Hausdorff 测度的覆盖数与均匀性数的分离需要大连续集合

Tatsuya Goto

Hausdorff 测度的覆盖数与均匀性数的分离需要大连续集合

经典分析与常微分方程 2025-07-18 v5 逻辑

作者: Tatsuya Goto

摘要

We show that if $\mathfrak{c} = \aleph_2$ then all covering numbers of Hausdorff measures $\operatorname{cov}(\mathcal{N}^s(\mathbb{R}^d))$ ( $0 < s < d, d \in \omega$ ) are equal and all uniformity numbers $\operatorname{non}(\mathcal{N}^s(\mathbb{R}^d))$ ( $0 < s < d, d \in \omega$ ) are equal. This is a partial answer to Problem 5.3 and 5.4 of [4].

关键词

Hausdorff 测度覆盖数均匀性数连续谱假设集合论基数

引用

@article{arxiv.2506.22592,
  title  = {Separating covering numbers and separating uniformity numbers of Hausdorff measures need large continuum},
  author = {Tatsuya Goto},
  journal= {arXiv preprint arXiv:2506.22592},
  year   = {2025}
}

备注

I found the gap in the proof of the main theorem (Theorem 13)

Hausdorff 测度的覆盖数与均匀性数的分离需要大连续集合

摘要

关键词

引用

备注

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