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April, 1974 The Rosenblatt Mixing Condition and Bernoulli Shifts
N. F. G. Martin
Ann. Probab. 2(2): 333-338 (April, 1974). DOI: 10.1214/aop/1176996715

Abstract

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 $k \rightarrow \infty$.

Citation

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N. F. G. Martin. "The Rosenblatt Mixing Condition and Bernoulli Shifts." Ann. Probab. 2 (2) 333 - 338, April, 1974. https://doi.org/10.1214/aop/1176996715

Information

Published: April, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0278.28008
MathSciNet: MR357740
Digital Object Identifier: 10.1214/aop/1176996715

Keywords: $\epsilon$-independence , $K$-automorphism , 2870 , 6050 , Bernoulli shifts , finitely determined , Rosenblatt mixing , weak Bernoulli

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 2 • April, 1974
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