Equation 11.45.637E96D4A1D80

\begin{equation} u\preceq \psi \quad \Longleftrightarrow \quad u=\psi +r,\quad r\in \mathrm{PSH}(X,\eta ),\qquad \mathrm{MA}^{\mathrm{ext}}_\theta (\psi +r) =\mathrm{MA}^{\mathrm{ext}}_\eta (r). \end{equation}