Math 621, Measure Theory and Integration, Fall 2007

Overview

We will begin with Lebesgue measure and integration in Euclidean spaces and then develop the general theory of measures and integration, including the powerful limit theorems that are not available for Riemann integration. This will lead us to Holder's and Minkowski's inequalities and to Lp spaces.

Textbook

Bartle, The Elements of Integration and Lebesgue Measure, Wiley Classics Library Edition.

Instructor

Marius Ionescu
Office: 588 Malott Hall
email: mionescu@math.cornell.edu
Office Hours: Monday 11:00--12:30pm, Tuesday 3:30--4:30pm

TA

Robyn Miller
email: rlm35@cornell.edu
Office Hours: TBA

Syllabus


Lectures and Homework

  1. Lecture 1, 08/27/07 Introduction, Syllabus, Chapter 11
  2. Lecture 2, 08/29/07 Chapter 11 (cont'd), Chapter 12
    Homework 1, due 09/03/07
  3. Lecture 3, 09/03/07 Chapter 13
  4. Lecture 4, 09/05/07 Chapter 13 (cont'd)
    Homework 2, due 09/10/07
  5. Lecture 5, 09/10/07 Chapter 14
  6. Lecture 6, 09/12/07 Chapter 15
    Homework 3, due 09/19/07 y
  7. Hommework 4, due 10/03/07 From the textbook: 2.D, 2.E, 2.I, 2.K, 2.N., pages 15-17.
  8. Homework 5, due 10/17/07 Textbook: 3.K, 3.L, 3.M; 4.A, 4.G
  9. Homework 6, due 10/31/07 Textbook 6.D, 6.G, 6.K (you can quote 6.J if you want), 6.N
  10. Homework 7, due 11/7/07 Textbook 10.F. and 10.G.
  11. Homework 8, due 11/14/07 Textbook 10.K, 10.L, and 10.O.
  12. Homework 9, due 11/28/07 Textbook 7.M, 7.Q, 8.E, 8.H, 8.N
  13. Final will be hand in class on Wednesday, November 28 and due on Thursday, December 6, by 5:00 pm. Good luck!
  14. Here you can find an updated version of the final.
Marius Ionescu, 03 Dec 2007