Measure Theory(MAT351)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| MAT351 | Measure Theory | 6 | 3 | 0 | 0 | 3 | 5 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | French |
| Course Type | Elective |
| Course Level | Bachelor Degree |
| Course Instructor(s) | Can Ozan OĞUZ canozanoguz@gmail.com (Email) |
| Assistant | |
| Objective | To introduce the fondamentals of measure theory, with its applications to integration theory and probability theory. |
| 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) |
| Course Learning Outcomes | |
| 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 |
Theory Topics
| 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 |
Practice Topics
| Week | Weekly Contents |
|---|
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 3 | 60 |
| Contribution of final exam to overall grade | 1 | 40 |
| Toplam | 4 | 100 |
In-Term Studies
| 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 |
| Toplam | 3 | 60 |
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 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 | ||