Models, coproducts and exchangeability: notes on states on Baire functions. (English) Zbl 07571160
Summary: We discuss exchangeability and independence in the setting of \(\sigma\)-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 \(\sigma\)-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.
MSC:
| 06B05 | Structure theory of lattices |
| 06D35 | MV-algebras |
| 35R30 | Inverse problems for PDEs |
| 39A10 | Additive difference equations |
Keywords:
Riesz MV-algebras; Baire functions; states; observables; de Finetti; exchangeable probabilities; co-product; statistical modelsReferences:
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