A note on a paper of J. D. Stein, Jr.: “Sequence of regular finitely additive set functions” (Trans. Amer. Math. Soc. 192 (1974), 59–66)

Author:

Khurana Surjit Singh

Abstract

Among other results, it is proved that if a sequence { μ n } \{ {\mu _n}\} of regular measures on a Hausdorff space, with values in a normed group, is convergent to zero for all σ \sigma -compact sets or all open sets, then there exists a maximal open set U such that μ ˙ n ( U ) 0 , { μ ˙ n } {\dot \mu _n}(U) \to 0,\{ {\dot \mu _n}\} being the associated submeasures.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference5 articles.

1. Topological rings of sets, continuous set functions, integration. I, II;Drewnowski, L.;Bull. Acad. Polon. Sci. S\'{e}r. Sci. Math. Astronom. Phys.,1972

2. Equivalence of Brooks-Jewett, Vitali-Hahn-Saks and Nikodym theorems;Drewnowski, L.;Bull. Acad. Polon. Sci. S\'{e}r. Sci. Math. Astronom. Phys.,1972

3. The Hahn-Vitali-Saks and the uniform boundedness theorem in topological groups;Landers, D.;Manuscripta Math.,1971

4. Cauchy convergent sequences of regular measures with values in a topological group;Landers, Dieter;Z. Wahrscheinlichkeitstheorie und Verw. Gebiete,1972

5. Sequence of regular finitely additive set functions;Stein, J. D., Jr.;Trans. Amer. Math. Soc.,1974

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