This course is an introduction to the theory of measure and integration. It covers basic material required for study of any area of mathematical analysis---ordinary and partial differential equations, harmonic analysis, probability and stochastic processes, complex analysis. A more detailed list of topics may be found in the course syllabus.
TEXT AND BOOKS ON RESERVE: The text for the course is:
Wheeden and Zygmund,
Measure and Integeral: An Introduction to Real Analysis,
Marcel Dekker, New York, 1977, ISBN 0-8247-6499-4.
This text is intended for reference and collateral reading.
The lectures will not follow order of presentation of the
book. Material that is not in the book or is taken out of context
will sometimes be summarized in lecture notes, which will be
available by links from this page. Also, there are several
books on reserves in the Math Library in the Hill Center for
this course, and students will be directed to these sources
from time to time. These reserve books are:
PREREQUISITES: It is assume that the student has a solid background in an undergraduate analysis course at the level of W. Rudin, Principles of Mathematical Analysis, and that the student can read and write mathematical proofs. In particular, the student should understand basic metric space topology---including compact sets, completeness, continuous functions and their properties---and the notion of countable set, the fact that the rationals are countable, but the reals are not, and similar basic facts. Summaries of basic points are contained in Chapter 1 of Wheeden and Zygmund and in sections P.5,P.6 of Folland.
COURSE WORK: This course emphasizes problem sets, which will be due weekly. Reading will be assigned for each class, and it is important that students prepare for class by doing the reading assignment. Current homeworks and reading assignments will be posted on a supplementary information page.