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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.

Thanks.

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    $\begingroup$ Because you mentioned probability theory, you could look at "First Look at Rigorous Probability Theory" by Rosenthal. This will teach you the measure theoretic probability theory that you'll need for grad school. $\endgroup$ – jmbejara Jan 26 '15 at 15:36
  • $\begingroup$ @jmbejara Does this book also develop measure theory? I have no background in it. If it does not, which measure theory book will complement "First Look at Rigorous Probability Theory". $\endgroup$ – user52932 Jan 26 '15 at 17:09
  • $\begingroup$ It does do measure theory--at least the fundamentals. It does it very well, in my opinion. I would recommend starting here. $\endgroup$ – jmbejara Jan 26 '15 at 18:12
  • $\begingroup$ Billingsley's Probability and Measure combines an introduction to Lebesgue integration and to probability. Williams' Weighing the Odds is good for intuition on probability and statistics. $\endgroup$ – user208259 Jan 28 '15 at 11:12
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You could start with Bartle - The Elements of Integration and Lebesgue Measure. You could also check here and here.

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"Measure Theory. Volume I" by V.I. Bogachev. It is one of the fullest book on measure theory. But I'm not sure that it will be easy enought to read it. And there is no chapter on probability.

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