## The Annals of Probability

### Zeros of the Densities of Infinitely Divisible Measures

#### Abstract

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 $\mu$.

#### Article information

Source
Ann. Probab., Volume 8, Number 2 (1980), 400-403.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994789

Digital Object Identifier
doi:10.1214/aop/1176994789

Mathematical Reviews number (MathSciNet)
MR566606

Zentralblatt MATH identifier
0428.60013

JSTOR