Corollary 3.3 . [033G]

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Corollary 3.3.

Let $K$ be a Borel subset of $X$ and set

{\mathcal{F}}_{K}:=\{\varphi\in PSH(X,\omega)\,/\,\sup_{K}\varphi=0\}.

Then ${\mathcal{F}}_{K}$ is relatively compact iff $K$ is not $PSH(X,\omega)$ -polar.