Measure theory practice problems

Question

Could anybody recommend any texts which have lots of practice problems for measure theory, in particular, integrating with respect to a measure.

I have always found that I understand conceptually the theory behind integrating with respect to a measure, but I have never been able to apply it to computations very well.

Thanks.

Answer 1

If you are looking for textbooks suitable to a beginning graduate student, I would recommend all three of these textbooks

1. Real Analysis: Modern Techniques and Their Applications by Gerald B. Folland.
2. Real and Complex Analysis by Walter by Walter Rudin.
3. Introduction to Measure Theory by Terence Tao. He also maintains lecture notes on his blog.

I went through most of the first six chapters of Folland in my first course on measure theory. The exercises in this textbook are wonderful. Papa Rudin also has outstanding exercises.