Conglomerability and Representations

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.