MTH 241, Fall 1997
Real Analysis I 
MWF 9:10-10:00, 218 Physics
Greg Lawler, 128B Physics

Office Hours: 1:30 - 3:00 M, 10:15 - 11:45, W

This will be a course in measure theory. We develop simultaneously the theory of Lebesgue measure/integration on the reals and the measure theory needed to do probability. Standard results about convergence and inequalities involving integrals will be done. There will also be an introduction to Fourier analysis including a proof of the central limit theorem using Fourier analysis.
 

Final Problem Set ---

due Thursday, December 11.   ps file  pdf file

(Note: Correction on Problem 10 as mentioned in class on 12/8/97).  

Schedule for Remainder of the Fall Semester

        Fri. Nov. 21 and Mon. Nov 24 --- class as usual
        Wed. Nov. 26 --- no class
        Mon. Dec 1 and Wed. Dec 3 --- class as usual
        Fri. Dec. 5 --- no class
        Mon. Dec. 8 and Wed. Dec 10 --- class will be held (this is officially reading week but these
             two classes compensate for the Nov. 26 and Dec. 5 classes being cancelled).
 

       The final problem set/take-home exam will be handed out on Wednesday, December 3 and
              will be due on Thursday, December 11 by 5:00 pm

Text

Adams and Guillemin, Measure Theory and Probability

Recommended Reading for latter part of course: Rudin, Real and Complex Analysis, especially Chapters 6, 2 (for Riesz Representation Theorem), and 8.

Assignments

There will be weekly homework assignments due on Wednesday. There will be a take-home examination at the end of the course, but there will be no in-class tests or examinations.

PS1 (due Sept. 10): pp 11-13: 1, 10, 11, 12, 15
PS2 (due Sept. 17): pp 39-42: 4, 5, 6, 12, 19, 20
PS3 (due Sept. 24): pp 49-52: 1, 8 , 10, 19; p 58: 2, and extra problem: ps file , pdf file
PS4 (due Oct. 1): pp 70-71: 3, 6, 10; pp 80-81: 4, 5, 6, 7, 8
PS5 (due Oct. 8): p. 81: 11, 12; p. 88: 2, 3, 4; p. 101, 6
PS6 (due Oct. 15): pp. 101 - 102: 10, 12; p. 108, 2, and extra problems: ps file , pdf file
PS7 (due Oct. 22)  ps file ,  pdf file
PS8 (due Oct 29)  p. 129: 6, 11; pp. 134- 136: 3, 6, 11 and extra problem:   ps file ,  pdf file
PS9 (due Nov 5)  pp. 143-145: 3, 5, 9; pp. 153-154: 1, 4, 7
PS10 (due Nov 12)  ps file ,  pdf file
PS11 (due Nov 19)  ps file ,  pdf file
PS12 (due Nov 26)  ps file ,  pdf file (Note: new version with corrections posted Nov. 26; an even newer version posted Nov. 29 -- on problem 3(ii) assume a finite measure space)

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Last modified: 3 December 1997