Advanced Analysis
For not-so-advanced mathematicians
Preface
These notes follow the course Advanced Analysis (MAT.A0001UF) taught by Univ.-Prof. Dipl.-Ing. Dr.techn. Peter Grabner at the Institute of Analysis and Number Theory, University of Technology, Graz, as it appeared in the Winter semester 2025.
Most of the material comes from my hand-written notes from the lectures, however there are some additions to make the material (in my opinion) more understandable and/or complete. Use of additional material is always explicitly pointed out and cited. Nevertheless, I would like to thank Laura Philomena Mossböck for their LaTeX notes, which I referenced at certain points.
The typesetting was done in Quarto, and hence they come in both PDF and web versions. Feel free to use whichever feels more comfortable for you. They were put together as a preparation for the final exam, and as such are bound to contain typos and errors. I will be very happy if you report and/or fix them, either by email (stepan@zapadlo.name) or by submitting an Issue/Merge Request on the git repository.