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.