MA598R: Measure Theory
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
Hi Francisco,
I’m a new graduate student in Purdue. I found some links in Prof. Bell’s homepage, including the nice problems you created in the 2007 summer to help students prepare quals. I spent a lot of time thinkng about the ” advanced problems 18″ but still don’t know where to start. I’m sorry to ask you about this now. It has been 7 years’ long since you gave the problems, but I’ve been tortured by it for a long long time.
I couldn’t get asleep these days because of this problem. I tood a glance of all the books you listed but didn’t find any hint. I think the key to the problem should be the Plancherel Theorem, but I don’t know where to start. Could you please give me some clues whenever you are free?
Best,
Qinfeng
Qinfeng, thanks for reading! I posted a solution to this problem at the following [link]. Let me know if that helps.