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Positivity

, Volume 22, Issue 1, pp 199–208 | Cite as

Measure extension by local approximation

  • Iosif Pinelis
Article
  • 63 Downloads

Abstract

Measurable sets are defined as those locally approximable, in a certain sense, by sets in the given algebra (or ring). A corresponding measure extension theorem is proved. It is also shown that a set is locally approximable in the mentioned sense if and only if it is Carathéodory-measurable.

Keywords

Measures Measure extension Rings of sets Algebras of sets Sigma-algebras of sets 

Mathematics Subject Classification

28A12 60A10 

References

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    von Weizsäcker, H.: Basic Measure Theory. Lecture Notes. Technische Universität Kaiserslautern (2008). Revised Translation. http://bit.ly/2jS1aPf
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    Wise, G.L., Hall, E.B.: Counterexamples in Probability and Real Analysis. The Clarendon Press, Oxford University Press, New York (1993)MATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematical SciencesMichigan Technological UniversityHoughtonUSA

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