MATS112 Measure and Integration Theory 2 (4 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, 2023-2024
Description
Lp -spaces, general measure spaces, measurable functions and integrals, s-dimensional Hausdorff measure.
Learning outcomes
After the course the student
- understands the basics of L^p spaces (in particular L^2)
- is able to define general outer measures and use the Caratheodory criterion for measurability
- knows and uses the definitions of general measures and measurable functions in abstract measure spaces.
- knows the basics of Hausdorff measures
Description of prerequisites
Introduction to mathematical analysis 3, Vector calculus 2, Vector analysis 1 and 2, Measure and integration 1
Study materials
Luentomoniste
Literature
- Andrew M. Bruckner, Judith B. Bruckner & Brian S. Thomson: Real Analysis, 2008, www.classicalrealanalysis.com
- Avner Friedman: Foundations of Modern Analysis.
- Terence Tao: An Introduction to Measure Theory
- Elias M. Stein & Rami Shakarchi: Real Analysis.
Completion methods
Method 1
Evaluation criteria:
Exam after the lectures. Extra benefits from approved homework assignments.
Time of teaching:
Period 2
Select all marked parts
Method 2
Evaluation criteria:
Final exam. At least 50% of total points is required for a passing grade.
Select all marked parts
Parts of the completion methods
x
Teaching (4 cr)
Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
Exam after the lectures. Extra benefits from approved homework assignments.
Language:
English, Finnish
Study methods:
24h lectures, 6 exercise sessions
Study materials:
Luentomoniste
Literature:
- Andrew M. Bruckner, Judith B. Bruckner & Brian S. Thomson: Real Analysis, 2008, www.classicalrealanalysis.com
- Avner Friedman: Foundations of Modern Analysis.
- Terence Tao: An Introduction to Measure Theory
- Elias M. Stein & Rami Shakarchi: Real Analysis.
Teaching
10/27–12/16/2022 Lectures
12/14–12/14/2022 Course exam
1/20–1/20/2023 Course exam
x
Exam (4 cr)
Type:
Exam
Grading scale:
0-5
Evaluation criteria:
Final exam. Minimum of 50% of total points is required.
Language:
English, Finnish
Study methods:
Final exam
Literature:
- Andrew M. Bruckner, Judith B. Bruckner & Brian S. Thomson: Real Analysis, 2008, www.classicalrealanalysis.com
- Avner Friedman: Foundations of Modern Analysis.
- Terence Tao: An Introduction to Measure Theory
- Elias M. Stein & Rami Shakarchi: Real Analysis.