info:eu-repo/semantics/article
Sets which are not tube null and intersection properties of random measures
Registro en:
Shmerkin, Pablo Sebastian; Suomala, Ville; Sets which are not tube null and intersection properties of random measures; Oxford University Press; Journal of the London Mathematical Society; 91; 2; 2-2015; 405-422
0024-6107
1469-7750
CONICET Digital
CONICET
Autor
Shmerkin, Pablo Sebastian
Suomala, Ville
Resumen
We show that in ℝd 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, Csörnyei 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. Fil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Suomala, Ville. Universidad de Oulu; Finlandia