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Pluripolar set
Analog of a polar set for plurisubharmonic functions From Wikipedia, the free encyclopedia
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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 if is not the zero function.
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References
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