pluripolar set

Definition.

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

If $f$ is a holomorphic function then $\log |f|$ is a plurisubharmonic function. The zero set of $f$ is thena pluripolar set.