Definition 6.3.110E4AE8BC531

Definition 6.3.1.10E4AE8BC531 Let $n\ge 1$ and let $\Omega \subset \mathbb C^ n$ be open. An exhaustion function of $\Omega $ is a function $\rho \colon \Omega \to \mathbb R$ such that the sublevel set $\{ z\in \Omega :\rho (z)\le c\} $ is compact for every $c\in \mathbb R$. The open set $\Omega $ is pseudoconvex if it has a continuous plurisubharmonic exhaustion function.