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Bulletin of the London Mathematical Society Advance Access originally published online on November 9, 2008
Bulletin of the London Mathematical Society 2008 40(6):1038-1044; doi:10.1112/blms/bdn088
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© 2008 London Mathematical Society

Probability measures on compact groups which have square-integrable densities

David Applebaum

Probability and Statistics Department
University of Sheffield
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
United Kingdom

Received 8 October 2007. Revision received 1 April 2008.

We apply Peter–Weyl theory to obtain necessary and sufficient conditions for a probability measure on a compact group to have a square-integrable density. Applications are given to measures on the d-dimensional torus.

2000 Mathematics Subject Classification 60B15, 60E07, 43A05, 43A30.


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