An Andô-Douglas type theorem in Riesz spaces with a conditional expectation
type: Item
instance of: scholarly article
title: An Andô-Douglas type theorem in Riesz spaces with a conditional expectation
zbMATH Open document ID: 1186.47038
published in: Positivity
publication date: 2009-09-02T00:00:00Z
review text: The paper is concerned with the existence and uniqueness of conditional expectations on Riesz spaces with specified range spaces. After an introductory section, the second section contains the definition of a conditional expectation on a Riesz space, and other necessary preliminaries. A Hahn-Jordan decomposition is given in terms of conditional expectations on Riesz spaces in the third section of the paper, while in the fourth section, a Riesz space Radon-Nikodým theorem is proved. In the last section, an Andô-Douglas type characterization theorem in Dedekind complete Riesz spaces is given, and the existence and uniqueness of conditional expectations with given range spaces is proved.
reviewed by: Ilie Valuşescu
Mathematics Subject Classification ID: 47B60
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 60G48
Mathematics Subject Classification ID: 60G42
zbMATH DE Number: 5601475
zbMATH Keywords: Riesz spaces
zbMATH Keywords: Andô-Douglas theorem
zbMATH Keywords: Radon-Nikodým theorem
zbMATH Keywords: Hahn-Jordan decomposition
author: Bruce A. Watson
MaRDI profile type: Publication
full work available at URL: s11117-008-2239-2
OpenAlex ID: W2030671173
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DOI: 10.1007/S11117-008-2239-2
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description: scientific article; zbMATH DE number 5601475