Measure extension by local approximation

2017/02/03 by Pinelis, Iosif
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary 28A12 #secondary 60A10

paper · doi:10.48550/arxiv.1702.01142

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.

Related

• A Realization of Measurable Sets as Limit Points
• A Carathéodory's Extension Theorem for Families Simpler Than an Algebras of Sets
• A categorical proof of the Carathéodory extension theorem
• Locally standard measure algebras
• Induced Measures on "Mu**"- measurable Sets