Measure theory

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

2 hour lectures and 2 hour exercise sessions weekly

Expected student activities

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

Assessment methods

Written midterm, written final exam

Supervision

Resources

Bibliography

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

Ressources en bibliothèque

• Find the references at the Library

Notes/Handbook

Lecture notes will be provided