Provider: JSTOR http://www.jstor.org Database: JSTOR Content: text/plain; charset="us-ascii" TY - CHAP TI - INTEGRALS OF STIELTJES TYPE A2 - McLEOD, ROBERT M. AB -

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

EP - 230 ET - 1 PB - Mathematical Association of America PY - 1980 SN - 9780883850459 SP - 177 T2 - The Generalized Riemann Integral UR - http://www.jstor.org/stable/10.4169/j.ctt5hhb4z.12 VL - 20 Y2 - 2021/09/19/ ER -