Utility representation theorems for Debreu separable preorders |
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| Authors: | Gerhard Herden Vladimir L. Levin |
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| Affiliation: | 1. Universität Duisburg-Essen, Campus Essen, Fakultät für Mathematik, Universitätsstrasse 2, D-45117 Essen, Germany;2. Central Economics and Mathematics Institute of the Russian Academy of Sciences, Nakhimovskii Prospect 47, 117418 Moscow, Russia |
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| Abstract: | We prove the existence of arbitrary (resp., semicontinuous, continuous) utility representations for arbitrary (resp., semicontinuous, continuous) preorders satisfying some weakened Debreu order separability conditions. In this way we widely generalize a classical result for total preorders that essentially is due to Debreu. |
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| Keywords: | Debreu separability Weak Debreu separability Topological space Continuous preorder Utility function Open decreasing set Separable system |
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