Products of non additive measures: A Fubini theorem

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 …nite spaces. The uniqueness result of Ghirardato (1997) for belief functions is also extended to non …nite 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. JEL: D81, D84