# 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:**

2024-2025, 2025-2026, 2026-2027, 2027-2028

## Description

- The first part of the course concerns fundamental tools in geometric measure theory such as Hausdorff measures and dimension, covering theorems, and density theorems.
The second part focuses on specific topics in geometric measure theory, for instance rectifiable and purely unrectifiable sets, projection theorems, theory of currents, or Fourier-analytic methods in geometric measure theory.

## 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

## Study materials

Lecture notes or other study materials will be announced separately.

## Literature

- P. Mattila: Geometry of Sets and Measures on Euclidean Spaces: Fractals and Rectifiability, Cambridge University Press (1995)

## Completion methods

### Method 1

**Evaluation criteria:**

Points from exercises and/or seminar presentation and/or exam, depending on the implementation of the course

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

**Language:**

English

#### Teaching

##### 3/17–5/25/2025 Lectures

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)