Overview

The central subject of this course is integration. We will begin by developing the Cauchy and Riemann theories of integration and discussing the properties and limitations of these approaches. The limitations will provide the motivation for developing both a more general approach. We will then turn to measure theory and the Lebesgue theory of integration. After covering the basics, we will work out some of the most important properties, including the relation to the Riemann integral and integration in several variables. We will discuss applications of measure theory and the Lebesgue integral to defining some important classes of functions and probability theory.

Prerequisites

Familiarity with some elementary facts about metric spaces and sequences of functions, such as obtained in M517. This course is more sophisticated than M517.

Course Work and Grades

The course work will consist of problem sets assigned periodically and a cumulative two hour Final Exam. Problems in the problem sets so marked by the instructor may be resubmitted.

Course Material

Course Text

Foundations of Modern Analysis, A. Friedman, Dover Publications, ISBN 0486640620

Supplemental Texts

Real Analysis, Royden, 1988.
Principles of Real Analysis, Aliprantas and Burkinshaw, Elsevier, 1998
Measure and Integration, Wheeden and Zygmund, Marcel Dekker, 1977
The Elements of Integration and Lebesgue Measure, by Bartle, John Wiley, 1995
Measure Theory and Probability, Adams and Guillemin, Birkhauser, 1996
Real Analysis, Folland, Wiley, 1984
Probability and Measure, Billingsley, Wiley, 1995
Analysis on Manifolds, J. Munkres, Addison-Wesley, 1970
Calculus on Manifolds, M. Spivak, Benjamin/Cummings Publishing Company, 1965
Measure, Integration, and Function Spaces, C. Swartz, World Scientific, 1994

Instructor: YOUR NAME

Department: Mathematics

Office: XXX Weber Building

Phone: 491-XXXX email: YOUR EMAIL (Be sure to fix link) URL: http://www.math.colostate.edu/~YOUR URL