MATH 312---Autumn, 2007
Analysis I: Measure, Integration, and Probability 
MWF 11:30 -- 12:20, 206 Eckhart
Greg Lawler , 415 Eckhart,
e-mail: lawler at
Grader: Catalin Carstea


Rudin, Real and Complex Analysis
Notes on Probability,

This is the first quarter of a three-quarter sequence on real and complex analysis intended primarily for first-year graduate students in the department of mathematics (but is open to all students with the appropriate background and mathematical maturity). The plan is to have lectures on Mondays and Wednesdays from the half of Rudin's book and for Friday lectures to be on probability.
There will be weekly homework exercises due on Wednesdays. That assignment will cover material from the lectures of the previous week. There will also be a large problem set at the end of the semester that will serve as a final exam. Students may work together on homework exercises EXCEPT FOR THE FINAL PROBLEM SET, but must write-up their work separately.
Problem Set 1 (due Oct 3)
Problem Set 2 (due Oct 10)
Problem Set 3 (due Oct 17)
Problem Set 4 (due Oct 24) (CORRECTION: In part 3 of the long extra exercise (which is part 4 if you downloaded this a few days ago), we want to show that there is a __G-measurable__ E(X|G) satisfying (1). Without that condition of G-measurability, the problem is really trivial! This then defines E(X|G) for all integrable X. In parts 5 and 6, assume that X is integrable. In part 4, XY must be integrable if X,Y are square integrable.)
Problem Set 5 (due Oct 31)
Problem Set 6 (due Nov 7)
Problem Set 7 (due Nov 14) (revised Nov. 9 --- problem 8 from Rudin removed and a new extra problem added)
Problem Set 8 (due Nov 21)

FINAL PROBLEM SET. REVISED: Nov 26, 12:30 pm . (NOTE: another typo was noticed Monday, Nov. 26, 12:30pm. On part 3 of the last problem the \leq should be a \geq. With \leq the statement is false.) This is due at 11:30 am on Friday, November 30 --- I will be in the usual class room to collect the papers. You may not discuss this with each other people, but it is open book(s). Corrections: Exercise 5 had a number of errors in it in the original version --- c_2 should be c_1 and throughout the problem log n should be log log n. The corrected version is above.