MAT 324, Real Analysis (Measure Theory)

Fall 2007

Christopher Bishop

Professor, Mathematics
SUNY Stony Brook

Office: 4-112 Mathematics Building
Phone: (631)-632-8274
Dept. Phone: (631)-632-8290
FAX: (631)-632-7631

Time and place: MWF 11:45-12:40, Harriman Hall 115

We will follow the text `Measure, Integral and Probability' by Marek Capinski and Ekkehard Kopp (Springer-Verlag, Springer Undergraduate Mathematics Series, ISBN 1-85233-781-8). We should cover all of Chapters 1-5, and perhaps parts of Chapters 6,7,8 as time permits.

This is definitely a course with proofs. Homework problems will be asssigned for each section and there will be an inclass midterm on Friday, Oct 27 and a final at a time to be set (Scheduled time is Monday Dec 18 at 2-4:30).

Please hand homework in on or before due date. I will try to discuss the problems on the following meeting. Incorrect problems may be rewritten and handed back in for partial credit.

MIDTERM in class on MOnday , Oct 29. Midterm 1 sample exam in PDF
Midterm 1 sample exam in postscript

Chapter 1: Motivation and preliminaries

Problem set 1 is due Wed, Sept 12
Problem set 1 in PDF
Problem set 1 in postscript
Problem set 1 in TeX

Chapter 2: Measure

Problem Set 2a due Oct 1
Problem set 2a in PDF
Problem set 2a in postscript
Problem set 2a in TeX

Problem Set 2b due Oct 8
Problem set 2b in PDF
Problem set 2b in postscript
Problem set 2b in TeX

Chapter 3: Measureable functions
Problem Set 3 --- Due Oct 15
Problem set 3 in PDF
Problem set 3 in postscript
Problem set 3 in TeX

Chapter 4: Integral --- Oct 31
Problem Set 4
Problem set 4 in PDF
Problem set 4 in postscript
Problem set 4 in TeX

Chapter 5: Spaces of Integrable functions
Problem Set 5 --- Due Nov 26
Problem set 5 in PDF
Problem set 5 in postscript
Problem set 5 in TeX

Chapter 6: Product measures

Chapter 7: The Radon-Nikodym theorem

Chapter 8: Limit theorems

Here are some `fun' problems to think about:
- Given a set X in the real numbers, how many different sets can you generate by taking complements and closures repeatedly?
-Show that every real number in the interval [0,2] Can be written as the sum of two real numbers in the Cantor middle thirds set.

postscript output for template.tex

Send me email at: bishop at

University final exam schedule

Link to Schroder-Bernstein theorem

Link to Freilng's dart argument against CH

Link to history of mathematics

Some specific topics from the history of math site: history of `e' , The Brachistochrome problem , Isaac Newton , Gottfried Willhelm von Leibniz , A brief history of calculus , The fundamental theorem of algebra , A brief history of mathematics , Jean Fourier , The number `Pi' , Discovery of Neptune and Pluto , ,