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Published 1991 | public
Book Section - Chapter

Integration with Respect to Finitely Additive Measures

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.

Additional Information

© Springer-Verlag Berlin Heidelberg 1991.

Additional details

Created:
August 22, 2023
Modified:
January 14, 2024