Subject: 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.
10 lectures with exercises
To be announced later
Jon Johnsen, email: email@example.com
Jon Johnsen, Aalborg University
Fredrik Bajers Vej 7G, room G5-109
Number of seats:
August 12, 2013
Important information concerning PhD courses
We have over some time experienced problems with no-show for both project and general courses. It has now reached a point where we are forced to take action. Therefore, the Doctoral School has decided to introduce a no-show fee of DKK 5,000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately three months before start. This can hopefully also provide new students a chance to register for courses during the year. We look forward to your registrations.
- Teacher: Jon Johnsen