*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)*