University at Buffalo 3 credits Mathematics
Metric spaces, Baire category argument, Stone-Weierstrass theorem, Daniell integral, theory of measure, measurable functions. Lusin’s theorem, Egoroff’s theorem. Lebesgue integral, Fatou’s lemma, convergence in measure, mean convergence, almost uniform convergence. Dominated Convergence Theorem. Riesz representation theorem, absolute continuity. Radon-Nikodym theorem, bounded variation, Lebesgue’s differentiation theorem, F.T.C. for Lebesgue integral, density, approximate continuity. Radon-Nikodym theorem, bounded variation, Lebesgue’s differentiation theorem, F.T.C. for Lebesgue integral, density, approximate continuity.
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