Limits of successive convolutions
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- by John C. Martin PDF
- Proc. Amer. Math. Soc. 59 (1976), 52-54 Request permission
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
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- M. Keane, Generalized Morse sequences, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 10 (1968), 335–353. MR 239047, DOI 10.1007/BF00531855
- Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 59 (1976), 52-54
- MSC: Primary 43A10
- DOI: https://doi.org/10.1090/S0002-9939-1976-0412734-X
- MathSciNet review: 0412734