pluripolar set

Definition.

Let $G\subset {ℂ}^n$ and let $f:G\to ℝ\cup \{-\mathrm{\infty }\}$ be a plurisubharmonic function which is not identically $-\mathrm{\infty }$. The set $𝒫:=\{z\in G\mid f(z)=-\mathrm{\infty }\}$ 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.

Title	pluripolar set
Canonical name	PluripolarSet
Date of creation	2013-03-22 14:29:15
Last modified on	2013-03-22 14:29:15
Owner	jirka (4157)
Last modified by	jirka (4157)
Numerical id	5
Author	jirka (4157)
Entry type	Definition
Classification	msc 32U05
Classification	msc 31C10