Portal de Periódicos da CAPES

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

2010; Springer Nature; Volume: 351; Issue: 3 Linguagem: Inglês

10.1007/s00208-010-0613-4

1432-1807

Michael Doré, Olga Maleva,

Advanced Topology and Set Theory

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.