IUMJ

Title: Continuity properties of finely plurisubharmonic functions and pluripolarity

Authors: Said El Marzguioui and Jan Wiegerinck

Issue: Volume 59 (2010), Issue 5, 1793-1800

Abstract:

We prove that every bounded finely plurisubharmonic function can be locally (in the pluri-fine topology) written as the difference of two usual plurisubharmonic functions. As a consequence, finely plurisubharmonic functions are continuous with respect to the pluri-fine topology. Moreover, we show that $-\infty$ sets of finely plurisubharmonic functions are pluripolar, hence graphs of finely holomorphic functions are pluripolar.