This note introduces the concepts of measures, measurable functions and
Lebesgue integrals. Topics covered includes: Measurable functions / random
variables , Dynkin’s Lemma and the Uniqueness Theorem, Borel-Cantelli’s First
Lemma, Independent random variables, Kolmogorov’s 0-1-law, Integration of
nonnegative functions , Jordan-Hahn Decompositions, The Lebesgue-Radon-Nikodym
Theorem, The law of large numbers.

**Author(s):** Johan
Jonasson

71**Pages**