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Normal numbers and ergodic theory

Part of the Lecture Notes in Mathematics book series (LNM,volume 550)

Keywords

  • Invariant Measure
  • Ergodic Theory
  • Haar Measure
  • Positive Entropy
  • Infinite Subset

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References

  1. P. Billingsley, Ergodic Theory and Information, John Wiley & Sons, New York, 1965.

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  2. R. Bowen, Periodic points and measures for axiom A diffeomorphisms, Trans. Amer. Math. Soc. 154 (1971).

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  3. H. Furstenberg, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation, Math. Systems Theory 1 (1967).

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  4. T. Kamae, Subsequences of normal sequences, Israel, J. Math. 16 (1973).

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  5. T. Kamae & B. Weiss, Normal numbers and selection rules, Israel J. Math. 21 (1975).

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  6. K. R. Parthasarathy, Probability Measures on Metric Spaces, Academic Press, New York, 1967.

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  7. G. Rauzy, Fonctions entièrs et répartition modulo un II, Bull. Soc. Math. France 101 (1973).

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  8. G. Rauzy, Normbres normaux et processus déterministes, to appear.

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  9. V, A, Rohlin, Metric propertes of endomorphisms of compact commutative groups, Amer. Math. Soc. Transl. (2) 64 (1967).

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  10. D. Ruelle, Statistical mechanics on a compact set with zv action satisfying expansiveness and specification, Bull. Amer. Math. Soc. 78 (1972).

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  12. H. Totoki, Introduction to Ergodic Theory, Kyoritsu Shuppan, Tokyo, 1971 (in Japanese).

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© 1976 Springer-Verlag

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Kamae, T. (1976). Normal numbers and ergodic theory. In: Maruyama, G., Prokhorov, J.V. (eds) Proceedings of the Third Japan — USSR Symposium on Probability Theory. Lecture Notes in Mathematics, vol 550. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077494

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  • DOI: https://doi.org/10.1007/BFb0077494

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07995-8

  • Online ISBN: 978-3-540-37966-9

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