Measure theory, probability theory and stochastic processes

Measure theory

Bartle, The elements of integration and Lebesgue measure

Saks, Theory of the integral

Halmos, Measure theory

Cohn, Measure theory

Bauer, Measure and integration theory

Bogachev, Measure theory, vols 1&2

Fremlin, Measure theory, vols 1--5

Oxtoby, Measure and category

Probability theory

Lamperti, Probability: a survey of the mathematical theory

Grimmett and Stirzaker, Probability and random processes

Chow and Teicher, Probability theory

Klenke, Probability theory: a comprehensive course

Kallenberg, Foundations of modern probability

Williams, Probability with martingales

Stochastic processes

Norris, Markov chains

Levin and Peres, Markov chains and mixing times

Karatsas and Shreve, Brownian motion and stochastic calculus

Applebaum, Levi processes and stochastic calculus

Le Gall, Brownian motion, martingales and stochastic calculus

Ikeda and Watanabe, Stochastic differential equations and diffusion processes

Protter, Stochastic integration and differential equations

Doob, Stochastic processes

Kloeden and Platen, Numerical solution of stochastic differential equations