A class of generalized Ornstein transformations with the weak mixing property (Q1594510)
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scientific article; zbMATH DE number 1559462
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A class of generalized Ornstein transformations with the weak mixing property |
scientific article; zbMATH DE number 1559462 |
Statements
A class of generalized Ornstein transformations with the weak mixing property (English)
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30 September 2001
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A family of rank-one measure-preserving transformations parametrized by a probability space were constructed by \textit{D. Ornstein} [Proc. 6th Berkeley Sympos. Math. Statist. Probab., Univ. Calif. 1970, 2, 347-356 (1972; Zbl 0262.28009)], who showed they are almost surely mixing. Here an analogous construction is made, for which it may be shown that almost every transformation is weak-mixing. The author points out that this construction is flexible enough to produce rigidity. The possibility of extending the approach to interval exchanges is discussed.
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weak-mixing
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cutting and stacking
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Ornstein transformations
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interval exchanges
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