COURSE INFORMATION PACKAGE · MAT351
Measure Theory
Elective · French Open to Erasmus+ exchange students
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Content Weekly Contents Assessment System ECTS
Course Instructor(s)
Can Ozan OĞUZ
canozanoguz@gmail.com
canozanoguz@gmail.com
Content
Objective
To introduce the fondamentals of measure theory, with its applications to integration theory and probability theory.
Course Content
Measures and sigma-algebras,
Borel and Lebesgue measurable sets,
Measurable functions,
Lebesgue measure on R^n,
Lebesgue integral,
Convergence theorems: Monotone Convergence Theorem (MCT), Fatou's Lemma, Dominated Convergence Theorem (DCT)
Teaching and Learning Methods
Lectures
Exercices
Discussions
References
Mesure, Intégration, Eléments d'Analyse Fonctionelle, lecture notes of Petru Mironescu, Université Claude Bernard Lyon 1:
https://math.univ-lyon1.fr/~mironescu/resources/complet_mesure_integration.pdf
Weekly Contents
| Week | Weekly Contents |
|---|---|
| 1 | Review of Riemann Integral, Motivation for the need of a more general theory |
| 2 | sigma-algebras, Borel sets |
| 3 | Measurable functions |
| 4 | Measures |
| 5 | Negligable sets, Lebesgue measure |
| 6 | Constrution of Lebesgue measure |
| 7 | Integral of a measurable function |
| 8 | Midterm |
| 9 | Integral of a measurable function, Monotone Convergence Theorem |
| 10 | Integration |
| 11 | Fatou's Lemma, Dominated Convergence Theorem |
| 12 | Product measure |
| 13 | Fubini-Tonelli Theorem |
| 14 | Fubini-Tonelli Theorem |
Assessment System
| Activities | Number | Contribution |
|---|---|---|
| Contribution of in-term studies to overall grade | 3 | 60 |
| Contribution of final exam to overall grade | 1 | 40 |
| Total | 4 | 100 |
| Activities | Number | Contribution |
|---|---|---|
| Assignments | 2 | 30 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 30 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 0 | 0 |
| Term Paper/ Project | 0 | 0 |
| Portfolio Study | 0 | 0 |
| Reports | 0 | 0 |
| Learning Diary | 0 | 0 |
| Thesis/ Project | 0 | 0 |
| Seminar | 0 | 0 |
| Other | 0 | 0 |
| Make-up | 0 | 0 |
| Total | 3 | 60 |
ECTS
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 3 | 42 |
| Working Hours out of Class | 14 | 3 | 42 |
| Assignments | 4 | 5 | 20 |
| Presentation | 0 | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 6 | 6 |
| Project | 0 | 0 | 0 |
| Laboratory | 0 | 0 | 0 |
| Other Applications | 0 | 0 | 0 |
| Final Examinations (including preparation) | 1 | 10 | 10 |
| Quiz | 0 | 0 | 0 |
| Term Paper/ Project | 0 | 0 | 0 |
| Portfolio Study | 0 | 0 | 0 |
| Reports | 0 | 0 | 0 |
| Learning Diary | 0 | 0 | 0 |
| Thesis/ Project | 0 | 0 | 0 |
| Seminar | 0 | 0 | 0 |
| Other | 0 | 0 | 0 |
| Make-up | 0 | 0 | 0 |
| Yıl Sonu | 0 | 0 | 0 |
| Hazırlık Yıl Sonu | 0 | 0 | 0 |
| Hazırlık Bütünleme | 0 | 0 | 0 |
| Total Workload | 120 | ||
| Total Workload / 25 | 4.80 | ||
| Credits ECTS | 5 | ||