We consider an infinitely divisible measure $\mu$ on a locally compact Abelian group. If $\mu \ll \lambda$ (Haar measure), and if the semigroup generated by the support of the corresponding Levy measure $\nu$ is the closure of an angular semigroup, then $\mu \sim \lambda$ over the support of $\mu$. In particular, if $\int|\chi(x) - 1|\nu(dx) < \infty$, for all characters $\chi$, or if $\nu \ll \lambda$ then $\mu \ll \lambda$ implies $\mu \sim \lambda$ over the support of $\mu$.
Publié le : 1980-04-14
Classification:
Infinitely divisible measures,
locally Compact Abelian group,
absolute continuity,
support of measures,
equivalence with Haar measure,
60B15,
60E05,
43A25
@article{1176994789,
author = {Brockett, Patrick L. and Hudson, William N.},
title = {Zeros of the Densities of Infinitely Divisible Measures},
journal = {Ann. Probab.},
volume = {8},
number = {6},
year = {1980},
pages = { 400-403},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994789}
}
Brockett, Patrick L.; Hudson, William N. Zeros of the Densities of Infinitely Divisible Measures. Ann. Probab., Tome 8 (1980) no. 6, pp. 400-403. http://gdmltest.u-ga.fr/item/1176994789/