Convex functions on superconvex spaces (Q1203564)

This note is about superconvex analysis, an axiomatic theory of infinite convex combinations first introduced by Rodé, and subsequently refined by König, Kremp and Kühn. In [``Ökonomie und Mathematik'' (pp. 29-34 (1987; Zbl 0662.46007)], \textit{H. König} showed that the main theorems of superconvex analysis can be deduced from an easily statable basic estimation which can, in turn, be deduced from an intersection theorem. This line of approach represented a considerable simplification on that previously used. In this note, we continue this simplification process by showing that the intersection theorem is not needed and that the basic estimation can, in fact, be deduced directly from the second superconvexity axiom.