Riemann Integration

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


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.

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© Sheldon Axler 2020

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Authors and Affiliations

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

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