Invariant and reducing subalgebras of measure preserving transformations
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- by Roy L. Adler PDF
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References
- L. M. Abramov, On the entropy of a flow, Dokl. Akad. Nauk SSSR 128 (1959), 873–875 (Russian). MR 0113985 R. L. Adler, Generalized commutativity properties of measure preserving transformations (to appear).
- Hirotada Anzai, Ergodic skew product transformations on the torus, Osaka Math. J. 3 (1951), 83–99. MR 40594
- Hirotada Anzai, On an example of a measure preserving transformation which is not conjugate to its inverse, Proc. Japan Acad. 27 (1951), 517–522. MR 47742
- Hirotada Anzai and Shizuo Kakutani, Bohr compactifications of a locally compact Abelian group. I, Proc. Imp. Acad. Tokyo 19 (1943), 476–480. MR 15122
- R. R. Bahadur, Measurable subspaces and subalgebras, Proc. Amer. Math. Soc. 6 (1955), 565–570. MR 72446, DOI 10.1090/S0002-9939-1955-0072446-8 J. Frampton, Unitary equivalence of a measure preserving transformation and its inverse, oral communication.
- Paul R. Halmos, Lectures on ergodic theory, Publications of the Mathematical Society of Japan, vol. 3, Mathematical Society of Japan, Tokyo, 1956. MR 0097489
- Paul R. Halmos, Measure Theory, D. Van Nostrand Co., Inc., New York, N. Y., 1950. MR 0033869
- Paul R. Halmos and John von Neumann, Operator methods in classical mechanics. II, Ann. of Math. (2) 43 (1942), 332–350. MR 6617, DOI 10.2307/1968872
- Paul R. Halmos and H. Samelson, On monothetic groups, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 254–258. MR 6543, DOI 10.1073/pnas.28.6.254
- A. N. Kolmogorov, A new metric invariant of transient dynamical systems and automorphisms in Lebesgue spaces, Dokl. Akad. Nauk SSSR (N.S.) 119 (1958), 861–864 (Russian). MR 0103254
- Lynn H. Loomis, An introduction to abstract harmonic analysis, D. Van Nostrand Co., Inc., Toronto-New York-London, 1953. MR 0054173
- M. S. Pinsker, Dynamical systems with completely positive or zero entropy, Soviet Math. Dokl. 1 (1960), 937–938. MR 0152628 L. Pontrjagin, Topological groups, Princeton Univ. Press, Princeton, N. J., 1948.
- V. A. Rohlin, Entropy of metric automorphism, Dokl. Akad. Nauk SSSR 124 (1959), 980–983 (Russian). MR 0103258
- V. A. Rohlin, On the fundamental ideas of measure theory, Amer. Math. Soc. Translation 1952 (1952), no. 71, 55. MR 0047744
- V. A. Rohlin and Ja. G. Sinaĭ, The structure and properties of invariant measurable partitions, Dokl. Akad. Nauk SSSR 141 (1961), 1038–1041 (Russian). MR 0152629 Ja. G. Sinaĭ, On the notion of entropy of a dynamical system, Dokl. Akad. Nauk SSSR 124 (1959), 768-771.
Additional Information
- © Copyright 1964 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 110 (1964), 350-360
- MSC: Primary 28.70
- DOI: https://doi.org/10.1090/S0002-9947-1964-0156941-9
- MathSciNet review: 0156941