Ascoli-Type Theorem for Baire 1 Functions

Abstract

Let X, Y be metric spaces and B1(X,Y) be the space of Baire 1 functions from X to Y. The main purpose of this paper is to study compact subsets of B1(X,Y) equipped with the topology τUC of uniform convergence on compacta and prove Ascoli-type theorem for locally bounded Baire 1 functions. The key notion in our paper is the notion of equi-Lebesgue family of functions from X to Y.