ZERO-ONE LAW FOR SYMMETRICAL CONVOLUTION SEMIGROUPS OF MEASURES ON GROUPS

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.