id	sid	tid	token	lemma	pos
bibechana-4051	1	1	microsoft	microsoft	PROPN
bibechana-4051	1	2	word	word	PROPN
bibechana-4051	1	3	mani	mani	PROPN
bibechana-4051	1	4	raj	raj	PROPN
bibechana-4051	1	5	bhattrai	bhattrai	VERB
bibechana-4051	1	6	_	_	NOUN
bibechana-4051	1	7	82	82	NUM
bibechana-4051	1	8	-	-	SYM
bibechana-4051	1	9	86_.doc	86_.doc	NUM
bibechana-4051	1	10	mani	mani	PROPN
bibechana-4051	1	11	raj	raj	PROPN
bibechana-4051	1	12	bhattrai	bhattrai	PROPN
bibechana-4051	1	13	/	/	SYM
bibechana-4051	1	14	bibechana	bibechana	NOUN
bibechana-4051	1	15	7	7	NUM
bibechana-4051	1	16	(	(	PUNCT
bibechana-4051	1	17	2011	2011	NUM
bibechana-4051	1	18	)	)	PUNCT
bibechana-4051	1	19	83	83	NUM
bibechana-4051	1	20	-	-	SYM
bibechana-4051	1	21	86	86	NUM
bibechana-4051	1	22	:	:	PUNCT
bibechana-4051	1	23	bmhss	bmhss	PROPN
bibechana-4051	1	24	83	83	NUM
bibechana-4051	1	25	bibechana	bibechana	NOUN
bibechana-4051	1	26	a	a	DET
bibechana-4051	1	27	multidisciplinary	multidisciplinary	ADJ
bibechana-4051	1	28	journal	journal	NOUN
bibechana-4051	1	29	of	of	ADP
bibechana-4051	1	30	science	science	NOUN
bibechana-4051	1	31	,	,	PUNCT
bibechana-4051	1	32	technology	technology	NOUN
bibechana-4051	1	33	and	and	CCONJ
bibechana-4051	1	34	mathematics	mathematic	NOUN
bibechana-4051	1	35	issn	issn	VERB
bibechana-4051	1	36	2091	2091	NUM
bibechana-4051	1	37	-	-	SYM
bibechana-4051	1	38	0762	0762	NUM
bibechana-4051	1	39	(	(	PUNCT
bibechana-4051	1	40	online	online	ADJ
bibechana-4051	1	41	)	)	PUNCT
bibechana-4051	1	42	journal	journal	NOUN
bibechana-4051	1	43	homepage	homepage	NOUN
bibechana-4051	1	44	:	:	PUNCT
bibechana-4051	2	1	http://nepjol.info/index.php/bibichana	http://nepjol.info/index.php/bibichana	X
bibechana-4051	2	2	riemann	riemann	PROPN
bibechana-4051	2	3	integral	integral	ADJ
bibechana-4051	2	4	and	and	CCONJ
bibechana-4051	2	5	its	its	PRON
bibechana-4051	2	6	relation	relation	NOUN
bibechana-4051	2	7	with	with	ADP
bibechana-4051	2	8	lebesgue	lebesgue	PROPN
bibechana-4051	2	9	integral	integral	ADJ
bibechana-4051	2	10	mani	mani	PROPN
bibechana-4051	2	11	raj	raj	PROPN
bibechana-4051	2	12	bhattrai∗∗∗∗	bhattrai∗∗∗∗	PROPN
bibechana-4051	2	13	dept	dept	PROPN
bibechana-4051	2	14	.	.	PROPN
bibechana-4051	2	15	of	of	ADP
bibechana-4051	2	16	mathematics	mathematics	PROPN
bibechana-4051	2	17	,	,	PUNCT
bibechana-4051	2	18	bhanu	bhanu	PROPN
bibechana-4051	2	19	m.h.s	m.h.s	PROPN
bibechana-4051	2	20	.	.	PUNCT
bibechana-4051	3	1	school	school	NOUN
bibechana-4051	3	2	,	,	PUNCT
bibechana-4051	3	3	biratnagar	biratnagar	NOUN
bibechana-4051	3	4	,	,	PUNCT
bibechana-4051	3	5	nepal	nepal	ADJ
bibechana-4051	3	6	article	article	NOUN
bibechana-4051	3	7	history	history	NOUN
bibechana-4051	3	8	:	:	PUNCT
bibechana-4051	3	9	received	receive	VERB
bibechana-4051	3	10	29	29	NUM
bibechana-4051	3	11	october	october	PROPN
bibechana-4051	3	12	2010	2010	NUM
bibechana-4051	3	13	;	;	PUNCT
bibechana-4051	3	14	revised	revise	VERB
bibechana-4051	3	15	25	25	NUM
bibechana-4051	3	16	november	november	PROPN
bibechana-4051	3	17	2010	2010	NUM
bibechana-4051	3	18	;	;	PUNCT
bibechana-4051	3	19	accepted	accept	VERB
bibechana-4051	3	20	5	5	NUM
bibechana-4051	3	21	december	december	PROPN
bibechana-4051	3	22	2010	2010	NUM
bibechana-4051	3	23	abstract	abstract	NOUN
bibechana-4051	3	24	this	this	DET
bibechana-4051	3	25	review	review	NOUN
bibechana-4051	3	26	explains	explain	VERB
bibechana-4051	3	27	the	the	DET
bibechana-4051	3	28	limitations	limitation	NOUN
bibechana-4051	3	29	of	of	ADP
bibechana-4051	3	30	the	the	DET
bibechana-4051	3	31	riemann	riemann	PROPN
bibechana-4051	3	32	integral	integral	PROPN
bibechana-4051	3	33	and	and	CCONJ
bibechana-4051	3	34	focuses	focus	VERB
bibechana-4051	3	35	on	on	ADP
bibechana-4051	3	36	the	the	DET
bibechana-4051	3	37	more	more	ADV
bibechana-4051	3	38	general	general	ADJ
bibechana-4051	3	39	concept	concept	NOUN
bibechana-4051	3	40	.	.	PUNCT
bibechana-4051	4	1	it	it	PRON
bibechana-4051	4	2	has	have	AUX
bibechana-4051	4	3	been	be	AUX
bibechana-4051	4	4	suggested	suggest	VERB
bibechana-4051	4	5	that	that	SCONJ
bibechana-4051	4	6	a	a	DET
bibechana-4051	4	7	better	well	ADJ
bibechana-4051	4	8	route	route	NOUN
bibechana-4051	4	9	is	be	AUX
bibechana-4051	4	10	to	to	PART
bibechana-4051	4	11	abandon	abandon	VERB
bibechana-4051	4	12	the	the	DET
bibechana-4051	4	13	riemann	riemann	PROPN
bibechana-4051	4	14	integral	integral	PROPN
bibechana-4051	4	15	for	for	ADP
bibechana-4051	4	16	lebesgue	lebesgue	NOUN
bibechana-4051	4	17	integral	integral	ADJ
bibechana-4051	4	18	and	and	CCONJ
bibechana-4051	4	19	explained	explain	VERB
bibechana-4051	4	20	the	the	DET
bibechana-4051	4	21	importance	importance	NOUN
bibechana-4051	4	22	of	of	ADP
bibechana-4051	4	23	lebesgue	lebesgue	NOUN
bibechana-4051	4	24	integral	integral	ADJ
bibechana-4051	4	25	in	in	ADP
bibechana-4051	4	26	real	real	ADJ
bibechana-4051	4	27	analysis	analysis	NOUN
bibechana-4051	4	28	and	and	CCONJ
bibechana-4051	4	29	other	other	ADJ
bibechana-4051	4	30	fields	field	NOUN
bibechana-4051	4	31	of	of	ADP
bibechana-4051	4	32	mathematical	mathematical	ADJ
bibechana-4051	4	33	science	science	NOUN
bibechana-4051	4	34	.	.	PUNCT
bibechana-4051	5	1	keywords	keyword	NOUN
bibechana-4051	5	2	:	:	PUNCT
bibechana-4051	5	3	riemann	riemann	PROPN
bibechana-4051	5	4	integral	integral	PROPN
bibechana-4051	5	5	;	;	PUNCT
bibechana-4051	5	6	lebesgue	lebesgue	NOUN
bibechana-4051	5	7	integral	integral	ADJ
bibechana-4051	5	8	;	;	PUNCT
bibechana-4051	5	9	fourier	fourier	NOUN
bibechana-4051	5	10	series	series	PROPN
bibechana-4051	5	11	1	1	NUM
bibechana-4051	5	12	.	.	PUNCT
bibechana-4051	6	1	introduction	introduction	NOUN
bibechana-4051	6	2	as	as	ADP
bibechana-4051	6	3	part	part	NOUN
bibechana-4051	6	4	of	of	ADP
bibechana-4051	6	5	a	a	DET
bibechana-4051	6	6	general	general	ADJ
bibechana-4051	6	7	movement	movement	NOUN
bibechana-4051	6	8	toward	toward	ADP
bibechana-4051	6	9	rigor	rigor	NOUN
bibechana-4051	6	10	in	in	ADP
bibechana-4051	6	11	mathematics	mathematic	NOUN
bibechana-4051	6	12	in	in	ADP
bibechana-4051	6	13	the	the	DET
bibechana-4051	6	14	nineteenth	nineteenth	ADJ
bibechana-4051	6	15	century	century	NOUN
bibechana-4051	6	16	,	,	PUNCT
bibechana-4051	6	17	attempts	attempt	NOUN
bibechana-4051	6	18	were	be	AUX
bibechana-4051	6	19	made	make	VERB
bibechana-4051	6	20	to	to	PART
bibechana-4051	6	21	put	put	VERB
bibechana-4051	6	22	the	the	DET
bibechana-4051	6	23	integral	integral	ADJ
bibechana-4051	6	24	calculus	calculus	NOUN
bibechana-4051	6	25	on	on	ADP
bibechana-4051	6	26	a	a	DET
bibechana-4051	6	27	firm	firm	ADJ
bibechana-4051	6	28	foundation	foundation	NOUN
bibechana-4051	6	29	.	.	PUNCT
bibechana-4051	7	1	the	the	DET
bibechana-4051	7	2	riemann	riemann	PROPN
bibechana-4051	7	3	integral	integral	PROPN
bibechana-4051	7	4	,	,	PUNCT
bibechana-4051	7	5	proposed	propose	VERB
bibechana-4051	7	6	by	by	ADP
bibechana-4051	7	7	bernhard	bernhard	PROPN
bibechana-4051	7	8	riemann	riemann	PROPN
bibechana-4051	7	9	(	(	PUNCT
bibechana-4051	7	10	1826–1866	1826–1866	NUM
bibechana-4051	7	11	)	)	PUNCT
bibechana-4051	8	1	[	[	X
bibechana-4051	8	2	1	1	NUM
bibechana-4051	8	3	]	]	PUNCT
bibechana-4051	8	4	,	,	PUNCT
bibechana-4051	8	5	is	be	AUX
bibechana-4051	8	6	a	a	DET
bibechana-4051	8	7	broadly	broadly	ADV
bibechana-4051	8	8	successful	successful	ADJ
bibechana-4051	8	9	attempt	attempt	NOUN
bibechana-4051	8	10	to	to	PART
bibechana-4051	8	11	provide	provide	VERB
bibechana-4051	8	12	such	such	DET
bibechana-4051	8	13	a	a	DET
bibechana-4051	8	14	foundation	foundation	NOUN
bibechana-4051	8	15	.	.	PUNCT
bibechana-4051	9	1	riemann	riemann	PROPN
bibechana-4051	9	2	's	's	PART
bibechana-4051	9	3	definition	definition	NOUN
bibechana-4051	9	4	starts	start	VERB
bibechana-4051	9	5	with	with	ADP
bibechana-4051	9	6	the	the	DET
bibechana-4051	9	7	construction	construction	NOUN
bibechana-4051	9	8	of	of	ADP
bibechana-4051	9	9	a	a	DET
bibechana-4051	9	10	sequence	sequence	NOUN
bibechana-4051	9	11	of	of	ADP
bibechana-4051	9	12	easily	easily	ADV
bibechana-4051	9	13	-	-	PUNCT
bibechana-4051	9	14	calculated	calculate	VERB
bibechana-4051	9	15	areas	area	NOUN
bibechana-4051	9	16	which	which	PRON
bibechana-4051	9	17	converge	converge	VERB
bibechana-4051	9	18	to	to	ADP
