On A Recent Characterization of Baire Class One Functions

Jonald Fenecios

Abstract

Recently, a new characterization of Baire class one functions is given based on the countable decomposition of their set of points of discontinuity which improves a theorem by Henri Lebesgue. The proof makes use of the $\epsilon$-$\delta$ characterization of Baire class one functions. In this note, we shall give another proof of this result that avoids the use of the $\epsilon$-$\delta$ characterization. Furthermore, we use the theorem in finding applications involving the class of cliquish functions.