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arXiv · 2607.08950

Integrability of a composition of functions

Alexander Kukush·Mykhailo Naumov
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Abstract

The paper deals with the Riemann and Lebesgue integrability of functions. Sufficient conditions and criteria are stated for the integrability of a composition of functions. Relevant counterexamples are constructed based on Cantor's perfect sets and the Cantor staircase function. The main tool of research is Lebesgue's criterion for Riemann integrability.

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Alexander Kukush, Mykhailo Naumov. 2026-07-09. Integrability of a composition of functions. https://arxiv.org/abs/2607.08950

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