On AP–Henstock–Kurzweil Integrals and Non-Atomic Radon Measure-Reference-Cited by-同舟云学术

On AP–Henstock–Kurzweil Integrals and Non-Atomic Radon Measure

Published:2023-03-22 Issue:6 Volume:11 Page:1552
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Kalita Hemanta¹,Hazarika Bipan²^ORCID,Becerra Tomás Pérez³^ORCID

Affiliation:

1. Department of Mathematics, Assam Don Bosco University, Guwahati 782402, Assam, India

2. Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India

3. Institute of Physics and Mathematics, Technological University of the Mixteca, Oaxaca 69000, Mexico

Abstract

The AP–Henstock–Kurzweil-type integral is defined on X, where X is a complete measure metric space. We present some properties of the integral, continuing the study’s use of a Radon measure μ. Finally, using locally finite measures, we extend the AP–Henstock–Kurzweil integral theory to second countable Hausdorff spaces that are locally compact. A Saks–Henstock-type Lemma is proved here.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/6/1552/pdf

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4. Saks, S. (1937). Theory of Integral, Hafner. [2nd revised ed.].

5. The approximately continuous Perron integral;Burkill;Math. Z.,1932

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