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

Author

Listed:
  • Hemanta Kalita

    (Department of Mathematics, Assam Don Bosco University, Guwahati 782402, Assam, India)

  • Bipan Hazarika

    (Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India)

  • Tomás Pérez Becerra

    (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.

Suggested Citation

  • Hemanta Kalita & Bipan Hazarika & Tomás Pérez Becerra, 2023. "On AP–Henstock–Kurzweil Integrals and Non-Atomic Radon Measure," Mathematics, MDPI, vol. 11(6), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1552-:d:1104405
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