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.