MATS311 Real Analysis (9 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
Description
The course in concerned with measure theory in Euclidean spaces. Main topics are Hausdorff measures and dimension, differentiation of measures, absolute continuity, covering and density theorems, and maximal function.
Learning outcomes
After the course, the student knows
- the definition of a measure and of the Hausdorff measure
- the basic properties of Hausdorff measures
- the basic convergence theorems and their proofs, and is able to apply the theorems
- the basic covering theorems
- absolute continuity and differentiation of measures.
Description of prerequisites
Measure and Integration Theory 1 and 2
Study materials
lecture notes
Literature
- Andrew M. Bruckner, Judith B. Bruckner ja Brian S. Thomson: Real analysis, 2008; www.classicalrealanalysis.com
- Olli Lehto: Reaalifunktioiden teoria, Limes ry, 1969.
- Pertti Mattila: Geometry of sets and measures in Euclidian spaces
Completion methods
Method 1
Evaluation criteria:
course exam 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 (9 cr)
Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
course exam points and exercise points
Language:
English, Finnish
Study methods:
lectures and exercises
Teaching
9/14–12/17/2021 Lectures
x
Exam (9 cr)
Type:
Exam
Grading scale:
0-5
Evaluation criteria:
final exam points
Language:
English, Finnish
Study methods:
Independent study and final exam.