Measure Theory: Sets and Algebras

This lecture covers the concepts of measurability and independence of sets, limits, and construction of sigma-algebras. It introduces the construction of a sigma-algebra from a collection of sets, along with the definition of cylinder sets and their properties. The lecture also discusses the concept of a co-algebra, the uniqueness of measures, and the extension of measures. The presentation concludes with the proof of the uniqueness of measures and the extension of measures from a T-system to a sigma-algebra.