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Some Fubini theorems on sigma-algebras for non additive measures

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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 sigma-algebras for non additive measures," Cahiers de la Maison des Sciences Economiques b06086, Université Panthéon-Sorbonne (Paris 1).
    • Handle: RePEc:mse:wpsorb:b06086
    DOI: 10.1016/j.ijar.2007.02.007
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    1. Yann Rébillé, 2005. "A Yosida-Hewitt decomposition for totally monotone games on locally compact sigma-compact topological spaces," Cahiers de la Maison des Sciences Economiques b05087, Université Panthéon-Sorbonne (Paris 1).
    2. Alain Chateauneuf & Fabio Maccheroni & Massimo Marinacci & Jean-Marc Tallon, 2005. "Monotone continuous multiple priors," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 973-982, November.
    3. 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.
    4. 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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    6. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
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    More about this item

    Keywords

    Choquet integral; product capacity;

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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