Local property of maximal plurifinely plurisubharmonic functions

Abstract

In this paper, we prove that a continuous $\mathcal{F}$-plurisubharmonic functions defined in an $\mathcal{F}$-open set in ${\mathbb{C}}^n$ is $\mathcal{F}$-maximal if and only if it is $\mathcal{F}$-locally $\mathcal{F}$-maximal.