Measure extension by local approximation

Published 3 Feb 2017 in math.CA | (1702.01142v2)

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 Carath\'eodory-measurable.

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Iosif Pinelis

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