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| MATH0209-3 | Measure Theory
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| Duration : | 30h Th, 10h Pr, 20h Mon. WS |
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| Number of credits : |
| Master in Mathematical Sciences, in-depth approach, 1st year | | First semester | | 8 |
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| Master in Mathematical Sciences, didactic approach, 1st year | | First semester | | 8 |
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| Master in Mathematical Sciences, professional focus in management, 1st year | | First semester | | 8 |
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| Master in Mathematical Sciences, professional focus in computer science, 1st year | | First semester | | 8 |
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| Master en sciences mathématiques, à finalité spécialisée en statistiques, 1st year | | First semester | | 8 |
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| Master in Mathematical Sciences, specialized approach, 1st year | | First semester | | 8 |
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| Master in Mathematical Sciences | | Toute l'année | | 8 |
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| Master in Mathematical Sciences | | First semester | | 8 |
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| Lecturer : | Samuel Nicolay |
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Language(s) of instruction :
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| French language |
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Course contents :
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| 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. |
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Learning outcomes of the course :
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| 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).
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Prerequisites and co-requisites/ Recommended optional programme components :
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| Analysis I, General Topology |
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Planned learning activities and teaching methods :
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| The exercises are directed by the assistants.
The theory presented in the cours is complemented by several examples and exercises. |
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Mode of delivery (face-to-face ; distance-learning) :
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| The course will be given during the first semester. The timetable will be available at the beginning of the academic year. |
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Recommended or required readings :
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| Course notes, following the main taught subjects, are aviable at the beginning of the year. |
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Assessment methods and criteria :
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| Oral examination. |
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Contacts :
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| 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) |
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