PomeDefinition 17.13.1.2105331E66C7 Let $\Gamma \in \mathrm{TC}(X,\theta ;\phi )$. We define its Legendre transform as the map $\Gamma ^*\colon (0,\infty )\rightarrow \mathrm{PSH}(X,\theta )$ given by
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17.13.2
\begin{equation} \Gamma ^*_ t=\sup _{\tau \in \mathbb {R}} \left(t\tau + \Gamma _{\tau }\right){}^{\href{#sgpt-a0000073394}{1}}. \end{equation}
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