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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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See also

References

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