Math 205a:
Measure Theory and Lebesgue Integration
(Autumn 2009)


Professor: Brian White
Email: white "at" math.stanford.edu
Office: Room 383-EE (third floor of math building)
Office Hours: Tue 1:15 - 4:15, and by appointment

Course assistant: David Sher
Email: dsher "at" stanford.edu
Office: 381A (first floor of math building)
Office hours: 4-6 Monday, 2:15-3:15 Wednesday, 1-2 Thursday, and by appointment.

Text: "Measure Theory" by Donald Cohn. The course corresponds roughly to the first seven chapters of the text, though we will cover a few additional topics.

Grading: the grade will be based on weekly homework assignments (20%), a midterm (30%), and the final exam (50%).

The final exam is 3:30-6:30 pm on Monday, December 7. This time is officially set by the university, and cannot be varied.
Do not take the course unless you can take the exam then.

Midterm date: TBD

Homework assignments will generally be posted here weekly. Homeworks will generally be due on Thursdays. (No hw due Thur, Sept 24.) Late homework assignments will not be accepted, so if you haven't finished an assignment when due, please go on and turn in the problems you have done.
Remark about completions.

Midterm date: Thursday, Nov 5. Time: 11-12:30. Place: classroom. The midterm will be on the material up to and including Dynkin's Theorem. (I.e., the material covered in class up to and including Thur, Oct 29.) Sample midterm (2006). Another sample midterm (2007). Yet another sample midterm (2005).

Solutions to the midterm.

Homework assignment 1 (due in class Thursday, October 1). Solutions.

Homework assignment 2 (due at 5pm, Thursday, October 8). Solutions.

Homework assignment 3 (due in my mailbox 5pm, Thursday, October 15). hint. Solutions.

Homework assignment 4 (due in my mailbox 11am, Friday, October 23). Solutions.

Homework assignment 5 (due in my mailbox 11am, Friday, October 30.) Solutions.

Homework assignment 6 (due in my mailbox 11am, Friday, November 6). Solutions.

Homework assignment 7 (due in my mailbox 11am, Friday, November 13.)

Lecture notes on the 5-Times Covering Lemma and on the Vitali Covering Theorem.

Homework assignment 8 (due in my mailbox 11am, Friday, November 20.)

Note on homework:
The homework problems form an integral part of the course. Some of the problems are meant to be quite challenging, so don't be discouraged if you are unable to solve every one. However, it is important that you work on them. You can learn a lot by working hard on a problem, even when you don't succeed in solving it. (Also, if you've worked hard on a problem you were unable to solve, you'll learn a lot from the reading a solution. Without having struggled with it, you'll learn little.)

Even when you have solved a problem, you should read the web page solution, which may be more elegant and/or more concise than your solution.

Finally, if a problem asks for a proof, you are allowed to use the results of any previous problems, including those you are unable to solve.