id	sid	tid	token	lemma	pos
ejpam-4424	1	1	european	european	PROPN
ejpam-4424	1	2	journal	journal	PROPN
ejpam-4424	1	3	of	of	ADP
ejpam-4424	1	4	pure	pure	ADJ
ejpam-4424	1	5	and	and	CCONJ
ejpam-4424	1	6	applied	apply	VERB
ejpam-4424	1	7	mathematics	mathematic	NOUN
ejpam-4424	1	8	vol	vol	NOUN
ejpam-4424	1	9	.	.	PROPN
ejpam-4424	2	1	15	15	NUM
ejpam-4424	2	2	,	,	PUNCT
ejpam-4424	2	3	no	no	INTJ
ejpam-4424	2	4	.	.	NOUN
ejpam-4424	2	5	3	3	NUM
ejpam-4424	2	6	,	,	PUNCT
ejpam-4424	2	7	2022	2022	NUM
ejpam-4424	2	8	,	,	PUNCT
ejpam-4424	2	9	1211	1211	NUM
ejpam-4424	2	10	-	-	SYM
ejpam-4424	2	11	1216	1216	NUM
ejpam-4424	2	12	issn	issn	PROPN
ejpam-4424	2	13	1307	1307	NUM
ejpam-4424	2	14	-	-	SYM
ejpam-4424	2	15	5543	5543	NUM
ejpam-4424	2	16	–	–	PUNCT
ejpam-4424	3	1	ejpam.com	ejpam.com	X
ejpam-4424	3	2	published	publish	VERB
ejpam-4424	3	3	by	by	ADP
ejpam-4424	3	4	new	new	PROPN
ejpam-4424	3	5	york	york	PROPN
ejpam-4424	3	6	business	business	PROPN
ejpam-4424	3	7	global	global	PROPN
ejpam-4424	3	8	on	on	ADP
ejpam-4424	3	9	the	the	DET
ejpam-4424	3	10	relationship	relationship	NOUN
ejpam-4424	3	11	between	between	ADP
ejpam-4424	3	12	the	the	DET
ejpam-4424	3	13	integral	integral	NOUN
ejpam-4424	3	14	of	of	ADP
ejpam-4424	3	15	derivative	derivative	NOUN
ejpam-4424	3	16	and	and	CCONJ
ejpam-4424	3	17	the	the	DET
ejpam-4424	3	18	derivative	derivative	NOUN
ejpam-4424	3	19	of	of	ADP
ejpam-4424	3	20	the	the	DET
ejpam-4424	3	21	integral	integral	ADJ
ejpam-4424	3	22	giljun	giljun	PROPN
ejpam-4424	3	23	han1	han1	PROPN
ejpam-4424	3	24	,	,	PUNCT
ejpam-4424	3	25	hwajoon	hwajoon	PROPN
ejpam-4424	3	26	kim2∗	kim2∗	PROPN
ejpam-4424	3	27	1departmet	1departmet	NUM
ejpam-4424	3	28	of	of	ADP
ejpam-4424	3	29	mathematics	mathematics	PROPN
ejpam-4424	3	30	education	education	NOUN
ejpam-4424	3	31	,	,	PUNCT
ejpam-4424	3	32	dankook	dankook	PROPN
ejpam-4424	3	33	university	university	NOUN
ejpam-4424	3	34	,	,	PUNCT
ejpam-4424	3	35	yongin	yongin	ADJ
ejpam-4424	3	36	-	-	PUNCT
ejpam-4424	3	37	si	si	NOUN
ejpam-4424	3	38	,	,	PUNCT
ejpam-4424	3	39	gyeonggi	gyeonggi	NOUN
ejpam-4424	3	40	-	-	PUNCT
ejpam-4424	3	41	do	do	VERB
ejpam-4424	3	42	,	,	PUNCT
ejpam-4424	3	43	s.	s.	PROPN
ejpam-4424	3	44	korea	korea	PROPN
ejpam-4424	3	45	2	2	NUM
ejpam-4424	3	46	it	it	PRON
ejpam-4424	3	47	engineering	engineering	NOUN
ejpam-4424	3	48	,	,	PUNCT
ejpam-4424	3	49	kyungdong	kyungdong	PROPN
ejpam-4424	3	50	university	university	PROPN
ejpam-4424	3	51	,	,	PUNCT
ejpam-4424	3	52	yangju	yangju	PROPN
ejpam-4424	3	53	,	,	PUNCT
ejpam-4424	3	54	gyeonggi	gyeonggi	NOUN
ejpam-4424	3	55	-	-	PUNCT
ejpam-4424	3	56	do	do	VERB
ejpam-4424	3	57	,	,	PUNCT
ejpam-4424	3	58	s.	s.	PROPN
ejpam-4424	3	59	korea	korea	PROPN
ejpam-4424	3	60	abstract	abstract	PROPN
ejpam-4424	3	61	.	.	PUNCT
ejpam-4424	4	1	we	we	PRON
ejpam-4424	4	2	would	would	AUX
ejpam-4424	4	3	like	like	VERB
ejpam-4424	4	4	to	to	PART
ejpam-4424	4	5	study	study	VERB
ejpam-4424	4	6	the	the	DET
ejpam-4424	4	7	relationship	relationship	NOUN
ejpam-4424	4	8	between	between	ADP
ejpam-4424	4	9	the	the	DET
ejpam-4424	4	10	integral	integral	NOUN
ejpam-4424	4	11	of	of	ADP
ejpam-4424	4	12	the	the	DET
ejpam-4424	4	13	derivative	derivative	NOUN
ejpam-4424	4	14	and	and	CCONJ
ejpam-4424	4	15	the	the	DET
ejpam-4424	4	16	derivative	derivative	NOUN
ejpam-4424	4	17	of	of	ADP
ejpam-4424	4	18	the	the	DET
ejpam-4424	4	19	integral	integral	NOUN
ejpam-4424	4	20	.	.	PUNCT
ejpam-4424	5	1	this	this	PRON
ejpam-4424	5	2	is	be	AUX
ejpam-4424	5	3	the	the	DET
ejpam-4424	5	4	study	study	NOUN
ejpam-4424	5	5	of	of	ADP
ejpam-4424	5	6	whether	whether	SCONJ
ejpam-4424	5	7	these	these	DET
ejpam-4424	5	8	two	two	NUM
ejpam-4424	5	9	are	be	AUX
ejpam-4424	5	10	the	the	DET
ejpam-4424	5	11	same	same	ADJ
ejpam-4424	5	12	or	or	CCONJ
ejpam-4424	5	13	not	not	PART
ejpam-4424	5	14	.	.	PUNCT
ejpam-4424	6	1	also	also	ADV
ejpam-4424	6	2	,	,	PUNCT
ejpam-4424	6	3	this	this	DET
ejpam-4424	6	4	study	study	NOUN
ejpam-4424	6	5	began	begin	VERB
ejpam-4424	6	6	with	with	ADP
ejpam-4424	6	7	the	the	DET
ejpam-4424	6	8	question	question	NOUN
ejpam-4424	6	9	of	of	ADP
ejpam-4424	6	10	kreyszig	kreyszig	PROPN
ejpam-4424	6	11	’s	’s	PART
ejpam-4424	6	12	assumptions	assumption	NOUN
ejpam-4424	6	13	presented	present	VERB
ejpam-4424	6	14	in	in	ADP
ejpam-4424	6	15	[	[	X
ejpam-4424	6	16	8	8	NUM
ejpam-4424	6	17	]	]	PUNCT
ejpam-4424	6	18	.	.	PUNCT
ejpam-4424	7	1	the	the	DET
ejpam-4424	7	2	research	research	NOUN
ejpam-4424	7	3	method	method	NOUN
ejpam-4424	7	4	used	use	VERB
ejpam-4424	7	5	two	two	NUM
ejpam-4424	7	6	tools	tool	NOUN
ejpam-4424	7	7	:	:	PUNCT
ejpam-4424	7	8	the	the	DET
ejpam-4424	7	9	riemann	riemann	PROPN
ejpam-4424	7	10	integral	integral	PROPN
ejpam-4424	7	11	and	and	CCONJ
ejpam-4424	7	12	its	its	PRON
ejpam-4424	7	13	generalized	generalized	ADJ
ejpam-4424	7	14	concept	concept	NOUN
ejpam-4424	7	15	,	,	PUNCT
ejpam-4424	7	16	the	the	DET
ejpam-4424	7	17	lebesgue	lebesgue	NOUN
ejpam-4424	7	18	integral	integral	ADJ
ejpam-4424	7	19	.	.	PUNCT
ejpam-4424	8	1	the	the	DET
ejpam-4424	8	2	obtained	obtain	VERB
ejpam-4424	8	3	research	research	NOUN
ejpam-4424	8	4	results	result	NOUN
ejpam-4424	8	5	give	give	VERB
ejpam-4424	8	6	some	some	DET
ejpam-4424	8	7	answer	answer	NOUN
ejpam-4424	8	8	to	to	ADP
ejpam-4424	8	9	this	this	DET
ejpam-4424	8	10	question	question	NOUN
ejpam-4424	8	11	.	.	PUNCT
ejpam-4424	9	1	2020	2020	NUM
ejpam-4424	9	2	mathematics	mathematic	NOUN
ejpam-4424	9	3	subject	subject	NOUN
ejpam-4424	9	4	classifications	classification	NOUN
ejpam-4424	9	5	:	:	PUNCT
ejpam-4424	9	6	35	35	NUM
ejpam-4424	9	7	-	-	SYM
ejpam-4424	9	8	02	02	NUM
ejpam-4424	9	9	key	key	ADJ
ejpam-4424	9	10	words	word	NOUN
ejpam-4424	9	11	and	and	CCONJ
ejpam-4424	9	12	phrases	phrase	NOUN
ejpam-4424	9	13	:	:	PUNCT
ejpam-4424	9	14	leibniz	leibniz	PROPN
ejpam-4424	9	15	integral	integral	ADJ
ejpam-4424	9	16	rule	rule	NOUN
ejpam-4424	9	17	,	,	PUNCT
ejpam-4424	9	18	interchange	interchange	NOUN
ejpam-4424	9	19	of	of	ADP
ejpam-4424	9	20	integral	integral	ADJ
ejpam-4424	9	21	and	and	CCONJ
ejpam-4424	9	22	derivative	derivative	ADJ
ejpam-4424	9	23	,	,	PUNCT
ejpam-4424	9	24	monotone	monotone	ADJ
ejpam-4424	9	25	convergence	convergence	NOUN
ejpam-4424	9	26	theorem	theorem	VERB
ejpam-4424	9	27	1	1	NUM
ejpam-4424	9	28	.	.	NOUN
ejpam-4424	10	1	introduction	introduction	NOUN
ejpam-4424	10	2	among	among	ADP
ejpam-4424	10	3	the	the	DET
ejpam-4424	10	4	various	various	ADJ
ejpam-4424	10	5	methods	method	NOUN
ejpam-4424	10	6	to	to	PART
ejpam-4424	10	7	find	find	VERB
ejpam-4424	10	8	the	the	DET
ejpam-4424	10	9	solution	solution	NOUN
ejpam-4424	10	10	of	of	ADP
ejpam-4424	10	11	pdes	pde	NOUN
ejpam-4424	10	12	,	,	PUNCT
ejpam-4424	10	13	there	there	PRON
ejpam-4424	10	14	is	be	VERB
ejpam-4424	10	15	a	a	DET
ejpam-4424	10	16	method	method	NOUN
ejpam-4424	10	17	using	use	VERB
ejpam-4424	10	18	integral	integral	ADJ
ejpam-4424	10	19	transform	transform	NOUN
ejpam-4424	10	20	[	[	X
ejpam-4424	10	21	3–9	3–9	NUM
ejpam-4424	10	22	]	]	PUNCT
ejpam-4424	10	23	.	.	PUNCT
ejpam-4424	11	1	there	there	PRON
ejpam-4424	11	2	is	be	VERB
ejpam-4424	11	3	one	one	NUM
ejpam-4424	11	4	problem	problem	NOUN
ejpam-4424	11	5	in	in	ADP
ejpam-4424	11	6	this	this	DET
ejpam-4424	11	7	solution	solution	NOUN
ejpam-4424	11	8	process	process	NOUN
ejpam-4424	11	9	.	.	PUNCT
ejpam-4424	12	1	that	that	PRON
ejpam-4424	12	2	is	is	ADV
ejpam-4424	12	3	,	,	PUNCT
ejpam-4424	12	4	the	the	DET
ejpam-4424	12	5	solution	solution	NOUN
ejpam-4424	12	6	is	be	AUX
ejpam-4424	12	7	made	make	VERB
ejpam-4424	12	8	under	under	ADP
ejpam-4424	12	9	the	the	DET
ejpam-4424	12	10	assumption	assumption	NOUN
ejpam-4424	12	11	that	that	SCONJ
ejpam-4424	12	12	the	the	DET
ejpam-4424	12	13	order	order	NOUN
ejpam-4424	12	14	of	of	ADP
ejpam-4424	12	15	differentiation	differentiation	NOUN
