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Entropy and Hausdorff dimension of a sequence of coordinate functions in base-r expansion

Part of the Lecture Notes in Mathematics book series (LNM,volume 330)

Keywords

  • Probability Measure
  • Fractional Dimension
  • Hausdorff Dimension
  • Coordinate Function
  • Dichotomy Theorem

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References

  1. H.G. Eggleston: The fractional dimension of a set defined by decimal properties, Quart. J. Math. Oxford Ser. 20 (1949), 31–36.

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  2. P. Billingsley: Ergodic theory and information, John Wiley, New York, 1965.

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  3. S. Kakutani: On equivalence of infinite product measures, Ann. of Math. 49 (1948), 214–224.

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  4. G. Marsaglia: Random variables with independent binary digits, Ann. Math. Statist. 42 (1971), 1922–1929.

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© 1973 Springer-Verlag

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Baba, Y. (1973). Entropy and Hausdorff dimension of a sequence of coordinate functions in base-r expansion. In: Maruyama, G., Prokhorov, Y.V. (eds) Proceedings of the Second Japan-USSR Symposium on Probability Theory. Lecture Notes in Mathematics, vol 330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061477

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  • DOI: https://doi.org/10.1007/BFb0061477

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06358-2

  • Online ISBN: 978-3-540-46956-8

  • eBook Packages: Springer Book Archive