Existence and computation of Riemann-Stieltjes integrals through Riemann integrals

Abstract

We study the existence of Riemann-Stieltjes integrals of bounded functions against a given integrator. We are also concerned with the possibility of computing the resulting integrals by means of related Riemann integrals. In particular, we present a new generalization to the well-known formula for continuous integrands and continuously differentiable integrators.

References in corpus (1)

• Mean value integral inequalities

Cited by in corpus (3)

• The change of variable formula for the Riemann integral
• The change of variable formula for Riemann-Stieltjes integrals
• Modified Riemann sums of Riemann-Stieltjes integrable functions