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The Kreps-Yan theorem for $L^\infty$

Dmitry B. Rokhlin
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Abstract

We prove the following version of the Kreps-Yan theorem. For any norm closed convex cone $C\subset L^\infty$ such that $C\cap L_+^\infty=\{0\}$ and $C\supset -L_+^\infty$, there exists a strictly positive continuous linear functional, whose restriction on $C$ is non-positive. The proof uses some tools from convex analysis in contrast to the case of a weakly Lindelöf Banach space, where such approach is not needed.

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Dmitry B. Rokhlin. 2004-12-31. The Kreps-Yan theorem for $L^\infty$. https://arxiv.org/abs/math/0412551

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