A Generalization of a Theorem of Arrow, Barankin, and Blackwell

Abstract

This paper presents a generalization of a known density theorem of Arrow, Barankin, and Blackwell (“Admissible points of convex sets,” in Contributions to the Theory of Games, H. W. Kuhn and A. W. Tucker, eds., Princeton University Press, Princeton, NJ, 1953). This result is shown to hold even in a real normed space partially ordered by a Bishop-Phelps cone.