Periodicity and absolute regularity
[A previous version of the paper has been reviewed in Zbl 0533.60038.] The ''total variation'' properties similar to 0-2 theorem for Markov chains are proved for a general ergodic stationary sequence \(\xi\). The conditions for the periodicity are given. It shows that when the period p is finite, the double tail \(\sigma\)-field of \(\xi\) is partitioned into atoms which are \(T^ p\)-invariant, and when \(p=1\), \(\xi\) is absolutely regular.
scientific article; zbMATH DE number 3992542
scientific article