In the summer of 2007, I had the pleasure to help a group of graduate students prepare for their Qualifying exams in Measure Theory. I taught the course MA598R, which was mainly a thorough review of Torchinsky's "Real Variables", together with guided sessions of problemsolving from previous Qualifying exams and lists of problems from Rudin, Torchinsky, LiebLoss, and other sources.
Real Variables  Analysis (Graduate Studies in Mathematics) (See all Mathematical Analysis Books)  Principles of Mathematical Analysis, Third Edition (See all Mathematical Analysis Books) 
Lesson Plan and Assignments
Feel free to download the different problem sets below. In a near future I will also present hints and solutions to some of the harder exercises.
Monday, June 11
RiemannStieltjes Integral

Wednesday, June 13
Abstract Measures. Lebesgue Measure.

Monday, June 18
Second chances: review of Measure Theory
Wednesday, June 20
Measurable Functions

Monday, June 25
Second chances: review of Measurable Functions.
Wednesday, June 27
Integration

Monday, July 2
Second chances: review of Integration
Wednesday, July 4
No class
Monday, July 9
Third chances: review of Integration
Wednesday, July 11
L_{p} Spaces

Monday, July 16
Second chances: review of L_{p} spaces
Wednesday, July 18
Advanced Topics:

Monday, July 23
Second chances: review of Advanced Topics.
Wednesday, July 25
Qual frenzy 
Monday, July 30
Qual frenzy