博文

Measure and Probability

已有 5561 次阅读 2013-11-15 10:14 |系统分类:科研笔记

Althoughnone of the books listed below cover the course as a whole, they may be helpfulin clarifying your understanding of specific topics.

1) Books on Measure Theory and Lebesgue Integration.

Donald L. Cohn, Measure Theory, Birkhauser (1980)

This is my favourite book on the topic.It’s maybe a little advanced for this course but is very comprehensive. [3B 517.29 (C)]

Terence Tao, AnIntroduction to MeasureTheory, American Mathematical Society (2011)

A new book by a Fields medal winningmathematician. It’s based on a graduate course so is again, quite high level. [515.42(T)]

Rene Schilling, Measures, Integrals and Martingales, Cambridge University Press(2005)

This is based on a comprehensiveundergraduate course. It takes a different approach to me to some of thetopics. [515.42 (S)]

2) Books on Measure Theory and Probability

Malcolm Adams and Victor Guillemin, Measure Theory and Probability,Birkhauser (1996)

I like this book very much and used itextensively in writing my course. In particular, Chapter 3 on Lebesgueintegration is based very closely on the account in here. [515.42(A)]

Jeffery S. Rosenthal, A First Look at Rigorous Probability, World Scientific (2000)

A very nice book that develops minimalmeasure theory in order to do probability theory properly. I used this book alot for writing Chapter 4. [519.2 (R)] (*)

D. Williams, Probability with Martingales, Cambridge UniversityPress (1991).

This is a classic book by one of theleading UK probabilists of the second half of the 20th century. PartA is relevant to this course. My treatment of the central limit theorem inChapter 4 is based on that given here. [519.236 (W)](**)

Patrick Billingsley, Probability and Measure, John Wiley and Sons (1979)

A classic text and one of the first tosystematically treat probability and measure together. Perhaps a littleadvanced for this course. [519.2 (B)]

1. 讲义：

Ch1Measure.pdf