PomeDefinition 19.3.20.0887D96E8350 Let $\pi \colon Z\rightarrow X$ be a proper bimeromorphic morphism from a normal compact Kähler space, and let $S$ be a closed positive $(1,1)$-current on $Z$. Choose a proper bimeromorphic morphism $h\colon \widehat Z\rightarrow Z$ from a compact Kähler manifold such that $Y_{\bullet }$ admits a lifting $(W_{\bullet },g)$ to $\widehat Z$ with respect to $\pi \circ h$, where
\[ g=\operatorname{cor}(Y_{\bullet },\pi \circ h). \]
We define
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\begin{equation} \nu _{Y_{\bullet }}(S)\coloneqq \nu _{W_{\bullet }}(h^*S)g^{-1}\in \mathbb {R}^ n. \end{equation}
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