Francesco Cellarosi's Generals Exam May 11th 2007, 2.30 pm - 4.30 pm
Committee:
Y.SINAI (chair)
J.MATHER
A.OBLOMKOV
Special Topics:
1) Probability Theory
2) Ergodic Theory and Dynamical Systems
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REAL ANALYSIS
Can you construct a closed nowhere dense of positive measure?
Baire categories & Baire theorem.
What is a density point? What can you say about them (a.e. point is a density point) ?
The fundamental theorem of calculus for Lebesgue integral.
Absolute continuity. Given f\in L1, what can you say about F(x):=\int_a^x f(t)dt ?
COMPLEX ANALYSIS
Consider f a holomorphic function on 0