Outer measure and utility

Mark Voorneveld (1) , Jörgen Weibull (1, 2)

1 SSE - Department of Economics
2 X-DEP-ECO - Département d'Économie de l'École Polytechnique

In most economics textbooks there is a gap between the non-existence of utility functions and the existence of continuous utility functions, although upper semi-continuity is sufficient for many purposes. Starting from a simple constructive approach for countable domains and combining this with basic measure theory, we obtain necessary and sufficient conditions for the existence of upper semi-continuous utility functions on a wide class of domains. Although links between utility theory and measure theory have been pointed out before, to the best of our knowledge this is the first time that the present route has been taken.

Mots clés: preferences; utility theory; measure theory; outer measure

Domaines: Gestion et management; Economies et finances

Mark Voorneveld, Jörgen Weibull. Outer measure and utility. 2008. ⟨hal-00354246⟩