实变函数(H)

This honors course provides an in-depth introduction to various topics and techniques in real analysis, including cardinality of sets, measure theory, types of convergence, the dominated convergence theorem, the Fubini-Tonelli theorem, Lebesgue’s differentiation theorem, the Hardy-Littlewood maximal function, the fundamental theorem of calculus, L^p spaces, and generalized functions. Compared with the regular real analysis course, this course provides capable students with more rigorous training in analysis.