Advanced analysis II: riemann integral properties

This lecture covers advanced topics in Riemann integral properties, including the definition of Riemann integrability, upper and lower Riemann sums, and the coherence of the definition. It also explores the concept of partitions, tensorial partitions, and the iterated integrals formula. The instructor demonstrates the proof of Riemann integrability for bounded functions and discusses the extension of functions on compact sets. Additionally, the lecture delves into the concept of Riemann integrals on bounded sets and the set of Riemann-integrable functions. Various examples and proofs are provided to illustrate the theoretical concepts discussed.