PomeDefinition 5.47.26.FF965EAEB1A3 Let $X$ be a complex manifold, let $W\subset X$ be a nonempty plurifine open set, let $Z\subset X$ be pluripolar, and let $f\colon W\setminus Z\to [-\infty ,\infty ]$. The quasi-supremum and the quasi-infimum of $f$ on $W$ are
\[ \operatorname *{q-sup}_ W f =\inf _{N}\, \sup _{W\setminus N}f, \qquad \operatorname *{q-inf}_ W f =\sup _{N}\, \inf _{W\setminus N}f, \]
where $N$ ranges over the pluripolar subsets of $X$ containing $Z$, and all suprema and infima are taken in $[-\infty ,\infty ]$.
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