A pair of adjoint classes of Riemann-Stieltjes integrable functions (Q1978858)

Let \(-\infty <a<b<\infty \) and let R stand for the set of functions Riemann integrable on \([a,b].\) The author shows that then the Riemann-Stieltjes integral \(\int _a^b f dg\) exists for all \(f\in \text R\) and any function \(g\) absolutely continuous on \([a,b]\) (\(g\in \) AC). Moreover, if \(\int _a^b f dg\) exists for all \(f\in \) R, then \(g\in \) AC and if \(\int _a^b f dg\) exists for all \(g\in \) AC, then \(f\in \) R. (In other words, the sets R and AC are adjoint with respect to the Riemann-Stieltjes integral).