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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Functions of the first Baire class with values in Banach spaces


Author: Charles Stegall
Journal: Proc. Amer. Math. Soc. 111 (1991), 981-991
MSC: Primary 26A21; Secondary 47H04
MathSciNet review: 1019283
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Abstract: We characterize functions of the first Baire class with values in Banach spaces and give a short self-contained proof of a result more general than the following: If $ T$ is a complete metric space, $ X$ is a Banach space, and $ \Phi :T \to \wp (X)$ (the power set of $ X$) is a mapping that is use in the weak topology then $ \Phi $ has a selector of the first Baire class. This extends some results of Hansell, Jayne, Rogers, and Talagrand.


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DOI: https://doi.org/10.1090/S0002-9939-1991-1019283-7
Keywords: First Baire class, Banach spaces
Article copyright: © Copyright 1991 American Mathematical Society