# Cornell University, Fall 2016

# Math 6210 -- Measure Theory and Lebesgue Integration

### Instructor:

Farbod Shokrieh

Office: 436 Malott Hall

Email: farbod@cornell.edu

Office Hours: Wednesdays 2:30PM - 3:30PM, and by appointment

### Teaching assistant:

Hannah Cairns

Email: ahc238@cornell.edu

Office Hours: Mondays 3:00PM - 4:00PM, 218 Malott Hall

### Course Webpage:

www.math.cornell.edu/~farbod/teaching/math6210.html

### Textbook:

Robert G. Bartle -- *The Elements of Integration and Lebesgue Measure*, 1995 Edition

The ebook is freely available to download (with a Cornell NetID).

I might also discuss some material not covered in this book, in which
case I will provide references and/or handouts if needed.

### Course Description:

The Riemann integral familiar from undergraduate calculus has poor convergence properties and does not behave well in higher dimensions. A much more convenient and flexible theory of integration, based on the notion of a countably additive measure, was developed by Henri Lebesgue. In this course we develop Lebesgue's theory from the ground up.
This course is designed for students who need the theory for applications to fields including probability, statistics, economics, functional analysis and PDEs.

### Prerequisite:

Undergraduate analysis and linear algebra as taught in MATH 4130 and 4310.

### Lecture time and place:

Tuesdays and Thursdays

8:40AM - 9:55AM

205 Malott Hall

### Homework:

Homework will be assigned (approximately) once a week.

All assignments are here.

Late homework will not be accepted.

### Collaboration:

On the homework sets, collaboration is both allowed and
encouraged.

However, you must write up yourself and understand your
own homework solutions.

You should give credit to any outside sources or collaborations.

### Exams:

There will be one (in class) exam on October 20

Books and electronics (calculators, phones, tablets, etc.) are not
allowed in the exam.

You are allowed to bring a one-page, one-sided, hand-written cheat
sheet (US letter size).

### Grading:

Homework: 40%

Exam: 30%

Project: 30%

### Auditing:

If you are taking this course on an "audit" basis, you will not turn
in homework/exam/project.

However, those auditing are expected to indeed audit the
course; if at some point you decide to stop coming to class, please drop the course.

### Projects:

Students will study and present the following material, and write a
short expository article.
- Radon measures

(Click here for the expository final article by David Kent and Lindsay Mercer)

- Hausdorff measure and Hausdorff dimension

(Click here for the expository final article by Jimmy Briggs and Timothy Tyree)

- Haar measures on (LCH) topological groups

(Click here for the expository final article by Shuxiao Chen and Joshua Hull)

- Hilbert spaces

(Click here for the expository final article by Jaden Chen and Shaoshu Li)

### Academic honesty:

All students are expected to comply with the Code of Academic
Integrity. The institute honor code is available at:

http://archive.theuniversityfaculty.cornell.edu/AcadInteg/code.html

(Last modified on: December 2, 2016)