2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127035We prove several approximation theorems of the complex Monge-Ampere operator on a compact Kahler manifold. As an application we give a new proof of a recent result of Guedj and Zeriahi on a complete description of the range of the complex Monge-Ampere operator in the class of w-plurisubharmonic functions with vanishing complex Monge-Ampere mass on all pluripolar sets. As a by-product we obtain a stability theorem of solutions of complex Monge-Ampere equations in some subclass.This is the second version of the paperComplex VariablesDifferential Geometry32W20; 32Q15text