Definition of the complex Monge-Ampère operator for arbitrary plurisubharmonic functions

In this paper we consider the problem of definition of the Monge-Ampère operator for an arbitrary plurisubharmonic function. The paper has a survey character; in it we discuss on the results related to this area. We give one construction of the definition of the Monge-Ampère operator, which will then be applied to maximal plurisubharmonic functions.