ejpam-4424	12	16	and	and	CCONJ
ejpam-4424	12	17	integration	integration	NOUN
ejpam-4424	12	18	can	can	AUX
ejpam-4424	12	19	be	be	AUX
ejpam-4424	12	20	changed	change	VERB
ejpam-4424	12	21	.	.	PUNCT
ejpam-4424	13	1	this	this	DET
ejpam-4424	13	2	problem	problem	NOUN
ejpam-4424	13	3	appears	appear	VERB
ejpam-4424	13	4	frequently	frequently	ADV
ejpam-4424	13	5	in	in	ADP
ejpam-4424	13	6	the	the	DET
ejpam-4424	13	7	calculation	calculation	NOUN
ejpam-4424	13	8	process	process	NOUN
ejpam-4424	13	9	of	of	ADP
ejpam-4424	13	10	£	£	SYM
ejpam-4424	13	11	(	(	PUNCT
ejpam-4424	13	12	uxx	uxx	NOUN
ejpam-4424	13	13	)	)	PUNCT
ejpam-4424	13	14	in	in	ADP
ejpam-4424	13	15	pdes	pde	NOUN
ejpam-4424	13	16	.	.	PUNCT
ejpam-4424	14	1	this	this	DET
ejpam-4424	14	2	point	point	NOUN
ejpam-4424	14	3	was	be	AUX
ejpam-4424	14	4	mentioned	mention	VERB
ejpam-4424	14	5	in	in	ADP
ejpam-4424	14	6	[	[	X
ejpam-4424	14	7	8	8	NUM
ejpam-4424	14	8	]	]	PUNCT
ejpam-4424	14	9	,	,	PUNCT
ejpam-4424	14	10	and	and	CCONJ
ejpam-4424	14	11	it	it	PRON
ejpam-4424	14	12	seems	seem	VERB
ejpam-4424	14	13	that	that	SCONJ
ejpam-4424	14	14	kreyszig	kreyszig	PROPN
ejpam-4424	14	15	was	be	AUX
ejpam-4424	14	16	also	also	ADV
ejpam-4424	14	17	aware	aware	ADJ
ejpam-4424	14	18	of	of	ADP
ejpam-4424	14	19	it(sec	it(sec	NOUN
ejpam-4424	14	20	.	.	PUNCT
ejpam-4424	15	1	12.11	12.11	NUM
ejpam-4424	15	2	of	of	ADP
ejpam-4424	15	3	[	[	X
ejpam-4424	15	4	8	8	NUM
ejpam-4424	15	5	]	]	NUM
ejpam-4424	15	6	)	)	PUNCT
ejpam-4424	15	7	.	.	PUNCT
ejpam-4424	15	8	is	be	AUX
ejpam-4424	15	9	it	it	PRON
ejpam-4424	15	10	possible	possible	ADJ
ejpam-4424	15	11	to	to	PART
ejpam-4424	15	12	interchange	interchange	VERB
ejpam-4424	15	13	the	the	DET
ejpam-4424	15	14	integral	integral	ADJ
ejpam-4424	15	15	and	and	CCONJ
ejpam-4424	15	16	derivative	derivative	ADJ
ejpam-4424	15	17	in	in	ADP
ejpam-4424	15	18	solving	solve	VERB
ejpam-4424	15	19	pdes	pde	NOUN
ejpam-4424	15	20	by	by	ADP
ejpam-4424	15	21	integral	integral	ADJ
ejpam-4424	15	22	transform	transform	NOUN
ejpam-4424	15	23	?	?	PUNCT
ejpam-4424	16	1	this	this	DET
ejpam-4424	16	2	study	study	NOUN
ejpam-4424	16	3	intends	intend	VERB
ejpam-4424	16	4	to	to	PART
ejpam-4424	16	5	start	start	VERB
ejpam-4424	16	6	with	with	ADP
ejpam-4424	16	7	this	this	DET
ejpam-4424	16	8	question	question	NOUN
ejpam-4424	16	9	.	.	PUNCT
ejpam-4424	17	1	since	since	SCONJ
ejpam-4424	17	2	the	the	DET
ejpam-4424	17	3	solution	solution	NOUN
ejpam-4424	17	4	by	by	ADP
ejpam-4424	17	5	integral	integral	ADJ
ejpam-4424	17	6	transform	transform	NOUN
ejpam-4424	17	7	is	be	AUX
ejpam-4424	17	8	almost	almost	ADV
ejpam-4424	17	9	similar	similar	ADJ
ejpam-4424	17	10	,	,	PUNCT
ejpam-4424	17	11	we	we	PRON
ejpam-4424	17	12	would	would	AUX
ejpam-4424	17	13	just	just	ADV
ejpam-4424	17	14	like	like	VERB
ejpam-4424	17	15	to	to	PART
ejpam-4424	17	16	approach	approach	VERB
ejpam-4424	17	17	by	by	ADP
ejpam-4424	17	18	the	the	DET
ejpam-4424	17	19	laplace	laplace	NOUN
ejpam-4424	17	20	transform	transform	NOUN
ejpam-4424	17	21	.	.	PUNCT
ejpam-4424	18	1	consider	consider	VERB
ejpam-4424	18	2	a	a	DET
ejpam-4424	18	3	function	function	NOUN
ejpam-4424	18	4	w(x	w(x	PROPN
ejpam-4424	18	5	,	,	PUNCT
ejpam-4424	18	6	t	t	PROPN
ejpam-4424	18	7	)	)	PUNCT
ejpam-4424	18	8	=	=	PUNCT
ejpam-4424	18	9	xn	xn	PROPN
ejpam-4424	19	1	+	+	NUM
ejpam-4424	19	2	tn	tn	PROPN
ejpam-4424	19	3	,	,	PUNCT
ejpam-4424	19	4	where	where	SCONJ
ejpam-4424	19	5	n	n	PRON
ejpam-4424	19	6	is	be	AUX
ejpam-4424	19	7	a	a	DET
ejpam-4424	19	8	positive	positive	ADJ
ejpam-4424	19	9	integer	integer	NOUN
ejpam-4424	19	10	.	.	PUNCT
ejpam-4424	20	1	by	by	ADP
ejpam-4424	20	2	simple	simple	ADJ
ejpam-4424	20	3	calculation	calculation	NOUN
ejpam-4424	20	4	,	,	PUNCT
ejpam-4424	20	5	we	we	PRON
ejpam-4424	20	6	get	get	VERB
ejpam-4424	20	7	∂n	∂n	PROPN
ejpam-4424	20	8	∂xn	∂xn	PROPN
ejpam-4424	20	9	∫	∫	PROPN
ejpam-4424	20	10	w(x	w(x	PROPN
ejpam-4424	20	11	,	,	PUNCT
ejpam-4424	20	12	t	t	PROPN
ejpam-4424	20	13	)	)	PUNCT
ejpam-4424	20	14	dt	dt	PUNCT
ejpam-4424	21	1	=	=	SYM
ejpam-4424	21	2	∫	∫	PROPN
ejpam-4424	21	3	∂n	∂n	PROPN
ejpam-4424	21	4	∂xn	∂xn	PROPN
ejpam-4424	21	5	w(x	w(x	PROPN
ejpam-4424	21	6	,	,	PUNCT
ejpam-4424	21	7	t	t	PROPN
ejpam-4424	21	8	)	)	PUNCT
ejpam-4424	21	9	dt	dt	X
ejpam-4424	21	10	∗corresponding	∗corresponde	VERB
ejpam-4424	21	11	author	author	NOUN
ejpam-4424	21	12	.	.	PUNCT
ejpam-4424	22	1	doi	doi	NOUN
ejpam-4424	22	2	:	:	PUNCT
ejpam-4424	22	3	https://doi.org/10.29020/nybg.ejpam.v15i3.4424	https://doi.org/10.29020/nybg.ejpam.v15i3.4424	NUM
ejpam-4424	22	4	email	email	NOUN
ejpam-4424	22	5	addresses	address	NOUN
ejpam-4424	22	6	:	:	PUNCT
ejpam-4424	22	7	gilhan@dankook.ac.kr	gilhan@dankook.ac.kr	X
ejpam-4424	22	8	(	(	PUNCT
ejpam-4424	22	9	gj	gj	PROPN
ejpam-4424	22	10	.	.	PUNCT
ejpam-4424	22	11	han	han	PROPN
ejpam-4424	22	12	)	)	PUNCT
ejpam-4424	22	13	,	,	PUNCT
ejpam-4424	22	14	cellmath@gmail.com	cellmath@gmail.com	X
ejpam-4424	22	15	(	(	PUNCT
ejpam-4424	22	16	hj	hj	PROPN
ejpam-4424	22	17	.	.	PUNCT
ejpam-4424	22	18	kim	kim	PROPN
ejpam-4424	22	19	)	)	PUNCT
ejpam-4424	22	20	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4424	22	21	1211	1211	NUM
ejpam-4424	23	1	©	©	PROPN
ejpam-4424	23	2	2022	2022	NUM
ejpam-4424	23	3	ejpam	ejpam	VERB
ejpam-4424	23	4	all	all	DET
ejpam-4424	23	5	rights	right	NOUN
ejpam-4424	23	6	reserved	reserve	VERB
ejpam-4424	23	7	.	.	PUNCT
ejpam-4424	24	1	gj	gj	NOUN
ejpam-4424	24	2	.	.	PUNCT
ejpam-4424	24	3	han	han	PROPN
ejpam-4424	24	4	,	,	PUNCT
ejpam-4424	24	5	hj	hj	PROPN
ejpam-4424	24	6	.	.	PROPN
ejpam-4424	25	1	kim	kim	PROPN
ejpam-4424	25	2	/	/	SYM
ejpam-4424	25	3	eur	eur	PROPN
ejpam-4424	25	4	.	.	PUNCT
ejpam-4424	26	1	j.	j.	PROPN
ejpam-4424	26	2	pure	pure	PROPN
ejpam-4424	26	3	appl	appl	PROPN
ejpam-4424	26	4	.	.	PROPN
ejpam-4424	26	5	math	math	PROPN
ejpam-4424	26	6	,	,	PUNCT
ejpam-4424	26	7	15	15	NUM
ejpam-4424	26	8	(	(	PUNCT
ejpam-4424	26	9	3	3	NUM
ejpam-4424	26	10	)	)	PUNCT
ejpam-4424	26	11	(	(	PUNCT
ejpam-4424	26	12	2022	2022	NUM
ejpam-4424	26	13	)	)	PUNCT
ejpam-4424	26	14	,	,	PUNCT
ejpam-4424	26	15	1211	1211	NUM
ejpam-4424	26	16	-	-	SYM
ejpam-4424	26	17	1216	1216	NUM
ejpam-4424	26	18	1212	1212	NUM
ejpam-4424	26	19	under	under	ADP
ejpam-4424	26	20	the	the	DET
ejpam-4424	26	21	assumption	assumption	NOUN
ejpam-4424	26	22	that	that	SCONJ
ejpam-4424	26	23	the	the	DET
ejpam-4424	26	24	difference	difference	NOUN
ejpam-4424	26	25	as	as	ADV
ejpam-4424	26	26	much	much	ADV
ejpam-4424	26	27	as	as	ADP
ejpam-4424	26	28	constant	constant	ADJ
ejpam-4424	26	29	is	be	AUX
ejpam-4424	26	30	accepted	accept	VERB
ejpam-4424	26	31	.	.	PUNCT
ejpam-4424	27	1	on	on	ADP
ejpam-4424	27	2	one	one	NUM
ejpam-4424	27	3	hand	hand	NOUN
ejpam-4424	27	4	,	,	PUNCT
ejpam-4424	27	5	as	as	ADP
ejpam-4424	27	6	a	a	DET
ejpam-4424	27	7	counter	counter	ADJ
ejpam-4424	27	8	example	example	NOUN
ejpam-4424	27	9	,	,	PUNCT
ejpam-4424	27	10	consider	consider	VERB
ejpam-4424	27	11	the	the	DET
ejpam-4424	27	12	following	follow	VERB
ejpam-4424	27	13	example	example	NOUN
ejpam-4424	27	14	:	:	PUNCT
ejpam-4424	27	15	let	let	VERB
ejpam-4424	27	16	y	y	PRON
ejpam-4424	27	17	be	be	AUX
ejpam-4424	27	18	the	the	DET
ejpam-4424	27	19	positive	positive	ADJ
ejpam-4424	27	20	integers	integer	NOUN
ejpam-4424	27	21	,	,	PUNCT
ejpam-4424	27	22	dy	dy	NOUN
ejpam-4424	27	23	be	be	VERB
ejpam-4424	27	24	the	the	DET
ejpam-4424	27	25	counting	counting	NOUN
ejpam-4424	27	26	measure	measure	NOUN
ejpam-4424	27	27	,	,	PUNCT
ejpam-4424	27	28	and	and	CCONJ
ejpam-4424	27	29	f(x	f(x	PROPN
ejpam-4424	27	30	,	,	PUNCT
ejpam-4424	27	31	y	y	NOUN
ejpam-4424	27	32	)	)	PUNCT
ejpam-4424	27	33	=	=	PRON
ejpam-4424	28	1	{	{	PUNCT
ejpam-4424	28	2	x	x	X
ejpam-4424	28	3	(	(	PUNCT
ejpam-4424	28	4	1	1	NUM
ejpam-4424	28	5	y	y	NOUN
ejpam-4424	28	6	+	+	NOUN
ejpam-4424	28	7	1	1	NUM
