PomeProposition 13.13.4.365687A6A087 Let $\pi \colon Y\rightarrow X$ be a proper bimeromorphic morphism from a Kähler manifold $Y$ and $T_1,\ldots ,T_ n$ be closed positive $(1,1)$-currents on $X$. Then
\[ \int _ Y (\pi ^*T_1)\wedge \cdots \wedge (\pi ^*T_ n)=\int _ X T_1\wedge \cdots \wedge T_ n. \]
Similarly, if $S_1,\ldots ,S_ n$ are closed positive $(1,1)$-currents on $Y$, then
\[ \int _ Y S_1\wedge \cdots \wedge S_ n=\int _ X \left(\pi _*S_1\right)\wedge \cdots \wedge \left(\pi _*S_ n\right). \]
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