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arXiv · 2211.09269

On the relation between Denjoy--Khintchine and HK$_{r}$-integrals

Valentin A. Skvortsov·Piotr Sworowski
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Abstract

We locate Musial\,\&\,Sagher's concept of HK$_r$-inte\-gration within the approximate Henstock--Kurzweil integral theory. If to restrict HK$_r$-integral by requirement that the indefinite HK$_r$-integral is {\em continuous}, then it is included even in the classical Denjoy--Khintchine integral. We provide a direct argument demonstrating that this inclusion is proper.

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Valentin A. Skvortsov, Piotr Sworowski. 2022-11-17. On the relation between Denjoy--Khintchine and HK$_{r}$-integrals. https://arxiv.org/abs/2211.09269

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