Following Sibony, we say that a bounded domain $\Omega$ in $C^n$ is $B$-regular if every continuous real valued function on the boundary of $\Omega$ can be extended continuously to a plurisubharmonic function on $\Omega$. The aim of this paper is to study an analogue of this concept in the category of unbounded domains in $C^n$. The use of Jensen measures relative to classes of plurisubharmonic functions plays a key role in our work