Math 501, Lecture Schedule and Problem Set Assignments

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The following table lists all reading and problem assignments according to the date by which they should be completed. All problem numbers refer to problems from the course problem sheets. The required reading is either from the course text (referred to as WZ) or lecture notes available on-line. Supplementary, recommend reading that gives further background on lecture or problem set material is also suggested from the books of Folland and Taylor on reserve in the Mathematics Library in Hill Center.

Lecture notes for lectures 9-14: Construction of Measures

Date Lecture Topic Reading due Problems due
1 9/3 Functions of bounded variation    
2 9/8 Cantor sets and functions WZ, 1.1-1.6, 2.1, 2.2, 3.1  
3 9/10 Riemann-Stieltes Integrals WZ, 1.7, 2.3, 2.4 1-6, 10-14
4 9/15 Drawbacks of Riemann integrals    
5 9/17 Drawbacks of Riemann integrals   7, 8, 9, 15-19, 25, 26
6 9/22 Outline of measure
and integration theory
   
7 9/24 Outine continued read lecture notes  
8 9/29 Algebras and sigma algebras: lecture notes    
9 10/1 Finitely additive measures   22,23,24
10 10/6 Construction of Lebesgue measure   22,23,24
11 10/8 Construction of Lebesgue measure   hand in 28-32
12 10/13 Lebesgue-Stieltjes measures
Lecture Notes
   
13 10/15 Coin-tossing measure; outer measures,
measurable sets
read WZ, chapter 11.1,2,3,5  
14 10/20 Caratheodory's theorem; proof read WZ, chapter 11.1,2,3,5  
15 10/22 Lebesgue measure: regularity read WZ, chapter 3  
16 10/27 Measurable functions read WZ, chapter 3 33-44 (42 optional),
hand in 33,34,36,38,42
17 10/29 Measurable functions read WZ, chapter 3  
18 11/3 The integral and basic convergence theorems   44-50
hand in 44, 45, 47, 50
19 11/5 The integral and basic convergence theorems   44-50
hand in 44, 45, 47, 50
20 11/10 EXAM   
21 11/12 Integration WZ, chapter 5  
22 11/17 Integration WZ, chapter 5  
23 11/19 Convergence in measure, a.e. and L^1 WZ, chapter 4, section 4  
24 11/24 Egorov, Lusin, Fubini-Tonelli WZ, Chapter 4, section 3, Chapter 6 56, 59, 61, 62, 66
25 12/1 Fubini-Tonelli theorem WZ, Chapter 6  
26 12/3 Differentiation WZ, Chapter 7 68, 69, 71, 79, 82
27 12/7 Differentiation WZ, Chapter 7  
28 12/10 Differentiation WZ, Chapter 7  

Problem Set 1 solutions

Problem Set 2 solutions