First read for rigorous probability theory

Question

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

Answer 1

You might try K.L. Chung, "Elementary Probability Theory with Stochastic Processes", or W. Feller, "An Introduction to Probability Theory and its Applications".

Answer 2

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.