Kreps-Yan theorem for Banach ideal spaces

Abstract

Let $C$ be a closed convex cone in a Banach ideal space $X$ on a measurable space with a $\sigma$-finite measure. We prove that conditions $C\cap X_{+}=\{0\}$ and $C\supset -X_{+}$ imply the existence of a strictly positive continuous functional on $X$, whose restriction to $C$ is non-positive.

6 pages

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