Course description: This course provides an introduction
into the Lebesgue theory of real functions and measures.
Topics:
Introduction: motivation from Fourier analysis, the Lebesgue measure;
Abstract measure theory: the abstract theory of measure and integration, motonone convergence, dominated convergence, product measures and Fubini's theorem, decompositions á lá Lebesgue and Radon-Nikodym;
More on the Lebesgue measure and the Lebesgue integral: regularity properties, affine transformations, connection to the Riemann integral, convolutions, applications to Fourier analysis and approximation theorems.