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Rearranging measures

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  09 April 2009

G. Brown  and
J. H. Williamson
G. Brown
Affiliation:
School of Mathematics University of New South WalesKensington, N.S.W. 2033, Australia
J. H. Williamson
Affiliation:
Mathematics Department Heriot-Watt UniversityRiccarton, Currie Edinburgh EHI 1HX, Scotland
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Abstract

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A churning transformation can be defined on probability measures by an infinite sequence of finite permutations of mass. Continuity and absolute continuity of measures are invariants for such transformations but it is shown that certain probability measures whose Fourier-Stieltjes transforms fail to vanish at infinity may be churned into measures whose transforms do vanish in this sense.

MSC classification

Secondary: 60E05: Distributions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 1 , February 1983 , pp. 16 - 30
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Blum, J. R. and Epstein, B., ‘On the Fourier transforms of an interesting class of measures’, Israel J. Math. 10 (1971), 302–305.CrossRefGoogle Scholar
[2]Brown, G., ‘M0 (G) has a symmetric maximal ideal off the Silov boundary’, Proc. London Math. Soc. (3) 27 (1973), 484–504.CrossRefGoogle Scholar
[3]Brown, G. and Moran, W., ‘Coin-tossing and powers of singular measures’, Math. Proc. Cambridge Philos. Soc. 77 (1975), 349–364.CrossRefGoogle Scholar
[4]Brown, G. and Sanders, J. W., ‘Lognormal genesis’, J. Appl. Probability 18 (1981).Google Scholar