Open Access
1998/1999 Integration by Parts and Other Theorems for R3S-Integrals
E. R. Love
Real Anal. Exchange 24(1): 315-336 (1998/1999).


This paper is a continuation of [3], in which was introduced the Refinement-Ross-Riemann-Stieltjes $(R^3S)$ Integral, and in which some of its advantages were exhibited. After a brief summary of [3], this paper proves an integration by parts theorem which shows incidentally that if $f$ is $R^3S$-integrable with respect to $g$ then $g$ is $R^3S$-integrable with respect to $f$. Theorems on term-by-term integration of sequences analogous to the Helly-Bray Theorem are next proved, in a context of Wiener's functions of bounded generalized variation as developed by L. C. Young and me. In a similar context I prove also a theorem resembling the classical theorem of Riesz representing linear functionals by Stieltje.


Download Citation

E. R. Love. "Integration by Parts and Other Theorems for R3S-Integrals." Real Anal. Exchange 24 (1) 315 - 336, 1998/1999.


Published: 1998/1999
First available in Project Euclid: 23 March 2011

MathSciNet: MR1691754

Primary: 26A42

Keywords: integration by parts

Rights: Copyright © 1998 Michigan State University Press

Vol.24 • No. 1 • 1998/1999
Back to Top