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.
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.
Illustration of the concepts and results of the course.
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. 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 7/20 in the written and oral exams, the final mark is the arithmetic mean of the marks. Otherwise, the final mark is the minimum of both scores.
"Measure Theory - A first Course", Carlos S. Kubrusly, Elsevier, 2007
"Measure Theory", Paul R. Halmos, Springer, 1974
"Measure Theory", J.L. Doob, Springer, 1993
| Training | Block | Credits | Mandatory |
|---|---|---|---|
| Bachelor in Mathematics | 3 | 5 | Yes |