Achim Klenke

Amazingly well-done

I taught a course in advanced probability out of the first half of Klenke's _Probability Theory_ during Fall 2009 at Brigham Young University, and I'm just starting to teach the follow-on course out of the second half. I am, therefore, thoroughly familiar with the first half of the book but admittedly only vaguely familiar with the second half. I've decided to go ahead and write a review now based on this incomplete information in order to help faculty who may be selecting a probability textbook now for the coming academic year.

In my opinion, this is an extraordinarily good textbook! I've taught classes out of some great books before (e.g., Rudin's _Real and Complex Analysis_, Jones' _Lebesgue Integration on Euclidean Space_, Abbott's _Understanding Analysis_) but I can't remember ever being as impressed with a textbook as I am with Klenke's. His logical arguments are amazingly precise and clear. Even little things like his choices of notation and fonts seem ideal. I think German is Klenke's native language, but his use of English in this book is not stilted at all. The book is mainly self-contained and, in particular, does measure theory from scratch. It was quite a revelation to me to see how clearly and concisely one could work up to Caratheodory's measure extension theorem.

Judging by the copies that appeared on the shelf of the campus bookstore this semester, Springer has not yet subjected Klenke's book to the print-on-demand treatment, so the printing is still nice and sharp. From the perspective of a mathematician and a book lover, _Probability Theory_ is a work of art, and it's been a genuine privilege to get to use it.… (mer)