Open Access
April, 1980 Zeros of the Densities of Infinitely Divisible Measures
Patrick L. Brockett, William N. Hudson
Ann. Probab. 8(2): 400-403 (April, 1980). DOI: 10.1214/aop/1176994789


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 $\mu$.


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Patrick L. Brockett. William N. Hudson. "Zeros of the Densities of Infinitely Divisible Measures." Ann. Probab. 8 (2) 400 - 403, April, 1980.


Published: April, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0428.60013
MathSciNet: MR566606
Digital Object Identifier: 10.1214/aop/1176994789

Primary: 60B15
Secondary: 43A25 , 60E05

Keywords: Absolute continuity , equivalence with Haar measure , Infinitely divisible measures , locally compact Abelian group , support of measures

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 2 • April, 1980
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