Measure Theory and probability

Objectifs

Objectives:
We will introduce the modern notion of integration established by H. Lebesgue at the beginning of the 20th century. At the end of the course, the student will be able to (among other things):
- show that a given function is measurable and integrable in the Lebesgue sense;
- use the notion of measure;
- switch a limit (or a derivative) and an integral sign;
- understand the various concepts of convergence (almost everywhere, Lp, etc);
- discuss the belonging of a given function in Lp;
- use Cauchy-Schwarz¿ and Hölder¿s inequalities;
- compute a convolution product.

Pré-requis

Évaluation

L’évaluation des acquis d’apprentissage est réalisée en continu tout le long du semestre. En fonction des enseignements, elle peut prendre différentes formes : examen écrit, oral, compte-rendu, rapport écrit, évaluation par les pairs…