Math 4121

Introduction to Lebesgue Integration, Spring 2023

Course Description

Riemann integration; measurable functions; measures; the Lebesgue integral; integrable functions; Lp spaces; modes of convergence; decomposition of measures; product measures; Lebesgue measure. Prerequisite: Math 4111 or permission of the instructor.

Contact Information

Instructor: Ari Stern
Office: Cupples I 211B
Office Hours: M 2-3:30pm, Th 10:30am-12pm


MWF 10-10:50am, Duncker 101. The first class will be on Wednesday, January 18, and the last will be on Friday, April 28. Class will be canceled for Spring Break (week of March 13-17).

Homework Assignments

Problem sets will be posted to Canvas, and students will submit their solutions electronically by uploading them before the specified due date and time. You are encouraged to discuss the homework with your fellow students, but your final write-up must be your own. Please make sure that your solutions are written clearly and legibly.


There will be one in-class midterm exam on Wednesday, March 8. The final exam will be held Monday, May 8, from 10:30am-12:30pm.


Grades will be based on a weighted average of homework (40%, lowest score dropped), midterm exam (20%), and final exam (40%).

Course Text

The main text we will use for this course is A Primer of Lebesgue Integration, by H.S. Bear (second edition, Academic Press, 2002). Click here for free eBook access through the WUSTL Library.

Academic Integrity

All students are expected to adhere to high standards of academic integrity, as specified in the undergraduate student academic integrity policy. Since this course is offered through the College of Arts & Sciences, any violations of this policy will be referred to the College’s Academic Integrity Officer. Violations of this policy include, but are not limited to:

If you have any questions, or are unsure about what is permitted/prohibited by this policy, please ask me.

In many cases, academic integrity violations are the result of getting behind in coursework and making bad decisions under pressure. Keep up with your assignments, ask questions when you are unsure what is expected of you, and do not give in to the temptation to cut corners.

COVID-19 Health and Safety Protocols

Students experiencing symptoms consistent with COVID-19 or concerned about a possible exposure should contact Habif Health and Wellness Center (314-935-6666) to arrange for testing as indicated. If instructed by Habif to quarantine or isolate, students should notify their instructor as soon as possible by forwarding the email they received from Habif. Any accommodation needs for COVID-related absence not covered in an instructor’s standard course policies should be discussed between the student and instructor.

While on campus, it is imperative that students follow all public health guidelines established to reduce the risk of COVID-19 transmission within our community. The full set of University protocols can be found at

Access to Classroom Content During Excused Absences (Including COVID)

To encourage in-person attendance and participation, WashU no longer requires that lectures be recorded or otherwise made available outside the classroom, aside from certain exceptional cases: "In the case of excused student absences due to COVID and other factors (e.g., illness, religious holidays, family emergencies, etc.), instructors should develop strategies for providing students access to the fundamental content of a given class session so that students are able to make progress in the course while complying with public health and university guidelines around quarantine and isolation and managing other challenges that disrupt their ability to attend class."

If you cannot attend class due to COVID or other factors similar to those listed above, and if you contact me at least 2 hours prior to the start of class, I will try to arrange for video recording of the lecture. If I am unable to record the lecture (e.g., due to technical difficulties) or do not receive advance notice to do so, I will provide written lecture notes instead.

Valid XHTML 1.0!