arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~

零可加集与填充测度

Null-additive sets and packing measures

Ond{ř}ej Zindulka

arXiv 2610.05283首次发表:更新:

发表机构

Czech Technical University(捷克理工大学)

机构由 AI 辅助整理,请以论文原文为准。

AI 中文总结

本文刻画了严格测度零集,证明其在波兰局部紧群中为零可加,并在康托集、欧氏空间和环面上与零可加性等价。

AI 中文摘要

一个可分度量空间具有严格测度零,如果其由任意规范诱导的填充测度为零。我们提供了严格测度零的几个刻画,考察笛卡尔积,并证明在每一个波兰局部紧群中,每个严格测度零的集合都是零可加的,且在康托集、欧几里得空间和环面上这两个概念是等价的。

英文摘要

A separable metric space has strict measure zero if its packing measure induced by any gauge is zero. We provide a few characterizations of strict measure zero, look at cartesian products and prove that in every Polish locally compact group every set of strict measure zero is null-additive and that in the Cantor set, Euclidean spaces and tori the two notions are equivalent.

论文原文

arXiv 摘要页 · PDF 原文 · HTML 原文

↑