English

On Lebesgue null sets

Classical Analysis and ODEs 2019-09-24 v2

Abstract

Letting A be a Borel subset of n dimensional Euclidean space, and W(x) be an m dimensional affine subspace containing x and varying in a Lipschitz way according to x, we establish that A is Lebesgue null if and only if AW(x)A \cap W(x) has m dimensional Hausdorff measure vanishing for almost every x.

Keywords

Cite

@article{arxiv.1904.12276,
  title  = {On Lebesgue null sets},
  author = {Thierry De Pauw},
  journal= {arXiv preprint arXiv:1904.12276},
  year   = {2019}
}
R2 v1 2026-06-23T08:51:27.109Z