The density and cellularity of the spaces of signed measures and probability measures

摘要

For a compact Hausdorff space X, let M(X) be a linear space of all signed Borel measures on X, M_+(X) be a positive cone of M(X). It is proved that c(M(X)) = C(M_+(X)) = C(X~ω) and d(M(X)) = d(M_+(X)) = d(P(X)). Similar results take place for spaces of τ-additive measures, Radon measures, and measures with compact supports on Tychonoff spaces.