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I need a good rigorous book to learn probability theory. So far, I've been suggested

  • Gnedenko’s Theory of Probability;

  • Shiyayev’s Probability;

  • Feller’s An Introduction to Probability Theory and Its Applications.

. Which one would you reccomend the most and why? Are there other books worth mentioning?

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  • $\begingroup$ I really like Probability & Measure Theory by Ash and Doléans-Dade. $\endgroup$ – Stefan Hansen Sep 9 '14 at 12:22
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    $\begingroup$ If you're a beginner, Probability Essentials by Jacod & Protter is really easy to read with short chapters and good exercises. $\endgroup$ – OBDA Sep 9 '14 at 13:56
  • $\begingroup$ @OBDA I prefer something more advanced $\endgroup$ – user62029 Sep 9 '14 at 13:57
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    $\begingroup$ Borovkov, Billingsley and Loève's books are all classics. $\endgroup$ – Dave Sep 9 '14 at 22:58
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As an introductory course, you can look into "Probability and Statistics in Engineering", by Hines, Montgomery, Goldman and Borror. It covers basic probability axioms, discrete and continuous distributions, before introducing statistics and data description techniques.

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It depends on the topics you want to do also, but I found Applied Stochastic Processes by Lefebvre pretty decent for some probability theory topics.

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