# pluripolar set

###### 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 $\log\lvert f\rvert$ is a plurisubharmonic function. The zero set of $f$ is then a pluripolar set.

## References

• 1 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
Title pluripolar set PluripolarSet 2013-03-22 14:29:15 2013-03-22 14:29:15 jirka (4157) jirka (4157) 5 jirka (4157) Definition msc 32U05 msc 31C10