 | | |
| MATH0209-3 | Measure Theory
|
|
| Duration : | 30h Th, 10h Pr, 20h Mon. WS |
|
| Number of credits : |
| Master in Mathematical Sciences, in-depth approach, 1st year | | 8 |
|
| Master in Mathematical Sciences, didactic approach, 1st year | | 8 |
|
| Master in Mathematical Sciences, professional focus in management, 1st year | | 8 |
|
| Master in Mathematical Sciences, professional focus in computer science, 1st year | | 8 |
|
| Master en sciences mathématiques, à finalité spécialisée en statistique, 1st year | | 8 |
|
| Master in Mathematical Sciences, specialized approach, 1st year | | 8 |
|
| Master in Mathematical Sciences | | 8 |
|
| Master in Mathematical Sciences | | 8 |
|
|
|
| Lecturer : | Samuel Nicolay |
|
Language(s) of instruction :
|
| French language |
|
Organisation and examination :
|
| Teaching in the first semester, review in January |
|
Course contents :
|
| Measure theory has many applications in mathematics, in particular in analysis, functional analysis, and probability theory.
The course will introduce the basic notions of measures as well as integration techniques. |
|
Learning outcomes of the course :
|
| The aims of this course are to:
- prove the results concerning the integral calculus stated during the first year of the Bachelor's degree (Analysis I),
- show the connections between the Riemann integral, the Darboux integral and the Lebesgue integral,
- if time is remaining, show some important results about the measure theory (the Radon-Nykodym theorem, the Lebesgue decomposition, the Riesz representation theorem).
|
|
Prerequisites and co-requisites/ Recommended optional programme components :
|
| Analysis I, General Topology |
|
Planned learning activities and teaching methods :
|
| The exercises are directed by the assistants.
The theory presented in the cours is complemented by several examples and exercises. |
|
Mode of delivery (face-to-face ; distance-learning) :
|
| The course will be given during the first semester. The timetable will be available at the beginning of the academic year. |
|
Recommended or required readings :
|
| Course notes, following the main taught subjects, are aviable at the beginning of the year. |
|
Assessment methods and criteria :
|
| Oral examination. |
|
Work placement(s) :
|
| |
|
Organizational remarks :
|
| |
|
Contacts :
|
| S. Nicolay
Analyse
Institut de Mathématique - Grande Traverse, 12 - Sart Tilman -Bât. B 37 - 4000 LIEGE 1
email: S.Nicolay@ulg.ac.be(S.Nicolay@ulg.ac.be)(S.Nicolay@ulg.ac.be) |
|
|
| Items online : |
|
| Théorie de la mesure |
| Notes du cours |
|
|
