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arXiv · 2403.11733

An HK$_r$-integrable function which is P$_s$-integrable for no $s$

Piotr Sworowski
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Abstract

Given arbitrary $r\ge1$, we construct an HK$_r$-integrable function which is not P$_1$-integrable. This is an extension of Musial et al.\ construction published recently in [Musial, P., Skvortsov, V., Tulone, F.: The HK$_r$-integral is not contained in the P$_r$-integral. Proc. Amer. Math. Soc. {\bf150}(5), 2107--2114 (2022)].

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Piotr Sworowski. 2024-03-18. An HK$_r$-integrable function which is P$_s$-integrable for no $s$. https://arxiv.org/abs/2403.11733

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