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1995/1996 An integral mean value theorem for regulated functions
Daniel Waterman
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Real Anal. Exchange 21(2): 817-820 (1995/1996).


An elementary but useful mean value theorem for integrals asserts that if \(f\) is a non-negative integrable function on \([a,b]\) and \(g\) is continuous there, then there is a \(\theta\in(a,b)\) such that \[g(\theta)\int^b_af(t)dt=\int^b_ag(t)f(t)dt.\] It does not seem to have been observed that this result has an equally useful extension to regulated \(g\), i.e, \(g\) which have right and left limits at each point.


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Daniel Waterman. "An integral mean value theorem for regulated functions." Real Anal. Exchange 21 (2) 817 - 820, 1995/1996.


Published: 1995/1996
First available in Project Euclid: 14 June 2012

zbMATH: 0879.26019
MathSciNet: MR1407299

Primary: 26A24

Keywords: Integral mean value theorem , regulated functions

Rights: Copyright © 1995 Michigan State University Press

Vol.21 • No. 2 • 1995/1996
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