Conversion formulas for the Lebesgue-Stieltjes integral (Q1898960)

The author derived some conversion formulas for the Lebesgue-Stieltjes integral which convert Lebesgue-Stieltjes integrals with a continuous integrator \(h\) of bounded variation into Lebesgue integrals over the range of \(h\). Hence Banach's indicatrix formula and Green's theorem were deduced. The integral used is the generalized Riemann integral involving differentials, some of which were developed by the author in his earlier papers [Real Anal. Exch. 12(1986/87), 144-175 (1987; Zbl 0638.26009); 16, No. 2, 508-515 (1991; Zbl 0747.26004)].