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manuscripta mathematica

, Volume 5, Issue 2, pp 123–131 | Cite as

Equicontinuity and convergence of measures

  • Dieter Landers
  • Lothar Rogge
Article

Abstract

It is shown in this paper that each family of measures with values in an abelian topological group which is equicontinuous on a ring is equicontinuous on the generated σ-ring. A family of measures is equicontinuous iff the corresponding family of “semivariations” is equicontinuous. It is furthermore shown that a family of measures which is equicontinuous and Cauchy convergent on a ring is Cauchy convergent on the generated σ-ring. A family of measures which is Cauchy convergent for all countable sums of elements of a ring is Cauchy convergent on the generated σ-ring.

Keywords

Number Theory Algebraic Geometry Topological Group Abelian Topological Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • Dieter Landers
    • 1
  • Lothar Rogge
    • 1
  1. 1.Mathematisches Institut der Universität zu KölnKöln 41

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