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

Author

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  • 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

Abstract

Since the seminal paper of Ghirardato, it is known that Fubini Theorem for non-additive measures can be available only for functions defined as "slice-comonotonic". We give different assumptions that provide such Fubini Theorems in the framework of product σ-algebras.

Suggested Citation

  • Alain Chateauneuf & Jean-Philippe Lefort, 2008. "Some Fubini theorems on product sigma-algebras for non-additive measures," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00271357, HAL.
    • Handle: RePEc:hal:cesptp:hal-00271357
    DOI: 10.1016/j.ijar.2007.02.007
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    References listed on IDEAS

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    1. Itzhak Gilboa & David Schmeidler, 1992. "Canonical Representation of Set Functions," Discussion Papers 986, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    3. Itzhak Gilboa & David Schmeidler, 1995. "Canonical Representation of Set Functions," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 197-212, February.
    4. 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.
    5. 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.
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    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.

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