PomeDefinition 17.14.5.03BED679B3AD Given $\Gamma \in \mathrm{TC}(X,\theta ;\phi )$, we define its $\mathcal{I}$-envelope $P_{\theta }[\Gamma ]_{\mathcal{I}}$ as the map
\[ (-\infty ,\Gamma _{\max })\rightarrow \mathrm{PSH}(X,\theta ),\quad \tau \mapsto P_{\theta }\left[\Gamma _{\tau }\right]_{\mathcal{I}}. \]
More generally, for any closed real smooth positive $(1,1)$-form $\omega $ on $X$, we define $P_{\theta +\omega }[\Gamma ]_{\mathcal{I}}$ as the map
\[ (-\infty ,\Gamma _{\max })\rightarrow \mathrm{PSH}(X,\theta +\omega ),\quad \tau \mapsto P_{\theta +\omega }\left[\Gamma _{\tau }\right]_{\mathcal{I}}. \]
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