Geodesic
Pairwise $\varepsilon$-Independence of the Sets $T^iA$ for a Mixing Transformation~$T$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 2, pp. 88-91

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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. 
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     author = {V. V. Ryzhikov},
     title = {Pairwise $\varepsilon${-Independence} of the {Sets} $T^iA$ for a {Mixing} {Transformation~}$T$},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {88--91},
     publisher = {mathdoc},
     volume = {43},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2009_43_2_a9/}
}
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V. V. Ryzhikov. Pairwise $\varepsilon$-Independence of the Sets $T^iA$ for a Mixing Transformation~$T$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 2, pp. 88-91. http://geodesic.mathdoc.fr/item/FAA_2009_43_2_a9/