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 $f\; colon\; G\; o\; \{mathbb\{R\; cup\; \{\; -\; infty\; \}$ 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.

See also

*Skoda-El Mir theorem

References

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

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