Book on Probability: Learn from Elementary to Advanced

[MIB]

Please , I want you to recommend me to a book on probability , I a have never read a probability book , or have a good background , I only Know what are probability measures , some theorems concerning it . I want a book that take me from the elementary probability , to advanced probability (which depend on Measure theory ) . I know some set theory , the basic axiomatic system of ZFC , Ordinals , Cardinals , Large Cardinals , operations on ordinals and cardinals ( including the infinite sum and product of cardinals) , some of Ramsey's theorems ... etc . I am reading in Tao's measure theory . I want the book to be as abstract as possible and to have an interesting introduction .


Thanks

 

[PAllen]

The classic is William Feller, in 2 volumes.

 

[Karlx]

Hello MIB.
I second the recommendation of PAllen.

Feller's book is a very recommendable book.
Volume I starts from a very intuitive conception of probability and then it goes on, from the very elementary concepts until more deep ones.
And always with a lot of very interesting exercises.
It is a classical of probability theory, and maybe one of the best books in order to build your "intuitive knowledge basis" about the matter. And for me, it is, too, a pleasure to read it.

Volume I deals with discrete probability, but don't let this to misslead you. As I said, it builds up the basis of probability concepts.

Volume II deals with infinite sample spaces, measure theory and so on. It widely extents the concepts introduced in Vol.I to the continuum case. This volume is as illuminating as the first one, but its reading is not as easy.

The complete references are:

William Feller, "An Introduction to Probability Theory and Its Applications", Vol I, 3rd.Ed.

William Feller, "An Introduction to Probability Theory and Its Applications", Vol II, 2nd.Ed.