Multiple Integration: Fubini Theorem

This lecture covers the concept of multiple integration in R², focusing on double integrals over closed rectangles and the Fubini theorem. The instructor explains the idea behind the theorem's proof, emphasizing the uniform continuity of functions on closed rectangles. Properties of double integrals, such as linearity and the ability to interchange the roles of x and y, are discussed. The lecture also explores the significance of double integrals in determining areas and volumes, along with the theorem of averages. Various properties of double integrals, including linearity, comparison, and the theorem of averages, are presented and explained.