Lecture 7 (Part 1): Consequences of Caratheodry Theorem; Borel sets are m^{*}-measurable

This course is about the mathematical foundations of randomness. Most advanced topics in stochastics and statistics rely on probability theory. The basic constructions are identical to measure theory, but there are a number of distinctly probabilistic features such as independence, notions of convergence of random variables, information contained in a sigma-algebra, conditional expectation, characteristic functions and generating functions, laws of large numbers and central limit theorems, etc. @RUeamHK0X6#