On the approximation of weakly plurifinely plurisubharmonic functions

TL;DR

This paper investigates how to approximate singular weakly plurifinely plurisubharmonic functions using increasing sequences of classical plurisubharmonic functions on Euclidean neighborhoods, enhancing understanding of their structure.

Contribution

It introduces conditions under which weakly plurifinely plurisubharmonic functions can be approximated by classical plurisubharmonic functions on Euclidean neighborhoods.

Findings

Approximation of singular plurifinely plurisubharmonic functions achieved.

Conditions for increasing approximation sequences established.

Improves understanding of plurifinely plurisubharmonic function structure.

Abstract

In this note, we study the approximation of singular plurifinely plurisubharmonic function $u$ defined on a plurifinely domain $\Omega$. Under some conditions, we prove that $u$ can be approximated by an increasing sequence of plurisubharmonic functions defined on Euclidean neighborhoods of $\Omega$.