id	sid	eid	entity	type
ejpam-3659	1	1	european journal	ORG
ejpam-3659	2	1	13	CARDINAL
ejpam-3659	2	2	2, 2020	DATE
ejpam-3659	2	3	303	CARDINAL
ejpam-3659	2	4	1307-5543	DATE
ejpam-3659	2	5	new york	GPE
ejpam-3659	2	6	r. sumalpong	PERSON
ejpam-3659	2	7	jr.1,∗	DATE
ejpam-3659	2	8	julius v. benitez1 1	PERSON
ejpam-3659	2	9	mindanao state university-iligan institute of technology	ORG
ejpam-3659	2	10	tibanga	GPE
ejpam-3659	2	11	iligan city	GPE
ejpam-3659	2	12	philippines	GPE
ejpam-3659	4	1	mcshane integrable	PERSON
ejpam-3659	4	2	mcshane integrable	PERSON
ejpam-3659	8	1	2020	DATE
ejpam-3659	8	2	26a39	CARDINAL
ejpam-3659	8	3	26a42	CARDINAL
ejpam-3659	8	4	mcshane δ	PERSON
ejpam-3659	8	5	zero	CARDINAL
ejpam-3659	9	1	1	CARDINAL
ejpam-3659	11	1	mcshane integrable	PERSON
ejpam-3659	12	1	5	CARDINAL
ejpam-3659	12	2	10.11	CARDINAL
ejpam-3659	13	1	mcshane integrable	PERSON
ejpam-3659	13	2	1	CARDINAL
ejpam-3659	15	1	mcshane integrable	PERSON
ejpam-3659	15	2	5	CARDINAL
ejpam-3659	15	3	10.4	CARDINAL
ejpam-3659	15	4	6	CARDINAL
ejpam-3659	15	5	10	CARDINAL
ejpam-3659	16	1	8	CARDINAL
ejpam-3659	17	1	∈	ORG
ejpam-3659	17	2	lim	PERSON
ejpam-3659	19	1	lim	PERSON
ejpam-3659	20	1	felipejr.sumalpong@g.msuiit.edu.ph	ORG
ejpam-3659	20	2	f. sumalpong jr.	PERSON
ejpam-3659	20	3	edu.ph	GPE
ejpam-3659	20	4	j. benitez	PERSON
ejpam-3659	21	1	303	CARDINAL
ejpam-3659	21	2	2020	DATE
ejpam-3659	22	1	f. sumalpong jr.	PERSON
ejpam-3659	22	2	j. benitez	PERSON
ejpam-3659	23	1	j. pure	PERSON
ejpam-3659	23	2	13	CARDINAL
ejpam-3659	23	3	2	CARDINAL
ejpam-3659	23	4	2020	DATE
ejpam-3659	23	5	303	CARDINAL
ejpam-3659	24	1	1	CARDINAL
ejpam-3659	25	1	mcshane integrable	PERSON
ejpam-3659	25	2	1	CARDINAL
ejpam-3659	25	3	lim	PERSON
ejpam-3659	26	1	1	CARDINAL
ejpam-3659	26	2	1)−	CARDINAL
ejpam-3659	26	3	1	CARDINAL
ejpam-3659	26	4	0	CARDINAL
ejpam-3659	26	5	1	CARDINAL
ejpam-3659	28	1	1	CARDINAL
ejpam-3659	29	1	0	CARDINAL
ejpam-3659	29	2	1]→	CARDINAL
ejpam-3659	29	3	6=	DATE
ejpam-3659	29	4	0	CARDINAL
ejpam-3659	31	1	0	CARDINAL
ejpam-3659	31	2	1]→	CARDINAL
ejpam-3659	31	3	f(x	ORG
ejpam-3659	32	1	0	CARDINAL
ejpam-3659	33	1	2x	CARDINAL
ejpam-3659	33	2	1 x2	QUANTITY
ejpam-3659	33	3	2	CARDINAL
ejpam-3659	33	4	1 x2	CARDINAL
ejpam-3659	34	1	0	CARDINAL
ejpam-3659	34	2	1	CARDINAL
ejpam-3659	35	1	0	CARDINAL
ejpam-3659	35	2	1	CARDINAL
ejpam-3659	36	1	0	CARDINAL
ejpam-3659	36	2	1	CARDINAL
ejpam-3659	36	3	0	CARDINAL
ejpam-3659	36	4	1	CARDINAL
ejpam-3659	37	1	0	CARDINAL
ejpam-3659	37	2	1	CARDINAL
ejpam-3659	38	1	2 2nπ±π	CARDINAL
ejpam-3659	39	1	n ∈ n	ORG
