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A utility representation theorem with weaker continuity condition

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Author Info
Tomoki Inoue () (Institute of Mathematical Economics, Bielefeld University)
Abstract

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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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-401.pdf
File Format: application/pdf
File Function: First version, 2008
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Publisher Info
Paper provided by Bielefeld University, Institute of Mathematical Economics in its series Working Papers with number 401.

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Length: 24 pages
Date of creation: Sep 2008
Date of revision:
Handle: RePEc:bie:wpaper:401

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Web page: http://www.imw.uni-bielefeld.de/
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Related research
Keywords: linear continuity; utility representation;

Find related papers by JEL classification:
C60 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - General
D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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  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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
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