Measure extension by local approximation

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.

8 pages. Version 2: A localized completion of the measure is now considered as well, in Theorem 1.4