ejpam-4424	28	8	<	<	X
ejpam-4424	28	9	x	x	X
ejpam-4424	28	10	<	<	X
ejpam-4424	28	11	1	1	NUM
ejpam-4424	28	12	y	y	PROPN
ejpam-4424	28	13	)	)	PUNCT
ejpam-4424	28	14	0	0	PUNCT
ejpam-4424	29	1	elsewhere	elsewhere	ADV
ejpam-4424	29	2	.	.	PUNCT
ejpam-4424	30	1	it	it	PRON
ejpam-4424	30	2	is	be	AUX
ejpam-4424	30	3	well	well	ADV
ejpam-4424	30	4	-	-	PUNCT
ejpam-4424	30	5	known	know	VERB
ejpam-4424	30	6	that	that	SCONJ
ejpam-4424	30	7	the	the	DET
ejpam-4424	30	8	integral	integral	NOUN
ejpam-4424	30	9	of	of	ADP
ejpam-4424	30	10	the	the	DET
ejpam-4424	30	11	derivative	derivative	NOUN
ejpam-4424	30	12	of	of	ADP
ejpam-4424	30	13	f	f	PROPN
ejpam-4424	30	14	is	be	AUX
ejpam-4424	30	15	0	0	NUM
ejpam-4424	30	16	at	at	ADP
ejpam-4424	30	17	x	x	X
ejpam-4424	31	1	=	=	SYM
ejpam-4424	31	2	0	0	NUM
ejpam-4424	31	3	and	and	CCONJ
ejpam-4424	31	4	the	the	DET
ejpam-4424	31	5	derivative	derivative	NOUN
ejpam-4424	31	6	of	of	ADP
ejpam-4424	31	7	the	the	DET
ejpam-4424	31	8	integral	integral	ADJ
ejpam-4424	31	9	is	be	AUX
ejpam-4424	31	10	1	1	NUM
ejpam-4424	31	11	at	at	ADP
ejpam-4424	31	12	x	x	X
ejpam-4424	31	13	=	=	NOUN
ejpam-4424	31	14	0	0	X
ejpam-4424	31	15	.	.	PUNCT
ejpam-4424	32	1	it	it	PRON
ejpam-4424	32	2	is	be	AUX
ejpam-4424	32	3	necessary	necessary	ADJ
ejpam-4424	32	4	to	to	PART
ejpam-4424	32	5	find	find	VERB
ejpam-4424	32	6	out	out	ADP
ejpam-4424	32	7	more	more	ADV
ejpam-4424	32	8	about	about	ADP
ejpam-4424	32	9	to	to	ADP
ejpam-4424	32	10	what	what	DET
ejpam-4424	32	11	extent	extent	NOUN
ejpam-4424	32	12	equality	equality	NOUN
ejpam-4424	32	13	holds	hold	VERB
ejpam-4424	32	14	and	and	CCONJ
ejpam-4424	32	15	where	where	SCONJ
ejpam-4424	32	16	equality	equality	NOUN
ejpam-4424	32	17	does	do	AUX
ejpam-4424	32	18	not	not	PART
ejpam-4424	32	19	hold	hold	VERB
ejpam-4424	32	20	.	.	PUNCT
ejpam-4424	33	1	in	in	ADP
ejpam-4424	33	2	the	the	DET
ejpam-4424	33	3	next	next	ADJ
ejpam-4424	33	4	section	section	NOUN
ejpam-4424	33	5	,	,	PUNCT
ejpam-4424	33	6	consider	consider	VERB
ejpam-4424	33	7	a	a	DET
ejpam-4424	33	8	further	further	ADJ
ejpam-4424	33	9	approach	approach	NOUN
ejpam-4424	33	10	to	to	ADP
ejpam-4424	33	11	this	this	DET
ejpam-4424	33	12	topic	topic	NOUN
ejpam-4424	33	13	.	.	PUNCT
ejpam-4424	34	1	2	2	X
ejpam-4424	34	2	.	.	X
ejpam-4424	34	3	on	on	ADP
ejpam-4424	34	4	the	the	DET
ejpam-4424	34	5	relationship	relationship	NOUN
ejpam-4424	34	6	between	between	ADP
ejpam-4424	34	7	the	the	DET
ejpam-4424	34	8	integral	integral	NOUN
ejpam-4424	34	9	of	of	ADP
ejpam-4424	34	10	derivative	derivative	NOUN
ejpam-4424	34	11	and	and	CCONJ
ejpam-4424	34	12	the	the	DET
ejpam-4424	34	13	derivative	derivative	NOUN
ejpam-4424	34	14	of	of	ADP
ejpam-4424	34	15	the	the	DET
ejpam-4424	34	16	integral	integral	ADJ
ejpam-4424	34	17	from	from	ADP
ejpam-4424	34	18	the	the	DET
ejpam-4424	34	19	point	point	NOUN
ejpam-4424	34	20	of	of	ADP
ejpam-4424	34	21	view	view	NOUN
ejpam-4424	34	22	of	of	ADP
ejpam-4424	34	23	the	the	DET
ejpam-4424	34	24	riemann	riemann	PROPN
ejpam-4424	34	25	integral	integral	PROPN
ejpam-4424	34	26	,	,	PUNCT
ejpam-4424	34	27	this	this	DET
ejpam-4424	34	28	interchange	interchange	NOUN
ejpam-4424	34	29	is	be	AUX
ejpam-4424	34	30	closely	closely	ADV
ejpam-4424	34	31	related	relate	VERB
ejpam-4424	34	32	to	to	ADP
ejpam-4424	34	33	the	the	DET
ejpam-4424	34	34	following	follow	VERB
ejpam-4424	34	35	leibniz	leibniz	PROPN
ejpam-4424	34	36	integral	integral	ADJ
ejpam-4424	34	37	rule	rule	NOUN
ejpam-4424	34	38	.	.	PUNCT
ejpam-4424	35	1	from	from	ADP
ejpam-4424	35	2	the	the	DET
ejpam-4424	35	3	point	point	NOUN
ejpam-4424	35	4	of	of	ADP
ejpam-4424	35	5	view	view	NOUN
ejpam-4424	35	6	of	of	ADP
ejpam-4424	35	7	the	the	DET
ejpam-4424	35	8	lebesgue	lebesgue	NOUN
ejpam-4424	35	9	integral	integral	ADJ
ejpam-4424	35	10	,	,	PUNCT
ejpam-4424	35	11	this	this	DET
ejpam-4424	35	12	interchange	interchange	NOUN
ejpam-4424	35	13	relates	relate	VERB
ejpam-4424	35	14	to	to	ADP
ejpam-4424	35	15	monotone	monotone	ADJ
ejpam-4424	35	16	convergence	convergence	NOUN
ejpam-4424	35	17	theorem	theorem	NOUN
ejpam-4424	35	18	,	,	PUNCT
ejpam-4424	35	19	beppo	beppo	PROPN
ejpam-4424	35	20	levi	levi	PROPN
ejpam-4424	35	21	’s	’s	PART
ejpam-4424	35	22	theorem	theorem	PROPN
ejpam-4424	35	23	and	and	CCONJ
ejpam-4424	35	24	lebesgue	lebesgue	NOUN
ejpam-4424	35	25	dominated	dominate	VERB
ejpam-4424	35	26	convergence	convergence	NOUN
ejpam-4424	35	27	theorem	theorem	VERB
ejpam-4424	35	28	.	.	PUNCT
ejpam-4424	36	1	therefore	therefore	ADV
ejpam-4424	36	2	,	,	PUNCT
ejpam-4424	36	3	let	let	VERB
ejpam-4424	36	4	us	we	PRON
ejpam-4424	36	5	take	take	VERB
ejpam-4424	36	6	a	a	DET
ejpam-4424	36	7	look	look	NOUN
ejpam-4424	36	8	at	at	ADP
ejpam-4424	36	9	these	these	DET
ejpam-4424	36	10	theorems	theorem	NOUN
ejpam-4424	36	11	first	first	ADV
ejpam-4424	36	12	as	as	ADP
ejpam-4424	36	13	lemmas	lemmas	PROPN
ejpam-4424	36	14	.	.	PUNCT
ejpam-4424	37	1	lemma	lemma	PROPN
ejpam-4424	37	2	1	1	NUM
ejpam-4424	37	3	.	.	PUNCT
ejpam-4424	38	1	(	(	PUNCT
ejpam-4424	38	2	leibniz	leibniz	PROPN
ejpam-4424	38	3	integral	integral	ADJ
ejpam-4424	38	4	rule	rule	NOUN
ejpam-4424	38	5	)	)	PUNCT
ejpam-4424	38	6	if	if	SCONJ
ejpam-4424	38	7	f	f	PROPN
ejpam-4424	38	8	and	and	CCONJ
ejpam-4424	38	9	fx	fx	PROPN
ejpam-4424	38	10	are	be	AUX
ejpam-4424	38	11	continuous	continuous	ADJ
ejpam-4424	38	12	functions	function	NOUN
ejpam-4424	38	13	,	,	PUNCT
ejpam-4424	38	14	then	then	ADV
ejpam-4424	38	15	d	d	X
ejpam-4424	38	16	dx	dx	PROPN
ejpam-4424	38	17	(	(	PUNCT
ejpam-4424	38	18	∫	∫	PROPN
ejpam-4424	38	19	b(x	b(x	NOUN
ejpam-4424	38	20	)	)	PUNCT
ejpam-4424	38	21	a(x	a(x	PROPN
ejpam-4424	38	22	)	)	PUNCT
ejpam-4424	38	23	f(x	f(x	PROPN
ejpam-4424	38	24	,	,	PUNCT
ejpam-4424	38	25	t	t	PROPN
ejpam-4424	38	26	)	)	PUNCT
ejpam-4424	38	27	dt	dt	NOUN
ejpam-4424	38	28	)	)	PUNCT
ejpam-4424	38	29	=	=	SYM
ejpam-4424	38	30	f(x	f(x	PROPN
ejpam-4424	38	31	,	,	PUNCT
ejpam-4424	38	32	b(x	b(x	NOUN
ejpam-4424	38	33	)	)	PUNCT
ejpam-4424	38	34	)	)	PUNCT
ejpam-4424	38	35	·	·	PUNCT
ejpam-4424	39	1	d	d	X
ejpam-4424	39	2	dx	dx	PROPN
ejpam-4424	39	3	b(x)−	b(x)−	PROPN
ejpam-4424	39	4	f(x	f(x	PROPN
ejpam-4424	39	5	,	,	PUNCT
ejpam-4424	39	6	a(x	a(x	PROPN
ejpam-4424	39	7	)	)	PUNCT
ejpam-4424	39	8	)	)	PUNCT
ejpam-4424	39	9	·	·	PUNCT
ejpam-4424	40	1	d	d	X
ejpam-4424	40	2	dx	dx	PROPN
ejpam-4424	40	3	a(x	a(x	PROPN
ejpam-4424	40	4	)	)	PUNCT
ejpam-4424	40	5	+	+	NUM
ejpam-4424	40	6	∫	∫	PROPN
ejpam-4424	40	7	b(x	b(x	NOUN
ejpam-4424	40	8	)	)	PUNCT
ejpam-4424	40	9	a(x	a(x	PROPN
ejpam-4424	40	10	)	)	PUNCT
ejpam-4424	40	11	∂	∂	PUNCT
ejpam-4424	40	12	∂x	∂x	PROPN
ejpam-4424	40	13	f(x	f(x	PROPN
ejpam-4424	40	14	,	,	PUNCT
ejpam-4424	40	15	t	t	PROPN
ejpam-4424	40	16	)	)	PUNCT
ejpam-4424	40	17	dt	dt	PUNCT
ejpam-4424	40	18	is	be	AUX
ejpam-4424	40	19	valid	valid	ADJ
ejpam-4424	40	20	for	for	ADP
ejpam-4424	40	21	a(x	a(x	NOUN
ejpam-4424	40	22	)	)	PUNCT
ejpam-4424	40	23	,	,	PUNCT
ejpam-4424	40	24	b(x	b(x	NOUN
ejpam-4424	40	25	)	)	PUNCT
ejpam-4424	40	26	,	,	PUNCT
ejpam-4424	40	27	a′(x	a′(x	PROPN
ejpam-4424	40	28	)	)	PUNCT
ejpam-4424	40	29	and	and	CCONJ
ejpam-4424	40	30	b′(x	b′(x	PRON
ejpam-4424	40	31	)	)	PUNCT
ejpam-4424	40	32	are	be	AUX
ejpam-4424	40	33	all	all	ADV
ejpam-4424	40	34	continuous	continuous	ADJ
ejpam-4424	40	35	.	.	PUNCT
ejpam-4424	41	1	if	if	SCONJ
ejpam-4424	41	2	a(x	a(x	NOUN
ejpam-4424	41	3	)	)	PUNCT
ejpam-4424	41	4	and	and	CCONJ
ejpam-4424	41	5	b(x	b(x	NOUN
ejpam-4424	41	6	)	)	PUNCT
ejpam-4424	41	7	are	be	AUX
ejpam-4424	41	8	constants	constant	NOUN
ejpam-4424	41	9	,	,	PUNCT
ejpam-4424	41	10	we	we	PRON
ejpam-4424	41	11	can	can	AUX
ejpam-4424	41	12	easily	easily	ADV
ejpam-4424	41	13	see	see	VERB
ejpam-4424	41	14	that	that	SCONJ
ejpam-4424	41	15	d	d	PROPN
ejpam-4424	41	16	dx	dx	PROPN
ejpam-4424	41	17	(	(	PUNCT
