On a measure of symmetry for stationary random sequences (Q1201197)

The classical theorem of de Finetti states that a sequence of exchangeable random variables is in fact conditionally independent and identically distributed given a certain \(\sigma\)-field, \({\mathcal I}\). The main result of this paper states that stationary sequences satisfying an asymptotic exchangeability criterion (defined in terms of shift transformations) have a conditional \(\varphi\)-mixing structure given \({\mathcal I}\). Here \({\mathcal I}\) is the \(\sigma\)-field left invariant by the shift transformation.