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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

    (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," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00130444, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00130444
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00130444
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    Cited by:

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    2. Mario Ghossoub, 2015. "Equimeasurable Rearrangements with Capacities," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 429-445, February.
    3. Ghossoub, Mario, 2011. "Monotone equimeasurable rearrangements with non-additive probabilities," MPRA Paper 37629, University Library of Munich, Germany, revised 23 Mar 2012.
    4. Chunyu Kao & Gaofeng Zong, 2025. "Borel–Cantelli Lemma for Capacities," Mathematics, MDPI, vol. 13(5), pages 1-10, February.

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