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A utility representation theorem with weaker continuity condition

  • Inoue, Tomoki
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    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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    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
    Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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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. Fishburn, P. C., 1983. "Utility functions on ordered convex sets," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 221-232, December.
    4. Fishburn, Peter C., 1983. "Transitive measurable utility," Journal of Economic Theory, Elsevier, vol. 31(2), pages 293-317, December.
    5. Tomoki Inoue, 2008. "A utility representation theorem with weaker continuity condition," Working Papers 401, Bielefeld University, Center for Mathematical Economics.
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