Course content

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 Theorems, ergodic theory. Hansdorff measures.

Lectures every second year, next time in 2012.

Learning outcome

The course aims at giving the students a fundamental understanding in advanced analysis, more specifically in the topics described above.

Learning methods and activities

Lectures, exercises and possibly projects. 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 total assessment of the problem
sheets and projects only counts if it has a positive effect on the total assessment. 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.

Recommended previous knowledge

TMA4225 Foundation of analysis.

Course materials

Will be announced at the start of the course.

Credit reductions