The existence of utility functions for weakly continuous preferences on a Banach space
In this note we prove that the weak topology of a Banach space has the Continuous Representability Property which means that every (weakly) continuous total preorder defined on a Banach space can be represented by a weakly continuous utility function. This shows that weak topologies are perfect to l...
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Veröffentlicht in: | Mathematical social sciences 2006-03, Vol.51 (2), p.227-237 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | In this note we prove that the weak topology of a Banach space has the Continuous Representability Property which means that every (weakly) continuous total preorder defined on a Banach space can be represented by a weakly continuous utility function. This shows that weak topologies are perfect to look for continuous utility functions that represent preferences on infinite-dimensional commodity spaces. |
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ISSN: | 0165-4896 1879-3118 |
DOI: | 10.1016/j.mathsocsci.2005.07.007 |