PomeDefinition 18.28.26.12F5599D8900 Given $\varphi \in \mathrm{PSH}(X,\theta )_{>0}$, we define the partial equilibrium energy functional $\mathcal{E}_{\theta ,K}^{\varphi }\colon C^0(K)\rightarrow \mathbb {R}$ as follows: given $v \in C^0(K)$, we set
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\begin{equation} \mathcal{E}_{\theta ,K}^{\varphi }(v)\coloneqq E_{\theta }^{P_{\theta }[\varphi ]_{\mathcal{I}}}\left(P_{\theta ,K}[\varphi ]_{\mathcal{I}}(v)\right). \end{equation}
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