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Abstract

Let $D$ be a domain in ${\mathbb{C}}^n$. The plurisubharmonic envelope of a function $\varphi \in C(\overline{D}{\hskip3.5pt I})$ is the supremum of all plurisubharmonic functions which are not greater than $\varphi$ on $D$. A bounded domain $D$ is called $c$-regular if the envelope of every function $\varphi \in C(\overline{D}{\hskip3.5pt I})$ is continuous on $D$ and extends continuously to $\overline{D}{\hskip3.5pt I}$. The purpose of this paper is to give a complete characterization of $c$-regular domains in terms of Jensen measures.