Products of convex measures: A Fubini theorem

Christian Bauer ()

Macroeconomics from Department of Economics, Economics I, Bayreuth University

Abstract: The concept of qualitative di¤erences in information, i.e. the distinction between risk and ambiguity, builds the framework of a growing strand of economic research. For non additive set functions as used in the Choquet Expected Utility framework, 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(1995)] to extend the Möbius product for non additive set functions to non finite spaces. The uniqueness result of [Ghirardato(1997)] for belief functions is also extended to non finite spaces. For this unique 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.

Keywords: Knightian uncertainty; multivariate capacity; product measure; totally monotone measure; Choqet integral (search for similar items in EconPapers)
JEL-codes: D81 D84 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-rmg
Date: 2006-11
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