-5165	255	17	b	b	NOUN
ejpam-5165	255	18	]	]	X
ejpam-5165	255	19	,	,	PUNCT
ejpam-5165	255	20	it	it	PRON
ejpam-5165	255	21	implies	imply	VERB
ejpam-5165	255	22	that	that	SCONJ
ejpam-5165	255	23	we	we	PRON
ejpam-5165	255	24	can	can	AUX
ejpam-5165	255	25	choose	choose	VERB
ejpam-5165	255	26	operators	operator	NOUN
ejpam-5165	255	27	x∗∗j	x∗∗j	PROPN
ejpam-5165	255	28	,	,	PUNCT
ejpam-5165	256	1	y∗∗j	y∗∗j	PROPN
ejpam-5165	256	2	∈	∈	PROPN
ejpam-5165	256	3	x∗∗	x∗∗	NOUN
ejpam-5165	256	4	such	such	ADJ
ejpam-5165	256	5	that	that	SCONJ
ejpam-5165	256	6	x∗∗j	x∗∗j	PROPN
ejpam-5165	256	7	(	(	PUNCT
ejpam-5165	256	8	x∗	x∗	PROPN
ejpam-5165	256	9	)	)	PUNCT
ejpam-5165	256	10	=	=	SYM
ejpam-5165	256	11	(	(	PUNCT
ejpam-5165	256	12	ms	ms	PROPN
ejpam-5165	256	13	)	)	PUNCT
ejpam-5165	256	14	∫	∫	PROPN
ejpam-5165	256	15	j	j	PROPN
ejpam-5165	256	16	x∗(f	x∗(f	PROPN
ejpam-5165	256	17	)	)	PUNCT
ejpam-5165	257	1	dg1	dg1	VERB
ejpam-5165	258	1	and	and	CCONJ
ejpam-5165	258	2	y∗∗j	y∗∗j	PROPN
ejpam-5165	258	3	(	(	PUNCT
ejpam-5165	258	4	x∗	x∗	PROPN
ejpam-5165	258	5	)	)	PUNCT
ejpam-5165	258	6	=	=	PUNCT
ejpam-5165	259	1	(	(	PUNCT
ejpam-5165	259	2	ms	ms	PROPN
ejpam-5165	259	3	)	)	PUNCT
ejpam-5165	259	4	∫	∫	PROPN
ejpam-5165	259	5	j	j	PROPN
ejpam-5165	259	6	x∗(f	x∗(f	PROPN
ejpam-5165	259	7	)	)	PUNCT
ejpam-5165	259	8	dg2	dg2	PROPN
ejpam-5165	259	9	∀x∗	∀x∗	PROPN
ejpam-5165	259	10	∈	∈	PROPN
ejpam-5165	259	11	x∗.	x∗.	PROPN
ejpam-5165	259	12	note	note	VERB
ejpam-5165	259	13	that	that	SCONJ
ejpam-5165	259	14	αx∗∗j	αx∗∗j	PRON
ejpam-5165	259	15	+	+	CCONJ
ejpam-5165	259	16	βy∗∗j	βy∗∗j	NUM
ejpam-5165	259	17	∈	∈	NOUN
ejpam-5165	259	18	x∗∗.	x∗∗.	PUNCT
ejpam-5165	259	19	then	then	ADV
ejpam-5165	259	20	write	write	VERB
ejpam-5165	259	21	w∗∗	w∗∗	PROPN
ejpam-5165	259	22	j	j	NOUN
ejpam-5165	259	23	=	=	SYM
ejpam-5165	259	24	αx∗∗j	αx∗∗j	PROPN
ejpam-5165	259	25	+	+	X
ejpam-5165	259	26	βy∗∗j	βy∗∗j	NUM
ejpam-5165	259	27	.	.	PUNCT
ejpam-5165	260	1	fix	fix	VERB
ejpam-5165	260	2	x∗	x∗	PROPN
ejpam-5165	260	3	∈	∈	PROPN
ejpam-5165	260	4	x∗.	x∗.	PUNCT
ejpam-5165	261	1	now	now	ADV
ejpam-5165	261	2	,	,	PUNCT
ejpam-5165	261	3	w∗∗	w∗∗	PROPN
ejpam-5165	261	4	j	j	PROPN
ejpam-5165	261	5	(	(	PUNCT
ejpam-5165	261	6	x∗	x∗	PROPN
ejpam-5165	261	7	)	)	PUNCT
ejpam-5165	261	8	=	=	SYM
ejpam-5165	261	9	(	(	PUNCT
ejpam-5165	261	10	αx∗∗j	αx∗∗j	NOUN
ejpam-5165	261	11	+	+	X
ejpam-5165	261	12	βy∗∗j	βy∗∗j	NUM
ejpam-5165	261	13	)	)	PUNCT
ejpam-5165	261	14	(	(	PUNCT
ejpam-5165	261	15	x∗	x∗	X
ejpam-5165	261	16	)	)	PUNCT
ejpam-5165	261	17	=	=	SYM
ejpam-5165	261	18	αx∗∗j	αx∗∗j	NOUN
ejpam-5165	261	19	(	(	PUNCT
ejpam-5165	261	20	x∗	x∗	PROPN
ejpam-5165	261	21	)	)	PUNCT
ejpam-5165	261	22	+	+	CCONJ
ejpam-5165	261	23	βy∗∗j	βy∗∗j	NUM
ejpam-5165	261	24	(	(	PUNCT
ejpam-5165	261	25	x∗	x∗	X
ejpam-5165	261	26	)	)	PUNCT
ejpam-5165	261	27	=	=	SYM
ejpam-5165	261	28	α(ms	α(ms	NUM
ejpam-5165	261	29	)	)	PUNCT
ejpam-5165	261	30	∫	∫	PROPN
ejpam-5165	261	31	j	j	PROPN
ejpam-5165	261	32	x∗(f	x∗(f	PROPN
ejpam-5165	261	33	)	)	PUNCT
ejpam-5165	261	34	dg1	dg1	VERB
ejpam-5165	262	1	+	+	CCONJ
ejpam-5165	263	1	β(ms	β(ms	NUM
ejpam-5165	263	2	)	)	PUNCT
ejpam-5165	264	1	∫	∫	PROPN
ejpam-5165	264	2	j	j	PROPN
ejpam-5165	264	3	x∗(f	x∗(f	PROPN
ejpam-5165	264	4	)	)	PUNCT
ejpam-5165	264	5	dg2	dg2	PROPN
ejpam-5165	265	1	=	=	SYM
ejpam-5165	265	2	(	(	PUNCT
ejpam-5165	265	3	ms	ms	PROPN
ejpam-5165	265	4	)	)	PUNCT
ejpam-5165	265	5	∫	∫	PROPN
ejpam-5165	266	1	j	j	PROPN
ejpam-5165	266	2	x∗(f)d[αg1	x∗(f)d[αg1	PROPN
ejpam-5165	267	1	+	+	PROPN
ejpam-5165	267	2	βg2	βg2	NOUN
ejpam-5165	267	3	]	]	X
ejpam-5165	267	4	.	.	PUNCT
ejpam-5165	268	1	and	and	CCONJ
ejpam-5165	268	2	so	so	ADV
ejpam-5165	268	3	,	,	PUNCT
ejpam-5165	268	4	we	we	PRON
ejpam-5165	268	5	see	see	VERB
ejpam-5165	268	6	that	that	SCONJ
ejpam-5165	268	7	f	f	PROPN
ejpam-5165	268	8	is	be	AUX
ejpam-5165	268	9	mds	mds	NOUN
ejpam-5165	268	10	-	-	PUNCT
ejpam-5165	268	11	integrable	integrable	ADJ
ejpam-5165	268	12	with	with	ADP
ejpam-5165	268	13	respect	respect	NOUN
ejpam-5165	268	14	to	to	ADP
ejpam-5165	268	15	αg1	αg1	NOUN
ejpam-5165	268	16	+	+	NOUN
ejpam-5165	268	17	βg2	βg2	X
ejpam-5165	268	18	.	.	PUNCT
ejpam-5165	269	1	thus	thus	ADV
ejpam-5165	269	2	,	,	PUNCT
ejpam-5165	269	3	(	(	PUNCT
ejpam-5165	269	4	mds	mds	PROPN
ejpam-5165	269	5	)	)	PUNCT
ejpam-5165	269	6	∫	∫	PROPN
ejpam-5165	270	1	j	j	PROPN
ejpam-5165	270	2	f	f	PROPN
ejpam-5165	270	3	d[αg1	d[αg1	PROPN
ejpam-5165	271	1	+	+	CCONJ
ejpam-5165	271	2	βg2	βg2	X
ejpam-5165	271	3	]	]	X
ejpam-5165	272	1	=	=	PUNCT
ejpam-5165	272	2	w∗∗	w∗∗	X
ejpam-5165	272	3	j	j	NOUN
ejpam-5165	272	4	=	=	SYM
ejpam-5165	272	5	αx∗∗j	αx∗∗j	PROPN
ejpam-5165	272	6	+	+	CCONJ
ejpam-5165	272	7	βy∗∗j	βy∗∗j	NUM
ejpam-5165	272	8	=	=	SYM
ejpam-5165	272	9	α	α	X
ejpam-5165	272	10	·	·	PUNCT
ejpam-5165	272	11	(	(	PUNCT
ejpam-5165	272	12	mds	mds	PROPN
ejpam-5165	272	13	)	)	PUNCT
ejpam-5165	272	14	∫	∫	PROPN
ejpam-5165	273	1	j	j	PROPN
ejpam-5165	273	2	f	f	PROPN
ejpam-5165	273	3	dg1	dg1	PROPN
ejpam-5165	274	1	+	+	X
ejpam-5165	274	2	β	β	X
ejpam-5165	274	3	·	·	PUNCT
ejpam-5165	274	4	(	(	PUNCT
ejpam-5165	274	5	mds	mds	PROPN
ejpam-5165	274	6	)	)	PUNCT
ejpam-5165	274	7	∫	∫	PROPN
ejpam-5165	275	1	j	j	PROPN
ejpam-5165	275	2	f	f	PROPN
ejpam-5165	275	3	dg2	dg2	PROPN
ejpam-5165	275	4	.	.	PUNCT
ejpam-5165	275	5	□	□	PUNCT
ejpam-5165	275	6	theorem	theorem	ADJ
ejpam-5165	275	7	5	5	NUM
ejpam-5165	275	8	.	.	PUNCT
ejpam-5165	276	1	let	let	VERB
ejpam-5165	276	2	g	g	NOUN
ejpam-5165	276	3	:	:	PUNCT
ejpam-5165	276	4	[	[	X
ejpam-5165	276	5	a	a	X
ejpam-5165	276	6	,	,	PUNCT
ejpam-5165	276	7	b	b	NOUN
ejpam-5165	276	8	]	]	X
ejpam-5165	276	9	→	→	PUNCT
ejpam-5165	276	10	r	r	NOUN
ejpam-5165	276	11	be	be	AUX
ejpam-5165	276	12	a	a	DET
ejpam-5165	276	13	function	function	NOUN
ejpam-5165	276	14	.	.	PUNCT
ejpam-5165	277	1	a	a	DET
ejpam-5165	277	2	function	function	NOUN
ejpam-5165	277	3	f	f	NOUN
ejpam-5165	277	4	:	:	PUNCT
ejpam-5165	278	1	[	[	X
ejpam-5165	278	2	a	a	X
ejpam-5165	278	3	,	,	PUNCT
ejpam-5165	278	4	b	b	NOUN
ejpam-5165	278	5	]	]	X
ejpam-5165	278	6	→	→	PUNCT
ejpam-5165	278	7	x	x	X
ejpam-5165	278	8	is	be	AUX
ejpam-5165	278	9	mcshanedunford	mcshanedunford	NOUN
ejpam-5165	278	10	-	-	PUNCT
ejpam-5165	278	11	stieltjes	stieltjes	NOUN
ejpam-5165	278	12	integrable	integrable	ADJ
ejpam-5165	278	13	with	with	ADP
ejpam-5165	278	14	respect	respect	NOUN
ejpam-5165	278	15	to	to	ADP
ejpam-5165	278	16	g	g	NOUN
ejpam-5165	278	17	on	on	ADP
ejpam-5165	278	18	[	[	X
ejpam-5165	278	19	a	a	X
ejpam-5165	278	20	,	,	PUNCT
ejpam-5165	278	21	b	b	NOUN
ejpam-5165	278	22	]	]	X
ejpam-5165	278	23	if	if	SCONJ
ejpam-5165	278	24	and	and	CCONJ
ejpam-5165	278	25	only	only	ADV
ejpam-5165	278	26	if	if	SCONJ
ejpam-5165	278	27	x∗(f	x∗(f	PROPN
ejpam-5165	278	28	)	)	PUNCT
ejpam-5165	278	29	:	:	PUNCT
ejpam-5165	279	1	[	[	X
ejpam-5165	279	2	a	a	X
ejpam-5165	279	3	,	,	PUNCT
ejpam-5165	279	4	b	b	NOUN
ejpam-5165	279	5	]	]	X
ejpam-5165	279	6	→	→	PUNCT
ejpam-5165	279	7	r	r	NOUN
ejpam-5165	279	8	is	be	AUX
ejpam-5165	279	9	mcshane	mcshane	NOUN
ejpam-5165	279	10	-	-	PUNCT
ejpam-5165	279	11	stieltjes	stieltjes	NOUN
ejpam-5165	279	12	integrable	integrable	ADJ
ejpam-5165	279	13	with	with	ADP
ejpam-5165	279	14	respect	respect	NOUN
ejpam-5165	279	15	to	to	ADP
ejpam-5165	279	16	g	g	NOUN
ejpam-5165	279	17	on	on	ADP
ejpam-5165	279	18	[	[	X
ejpam-5165	279	19	a	a	X
ejpam-5165	279	20	,	,	PUNCT
ejpam-5165	279	21	b	b	NOUN
ejpam-5165	279	22	]	]	X
ejpam-5165	279	23	for	for	ADP
ejpam-5165	279	24	all	all	DET
ejpam-5165	279	25	x∗	x∗	PROPN
ejpam-5165	279	26	∈	∈	PROPN
ejpam-5165	279	27	x∗.	x∗.	PUNCT
ejpam-5165	280	1	proof	proof	NOUN
ejpam-5165	280	2	.	.	PUNCT
ejpam-5165	281	1	suppose	suppose	VERB
ejpam-5165	281	2	that	that	SCONJ
ejpam-5165	281	3	f	f	PROPN
ejpam-5165	281	4	is	be	AUX
ejpam-5165	281	5	mds	mds	NOUN
ejpam-5165	281	6	-	-	PUNCT
ejpam-5165	281	7	integrable	integrable	ADJ
ejpam-5165	281	8	with	with	ADP
ejpam-5165	281	9	respect	respect	NOUN
ejpam-5165	281	10	to	to	ADP
ejpam-5165	281	11	g	g	NOUN
ejpam-5165	281	12	on	on	ADP
ejpam-5165	281	13	[	[	X
ejpam-5165	281	14	a	a	X
ejpam-5165	281	15	,	,	PUNCT
ejpam-5165	281	16	b	b	NOUN
ejpam-5165	281	17	]	]	PUNCT
ejpam-5165	281	18	.	.	PUNCT
ejpam-5165	282	1	by	by	ADP
ejpam-5165	282	2	definition	definition	NOUN
ejpam-5165	282	3	18	18	NUM
ejpam-5165	282	4	,	,	PUNCT
ejpam-5165	282	5	x∗(f	x∗(f	PROPN
ejpam-5165	282	6	)	)	PUNCT
ejpam-5165	282	7	is	be	AUX
ejpam-5165	282	8	mcshane	mcshane	NOUN
ejpam-5165	282	9	-	-	PUNCT
ejpam-5165	282	10	stieltjes	stieltjes	NOUN
ejpam-5165	282	11	integrable	integrable	ADJ
ejpam-5165	282	12	with	with	ADP
ejpam-5165	282	13	respect	respect	NOUN
ejpam-5165	282	14	to	to	ADP
ejpam-5165	282	15	g	g	NOUN
ejpam-5165	282	16	on	on	ADP
ejpam-5165	282	17	[	[	X
ejpam-5165	282	18	a	a	X
ejpam-5165	282	19	,	,	PUNCT
ejpam-5165	282	20	b	b	NOUN
ejpam-5165	282	21	]	]	PUNCT
ejpam-5165	282	22	and	and	CCONJ
ejpam-5165	282	23	so	so	ADV
ejpam-5165	282	24	we	we	PRON
ejpam-5165	282	25	are	be	AUX
ejpam-5165	282	26	done	do	VERB
ejpam-5165	282	27	.	.	PUNCT
ejpam-5165	283	1	conversely	conversely	ADV
ejpam-5165	283	2	,	,	PUNCT
ejpam-5165	283	3	assume	assume	VERB
ejpam-5165	283	4	that	that	SCONJ
ejpam-5165	283	5	x∗(f	x∗(f	PROPN
ejpam-5165	283	6	)	)	PUNCT
ejpam-5165	283	7	:	:	PUNCT
ejpam-5165	284	1	[	[	X
ejpam-5165	284	2	a	a	X
ejpam-5165	284	3	,	,	PUNCT
ejpam-5165	284	4	b	b	NOUN
ejpam-5165	284	5	]	]	X
ejpam-5165	284	6	→	→	PUNCT
ejpam-5165	284	7	r	r	NOUN
ejpam-5165	284	8	is	be	AUX
ejpam-5165	284	9	mcshane	mcshane	NOUN
ejpam-5165	284	10	-	-	PUNCT
ejpam-5165	284	11	stieltjes	stieltjes	NOUN
ejpam-5165	284	12	integrable	integrable	ADJ
ejpam-5165	284	13	with	with	ADP
ejpam-5165	284	14	respect	respect	NOUN
ejpam-5165	284	15	to	to	ADP
ejpam-5165	284	16	g	g	NOUN
ejpam-5165	284	17	on	on	ADP
ejpam-5165	284	18	[	[	X
ejpam-5165	284	19	a	a	X
ejpam-5165	284	20	,	,	PUNCT
ejpam-5165	284	21	b	b	NOUN
ejpam-5165	284	22	]	]	X
ejpam-5165	284	23	for	for	ADP
ejpam-5165	284	24	all	all	DET
ejpam-5165	284	25	x∗	x∗	PROPN
ejpam-5165	284	26	∈	∈	PROPN
ejpam-5165	284	27	x∗.	x∗.	PROPN
ejpam-5165	285	1	let	let	VERB
ejpam-5165	285	2	an	an	DET
ejpam-5165	285	3	interval	interval	NOUN
ejpam-5165	285	4	j	j	NOUN
ejpam-5165	286	1	⊆	⊆	NUM
ejpam-5165	286	2	[	[	X
ejpam-5165	286	3	a	a	X
ejpam-5165	286	4	,	,	PUNCT
ejpam-5165	286	5	b	b	NOUN
ejpam-5165	286	6	]	]	X
ejpam-5165	286	7	.	.	PUNCT
ejpam-5165	287	1	then	then	ADV
ejpam-5165	287	2	x∗(f	x∗(f	PROPN
ejpam-5165	287	3	)	)	PUNCT
ejpam-5165	287	4	is	be	AUX
ejpam-5165	287	5	mcshanestieltjes	mcshanestieltjes	NOUN
ejpam-5165	287	6	integrable	integrable	ADJ
ejpam-5165	287	7	with	with	ADP
ejpam-5165	287	8	respect	respect	NOUN
ejpam-5165	287	9	to	to	ADP
ejpam-5165	287	10	g	g	NOUN
ejpam-5165	287	11	on	on	ADP
ejpam-5165	287	12	j	j	PROPN
ejpam-5165	287	13	implying	imply	VERB
ejpam-5165	287	14	that	that	SCONJ
ejpam-5165	287	15	(	(	PUNCT
ejpam-5165	287	16	ms	ms	PROPN
ejpam-5165	287	17	)	)	PUNCT
ejpam-5165	287	18	∫	∫	PROPN
ejpam-5165	287	19	j	j	PROPN
ejpam-5165	287	20	x∗(f)dg	x∗(f)dg	PROPN
ejpam-5165	287	21	∈	∈	PROPN
ejpam-5165	287	22	r.	r.	PROPN
ejpam-5165	287	23	now	now	ADV
ejpam-5165	287	24	,	,	PUNCT
ejpam-5165	287	25	let	let	VERB
ejpam-5165	287	26	d.	d.	PROPN
ejpam-5165	287	27	omayan	omayan	PROPN
ejpam-5165	287	28	,	,	PUNCT
ejpam-5165	287	29	g.b	g.b	PROPN
ejpam-5165	287	30	.	.	PROPN
ejpam-5165	287	31	flores	flores	PROPN
ejpam-5165	287	32	/	/	SYM
ejpam-5165	287	33	eur	eur	PROPN
ejpam-5165	287	34	.	.	PUNCT
ejpam-5165	288	1	j.	j.	PROPN
ejpam-5165	288	2	pure	pure	PROPN
ejpam-5165	288	3	appl	appl	PROPN
ejpam-5165	288	4	.	.	PROPN
ejpam-5165	288	5	math	math	PROPN
ejpam-5165	288	6	,	,	PUNCT
ejpam-5165	288	7	17	17	NUM
ejpam-5165	288	8	(	(	PUNCT
ejpam-5165	288	9	2	2	NUM
ejpam-5165	288	10	)	)	PUNCT
ejpam-5165	288	11	(	(	PUNCT
ejpam-5165	288	12	2024	2024	NUM
ejpam-5165	288	13	)	)	PUNCT
ejpam-5165	288	14	,	,	PUNCT
ejpam-5165	288	15	1183	1183	NUM
ejpam-5165	288	16	-	-	SYM
ejpam-5165	288	17	1196	1196	NUM
ejpam-5165	288	18	1191	1191	NUM
ejpam-5165	288	19	x∗∗	x∗∗	PROPN
ejpam-5165	288	20	:	:	PUNCT
ejpam-5165	288	21	x∗	x∗	PROPN
ejpam-5165	288	22	→	→	PUNCT
ejpam-5165	289	1	r	r	NOUN
ejpam-5165	289	2	by	by	ADP
ejpam-5165	289	3	setting	set	VERB
ejpam-5165	289	4	x∗∗j	x∗∗j	PROPN
ejpam-5165	289	5	(	(	PUNCT
ejpam-5165	289	6	x∗	x∗	PROPN
ejpam-5165	289	7	)	)	PUNCT
ejpam-5165	289	8	=	=	SYM
ejpam-5165	289	9	(	(	PUNCT
ejpam-5165	289	10	ms	ms	PROPN
ejpam-5165	289	11	)	)	PUNCT
ejpam-5165	289	12	∫	∫	PROPN
ejpam-5165	289	13	j	j	PROPN
ejpam-5165	289	14	x∗(f)dg	x∗(f)dg	PROPN
ejpam-5165	289	15	for	for	ADP
ejpam-5165	289	16	all	all	DET
ejpam-5165	289	17	x∗	x∗	PROPN
ejpam-5165	289	18	∈	∈	PROPN
ejpam-5165	289	19	x∗.	x∗.	PROPN
ejpam-5165	290	1	this	this	PRON
ejpam-5165	290	2	means	mean	VERB
ejpam-5165	290	3	that	that	SCONJ
ejpam-5165	290	4	x∗∗j	x∗∗j	PROPN
ejpam-5165	290	5	∈	∈	PROPN
ejpam-5165	290	6	x∗∗.	x∗∗.	X
ejpam-5165	290	7	hence	hence	ADV
ejpam-5165	290	8	,	,	PUNCT
ejpam-5165	290	9	f	f	PROPN
ejpam-5165	290	10	is	be	AUX
ejpam-5165	290	11	mds	mds	NOUN
ejpam-5165	290	12	-	-	PUNCT
ejpam-5165	290	13	integrable	integrable	ADJ
ejpam-5165	290	14	with	with	ADP
ejpam-5165	290	15	respect	respect	NOUN
ejpam-5165	290	16	to	to	ADP
ejpam-5165	290	17	g	g	NOUN
ejpam-5165	290	18	on	on	ADP
ejpam-5165	290	19	[	[	X
ejpam-5165	290	20	a	a	X
ejpam-5165	290	21	,	,	PUNCT
ejpam-5165	290	22	b	b	NOUN
ejpam-5165	290	23	]	]	X
ejpam-5165	290	24	.	.	PUNCT
ejpam-5165	291	1	□	□	PUNCT
ejpam-5165	291	2	theorem	theorem	ADJ
ejpam-5165	291	3	6	6	NUM
ejpam-5165	291	4	.	.	PUNCT
ejpam-5165	292	1	(	(	PUNCT
ejpam-5165	292	2	cauchy	cauchy	ADJ
ejpam-5165	292	3	criterion	criterion	NOUN
ejpam-5165	292	4	of	of	ADP
ejpam-5165	292	5	the	the	DET
