The previous lecture in this series is here. The next lecture in this series is here.
Last time, we introduced outer measures, which have most properties we want for a measure. We define Lebesgue measurable sets and ultimately the Lebesgue measure. We also define σ-algebras, including the important Borel σ-algebra.
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.