Dominated sets, microscopic sets and Hausdorff measures
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910061407764480 |
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| author | Zindulka, Ondřej Nowakowski, Piotr |
| author_facet | Zindulka, Ondřej Nowakowski, Piotr |
| contents | Let $S$ be a family of sequences of positive numbers that decrease to 0, let $X$ be a metric space and $A \subset X$. $A$ is said to be $S$-dominated if, for every $s\in S$, a countable cover $\{E_n\}$ of $E$ can be found such that $diam E_n < s_n$ for all $n$. We examine the family of all $S$-dominated sets, denoted by $\mathcal{D}(S)$. In particular, we examine the connections between $\mathcal{D}(S)$ and families of sets with zero Hausdorff measure for some gauges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20050 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dominated sets, microscopic sets and Hausdorff measures Zindulka, Ondřej Nowakowski, Piotr Classical Analysis and ODEs 28A78, 28A75 Let $S$ be a family of sequences of positive numbers that decrease to 0, let $X$ be a metric space and $A \subset X$. $A$ is said to be $S$-dominated if, for every $s\in S$, a countable cover $\{E_n\}$ of $E$ can be found such that $diam E_n < s_n$ for all $n$. We examine the family of all $S$-dominated sets, denoted by $\mathcal{D}(S)$. In particular, we examine the connections between $\mathcal{D}(S)$ and families of sets with zero Hausdorff measure for some gauges. |
| title | Dominated sets, microscopic sets and Hausdorff measures |
| topic | Classical Analysis and ODEs 28A78, 28A75 |
| url | https://arxiv.org/abs/2603.20050 |