Measure extension by local approximation
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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.
KeywordsMeasures Measure extension Rings of sets Algebras of sets Sigma-algebras of sets
Mathematics Subject Classification28A12 60A10
- 2.Borovkov, A.A.: Probability theory. Gordon and Breach Science Publishers, Amsterdam (1998). Translated from the 1986 Russian original by O. Borovkova and revised by the authorGoogle Scholar
- 4.von Weizsäcker, H.: Basic Measure Theory. Lecture Notes. Technische Universität Kaiserslautern (2008). Revised Translation. http://bit.ly/2jS1aPf