A Lipschitz function is a map that does not increase distance between points more than a multiplicative factor. They are generalizations of C^{1} functions: while they aren?t necessarily differentiable, they are almost everywhere, and with the benefit that they are easier to construct and can be defined between arbitrary metric spaces.

- Notes (Alternatively Chapter 7 in Mattila and the section on the lip bi-lip theorem in David’s book.)
- Videos: SVD, Rademacher’s Theorem, Dorronsoro’s Theorem, Arzela-Ascoli, Extensions, Sard’s Theorem, Lip bi-Lip, Area Formulas and Level Sets

(No need to watch the proof of the Lip bi-Lip theorem, but be familiar with the statement) - Exercises, prepare any 4 problems.