The Rosenblatt Mixing Condition and Bernoulli Shifts

Martin, N. F. G.

Ann. Probab., Tome 2 (1974) no. 6, p. 333-338 / Harvested from Project Euclid

Résumé

If $T$ is an automorphism on a Lebesgue space and $P$ a finite generator for $T$, then $T$ is a Bernoulli shift if $$\sup \{|\mu(A \cap B) - \mu(A)\mu(B)|: A \in \vee^{-1}_{-\infty} T^j P, B \in \vee^\infty_k T^j P\}$$ is $o(|P|^{-a}k)$ where $a_k/k \rightarrow \infty$ as $k \rightarrow \infty$.

Détail

Publié le : 1974-04-14
Classification:  2870,  6050,  Rosenblatt mixing,  Bernoulli shifts,  $\epsilon$-independence,  weak Bernoulli,  finitely determined,  $K$-automorphism