Quasi-pseudometric properties of the Nikodym-Saks space

Jesús Ferrer

doi:10.4995/agt.2003.2029

Authors

Jesús Ferrer Universitat de València

DOI:

https://doi.org/10.4995/agt.2003.2029

Keywords:

Quasi-pseudometric space, Nikodym-Saks space

Abstract

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.

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Author Biography

Jesús Ferrer, Universitat de València

Departamento de Analisis Matematico

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