Add to ORKGAbstract. We prove an asymptotically sharp dimension estimate for sets with large porosity in a collection of metric spaces. This generalizes a dimension estimate first proven by A. Salli. From the metric space we assume, among other properties, that it can be locally mapped into R n in a way that allows us to use Euclidean projections. We show that Rn with any norm satisfies these conditions as well as every step two Carnot group. We also discuss the necessity of the conditions by examining various metric spaces where the estimates fail. 1
We prove that the packing dimension of any mean porous Radon measure on $mathbb R^d$ may be estimate...
For CAT(κ)-spaces with κ < 0 having nicely n-covered spheres (compare Definition 1.1) we prove th...
Abstract. We prove that the packing dimension of any mean porous Radon measure on Rd may be estimate...
Abstract. A. Salli proved in [14] an asymptotically sharp dimension estimate for sets in Rn with lar...
Abstract. In Rn, we establish an asymptotically sharp upper bound for the upper Minkowski dimension ...
In ${\mathsf R}^n$, we establish an asymptotically sharp upper bound for the upper Minkowski dimensi...
Abstract. Let X be a metric measure space with an s-regular measure µ. We prove that if A ⊂ X is ̺-p...
Abstract. Let X be a metric measure space with an s-regular measure . We prove that if A X is %-por...
Abstract. We dene the class of weakly mean porous sets and prove a sharp dimension estimate for the ...
Using probabilistic ideas, we prove that the packing dimension of a mean porous measure is strictly ...
We give an essentially sharp estimate in terms of generalized Hausdorff measures for images of porou...
AbstractFor a large class of metric spaces X including discrete groups we prove that the asymptotic ...
We introduce a notion of mean porosity for measures and obtain dimensional bounds for mean-porous an...
Abstract We study the porosity properties of fractal percolation sets E ⊂ Rd. Among other things, f...
AbstractIt is shown that every locally compact σ-compact metric space endowed with a Borel measure r...
We prove that the packing dimension of any mean porous Radon measure on $mathbb R^d$ may be estimate...
For CAT(κ)-spaces with κ < 0 having nicely n-covered spheres (compare Definition 1.1) we prove th...
Abstract. We prove that the packing dimension of any mean porous Radon measure on Rd may be estimate...
Abstract. A. Salli proved in [14] an asymptotically sharp dimension estimate for sets in Rn with lar...
Abstract. In Rn, we establish an asymptotically sharp upper bound for the upper Minkowski dimension ...
In ${\mathsf R}^n$, we establish an asymptotically sharp upper bound for the upper Minkowski dimensi...
Abstract. Let X be a metric measure space with an s-regular measure µ. We prove that if A ⊂ X is ̺-p...
Abstract. Let X be a metric measure space with an s-regular measure . We prove that if A X is %-por...
Abstract. We dene the class of weakly mean porous sets and prove a sharp dimension estimate for the ...
Using probabilistic ideas, we prove that the packing dimension of a mean porous measure is strictly ...
We give an essentially sharp estimate in terms of generalized Hausdorff measures for images of porou...
AbstractFor a large class of metric spaces X including discrete groups we prove that the asymptotic ...
We introduce a notion of mean porosity for measures and obtain dimensional bounds for mean-porous an...
Abstract We study the porosity properties of fractal percolation sets E ⊂ Rd. Among other things, f...
AbstractIt is shown that every locally compact σ-compact metric space endowed with a Borel measure r...
We prove that the packing dimension of any mean porous Radon measure on $mathbb R^d$ may be estimate...
For CAT(κ)-spaces with κ < 0 having nicely n-covered spheres (compare Definition 1.1) we prove th...
Abstract. We prove that the packing dimension of any mean porous Radon measure on Rd may be estimate...