PomeCorollary 19.5.39.0EE135D07034 For any $T\in \mathcal{Z}_+(X,\alpha )$,
\[ \nu _{Y_{\bullet }}(T)\in \Delta _{Y_{\bullet }}(T)\subseteq \Delta _{Y_{\bullet }}(\alpha ). \]
Corollary 19.5.390EE135D07034
Proof. When $T$ is a Kähler current, this follows from theorem 19.5.37.
In general, by definition, $\nu _{Y_{\bullet }}(T)=\nu _{Y_{\bullet }}(T+\omega )$ for any Kähler form $\omega $ on $X$. It follows that
\[ \nu _{Y_{\bullet }}(T)\in \Delta _{Y_{\bullet }}(T+\omega ) \]
for any Kähler form $\omega $. It follows that $\nu _{Y_{\bullet }}(T)\in \Delta _{Y_{\bullet }}(T)$. $\square$
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