We prove that a Baire measure (or a regular Borel measure) on a compact Hausdorff space is sequentially order continuous as a linear functional on the Banach space of all continuous functions if and ...

Let S be a complete and separable metric space and μ a σ-finite, complete Borel measure on S with $\mu(S) > 0$. Let Φ be the family of all real-valued functions defined on S whose set of points of ...