MATH 3969 Measure Theory and Fourier Analysis
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Measurement theory is the study of basic concepts such as length, area, volume, arc length and surface area. Since it was proposed by Henri Lebesgue around 1900, it has been the basis for the use of integral theory in advanced mathematics. Moreover, it is the basis of modern probability theory. The course starts with the establishment of measurement and integration theories and establishes actual results, such as Fubini's theorem and the explicit convergence theorem, which allow us to control the integration. Then apply it to Fourier analysis and obtain products such as the inversion formula and Plancherel's theorem. Then the theory of probability was discussed.
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