Zero-One Law for Symmetric Convolution Semigroups of Measures on Groups

Let (μ t )t>0 be a symmetric weakly continuous semigroup of probability measures on a nonabelien complete separable group G and let v be its Levy measure. The purpose of this paper is to provide a relatively simple proof of the zero-one law for semigroups with the Levy measure satisfying either v(Hc) = ∞ or v(Hc) = 0.