Problem 24.2.2FBE8C5BA5CA4

Problem 24.2.2.FBE8C5BA5CA4 Let $h$ be a Hermitian form on $X$ with zero lower mass, $v_-(h)=0$, and let $\mathrm{d}V$ be a smooth positive probability volume form. Let $0\leq f\in L^1(\mathrm{d}V)$ be nonzero, with positive density threshold $b_ h(f)>0$. Does there exist $u\in \mathrm{PSH}(X,h)$ such that

Determine the singularity type or envelope class in which such an equation should be posed.