Prob/Stats Which Book for Learning Probability with Measure Theory?

[mr.tea]

Hi,

I am looking for a book for studying probability theory using measure theory. This is the first course I am taking of probability. Notions and theorems from measure theory are part of this course.
As it turns out, this is a catastrophic disaster, and the textbook for this course is also not helping a lot(and doesn't even use measure theory).
Therefore I need a recommendation on a book that develops the theory of probability using measure theory, and if it is possible, suitable for self study.

Thank you.

 

[S.G. Janssens]

Nice question. I think the book "A First Look at Rigorous Probability Theory" by J.S. Rosenthal may be suitable for this purpose. It does not contain enough material to serve as a long-time reference, but it does a very good job introducing the subject.

 

[mr.tea]

Nice question. I think the book "A First Look at Rigorous Probability Theory" by J.S. Rosenthal may be suitable for this purpose. It does not contain enough material to serve as a long-time reference, but it does a very good job introducing the subject.

Thank you for the answer. But unfortunately it seems that the book assumes some knowledge in probability.

 

[S.G. Janssens]

Thank you for the answer. But unfortunately it seems that the book assumes some knowledge in probability.

Most of the times people first take a non-measure-theory based course on probability. Then for a second course everything is placed in the proper measure-theoretic context. So, I conjecture that it will be hard to find a "first course in probability" based on measure theory.

With that being said, I believe that Rosenthal's book can be read by someone who has no prior exposure to probability. It may be more important that you have an understanding of introductory analysis and some experience with proof writing. Another title you could consider is Resnick's "A Probability Path".

 

[mr.tea]

Most of the times people first take a non-measure-theory based course on probability. Then for a second course everything is placed in the proper measure-theoretic context. So, I conjecture that it will be hard to find a "first course in probability" based on measure theory.

This course is called "Basic..", and suppose to be the first course in probability that we should take(math major).

With that being said, I believe that Rosenthal's book can be read by someone who has no prior exposure to probability. It may be more important that you have an understanding of introductory analysis and some experience with proof writing. Another title you could consider is Resnick's "A Probability Path".

I will give Rosenthal's book another chance, and also look at the other book. Thank you.