MATH 3002, Real Analysis
Description: A course on the theory of the Lebesgue measure and integration. The contents include: Lebesgue measure and integral, convergence theorem (Monotone convergence theorem, Fatou’s lemma, Lebesgue’s dominated convergence theorem), product measure and Fubini’s theorem, L^p space, the Hardy-Littlewood maximal function and Lebesgue differentiation theorem, functions of bounded variation, absolutely continuous functions, and the fundamental theorem of calculus.
E.M.Stein and R. Shakarchi, Real Analysis - Measure Theory, Integration, and Hilbert Spaces, Princeton University Press, 2005 参考教材-
The fifth teaching building 5203, Wednesday 14:00-15:35, Friday 9:45-11:20 .