Certain strict topologies on the space of regular Borel measures on locally compact groups

Let G denote a locally compact Hausdorff group and M(G) be the space of all bounded complex-valued regular Borel measures on G. In this paper, we define two strict topologies on M(G) and study various properties of these topologies such as metrizability, barrelledness and completeness. We also determine the dual space of M(G) and consider various continuity properties for the convolution product on M(G) under these topologies.