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2009/2010 Monotonicity Properties of Darboux Sums
Ioanna Kyrezi
Real Anal. Exchange 35(1): 43-64 (2009/2010).


Let $f:[a, b]\to \R$ be a continuous function. Dividing the interval $[a, b]$ into subintervals of equal length, we obtain partitions of $[a, b]$ for which the upper and lower Darboux sums of $f$ constitute two sequences, which converge to the definite integral of $f$ in $[a, b]$ from above and below respectively. We study the monotonicity properties of these sequence and we prove that their non-monotonicity is a generic (quasi-sure) property in the space $C([a, b])$.


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Ioanna Kyrezi. "Monotonicity Properties of Darboux Sums." Real Anal. Exchange 35 (1) 43 - 64, 2009/2010.


Published: 2009/2010
First available in Project Euclid: 27 April 2010

zbMATH: 1200.26010
MathSciNet: MR2657287

Primary: 26A42

Keywords: Darboux sums

Rights: Copyright © 2009 Michigan State University Press

Vol.35 • No. 1 • 2009/2010
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