On the dual of certain locally convex function spaces

In this paper‎, ‎we first introduce some‎ ‎function spaces‎, ‎with certain locally convex topologies‎, ‎closely‎ ‎related to the space of real-valued continuous functions on $X$‎, ‎where $X$ is a $C$-distinguished topological space‎. ‎Then‎, ‎we show‎ ‎that their dual spaces can be identified in a natural way with‎ ‎certain spaces of Radon measures‎.