THE SEMI-BOREL CLASSIFICATION OF THE EXTREME PATH DERIVATIVES

Abstract

The goal of this paper is to investigate of the semi-Borel and Baire classification of the multifunction of all path derived numbers of a semi-Borel and Baire function of the class $\alpha$. Consequently the classification of the extreme path derivatives is given. The results hold in the setting of ordinary qualitative and approximate path differentiation, and the proofs are based on a classification of the collection of paths which is considered as a multifunction of the semi-Borel class $\alpha$.