H. Byczkowska et T. Byczkowski, ZERO-ONE LAW FOR SYMMETRICAL CONVOLUTION SEMIGROUPS OF MEASURES ON GROUPS, Journal of theoretical probability, 11(3), 1998, pp. 633-643
Let (mu(t))(t > 0) be a symmetric weakly continuous semigroup of proba
bility measures on a nonabelien complete separable group G and let nu
be its Levy measure. The purpose of this paper is to provide a relativ
ely simple proof of the zero-one law for semigroups with the Levy meas
ure satisfying either nu(H-c) = infinity or nu(H-c) = 0.