This article is cited in 2 papers

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

S. V. Tikhonov

M. V. Lomonosov Moscow State University

Abstract: It is shown how using the $\kappa$-mixing property one can construct finite measure-preserving $\mathbb{Z}^{d}$-actions possessing different and even unusual properties. In the case of a “classical time” $\mathbb{Z}$ 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.

UDC: 517.987

Received: 01.12.2002

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