FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2002, VOLUME 8, NUMBER 4, PAGES 1179-1192

On relation of measure-theoretic and special properties of $$Z^d-actions

S. V. Tikhonov

Abstract

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It is shown how using the $$k-mixing property one can construct finite measure-preserving $$Z^d-actions possessing different and even unusual properties. In the case of a "classical time" $$Z this approach was applied by Lemanczik and del Junco as an alternative to the so-called Rudolf's "counterexamples machine", based on the notion of joining.

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Last modified: April 10, 2003