bibechana-4051	9	19	the	the	DET
bibechana-4051	9	20	integral	integral	NOUN
bibechana-4051	9	21	of	of	ADP
bibechana-4051	9	22	a	a	DET
bibechana-4051	9	23	given	give	VERB
bibechana-4051	9	24	function	function	NOUN
bibechana-4051	9	25	.	.	PUNCT
bibechana-4051	10	1	this	this	DET
bibechana-4051	10	2	definition	definition	NOUN
bibechana-4051	10	3	is	be	AUX
bibechana-4051	10	4	successful	successful	ADJ
bibechana-4051	10	5	in	in	ADP
bibechana-4051	10	6	the	the	DET
bibechana-4051	10	7	sense	sense	NOUN
bibechana-4051	10	8	that	that	SCONJ
bibechana-4051	10	9	it	it	PRON
bibechana-4051	10	10	gives	give	VERB
bibechana-4051	10	11	the	the	DET
bibechana-4051	10	12	expected	expect	VERB
bibechana-4051	10	13	answer	answer	NOUN
bibechana-4051	10	14	for	for	ADP
bibechana-4051	10	15	many	many	ADJ
bibechana-4051	10	16	already	already	ADV
bibechana-4051	10	17	-	-	PUNCT
bibechana-4051	10	18	solved	solve	VERB
bibechana-4051	10	19	problems	problem	NOUN
bibechana-4051	10	20	,	,	PUNCT
bibechana-4051	10	21	and	and	CCONJ
bibechana-4051	10	22	gives	give	VERB
bibechana-4051	10	23	useful	useful	ADJ
bibechana-4051	10	24	results	result	NOUN
bibechana-4051	10	25	for	for	ADP
bibechana-4051	10	26	many	many	ADJ
bibechana-4051	10	27	other	other	ADJ
bibechana-4051	10	28	problems	problem	NOUN
bibechana-4051	10	29	.	.	PUNCT
bibechana-4051	11	1	in	in	ADP
bibechana-4051	11	2	the	the	DET
bibechana-4051	11	3	branch	branch	NOUN
bibechana-4051	11	4	of	of	ADP
bibechana-4051	11	5	mathematics	mathematic	NOUN
bibechana-4051	11	6	called	call	VERB
bibechana-4051	11	7	real	real	ADJ
bibechana-4051	11	8	analysis	analysis	NOUN
bibechana-4051	11	9	,	,	PUNCT
bibechana-4051	11	10	the	the	DET
bibechana-4051	11	11	riemann	riemann	PROPN
bibechana-4051	11	12	integral	integral	PROPN
bibechana-4051	11	13	was	be	AUX
bibechana-4051	11	14	the	the	DET
bibechana-4051	11	15	first	first	ADJ
bibechana-4051	11	16	definition	definition	NOUN
bibechana-4051	11	17	of	of	ADP
bibechana-4051	11	18	the	the	DET
bibechana-4051	11	19	integral	integral	NOUN
bibechana-4051	11	20	of	of	ADP
bibechana-4051	11	21	a	a	DET
bibechana-4051	11	22	function	function	NOUN
bibechana-4051	11	23	on	on	ADP
bibechana-4051	11	24	an	an	DET
bibechana-4051	11	25	interval	interval	NOUN
bibechana-4051	11	26	,	,	PUNCT
bibechana-4051	11	27	created	create	VERB
bibechana-4051	11	28	by	by	ADP
bibechana-4051	11	29	bernhard	bernhard	PROPN
bibechana-4051	11	30	riemann	riemann	PROPN
bibechana-4051	11	31	,	,	PUNCT
bibechana-4051	11	32	.	.	PUNCT
bibechana-4051	12	1	while	while	SCONJ
bibechana-4051	12	2	the	the	DET
bibechana-4051	12	3	riemann	riemann	PROPN
bibechana-4051	12	4	integral	integral	PROPN
bibechana-4051	12	5	is	be	AUX
bibechana-4051	12	6	unsuitable	unsuitable	ADJ
bibechana-4051	12	7	for	for	ADP
bibechana-4051	12	8	many	many	ADJ
bibechana-4051	12	9	theoretical	theoretical	ADJ
bibechana-4051	12	10	purposes	purpose	NOUN
bibechana-4051	12	11	,	,	PUNCT
bibechana-4051	12	12	it	it	PRON
bibechana-4051	12	13	is	be	AUX
bibechana-4051	12	14	one	one	NUM
bibechana-4051	12	15	of	of	ADP
bibechana-4051	12	16	the	the	DET
bibechana-4051	12	17	easiest	easy	ADJ
bibechana-4051	12	18	integrals	integral	NOUN
bibechana-4051	12	19	to	to	PART
bibechana-4051	12	20	define	define	VERB
bibechana-4051	12	21	.	.	PUNCT
bibechana-4051	13	1	some	some	PRON
bibechana-4051	13	2	of	of	ADP
bibechana-4051	13	3	these	these	DET
bibechana-4051	13	4	technical	technical	ADJ
bibechana-4051	13	5	deficiencies	deficiency	NOUN
bibechana-4051	13	6	can	can	AUX
bibechana-4051	13	7	be	be	AUX
bibechana-4051	13	8	remedied	remedie	VERB
bibechana-4051	13	9	by	by	ADP
bibechana-4051	13	10	the	the	DET
bibechana-4051	13	11	riemann	riemann	PROPN
bibechana-4051	13	12	–	–	PUNCT
bibechana-4051	13	13	satieties	satiety	NOUN
bibechana-4051	13	14	integral	integral	ADJ
bibechana-4051	13	15	,	,	PUNCT
bibechana-4051	13	16	and	and	CCONJ
bibechana-4051	13	17	most	most	ADJ
bibechana-4051	13	18	of	of	ADP
bibechana-4051	13	19	them	they	PRON
bibechana-4051	13	20	disappear	disappear	VERB
bibechana-4051	13	21	in	in	ADP
bibechana-4051	13	22	the	the	DET
bibechana-4051	13	23	lebesgue	lebesgue	NOUN
bibechana-4051	13	24	integral	integral	ADJ
bibechana-4051	14	1	[	[	X
bibechana-4051	14	2	2	2	NUM
bibechana-4051	14	3	]	]	PUNCT
bibechana-4051	14	4	.	.	PUNCT
bibechana-4051	15	1	bernhard	bernhard	PROPN
bibechana-4051	15	2	riemann	riemann	PROPN
bibechana-4051	15	3	,	,	PUNCT
bibechana-4051	15	4	no	no	ADV
bibechana-4051	15	5	doubt	doubt	ADV
bibechana-4051	15	6	acquired	acquire	VERB
bibechana-4051	15	7	his	his	PRON
bibechana-4051	15	8	interest	interest	NOUN
bibechana-4051	15	9	in	in	ADP
bibechana-4051	15	10	problems	problem	NOUN
bibechana-4051	15	11	connected	connect	VERB
bibechana-4051	15	12	with	with	ADP
bibechana-4051	15	13	trigonometric	trigonometric	ADJ
bibechana-4051	15	14	series	series	NOUN
bibechana-4051	15	15	through	through	ADP
bibechana-4051	15	16	contact	contact	NOUN
bibechana-4051	15	17	with	with	ADP
bibechana-4051	15	18	dirichlet	dirichlet	PROPN
bibechana-4051	15	19	when	when	SCONJ
bibechana-4051	15	20	he	he	PRON
bibechana-4051	15	21	spent	spend	VERB
bibechana-4051	15	22	a	a	DET
bibechana-4051	15	23	year	year	NOUN
bibechana-4051	15	24	in	in	ADP
bibechana-4051	15	25	berlin	berlin	PROPN
bibechana-4051	15	26	.	.	PUNCT
bibechana-4051	16	1	he	he	PRON
bibechana-4051	16	2	almost	almost	ADV
bibechana-4051	16	3	certainly	certainly	ADV
bibechana-4051	16	4	attended	attend	VERB
bibechana-4051	16	5	dirichlet	dirichlet	PROPN
bibechana-4051	16	6	's	's	PART
bibechana-4051	16	7	lectures	lecture	NOUN
bibechana-4051	16	8	.	.	PUNCT
bibechana-4051	17	1	for	for	ADP
bibechana-4051	17	2	his	his	PRON
bibechana-4051	17	3	habilitationsschrift	habilitationsschrift	NOUN
bibechana-4051	17	4	(	(	PUNCT
bibechana-4051	17	5	1854	1854	NUM
bibechana-4051	17	6	)	)	PUNCT
bibechana-4051	17	7	riemann	riemann	PROPN
bibechana-4051	17	8	under	under	AUX
bibechana-4051	17	9	-	-	PUNCT
bibechana-4051	17	10	took	take	VERB
bibechana-4051	17	11	to	to	PART
bibechana-4051	17	12	study	study	VERB
bibechana-4051	17	13	the	the	DET
bibechana-4051	17	14	representation	representation	NOUN
bibechana-4051	17	15	of	of	ADP
bibechana-4051	17	16	functions	function	NOUN
bibechana-4051	17	17	by	by	ADP
bibechana-4051	17	18	trigonometric	trigonometric	ADJ
bibechana-4051	17	19	functions	function	NOUN
bibechana-4051	17	20	.	.	PUNCT
bibechana-4051	18	1	he	he	PRON
bibechana-4051	18	2	concluded	conclude	VERB
bibechana-4051	18	3	that	that	SCONJ
bibechana-4051	18	4	continuous	continuous	ADJ
bibechana-4051	18	5	functions	function	NOUN
bibechana-4051	18	6	are	be	AUX
bibechana-4051	18	7	represented	represent	VERB
bibechana-4051	18	8	by	by	ADP
bibechana-4051	18	9	fourier	fourier	NOUN
bibechana-4051	18	10	series	series	NOUN
bibechana-4051	18	11	.	.	PUNCT
bibechana-4051	19	1	he	he	PRON
bibechana-4051	19	2	also	also	ADV
bibechana-4051	19	3	concluded	conclude	VERB
bibechana-4051	19	4	that	that	SCONJ
bibechana-4051	19	5	functions	function	NOUN
bibechana-4051	19	6	not	not	PART
bibechana-4051	19	7	covered	cover	VERB
bibechana-4051	19	8	by	by	ADP
bibechana-4051	19	9	dirichlet	dirichlet	PROPN
bibechana-4051	19	10	do	do	AUX
bibechana-4051	19	11	not	not	PART
bibechana-4051	19	12	exist	exist	VERB
bibechana-4051	19	13	in	in	ADP
bibechana-4051	19	14	nature	nature	NOUN
bibechana-4051	19	15	.	.	PUNCT
bibechana-4051	20	1	but	but	CCONJ
bibechana-4051	20	2	there	there	PRON
bibechana-4051	20	3	were	be	VERB
bibechana-4051	20	4	new	new	ADJ
bibechana-4051	20	5	applications	application	NOUN
bibechana-4051	20	6	of	of	ADP
bibechana-4051	20	7	trigonometric	trigonometric	ADJ
bibechana-4051	20	8	series	series	NOUN
bibechana-4051	20	9	to	to	ADP
bibechana-4051	20	10	number	number	NOUN
bibechana-4051	20	11	theory	theory	NOUN
bibechana-4051	20	12	and	and	CCONJ
bibechana-4051	20	13	other	other	ADJ
bibechana-4051	20	14	places	place	NOUN
bibechana-4051	20	15	in	in	ADP
bibechana-4051	20	16	pure	pure	ADJ
bibechana-4051	20	17	mathematics	mathematic	NOUN
bibechana-4051	20	18	.	.	PUNCT
bibechana-4051	21	1	this	this	PRON
bibechana-4051	21	2	provided	provide	VERB
bibechana-4051	21	3	impetus	impetus	NOUN
bibechana-4051	21	4	to	to	PART
bibechana-4051	21	5	pursue	pursue	VERB
