On Lebesgue null sets

2019/04/28 by De Pauw, Thierry
#26B15 #28A75 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1904.12276

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 A ∩ W(x) has m dimensional Hausdorff measure vanishing for almost every x.

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