Corollary 16.9.1194B2CC4C30BB

Corollary 16.9.11.94B2CC4C30BB Let $\pi \colon Y\rightarrow X$ be a proper bimeromorphic morphism from a Kähler manifold. Given a net $(\varphi _ i)_{i\in I}$ in $\mathrm{PSH}(X,\theta )$ and $\varphi \in \mathrm{PSH}(X,\theta )$, the following are equivalent:

1. $\varphi _ i\xrightarrow {d_ S}\varphi $;

2. $\pi ^*\varphi _ i\xrightarrow {d_ S}\pi ^*\varphi $.