bibechana-4051	21	6	these	these	DET
bibechana-4051	21	7	foundational	foundational	ADJ
bibechana-4051	21	8	questions	question	NOUN
bibechana-4051	21	9	.	.	PUNCT
bibechana-4051	22	1	riemann	riemann	PROPN
bibechana-4051	22	2	began	begin	VERB
bibechana-4051	22	3	with	with	ADP
bibechana-4051	22	4	the	the	DET
bibechana-4051	22	5	question	question	NOUN
bibechana-4051	22	6	:	:	PUNCT
bibechana-4051	22	7	when	when	SCONJ
bibechana-4051	22	8	is	be	AUX
bibechana-4051	22	9	a	a	DET
bibechana-4051	22	10	function	function	NOUN
bibechana-4051	22	11	integrable	integrable	ADJ
bibechana-4051	22	12	?	?	PUNCT
bibechana-4051	23	1	by	by	SCONJ
bibechana-4051	23	2	that	that	SCONJ
bibechana-4051	23	3	he	he	PRON
bibechana-4051	23	4	meant	mean	VERB
bibechana-4051	23	5	,	,	PUNCT
bibechana-4051	23	6	when	when	SCONJ
bibechana-4051	23	7	do	do	AUX
bibechana-4051	23	8	the	the	DET
bibechana-4051	23	9	cauchy	cauchy	NOUN
bibechana-4051	23	10	sums	sum	NOUN
bibechana-4051	23	11	converge	converge	VERB
bibechana-4051	23	12	?	?	PUNCT
bibechana-4051	24	1	∗	∗	NOUN
bibechana-4051	24	2	corresponding	correspond	VERB
bibechana-4051	24	3	author	author	NOUN
bibechana-4051	24	4	:	:	PUNCT
bibechana-4051	24	5	mani	mani	PROPN
bibechana-4051	24	6	raj	raj	PROPN
bibechana-4051	24	7	bhattrai	bhattrai	PROPN
bibechana-4051	24	8	,	,	PUNCT
bibechana-4051	24	9	dept	dept	NOUN
bibechana-4051	24	10	.	.	PROPN
bibechana-4051	24	11	of	of	ADP
bibechana-4051	24	12	mathematics	mathematics	PROPN
bibechana-4051	24	13	,	,	PUNCT
bibechana-4051	24	14	bhanu	bhanu	PROPN
bibechana-4051	24	15	m.h.s	m.h.s	PROPN
bibechana-4051	24	16	.	.	PUNCT
bibechana-4051	25	1	school	school	NOUN
bibechana-4051	25	2	,	,	PUNCT
bibechana-4051	25	3	biratnagar	biratnagar	NOUN
bibechana-4051	25	4	,	,	PUNCT
bibechana-4051	25	5	nepal	nepal	ADJ
bibechana-4051	25	6	,	,	PUNCT
bibechana-4051	25	7	email	email	NOUN
bibechana-4051	25	8	:	:	PUNCT
bibechana-4051	25	9	manirb08@yahoo.co.in	manirb08@yahoo.co.in	PROPN
bibechana-4051	25	10	mani	mani	PROPN
bibechana-4051	25	11	raj	raj	PROPN
bibechana-4051	25	12	bhattrai	bhattrai	PROPN
bibechana-4051	25	13	/	/	SYM
bibechana-4051	25	14	bibechana	bibechana	NOUN
bibechana-4051	25	15	7	7	NUM
bibechana-4051	25	16	(	(	PUNCT
bibechana-4051	25	17	2011	2011	NUM
bibechana-4051	25	18	)	)	PUNCT
bibechana-4051	25	19	83	83	NUM
bibechana-4051	25	20	-	-	SYM
bibechana-4051	25	21	86	86	NUM
bibechana-4051	25	22	:	:	PUNCT
bibechana-4051	25	23	bmhss	bmhss	PROPN
bibechana-4051	25	24	84	84	NUM
bibechana-4051	25	25	however	however	ADV
bibechana-4051	25	26	,	,	PUNCT
bibechana-4051	25	27	riemann	riemann	PROPN
bibechana-4051	25	28	integration	integration	NOUN
bibechana-4051	25	29	does	do	AUX
bibechana-4051	25	30	not	not	PART
bibechana-4051	25	31	interact	interact	VERB
bibechana-4051	25	32	well	well	ADV
bibechana-4051	25	33	with	with	ADP
bibechana-4051	25	34	taking	take	VERB
bibechana-4051	25	35	limits	limit	NOUN
bibechana-4051	25	36	of	of	ADP
bibechana-4051	25	37	sequences	sequence	NOUN
bibechana-4051	25	38	of	of	ADP
bibechana-4051	25	39	functions	function	NOUN
bibechana-4051	25	40	,	,	PUNCT
bibechana-4051	25	41	making	make	VERB
bibechana-4051	25	42	such	such	ADJ
bibechana-4051	25	43	limiting	limiting	NOUN
bibechana-4051	25	44	processes	process	NOUN
bibechana-4051	25	45	difficult	difficult	ADJ
bibechana-4051	25	46	to	to	PART
bibechana-4051	25	47	analyze	analyze	VERB
bibechana-4051	25	48	.	.	PUNCT
bibechana-4051	26	1	this	this	PRON
bibechana-4051	26	2	is	be	AUX
bibechana-4051	26	3	of	of	ADP
bibechana-4051	26	4	prime	prime	ADJ
bibechana-4051	26	5	importance	importance	NOUN
bibechana-4051	26	6	,	,	PUNCT
bibechana-4051	26	7	for	for	ADP
bibechana-4051	26	8	instance	instance	NOUN
bibechana-4051	26	9	,	,	PUNCT
bibechana-4051	26	10	in	in	ADP
bibechana-4051	26	11	the	the	DET
bibechana-4051	26	12	study	study	NOUN
bibechana-4051	26	13	of	of	ADP
bibechana-4051	26	14	fourier	fourier	PROPN
bibechana-4051	26	15	series	series	NOUN
bibechana-4051	26	16	,	,	PUNCT
bibechana-4051	26	17	fourier	fourier	NOUN
bibechana-4051	26	18	transforms	transform	VERB
bibechana-4051	26	19	and	and	CCONJ
bibechana-4051	26	20	other	other	ADJ
bibechana-4051	26	21	topics	topic	NOUN
bibechana-4051	26	22	.	.	PUNCT
bibechana-4051	27	1	the	the	DET
bibechana-4051	27	2	lebesgue	lebesgue	NOUN
bibechana-4051	27	3	integral	integral	NOUN
bibechana-4051	27	4	is	be	AUX
bibechana-4051	27	5	better	well	ADJ
bibechana-4051	27	6	able	able	ADJ
bibechana-4051	27	7	to	to	PART
bibechana-4051	27	8	describe	describe	VERB
bibechana-4051	27	9	how	how	SCONJ
bibechana-4051	27	10	and	and	CCONJ
bibechana-4051	27	11	when	when	SCONJ
bibechana-4051	27	12	it	it	PRON
bibechana-4051	27	13	is	be	AUX
bibechana-4051	27	14	possible	possible	ADJ
bibechana-4051	27	15	to	to	PART
bibechana-4051	27	16	take	take	VERB
bibechana-4051	27	17	limits	limit	NOUN
bibechana-4051	27	18	under	under	ADP
bibechana-4051	27	19	the	the	DET
bibechana-4051	27	20	integral	integral	ADJ
bibechana-4051	27	21	sign	sign	NOUN
bibechana-4051	27	22	.	.	PUNCT
bibechana-4051	28	1	the	the	DET
bibechana-4051	28	2	lebesgue	lebesgue	ADJ
bibechana-4051	28	3	definition	definition	NOUN
bibechana-4051	28	4	considers	consider	VERB
bibechana-4051	28	5	a	a	DET
bibechana-4051	28	6	different	different	ADJ
bibechana-4051	28	7	class	class	NOUN
bibechana-4051	28	8	of	of	ADP
bibechana-4051	28	9	easily	easily	ADV
bibechana-4051	28	10	-	-	PUNCT
bibechana-4051	28	11	calculated	calculate	VERB
bibechana-4051	28	12	areas	area	NOUN
bibechana-4051	28	13	than	than	ADP
bibechana-4051	28	14	the	the	DET
bibechana-4051	28	15	riemann	riemann	PROPN
bibechana-4051	28	16	definition	definition	NOUN
bibechana-4051	28	17	,	,	PUNCT
bibechana-4051	28	18	which	which	PRON
bibechana-4051	28	19	is	be	AUX
bibechana-4051	28	20	the	the	DET
bibechana-4051	28	21	main	main	ADJ
bibechana-4051	28	22	reason	reason	NOUN
bibechana-4051	28	23	the	the	DET
bibechana-4051	28	24	lebesgue	lebesgue	NOUN
bibechana-4051	28	25	integral	integral	ADJ
bibechana-4051	28	26	is	be	AUX
bibechana-4051	28	27	better	well	ADV
bibechana-4051	28	28	behaved	behave	VERB
bibechana-4051	28	29	.	.	PUNCT
bibechana-4051	29	1	the	the	DET
bibechana-4051	29	2	lebesgue	lebesgue	PROPN
bibechana-4051	29	3	definition	definition	NOUN
bibechana-4051	29	4	also	also	ADV
bibechana-4051	29	5	makes	make	VERB
bibechana-4051	29	6	it	it	PRON
bibechana-4051	29	7	possible	possible	ADJ
bibechana-4051	29	8	to	to	PART
bibechana-4051	29	9	calculate	calculate	VERB
bibechana-4051	29	10	integrals	integral	NOUN
bibechana-4051	29	11	for	for	ADP
bibechana-4051	29	12	a	a	DET
bibechana-4051	29	13	broader	broad	ADJ
bibechana-4051	29	14	class	class	NOUN
bibechana-4051	29	15	of	of	ADP
bibechana-4051	29	16	functions	function	NOUN
bibechana-4051	29	17	.	.	PUNCT
bibechana-4051	30	1	in	in	ADP
bibechana-4051	30	2	mathematics	mathematic	NOUN
bibechana-4051	30	3	,	,	PUNCT
bibechana-4051	30	4	lebesgue	lebesgue	NOUN
bibechana-4051	30	5	integration	integration	NOUN
bibechana-4051	30	6	refers	refer	VERB
bibechana-4051	30	7	to	to	ADP
bibechana-4051	30	8	both	both	CCONJ
bibechana-4051	30	9	the	the	DET
bibechana-4051	30	10	general	general	ADJ
bibechana-4051	30	11	theory	theory	NOUN
bibechana-4051	30	12	of	of	ADP
bibechana-4051	30	13	integration	integration	NOUN
bibechana-4051	30	14	of	of	ADP
bibechana-4051	30	15	a	a	DET
bibechana-4051	30	16	function	function	NOUN
bibechana-4051	30	17	with	with	ADP
bibechana-4051	30	18	respect	respect	NOUN
bibechana-4051	30	19	to	to	ADP
bibechana-4051	30	20	a	a	DET
bibechana-4051	30	21	general	general	ADJ
bibechana-4051	30	22	measure	measure	NOUN
bibechana-4051	30	23	,	,	PUNCT
bibechana-4051	30	24	and	and	CCONJ
bibechana-4051	30	25	to	to	ADP
bibechana-4051	30	26	the	the	DET
bibechana-4051	30	27	specific	specific	ADJ
bibechana-4051	30	28	case	case	NOUN
bibechana-4051	30	29	of	of	ADP
bibechana-4051	30	30	integration	integration	NOUN
bibechana-4051	30	31	of	of	ADP
bibechana-4051	30	32	a	a	DET
bibechana-4051	30	33	function	function	NOUN
bibechana-4051	30	34	defined	define	VERB
bibechana-4051	30	35	on	on	ADP
bibechana-4051	30	36	a	a	DET
bibechana-4051	30	37	sub	sub	NOUN
bibechana-4051	30	38	-	-	NOUN
bibechana-4051	30	39	domain	domain	NOUN
bibechana-4051	30	40	of	of	ADP
bibechana-4051	30	41	the	the	DET
