Approximation of plurifinely plurisubharmonic functions

TL;DR

This paper investigates how negative plurifinely plurisubharmonic functions can be approximated by increasing sequences of classical plurisubharmonic functions within Euclidean domains, enhancing understanding of their structure.

Contribution

It introduces a method to approximate plurifinely plurisubharmonic functions with classical ones, bridging the gap between plurifine and Euclidean potential theories.

Findings

Successful approximation of plurifinely plurisubharmonic functions by classical functions.

Establishment of conditions for increasing sequences of approximations.

Improved understanding of plurifine potential theory.

Abstract

In this paper, we study the approximation of negative plurifinely plurisubharmonic function defined on a plurifinely domain by an increasing sequence of plurisubharmonic functions defined in Euclidean domains.