On the relation between Denjoy--Khintchine and HK$_{r}$-integrals
Classical Analysis and ODEs
2023-11-14 v2
Abstract
We locate Musial\,\&\,Sagher's concept of HK-inte\-gration within the approximate Henstock--Kurzweil integral theory. If to restrict HK-integral by requirement that the indefinite HK-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.
Cite
@article{arxiv.2211.09269,
title = {On the relation between Denjoy--Khintchine and HK$_{r}$-integrals},
author = {Valentin A. Skvortsov and Piotr Sworowski},
journal= {arXiv preprint arXiv:2211.09269},
year = {2023}
}