MEASURE THEORY
| Title | ΘΕΩΡΙΑ ΜΕΤΡΟΥ ΚΑΙ ΟΛΟΚΛΗΡΩΣΗΣ / MEASURE THEORY |
| Code | Θ017 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Dimitrios Ntalampekos |
| Common | No |
| Status | Active |
| Course ID | 600025906 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2025-2030)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Elective Courses belonging to the selected specialization | Winter | - | 10 |
| Academic Year | 2025 – 2026 |
| Class Period | Winter |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600268383
|
Course Type 2021
General Foundation
Course Type 2011-2015
General Foundation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600268383
- eLearning: https://elearning.auth.gr/course/view.php?id=8303
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
Course Content (Syllabus)
Outer Lebesgue measure, measurable sets, measurable functions, integrable functions. Fubini's theorem. Modes of convergence. Hardy-Littlewood inequality, Lebesgue differentiation theorem and application to convolution kernels. Differentiability of increasing functions, functions of bounded variation, absolutely continuous functions, fundamental theorem of calculus. Abstract measure theory, Carathéodory's theorem, absolutely continuous and singular measures, Radon-Nikodym theorem.
Keywords
Lebesgue measure, integral, Fubini's theorem, Hardy-Littlewoord inequality, Lebesgue differentiation theorem, absolutely continuous functions, functions of bounded variation, absolutely continuous measures, singular measures, Radon-Nikodym theorem
Educational Material Types
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | ||||
| Reading Assigment | 258 | ||||
| Exams | 3 | ||||
| Total | 300 |
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. E. M. Stein and R. Shakarchi, Real Analysis: Measure Theory, Integration, and Hilbert Spaces, Princeton University Press, 2005.
2. Gerald B. Folland, Real Analysis: Modern Techniques and Applications, Wiley Interscience, second ed., 1999.
Last Update
15-09-2025