ejpam-4424	41	18	∫	∫	PROPN
ejpam-4424	41	19	b	b	PROPN
ejpam-4424	41	20	a	a	DET
ejpam-4424	41	21	f(x	f(x	PROPN
ejpam-4424	41	22	,	,	PUNCT
ejpam-4424	41	23	t	t	PROPN
ejpam-4424	41	24	)	)	PUNCT
ejpam-4424	41	25	dt	dt	NOUN
ejpam-4424	41	26	)	)	PUNCT
ejpam-4424	41	27	=	=	SYM
ejpam-4424	42	1	∫	∫	PROPN
ejpam-4424	42	2	b	b	PROPN
ejpam-4424	42	3	a	a	DET
ejpam-4424	42	4	∂	∂	NUM
ejpam-4424	42	5	∂x	∂x	PROPN
ejpam-4424	42	6	f(x	f(x	PROPN
ejpam-4424	42	7	,	,	PUNCT
ejpam-4424	42	8	t	t	PROPN
ejpam-4424	42	9	)	)	PUNCT
ejpam-4424	42	10	dt	dt	PROPN
ejpam-4424	42	11	.	.	PUNCT
ejpam-4424	43	1	lemma	lemma	PROPN
ejpam-4424	43	2	2	2	NUM
ejpam-4424	43	3	.	.	PUNCT
ejpam-4424	44	1	(	(	PUNCT
ejpam-4424	44	2	monotone	monotone	ADJ
ejpam-4424	44	3	convergence	convergence	NOUN
ejpam-4424	44	4	theorem(mct	theorem(mct	NOUN
ejpam-4424	44	5	)	)	PUNCT
ejpam-4424	45	1	[	[	X
ejpam-4424	45	2	1	1	NUM
ejpam-4424	45	3	,	,	PUNCT
ejpam-4424	45	4	2	2	NUM
ejpam-4424	45	5	]	]	PUNCT
ejpam-4424	45	6	)	)	PUNCT
ejpam-4424	45	7	.	.	PUNCT
ejpam-4424	46	1	let	let	VERB
ejpam-4424	46	2	m+	m+	PRON
ejpam-4424	46	3	be	be	AUX
ejpam-4424	46	4	the	the	DET
ejpam-4424	46	5	collection	collection	NOUN
ejpam-4424	46	6	of	of	ADP
ejpam-4424	46	7	all	all	DET
ejpam-4424	46	8	non	non	ADJ
ejpam-4424	46	9	-	-	ADJ
ejpam-4424	46	10	negative	negative	ADJ
ejpam-4424	46	11	measurable	measurable	ADJ
ejpam-4424	46	12	functions	function	NOUN
ejpam-4424	46	13	and	and	CCONJ
ejpam-4424	46	14	let	let	VERB
ejpam-4424	46	15	µ	µ	X
ejpam-4424	46	16	be	be	AUX
ejpam-4424	46	17	a	a	DET
ejpam-4424	46	18	measure	measure	NOUN
ejpam-4424	46	19	.	.	PUNCT
ejpam-4424	47	1	if	if	SCONJ
ejpam-4424	47	2	(	(	PUNCT
ejpam-4424	47	3	fn	fn	NOUN
ejpam-4424	47	4	)	)	PUNCT
ejpam-4424	47	5	is	be	AUX
ejpam-4424	47	6	a	a	DET
ejpam-4424	47	7	monotone	monotone	ADJ
ejpam-4424	47	8	increasing	increase	VERB
ejpam-4424	47	9	sequence	sequence	NOUN
ejpam-4424	47	10	of	of	ADP
ejpam-4424	47	11	functions	function	NOUN
ejpam-4424	47	12	in	in	ADP
ejpam-4424	47	13	m+	m+	NUM
ejpam-4424	47	14	which	which	PRON
ejpam-4424	47	15	converges	converge	VERB
ejpam-4424	47	16	to	to	ADP
ejpam-4424	47	17	f	f	PROPN
ejpam-4424	47	18	,	,	PUNCT
ejpam-4424	47	19	then∫	then∫	NOUN
ejpam-4424	47	20	f	f	PROPN
ejpam-4424	48	1	dµ	dµ	PROPN
ejpam-4424	49	1	=	=	SYM
ejpam-4424	49	2	lim	lim	PROPN
ejpam-4424	49	3	∫	∫	PROPN
ejpam-4424	49	4	fn	fn	PROPN
ejpam-4424	49	5	dµ.	dµ.	PROPN
ejpam-4424	49	6	in	in	ADP
ejpam-4424	49	7	other	other	ADJ
ejpam-4424	49	8	words	word	NOUN
ejpam-4424	49	9	,	,	PUNCT
ejpam-4424	49	10	this	this	DET
ejpam-4424	49	11	theorem	theorem	NOUN
ejpam-4424	49	12	can	can	AUX
ejpam-4424	49	13	be	be	AUX
ejpam-4424	49	14	expressed	express	VERB
ejpam-4424	49	15	as∫	as∫	PROPN
ejpam-4424	49	16	f	f	PROPN
ejpam-4424	49	17	dµ	dµ	PROPN
ejpam-4424	50	1	=	=	SYM
ejpam-4424	50	2	∫	∫	PROPN
ejpam-4424	50	3	lim	lim	PROPN
ejpam-4424	50	4	fn	fn	PROPN
ejpam-4424	50	5	dµ	dµ	PROPN
ejpam-4424	51	1	=	=	SYM
ejpam-4424	51	2	lim	lim	PROPN
ejpam-4424	51	3	∫	∫	PROPN
ejpam-4424	51	4	fn	fn	PROPN
ejpam-4424	51	5	dµ.	dµ.	PROPN
ejpam-4424	51	6	gj	gj	PROPN
ejpam-4424	51	7	.	.	PUNCT
ejpam-4424	51	8	han	han	PROPN
ejpam-4424	51	9	,	,	PUNCT
ejpam-4424	51	10	hj	hj	PROPN
ejpam-4424	51	11	.	.	PROPN
ejpam-4424	52	1	kim	kim	PROPN
ejpam-4424	52	2	/	/	SYM
ejpam-4424	52	3	eur	eur	PROPN
ejpam-4424	52	4	.	.	PUNCT
ejpam-4424	53	1	j.	j.	PROPN
ejpam-4424	53	2	pure	pure	PROPN
ejpam-4424	53	3	appl	appl	PROPN
ejpam-4424	53	4	.	.	PROPN
ejpam-4424	53	5	math	math	PROPN
ejpam-4424	53	6	,	,	PUNCT
ejpam-4424	53	7	15	15	NUM
ejpam-4424	53	8	(	(	PUNCT
ejpam-4424	53	9	3	3	NUM
ejpam-4424	53	10	)	)	PUNCT
ejpam-4424	53	11	(	(	PUNCT
ejpam-4424	53	12	2022	2022	NUM
ejpam-4424	53	13	)	)	PUNCT
ejpam-4424	53	14	,	,	PUNCT
ejpam-4424	53	15	1211	1211	NUM
ejpam-4424	53	16	-	-	SYM
ejpam-4424	53	17	1216	1216	NUM
ejpam-4424	53	18	1213	1213	NUM
ejpam-4424	53	19	putting	put	VERB
ejpam-4424	53	20	fn	fn	NOUN
ejpam-4424	53	21	=	=	NOUN
ejpam-4424	53	22	g1	g1	PROPN
ejpam-4424	53	23	+	+	X
ejpam-4424	53	24	·	·	PUNCT
ejpam-4424	53	25	·	·	PUNCT
ejpam-4424	53	26	·	·	PUNCT
ejpam-4424	54	1	+	+	NUM
ejpam-4424	54	2	gn	gn	X
ejpam-4424	54	3	and	and	CCONJ
ejpam-4424	54	4	applying	apply	VERB
ejpam-4424	54	5	the	the	DET
ejpam-4424	54	6	mct	mct	NOUN
ejpam-4424	54	7	,	,	PUNCT
ejpam-4424	54	8	then∫	then∫	NOUN
ejpam-4424	54	9	∞∑	∞∑	NUM
ejpam-4424	54	10	n=1	n=1	PROPN
ejpam-4424	54	11	gn	gn	PROPN
ejpam-4424	54	12	dµ	dµ	PROPN
ejpam-4424	54	13	=	=	SYM
ejpam-4424	54	14	∫	∫	PROPN
ejpam-4424	54	15	lim	lim	PROPN
ejpam-4424	54	16	m∑	m∑	VERB
ejpam-4424	54	17	n=1	n=1	PROPN
ejpam-4424	54	18	gn	gn	PROPN
ejpam-4424	54	19	dµ	dµ	PROPN
ejpam-4424	54	20	=	=	PROPN
ejpam-4424	54	21	lim	lim	PROPN
ejpam-4424	54	22	m∑	m∑	VERB
ejpam-4424	54	23	n=1	n=1	PROPN
ejpam-4424	55	1	∫	∫	PROPN
ejpam-4424	55	2	gn	gn	PROPN
ejpam-4424	55	3	dµ	dµ	PROPN
ejpam-4424	55	4	=	=	PROPN
ejpam-4424	55	5	∞∑	∞∑	NUM
ejpam-4424	55	6	n=1	n=1	NUM
ejpam-4424	55	7	∫	∫	PROPN
ejpam-4424	55	8	gn	gn	PROPN
ejpam-4424	55	9	dµ	dµ	PROPN
ejpam-4424	55	10	for	for	ADP
ejpam-4424	55	11	gn	gn	PROPN
ejpam-4424	55	12	is	be	AUX
ejpam-4424	55	13	measurable	measurable	ADJ
ejpam-4424	55	14	.	.	PUNCT
ejpam-4424	56	1	this	this	PRON
ejpam-4424	56	2	is	be	AUX
ejpam-4424	56	3	the	the	DET
ejpam-4424	56	4	famous	famous	PROPN
ejpam-4424	56	5	beppo	beppo	PROPN
ejpam-4424	56	6	levi	levi	PROPN
ejpam-4424	56	7	’s	’s	PART
ejpam-4424	56	8	theorem	theorem	PROPN
ejpam-4424	56	9	.	.	PUNCT
ejpam-4424	57	1	lemma	lemma	PROPN
ejpam-4424	57	2	3	3	X
ejpam-4424	57	3	.	.	PUNCT
ejpam-4424	58	1	(	(	PUNCT
ejpam-4424	58	2	beppo	beppo	PROPN
ejpam-4424	58	3	levi	levi	PROPN
ejpam-4424	58	4	’s	’s	PART
ejpam-4424	58	5	theorem[2	theorem[2	PROPN
ejpam-4424	58	6	]	]	PUNCT
ejpam-4424	58	7	)	)	PUNCT
ejpam-4424	58	8	.	.	PUNCT
ejpam-4424	59	1	let	let	AUX
ejpam-4424	59	2	(	(	PUNCT
ejpam-4424	59	3	gn	gn	AUX
ejpam-4424	59	4	)	)	PUNCT
ejpam-4424	59	5	be	be	AUX
ejpam-4424	59	6	a	a	DET
ejpam-4424	59	7	sequence	sequence	NOUN
ejpam-4424	59	8	in	in	ADP
ejpam-4424	59	9	m+	m+	NOUN
ejpam-4424	59	10	,	,	PUNCT
ejpam-4424	59	11	then∫	then∫	NUM
ejpam-4424	59	12	∞∑	∞∑	NUM
ejpam-4424	59	13	n=1	n=1	PROPN
ejpam-4424	59	14	gn	gn	PROPN
ejpam-4424	59	15	dµ	dµ	PROPN
ejpam-4424	59	16	=	=	SYM
ejpam-4424	59	17	∞∑	∞∑	NUM
ejpam-4424	59	18	n=1	n=1	PROPN
ejpam-4424	59	19	∫	∫	PROPN
ejpam-4424	59	20	gn	gn	PROPN
ejpam-4424	59	21	dµ.	dµ.	PROPN
ejpam-4424	59	22	lemma	lemma	PROPN
ejpam-4424	59	23	4	4	X
ejpam-4424	59	24	.	.	PUNCT
ejpam-4424	60	1	(	(	PUNCT
ejpam-4424	60	2	lebesgue	lebesgue	NOUN
ejpam-4424	60	3	dominated	dominate	VERB
ejpam-4424	60	4	convergence	convergence	NOUN
ejpam-4424	60	5	theorem(ldct	theorem(ldct	PROPN
ejpam-4424	60	6	)	)	PUNCT
ejpam-4424	61	1	[	[	X
ejpam-4424	61	2	1	1	NUM
ejpam-4424	61	3	,	,	PUNCT
ejpam-4424	61	4	2	2	NUM
ejpam-4424	61	5	]	]	PUNCT
ejpam-4424	61	6	)	)	PUNCT
ejpam-4424	61	7	.	.	PUNCT
ejpam-4424	62	1	let	let	VERB
ejpam-4424	62	2	(	(	PUNCT
ejpam-4424	62	3	fn	fn	AUX
ejpam-4424	62	4	)	)	PUNCT
ejpam-4424	62	5	be	be	AUX
ejpam-4424	62	6	a	a	DET
ejpam-4424	62	7	sequence	sequence	NOUN
ejpam-4424	62	8	of	of	ADP
ejpam-4424	62	9	integrable	integrable	ADJ
ejpam-4424	62	10	functions	function	NOUN
ejpam-4424	62	11	which	which	PRON
ejpam-4424	62	12	converges	converge	VERB
ejpam-4424	62	13	almost	almost	ADV
ejpam-4424	62	14	everywhere	everywhere	ADV
ejpam-4424	62	15	to	to	ADP
ejpam-4424	62	16	a	a	DET
ejpam-4424	62	17	real	real	ADV
ejpam-4424	62	18	-	-	PUNCT
ejpam-4424	62	19	valued	value	VERB
ejpam-4424	62	20	measurable	measurable	ADJ
ejpam-4424	62	21	function	function	NOUN
ejpam-4424	62	22	f	f	PROPN
ejpam-4424	62	23	.	.	PUNCT
ejpam-4424	63	1	if	if	SCONJ
ejpam-4424	63	2	there	there	PRON
ejpam-4424	63	3	exists	exist	VERB
ejpam-4424	63	4	an	an	DET
ejpam-4424	63	5	integrable	integrable	ADJ
ejpam-4424	63	6	function	function	NOUN
