Topics: Measure and integration over abstract measure spaces, Radon-Nikodym theorem, Fubini’s theorem, convergence theorems, differentiation.
Instructor: Larry Goldstein, KAP 406D, x02405
Lecture 39735R, KAP 140
Office hours: M 12:50-1:50, W 11-12
Grader: Fei Wang, wang828 at usc dot edu
Office hours: M 5-7 and F 11-12 in the Math Center
Materials
Required Text: Real Analysis, Modern Techniques and Their Applications, Second Edition
Gerald Folland, Wiley Interscience. Errata
Supplemental References:
- Real and Complex Analysis, Walter Rudin
- Real Analysis, Royden
- Measure Theory, Halmos
Assignments
Assignments are not finalized until their due dates appear in bold.
Chapter 1:
1, 3, 4, 5 Due 9/8
6, 8, 9, 12, 14.5, 15 Due 9/17
17, 18, 19, 20, 22a, 23 Due 9/28
27, 29, 30, 31, 32 Due 10/9
Chapter 2:
3,4,5,6,7,8,9,11 Due 10/20
13,14,16,17,20,21,23 Due 10/30
25,28,32,34,36,40,44 Due 11/10
46,48,49,50,51 Due 11/17
Chapter 3:
1,2,3,4,7,8,10,13,16,17* Due 12/1
22,23,25,26
28,30,31,37,40,41,42 Due 12/9
*) You may take f to be real valued, to avoid the use of the complex Lebesgue-Radon-Nikodym
Exams and Grading Policy
Grading Policy
- 25% Homework: If you are a Math student and have access to the graduate mailroom, please drop off your homework in Fei Wang’s mailbox, 4th floor KAP. Otherwise, submit at the front desk of the Math Center, KAP 263, or just slide them under the door of KAP 248B. No electronic submissions. Points on homework turned in past the due date are reduced by 20% for each week late.
- 40% Two Midterms
Midterm 1: Monday Sept 28th, coverage 1.1-1.4
200 possible points: High score 200, 3rd quartile 155, median 123, 1st quartile 83. Average 123
Midterm 2: Monday November 2nd, coverage 1.5, 2.1-2.4
140 possible points: High score 136, 3rd quartile 123, median 67, 1st quartile 36. Average 74
- 35% Final Exam, Wednesday, December 9th, 8-10AM, will be comprehensive.
Links
The Banach Tarski Paradox
Karl Stromberg
The American Mathematical Monthly, Vol. 86, No. 3. (Mar., 1979), pp. 151-161.
Important Dates and Information
- September 11th, last day to register and add, or to drop without mark of W
- November 13th, last day to drop a class with mark of W.
- December 4th, classes end.