Compactly bounded convolutions of measures

In this paper we extend classical results concerning generalized convolution structures on measure spaces. Given a locally compact Hausdorff space $X$, we show that a compactly bounded convolution of point masses that is continuous in the topology of weak convergence with respect to $C_{c}(X)$ can be extended to a general convolution of measures which is separately continuous in the topology of weak convergence with respect to $C_{b}(X)$.