Geometric measure theory, spring 2008

Lecturer

prof. Pertti Mattila

Scope

10 op.

Type

Advanced studies.

Prerequisites

Basic knowledge of measure and integration theory such as the courses "Mitta ja integraali" and "Reaalianalyysi I". "Reaalianalyysi II is useful but not necessary.

Lectures

Weeks 3-9 and 11-17, Tuesday 10-12, Friday 10-12 in room C123. Two hours of exercise classes per week.

Easter holiday 20.-26.3.

No lectures and exercises during week 4.

Contents

• Hausdorff measures
• fractal type measures and sets
• rectifiable sets
• area and coarea formulae
• some other topics

Bibliography

K.J. Falconer, Geometry of Fractal Sets
 H. Federer, Geometric Measure theory
 P. Mattila, Geometry of Sets and Measures in Euclidean Spaces
 F: Morgan, Geometric Measure Theory, a Beginner's Guide
 L. Simon, Lectures on Geometric Measure Theory
 F. Lin and X. Yang, Geometric Measure Theory - an Introduction

Exercise groups