A dichotomy for infinite convolutions of discrete measures
- 1 March 1973
- journal article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 73 (2) , 307-316
- https://doi.org/10.1017/s0305004100076878
Abstract
Measures, μ which can be realized as an infinite convolution where each measure μ n 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.Keywords
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