Real Functions and Measures

  • Instructor: Peter MAGA
  • Contact: magapeter - at - gmail dot com
  • Prerequisites: calculus or rather an introductory analysis course; some elementary knowledge of topology and linear algebra is desirable, but a short introduction will be offered to make the course self contained.
  • Text: will be posted ( click here for the draft; posted FYI)

Course description: This course provides an introduction into the Lebesgue theory of real functions and measures.


  • Introduction: motivation from Fourier analysis, the Lebesgue measure;
  • Abstract measure theory: the abstract theory of measure and integration, motonone convergence, dominated convergence, product measures and Fubini's theorem, decompositions á lá Lebesgue and Radon-Nikodym;
  • More on the Lebesgue measure and the Lebesgue integral: regularity properties, affine transformations, connection to the Riemann integral, convolutions, applications to Fourier analysis and approximation theorems.