Definition 17.15.4DAA4083947C1

Definition 17.15.4.DAA4083947C1 Let $\Gamma \in \mathrm{TC}(X,\theta )_{>0}$ and $\Gamma ' \in \mathrm{TC}(X,\theta ')_{>0}$. Then we define $\Gamma +\Gamma '\in \mathrm{TC}(X,\theta +\theta ')_{>0}$ as follows:

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   We set

   \[ (\Gamma +\Gamma ')_{\max }\coloneqq \Gamma _{\max }+\Gamma '_{\max }; \]
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   for any $\tau <(\Gamma +\Gamma ')_{\max }$, we define²

   6C3AF1760F9F 17.15.5

   \begin{equation} (\Gamma +\Gamma ')_{\tau }\coloneqq P_{\theta +\theta '}\left[\sup _{\delta \in \mathbb {R}} \left(\Gamma _\delta +\Gamma '_{\tau -\delta }\right)\right]. \end{equation}