Rocky Mountain Journal of Mathematics

Borel and continuous systems of measures

Aviv Censor and Daniele Grandini

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Abstract

We study Borel systems and continuous systems of measures, with a focus on mapping properties: compositions, liftings, fibred products and disintegration. Parts of the theory we develop can be derived from known work in the literature, and in that sense this paper is of an expository nature. However, we put the above notions in the spotlight and provide a self-contained, purely measure-theoretic, detailed and thorough investigation of their properties, and in that aspect our paper enhances and complements the existing literature. Our work constitutes part of the necessary theoretical framework for categorical constructions involving measured and topological groupoids with Haar systems, a line of research we pursue in separate papers.

Article information

Source
Rocky Mountain J. Math., Volume 44, Number 4 (2014), 1073-1110.

Dates
First available in Project Euclid: 31 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1414760943

Digital Object Identifier
doi:10.1216/RMJ-2014-44-4-1073

Mathematical Reviews number (MathSciNet)
MR3274338

Zentralblatt MATH identifier
1316.28003

Subjects
Primary: 28A50: Integration and disintegration of measures 22A22: Topological groupoids (including differentiable and Lie groupoids) [See also 58H05]

Keywords
System of measures Borel system of measures lifting fibred product disintegration groupoid Haar system

Citation

Censor, Aviv; Grandini, Daniele. Borel and continuous systems of measures. Rocky Mountain J. Math. 44 (2014), no. 4, 1073--1110. doi:10.1216/RMJ-2014-44-4-1073. https://projecteuclid.org/euclid.rmjm/1414760943


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