PomeRemark 17.12.3.3D73AB2E32CB Sometimes it is convenient to extend $\Gamma _{\tau }$ to $\tau \geq \Gamma _{\max }$ as well. This can be done as follows: for $\tau >\Gamma _{\max }$, we set $\Gamma _{\tau }\equiv -\infty $. For $\tau =\Gamma _{\max }$, we set
\[ \Gamma _{\tau }\coloneqq \inf _{\tau '<\Gamma _{\max }}\Gamma _{\tau '}\in \mathrm{PSH}(X,\theta ). \]
Note that $\Gamma _{\tau }\in \mathrm{PSH}(X,\theta )$ by corollary 5.17.5.
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