Add to ORKGAbstract. We prove that the packing dimension of any mean porous Radon measure on Rd may be estimated from above by a function which depends on mean porosity. The upper bound tends to d − 1 as mean porosity tends to its maximum value. This result was stated in [BS], and in a weaker form in [JJ1], but the proofs are not correct. Quite surprisingly, it turns out that mean porous measures are not necessarily approximable by mean porous sets. We verify this by constructing an example of a mean porous measure µ on R such that µ(A) = 0 for all mean porous sets A ⊂ R. 1
AbstractWe study how measures with finite lower density are distributed around (n−m)-planes in small...
We give an essentially sharp estimate in terms of generalized Hausdorff measures for images of porou...
Abstract. A. Salli proved in [14] an asymptotically sharp dimension estimate for sets in Rn with lar...
We prove that the packing dimension of any mean porous Radon measure on $mathbb R^d$ may be estimate...
We prove that the packing dimension of any mean porous Radon measure on Rd may be estimated from abo...
We prove that the packing dimension of any mean porous Radon measure on Rd may be estimated from abo...
Using probabilistic ideas, we prove that the packing dimension of a mean porous measure is strictly ...
Abstract. We introduce a notion of mean porosity for measures and obtain dimensional bounds for mean...
Abstract. We dene the class of weakly mean porous sets and prove a sharp dimension estimate for the ...
Abstract. Let X be a metric measure space with an s-regular measure µ. We prove that if A ⊂ X is ̺-p...
Porosity and dimension are two useful, but different, concepts that quantify the size of fractal set...
Abstract. Porosity and dimension are two useful, but different, concepts that quantify the size of f...
Abstract. Let X be a metric measure space with an s-regular measure . We prove that if A X is %-por...
In ${\mathsf R}^n$, we establish an asymptotically sharp upper bound for the upper Minkowski dimensi...
Abstract. In Rn, we establish an asymptotically sharp upper bound for the upper Minkowski dimension ...
AbstractWe study how measures with finite lower density are distributed around (n−m)-planes in small...
We give an essentially sharp estimate in terms of generalized Hausdorff measures for images of porou...
Abstract. A. Salli proved in [14] an asymptotically sharp dimension estimate for sets in Rn with lar...
We prove that the packing dimension of any mean porous Radon measure on $mathbb R^d$ may be estimate...
We prove that the packing dimension of any mean porous Radon measure on Rd may be estimated from abo...
We prove that the packing dimension of any mean porous Radon measure on Rd may be estimated from abo...
Using probabilistic ideas, we prove that the packing dimension of a mean porous measure is strictly ...
Abstract. We introduce a notion of mean porosity for measures and obtain dimensional bounds for mean...
Abstract. We dene the class of weakly mean porous sets and prove a sharp dimension estimate for the ...
Abstract. Let X be a metric measure space with an s-regular measure µ. We prove that if A ⊂ X is ̺-p...
Porosity and dimension are two useful, but different, concepts that quantify the size of fractal set...
Abstract. Porosity and dimension are two useful, but different, concepts that quantify the size of f...
Abstract. Let X be a metric measure space with an s-regular measure . We prove that if A X is %-por...
In ${\mathsf R}^n$, we establish an asymptotically sharp upper bound for the upper Minkowski dimensi...
Abstract. In Rn, we establish an asymptotically sharp upper bound for the upper Minkowski dimension ...
AbstractWe study how measures with finite lower density are distributed around (n−m)-planes in small...
We give an essentially sharp estimate in terms of generalized Hausdorff measures for images of porou...
Abstract. A. Salli proved in [14] an asymptotically sharp dimension estimate for sets in Rn with lar...