Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-00130444.html
   My bibliography  Save this paper

Some Fubini theorems on product sigma-algebras for non-additive measures

Author

Listed:
  • Alain Chateauneuf

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Jean-Philippe Lefort

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract
We give some Fubini's theorems (interversion of the order of integration and product capacities) in the framework of the Choquet integral for product sigma-algebras. Following Ghirardato this is performed by considering slice-comonotonic functions. Our results can be easily interpreted for belief functions, in the Dempster and Shafer setting.

Suggested Citation

  • Alain Chateauneuf & Jean-Philippe Lefort, 2006. "Some Fubini theorems on product sigma-algebras for non-additive measures," Post-Print halshs-00130444, HAL.
    • Handle: RePEc:hal:journl:halshs-00130444
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00130444
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-00130444/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ghirardato, Paolo, 1997. "On Independence for Non-Additive Measures, with a Fubini Theorem," Journal of Economic Theory, Elsevier, vol. 73(2), pages 261-291, April.
    2. Hendon, Ebbe & Jacobsen, Hans Jorgen & Sloth, Birgitte & Tranaes, Torben, 1996. "The product of capacities and belief functions," Mathematical Social Sciences, Elsevier, vol. 32(2), pages 95-108, October.
    3. Itzhak Gilboa & David Schmeidler, 1992. "Canonical Representation of Set Functions," Discussion Papers 986, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    5. Itzhak Gilboa & David Schmeidler, 1995. "Canonical Representation of Set Functions," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 197-212, February.
    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. Mario Ghossoub, 2015. "Equimeasurable Rearrangements with Capacities," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 429-445, February.
    2. Ghossoub, Mario, 2011. "Monotone equimeasurable rearrangements with non-additive probabilities," MPRA Paper 37629, University Library of Munich, Germany, revised 23 Mar 2012.

    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. Alain Chateauneuf & Jean-Philippe Lefort, 2006. "Some Fubini theorems on sigma-algebras for non additive measures," Cahiers de la Maison des Sciences Economiques b06086, Université Panthéon-Sorbonne (Paris 1).
    2. Ronald Stauber, 2019. "A strategic product for belief functions," ANU Working Papers in Economics and Econometrics 2019-668, Australian National University, College of Business and Economics, School of Economics.
    3. Stauber, Ronald, 2019. "A strategic product for belief functions," Games and Economic Behavior, Elsevier, vol. 116(C), pages 38-64.
    4. repec:dau:papers:123456789/7324 is not listed on IDEAS
    5. Marinacci, Massimo, 1999. "Limit Laws for Non-additive Probabilities and Their Frequentist Interpretation," Journal of Economic Theory, Elsevier, vol. 84(2), pages 145-195, February.
    6. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
    7. Aouani, Zaier & Chateauneuf, Alain, 2008. "Exact capacities and star-shaped distorted probabilities," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 185-194, September.
    8. Sujoy Mukerji & Jean-Marc Tallon, 2001. "Ambiguity Aversion and Incompleteness of Financial Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(4), pages 883-904.
    9. Lo, Kin Chung, 2000. "Epistemic conditions for agreement and stochastic independence of [epsi]-contaminated beliefs," Mathematical Social Sciences, Elsevier, vol. 39(2), pages 207-234, March.
    10. Gilboa, Itzhak & Samuelson, Larry & Schmeidler, David, 2013. "Dynamics of inductive inference in a unified framework," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1399-1432.
    11. Ghirardato, Paolo & Le Breton, Michel, 2000. "Choquet Rationality," Journal of Economic Theory, Elsevier, vol. 90(2), pages 277-285, February.
    12. Ghirardato, Paolo, 1997. "On Independence for Non-Additive Measures, with a Fubini Theorem," Journal of Economic Theory, Elsevier, vol. 73(2), pages 261-291, April.
    13. repec:bos:wpaper:wp2013-001 is not listed on IDEAS
    14. Epstein, Larry G. & Seo, Kyoungwon, 2015. "Exchangeable capacities, parameters and incomplete theories," Journal of Economic Theory, Elsevier, vol. 157(C), pages 879-917.
    15. Silvia Bortot & Ricardo Alberto Marques Pereira & Thuy H. Nguyen, 2015. "Welfare functions and inequality indices in the binomial decomposition of OWA functions," DEM Discussion Papers 2015/08, Department of Economics and Management.
    16. Eichberger, Jürgen & Oechssler, Jörg & Schnedler, Wendelin, 2012. "How do people cope with an ambiguous situation when it becomes even more ambiguous?," Working Papers 0528, University of Heidelberg, Department of Economics.
    17. Ralph W. Bailey & Jürgen Eichberger & David Kelsey, 2005. "Ambiguity and Public Good Provision in Large Societies," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 7(5), pages 741-759, December.
    18. Epstein, Larry G. & Schneider, Martin, 2003. "IID: independently and indistinguishably distributed," Journal of Economic Theory, Elsevier, vol. 113(1), pages 32-50, November.
    19. De Waegenaere, Anja & Wakker, Peter P., 2001. "Nonmonotonic Choquet integrals," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 45-60, September.
    20. Lo, Kin Chung, 2006. "Agreement and stochastic independence of belief functions," Mathematical Social Sciences, Elsevier, vol. 51(1), pages 1-22, January.
    21. Kin Chung Lo, 1998. "Epistemic Conditions for Agreement and Stochastic Independence of epsilon-Contaminated Beliefs," Working Papers 1998_02, York University, Department of Economics.
    22. Philippe, Fabrice, 2000. "Cumulative prospect theory and imprecise risk," Mathematical Social Sciences, Elsevier, vol. 40(3), pages 237-263, November.

    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:hal:journl:halshs-00130444. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.