On the weighted m-energy classes

TL;DR

This paper explores properties and relationships of weighted m-subharmonic functions, establishing key theorems on integration and convergence, thereby advancing understanding of this mathematical class.

Contribution

It introduces new properties of weighted m-subharmonic functions and proves integration and convergence theorems, linking them to m-Cegrell classes.

Findings

Established properties of weighted m-subharmonic functions

Proved an integration theorem for this class

Demonstrated an almost everywhere convergence theorem

Abstract

In this article, we investigate the weighted $m-$subharmonic functions. We shall give some properties of this class and consider its relation to the $m-$Cegrell classes. We also prove an integration theorem and an almost everywhere convergence theorem for this class.