# 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.