On the double Lusin condition and convergence theorem for Kurzweil-Henstock type integrals
Equiintegrability in a compact interval E may be defined as a uniform integrability property that involves both the integrand fn and the corresponding primitive Fn. The pointwise convergence of the integrands fn to some f and the equiintegrability of the functions fn together imply that f is also in...
Saved in:
Main Authors: | , |
---|---|
Format: | text |
Published: |
Archīum Ateneo
2016
|
Subjects: | |
Online Access: | https://archium.ateneo.edu/mathematics-faculty-pubs/63 http://mb.math.cas.cz/full/141/2/mb141_2_4.pdf |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Institution: | Ateneo De Manila University |
id |
ph-ateneo-arc.mathematics-faculty-pubs-1062 |
---|---|
record_format |
eprints |
spelling |
ph-ateneo-arc.mathematics-faculty-pubs-10622020-03-13T07:02:33Z On the double Lusin condition and convergence theorem for Kurzweil-Henstock type integrals Racca, Abraham P Cabral, Emmanuel A Equiintegrability in a compact interval E may be defined as a uniform integrability property that involves both the integrand fn and the corresponding primitive Fn. The pointwise convergence of the integrands fn to some f and the equiintegrability of the functions fn together imply that f is also integrable with primitive F and that the primitives Fn converge uniformly to F. In this paper, another uniform integrability property called uniform double Lusin condition introduced in the papers E. Cabral and P. Y. Lee (2001/2002) is revisited. Under the assumption of pointwise convergence of the integrands fn, the three uniform integrability properties, namely equiintegrability and the two versions of the uniform double Lusin condition, are all equivalent. The first version of the double Lusin condition and its corresponding uniform double Lusin convergence theorem are also extended into the division space. 2016-01-01T08:00:00Z text https://archium.ateneo.edu/mathematics-faculty-pubs/63 http://mb.math.cas.cz/full/141/2/mb141_2_4.pdf Mathematics Faculty Publications Archīum Ateneo Kurzweil-Henstock integral g-integral double Lusin condition uniform double Lusin condition Mathematics |
institution |
Ateneo De Manila University |
building |
Ateneo De Manila University Library |
country |
Philippines |
collection |
archium.Ateneo Institutional Repository |
topic |
Kurzweil-Henstock integral g-integral double Lusin condition uniform double Lusin condition Mathematics |
spellingShingle |
Kurzweil-Henstock integral g-integral double Lusin condition uniform double Lusin condition Mathematics Racca, Abraham P Cabral, Emmanuel A On the double Lusin condition and convergence theorem for Kurzweil-Henstock type integrals |
description |
Equiintegrability in a compact interval E may be defined as a uniform integrability property that involves both the integrand fn and the corresponding primitive Fn. The pointwise convergence of the integrands fn to some f and the equiintegrability of the functions fn together imply that f is also integrable with primitive F and that the primitives Fn converge uniformly to F. In this paper, another uniform integrability property called uniform double Lusin condition introduced in the papers E. Cabral and P. Y. Lee (2001/2002) is revisited. Under the assumption of pointwise convergence of the integrands fn, the three uniform integrability properties, namely equiintegrability and the two versions of the uniform double Lusin condition, are all equivalent. The first version of the double Lusin condition and its corresponding uniform double Lusin convergence theorem are also extended into the division space. |
format |
text |
author |
Racca, Abraham P Cabral, Emmanuel A |
author_facet |
Racca, Abraham P Cabral, Emmanuel A |
author_sort |
Racca, Abraham P |
title |
On the double Lusin condition and convergence theorem for Kurzweil-Henstock type integrals |
title_short |
On the double Lusin condition and convergence theorem for Kurzweil-Henstock type integrals |
title_full |
On the double Lusin condition and convergence theorem for Kurzweil-Henstock type integrals |
title_fullStr |
On the double Lusin condition and convergence theorem for Kurzweil-Henstock type integrals |
title_full_unstemmed |
On the double Lusin condition and convergence theorem for Kurzweil-Henstock type integrals |
title_sort |
on the double lusin condition and convergence theorem for kurzweil-henstock type integrals |
publisher |
Archīum Ateneo |
publishDate |
2016 |
url |
https://archium.ateneo.edu/mathematics-faculty-pubs/63 http://mb.math.cas.cz/full/141/2/mb141_2_4.pdf |
_version_ |
1681506546114101248 |