Proposition 11.25.13E5CF25D6E23

Proposition 11.25.1.3E5CF25D6E23 Assume that $\omega _ v$ is Gauduchon for every $v\in \mathcal H_\omega $. For every $u\in \mathrm{PSH}(X,\omega )\cap L^\infty (X)$, the measure

is a probability measure, which agrees with the preceding definition when $u\in \mathcal H_\omega $. If $u_ j,u\in \mathrm{PSH}(X,\omega )\cap L^\infty (X)$ are uniformly bounded and $u_ j\to u$ in capacity, then $\mu _{u_ j}\rightharpoonup \mu _ u$.