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Unformatted text preview: MATH3969: Measure Theory and Fourier Analysis (Advanced) Daniel Daners The University of Sydney Semester 2, 2009 Overview In this course we study 1. measure theory 2. the Lebesgue integral I an alternative to the Riemann integral with better properties and larger scope. 3. the Fourier transform I widely used in applied mathematics, partial differential equations, probability theory and statistics and more 4. modern measure theoretic foundations of probability theory I widely used in statistics, stochastic differential equations, partial differential equations, financial mathematics and more (no prior knowledge of probability required) What is measure theory? Measure theory provides a way to I measure length, area, volume I compute the mass of a body, given a mass density I measure probability of events I build a theory of integration with better properties than that of the Riemann integral Measure Theory How to define area?...
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