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:
2024-2025, 2025-2026, 2026-2027, 2027-2028
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.
Additional information
Lectured in the fall 2025 and fall 2027.
Description of prerequisites
Measure and Integration Theory 1 and 2
Study materials
lecture notes
Andrew M. Bruckner, Judith B. Bruckner ja Brian S. Thomson: Real analysis, 2008; www.classicalrealanalysis.com
Literature
- 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
Language:
English, Finnish
x
Exam (9 cr)
Type:
Exam
Grading scale:
0-5
Language:
English, Finnish