English

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 HKr_r-inte\-gration within the approximate Henstock--Kurzweil integral theory. If to restrict HKr_r-integral by requirement that the indefinite HKr_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.

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}
}
R2 v1 2026-06-28T06:05:11.382Z