PomeDefinition 16.5.10.8A07570966F8 We define the Monge–Ampère energy $E^{\phi }_{\theta }\colon \mathcal{E}^{\infty }(X,\theta ;\phi )\rightarrow \mathbb {R}$ as follows
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\begin{equation} E^{\phi }_{\theta }(\varphi )\coloneqq \frac{1}{n+1}\sum _{j=0}^ n \int _ X (\varphi -\phi )\, \theta _{\varphi }^ j\wedge \theta _{\phi }^{n-j}. \end{equation}
More generally, we extend $E_{\theta }^{\phi }$ to a functional $E^{\phi }_{\theta }\colon \mathrm{PSH}(X,\theta ;\phi )\rightarrow [-\infty ,\infty )$ as follows
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\begin{equation} E^{\phi }_{\theta }(\varphi )\coloneqq \inf \left\{ E^{\phi }_{\theta }(\psi ):\psi \in \mathcal{E}^{\infty }(X,\theta ;\phi ),\varphi \leq \psi \right\} . \end{equation}
We write $E_{\theta }$ instead of $E_{\theta }^{\phi }$ when $\phi =V_{\theta }$.
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