Continuity properties of finely plurisubharmonic functions and pluripolarity
Said El MarzguiouiJan Wiegerinck
32U1532U0530G1231C40finely plurisubharmonic functionpluripolarity
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.
Indiana University Mathematics Journal
2010
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10.1512/iumj.2010.59.4078
10.1512/iumj.2010.59.4078
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Indiana Univ. Math. J. 59 (2010) 1793 - 1800
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