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Outer measure and utility

Author

Listed:
  • Mark Voorneveld

    (SSE - Department of Economics - SSE - Stockholm School of Economics)

  • Jörgen Weibull

    (SSE - Department of Economics - SSE - Stockholm School of Economics, X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris)

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.

Suggested Citation

  • Mark Voorneveld & Jörgen Weibull, 2008. "Outer measure and utility," Working Papers hal-00354246, HAL.
    • Handle: RePEc:hal:wpaper:hal-00354246
    Note: View the original document on HAL open archive server: https://hal.science/hal-00354246
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    File URL: https://hal.science/hal-00354246/document
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    References listed on IDEAS

    as
    1. NEUEFEIND, Wilhellm, 1972. "On continuous utility," LIDAM Reprints CORE 113, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Jaffray, Jean-Yves, 1975. "Existence of a Continuous Utility Function: An Elementary Proof," Econometrica, Econometric Society, vol. 43(5-6), pages 981-983, Sept.-Nov.
    3. Neuefeind, Wilhelm, 1972. "On continuous utility," Journal of Economic Theory, Elsevier, vol. 5(1), pages 174-176, August.
    4. Trout Rader, 1963. "The Existence of a Utility Function to Represent Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 229-232.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Tapan Mitra & M. Ozbek, 2013. "On representation of monotone preference orders in a sequence space," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 473-487, September.

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    More about this item

    Keywords

    preferences; utility theory; measure theory; outer measure;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles

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