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arXiv · 2311.05751

On points avoiding measures

Piotr Borodulin-Nadzieja·Artsiom Ranchynski
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Abstract

We say that an element $x$ of a topological space $X$ avoids measures if for every Borel measure $\mu$ on $X$ if $\mu(\{x\})=0$, then there is an open $U\ni x$ such that $\mu(U)=0$. The negation of this property can viewed as a local version of the property of supporting a strictly positive measure. We study points avoiding measures in the general setting as well as in the context of $\omega^\ast$, the remainder of Stone-\v{C}ech compactification of $\omega$.

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Piotr Borodulin-Nadzieja, Artsiom Ranchynski. 2023-11-09. On points avoiding measures. https://arxiv.org/abs/2311.05751

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