Gaussian Measure of Normal Subgroups

Byczkowski, T.; Hulanicki, A.

Ann. Probab., Tome 11 (1983) no. 4, p. 685-691 / Harvested from Project Euclid

Résumé

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 $t$.

Publié le : 1983-08-14
Classification: Gaussian semigroups of measures, Trotter approximation theorem, 60B15, 22E30

@article{1176993513,
     author = {Byczkowski, T. and Hulanicki, A.},
     title = {Gaussian Measure of Normal Subgroups},
     journal = {Ann. Probab.},
     volume = {11},
     number = {4},
     year = {1983},
     pages = { 685-691},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993513}
}

Byczkowski, T.; Hulanicki, A. Gaussian Measure of Normal Subgroups. Ann. Probab., Tome 11 (1983) no. 4, pp.  685-691. http://gdmltest.u-ga.fr/item/1176993513/