Open Access
August, 1983 Gaussian Measure of Normal Subgroups
T. Byczkowski, A. Hulanicki
Ann. Probab. 11(3): 685-691 (August, 1983). DOI: 10.1214/aop/1176993513


Let $(\mu_t)_{t>0}$ be a Gaussian semigroup on a metric, separable, complete group $G$. If $H$ is a Borel measurable normal subgroup of $G$ such that $\mu_t(H) > 0$ for all $t$, then $\mu_t(H) = 1$ for every $t$. If, in addition, $\mu_t$ are symmetric, then $\mu_t(H) > 0$ for a single $t$ implies $\mu_t(H) = 1$ for all $t$.


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T. Byczkowski. A. Hulanicki. "Gaussian Measure of Normal Subgroups." Ann. Probab. 11 (3) 685 - 691, August, 1983.


Published: August, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0523.60012
MathSciNet: MR704555
Digital Object Identifier: 10.1214/aop/1176993513

Primary: 60B15
Secondary: 22E30

Keywords: Gaussian semigroups of measures , Trotter approximation theorem

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 3 • August, 1983
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