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Integration with Respect to Finitely Additive Measures

Luxemburg, Wilhelmus A. J. (1991) Integration with Respect to Finitely Additive Measures. In: Positive Operators, Riesz Spaces, and Economics: Proceedings of a Conference at Caltech, Pasadena, California, April 16–20, 1990. Studies in Economic Theory. No.2. Springer , Berlin, pp. 109-150. ISBN 9783642635021. https://resolver.caltech.edu/CaltechAUTHORS:20181003-155855248

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Abstract

This essay interprets the theory of finitely additive measures within the framework of the theory of Riesz spaces. The following topics are discussed: the extension procedures of measures, the Riemann and the Dunford integration procedures, the Radon-Nikodym Theorem and the Hahn Decomposition Theorem, the representation theory of the Radon- Nikodym derivatives as generalized functions, conditional expectation operators, the theory of L^p -spaces, and the norm completeness problem. The nature of the classical axiom of countable additivity is examined from Carathéodory’s algebraic measure-theoretic point of view.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/978-3-642-58199-1_6DOIArticle
Additional Information:© Springer-Verlag Berlin Heidelberg 1991.
Subject Keywords:Boolean Algebra; Banach Lattice; Riesz Space; Outer Measure; Complete Boolean Algebra
Series Name:Studies in Economic Theory
Issue or Number:2
Record Number:CaltechAUTHORS:20181003-155855248
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20181003-155855248
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90121
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:08 Oct 2018 16:05
Last Modified:03 Oct 2019 20:22

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