bibechana-4051	30	42	real	real	ADJ
bibechana-4051	30	43	line	line	NOUN
bibechana-4051	30	44	or	or	CCONJ
bibechana-4051	30	45	a	a	DET
bibechana-4051	30	46	higher	high	ADJ
bibechana-4051	30	47	dimensional	dimensional	ADJ
bibechana-4051	30	48	euclidean	euclidean	ADJ
bibechana-4051	30	49	space	space	NOUN
bibechana-4051	30	50	with	with	ADP
bibechana-4051	30	51	respect	respect	NOUN
bibechana-4051	30	52	to	to	ADP
bibechana-4051	30	53	the	the	DET
bibechana-4051	30	54	lebesgue	lebesgue	NOUN
bibechana-4051	30	55	measure	measure	NOUN
bibechana-4051	30	56	.	.	PUNCT
bibechana-4051	31	1	2	2	X
bibechana-4051	31	2	.	.	NUM
bibechana-4051	31	3	limitations	limitation	NOUN
bibechana-4051	31	4	of	of	ADP
bibechana-4051	31	5	the	the	DET
bibechana-4051	31	6	riemann	riemann	PROPN
bibechana-4051	31	7	integral	integral	PROPN
bibechana-4051	31	8	here	here	ADV
bibechana-4051	31	9	we	we	PRON
bibechana-4051	31	10	discuss	discuss	VERB
bibechana-4051	31	11	the	the	DET
bibechana-4051	31	12	limitations	limitation	NOUN
bibechana-4051	31	13	of	of	ADP
bibechana-4051	31	14	the	the	DET
bibechana-4051	31	15	riemann	riemann	PROPN
bibechana-4051	31	16	integral	integral	PROPN
bibechana-4051	31	17	and	and	CCONJ
bibechana-4051	31	18	the	the	DET
bibechana-4051	31	19	greater	great	ADJ
bibechana-4051	31	20	scope	scope	NOUN
bibechana-4051	31	21	offered	offer	VERB
bibechana-4051	31	22	by	by	ADP
bibechana-4051	31	23	the	the	DET
bibechana-4051	31	24	lebesgue	lebesgue	NOUN
bibechana-4051	31	25	integral	integral	ADJ
bibechana-4051	31	26	.	.	PUNCT
bibechana-4051	32	1	we	we	PRON
bibechana-4051	32	2	presume	presume	VERB
bibechana-4051	32	3	a	a	DET
bibechana-4051	32	4	working	work	VERB
bibechana-4051	32	5	understanding	understanding	NOUN
bibechana-4051	32	6	of	of	ADP
bibechana-4051	32	7	the	the	DET
bibechana-4051	32	8	riemann	riemann	PROPN
bibechana-4051	32	9	integral	integral	PROPN
bibechana-4051	32	10	.	.	PUNCT
bibechana-4051	33	1	with	with	ADP
bibechana-4051	33	2	the	the	DET
bibechana-4051	33	3	advent	advent	NOUN
bibechana-4051	33	4	of	of	ADP
bibechana-4051	33	5	fourier	fourier	ADJ
bibechana-4051	33	6	series	series	NOUN
bibechana-4051	33	7	,	,	PUNCT
bibechana-4051	33	8	many	many	ADJ
bibechana-4051	33	9	analytical	analytical	ADJ
bibechana-4051	33	10	problems	problem	NOUN
bibechana-4051	33	11	involving	involve	VERB
bibechana-4051	33	12	integrals	integral	NOUN
bibechana-4051	33	13	came	come	VERB
bibechana-4051	33	14	up	up	ADP
bibechana-4051	33	15	whose	whose	DET
bibechana-4051	33	16	satisfactory	satisfactory	ADJ
bibechana-4051	33	17	solution	solution	NOUN
bibechana-4051	33	18	required	require	VERB
bibechana-4051	33	19	interchanging	interchanging	ADJ
bibechana-4051	33	20	limit	limit	NOUN
bibechana-4051	33	21	processes	process	NOUN
bibechana-4051	33	22	and	and	CCONJ
bibechana-4051	33	23	integral	integral	ADJ
bibechana-4051	33	24	signs	sign	NOUN
bibechana-4051	33	25	.	.	PUNCT
bibechana-4051	34	1	however	however	ADV
bibechana-4051	34	2	,	,	PUNCT
bibechana-4051	34	3	the	the	DET
bibechana-4051	34	4	conditions	condition	NOUN
bibechana-4051	34	5	under	under	ADP
bibechana-4051	34	6	which	which	PRON
bibechana-4051	34	7	the	the	DET
bibechana-4051	34	8	integrals	integral	NOUN
bibechana-4051	34	9	(	(	PUNCT
bibechana-4051	34	10	)	)	PUNCT
bibechana-4051	34	11	(	(	PUNCT
bibechana-4051	34	12	)	)	PUNCT
bibechana-4051	35	1	k	k	X
bibechana-4051	36	1	k	k	PROPN
bibechana-4051	36	2	k	k	PROPN
bibechana-4051	37	1	k	k	PROPN
bibechana-4051	37	2	f	f	PROPN
bibechana-4051	37	3	x	x	X
bibechana-4051	37	4	dx	dx	PROPN
bibechana-4051	37	5	and	and	CCONJ
bibechana-4051	37	6	f	f	PROPN
bibechana-4051	37	7	x	x	PROPN
bibechana-4051	37	8	dx	dx	PROPN
bibechana-4051	37	9			VERB
bibechana-4051	37	10			PROPN
bibechana-4051	37	11			ADJ
bibechana-4051	37	12			PROPN
bibechana-4051	37	13			NOUN
bibechana-4051	37	14			SYM
bibechana-4051	37	15	∑	∑	PROPN
bibechana-4051	37	16	∑∫	∑∫	PROPN
bibechana-4051	37	17	∫	∫	PROPN
bibechana-4051	37	18	are	be	AUX
bibechana-4051	37	19	equally	equally	ADV
bibechana-4051	37	20	proved	prove	VERB
bibechana-4051	37	21	quite	quite	ADV
bibechana-4051	37	22	elusive	elusive	ADJ
bibechana-4051	37	23	in	in	ADP
bibechana-4051	37	24	the	the	DET
bibechana-4051	37	25	riemann	riemann	PROPN
bibechana-4051	37	26	framework	framework	NOUN
bibechana-4051	37	27	.	.	PUNCT
bibechana-4051	38	1	there	there	PRON
bibechana-4051	38	2	are	be	VERB
bibechana-4051	38	3	some	some	DET
bibechana-4051	38	4	other	other	ADJ
bibechana-4051	38	5	technical	technical	ADJ
bibechana-4051	38	6	difficulties	difficulty	NOUN
bibechana-4051	38	7	with	with	ADP
bibechana-4051	38	8	the	the	DET
bibechana-4051	38	9	riemann	riemann	PROPN
bibechana-4051	38	10	integral	integral	PROPN
bibechana-4051	38	11	.	.	PUNCT
bibechana-4051	39	1	these	these	PRON
bibechana-4051	39	2	are	be	AUX
bibechana-4051	39	3	linked	link	VERB
bibechana-4051	39	4	with	with	ADP
bibechana-4051	39	5	the	the	DET
bibechana-4051	39	6	limit	limit	NOUN
bibechana-4051	39	7	taking	take	VERB
bibechana-4051	39	8	difficulty	difficulty	NOUN
bibechana-4051	39	9	discussed	discuss	VERB
bibechana-4051	39	10	above	above	ADV
bibechana-4051	39	11	.	.	PUNCT
bibechana-4051	40	1	2.1	2.1	NUM
bibechana-4051	40	2	unsuitability	unsuitability	NOUN
bibechana-4051	40	3	for	for	ADP
bibechana-4051	40	4	unbounded	unbounded	ADJ
bibechana-4051	40	5	intervals	interval	NOUN
bibechana-4051	40	6	.	.	PUNCT
bibechana-4051	41	1	the	the	DET
bibechana-4051	41	2	riemann	riemann	PROPN
bibechana-4051	41	3	integral	integral	PROPN
bibechana-4051	41	4	can	can	AUX
bibechana-4051	41	5	only	only	ADV
bibechana-4051	41	6	integrate	integrate	VERB
bibechana-4051	41	7	functions	function	NOUN
bibechana-4051	41	8	on	on	ADP
bibechana-4051	41	9	a	a	DET
bibechana-4051	41	10	bounded	bounded	ADJ
bibechana-4051	41	11	interval	interval	NOUN
bibechana-4051	41	12	.	.	PUNCT
bibechana-4051	42	1	it	it	PRON
bibechana-4051	42	2	can	can	AUX
bibechana-4051	42	3	however	however	ADV
bibechana-4051	42	4	be	be	AUX
bibechana-4051	42	5	extended	extend	VERB
bibechana-4051	42	6	to	to	ADP
bibechana-4051	42	7	unbounded	unbounded	ADJ
bibechana-4051	42	8	intervals	interval	NOUN
bibechana-4051	42	9	by	by	ADP
bibechana-4051	42	10	taking	take	VERB
bibechana-4051	42	11	limits	limit	NOUN
bibechana-4051	42	12	,	,	PUNCT
bibechana-4051	42	13	so	so	ADV
bibechana-4051	42	14	long	long	ADV
bibechana-4051	42	15	as	as	SCONJ
bibechana-4051	42	16	this	this	PRON
bibechana-4051	42	17	does	do	AUX
bibechana-4051	42	18	n't	not	PART
bibechana-4051	42	19	yield	yield	VERB
bibechana-4051	42	20	an	an	DET
bibechana-4051	42	21	answer	answer	NOUN
bibechana-4051	42	22	such	such	ADJ
bibechana-4051	42	23	as	as	ADP
bibechana-4051	42	24	∞÷∞	∞÷∞	NUM
bibechana-4051	42	25	.	.	PUNCT
bibechana-4051	43	1	3	3	X
bibechana-4051	43	2	.	.	X
bibechana-4051	43	3	domain	domain	NOUN
bibechana-4051	43	4	of	of	ADP
bibechana-4051	43	5	integration	integration	NOUN
bibechana-4051	43	6	a	a	DET
bibechana-4051	43	7	technical	technical	ADJ
bibechana-4051	43	8	issue	issue	NOUN
bibechana-4051	43	9	in	in	ADP
bibechana-4051	43	10	lebesgue	lebesgue	ADJ
bibechana-4051	43	11	integration	integration	NOUN
bibechana-4051	43	12	is	be	AUX
bibechana-4051	43	13	that	that	SCONJ
bibechana-4051	43	14	the	the	DET
bibechana-4051	43	15	domain	domain	NOUN
bibechana-4051	43	16	of	of	ADP
bibechana-4051	43	17	integration	integration	NOUN
bibechana-4051	43	18	is	be	AUX
bibechana-4051	43	19	defined	define	VERB
bibechana-4051	43	20	as	as	ADP
bibechana-4051	43	21	a	a	DET
bibechana-4051	43	22	set	set	NOUN
bibechana-4051	43	23	(	(	PUNCT
bibechana-4051	43	24	a	a	DET
bibechana-4051	43	25	subset	subset	NOUN
bibechana-4051	43	26	of	of	ADP
bibechana-4051	43	27	a	a	DET
bibechana-4051	43	28	measure	measure	NOUN
bibechana-4051	43	29	space	space	NOUN
bibechana-4051	43	30	)	)	PUNCT
bibechana-4051	43	31	,	,	PUNCT
bibechana-4051	43	32	with	with	ADP
bibechana-4051	43	33	no	no	DET
bibechana-4051	43	34	notion	notion	NOUN
bibechana-4051	43	35	of	of	ADP
bibechana-4051	43	36	orientation	orientation	NOUN
bibechana-4051	43	37	.	.	PUNCT
bibechana-4051	44	1	in	in	ADP
bibechana-4051	44	2	elementary	elementary	ADJ
bibechana-4051	44	3	calculus	calculus	NOUN
bibechana-4051	44	4	,	,	PUNCT
bibechana-4051	44	5	one	one	NUM
