Class InfoClass Number: Math 307001Dates: Sep 3, 2011  Dec 8, 2012 Room: NS 319 Meeting time:
Purpose: Introduction to Lebesgue Measure Text: Robert G. Bartle, The Elements of Integration and Lebesgue Measure, Wiley 1995 Optional suggested reading: Tom M. Apostol, Mathematical Analysis, 5. ed., AddisonWesley 1981 Walter Rudin, Real & Complex Analysis, 3. ed., McGraw Hill 1986 In these lectures we will derive the Lebesgue Measure and important properties of measurable sets. 

Week  Topics  Chapters 
1  Elements of Integration  17 
2  Elements of Integration, Algebras  17 & 9 
3  Extension of Measures  9 
4  Lebesgue Measure  9 
5  Riesz Representation Theorem  9 
6  Product Measures  10 
7  Volumes  11 
8  Midterm Exam  
9  The Outer Measure  12 
10  Carathéodory's Theorem  13 
11  Properties of Lebesgue Measure  13 
12  Examples of Measurable Sets  14 
13  Approximation  15 
14  Nonmeasurable Sets  17 
15  Final Exam 
Attendance  10% 
Midterm:  40% 
Final:  50% 