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

Dudley, E.

doi:10.1090/S0002-9947-1975-0380246-1

The Gaussian law and the law of the iterated logarithm for lacunary sets of characters
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Trans. Amer. Math. Soc. 214 (1975), 187-214 Request permission

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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