MATHEMATICS 7600
Class Ref. No. 16566
Fall, 2010
M W F 10:40 – 11:35, Room 171 Education Bldg.
Prof. B. Schreiber
Office
Room 1089 Faculty/Administration Building
Office Hours: Wed. 2:45 ─ 3:45, Fri. 1:00 ─ 2:00, or by appointment.
Telephone: (313) 577─8838
Electronic Mail: bert@math.wayne.edu URL: http://www.math.wayne.edu/~bert
Class URL: http://www.math.wayne.edu/~bert/courses/7600
Text
G.B. Folland, Real Analysis: Modern Techniques and Their Applications, 2nd ed., WileyInterscience, John Wiley and Sons, New York, 1999.
Summary
MAT 7600-7610 will present the fundamentals of measure theory and integration from a
functional-analytic point of view. The course(s) will be broken down into the following topical
sections:
 Background and Topological Preliminaries
 Measures and Integration Theory
 Measures on Product Spaces
 Introduction to Banach and Hilbert Spaces
 Complex Measures, the Radon-Nikodym Theorem, and the Dual of Lp
 Integration on Locally Compact Spaces
 Differentiability and Absolutely Continuous Functions
 Measures on Infinite Product Spaces
 Convex sets in Banach Spaces and the Krein-Milman-Choquet Theorem (time
permitting)
Homework and Grading
Homework will be assigned approximately weekly. Grading will be based on solutions to
homework exercises; there will be no in-class examinations. Homework will not be accepted
after the due date. Solutions should be written as full sentences in good English with clear
exposition. Assume that the reader does not know how to solve a given problem and you are
explaining the solution. Students are encouraged to discuss material presented in class and the
ideas behind solutions to homework problems, but each student is expected to write up his/her
own solutions to homework problems and not to copy the solutions of others with only minor
changes. Such “copying” will be treated as cheating and may lead to no credit for solutions
submitted by all parties concerned.
MATHEMATICS 7600–7610
Fall, 2010, Winter, 2011
Prof. B. Schreiber
Selected Bibliography
C.D. Aliprantis and O. Burkinshaw, Principles of Real Analysis, 3rd ed., Academic Press, San
Diego, CA, 1998. (QA 300 .A48 1990)
C.D. Aliprantis and O. Burkinshaw, Problems in Real Analysis, 2nd ed., Academic Press, San
Diego, CA, 1999.
P. Billingsley, Probability and Measure, 3rd ed., Wiley, New York, 1995. (QA273 .B575 1986)
A.M. Bruckner, J.B. Bruckner, and B.S. Thomson, Real Analysis, Prentice-Hall, Upper Saddle
River, NJ, 1997.
N. Dunford and J.T. Schwartz, Linear Operators PartI: General Theory, Interscience, Wiley, New
York, 1965. (QA329.2 .D85 v.1)
E. Hewitt and K. Stromberg, Real and Abstract Analysis, Graduate Texts in Mathematics No. 25,
Springer-Verlag, Berlin-New York, 1975.
P.R. Halmos, Measure Theory, van Nostrand, New York, 1950. (QA611 .H25)
J.N. McDonald and N.A. Weiss, A Course in Real Analysis, Academic Press, San Diego, CA, 1999.
H.L. Royden, Real Analysis, 3rd ed., Macmillan, New York, 1988. (QA331.5 .R6 1988)
W. Rudin, Functional Analysis, 2nd ed., McGraw-Hill, New York, 1991. (QA 320 .R83 1991)
W. Rudin, Real and Complex Analysis, 2nd ed., McGraw Hill, New York, 1974. (QA300 .R82
1974)
S. Saks, Theory of the Integral, Dover, New York, 1964. (517.3 .Sa29t 1964)
K. Yosida, Functional Analysis, 6th ed., Springer-Verlag, Berlin-New York, 1980. (QA320 .Y6
1980)