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The exactness of generalized skew products. (English) Zbl 0787.28012

The author studies certain types of skew products of the form \(\widehat T(x,y)= (\sigma(x),\;T_{x(0)}y)\), where \(\sigma: X\to X\) is a discrete endomorphism (defined on \(X\subseteq \{1,\dots,s\}^ N\), preserving \(\mu\)), and \(T_ 1,T_ 2,\dots,T_ s\) are piecewise monotonic and piecewise continuous maps, preserving a Borel measure \(p\) on \([0,1)\) [see the author, Stud. Math. 87, 215-222 (1987; Zbl 0651.28013)]. Using the Pinsker algebra, sufficient conditions for the exactness of \(\widehat T\) are given, together with applications to a particular class of random maps.

MSC:

28D05 Measure-preserving transformations

Citations:

Zbl 0651.28013
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