On the Riemann-Stieltjes Integral

Document Type : Original Scientific Paper


Department of Mathematics, Tafresh University, Tafresh, 39518-79611, I. R. Iran


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.


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