Sets of non-differentiability for functions with finite lower scaled oscillation (Q1704492)

Characterization of sets of non-differentiability for real-valued functions which satisfy certain Lipschitz-like conditions initiated the theme of writing the present paper. Notations and terminologies begin the paper, giving the concept that Lebesgue's result can be generalized by employing the upper scaled oscillation function defined by equation (1). The claim of the paper is that the results can be (and in fact that is endeavored also) explored by replacing the upper scaled oscillation function with the lower scaled oscillation. This fact and analysis helped the proof of Theorems 8 and 9, where perfect nowhere dense sets are considered and simultaneously, dyadic decompositions of set are also invoked.