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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Ergodic measure preserving transformations with quasi-discrete spectrum


Author: James B. Robertson
Journal: Trans. Amer. Math. Soc. 190 (1974), 301-311
MSC: Primary 28A65
MathSciNet review: 0344419
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Abstract: It is shown that an ergodic measure preserving transformation with quasi-discrete spectrum is conjugate to: (a) the skew-product of an ergodic measure preserving transformation with discrete spectrum and a measurable family of totally ergodic measure preserving transformations with quasi-discrete spectrum; (b) a factor of the direct product of an ergodic measure preserving transformation with discrete spectrum and a totally ergodic measure preserving transformation with quasi-discrete spectrum. Sufficient conditions are given to insure that an ergodic measure preserving transformation with quasi-discrete spectrum is conjugate to the direct product of an ergodic measure preserving transformation with discrete spectrum and a totally ergodic measure preserving transformation with quasi-discrete spectrum.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0344419-5
Keywords: Measure preserving, totally ergodic, quasi-discrete spectrum, quasi-eigenvalues
Article copyright: © Copyright 1974 American Mathematical Society