A note on $\varrho$-upper continuous functions

Abstract

In the present paper, we introduce the notion of classes of $\varrho$-upper continuous functions. We show that $\varrho$-upper continuous functions are Lebesgue measurable and, for $\varrho<\frac{1}{2}$, may not belong to Baire class 1. We also prove that a function with Denjoy property can be non-measurable.