Abstract
The class of nonatomic finite measure spaces with the saturation property, as developed in Maharam (1942) and Hoover–Keisler (1984), is characterized by the Fatou (and Lebesgue) property of a well-dominated sequence of multifunctions taking values in a Banach space. With multifunctions reduced to functions, this Fatou characterization also extends to a variant of the closure property found in optimal control theory. The results are developed through a considered overview of the relevant literature on the exact and approximate Fatou lemma phrased in terms of Bochner integration.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.