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The Gaussian law and lacunary sets of characters

Part of: Limit theorems

Published online by Cambridge University Press:  09 April 2009

E. Dudley  and
P. Hall
E. Dudley
Affiliation:
Department of MathematicsUniversity of MelbourneParkville, Victoria 3052, Australia
P. Hall
Affiliation:
Department of StatisticsUniversity of MelbourneParkville, Victoria 3052, Australia
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Abstract

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Salem and Zygmund (1947, 1948), Baker (1972) and Dudley (1975) have shown that certain lacunary sets P of characters of a compact abelian group have sequences of the form where фk∈P converge to the normal distribution if suitably normalized. In this paper, a theorem of probability due to McLeish (1974) is applied to clarify and extend the previous results.

MSC classification

Secondary: 60F05: Central limit and other weak theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 1 , February 1979 , pp. 91 - 107
Copyright
Copyright © Australian Mathematical Society 1979

References

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