How well can we partition a set if we can only partition it using a specified collection of balls? We introduce several ways of approaching this, particularly the Besicovitch Covering Theorem, then use this to study Radon-Nikodym derivatives more in depth.
- Notes (or Chapter 2 of Mattila)
- Videos: Cubes, 5r Covering Lemma, Besicovitch Covering Theorem, Vitali’s Covering Theorem Differentiation of Radon Measures
Optional Videos: Besicovitch Covering Theorem (with proof) - Exercises and Partial Solutions (prepare to discuss problems 1,2, 6, 7, 9, 10)
- Videos: Cubes, 5r Covering Lemma, Besicovitch Covering Theorem, Vitali’s Covering Theorem Differentiation of Radon Measures