Probability theory, II / M. Loève

This popular book, on which many of today's probabalists cut their eye teeth, appears in its fourth edition. The first edition appeared in 1955 and each successive revision has included new material. The size has consequently increased so as to necessitate the present edition appearing in two volumes. Also the present edition has a different publisher, Springer-Verlag, which has done its usual fine job with the editing and printing. The current edition treats several topics not in earlier editions. Chief among these are Brownian motion, functional central limit theorems and the invariance principle, random walk and fluctuation theory.
The author has attempted to retain the encyclopaedic character of his treatise, starting off with the elements of measure and integration theory and proceeding to the end. But his task has become more and more difficult as time progresses because of the continuing great expansion of his subject. Thus there are a number of topics of intense current interest not mentioned. Included in these are boundary theory, potential theory, general theory of processes, Markov processes and function theory. It would, of course, be impossible to write a text covering all of probability theory. The author's compromise of topics covered seems to be about right. (MathSciNet)

Bibliogr. p. 384-389. Index