@inbook{10.4169/j.ctt5hhb4z.12,
ISBN = {9780883850459},
URL = {http://www.jstor.org/stable/10.4169/j.ctt5hhb4z.12},
abstract = {The Stieltjes integral is a generalization of the Riemann integral on intervals of real numbers. It employs a function a in place of the identity function in forming the measure of subintervals of [a, b]. A Riemann sum$f\Delta \alpha \left( D \right)$is made up of terms$f\left( z \right)\left( {\alpha \left( v \right) - \alpha \left( u \right)} \right)$. The resulting integral is denoted$\int_a^b {fd\alpha } $or$\int_a^b {f\left( x \right)d\alpha \left( x \right)} $. The function$\alpha $is called the integrator andfis the integrand.The level of generality of$\int_a^b {fd\alpha } $depends on the limit process which is applied to the Riemann sum. There are three which should claim our attention. The least general of them is the limit used},
bookauthor = {ROBERT M. McLEOD},
booktitle = {The Generalized Riemann Integral},
edition = {1},
pages = {177--230},
publisher = {Mathematical Association of America},
title = {INTEGRALS OF STIELTJES TYPE},
volume = {20},
year = {1980}
}