Vector Measures

For a non-negative finite countably additive measure µ defined on the σ-field Σ of subsets of Ω, it is well known that a certain quotient of Σ can be turned into a complete metric space Σ(Ω), known as the Nikodym-Saks space, which yields such important results in Measure Theory and Functional Analysis as Vitali-Hahn-Saks and Nikodym's theorems.Here we study some topological properties of Σ(Ω) regarded as a quasi-pseudometric space.