Solution of a problem of S. Marcus concerning Jensen-convex functions

Summary.

This paper is devoted to the problem of characterizing the class $\cal S$ of the stationary sets for J-convex functions $\Delta \to {\Bbb R}$, where $\Delta$ is a convex open subset of ${\Bbb R}^n$. We prove, among others, that a set T belongs to the class $\cal S$ if and only if T satisfies two conditions: the closure of the convex hull of T in the relative topology is the whole set $\Delta$, and each J-convex function bounded above on T is continuous.