MATS2110 Geometric Measure Theory (5 cr)
Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023, 2023-2024
Description
- 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
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.
Description of 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
MATS111 Measure and Integration Theory 1
MATS112 Measure and Integration Theory 2
Literature
- P. Mattila: Geometry of Sets and Measures on Euclidean Spaces: Fractals and Rectifiability, Cambridge University Press (1995)
Completion methods
Method 1
Evaluation criteria:
course exam/presentation points and exercise points
Select all marked parts
Method 2
Evaluation criteria:
final exam points
Select all marked parts
Parts of the completion methods
x
Teaching (5 cr)
Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
course exam/presentation points and exercise points
Language:
English, Finnish
Study methods:
lectures and exercises
x
Exam (5 cr)
Type:
Exam
Grading scale:
0-5
Evaluation criteria:
final exam points
Language:
English, Finnish
Study materials:
P. Mattila: Geometry of Sets and Measures on Euclidean Spaces: Fractals and Rectifiability, Cambridge University Press (1995)