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 G \subset {\mathbb{C}}^n and let f \colon G \to {\mathbb{R}} \cup \{ - \infty \} be a plurisubharmonic function which is not identically -\infty. The set

{\mathcal{P}} := \{ z \in G \mid f(z) = - \infty \}

is called a complete pluripolar set. A pluripolar set is any subset of a complete pluripolar set.

If f is a holomorphic function then \log | f | is a plurisubharmonic function. The zero set of f is then a pluripolar set.

See also

References

  • Steven G. Krantz. Function Theory of Several Complex Variables, AMS Chelsea Publishing, Providence, Rhode Island, 1992.

This article incorporates material from pluripolar set on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.

Last modified on 23 January 2013, at 23:29