ejpam-3659	40	1	2 2nπ+π	CARDINAL
ejpam-3659	41	1	n ∈ n	PRODUCT
ejpam-3659	41	2	2 ·	CARDINAL
ejpam-3659	41	3	2nπ +	DATE
ejpam-3659	42	1	∞∑ n=0	PERSON
ejpam-3659	42	2	n=0	PERSON
ejpam-3659	42	3	2nπ +	DATE
ejpam-3659	42	4	2	CARDINAL
ejpam-3659	43	1	2	CARDINAL
ejpam-3659	44	1	2	CARDINAL
ejpam-3659	44	2	n=0 1	DATE
ejpam-3659	44	3	1	CARDINAL
ejpam-3659	44	4	2	CARDINAL
ejpam-3659	44	5	n=0	DATE
ejpam-3659	45	1	0	CARDINAL
ejpam-3659	45	2	1	CARDINAL
ejpam-3659	46	1	n=0	DATE
ejpam-3659	46	2	xn+1)|	ORG
ejpam-3659	46	3	f. sumalpong jr.	PERSON
ejpam-3659	46	4	j. benitez	PERSON
ejpam-3659	47	1	j. pure	PERSON
ejpam-3659	47	2	13	CARDINAL
ejpam-3659	47	3	2	CARDINAL
ejpam-3659	47	4	2020	DATE
ejpam-3659	47	5	303	CARDINAL
ejpam-3659	48	1	0	CARDINAL
ejpam-3659	48	2	1	CARDINAL
ejpam-3659	50	1	4	CARDINAL
ejpam-3659	51	1	mcshane integrable	PERSON
ejpam-3659	52	1	0	CARDINAL
ejpam-3659	52	2	1	CARDINAL
ejpam-3659	53	1	0	CARDINAL
ejpam-3659	53	2	1	CARDINAL
ejpam-3659	53	3	1	CARDINAL
ejpam-3659	53	4	mcshane integrable	PERSON
ejpam-3659	54	1	1	CARDINAL
ejpam-3659	55	1	16	CARDINAL
ejpam-3659	55	2	11	CARDINAL
ejpam-3659	55	3	0	CARDINAL
ejpam-3659	55	4	1	CARDINAL
ejpam-3659	56	1	5	CARDINAL
ejpam-3659	56	2	9.13	CARDINAL
ejpam-3659	57	1	mcshane integrable	PERSON
ejpam-3659	57	2	mcshane integrable	PERSON
ejpam-3659	58	1	3	CARDINAL
ejpam-3659	59	1	mcshane integrable	PERSON
ejpam-3659	59	2	mcshane integrable	PERSON
ejpam-3659	60	1	5	CARDINAL
ejpam-3659	60	2	9.19	CARDINAL
ejpam-3659	60	3	8	CARDINAL
ejpam-3659	62	1	mcshane integrable	PERSON
ejpam-3659	62	2	⊆	CARDINAL
ejpam-3659	62	3	x.	GPE
ejpam-3659	63	1	⊆	CARDINAL
ejpam-3659	64	1	2	CARDINAL
ejpam-3659	66	1	ξi)}ni=1	GPE
ejpam-3659	66	2	1	CARDINAL
ejpam-3659	66	3	2	DATE
ejpam-3659	68	1	⊆	CARDINAL
ejpam-3659	71	1	ξi)}ni=1	GPE
ejpam-3659	71	2	1	CARDINAL
ejpam-3659	71	3	2	DATE
ejpam-3659	74	1	⊆	CARDINAL
ejpam-3659	74	2	∈	ORG
ejpam-3659	78	1	mcshane δ	PERSON
ejpam-3659	79	1	∈	ORG
ejpam-3659	79	2	∪[u	PERSON
ejpam-3659	79	3	⊆	CARDINAL
ejpam-3659	80	1	10	CARDINAL
ejpam-3659	81	1	f. sumalpong jr.	PERSON
ejpam-3659	81	2	j. benitez	PERSON
ejpam-3659	82	1	j. pure	PERSON
ejpam-3659	82	2	13	CARDINAL
ejpam-3659	82	3	2	CARDINAL
ejpam-3659	82	4	2020	DATE
ejpam-3659	82	5	303	CARDINAL
ejpam-3659	82	6	306	CARDINAL
ejpam-3659	82	7	1	CARDINAL
ejpam-3659	83	1	6	CARDINAL
ejpam-3659	84	1	1	CARDINAL
ejpam-3659	85	1	5–7	CARDINAL
ejpam-3659	85	2	10	CARDINAL
ejpam-3659	87	1	mcshane integrable	PERSON
ejpam-3659	87	2	0	CARDINAL
ejpam-3659	90	1	mcshane integrable	PERSON
