The strict topology for the space of Radon measures on a locally compact Hausdorff space

In this paper, we deal with the dual of the measure space M ( X ) for a locally compact Hausdorff space X under certain locally convex topologies. We first introduce and study a strict topology β ( X ) on M ( X ) under which its strong dual can be identified with L 0 ∞ ( M ( X ) ) , the Banach space of all F ∈ L ∞ ( M ( X ) ) that vanishes at infinity. Under this duality, we investigate some attributes of ( M ( X ) , β ( X ) ) as a locally convex space.