Monge-Ampère measures of bounded potentials

Abstract

Let $X$ be a compact Kähler manifold and let $\mu$ be a non-pluripolar measure on $X$. We give a necessary and sufficient condition for $\mu$ so that the complex Monge-Ampère equation (in a Kähler class in $X$) having $\mu$ as the right-hand side admits a bounded solution. This implies in particular a well-known conjecture of Kolodziej that a complex Monge-Ampère equation on $X$ admits a bounded solution if it has a bounded subsolution.

There is a gap in the proof. So the paper is withdrawn