Baire 1 functions and the strong Choquet property

Abstract

Let X be a Tychonoff space and B_1(X) be the space of real-valued Baire 1 functions. Using the classical Lebesgue's characterization of Baire 1 functions and the strong Choquet game we prove that if X is locally compact or a topological sum of sigma-compact spaces, the space B_1(X) equipped with the topology τ_UC of uniform convergence on compacta, is a strong Choquet space. For the Sorgenfrey line S, the space (B_1(S); τ_UC) is of the first Baire category in itself.