Measurable Functions: Independence

This lecture covers the concept of independence between sigma-algebras, focusing on the proof and lemma that demonstrate the independence of certain algebras. It also discusses the conditions under which algebras are considered independent, emphasizing the role of measurable functions. The lecture further explores the notion of independent T-systems and their implications in probability theory, illustrating how to determine independence through specific measures and systems. Additionally, it delves into countably additive measures and their significance in defining independence within a given space.