bibechana-4051	44	6	defines	define	VERB
bibechana-4051	44	7	integration	integration	NOUN
bibechana-4051	44	8	with	with	ADP
bibechana-4051	44	9	respect	respect	NOUN
bibechana-4051	44	10	to	to	ADP
bibechana-4051	44	11	an	an	DET
bibechana-4051	44	12	orientation	orientation	NOUN
bibechana-4051	44	13	:	:	PUNCT
bibechana-4051	44	14	∫	∫	PROPN
bibechana-4051	44	15	∫−=	∫−=	PROPN
bibechana-4051	44	16	a	a	DET
bibechana-4051	44	17	b	b	PROPN
bibechana-4051	44	18	b	b	NOUN
bibechana-4051	44	19	a	a	DET
bibechana-4051	44	20	ff	ff	NOUN
bibechana-4051	44	21	.	.	PUNCT
bibechana-4051	45	1	generalizing	generalize	VERB
bibechana-4051	45	2	this	this	PRON
bibechana-4051	45	3	to	to	ADP
bibechana-4051	45	4	higher	high	ADJ
bibechana-4051	45	5	dimensions	dimension	NOUN
bibechana-4051	45	6	yields	yield	NOUN
bibechana-4051	45	7	integration	integration	NOUN
bibechana-4051	45	8	of	of	ADP
bibechana-4051	45	9	differential	differential	ADJ
bibechana-4051	45	10	forms	form	NOUN
bibechana-4051	45	11	.	.	PUNCT
bibechana-4051	46	1	by	by	ADP
bibechana-4051	46	2	contrast	contrast	NOUN
bibechana-4051	46	3	,	,	PUNCT
bibechana-4051	46	4	lebesgue	lebesgue	ADJ
bibechana-4051	46	5	integration	integration	NOUN
bibechana-4051	46	6	provides	provide	VERB
bibechana-4051	46	7	an	an	DET
bibechana-4051	46	8	alternative	alternative	ADJ
bibechana-4051	46	9	generalization	generalization	NOUN
bibechana-4051	46	10	,	,	PUNCT
bibechana-4051	46	11	integrating	integrate	VERB
bibechana-4051	46	12	over	over	ADP
bibechana-4051	46	13	subsets	subset	NOUN
bibechana-4051	46	14	with	with	ADP
bibechana-4051	46	15	respect	respect	NOUN
bibechana-4051	46	16	to	to	ADP
bibechana-4051	46	17	a	a	DET
bibechana-4051	46	18	measure	measure	NOUN
bibechana-4051	46	19	;	;	PUNCT
bibechana-4051	46	20	this	this	PRON
bibechana-4051	46	21	can	can	AUX
bibechana-4051	46	22	be	be	AUX
bibechana-4051	46	23	notated	notate	VERB
bibechana-4051	46	24	as	as	ADP
bibechana-4051	46	25	∫	∫	PROPN
bibechana-4051	46	26	∫	∫	PROPN
bibechana-4051	46	27	µ=µ	µ=µ	PROPN
bibechana-4051	46	28	a	a	DET
bibechana-4051	46	29	]	]	X
bibechana-4051	46	30	b	b	NOUN
bibechana-4051	46	31	,	,	PUNCT
bibechana-4051	46	32	a	a	DET
bibechana-4051	46	33	[	[	PUNCT
bibechana-4051	46	34	fdfd	fdfd	NOUN
bibechana-4051	46	35	to	to	PART
bibechana-4051	46	36	indicate	indicate	VERB
bibechana-4051	46	37	integration	integration	NOUN
bibechana-4051	46	38	over	over	ADP
bibechana-4051	46	39	a	a	DET
bibechana-4051	46	40	subset	subset	NOUN
bibechana-4051	46	41	a.	a.	NOUN
bibechana-4051	46	42	for	for	ADP
bibechana-4051	46	43	details	detail	NOUN
bibechana-4051	46	44	on	on	ADP
bibechana-4051	46	45	the	the	DET
bibechana-4051	46	46	relation	relation	NOUN
bibechana-4051	46	47	between	between	ADP
bibechana-4051	46	48	these	these	DET
bibechana-4051	46	49	generalizations	generalization	NOUN
bibechana-4051	46	50	,	,	PUNCT
bibechana-4051	46	51	see	see	VERB
bibechana-4051	46	52	differential	differential	ADJ
bibechana-4051	46	53	form	form	NOUN
bibechana-4051	46	54	:	:	PUNCT
bibechana-4051	46	55	relation	relation	NOUN
bibechana-4051	46	56	with	with	ADP
bibechana-4051	46	57	measures	measure	NOUN
bibechana-4051	46	58	.	.	PUNCT
bibechana-4051	47	1	4	4	X
bibechana-4051	47	2	.	.	X
bibechana-4051	47	3	intuitive	intuitive	ADJ
bibechana-4051	47	4	interpretation	interpretation	NOUN
bibechana-4051	47	5	to	to	PART
bibechana-4051	47	6	get	get	VERB
bibechana-4051	47	7	some	some	DET
bibechana-4051	47	8	intuition	intuition	NOUN
bibechana-4051	47	9	about	about	ADP
bibechana-4051	47	10	the	the	DET
bibechana-4051	47	11	different	different	ADJ
bibechana-4051	47	12	approaches	approach	NOUN
bibechana-4051	47	13	to	to	ADP
bibechana-4051	47	14	integration	integration	NOUN
bibechana-4051	47	15	,	,	PUNCT
bibechana-4051	47	16	let	let	VERB
bibechana-4051	47	17	us	we	PRON
bibechana-4051	47	18	imagine	imagine	VERB
bibechana-4051	47	19	that	that	SCONJ
bibechana-4051	47	20	it	it	PRON
bibechana-4051	47	21	is	be	AUX
bibechana-4051	47	22	desired	desire	VERB
bibechana-4051	47	23	to	to	PART
bibechana-4051	47	24	find	find	VERB
bibechana-4051	47	25	a	a	DET
bibechana-4051	47	26	mountain	mountain	NOUN
bibechana-4051	47	27	's	's	PART
bibechana-4051	47	28	volume	volume	NOUN
bibechana-4051	47	29	(	(	PUNCT
bibechana-4051	47	30	above	above	ADP
bibechana-4051	47	31	sea	sea	NOUN
bibechana-4051	47	32	level	level	NOUN
bibechana-4051	47	33	)	)	PUNCT
bibechana-4051	47	34	.	.	PUNCT
bibechana-4051	48	1	mani	mani	PROPN
bibechana-4051	48	2	raj	raj	PROPN
bibechana-4051	48	3	bhattrai	bhattrai	PROPN
bibechana-4051	48	4	/	/	SYM
bibechana-4051	48	5	bibechana	bibechana	NOUN
bibechana-4051	48	6	7	7	NUM
bibechana-4051	48	7	(	(	PUNCT
bibechana-4051	48	8	2011	2011	NUM
bibechana-4051	48	9	)	)	PUNCT
bibechana-4051	48	10	83	83	NUM
bibechana-4051	48	11	-	-	SYM
bibechana-4051	48	12	86	86	NUM
bibechana-4051	48	13	:	:	PUNCT
bibechana-4051	48	14	bmhss	bmhss	PROPN
bibechana-4051	48	15	85	85	NUM
bibechana-4051	48	16	4.1	4.1	NUM
bibechana-4051	48	17	the	the	DET
bibechana-4051	48	18	riemann	riemann	PROPN
bibechana-4051	48	19	-	-	PUNCT
bibechana-4051	48	20	darboux	darboux	VERB
bibechana-4051	48	21	approach	approach	NOUN
bibechana-4051	48	22	divide	divide	VERB
bibechana-4051	48	23	the	the	DET
bibechana-4051	48	24	base	base	NOUN
bibechana-4051	48	25	of	of	ADP
bibechana-4051	48	26	the	the	DET
bibechana-4051	48	27	mountain	mountain	NOUN
bibechana-4051	48	28	into	into	ADP
bibechana-4051	48	29	a	a	DET
bibechana-4051	48	30	grid	grid	NOUN
bibechana-4051	48	31	of	of	ADP
bibechana-4051	48	32	1	1	NUM
bibechana-4051	48	33	meter	meter	NOUN
bibechana-4051	48	34	squares	square	NOUN
bibechana-4051	48	35	.	.	PUNCT
bibechana-4051	49	1	measure	measure	VERB
bibechana-4051	49	2	the	the	DET
bibechana-4051	49	3	altitude	altitude	NOUN
bibechana-4051	49	4	of	of	ADP
bibechana-4051	49	5	the	the	DET
bibechana-4051	49	6	mountain	mountain	NOUN
bibechana-4051	49	7	at	at	ADP
bibechana-4051	49	8	the	the	DET
bibechana-4051	49	9	center	center	NOUN
bibechana-4051	49	10	of	of	ADP
bibechana-4051	49	11	each	each	DET
bibechana-4051	49	12	square	square	NOUN
bibechana-4051	49	13	.	.	PUNCT
bibechana-4051	50	1	the	the	DET
bibechana-4051	50	2	volume	volume	NOUN
bibechana-4051	50	3	on	on	ADP
bibechana-4051	50	4	a	a	DET
bibechana-4051	50	5	single	single	ADJ
bibechana-4051	50	6	grid	grid	NOUN
bibechana-4051	50	7	square	square	NOUN
bibechana-4051	50	8	is	be	AUX
bibechana-4051	50	9	approximately	approximately	ADV
bibechana-4051	50	10	1x1(altitude	1x1(altitude	NUM
bibechana-4051	50	11	)	)	PUNCT
bibechana-4051	50	12	,	,	PUNCT
bibechana-4051	50	13	so	so	CCONJ
bibechana-4051	50	14	the	the	DET
bibechana-4051	50	15	total	total	ADJ
bibechana-4051	50	16	volume	volume	NOUN
bibechana-4051	50	17	is	be	AUX
bibechana-4051	50	18	the	the	DET
bibechana-4051	50	19	sum	sum	NOUN
bibechana-4051	50	20	of	of	ADP
bibechana-4051	50	21	the	the	DET
bibechana-4051	50	22	altitudes	altitude	NOUN
bibechana-4051	50	23	.	.	PUNCT
bibechana-4051	51	1	4.2	4.2	NUM
bibechana-4051	51	2	the	the	DET
bibechana-4051	51	3	lebesgue	lebesgue	NOUN
bibechana-4051	51	4	approach	approach	NOUN
bibechana-4051	51	5	draw	draw	VERB
bibechana-4051	51	6	a	a	DET
bibechana-4051	51	7	contour	contour	NOUN
bibechana-4051	51	8	map	map	NOUN
bibechana-4051	51	9	of	of	ADP
bibechana-4051	51	10	the	the	DET
bibechana-4051	51	11	mountain	mountain	NOUN
bibechana-4051	51	12	,	,	PUNCT
bibechana-4051	51	13	where	where	SCONJ
bibechana-4051	51	14	each	each	DET
bibechana-4051	51	15	contour	contour	NOUN
bibechana-4051	51	16	is	be	AUX
bibechana-4051	51	17	1	1	NUM
bibechana-4051	51	18	meter	meter	NOUN
bibechana-4051	51	19	of	of	ADP
bibechana-4051	51	20	altitude	altitude	NOUN
bibechana-4051	51	21	apart	apart	ADV
bibechana-4051	51	22	.	.	PUNCT
bibechana-4051	52	1	the	the	DET
bibechana-4051	52	2	volume	volume	NOUN
bibechana-4051	52	3	of	of	ADP
bibechana-4051	52	4	earth	earth	NOUN
bibechana-4051	52	5	contained	contain	VERB
bibechana-4051	52	6	in	in	ADP
bibechana-4051	52	7	a	a	DET
bibechana-4051	52	8	single	single	ADJ
bibechana-4051	52	9	contour	contour	NOUN
bibechana-4051	52	10	is	be	AUX
bibechana-4051	52	11	approximately	approximately	ADV
bibechana-4051	52	12	that	that	PRON
bibechana-4051	52	13	contour	contour	NOUN
