Equation 13.13.3323948CFE8AEE

\begin{equation} \begin{aligned} P_{\theta }\Bigl (a\varphi +(1-a)\psi \Bigr )\coloneqq & \operatorname *{sup}_{}{}\! {}^{*}\left\{ \eta \in \mathrm{PSH}(X,\theta ): a^{-1}\eta +\left(1-a^{-1}\right)\psi \leq \varphi \right\} \\ \in & \mathrm{PSH}(X,\theta ). \end{aligned} \end{equation}