Μeasure Theory
| Title | ΘΕΩΡΙΑ ΜΕΤΡΟΥ ΚΑΙ ΟΛΟΚΛΗΡΩΣΗΣ / Μeasure Theory |
| Code | 0643 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter |
| Coordinator | Romanos diogenis Malikiosis |
| Common | Yes |
| Status | Active |
| Course ID | 40000031 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2018-sīmera)
Registered students: 16
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Core Courses A2 | 1 | 1 | 10 |
| Academic Year | 2021 – 2022 |
| Class Period | Winter |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Class ID | 600193589
|
Course Type 2011-2015
General Foundation
Mode of Delivery
- Face to face
Digital Course Content
Language of Instruction
- Greek (Instruction, Examination)
Course Content (Syllabus)
σ-algebras. Measures. Borel measures. Measurable and integrable functions. Modes of convergence. Product measure. Fubini's theorem. Lebesgue integral on R^n. Signed measures. Absolutely continuous and singular measures. Hahn decomposition theorem. Jordan decomposition theorem. Lebesgue-Radon-Nikodym theorem. Functions of bounded variation. Basic theory of L^p spaces.
Keywords
Lebesgue measure and integral
Educational Material Types
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | 1.3 | |||
| Reading Assigment | 259 | 8.6 | |||
| Exams | 2 | 0.1 | |||
| Total | 300 | 10 |
Student Assessment
Student Assessment methods
- Oral Exams (Summative)
- Written Exam with Problem Solving (Summative)
Bibliography
Course Bibliography (Eudoxus)
Δ. Μπετσάκος, Εισαγωγή στην Πραγματική Ανάλυση, Εκδόσεις Αφοί Κυριακίδη, 2016.
Additional bibliography for study
1. Gerald B. Folland, Real Analysis (Modern Techniques and Applications), Wiley Interscience, second ed. 1999.
2. Σημειώσεις Θεωρίας Μέτρου του Μιχ. Παπαδημητράκη (αγγλικά).
3. Σημειώσεις Θεωρίας Μέτρου του Απ. Γιαννόπουλου.
Last Update
13-03-2020
