My current Math background is as follows:
1) Read first 7 chapters of Rudin "Principles of Mathematical Analysis" and solved a lot of the given problems.
2) Completed Munkres "Analysis on Manifolds" cover to cover and solved a lot of given problems.
3) Also read Rosenlicht "Introduction to Analysis" and solved a lot of its problems.
Based on this, I think my math experience is equivalent to doing a year-long undergraduate course in Analysis.
In the future I want to do an Economics PhD. To better understand stuff (such as econometrics etc.), I want to self-study Measure Theory and Probability Theory.
I intend to use Grinstead and Snell's "Introduction to Probability", to develop intuition regarding probability. I have heard good things about this book. Is my background sufficient for this? I have taken statistics courses before but never a formal Probability course.
I am not sure that which Measure Theory book will best suit my needs:
1) Since I am self-studying, I want a book that picks up from the very basics of Measure theory (i.e. it should not assume a math background more advanced than mine).
2) It should not skimp on rigor but should also be easy to read (i.e. the proofs do not skip huge amounts of steps, which would be very bad for me since I will be studying by myself).
3) It would be helpful if the book has informative problems, to which I may be able to find solutions if I absolutely need to.
4) Also it would be great if the book has a chapter on Probability Theory.