This is the lecture notes for the Advanced Probability Theory course in the Department of Statistics at the University of Hong Kong. Thanks to Professor Marius Hofert, it has been my privilege to study what I consider the best course in probability theory.

Introduction to ZFC Set Theory and Measure Theory (including Carathéodory-Klenke extension theorem)

• Slide 1

Basic concepts in advanced probability (including: random variable, conditional probability, integration and expectation, conditional expectation, martingales and modes of convergence)

• Slide 2