Course Description: Upon completion of this two-semester series, students should master concepts and theories of outer measure, the Caratheodory extension theorem, general measures, Lebesgue integrals with respect to a measure, Lebesgue measures, Lebesgue-Stieltjes measures, product measures, convergence theorems, Fubine-Tonelli theorem, signed measures, functions of bounded variation, absolutely continuous functions, differentiation theory, differentiation of a measure, metric spaces, compactness, Banach spaces, Lp spaces, Hilbert spaces, basic Fourier analysis, bounded linear functionals, dual spaces, and bounded linear operators.
Textbook: REAL ANALYSIS, Modern Techniques and Their Applications, by G.B. Folland, 2nd Ed.
MATH 5322 – Exam 1 w Key (F2011) – Real Analysis 1 (Alex Wang)
MATH 5322 – Exam 2 w Key (F2011) – Real Analysis 1 (Alex Wang)
MATH 5322 – Exam 3 w Key (F2011) – Real Analysis 1 (Alex Wang)
MATH 5322 – Final w Key (F2011) – Real Analysis 1 (Alex Wang)
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