Abstract
In this chapter we study elementary integration theory for functions defined on closed intervals. Although we expect that the reader has had experience with integral calculus and that the ideas are familiar, we shall not require any special results to be known. For pedagogical reasons we shall first treat the Cauchy integral. After this has been done, we will study in §3 the Riemann integral. Our attention here is focused exclusively on the definition and existence, since these concepts are often mysterious even to students who have ample knowledge of the numerous applications and techniques of evaluating Riemann integrals from their study of calculus.
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© 1995 Springer Science+Business Media New York
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Chae, S.B. (1995). The Riemann Integral. In: Lebesgue Integration. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0781-8_2
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DOI: https://doi.org/10.1007/978-1-4612-0781-8_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94357-2
Online ISBN: 978-1-4612-0781-8
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