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MATH-501 Real Analysis - I Lecture 13

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Xuất bản 29/06/2016
Lecture 13 (2009-10-26) Review of mid-term exam MATH-501 Real Analysis - I Assoc. Prof. Dr. Alexandre Gontcharov 2009-2010- Fall Concepts of integration. Henstock-Kurzweil integral. Borel sets, Bair functions. Outer measures. Measurable sets. Lebesgue and Lebesgue-Stieltjes measures. Lebesgue density theorem. Hausdorff measures and Hausdorff dimension. Measurable functions. Lusin’s and Egorov’s theorems. Convergence in measure. Lebesgue integral. Basic theorems of Lebesgue integral. Modes of convergence. Differentiation of indefinite Lebesgue integral. Signed measures. The Radon- Nikodym theorem. Product measures. Spaces of integrable functions.
integration mathematics Henstock-Kurzweil integral Borel sets Bair functions Outer measures Measurable sets Lebesgue measures Lebesgue-Stieltjes measures Lebesgue density theorem Hausdorff measures Hausdorff dimension Measurable functions Lusin s theorem Egorov s theorems Convergence in measure Lebesgue integral Product measures Spaces of integrable functions bilkent university