Probability Measure
Delve into a comprehensive 7-hour tutorial on probability measure, covering essential topics in set theory, fields, sigma fields, measurable spaces, and probability measures. Learn about limit supremum and infimum, construct fields and sigma fields, explore set functions and their properties, and understand probability measures and their extensions. Examine concepts like outer measure, complete measure, and the Monotone Class Theorem. Study conditional probability, independence, random variables, and cumulative distribution functions. Gain insights into the Borel-Cantelli Lemmas, Erdos-Renyi Lemma, and Riemann Stieltjes Integration. Explore real-world applications through examples, including the independence of polar coordinates and the construction of non-measurable sets.