We decided to write this book largely as a result of experience in teaching at the Instructional Conference on Probability held at Durham in 1963 under the auspices of the London Mathematical Society. It seemed that a proper treatment of probability theory required an adequate background in the theory of finite measures in general spaces. The first part of the book attempts to set out this material in a form which not only provides an introduction for the intending specialist in measure theory, but also meets the needs of students of probability.

The theory of measure and integration is presented in the first instance for general spaces, though at each stage Lebesgue measure and the Lebesgue integral are considered as important examples, and their detailed properties are obtained. An introduction to functional analysis is given in Chapters 7 and 8; this contains not only the material (such as the various notions of convergence) which is relevant to probability theory, but also covers the basic theory of L2-spaces important, for instance, in modern physics.

The second part of the book is an account of the fundamental theoretical ideas which underlie the applications of probability in statistics and elsewhere. The treatment leans heavily on the machinery developed in the first half of the book, and indeed some of the most important results are merely restatements of standard theorems of measure theory.