## Abstract

We provide sufficient conditions for a set E ⊂ ℝ
^{n} to be a non-universal differentiability set, i.e., to be contained in the set of points of non-differentiability of a real-valued Lipschitz function. These conditions are motivated by a description of the ideal generated by sets of non-differentiability of Lipschitz self-maps of ℝ
^{n} given by Alberti, Csörnyei and Preiss, which eventually led to the result of Jones and Csörnyei that for every Lebesgue null set E in ℝ
^{n} there is a Lipschitz map f: ℝ
^{n} → ℝ
^{n} not differentiable at any point of E, even though for n > 1 and for Lipschitz functions from ℝ
^{n} to ℝ there exist Lebesgue null universal differentiability sets. Among other results, we show that the new class of Lebesgue null sets introduced here contains all uniformly purely unrectifiable sets and gives a quantified version of the result about non-differentiability in directions outside the decomposability bundle with respect to a Radon measure.

Original language | English |
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Pages (from-to) | 75-108 |

Number of pages | 34 |

Journal | Israel Journal of Mathematics |

Volume | 232 |

Issue number | 1 |

Early online date | 30 Apr 2019 |

DOIs | |

Publication status | Published - Aug 2019 |

## ASJC Scopus subject areas

- General Mathematics