ejpam-5165	292	6	mds	mds	NOUN
ejpam-5165	292	7	-	-	PUNCT
ejpam-5165	292	8	integral	integral	ADJ
ejpam-5165	292	9	)	)	PUNCT
ejpam-5165	292	10	let	let	VERB
ejpam-5165	292	11	f	f	NOUN
ejpam-5165	292	12	:	:	PUNCT
ejpam-5165	293	1	[	[	X
ejpam-5165	293	2	a	a	X
ejpam-5165	293	3	,	,	PUNCT
ejpam-5165	293	4	b	b	NOUN
ejpam-5165	293	5	]	]	X
ejpam-5165	293	6	→	→	SYM
ejpam-5165	293	7	x	x	X
ejpam-5165	293	8	and	and	CCONJ
ejpam-5165	293	9	g	g	NOUN
ejpam-5165	293	10	:	:	PUNCT
ejpam-5165	294	1	[	[	X
ejpam-5165	294	2	a	a	X
ejpam-5165	294	3	,	,	PUNCT
ejpam-5165	294	4	b	b	NOUN
ejpam-5165	294	5	]	]	X
ejpam-5165	294	6	→	→	PUNCT
ejpam-5165	294	7	r	r	NOUN
ejpam-5165	294	8	be	be	NOUN
ejpam-5165	294	9	functions	function	NOUN
ejpam-5165	294	10	.	.	PUNCT
ejpam-5165	295	1	a	a	DET
ejpam-5165	295	2	function	function	NOUN
ejpam-5165	295	3	f	f	PROPN
ejpam-5165	295	4	is	be	AUX
ejpam-5165	295	5	mcshane	mcshane	PROPN
ejpam-5165	295	6	-	-	PUNCT
ejpam-5165	295	7	dunfordstieltjes	dunfordstieltjes	PROPN
ejpam-5165	295	8	integrable	integrable	ADJ
ejpam-5165	295	9	with	with	ADP
ejpam-5165	295	10	respect	respect	NOUN
ejpam-5165	295	11	to	to	ADP
ejpam-5165	295	12	g	g	NOUN
ejpam-5165	295	13	on	on	ADP
ejpam-5165	295	14	[	[	X
ejpam-5165	295	15	a	a	X
ejpam-5165	295	16	,	,	PUNCT
ejpam-5165	295	17	b	b	NOUN
ejpam-5165	295	18	]	]	X
ejpam-5165	295	19	if	if	SCONJ
ejpam-5165	295	20	and	and	CCONJ
ejpam-5165	295	21	only	only	ADV
ejpam-5165	295	22	if	if	SCONJ
ejpam-5165	295	23	for	for	ADP
ejpam-5165	295	24	every	every	DET
ejpam-5165	295	25	ε	ε	PROPN
ejpam-5165	295	26	>	>	X
ejpam-5165	295	27	0	0	PROPN
ejpam-5165	295	28	,	,	PUNCT
ejpam-5165	295	29	there	there	PRON
ejpam-5165	295	30	exists	exist	VERB
ejpam-5165	295	31	a	a	DET
ejpam-5165	295	32	gauge	gauge	NOUN
ejpam-5165	295	33	δ	δ	NOUN
ejpam-5165	295	34	:	:	PUNCT
ejpam-5165	296	1	[	[	X
ejpam-5165	296	2	a	a	X
ejpam-5165	296	3	,	,	PUNCT
ejpam-5165	296	4	b	b	NOUN
ejpam-5165	296	5	]	]	X
ejpam-5165	296	6	→	→	PUNCT
ejpam-5165	296	7	r+	r+	NOUN
ejpam-5165	296	8	such	such	ADJ
ejpam-5165	296	9	that	that	SCONJ
ejpam-5165	296	10	if	if	SCONJ
ejpam-5165	296	11	n1	n1	PROPN
ejpam-5165	296	12	and	and	CCONJ
ejpam-5165	296	13	n2	n2	NOUN
ejpam-5165	296	14	are	be	AUX
ejpam-5165	296	15	two	two	NUM
ejpam-5165	296	16	δ	δ	PROPN
ejpam-5165	296	17	-	-	PUNCT
ejpam-5165	296	18	fine	fine	ADJ
ejpam-5165	296	19	m	m	PROPN
ejpam-5165	296	20	-partitions	-partition	NOUN
ejpam-5165	296	21	,	,	PUNCT
ejpam-5165	296	22	then	then	ADV
ejpam-5165	296	23	∥s(f	∥s(f	ADJ
ejpam-5165	296	24	,	,	PUNCT
ejpam-5165	296	25	g	g	NOUN
ejpam-5165	296	26	,	,	PUNCT
ejpam-5165	296	27	n1)−	n1)−	PROPN
ejpam-5165	296	28	s(f	s(f	PROPN
ejpam-5165	296	29	,	,	PUNCT
ejpam-5165	296	30	g	g	PROPN
ejpam-5165	296	31	,	,	PUNCT
ejpam-5165	296	32	n2)∥x	n2)∥x	PRON
ejpam-5165	296	33	<	<	X
ejpam-5165	296	34	ε	ε	PROPN
ejpam-5165	296	35	.	.	PUNCT
ejpam-5165	296	36	proof	proof	NOUN
ejpam-5165	296	37	.	.	PUNCT
ejpam-5165	297	1	suppose	suppose	VERB
ejpam-5165	297	2	that	that	SCONJ
ejpam-5165	297	3	f	f	PROPN
ejpam-5165	297	4	is	be	AUX
ejpam-5165	297	5	mcshane	mcshane	PROPN
ejpam-5165	297	6	-	-	PUNCT
ejpam-5165	297	7	dunford	dunford	NOUN
ejpam-5165	297	8	-	-	PUNCT
ejpam-5165	297	9	stieltjes	stieltjes	NOUN
ejpam-5165	297	10	integrable	integrable	ADJ
ejpam-5165	297	11	with	with	ADP
ejpam-5165	297	12	respect	respect	NOUN
ejpam-5165	297	13	to	to	ADP
ejpam-5165	297	14	g	g	NOUN
ejpam-5165	297	15	on	on	ADP
ejpam-5165	297	16	[	[	X
ejpam-5165	297	17	a	a	X
ejpam-5165	297	18	,	,	PUNCT
ejpam-5165	297	19	b	b	NOUN
ejpam-5165	297	20	]	]	PUNCT
ejpam-5165	297	21	.	.	PUNCT
ejpam-5165	298	1	by	by	ADP
ejpam-5165	298	2	theorem	theorem	NOUN
ejpam-5165	298	3	5	5	NUM
ejpam-5165	298	4	,	,	PUNCT
ejpam-5165	298	5	x∗(f	x∗(f	PROPN
ejpam-5165	298	6	)	)	PUNCT
ejpam-5165	298	7	:	:	PUNCT
ejpam-5165	299	1	[	[	X
ejpam-5165	299	2	a	a	X
ejpam-5165	299	3	,	,	PUNCT
ejpam-5165	299	4	b	b	NOUN
ejpam-5165	299	5	]	]	X
ejpam-5165	299	6	→	→	PUNCT
ejpam-5165	299	7	r	r	NOUN
ejpam-5165	299	8	is	be	AUX
ejpam-5165	299	9	mcshane	mcshane	NOUN
ejpam-5165	299	10	-	-	PUNCT
ejpam-5165	299	11	stieltjes	stieltjes	NOUN
ejpam-5165	299	12	integrable	integrable	ADJ
ejpam-5165	299	13	with	with	ADP
ejpam-5165	299	14	respect	respect	NOUN
ejpam-5165	299	15	to	to	ADP
ejpam-5165	299	16	to	to	ADP
ejpam-5165	299	17	g	g	NOUN
ejpam-5165	299	18	on	on	ADP
ejpam-5165	299	19	[	[	X
ejpam-5165	299	20	a	a	X
ejpam-5165	299	21	,	,	PUNCT
ejpam-5165	299	22	b	b	NOUN
ejpam-5165	299	23	]	]	X
ejpam-5165	299	24	for	for	ADP
ejpam-5165	299	25	all	all	DET
ejpam-5165	299	26	x∗	x∗	PROPN
ejpam-5165	299	27	∈	∈	PROPN
ejpam-5165	299	28	x∗.	x∗.	PUNCT
ejpam-5165	300	1	if	if	SCONJ
ejpam-5165	300	2	x∗	x∗	PROPN
ejpam-5165	300	3	∈	∈	PROPN
ejpam-5165	300	4	x∗	x∗	PROPN
ejpam-5165	300	5	is	be	AUX
ejpam-5165	300	6	the	the	DET
ejpam-5165	300	7	zero	zero	NUM
ejpam-5165	300	8	map	map	NOUN
ejpam-5165	300	9	so	so	SCONJ
ejpam-5165	300	10	that	that	SCONJ
ejpam-5165	300	11	x∗(x	x∗(x	NOUN
ejpam-5165	300	12	)	)	PUNCT
ejpam-5165	300	13	=	=	SYM
ejpam-5165	300	14	0	0	NUM
ejpam-5165	300	15	for	for	ADP
ejpam-5165	300	16	all	all	PRON
ejpam-5165	300	17	x	x	SYM
ejpam-5165	300	18	∈	∈	NOUN
ejpam-5165	300	19	x.	x.	NOUN
ejpam-5165	300	20	then	then	ADV
ejpam-5165	300	21	we	we	PRON
ejpam-5165	300	22	can	can	AUX
ejpam-5165	300	23	choose	choose	VERB
ejpam-5165	300	24	δ	δ	NOUN
ejpam-5165	300	25	:	:	PUNCT
ejpam-5165	301	1	[	[	X
ejpam-5165	301	2	a	a	X
ejpam-5165	301	3	,	,	PUNCT
ejpam-5165	301	4	b	b	NOUN
ejpam-5165	301	5	]	]	X
ejpam-5165	301	6	→	→	PUNCT
ejpam-5165	301	7	r+	r+	NOUN
ejpam-5165	301	8	such	such	ADJ
ejpam-5165	301	9	that	that	PRON
ejpam-5165	301	10	for	for	ADP
ejpam-5165	301	11	any	any	DET
ejpam-5165	301	12	two	two	NUM
ejpam-5165	301	13	δ	δ	PROPN
ejpam-5165	301	14	-	-	PUNCT
ejpam-5165	301	15	fine	fine	ADJ
ejpam-5165	301	16	m	m	PROPN
ejpam-5165	301	17	-partitions	-partition	NOUN
ejpam-5165	301	18	n1	n1	NOUN
ejpam-5165	301	19	and	and	CCONJ
ejpam-5165	301	20	n2	n2	NOUN
ejpam-5165	301	21	of	of	ADP
ejpam-5165	301	22	[	[	X
ejpam-5165	301	23	a	a	X
ejpam-5165	301	24	,	,	PUNCT
ejpam-5165	301	25	b	b	NOUN
ejpam-5165	301	26	]	]	X
ejpam-5165	301	27	,	,	PUNCT
ejpam-5165	301	28	∥s(x∗(f	∥s(x∗(f	PROPN
ejpam-5165	301	29	)	)	PUNCT
ejpam-5165	301	30	,	,	PUNCT
ejpam-5165	301	31	g	g	PROPN
ejpam-5165	301	32	,	,	PUNCT
ejpam-5165	301	33	n1)−	n1)−	PROPN
ejpam-5165	301	34	s(x∗(f	s(x∗(f	PROPN
ejpam-5165	301	35	)	)	PUNCT
ejpam-5165	301	36	,	,	PUNCT
ejpam-5165	301	37	g	g	NOUN
ejpam-5165	301	38	,	,	PUNCT
ejpam-5165	301	39	n2)∥x∗	n2)∥x∗	X
ejpam-5165	301	40	=	=	SYM
ejpam-5165	301	41	∥x∗s(f	∥x∗s(f	X
ejpam-5165	301	42	,	,	PUNCT
ejpam-5165	301	43	g	g	NOUN
ejpam-5165	301	44	,	,	PUNCT
ejpam-5165	301	45	n1)−	n1)−	PROPN
ejpam-5165	301	46	x∗s(f	x∗s(f	PROPN
ejpam-5165	301	47	,	,	PUNCT
ejpam-5165	301	48	g	g	NOUN
ejpam-5165	301	49	,	,	PUNCT
ejpam-5165	301	50	n2)∥x∗	n2)∥x∗	X
ejpam-5165	301	51	=	=	SYM
ejpam-5165	301	52	∥0−	∥0−	PROPN
ejpam-5165	301	53	0∥	0∥	NUM
ejpam-5165	301	54	<	<	X
ejpam-5165	301	55	ε	ε	PROPN
ejpam-5165	301	56	.	.	PUNCT
ejpam-5165	302	1	if	if	SCONJ
ejpam-5165	302	2	x∗	x∗	PROPN
ejpam-5165	302	3	∈	∈	PROPN
ejpam-5165	302	4	x∗	x∗	PROPN
ejpam-5165	302	5	is	be	AUX
ejpam-5165	302	6	not	not	PART
ejpam-5165	302	7	the	the	DET
ejpam-5165	302	8	zero	zero	NUM
ejpam-5165	302	9	map	map	NOUN
ejpam-5165	302	10	.	.	PUNCT
ejpam-5165	303	1	then	then	ADV
ejpam-5165	303	2	we	we	PRON
ejpam-5165	303	3	can	can	AUX
ejpam-5165	303	4	pick	pick	VERB
ejpam-5165	303	5	δ	δ	PROPN
ejpam-5165	303	6	:	:	PUNCT
ejpam-5165	304	1	[	[	X
ejpam-5165	304	2	a	a	X
ejpam-5165	304	3	,	,	PUNCT
ejpam-5165	304	4	b	b	NOUN
ejpam-5165	304	5	]	]	X
ejpam-5165	304	6	→	→	PUNCT
ejpam-5165	304	7	r+	r+	NOUN
ejpam-5165	304	8	such	such	ADJ
ejpam-5165	304	9	that	that	PRON
ejpam-5165	304	10	for	for	ADP
ejpam-5165	304	11	every	every	DET
ejpam-5165	304	12	two	two	NUM
ejpam-5165	304	13	δ	δ	PROPN
ejpam-5165	304	14	-	-	PUNCT
ejpam-5165	304	15	fine	fine	ADJ
ejpam-5165	304	16	m	m	PROPN
ejpam-5165	304	17	-partitions	-partition	NOUN
ejpam-5165	304	18	n1	n1	NOUN
ejpam-5165	304	19	and	and	CCONJ
ejpam-5165	304	20	n2	n2	NOUN
ejpam-5165	304	21	of	of	ADP
ejpam-5165	304	22	[	[	X
ejpam-5165	304	23	a	a	X
ejpam-5165	304	24	,	,	PUNCT
ejpam-5165	304	25	b	b	NOUN
ejpam-5165	304	26	]	]	X
ejpam-5165	304	27	,	,	PUNCT
ejpam-5165	304	28	we	we	PRON
ejpam-5165	304	29	have	have	AUX
ejpam-5165	304	30	∥x∗[s(f	∥x∗[s(f	NUM
ejpam-5165	304	31	,	,	PUNCT
ejpam-5165	304	32	g	g	NOUN
ejpam-5165	304	33	,	,	PUNCT
ejpam-5165	304	34	n1)−	n1)−	PROPN
ejpam-5165	304	35	s(f	s(f	PROPN
ejpam-5165	304	36	,	,	PUNCT
ejpam-5165	304	37	g	g	NOUN
ejpam-5165	304	38	,	,	PUNCT
ejpam-5165	304	39	n2)]∥x∗	n2)]∥x∗	NOUN
ejpam-5165	304	40	=	=	SYM
ejpam-5165	304	41	∥s(x∗(f	∥s(x∗(f	PROPN
ejpam-5165	304	42	)	)	PUNCT
ejpam-5165	304	43	,	,	PUNCT
ejpam-5165	304	44	g	g	PROPN
ejpam-5165	304	45	,	,	PUNCT
ejpam-5165	304	46	n1)−	n1)−	PROPN
ejpam-5165	304	47	s(x∗(f	s(x∗(f	PROPN
ejpam-5165	304	48	)	)	PUNCT
ejpam-5165	304	49	,	,	PUNCT
ejpam-5165	304	50	g	g	NOUN
ejpam-5165	304	51	,	,	PUNCT
ejpam-5165	304	52	n2)∥x∗	n2)∥x∗	ADP
ejpam-5165	304	53	<	<	X
ejpam-5165	304	54	∥x∗∥x∗	∥x∗∥x∗	PROPN
ejpam-5165	304	55	·	·	PUNCT
ejpam-5165	304	56	ε	ε	PROPN
ejpam-5165	304	57	.	.	PUNCT
ejpam-5165	305	1	this	this	PRON
ejpam-5165	305	2	implies	imply	VERB
ejpam-5165	305	3	that	that	SCONJ
ejpam-5165	305	4	∥x∗∥x∗∥s(f	∥x∗∥x∗∥s(f	PROPN
ejpam-5165	305	5	,	,	PUNCT
ejpam-5165	305	6	g	g	PROPN
ejpam-5165	305	7	,	,	PUNCT
ejpam-5165	305	8	n1)−	n1)−	PROPN
ejpam-5165	305	9	s(f	s(f	PROPN
ejpam-5165	305	10	,	,	PUNCT
ejpam-5165	305	11	g	g	NOUN
ejpam-5165	305	12	,	,	PUNCT
ejpam-5165	305	13	n2)∥x∗	n2)∥x∗	ADP
ejpam-5165	306	1	<	<	X
ejpam-5165	306	2	∥x∗∥x∗	∥x∗∥x∗	PROPN
ejpam-5165	306	3	·	·	PUNCT
ejpam-5165	306	4	ε	ε	AUX
ejpam-5165	306	5	.	.	PROPN
ejpam-5165	306	6	in	in	ADP
ejpam-5165	306	7	other	other	ADJ
ejpam-5165	306	8	words	word	NOUN
ejpam-5165	306	9	,	,	PUNCT
ejpam-5165	306	10	∥s(f	∥s(f	ADJ
ejpam-5165	306	11	,	,	PUNCT
ejpam-5165	306	12	g	g	NOUN
ejpam-5165	306	13	,	,	PUNCT
ejpam-5165	306	14	n1)−	n1)−	PROPN
ejpam-5165	306	15	s(f	s(f	PROPN
ejpam-5165	306	16	,	,	PUNCT
ejpam-5165	306	17	g	g	PROPN
ejpam-5165	306	18	,	,	PUNCT
ejpam-5165	306	19	n2)∥x	n2)∥x	PRON
ejpam-5165	306	20	<	<	X
ejpam-5165	306	21	ε	ε	PROPN
ejpam-5165	306	22	.	.	PUNCT
ejpam-5165	306	23	conversely	conversely	ADV
ejpam-5165	306	24	,	,	PUNCT
ejpam-5165	306	25	let	let	VERB
ejpam-5165	306	26	x∗	x∗	PROPN
ejpam-5165	306	27	∈	∈	PROPN
ejpam-5165	306	28	x∗.	x∗.	PROPN
ejpam-5165	306	29	suppose	suppose	VERB
ejpam-5165	306	30	that	that	SCONJ
ejpam-5165	306	31	for	for	ADP
ejpam-5165	306	32	every	every	DET
ejpam-5165	306	33	ε	ε	PROPN
ejpam-5165	306	34	>	>	X
ejpam-5165	306	35	0	0	PROPN
ejpam-5165	306	36	,	,	PUNCT
ejpam-5165	306	37	there	there	PRON
ejpam-5165	306	38	exists	exist	VERB
ejpam-5165	306	39	a	a	DET
ejpam-5165	306	40	gauge	gauge	NOUN
ejpam-5165	306	41	δ	δ	NOUN
ejpam-5165	306	42	:	:	PUNCT
ejpam-5165	307	1	[	[	X
ejpam-5165	307	2	a	a	X
ejpam-5165	307	3	,	,	PUNCT
ejpam-5165	307	4	b	b	NOUN
ejpam-5165	307	5	]	]	X
ejpam-5165	307	6	→	→	PUNCT
ejpam-5165	307	7	r+	r+	NOUN
ejpam-5165	307	8	such	such	ADJ
ejpam-5165	307	9	that	that	SCONJ
ejpam-5165	307	10	if	if	SCONJ
ejpam-5165	307	11	n1	n1	PROPN
ejpam-5165	307	12	and	and	CCONJ
ejpam-5165	307	13	n2	n2	NOUN
ejpam-5165	307	14	are	be	AUX
ejpam-5165	307	15	two	two	NUM
ejpam-5165	307	16	δ	δ	PROPN
ejpam-5165	307	17	-	-	PUNCT
ejpam-5165	307	18	fine	fine	ADJ
ejpam-5165	307	19	m	m	PROPN
ejpam-5165	307	20	-partitions	-partition	NOUN
ejpam-5165	307	21	,	,	PUNCT
ejpam-5165	307	22	then	then	ADV
ejpam-5165	307	23	∥s(f	∥s(f	ADJ
ejpam-5165	307	24	,	,	PUNCT
ejpam-5165	307	25	g	g	NOUN
ejpam-5165	307	26	,	,	PUNCT
ejpam-5165	307	27	n1)−	n1)−	PROPN
ejpam-5165	307	28	s(f	s(f	PROPN
ejpam-5165	307	29	,	,	PUNCT
ejpam-5165	307	30	g	g	PROPN
ejpam-5165	307	31	,	,	PUNCT
ejpam-5165	307	32	n2)∥x	n2)∥x	PRON
ejpam-5165	308	1	<	<	X
ejpam-5165	308	2	ε	ε	PROPN
ejpam-5165	308	3	∥x∗∥x∗	∥x∗∥x∗	VERB
ejpam-5165	308	4	+	+	CCONJ
ejpam-5165	308	5	1	1	NUM
ejpam-5165	308	6	(	(	PUNCT
ejpam-5165	308	7	1	1	NUM
ejpam-5165	308	8	)	)	PUNCT
ejpam-5165	308	9	by	by	ADP
ejpam-5165	308	10	(	(	PUNCT
ejpam-5165	308	11	1	1	NUM
ejpam-5165	308	12	)	)	PUNCT
ejpam-5165	308	13	,	,	PUNCT
ejpam-5165	308	14	we	we	PRON
ejpam-5165	308	15	obtain	obtain	VERB
ejpam-5165	308	16	∥s(x∗(f	∥s(x∗(f	NOUN
ejpam-5165	308	17	)	)	PUNCT
ejpam-5165	308	18	,	,	PUNCT
ejpam-5165	308	19	g	g	PROPN
ejpam-5165	308	20	,	,	PUNCT
ejpam-5165	308	21	n1)−	n1)−	PROPN
ejpam-5165	308	22	s(x∗(f	s(x∗(f	PROPN
ejpam-5165	308	23	)	)	PUNCT
ejpam-5165	308	24	,	,	PUNCT
ejpam-5165	308	25	g	g	NOUN
ejpam-5165	308	26	,	,	PUNCT
ejpam-5165	308	27	n2)∥x∗	n2)∥x∗	X
ejpam-5165	308	28	=	=	SYM
ejpam-5165	308	29	∥x∗[s(f	∥x∗[s(f	PROPN
ejpam-5165	308	30	,	,	PUNCT
ejpam-5165	308	31	g	g	NOUN
ejpam-5165	308	32	,	,	PUNCT
ejpam-5165	308	33	n1)−	n1)−	PROPN
ejpam-5165	308	34	s(f	s(f	PROPN
ejpam-5165	308	35	,	,	PUNCT
ejpam-5165	308	36	g	g	PROPN
ejpam-5165	308	37	,	,	PUNCT
ejpam-5165	308	38	n2)]∥x	n2)]∥x	PROPN
ejpam-5165	308	39	≤	≤	PROPN
ejpam-5165	308	40	∥x∗∥x∗∥s(f	∥x∗∥x∗∥s(f	PROPN
ejpam-5165	308	41	,	,	PUNCT
ejpam-5165	308	42	g	g	PROPN
ejpam-5165	308	43	,	,	PUNCT
ejpam-5165	308	44	n1)−	n1)−	PROPN
ejpam-5165	308	45	s(f	s(f	PROPN
ejpam-5165	308	46	,	,	PUNCT
ejpam-5165	308	47	g	g	PROPN
ejpam-5165	308	48	,	,	PUNCT
ejpam-5165	308	49	n2)∥x	n2)∥x	PRON
ejpam-5165	308	50	<	<	X
ejpam-5165	308	51	∥x∗∥x∗	∥x∗∥x∗	PROPN
ejpam-5165	308	52	·	·	PUNCT
ejpam-5165	308	53	ε	ε	PROPN
ejpam-5165	308	54	∥x∗∥x∗	∥x∗∥x∗	NOUN
ejpam-5165	308	55	+	+	CCONJ
ejpam-5165	308	56	1	1	NUM
ejpam-5165	308	57	<	<	X
ejpam-5165	308	58	ε	ε	PROPN
ejpam-5165	308	59	.	.	PUNCT
ejpam-5165	309	1	this	this	PRON
ejpam-5165	309	2	implies	imply	VERB
