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An example of an automorphism which is a mixing of all degrees but which is not a Kolmogorov automorphism

Published online by Cambridge University Press:  24 October 2008

J. K. Dugdale
J. K. Dugdale
Affiliation:
Imperial College, London
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Extract

Rohlin (7) has shown that Kolmogorov automorphisms are mixings of all degrees. Later Sucheston(9) introduced regular automorphisms and after showing that they are mixings of all degrees asks if the converse of either of the above theorems holds. Since the equivalence of Kolmogorov and regular automorphisms follows from (1) and (8) we have only one problem. We show that the converse of either of the above theorems is false by constructing a stationary Gaussian process which is a mixing of all degrees but which is not a Kolmogorov automorphism.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 4 , October 1966 , pp. 687 - 691
Copyright
Copyright © Cambridge Philosophical Society 1966

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References

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