Advanced Real Analysis

The Radon-Nikodym theorem, Radon measure on locally compact spaces and Riesz' representation theorem. Applications to Fourier analysis and probability theory: Heisenberg's inequality, the Prime Number Theorem, ergodic theory. Hausdorff measures.

Lectures every second year, next time spring 2016.

1. Knowledge. The student understands concepts and methods from advanced real analysis, as specified under "academic content". The student is familiar with applications of measure theory in Fourier analysis, functional analysis and probability theory.

2. Skills. The student is able to apply measure theory and Lebesgue spaces to formulate and solve mathematical problems.

Lectures, exercises and possibly projects. The lectures will be given in English if they are attended by students from the Master's Programme in Mathematics for International students. Portfolio assessment is the basis for the grade awarded in the course. This portfolio comprises an oral final examination 80%, and a total assessment of the problem sheets, and the semester assignment 20%. The exercises and projects only count if they have a positive effect on the final grade. The results for the constituent parts are to be given in %-points, while the grade for the whole portfolio (course grade) is given by the letter grading system.