Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Limits of successive convolutions

Author: John C. Martin
Journal: Proc. Amer. Math. Soc. 59 (1976), 52-54
MSC: Primary 43A10
MathSciNet review: 0412734
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: On an arbitrary compact, zero-dimensional, Abelian group, if $ {\mu _0},{\mu _1}, \ldots $ is a sequence of probability measures, a condition on these measures is given which is necessary and sufficient for each of the sequences $ {\mu _t},{\mu _t}{\ast}{\mu _{t + 1}},{\mu _t}{\ast}{\mu _{t + 1}}{\ast}{\mu _{t + 2}}, \ldots $ of successive convolutions to converge to Haar measure in the weak-star topology. Some simple consequences of the theorem are noted.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 43A10

Retrieve articles in all journals with MSC: 43A10

Additional Information

Keywords: Compact zero-dimensional Abelian group, probability measure, convolution, weak-star topology, Fourier-Stieltjes transform
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society