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2004-2005 A new necessary condition for existence of the Stieltjes integral
V. Chernyatin
Real Anal. Exchange 30(1): 207-216 (2004-2005).


The paper is devoted to establishing a necessary condition for the existence of the Riemann-Stieltjes integral of continuous functions and simultaneously to finding a limit form of its relationship with the classical Riemann integral depending on a parameter. The mathematical technique for this study is based on changing the weighted first difference of a given function into the simple difference of a function determined by a first-order difference equation.


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V. Chernyatin. "A new necessary condition for existence of the Stieltjes integral." Real Anal. Exchange 30 (1) 207 - 216, 2004-2005.


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

zbMATH: 1060.26012
MathSciNet: MR2127527

Primary: 26A42
Secondary: 28A75 , 39A10

Keywords: difference equation , Riemann-Stieltjes integral , weighted first difference

Rights: Copyright © 2004 Michigan State University Press

Vol.30 • No. 1 • 2004-2005
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