Casey Rodriguez: Introduction to Functional Analysis, XI. The Lebesgue Integral of a Non-negative Function and Convergence Theorems

The previous lecture in this series is here. The next lecture in this series is here.

We define the Lebesgue integral for non-negative functions via a limiting process involving simple functions. We then prove two fundamental results of Lebesgue integration: the Monotone Convergence Theorem and Fatou’s Lemma.

These videos are of a lecture course by Casey Rodriguez at the Massachusetts Institute of Technology in 2021, and made available as part of its OpenCourseWare initiative.