ejpam-3659	90	2	⊆	CARDINAL
ejpam-3659	91	1	mcshane integrable	PERSON
ejpam-3659	96	1	1	CARDINAL
ejpam-3659	98	1	mcshane integrable	PERSON
ejpam-3659	100	1	mcshane integrable	PERSON
ejpam-3659	104	1	2	CARDINAL
ejpam-3659	105	1	6	CARDINAL
ejpam-3659	106	1	0	CARDINAL
ejpam-3659	110	1	yang	PERSON
ejpam-3659	111	1	12	CARDINAL
ejpam-3659	112	1	2	CARDINAL
ejpam-3659	113	1	⊆	CARDINAL
ejpam-3659	113	2	⊆	CARDINAL
ejpam-3659	113	3	r.	NORP
ejpam-3659	113	4	r.	NORP
ejpam-3659	114	1	9	CARDINAL
ejpam-3659	114	2	quindala	GPE
ejpam-3659	114	3	benitez	PERSON
ejpam-3659	115	1	µ(e	NORP
ejpam-3659	116	1	∈	ORG
ejpam-3659	116	2	f. sumalpong	PERSON
ejpam-3659	117	1	j. benitez	PERSON
ejpam-3659	118	1	j. pure	PERSON
ejpam-3659	118	2	13	CARDINAL
ejpam-3659	118	3	2	CARDINAL
ejpam-3659	118	4	2020	DATE
ejpam-3659	118	5	303	CARDINAL
ejpam-3659	119	1	⊆	CARDINAL
ejpam-3659	120	1	1	CARDINAL
ejpam-3659	120	2	p.85	ORG
ejpam-3659	120	3	heine-borel	PERSON
ejpam-3659	121	1	2	CARDINAL
ejpam-3659	122	1	1	CARDINAL
ejpam-3659	122	2	mcshane integrable	PERSON
ejpam-3659	123	1	⊆	CARDINAL
ejpam-3659	123	2	e ⊆ o	ORG
ejpam-3659	124	1	⊆	CARDINAL
ejpam-3659	125	1	3	CARDINAL
ejpam-3659	126	1	12	CARDINAL
ejpam-3659	127	1	mcshane integrable	PERSON
ejpam-3659	129	1	3	CARDINAL
ejpam-3659	130	1	⊆	CARDINAL
ejpam-3659	130	2	zero	CARDINAL
ejpam-3659	130	3	if∫	NORP
ejpam-3659	130	4	0	CARDINAL
ejpam-3659	131	1	zero	CARDINAL
ejpam-3659	131	2	zero	CARDINAL
ejpam-3659	132	1	4	CARDINAL
ejpam-3659	133	1	a.e.	GPE
ejpam-3659	134	1	zero	CARDINAL
ejpam-3659	135	1	9	CARDINAL
ejpam-3659	135	2	mcshane integrable	PERSON
ejpam-3659	136	1	zero	CARDINAL
ejpam-3659	136	2	zero	CARDINAL
ejpam-3659	137	1	4	CARDINAL
ejpam-3659	138	1	mcshane integrable	PERSON
ejpam-3659	140	1	two	CARDINAL
ejpam-3659	140	2	a.e.	GPE
ejpam-3659	141	1	one	CARDINAL
ejpam-3659	141	2	mcshane integrable	PERSON
ejpam-3659	142	1	3	CARDINAL
ejpam-3659	143	1	9.5	CARDINAL
ejpam-3659	143	2	5	CARDINAL
ejpam-3659	143	3	10	CARDINAL
ejpam-3659	143	4	11	CARDINAL
ejpam-3659	144	1	f. sumalpong jr.	PERSON
ejpam-3659	144	2	j. benitez	PERSON
ejpam-3659	145	1	j. pure	PERSON
ejpam-3659	145	2	13	CARDINAL
ejpam-3659	145	3	2	CARDINAL
ejpam-3659	145	4	2020	DATE
ejpam-3659	145	5	303	CARDINAL
ejpam-3659	145	6	3	CARDINAL
ejpam-3659	151	1	3	CARDINAL
ejpam-3659	151	2	5	CARDINAL
ejpam-3659	154	1	4	CARDINAL
ejpam-3659	155	1	4	CARDINAL
ejpam-3659	157	1	lim n→∞	ORG
ejpam-3659	159	1	∈	ORG
ejpam-3659	162	1	5	CARDINAL
ejpam-3659	163	1	2	CARDINAL
ejpam-3659	165	1	mcshane integrable	PERSON
ejpam-3659	171	1	χe(f≤c	GPE
