Pluripolar set

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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.

[edit] 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 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.

[edit] 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 GFDL.

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