An Alternative Definition of the Henstock-Kurzweil Integral Using Primitives

Abstract

We introduce the notion of an H-primitive being the limit of a sequence of absolutely continuous functions satisfying certain conditions and use it to formulate an alternative definition of the Henstock-Kurzweil integral on a closed bounded interval. Furthermore, the definition provides a characterisation of the primitive of a Henstock-Kurzweil integrable function.