Real Functions and Measures— RFM

Instructor: Dr. Viktor HARANGI

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.

Topics:

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)