ejpam-5165	309	3	that	that	SCONJ
ejpam-5165	309	4	x∗(f	x∗(f	PROPN
ejpam-5165	309	5	)	)	PUNCT
ejpam-5165	309	6	:	:	PUNCT
ejpam-5165	310	1	[	[	X
ejpam-5165	310	2	a	a	X
ejpam-5165	310	3	,	,	PUNCT
ejpam-5165	310	4	b	b	NOUN
ejpam-5165	310	5	]	]	X
ejpam-5165	310	6	→	→	PUNCT
ejpam-5165	310	7	r	r	NOUN
ejpam-5165	310	8	is	be	AUX
ejpam-5165	310	9	ms	ms	NOUN
ejpam-5165	310	10	-	-	PUNCT
ejpam-5165	310	11	integrable	integrable	ADJ
ejpam-5165	310	12	with	with	ADP
ejpam-5165	310	13	respect	respect	NOUN
ejpam-5165	310	14	to	to	ADP
ejpam-5165	310	15	g	g	NOUN
ejpam-5165	310	16	on	on	ADP
ejpam-5165	310	17	[	[	X
ejpam-5165	310	18	a	a	X
ejpam-5165	310	19	,	,	PUNCT
ejpam-5165	310	20	b	b	NOUN
ejpam-5165	310	21	]	]	PUNCT
ejpam-5165	310	22	.	.	PUNCT
ejpam-5165	311	1	fix	fix	VERB
ejpam-5165	311	2	j	j	PROPN
ejpam-5165	311	3	⊆	⊆	NUM
ejpam-5165	311	4	[	[	X
ejpam-5165	311	5	a	a	X
ejpam-5165	311	6	,	,	PUNCT
ejpam-5165	311	7	b	b	AUX
ejpam-5165	311	8	]	]	PUNCT
ejpam-5165	311	9	be	be	AUX
ejpam-5165	311	10	a	a	DET
ejpam-5165	311	11	compact	compact	ADJ
ejpam-5165	311	12	interval	interval	NOUN
ejpam-5165	311	13	.	.	PUNCT
ejpam-5165	312	1	define	define	VERB
ejpam-5165	312	2	x∗∗	x∗∗	PROPN
ejpam-5165	312	3	:	:	PUNCT
ejpam-5165	312	4	x∗	x∗	PROPN
ejpam-5165	312	5	→	→	PUNCT
ejpam-5165	312	6	r	r	NOUN
ejpam-5165	312	7	such	such	ADJ
ejpam-5165	312	8	that	that	SCONJ
ejpam-5165	312	9	x∗∗j	x∗∗j	PROPN
ejpam-5165	312	10	(	(	PUNCT
ejpam-5165	312	11	x∗	x∗	PROPN
ejpam-5165	312	12	)	)	PUNCT
ejpam-5165	313	1	=	=	SYM
ejpam-5165	313	2	(	(	PUNCT
ejpam-5165	313	3	ms	ms	PROPN
ejpam-5165	313	4	)	)	PUNCT
ejpam-5165	313	5	∫	∫	PROPN
ejpam-5165	313	6	j	j	PROPN
ejpam-5165	313	7	x∗(f)dg	x∗(f)dg	PROPN
ejpam-5165	313	8	.	.	PUNCT
ejpam-5165	314	1	d.	d.	PROPN
ejpam-5165	314	2	omayan	omayan	PROPN
ejpam-5165	314	3	,	,	PUNCT
ejpam-5165	314	4	g.b	g.b	PROPN
ejpam-5165	314	5	.	.	PROPN
ejpam-5165	314	6	flores	flores	PROPN
ejpam-5165	314	7	/	/	SYM
ejpam-5165	314	8	eur	eur	PROPN
ejpam-5165	314	9	.	.	PUNCT
ejpam-5165	315	1	j.	j.	PROPN
ejpam-5165	315	2	pure	pure	PROPN
ejpam-5165	315	3	appl	appl	PROPN
ejpam-5165	315	4	.	.	PROPN
ejpam-5165	315	5	math	math	PROPN
ejpam-5165	315	6	,	,	PUNCT
ejpam-5165	315	7	17	17	NUM
ejpam-5165	315	8	(	(	PUNCT
ejpam-5165	315	9	2	2	NUM
ejpam-5165	315	10	)	)	PUNCT
ejpam-5165	315	11	(	(	PUNCT
ejpam-5165	315	12	2024	2024	NUM
ejpam-5165	315	13	)	)	PUNCT
ejpam-5165	315	14	,	,	PUNCT
ejpam-5165	315	15	1183	1183	NUM
ejpam-5165	315	16	-	-	SYM
ejpam-5165	315	17	1196	1196	NUM
ejpam-5165	315	18	1192	1192	NUM
ejpam-5165	315	19	now	now	ADV
ejpam-5165	315	20	,	,	PUNCT
ejpam-5165	315	21	by	by	ADP
ejpam-5165	315	22	definition	definition	NOUN
ejpam-5165	315	23	of	of	ADP
ejpam-5165	315	24	x∗∗	x∗∗	PROPN
ejpam-5165	315	25	,	,	PUNCT
ejpam-5165	315	26	x∗∗j	x∗∗j	PROPN
ejpam-5165	315	27	∈	∈	PROPN
ejpam-5165	315	28	x∗∗	x∗∗	PROPN
ejpam-5165	315	29	which	which	PRON
ejpam-5165	315	30	means	mean	VERB
ejpam-5165	315	31	that	that	SCONJ
ejpam-5165	315	32	x∗∗j	x∗∗j	PROPN
ejpam-5165	315	33	is	be	AUX
ejpam-5165	315	34	linear	linear	ADJ
ejpam-5165	315	35	.	.	PUNCT
ejpam-5165	316	1	consequently	consequently	ADV
ejpam-5165	316	2	,	,	PUNCT
ejpam-5165	316	3	x∗∗j	x∗∗j	PROPN
ejpam-5165	316	4	=	=	SYM
ejpam-5165	316	5	(	(	PUNCT
ejpam-5165	316	6	mds	mds	PROPN
ejpam-5165	316	7	)	)	PUNCT
ejpam-5165	316	8	∫	∫	PROPN
ejpam-5165	316	9	j	j	PROPN
ejpam-5165	316	10	fdg	fdg	PROPN
ejpam-5165	316	11	.	.	PUNCT
ejpam-5165	316	12	thus	thus	ADV
ejpam-5165	316	13	,	,	PUNCT
ejpam-5165	316	14	f	f	PROPN
ejpam-5165	316	15	is	be	AUX
ejpam-5165	316	16	mds	mds	NOUN
ejpam-5165	316	17	-	-	PUNCT
ejpam-5165	316	18	integrable	integrable	ADJ
ejpam-5165	316	19	with	with	ADP
ejpam-5165	316	20	respect	respect	NOUN
ejpam-5165	316	21	to	to	ADP
ejpam-5165	316	22	g	g	NOUN
ejpam-5165	316	23	on	on	ADP
ejpam-5165	316	24	[	[	X
ejpam-5165	316	25	a	a	X
ejpam-5165	316	26	,	,	PUNCT
ejpam-5165	316	27	b	b	NOUN
ejpam-5165	316	28	]	]	X
ejpam-5165	316	29	.	.	PUNCT
ejpam-5165	317	1	□	□	PUNCT
ejpam-5165	317	2	theorem	theorem	ADJ
ejpam-5165	317	3	7	7	NUM
ejpam-5165	317	4	.	.	PUNCT
ejpam-5165	318	1	(	(	PUNCT
ejpam-5165	318	2	additivity	additivity	NOUN
ejpam-5165	318	3	of	of	ADP
ejpam-5165	318	4	the	the	DET
ejpam-5165	318	5	mds	mds	NOUN
ejpam-5165	318	6	-	-	PUNCT
ejpam-5165	318	7	integral	integral	ADJ
ejpam-5165	318	8	)	)	PUNCT
ejpam-5165	318	9	let	let	VERB
ejpam-5165	318	10	f	f	NOUN
ejpam-5165	318	11	:	:	PUNCT
ejpam-5165	319	1	[	[	X
ejpam-5165	319	2	a	a	X
ejpam-5165	319	3	,	,	PUNCT
ejpam-5165	319	4	b	b	NOUN
ejpam-5165	319	5	]	]	X
ejpam-5165	319	6	→	→	SYM
ejpam-5165	319	7	x	x	SYM
ejpam-5165	319	8	,	,	PUNCT
ejpam-5165	319	9	g	g	NOUN
ejpam-5165	319	10	:	:	PUNCT
ejpam-5165	319	11	[	[	X
ejpam-5165	319	12	a	a	X
ejpam-5165	319	13	,	,	PUNCT
ejpam-5165	319	14	b	b	NOUN
ejpam-5165	319	15	]	]	X
ejpam-5165	319	16	→	→	SYM
ejpam-5165	319	17	r	r	NOUN
ejpam-5165	319	18	and	and	CCONJ
ejpam-5165	319	19	i	i	PRON
ejpam-5165	319	20	,	,	PUNCT
ejpam-5165	319	21	j	j	PROPN
ejpam-5165	319	22	∈	∈	PROPN
ejpam-5165	319	23	in	in	ADP
ejpam-5165	319	24	(	(	PUNCT
ejpam-5165	319	25	[	[	X
ejpam-5165	319	26	a	a	X
ejpam-5165	319	27	,	,	PUNCT
ejpam-5165	319	28	b	b	NOUN
ejpam-5165	319	29	]	]	PUNCT
ejpam-5165	319	30	)	)	PUNCT
ejpam-5165	319	31	that	that	PRON
ejpam-5165	319	32	forms	form	VERB
ejpam-5165	319	33	an	an	DET
ejpam-5165	319	34	m	m	NOUN
ejpam-5165	319	35	-partition	-partition	NOUN
ejpam-5165	319	36	of	of	ADP
ejpam-5165	319	37	[	[	X
ejpam-5165	319	38	a	a	X
ejpam-5165	319	39	,	,	PUNCT
ejpam-5165	319	40	b	b	NOUN
ejpam-5165	319	41	]	]	PUNCT
ejpam-5165	319	42	.	.	PUNCT
ejpam-5165	320	1	assume	assume	VERB
ejpam-5165	320	2	that	that	SCONJ
ejpam-5165	320	3	f	f	PROPN
ejpam-5165	320	4	∈	∈	PROPN
ejpam-5165	320	5	mds(i	mds(i	PROPN
ejpam-5165	320	6	,	,	PUNCT
ejpam-5165	320	7	g	g	NOUN
ejpam-5165	320	8	)	)	PUNCT
ejpam-5165	320	9	∩mds(j	∩mds(j	PUNCT
ejpam-5165	320	10	,	,	PUNCT
ejpam-5165	320	11	g	g	NOUN
ejpam-5165	320	12	)	)	PUNCT
ejpam-5165	320	13	,	,	PUNCT
ejpam-5165	320	14	then	then	ADV
ejpam-5165	320	15	f	f	PROPN
ejpam-5165	320	16	∈	∈	PROPN
ejpam-5165	320	17	mds([a	mds([a	NOUN
ejpam-5165	320	18	,	,	PUNCT
ejpam-5165	320	19	b	b	NOUN
ejpam-5165	320	20	]	]	X
ejpam-5165	320	21	,	,	PUNCT
ejpam-5165	320	22	g	g	NOUN
ejpam-5165	320	23	)	)	PUNCT
ejpam-5165	320	24	and	and	CCONJ
ejpam-5165	320	25	(	(	PUNCT
ejpam-5165	320	26	mds	mds	PROPN
ejpam-5165	320	27	)	)	PUNCT
ejpam-5165	320	28	∫	∫	PROPN
ejpam-5165	321	1	[	[	X
ejpam-5165	321	2	a	a	X
ejpam-5165	321	3	,	,	PUNCT
ejpam-5165	321	4	b	b	NOUN
ejpam-5165	321	5	]	]	X
ejpam-5165	321	6	fdg	fdg	PROPN
ejpam-5165	321	7	=	=	SYM
ejpam-5165	321	8	(	(	PUNCT
ejpam-5165	321	9	mds	mds	PROPN
ejpam-5165	321	10	)	)	PUNCT
ejpam-5165	321	11	∫	∫	PROPN
ejpam-5165	322	1	i	i	PROPN
ejpam-5165	322	2	fdg	fdg	PROPN
ejpam-5165	323	1	+	+	X
ejpam-5165	323	2	(	(	PUNCT
ejpam-5165	323	3	mds	mds	PROPN
ejpam-5165	323	4	)	)	PUNCT
ejpam-5165	323	5	∫	∫	PROPN
ejpam-5165	323	6	j	j	PROPN
ejpam-5165	323	7	fdg	fdg	PROPN
ejpam-5165	323	8	.	.	PROPN
ejpam-5165	323	9	theorem	theorem	VERB
ejpam-5165	323	10	8	8	NUM
ejpam-5165	323	11	.	.	PUNCT
ejpam-5165	324	1	let	let	VERB
ejpam-5165	324	2	f	f	NOUN
ejpam-5165	324	3	:	:	PUNCT
ejpam-5165	325	1	[	[	X
ejpam-5165	325	2	a	a	X
ejpam-5165	325	3	,	,	PUNCT
ejpam-5165	325	4	b	b	NOUN
ejpam-5165	325	5	]	]	X
ejpam-5165	325	6	→	→	SYM
ejpam-5165	325	7	x	x	X
ejpam-5165	325	8	and	and	CCONJ
ejpam-5165	325	9	g	g	NOUN
ejpam-5165	325	10	:	:	PUNCT
ejpam-5165	326	1	[	[	X
ejpam-5165	326	2	a	a	X
ejpam-5165	326	3	,	,	PUNCT
ejpam-5165	326	4	b	b	NOUN
ejpam-5165	326	5	]	]	X
ejpam-5165	326	6	→	→	PUNCT
ejpam-5165	326	7	r	r	NOUN
ejpam-5165	326	8	be	be	NOUN
ejpam-5165	326	9	functions	function	NOUN
ejpam-5165	326	10	.	.	PUNCT
ejpam-5165	327	1	if	if	SCONJ
ejpam-5165	327	2	f	f	PROPN
ejpam-5165	327	3	is	be	AUX
ejpam-5165	327	4	mds	mds	NOUN
ejpam-5165	327	5	-	-	PUNCT
ejpam-5165	327	6	integrable	integrable	ADJ
ejpam-5165	327	7	with	with	ADP
ejpam-5165	327	8	respect	respect	NOUN
ejpam-5165	327	9	to	to	ADP
ejpam-5165	327	10	g	g	NOUN
ejpam-5165	327	11	on	on	ADP
ejpam-5165	327	12	[	[	X
ejpam-5165	327	13	a	a	PRON
ejpam-5165	327	14	,	,	PUNCT
ejpam-5165	327	15	b	b	NOUN
ejpam-5165	327	16	,	,	PUNCT
ejpam-5165	327	17	then	then	ADV
ejpam-5165	327	18	for	for	ADP
ejpam-5165	327	19	each	each	DET
ejpam-5165	327	20	j	j	PROPN
ejpam-5165	327	21	⊆	⊆	NUM
ejpam-5165	327	22	in	in	ADP
ejpam-5165	327	23	(	(	PUNCT
ejpam-5165	327	24	[	[	X
ejpam-5165	327	25	a	a	X
ejpam-5165	327	26	,	,	PUNCT
ejpam-5165	327	27	b	b	NOUN
ejpam-5165	327	28	]	]	PUNCT
ejpam-5165	327	29	)	)	PUNCT
ejpam-5165	327	30	,	,	PUNCT
ejpam-5165	327	31	(	(	PUNCT
ejpam-5165	327	32	mds	mds	PROPN
ejpam-5165	327	33	)	)	PUNCT
ejpam-5165	327	34	∫	∫	PROPN
ejpam-5165	328	1	j	j	PROPN
ejpam-5165	328	2	fdg	fdg	PROPN
ejpam-5165	328	3	=	=	X
ejpam-5165	328	4	(	(	PUNCT
ejpam-5165	328	5	mds	mds	PROPN
ejpam-5165	328	6	)	)	PUNCT
ejpam-5165	328	7	∫	∫	PROPN
ejpam-5165	329	1	[	[	X
ejpam-5165	329	2	a	a	X
ejpam-5165	329	3	,	,	PUNCT
ejpam-5165	329	4	b	b	NOUN
ejpam-5165	329	5	]	]	X
ejpam-5165	329	6	f	f	X
ejpam-5165	329	7	·	·	PUNCT
ejpam-5165	329	8	χjdg	χjdg	ADV
ejpam-5165	329	9	.	.	PUNCT
ejpam-5165	330	1	proof	proof	NOUN
ejpam-5165	330	2	.	.	PUNCT
ejpam-5165	331	1	let	let	VERB
ejpam-5165	331	2	f	f	X
ejpam-5165	331	3	,	,	PUNCT
ejpam-5165	331	4	g	g	NOUN
ejpam-5165	331	5	:	:	PUNCT
ejpam-5165	332	1	[	[	X
ejpam-5165	332	2	a	a	X
ejpam-5165	332	3	,	,	PUNCT
ejpam-5165	332	4	b	b	NOUN
ejpam-5165	332	5	]	]	X
ejpam-5165	332	6	→	→	PUNCT
ejpam-5165	332	7	x	x	PART
ejpam-5165	332	8	be	be	AUX
ejpam-5165	332	9	functions	function	NOUN
ejpam-5165	332	10	and	and	CCONJ
ejpam-5165	332	11	j	j	PROPN
ejpam-5165	332	12	∈	∈	PROPN
ejpam-5165	332	13	in	in	ADP
ejpam-5165	332	14	(	(	PUNCT
ejpam-5165	332	15	[	[	X
ejpam-5165	332	16	a	a	X
ejpam-5165	332	17	,	,	PUNCT
ejpam-5165	332	18	b	b	NOUN
ejpam-5165	332	19	]	]	PUNCT
ejpam-5165	332	20	)	)	PUNCT
ejpam-5165	332	21	.	.	PUNCT
ejpam-5165	333	1	assume	assume	VERB
ejpam-5165	333	2	that	that	SCONJ
ejpam-5165	333	3	f	f	PROPN
ejpam-5165	333	4	is	be	AUX
ejpam-5165	333	5	mdsintegrable	mdsintegrable	ADJ
ejpam-5165	333	6	with	with	ADP
ejpam-5165	333	7	respect	respect	NOUN
ejpam-5165	333	8	to	to	ADP
ejpam-5165	333	9	g	g	NOUN
ejpam-5165	333	10	over	over	ADP
ejpam-5165	333	11	[	[	X
ejpam-5165	333	12	a	a	X
ejpam-5165	333	13	,	,	PUNCT
ejpam-5165	333	14	b	b	NOUN
ejpam-5165	333	15	]	]	X
ejpam-5165	333	16	.	.	PUNCT
ejpam-5165	334	1	if	if	SCONJ
ejpam-5165	334	2	j	j	PROPN
ejpam-5165	335	1	=	=	PUNCT
ejpam-5165	336	1	[	[	X
ejpam-5165	336	2	a	a	X
ejpam-5165	336	3	,	,	PUNCT
ejpam-5165	336	4	b	b	NOUN
ejpam-5165	336	5	]	]	X
ejpam-5165	336	6	,	,	PUNCT
ejpam-5165	336	7	then	then	ADV
ejpam-5165	336	8	(	(	PUNCT
ejpam-5165	336	9	mds	mds	PROPN
ejpam-5165	336	10	)	)	PUNCT
ejpam-5165	336	11	∫	∫	PROPN
ejpam-5165	337	1	j	j	PROPN
ejpam-5165	337	2	f	f	PROPN
ejpam-5165	337	3	·	·	PUNCT
ejpam-5165	337	4	χj	χj	ADP
ejpam-5165	337	5	dg	dg	PROPN
ejpam-5165	337	6	=	=	SYM
ejpam-5165	337	7	(	(	PUNCT
ejpam-5165	337	8	mds	mds	PROPN
ejpam-5165	337	9	)	)	PUNCT
ejpam-5165	337	10	∫	∫	PROPN
ejpam-5165	338	1	[	[	X
ejpam-5165	338	2	a	a	X
ejpam-5165	338	3	,	,	PUNCT
ejpam-5165	338	4	b	b	NOUN
ejpam-5165	338	5	]	]	X
ejpam-5165	338	6	f	f	X
ejpam-5165	338	7	·	·	PUNCT
ejpam-5165	338	8	χ[a	χ[a	PROPN
ejpam-5165	338	9	,	,	PUNCT
ejpam-5165	338	10	b	b	NOUN
ejpam-5165	338	11	]	]	X
ejpam-5165	338	12	dg	dg	X
ejpam-5165	338	13	=	=	SYM
ejpam-5165	338	14	(	(	PUNCT
ejpam-5165	338	15	mds	mds	PROPN
ejpam-5165	338	16	)	)	PUNCT
ejpam-5165	338	17	∫	∫	PROPN
ejpam-5165	339	1	[	[	X
ejpam-5165	339	2	a	a	X
ejpam-5165	339	3	,	,	PUNCT
ejpam-5165	339	4	b	b	NOUN
ejpam-5165	339	5	]	]	X
ejpam-5165	339	6	f	f	X
ejpam-5165	339	7	dg	dg	PROPN
ejpam-5165	339	8	=	=	SYM
ejpam-5165	339	9	(	(	PUNCT
ejpam-5165	339	10	mds	mds	PROPN
ejpam-5165	339	11	)	)	PUNCT
ejpam-5165	339	12	∫	∫	PROPN
ejpam-5165	340	1	j	j	PROPN
ejpam-5165	340	2	f	f	PROPN
ejpam-5165	340	3	dg	dg	PROPN
ejpam-5165	340	4	.	.	PUNCT
ejpam-5165	341	1	if	if	SCONJ
ejpam-5165	341	2	i	i	PRON
ejpam-5165	341	3	⊂	⊂	PRON
ejpam-5165	342	1	[	[	X
ejpam-5165	342	2	a	a	X
ejpam-5165	342	3	,	,	PUNCT
ejpam-5165	342	4	b	b	NOUN
ejpam-5165	342	5	]	]	X
ejpam-5165	342	6	,	,	PUNCT
ejpam-5165	342	7	then	then	ADV
ejpam-5165	342	8	f	f	PROPN
ejpam-5165	342	9	is	be	AUX
ejpam-5165	342	10	mds	mds	NOUN
ejpam-5165	342	11	-	-	PUNCT
ejpam-5165	342	12	integrable	integrable	ADJ
ejpam-5165	342	13	with	with	ADP
ejpam-5165	342	14	respect	respect	NOUN
ejpam-5165	342	15	to	to	ADP
ejpam-5165	342	16	g	g	NOUN
ejpam-5165	342	17	on	on	ADP
ejpam-5165	342	18	j	j	PROPN
ejpam-5165	342	19	.	.	PUNCT
ejpam-5165	343	1	notice	notice	VERB
ejpam-5165	343	2	that	that	SCONJ
ejpam-5165	343	3	[	[	X
ejpam-5165	343	4	a	a	DET
ejpam-5165	343	5	,	,	PUNCT
ejpam-5165	343	6	b	b	NOUN
ejpam-5165	343	7	]	]	X
ejpam-5165	343	8	=	=	SYM
ejpam-5165	343	9	(	(	PUNCT
ejpam-5165	344	1	[	[	X
ejpam-5165	344	2	a	a	X
ejpam-5165	344	3	,	,	PUNCT
ejpam-5165	344	4	b]∖	b]∖	PROPN
ejpam-5165	344	5	j	j	PROPN
ejpam-5165	344	6	)	)	PUNCT
ejpam-5165	344	7	∪	∪	ADP
ejpam-5165	344	8	j	j	PROPN
ejpam-5165	344	9	.	.	PUNCT
ejpam-5165	345	1	now	now	ADV
ejpam-5165	345	2	,	,	PUNCT
ejpam-5165	345	3	(	(	PUNCT
ejpam-5165	345	4	mds	mds	PROPN
ejpam-5165	345	5	)	)	PUNCT
ejpam-5165	345	6	∫	∫	PROPN
ejpam-5165	346	1	[	[	X
ejpam-5165	346	2	a	a	X
ejpam-5165	346	3	,	,	PUNCT
ejpam-5165	346	4	b	b	NOUN
ejpam-5165	346	5	]	]	X
ejpam-5165	346	6	f	f	X
ejpam-5165	346	7	·	·	PUNCT
ejpam-5165	346	8	χj	χj	ADP
ejpam-5165	346	9	dg	dg	PROPN
ejpam-5165	346	10	=	=	SYM
ejpam-5165	346	11	(	(	PUNCT
ejpam-5165	346	12	mds	mds	PROPN
ejpam-5165	346	13	)	)	PUNCT
ejpam-5165	346	14	∫	∫	PROPN
ejpam-5165	347	1	[	[	X
ejpam-5165	347	2	a	a	DET
