In this note, we present an alternative proof of the classical theorem by Banach and Zarecki, utilizing the Vitali covering lemma.

Absolutely continuous functions;Vitali covering lemma;Banach-Zarecki Theorem

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The work is supported by the Top-Notch Student Training Program 2.0 in Basic Disciplines (20212028); 2010 Mathematics Subject Classification. 26A46.

DOI： https://doi.org/10.62639/sspjinss10.20240101

Published： 2024