V. V. Ryzhikov, “Pairwise $\varepsilon$-Independence of the Sets $T^iA$ for a Mixing Transformation $T$”, Funktsional. Anal. i Prilozhen., 2009, Volume 43, Issue 2,Pages 88

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Brief communications

Pairwise $\varepsilon$-Independence of the Sets $T^iA$ for a Mixing Transformation $T$

V. V. Ryzhikov

M. V. Lomonosov Moscow State University

Abstract: If an ergodic automorphism $T$ of a probability space is not partially rigid, then for any numbers $a\in(0,1)$ and $\varepsilon>0$ there exists a set $A$ such that all sets $T^i\!A$, $i>0$, are pairwise $\varepsilon$-independent.

Keywords: mixing, partial rigidity, measure-preserving transformation, $\varepsilon$-independence.

UDC: 517.9

Received: 07.05.2007

DOI: 10.4213/faa2935