2023/12/26 by Peter Potaptchik, Daniel M. Roy, Potaptchik, Peter +3
Computer Science · Mathematics · #28C15 #60G05 #60G09 #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2312.16349
openalex publication_date 2023/12/26 · openalex created_date 2023/12/30 · openalex updated_date 2026/07/28
We show the following generalizations of the de Finetti--Hewitt--Savage theorem: Given an exchangeable sequence of random elements, the sequence is conditionally i.i.d. if and only if each random element admits a regular conditional distribution given the exchangeable σ-algebra (equivalently, the shift invariant or the tail algebra). We use this result, which holds without any regularity or technical conditions, to demonstrate that any exchangeable sequence of random elements whose common distribution is Radon is conditional iid.