Measure Theory and Probability Theory Basics: Series of Mathematics Teaching Books from Peking University

Author: Cheng Shihong
Publisher:
Publish Date: 2004-02-01
Features: This book serves as a textbook for undergraduate students in probability and statistics departments of higher education institutions for the course "Measure Theory and Foundations of Probability Theory." The content of measure theory aims to provide a "short, flat, and fast" bridge between elementary probability theory and axiomatic probability theory. By selecting essential measure theory content necessary for establishing the axiomatic system of probability theory in abstract analysis, the book focuses on explaining and elaborating concepts and formulas that are not fully covered or cannot be fully explained in elementary probability. The book is divided into six chapters, covering topics such as measurable spaces and measurable functions, measure spaces, integration, signed measures, product spaces, and sequences of independent random variables. The book is concise and well-structured, with explanations progressing from simple to complex, making it easy to understand. Difficult concepts are broken down into manageable sections, and the arguments are rigorous. To meet the needs of readers from non-mathematics backgrounds who must study axiomatic probability theory, the book provides detailed explanations of concepts and proofs of theorems, making it suitable for self-study. Each chapter includes a selection of exercises, and solutions or hints to most of the exercises are provided at the end of the book. This book can be used as a textbook for undergraduate and graduate students in mathematics and probability and statistics departments of comprehensive universities, universities of science and engineering, and normal universities. It can also serve as a reference book for graduate students and scientific and technological workers in economics and finance. This book is a required prerequisite for university students studying "Advanced Probability Theory," "Advanced Statistics," and "Stochastic Processes."