PomeDefinition 16.5.1.6444F0A28464 We define
\[ \begin{aligned} \mathrm{PSH}(X,\theta ;\phi )\coloneqq & \left\{ \eta \in \mathrm{PSH}(X,\theta ): \eta \preceq \phi \right\} ,\\ \mathcal{E}^{\infty }(X,\theta ;\phi )\coloneqq & \left\{ \eta \in \mathrm{PSH}(X,\theta ): \eta \sim \phi \right\} ,\\ \mathcal{E}(X,\theta ;\phi )\coloneqq & \left\{ \eta \in \mathrm{PSH}(X,\theta ;\phi ): \int _ X \theta _{\eta }^ n=\int _ X \theta _{\phi }^ n\right\} ,\\ \mathcal{E}^1(X,\theta ;\phi )\coloneqq & \left\{ \eta \in \mathcal{E}(X,\theta ;\phi ): \int _ X |\phi -\eta |\, \theta _{\eta }^ n<\infty \right\} . \end{aligned} \]
Potentials in the last three classes are said to have relatively minimal singularities, full mass and finite energy relative to $\phi $ respectively.
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