MATS2110 Geometric Measure Theory (5 cr)
Learning outcomes
After the course the students know techniques to investigate geometric properties of general Borel sets and measures, and they are familiar with the notion and some properties of rectifiable sets in Euclidean spaces. The students will be provided with the necessary background to study advanced topics in modern geometric measure theory.
Content
- Hausdorff measure and dimension, density theorems
- Mass distribution principle, Frostman's lemma, Riesz energies of measures
- Haar measures, uniformly distributed measures
- Projection theorems by Marstrand, Kaufman, and Mattila
- Fourier transforms of measures
- Rectifiable and purely unrectifiable sets
- Besicovitch's projection theorem
Materials
P. Mattila: Geometry of Sets and Measures on Euclidean Spaces: Fractals and Rectifiability, Cambridge University Press (1995)
Prerequisites
Requires knowledge of basic theory of measure and integration, as covered in the courses
MATS111 Measure and Integration Theory 1
MATS112 Measure and Integration Theory 2