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A utility representation theorem with weaker continuity condition

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  • Inoue, Tomoki
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    Abstract

    We prove that a mixture continuous preference relation has a utility representation if its domain is a convex subset of a finite dimensional vector space. Our condition on the domain of a preference relation is stronger than Eilenberg (1941) and Debreu (1959, 1964), but our condition on the continuity of a preference relation is strictly weaker than the usual continuity assumed by them.

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    File URL: http://www.sciencedirect.com/science/article/B6VBY-4X7R85R-2/2/93071af0c3f81369e817d22c4d6be8b0
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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 46 (2010)
    Issue (Month): 1 (January)
    Pages: 122-127

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    Handle: RePEc:eee:mateco:v:46:y:2010:i:1:p:122-127

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    Web page: http://www.elsevier.com/locate/jmateco

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    Keywords: Mixture continuity Utility representation;

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    1. Monteiro, Paulo Klinger, 1987. "Some results on the existence of utility functions on path connected spaces," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 147-156, April.
    2. Toranzo, Margarita Estevez & Beloso, Carlos Herves, 1995. "On the existence of continuous preference orderings without utility representations," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 305-309.
    3. Tomoki Inoue, 2008. "A utility representation theorem with weaker continuity condition," Working Papers 401, Bielefeld University, Center for Mathematical Economics.
    4. Fishburn, Peter C., 1983. "Transitive measurable utility," Journal of Economic Theory, Elsevier, vol. 31(2), pages 293-317, December.
    5. Fishburn, P. C., 1983. "Utility functions on ordered convex sets," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 221-232, December.
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