## Real Analysis Exchange

### On the Carathéodory Approach to the Construction of a Measure

Ivan Werner

#### Abstract

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

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

Dates
First available in Project Euclid: 10 May 2018

https://projecteuclid.org/euclid.rae/1525917692

Digital Object Identifier
doi:10.14321/realanalexch.42.2.0345

Mathematical Reviews number (MathSciNet)
MR3721806

Zentralblatt MATH identifier
06870334

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

#### Citation

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. https://projecteuclid.org/euclid.rae/1525917692