Open Access
2004-2005 On integrals with integrators in BVp
Varayu Boonpogkrong, Chew Tuan Seng
Real Anal. Exchange 30(1): 193-200 (2004-2005).


n 1936, L. C. Young proved that the Riemann-Stieltjes integral$\int^b_a$ $f$ $dg$ exists, if $f\in BV_p,\,g\in BV_q, \frac{1}{p}+\frac{1}{q}>1$ and $f,g$ do not have common discontinuous points. In this note, using Henstock's approach, we prove that $\int^b_a$ $f$ $dg$ still exists without assuming the condition on discontinuous points. Some convergence theorems are also proved.


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Varayu Boonpogkrong. Chew Tuan Seng. "On integrals with integrators in BVp." Real Anal. Exchange 30 (1) 193 - 200, 2004-2005.


Published: 2004-2005
First available in Project Euclid: 27 July 2005

zbMATH: 1060.26010
MathSciNet: MR2127525

Primary: 26A21 , 28B16

Keywords: Henstock , integral , p-variation , Stieltjes , Young

Rights: Copyright © 2004 Michigan State University Press

Vol.30 • No. 1 • 2004-2005
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