Course in Probability Theory

Preface to the second editionThis edition contains a good number of additions scattered throughout thebook as well as numerous voluntary and involuntary changes . The reader whois familiar with the first edition will have the joy (or chagrin) of spotting newentries . Several sections in Chapters 4 and 9 have been rewritten to make thematerial more adaptable to application in stochastic processes . Let me reiteratethat this book was designed as a basic study course prior to various possiblespecializations . There is enough material in it to cover an academic year inclass instruction, if the contents are taken seriously, including the exercises .On the other hand, the ordering of the topics may be varied considerably tosuit individual tastes. For instance, Chapters 6 and 7 dealing with limitingdistributions can be easily made to precede Chapter 5 which treats almostsure convergence . A specific recommendation is to take up Chapter 9, whereconditioning makes a belated appearance, before much of Chapter 5 or evenChapter 4 . This would be more in the modern spirit of an early weaning fromthe independence concept, and could be followed by an excursion into theMarkovian territory .Thanks are due to many readers who have told me about errors, obscurities,and inanities in the first edition . An incomplete record includes the namesbelow (with apology for forgotten ones) : Geoff Eagleson, Z . Govindarajulu,David Heath, Bruce Henry, Donald Iglehart, Anatole Joffe, Joseph Marker,P. Masani, Warwick Millar, Richard Olshen, S . M. Samuels, David Siegmund .T. Thedeen, A . Gonzalez Villa lobos, Michel Weil, and Ward Whitt . Therevised manuscript was checked in large measure by Ditlev Monrad . The