MATH 501 Real Analysis I
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Algebras of sets. The Cantor-Bernstein theorem. Borel Sets. Measurable sets, Lebesgue measure. Measurable functions. Luzin's and Egerov's theorems. The Riemann and the Lebesgue integrals. Convergence in measure. Differentiation and integration. The Lp spaces. The Minkowski and Holder inequalities. Convergence and completeness. General measure and integration theory. The Radon-Nikodym theorem.
Credit units: 3 ECTS Credit units: 6.
Autumn Semester (Alexandre Gontcharov)
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