Pluripolar set
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
References
- Steven G. Krantz. Function Theory of Several Complex Variables, AMS Chelsea Publishing, Providence, Rhode Island, 1992.
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