- Definition
- See also
- References
In mathematics, in the area of potential theory, a pluripolar set is the analog of a polar set for plurisubharmonic functions.
Definition
Let 
and let 
be a plurisubharmonic function which is not identically 
. The set
is called a complete pluripolar set. A pluripolar set is any subset of a complete pluripolar set. Pluripolar sets are of Hausdorff dimension at most 
and have zero Lebesgue measure.[1]
If 
is a holomorphic function then 
is a plurisubharmonic function. The zero set of is then a pluripolar set.
See also
- Skoda-El Mir theorem
References
1. ^{{cite book|last=Patrizio|first=Marco Abate ... [et al.] ; editors, Graziano Gentili, Jacques Guenot, Giorgio|title=Holomorphic dynamical systems : lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 7-12, 2008|year=2010|publisher=Springer|location=Berlin|isbn=9783642131707|page=275}}
- Steven G. Krantz. Function Theory of Several Complex Variables, AMS Chelsea Publishing, Providence, Rhode Island, 1992.
1 : Potential theory
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