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Mathematics Colloquium, CSU Friday, April 10, 2015 3:30–4:30 pm in RT 1516 Coin Tossing and Fubini’s Nightmare Ali Tahzibi, University of Sao Paulo at Sao Carlos, Brazil Abstract. Flipping a coin (fair or unfair) is a very first example studied in probability theory. If we toss a fair coin a very large number of times, with a large probability half time we get heads. What happens, if the coin is not fair? The law of large numbers in probability theory deals with this question. In this talk, we show the construction (due to Katok-Milnor) of a full Lebesgue measurable subset A, of unit square and a foliation by analytic curves in the square such that any leaf intersects A in at most one point. The construction is related to the coin tossing of non-fair toss. Finally, we relate the above ”pathological” example to the rigidity in dynamical systems. * Refreshments at 3:00 PM in RT 1517