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I'm looking for a book that serves as an introduction to probability theory. I barely know anything about this branch of mathematics but if possible I'd like it to involve plenty of analysis since that's what i've studied a bit of thus far. I'd like it to have a lot assignments as well. I'd prefer if it's more focused on pure mathematics and I want plenty of rigorous proofs.

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I used 'Elementary Probability', by D. Stirzaker, and 'A First Course on Probability', by S. Ross.

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  • $\begingroup$ Thank you. It turns out that they're available online for free which is great. $\endgroup$ – David Nov 11 '16 at 22:34
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I heard from my friend who is a PhD student doing research in Probability, that he recommends "Real Analysis and Probability", by Dudley. Here is its amazon page .
He said it is clear, detailed, thorough, and doesn't skip steps. Also, it helped him transition from "undergraduate" probability to measure-theoretic probability. From his comments and the amazon reviews, it seems to match your criteria of "plenty of analysis", "focused on pure mathematics", and "plenty of rigorous proofs". I haven't read it yet, but it's definitely on my reading list.

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  • $\begingroup$ Perhaps i'll get around to it at a later point, it seems a bit too advanced for me at this moment. It does sound intressting however. I've never studied probability theory before so perhaps it's a good idea to settle for something simpler initially. $\endgroup$ – David Nov 11 '16 at 22:49
  • $\begingroup$ No problem, wish you the best as you learn probability; it is a beautiful area of study. $\endgroup$ – Jason Nov 11 '16 at 22:53

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