Quasi-pseudometric properties of the Nikodym-Saks space


  • Jesús Ferrer Universitat de València




Quasi-pseudometric space, Nikodym-Saks space


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


De Guzmán; M., Rubio, B.: Integración: Teoría y técnicas, Alhambra S. A., Madrid (1979).

Diestel, J.; Uhl, J.J.: Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence (1977). http://dx.doi.org/10.1090/surv/015

Diestel, J.: Sequences and Series in Banach Spaces, Springer-Verlag, New York (1984). http://dx.doi.org/10.1007/978-1-4612-5200-9

Drewnowski, L.: Topological Rings, Continuous Set Functions, Integration, Bull. Acad. Polon. Scien. 20 , 269-276 (1972). 1981.

Dunford, N.; Schwartz, J.T.: Linear Operators (I), Wiley, New York (1976).

Fletcher, P.; Lindgren, W.: Quasi-Uniform Spaces, Marcel Dekker, (1982).

Halmos, P.R.: Measure Theory, Springer-Verlag, New York (1974).

Munroe, M.E.: Measure and Integration, Addison-Wesley, London (1968).

Oxtoby, J.C.: Measure and Category, Springer-Verlag, New York (1980). http://dx.doi.org/10.1007/978-1-4684-9339-9

Reilly, I.L.; Subrahmanyam, P.V.; Vamanamurthy, M.K.: Cauchy sequences in quasipseudometric spaces, Mh. Math. 93, 127-140 (1982). http://dx.doi.org/10.1007/BF01301400

Williamson, J.H.: Integración Lebesgue, Tecnos , Madrid (1973).




How to Cite

J. Ferrer, “Quasi-pseudometric properties of the Nikodym-Saks space”, Appl. Gen. Topol., vol. 4, no. 2, pp. 243–253, Oct. 2003.



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