RealAnalysisExamTopics - graph theorem • Complex measures...

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Topics for Qualifying Exam in Analysis r-algebras Measures, outer measures, Borel measures Measurable Functions Lebergee integration in abstract measure spaces and in R , Lebesgue measure Riesz representation theorem for positive Borel measures and for complex Borel measures. Lp spaces, approximation by continuous functions Elementary Hilbert space theory, linear product, linear functionals, Riesz-Fischer theorem Elementary Barach spaces, Banach-Sternhaus, open mapping theorem, closed
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Unformatted text preview: graph theorem • Complex measures, Radon-Nikodym theorem, bounded linear functionals on Lp, duality, • Derivatives of measures, Lebesgue points, absolutely continuous functions, functions of bounded variation, fundamental theorem of calculus • Product measures, Fubino theorem References: • Real and Complex Analysis, 3 rd ed., Walter Rudin • Real Analysis, 3 rd ed., H.L. Royden...
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