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A limit theorem for the fractional parts of the sequence $ \{2\sp{k}t\}$


Authors: Z. Ciesielski and H. Kesten
Journal: Proc. Amer. Math. Soc. 13 (1962), 596-600
MSC: Primary 10.50; Secondary 10.33
DOI: https://doi.org/10.1090/S0002-9939-1962-0138612-1
MathSciNet review: 0138612
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References [Enhancements On Off] (What's this?)

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  • [2] N. J. Fine, On the asymptotic distributions of certain sums, Proc. Amer. Math. Soc. 5 (1954), 243-252. MR 0064337 (16:267f)
  • [3] M. Kac, On the distributions of values of sums of type $ \sum {f({2^k}t)} $, Ann. of Math. 47 (1946), 33-49. MR 0015548 (7:436f)
  • [4] G. G. Lorenz, Bernstein polynomials, Toronto, 1953. MR 0057370 (15:217a)
  • [5] A. V. Skorokhod, Limit theorems for stochastic processes, Theory of Probability and its Applications 1 (1956), 261-290 (An English translation of the Soviet journal, Teor. Veroyatnost. i. Primenen.) MR 0084897 (18:943c)

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DOI: https://doi.org/10.1090/S0002-9939-1962-0138612-1
Article copyright: © Copyright 1962 American Mathematical Society

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