On points avoiding measures

Piotr Borodulin-Nadzieja, Artsiom Ranchynski

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…