**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