Unbounded weighted radon measures and dual of certain function spaces with strict topology

Let X be a C-distinguished topological space, and let ? be a weight function on X. Denote by Cb(X,?) the space of all real-valued functions f with f/??Cb(X), and by C?b(X,?) the space of all real-valued continuous functions f such that f/? is bounded. We introduce certain locally convex topologies on Cb(X,?) and C?b(X,?), and as our main results we determine their duals.