Remark 13.13.2218A02F6B9E0

Remark 13.13.2.218A02F6B9E0 Suppose that $X$ is a connected complex manifold of dimension $0$, namely, $X$ is a single point. In this case, by definition, the non-pluripolar product $\theta _{\varphi }^ n$ is given by the current of integration at the unique point. So $\mathrm{PSH}(X,\theta )_{>0}=\mathrm{PSH}(X,\theta )\cong \mathbb {R}$ in this case and $\int _ X \theta _{\varphi }^ n=1$ for all $\varphi \in \mathrm{PSH}(X,\theta )$.