Outer measure and utility
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.
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- Jaffray, Jean-Yves, 1975. "Existence of a Continuous Utility Function: An Elementary Proof," Econometrica, Econometric Society, vol. 43(5-6), pages 981-83, Sept.-Nov.
- Neuefeind, Wilhelm, 1972. "On continuous utility," Journal of Economic Theory, Elsevier, vol. 5(1), pages 174-176, August.
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