The Riesz-Kakutani Theorem

This lecture covers the construction of measures, focusing on positive functionals and their inner and outer measures. It discusses the properties of o-additivity, measurability of sets, and the concept of a measurable collection. The lecture also presents propositions related to measurable disjoint sets and concludes with the Riesz-Kakutani Theorem, which establishes the existence of a regular and complete measure on a Borel o-algebra. The theorem connects positive functionals to measures, showcasing the significance of the Lebesgue measure in this context.