Math 205a:
Measure Theory and Lebesgue Integration
(Autumn 2018)


Professor: Brian White
Email: bcwhite "at" stanford.edu
Office: Room 383-EE (third floor of math building)
Office Hours: TTh 10:30-12:00, and by appointment

Course assistant: Jupiter Zhu
Email: jupiterz "at" stanford.edu
Office: 380G (basement floor of math building)
Office hours: Tuesday, Wednesday 2-3:30.

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.

You can download the text for free as follows. Go the Stanford Library webpage and search for "donald cohn measure theory". Then click on "view on content provider's site" (next to "full text".)

Prerequisites: the main prerequisite is math 171 or the equivalent. For example, it is essential that you know and understand compact sets and their basic properties. You also need to know and understand the basic facts about countable and uncountable sets (e.g. a countable union of countable sets is countable.) If your background in such matters is shaky, then you should take math 171 (and perhaps also math 161) instead of math 205a; you can then take the undergraduate measure theory course (math 172) in the winter, and/or math 205a next fall.

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

Homework

Homework assignments (and solutions) will generally be posted here weekly.

Hw will be due 11:59 pm Thursday. The first hw will be due during the 2nd week of class (Thur, Oct 4).

You will submit hw online with GRADESCOPE: instructions will be posted in the next few days.

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.

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.

Lecture Notes

Lecture 4.

The Five-Times Covering Theorem.

The Vitali Covering Theorem.

Exams

The midterm is in class on Thursday, November 8. The midterm covers material up through Thur Nov 1 (i.e., up to and including the 5-times-covering lemma.)

The final exam is 8:30 - 11:30 am on Wed, December 12. Room: TBD. This time is officially set by the university, and cannot be varied.
Do not take the course unless you can take the exam then.