ejpam-5165	347	3	,	,	PUNCT
ejpam-5165	347	4	b]∖j	b]∖j	ADJ
ejpam-5165	347	5	f	f	X
ejpam-5165	347	6	·	·	PUNCT
ejpam-5165	347	7	χj	χj	ADP
ejpam-5165	347	8	dg	dg	PROPN
ejpam-5165	347	9	+	+	CCONJ
ejpam-5165	347	10	(	(	PUNCT
ejpam-5165	347	11	mds	mds	PROPN
ejpam-5165	347	12	)	)	PUNCT
ejpam-5165	347	13	∫	∫	PROPN
ejpam-5165	348	1	j	j	PROPN
ejpam-5165	348	2	f	f	PROPN
ejpam-5165	348	3	·	·	PUNCT
ejpam-5165	348	4	χj	χj	ADP
ejpam-5165	348	5	dg	dg	PROPN
ejpam-5165	348	6	=	=	SYM
ejpam-5165	348	7	(	(	PUNCT
ejpam-5165	348	8	mds	mds	PROPN
ejpam-5165	348	9	)	)	PUNCT
ejpam-5165	348	10	∫	∫	PROPN
ejpam-5165	349	1	[	[	X
ejpam-5165	349	2	a	a	PRON
ejpam-5165	349	3	,	,	PUNCT
ejpam-5165	349	4	b]∖j	b]∖j	ADJ
ejpam-5165	349	5	f	f	X
ejpam-5165	349	6	·	·	PUNCT
ejpam-5165	349	7	(	(	PUNCT
ejpam-5165	349	8	0	0	NUM
ejpam-5165	349	9	)	)	PUNCT
ejpam-5165	349	10	dg	dg	NOUN
ejpam-5165	349	11	+	+	CCONJ
ejpam-5165	349	12	(	(	PUNCT
ejpam-5165	349	13	mds	mds	PROPN
ejpam-5165	349	14	)	)	PUNCT
ejpam-5165	349	15	∫	∫	PROPN
ejpam-5165	350	1	j	j	PROPN
ejpam-5165	350	2	f	f	PROPN
ejpam-5165	350	3	·	·	PUNCT
ejpam-5165	350	4	(	(	PUNCT
ejpam-5165	350	5	1	1	X
ejpam-5165	350	6	)	)	PUNCT
ejpam-5165	350	7	dg	dg	NOUN
ejpam-5165	350	8	=	=	SYM
ejpam-5165	350	9	(	(	PUNCT
ejpam-5165	350	10	mds	mds	PROPN
ejpam-5165	350	11	)	)	PUNCT
ejpam-5165	351	1	∫	∫	PROPN
ejpam-5165	352	1	j	j	PROPN
ejpam-5165	352	2	f	f	PROPN
ejpam-5165	352	3	dg	dg	PROPN
ejpam-5165	352	4	.	.	PUNCT
ejpam-5165	353	1	thus	thus	ADV
ejpam-5165	353	2	,	,	PUNCT
ejpam-5165	353	3	(	(	PUNCT
ejpam-5165	353	4	mds	mds	PROPN
ejpam-5165	353	5	)	)	PUNCT
ejpam-5165	353	6	∫	∫	PROPN
ejpam-5165	354	1	[	[	X
ejpam-5165	354	2	a	a	X
ejpam-5165	354	3	,	,	PUNCT
ejpam-5165	354	4	b	b	NOUN
ejpam-5165	354	5	]	]	X
ejpam-5165	354	6	f	f	X
ejpam-5165	354	7	·	·	PUNCT
ejpam-5165	354	8	χj	χj	ADP
ejpam-5165	354	9	dg	dg	PROPN
ejpam-5165	354	10	=	=	SYM
ejpam-5165	354	11	(	(	PUNCT
ejpam-5165	354	12	mds	mds	PROPN
ejpam-5165	354	13	)	)	PUNCT
ejpam-5165	354	14	∫	∫	PROPN
ejpam-5165	355	1	j	j	PROPN
ejpam-5165	355	2	f	f	PROPN
ejpam-5165	355	3	dg	dg	PROPN
ejpam-5165	355	4	.	.	PUNCT
ejpam-5165	355	5	□	□	PUNCT
ejpam-5165	355	6	.	.	PUNCT
ejpam-5165	356	1	proposition	proposition	NOUN
ejpam-5165	356	2	2	2	NUM
ejpam-5165	356	3	.	.	PUNCT
ejpam-5165	357	1	if	if	SCONJ
ejpam-5165	357	2	f	f	PROPN
ejpam-5165	357	3	:	:	PUNCT
ejpam-5165	358	1	[	[	X
ejpam-5165	358	2	a	a	X
ejpam-5165	358	3	,	,	PUNCT
ejpam-5165	358	4	b	b	NOUN
ejpam-5165	358	5	]	]	X
ejpam-5165	358	6	→	→	PUNCT
ejpam-5165	358	7	x	x	X
ejpam-5165	358	8	is	be	AUX
ejpam-5165	358	9	continuous	continuous	ADJ
ejpam-5165	358	10	on	on	ADP
ejpam-5165	358	11	[	[	X
ejpam-5165	358	12	a	a	X
ejpam-5165	358	13	,	,	PUNCT
ejpam-5165	358	14	b	b	NOUN
ejpam-5165	358	15	]	]	X
ejpam-5165	358	16	,	,	PUNCT
ejpam-5165	358	17	then	then	ADV
ejpam-5165	358	18	for	for	ADP
ejpam-5165	358	19	each	each	DET
ejpam-5165	358	20	x∗	x∗	PROPN
ejpam-5165	358	21	∈	∈	PROPN
ejpam-5165	358	22	x∗	x∗	PROPN
ejpam-5165	358	23	,	,	PUNCT
ejpam-5165	358	24	x∗(f	x∗(f	PROPN
ejpam-5165	358	25	)	)	PUNCT
ejpam-5165	358	26	:	:	PUNCT
ejpam-5165	359	1	[	[	X
ejpam-5165	359	2	a	a	X
ejpam-5165	359	3	,	,	PUNCT
ejpam-5165	359	4	b	b	NOUN
ejpam-5165	359	5	]	]	X
ejpam-5165	359	6	→	→	PUNCT
ejpam-5165	359	7	r	r	NOUN
ejpam-5165	359	8	is	be	AUX
ejpam-5165	359	9	also	also	ADV
ejpam-5165	359	10	continuous	continuous	ADJ
ejpam-5165	359	11	on	on	ADP
ejpam-5165	359	12	[	[	X
ejpam-5165	359	13	a	a	X
ejpam-5165	359	14	,	,	PUNCT
ejpam-5165	359	15	b	b	NOUN
ejpam-5165	359	16	]	]	PUNCT
ejpam-5165	359	17	.	.	PUNCT
ejpam-5165	360	1	proof	proof	NOUN
ejpam-5165	360	2	.	.	PUNCT
ejpam-5165	361	1	let	let	VERB
ejpam-5165	361	2	ε	ε	PROPN
ejpam-5165	361	3	>	>	X
ejpam-5165	361	4	0	0	PUNCT
ejpam-5165	362	1	and	and	CCONJ
ejpam-5165	362	2	x∗	x∗	PROPN
ejpam-5165	362	3	∈	∈	PROPN
ejpam-5165	362	4	x∗.	x∗.	PROPN
ejpam-5165	362	5	suppose	suppose	VERB
ejpam-5165	362	6	that	that	SCONJ
ejpam-5165	362	7	f	f	X
ejpam-5165	362	8	:	:	PUNCT
ejpam-5165	363	1	[	[	X
ejpam-5165	363	2	a	a	X
ejpam-5165	363	3	,	,	PUNCT
ejpam-5165	363	4	b	b	NOUN
ejpam-5165	363	5	]	]	X
ejpam-5165	363	6	→	→	PUNCT
ejpam-5165	363	7	x	x	X
ejpam-5165	363	8	is	be	AUX
ejpam-5165	363	9	continuous	continuous	ADJ
ejpam-5165	363	10	on	on	ADP
ejpam-5165	363	11	[	[	X
ejpam-5165	363	12	a	a	X
ejpam-5165	363	13	,	,	PUNCT
ejpam-5165	363	14	b	b	NOUN
ejpam-5165	363	15	]	]	X
ejpam-5165	363	16	.	.	PUNCT
ejpam-5165	364	1	then	then	ADV
ejpam-5165	364	2	for	for	ADP
ejpam-5165	364	3	every	every	DET
ejpam-5165	364	4	ε	ε	PROPN
ejpam-5165	364	5	>	>	X
ejpam-5165	364	6	0	0	PROPN
ejpam-5165	364	7	,	,	PUNCT
ejpam-5165	364	8	there	there	PRON
ejpam-5165	364	9	exists	exist	VERB
ejpam-5165	364	10	a	a	DET
ejpam-5165	364	11	δ	δ	PROPN
ejpam-5165	364	12	>	>	X
ejpam-5165	364	13	0	0	NUM
ejpam-5165	365	1	such	such	ADJ
ejpam-5165	365	2	that	that	PRON
ejpam-5165	365	3	for	for	ADP
ejpam-5165	365	4	every	every	DET
ejpam-5165	365	5	u	u	NOUN
ejpam-5165	365	6	,	,	PUNCT
ejpam-5165	365	7	v	v	NOUN
ejpam-5165	365	8	∈	∈	PROPN
ejpam-5165	365	9	[	[	X
ejpam-5165	365	10	a	a	X
ejpam-5165	365	11	,	,	PUNCT
ejpam-5165	365	12	b	b	NOUN
ejpam-5165	365	13	]	]	PUNCT
ejpam-5165	365	14	with	with	ADP
ejpam-5165	365	15	∥u−	∥u−	PROPN
ejpam-5165	365	16	v∥rn	v∥rn	PROPN
ejpam-5165	365	17	<	<	X
ejpam-5165	365	18	δ	δ	PROPN
ejpam-5165	365	19	,	,	PUNCT
ejpam-5165	365	20	we	we	PRON
ejpam-5165	365	21	have	have	VERB
ejpam-5165	365	22	|f(u)−	|f(u)−	PRON
ejpam-5165	365	23	f(v)|	f(v)|	NOUN
ejpam-5165	365	24	<	<	X
ejpam-5165	365	25	ε	ε	PROPN
ejpam-5165	365	26	∥x∗∥x∗	∥x∗∥x∗	PROPN
ejpam-5165	366	1	+	+	ADP
ejpam-5165	366	2	1	1	NUM
ejpam-5165	366	3	.	.	PUNCT
ejpam-5165	367	1	d.	d.	PROPN
ejpam-5165	367	2	omayan	omayan	PROPN
ejpam-5165	367	3	,	,	PUNCT
ejpam-5165	367	4	g.b	g.b	PROPN
ejpam-5165	367	5	.	.	PROPN
ejpam-5165	367	6	flores	flores	PROPN
ejpam-5165	367	7	/	/	SYM
ejpam-5165	367	8	eur	eur	PROPN
ejpam-5165	367	9	.	.	PUNCT
ejpam-5165	368	1	j.	j.	PROPN
ejpam-5165	368	2	pure	pure	PROPN
ejpam-5165	368	3	appl	appl	PROPN
ejpam-5165	368	4	.	.	PROPN
ejpam-5165	368	5	math	math	PROPN
ejpam-5165	368	6	,	,	PUNCT
ejpam-5165	368	7	17	17	NUM
ejpam-5165	368	8	(	(	PUNCT
ejpam-5165	368	9	2	2	NUM
ejpam-5165	368	10	)	)	PUNCT
ejpam-5165	368	11	(	(	PUNCT
ejpam-5165	368	12	2024	2024	NUM
ejpam-5165	368	13	)	)	PUNCT
ejpam-5165	368	14	,	,	PUNCT
ejpam-5165	368	15	1183	1183	NUM
ejpam-5165	368	16	-	-	SYM
ejpam-5165	368	17	1196	1196	NUM
ejpam-5165	368	18	1193	1193	NUM
ejpam-5165	368	19	now	now	ADV
ejpam-5165	368	20	,	,	PUNCT
ejpam-5165	368	21	∥x∗(f(u))−	∥x∗(f(u))−	NOUN
ejpam-5165	368	22	x∗(f(v))∥x∗	x∗(f(v))∥x∗	NOUN
ejpam-5165	368	23	=	=	PUNCT
ejpam-5165	368	24	∥x∗[f(u)−	∥x∗[f(u)−	NOUN
ejpam-5165	368	25	f(v)]∥x∗	f(v)]∥x∗	NOUN
ejpam-5165	368	26	≤	≤	PUNCT
ejpam-5165	368	27	∥x∗∥x∗∥f(u)−	∥x∗∥x∗∥f(u)−	PROPN
ejpam-5165	368	28	f(v)∥	f(v)∥	X
ejpam-5165	368	29	≤	≤	NOUN
ejpam-5165	368	30	∥x∗∥x∗	∥x∗∥x∗	ADJ
ejpam-5165	368	31	|f(u)−	|f(u)−	PRON
ejpam-5165	368	32	f(v)|	f(v)|	NOUN
ejpam-5165	368	33	<	<	X
ejpam-5165	368	34	∥x∗∥x∗	∥x∗∥x∗	PROPN
ejpam-5165	368	35	ε	ε	PROPN
ejpam-5165	368	36	∥x∗∥x∗	∥x∗∥x∗	PROPN
ejpam-5165	368	37	+	+	CCONJ
ejpam-5165	368	38	1	1	NUM
ejpam-5165	368	39	=	=	SYM
ejpam-5165	368	40	ε	ε	PROPN
ejpam-5165	368	41	.	.	PUNCT
ejpam-5165	369	1	and	and	CCONJ
ejpam-5165	369	2	so	so	ADV
ejpam-5165	369	3	,	,	PUNCT
ejpam-5165	369	4	x∗(f	x∗(f	PROPN
ejpam-5165	369	5	)	)	PUNCT
ejpam-5165	369	6	is	be	AUX
ejpam-5165	369	7	continuous	continuous	ADJ
ejpam-5165	369	8	.	.	PUNCT
ejpam-5165	370	1	□	□	PUNCT
ejpam-5165	370	2	theorem	theorem	ADJ
ejpam-5165	370	3	9	9	NUM
ejpam-5165	370	4	.	.	PUNCT
ejpam-5165	371	1	(	(	PUNCT
ejpam-5165	371	2	existence	existence	NOUN
ejpam-5165	371	3	theorem	theorem	NOUN
ejpam-5165	371	4	of	of	ADP
ejpam-5165	371	5	mds	mds	NOUN
ejpam-5165	371	6	-	-	PUNCT
ejpam-5165	371	7	integral	integral	ADJ
ejpam-5165	371	8	)	)	PUNCT
ejpam-5165	371	9	let	let	VERB
ejpam-5165	371	10	f	f	PRON
ejpam-5165	371	11	be	be	AUX
ejpam-5165	371	12	continuous	continuous	ADJ
ejpam-5165	371	13	on	on	ADP
ejpam-5165	371	14	[	[	X
ejpam-5165	371	15	a	a	X
ejpam-5165	371	16	,	,	PUNCT
ejpam-5165	371	17	b	b	NOUN
ejpam-5165	371	18	]	]	PUNCT
ejpam-5165	371	19	and	and	CCONJ
ejpam-5165	371	20	g	g	PROPN
ejpam-5165	371	21	be	be	AUX
ejpam-5165	371	22	a	a	DET
ejpam-5165	371	23	function	function	NOUN
ejpam-5165	371	24	of	of	ADP
ejpam-5165	371	25	bounded	bounded	ADJ
ejpam-5165	371	26	variation	variation	NOUN
ejpam-5165	371	27	.	.	PUNCT
ejpam-5165	372	1	then	then	ADV
ejpam-5165	372	2	f	f	PROPN
ejpam-5165	372	3	is	be	AUX
ejpam-5165	372	4	mds	mds	NOUN
ejpam-5165	372	5	-	-	PUNCT
ejpam-5165	372	6	integrable	integrable	ADJ
ejpam-5165	372	7	with	with	ADP
ejpam-5165	372	8	respect	respect	NOUN
ejpam-5165	372	9	to	to	ADP
ejpam-5165	372	10	g	g	NOUN
ejpam-5165	372	11	on	on	ADP
ejpam-5165	372	12	[	[	X
ejpam-5165	372	13	a	a	X
ejpam-5165	372	14	,	,	PUNCT
ejpam-5165	372	15	b	b	NOUN
ejpam-5165	372	16	]	]	PUNCT
ejpam-5165	372	17	.	.	PUNCT
ejpam-5165	373	1	proof	proof	NOUN
ejpam-5165	373	2	.	.	PUNCT
ejpam-5165	374	1	fix	fix	VERB
ejpam-5165	374	2	x∗	x∗	PROPN
ejpam-5165	374	3	∈	∈	PROPN
ejpam-5165	374	4	x∗.	x∗.	PROPN
ejpam-5165	374	5	suppose	suppose	VERB
ejpam-5165	374	6	that	that	SCONJ
ejpam-5165	374	7	f	f	PROPN
ejpam-5165	374	8	is	be	AUX
ejpam-5165	374	9	continuous	continuous	ADJ
ejpam-5165	374	10	on	on	ADP
ejpam-5165	374	11	[	[	X
ejpam-5165	374	12	a	a	X
ejpam-5165	374	13	,	,	PUNCT
ejpam-5165	374	14	b	b	NOUN
ejpam-5165	374	15	]	]	PUNCT
ejpam-5165	374	16	and	and	CCONJ
ejpam-5165	374	17	g	g	PROPN
ejpam-5165	374	18	be	be	AUX
ejpam-5165	374	19	a	a	DET
ejpam-5165	374	20	function	function	NOUN
ejpam-5165	374	21	of	of	ADP
ejpam-5165	374	22	bounded	bounded	ADJ
ejpam-5165	374	23	variation	variation	NOUN
ejpam-5165	374	24	.	.	PUNCT
ejpam-5165	375	1	applying	apply	VERB
ejpam-5165	375	2	proposition	proposition	NOUN
ejpam-5165	375	3	2	2	NUM
ejpam-5165	375	4	,	,	PUNCT
ejpam-5165	375	5	x∗(f	x∗(f	PROPN
ejpam-5165	375	6	)	)	PUNCT
ejpam-5165	375	7	is	be	AUX
ejpam-5165	375	8	continuous	continuous	ADJ
ejpam-5165	375	9	.	.	PUNCT
ejpam-5165	376	1	by	by	ADP
ejpam-5165	376	2	the	the	DET
ejpam-5165	376	3	existence	existence	NOUN
ejpam-5165	376	4	theorem	theorem	NOUN
ejpam-5165	376	5	of	of	ADP
ejpam-5165	376	6	the	the	DET
ejpam-5165	376	7	pul	pul	NOUN
ejpam-5165	376	8	-	-	PUNCT
ejpam-5165	376	9	stieltjes	stieltjes	NOUN
ejpam-5165	376	10	integral	integral	ADJ
ejpam-5165	376	11	and	and	CCONJ
ejpam-5165	376	12	theorem	theorem	ADJ
ejpam-5165	376	13	1	1	NUM
ejpam-5165	376	14	,	,	PUNCT
ejpam-5165	376	15	x∗(f	x∗(f	PROPN
ejpam-5165	376	16	)	)	PUNCT
ejpam-5165	376	17	is	be	AUX
ejpam-5165	376	18	continuous	continuous	ADJ
ejpam-5165	376	19	and	and	CCONJ
ejpam-5165	376	20	g	g	NOUN
ejpam-5165	376	21	is	be	AUX
ejpam-5165	376	22	a	a	DET
ejpam-5165	376	23	function	function	NOUN
ejpam-5165	376	24	of	of	ADP
ejpam-5165	376	25	bounded	bounded	ADJ
ejpam-5165	376	26	variation	variation	NOUN
ejpam-5165	376	27	means	mean	VERB
ejpam-5165	376	28	that	that	SCONJ
ejpam-5165	376	29	the	the	DET
ejpam-5165	376	30	mcshane	mcshane	PROPN
ejpam-5165	376	31	-	-	PUNCT
ejpam-5165	376	32	stieltjes	stieltjes	PROPN
ejpam-5165	376	33	integral	integral	ADJ
ejpam-5165	376	34	of	of	ADP
ejpam-5165	376	35	x∗(f	x∗(f	PROPN
ejpam-5165	376	36	)	)	PUNCT
ejpam-5165	376	37	with	with	ADP
ejpam-5165	376	38	respect	respect	NOUN
ejpam-5165	376	39	to	to	ADP
ejpam-5165	376	40	g	g	NOUN
ejpam-5165	376	41	on	on	ADP
ejpam-5165	376	42	[	[	X
ejpam-5165	376	43	a	a	X
ejpam-5165	376	44	,	,	PUNCT
ejpam-5165	376	45	b	b	NOUN
ejpam-5165	376	46	]	]	PUNCT
ejpam-5165	376	47	exists	exist	VERB
ejpam-5165	376	48	.	.	PUNCT
ejpam-5165	377	1	and	and	CCONJ
ejpam-5165	377	2	so	so	ADV
ejpam-5165	377	3	,	,	PUNCT
ejpam-5165	377	4	x∗(f	x∗(f	PROPN
ejpam-5165	377	5	)	)	PUNCT
ejpam-5165	377	6	is	be	AUX
ejpam-5165	377	7	ms	ms	NOUN
ejpam-5165	377	8	-	-	PUNCT
ejpam-5165	377	9	integrable	integrable	ADJ
ejpam-5165	377	10	with	with	ADP
ejpam-5165	377	11	respect	respect	NOUN
ejpam-5165	377	12	to	to	ADP
ejpam-5165	377	13	g	g	NOUN
ejpam-5165	377	14	on	on	ADP
ejpam-5165	377	15	[	[	X
ejpam-5165	377	16	a	a	X
ejpam-5165	377	17	,	,	PUNCT
ejpam-5165	377	18	b	b	NOUN
ejpam-5165	377	19	]	]	PUNCT
ejpam-5165	377	20	.	.	PUNCT
ejpam-5165	378	1	let	let	VERB
ejpam-5165	378	2	j	j	PROPN
ejpam-5165	378	3	be	be	AUX
ejpam-5165	378	4	a	a	DET
ejpam-5165	378	5	compact	compact	ADJ
ejpam-5165	378	6	subinterval	subinterval	NOUN
ejpam-5165	378	7	of	of	ADP
ejpam-5165	378	8	[	[	X
ejpam-5165	378	9	a	a	X
ejpam-5165	378	10	,	,	PUNCT
ejpam-5165	378	11	b	b	NOUN
ejpam-5165	378	12	]	]	X
ejpam-5165	378	13	.	.	PUNCT
ejpam-5165	379	1	then	then	ADV
ejpam-5165	379	2	x∗(f	x∗(f	PROPN
ejpam-5165	379	3	)	)	PUNCT
ejpam-5165	379	4	is	be	AUX
ejpam-5165	379	5	also	also	ADV
ejpam-5165	379	6	ms	ms	ADJ
ejpam-5165	379	7	-	-	PUNCT
ejpam-5165	379	8	integrable	integrable	ADJ
ejpam-5165	379	9	with	with	ADP
ejpam-5165	379	10	respect	respect	NOUN
ejpam-5165	379	11	to	to	ADP
ejpam-5165	379	12	g	g	NOUN
ejpam-5165	379	13	on	on	ADP
ejpam-5165	379	14	j	j	PROPN
ejpam-5165	379	15	.	.	PUNCT
ejpam-5165	380	1	take	take	VERB
ejpam-5165	380	2	x∗∗j	x∗∗j	PROPN
ejpam-5165	380	3	(	(	PUNCT
ejpam-5165	380	4	x∗	x∗	PROPN
ejpam-5165	380	5	)	)	PUNCT
ejpam-5165	381	1	=	=	SYM
ejpam-5165	381	2	(	(	PUNCT
ejpam-5165	381	3	ms	ms	PROPN
ejpam-5165	381	4	)	)	PUNCT
ejpam-5165	381	5	∫	∫	PROPN
ejpam-5165	382	1	j	j	PROPN
ejpam-5165	382	2	x∗(f)dg	x∗(f)dg	PROPN
ejpam-5165	382	3	implying	imply	VERB
ejpam-5165	382	4	that	that	SCONJ
ejpam-5165	382	5	x∗∗j	x∗∗j	PROPN
ejpam-5165	382	6	∈	∈	PROPN
ejpam-5165	382	7	x∗∗.	x∗∗.	X
ejpam-5165	383	1	this	this	PRON
ejpam-5165	383	2	means	mean	VERB
ejpam-5165	383	3	that	that	SCONJ
ejpam-5165	383	4	x∗∗j	x∗∗j	PROPN
