6533b858fe1ef96bd12b5a40

RESEARCH PRODUCT

Quasi-pseudometric properties of the Nikodym-Saks space

Jesús Ferrer

subject

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsFunctional analysislcsh:MathematicsQuasi-pseudometric spaceMathematics::General Topologylcsh:QA299.6-433lcsh:AnalysisPseudometric spacelcsh:QA1-939Space (mathematics)Measure (mathematics)Complete metric spaceNikodym-Saks spaceGeometry and TopologyQuotientMathematics

description

[EN] 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.

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