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.


  • Topological and measurable spaces. The abstract theory of measurable sets and functions, integration.
  • Borel measures, linear functionals, the Riesz theorem.
  • Bounded variation and absolute continuity. The Lebesgue-Radon--Nikodym theorem.
  • The maximal theorem. Differentiation of measures and functions. Density. Haar measure. (if time permits)