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For ergodic theory, there were a few really good lectures, and I have good notes, in a course I took from a star student of E. Cinlar. For Breiman Probability: (1) I liked his start, nice, simple, intuitive, on how the law of large numbers works. Of course the super nice proof is from the martingale convergence theorem, but Breiman's start is nice. (2) His book has the nicest start on diffusions I have seen. (3) Once in some of my work I ran into a martingale. So, then, when I wanted to review martingale theory, I went to Breiman. Nice. (4) Since I was interested in stochastic optimal control, I was interested in measurable selection and regular conditional distributions, and I got those from Breiman -- thanks Leo!!!! Yes, IIRC, there is the relevant Sierpinski exercise in Halmos, Measure Theory and also in Loeve, Probability, but it was Breiman who gave me what I really needed. (5) Generally Breiman is easy to read. He writes like he is trying to help the reader learn. |