PomeLemma 17.15.30.B6D60981A394 Let $(\Gamma ^ i)_{i\in I}$ be a non-empty family in $\mathrm{TC}(X,\theta )_{>0}$ satisfying (17.15.21). Assume that $\omega $ is a closed smooth positive $(1,1)$-form on $X$. Then
\[ P_{\theta +\omega }\left[ \operatorname *{sup}_{i\in I}{}\! {}^{*} \Gamma ^{i} \right]= \operatorname *{sup}_{i\in I}{}\! {}^{*} P_{\theta +\omega }\left[ \Gamma ^{i} \right]. \]
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