MATS311 Real Analysis (9 cr)

Open the course unit brochure on Sisu
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

No published teaching
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.

Teaching