Some remarks on differential equivalence (Q1113300)

This paper is related to S. Leader's concept of differential df of a function f based upon the Henstock-Kurzweil integral. A nice theory of the differential works for a class of functions called ``dampable'' by S. Leader and it is the purpose of the note to characterize this class of functions in terms of the old concept of ``differential equivalence'' in the language of Kolmogorov, or of ``variational equivalence'' in the language of Henstock. Indeed, the differentials of Leader are the equivalence classes for this equivalence relation. The characterization of the dampable functions is given in terms of the classical concepts of VBG* and ACG* functions which are fundamental in Perron-like integration theories.