Learning Outcomes for 3450:621 Real Analysis

 Students are expected to be able to 

  • Know basic properties of  closed sets, open sets, compact sets, metric spaces, and normed spaces.
  • Calculate liminf and limsup of a sequence of sets.
  • Understand  fundamental properties of  outer Lebesgue measure, Lebesgue measure, and Lebesgue measurable and integrable functions. Students are also expected to be able to calculate Lebesgue measure of some basic sets in Euclidean space.
  • Use Tchebyshev's inequality, Fatou's lemma, the monotone convergence theorem, and Lebesgue's dominated convergence theorem.
  • Do standard proofs using  set theory, measure theory, and Lebesgue integral.