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arXiv · 2507.15333

A Vitali-type lemma for the boundary

Julian Weigt
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Abstract

Take a set of balls in $\mathbb R^d$. We find a subset of pairwise disjoint balls whose combined perimeter controls the perimeter of the union of the original balls. This can be seen as a boundary version of the Vitali covering lemma. We further prove combined volume-perimeter results and counterexamples and apply them to find short proofs of some regularity statements for maximal functions.

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Julian Weigt. 2025-07-21. A Vitali-type lemma for the boundary. https://arxiv.org/abs/2507.15333

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