In this paper we give a representation theorem for the orthogonally additive functionals on the space BV in terms of a non-linear integral of the Henstock-Kurzweil-Stieltjes type.
In the paper, we show that the space of functions of bounded variation and the space of regulated functions are, in some sense, the dual space of each other, involving the Henstock-Kurzweil-Stieltjes integral.