Definition 17.15.12D347D46F3537

Definition 17.15.12.D347D46F3537 Let $\Gamma ,\Gamma '\in \mathrm{TC}(X,\theta )_{>0}$. We define $\Gamma \lor \Gamma '\in \mathrm{TC}(X,\theta )_{>0}$ as follows:

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   We set

   \[ (\Gamma \lor \Gamma ')_{\max }\coloneqq \Gamma _{\max }\lor \Gamma '_{\max }; \]
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   for any $\tau <(\Gamma \lor \Gamma ')_{\max }$, we define

   CFA9EE6DC1ED 17.15.13

   \begin{equation} (\Gamma \lor \Gamma ')_{\tau }\coloneqq P_{\theta }\left[ \operatorname{CE}\left( \rho \mapsto \Gamma _{\rho }\lor \Gamma '_{\rho } \right)_{\tau } \right]. \end{equation}