MAT 324, Real Analysis (Measure Theory)

Fall 2015

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: Tu-Th 10:00-11:20am, Library W4530

Grader: David Hu

Final Exam: Friday, Dec 11, 2015 11:15am-1:45pm, W4530 Melville Library (usual lecture room)

The Grader will have a Review Session to go over the problem sets 1-4 on Tuesday, Oct 13 at 6-8pm in P-131 of the Math Tower.

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). I hope to cover the entire book, at a rate of about 1 chapter every two weeks.

This is definitely a course with proofs. Homework problems will be asssigned for each section and there will be an in-class midterm and a final.

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.

Office Hours: Tu 9-10, Th 9-10 and 1-2

Links to the problems sets will be posted here later.

Quick review of real analysis

Problem Set 1, Prerequisites, Due Thursday, Sept 3

Problem Set 2, Measure zero sets, Due Tuesday, Sept 15

Problem Set 3, Measurable sets, Due Thursday, Sept 25

Problem Set 4, Measurable functions, Due Thursday, October 8

Midterm Review.
This describes the format of the Midterm on Thursday, Oct 15 (same time and place as class usually meets).

Problem Set 5, Lebesgue integration, Due Thursday, October 29

Problem Set 6, L^p spaces, Due Thursday, November 13

Problem Set 7, Product measures , Due Tuesday, December 1

Alternate treatment of Fubini's theorem

Final Review.
This describes the format of the Final exam on Friday, Dec 11 (same place as class usually meets).

Fractals in probability and analysis
Chapter 1 contains a simple proof of the strong law of large numbers

tentative lecture schedule


Send me email at: bishop at

University final exam schedule

Additional links

Hugh Woodin, The Continuum Hypothesis, Part I

This gives an introduction to set theory with a discussion of the the role of the axiom of choice and the existence of non-measurable sets.

Hugh Woodin, The Continuum Hypothesis, Part II

This continues the previous article and discusses in what sense the continuum hypothesis can be considered true or false, even through it is formally independent of ZFC.

paper giving careful proof of Banach-Tarski paradox

Wikipedia article on the Banach-Tarski paradox

Wikipedia article on Carleson's a.e. convergence theorem

Wikipedia article on Weierstrass' nowhere differentiable function

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 , ,