Mass und Integral - 2020

Dave, 24.08., 15:00 - 15:20

First, I had to prove that every metric measure on \( \mathbb{R}^n \) is a Borel measure. Prof. Da Lio only wanted to hear the proof and wasn't interested in additional things around the statement (e.g. didn't want to hear why we only have to consider closed sets). Then I just copied the proof from the lecture notes and when I came to the step, where one has to show that \( \sum_{l=k}^\infty R_{l} < \infty \), she stopped me and moved on.

The second question was about what types of convergence there are and their relations. I mentioned convergence \(\mu\)-a.e. and convergence in measure and proved (again, just copying the script word by word) that convergence \(\mu\)-a.e. implies convergence in measure. To my surprise I didn't have to show the converse direction (conv. in measure yields subsequence with conv. \(\mu\)-a.e.) and she ended the exam there.

During the exam, Prof. Da Lio only spoke when she posed her questions, or when I asked her if I have to explain something more explicit, to which the answer was always no. Otherwise she just sat there and didn't show any reaction. As long as you just present things like they are in the script, she seems to be happy with it.