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MTH-107.4 Measure Theory

Construction of Lebesgue measure on ℝ using inner measure and outer measure, σ - algebras, abstract measures, measurable functions.

Lebesgue integration, Fatou, Monotone and dominated convergence theorems, product measures, Fubini theorem.

Lebesgue decomposition, Radon-Nikodym theorem, Lp spaces, duality, Lebesgue differentiation theorem, absolutely continuous functions, monotone functions.

Convolution and Fourier transforms.