Definition 13.12.3BA13EE505D9B

Definition 13.12.3.BA13EE505D9B Let $U$ be an open subset of $X$. A function $f\colon U\rightarrow [-\infty ,\infty ]$ is quasi-continuous if it is Borel measurable and for any $\epsilon >0$, there is an open subset $G\subseteq U$ such that

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   $\operatorname{Cap}_{\theta }(G)\leq \epsilon $;

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   $f|_{U\setminus G}$ is real-valued and continuous.