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

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

Hossein Javanshiri

Rasoul Nasr-Isfahani

Abstract

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  , 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.

Keywords: Dual space; Locally compact space; Locally convex topology; Radon measure; Strict topology.

MSC: 28C05; 28C15; 46A03; 54C35; 54C60.