Instructor: Dr. Dr. Péter SIMON
Text: W. Rudin, Real and Complex Analysis (3rd edition)
Prerequisite: 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.
(please consult the syllabus of the ANT course; if most of the material it covers is unfamiliar for you, take that instead of the RFM course)
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. (if time permits)