Duration
30h Th, 10h Pr, 20h Mon. WS
Number of credits
| Master in mathematics (120 ECTS) | 8 crédits | |||
| Master in mathematics (60 ECTS) | 8 crédits |
Lecturer
Language(s) of instruction
French language
Organisation and examination
Teaching in the second semester
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
Measure theory has many applications in mathematics, in particular in analysis, functional analysis, and probability theory. The course will begin where the preceding ended, by introducing themes such as the theorems of Radon-Nykodym, Lebesgue, the main result being the representation theorem for linear functionals.
Learning outcomes of the learning unit
The aims of this course are to:
- show some important results about the measure theory (the Radon-Nykodym theorem, the Lebesgue decomposition, the Riesz representation theorem).
Prerequisite knowledge and skills
Analysis I, General Topology, Measure Theory.
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 second semester. The timetable will be available at the beginning of the academic year.
If the number of students is lower or equal to three, the course will consist in a personal work.
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)
Adaptation of teaching commitments following the COVID-19 pandemic for the May-June 2020 session
Teaching methods implemented : distance-learning
The necessary theory has be been taught face-to-face.
Assessment subjects
Each student has to write a project concerning measure theory. The subject has to be validated by the titular.
Assessment methods
The project will be evaluated by the titular and eventually by another member of the Mathematic Department.
Contacts
Adaptation of teaching commitments following the COVID-19 pandemic for the Aug-Sept 2020 session
Assessment subjects
Personal work. The subject must be validated by the titular
Assessment methods
Personal work.
Contacts
Items online
Théorie de la mesure
Notes du cours