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Riemann Integration

  • Sheldon Axler
Open Access
Chapter
Part of the Graduate Texts in Mathematics book series (GTM, volume 282)

Abstract

This brief chapter reviews Riemann integration. Riemann integration uses rectangles to approximate areas under graphs. This chapter begins by carefully presenting the definitions leading to the Riemann integral. The big result in the first section states that a continuous real-valued function on a closed bounded interval is Riemann integrable. The proof depends upon the theorem that continuous functions on closed bounded intervals are uniformly continuous.

Copyright information

© Sheldon Axler 2020

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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Authors and Affiliations

  • Sheldon Axler
    • 1
  1. 1.Department of MathematicsSan Francisco State UniversitySan FranciscoUSA

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