Moduli of continuity and absolute continuity: any relation?
Classical Analysis and ODEs
2025-01-03 v1 Functional Analysis
Abstract
We construct a monotone, continuous, but not absolutely continuous function whose minimal modulus of continuity is absolutely continuous. In particular, we establish that there is no equivalence between the absolute continuity of a function and the absolute continuity of its modulus of continuity, in contrast with a well-known property of Lipschitz functions.
Keywords
Cite
@article{arxiv.2501.00441,
title = {Moduli of continuity and absolute continuity: any relation?},
author = {Matteo Muratori and Jacopo Somaglia},
journal= {arXiv preprint arXiv:2501.00441},
year = {2025}
}