Some quantities related to monotonicity and bounded variation of functions

The aim of this paper is to introduce and study some quantities connected with monotonicity and bounded variation of real functions. These quantities will also be considered for bounded subsets of spaces of bounded or continuous functions on a compact interval, equipped with the standard supremum norm. Several properties of such quantities are established, and possible applications are briefly sketched. Moreover, some relation with the theory of measures of noncompactness is discussed as well.