ejpam-3659	171	2	mcshane integrable	PERSON
ejpam-3659	172	1	e(f	PERSON
ejpam-3659	172	2	e(f	PERSON
ejpam-3659	172	3	mcshane integrable	PERSON
ejpam-3659	173	1	3	CARDINAL
ejpam-3659	173	2	5	CARDINAL
ejpam-3659	174	1	1	CARDINAL
ejpam-3659	177	1	e(f	PERSON
ejpam-3659	178	1	mct	PRODUCT
ejpam-3659	179	1	6	CARDINAL
ejpam-3659	179	2	convergence theorem	PERSON
ejpam-3659	180	1	1	CARDINAL
ejpam-3659	180	2	lim n→∞	ORG
ejpam-3659	181	1	f. sumalpong jr.	PERSON
ejpam-3659	181	2	j. benitez	PERSON
ejpam-3659	182	1	j. pure	PERSON
ejpam-3659	182	2	13	CARDINAL
ejpam-3659	182	3	2	CARDINAL
ejpam-3659	182	4	2020	DATE
ejpam-3659	182	5	303	CARDINAL
ejpam-3659	183	1	mcshane integrable	PERSON
ejpam-3659	183	2	lim n→∞	ORG
ejpam-3659	186	1	mcshane integrable	PERSON
ejpam-3659	186	2	mcshane integrable	PERSON
ejpam-3659	188	1	one	CARDINAL
ejpam-3659	188	2	⊆	CARDINAL
ejpam-3659	189	1	7	CARDINAL
ejpam-3659	190	1	3	CARDINAL
ejpam-3659	191	1	mcshane integrable	PERSON
ejpam-3659	192	1	3	CARDINAL
ejpam-3659	193	1	5	CARDINAL
ejpam-3659	194	1	8	CARDINAL
ejpam-3659	194	2	v)|	DATE
ejpam-3659	195	1	vmf	PERSON
ejpam-3659	198	1	mcshane integrable	PERSON
ejpam-3659	200	1	4	CARDINAL
ejpam-3659	202	1	⊆	CARDINAL
ejpam-3659	203	1	mcshane integrable	PERSON
ejpam-3659	204	1	vmf	PERSON
ejpam-3659	206	1	0	CARDINAL
ejpam-3659	207	1	henstock lemma	PERSON
ejpam-3659	207	2	3	CARDINAL
ejpam-3659	208	1	f. sumalpong jr.	PERSON
ejpam-3659	208	2	j. benitez	PERSON
ejpam-3659	209	1	j. pure	PERSON
ejpam-3659	209	2	13	CARDINAL
ejpam-3659	209	3	2	CARDINAL
ejpam-3659	209	4	2020	DATE
ejpam-3659	209	5	303	CARDINAL
ejpam-3659	209	6	mcshane integrable	PERSON
ejpam-3659	209	7	⊆	CARDINAL
ejpam-3659	209	8	mcshane integrable	PERSON
ejpam-3659	211	1	mcshane integrable	PERSON
ejpam-3659	212	1	3	CARDINAL
ejpam-3659	213	1	∑	PERSON
ejpam-3659	214	1	3 +	DATE
ejpam-3659	214	2	∑	PERSON
ejpam-3659	217	1	2ε	CARDINAL
ejpam-3659	220	1	vmf	ORG
ejpam-3659	225	1	1	CARDINAL
ejpam-3659	225	2	vmf	ORG
ejpam-3659	225	3	0	CARDINAL
ejpam-3659	227	1	3	CARDINAL
ejpam-3659	237	1	− u	PERSON
ejpam-3659	237	2	f. sumalpong jr.	PERSON
ejpam-3659	237	3	j. benitez	PERSON
ejpam-3659	238	1	j. pure	PERSON
ejpam-3659	238	2	13	CARDINAL
ejpam-3659	238	3	2	CARDINAL
ejpam-3659	238	4	2020	DATE
ejpam-3659	238	5	303	CARDINAL
ejpam-3659	241	1	3 +	DATE
ejpam-3659	241	2	3 +	CARDINAL
ejpam-3659	241	3	2ε 3 +	CARDINAL
ejpam-3659	245	1	2	CARDINAL
ejpam-3659	245	2	1	CARDINAL
ejpam-3659	245	3	2	CARDINAL
ejpam-3659	246	1	vmf	PERSON
ejpam-3659	247	1	8	CARDINAL
ejpam-3659	249	1	⊆	CARDINAL
