On stability and continuity of bounded solutions of degenerate complex Monge–Ampère equations over compact Kähler manifolds

We obtain a stability estimate for the degenerate complex Monge–Ampère operator which generalizes a result of Kołodziej (2003) [12], . In particular, we obtain the optimal stability exponent and also treat the case when the right-hand side is a general Borel measure satisfying certain regularity conditions. Moreover, our result holds for functions plurisubharmonic with respect to a big form, thus generalizing the Kähler form setting in Kołodziej (2003) [12], . Independently, we also provide more detail for the proof in Zhang (2006) [18] on continuity of the solution with respect to a special big form when the right-hand side is Lp-measure with p>1.