Functions of the first Baire class with values in Banach spaces

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 Φ:T→γ(X) (the power set of X) is a mapping that is usc in the weak topology then Φ has a selector of the first Baire class. This extends some results of Hansell, Jayne, Rogers, and Talagrand