The Annals of Probability

Convergence and Convolutions of Probability Measures on a Topological Group

Eberhard Siebert

Full-text: Open access

Abstract

A new technique is developed for studying the convergence of nets of probability measures on a topological group. It is applied to results concerned with the interplay between convergence and convolutions of measures like properties of the convolution mapping, divisibility of measures and convolution semigroups. Our method gives a unified and simple approach to these results.

Article information

Source
Ann. Probab., Volume 4, Number 3 (1976), 433-443.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996091

Digital Object Identifier
doi:10.1214/aop/1176996091

Mathematical Reviews number (MathSciNet)
MR413217

Zentralblatt MATH identifier
0338.60012

JSTOR
links.jstor.org

Subjects
Primary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization
Secondary: 22A10: Analysis on general topological groups

Keywords
Quasi-tight and tight nets of measures convolution mapping root compactness divisibility convolution operator convolution semigroup

Citation

Siebert, Eberhard. Convergence and Convolutions of Probability Measures on a Topological Group. Ann. Probab. 4 (1976), no. 3, 433--443. doi:10.1214/aop/1176996091. https://projecteuclid.org/euclid.aop/1176996091


Export citation