Lecture 21: The Riemann Integral of a Continuous Function

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MIT 18.100A Real Analysis, Fall 2020
Instructor: Dr. Casey Rodriguez

We continue studying the Riemann integral, proving the convergence of Riemann sums of a continuous function on a bounded interval. We also begin studying properties of the Riemann integral, which we explore more in the next lecture.

License: Creative Commons BY-NC-SA

  1. MIT OpenCourseWare
  2. Riemann integral
  3. Riemann sums
  4. convergence of Riemann sums
  5. properties of Riemann integrals
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Автор

I am confused with Thm2, the instructor said and explained like x is coarser than x' but since x' is contained in x and considering the definition of the partition, isn't his explain should be opposite while he is proving Thm2? so x contains x' and more I think

배현성-on
Автор

There is a minor typo at 28:49, where sigma index goes from j = L+1 to M (not K)

nicolasg.b.