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This is an archived course. A more recent version may be available at ocw.mit.edu.
The textbook that is used for problem 5 in the second problem set is the required book: 
Dudley, R. M. Real Analysis and Probability. Cambridge, UK: Cambridge University Press, 2002. ISBN: 9780521007542.
Problem Set 1 (PDF)
Problem Set 2 (PDF)
Problem Set 3 (PDF)
Problem Set 4 (PDF)
Note: A more recent version of this course, taught by Prof. Dmitry Panchenko at Texas A&M University, is available here. Updated Lecture Notes include some new material and many more exercises.
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