Corollary 14.19.117C5FAB3BA5DA

Proof. Let $u$ be a bounded $\omega $-plurisubharmonic function. If $\omega _ u^ n=0$, then theorem 14.19.10, applied with $c=0$ and the constant potential $v=\sup _ Xu+1$, would give $u\geq v$, a contradiction. $\square$