Back to Spielberg's webpage

Fall 2005
MAT 570
REAL ANALYSIS I

Instructor:  Jack Spielberg
Time:  TTh, 12:15 - 1:30
Location:  ARCH-147
Line Number:  38866

Course Description:

This is the first half of a basic graduate level course in real
analysis.  The central topic is abstract measure and integration
theory.  The Lebesgue integral is treated as a special case.  Lebesgue
integration was developed in the early part of the twentieth century,
and is a much more general and flexible integral than the Riemann or
Riemann-Stieltjes integral.  It has applications virtually everywhere
in pure and applied mathematics.  Once the door had been opened, it
was seen that the same methods lead to a general integration theory
that is foundational in analysis and probability.

In MAT 570 we will cover chapters 1, 2, 3, and parts of chapters 5 and
6, of Folland.  There will be regular homework assignments.  If
necessary there will be a final exam for students whose performance on
homework is inadequate.

Prerequisites:

A solid understanding of Advanced Calculus, i.e., MAT 371 or MAT 472.
The student should be completely comfortable with the notion of least
upper bound in the real numbers, and its consequences for continuity,
differentiation, Riemann integration, and uniform convergence.  Basic
knowledge of metric space topology (open and closed sets, Cauchy
sequences, compactness), at least in R^n, will be assumed.  If you
have not taken MAT 472, or are otherwise uncertain about your
background for this course, you are welcome to contact the instructor
at jack.spielberg@asu.edu.

Textbook:

The lectures will be self-contained, so strictly speaking, no text is 
necessary.  As a reference, any book on measure theory can be used.
The organization of the course will follow:

Real Analysis (either edition), Gerald B. Folland, Wiley Interscience.