Approximations by Darboux Functions in the Baire One Class

In the paper [Sur la premiére dérivée, Trans. Amer. Math. Soc. (N.S.) 2 (1940), 17-23], Z. Zahorski designed a way of constructing the real semicontinuous functions. Throughout the present paper, it is shown that a modification of Zahorski’s approach is usefull for approximation of a Baire one function by a Darboux Baire one function.