Abstract: | Let λ, μ be regular probability measures on a locally compact abelian semigroup S, λ * μ the convolution of λ and μ, λn the nth iterated convolution of λ, δx the point measure of x?S. We study the totalvariation of λn–δx * λn for n → ∞. We shall see that for a certain class of semigroups the limit of this sequence is either 0 or 2. |