Real Analysis II (실해석학)

Class Info

Class Number: Math 307001
Dates: Sep 3, 2011 - Dec 8, 2012
Room: NS 319
Meeting time:
Monday 10:30 - 11:45
Friday 9:00 - 10:15

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

In these lectures we will derive the Lebesgue Measure and important properties of measurable sets.
Links
Homework
The Cantor Set

Final Exam: December 10, 10:30 - 12:30, room NS 218.


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: Fri Nov 30 14:54:06 KST 2012