Dual spaces of \(C_{\infty}(X)\) (Q1822009)

Characterizations of the important dual spaces of the Riesz space \(C_{\infty}(X)\) of extended-real-valued continuous functions with dense set of points of finiteness on some locally compact Stonian space X are given. In particular, the extended order dual of \(C_{\infty}(X)\) (introduced by Luxemburg and Masterson) can be described as an inductive limit of Riesz spaces of normal Radon measures, which can even be identified with \(C_{\infty}(X)\) if X is hyperstonian.