Real Analysis Exchange

On the Carathéodory Approach to the Construction of a Measure

Ivan Werner

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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.

Article information

Real Anal. Exchange, Volume 42, Number 2 (2017), 345-384.

First available in Project Euclid: 10 May 2018

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 28A99: None of the above, but in this section
Secondary: 28A12: Contents, measures, outer measures, capacities

outer measure outer measure approximation Caratheodory measurability dynamically defined measure


Werner, Ivan. On the Carathéodory Approach to the Construction of a Measure. Real Anal. Exchange 42 (2017), no. 2, 345--384. doi:10.14321/realanalexch.42.2.0345.

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