ejpam-3659	250	1	mcshane integrable	PERSON
ejpam-3659	252	1	vmf	PERSON
ejpam-3659	254	1	lemma 4.	ORG
ejpam-3659	254	2	vmf	ORG
ejpam-3659	255	1	n ∈ n	ORG
ejpam-3659	257	1	⊆	CARDINAL
ejpam-3659	258	1	mcshane integrable	PERSON
ejpam-3659	258	2	lemma 4	PERSON
ejpam-3659	258	3	vmf	ORG
ejpam-3659	260	1	vmf	PERSON
ejpam-3659	261	1	312	CARDINAL
ejpam-3659	262	1	n ∈ n	ORG
ejpam-3659	262	2	vmf	ORG
ejpam-3659	262	3	n ∈ n	PERSON
ejpam-3659	262	4	6	DATE
ejpam-3659	263	1	mcshane integrable	PERSON
ejpam-3659	264	1	lim	PERSON
ejpam-3659	264	2	n→∞	CARDINAL
ejpam-3659	266	1	lim	PERSON
ejpam-3659	266	2	n→∞	CARDINAL
ejpam-3659	267	1	vmf	PERSON
ejpam-3659	268	1	4.	CARDINAL
ejpam-3659	270	1	⊆	CARDINAL
ejpam-3659	271	1	1	CARDINAL
ejpam-3659	271	2	j.v.	GPE
ejpam-3659	271	3	ph.d	ORG
ejpam-3659	272	1	msu-iligan institute of technology	ORG
ejpam-3659	272	2	2012	DATE
ejpam-3659	273	1	2	CARDINAL
ejpam-3659	273	2	j.v.	GPE
ejpam-3659	273	3	jamil	GPE
ejpam-3659	273	4	f.p.	GPE
ejpam-3659	273	5	t.s.	GPE
ejpam-3659	273	6	mcshane integrability	PERSON
ejpam-3659	273	7	32(2	CARDINAL
ejpam-3659	273	8	13-20	CARDINAL
ejpam-3659	274	1	3	CARDINAL
ejpam-3659	274	2	j.v.	GPE
ejpam-3659	274	3	3(1	CARDINAL
ejpam-3659	274	4	2012	DATE
ejpam-3659	275	1	4	CARDINAL
ejpam-3659	275	2	t.s.	GPE
ejpam-3659	275	3	riemann	PERSON
ejpam-3659	275	4	chulalongkorn university	ORG
ejpam-3659	275	5	2004	DATE
ejpam-3659	276	1	5	CARDINAL
ejpam-3659	276	2	r.	NORP
ejpam-3659	276	3	denjoy	PERSON
ejpam-3659	276	4	perron	ORG
ejpam-3659	276	5	4	DATE
ejpam-3659	276	6	amer	PERSON
ejpam-3659	277	1	1994	DATE
ejpam-3659	278	1	6	CARDINAL
ejpam-3659	278	2	p.y.	GPE
ejpam-3659	278	3	lanzhou	GPE
ejpam-3659	278	4	1989	DATE
ejpam-3659	279	1	7	CARDINAL
ejpam-3659	279	2	p.y.	GPE
ejpam-3659	279	3	r.	NORP
ejpam-3659	279	4	kurzweil	ORG
ejpam-3659	279	5	cambridge university press	ORG
ejpam-3659	279	6	2000	DATE
ejpam-3659	280	1	8	CARDINAL
ejpam-3659	280	2	t.y.	GPE
ejpam-3659	280	3	12, 2011	DATE
ejpam-3659	281	1	313	CARDINAL
ejpam-3659	281	2	9	CARDINAL
ejpam-3659	281	3	j.v.	GPE
ejpam-3659	281	4	quindala iii	PERSON
ejpam-3659	281	5	mcshane integrable	PERSON
ejpam-3659	281	6	9(3	CARDINAL
ejpam-3659	281	7	127	CARDINAL
ejpam-3659	281	8	2015	DATE
ejpam-3659	282	1	10	CARDINAL
ejpam-3659	282	2	swartz	ORG
ejpam-3659	282	3	2001	DATE
ejpam-3659	283	1	11	CARDINAL
ejpam-3659	283	2	riemann	PERSON
ejpam-3659	283	3	2011	DATE
ejpam-3659	284	1	12	CARDINAL
ejpam-3659	284	2	c.h.	GPE
ejpam-3659	284	3	national university of singapore	ORG
ejpam-3659	284	4	singapore	GPE
ejpam-3659	284	5	1996-97	DATE