bibechana-4051	52	14	's	's	PART
bibechana-4051	52	15	area	area	NOUN
bibechana-4051	52	16	times	time	VERB
bibechana-4051	52	17	its	its	PRON
bibechana-4051	52	18	height	height	NOUN
bibechana-4051	52	19	.	.	PUNCT
bibechana-4051	53	1	so	so	ADV
bibechana-4051	53	2	the	the	DET
bibechana-4051	53	3	total	total	ADJ
bibechana-4051	53	4	volume	volume	NOUN
bibechana-4051	53	5	is	be	AUX
bibechana-4051	53	6	the	the	DET
bibechana-4051	53	7	sum	sum	NOUN
bibechana-4051	53	8	of	of	ADP
bibechana-4051	53	9	these	these	DET
bibechana-4051	53	10	volumes	volume	NOUN
bibechana-4051	53	11	.	.	PUNCT
bibechana-4051	54	1	folland	folland	PROPN
bibechana-4051	55	1	[	[	X
bibechana-4051	55	2	1	1	NUM
bibechana-4051	55	3	]	]	PUNCT
bibechana-4051	55	4	summarizes	summarize	VERB
bibechana-4051	55	5	the	the	DET
bibechana-4051	55	6	difference	difference	NOUN
bibechana-4051	55	7	between	between	ADP
bibechana-4051	55	8	the	the	DET
bibechana-4051	55	9	riemann	riemann	PROPN
bibechana-4051	55	10	and	and	CCONJ
bibechana-4051	55	11	lebesgue	lebesgue	PROPN
bibechana-4051	55	12	approaches	approach	NOUN
bibechana-4051	55	13	thus	thus	ADV
bibechana-4051	55	14	:	:	PUNCT
bibechana-4051	55	15	"	"	PUNCT
bibechana-4051	55	16	to	to	PART
bibechana-4051	55	17	compute	compute	VERB
bibechana-4051	55	18	the	the	DET
bibechana-4051	55	19	riemann	riemann	PROPN
bibechana-4051	55	20	integral	integral	NOUN
bibechana-4051	55	21	of	of	ADP
bibechana-4051	55	22	f	f	PROPN
bibechana-4051	55	23	,	,	PUNCT
bibechana-4051	55	24	one	one	NUM
bibechana-4051	55	25	partitions	partition	VERB
bibechana-4051	55	26	the	the	DET
bibechana-4051	55	27	domain	domain	NOUN
bibechana-4051	55	28	[	[	X
bibechana-4051	55	29	a	a	X
bibechana-4051	55	30	,	,	PUNCT
bibechana-4051	55	31	b	b	NOUN
bibechana-4051	55	32	]	]	X
bibechana-4051	55	33	into	into	ADP
bibechana-4051	55	34	subintervals	subinterval	NOUN
bibechana-4051	55	35	"	"	PUNCT
bibechana-4051	55	36	,	,	PUNCT
bibechana-4051	55	37	while	while	SCONJ
bibechana-4051	55	38	in	in	ADP
bibechana-4051	55	39	the	the	DET
bibechana-4051	55	40	lebesgue	lebesgue	NOUN
bibechana-4051	55	41	integral	integral	ADJ
bibechana-4051	55	42	,	,	PUNCT
bibechana-4051	55	43	"	"	PUNCT
bibechana-4051	55	44	one	one	NUM
bibechana-4051	55	45	is	be	AUX
bibechana-4051	55	46	in	in	ADP
bibechana-4051	55	47	effect	effect	NOUN
bibechana-4051	55	48	partitioning	partition	VERB
bibechana-4051	55	49	the	the	DET
bibechana-4051	55	50	range	range	NOUN
bibechana-4051	55	51	of	of	ADP
bibechana-4051	55	52	f	f	X
bibechana-4051	55	53	"	"	PUNCT
bibechana-4051	55	54	.	.	PUNCT
bibechana-4051	56	1	the	the	DET
bibechana-4051	56	2	riemann	riemann	PROPN
bibechana-4051	56	3	integral	integral	PROPN
bibechana-4051	56	4	is	be	AUX
bibechana-4051	56	5	a	a	DET
bibechana-4051	56	6	linear	linear	ADJ
bibechana-4051	56	7	transformation	transformation	NOUN
bibechana-4051	56	8	;	;	PUNCT
bibechana-4051	56	9	that	that	PRON
bibechana-4051	56	10	is	is	ADV
bibechana-4051	56	11	,	,	PUNCT
bibechana-4051	56	12	if	if	SCONJ
bibechana-4051	56	13	f	f	PROPN
bibechana-4051	56	14	and	and	CCONJ
bibechana-4051	56	15	g	g	PROPN
bibechana-4051	56	16	are	be	AUX
bibechana-4051	56	17	riemann	riemann	NOUN
bibechana-4051	56	18	-	-	PUNCT
bibechana-4051	56	19	integrable	integrable	ADJ
bibechana-4051	56	20	on	on	ADP
bibechana-4051	56	21	[	[	X
bibechana-4051	56	22	a	a	DET
bibechana-4051	56	23	,	,	PUNCT
bibechana-4051	56	24	b	b	NOUN
bibechana-4051	56	25	]	]	PUNCT
bibechana-4051	56	26	and	and	CCONJ
bibechana-4051	56	27	α	α	NOUN
bibechana-4051	56	28	and	and	CCONJ
bibechana-4051	56	29	β	β	PROPN
bibechana-4051	56	30	are	be	AUX
bibechana-4051	56	31	constants	constant	NOUN
bibechana-4051	56	32	,	,	PUNCT
bibechana-4051	56	33	then	then	ADV
bibechana-4051	56	34	(	(	PUNCT
bibechana-4051	56	35	)	)	PUNCT
bibechana-4051	56	36	(	(	PUNCT
bibechana-4051	56	37	)	)	PUNCT
bibechana-4051	56	38	(	(	PUNCT
bibechana-4051	56	39	)	)	PUNCT
bibechana-4051	56	40	b	b	X
bibechana-4051	56	41	b	b	X
bibechana-4051	56	42	b	b	PROPN
bibechana-4051	56	43	a	a	PRON
bibechana-4051	56	44	a	a	PRON
bibechana-4051	56	45	a	a	DET
bibechana-4051	56	46	f	f	NOUN
bibechana-4051	56	47	g	g	PROPN
bibechana-4051	56	48	dx	dx	PROPN
bibechana-4051	57	1	f	f	PROPN
bibechana-4051	57	2	x	x	X
bibechana-4051	57	3	dx	dx	PROPN
bibechana-4051	57	4	g	g	PROPN
bibechana-4051	57	5	x	x	PROPN
bibechana-4051	57	6	dxα	dxα	PROPN
bibechana-4051	57	7	+	+	X
bibechana-4051	57	8	β	β	X
bibechana-4051	57	9	=	=	VERB
bibechana-4051	57	10	α	α	PROPN
bibechana-4051	57	11	+	+	NOUN
bibechana-4051	57	12	β∫	β∫	NUM
bibechana-4051	57	13	∫	∫	PROPN
bibechana-4051	57	14	∫	∫	PROPN
bibechana-4051	57	15	because	because	SCONJ
bibechana-4051	57	16	the	the	DET
bibechana-4051	57	17	riemann	riemann	PROPN
bibechana-4051	57	18	integral	integral	NOUN
bibechana-4051	57	19	of	of	ADP
bibechana-4051	57	20	a	a	DET
bibechana-4051	57	21	function	function	NOUN
bibechana-4051	57	22	is	be	AUX
bibechana-4051	57	23	a	a	DET
bibechana-4051	57	24	number	number	NOUN
bibechana-4051	57	25	,	,	PUNCT
bibechana-4051	57	26	this	this	PRON
bibechana-4051	57	27	makes	make	VERB
bibechana-4051	57	28	the	the	DET
bibechana-4051	57	29	riemann	riemann	PROPN
bibechana-4051	57	30	integral	integral	ADJ
bibechana-4051	57	31	a	a	DET
bibechana-4051	57	32	linear	linear	ADJ
bibechana-4051	57	33	functional	functional	NOUN
bibechana-4051	57	34	on	on	ADP
bibechana-4051	57	35	the	the	DET
bibechana-4051	57	36	vector	vector	NOUN
bibechana-4051	57	37	space	space	NOUN
bibechana-4051	57	38	of	of	ADP
bibechana-4051	57	39	riemann	riemann	PROPN
bibechana-4051	57	40	-	-	PUNCT
bibechana-4051	57	41	integrable	integrable	ADJ
bibechana-4051	57	42	functions	function	NOUN
bibechana-4051	57	43	.	.	PUNCT
bibechana-4051	58	1	it	it	PRON
bibechana-4051	58	2	can	can	AUX
bibechana-4051	58	3	be	be	AUX
bibechana-4051	58	4	shown	show	VERB
bibechana-4051	58	5	that	that	SCONJ
bibechana-4051	58	6	a	a	DET
bibechana-4051	58	7	real	real	ADV
bibechana-4051	58	8	-	-	PUNCT
bibechana-4051	58	9	valued	value	VERB
bibechana-4051	58	10	function	function	NOUN
bibechana-4051	58	11	f	f	PROPN
bibechana-4051	58	12	on	on	ADP
bibechana-4051	58	13	[	[	X
bibechana-4051	58	14	a	a	DET
bibechana-4051	58	15	,	,	PUNCT
bibechana-4051	58	16	b	b	NOUN
bibechana-4051	58	17	]	]	X
bibechana-4051	58	18	is	be	AUX
bibechana-4051	58	19	riemann	riemann	PROPN
bibechana-4051	58	20	-	-	PUNCT
bibechana-4051	58	21	integrable	integrable	ADJ
bibechana-4051	58	22	if	if	SCONJ
bibechana-4051	58	23	and	and	CCONJ
bibechana-4051	58	24	only	only	ADV
bibechana-4051	58	25	if	if	SCONJ
bibechana-4051	58	26	it	it	PRON
bibechana-4051	58	27	is	be	AUX
bibechana-4051	58	28	bounded	bound	VERB
bibechana-4051	58	29	and	and	CCONJ
bibechana-4051	58	30	continuous	continuous	ADJ
bibechana-4051	58	31	almost	almost	ADV
bibechana-4051	58	32	everywhere	everywhere	ADV
bibechana-4051	58	33	in	in	ADP
bibechana-4051	58	34	the	the	DET
bibechana-4051	58	35	sense	sense	NOUN
bibechana-4051	58	36	of	of	ADP
bibechana-4051	58	37	lebesgue	lebesgue	ADJ
bibechana-4051	58	38	measure	measure	NOUN
bibechana-4051	58	39	.	.	PUNCT
bibechana-4051	59	1	if	if	SCONJ
bibechana-4051	59	2	a	a	DET
bibechana-4051	59	3	real	real	ADV
bibechana-4051	59	4	-	-	PUNCT
bibechana-4051	59	5	valued	value	VERB
bibechana-4051	59	6	function	function	NOUN
bibechana-4051	59	7	on	on	ADP
bibechana-4051	59	8	[	[	X
bibechana-4051	59	9	a	a	X
bibechana-4051	59	10	,	,	PUNCT
bibechana-4051	59	11	b	b	NOUN
bibechana-4051	59	12	]	]	X
bibechana-4051	59	13	is	be	AUX
bibechana-4051	59	14	riemann	riemann	PROPN
bibechana-4051	59	15	-	-	PUNCT
bibechana-4051	59	16	integrable	integrable	ADJ
bibechana-4051	59	17	,	,	PUNCT
bibechana-4051	59	18	it	it	PRON
bibechana-4051	59	19	is	be	AUX
bibechana-4051	59	20	lebesgue	lebesgue	NOUN
bibechana-4051	59	21	-	-	PUNCT
bibechana-4051	59	22	integrable	integrable	ADJ
bibechana-4051	59	23	.	.	PUNCT
bibechana-4051	60	1	if	if	SCONJ
bibechana-4051	60	2	function	function	NOUN
bibechana-4051	60	3	is	be	AUX
bibechana-4051	60	4	a	a	DET
bibechana-4051	60	5	uniformly	uniformly	ADV
bibechana-4051	60	6	convergent	convergent	ADJ
bibechana-4051	60	7	sequence	sequence	NOUN
bibechana-4051	60	8	on	on	ADP
bibechana-4051	60	9	[	[	X
bibechana-4051	60	10	a	a	DET
bibechana-4051	60	11	,	,	PUNCT
