Lecture
This lecture delves into the concept of Fubini's theorem in multiple dimensions, exploring the integration of functions over various domains, such as rectangles and closed unit balls. The instructor demonstrates how to generalize the theorem by using rectangles as building blocks and extends the integration to more complex regions. Through detailed examples, the lecture illustrates the process of splitting the integral over different domains and showcases the application of Fubini's theorem in practical scenarios, such as integrating over triangles and closed unit balls with specific constraints. The lecture concludes by hinting at further exploration of the topic in the upcoming session.