Open Access
May 2014 Lebesgue's Remarkable Result
Charles A. Coppin
Missouri J. Math. Sci. 26(1): 88-97 (May 2014). DOI: 10.35834/mjms/1404997112


We present a proof based on a 1905 paper by Henri Lebesgue that any continuous function defined on an interval has an antiderivative {\em without first proving the existence of the definite integral of the function}. We also demonstrate how the definite integral is a byproduct of this proof. Instead of merely presenting an efficient proof using modern techniques, we have chosen to present a more instructive proof actually following the steps of Lebesgue in the spirit of Otto Toeplitz's~\cite{Toeplitz} genetic approach.


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Charles A. Coppin. "Lebesgue's Remarkable Result." Missouri J. Math. Sci. 26 (1) 88 - 97, May 2014.


Published: May 2014
First available in Project Euclid: 10 July 2014

zbMATH: 1301.26005
MathSciNet: MR3263544
Digital Object Identifier: 10.35834/mjms/1404997112

Primary: 00-01
Secondary: 26-01

Keywords: antiderivative , Riemann integral

Rights: Copyright © 2014 Central Missouri State University, Department of Mathematics and Computer Science

Vol.26 • No. 1 • May 2014
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