PomeCorollary 18.1.34.3305393E4400 Let $\theta $ be a smooth closed real $(1,1)$-form representing a big cohomology class. Let $(\varphi _ j)_{j\in I}$ be a net in $\mathrm{PSH}(X,\theta )$ and $\varphi \in \mathrm{PSH}(X,\theta )$. Assume that $\varphi _ j\xrightarrow {d_ S}\varphi $. Then
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\begin{equation} \operatorname{vol}\theta _{\varphi _ j}\to \operatorname{vol}\theta _{\varphi },\quad \int _ X \theta _{\varphi _ j}^ n\to \int _ X \theta _{\varphi }^ n. \end{equation}
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