Measure extension by local approximation
Classical Analysis and ODEs
2017-02-14 v2
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.
Cite
@article{arxiv.1702.01142,
title = {Measure extension by local approximation},
author = {Iosif Pinelis},
journal= {arXiv preprint arXiv:1702.01142},
year = {2017}
}
Comments
8 pages. Version 2: A localized completion of the measure is now considered as well, in Theorem 1.4