A utility representation theorem with weaker continuity condition

Inoue T (2008) Working Papers. Institute of Mathematical Economics; 401.
Bielefeld: Universität Bielefeld.

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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 T. A utility representation theorem with weaker continuity condition. Working Papers. Institute of Mathematical Economics. Vol 401. Bielefeld: Universität Bielefeld; 2008.
Inoue, T. (2008). A utility representation theorem with weaker continuity condition (Working Papers. Institute of Mathematical Economics, 401). Bielefeld: Universität Bielefeld.
Inoue, T. (2008). A utility representation theorem with weaker continuity condition. Working Papers. Institute of Mathematical Economics, 401, Bielefeld: Universität Bielefeld.
Inoue, T., 2008. A utility representation theorem with weaker continuity condition, Working Papers. Institute of Mathematical Economics, no.401, Bielefeld: Universität Bielefeld.
T. Inoue, A utility representation theorem with weaker continuity condition, Working Papers. Institute of Mathematical Economics, vol. 401, Bielefeld: Universität Bielefeld, 2008.
Inoue, T.: A utility representation theorem with weaker continuity condition. Working Papers. Institute of Mathematical Economics, 401. Universität Bielefeld, Bielefeld (2008).
Inoue, Tomoki. A utility representation theorem with weaker continuity condition. Bielefeld: Universität Bielefeld, 2008. Working Papers. Institute of Mathematical Economics. 401.
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