Preface to the Second Edition

Summary

This Tract has now been out of print for a number of years. Since there still seems to be some demand for it, the Syndics of the Cambridge University Press have judged it desirable to publish a new edition.

However, owing to the vigorous development of Mathematical Probability Theory since 1937, any attempt to bring the book up to date would have meant rewriting it completely, a task that would have been utterly beyond my possibilities under present conditions. Thus I have had to restrict myself in the main to a number of minor corrections, otherwise leaving the work—including the Bibliography—where it was in 1937.

Besides the minor corrections, most of which are concerned with questions of terminology, there are, in fact, only two major alterations. In the first place, a serious error in the statement and proof of Theorem 11 has been put right. Further, the contents of Chapter IV, § 4, which are fundamental for the theory of asymptotic expansions, etc., developed in Chapter VII, have been revised and simplified. This permits a new formulation of the important Lemma 4, on which the proofs of Theorems 24-26 are based. Finally a brief list of recent works on the subject in the English language has been added.