Daily Diary

• Wednesday, January 9: The limits of the Riemann Integral
• Friday, January 11: Overview of measure theory, outer measure
• Monday, January 14: In-class exercise on outer measure
• Wednesday, January 16: Observations on outer measure
• Friday, January 18: Observations on outer measure; properties of Lebesgue measure
• Wednesday, January 23: Properties of Lebesgue measure, concluded; countable additivity of Lebesgue measure on disjoint measurable sets
• Friday, January 25: Properties of Lebesgue measure, continued
• Monday, January 28: Construction of a non-measurable set
• Wednesday, January 30: Polar vortex day, no class
• Friday, February 1: Introduction to measurable functions (Mihai Tohaneanu)
• Monday, February 4: Measurable functions, continued
• Wednesday, February 6: Approximation of measurable functions by step functions
• Friday, February 8: Approximation of measurable functions by step functions, continued
• Monday, February 11: Littlewood's Three Principles, Part I (Egorov's Theorem)
• Wednesday, February 13: Littlewood's Three Principles, Part II (Lusin's Theorem) and introduction to Lebesgue Integration
• Friday, February 15: Lebesgue integration: simple functions
• Monday, February 18: Lebesgue integration: simple functions (continued)
• Wednesday, February 20: Lebesgue integration: bounded measurable functions with support of finite measure (BMFSSFM's
• Friday, Feburary 22: Lebesgue Integration: Nonnnegative measurable functions