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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Gaussian law and the law of the iterated logarithm for lacunary sets of characters


Author: E. Dudley
Journal: Trans. Amer. Math. Soc. 214 (1975), 187-214
MSC: Primary 42A44; Secondary 43A46, 60F15
MathSciNet review: 0380246
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Abstract: Salem and Zygmund showed that the Gaussian law holds for Hadamard sequences of real numbers while Mary Weiss proved a similar result for the law of the iterated logarithm. In the present paper, the author obtains corresponding results for lacunary sets of characters of an arbitrary infinite compact abelian group. It is shown that the laws are best satisfied for a certain class of lacunary sets but that modified results apply to more general classes.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0380246-1
PII: S 0002-9947(1975)0380246-1
Keywords: Compact abelian group, lacunary sets of characters, Stečkin sets, dissociate sets, Hadamard sequences, normal distribution, integral estimates, dyadic representation of natural numbers
Article copyright: © Copyright 1975 American Mathematical Society