PomeDefinition 17.3.1.8F92EE4FC37C Put
\[ \begin{aligned} \mathcal E^\infty (X,\theta ,\phi ) & =\{ u\in \mathrm{PSH}(X,\theta ):u\sim \phi \} ,\\ \mathcal E^1(X,\theta ,\phi ) & =\left\{ u\in \mathcal E(X,\theta ,\phi ): \int _ X|u-\phi |\, \mu _ u<\infty \right\} . \end{aligned} \]
The potentials in $\mathcal E^\infty (X,\theta ,\phi )$ have bounded difference from $\phi $, but they need not be bounded functions. The class $\mathcal E^1(X,\theta ,\phi )$ is the relative finite-energy class. For the potential $\phi =V_\theta $ with minimal singularities (definition 10.3.7) we omit the reference from these notations.
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