The General Definition of the Complex Monge-Ampere Operator on Compact Kahler Manifolds
We introduce a wide subclass F(X, w) of quasi-plurisubharmonic functions in a compact Kahler manifold, on which the complex Monge-Ampere operator is well defined and the convergence theorem is valid. We also prove that F(X, w) is a convex cone and includes all quasi-plurisubharmonic functions that are in the Cegrell class.