Change of variable in Kurzweil-Henstock Stieltjes integrals.

Abstract

We present conditions under which one may substitute the identity function for $h$ in Kurzweil-Henstock integrals of the form $\int(f\circ h)\,d(g\circ h)$ reducing them to equivalent integrals of the form $\int f\,dg$\,. Our study requires that we also consider reduction of $\int (f\circ g) |d(g\circ h)|$ to $\int Nf|dg|$ where $N$ is the Banach indicatrix of $h$.