By classical results of G.C. Evans and G. Choquet on "good kernels $G$ in potential theory", for every polar $K_\sigma$-set $P$, there exists a finite measure $\mu$ on $P$ such that $G\mu=\infty$ on $P$, and a set $P$ admits a finite measure $\mu$ on $P$ such that $\{G\mu=\infty\}=P$ if and only if $P$ is a polar $G_\delta$-set... (read more)

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