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.
Textbook: "Real Analysis" by G. B. Folland, second edition (1999, 978-0-471-31716-6).
Notes: (1) Here is
a link to errata (list of misprints, mostly). (2) 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.
Prerequisites: This course assumes that you took an undergraduate analysis
course or achieved an equivalent expertise by other means. See announcements in Canvas for details.
Grades: Your Final Grade in the course will be based on
Attendance/Assignments/Various Forms of Class Participation (35%),
Midterm Exam (25%, early to mid-October) and Final Exam (40%, Mon, Dec 14, 8:30-11 AM).
(Students with special needs should contact
Division of Student Affairs/Disability Resources.
Please keep in mind that accommodations are not retroactive.)
Integrity: It is OK (and indeed encouraged) to discuss homework assignments with fellow students.
However, any submitted work must be your own.
Merely copying someone else's work is unethical,
a waste of time, and may be penalized.
(This includes copying solutions found on the internet.)
Any substantive collaboration and/or usage of sources or AI tools has to be properly acknowledged.
See CWRU
academic integrity policy and
Academic Integrity Board.
Any violation of the policy will be reported to the Dean of Undergraduate Studies and the Office of Student Conduct & Community Standards.
SYLLABUS & ASSIGNMENTS
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.
Homework will be assigned (roughly) weekly.
A tentative schedule of assignments can be found
here.
Finalized assignments and solutions, handouts, and other documents will be progressively posted on Canvas under Assignments and Modules, as appropriate. However, the information posted under "tentative assignments" is a close approximation of the "finalized assignments" and so you are advised to start working on the problems as soon as the relevant material is covered in class. The scores for the assignments will be awarded primarily for "good faith effort."
