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Bilkent University

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Undergraduate and Graduate Programs 2020-2021

MATH 501 Real Analysis I

Concepts of integration. Generalized Riemann Integral. Borel Sets, Bair Functions. Outer Measures. Measurable Sets. Lebesgue Measure. Lebesgue density theorem. Hausdorff Dimension. Measurable Functions. Lusin's and Egorov's Theorems. Limit Theorems for Lebesgue Integral. Differentiation of Lebesgue Integral. Spaces of Integrable Functions. Signed Measures. The Radon-Nikodym Theorem. Credit units: 3 ECTS Credit units: 5.

Autumn Semester (Alexandre Goncharov)

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