bibechana-4051	60	12	b	b	NOUN
bibechana-4051	60	13	]	]	PUNCT
bibechana-4051	60	14	with	with	ADP
bibechana-4051	60	15	limit	limit	NOUN
bibechana-4051	60	16	f	f	X
bibechana-4051	60	17	,	,	PUNCT
bibechana-4051	60	18	then	then	ADV
bibechana-4051	60	19	riemann	riemann	PROPN
bibechana-4051	60	20	integrability	integrability	NOUN
bibechana-4051	60	21	of	of	ADP
bibechana-4051	60	22	all	all	DET
bibechana-4051	60	23	function	function	NOUN
bibechana-4051	60	24	implies	imply	VERB
bibechana-4051	60	25	riemann	riemann	PROPN
bibechana-4051	60	26	integrability	integrability	NOUN
bibechana-4051	60	27	of	of	ADP
bibechana-4051	60	28	f	f	PROPN
bibechana-4051	60	29	,	,	PUNCT
bibechana-4051	60	30	and	and	CCONJ
bibechana-4051	61	1	b	b	X
bibechana-4051	61	2	b	b	PROPN
bibechana-4051	61	3	b	b	PROPN
bibechana-4051	61	4	n	n	CCONJ
bibechana-4051	61	5	n	n	CCONJ
bibechana-4051	61	6	n	n	PROPN
bibechana-4051	61	7	n	n	ADV
bibechana-4051	61	8	a	a	PRON
bibechana-4051	61	9	a	a	PRON
bibechana-4051	61	10	a	a	PRON
bibechana-4051	61	11	f	f	NOUN
bibechana-4051	61	12	dx	dx	PROPN
bibechana-4051	62	1	lim	lim	PROPN
bibechana-4051	62	2	f	f	PROPN
bibechana-4051	63	1	dx	dx	PROPN
bibechana-4051	64	1	lim	lim	PROPN
bibechana-4051	64	2	f	f	PROPN
bibechana-4051	64	3	dx	dx	PROPN
bibechana-4051	64	4	→	→	SYM
bibechana-4051	64	5	∞	∞	PROPN
bibechana-4051	64	6	→	→	SYM
bibechana-4051	64	7	∞	∞	NUM
bibechana-4051	64	8	=	=	SYM
bibechana-4051	64	9	=	=	NUM
bibechana-4051	64	10	∫	∫	PROPN
bibechana-4051	64	11	∫	∫	PROPN
bibechana-4051	64	12	∫	∫	PROPN
bibechana-4051	64	13	if	if	SCONJ
bibechana-4051	64	14	a	a	DET
bibechana-4051	64	15	real	real	ADV
bibechana-4051	64	16	-	-	PUNCT
bibechana-4051	64	17	valued	value	VERB
bibechana-4051	64	18	function	function	NOUN
bibechana-4051	64	19	is	be	AUX
bibechana-4051	64	20	monotone	monotone	ADJ
bibechana-4051	64	21	on	on	ADP
bibechana-4051	64	22	the	the	DET
bibechana-4051	64	23	interval	interval	NOUN
bibechana-4051	64	24	[	[	X
bibechana-4051	64	25	a	a	X
bibechana-4051	64	26	,	,	PUNCT
bibechana-4051	64	27	b	b	NOUN
bibechana-4051	64	28	]	]	X
bibechana-4051	64	29	,	,	PUNCT
bibechana-4051	64	30	it	it	PRON
bibechana-4051	64	31	is	be	AUX
bibechana-4051	64	32	riemann	riemann	PROPN
bibechana-4051	64	33	-	-	PUNCT
bibechana-4051	64	34	integrable	integrable	ADJ
bibechana-4051	64	35	,	,	PUNCT
bibechana-4051	64	36	since	since	SCONJ
bibechana-4051	64	37	its	its	PRON
bibechana-4051	64	38	set	set	NOUN
bibechana-4051	64	39	of	of	ADP
bibechana-4051	64	40	discontinuities	discontinuity	NOUN
bibechana-4051	64	41	is	be	AUX
bibechana-4051	64	42	denumerable	denumerable	ADJ
bibechana-4051	64	43	,	,	PUNCT
bibechana-4051	64	44	and	and	CCONJ
bibechana-4051	64	45	therefore	therefore	ADV
bibechana-4051	64	46	of	of	ADP
bibechana-4051	64	47	lebesgue	lebesgue	ADJ
bibechana-4051	64	48	measure	measure	NOUN
bibechana-4051	64	49	zero	zero	NUM
bibechana-4051	64	50	.	.	PUNCT
bibechana-4051	65	1	5	5	NUM
bibechana-4051	65	2	.	.	NOUN
bibechana-4051	65	3	alternative	alternative	ADJ
bibechana-4051	65	4	formulations	formulation	NOUN
bibechana-4051	65	5	it	it	PRON
bibechana-4051	65	6	is	be	AUX
bibechana-4051	65	7	possible	possible	ADJ
bibechana-4051	65	8	to	to	PART
bibechana-4051	65	9	develop	develop	VERB
bibechana-4051	65	10	the	the	DET
bibechana-4051	65	11	integral	integral	ADJ
bibechana-4051	65	12	with	with	ADP
bibechana-4051	65	13	respect	respect	NOUN
bibechana-4051	65	14	to	to	ADP
bibechana-4051	65	15	the	the	DET
bibechana-4051	65	16	lebesgue	lebesgue	ADJ
bibechana-4051	65	17	measure	measure	NOUN
bibechana-4051	65	18	without	without	ADP
bibechana-4051	65	19	relying	rely	VERB
bibechana-4051	65	20	on	on	ADP
bibechana-4051	65	21	the	the	DET
bibechana-4051	65	22	full	full	ADJ
bibechana-4051	65	23	machinery	machinery	NOUN
bibechana-4051	65	24	of	of	ADP
bibechana-4051	65	25	measure	measure	NOUN
bibechana-4051	65	26	theory	theory	NOUN
bibechana-4051	65	27	.	.	PUNCT
bibechana-4051	66	1	one	one	NUM
bibechana-4051	66	2	such	such	ADJ
bibechana-4051	66	3	approach	approach	NOUN
bibechana-4051	66	4	is	be	AUX
bibechana-4051	66	5	provided	provide	VERB
bibechana-4051	66	6	by	by	ADP
bibechana-4051	66	7	daniell	daniell	PROPN
bibechana-4051	66	8	integral	integral	PROPN
bibechana-4051	67	1	[	[	X
bibechana-4051	67	2	3	3	NUM
bibechana-4051	67	3	]	]	PUNCT
bibechana-4051	67	4	.	.	PUNCT
bibechana-4051	68	1	there	there	PRON
bibechana-4051	68	2	is	be	VERB
bibechana-4051	68	3	also	also	ADV
bibechana-4051	68	4	an	an	DET
bibechana-4051	68	5	alternative	alternative	ADJ
bibechana-4051	68	6	approach	approach	NOUN
bibechana-4051	68	7	to	to	ADP
bibechana-4051	68	8	developing	develop	VERB
bibechana-4051	68	9	the	the	DET
bibechana-4051	68	10	theory	theory	NOUN
bibechana-4051	68	11	of	of	ADP
bibechana-4051	68	12	integration	integration	NOUN
bibechana-4051	68	13	via	via	ADP
bibechana-4051	68	14	methods	method	NOUN
bibechana-4051	68	15	of	of	ADP
bibechana-4051	68	16	functional	functional	ADJ
bibechana-4051	68	17	analysis	analysis	NOUN
bibechana-4051	68	18	.	.	PUNCT
bibechana-4051	69	1	the	the	DET
bibechana-4051	69	2	riemann	riemann	PROPN
bibechana-4051	69	3	integral	integral	PROPN
bibechana-4051	69	4	exists	exist	VERB
bibechana-4051	69	5	for	for	ADP
bibechana-4051	69	6	any	any	DET
bibechana-4051	69	7	continuous	continuous	ADJ
bibechana-4051	69	8	function	function	NOUN
bibechana-4051	69	9	f	f	PROPN
bibechana-4051	69	10	of	of	ADP
bibechana-4051	69	11	compact	compact	ADJ
bibechana-4051	69	12	support	support	NOUN
bibechana-4051	69	13	defined	define	VERB
bibechana-4051	69	14	on	on	ADP
bibechana-4051	69	15	rn	rn	PROPN
bibechana-4051	69	16	(	(	PUNCT
bibechana-4051	69	17	or	or	CCONJ
bibechana-4051	69	18	a	a	DET
bibechana-4051	69	19	fixed	fix	VERB
bibechana-4051	69	20	open	open	ADJ
bibechana-4051	69	21	subset	subset	NOUN
bibechana-4051	69	22	)	)	PUNCT
bibechana-4051	69	23	.	.	PUNCT
bibechana-4051	70	1	integrals	integral	NOUN
bibechana-4051	70	2	of	of	ADP
bibechana-4051	70	3	more	more	ADJ
bibechana-4051	70	4	general	general	ADJ
bibechana-4051	70	5	functions	function	NOUN
bibechana-4051	70	6	can	can	AUX
bibechana-4051	70	7	be	be	AUX
bibechana-4051	70	8	built	build	VERB
bibechana-4051	70	9	starting	start	VERB
bibechana-4051	70	10	from	from	ADP
bibechana-4051	70	11	these	these	DET
bibechana-4051	70	12	integrals	integral	NOUN
bibechana-4051	70	13	.	.	PUNCT
bibechana-4051	71	1	let	let	VERB
bibechana-4051	71	2	cc	cc	PART
bibechana-4051	71	3	be	be	AUX
bibechana-4051	71	4	the	the	DET
bibechana-4051	71	5	space	space	NOUN
bibechana-4051	71	6	of	of	ADP
bibechana-4051	71	7	all	all	PRON
bibechana-4051	71	8	real	real	ADV
bibechana-4051	71	9	-	-	PUNCT
bibechana-4051	71	10	valued	value	VERB
bibechana-4051	71	11	compactly	compactly	ADV
bibechana-4051	71	12	supported	support	VERB
bibechana-4051	71	13	continuous	continuous	ADJ
bibechana-4051	71	14	functions	function	NOUN
bibechana-4051	71	15	of	of	ADP
bibechana-4051	71	16	r.	r.	PROPN
bibechana-4051	71	17	define	define	VERB
bibechana-4051	71	18	a	a	DET
bibechana-4051	71	19	norm	norm	NOUN
bibechana-4051	71	20	on	on	ADP
bibechana-4051	71	21	cc	cc	X
bibechana-4051	71	22	by	by	ADP
bibechana-4051	71	23	(	(	PUNCT
bibechana-4051	71	24	)	)	PUNCT
bibechana-4051	71	25	.=	.=	VERB
bibechana-4051	72	1	∫f	∫f	NOUN
bibechana-4051	73	1	f	f	X
bibechana-4051	73	2	x	x	SYM
bibechana-4051	73	3	d	d	NOUN
bibechana-4051	73	4	x	x	X
bibechana-4051	73	5	then	then	ADV
bibechana-4051	73	6	cc	cc	PROPN
bibechana-4051	73	7	is	be	AUX
bibechana-4051	73	8	a	a	DET
bibechana-4051	73	9	normed	normed	ADJ
bibechana-4051	73	10	vector	vector	NOUN
bibechana-4051	73	11	space	space	NOUN
bibechana-4051	73	12	(	(	PUNCT
bibechana-4051	73	13	and	and	CCONJ
bibechana-4051	73	14	in	in	ADP
bibechana-4051	73	15	particular	particular	ADJ
bibechana-4051	73	16	,	,	PUNCT
bibechana-4051	73	17	it	it	PRON
bibechana-4051	73	18	is	be	AUX
bibechana-4051	73	19	a	a	DET
bibechana-4051	73	20	metric	metric	ADJ
bibechana-4051	73	21	space	space	NOUN
bibechana-4051	73	22	.	.	PUNCT
bibechana-4051	73	23	)	)	PUNCT
bibechana-4051	74	1	all	all	DET
bibechana-4051	74	2	metric	metric	ADJ
bibechana-4051	74	3	spaces	space	NOUN
bibechana-4051	74	4	have	have	VERB
bibechana-4051	74	5	hausdorff	hausdorff	NOUN
bibechana-4051	74	6	completions	completion	NOUN
