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Some Fubini theorems on sigma-algebras for non additive measures

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.

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File URL: ftp://mse.univ-paris1.fr/pub/mse/cahiers2006/B06086.pdf
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Paper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number b06086.

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Length: 21 pages
Date of creation: Dec 2006
Handle: RePEc:mse:wpsorb:b06086
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  1. 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.
  2. 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.
  3. 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.
  4. Itzhak Gilboa & David Schmeidler, 1995. "Canonical Representation of Set Functions," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 197-212, February.
  5. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
  6. Massimo Marinacci, 1997. "Finitely Additive and Epsilon Nash Equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(3), pages 315-333.
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