The convergence determining class of connected open sets in product spaces
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- by Dieter Landers PDF
- Proc. Amer. Math. Soc. 33 (1972), 529-533 Request permission
Abstract:
It is proved in this paper that each sequence of measures with values in a topological group—defined on the Borel field of a finite or countable product of connected, locally connected, separable metric spaces—which is Cauchy convergent for all connected open sets is Cauchy convergent for all Borel sets, too.References
- D. Landers and L. Rogge, The Hahn-Vitali-Saks and the uniform boundedness theorem in topological groups, Manuscripta Math. 4 (1971), 351–359. MR 283169, DOI 10.1007/BF01168702
- Dieter Landers and Lothar Rogge, Cauchy convergent sequences of regular measures with values in a topological group, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 21 (1972), 188–196. MR 310170, DOI 10.1007/BF00538391
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 529-533
- MSC: Primary 60B15; Secondary 28A45
- DOI: https://doi.org/10.1090/S0002-9939-1972-0298718-X
- MathSciNet review: 0298718