Measures and integration

Summary

This course provides an introduction to the theory of measures and integration on abstract measure spaces.

Content

Keywords

analysis, measure theory, Lebesgue integration, L^p spaces

Learning Outcomes

By the end of the course, the student must be able to:

• Define fundamental objects such as sigma-algebras, measures, measurable functions, etc.
• Apply the main theorems to problems in analysis and other areas
• Prove results in measure theory
• Identify common proof techniques used in analysis

Transversal skills

• Use a work methodology appropriate to the task.
• Continue to work through difficulties or initial failure to find optimal solutions.
• Demonstrate a capacity for creativity.
• Demonstrate the capacity for critical thinking

Teaching methods

Weekly lectures and exercise sessions

Expected student activities

Participate in lectures and exercise sessions and complete homework problems outside of class meetings

Assessment methods

Written homeworks and a written exam

Supervision

Resources

Bibliography

• G. B. Folland, Real Analysis (second edition), John Wiley & Sons, Inc., New York, 1999.
• W. Rudin, Real and Complex Analysis (third edition), McGraw-Hill Book Co., New York, 1987.
• E. M. Stein and R. Shakarchi, Real Analysis, Princeton University Press, Princeton, NJ, 2005.
• T. Tao, Introduction to Measure Theory, American Mathematical Society, Providence, RI, 2011.

Notes/Handbook

Lecture notes will be provided

Moodle Link

• https://go.epfl.ch/MATH-303