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On the work of V. A. Rokhlin in ergodic theory

Published online by Cambridge University Press:  19 September 2008

Benjamin Weiss
Benjamin Weiss
Affiliation:
Institute of Mathematics and Computer Science, The Hebrew University of Jerusalem, Givat Ram 91904 Jerusalem, Israel
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Abstract

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The impact of V. A. Rokhlin's work in ergodic theory is discussed with particular emphasis on his famous lemma and its generalizations and his foundational work on measurable partitions.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 9 , Issue 4 , December 1989 , pp. 619 - 627
Copyright
Copyright © Cambridge University Press 1989

References

REFERENCES

[A]Alpern, S.. Generic properties of measure preserving homeomorphisms in ergodic theory. (eds Denker, M. & Jacobs, K.) LNM # 729 pp. 16–27. Springer: Berlin, 1979.Google Scholar
[B]Belinskaya, R.. Partitions of a Lebesgue space into orbits defined by ergodic automorphisms. Funkt. Analiz. i. Priloz. 2 (1968), 4–16.Google Scholar
[C-F]Chacon, R.V. & Friedman, N.. Approximation and invariant measures. Z. Wahrsch. verw. Geb. 3 (1965), 286–95.CrossRefGoogle Scholar
[C-K]Connes, A. & Krieger, W.. Measure space automorphisms the normalizer of their full groups and approximate finiteness. J. Fund. Anal. 29 (1977).Google Scholar
[C]Conze, J.P.. Entropie d'un group abelien de transformations. Z. Wahrsch verw. Geb. 25 (1972), 11–30.CrossRefGoogle Scholar
[D]Doob, J.. Stochastic Processes. J. Wiley: New York, 1953.Google Scholar
[DGS]Denker, M., Grillenberger, C. & Sigmund, K.. Ergodic Theory on Compact Spaces. LNM #527. Springer: Berlin, 1976.CrossRefGoogle Scholar
[D1]Dye, H.. On groups of measure preserving transformations I. Amer. J. Math. 81 (1959), 119–59.CrossRefGoogle Scholar
[D2]Dye, H.. On groups of measure preserving transformations II. Amer. J. Math. 85 (1963), 551–76.CrossRefGoogle Scholar
[F]Furstenberg, H.. Recurrence in Ergodic Theory and Combinatorial Number Theory. Princeton, 1981.CrossRefGoogle Scholar
[H]Halmos, P.. Lectures on Ergodic Theory. Chelsea: New York, 1956.Google Scholar
[IT]Ionescu-Tulcea, A.. On the category of certain classes of transformations in ergodic theory. Trans. Amer. M. Soc. 114 (1965), 261–79.CrossRefGoogle Scholar
[K]Kalikow, S.. Twofold mixing implies threefold mixing for rank one transformations. Ergod. Th. & Dynam. Syst. 4 (1984), 237–259.CrossRefGoogle Scholar
[K-S]Katok, A. and Stepin, A.. Approximations in ergodic theory. Usp. Math. Nauk 22 (1967), 81–106.Google Scholar
[K-W]Katznelson, Y. and Weiss, B.. Commuting measure preserving transformations. Israel J. Math. 12 (1972), 161–173.CrossRefGoogle Scholar
[KI]King, J.. The commutant is the weak closure of the powers, for rank-1 transformations. Ergod. Th. & Dynam. Syst. 6 (1986), 363–384.CrossRefGoogle Scholar
[L-W]Lehrer, E. and Weiss, B.. An e-free version of Rohlin's lemma. Ergod. Th. & Dynam. Syst. 2 (1982), 45–48.Google Scholar
[M-vN]Murray, F.J. and Neumann, J.von. Rings of Operators IV. Ann. of Math. 44 (1943), 716–804.CrossRefGoogle Scholar
[O]Ornstein, D.. Bernoulli shifts with the same entropy are isomorphic. Adv. in Math. 4 (1970), 337–352.Google Scholar
[O-W-1980]Ornstein, D. and Weiss, B.. Ergodic theory of amenable group actions I. The Rohlin lemma. Bull. Amer. Math. Soc. 2 (1980), 161–165.Google Scholar
[OW-1987]Ornstein, D. and Weiss, B.. Entropy and isomorphism theorems for actions of amenable groups. J. d'Analyse 48 (1987), 1–141.CrossRefGoogle Scholar
[R-1948]Rokhlin, V.. A ‘general’ measure preserving transformation is not mixing. Dokl. Akad. Nauk SSSR 60 (1948), 349–351.Google Scholar
[R-1949a]Rokhlin, V.. On the fundamental concepts of measure theory. Math. Sb. 25 (1949), 107–150.Google Scholar
[R-1949b]Rokhlin, V.. Selected topics from the metric theory of dynamical systems. Usp. Math. Nauk. 4 (1949), 57–128.Google Scholar
[V]Vershik, A.. Amenability and approximation of infinite groups. Selecta Sovietka Math. 2 (1982), 311–330.Google Scholar
[W]Weiss, B.. Measurable dynamics, in Conference in Modern Analysis and Probability. Contemp. Math. V. 26 (1984).Google Scholar