Probability with Martingales (Cambridge Mathematical Textbooks)
Cambridge University Press (February 22, 1991) | ISBN: [url=]0521406056[/url]
Thisis a masterly introduction to the modern and rigorous theory ofprobability. The author adopts the martingale theory as his main themeand moves at a lively pace through the subject's rigorous foundations.Measure theory is introduced and then immediately exploited by beingapplied to real probability theory. Classical results, such asKolmogorov's Strong Law of Large Numbers and Three-Series Theorem areproved by martingale techniques. A proof of the Central Limit Theoremis also given. The author's style is entertaining and inimitable withpedagogy to the fore. Exercises play a vital role; there is a fullquota of interesting and challenging problems, some with hints.