Strict topology on locally compact groups

Abstract

Let G be a locally compact group, A a subalgebra of the measure algebra M ( G ) , and A a family of Borel subsets of G that is closed under finite unions. In this paper, among other results, we find sufficient conditions on A , that imply A is a semi-topological algebra with respect to the strict topology β A . We also find necessary and sufficient conditions on G , that imply A is a topological algebra with respect to the strict topology β A , where A is a family of Borel subsets of G with finite Haar measure.