The aim of this book is to provide the reader with a fairly thorough treatment
of the main body of basic and classical probability theory, preceded by
an introduction to the mathematics which is necessary for a solid treatment
of the material. This means that we begin with basics from measure theory,
such as σ-algebras, set theory, measurability (random variables) and Lebesgue
integration (expectation), after which we turn to the Borel-Cantelli lemmas,
inequalities, transforms and the three classical limit theorems: the law of large
numbers, the central limit theorem and the law of the iterated logarithm. A
final chapter on martingales – one of the most efficient, important, and useful
tools in probability theory – is preceded by a chapter on topics that could
have been included with the hope that the reader will be tempted to look further
into the literature. The reason that these topics did not get a chapter of
their own is that beyond a certain number of pages a book becomes deterring
rather than tempting (or, as somebody said with respect to an earlier book
of mine: “It is a nice format for bedside reading”).