ejpam-5165	383	5	=	=	SYM
ejpam-5165	383	6	(	(	PUNCT
ejpam-5165	383	7	mds	mds	PROPN
ejpam-5165	383	8	)	)	PUNCT
ejpam-5165	383	9	∫	∫	PROPN
ejpam-5165	383	10	j	j	PROPN
ejpam-5165	383	11	fdg	fdg	PROPN
ejpam-5165	383	12	.	.	PUNCT
ejpam-5165	384	1	therefore	therefore	ADV
ejpam-5165	384	2	,	,	PUNCT
ejpam-5165	384	3	f	f	PROPN
ejpam-5165	384	4	is	be	AUX
ejpam-5165	384	5	mds	mds	NOUN
ejpam-5165	384	6	-	-	PUNCT
ejpam-5165	384	7	integrable	integrable	ADJ
ejpam-5165	384	8	with	with	ADP
ejpam-5165	384	9	respect	respect	NOUN
ejpam-5165	384	10	to	to	ADP
ejpam-5165	384	11	g	g	NOUN
ejpam-5165	384	12	on	on	ADP
ejpam-5165	384	13	[	[	X
ejpam-5165	384	14	a	a	X
ejpam-5165	384	15	,	,	PUNCT
ejpam-5165	384	16	b	b	NOUN
ejpam-5165	384	17	]	]	X
ejpam-5165	384	18	.	.	PUNCT
ejpam-5165	385	1	□	□	PUNCT
ejpam-5165	385	2	definition	definition	NOUN
ejpam-5165	385	3	19	19	NUM
ejpam-5165	385	4	.	.	PUNCT
ejpam-5165	386	1	let	let	VERB
ejpam-5165	386	2	f	f	NOUN
ejpam-5165	386	3	:	:	PUNCT
ejpam-5165	387	1	[	[	X
ejpam-5165	387	2	a	a	X
ejpam-5165	387	3	,	,	PUNCT
ejpam-5165	387	4	b	b	NOUN
ejpam-5165	387	5	]	]	X
ejpam-5165	387	6	→	→	SYM
ejpam-5165	387	7	x	x	X
ejpam-5165	387	8	and	and	CCONJ
ejpam-5165	387	9	g	g	NOUN
ejpam-5165	387	10	:	:	PUNCT
ejpam-5165	388	1	[	[	X
ejpam-5165	388	2	a	a	X
ejpam-5165	388	3	,	,	PUNCT
ejpam-5165	388	4	b	b	NOUN
ejpam-5165	388	5	]	]	X
ejpam-5165	388	6	→	→	PUNCT
ejpam-5165	388	7	r	r	NOUN
ejpam-5165	388	8	be	be	NOUN
ejpam-5165	388	9	functions	function	NOUN
ejpam-5165	388	10	.	.	PUNCT
ejpam-5165	389	1	if	if	SCONJ
ejpam-5165	389	2	f	f	PROPN
ejpam-5165	389	3	is	be	AUX
ejpam-5165	389	4	mdsintegrable	mdsintegrable	ADJ
ejpam-5165	389	5	with	with	ADP
ejpam-5165	389	6	respect	respect	NOUN
ejpam-5165	389	7	to	to	ADP
ejpam-5165	389	8	g	g	NOUN
ejpam-5165	389	9	on	on	ADP
ejpam-5165	389	10	[	[	X
ejpam-5165	389	11	a	a	X
ejpam-5165	389	12	,	,	PUNCT
ejpam-5165	389	13	b	b	NOUN
ejpam-5165	389	14	]	]	X
ejpam-5165	389	15	where	where	SCONJ
ejpam-5165	389	16	(	(	PUNCT
ejpam-5165	389	17	mds	mds	PROPN
ejpam-5165	389	18	)	)	PUNCT
ejpam-5165	389	19	∫	∫	PROPN
ejpam-5165	389	20	j	j	PROPN
ejpam-5165	389	21	fdg	fdg	PROPN
ejpam-5165	389	22	∈	∈	PROPN
ejpam-5165	389	23	x	x	PUNCT
ejpam-5165	389	24	for	for	ADP
ejpam-5165	389	25	every	every	DET
ejpam-5165	389	26	interval	interval	NOUN
ejpam-5165	389	27	j	j	PROPN
ejpam-5165	390	1	⊆	⊆	NUM
ejpam-5165	390	2	[	[	X
ejpam-5165	390	3	a	a	X
ejpam-5165	390	4	,	,	PUNCT
ejpam-5165	390	5	b	b	NOUN
ejpam-5165	390	6	]	]	X
ejpam-5165	390	7	(	(	PUNCT
ejpam-5165	390	8	more	more	ADV
ejpam-5165	390	9	precisely	precisely	ADV
ejpam-5165	390	10	(	(	PUNCT
ejpam-5165	390	11	mds	mds	PROPN
ejpam-5165	390	12	)	)	PUNCT
ejpam-5165	390	13	∫	∫	PROPN
ejpam-5165	390	14	j	j	PROPN
ejpam-5165	390	15	fdg	fdg	PROPN
ejpam-5165	390	16	∈	∈	PROPN
ejpam-5165	390	17	e(x	e(x	NUM
ejpam-5165	390	18	)	)	PUNCT
ejpam-5165	390	19	⊆	⊆	NUM
ejpam-5165	390	20	x∗∗	x∗∗	NOUN
ejpam-5165	390	21	,	,	PUNCT
ejpam-5165	390	22	where	where	SCONJ
ejpam-5165	390	23	e	e	NOUN
ejpam-5165	390	24	is	be	AUX
ejpam-5165	390	25	the	the	DET
ejpam-5165	390	26	canonical	canonical	ADJ
ejpam-5165	390	27	embedding	embedding	NOUN
ejpam-5165	390	28	of	of	ADP
ejpam-5165	390	29	x	x	PUNCT
ejpam-5165	390	30	into	into	ADP
ejpam-5165	390	31	x∗∗	x∗∗	NOUN
ejpam-5165	390	32	)	)	PUNCT
ejpam-5165	390	33	,	,	PUNCT
ejpam-5165	390	34	then	then	ADV
ejpam-5165	390	35	f	f	PROPN
ejpam-5165	390	36	is	be	AUX
ejpam-5165	390	37	called	call	VERB
ejpam-5165	390	38	mcshane	mcshane	PROPN
ejpam-5165	390	39	-	-	PUNCT
ejpam-5165	390	40	pettis	pettis	PROPN
ejpam-5165	390	41	-	-	PUNCT
ejpam-5165	390	42	stieltjes	stieltjes	NOUN
ejpam-5165	390	43	integrable	integrable	ADJ
ejpam-5165	390	44	(	(	PUNCT
ejpam-5165	390	45	or	or	CCONJ
ejpam-5165	390	46	simply	simply	ADV
ejpam-5165	390	47	mpsintegrable	mpsintegrable	ADJ
ejpam-5165	390	48	)	)	PUNCT
ejpam-5165	390	49	with	with	ADP
ejpam-5165	390	50	respect	respect	NOUN
ejpam-5165	390	51	to	to	ADP
ejpam-5165	390	52	g	g	NOUN
ejpam-5165	390	53	on	on	ADP
ejpam-5165	390	54	[	[	X
ejpam-5165	390	55	a	a	X
ejpam-5165	390	56	,	,	PUNCT
ejpam-5165	390	57	b	b	NOUN
ejpam-5165	390	58	]	]	PUNCT
ejpam-5165	390	59	and	and	CCONJ
ejpam-5165	390	60	(	(	PUNCT
ejpam-5165	390	61	mds	mds	PROPN
ejpam-5165	390	62	)	)	PUNCT
ejpam-5165	390	63	∫	∫	PROPN
ejpam-5165	391	1	j	j	PROPN
ejpam-5165	391	2	f	f	X
ejpam-5165	391	3	dg	dg	PROPN
ejpam-5165	391	4	=	=	SYM
ejpam-5165	391	5	(	(	PUNCT
ejpam-5165	391	6	mps	mps	PROPN
ejpam-5165	391	7	)	)	PUNCT
ejpam-5165	391	8	∫	∫	PROPN
ejpam-5165	392	1	j	j	PROPN
ejpam-5165	392	2	f	f	PROPN
ejpam-5165	392	3	dg	dg	PROPN
ejpam-5165	392	4	∈	∈	PROPN
ejpam-5165	392	5	x	x	PUNCT
ejpam-5165	392	6	is	be	AUX
ejpam-5165	392	7	the	the	DET
ejpam-5165	392	8	mcshane	mcshane	PROPN
ejpam-5165	392	9	-	-	PUNCT
ejpam-5165	392	10	pettis	pettis	PROPN
ejpam-5165	392	11	-	-	PUNCT
ejpam-5165	392	12	stieltjes	stieltjes	NOUN
ejpam-5165	392	13	integral	integral	ADJ
ejpam-5165	392	14	of	of	ADP
ejpam-5165	392	15	f	f	PROPN
ejpam-5165	392	16	with	with	ADP
ejpam-5165	392	17	respect	respect	NOUN
ejpam-5165	392	18	to	to	ADP
ejpam-5165	392	19	g	g	NOUN
ejpam-5165	392	20	on	on	ADP
ejpam-5165	392	21	j	j	PROPN
ejpam-5165	392	22	⊆	⊆	NUM
ejpam-5165	392	23	[	[	X
ejpam-5165	392	24	a	a	X
ejpam-5165	392	25	,	,	PUNCT
ejpam-5165	392	26	b	b	NOUN
ejpam-5165	392	27	]	]	X
ejpam-5165	392	28	.	.	PUNCT
ejpam-5165	393	1	here	here	ADV
ejpam-5165	393	2	,	,	PUNCT
ejpam-5165	393	3	we	we	PRON
ejpam-5165	393	4	write	write	VERB
ejpam-5165	393	5	mps([a	mps([a	PROPN
ejpam-5165	393	6	,	,	PUNCT
ejpam-5165	393	7	b	b	NOUN
ejpam-5165	393	8	]	]	X
ejpam-5165	393	9	,	,	PUNCT
ejpam-5165	393	10	g	g	NOUN
ejpam-5165	393	11	)	)	PUNCT
ejpam-5165	393	12	the	the	DET
ejpam-5165	393	13	set	set	NOUN
ejpam-5165	393	14	of	of	ADP
ejpam-5165	393	15	all	all	DET
ejpam-5165	393	16	mcshane	mcshane	PROPN
ejpam-5165	393	17	-	-	PUNCT
ejpam-5165	393	18	pettis	pettis	PROPN
ejpam-5165	393	19	-	-	PUNCT
ejpam-5165	393	20	stieltjes	stieltjes	NOUN
ejpam-5165	393	21	integrable	integrable	ADJ
ejpam-5165	393	22	functions	function	NOUN
ejpam-5165	393	23	f	f	NOUN
ejpam-5165	393	24	:	:	PUNCT
ejpam-5165	394	1	[	[	X
ejpam-5165	394	2	a	a	X
ejpam-5165	394	3	,	,	PUNCT
ejpam-5165	394	4	b	b	NOUN
ejpam-5165	394	5	]	]	X
ejpam-5165	394	6	→	→	PUNCT
ejpam-5165	394	7	x	x	SYM
ejpam-5165	394	8	with	with	ADP
ejpam-5165	394	9	respect	respect	NOUN
ejpam-5165	394	10	to	to	ADP
ejpam-5165	394	11	g	g	NOUN
ejpam-5165	394	12	on	on	ADP
ejpam-5165	394	13	j	j	PROPN
ejpam-5165	394	14	⊆	⊆	NUM
ejpam-5165	394	15	[	[	X
ejpam-5165	394	16	a	a	X
ejpam-5165	394	17	,	,	PUNCT
ejpam-5165	394	18	b	b	NOUN
ejpam-5165	394	19	]	]	PUNCT
ejpam-5165	394	20	.	.	PUNCT
ejpam-5165	395	1	theorem	theorem	ADJ
ejpam-5165	395	2	10	10	NUM
ejpam-5165	395	3	.	.	PUNCT
ejpam-5165	396	1	there	there	PRON
ejpam-5165	396	2	is	be	VERB
ejpam-5165	396	3	at	at	ADP
ejpam-5165	396	4	most	most	ADV
ejpam-5165	396	5	one	one	NUM
ejpam-5165	396	6	value	value	NOUN
ejpam-5165	396	7	satisfying	satisfy	VERB
ejpam-5165	396	8	definition	definition	NOUN
ejpam-5165	396	9	19	19	NUM
ejpam-5165	396	10	proof	proof	NOUN
ejpam-5165	396	11	.	.	PUNCT
ejpam-5165	397	1	suppose	suppose	VERB
ejpam-5165	397	2	that	that	SCONJ
ejpam-5165	397	3	(	(	PUNCT
ejpam-5165	397	4	mps	mp	NOUN
ejpam-5165	397	5	)	)	PUNCT
ejpam-5165	397	6	∫	∫	PROPN
ejpam-5165	397	7	j	j	PROPN
ejpam-5165	397	8	f	f	PROPN
ejpam-5165	397	9	dg	dg	PROPN
ejpam-5165	397	10	exists	exist	VERB
ejpam-5165	397	11	∀	∀	X
ejpam-5165	397	12	j	j	PROPN
ejpam-5165	397	13	⊆	⊆	NUM
ejpam-5165	397	14	[	[	X
ejpam-5165	397	15	a	a	X
ejpam-5165	397	16	,	,	PUNCT
ejpam-5165	397	17	b	b	NOUN
ejpam-5165	397	18	]	]	PUNCT
ejpam-5165	397	19	.	.	PUNCT
ejpam-5165	398	1	by	by	ADP
ejpam-5165	398	2	definition	definition	NOUN
ejpam-5165	398	3	19	19	NUM
ejpam-5165	398	4	,	,	PUNCT
ejpam-5165	398	5	(	(	PUNCT
ejpam-5165	398	6	mds	mds	PROPN
ejpam-5165	398	7	)	)	PUNCT
ejpam-5165	398	8	∫	∫	PROPN
ejpam-5165	399	1	j	j	PROPN
ejpam-5165	399	2	f	f	X
ejpam-5165	399	3	dg	dg	PROPN
ejpam-5165	399	4	=	=	SYM
ejpam-5165	399	5	(	(	PUNCT
ejpam-5165	399	6	mps	mps	PROPN
ejpam-5165	399	7	)	)	PUNCT
ejpam-5165	399	8	∫	∫	PROPN
ejpam-5165	400	1	j	j	PROPN
ejpam-5165	400	2	f	f	PROPN
ejpam-5165	400	3	dg	dg	PROPN
ejpam-5165	400	4	.	.	PUNCT
ejpam-5165	401	1	d.	d.	PROPN
ejpam-5165	401	2	omayan	omayan	PROPN
ejpam-5165	401	3	,	,	PUNCT
ejpam-5165	401	4	g.b	g.b	PROPN
ejpam-5165	401	5	.	.	PROPN
ejpam-5165	401	6	flores	flores	PROPN
ejpam-5165	401	7	/	/	SYM
ejpam-5165	401	8	eur	eur	PROPN
ejpam-5165	401	9	.	.	PUNCT
ejpam-5165	402	1	j.	j.	PROPN
ejpam-5165	402	2	pure	pure	PROPN
ejpam-5165	402	3	appl	appl	PROPN
ejpam-5165	402	4	.	.	PROPN
ejpam-5165	402	5	math	math	PROPN
ejpam-5165	402	6	,	,	PUNCT
ejpam-5165	402	7	17	17	NUM
ejpam-5165	402	8	(	(	PUNCT
ejpam-5165	402	9	2	2	NUM
ejpam-5165	402	10	)	)	PUNCT
ejpam-5165	402	11	(	(	PUNCT
ejpam-5165	402	12	2024	2024	NUM
ejpam-5165	402	13	)	)	PUNCT
ejpam-5165	402	14	,	,	PUNCT
ejpam-5165	402	15	1183	1183	NUM
ejpam-5165	402	16	-	-	SYM
ejpam-5165	402	17	1196	1196	NUM
ejpam-5165	402	18	1194	1194	NUM
ejpam-5165	402	19	now	now	ADV
ejpam-5165	402	20	,	,	PUNCT
ejpam-5165	402	21	fix	fix	VERB
ejpam-5165	402	22	j	j	NOUN
ejpam-5165	402	23	⊆	⊆	NUM
ejpam-5165	402	24	[	[	X
ejpam-5165	402	25	a	a	X
ejpam-5165	402	26	,	,	PUNCT
ejpam-5165	402	27	b	b	NOUN
ejpam-5165	402	28	]	]	PUNCT
ejpam-5165	402	29	.	.	PUNCT
ejpam-5165	403	1	from	from	ADP
ejpam-5165	403	2	theorem	theorem	ADJ
ejpam-5165	403	3	2	2	NUM
ejpam-5165	403	4	,	,	PUNCT
ejpam-5165	403	5	(	(	PUNCT
ejpam-5165	403	6	mds	mds	PROPN
ejpam-5165	403	7	)	)	PUNCT
ejpam-5165	403	8	∫	∫	PROPN
ejpam-5165	404	1	j	j	PROPN
ejpam-5165	404	2	f	f	PROPN
ejpam-5165	404	3	dg	dg	PROPN
ejpam-5165	404	4	is	be	AUX
ejpam-5165	404	5	unique	unique	ADJ
ejpam-5165	404	6	,	,	PUNCT
ejpam-5165	404	7	then	then	ADV
ejpam-5165	404	8	(	(	PUNCT
ejpam-5165	404	9	mps	mps	PROPN
ejpam-5165	404	10	)	)	PUNCT
ejpam-5165	404	11	∫	∫	PROPN
ejpam-5165	405	1	j	j	PROPN
ejpam-5165	405	2	f	f	PROPN
ejpam-5165	405	3	dg	dg	PROPN
ejpam-5165	405	4	is	be	AUX
ejpam-5165	405	5	also	also	ADV
ejpam-5165	405	6	unique	unique	ADJ
ejpam-5165	405	7	.	.	PUNCT
ejpam-5165	406	1	□	□	PUNCT
ejpam-5165	406	2	theorem	theorem	ADJ
ejpam-5165	406	3	11	11	NUM
ejpam-5165	406	4	.	.	PUNCT
ejpam-5165	407	1	(	(	PUNCT
ejpam-5165	407	2	linearity	linearity	NOUN
ejpam-5165	407	3	of	of	ADP
ejpam-5165	407	4	integrand	integrand	NOUN
ejpam-5165	407	5	of	of	ADP
ejpam-5165	407	6	the	the	DET
ejpam-5165	407	7	mps	mps	PROPN
ejpam-5165	407	8	-	-	ADJ
ejpam-5165	407	9	integral	integral	ADJ
ejpam-5165	407	10	)	)	PUNCT
ejpam-5165	407	11	let	let	VERB
ejpam-5165	407	12	f1	f1	NOUN
ejpam-5165	407	13	,	,	PUNCT
ejpam-5165	407	14	f2	f2	PROPN
ejpam-5165	407	15	:	:	PUNCT
ejpam-5165	407	16	[	[	X
ejpam-5165	407	17	a	a	X
ejpam-5165	407	18	,	,	PUNCT
ejpam-5165	407	19	b	b	NOUN
ejpam-5165	407	20	]	]	X
ejpam-5165	407	21	→	→	SYM
ejpam-5165	407	22	x	x	X
ejpam-5165	407	23	and	and	CCONJ
ejpam-5165	407	24	g	g	NOUN
ejpam-5165	407	25	:	:	PUNCT
ejpam-5165	408	1	[	[	X
ejpam-5165	408	2	a	a	X
ejpam-5165	408	3	,	,	PUNCT
ejpam-5165	408	4	b	b	NOUN
ejpam-5165	408	5	]	]	X
ejpam-5165	408	6	→	→	PUNCT
ejpam-5165	408	7	r	r	NOUN
ejpam-5165	408	8	be	be	NOUN
ejpam-5165	408	9	functions	function	NOUN
ejpam-5165	408	10	.	.	PUNCT
ejpam-5165	409	1	if	if	SCONJ
ejpam-5165	409	2	f1	f1	PROPN
ejpam-5165	409	3	,	,	PUNCT
ejpam-5165	409	4	f2	f2	PROPN
ejpam-5165	409	5	∈	∈	PROPN
ejpam-5165	409	6	mps([a	mps([a	NOUN
ejpam-5165	409	7	,	,	PUNCT
ejpam-5165	409	8	b	b	NOUN
ejpam-5165	409	9	]	]	X
ejpam-5165	409	10	,	,	PUNCT
ejpam-5165	409	11	g	g	NOUN
ejpam-5165	409	12	)	)	PUNCT
ejpam-5165	409	13	,	,	PUNCT
ejpam-5165	409	14	then	then	ADV
ejpam-5165	409	15	for	for	ADP
ejpam-5165	409	16	every	every	DET
ejpam-5165	409	17	α	α	NOUN
ejpam-5165	409	18	,	,	PUNCT
ejpam-5165	409	19	β	β	X
ejpam-5165	409	20	∈	∈	NOUN
ejpam-5165	409	21	r	r	NOUN
ejpam-5165	409	22	,	,	PUNCT
ejpam-5165	409	23	αf1	αf1	X
ejpam-5165	409	24	+	+	CCONJ
ejpam-5165	409	25	βf2	βf2	PROPN
ejpam-5165	409	26	∈	∈	PROPN
ejpam-5165	409	27	mps([a	mps([a	PROPN
ejpam-5165	409	28	,	,	PUNCT
ejpam-5165	409	29	b	b	NOUN
ejpam-5165	409	30	]	]	X
ejpam-5165	409	31	,	,	PUNCT
ejpam-5165	409	32	g	g	NOUN
ejpam-5165	409	33	)	)	PUNCT
ejpam-5165	409	34	and	and	CCONJ
ejpam-5165	409	35	for	for	ADP
ejpam-5165	409	36	all	all	DET
ejpam-5165	409	37	j	j	NOUN
ejpam-5165	409	38	⊆	⊆	NUM
ejpam-5165	409	39	[	[	X
ejpam-5165	409	40	a	a	X
ejpam-5165	409	41	,	,	PUNCT
ejpam-5165	409	42	b	b	NOUN
ejpam-5165	409	43	]	]	X
ejpam-5165	409	44	(	(	PUNCT
ejpam-5165	409	45	mps	mps	PROPN
ejpam-5165	409	46	)	)	PUNCT
ejpam-5165	409	47	∫	∫	PROPN
ejpam-5165	409	48	j	j	PROPN
ejpam-5165	409	49	(	(	PUNCT
ejpam-5165	409	50	αf1	αf1	X
ejpam-5165	409	51	+	+	CCONJ
ejpam-5165	409	52	βf2	βf2	X
ejpam-5165	409	53	)	)	PUNCT
ejpam-5165	409	54	dg	dg	PROPN
ejpam-5165	409	55	=	=	SYM
ejpam-5165	409	56	α	α	PROPN
ejpam-5165	409	57	·	·	PUNCT
ejpam-5165	409	58	(	(	PUNCT
ejpam-5165	409	59	mps	mps	PROPN
ejpam-5165	409	60	)	)	PUNCT
ejpam-5165	409	61	∫	∫	PROPN
ejpam-5165	410	1	j	j	PROPN
ejpam-5165	410	2	f1	f1	PROPN
ejpam-5165	410	3	dg	dg	VERB
ejpam-5165	410	4	+	+	X
ejpam-5165	411	1	β	β	X
ejpam-5165	411	2	·	·	PUNCT
ejpam-5165	411	3	(	(	PUNCT
ejpam-5165	411	4	mps	mps	PROPN
ejpam-5165	411	5	)	)	PUNCT
ejpam-5165	411	6	∫	∫	PROPN
ejpam-5165	411	7	j	j	PROPN
ejpam-5165	411	8	f2	f2	PROPN
ejpam-5165	411	9	dg	dg	VERB
ejpam-5165	411	10	.	.	PUNCT
ejpam-5165	412	1	proof	proof	NOUN
ejpam-5165	412	2	.	.	PUNCT
ejpam-5165	413	1	suppose	suppose	VERB
ejpam-5165	413	2	that	that	SCONJ
ejpam-5165	413	3	f1	f1	PROPN
ejpam-5165	413	4	,	,	PUNCT
ejpam-5165	413	5	f2	f2	PROPN
ejpam-5165	413	6	are	be	AUX
ejpam-5165	413	7	mps	mp	NOUN
