Complement of studies in the theory of measurement

Duration

30h Th, 10h Pr, 20h Mon. WS

Number of credits

Lecturer

Samuel Nicolay

Language(s) of instruction

French language

Organisation and examination

Teaching in the second semester

Schedule

Schedule online

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, hybrid 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.

Organisational adjustments related to the current health context

Recommended or required readings

Course notes, following the main taught subjects, are aviable at the beginning of the year.

Assessment methods and criteria

Below you will find information on the evaluation methods planned for in-person and remote exams as well as those planned for hybrid sessions. Depending on how the health crisis evolves, the chosen method will be communicated to you no later than one month before the start of the exam session.

Oral examination.

Work placement(s)

Organizational remarks

In case of restrictions related to a health crisis, the teaching can be adapted in order to respect the imposed constraints. For example the flipped classroom strategy could be adopted.

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