Calculus of Variations and Geometric Measure Theory

N. Gigli

Pills of measure theory on Polish spaces

created by gigli on 24 Jul 2025
modified on 14 Jan 2026

[BibTeX]

Lecture Notes

Inserted: 24 jul 2025
Last Updated: 14 jan 2026

Year: 2025

Abstract:

These are notes of a short course I gave in SISSA in 2024 and have been written with the intent to give a straight to the point presentation of some fundamental results about measure theory on Polish spaces. Among others, they contain full proofs of some key theorems, such as the disintegration and Kolmogorov’s ones, that in the literature are often presented from a probabilistic perspective. Hopefully, they will convince students that, all in all, the proofs of these crucial statements fit in just a handful of pages, at least if one writes them with a sufficiently small font.

The material collected here is very classical. For more on the topic and references I shall refer to the beautiful textbooks Bog18 and Dud02.


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