ejpam-5165	413	8	-	-	PUNCT
ejpam-5165	413	9	integrable	integrable	ADJ
ejpam-5165	413	10	with	with	ADP
ejpam-5165	413	11	respect	respect	NOUN
ejpam-5165	413	12	to	to	ADP
ejpam-5165	413	13	g	g	NOUN
ejpam-5165	413	14	on	on	ADP
ejpam-5165	413	15	[	[	X
ejpam-5165	413	16	a	a	X
ejpam-5165	413	17	,	,	PUNCT
ejpam-5165	413	18	b	b	NOUN
ejpam-5165	413	19	]	]	PUNCT
ejpam-5165	413	20	.	.	PUNCT
ejpam-5165	414	1	by	by	ADP
ejpam-5165	414	2	definition	definition	NOUN
ejpam-5165	414	3	19	19	NUM
ejpam-5165	414	4	,	,	PUNCT
ejpam-5165	414	5	f1	f1	NOUN
ejpam-5165	414	6	,	,	PUNCT
ejpam-5165	414	7	f2	f2	PROPN
ejpam-5165	414	8	are	be	AUX
ejpam-5165	414	9	mds	mds	NOUN
ejpam-5165	414	10	-	-	PUNCT
ejpam-5165	414	11	integrable	integrable	ADJ
ejpam-5165	414	12	with	with	ADP
ejpam-5165	414	13	respect	respect	NOUN
ejpam-5165	414	14	to	to	ADP
ejpam-5165	414	15	g	g	NOUN
ejpam-5165	414	16	on	on	ADP
ejpam-5165	414	17	[	[	X
ejpam-5165	414	18	a	a	X
ejpam-5165	414	19	,	,	PUNCT
ejpam-5165	414	20	b	b	NOUN
ejpam-5165	414	21	]	]	X
ejpam-5165	414	22	.	.	PUNCT
ejpam-5165	415	1	now	now	ADV
ejpam-5165	415	2	,	,	PUNCT
ejpam-5165	415	3	let	let	VERB
ejpam-5165	415	4	α	α	PRON
ejpam-5165	415	5	,	,	PUNCT
ejpam-5165	415	6	β	β	X
ejpam-5165	415	7	∈	∈	NOUN
ejpam-5165	415	8	r	r	NOUN
ejpam-5165	415	9	and	and	CCONJ
ejpam-5165	415	10	j	j	PROPN
ejpam-5165	415	11	⊆	⊆	NUM
ejpam-5165	415	12	[	[	X
ejpam-5165	415	13	a	a	X
ejpam-5165	415	14	,	,	PUNCT
ejpam-5165	415	15	b	b	NOUN
ejpam-5165	415	16	]	]	PUNCT
ejpam-5165	415	17	.	.	PUNCT
ejpam-5165	416	1	by	by	ADP
ejpam-5165	416	2	linearity	linearity	NOUN
ejpam-5165	416	3	property	property	NOUN
ejpam-5165	416	4	of	of	ADP
ejpam-5165	416	5	functions	function	NOUN
ejpam-5165	416	6	,	,	PUNCT
ejpam-5165	416	7	α	α	NOUN
ejpam-5165	416	8	·	·	PUNCT
ejpam-5165	416	9	f1	f1	NOUN
ejpam-5165	416	10	+	+	CCONJ
ejpam-5165	416	11	β	β	X
ejpam-5165	416	12	·	·	PUNCT
ejpam-5165	416	13	f2	f2	PRON
ejpam-5165	416	14	is	be	AUX
ejpam-5165	416	15	also	also	ADV
ejpam-5165	416	16	mds	mds	NOUN
ejpam-5165	416	17	-	-	PUNCT
ejpam-5165	416	18	integrable	integrable	ADJ
ejpam-5165	416	19	with	with	ADP
ejpam-5165	416	20	respect	respect	NOUN
ejpam-5165	416	21	to	to	ADP
ejpam-5165	416	22	g	g	NOUN
ejpam-5165	416	23	on	on	ADP
ejpam-5165	416	24	[	[	X
ejpam-5165	416	25	a	a	X
ejpam-5165	416	26	,	,	PUNCT
ejpam-5165	416	27	b	b	NOUN
ejpam-5165	416	28	]	]	PUNCT
ejpam-5165	416	29	and	and	CCONJ
ejpam-5165	416	30	(	(	PUNCT
ejpam-5165	416	31	mds	mds	PROPN
ejpam-5165	416	32	)	)	PUNCT
ejpam-5165	416	33	∫	∫	PROPN
ejpam-5165	417	1	j	j	PROPN
ejpam-5165	417	2	(	(	PUNCT
ejpam-5165	417	3	α	α	NOUN
ejpam-5165	417	4	·	·	PUNCT
ejpam-5165	417	5	f1	f1	NOUN
ejpam-5165	417	6	+	+	CCONJ
ejpam-5165	417	7	β	β	X
ejpam-5165	417	8	·	·	PUNCT
ejpam-5165	417	9	f2	f2	X
ejpam-5165	417	10	)	)	PUNCT
ejpam-5165	417	11	dg	dg	PROPN
ejpam-5165	417	12	=	=	SYM
ejpam-5165	417	13	α	α	PROPN
ejpam-5165	417	14	·	·	PUNCT
ejpam-5165	417	15	(	(	PUNCT
ejpam-5165	417	16	mds	mds	PROPN
ejpam-5165	417	17	)	)	PUNCT
ejpam-5165	417	18	∫	∫	PROPN
ejpam-5165	418	1	j	j	PROPN
ejpam-5165	418	2	f1	f1	PROPN
ejpam-5165	418	3	dg	dg	VERB
ejpam-5165	418	4	+	+	X
ejpam-5165	418	5	β	β	X
ejpam-5165	418	6	·	·	PUNCT
ejpam-5165	418	7	(	(	PUNCT
ejpam-5165	418	8	mds	mds	PROPN
ejpam-5165	418	9	)	)	PUNCT
ejpam-5165	418	10	∫	∫	PROPN
ejpam-5165	419	1	j	j	PROPN
ejpam-5165	419	2	f2	f2	PROPN
ejpam-5165	419	3	dg	dg	PROPN
ejpam-5165	419	4	.	.	PUNCT
ejpam-5165	420	1	(	(	PUNCT
ejpam-5165	420	2	2	2	X
ejpam-5165	420	3	)	)	PUNCT
ejpam-5165	420	4	by	by	ADP
ejpam-5165	420	5	the	the	DET
ejpam-5165	420	6	definition	definition	NOUN
ejpam-5165	420	7	of	of	ADP
ejpam-5165	420	8	mps	mp	NOUN
ejpam-5165	420	9	-	-	ADJ
ejpam-5165	420	10	integral	integral	ADJ
ejpam-5165	420	11	,	,	PUNCT
ejpam-5165	420	12	(	(	PUNCT
ejpam-5165	420	13	mds	mds	PROPN
ejpam-5165	420	14	)	)	PUNCT
ejpam-5165	420	15	∫	∫	PROPN
ejpam-5165	420	16	j	j	PROPN
ejpam-5165	420	17	f1	f1	PROPN
ejpam-5165	420	18	dg	dg	PROPN
ejpam-5165	420	19	,	,	PUNCT
ejpam-5165	420	20	(	(	PUNCT
ejpam-5165	420	21	mds	mds	PROPN
ejpam-5165	420	22	)	)	PUNCT
ejpam-5165	420	23	∫	∫	PROPN
ejpam-5165	421	1	j	j	PROPN
ejpam-5165	421	2	f2	f2	PROPN
ejpam-5165	421	3	dg	dg	VERB
ejpam-5165	421	4	∈	∈	NOUN
ejpam-5165	421	5	e(x	e(x	NUM
ejpam-5165	421	6	)	)	PUNCT
ejpam-5165	421	7	.	.	PUNCT
ejpam-5165	422	1	set	set	VERB
ejpam-5165	422	2	m1,m2	m1,m2	PROPN
ejpam-5165	422	3	∈	∈	PROPN
ejpam-5165	422	4	x	x	PUNCT
ejpam-5165	423	1	so	so	ADV
ejpam-5165	423	2	that	that	SCONJ
ejpam-5165	423	3	(	(	PUNCT
ejpam-5165	423	4	mds	mds	PROPN
ejpam-5165	423	5	)	)	PUNCT
ejpam-5165	423	6	∫	∫	PROPN
ejpam-5165	423	7	j	j	PROPN
ejpam-5165	423	8	f1	f1	PROPN
ejpam-5165	423	9	dg	dg	PROPN
ejpam-5165	423	10	=	=	SYM
ejpam-5165	423	11	m1	m1	PROPN
ejpam-5165	423	12	and	and	CCONJ
ejpam-5165	423	13	(	(	PUNCT
ejpam-5165	423	14	mds	mds	PROPN
ejpam-5165	423	15	)	)	PUNCT
ejpam-5165	423	16	∫	∫	PROPN
ejpam-5165	424	1	j	j	PROPN
ejpam-5165	424	2	f2	f2	PROPN
ejpam-5165	424	3	dg	dg	PROPN
ejpam-5165	424	4	=	=	SYM
ejpam-5165	424	5	m2	m2	PROPN
ejpam-5165	424	6	.	.	PUNCT
ejpam-5165	425	1	so	so	ADV
ejpam-5165	425	2	we	we	PRON
ejpam-5165	425	3	have	have	VERB
ejpam-5165	425	4	α	α	PRON
ejpam-5165	425	5	·	·	PUNCT
ejpam-5165	425	6	m1	m1	PROPN
ejpam-5165	425	7	+	+	CCONJ
ejpam-5165	425	8	β	β	X
ejpam-5165	425	9	·	·	PUNCT
ejpam-5165	425	10	m2	m2	PROPN
ejpam-5165	425	11	∈	∈	PROPN
ejpam-5165	425	12	x.	x.	NOUN
ejpam-5165	425	13	by	by	ADP
ejpam-5165	425	14	equation	equation	NOUN
ejpam-5165	425	15	(	(	PUNCT
ejpam-5165	425	16	2	2	NUM
ejpam-5165	425	17	)	)	PUNCT
ejpam-5165	425	18	,	,	PUNCT
ejpam-5165	425	19	(	(	PUNCT
ejpam-5165	425	20	mds	mds	PROPN
ejpam-5165	425	21	)	)	PUNCT
ejpam-5165	425	22	∫	∫	PROPN
ejpam-5165	426	1	j	j	PROPN
ejpam-5165	426	2	(	(	PUNCT
ejpam-5165	426	3	α	α	NOUN
ejpam-5165	426	4	·	·	PUNCT
ejpam-5165	426	5	f1	f1	NOUN
ejpam-5165	426	6	+	+	CCONJ
ejpam-5165	426	7	β	β	X
ejpam-5165	426	8	·	·	PUNCT
ejpam-5165	426	9	f2	f2	X
ejpam-5165	426	10	)	)	PUNCT
ejpam-5165	426	11	dg	dg	PROPN
ejpam-5165	426	12	=	=	SYM
ejpam-5165	426	13	α	α	PROPN
ejpam-5165	426	14	·	·	PUNCT
ejpam-5165	426	15	(	(	PUNCT
ejpam-5165	426	16	mds	mds	PROPN
ejpam-5165	426	17	)	)	PUNCT
ejpam-5165	426	18	∫	∫	PROPN
ejpam-5165	427	1	j	j	PROPN
ejpam-5165	427	2	f1	f1	PROPN
ejpam-5165	427	3	dg	dg	VERB
ejpam-5165	427	4	+	+	X
ejpam-5165	427	5	β	β	X
ejpam-5165	427	6	·	·	PUNCT
ejpam-5165	427	7	(	(	PUNCT
ejpam-5165	427	8	mds	mds	PROPN
ejpam-5165	427	9	)	)	PUNCT
ejpam-5165	427	10	∫	∫	PROPN
ejpam-5165	428	1	j	j	PROPN
ejpam-5165	428	2	f2	f2	PROPN
ejpam-5165	428	3	dg	dg	VERB
ejpam-5165	428	4	=	=	SYM
ejpam-5165	428	5	α	α	PROPN
ejpam-5165	428	6	·	·	PUNCT
ejpam-5165	428	7	e(m1	e(m1	NOUN
ejpam-5165	428	8	)	)	PUNCT
ejpam-5165	429	1	+	+	CCONJ
ejpam-5165	429	2	β	β	X
ejpam-5165	429	3	·	·	PUNCT
ejpam-5165	429	4	e(m2	e(m2	X
ejpam-5165	429	5	)	)	PUNCT
ejpam-5165	430	1	=	=	PUNCT
ejpam-5165	430	2	e(αm1	e(αm1	PROPN
ejpam-5165	430	3	+	+	CCONJ
ejpam-5165	430	4	βm2	βm2	NOUN
ejpam-5165	430	5	)	)	PUNCT
ejpam-5165	430	6	∈	∈	NOUN
ejpam-5165	430	7	e(x	e(x	NUM
ejpam-5165	430	8	)	)	PUNCT
ejpam-5165	430	9	.	.	PUNCT
ejpam-5165	431	1	this	this	PRON
ejpam-5165	431	2	implies	imply	VERB
ejpam-5165	431	3	that	that	SCONJ
ejpam-5165	431	4	α	α	PROPN
ejpam-5165	431	5	·	·	PUNCT
ejpam-5165	431	6	f1	f1	NOUN
ejpam-5165	431	7	+	+	CCONJ
ejpam-5165	431	8	β	β	X
ejpam-5165	431	9	·	·	PUNCT
ejpam-5165	431	10	f2	f2	PRON
ejpam-5165	431	11	is	be	AUX
ejpam-5165	431	12	mps	mp	NOUN
ejpam-5165	431	13	-	-	PUNCT
ejpam-5165	431	14	integrable	integrable	ADJ
ejpam-5165	431	15	with	with	ADP
ejpam-5165	431	16	respect	respect	NOUN
ejpam-5165	431	17	to	to	ADP
ejpam-5165	431	18	g	g	NOUN
ejpam-5165	431	19	on	on	ADP
ejpam-5165	431	20	[	[	X
ejpam-5165	431	21	a	a	X
ejpam-5165	431	22	,	,	PUNCT
ejpam-5165	431	23	b	b	NOUN
ejpam-5165	431	24	]	]	PUNCT
ejpam-5165	431	25	and	and	CCONJ
ejpam-5165	431	26	(	(	PUNCT
ejpam-5165	431	27	mps	mps	PROPN
ejpam-5165	431	28	)	)	PUNCT
ejpam-5165	432	1	∫	∫	PROPN
ejpam-5165	432	2	j	j	PROPN
ejpam-5165	432	3	(	(	PUNCT
ejpam-5165	432	4	α	α	NOUN
ejpam-5165	432	5	·	·	PUNCT
ejpam-5165	432	6	f1	f1	NOUN
ejpam-5165	432	7	+	+	CCONJ
ejpam-5165	432	8	β	β	X
ejpam-5165	432	9	·	·	PUNCT
ejpam-5165	432	10	f2	f2	X
ejpam-5165	432	11	)	)	PUNCT
ejpam-5165	432	12	dg	dg	PROPN
ejpam-5165	432	13	=	=	SYM
ejpam-5165	432	14	(	(	PUNCT
ejpam-5165	432	15	mds	mds	PROPN
ejpam-5165	432	16	)	)	PUNCT
ejpam-5165	433	1	∫	∫	PROPN
ejpam-5165	433	2	j	j	PROPN
ejpam-5165	433	3	(	(	PUNCT
ejpam-5165	433	4	α	α	NOUN
ejpam-5165	433	5	·	·	PUNCT
ejpam-5165	433	6	f1	f1	NOUN
ejpam-5165	433	7	+	+	CCONJ
ejpam-5165	433	8	β	β	X
ejpam-5165	433	9	·	·	PUNCT
ejpam-5165	433	10	f2	f2	X
ejpam-5165	433	11	)	)	PUNCT
ejpam-5165	433	12	dg	dg	PROPN
ejpam-5165	433	13	=	=	SYM
ejpam-5165	433	14	α	α	PROPN
ejpam-5165	433	15	·	·	PUNCT
ejpam-5165	433	16	(	(	PUNCT
ejpam-5165	433	17	mds	mds	PROPN
ejpam-5165	433	18	)	)	PUNCT
ejpam-5165	433	19	∫	∫	PROPN
ejpam-5165	434	1	j	j	PROPN
ejpam-5165	434	2	f1	f1	PROPN
ejpam-5165	434	3	dg	dg	VERB
ejpam-5165	434	4	+	+	X
ejpam-5165	434	5	β	β	X
ejpam-5165	434	6	·	·	PUNCT
ejpam-5165	434	7	(	(	PUNCT
ejpam-5165	434	8	mds	mds	PROPN
ejpam-5165	434	9	)	)	PUNCT
ejpam-5165	434	10	∫	∫	PROPN
ejpam-5165	435	1	j	j	PROPN
ejpam-5165	435	2	f2	f2	PROPN
ejpam-5165	435	3	dg	dg	VERB
ejpam-5165	435	4	=	=	SYM
ejpam-5165	435	5	α	α	PROPN
ejpam-5165	435	6	·	·	PUNCT
ejpam-5165	435	7	(	(	PUNCT
ejpam-5165	435	8	mps	mps	PROPN
ejpam-5165	435	9	)	)	PUNCT
ejpam-5165	435	10	∫	∫	PROPN
ejpam-5165	436	1	j	j	PROPN
ejpam-5165	436	2	f1	f1	PROPN
ejpam-5165	436	3	dg	dg	VERB
ejpam-5165	436	4	+	+	X
ejpam-5165	437	1	β	β	X
ejpam-5165	437	2	·	·	PUNCT
ejpam-5165	437	3	(	(	PUNCT
ejpam-5165	437	4	mps	mps	PROPN
ejpam-5165	437	5	)	)	PUNCT
ejpam-5165	437	6	∫	∫	PROPN
ejpam-5165	437	7	j	j	PROPN
ejpam-5165	437	8	f2	f2	PROPN
ejpam-5165	437	9	dg	dg	PROPN
ejpam-5165	437	10	.	.	PUNCT
ejpam-5165	438	1	hence	hence	ADV
ejpam-5165	438	2	,	,	PUNCT
ejpam-5165	438	3	the	the	DET
ejpam-5165	438	4	proof	proof	NOUN
ejpam-5165	438	5	.	.	PUNCT
ejpam-5165	439	1	□	□	PUNCT
ejpam-5165	439	2	d.	d.	PROPN
ejpam-5165	439	3	omayan	omayan	NOUN
ejpam-5165	439	4	,	,	PUNCT
ejpam-5165	439	5	g.b	g.b	PROPN
ejpam-5165	439	6	.	.	PROPN
ejpam-5165	439	7	flores	flores	PROPN
ejpam-5165	439	8	/	/	SYM
ejpam-5165	439	9	eur	eur	PROPN
ejpam-5165	439	10	.	.	PUNCT
ejpam-5165	440	1	j.	j.	PROPN
ejpam-5165	440	2	pure	pure	PROPN
ejpam-5165	440	3	appl	appl	PROPN
ejpam-5165	440	4	.	.	PROPN
ejpam-5165	440	5	math	math	PROPN
ejpam-5165	440	6	,	,	PUNCT
ejpam-5165	440	7	17	17	NUM
ejpam-5165	440	8	(	(	PUNCT
ejpam-5165	440	9	2	2	NUM
ejpam-5165	440	10	)	)	PUNCT
ejpam-5165	440	11	(	(	PUNCT
ejpam-5165	440	12	2024	2024	NUM
ejpam-5165	440	13	)	)	PUNCT
ejpam-5165	440	14	,	,	PUNCT
ejpam-5165	440	15	1183	1183	NUM
ejpam-5165	440	16	-	-	SYM
ejpam-5165	440	17	1196	1196	NUM
ejpam-5165	440	18	1195	1195	NUM
ejpam-5165	440	19	theorem	theorem	NOUN
ejpam-5165	440	20	12	12	NUM
ejpam-5165	440	21	.	.	PUNCT
ejpam-5165	441	1	(	(	PUNCT
ejpam-5165	441	2	linearity	linearity	NOUN
ejpam-5165	441	3	of	of	ADP
ejpam-5165	441	4	integrator	integrator	NOUN
ejpam-5165	441	5	of	of	ADP
ejpam-5165	441	6	the	the	DET
ejpam-5165	441	7	mps	mps	PROPN
ejpam-5165	441	8	-	-	ADJ
ejpam-5165	441	9	integral	integral	ADJ
ejpam-5165	441	10	)	)	PUNCT
ejpam-5165	441	11	let	let	VERB
ejpam-5165	441	12	f	f	NOUN
ejpam-5165	441	13	:	:	PUNCT
ejpam-5165	442	1	[	[	X
ejpam-5165	442	2	a	a	X
ejpam-5165	442	3	,	,	PUNCT
ejpam-5165	442	4	b	b	NOUN
ejpam-5165	442	5	]	]	X
ejpam-5165	442	6	→	→	SYM
ejpam-5165	442	7	x	x	X
ejpam-5165	442	8	and	and	CCONJ
ejpam-5165	442	9	g1	g1	PROPN
ejpam-5165	442	10	,	,	PUNCT
ejpam-5165	442	11	g2	g2	PROPN
ejpam-5165	442	12	:	:	PUNCT
ejpam-5165	443	1	[	[	X
ejpam-5165	443	2	a	a	X
ejpam-5165	443	3	,	,	PUNCT
ejpam-5165	443	4	b	b	NOUN
ejpam-5165	443	5	]	]	X
ejpam-5165	443	6	→	→	PUNCT
ejpam-5165	443	7	r	r	NOUN
ejpam-5165	443	8	be	be	NOUN
ejpam-5165	443	9	functions	function	NOUN
ejpam-5165	443	10	.	.	PUNCT
ejpam-5165	444	1	if	if	SCONJ
ejpam-5165	444	2	f	f	PROPN
ejpam-5165	444	3	is	be	AUX
ejpam-5165	444	4	mps	mp	NOUN
ejpam-5165	444	5	-	-	PUNCT
ejpam-5165	444	6	integrable	integrable	ADJ
ejpam-5165	444	7	with	with	ADP
ejpam-5165	444	8	respect	respect	NOUN
ejpam-5165	444	9	to	to	ADP
ejpam-5165	444	10	g1	g1	VERB
ejpam-5165	444	11	and	and	CCONJ
ejpam-5165	444	12	g2	g2	PROPN
ejpam-5165	444	13	on	on	ADP
ejpam-5165	444	14	[	[	X
ejpam-5165	444	15	a	a	PRON
ejpam-5165	444	16	,	,	PUNCT
ejpam-5165	444	17	b	b	NOUN
ejpam-5165	444	18	]	]	X
ejpam-5165	444	19	,	,	PUNCT
ejpam-5165	444	20	then	then	ADV
ejpam-5165	444	21	for	for	ADP
ejpam-5165	444	22	any	any	DET
ejpam-5165	444	23	α	α	NOUN
ejpam-5165	444	24	,	,	PUNCT
ejpam-5165	444	25	β	β	X
ejpam-5165	444	26	∈	∈	PROPN
ejpam-5165	444	27	r	r	NOUN
ejpam-5165	444	28	,	,	PUNCT
ejpam-5165	444	29	f	f	PROPN
ejpam-5165	444	30	∈	∈	PROPN
ejpam-5165	444	31	mps([a	mps([a	PROPN
ejpam-5165	444	32	,	,	PUNCT
ejpam-5165	444	33	b	b	NOUN
ejpam-5165	444	34	]	]	X
ejpam-5165	444	35	,	,	PUNCT
ejpam-5165	444	36	αg1	αg1	X
ejpam-5165	444	37	+	+	X
ejpam-5165	444	38	βg2	βg2	X
ejpam-5165	444	39	)	)	PUNCT
ejpam-5165	444	40	and	and	CCONJ
ejpam-5165	444	41	(	(	PUNCT
ejpam-5165	444	42	mps	mps	PROPN
ejpam-5165	444	43	)	)	PUNCT
ejpam-5165	444	44	∫	∫	PROPN
ejpam-5165	445	1	j	j	PROPN
ejpam-5165	445	2	f	f	PROPN
ejpam-5165	445	3	d[αg1	d[αg1	PROPN
ejpam-5165	446	1	+	+	CCONJ
ejpam-5165	446	2	βg2	βg2	X
ejpam-5165	446	3	]	]	X
ejpam-5165	446	4	=	=	SYM
ejpam-5165	446	5	α	α	X
ejpam-5165	446	6	·	·	PUNCT
ejpam-5165	446	7	(	(	PUNCT
ejpam-5165	446	8	mps	mps	PROPN
ejpam-5165	446	9	)	)	PUNCT
ejpam-5165	446	10	∫	∫	PROPN
ejpam-5165	447	1	j	j	PROPN
ejpam-5165	447	2	f	f	PROPN
ejpam-5165	447	3	dg1	dg1	PROPN
ejpam-5165	448	1	+	+	X