ejpam-4424	63	7	g	g	ADP
ejpam-4424	63	8	such	such	ADJ
ejpam-4424	63	9	that	that	DET
ejpam-4424	63	10	|fn|	|fn|	PROPN
ejpam-4424	63	11	≤	≤	NUM
ejpam-4424	63	12	g	g	NOUN
ejpam-4424	63	13	for	for	ADP
ejpam-4424	63	14	all	all	DET
ejpam-4424	63	15	n	n	CCONJ
ejpam-4424	63	16	,	,	PUNCT
ejpam-4424	63	17	then	then	ADV
ejpam-4424	63	18	f	f	PROPN
ejpam-4424	63	19	is	be	AUX
ejpam-4424	63	20	integrable	integrable	ADJ
ejpam-4424	63	21	and	and	CCONJ
ejpam-4424	63	22	∫	∫	PROPN
ejpam-4424	64	1	f	f	PROPN
ejpam-4424	64	2	dµ	dµ	PROPN
ejpam-4424	65	1	=	=	PROPN
ejpam-4424	65	2	lim	lim	PROPN
ejpam-4424	65	3	∫	∫	PROPN
ejpam-4424	65	4	fndµ.	fndµ.	PROPN
ejpam-4424	65	5	as	as	ADP
ejpam-4424	65	6	an	an	DET
ejpam-4424	65	7	intuitive	intuitive	ADJ
ejpam-4424	65	8	approach	approach	NOUN
ejpam-4424	65	9	,	,	PUNCT
ejpam-4424	65	10	consider	consider	VERB
ejpam-4424	65	11	whether	whether	SCONJ
ejpam-4424	65	12	d	d	PRON
ejpam-4424	65	13	dx	dx	PROPN
ejpam-4424	65	14	∫	∫	PROPN
ejpam-4424	65	15	b	b	PROPN
ejpam-4424	65	16	a	a	DET
ejpam-4424	65	17	f(x	f(x	PROPN
ejpam-4424	65	18	,	,	PUNCT
ejpam-4424	65	19	t	t	PROPN
ejpam-4424	65	20	)	)	PUNCT
ejpam-4424	65	21	dt	dt	PUNCT
ejpam-4424	66	1	=	=	SYM
ejpam-4424	66	2	∫	∫	PROPN
ejpam-4424	66	3	b	b	PROPN
ejpam-4424	66	4	a	a	DET
ejpam-4424	66	5	fx(x	fx(x	ADJ
ejpam-4424	66	6	,	,	PUNCT
ejpam-4424	66	7	t	t	PROPN
ejpam-4424	66	8	)	)	PUNCT
ejpam-4424	66	9	dt	dt	NOUN
ejpam-4424	66	10	or	or	CCONJ
ejpam-4424	66	11	not	not	PART
ejpam-4424	66	12	.	.	PUNCT
ejpam-4424	67	1	putting	put	VERB
ejpam-4424	67	2	g(x	g(x	NOUN
ejpam-4424	67	3	)	)	PUNCT
ejpam-4424	68	1	=	=	SYM
ejpam-4424	69	1	∫	∫	PROPN
ejpam-4424	69	2	b	b	PROPN
ejpam-4424	69	3	a	a	DET
ejpam-4424	69	4	f(x	f(x	PROPN
ejpam-4424	69	5	,	,	PUNCT
ejpam-4424	69	6	t	t	PROPN
ejpam-4424	69	7	)	)	PUNCT
ejpam-4424	69	8	dt	dt	NOUN
ejpam-4424	69	9	,	,	PUNCT
ejpam-4424	69	10	we	we	PRON
ejpam-4424	69	11	have	have	VERB
ejpam-4424	69	12	g′(x	g′(x	PRON
ejpam-4424	69	13	)	)	PUNCT
ejpam-4424	70	1	=	=	SYM
ejpam-4424	70	2	lim	lim	PROPN
ejpam-4424	70	3	h→0	h→0	ADV
ejpam-4424	70	4	g(x+	g(x+	ADV
ejpam-4424	70	5	h)−	h)−	PROPN
ejpam-4424	70	6	g(x	g(x	NOUN
ejpam-4424	70	7	)	)	PUNCT
ejpam-4424	70	8	h	h	NOUN
ejpam-4424	71	1	=	=	SYM
ejpam-4424	71	2	lim	lim	PROPN
ejpam-4424	72	1	h→0	h→0	ADV
ejpam-4424	72	2	∫	∫	PROPN
ejpam-4424	72	3	b	b	PROPN
ejpam-4424	72	4	a	a	DET
ejpam-4424	72	5	f(x+	f(x+	NOUN
ejpam-4424	72	6	h	h	NOUN
ejpam-4424	72	7	,	,	PUNCT
ejpam-4424	72	8	t	t	PROPN
ejpam-4424	72	9	)	)	PUNCT
ejpam-4424	72	10	dt−	dt−	CCONJ
ejpam-4424	72	11	∫	∫	PROPN
ejpam-4424	72	12	b	b	PROPN
ejpam-4424	72	13	a	a	DET
ejpam-4424	72	14	f(x	f(x	PROPN
ejpam-4424	72	15	,	,	PUNCT
ejpam-4424	72	16	t	t	PROPN
ejpam-4424	72	17	)	)	PUNCT
ejpam-4424	72	18	dt	dt	PROPN
ejpam-4424	73	1	h	h	NOUN
ejpam-4424	73	2	=	=	PROPN
ejpam-4424	73	3	lim	lim	PROPN
ejpam-4424	74	1	h→0	h→0	ADV
ejpam-4424	74	2	∫	∫	PROPN
ejpam-4424	74	3	b	b	PROPN
ejpam-4424	74	4	a	a	DET
ejpam-4424	74	5	(	(	PUNCT
ejpam-4424	74	6	f(x+	f(x+	NOUN
ejpam-4424	74	7	h	h	NOUN
ejpam-4424	74	8	,	,	PUNCT
ejpam-4424	74	9	t)−	t)−	PROPN
ejpam-4424	74	10	f(x	f(x	PROPN
ejpam-4424	74	11	,	,	PUNCT
ejpam-4424	74	12	t	t	PROPN
ejpam-4424	74	13	)	)	PUNCT
ejpam-4424	74	14	)	)	PUNCT
ejpam-4424	74	15	h	h	NOUN
ejpam-4424	74	16	dt	dt	NOUN
ejpam-4424	75	1	=	=	SYM
ejpam-4424	75	2	lim	lim	PROPN
ejpam-4424	75	3	h→0	h→0	ADV
ejpam-4424	75	4	∫	∫	PROPN
ejpam-4424	75	5	b	b	PROPN
ejpam-4424	75	6	a	a	DET
ejpam-4424	75	7	f(x+	f(x+	NOUN
ejpam-4424	75	8	h	h	NOUN
ejpam-4424	75	9	,	,	PUNCT
ejpam-4424	75	10	t)−	t)−	PROPN
ejpam-4424	75	11	f(x	f(x	PROPN
ejpam-4424	75	12	,	,	PUNCT
ejpam-4424	75	13	t	t	PROPN
ejpam-4424	75	14	)	)	PUNCT
ejpam-4424	75	15	h	h	NOUN
ejpam-4424	75	16	dt	dt	NOUN
ejpam-4424	76	1	=	=	SYM
ejpam-4424	76	2	∫	∫	PROPN
ejpam-4424	76	3	b	b	PROPN
ejpam-4424	76	4	a	a	DET
ejpam-4424	76	5	fx(x	fx(x	ADJ
ejpam-4424	76	6	,	,	PUNCT
ejpam-4424	76	7	t	t	PROPN
ejpam-4424	76	8	)	)	PUNCT
ejpam-4424	76	9	dt	dt	PUNCT
ejpam-4424	76	10	by	by	ADP
ejpam-4424	76	11	ldct	ldct	PROPN
ejpam-4424	76	12	and	and	CCONJ
ejpam-4424	76	13	mean	mean	VERB
ejpam-4424	76	14	value	value	NOUN
ejpam-4424	76	15	theorem	theorem	VERB
ejpam-4424	76	16	.	.	PUNCT
ejpam-4424	77	1	therefore	therefore	ADV
ejpam-4424	77	2	,	,	PUNCT
ejpam-4424	77	3	d	d	PROPN
ejpam-4424	77	4	dx	dx	PROPN
ejpam-4424	77	5	∫	∫	PROPN
ejpam-4424	77	6	b	b	PROPN
ejpam-4424	77	7	a	a	DET
ejpam-4424	77	8	f(x	f(x	PROPN
ejpam-4424	77	9	,	,	PUNCT
ejpam-4424	77	10	t	t	PROPN
ejpam-4424	77	11	)	)	PUNCT
ejpam-4424	77	12	dt	dt	PUNCT
ejpam-4424	78	1	=	=	SYM
ejpam-4424	78	2	∫	∫	PROPN
ejpam-4424	78	3	b	b	PROPN
ejpam-4424	78	4	a	a	DET
ejpam-4424	78	5	fx(x	fx(x	ADJ
ejpam-4424	78	6	,	,	PUNCT
ejpam-4424	78	7	t	t	PROPN
ejpam-4424	78	8	)	)	PUNCT
ejpam-4424	78	9	dt	dt	NOUN
ejpam-4424	78	10	,	,	PUNCT
ejpam-4424	78	11	where	where	SCONJ
ejpam-4424	78	12	fx	fx	PROPN
ejpam-4424	78	13	is	be	AUX
ejpam-4424	78	14	the	the	DET
ejpam-4424	78	15	partial	partial	ADJ
ejpam-4424	78	16	derivative	derivative	NOUN
ejpam-4424	78	17	with	with	ADP
ejpam-4424	78	18	respect	respect	NOUN
ejpam-4424	78	19	to	to	ADP
ejpam-4424	78	20	x.	x.	NOUN
ejpam-4424	78	21	in	in	ADP
ejpam-4424	78	22	this	this	DET
ejpam-4424	78	23	regard	regard	NOUN
ejpam-4424	78	24	,	,	PUNCT
ejpam-4424	78	25	the	the	DET
ejpam-4424	78	26	following	follow	VERB
ejpam-4424	78	27	lemma	lemma	PROPN
ejpam-4424	78	28	can	can	AUX
ejpam-4424	78	29	be	be	AUX
ejpam-4424	78	30	constructed	construct	VERB
ejpam-4424	78	31	:	:	PUNCT
ejpam-4424	79	1	gj	gj	NOUN
ejpam-4424	79	2	.	.	PUNCT
ejpam-4424	79	3	han	han	PROPN
ejpam-4424	79	4	,	,	PUNCT
ejpam-4424	79	5	hj	hj	PROPN
ejpam-4424	79	6	.	.	PROPN
ejpam-4424	80	1	kim	kim	PROPN
ejpam-4424	80	2	/	/	SYM
ejpam-4424	80	3	eur	eur	PROPN
ejpam-4424	80	4	.	.	PUNCT
ejpam-4424	81	1	j.	j.	PROPN
ejpam-4424	81	2	pure	pure	PROPN
ejpam-4424	81	3	appl	appl	PROPN
ejpam-4424	81	4	.	.	PROPN
ejpam-4424	81	5	math	math	PROPN
ejpam-4424	81	6	,	,	PUNCT
ejpam-4424	81	7	15	15	NUM
ejpam-4424	81	8	(	(	PUNCT
ejpam-4424	81	9	3	3	NUM
ejpam-4424	81	10	)	)	PUNCT
ejpam-4424	81	11	(	(	PUNCT
ejpam-4424	81	12	2022	2022	NUM
ejpam-4424	81	13	)	)	PUNCT
ejpam-4424	81	14	,	,	PUNCT
ejpam-4424	81	15	1211	1211	NUM
ejpam-4424	81	16	-	-	SYM
ejpam-4424	81	17	1216	1216	NUM
ejpam-4424	81	18	1214	1214	NUM
ejpam-4424	81	19	lemma	lemma	PROPN
ejpam-4424	81	20	5	5	NUM
ejpam-4424	81	21	.	.	PUNCT
ejpam-4424	82	1	let	let	VERB
ejpam-4424	82	2	x	x	PRON
ejpam-4424	82	3	be	be	AUX
ejpam-4424	82	4	an	an	DET
ejpam-4424	82	5	open	open	ADJ
ejpam-4424	82	6	subset	subset	NOUN
ejpam-4424	82	7	of	of	ADP
ejpam-4424	82	8	r	r	NOUN
ejpam-4424	82	9	,	,	PUNCT
ejpam-4424	82	10	and	and	CCONJ
ejpam-4424	82	11	ω	ω	NUM
ejpam-4424	82	12	be	be	AUX
ejpam-4424	82	13	a	a	DET
ejpam-4424	82	14	measure	measure	NOUN
ejpam-4424	82	15	space	space	NOUN
ejpam-4424	82	16	.	.	PUNCT
ejpam-4424	83	1	if	if	SCONJ
ejpam-4424	83	2	f	f	PROPN
ejpam-4424	83	3	:	:	PUNCT
ejpam-4424	83	4	x×ω	x×ω	PUNCT
ejpam-4424	84	1	→	→	SYM
ejpam-4424	84	2	r	r	NOUN
ejpam-4424	84	3	satisfies	satisfy	VERB
ejpam-4424	84	4	the	the	DET
ejpam-4424	84	5	following	follow	VERB
ejpam-4424	84	6	conditions	condition	NOUN
ejpam-4424	84	7	:	:	PUNCT
ejpam-4424	84	8	(	(	PUNCT
ejpam-4424	84	9	i)f	i)f	X
ejpam-4424	84	10	is	be	AUX
ejpam-4424	84	11	lebesgue	lebesgue	NOUN
ejpam-4424	84	12	-	-	PUNCT
ejpam-4424	84	13	integrable	integrable	ADJ
ejpam-4424	84	14	,	,	PUNCT
ejpam-4424	84	15	(	(	PUNCT
ejpam-4424	84	16	ii)fx	ii)fx	PROPN
ejpam-4424	84	17	exists	exist	VERB
ejpam-4424	84	18	almost	almost	ADV
ejpam-4424	84	19	everywhere	everywhere	ADV
ejpam-4424	84	20	,	,	PUNCT
ejpam-4424	84	21	and	and	CCONJ
ejpam-4424	84	22	(	(	PUNCT
ejpam-4424	84	23	iii	iii	X
ejpam-4424	84	24	)	)	PUNCT
ejpam-4424	84	25	there	there	PRON
ejpam-4424	84	26	is	be	VERB
ejpam-4424	84	27	an	an	DET
ejpam-4424	84	28	integrable	integrable	ADJ
