Double Integrals: Definitions and Properties

This lecture covers the definitions and properties of double integrals in the context of continuous functions over compact regions in the plane, emphasizing the importance of reasonable boundaries. It also discusses the concept of nested regions and the independence of the result on the choice of points. The presentation includes the demonstration of double integrals modulo boundary issues and the application of Riemann sums. The lecture concludes with remarks on volume calculations and the significance of the first square's size in the process.