A Vitali-type lemma for the boundary
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918099233538048 |
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| 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 |