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A utility representation theorem with weaker continuity condition


  • Inoue, Tomoki

    (Center for Mathematical Economics, Bielefeld University)


We prove that a preference relation which is continuous on every straight line 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 theirs.

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  • Inoue, Tomoki, 2011. "A utility representation theorem with weaker continuity condition," Center for Mathematical Economics Working Papers 401, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:401

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    References listed on IDEAS

    1. 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.
    2. 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.
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    Cited by:

    1. Inoue, Tomoki, 2010. "A utility representation theorem with weaker continuity condition," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 122-127, January.

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    Linear continuity; Utility representation;

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