Teaching directory
Course 2022-2023

Measure and Integration Theory [SMATB302]

  • 6 credits
  • 30h+30h
  • 1st quarter
Language of instruction: French / Français
Teacher: Winkin Joseph

Learning outcomes

The first part of the course presents the main results of the Measure and Integration theory within the framework of measured spaces. The second part deals with the theory of the Fourier transform of Lebesgue integrable functions, as well as the Laplace transform.

Objectives

The objective is to introduce to the theory of the Lebesgue integral, and to show the main contributions of this theory compared to the Riemann integral.

Content

The table of contents consists of ten chapters: Introduction. Measurable space and measure function. Measurable functions. Integral of a non-negative measurable function. Integrated functions. Lp spaces. Lebesgue measurement on R. Product measurement. Fourier transform in L1. Fourier transform in L2. La place transform.
 

Table of contents

The table of contents consists of ten chapters: I. Introduction. II. Measure and measured space. III. Measurable functions. IV. Integral of a non-negative measurable function. V. Integrable functions. VI. Lp spaces. VII. Lebesgue measurement on R. VIII. Product space. IX. Fourier transform in L1. X. Fourier transform in L2. Laplace transform.
 

Exercises description

Illustration of the concepts and results of the course.


Prerequisites

Analyse réelle II [SMATB102] et Analyse réelle I [SMATB103]

Teaching methods

Lecture. A theory syllabus and an exercise syllabus are available on webcampus.unamur.be
 

Evaluations

The evaluation has two parts. 1) An individual oral exam which aims to assess the student's knowledge and level of understanding of the course (definitions, statements and demonstrations of theorems, summary questions ...). 2) A written exercise exam which aims to test the student's ability to apply the results seen in the course. If the student obtains a mark higher than 10/20 in the written and oral exams, the final mark is the arithmetic mean of the marks. Otherwise, the final dimension is the integer part of the geometric mean of the dimensions, with at least 7/20 or more for each part of the exam (=> minimum of both marks).
 

Recommended readings

"Measure Theory - A first Course", Carlos S. Kubrusly, Elsevier, 2007

"Measure Theory", Paul R. Halmos, Springer, 1974

"Measure Theory", J.L. Doob, Springer, 1993

 

Language of instruction

French / Français

Location for course

NAMUR

Organizer

Faculté des sciences
Rue de Bruxelles, 61
5000 NAMUR

Degree of Reference

Undergraduate Degree