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

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.