About the Course:

• Class time: Saturday 16:00 - 17:50.

• Office hours: Saturday 18:00 - 18:50.

• Main Textbook: Real Analysis, by Gerald Folland.

• Recommended Textbook: Real Analysis, by Elias M. Stein and Rami Shakarchi.

• Syllabus (pdf)

Exams:

• Take-home Midterm 1 (pdf)

• Take-home Midterm 2 (pdf)

• Take-home Final (pdf)

Lecture Notes and Videos:

• Lecture 1: Measures (pdf) (video)

• Lecture 2: Complete Measures and Outer Measures (pdf) (video)

• Lecture 3: Outer Measures and Premeasures (pdf) (video)

• Lecture 4: Construction of an algebra on R^n (pdf) (video)

• Lecture 5: Construction of a premeasure on R^n (pdf) (video)

• Lecture 6: Lebesgue Measure (pdf) (video)

• Lecture 7: Examples (pdf) (video)

• Lecture 8: Measurable Functions (pdf) (video)

• Lecture 9: Measurable and Simple Functions (pdf) (video)

• Lecture 10: Integration Theory (pdf) (video)

• Lecture 11: Integration Theory (pdf) (video)

• Lecture 12: Dominated Convergence Theorem (pdf) (video)

• Lecture 13: Lebesgue and Riemann Integrals, Product Spaces (pdf) (video)