Existence of subset with given Hausdorff dimensionQuestion on geometric measure theorySubsets of sets of positive Hausdorff dimension with controlled upper Minkowski dimensionHow can dimension depend on the point?Multiplicity of a subcovering in spaces of given Hausdorff dimensionHausdorff dimension of sequence spaceConstruction of null sets with prescribed Hausdorff dimension and generalizationsHausdorff dimension of boundaries of open sets diffeomorphic to $mathbbR^n$Hausdorff approximating measures and Borel setsWhen is Hausdorff measure locally finite?Existence of a discrete subset
Existence of subset with given Hausdorff dimension Question on geometric measure theorySubsets of sets of positive Hausdorff dimension with controlled upper Minkowski dimensionHow can dimension depend on the point?Multiplicity of a subcovering in spaces of given Hausdorff dimensionHausdorff dimension of sequence spaceConstruction of null sets with prescribed Hausdorff dimension and generalizationsHausdorff dimension of boundaries of open sets diffeomorphic to $mathbbR^n$Hausdorff approximating measures and Borel setsWhen is Hausdorff measure locally finite?Existence of a discrete subset 9 $begingroup$ Let $Asubseteq mathbbR$ be Lebesgue-measurable and let $0<alpha<1$ be its Hausdorff dimension. For a given $0<beta <alpha$ can we find a subset $Bsubset A$ with Hausdorff dimension $beta$ ? In case this is true, could you provide a reference for this statement? Added: Actually I am happy if $A$ is compact. reference-request geometric-measure-theory