Mathematics 420/507 (Real Analysis)
Textbook: H.L. Royden, Real Analysis, Macmillan 1998 (3rd ed.)
Topics to be covered:
- Lebesgue measure and integration (Chapters 3 and 4)
- Abstract measure theory (parts of Chapters 11 and 12)
- Differentiation (Chapter 5)
- L^p spaces (Chapter 6)
- Hausdorff measure and selected topics in geometric measure theory
Additional recommended books:
- W. Rudin: Real and Complex Analysis. A classic!
- M. Capinski, E. Kopp: Measure, Integral and Probability. A nice
introductory book, written for undergraduates. On reserve in
the math library.
- F. Morgan: Geometric measure theory. Nice, short, a lot of pictures.
If you prefer (rather a lot of) substance over style, skip to the next item:
- H. Federer: Geometric measure theory. Long,
more like a reference book than like a textbook.
- K. J. Falconer: The Geometry of Fractal Sets. My personal favourite
book on Hausdorff measure, fractal sets, etc.
- H. Furstenberg: Recurrence in Ergodic Theory and Combinatorial
Number Theory. A mind-opening experience.
Your course mark will be based on the homeworks (25%),
midterm (25%), and the final exam (50%). If you do better on
the final exam than you did on the midterm, I will count your
final score instead of your midterm score. The homeworks
are due on September 18, October 2 and 16, November 13 and 27.
The final exam will be available from Helga in the math office
between December 11 and 15. (If you have to write the exam
before December 11, let me know.) The exam will consist of
five problems. You will have three days to solve it.
I will mark all five questions, and count only the best
four scores. The level of difficulty will be about the same
as on the midterm exam.
A handout on Hausdorff measure and dimension
(a .dvi file)
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