The Kreps-Yan theorem for L∞

Abstract

We prove the following version of the Kreps-Yan theorem. For any norm-closed convex cone C⊂L∞ such that C∩L+∞={0} and C⊃−L+∞, there exists a strictly positive continuous linear functional, whose restriction on C is nonpositive. The technique of the proof differs from the usual approach, applicable to a weakly Lindelöf Banach space.