(Graduate Level, FALL 2014)

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*Class Number: 1281**Class meets:*MW 12:30-1:45 in Yost 112

*Instructor:*Stanislaw J. Szarek (pronounced 'Shareck')*Office:*Yost 332*Office hours:*Currently M 2-3, W 11-12, and by appointment or by luck*Phone:*216-368-2913*E-mail:*szarek at cwru.edu (the preferred mode of communication)*WWW Home Page:*http://www.cwru.edu/artsci/math/szarek/*Class WWW Page (this page):*http://www.cwru.edu/artsci/math/szarek/MATH423/*Catalog Course Description:*General theory of measure and integration. Measures and outer measures. Lebesgue measure on-N-space. Integration. Convergence theorems. Product measures and Fubini's theorem. Signed measures. Hahn-Jordan decomposition, Radon-Nikodym theorem, and Lebesgue decomposition. Lp spaces. Lebesgue differentiation theorem in N-space. Prereq: MATH 322.*Text:*"Real Analysis" by Folland, second edition (1999, 978-0471317166).*Note:*If you want to use an earlier edition, you may try AT YOUR OWN risk.

**The course:** This is the first course of the MATH 423-424 sequence.
MATH 423 covers general theory of measure and integration.
When you hear someone invoking integrals or probabilities, this class will help
you understand what they are *really* talking about.
The second course, MATH 424, covers elements of functional analysis and some of its applications.
The sequence is required of most mathematics graduate students.
It can also be useful to graduate students in other mathematical sciences (such as statistics
and operation research) or in engineering.
Finally, the course (or the sequence) can be taken by advanced undergraduates.

**Grades:** Your Final Grade in the course will be based on
Attendance/Assignments/Various Forms of Class Participation (30%),
Midterm Exam (20%) and Final Exam (50%).
(Students with special needs should contact
Educational Services for Students.)

**Integrity:** It is OK (and indeed encouraged) to discuss homework assignments with fellow students.
However, **any** submitted work must be your own.
See
CWRU academic integrity policy.

- We will cover approximately Chapters 1-3 from the textbook. It is assumed that the students will familiarize themselves (at least roughly) with the "Prologue" on their own; but the more "sophisticated" points from there may be redone in class if and when needed.
- More detailed syllabus, including regularly updated assignments
- Solutions (and handouts etc.) will be posted on Blackboard.

Dr. Szarek's Home Page

Math Graduate Courses

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