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arXiv · 2501.00441

Moduli of continuity and absolute continuity: any relation?

Matteo Muratori·Jacopo Somaglia
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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.

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Matteo Muratori, Jacopo Somaglia. 2024-12-31. Moduli of continuity and absolute continuity: any relation?. https://arxiv.org/abs/2501.00441

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