Continuous solutions to Monge–Ampère equations on Hermitian manifolds for measures dominated by capacity

Abstract We prove the existence of a continuous quasi-plurisubharmonic solution to Monge–Ampère equation on compact Hermitian manifold for very general measure right hand side. admit measures dominated by capacity in certain manner, particular, moderate studied Dinh–Nguyen–Sibony. As consequence, we give characterization admitting Hölder potential, inspired work Dinh–Nguyen.