Corollary 10.18.5A786309EB514

Corollary 10.18.5.A786309EB514 Assume $b>0$ and that $D_ p$ has a smooth maximizing sequence $(T_ j)$ with uniformly integrable densities $p k_{T_ j}$. Let $u\in \mathrm{PSH}(X,\omega )$ be a threshold subsolution for $f$, and suppose that $\omega +\mathrm{dd}^{\mathrm{c}}u\geq [E]$ for an effective real divisor $E$ whose Bott–Chern class is nef. Let $\beta _ E$ be any smooth closed representative of that class. Then for every smooth strictly positive probability measure $\mu $, the Gauduchon root volume of definition 12.2.1 satisfies