In this video, we explore basic concepts of Measure Theory and the Lebesgue Integral. We will learn about important theorems of Lebesgue Integration like the Monotone convergence theorem, the Dominated convergence theorem and Fatous Lemma. Measure Theory also naturally leads to a formal theory of probability, which will be presented.
00:00 Introduction
02:12 Basic Concepts of Measure Theory
08:25 Lebesgue Integration
12:18 Fundamental Theorems of Lebesgue Integration
14:19 Application: Probability Theory