Postgraduate Studies
Courses
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AN3 - Real Analysis Ι |
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Topology and continuity, σ-algebra and measurable functions, Borel sets, Simple functions, Measure, Monotone Convergence theorem Fatou's Lemma, -space, Almost everywhere equality, Lebesgue Dominated Convergence theorem, Measure completion, Some Topological facts of Hausdorff spaces, Semicontinuity, Topological support, Urysohn's Lemma, Riesz's Representation theorem, Borel measure, Lebesque measure, Five ways of construction of Lebesgue measure, Completion of topological spaces, (Pointwise, uniform, almost uniform) convergence of sequences of functions, Egoroff theorem, Convergence with respect to measure, Almost everywhere convergence,Absolute continuous measures, -spaces, p1, -space, Radon-Nikodym theorem, -spaces, -space, Grothendieck's theorem, Orthogonal expansions, Riesz-Fisher theorem, Bessel's inequality, space, Fejer theorem. |
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