Functions of the first Baire class with values in metrizable spaces

Abstract

We show that every mapping of the first functional Lebesgue class that acts from a topological space into a separable metrizable space that is linearly connected and locally linearly connected belongs to the first Baire class. We prove that the uniform limit of functions of the first Baire class $f_n : \; X \rightarrow Y$ belongs to the first Baire class if $X$ is a topological space and $Y$ is a metric space that is linearly connected and locally linearly connected.