Study Programmes 2015-2016
MATH0209-3  
Measure Theory
Duration :
30h Th, 10h Pr, 20h Mon. WS
Number of credits :
Master in mathematics (120 ECTS)8
Master in mathematics (120 ECTS)8
Master in mathematics (120 ECTS)8
Master in mathematics (120 ECTS)8
Master in mathematics (120 ECTS)8
Master in mathematics (120 ECTS)8
Master in mathematics (60 ECTS)8
Lecturer :
Samuel Nicolay
Language(s) of instruction :
French language
Organisation and examination :
Teaching in the first semester, review in January
Units courses prerequisite and corequisite :
Prerequisite or corequisite units are presented within each program
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).
Prerequisite knowledge and skills :
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