Syllabus

Week 1. August 21 - 25

1.1: Measures: Introduction

1.2: Sigma-algebras

1.3: Measures

Drop/Add Deadline: August 25

Week 2. August 28 - September 1

1.3: Measures, continued

1.4: Outer measures

1.5: Borel measures on R

Week 3. September 5 - 8

Labor Day: September 4

1.5 ...continued

Week 4. September 11 - 15

2.1: Measurable functions

2.2: Integration of non-negative functions

Week 5. September 18 - 22

2.2 ...continued

2.3: Integration of complex functions

Week 6. September 25 - 29

2.3 ...continued

2.4: Modes of convergence

2.5: Product measures

Week 7. October 2 - 6

2.5 ...continued

2.6: The Lebesgue integral

Week 8. October 9 - 13

2.6 ...continued

Midterm Grades Due: October 13

Week 9. October 16 - 20

3.1: Signed measures

Week 10. October 23 - 27

3.2: The Lebesgue-Radon-Nikodym Theorem

3.3: Complex measures

Withdrawal Deadline: October 27

Week 11. October 30 - November 3

3.4: Differentiation on Euclidean space

Week 12. November 6 - 9

3.4 ...continued

Veterans' Day: November 10

Week 13. November 13 - 17

3.5: Functions of bounded variation

5.1: Normed vector spaces

5.2: Linear functionals

Week 14. November 20 - 22

6.1: Basic theory of L^p spaces

Thanksgiving Break: November 23 - 24

Week 15. November 27 - December 1

6.2: The dual of L^p

Week 16. December 4 - 5

6.2 ...continued