**Description:** The purpose of this course is to introduce the participants to the fundamentals of the Lebesgue integral, which is a core ingredient in mathematical analysis, probability theory and quantum mechanics etc. Working with functions on general sets, we shall show that every measure (like length, area, volume, probability etc.) induce an integral on practically every function.

The classical dominated convergence theorem (parameter dependent integrals), Fubini's theorem on product integrals, Hölder's and Minkowski's inequalities, completeness of Lebesgue spaces and convolution estimates will be the main themes of the course, and in the applications. Consequences for functions on Euclidean space and stochastic variables will be emphasized.

Form: 8 lectures with exercises.

Literature: To be announced.**Organizer:** Associate Professor Jon Johnsen, e-mail: jjohsen@math.aau.dk**Lecturers:** Associate Professsor Jon Johnsen, Department of Mathematical Sciences, AAU.**ECTS:** 1.5**Time:** 7 and 28 February; 7, 14, 21 and 28 March; 4 and 11 April, 2014**Place:** Department of Mathematical Sciences, Aalborg University**Zip code: **9220**City: **Aalborg**Number of seats: ****Deadline:** 20 January, 2014

- Teacher: Jon Johnsen