Math 420/507: Notes

• Lecture 1: Introduction
• Part A: Lebesgue Measure on R, and Abstract Measure Theory (Folland 1.1-1.5)
  • Lecture 2: Measures and sigma-algebras (Folland 1.2,1.3)
  • Lecture 3: Toward Lebesgue measure: premesures (Folland 1.4, 1.5)
  • Lecture 4: Toward Lebesgue meaure: outer measures (Folland 1.4, 1.5)
  • Lecture 5: Toward Lebesgue measure: Caratheodory's theorem (Folland 1.4)
  • Lecture 6: Lebesgue measure on R (Folland 1.5)
  • Lecture 7: Regularity of Lebesgue measure (Folland 1.5)
  • Lecture 8: Example: Cantor Sets (Folland 1.5)
• Part B: Integration and Convergence Theorems (Folland 2.1-2.3)
  • Lecture 9: Measurable functions (Folland 1.5)
  • Lecture 10: Integration of Simple and Nonnegative Functions (Folland 2.2)
  • Lecture 11: Integration and Convergence Theorems (Folland 2.2)
  • Lecture 12: Integration of Complex Functions (Folland 2.3)
• Part C: Approximation of Functions and Modes of Convergence (Folland 2.4)
  • Lecture 13: Modes of Convergence Theorems (Folland 2.4)
  • Lecture 14: Several Convergence and Approximation Theorems (Folland 2.4)
• Part D: Product Measures and Integration on R^n (Folland 2.5-2.6)
  • Lecture 15: Product Measures (Folland 2.5)

Some Overview Notes (courtesy of Joel Feldman)

• cardinality
• meaure theory
• measurable functions
• integration
• Radon-Nikodym theorem