This material was created for the 2024 Fall Semester Mathematics Teacher Professional Learning Community Seminar. It covers an overview of the concept of the Lebesgue integral and its properties. The material was used in a seminar for high school mathematics teachers, held over four weeks with two hours per week.
It is not suitable as a self-study resource for those encountering Lebesgue integration for the first time. This material is suitable for use in lectures by an instructor with a solid understanding of the Lebesgue integral and real analysis.
Contents:
- Invitation
- Measure
- Lebesgue Integral
- Properties of Lebesgue Integral
- Lp Space
- A Few Fundamental Theorems
- Radon-Nikodym Theorem
- Further Topics for Study
- References