Real Analysis II (실해석학)

Class Info

Class Number: Math 307
Dates: Sep 1, 2011 - Dec 5, 2011
Room: NS 319
Meeting time:
Monday 13:30 - 14:45
Friday 13:30 - 14:45

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., Addison-Wesley 1981
Walter Rudin, Real & Complex Analysis, 3. ed., McGraw Hill 1986
Links
Homework
The Cantor Set

Final Exam: Monday December 12, 13:30 - 15:00, Room NS 319.


The exam is a closed book test.


Syllabus

Week Topics Chapters
1 Elements of Integration 1-7
2 Elements of Integration, Algebras 1-7 & 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

Grading

We will have a mid-term test in October and a final exam in December.
The grades will be accorded the following weights.
Attendance 10%
Mid-term: 40%
Final: 50%

Homework

I will assign homework every Friday for the material covered that week.
It will be due to hand in on the following Friday.
Last modified: Sat Nov 19 14:40:23 KST 2011