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Sets which are not tube null and intersection properties of random measures

Shmerkin, P and Suomala, V (2012) Sets which are not tube null and intersection properties of random measures arXiv.

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Abstract

We show that in $\mathbb{R}^d$ there are purely unrectifiable sets of Hausdorff (and even box counting) dimension $d-1$ which are not tube null, settling a question of Carbery, Soria and Vargas, and improving a number of results by the same authors and by Carbery. Our method extends also to "convex tube null sets", establishing a contrast with a theorem of Alberti, Cs\"{o}rnyei and Preiss on Lipschitz-null sets. The sets we construct are random, and the proofs depend on intersection properties of certain random fractal measures with curves.

Item Type: Article
Authors :
NameEmailORCID
Shmerkin, Pp.shmerkin@surrey.ac.ukUNSPECIFIED
Suomala, VUNSPECIFIEDUNSPECIFIED
Date : 26 April 2012
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 17 May 2017 12:24
Last Modified : 17 May 2017 15:03
URI: http://epubs.surrey.ac.uk/id/eprint/835186

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