Generalized Stepanov type theorem with applications over metric-measure spaces

The main purpose of this article is to extend an L(p)-type generalization of Stepanov's differentiability theorem in metric-measure space. This generalized Stepanov type theorem is applied to the Sobolev and bounded variation functions in order to show the L(p)-type generalized differentiability for such functions. The proof of this generalized differentiability theorem is a combination of the proofs of Campanato and Stepanov theorems which is an extension of author's work to abstract spaces. Moreover, we give a positive answer to a question of Balogh-Rogovin-Zurchcr about L(p)-type generalized differentiability of BV functions over metric-measure spaces.