The roadmap would be to first learn analysis (advanced calculus), then measure theory, then get a measure theory probability book. I'll assume you are teaching

The roadmap would be to first learn analysis (advanced calculus), then measure theory, then get a measure theory probability book. I'll assume you are teaching this to yourself. For analysis, I wouldn't get Rudin's book (concepts are poorly motivated). There are plenty of good Dover books. But I haven't read them because, well, I learned from Rudin. For measure theory, I'd read Kolmogorov and Fomin's book. Rudin also has a measure theory book, which is much better than his analysis book, but it's hefty. Good problems though. For a book on Probability, we read A Probability Path at my university. I wasn't fond of it. Someone referred me to Probability with Martingales, and though I didn't read it, it looked very good.