On the CarathÉodory Approach to the Construction of a Measure

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 re...

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Bibliographic Details
Published inReal analysis exchange Vol. 42; no. 2; pp. 345 - 384
Main Author Werner, Ivan
Format Journal Article
LanguageEnglish
Published East Lansing Michigan State University Press 01.01.2017
Subjects
Algebra
Approximation
Logical theorems
Mathematical functions
Mathematical theorems
Measurability
Measure theory
Measurement
Theorems
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Summary: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 refiningσ-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 initialσ-algebra and a measure on it is also considered. Mathematical Reviews subject classification: Primary: 28A99; Secondary: 28A12 Key words: outer measure, outer measure approximation, Carathéodory measurability, dynamically defined measure
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0147-1937
1930-1219
DOI:10.14321/realanalexch.42.2.0345