ejpam-4424	84	29	function	function	NOUN
ejpam-4424	84	30	g	g	ADP
ejpam-4424	85	1	such	such	ADJ
ejpam-4424	85	2	that	that	SCONJ
ejpam-4424	85	3	|fx|	|fx|	PRON
ejpam-4424	85	4	≤	≤	NOUN
ejpam-4424	85	5	g	g	NOUN
ejpam-4424	85	6	,	,	PUNCT
ejpam-4424	85	7	then	then	ADV
ejpam-4424	85	8	d	d	X
ejpam-4424	85	9	dx	dx	PROPN
ejpam-4424	85	10	∫	∫	PROPN
ejpam-4424	86	1	ω	ω	PROPN
ejpam-4424	86	2	f	f	PROPN
ejpam-4424	87	1	=	=	SYM
ejpam-4424	87	2	∫	∫	PROPN
ejpam-4424	87	3	ω	ω	PROPN
ejpam-4424	87	4	fx	fx	PROPN
ejpam-4424	87	5	.	.	PUNCT
ejpam-4424	88	1	proof	proof	NOUN
ejpam-4424	88	2	.	.	PUNCT
ejpam-4424	89	1	the	the	DET
ejpam-4424	89	2	proof	proof	NOUN
ejpam-4424	89	3	follows	follow	VERB
ejpam-4424	89	4	from	from	ADP
ejpam-4424	89	5	the	the	DET
ejpam-4424	89	6	ldct	ldct	NOUN
ejpam-4424	89	7	and	and	CCONJ
ejpam-4424	89	8	the	the	DET
ejpam-4424	89	9	mean	mean	ADJ
ejpam-4424	89	10	value	value	NOUN
ejpam-4424	89	11	theorem	theorem	VERB
ejpam-4424	89	12	.	.	PUNCT
ejpam-4424	90	1	regarding	regard	VERB
ejpam-4424	90	2	this	this	DET
ejpam-4424	90	3	problem	problem	NOUN
ejpam-4424	90	4	,	,	PUNCT
ejpam-4424	90	5	consider	consider	VERB
ejpam-4424	90	6	three	three	NUM
ejpam-4424	90	7	places	place	NOUN
ejpam-4424	90	8	in	in	ADP
ejpam-4424	90	9	kreyszig	kreyszig	PROPN
ejpam-4424	90	10	’s	’s	PART
ejpam-4424	90	11	advanced	advanced	ADJ
ejpam-4424	90	12	engineering	engineering	NOUN
ejpam-4424	90	13	mathematics	mathematic	NOUN
ejpam-4424	91	1	[	[	X
ejpam-4424	91	2	8	8	NUM
ejpam-4424	91	3	]	]	PUNCT
ejpam-4424	91	4	.	.	PUNCT
ejpam-4424	92	1	one	one	NOUN
ejpam-4424	92	2	is	be	AUX
ejpam-4424	92	3	shown	show	VERB
ejpam-4424	92	4	in	in	ADP
ejpam-4424	92	5	the	the	DET
ejpam-4424	92	6	proof	proof	NOUN
ejpam-4424	92	7	of	of	ADP
ejpam-4424	92	8	theorem	theorem	NOUN
ejpam-4424	92	9	1	1	NUM
ejpam-4424	92	10	of	of	ADP
ejpam-4424	92	11	section	section	NOUN
ejpam-4424	92	12	11.1	11.1	NUM
ejpam-4424	92	13	,	,	PUNCT
ejpam-4424	92	14	and	and	CCONJ
ejpam-4424	92	15	the	the	DET
ejpam-4424	92	16	other	other	ADJ
ejpam-4424	92	17	two	two	NUM
ejpam-4424	92	18	are	be	AUX
ejpam-4424	92	19	shown	show	VERB
ejpam-4424	92	20	in	in	ADP
ejpam-4424	92	21	the	the	DET
ejpam-4424	92	22	solution	solution	NOUN
ejpam-4424	92	23	of	of	ADP
ejpam-4424	92	24	example	example	NOUN
ejpam-4424	92	25	1	1	NUM
ejpam-4424	92	26	of	of	ADP
ejpam-4424	92	27	section	section	NOUN
ejpam-4424	92	28	12.12	12.12	NUM
ejpam-4424	92	29	.	.	PUNCT
ejpam-4424	93	1	theorem	theorem	NOUN
ejpam-4424	93	2	1	1	NUM
ejpam-4424	93	3	.	.	PUNCT
ejpam-4424	94	1	(	(	PUNCT
ejpam-4424	94	2	1)(interchange	1)(interchange	NOUN
ejpam-4424	94	3	of	of	ADP
ejpam-4424	94	4	infinite	infinite	ADJ
ejpam-4424	94	5	series	series	NOUN
ejpam-4424	94	6	and	and	CCONJ
ejpam-4424	94	7	integral)∫	integral)∫	NOUN
ejpam-4424	94	8	π	π	PROPN
ejpam-4424	94	9	−π	−π	ADJ
ejpam-4424	94	10	∞∑	∞∑	PROPN
ejpam-4424	94	11	n=1	n=1	PROPN
ejpam-4424	94	12	(	(	PUNCT
ejpam-4424	94	13	ancosnx+	ancosnx+	PROPN
ejpam-4424	94	14	bnsinnx	bnsinnx	PROPN
ejpam-4424	94	15	)	)	PUNCT
ejpam-4424	94	16	dx	dx	PROPN
ejpam-4424	95	1	=	=	PUNCT
ejpam-4424	95	2	∞∑	∞∑	NUM
ejpam-4424	95	3	n=1	n=1	PROPN
ejpam-4424	95	4	(	(	PUNCT
ejpam-4424	95	5	an	an	DET
ejpam-4424	95	6	∫	∫	PROPN
ejpam-4424	95	7	π	π	PROPN
ejpam-4424	95	8	−π	−π	ADJ
ejpam-4424	95	9	cosnx	cosnx	NOUN
ejpam-4424	95	10	dx+	dx+	NOUN
ejpam-4424	96	1	bn	bn	INTJ
ejpam-4424	96	2	∫	∫	PROPN
ejpam-4424	97	1	π	π	PROPN
ejpam-4424	97	2	−π	−π	PROPN
ejpam-4424	97	3	sinnx	sinnx	PROPN
ejpam-4424	97	4	dx	dx	PROPN
ejpam-4424	97	5	)	)	PUNCT
ejpam-4424	97	6	.	.	PUNCT
ejpam-4424	98	1	(	(	PUNCT
ejpam-4424	98	2	2	2	X
ejpam-4424	98	3	)	)	PUNCT
ejpam-4424	98	4	(	(	PUNCT
ejpam-4424	98	5	interchange	interchange	NOUN
ejpam-4424	98	6	of	of	ADP
ejpam-4424	98	7	limit	limit	NOUN
ejpam-4424	98	8	and	and	CCONJ
ejpam-4424	98	9	integral	integral	ADJ
ejpam-4424	98	10	)	)	PUNCT
ejpam-4424	98	11	let	let	VERB
ejpam-4424	98	12	w	w	NOUN
ejpam-4424	98	13	be	be	AUX
ejpam-4424	98	14	the	the	DET
ejpam-4424	98	15	displacement	displacement	NOUN
ejpam-4424	98	16	of	of	ADP
ejpam-4424	98	17	an	an	DET
ejpam-4424	98	18	elastic	elastic	ADJ
ejpam-4424	98	19	string	string	NOUN
ejpam-4424	98	20	such	such	ADJ
ejpam-4424	98	21	that	that	SCONJ
ejpam-4424	98	22	w(0	w(0	PROPN
ejpam-4424	98	23	,	,	PUNCT
ejpam-4424	98	24	t	t	PROPN
ejpam-4424	98	25	)	)	PUNCT
ejpam-4424	98	26	=	=	SYM
ejpam-4424	98	27	f(t	f(t	NOUN
ejpam-4424	98	28	)	)	PUNCT
ejpam-4424	99	1	=	=	PRON
ejpam-4424	99	2	{	{	PUNCT
ejpam-4424	99	3	sin	sin	PROPN
ejpam-4424	99	4	t	t	PROPN
ejpam-4424	99	5	(	(	PUNCT
ejpam-4424	99	6	0	0	NUM
ejpam-4424	99	7	≤	≤	PROPN
ejpam-4424	99	8	t	t	NOUN
ejpam-4424	99	9	≤	≤	ADJ
ejpam-4424	99	10	2π	2π	NOUN
ejpam-4424	99	11	)	)	PUNCT
ejpam-4424	99	12	0	0	PUNCT
ejpam-4424	100	1	otherwise	otherwise	ADV
ejpam-4424	100	2	.	.	PUNCT
ejpam-4424	101	1	then	then	ADV
ejpam-4424	101	2	lim	lim	PROPN
ejpam-4424	101	3	x→∞	x→∞	X
ejpam-4424	101	4	∫	∫	PROPN
ejpam-4424	101	5	∞	∞	PROPN
ejpam-4424	101	6	0	0	PROPN
ejpam-4424	101	7	e−stw(x	e−stw(x	PROPN
ejpam-4424	101	8	,	,	PUNCT
ejpam-4424	101	9	t	t	PROPN
ejpam-4424	101	10	)	)	PUNCT
ejpam-4424	101	11	dt	dt	PUNCT
ejpam-4424	102	1	=	=	SYM
ejpam-4424	102	2	∫	∫	PROPN
ejpam-4424	102	3	∞	∞	PROPN
ejpam-4424	102	4	0	0	NUM
ejpam-4424	102	5	e−st	e−st	ADJ
ejpam-4424	102	6	lim	lim	PROPN
ejpam-4424	102	7	x→∞	x→∞	PROPN
ejpam-4424	103	1	w(x	w(x	PROPN
ejpam-4424	103	2	,	,	PUNCT
ejpam-4424	103	3	t	t	PROPN
ejpam-4424	103	4	)	)	PUNCT
ejpam-4424	103	5	dt	dt	PUNCT
ejpam-4424	103	6	is	be	AUX
ejpam-4424	103	7	valid	valid	ADJ
ejpam-4424	103	8	for	for	ADP
ejpam-4424	103	9	lim	lim	PROPN
ejpam-4424	103	10	x→∞	x→∞	PROPN
ejpam-4424	104	1	w(x	w(x	PROPN
ejpam-4424	104	2	,	,	PUNCT
ejpam-4424	104	3	t	t	PROPN
ejpam-4424	104	4	)	)	PUNCT
ejpam-4424	104	5	=	=	SYM
ejpam-4424	105	1	0	0	X
ejpam-4424	105	2	.	.	PUNCT
ejpam-4424	106	1	(	(	PUNCT
ejpam-4424	106	2	3	3	NUM
ejpam-4424	106	3	)	)	PUNCT
ejpam-4424	106	4	(	(	PUNCT
ejpam-4424	106	5	interchange	interchange	NOUN
ejpam-4424	106	6	of	of	ADP
ejpam-4424	106	7	derivative	derivative	ADJ
ejpam-4424	106	8	and	and	CCONJ
ejpam-4424	106	9	integral	integral	ADJ
ejpam-4424	106	10	)	)	PUNCT
ejpam-4424	106	11	in	in	ADP
ejpam-4424	106	12	the	the	DET
ejpam-4424	106	13	function	function	NOUN
ejpam-4424	106	14	of	of	ADP
ejpam-4424	106	15	(	(	PUNCT
ejpam-4424	106	16	2),∫	2),∫	NOUN
ejpam-4424	106	17	∞	∞	NOUN
ejpam-4424	106	18	0	0	NUM
ejpam-4424	107	1	e−st∂	e−st∂	PROPN
ejpam-4424	107	2	2w	2w	NUM
ejpam-4424	107	3	∂x2	∂x2	NOUN
ejpam-4424	107	4	dt	dt	NOUN
ejpam-4424	107	5	=	=	SYM
ejpam-4424	107	6	∂2	∂2	PROPN
ejpam-4424	107	7	∂x2	∂x2	NOUN
ejpam-4424	107	8	∫	∫	PROPN
ejpam-4424	107	9	∞	∞	PROPN
ejpam-4424	107	10	0	0	NUM
ejpam-4424	107	11	e−stw	e−stw	NOUN
ejpam-4424	107	12	dt	dt	X
ejpam-4424	107	13	is	be	AUX
ejpam-4424	107	14	established	establish	VERB
ejpam-4424	107	15	.	.	PUNCT
ejpam-4424	108	1	proof	proof	NOUN
ejpam-4424	108	2	.	.	PUNCT
ejpam-4424	109	1	(	(	PUNCT
ejpam-4424	109	2	1	1	X
ejpam-4424	109	3	)	)	PUNCT
ejpam-4424	109	4	it	it	PRON
ejpam-4424	109	5	suffices	suffice	VERB
ejpam-4424	109	6	to	to	PART
ejpam-4424	109	7	show	show	VERB
ejpam-4424	109	8	that	that	SCONJ
ejpam-4424	109	9	the	the	DET
ejpam-4424	109	10	assumptions	assumption	NOUN
ejpam-4424	109	11	of	of	ADP
ejpam-4424	109	12	beppo	beppo	PROPN
ejpam-4424	109	13	levi	levi	PROPN
ejpam-4424	109	14	’s	’s	PART
ejpam-4424	109	15	theorem	theorem	PROPN
ejpam-4424	109	16	are	be	AUX
ejpam-4424	109	17	satisfied	satisfied	ADJ
ejpam-4424	109	18	.	.	PUNCT
ejpam-4424	110	1	since	since	SCONJ
ejpam-4424	110	2	∞∑	∞∑	NUM
ejpam-4424	110	3	n=1	n=1	PROPN
ejpam-4424	110	4	(	(	PUNCT
ejpam-4424	110	5	ancosnx+	ancosnx+	PROPN
ejpam-4424	110	6	bnsinnx	bnsinnx	NOUN
ejpam-4424	110	7	)	)	PUNCT
ejpam-4424	110	8	is	be	AUX
ejpam-4424	110	9	nonnegative	nonnegative	ADJ
