On summability of pairs of convolution sequences of probability measures on locally compact semigroups

Abstract

In this paper we study the problem of convergence in the weak and the vague topology of the sequence $$\left( {\mathop \Sigma \limits_{i = 1}^\infty \mathop \Sigma \limits_{j = 1}^\infty a_{ij}^{(n)} \mu ^i *v^j ,n \in \mathbb{N}} \right)$$ where μ and ν are probability measures on locally compact commutative semigroupS andAn=[aij(n)(i, j, n ɛ N) are double stochastic matrices satisfying some additional conditions. Our results generalize the results in [9]. Theorem 1 also holds if we make some changes on the topological assumptions onS, i.e. if we suppose thatS is a polish space.