Probability Theory: STAT310/MATH230 Lecture Notes
by Amir Dembo · Stanford University
Stanford PhD-level notes developing probability from its measure-theoretic base: probability spaces, random variables as measurable functions, expectation as a Lebesgue integral, independence, modes of convergence, characteristic functions, martingales and Markov chains, with exercises embedded in the text. The best free, self-contained written alternative to a textbook, and structured exactly around this topic's centre of gravity — it spends its opening chapters on constructing probability measures and defining random variables and expectation measure-theoretically before moving to limit theorems. Complements Durrett rather than repeating it: fewer examples, more explicit proof technique and exercises.
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