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

  1. Sibony, Nessim; Schleicher, Dierk; Cuong, Dinh Tien; Brunella, Marco; Bedford, Eric; Abate, Marco (2010). Gentili, Graziano; Patrizio, Giorgio; Guenot, Jacques (eds.). Holomorphic Dynamical Systems: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 7-12, 2008. Springer Science & Business Media. p. 275. ISBN 978-3-642-13170-7.
  • Steven G. Krantz. Function Theory of Several Complex Variables, AMS Chelsea Publishing, Providence, Rhode Island, 1992.

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