## 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
**2/21 - Lecture 12: Abstract measure spaces. [SS, Ch 6, Sec 1] ** Outline
**2/26 - Lecture 13: Extension theorem. Integration on Measure spaces. Product measures and Fubini. [SS, Ch 6] ** Outline
**2/28 - Lecture 14: Completeness, Fubini, the Lebesgue-Stieltjes integral. [SS, Ch 6] ** Outline
**3/5 - Lecture 15: Signed measures, the Lebesgue-Radon-Nikodym theorem. [SS, Ch 6] ** Outline
**3/7 - Lecture 16: Hausdorff measures and fractals. [SS, Ch 7] ** Outline
**3/12 - Lecture 17: The Spectral Theorem 1/2. ** Outline
**3/14 - Lecture 18: The Spectral Theorem 2/2. ** 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).**
**2/21 - HW5 - due 2/28.**
**2/28 - HW6 - due 3/07.**
**3/8 - HW7 - due 3/14.**