ejpam-5165	448	2	β	β	X
ejpam-5165	448	3	·	·	PUNCT
ejpam-5165	448	4	(	(	PUNCT
ejpam-5165	448	5	mps	mps	PROPN
ejpam-5165	448	6	)	)	PUNCT
ejpam-5165	448	7	∫	∫	PROPN
ejpam-5165	449	1	j	j	PROPN
ejpam-5165	449	2	f	f	PROPN
ejpam-5165	449	3	dg2	dg2	PROPN
ejpam-5165	449	4	.	.	PROPN
ejpam-5165	450	1	for	for	ADP
ejpam-5165	450	2	every	every	DET
ejpam-5165	450	3	j	j	PROPN
ejpam-5165	450	4	⊆	⊆	NUM
ejpam-5165	450	5	[	[	X
ejpam-5165	450	6	a	a	X
ejpam-5165	450	7	,	,	PUNCT
ejpam-5165	450	8	b	b	NOUN
ejpam-5165	450	9	]	]	PUNCT
ejpam-5165	450	10	.	.	PUNCT
ejpam-5165	451	1	proof	proof	NOUN
ejpam-5165	451	2	.	.	PUNCT
ejpam-5165	452	1	the	the	DET
ejpam-5165	452	2	proof	proof	NOUN
ejpam-5165	452	3	is	be	AUX
ejpam-5165	452	4	analogous	analogous	ADJ
ejpam-5165	452	5	to	to	AUX
ejpam-5165	452	6	theorem	theorem	VERB
ejpam-5165	452	7	(	(	PUNCT
ejpam-5165	452	8	11	11	NUM
ejpam-5165	452	9	)	)	PUNCT
ejpam-5165	452	10	.	.	PUNCT
ejpam-5165	453	1	□	□	PUNCT
ejpam-5165	453	2	theorem	theorem	ADJ
ejpam-5165	453	3	13	13	NUM
ejpam-5165	453	4	.	.	PUNCT
ejpam-5165	454	1	(	(	PUNCT
ejpam-5165	454	2	cauchy	cauchy	ADJ
ejpam-5165	454	3	criterion	criterion	NOUN
ejpam-5165	454	4	of	of	ADP
ejpam-5165	454	5	the	the	DET
ejpam-5165	454	6	mps	mps	PROPN
ejpam-5165	454	7	-	-	ADJ
ejpam-5165	454	8	integral	integral	ADJ
ejpam-5165	454	9	)	)	PUNCT
ejpam-5165	454	10	let	let	VERB
ejpam-5165	454	11	f	f	NOUN
ejpam-5165	454	12	:	:	PUNCT
ejpam-5165	455	1	[	[	X
ejpam-5165	455	2	a	a	X
ejpam-5165	455	3	,	,	PUNCT
ejpam-5165	455	4	b	b	NOUN
ejpam-5165	455	5	]	]	X
ejpam-5165	455	6	→	→	SYM
ejpam-5165	455	7	x	x	X
ejpam-5165	455	8	and	and	CCONJ
ejpam-5165	455	9	g	g	NOUN
ejpam-5165	455	10	:	:	PUNCT
ejpam-5165	456	1	[	[	X
ejpam-5165	456	2	a	a	X
ejpam-5165	456	3	,	,	PUNCT
ejpam-5165	456	4	b	b	NOUN
ejpam-5165	456	5	]	]	X
ejpam-5165	456	6	→	→	PUNCT
ejpam-5165	456	7	r	r	NOUN
ejpam-5165	456	8	be	be	NOUN
ejpam-5165	456	9	functions	function	NOUN
ejpam-5165	456	10	.	.	PUNCT
ejpam-5165	457	1	then	then	ADV
ejpam-5165	457	2	f	f	PROPN
ejpam-5165	457	3	is	be	AUX
ejpam-5165	457	4	mcshane	mcshane	PROPN
ejpam-5165	457	5	-	-	PUNCT
ejpam-5165	457	6	pettis	pettis	PROPN
ejpam-5165	457	7	-	-	PUNCT
ejpam-5165	457	8	stieltjes	stieltjes	NOUN
ejpam-5165	457	9	integrable	integrable	ADJ
ejpam-5165	457	10	with	with	ADP
ejpam-5165	457	11	respect	respect	NOUN
ejpam-5165	457	12	to	to	ADP
ejpam-5165	457	13	g	g	NOUN
ejpam-5165	457	14	on	on	ADP
ejpam-5165	457	15	[	[	X
ejpam-5165	457	16	a	a	X
ejpam-5165	457	17	,	,	PUNCT
ejpam-5165	457	18	b	b	NOUN
ejpam-5165	457	19	]	]	X
ejpam-5165	457	20	if	if	SCONJ
ejpam-5165	457	21	and	and	CCONJ
ejpam-5165	457	22	only	only	ADV
ejpam-5165	457	23	if	if	SCONJ
ejpam-5165	457	24	for	for	ADP
ejpam-5165	457	25	every	every	DET
ejpam-5165	457	26	ε	ε	PROPN
ejpam-5165	457	27	>	>	X
ejpam-5165	457	28	0	0	PROPN
ejpam-5165	457	29	,	,	PUNCT
ejpam-5165	457	30	there	there	PRON
ejpam-5165	457	31	exists	exist	VERB
ejpam-5165	457	32	a	a	DET
ejpam-5165	457	33	gauge	gauge	NOUN
ejpam-5165	457	34	δ	δ	NOUN
ejpam-5165	457	35	:	:	PUNCT
ejpam-5165	458	1	[	[	X
ejpam-5165	458	2	a	a	X
ejpam-5165	458	3	,	,	PUNCT
ejpam-5165	458	4	b	b	NOUN
ejpam-5165	458	5	]	]	X
ejpam-5165	458	6	→	→	PUNCT
ejpam-5165	458	7	r+	r+	NOUN
ejpam-5165	458	8	such	such	ADJ
ejpam-5165	458	9	that	that	SCONJ
ejpam-5165	458	10	if	if	SCONJ
ejpam-5165	458	11	m1	m1	PROPN
ejpam-5165	458	12	and	and	CCONJ
ejpam-5165	458	13	m2	m2	PROPN
ejpam-5165	458	14	are	be	AUX
ejpam-5165	458	15	two	two	NUM
ejpam-5165	458	16	δ	δ	PROPN
ejpam-5165	458	17	-	-	PUNCT
ejpam-5165	458	18	fine	fine	ADJ
ejpam-5165	458	19	m	m	PROPN
ejpam-5165	458	20	-partitions	-partition	NOUN
ejpam-5165	458	21	,	,	PUNCT
ejpam-5165	458	22	then	then	ADV
ejpam-5165	458	23	∥s(f	∥s(f	ADJ
ejpam-5165	458	24	,	,	PUNCT
ejpam-5165	458	25	g	g	NOUN
ejpam-5165	458	26	,	,	PUNCT
ejpam-5165	458	27	m1)−	m1)−	PROPN
ejpam-5165	458	28	s(f	s(f	PROPN
ejpam-5165	458	29	,	,	PUNCT
ejpam-5165	458	30	g	g	PROPN
ejpam-5165	458	31	,	,	PUNCT
ejpam-5165	458	32	m2)∥x	m2)∥x	X
ejpam-5165	458	33	<	<	X
ejpam-5165	458	34	ε	ε	PROPN
ejpam-5165	458	35	.	.	PUNCT
ejpam-5165	458	36	proof	proof	NOUN
ejpam-5165	458	37	.	.	PUNCT
ejpam-5165	459	1	suppose	suppose	VERB
ejpam-5165	459	2	that	that	SCONJ
ejpam-5165	459	3	f	f	PROPN
ejpam-5165	459	4	is	be	AUX
ejpam-5165	459	5	mps	mp	NOUN
ejpam-5165	459	6	-	-	PUNCT
ejpam-5165	459	7	integrable	integrable	ADJ
ejpam-5165	459	8	with	with	ADP
ejpam-5165	459	9	respect	respect	NOUN
ejpam-5165	459	10	to	to	ADP
ejpam-5165	459	11	g	g	NOUN
ejpam-5165	459	12	on	on	ADP
ejpam-5165	459	13	[	[	X
ejpam-5165	459	14	a	a	X
ejpam-5165	459	15	,	,	PUNCT
ejpam-5165	459	16	b	b	NOUN
ejpam-5165	459	17	]	]	PUNCT
ejpam-5165	459	18	.	.	PUNCT
ejpam-5165	460	1	by	by	ADP
ejpam-5165	460	2	definition	definition	NOUN
ejpam-5165	460	3	19	19	NUM
ejpam-5165	460	4	,	,	PUNCT
ejpam-5165	460	5	f	f	PROPN
ejpam-5165	460	6	is	be	AUX
ejpam-5165	460	7	mds	mds	NOUN
ejpam-5165	460	8	-	-	PUNCT
ejpam-5165	460	9	integrable	integrable	ADJ
ejpam-5165	460	10	with	with	ADP
ejpam-5165	460	11	respect	respect	NOUN
ejpam-5165	460	12	to	to	ADP
ejpam-5165	460	13	g	g	NOUN
ejpam-5165	460	14	on	on	ADP
ejpam-5165	460	15	[	[	X
ejpam-5165	460	16	a	a	X
ejpam-5165	460	17	,	,	PUNCT
ejpam-5165	460	18	b	b	NOUN
ejpam-5165	460	19	]	]	PUNCT
ejpam-5165	460	20	.	.	PUNCT
ejpam-5165	461	1	using	use	VERB
ejpam-5165	461	2	the	the	DET
ejpam-5165	461	3	cauchy	cauchy	ADJ
ejpam-5165	461	4	criterion	criterion	NOUN
ejpam-5165	461	5	of	of	ADP
ejpam-5165	461	6	the	the	DET
ejpam-5165	461	7	mdsintegral	mdsintegral	NOUN
ejpam-5165	461	8	,	,	PUNCT
ejpam-5165	461	9	there	there	PRON
ejpam-5165	461	10	exists	exist	VERB
ejpam-5165	461	11	a	a	DET
ejpam-5165	461	12	gauge	gauge	NOUN
ejpam-5165	461	13	δ	δ	NOUN
ejpam-5165	461	14	:	:	PUNCT
ejpam-5165	462	1	[	[	X
ejpam-5165	462	2	a	a	X
ejpam-5165	462	3	,	,	PUNCT
ejpam-5165	462	4	b	b	NOUN
ejpam-5165	462	5	]	]	X
ejpam-5165	462	6	→	→	PUNCT
ejpam-5165	462	7	r+	r+	NOUN
ejpam-5165	462	8	such	such	ADJ
ejpam-5165	462	9	that	that	SCONJ
ejpam-5165	462	10	if	if	SCONJ
ejpam-5165	462	11	m1	m1	PROPN
ejpam-5165	462	12	and	and	CCONJ
ejpam-5165	462	13	m2	m2	PROPN
ejpam-5165	462	14	are	be	AUX
ejpam-5165	462	15	two	two	NUM
ejpam-5165	462	16	δ	δ	PROPN
ejpam-5165	462	17	-	-	PUNCT
ejpam-5165	462	18	fine	fine	ADJ
ejpam-5165	462	19	m	m	PROPN
ejpam-5165	462	20	-partitions	-partition	NOUN
ejpam-5165	462	21	,	,	PUNCT
ejpam-5165	462	22	then	then	ADV
ejpam-5165	462	23	∥s(f	∥s(f	ADJ
ejpam-5165	462	24	,	,	PUNCT
ejpam-5165	462	25	g	g	NOUN
ejpam-5165	462	26	,	,	PUNCT
ejpam-5165	462	27	m1)−	m1)−	PROPN
ejpam-5165	462	28	s(f	s(f	PROPN
ejpam-5165	462	29	,	,	PUNCT
ejpam-5165	462	30	g	g	PROPN
ejpam-5165	462	31	,	,	PUNCT
ejpam-5165	462	32	m2)∥x	m2)∥x	X
ejpam-5165	462	33	<	<	X
ejpam-5165	462	34	ε	ε	PROPN
ejpam-5165	462	35	.	.	PUNCT
ejpam-5165	462	36	conversely	conversely	ADV
ejpam-5165	462	37	,	,	PUNCT
ejpam-5165	462	38	assume	assume	VERB
ejpam-5165	462	39	that	that	SCONJ
ejpam-5165	462	40	for	for	ADP
ejpam-5165	462	41	every	every	DET
ejpam-5165	462	42	ε	ε	PROPN
ejpam-5165	462	43	>	>	X
ejpam-5165	462	44	0	0	PROPN
ejpam-5165	462	45	,	,	PUNCT
ejpam-5165	462	46	there	there	PRON
ejpam-5165	462	47	exists	exist	VERB
ejpam-5165	462	48	a	a	DET
ejpam-5165	462	49	gauge	gauge	NOUN
ejpam-5165	462	50	δ	δ	NOUN
ejpam-5165	462	51	:	:	PUNCT
ejpam-5165	463	1	[	[	X
ejpam-5165	463	2	a	a	X
ejpam-5165	463	3	,	,	PUNCT
ejpam-5165	463	4	b	b	NOUN
ejpam-5165	463	5	]	]	X
ejpam-5165	463	6	→	→	PUNCT
ejpam-5165	463	7	r+	r+	NOUN
ejpam-5165	463	8	such	such	ADJ
ejpam-5165	463	9	that	that	SCONJ
ejpam-5165	463	10	if	if	SCONJ
ejpam-5165	463	11	m1	m1	PROPN
ejpam-5165	463	12	and	and	CCONJ
ejpam-5165	463	13	m2	m2	PROPN
ejpam-5165	463	14	are	be	AUX
ejpam-5165	463	15	two	two	NUM
ejpam-5165	463	16	δ	δ	PROPN
ejpam-5165	463	17	-	-	PUNCT
ejpam-5165	463	18	fine	fine	ADJ
ejpam-5165	463	19	m	m	PROPN
ejpam-5165	463	20	-partitions	-partition	NOUN
ejpam-5165	463	21	,	,	PUNCT
ejpam-5165	463	22	then	then	ADV
ejpam-5165	463	23	∥s(f	∥s(f	ADJ
ejpam-5165	463	24	,	,	PUNCT
ejpam-5165	463	25	g	g	NOUN
ejpam-5165	463	26	,	,	PUNCT
ejpam-5165	463	27	m1)−	m1)−	PROPN
ejpam-5165	463	28	s(f	s(f	PROPN
ejpam-5165	463	29	,	,	PUNCT
ejpam-5165	463	30	g	g	PROPN
ejpam-5165	463	31	,	,	PUNCT
ejpam-5165	463	32	m2)∥e(x	m2)∥e(x	PROPN
ejpam-5165	463	33	)	)	PUNCT
ejpam-5165	463	34	<	<	X
ejpam-5165	463	35	ε	ε	PROPN
ejpam-5165	463	36	.	.	PUNCT
ejpam-5165	464	1	by	by	ADP
ejpam-5165	464	2	cauchy	cauchy	ADJ
ejpam-5165	464	3	criterion	criterion	NOUN
ejpam-5165	464	4	on	on	ADP
ejpam-5165	464	5	mds	mds	NOUN
ejpam-5165	464	6	-	-	PUNCT
ejpam-5165	464	7	integral	integral	ADJ
ejpam-5165	464	8	,	,	PUNCT
ejpam-5165	464	9	x∗(f	x∗(f	PROPN
ejpam-5165	464	10	)	)	PUNCT
ejpam-5165	464	11	:	:	PUNCT
ejpam-5165	465	1	[	[	X
ejpam-5165	465	2	a	a	X
ejpam-5165	465	3	,	,	PUNCT
ejpam-5165	465	4	b	b	NOUN
ejpam-5165	465	5	]	]	X
ejpam-5165	465	6	→	→	PUNCT
ejpam-5165	465	7	r	r	NOUN
ejpam-5165	465	8	is	be	AUX
ejpam-5165	465	9	ms	ms	ADJ
ejpam-5165	465	10	-	-	PUNCT
ejpam-5165	465	11	integrable	integrable	ADJ
ejpam-5165	465	12	.	.	PUNCT
ejpam-5165	466	1	let	let	VERB
ejpam-5165	466	2	an	an	DET
ejpam-5165	466	3	interval	interval	NOUN
ejpam-5165	466	4	j	j	NOUN
ejpam-5165	466	5	⊆	⊆	NUM
ejpam-5165	466	6	[	[	X
ejpam-5165	466	7	a	a	X
ejpam-5165	466	8	,	,	PUNCT
ejpam-5165	466	9	b	b	NOUN
ejpam-5165	466	10	]	]	PUNCT
ejpam-5165	466	11	.	.	PUNCT
ejpam-5165	467	1	define	define	VERB
ejpam-5165	467	2	x∗∗	x∗∗	PROPN
ejpam-5165	467	3	:	:	PUNCT
ejpam-5165	467	4	x∗	x∗	PROPN
ejpam-5165	467	5	→	→	PUNCT
ejpam-5165	468	1	r	r	NOUN
ejpam-5165	468	2	such	such	ADJ
ejpam-5165	468	3	that	that	SCONJ
ejpam-5165	468	4	x∗∗j	x∗∗j	PROPN
ejpam-5165	468	5	(	(	PUNCT
ejpam-5165	468	6	x∗	x∗	PROPN
ejpam-5165	468	7	)	)	PUNCT
ejpam-5165	468	8	=	=	SYM
ejpam-5165	468	9	(	(	PUNCT
ejpam-5165	468	10	ms	ms	PROPN
ejpam-5165	468	11	)	)	PUNCT
ejpam-5165	468	12	∫	∫	PROPN
ejpam-5165	469	1	[	[	X
ejpam-5165	469	2	a	a	X
ejpam-5165	469	3	,	,	PUNCT
ejpam-5165	469	4	b	b	NOUN
ejpam-5165	469	5	]	]	X
ejpam-5165	469	6	x∗(f)dg	x∗(f)dg	NUM
ejpam-5165	469	7	.	.	PUNCT
ejpam-5165	470	1	by	by	ADP
ejpam-5165	470	2	definition	definition	NOUN
ejpam-5165	470	3	of	of	ADP
ejpam-5165	470	4	x∗∗	x∗∗	PROPN
ejpam-5165	470	5	,	,	PUNCT
ejpam-5165	470	6	x∗∗j	x∗∗j	PROPN
ejpam-5165	470	7	∈	∈	PROPN
ejpam-5165	470	8	x∗∗.	x∗∗.	X
ejpam-5165	471	1	this	this	PRON
ejpam-5165	471	2	means	mean	VERB
ejpam-5165	471	3	that	that	SCONJ
ejpam-5165	471	4	x∗∗j	x∗∗j	PROPN
ejpam-5165	471	5	=	=	SYM
ejpam-5165	471	6	(	(	PUNCT
ejpam-5165	471	7	mds	mds	PROPN
ejpam-5165	471	8	)	)	PUNCT
ejpam-5165	471	9	∫	∫	PROPN
ejpam-5165	472	1	[	[	X
ejpam-5165	472	2	a	a	X
ejpam-5165	472	3	,	,	PUNCT
ejpam-5165	472	4	b	b	NOUN
ejpam-5165	472	5	]	]	X
ejpam-5165	472	6	fdg	fdg	PROPN
ejpam-5165	472	7	∈	∈	PROPN
ejpam-5165	472	8	e(x	e(x	NUM
ejpam-5165	472	9	)	)	PUNCT
ejpam-5165	472	10	.	.	PUNCT
ejpam-5165	473	1	hence	hence	ADV
ejpam-5165	473	2	,	,	PUNCT
ejpam-5165	473	3	(	(	PUNCT
ejpam-5165	473	4	mds	mds	PROPN
ejpam-5165	473	5	)	)	PUNCT
ejpam-5165	473	6	∫	∫	PROPN
ejpam-5165	474	1	[	[	X
ejpam-5165	474	2	a	a	X
ejpam-5165	474	3	,	,	PUNCT
ejpam-5165	474	4	b	b	NOUN
ejpam-5165	474	5	]	]	X
ejpam-5165	474	6	fdg	fdg	PROPN
ejpam-5165	474	7	=	=	SYM
ejpam-5165	474	8	(	(	PUNCT
ejpam-5165	474	9	mps	mps	PROPN
ejpam-5165	474	10	)	)	PUNCT
ejpam-5165	474	11	∫	∫	PROPN
ejpam-5165	475	1	[	[	X
ejpam-5165	475	2	a	a	X
ejpam-5165	475	3	,	,	PUNCT
ejpam-5165	475	4	b	b	NOUN
ejpam-5165	475	5	]	]	X
ejpam-5165	475	6	fdg	fdg	PROPN
ejpam-5165	475	7	.	.	PUNCT
ejpam-5165	476	1	therefore	therefore	ADV
ejpam-5165	476	2	,	,	PUNCT
ejpam-5165	476	3	f	f	PROPN
ejpam-5165	476	4	is	be	AUX
ejpam-5165	476	5	mps	mp	NOUN
ejpam-5165	476	6	-	-	PUNCT
ejpam-5165	476	7	integrable	integrable	ADJ
ejpam-5165	476	8	with	with	ADP
ejpam-5165	476	9	respect	respect	NOUN
ejpam-5165	476	10	to	to	ADP
ejpam-5165	476	11	g	g	NOUN
ejpam-5165	476	12	on	on	ADP
ejpam-5165	476	13	[	[	X
ejpam-5165	476	14	a	a	X
ejpam-5165	476	15	,	,	PUNCT
ejpam-5165	476	16	b	b	NOUN
ejpam-5165	476	17	]	]	X
ejpam-5165	476	18	.	.	PUNCT
ejpam-5165	477	1	□	□	PUNCT
ejpam-5165	477	2	theorem	theorem	ADJ
ejpam-5165	477	3	14	14	NUM
ejpam-5165	477	4	.	.	PUNCT
ejpam-5165	478	1	(	(	PUNCT
ejpam-5165	478	2	additivity	additivity	NOUN
ejpam-5165	478	3	of	of	ADP
ejpam-5165	478	4	the	the	DET
ejpam-5165	478	5	mps	mps	PROPN
ejpam-5165	478	6	-	-	ADJ
ejpam-5165	478	7	integral	integral	ADJ
ejpam-5165	478	8	)	)	PUNCT
ejpam-5165	478	9	let	let	VERB
ejpam-5165	478	10	f	f	NOUN
ejpam-5165	478	11	:	:	PUNCT
ejpam-5165	479	1	[	[	X
ejpam-5165	479	2	a	a	X
ejpam-5165	479	3	,	,	PUNCT
ejpam-5165	479	4	b	b	NOUN
ejpam-5165	479	5	]	]	X
ejpam-5165	479	6	→	→	SYM
ejpam-5165	479	7	x	x	X
ejpam-5165	479	8	and	and	CCONJ
ejpam-5165	479	9	g	g	NOUN
ejpam-5165	479	10	:	:	PUNCT
ejpam-5165	480	1	[	[	X
ejpam-5165	480	2	a	a	X
ejpam-5165	480	3	,	,	PUNCT
ejpam-5165	480	4	b	b	NOUN
ejpam-5165	480	5	]	]	X
ejpam-5165	480	6	→	→	PUNCT
ejpam-5165	480	7	r	r	NOUN
ejpam-5165	480	8	be	be	NOUN
ejpam-5165	480	9	functions	function	NOUN
ejpam-5165	480	10	and	and	CCONJ
ejpam-5165	480	11	i	i	PRON
ejpam-5165	480	12	,	,	PUNCT
ejpam-5165	480	13	j	j	PROPN
ejpam-5165	480	14	∈	∈	PROPN
ejpam-5165	480	15	in	in	ADP
ejpam-5165	480	16	(	(	PUNCT
ejpam-5165	480	17	[	[	X
ejpam-5165	480	18	a	a	X
ejpam-5165	480	19	,	,	PUNCT
ejpam-5165	480	20	b	b	NOUN
ejpam-5165	480	21	]	]	PUNCT
ejpam-5165	480	22	)	)	PUNCT
ejpam-5165	480	23	that	that	PRON
ejpam-5165	480	24	forms	form	VERB
ejpam-5165	480	25	an	an	DET
ejpam-5165	480	26	m	m	NOUN
ejpam-5165	480	27	-partition	-partition	NOUN
ejpam-5165	480	28	of	of	ADP
ejpam-5165	480	29	[	[	X
ejpam-5165	480	30	a	a	X
ejpam-5165	480	31	,	,	PUNCT
ejpam-5165	480	32	b	b	NOUN
ejpam-5165	480	33	]	]	X
