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2017 On the Carathéodory Approach to the Construction of a Measure
Ivan Werner
Real Anal. Exchange 42(2): 345-384 (2017). DOI: 10.14321/realanalexch.42.2.0345


The Carathéodory theorem on the construction of a measure is generalized by replacing the outer measure with an approximation of it and generalizing the Carathéodory measurability. The new theorem is applied to obtain dynamically defined measures from constructions of outer measure approximations resulting from sequences of measurement pairs consisting of refining \(\sigma\)-algebras and measures on them which need not be consistent. A particular case when the measurement pairs are given by the action of an invertible map on an initial \(\sigma\)-algebra and a measure on it is also considered.


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Ivan Werner. "On the Carathéodory Approach to the Construction of a Measure." Real Anal. Exchange 42 (2) 345 - 384, 2017.


Published: 2017
First available in Project Euclid: 10 May 2018

zbMATH: 06870334
MathSciNet: MR3721806
Digital Object Identifier: 10.14321/realanalexch.42.2.0345

Primary: 28A99
Secondary: 28A12

Keywords: Caratheodory measurability , dynamically defined measure , outer measure , outer measure approximation

Rights: Copyright © 2017 Michigan State University Press

Vol.42 • No. 2 • 2017
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