IFIMAR 20926
INSTITUTO DE INVESTIGACIONES FISICAS DE MAR DEL PLATA
Unidad Ejecutora - UE
artículos
Título:
On packing measures and a theorem of Besicovitch
Autor/es:
GARCIA, IGNACIO ; SHMERKIN, PABLO
Revista:
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Editorial:
AMER MATHEMATICAL SOC
Referencias:
Lugar: Providence; Año: 2014 vol. 142 p. 2661 - 2669
ISSN:
0002-9939
Resumen:
Let $mathcal{H}^h$ be the $h$-dimensional Hausdorff measure on $R^d$. Besicovitch showed that if a set $E$ is null for $mathcal{H}^h$, then it is null for $mathcal{H}^g$, for some dimension $g$ smaller than $h$. We prove that this is not true for packing measures. Moreover, we consider the corresponding questions for sets of non-$sigma$-finite packing measure, and for pre-packing measure instead of packing measure.
