Well you can just read the reviews to see that the Durrett text isn't well regarded while others like Chung's are. And the criticism about a probability space not being a sample space is correct, but I think it's clear what Tao meant there, namely that the sample space would be a part of a probability space.

Thanks

The Amazon UK reviews of Chung's book lead me to A Probability Path by Sidney Resnick which appears to be aimed at non-mathematicians. I have invested (speaking as a renegade physicist lacking a systematic exploration of measure theory).

Being a great mathematician doesn't necessarily make a great math educator. It is odd Tao chose Durret, but I assume it's due to the book being freely available online.

As the blog comments suggest there's a difference between a good self-study book and a good textbook for a class. The book will be accompanied by (at least) what look to be a good set of course notes.

Some googling around suggests his students are quite pleased with him. He has, according to Wikipedia's intro for him, the undisputed king of math blogs. Both of these point to him being at least a good or above average educator.

Background: From a famous, world class research university, Ph.D. from research on stochastic optimal control. Good to see that Durrett's book touches on regular conditional probabilities -- I needed that topic!

I learned from a star student of E. Cinlar, long at Princeton. We used Royden, Rudin, Neveu, and Chung, and there were some nice topics in the course not in any of those texts, e.g., the Lindeberg-Feller version of the central limit theorem, a really nice, astounding, result on an envelope for Brownian motion, more on ergodic theory, some on additive processes, and more. Super nice course.

Are you advocating "proof by authority "?

Of course. Appeal to authority was never a fallacy; the fallacy is "appeal to false authority". "Terry Tao knows much more about math in general and this in particular than I do, so I'll trust what he says here" is completely valid.

A fields medal doesn't indicate general authority in mathematics, only authority with regards to what was necessary for getting the medal.

OK, but being a math professor does indicate general authority in mathematics.

Appeal to authority is a dumb logical fallacy in reality geniuses are better at everything and we should prioritize their opinions by some decent weight over everyone else. Obviously.