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Subsequences of normal sequences. (English) Zbl 0272.28012


MSC:

28D05 Measure-preserving transformations
11K06 General theory of distribution modulo \(1\)
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References:

[1] Abramov, L. M., The entropy of the derived automorphism, Dokl. Akad. Nauk. SSSR, 128, 647-650 (1959) · Zbl 0094.10001
[2] Billingsley, P., Ergodic Theory and Information (1965), New York: John Wiley and Sons, New York · Zbl 0141.16702
[3] Furstenberg, H., Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation, Math. Systems Theory, 1-1, 1-49 (1967) · Zbl 0146.28502
[4] Gottschalk, W. H., Substitution minimal sets, Trans. Amer. Math. Soc., 109, 467-491 (1963) · Zbl 0121.18002
[5] Jacobs, K.; Keane, M., 0-1 Sequences of Toeplitz type, Z. Wahrscheinlichkeitstheorie Verw. Gebiete, 13, 123-131 (1969) · Zbl 0195.52703
[6] Kamae, Teturo, Spectrum of a substitution minimal set, J. Math. Soc. Japan, 22, 567-578 (1970) · Zbl 0197.49901
[7] Kamae, Teturo, A topological invariant of substitution minimal sets, J. Math. Soc. Japan, 24, 285-306 (1972) · Zbl 0232.54052
[8] Keane, M., Generalized Morse sequences, Z. Wahrscheinlichkeitstheorie Verw. Gebiete, 10, 335-353 (1968) · Zbl 0162.07201
[9] Oxtoby, J. C., Ergodic sets, Bull. Amer. Math. Soc., 58, 116-136 (1961) · Zbl 0046.11504
[10] Oxtoby, J. C.; Wright, Fred B., On two theorems of Parthasarathy and Kakutani concerning the shift transformation (1962), New York: Academic Press, New York
[11] Parthasarathy, K. R., Probability Measures on Metric Spaces (1967), New York: Academic Press, New York · Zbl 0153.19101
[12] Rokhlin, V. A., New progress in the theory of transformations with invariant measure, Russian Math. Surveys, 15, 1-22 (1960) · Zbl 0102.33001
[13] Totoki, H., Introduction to Ergodic Theory (1971), Tokyo: Kyoritsu Shuppan, Tokyo
[14] B. Weiss,Normal sequences as collectives, Proc. Symp. on Topological Dynamics and Ergodic Theory, Univ. of Kentucky, 1971.
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