Math 205A: Real Analysis (graduate, Stanford)

Lebesgue's theorem on Riemann integration, sigma-algebras, Borel sets, abstract measure spaces, outer measures, Caratheodory's theorem on measurability, measurable functions and the Lebesgue integral, Fatou's lemma, convergence theorems, product outer measures, Fubini theorem, Tonelli's theorem, covering theorem, differentiation theory, functions of bounded variation and absolutely continuous functions, Borel outer measures in topological spaces, Hahn decomposition, Radon-Nikodym theorem, Lebesgue decomposition theorem, Riesz representation theorem.

 

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