June 16, 2005

Analysis cheat sheet

[Math_] Notes on analysis... --DRAFT--

  • Function spaces
  • Metric spaces
  • Convergence
  • Measure
  • Lebesgue measure
  • Lebesgue integral
  • Riemann integral
  • Lebesgue-Stieltjes integral

  • Dense subsets
  • Separable spaces
  • Complete metric spaces
  • Compact metric spaces
  • Compactness and continuity
  • Linear spaces
  • Linear functionals
  • Norms and semi-norms of linear spaces
  • Convergence revisited
  • Euclidean spaces
  • Orthogonality and bases
  • Hilbert spaces
  • Delta functions
  • Fourier transform
  • Functional derivatives
  • Expectations
  • Law of large numbers


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