Measure Theory Lectures (Second Edition)

Author: Yan Jia'an
Publisher:
Publish Date: 1998-10-03
Features: This book systematically introduces measures and integrals on general measurable spaces and Hausdorff spaces, weak convergence and vague convergence of measures, as well as basic probability theory related to measure theory. The second edition adds Chapters 8 and 9, covering discrete-time martingales, measures on Hilbert spaces, and measures on Banach spaces. The book includes some research achievements of the author in measure theory. It is suitable as a graduate textbook for students in probability and statistics and other mathematics disciplines, as well as a reference book for university teachers and probability researchers for teaching and research purposes.
It systematically introduces measures and integrals on general measurable spaces, measures and integrals on Hausdorff spaces, and weak convergence of measures. Additionally, it covers related knowledge in probability and statistics related to measure theory, such as conditional mathematical expectation, regular conditional probability, uniform integrability of families of random variables, analytic sets, and classical martingale theory. The second edition adds content on measures on Hilbert spaces and Banach spaces, and some chapters have been supplemented with new content and the author's research findings.