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.
