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I am looking for a book for self-study of rigorous probability theory. I would like a book which is at a completly introductory level, but which is rigorously written. Especially not welcome are books like Introduction to Probability by Sheldon Ross ( which is a great book in its own right ).

The book should have as little assumptions as previous knowledge as possible.

Analog to the book I am looking for is something like Spivaks Calculus or Apostols Calculus but for probability theory.

I am really really stuck,since I suck at learning non-rigorous mathematics,and I always happen to land into some corner case when I try to apply it.

Thanks in advance

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    $\begingroup$ Learn measure theory first. There's no way around it. $\endgroup$ – user370967 Nov 9 '18 at 18:08
  • $\begingroup$ What path would you recommend ( as in books and in which order ) ? Thing is I really need it for application, but if it is laid out badly and slopy I cant connect the dots $\endgroup$ – TheCoolDrop Nov 9 '18 at 18:13
  • $\begingroup$ If your goal is to apply, measure theory might not be such a good idea. Maybe have a look here: math.stackexchange.com/questions/977490/… $\endgroup$ – user370967 Nov 9 '18 at 18:23
  • $\begingroup$ What I really deseprately need is rigorous treatment of conditional probabilities and Bayes theorem,everything else is not so urgent $\endgroup$ – TheCoolDrop Nov 9 '18 at 18:34
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    $\begingroup$ Does this answer your question? Good books on "advanced" probabilities $\endgroup$ – Intellectually disabled Dec 22 '20 at 3:01
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You might try K.L. Chung, "Elementary Probability Theory with Stochastic Processes", or W. Feller, "An Introduction to Probability Theory and its Applications".

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I would recommend Kai Lai Chung's Elementary Probability Theory with Stochastic Processes. The author was a reowned probabilist. It's tailor made for undergraduates who wish to learn probability theory from scratch. This books gives simple examples that have deep interpretations.

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