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.

Full text not available from this repository.

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
Divisions :	Surrey research (other units)
Authors :	Name Email ORCID Shmerkin, P p.shmerkin@surrey.ac.uk Suomala, V
Date :	26 April 2012
Related URLs :	Author
Depositing User :	Symplectic Elements
Date Deposited :	17 May 2017 12:24
Last Modified :	24 Jan 2020 22:10
URI:	http://epubs.surrey.ac.uk/id/eprint/835186

Actions (login required)

View Item

Downloads