Scandinavian Working Papers in Economics

SSE/EFI Working Paper Series in Economics and Finance,
Stockholm School of Economics

No 704: Outer measure and utility

Mark Voorneveld () and Jörgen W. Weibull ()
Additional contact information
Mark Voorneveld: Dept. of Economics, Stockholm School of Economics, Postal: P.O. Box 6501, SE-113 83 Stockholm, Sweden
Jörgen W. Weibull: Dept. of Economics, Stockholm School of Economics, Postal: P.O. Box 6501, SE-113 83 Stockholm, Sweden

Abstract: 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.

Keywords: preferences; utility theory; measure theory; outer measure

JEL-codes: C60; D01

8 pages, First version: October 16, 2008. Revised: April 6, 2009.

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