General info

Lectures

  • 1/8 - Lecture 1: Preliminaries. The Exterior Measure. [SS, Ch. 1, Sec 1-2] Outline
  • 1/10 - Lecture 2: Properties of the Exterior Measure. Measurable sets, the Lebesgue measure. [SS, Ch. 1, Sec 2-3] Outline
  • 1/17 - Lecture 3: Measurable functions. [SS, Ch. 1, Sec 3-4] Outline
  • 1/18 - Lecture 4: Approximation of measurable functions. Egorov's and Lusin's theorems. [SS, Ch. 1, Sec 4] Outline
  • 1/22 - Lecture 5: Construction of the Lebesgue integral, convergence theorems. [SS, Ch. 2, Sec 1] Outline
  • 1/24 - Lecture 6: The Lebesgue integral (continued). The Banach space L1. [SS, Ch. 2, Sec 1-2] Outline
  • 1/29 - Lecture 7: The Banach space L1. Theorems of Fubini and Tonelli. [SS, Ch. 2, Sec 2-3] Outline
  • 2/5 - Lecture 8: Differentiation of the integral. Lebesgue differentiation theorem. [SS, Ch. 3, Sec 1-2] Outline
  • 2/7 - Lecture 9: Integration of the derivative. Bounded variation. Absolute continuity. [SS, Ch. 3, Sec 3] Outline
  • 2/12 - Lecture 10: Hilbert spaces. The space L2. Riesz representation. [SS, Ch. 4, Sec 1,2,5] Outline
  • 2/14 - Lecture 11: Lp spaces. [Royden, Ch. 3,4][Brezis, Ch. 7,8] Outline

Problem sets

  • 1/9 - HW1 - due 1/17.
  • 1/17 - HW2 - due 1/24.
  • 1/24 - HW3 - due 2/7 (due date updated).
  • 2/8 - HW4 - due 2/21 (due date updated).