Example 13.12.5`472C675FCEA8`

Example 13.12.5.472C675FCEA8 A quasi-plurisubharmonic function on an open subset $U\subseteq X$ is always quasi-continuous. See [Theorem 4.20, GZ17] for the proof.

More generally, if $\varphi ,\psi $ are two quasi-plurisubharmonic functions on $U$, then the following function

\[ f(x)\coloneqq \begin{cases} \varphi (x)-\psi (x),& \textup{if }(\varphi \lor \psi )(x)\neq -\infty ;\\ \infty ,& \textup{otherwise} \end{cases} \]

is quasi-continuous.²

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@misc{pome-tag-472C675FCEA8,
  author = {{Pome contributors}},
  title = {Example 13.12.5},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/472C675FCEA8/}
}

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Example 13.12.5472C675FCEA8

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Example 13.12.5`472C675FCEA8`