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Four definitions of the scale of an automorphism. (English. Russian original) Zbl 0299.28016

Funct. Anal. Appl. 7, 169-181 (1974); translation from Funkts. Anal. Prilozh. 7, No. 3, 1-17 (1973).

MSC:

28D05 Measure-preserving transformations
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References:

[1] A. M. Vershik, ”Metric invariant of automorphisms of a space having a measure connected with a uniform approximation and sequences of partitions,” Dokl. Akad. Nauk SSSR,209, No. 1, 15-18 (1973). · Zbl 0289.28014
[2] A. M. Vershik, ”Denumerable groups, close to finite,” in: F. Greenleaf, Invariant Means on Topological Groups and Their Applications, Van Nostrand (1969).
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[4] A. M. Vershik, ”Decreasing sequences of measurable partitions and their applications,” Dokl. Akad. Nauk SSSR,193, No. 4, 748-751 (1970). · Zbl 0238.28011
[5] A. M. Vershik, ”The continuum of pairwise nonisomorphic dyadic sequences,” Funktsional’. Analiz i Ego Prilozhen.,5, No. 3, 16-18 (1971).
[6] R. M. Belinskaya, ”Partition of Lebesgue space on a trajectory defined by ergodic automorphisms,” Funktsional’. Analiz i Ego Prilozhen.,2, No. 3, 4-16 (1968).
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[10] H. Dye, ”On groups of measure preserving transformation,” Amer. J. Math.,85, No. 4, 551-576 (1963). · Zbl 0191.42803
[11] A. M. Vershik, ”Nonmeasurable partitions, trajectory theory, operator algebra,” Dokl. Akad. Nauk SSSR,199, No. 5, 1004-1007 (1971).
[12] A. M. Stepin, ”On the entropy invariant of decreasing sequences of measurable partitions,” Funktsional’. Analiz Ego Prilozhen.,5, No. 3, 80-84 (1971).
[13] A. B. Katok and A. M. Stepin, ”Approximation in ergodic theory,” Uspekhi Matem. Nauk,22, No. 5, 81-106 (1967). · Zbl 0172.07202
[14] D. Ornshtein, ”Kolmogorov automorphisms which are not Bernoulli shifts,” Matematika,15, No. 1, 130-150 (1971).
[15] R. V. Chacon, ”Approximation and spectral multiplicity,” Lecture Notes in Math.,160, 18-27 (1970). · Zbl 0212.40101
[16] T. Schwartzbauer, ”A general method for approximating measure preserving transformations,” Proc. Amer. Math. Soc.,24, 643-648 (1970). · Zbl 0197.04002
[17] A. M. Vershik and A. A. Shmidt, ”High-degree symmetric groups,” Dokl. Akad. Nauk SSSR,206, No. 2, 269-272 (1972). · Zbl 0285.60015
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