Kolmogorov: Foundations of the Theory of Probability

The book “Kolmogorov: Foundations of the Theory of Probability” by Andrey Nikolaevich Kolmogorov is historically very important. It is the foundation of modern probability theory. The monograph appeared as “Grundbegriffe der Wahrscheinlichkeitsrechnung” in 1933 and build up probability theory in a rigorous way similar as Euclid did with geometry. Today, it is mainly a historical document and can hardly be used as a textbook any more. The book is still readable and its structure survived in many modern probability books. Still, there are changes. The distribution function F for example is defined as F(s) = P[X < s], with an inquality, not “smaller equal” as today. The book is out of print and can only be purchased on the (now often electronic) flea markets.

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