Fubini Theorem on Closed Rectangles

This lecture covers the Fubini theorem applied to closed rectangles in R², discussing the integrability of functions over closed rectangles, the concept of iterated integrals, and the order of integration. Examples are provided to illustrate the application of the theorem, showing how to compute double integrals over different regions. The lecture also delves into the properties of zero-measure sets, the integrability of functions, and the concept of compact sets in R². The instructor emphasizes the importance of understanding the Fubini theorem for calculating integrals over various regions in two-dimensional space.