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
The maximal theorem. Differentiation of measures and functions. Density. Haar measure.