Integrability of a composition of functions

Alexander Kukush; Mykhailo Naumov

Integrability of a composition of functions

Classical Analysis and ODEs 2026-07-09 v1

Authors: Alexander Kukush , Mykhailo Naumov

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.

Keywords

积分性复合函数黎曼积分勒贝格积分康托尔集反例

Cite

@article{arxiv.2607.08950,
  title  = {Integrability of a composition of functions},
  author = {Alexander Kukush and Mykhailo Naumov},
  journal= {arXiv preprint arXiv:2607.08950},
  year   = {2026}
}

Comments

21 pages