A New Proof for The Banach–Zarecki Theorem
We present a modern and transparent proof of the Banach–Zarecki theorem, characterizing absolute continuity via continuity, bounded variation, and the preservation of Lebesgue null sets, while avoiding cumbersome estimates and classical summation arguments.
Authors
- Jia-Ming Li (ORCID: https://orcid.org/0009-0004-4573-761X)
Publication Details
- Journal
- American Mathematical Monthly
- Published
- 2026-08-24
- DOI
- https://doi.org/10.1080/00029890.2026.2702822
- Primary Topic
- Advanced Banach Space Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00