A Vitali-type lemma for the boundary
Classical Analysis and ODEs
2025-07-22 v1
Abstract
Take a set of balls in . 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.
Cite
@article{arxiv.2507.15333,
title = {A Vitali-type lemma for the boundary},
author = {Julian Weigt},
journal= {arXiv preprint arXiv:2507.15333},
year = {2025}
}