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Integrability of a composition of functions
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.
Related
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BibTeX
@misc{kukush2026integrability,
title = {{Integrability of a composition of functions}},
author = {Alexander Kukush and Mykhailo Naumov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.08950},
eprint = {2607.08950},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.08950},
}
RIS
TY - UNPB
TI - Integrability of a composition of functions
AU - Alexander Kukush
AU - Mykhailo Naumov
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2607.08950
UR - https://arxiv.org/abs/2607.08950
AB - 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.
ER -