Some properties of the complex Monge-Ampere operator in Cegrell's classes and applications

TL;DR

This paper investigates convergence properties and decomposition theorems for the complex Monge-Ampère operator within Cegrell's classes, leading to a comparison principle applicable in complex analysis.

Contribution

It introduces a new convergence result in capacity and a general decomposition theorem for Monge-Ampère measures, enhancing understanding of the operator's properties.

Findings

Proved a convergence result in capacity for the Monge-Ampère operator.

Established a general decomposition theorem for Monge-Ampère measures.

Derived a comparison principle for the complex Monge-Ampère operator.

Abstract

In this article we will first prove a result about convergence in capacity. Using the achieved result we will obtain a general decompositon theorem for complex Monge-Ampere measues which will be used to prove a comparison principle for the complex Monge-Ampere operator.