On the Riemann-Stieltjes Integral

Abstract

This study contributes to the theory of Riemann-Stieltjes integral. We prove that if all continuous piecewise linear functions are Riemann-Stieltjes integrable with respect to a bounded integrator α : [a,b] → R, then α must be of bounded variation on [a,b]. We also provide some other consequences.

Keywords

• cantor’s intersection theorem
• function of bounded variation
• riemann-stieltjes integral