Abstract
The development of a rigorous theory of the definite integral in the nineteenth century is associated particularly with the work of Augustin-Louis Cauchy (1789-1857) in France, and Bernhard Riemann (1826-1866) in Germany. In order to give some background to the modern theory, we will describe briefly a definition of an integral equivalent to that introduced by Riemann in 1854, and discuss some of the weaknesses in this definition that suggest the need for a more general theory.
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© 2000 Springer Science+Business Media New York
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Carter, M., van Brunt, B. (2000). The Riemann Integral. In: The Lebesgue-Stieltjes Integral. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1174-7_3
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DOI: https://doi.org/10.1007/978-1-4612-1174-7_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7033-1
Online ISBN: 978-1-4612-1174-7
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