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 problem-solving from previous Qualifying exams and lists of problems from Rudin, Torchinsky, Lieb-Loss, 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
Riemann-Stieltjes Integral
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Wednesday, June 13
Abstract Measures. Lebesgue Measure.
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Monday, June 18
Second chances: review of Measure Theory
Wednesday, June 20
Measurable Functions
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Monday, June 25
Second chances: review of Measurable Functions.
Wednesday, June 27
Integration
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Monday, July 2
Second chances: review of Integration
Wednesday, July 4
No class
Monday, July 9
Third chances: review of Integration
Wednesday, July 11
Lp Spaces
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Monday, July 16
Second chances: review of Lp spaces
Wednesday, July 18
Advanced Topics:
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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.