Vershik, A. M. 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). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 8 Documents MSC: 28D05 Measure-preserving transformations PDFBibTeX XMLCite \textit{A. M. Vershik}, Funct. Anal. Appl. 7, 169--181 (1974; Zbl 0299.28016); translation from Funkts. Anal. Prilozh. 7, No. 3, 1--17 (1973) Full Text: DOI 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). [3] A. M. Vershik, ”A theorem on lacunary isomorphisms,” Funktsional’. Analiz i Ego Prilozhen.,2, No. 3, 17-21 (1968). [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). [7] P. Halmos, Lectures on Ergodic Theory, Chelsea, New York (1960). [8] V. A. Rokhlin, ”Selected questions of the metric theory of dynamic systems,” Uspekhi Matem. Nauk,4, No. 2, 57-128 (1949). [9] S. A. Yuzvinskii, ”Distinction of K-automorphisms by the scale,” Funktsional’. Analiz i Ego Prilozhen.,7, No. 4 (1973). [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.