ejpam-4424	110	10	valued	value	VERB
ejpam-4424	110	11	on	on	ADP
ejpam-4424	110	12	(	(	PUNCT
ejpam-4424	110	13	−π	−π	PROPN
ejpam-4424	110	14	,	,	PUNCT
ejpam-4424	110	15	π	π	NOUN
ejpam-4424	110	16	)	)	PUNCT
ejpam-4424	110	17	and	and	CCONJ
ejpam-4424	110	18	measurable	measurable	ADJ
ejpam-4424	110	19	,	,	PUNCT
ejpam-4424	110	20	the	the	DET
ejpam-4424	110	21	proof	proof	NOUN
ejpam-4424	110	22	is	be	AUX
ejpam-4424	110	23	complete	complete	ADJ
ejpam-4424	110	24	.	.	PUNCT
ejpam-4424	111	1	references	reference	NOUN
ejpam-4424	111	2	1215	1215	NUM
ejpam-4424	111	3	(	(	PUNCT
ejpam-4424	111	4	2	2	NUM
ejpam-4424	111	5	)	)	PUNCT
ejpam-4424	111	6	let	let	VERB
ejpam-4424	111	7	us	we	PRON
ejpam-4424	111	8	check	check	VERB
ejpam-4424	111	9	whether	whether	SCONJ
ejpam-4424	111	10	the	the	DET
ejpam-4424	111	11	assumption	assumption	NOUN
ejpam-4424	111	12	of	of	ADP
ejpam-4424	111	13	ldct	ldct	PROPN
ejpam-4424	111	14	is	be	AUX
ejpam-4424	111	15	satisfied	satisfied	ADJ
ejpam-4424	111	16	.	.	PUNCT
ejpam-4424	112	1	note	note	VERB
ejpam-4424	112	2	that	that	SCONJ
ejpam-4424	113	1	|w(x	|w(x	NOUN
ejpam-4424	113	2	,	,	PUNCT
ejpam-4424	113	3	t)|	t)|	ADJ
ejpam-4424	113	4	≤	≤	NUM
ejpam-4424	113	5	1	1	NUM
ejpam-4424	113	6	for	for	ADP
ejpam-4424	113	7	all	all	DET
ejpam-4424	113	8	t	t	NOUN
ejpam-4424	113	9	and	and	CCONJ
ejpam-4424	113	10	lim	lim	PROPN
ejpam-4424	113	11	x→∞	x→∞	PROPN
ejpam-4424	114	1	w(x	w(x	PROPN
ejpam-4424	114	2	,	,	PUNCT
ejpam-4424	114	3	t	t	PROPN
ejpam-4424	114	4	)	)	PUNCT
ejpam-4424	114	5	=	=	SYM
ejpam-4424	114	6	0	0	NUM
ejpam-4424	115	1	for	for	ADP
ejpam-4424	115	2	t	t	PROPN
ejpam-4424	115	3	≥	≥	PROPN
ejpam-4424	115	4	0	0	NUM
ejpam-4424	115	5	.	.	PUNCT
ejpam-4424	116	1	therefore	therefore	ADV
ejpam-4424	116	2	,	,	PUNCT
ejpam-4424	116	3	the	the	DET
ejpam-4424	116	4	result	result	NOUN
ejpam-4424	116	5	of	of	ADP
ejpam-4424	116	6	(	(	PUNCT
ejpam-4424	116	7	2	2	X
ejpam-4424	116	8	)	)	PUNCT
ejpam-4424	116	9	is	be	AUX
ejpam-4424	116	10	naturally	naturally	ADV
ejpam-4424	116	11	derived	derive	VERB
ejpam-4424	116	12	.	.	PUNCT
ejpam-4424	117	1	(	(	PUNCT
ejpam-4424	117	2	3	3	X
ejpam-4424	117	3	)	)	PUNCT
ejpam-4424	117	4	from	from	ADP
ejpam-4424	117	5	the	the	DET
ejpam-4424	117	6	point	point	NOUN
ejpam-4424	117	7	of	of	ADP
ejpam-4424	117	8	view	view	NOUN
ejpam-4424	117	9	of	of	ADP
ejpam-4424	117	10	the	the	DET
ejpam-4424	117	11	riemann	riemann	PROPN
ejpam-4424	117	12	integral	integral	ADJ
ejpam-4424	117	13	,	,	PUNCT
ejpam-4424	117	14	e−st	e−st	ADJ
ejpam-4424	117	15	and	and	CCONJ
ejpam-4424	117	16	−se−st	−se−st	NOUN
ejpam-4424	117	17	are	be	AUX
ejpam-4424	117	18	continuous	continuous	ADJ
ejpam-4424	117	19	,	,	PUNCT
ejpam-4424	117	20	so	so	CCONJ
ejpam-4424	117	21	the	the	DET
ejpam-4424	117	22	result	result	NOUN
ejpam-4424	117	23	is	be	AUX
ejpam-4424	117	24	obtained	obtain	VERB
ejpam-4424	117	25	by	by	ADP
ejpam-4424	117	26	the	the	DET
ejpam-4424	117	27	leibniz	leibniz	PROPN
ejpam-4424	117	28	integral	integral	ADJ
ejpam-4424	117	29	rule	rule	NOUN
ejpam-4424	117	30	.	.	PUNCT
ejpam-4424	118	1	next	next	ADV
ejpam-4424	118	2	,	,	PUNCT
ejpam-4424	118	3	let	let	VERB
ejpam-4424	118	4	us	we	PRON
ejpam-4424	118	5	check	check	VERB
ejpam-4424	118	6	it	it	PRON
ejpam-4424	118	7	in	in	ADP
ejpam-4424	118	8	terms	term	NOUN
ejpam-4424	118	9	of	of	ADP
ejpam-4424	118	10	the	the	DET
ejpam-4424	118	11	more	more	ADV
ejpam-4424	118	12	general	general	ADJ
ejpam-4424	118	13	lebesgue	lebesgue	NOUN
ejpam-4424	118	14	integral	integral	ADJ
ejpam-4424	118	15	.	.	PUNCT
ejpam-4424	119	1	since	since	SCONJ
ejpam-4424	119	2	e−st	e−st	ADJ
ejpam-4424	119	3	is	be	AUX
ejpam-4424	119	4	lebesgue	lebesgue	NOUN
ejpam-4424	119	5	integrable	integrable	ADJ
ejpam-4424	119	6	on	on	ADP
ejpam-4424	119	7	[	[	X
ejpam-4424	119	8	0,∞	0,∞	NOUN
ejpam-4424	119	9	)	)	PUNCT
ejpam-4424	119	10	,	,	PUNCT
ejpam-4424	119	11	−se−st	−se−st	NOUN
ejpam-4424	119	12	exists	exist	VERB
ejpam-4424	119	13	,	,	PUNCT
ejpam-4424	119	14	and	and	CCONJ
ejpam-4424	119	15	for	for	ADP
ejpam-4424	119	16	some	some	DET
ejpam-4424	119	17	constants	constant	NOUN
ejpam-4424	119	18	m	m	VERB
ejpam-4424	119	19	and	and	CCONJ
ejpam-4424	119	20	k	k	PRON
ejpam-4424	119	21	it	it	PRON
ejpam-4424	119	22	satisfies	satisfy	VERB
ejpam-4424	119	23	|	|	ADV
ejpam-4424	119	24	−	−	PROPN
ejpam-4424	119	25	se−st|	se−st|	PROPN
ejpam-4424	119	26	≤	≤	NUM
ejpam-4424	119	27	mekt	mekt	NOUN
ejpam-4424	119	28	,	,	PUNCT
ejpam-4424	119	29	by	by	ADP
ejpam-4424	119	30	lemma	lemma	PROPN
ejpam-4424	119	31	5	5	NUM
ejpam-4424	119	32	,	,	PUNCT
ejpam-4424	119	33	the	the	DET
ejpam-4424	119	34	proof	proof	NOUN
ejpam-4424	119	35	is	be	AUX
ejpam-4424	119	36	complete	complete	ADJ
ejpam-4424	119	37	.	.	PUNCT
ejpam-4424	120	1	based	base	VERB
ejpam-4424	120	2	on	on	ADP
ejpam-4424	120	3	the	the	DET
ejpam-4424	120	4	above	above	ADJ
ejpam-4424	120	5	results	result	NOUN
ejpam-4424	120	6	,	,	PUNCT
ejpam-4424	120	7	kreyszig	kreyszig	PROPN
ejpam-4424	120	8	’s	’s	PART
ejpam-4424	120	9	assumption	assumption	NOUN
ejpam-4424	120	10	(	(	PUNCT
ejpam-4424	120	11	p	p	NOUN
ejpam-4424	120	12	601	601	NUM
ejpam-4424	120	13	of	of	ADP
ejpam-4424	120	14	[	[	X
ejpam-4424	120	15	8	8	NUM
ejpam-4424	120	16	]	]	PUNCT
ejpam-4424	120	17	)	)	PUNCT
ejpam-4424	120	18	can	can	AUX
ejpam-4424	120	19	be	be	AUX
ejpam-4424	120	20	considered	consider	VERB
ejpam-4424	120	21	unnecessary	unnecessary	ADJ
ejpam-4424	120	22	.	.	PUNCT
ejpam-4424	121	1	the	the	DET
ejpam-4424	121	2	reason	reason	NOUN
ejpam-4424	121	3	is	be	AUX
ejpam-4424	121	4	that	that	PRON
ejpam-4424	121	5	e−stw	e−stw	NOUN
ejpam-4424	121	6	and	and	CCONJ
ejpam-4424	121	7	its	its	PRON
ejpam-4424	121	8	derivative	derivative	NOUN
ejpam-4424	121	9	are	be	AUX
ejpam-4424	121	10	continuous	continuous	ADJ
ejpam-4424	121	11	.	.	PUNCT
ejpam-4424	122	1	conflict	conflict	NOUN
ejpam-4424	122	2	of	of	ADP
ejpam-4424	122	3	interest	interest	NOUN
ejpam-4424	122	4	.	.	PUNCT
ejpam-4424	123	1	the	the	DET
ejpam-4424	123	2	authors	author	NOUN
ejpam-4424	123	3	declare	declare	VERB
ejpam-4424	123	4	no	no	DET
ejpam-4424	123	5	conflicts	conflict	NOUN
ejpam-4424	123	6	of	of	ADP
ejpam-4424	123	7	interest	interest	NOUN
ejpam-4424	123	8	.	.	PUNCT
ejpam-4424	124	1	acknowledgements	acknowledgement	VERB
ejpam-4424	124	2	the	the	DET
ejpam-4424	124	3	corresponding	corresponding	ADJ
ejpam-4424	124	4	author	author	NOUN
ejpam-4424	124	5	(	(	PUNCT
ejpam-4424	124	6	hj	hj	PROPN
ejpam-4424	124	7	.	.	PUNCT
ejpam-4424	124	8	kim	kim	PROPN
ejpam-4424	124	9	)	)	PUNCT
ejpam-4424	124	10	acknowledges	acknowledge	VERB
ejpam-4424	124	11	the	the	DET
ejpam-4424	124	12	support	support	NOUN
ejpam-4424	124	13	of	of	ADP
ejpam-4424	124	14	kyungdong	kyungdong	PROPN
ejpam-4424	124	15	university	university	PROPN
ejpam-4424	124	16	research	research	NOUN
ejpam-4424	124	17	fund	fund	NOUN
ejpam-4424	124	18	,	,	PUNCT
ejpam-4424	124	19	2022	2022	NUM
ejpam-4424	124	20	.	.	PUNCT
ejpam-4424	125	1	references	reference	NOUN
ejpam-4424	125	2	[	[	X
ejpam-4424	125	3	1	1	NUM
ejpam-4424	125	4	]	]	PUNCT
ejpam-4424	125	5	r.	r.	PROPN
ejpam-4424	125	6	g.	g.	PROPN
ejpam-4424	125	7	bartle	bartle	PROPN
ejpam-4424	125	8	.	.	PUNCT
ejpam-4424	126	1	the	the	DET
ejpam-4424	126	2	elements	element	NOUN
ejpam-4424	126	3	of	of	ADP
ejpam-4424	126	4	integration	integration	NOUN
ejpam-4424	126	5	and	and	CCONJ
ejpam-4424	126	6	lebesgue	lebesgue	NOUN
ejpam-4424	126	7	measure	measure	NOUN
ejpam-4424	126	8	.	.	PUNCT
ejpam-4424	127	1	john	john	PROPN
ejpam-4424	127	2	willy	willy	PROPN
ejpam-4424	127	3	sons	sons	PROPN
ejpam-4424	127	4	,	,	PUNCT
ejpam-4424	127	5	inc	inc	PROPN
ejpam-4424	127	6	.	.	PROPN
ejpam-4424	127	7	,	,	PUNCT
ejpam-4424	127	8	new	new	PROPN
ejpam-4424	127	9	york	york	PROPN
ejpam-4424	127	10	,	,	PUNCT
ejpam-4424	127	11	1995	1995	NUM
ejpam-4424	127	12	.	.	PUNCT
