Homework 1 (due 9/07/10) :
Chapter 1 - Exercises 5, 18, 25.
Chapter 6 - Exercise 3 (p. 312)
Group Work 1:
Each team will submit a report and will present their results to the class.
TEAM 1 (decreasing sequence of positive continuous functions
whose pointwise limit is NOT Riemann integrable): Exercises 10, Problem 4
(will need to understand Cantor-like sets as in Exercise 4).
TEAM 2 (Borel-Cantelli): Exercises 16, 17, Problem 1
report (pdf)
TEAM 3 (Jordan content): Exercise 14
report (pdf)
Homework 2 (due 10/28/10) :
Chapter 2 - choose 3 from Exercises 2, 5, 6, 9, 10, 11, 19
do Problem 3 in page 95.
Homework 3 (due 11/23/10) :
Read Section 11.5.3 in this notes (ps),
then do exercise 11.54, 11.55
and 11.56 (the proof of the Marcinkiewicz Interpolation Theorem). You may choose
instead to read Section 11.5.4, and write a proof of the Riesz-Thorin
Interpolation Theorem which you will find in the references in the section.
You can work in groups if you want.
Homework 4 (LAST!!! due on final exam day) :
Exercise 24 in Chapter 3 (about Lebesgue decompositon). You can work in
groups if you want.
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Last updated: Nov 30, 2010