On the Differentiation of Henstock and McShane Integrals

It is well known that the derivative of the primitive of one-dimensional Henstock integral exists almost everywhere. Point -interval pairs used in the derivative are Henstock point-interval pairs; which are consistent with point-interval pairs used in the Henstock integral. Note that almost everywhe...

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Main Authors: Chew, Tuan Seng, Cabral, Emmanuel A, Benitez, Julius V
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出版: Archīum Ateneo 2021
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在線閱讀:https://archium.ateneo.edu/mathematics-faculty-pubs/165
https://www.worldscientific.com/doi/epdf/10.1142/S2591722621400019
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spelling ph-ateneo-arc.mathematics-faculty-pubs-11692022-02-03T08:49:03Z On the Differentiation of Henstock and McShane Integrals Chew, Tuan Seng Cabral, Emmanuel A Benitez, Julius V It is well known that the derivative of the primitive of one-dimensional Henstock integral exists almost everywhere. Point -interval pairs used in the derivative are Henstock point-interval pairs; which are consistent with point-interval pairs used in the Henstock integral. Note that almost everywhere" is a set of points; more precisely; the derivative does not exist on a set of points with measure zero. We can transform a set of Henstock point-interval pairs to a set of points with measure zero because of Vitali's covering theorem. For one-dimensional McShane integrals; n-dimensional McShane and Henstock integrals; covering theorems of the Vitali type cannot be applied. In this paper; we shall discuss differentiation of n-dimensional McShane and Henstock integrals." 2021-03-08T08:00:00Z text https://archium.ateneo.edu/mathematics-faculty-pubs/165 https://www.worldscientific.com/doi/epdf/10.1142/S2591722621400019 Mathematics Faculty Publications Archīum Ateneo Henstock-Kurzweil integral derivative of an integral Vitali covering theorem Mathematics
institution Ateneo De Manila University
building Ateneo De Manila University Library
continent Asia
country Philippines
Philippines
content_provider Ateneo De Manila University Library
collection archium.Ateneo Institutional Repository
topic Henstock-Kurzweil integral
derivative of an integral
Vitali covering theorem
Mathematics
spellingShingle Henstock-Kurzweil integral
derivative of an integral
Vitali covering theorem
Mathematics
Chew, Tuan Seng
Cabral, Emmanuel A
Benitez, Julius V
On the Differentiation of Henstock and McShane Integrals
description It is well known that the derivative of the primitive of one-dimensional Henstock integral exists almost everywhere. Point -interval pairs used in the derivative are Henstock point-interval pairs; which are consistent with point-interval pairs used in the Henstock integral. Note that almost everywhere" is a set of points; more precisely; the derivative does not exist on a set of points with measure zero. We can transform a set of Henstock point-interval pairs to a set of points with measure zero because of Vitali's covering theorem. For one-dimensional McShane integrals; n-dimensional McShane and Henstock integrals; covering theorems of the Vitali type cannot be applied. In this paper; we shall discuss differentiation of n-dimensional McShane and Henstock integrals."
format text
author Chew, Tuan Seng
Cabral, Emmanuel A
Benitez, Julius V
author_facet Chew, Tuan Seng
Cabral, Emmanuel A
Benitez, Julius V
author_sort Chew, Tuan Seng
title On the Differentiation of Henstock and McShane Integrals
title_short On the Differentiation of Henstock and McShane Integrals
title_full On the Differentiation of Henstock and McShane Integrals
title_fullStr On the Differentiation of Henstock and McShane Integrals
title_full_unstemmed On the Differentiation of Henstock and McShane Integrals
title_sort on the differentiation of henstock and mcshane integrals
publisher Archīum Ateneo
publishDate 2021
url https://archium.ateneo.edu/mathematics-faculty-pubs/165
https://www.worldscientific.com/doi/epdf/10.1142/S2591722621400019
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