Other references for Stat 330/600

Ash, R. B. Real Analysis and Probability
Good background on measure theory, particularly the connections between topology and measure. Recommended for martingales and conditioning.
Billingsley, P. Probability and Measure
Very well written. Particularly recommended for the discussion on conditioning. Covers many topics that might have been included in this course.
Breiman, L. Probability
A good book to look at after you think you know what is going on. Deceptive at times, because hard ideas are made to seem easy. Very good for weak convergence, characteristic functions, and more advanced topics. Worth owning.
Chow, Y. S. and Teicher, H. Probability theory: Independence, Interchangeability, Martingales
Written in a technical style, but full of information. Good on martingales and exchangeability. When I first looked at this book I didn't like it, but now I refer to it often.
Chung, K. L. A Course in Probability Theory
A standard text. Too dry for my taste. A good place to look for standard proofs.
Dudley, R. M. Real Analysis and Probability
A thorough text that has become one of my favourites. Read the notes at the end of each chapter to see how a real scholar works. Highly recommended.
Feller, W. An Introduction to Probability Theory and Its Applications, Volume~II
A classic. If you are serious about probability theory you need to own this book (and the companion volume~I). Covers lots of material not found in other texts. Very good on characteristic functions; very little on martingales. Unfortunately, Feller tried to avoid measure theory.
Folland, G. B. Real Analysis:Modern Techniques and Their Applications
Excellent source for measure theory and real analysis.
Kolmogorov, A. N. Foundations of the Theory of Probability
The original. It contains most of what goes into a modern probability course, in under a hundred pages. Hard reading, because notation and fashion have changed, but the ideas are mostly all there. Martingale theory wasn't invented in~1933, when the book first appeared. A landmark in the history of probability.
Loève, M. Probability Theory
The classic text on probability. I refer to it occasionally. The latest edition comes in two volumes.
Pollard, D. Convergence of Stochastic Processes
I will borrow (with modifications) some material from Chapter~III for weak convergence and the central limit theorem.
Royden, H. L. Real Analysis
An excellent reference for measure theory. Read Chapters~11 and~12 in particular.
Whittle, P. Probability via Expectation
Expectations as the starting point for the development of probability theory; similar to my approach. Very clear.
Williams, D. Probability with Martingales
A tad eccentric, but superbly clear. An author who conveys his enthusiasm for a great subject. Worth at least a browse at some stage during the course.