bibechana-4051	74	7	,	,	PUNCT
bibechana-4051	74	8	so	so	ADV
bibechana-4051	74	9	let	let	VERB
bibechana-4051	74	10	l	l	NOUN
bibechana-4051	74	11	1	1	NUM
bibechana-4051	74	12	be	be	AUX
bibechana-4051	74	13	its	its	PRON
bibechana-4051	74	14	completion	completion	NOUN
bibechana-4051	74	15	.	.	PUNCT
bibechana-4051	75	1	this	this	DET
bibechana-4051	75	2	space	space	NOUN
bibechana-4051	75	3	is	be	AUX
bibechana-4051	75	4	isomorphic	isomorphic	ADJ
bibechana-4051	75	5	to	to	ADP
bibechana-4051	75	6	the	the	DET
bibechana-4051	75	7	space	space	NOUN
bibechana-4051	75	8	of	of	ADP
bibechana-4051	75	9	lebesgue	lebesgue	PROPN
bibechana-4051	75	10	integrable	integrable	ADJ
bibechana-4051	75	11	functions	function	NOUN
bibechana-4051	75	12	modulo	modulo	VERB
bibechana-4051	75	13	the	the	DET
bibechana-4051	75	14	subspace	subspace	NOUN
bibechana-4051	75	15	of	of	ADP
bibechana-4051	75	16	functions	function	NOUN
bibechana-4051	75	17	with	with	ADP
bibechana-4051	75	18	integral	integral	ADJ
bibechana-4051	75	19	zero	zero	NUM
bibechana-4051	75	20	.	.	PUNCT
bibechana-4051	76	1	furthermore	furthermore	ADV
bibechana-4051	76	2	,	,	PUNCT
bibechana-4051	76	3	the	the	DET
bibechana-4051	76	4	riemann	riemann	PROPN
bibechana-4051	76	5	integral	integral	PROPN
bibechana-4051	76	6	∫	∫	PROPN
bibechana-4051	76	7	is	be	AUX
bibechana-4051	76	8	a	a	DET
bibechana-4051	76	9	uniformly	uniformly	ADV
bibechana-4051	76	10	continuous	continuous	ADJ
bibechana-4051	76	11	functional	functional	ADJ
bibechana-4051	76	12	with	with	ADP
bibechana-4051	76	13	respect	respect	NOUN
bibechana-4051	76	14	to	to	ADP
bibechana-4051	76	15	the	the	DET
bibechana-4051	76	16	norm	norm	NOUN
bibechana-4051	76	17	on	on	ADP
bibechana-4051	76	18	cc	cc	PROPN
bibechana-4051	76	19	,	,	PUNCT
bibechana-4051	76	20	which	which	PRON
bibechana-4051	76	21	is	be	AUX
bibechana-4051	76	22	dense	dense	ADJ
bibechana-4051	76	23	in	in	ADP
bibechana-4051	76	24	l	l	PROPN
bibechana-4051	76	25	1	1	NUM
bibechana-4051	76	26	.	.	PUNCT
bibechana-4051	77	1	hence	hence	ADV
bibechana-4051	77	2	∫	∫	PROPN
bibechana-4051	77	3	has	have	VERB
bibechana-4051	77	4	a	a	DET
bibechana-4051	77	5	unique	unique	ADJ
bibechana-4051	77	6	extension	extension	NOUN
bibechana-4051	77	7	to	to	ADP
bibechana-4051	77	8	all	all	PRON
bibechana-4051	77	9	of	of	ADP
bibechana-4051	77	10	l	l	NOUN
bibechana-4051	77	11	1	1	NUM
bibechana-4051	77	12	.	.	PUNCT
bibechana-4051	78	1	this	this	DET
bibechana-4051	78	2	integral	integral	NOUN
bibechana-4051	78	3	is	be	AUX
bibechana-4051	78	4	precisely	precisely	ADV
bibechana-4051	78	5	the	the	DET
bibechana-4051	78	6	lebesgue	lebesgue	NOUN
bibechana-4051	78	7	integral	integral	ADJ
bibechana-4051	78	8	.	.	PUNCT
bibechana-4051	79	1	mani	mani	PROPN
bibechana-4051	79	2	raj	raj	PROPN
bibechana-4051	79	3	bhattrai	bhattrai	PROPN
bibechana-4051	79	4	/	/	SYM
bibechana-4051	79	5	bibechana	bibechana	NOUN
bibechana-4051	79	6	7	7	NUM
bibechana-4051	79	7	(	(	PUNCT
bibechana-4051	79	8	2011	2011	NUM
bibechana-4051	79	9	)	)	PUNCT
bibechana-4051	79	10	83	83	NUM
bibechana-4051	79	11	-	-	SYM
bibechana-4051	79	12	86	86	NUM
bibechana-4051	79	13	:	:	PUNCT
bibechana-4051	79	14	bmhss	bmhss	PROPN
bibechana-4051	79	15	86	86	NUM
bibechana-4051	79	16	this	this	DET
bibechana-4051	79	17	approach	approach	NOUN
bibechana-4051	79	18	can	can	AUX
bibechana-4051	79	19	be	be	AUX
bibechana-4051	79	20	generalized	generalize	VERB
bibechana-4051	79	21	to	to	PART
bibechana-4051	79	22	build	build	VERB
bibechana-4051	79	23	the	the	DET
bibechana-4051	79	24	theory	theory	NOUN
bibechana-4051	79	25	of	of	ADP
bibechana-4051	79	26	integration	integration	NOUN
bibechana-4051	79	27	with	with	ADP
bibechana-4051	79	28	respect	respect	NOUN
bibechana-4051	79	29	to	to	ADP
bibechana-4051	79	30	radon	radon	NOUN
bibechana-4051	79	31	measures	measure	NOUN
bibechana-4051	79	32	on	on	ADP
bibechana-4051	79	33	locally	locally	ADV
bibechana-4051	79	34	compact	compact	ADJ
bibechana-4051	79	35	spaces	space	NOUN
bibechana-4051	79	36	.	.	PUNCT
bibechana-4051	80	1	it	it	PRON
bibechana-4051	80	2	is	be	AUX
bibechana-4051	80	3	the	the	DET
bibechana-4051	80	4	approach	approach	NOUN
bibechana-4051	80	5	adopted	adopt	VERB
bibechana-4051	80	6	by	by	ADP
bibechana-4051	80	7	bourbaki	bourbaki	NOUN
bibechana-4051	80	8	[	[	X
bibechana-4051	80	9	4	4	X
bibechana-4051	80	10	]	]	PUNCT
bibechana-4051	80	11	for	for	SCONJ
bibechana-4051	80	12	more	more	ADJ
bibechana-4051	80	13	details	detail	NOUN
bibechana-4051	80	14	see	see	VERB
bibechana-4051	80	15	radon	radon	NOUN
bibechana-4051	80	16	measures	measure	NOUN
bibechana-4051	80	17	on	on	ADP
bibechana-4051	80	18	locally	locally	ADV
bibechana-4051	80	19	compact	compact	ADJ
bibechana-4051	80	20	spaces	space	NOUN
bibechana-4051	80	21	.	.	PUNCT
bibechana-4051	81	1	references	reference	NOUN
bibechana-4051	81	2	[	[	X
bibechana-4051	81	3	1	1	NUM
bibechana-4051	81	4	]	]	X
bibechana-4051	81	5	w.k.clifford	w.k.clifford	NOUN
bibechana-4051	81	6	,	,	PUNCT
bibechana-4051	81	7	“	"	PUNCT
bibechana-4051	81	8	on	on	ADP
bibechana-4051	81	9	the	the	DET
bibechana-4051	81	10	hypotheses	hypothesis	NOUN
bibechana-4051	81	11	which	which	PRON
bibechana-4051	81	12	lie	lie	VERB
bibechana-4051	81	13	at	at	ADP
bibechana-4051	81	14	the	the	DET
bibechana-4051	81	15	foundation	foundation	NOUN
bibechana-4051	81	16	of	of	ADP
bibechana-4051	81	17	geometry	geometry	NOUN
bibechana-4051	81	18	”	"	PUNCT
bibechana-4051	81	19	,	,	PUNCT
bibechana-4051	81	20	nature	nature	NOUN
bibechana-4051	81	21	,	,	PUNCT
bibechana-4051	81	22	8	8	NUM
bibechana-4051	81	23	(	(	PUNCT
bibechana-4051	81	24	1873	1873	NUM
bibechana-4051	81	25	)	)	PUNCT
bibechana-4051	81	26	183	183	NUM
bibechana-4051	81	27	.	.	PUNCT
bibechana-4051	82	1	[	[	X
bibechana-4051	82	2	2	2	X
bibechana-4051	82	3	]	]	X
bibechana-4051	82	4	h.j	h.j	PROPN
bibechana-4051	82	5	.	.	PROPN
bibechana-4051	82	6	wilcox	wilcox	PROPN
bibechana-4051	82	7	and	and	CCONJ
bibechana-4051	82	8	d.l	d.l	PROPN
bibechana-4051	82	9	.	.	PROPN
bibechana-4051	82	10	myers	myers	PROPN
bibechana-4051	82	11	,	,	PUNCT
bibechana-4051	82	12	an	an	DET
bibechana-4051	82	13	introduction	introduction	NOUN
bibechana-4051	82	14	to	to	ADP
bibechana-4051	82	15	lebesgue	lebesgue	NOUN
bibechana-4051	82	16	integration	integration	NOUN
bibechana-4051	82	17	and	and	CCONJ
bibechana-4051	82	18	fourier	fourier	NOUN
bibechana-4051	82	19	series	series	NOUN
bibechana-4051	82	20	,	,	PUNCT
bibechana-4051	82	21	dover	dover	PROPN
bibechana-4051	82	22	publications	publications	PROPN
bibechana-4051	82	23	,	,	PUNCT
bibechana-4051	82	24	inc	inc	PROPN
bibechana-4051	82	25	.	.	PROPN
bibechana-4051	82	26	,	,	PUNCT
bibechana-4051	82	27	new	new	PROPN
bibechana-4051	82	28	york	york	PROPN
bibechana-4051	82	29	,	,	PUNCT
bibechana-4051	82	30	(	(	PUNCT
bibechana-4051	82	31	1978	1978	NUM
bibechana-4051	82	32	)	)	PUNCT
bibechana-4051	82	33	.	.	PUNCT
bibechana-4051	83	1	[	[	X
bibechana-4051	83	2	3	3	X
bibechana-4051	83	3	]	]	PUNCT
bibechana-4051	83	4	p.	p.	PROPN
bibechana-4051	83	5	daniell	daniell	PROPN
bibechana-4051	83	6	,	,	PUNCT
bibechana-4051	83	7	"	"	PUNCT
bibechana-4051	83	8	a	a	DET
bibechana-4051	83	9	general	general	ADJ
bibechana-4051	83	10	form	form	NOUN
bibechana-4051	83	11	of	of	ADP
bibechana-4051	83	12	integral	integral	ADJ
bibechana-4051	83	13	"	"	PUNCT
bibechana-4051	83	14	ann	ann	PROPN
bibechana-4051	83	15	.	.	PROPN
bibechana-4051	83	16	of	of	ADP
bibechana-4051	83	17	math	math	NOUN
bibechana-4051	83	18	.	.	PUNCT
bibechana-4051	84	1	,	,	PUNCT
bibechana-4051	84	2	19	19	NUM
bibechana-4051	84	3	(	(	PUNCT
bibechana-4051	84	4	1917	1917	NUM
bibechana-4051	84	5	)	)	PUNCT
bibechana-4051	84	6	279	279	NUM
bibechana-4051	84	7	.	.	PUNCT
bibechana-4051	85	1	[	[	X
bibechana-4051	85	2	4	4	NUM
bibechana-4051	85	3	]	]	X
bibechana-4051	85	4	n.	n.	NOUN
bibechana-4051	85	5	bourbaki	bourbaki	PROPN
bibechana-4051	85	6	,	,	PUNCT
bibechana-4051	85	7	elements	element	NOUN
bibechana-4051	85	8	of	of	ADP
bibechana-4051	85	9	mathematics	mathematic	NOUN
bibechana-4051	85	10	,	,	PUNCT
bibechana-4051	85	11	springer	springer	NOUN
bibechana-4051	85	12	,	,	PUNCT
bibechana-4051	85	13	(	(	PUNCT
bibechana-4051	85	14	2004	2004	NUM
bibechana-4051	85	15	)	)	PUNCT
bibechana-4051	85	16	.	.	PUNCT