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The Kreps-Yan theorem for L ∞

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  • D. B. Rokhlin

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.

Suggested Citation

  • D. B. Rokhlin, 2005. "The Kreps-Yan theorem for L ∞," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-8, January.
    • Handle: RePEc:hin:jijmms:316349
    DOI: 10.1155/IJMMS.2005.2749
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    Cited by:

    1. Maria Arduca & Cosimo Munari, 2020. "Fundamental theorem of asset pricing with acceptable risk in markets with frictions," Papers 2012.08351, arXiv.org, revised Apr 2022.

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