This textbook offers an approachable introduction to measure-theoretic probability, illustrating core concepts with examples from statistics and engineering. The author presents complex concepts in a succinct manner, making otherwise intimidating material approachable to undergraduates who are not necessarily studying mathematics as their major. Throughout, readers will learn how probability serves as the language in a variety of exciting fields. Specific applications covered include the coupon collectors problem, Monte Carlo integration in finance, data compression in information theory, and more.
Measure-Theoretic Probability is ideal for a one-semester course and will best suit undergraduates studying statistics, data science, financial engineering, and economics who want to understand and apply more advanced ideas from probability to their disciplines. As a concise and rigorous introduction to measure-theoretic probability, it is also suitable for self-study.Prerequisites include a basic knowledge of probability and elementary concepts from real analysis.
Preface.- Beyond discrete and continuous random variables.- Probability
spaces.- LebesgueStieltjes measures.- Measurable functions and random
variables.- Statistical independence.- Lebesgue integral and mathematical
expectation.- Properties of Lebesgue integral and convergence theorems.-
Product space and coupling.- Moment generating functions and characteristic
functions.- Modes of convergence.- Laws of large numbers.- Techniques from
Hilbert space theory.- Conditional expectation.- Levys continuity theorem
and central limit theorem.- References.- Index.
Kenneth Shum received his PhD degree in Electrical Engineering at University of Southern California. Currently, he is an Associate Professor in the School of Science and Engineering at The Chinese University of Hong Kong, Shenzhen. His research interests include information theory and coding theory, probability, and combinatorics.
