Continuity Properties of Finely Plurisubharmonic Functions and pluripolarity

Details Continuity Properties of Finely Plurisubharmonic Functions and pluripolarity Continuity Properties of Finely Plurisubharmonic Functions and pluripolarity

2009-06-11

arxiv.org/abs/0906.2081v1

Mathematics

Complex Variables

8 pages

Scientific paper

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 -infinity sets of finely plurisubharmonic functions are pluripolar, hence graphs of finely holomorphic functions are pluripolar.

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