An Andô-Douglas type theorem in Riesz spaces with a conditional expectation
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.
scientific article; zbMATH DE number 5601475
scientific article