The previous lecture in this series is here. The next lecture in this series is here.
We define the class of Lebesgue integrable functions and the Lebesgue integral, and we prove the powerful Dominated Convergence Theorem! We conclude by showing that the Riemann and Lebesgue integrals agree for continuous functions on a bounded interval.
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.