We obtain a stability estimate for the degenerate complex Monge-Ampère operator which generalizes a result of Kołodziej (2003) . 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) . Independently, we also provide more detail for the proof in Zhang (2006)  on continuity of the solution with respect to a special big form when the right-hand side is Lp-measure with p>1. © 2010.
Dinew, S., & Zhang, Z. (2010). On stability and continuity of bounded solutions of degenerate complex Monge-Ampère equations over compact Kähler manifolds. Advances in Mathematics, 225(1), 367–388. https://doi.org/10.1016/j.aim.2010.03.001