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I don't know about the quality of it, but you can't argue with the price.

math.berkeley.edu/~evans/SDE.course.pdf

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Meet all your requirements, I think.
[I'm looking for a book that goes through probability theory in a rigorous/measure-theoretic manner. Specifically, I'd prefer something that goes through stochastic calculus/pde's, brownian motion, and markov chain]