Integral Properties on Closed Pavés

This lecture covers the theorem stating that a continuous function on a closed pavé is integrable, along with the properties of the integral on a closed pavé. It discusses the integrability of functions, the concept of boundedness, the volume of a pavé, and the sums of Darboux. The lecture also explores the relationship between continuous functions and integrability, the overlap of pavés by open balls, and the compactness of subsets. Additionally, it delves into the maxima and minima of continuous functions on pavés, the definition of integrability, and the subdivision of pavés for calculating Darboux sums.