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
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