A utility representation theorem with weaker continuity condition
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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- 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.
- 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.
- Fishburn, P. C., 1983. "Utility functions on ordered convex sets," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 221-232, December.
- Inoue, Tomoki, 2011. "A utility representation theorem with weaker continuity condition," Center for Mathematical Economics Working Papers 401, Center for Mathematical Economics, Bielefeld University.
- Fishburn, Peter C., 1983. "Transitive measurable utility," Journal of Economic Theory, Elsevier, vol. 31(2), pages 293-317, December.
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