A Vitali-type lemma for the boundary

Fuente: arXiv
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Main Author: Weigt, Julian
Format: Preprint
Published: 2025
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_version_ 1866918099233538048
author Weigt, Julian
author_facet Weigt, Julian
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2507_15333
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Vitali-type lemma for the boundary
Weigt, Julian
Classical Analysis and ODEs
28A75, 42B25
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.
title A Vitali-type lemma for the boundary
topic Classical Analysis and ODEs
28A75, 42B25
url https://arxiv.org/abs/2507.15333