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Journal of Convex Analysis 25 (2018), No. 3, 789--815
Copyright Heldermann Verlag 2018

Conglomerability and Representations

Gianluca Cassese
Dept. of Economics, Statistics and Management, UniversitÓ Milano Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy

We prove results concerning the representation of linear functionals as integrals of a given random quantity X. The existence of such representation is related to the notion of conglomerability, originally introduced by de Finetti and Dubins. We show that this property has interesting applications in probability and in analysis. These include a version of Skorohod theorem, a proof that Brownian motion assumes whatever family of finite dimensional distributions upon a change of the probability measure and a version of the extremal representation theorem of Choquet.

Keywords: Choquet integral representation, conglomerability, Riesz representation, Skhorohod representation, vector lattice.

MSC: 28A25; 46A22, 52A41

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