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 -------------------------------------------- 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