University of Kashan Mathematics Interdisciplinary Research 2538-3639 7 2 2022 06 01 On the Riemann-Stieltjes Integral 131 138 111967 10.22052/mir.2022.243334.1322 EN Ali Parsian Department of Mathematics, Tafresh University, Tafresh, 39518-79611, I. R. Iran Journal Article 2021 12 03 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. Cantor’s intersection theorem Function of bounded variation Riemann-Stieltjes integral https://mir.kashanu.ac.ir/article_111967_38e1e40e7615202c24ada1b09fba3a91.pdf