Models, coproducts and exchangeability: Notes on states on Baire functions

Abstract

We discuss exchangeability and independence in the setting of σ-complete Riesz MV-algebras. We define and link to each other the notions of exchangeability and distribution law for a sequence of observables (i.e. non classical random variables), as well as the notion of independence for a sequence of algebras. We obtain two categorical dualities for σ-complete Riesz MV-algebras endowed with states and we define a “canonical” state on the coproduct of a sequence of probability Riesz tribes, giving a weak version of de Finetti’s result. Finally, we discuss statistical models.