PomeDefinition 13.13.18.434FC63292E2 Given a function $f\colon X\rightarrow [-\infty ,\infty ]$, we define $P_{\theta }(f)$ as follows:
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13.13.19
\begin{equation} P_{\theta }(f)\coloneqq \operatorname *{sup}_{}{}\! {}^{*}\left\{ \varphi \in \mathrm{PSH}(X,\theta ): \varphi \leq f\textup{ quasi-everywhere} \right\} {}^{\href{#sgpt-a0000013831}{5}}. \end{equation}
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