We continue our study of projections by showing what can happen when we take projections, which is essentially anything! In particular, we cover the miraculous Falconer Sundial, a theorem that says we can make sets with projections equal to whatever want (up to Lebesgue measure zero). This is based on the classical method of Venetian Blinds.
- Notes: Venetian Blinds, Sundials and Duality
Alternatively: Read 18.3 of Mattila and Falconer 7.1, 7.3-7.5. - Videos: Venetian Blinds, Sundials
- Exercises and Partial Solutions(prepare 1,2,4, and 5)