MAT 524 -- Real Variables II
Spring 1999 Course Description
Professor: D. Bradley
Text: Halsey L. Royden, "Real Analysis," (3rd ed.) MacMillan,
New York, 1988. Chapters 7-10, 13 & 16.
References:
-
Gerald B. Folland, "Real Analysis: Modern Techniques and their Applications,"
John Wiley and Sons, New York, 1984. Chapters 3, 5, 7 & 9.
-
Paul R. Halmos, "Measure Theory," Springer Graduate Texts in Mathematics,
New York, 1950. Chapters VI, IX & X.
-
Walter Rudin, "Real and Complex Analysis," McGraw-Hill, New York,
1987. Chapters 2 & 5-7.
This course is a continuation of MAT 523.
As such, we will be reinforcing many of the concepts and topics of
MAT 523 as well as forging ahead with new
material in the study of real analysis, measure theory and functional
analysis.
Syllabus:
-
Borel Measures on R
-
The Lebesgue Integral on Rn
- Decomposition and Differentiation of Measures
- Signed Measures
- The Lebesgue-Radon-Nikodym Theorem
- Complex Measures
- Differentiation on Rn
- Baire Category
- Radon Measures
- Positive Linear Functionals on Cc(X)
- Bounded Linear Functionals on C(X)
- The Dual of C0(X)
- The Daniell Integral
- Topics in Probability Theory