Book Review — Wahrscheinlichkeitsrechnung mit einem Anhang über Informations-theorie

Until recently, probability theory has been called “calculus of probabilities” in the French and German languages. This book is so called and deserved the name in the best sense of the word. It is essentially a textbook of mathematical analysis as applied to the field of probability. By this it is not implied that the measure-theoretic foundations are not given adequately and rigorously. Indeed, the book begins with axiomatic Boolean algebra including a proof of M. H. Stone's isomorphism theorem, albeit in fine print. Kolmogorov's extension theorem is also given its full treatment while the Radon-Nikodym theorem, though not proved, is discussed in some detail with examples—which is probably more helpful than reproducing a standard proof. However, the unmistakable flavor of this book is the abundance of classical analytic techniques vigorously and interestingly employed to calculate the probabilities…