Property of almost independent images for ergodic transformations without partial rigidity
A. I. Bashtanov · Proceedings of the Steklov Institute of Mathematics · 2010
S.V. Tikhonov, in his paper of 2007 devoted to a new metric on the class of mixing transformations, faced the following natural question when studying the properties of such transformations: Does there exist a set A with µ(A) = 1/2 such that the inequality |µ(A ∩ T i A) − µ(A)2| 0? V.V. Ryzhikov (2009) obtained the following criterion: For an ergodic transformation T, a set A of given measure such that A and its images under T are ɛ-independent exists if and only if T does not possess the property of partial rigidity. The aim of the present study is to generalize this proposition to the case of multiple ɛ-independence of images.