Real Analysis I, Fall 2002

Real Analysis I
MAA 6306-4776

Fall 2002

Instructor: Tomas Schonbek

S & E 218, Ext. 7-3355

e-mailschonbek@acc.fau.edu

Office Hours: MWF 10:00AM-12:00PM

Textbook: There is no official textbook.
Lectures will be posted on the web
(see the links below).

A list of references for further reading will be provided.

Course Description

We'll begin by covering the basics of measure theory and integration, discussing measurable spaces and measure spaces, integration with respect to a measure, and the classical theorems (Beppo Levi, Fatou, Lebesgue; etc.). We'll continue with Caratheodory's extension theory of measures and use it to construct Hausdorff measures in general and the Lebesgue measure in particular. This may very well take us to the end of the semester, but if there is time, we'll do product of measures next. Otherwise, the second part of the course will start with products of measures, continue with the Radon-Nikodym Theorem and derivatives of measures; finally get to some geometric measure theory and fractal sets.

Grading Procedures

I'll be assigning homework on a regular basis. Assume that homework is due one week after being assigned. Your grade will be based on the homework.

LINKS

Lectures, Homeworks, etc.

Lectures
1. First (introductory) lecture; Riemann vs. Lebesgue.
2. The bulk of the lectures, in pdf format These notes will grow as the course progresses.
Homeworks
1. Homework 1, pdf format.
2. Homework 2, pdf format.
3. Homework 3, pdf format.
4. Homework 4, pdf format.
5. Homework 5, pdf format.
6. Homework 6, pdf format.
Some Textbooks
1. Paul Halmos, Measure Theory, Van Nostrand 1950, Springer Verlag 1974.
  A classic, so it must be mentioned.
2. Walter Rudin, Real and Complex Analysis, McGraw Hill 1987.
  Also a classic; Chapters 1 and 2 deal with measure theory. Rudin's presentation is always very elegant, occasionally too elegant. The main defect of his presentation might be that he avoids extension of measures.
3. Gerald Folland, Real Analysis, Wiley 1999.
  Excellent presentation of the fundamentals of measure theory and integration.

Instructor:	Tomas Schonbek
	S & E 218, Ext. 7-3355
	e-mailschonbek@acc.fau.edu
Office Hours:	MWF 10:00AM-12:00PM

Textbook:	There is no official textbook. Lectures will be posted on the web (see the links below). A list of references for further reading will be provided.