The General Definition of the Complex Monge--Ampère Operator on Compact Kähler Manifolds

http://dx.doi.org/10.4153/CJM-2010-012-7
Canad. J. Math. 62(2010), 218-239

  Published:2009-12-04
 Printed: Feb 2010

We introduce a wide subclass ${\mathcal F}(X,\omega)$ of quasi-plurisubharmonic functions in a compact Kähler manifold, on which the complex Monge-Ampère operator is well defined and the convergence theorem is valid. We also prove that ${\mathcal F}(X,\omega)$ is a convex cone and includes all quasi-plurisubharmonic functions that are in the Cegrell class.