A new characterization of the dual space of the HK-integrable functions

Abstract

<abstract><p>We construct the Henstock-Kurzweil (HK) integral as an extension of a linear form initially defined on $ L^{1} $, but which is not continuous in this space. This gives us an alternative way to prove existing results. In particular, we give a new characterization of the dual space of Henstock-Kurzweil integrable functions in terms of a quotient space.</p></abstract>