IDEAS home Printed from https://ideas.repec.org/p/hhs/hastef/0704.html
   My bibliography  Save this paper

Outer measure and utility

Author

Listed:
  • Voorneveld, Mark

    (Dept. of Economics, Stockholm School of Economics)

  • Weibull, Jörgen W.

    (Dept. of Economics, Stockholm School of Economics)

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

  • Voorneveld, Mark & Weibull, Jörgen W., 2008. "Outer measure and utility," SSE/EFI Working Paper Series in Economics and Finance 704, Stockholm School of Economics, revised 06 Apr 2009.
    • Handle: RePEc:hhs:hastef:0704
    as

    Download full text from publisher

    File URL: http://swopec.hhs.se/hastef/papers/hastef0704.pdf
    File Function: Complete Rendering
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. Neuefeind, Wilhelm, 1972. "On continuous utility," Journal of Economic Theory, Elsevier, vol. 5(1), pages 174-176, August.
    3. 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.
    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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bosi, G. & Mehta, G. B., 2002. "Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 311-328, November.
    2. Kopylov, Igor, 2016. "Canonical utility functions and continuous preference extensions," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 32-37.
    3. Beth Allen, 1996. "A remark on a social choice problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 11-16, January.
    4. Trockel, W., 2008. "The Nash product is a utility representation of the Pareto ordering," Economics Letters, Elsevier, vol. 99(2), pages 220-222, May.
    5. Kuntal Banerjee, 2014. "On the representation of preference orders on sequence spaces," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 497-506, August.
    6. Nosratabadi, Hassan, 2014. "Partially upper continuous preferences: Representation and maximal elements," Economics Letters, Elsevier, vol. 125(3), pages 408-410.
    7. Itzhak Gilboa & Andrew Postlewaite & Larry Samuelson & David Schmeidler, 2019. "What are axiomatizations good for?," Theory and Decision, Springer, vol. 86(3), pages 339-359, May.
    8. Aleksandr G. Alekseev & Mikhail V. Sokolov, 2016. "Benchmark-based evaluation of portfolio performance: a characterization," Annals of Finance, Springer, vol. 12(3), pages 409-440, December.
    9. Yann Rébillé, 2019. "Continuous utility on connected separable topological spaces," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 147-153, May.
    10. Lu Hong & Scott Page, 1994. "Reducing informational costs in endowment mechanisms," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 103-117, December.
    11. Subiza, Begona & Peris, Josep E., 1997. "Numerical representation for lower quasi-continuous preferences," Mathematical Social Sciences, Elsevier, vol. 33(2), pages 149-156, April.
    12. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 19(1), pages 113-185, March.
    13. Michèle Cohen & Alain Chateauneuf & Eric Danan & Thibault Gajdos & Raphaël Giraud & Meglena Jeleva & Fabrice Philippe & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2011. "Tribute to Jean-Yves Jaffray," Theory and Decision, Springer, vol. 71(1), pages 1-10, July.
    14. Epstein, Larry G. & Seo, Kyoungwon, 2009. "Subjective states: A more robust model," Games and Economic Behavior, Elsevier, vol. 67(2), pages 408-427, November.
    15. Jay Simon, 2016. "On the existence of altruistic value and utility functions," Theory and Decision, Springer, vol. 81(3), pages 371-391, September.
    16. Romano Isler, 1997. "Semicontinuous utility functions in topological spaces," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 20(1), pages 111-116, June.
    17. Enrico G. De Giorgi & David B. Brown & Melvyn Sim, 2010. "Dual representation of choice and aspirational preferences," University of St. Gallen Department of Economics working paper series 2010 2010-07, Department of Economics, University of St. Gallen.
    18. M. Ali Khan & Metin Uyanık, 2021. "Topological connectedness and behavioral assumptions on preferences: a two-way relationship," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 411-460, March.
    19. Mikhail V. Sokolov, 2023. "NPV, IRR, PI, PP, and DPP: a unified view," Papers 2302.02875, arXiv.org, revised Nov 2023.
    20. Guney, Begum & Richter, Michael, 2018. "Costly switching from a status quo," Journal of Economic Behavior & Organization, Elsevier, vol. 156(C), pages 55-70.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hhs:hastef:0704. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Helena Lundin (email available below). General contact details of provider: https://edirc.repec.org/data/erhhsse.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.