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A dichotomy for infinite convolutions of discrete measures

Published online by Cambridge University Press:  24 October 2008

G. Brown  and
W. Moran
G. Brown
Affiliation:
The University of Liverpool
W. Moran
Affiliation:
The University of Liverpool
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Extract

Measures, μ which can be realized as an infinite convolution

where each measure μn is a discrete measure, arise naturally in many parts of analysis and number theory (see (15)). The basic property of these measures is ‘purity’; i.e. such a measure μ 1must be absolutely continuous, continuous and singular, or discrete.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 2 , March 1973 , pp. 307 - 316
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

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