arXiv subjects
Publications and source records attributed to Doureid Hamdan.
We prove that a shift ergodic measure on a topologically mixing sub-shift is isomorphic to a Bernoulli shift whenever it is quasi invariant under permutations of finite number of coordinates. We prove also that Gibbs measures on topologically mixing subshift of finite type are quasi invariant.
{\abstract{\textwidth=4,5 in} A discrete time process, with law $μ$, is quasi-exchangeable if for any finite permutation $σ$ of time indices, the law $μ_σ$ of the resulting process is equivalent to $μ$. For a quasi-exchangeable stationary process we prove mainly (1) that if the process is ergodic then it is isomorphic to a Bernoulli process and (2) that if the family of all Radon-Nikodym derivatives $\{{dμ_σ\over dμ}\}$ is uniformly integrable then the process is a mixture of Bernoulli processes, which generalizes De Finetti's Theorem. We give application of (1) to some determinantal processes. }