Math 206: Measure Theory (Spring, 2011)

Syllabus

Here is a tentative outline of the topic we'll cover:

• 1. Measures
• 2. Lebesgue measure
• 3. Measurable functions
• 4. Integration and convergence theorems
• 5. Product measures and Fubini's theorem
• 6. Differentiation and Lebesgue's theorem
• 7. L^p spaces
• 8. Radon measures and integrals as linear functionals
• 9. Other topics (if time permits)

This material is covered in the following Chapters of Folland:

• Chapter 1. Measures
• Chapter 2. Integration
• Chapter 3. Signed Measures and Differentiation
• Chapter 6. L^p Spaces
• Chapter 7. Radon Measures
• Chapter 11. More Measures and Integrals

The Department syllabus is here

Notes

Here are some notes

Contents

Chapter 1. Measures
Chapter 2. Lebesgue Measure
Chapter 3. Measurable Functions
Chapter 4. Integration
Chapter 5. Product Measures
Chapter 6. Differentiation
Chapter 7. L^p spaces

References

Measure Theory (full set of notes)

Homework

Problem set 1 (Due Friday, Apr 8)

Problem set 2 (Due Monday, Apr 18)

Problem set 3 (Due Monday, Apr 25)

Problem set 4 (Due Monday, May 9)

Problem set 5 (Due Friday, May 20)

Problem set 6 (Due Wednesday, Jun 1)