ZEROS OF THE DENSITIES OF INFINITELY DIVISIBLE MEASURES ON R(N)

Let mu be an infinitely divisible probability measure on R(n) without Gaussian component and let nu be its Levy measure. Suppose that mu is absolutely continuous with respect to the Lebesgue measure lambda. We investigate the structure of the set P of admissible translates of mu. This yields a unified presentation of previously known results. We al so show that if lambda(P) > 0 then mu is equivalent to lambda, under t he assumption that supp mu = R(n), where P is the closure of the semig roup generated by the support of nu.