PomeDefinition 5.15.22.8485EC5E3BC1 Let $Z\subseteq X$ be a pluripolar set, and $f\colon X\setminus Z\rightarrow [-\infty ,\infty ]$ be a function. We define the quasi-supremum and the quasi-infimum of $f$ as follows:
\[ \begin{split} \operatorname *{q-sup}_ X f\coloneqq & \inf \left\{ \sup _{X\setminus W} f:W\supseteq Z, W \textup{ is pluripolar}\right\} ,\\ \operatorname *{q-inf}_ X f\coloneqq & \sup \left\{ \inf _{X\setminus W} f:W\supseteq Z, W \textup{ is pluripolar}\right\} . \end{split} \]
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