ejpam-5165	480	34	.	.	PUNCT
ejpam-5165	481	1	if	if	SCONJ
ejpam-5165	481	2	f	f	PROPN
ejpam-5165	481	3	∈	∈	PROPN
ejpam-5165	481	4	mps(i	mps(i	PROPN
ejpam-5165	481	5	,	,	PUNCT
ejpam-5165	481	6	g	g	NOUN
ejpam-5165	481	7	)	)	PUNCT
ejpam-5165	481	8	∩mps(j	∩mps(j	PRON
ejpam-5165	481	9	,	,	PUNCT
ejpam-5165	481	10	g	g	NOUN
ejpam-5165	481	11	)	)	PUNCT
ejpam-5165	481	12	,	,	PUNCT
ejpam-5165	481	13	then	then	ADV
ejpam-5165	481	14	f	f	PROPN
ejpam-5165	481	15	∈	∈	PROPN
ejpam-5165	481	16	mps([a	mps([a	PROPN
ejpam-5165	481	17	,	,	PUNCT
ejpam-5165	481	18	b	b	NOUN
ejpam-5165	481	19	]	]	X
ejpam-5165	481	20	,	,	PUNCT
ejpam-5165	481	21	g	g	NOUN
ejpam-5165	481	22	)	)	PUNCT
ejpam-5165	481	23	and	and	CCONJ
ejpam-5165	481	24	(	(	PUNCT
ejpam-5165	481	25	mps	mps	PROPN
ejpam-5165	481	26	)	)	PUNCT
ejpam-5165	481	27	∫	∫	PROPN
ejpam-5165	482	1	[	[	X
ejpam-5165	482	2	a	a	X
ejpam-5165	482	3	,	,	PUNCT
ejpam-5165	482	4	b	b	NOUN
ejpam-5165	482	5	]	]	X
ejpam-5165	482	6	fdg	fdg	PROPN
ejpam-5165	482	7	=	=	SYM
ejpam-5165	482	8	(	(	PUNCT
ejpam-5165	482	9	mps	mps	PROPN
ejpam-5165	482	10	)	)	PUNCT
ejpam-5165	482	11	∫	∫	PROPN
ejpam-5165	483	1	i	i	PROPN
ejpam-5165	483	2	fdg	fdg	PROPN
ejpam-5165	484	1	+	+	CCONJ
ejpam-5165	484	2	(	(	PUNCT
ejpam-5165	484	3	mps	mps	PROPN
ejpam-5165	484	4	)	)	PUNCT
ejpam-5165	484	5	∫	∫	PROPN
ejpam-5165	484	6	j	j	PROPN
ejpam-5165	484	7	fdg	fdg	PROPN
ejpam-5165	484	8	.	.	PROPN
ejpam-5165	484	9	references	reference	NOUN
ejpam-5165	484	10	1196	1196	NUM
ejpam-5165	484	11	acknowledgements	acknowledgement	NOUN
ejpam-5165	484	12	the	the	DET
ejpam-5165	484	13	authors	author	NOUN
ejpam-5165	484	14	express	express	VERB
ejpam-5165	484	15	their	their	PRON
ejpam-5165	484	16	gratitude	gratitude	NOUN
ejpam-5165	484	17	to	to	ADP
ejpam-5165	484	18	the	the	DET
ejpam-5165	484	19	department	department	NOUN
ejpam-5165	484	20	of	of	ADP
ejpam-5165	484	21	science	science	NOUN
ejpam-5165	484	22	and	and	CCONJ
ejpam-5165	484	23	technologyscience	technologyscience	ADJ
ejpam-5165	484	24	education	education	NOUN
ejpam-5165	484	25	intitutescience	intitutescience	NOUN
ejpam-5165	484	26	and	and	CCONJ
ejpam-5165	484	27	technology	technology	NOUN
ejpam-5165	484	28	regional	regional	ADJ
ejpam-5165	484	29	alliance	alliance	NOUN
ejpam-5165	484	30	of	of	ADP
ejpam-5165	484	31	inclusive	inclusive	ADJ
ejpam-5165	484	32	universities	university	NOUN
ejpam-5165	484	33	for	for	ADP
ejpam-5165	484	34	national	national	ADJ
ejpam-5165	484	35	development	development	NOUN
ejpam-5165	484	36	(	(	PUNCT
ejpam-5165	484	37	dost	dost	NOUN
ejpam-5165	484	38	-	-	PUNCT
ejpam-5165	484	39	sei	sei	ADJ
ejpam-5165	484	40	-	-	PUNCT
ejpam-5165	484	41	strand	strand	NOUN
ejpam-5165	484	42	)	)	PUNCT
ejpam-5165	484	43	for	for	ADP
ejpam-5165	484	44	their	their	PRON
ejpam-5165	484	45	financial	financial	ADJ
ejpam-5165	484	46	support	support	NOUN
ejpam-5165	484	47	in	in	ADP
ejpam-5165	484	48	conducting	conduct	VERB
ejpam-5165	484	49	this	this	DET
ejpam-5165	484	50	research	research	NOUN
ejpam-5165	484	51	.	.	PUNCT
ejpam-5165	485	1	references	reference	NOUN
ejpam-5165	485	2	[	[	X
ejpam-5165	485	3	1	1	NUM
ejpam-5165	485	4	]	]	X
ejpam-5165	485	5	r	r	NOUN
ejpam-5165	485	6	bartle	bartle	NOUN
ejpam-5165	485	7	and	and	CCONJ
ejpam-5165	485	8	d	d	PROPN
ejpam-5165	485	9	sherbert	sherbert	PROPN
ejpam-5165	485	10	.	.	PUNCT
ejpam-5165	486	1	introduction	introduction	NOUN
ejpam-5165	486	2	to	to	ADP
ejpam-5165	486	3	real	real	ADJ
ejpam-5165	486	4	analysis	analysis	NOUN
ejpam-5165	486	5	.	.	PUNCT
ejpam-5165	487	1	john	john	PROPN
ejpam-5165	487	2	wiley	wiley	PROPN
ejpam-5165	487	3	and	and	CCONJ
ejpam-5165	487	4	sons	son	NOUN
ejpam-5165	487	5	,	,	PUNCT
ejpam-5165	487	6	inc	inc	PROPN
ejpam-5165	487	7	.	.	PROPN
ejpam-5165	487	8	,	,	PUNCT
ejpam-5165	487	9	new	new	PROPN
ejpam-5165	487	10	york	york	PROPN
ejpam-5165	487	11	,	,	PUNCT
ejpam-5165	487	12	2000	2000	NUM
ejpam-5165	487	13	.	.	PUNCT
ejpam-5165	488	1	[	[	X
ejpam-5165	488	2	2	2	NUM
ejpam-5165	488	3	]	]	X
ejpam-5165	488	4	g.b	g.b	PROPN
ejpam-5165	488	5	.	.	PROPN
ejpam-5165	488	6	flores	flores	PROPN
ejpam-5165	488	7	.	.	PUNCT
ejpam-5165	489	1	the	the	DET
ejpam-5165	489	2	pul	pul	NOUN
ejpam-5165	489	3	–	–	PUNCT
ejpam-5165	489	4	stieltjes	stieltjes	NOUN
ejpam-5165	489	5	integral	integral	ADJ
ejpam-5165	489	6	in	in	ADP
ejpam-5165	489	7	banach	banach	NOUN
ejpam-5165	489	8	space	space	NOUN
ejpam-5165	489	9	.	.	PUNCT
ejpam-5165	490	1	phd	phd	NOUN
ejpam-5165	490	2	thesis	thesis	PROPN
ejpam-5165	490	3	,	,	PUNCT
ejpam-5165	490	4	mindanao	mindanao	PROPN
ejpam-5165	490	5	state	state	PROPN
ejpam-5165	490	6	university	university	PROPN
ejpam-5165	490	7	iligan	iligan	PROPN
ejpam-5165	490	8	institute	institute	PROPN
ejpam-5165	490	9	of	of	ADP
ejpam-5165	490	10	technology	technology	PROPN
ejpam-5165	490	11	(	(	PUNCT
ejpam-5165	490	12	msu	msu	PROPN
ejpam-5165	490	13	-	-	PUNCT
ejpam-5165	490	14	iit	iit	NOUN
ejpam-5165	490	15	)	)	PUNCT
ejpam-5165	490	16	,	,	PUNCT
ejpam-5165	490	17	2017	2017	NUM
ejpam-5165	490	18	.	.	PUNCT
ejpam-5165	491	1	[	[	X
ejpam-5165	491	2	3	3	X
ejpam-5165	491	3	]	]	X
ejpam-5165	491	4	g.b	g.b	PROPN
ejpam-5165	491	5	.	.	PROPN
ejpam-5165	491	6	flores	flores	PROPN
ejpam-5165	491	7	and	and	CCONJ
ejpam-5165	491	8	j	j	PROPN
ejpam-5165	491	9	benitez	benitez	PROPN
ejpam-5165	491	10	.	.	PUNCT
ejpam-5165	492	1	simple	simple	ADJ
ejpam-5165	492	2	properties	property	NOUN
ejpam-5165	492	3	of	of	ADP
ejpam-5165	492	4	pul	pul	NOUN
ejpam-5165	492	5	-	-	PUNCT
ejpam-5165	492	6	stieltjes	stieltjes	NOUN
ejpam-5165	492	7	integral	integral	ADJ
ejpam-5165	492	8	in	in	ADP
ejpam-5165	492	9	banach	banach	NOUN
ejpam-5165	492	10	space	space	NOUN
ejpam-5165	492	11	.	.	PUNCT
ejpam-5165	493	1	journal	journal	NOUN
ejpam-5165	493	2	of	of	ADP
ejpam-5165	493	3	ultra	ultra	ADJ
ejpam-5165	493	4	scientist	scientist	NOUN
ejpam-5165	493	5	of	of	ADP
ejpam-5165	493	6	physical	physical	ADJ
ejpam-5165	493	7	sciences	science	NOUN
ejpam-5165	493	8	,	,	PUNCT
ejpam-5165	493	9	29:126–134	29:126–134	PROPN
ejpam-5165	493	10	,	,	PUNCT
ejpam-5165	493	11	2017	2017	NUM
ejpam-5165	493	12	.	.	PUNCT
ejpam-5165	494	1	[	[	X
ejpam-5165	494	2	4	4	NUM
ejpam-5165	494	3	]	]	X
ejpam-5165	494	4	r	r	NOUN
ejpam-5165	494	5	gordon	gordon	PROPN
ejpam-5165	494	6	.	.	PUNCT
ejpam-5165	495	1	the	the	DET
ejpam-5165	495	2	mcshane	mcshane	PROPN
ejpam-5165	495	3	integral	integral	ADJ
ejpam-5165	495	4	of	of	ADP
ejpam-5165	495	5	banach	banach	ADV
ejpam-5165	495	6	-	-	PUNCT
ejpam-5165	495	7	valued	value	VERB
ejpam-5165	495	8	functions	function	NOUN
ejpam-5165	495	9	.	.	PUNCT
ejpam-5165	496	1	illinois	illinois	PROPN
ejpam-5165	496	2	j	j	PROPN
ejpam-5165	496	3	math	math	PROPN
ejpam-5165	496	4	.	.	PUNCT
ejpam-5165	496	5	,	,	PUNCT
ejpam-5165	496	6	34:557–567	34:557–567	NUM
ejpam-5165	496	7	,	,	PUNCT
ejpam-5165	496	8	1990	1990	NUM
ejpam-5165	496	9	.	.	PUNCT
ejpam-5165	497	1	[	[	X
ejpam-5165	497	2	5	5	NUM
ejpam-5165	497	3	]	]	X
ejpam-5165	497	4	y	y	PROPN
ejpam-5165	497	5	gouju	gouju	PROPN
ejpam-5165	497	6	and	and	CCONJ
ejpam-5165	497	7	a	a	DET
ejpam-5165	497	8	schwabik	schwabik	PROPN
ejpam-5165	497	9	.	.	PUNCT
ejpam-5165	498	1	the	the	DET
ejpam-5165	498	2	mcshane	mcshane	PROPN
ejpam-5165	498	3	and	and	CCONJ
ejpam-5165	498	4	the	the	DET
ejpam-5165	498	5	pettis	pettis	NOUN
ejpam-5165	498	6	integral	integral	NOUN
ejpam-5165	498	7	of	of	ADP
ejpam-5165	498	8	banach	banach	NOUN
ejpam-5165	498	9	space	space	NOUN
ejpam-5165	498	10	-	-	PUNCT
ejpam-5165	498	11	valued	value	VERB
ejpam-5165	498	12	functions	function	NOUN
ejpam-5165	498	13	defined	define	VERB
ejpam-5165	498	14	on	on	ADP
ejpam-5165	498	15	rm	rm	PROPN
ejpam-5165	498	16	.	.	PUNCT
ejpam-5165	499	1	illinois	illinois	PROPN
ejpam-5165	499	2	j	j	PROPN
ejpam-5165	499	3	math	math	PROPN
ejpam-5165	499	4	.	.	PUNCT
ejpam-5165	499	5	,	,	PUNCT
ejpam-5165	499	6	46:1125–1144	46:1125–1144	NUM
ejpam-5165	499	7	,	,	PUNCT
ejpam-5165	499	8	2002	2002	NUM
ejpam-5165	499	9	.	.	PUNCT
ejpam-5165	500	1	[	[	X
ejpam-5165	500	2	6	6	NUM
ejpam-5165	500	3	]	]	X
ejpam-5165	500	4	r	r	NOUN
ejpam-5165	500	5	henstock	henstock	NOUN
ejpam-5165	500	6	.	.	PUNCT
ejpam-5165	501	1	a	a	DET
ejpam-5165	501	2	riemann	riemann	NOUN
ejpam-5165	501	3	-	-	PUNCT
ejpam-5165	501	4	type	type	NOUN
ejpam-5165	501	5	integral	integral	ADJ
ejpam-5165	501	6	of	of	ADP
ejpam-5165	501	7	lebesgue	lebesgue	NOUN
ejpam-5165	501	8	power	power	NOUN
ejpam-5165	501	9	.	.	PUNCT
ejpam-5165	502	1	canadian	canadian	ADJ
ejpam-5165	502	2	journal	journal	PROPN
ejpam-5165	502	3	of	of	ADP
ejpam-5165	502	4	mathematics	mathematic	NOUN
ejpam-5165	502	5	,	,	PUNCT
ejpam-5165	502	6	20:79–87	20:79–87	NUM
ejpam-5165	502	7	,	,	PUNCT
ejpam-5165	502	8	1968	1968	NUM
ejpam-5165	502	9	.	.	PUNCT
ejpam-5165	503	1	[	[	X
ejpam-5165	503	2	7	7	NUM
ejpam-5165	503	3	]	]	X
ejpam-5165	503	4	e	e	X
ejpam-5165	503	5	kreyszig	kreyszig	PROPN
ejpam-5165	503	6	.	.	PUNCT
ejpam-5165	504	1	introductory	introductory	ADJ
ejpam-5165	504	2	functional	functional	ADJ
ejpam-5165	504	3	analysis	analysis	NOUN
ejpam-5165	504	4	with	with	ADP
ejpam-5165	504	5	applications	application	NOUN
ejpam-5165	504	6	.	.	PUNCT
ejpam-5165	505	1	john	john	PROPN
ejpam-5165	505	2	wiley	wiley	PROPN
ejpam-5165	505	3	&	&	CCONJ
ejpam-5165	505	4	sons	sons	PROPN
ejpam-5165	505	5	,	,	PUNCT
ejpam-5165	505	6	inc	inc	PROPN
ejpam-5165	505	7	.	.	PROPN
ejpam-5165	505	8	,	,	PUNCT
ejpam-5165	505	9	canada	canada	PROPN
ejpam-5165	505	10	,	,	PUNCT
ejpam-5165	505	11	1978	1978	NUM
ejpam-5165	505	12	.	.	PUNCT
ejpam-5165	506	1	[	[	X
ejpam-5165	506	2	8	8	NUM
ejpam-5165	506	3	]	]	X
ejpam-5165	506	4	t.y	t.y	PROPN
ejpam-5165	506	5	.	.	PROPN
ejpam-5165	506	6	lee	lee	PROPN
ejpam-5165	506	7	.	.	PUNCT
ejpam-5165	506	8	henstock	henstock	PROPN
ejpam-5165	506	9	-	-	PUNCT
ejpam-5165	506	10	kurzweil	kurzweil	NOUN
ejpam-5165	506	11	integration	integration	NOUN
ejpam-5165	506	12	on	on	ADP
ejpam-5165	506	13	euclidean	euclidean	ADJ
ejpam-5165	506	14	spaces	space	NOUN
ejpam-5165	506	15	.	.	PUNCT
ejpam-5165	507	1	world	world	NOUN
ejpam-5165	507	2	scientific	scientific	PROPN
ejpam-5165	507	3	,	,	PUNCT
ejpam-5165	507	4	singapore	singapore	PROPN
ejpam-5165	507	5	,	,	PUNCT
ejpam-5165	507	6	2011	2011	NUM
ejpam-5165	507	7	.	.	PUNCT
ejpam-5165	508	1	[	[	X
ejpam-5165	508	2	9	9	NUM
ejpam-5165	508	3	]	]	X
ejpam-5165	508	4	e	e	X
ejpam-5165	508	5	mcshane	mcshane	PROPN
ejpam-5165	508	6	.	.	PUNCT
ejpam-5165	509	1	a	a	DET
ejpam-5165	509	2	riemann	riemann	NOUN
ejpam-5165	509	3	-	-	PUNCT
ejpam-5165	509	4	type	type	NOUN
ejpam-5165	509	5	integral	integral	ADJ
ejpam-5165	509	6	that	that	PRON
ejpam-5165	509	7	includes	include	VERB
ejpam-5165	509	8	lebesgue	lebesgue	NOUN
ejpam-5165	509	9	-	-	PUNCT
ejpam-5165	509	10	stieltjes	stieltjes	NOUN
ejpam-5165	509	11	,	,	PUNCT
ejpam-5165	509	12	bochner	bochn	ADJ
ejpam-5165	509	13	and	and	CCONJ
ejpam-5165	509	14	stochastic	stochastic	ADJ
ejpam-5165	509	15	integrals	integral	NOUN
ejpam-5165	509	16	.	.	PUNCT
ejpam-5165	510	1	american	american	PROPN
ejpam-5165	510	2	mathematical	mathematical	PROPN
ejpam-5165	510	3	society	society	NOUN
ejpam-5165	510	4	,	,	PUNCT
ejpam-5165	510	5	providence	providence	NOUN
ejpam-5165	510	6	,	,	PUNCT
ejpam-5165	510	7	rhode	rhode	NOUN
ejpam-5165	510	8	island	island	NOUN
ejpam-5165	510	9	,	,	PUNCT
ejpam-5165	510	10	1969	1969	NUM
ejpam-5165	510	11	.	.	PUNCT
ejpam-5165	511	1	[	[	X
ejpam-5165	511	2	10	10	NUM
ejpam-5165	511	3	]	]	X
ejpam-5165	511	4	s	s	AUX
ejpam-5165	511	5	schwabik	schwabik	PROPN
ejpam-5165	511	6	and	and	CCONJ
ejpam-5165	511	7	g	g	PROPN
ejpam-5165	511	8	ye	ye	PROPN
ejpam-5165	511	9	.	.	PUNCT
ejpam-5165	511	10	topics	topic	NOUN
ejpam-5165	511	11	in	in	ADP
ejpam-5165	511	12	banach	banach	NOUN
ejpam-5165	511	13	space	space	NOUN
ejpam-5165	511	14	integration	integration	NOUN
ejpam-5165	511	15	.	.	PUNCT
ejpam-5165	512	1	world	world	NOUN
ejpam-5165	512	2	scientific	scientific	PROPN
ejpam-5165	512	3	,	,	PUNCT
ejpam-5165	512	4	singapore	singapore	PROPN
ejpam-5165	512	5	,	,	PUNCT
ejpam-5165	512	6	2005	2005	NUM
ejpam-5165	512	7	.	.	PUNCT
ejpam-5165	513	1	[	[	X
ejpam-5165	513	2	11	11	NUM
ejpam-5165	513	3	]	]	PUNCT
ejpam-5165	513	4	a	a	DET
ejpam-5165	513	5	solikhin	solikhin	NOUN
ejpam-5165	513	6	,	,	PUNCT
ejpam-5165	513	7	y.d	y.d	PROPN
ejpam-5165	513	8	.	.	PROPN
ejpam-5165	513	9	aziz	aziz	PROPN
ejpam-5165	513	10	,	,	PUNCT
ejpam-5165	513	11	sumanto	sumanto	VERB
ejpam-5165	513	12	r	r	NOUN
ejpam-5165	513	13	,	,	PUNCT
ejpam-5165	513	14	and	and	CCONJ
ejpam-5165	513	15	s.u	s.u	PROPN
ejpam-5165	513	16	.	.	PROPN
ejpam-5165	513	17	heri	heri	PROPN
ejpam-5165	513	18	.	.	PUNCT
ejpam-5165	514	1	a	a	DET
ejpam-5165	514	2	convergence	convergence	NOUN
ejpam-5165	514	3	theorem	theorem	VERB
ejpam-5165	514	4	on	on	ADP
ejpam-5165	514	5	the	the	DET
ejpam-5165	514	6	dunford	dunford	PROPN
ejpam-5165	514	7	integral	integral	PROPN
ejpam-5165	514	8	.	.	PUNCT
ejpam-5165	515	1	journal	journal	PROPN
ejpam-5165	515	2	of	of	ADP
ejpam-5165	515	3	physics	physics	PROPN
ejpam-5165	515	4	:	:	PUNCT
ejpam-5165	515	5	conference	conference	NOUN
ejpam-5165	515	6	series	series	NOUN
ejpam-5165	515	7	,	,	PUNCT
ejpam-5165	515	8	2021	2021	NUM
ejpam-5165	515	9	.	.	PUNCT
ejpam-5165	516	1	[	[	X
ejpam-5165	516	2	12	12	NUM
ejpam-5165	516	3	]	]	X
ejpam-5165	516	4	l	l	PROPN
ejpam-5165	516	5	tu	tu	PROPN
ejpam-5165	516	6	.	.	PUNCT
ejpam-5165	517	1	an	an	DET
ejpam-5165	517	2	introduction	introduction	NOUN
ejpam-5165	517	3	to	to	ADP
ejpam-5165	517	4	manifolds	manifold	NOUN
ejpam-5165	517	5	.	.	PUNCT
ejpam-5165	518	1	springer	springer	NOUN
ejpam-5165	518	2	,	,	PUNCT
ejpam-5165	518	3	new	new	PROPN
ejpam-5165	518	4	york	york	PROPN
ejpam-5165	518	5	,	,	PUNCT
ejpam-5165	518	6	2010	2010	NUM
ejpam-5165	518	7	.	.	PUNCT