PomeProposition 22.1.44.07B251D899EF Let $(\Gamma ^ i)_{i\in I}$ be a decreasing net in $\mathrm{PSH}^{\mathrm{NA}}(X,\theta )$ satisfying (22.1.42). Assume that $\omega $ is a closed smooth positive $(1,1)$-form on $X$. Then
\[ P_{\theta +\omega }\left[ \inf _{i\in I} \Gamma ^{i} \right]_{\mathcal{I}}= \inf _{i\in I} P_{\theta +\omega }\left[ \Gamma ^{i} \right]_{\mathcal{I}}. \]
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