Ergodic measure preserving transformations with quasi-discrete spectrum

Robertson, James B.

doi:10.1090/S0002-9947-1974-0344419-5

Ergodic measure preserving transformations with quasi-discrete spectrum
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by James B. Robertson PDF

Trans. Amer. Math. Soc. 190 (1974), 301-311 Request permission

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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