A compact null set containing a differentiability point of every Lipschitz function

Abstract

We prove that in a Euclidean space of dimension at least two, there exists a compact set of Lebesgue measure zero such that any real-valued Lipschitz function defined on the space is differentiable at some point in the set. Such a set is constructed explicitly.

28 pages; minor modifications throughout; Lemma 4.2 is proved for general Banach space rather than for Hilbert space

Cited by in corpus (3)

• Modulus and Poincaré inequalities on non-self-similar Sierpinski carpets
• Full non-differentiability sets of typical Lipschitz functions
• Typical Lipschitz mappings are typically non-differentiable