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Recent progress in ergodic theory. (English) Zbl 0161.11401


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[1] L. M. Abramov, The entropy of an automorphism of a solenoidal group, Teor. Veroyatnost. i Primenen 4 (1959), 249 – 254 (Russian, with English summary). · Zbl 0201.49201
[2] Leo Breiman, The individual ergodic theorem of information theory, Ann. Math. Statist. 28 (1957), 809 – 811. · Zbl 0078.31801 · doi:10.1214/aoms/1177706899
[3] Leo Breiman, The individual ergodic theorem of information theory, Ann. Math. Statist. 28 (1957), 809 – 811. · Zbl 0078.31801 · doi:10.1214/aoms/1177706899
[4] R. V. Chacon and D. S. Ornstein, A general ergodic theorem, Illinois J. Math. 4 (1960), 153 – 160. · Zbl 0134.12102
[5] Nelson Dunford and J. T. Schwartz, Convergence almost everywhere of operator averages, J. Rational Mech. Anal. 5 (1956), 129 – 178. · Zbl 0075.12102
[6] Arshag B. Hajian and Shizuo Kakutani, Weakly wandering sets and invariant measures, Trans. Amer. Math. Soc. 110 (1964), 136 – 151. · Zbl 0122.29804
[7] Eberhard Hopf, The general temporally discrete Markoff process, J. Rational Mech. Anal. 3 (1954), 13 – 45. · Zbl 0055.36705
[8] Alexandra Ionescu Tulcea, Contributions to information theory for abstract alphabets, Ark. Mat. 4 (1961), 235 – 247 (1961). · Zbl 0107.34601 · doi:10.1007/BF02592011
[9] 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). A. N. Kolmogorov, Entropy per unit time as a metric invariant of automorphisms, Dokl. Akad. Nauk SSSR 124 (1959), 754 – 755 (Russian). · Zbl 0083.10602
[10] 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). A. N. Kolmogorov, Entropy per unit time as a metric invariant of automorphisms, Dokl. Akad. Nauk SSSR 124 (1959), 754 – 755 (Russian). · Zbl 0083.10602
[11] Donald S. Ornstein, On invariant measures, Bull. Amer. Math. Soc. 66 (1960), 297 – 300. · Zbl 0154.30502
[12] Brockway McMillan, The basic theorems of information theory, Ann. Math. Statistics 24 (1953), 196 – 219. · Zbl 0050.35501
[13] V. A. Rohlin, Entropy of metric automorphism, Dokl. Akad. Nauk SSSR 124 (1959), 980 – 983 (Russian). · Zbl 0096.31405
[14] Ja. Sinaĭ, On the concept of entropy for a dynamic system, Dokl. Akad. Nauk SSSR 124 (1959), 768 – 771 (Russian). Ja. Sinaĭ, Flows with finite entropy, Dokl. Akad. Nauk SSSR 125 (1959), 1200 – 1202 (Russian).
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