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The existence of utility functions for weakly continuous preferences on a Banach space

2005; Elsevier BV; Volume: 51; Issue: 2 Linguagem: Inglês

10.1016/j.mathsocsci.2005.07.007

1879-3118

María Jesús Campión, Juan C. Candeal, Esteban Induráin,

Decision-Making and Behavioral Economics

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.