MATS111 Measure and Integration Theory 1 (5 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
Lebesgue measure and measurable sets, Lebesgue integral and integrable functions, the connection between Lebesgue integral and Riemann integral, convergence theorems, absolutely continuous functions.
Learning outcomes
After the course one is able
- to define Lebesgue measure and integral
- to study integrability of a function
- to establish and employ basic properties of Lebesgue measure
- to state, prove, and apply the most important convergence theorems
- to explain the relations between Lebesgue and Riemann integrals
Description of prerequisites
Introduction to mathematical analysis 3, Vector calculus 2, Vector analysis 1
Study materials
Luentomoniste
Literature
- Bruce D. Craven: Lebesgue measure and integral
- Elias M. Stein & Rami Shakarchi: Real Analysis.
- Andrew M. Bruckner, Judith B. Bruckner & Brian S. Thomson: Real Analysis, 2008, www.classicalrealanalysis.com
- Terence Tao: An Introduction to Measure Theory
- Friedman: Foundations of Modern Analysis.
Completion methods
Method 1
Evaluation criteria:
Exam after the lectures. Extra benefits from approved homework assignments.
Time of teaching:
Period 1
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 (5 cr)
Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
Exam after the lectures. Extra benefits from approved homework assignments.
Language:
Finnish
Study methods:
28h lectures, 7 exercise sessions
Study materials:
Luentomoniste
Literature:
- Bruce D. Craven: Lebesgue measure and integral
- Elias M. Stein & Rami Shakarchi: Real Analysis.
- Andrew M. Bruckner, Judith B. Bruckner & Brian S. Thomson: Real Analysis, 2008, www.classicalrealanalysis.com
- Terence Tao: An Introduction to Measure Theory
- Friedman: Foundations of Modern Analysis.
Teaching
9/1–10/23/2022 Lectures
10/26–10/26/2022 Exam
11/9–11/9/2022 Exam
x
Exam (5 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
Study materials:
Luentomoniste
Literature:
- Bruce D. Craven: Lebesgue measure and integral
- Elias M. Stein & Rami Shakarchi: Real Analysis.
- Andrew M. Bruckner, Judith B. Bruckner & Brian S. Thomson: Real Analysis, 2008, www.classicalrealanalysis.com
- Terence Tao: An Introduction to Measure Theory
- Friedman: Foundations of Modern Analysis.