ejpam-4424	128	1	[	[	X
ejpam-4424	128	2	2	2	X
ejpam-4424	128	3	]	]	X
ejpam-4424	128	4	d.	d.	PROPN
ejpam-4424	128	5	l.	l.	PROPN
ejpam-4424	128	6	cohn	cohn	PROPN
ejpam-4424	128	7	.	.	PROPN
ejpam-4424	129	1	measure	measure	PROPN
ejpam-4424	129	2	theory	theory	NOUN
ejpam-4424	129	3	.	.	PUNCT
ejpam-4424	130	1	birkh¨auser	birkh¨auser	PROPN
ejpam-4424	130	2	,	,	PUNCT
ejpam-4424	130	3	boston	boston	PROPN
ejpam-4424	130	4	,	,	PUNCT
ejpam-4424	130	5	1980	1980	NUM
ejpam-4424	130	6	.	.	PUNCT
ejpam-4424	131	1	[	[	X
ejpam-4424	131	2	3	3	X
ejpam-4424	131	3	]	]	X
ejpam-4424	131	4	y.	y.	PROPN
ejpam-4424	131	5	h.	h.	PROPN
ejpam-4424	131	6	geum	geum	PROPN
ejpam-4424	131	7	,	,	PUNCT
ejpam-4424	131	8	a.k	a.k	PROPN
ejpam-4424	131	9	.	.	PROPN
ejpam-4424	131	10	rathie	rathie	NOUN
ejpam-4424	131	11	,	,	PUNCT
ejpam-4424	131	12	and	and	CCONJ
ejpam-4424	131	13	hj	hj	PROPN
ejpam-4424	131	14	.	.	PUNCT
ejpam-4424	132	1	kim	kim	PROPN
ejpam-4424	132	2	.	.	PROPN
ejpam-4424	132	3	matrix	matrix	NOUN
ejpam-4424	132	4	expression	expression	NOUN
ejpam-4424	132	5	of	of	ADP
ejpam-4424	132	6	convolution	convolution	NOUN
ejpam-4424	132	7	and	and	CCONJ
ejpam-4424	132	8	its	its	PRON
ejpam-4424	132	9	generalized	generalized	ADJ
ejpam-4424	132	10	continuous	continuous	ADJ
ejpam-4424	132	11	form	form	NOUN
ejpam-4424	132	12	.	.	PUNCT
ejpam-4424	133	1	symmetry	symmetry	NOUN
ejpam-4424	133	2	,	,	PUNCT
ejpam-4424	133	3	2020(12):1791	2020(12):1791	NUM
ejpam-4424	133	4	,	,	PUNCT
ejpam-4424	133	5	2020	2020	NUM
ejpam-4424	133	6	.	.	PUNCT
ejpam-4424	134	1	[	[	X
ejpam-4424	134	2	4	4	X
ejpam-4424	134	3	]	]	PUNCT
ejpam-4424	134	4	s.	s.	PROPN
ejpam-4424	134	5	jirakulchaiwong	jirakulchaiwong	PROPN
ejpam-4424	134	6	,	,	PUNCT
ejpam-4424	134	7	k.	k.	PROPN
ejpam-4424	134	8	nonlaopon	nonlaopon	PROPN
ejpam-4424	134	9	,	,	PUNCT
ejpam-4424	134	10	j.	j.	PROPN
ejpam-4424	134	11	tariboon	tariboon	PROPN
ejpam-4424	134	12	,	,	PUNCT
ejpam-4424	134	13	s.	s.	PROPN
ejpam-4424	134	14	k.	k.	PROPN
ejpam-4424	134	15	ntouyas	ntouyas	PROPN
ejpam-4424	134	16	,	,	PUNCT
ejpam-4424	134	17	and	and	CCONJ
ejpam-4424	134	18	hj	hj	PROPN
ejpam-4424	134	19	.	.	PUNCT
ejpam-4424	135	1	kim	kim	PROPN
ejpam-4424	135	2	.	.	PUNCT
ejpam-4424	136	1	on	on	ADP
ejpam-4424	136	2	(	(	PUNCT
ejpam-4424	136	3	p	p	X
ejpam-4424	136	4	,	,	PUNCT
ejpam-4424	136	5	q)-analogues	q)-analogue	NOUN
ejpam-4424	136	6	of	of	ADP
ejpam-4424	136	7	laplace	laplace	NOUN
ejpam-4424	136	8	-	-	PUNCT
ejpam-4424	136	9	typed	type	VERB
ejpam-4424	136	10	integral	integral	ADJ
ejpam-4424	136	11	transforms	transform	NOUN
ejpam-4424	136	12	and	and	CCONJ
ejpam-4424	136	13	applications	application	NOUN
ejpam-4424	136	14	.	.	PUNCT
ejpam-4424	136	15	symmetry	symmetry	NOUN
ejpam-4424	136	16	,	,	PUNCT
ejpam-4424	136	17	2021(13):631	2021(13):631	NUM
ejpam-4424	136	18	,	,	PUNCT
ejpam-4424	136	19	2021	2021	NUM
ejpam-4424	136	20	.	.	PUNCT
ejpam-4424	137	1	[	[	X
ejpam-4424	137	2	5	5	X
ejpam-4424	137	3	]	]	X
ejpam-4424	137	4	arjun	arjun	PROPN
ejpam-4424	137	5	k	k	PROPN
ejpam-4424	137	6	,	,	PUNCT
ejpam-4424	137	7	y.	y.	PROPN
ejpam-4424	137	8	h.	h.	PROPN
ejpam-4424	137	9	geum	geum	PROPN
ejpam-4424	137	10	rathie	rathie	NOUN
ejpam-4424	137	11	,	,	PUNCT
ejpam-4424	137	12	and	and	CCONJ
ejpam-4424	137	13	hj	hj	PROPN
ejpam-4424	137	14	.	.	PUNCT
ejpam-4424	138	1	kim	kim	PROPN
ejpam-4424	138	2	.	.	PUNCT
ejpam-4424	139	1	a	a	DET
ejpam-4424	139	2	note	note	NOUN
ejpam-4424	139	3	on	on	ADP
ejpam-4424	139	4	certain	certain	ADJ
ejpam-4424	139	5	laplace	laplace	NOUN
ejpam-4424	139	6	transforms	transform	VERB
ejpam-4424	139	7	of	of	ADP
ejpam-4424	139	8	convolution	convolution	NOUN
ejpam-4424	139	9	-	-	PUNCT
ejpam-4424	139	10	type	type	NOUN
ejpam-4424	139	11	integrals	integral	NOUN
ejpam-4424	139	12	involving	involve	VERB
ejpam-4424	139	13	product	product	NOUN
ejpam-4424	139	14	of	of	ADP
ejpam-4424	139	15	two	two	NUM
ejpam-4424	139	16	generalized	generalized	ADJ
ejpam-4424	139	17	hypergeometric	hypergeometric	ADJ
ejpam-4424	139	18	functions	function	NOUN
ejpam-4424	139	19	.	.	PUNCT
ejpam-4424	140	1	mathematical	mathematical	ADJ
ejpam-4424	140	2	problem	problem	NOUN
ejpam-4424	140	3	in	in	ADP
ejpam-4424	140	4	engineering	engineering	NOUN
ejpam-4424	140	5	,	,	PUNCT
ejpam-4424	140	6	2021:8827275	2021:8827275	NUM
ejpam-4424	140	7	,	,	PUNCT
ejpam-4424	140	8	2021	2021	NUM
ejpam-4424	140	9	.	.	PUNCT
ejpam-4424	141	1	[	[	X
ejpam-4424	141	2	6	6	NUM
ejpam-4424	141	3	]	]	PUNCT
ejpam-4424	141	4	hj	hj	PROPN
ejpam-4424	141	5	.	.	PUNCT
ejpam-4424	141	6	kim	kim	PROPN
ejpam-4424	141	7	.	.	PUNCT
ejpam-4424	142	1	the	the	DET
ejpam-4424	142	2	intrinsic	intrinsic	ADJ
ejpam-4424	142	3	structure	structure	NOUN
ejpam-4424	142	4	and	and	CCONJ
ejpam-4424	142	5	properties	property	NOUN
ejpam-4424	142	6	of	of	ADP
ejpam-4424	142	7	laplace	laplace	NOUN
ejpam-4424	142	8	-	-	PUNCT
ejpam-4424	142	9	typed	type	VERB
ejpam-4424	142	10	integral	integral	ADJ
ejpam-4424	142	11	transforms	transform	NOUN
ejpam-4424	142	12	.	.	PUNCT
ejpam-4424	143	1	mathematical	mathematical	ADJ
ejpam-4424	143	2	problem	problem	NOUN
ejpam-4424	143	3	in	in	ADP
ejpam-4424	143	4	engineering	engineering	NOUN
ejpam-4424	143	5	,	,	PUNCT
ejpam-4424	143	6	2017:1–8	2017:1–8	PROPN
ejpam-4424	143	7	,	,	PUNCT
ejpam-4424	143	8	2017	2017	NUM
ejpam-4424	143	9	.	.	PUNCT
ejpam-4424	144	1	references	reference	NOUN
ejpam-4424	144	2	1216	1216	NUM
ejpam-4424	144	3	[	[	X
ejpam-4424	144	4	7	7	NUM
ejpam-4424	144	5	]	]	SYM
ejpam-4424	144	6	hj	hj	PROPN
ejpam-4424	144	7	.	.	PUNCT
ejpam-4424	145	1	kim	kim	PROPN
ejpam-4424	145	2	.	.	PUNCT
ejpam-4424	146	1	the	the	DET
ejpam-4424	146	2	solution	solution	NOUN
ejpam-4424	146	3	of	of	ADP
ejpam-4424	146	4	the	the	DET
ejpam-4424	146	5	heat	heat	NOUN
ejpam-4424	146	6	equation	equation	NOUN
ejpam-4424	146	7	without	without	ADP
ejpam-4424	146	8	boundary	boundary	ADJ
ejpam-4424	146	9	conditions	condition	NOUN
ejpam-4424	146	10	.	.	PUNCT
ejpam-4424	147	1	dynamic	dynamic	ADJ
ejpam-4424	147	2	systems	system	NOUN
ejpam-4424	147	3	and	and	CCONJ
ejpam-4424	147	4	applications	application	NOUN
ejpam-4424	147	5	,	,	PUNCT
ejpam-4424	147	6	27:653–662	27:653–662	NUM
ejpam-4424	147	7	,	,	PUNCT
ejpam-4424	147	8	2018	2018	NUM
ejpam-4424	147	9	.	.	PUNCT
ejpam-4424	148	1	[	[	X
ejpam-4424	148	2	8	8	NUM
ejpam-4424	148	3	]	]	X
ejpam-4424	148	4	e.	e.	PROPN
ejpam-4424	148	5	kreyszig	kreyszig	PROPN
ejpam-4424	148	6	.	.	PUNCT
ejpam-4424	149	1	advanced	advanced	ADJ
ejpam-4424	149	2	engineering	engineering	NOUN
ejpam-4424	149	3	mathematics	mathematic	NOUN
ejpam-4424	149	4	.	.	PUNCT
ejpam-4424	150	1	wiley	wiley	PROPN
ejpam-4424	150	2	,	,	PUNCT
ejpam-4424	150	3	singapore	singapore	PROPN
ejpam-4424	150	4	,	,	PUNCT
ejpam-4424	150	5	2013	2013	NUM
ejpam-4424	150	6	.	.	PUNCT
ejpam-4424	151	1	[	[	X
ejpam-4424	151	2	9	9	NUM
ejpam-4424	151	3	]	]	PUNCT
ejpam-4424	151	4	s.	s.	PROPN
ejpam-4424	151	5	supaknaree	supaknaree	PROPN
ejpam-4424	151	6	,	,	PUNCT
ejpam-4424	151	7	k.	k.	PROPN
ejpam-4424	151	8	nonlaopon	nonlaopon	NOUN
ejpam-4424	151	9	,	,	PUNCT
ejpam-4424	151	10	and	and	CCONJ
ejpam-4424	151	11	hj	hj	PROPN
ejpam-4424	151	12	.	.	PUNCT
ejpam-4424	152	1	kim	kim	PROPN
ejpam-4424	152	2	.	.	PUNCT
ejpam-4424	153	1	further	further	ADJ
ejpam-4424	153	2	properties	property	NOUN
ejpam-4424	153	3	of	of	ADP
ejpam-4424	153	4	laplace	laplace	NOUN
ejpam-4424	153	5	-	-	PUNCT
ejpam-4424	153	6	type	type	NOUN
ejpam-4424	153	7	integral	integral	ADJ
ejpam-4424	153	8	transforms	transform	NOUN
ejpam-4424	153	9	.	.	PUNCT
ejpam-4424	154	1	dynamic	dynamic	ADJ
ejpam-4424	154	2	systems	system	NOUN
ejpam-4424	154	3	and	and	CCONJ
ejpam-4424	154	4	applications	application	NOUN
ejpam-4424	154	5	,	,	PUNCT
ejpam-4424	154	6	28:195–215	28:195–215	NUM
ejpam-4424	154	7	,	,	PUNCT
ejpam-4424	154	8	2019	2019	NUM
ejpam-4424	154	9	.	.	PUNCT