Proposition 22.1.7485809FFB162F

Proposition 22.1.74.85809FFB162F Let $H$ be an ample line bundle on $X$. Consider $\phi \in \mathrm{PSH}((L+H)^{\mathrm{An}})$. Assume that for each $m\in \mathbb {Z}_{>0}$, we have $\phi \in \mathrm{PSH}((L+m^{-1}H)^{\mathrm{An}})$. Then $\phi \in \mathrm{PSH}(L^{\mathrm{An}})$.