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.