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Summary

Probability theory is a comprehensive subject that covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion.
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It is suitable for beginning graduate students
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and includes 200 examples and 450 problems.
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Measure theory is also included in the fourth edition.
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According to

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duke.edu

Summary
This lively introduction to measure-theoretic probability theory covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion.

Probability
cambridge.org

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cornell.edu

Summary
This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications, and includes 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.

Probability: Theory and Examples | Request PDF
researchgate.net

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tamu.edu