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Products of non-additive measures: a Fubini-like theorem

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  • Christian Bauer

Abstract

For non-additive set functions, the independent product, in general, is not unique and the Fubini theorem is restricted to slice-comonotonic functions. In this paper, we use the representation theorem of Gilboa and Schmeidler (Math Oper Res 20:197–212, 1995 ) to extend the Möbius product for non-additive set functions to non-finite spaces. We extend the uniqueness result of Ghirardato (J Econ Theory 73:261–291, 1997 ) for products of two belief functions and weaken the requirements on the marginals necessary to obtain the Fubini property in the product. More importantly, we show that for the Möbius product one side of the Fubini theorem holds for all integrable functions if one of the marginals either is a probability or a convex combination of a chain of unanimity games, i.e., we relax the requirement of slice-comonotonicity and enrich the set of possible applications. Copyright Springer Science+Business Media New York 2012

Suggested Citation

  • Christian Bauer, 2012. "Products of non-additive measures: a Fubini-like theorem," Theory and Decision, Springer, vol. 73(4), pages 621-647, October.
    • Handle: RePEc:kap:theord:v:73:y:2012:i:4:p:621-647
    DOI: 10.1007/s11238-012-9324-5
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    More about this item

    Keywords

    Möbius inverse; Fubini; Capacity; Product measure; Totally monotone; Belief function; Choquet integral; Knightian uncertainty; D81; D84;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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