1 citations · 1 across the 2 of their papers we have counts for
7 papers
Schmidt's game on Hausdorff metric and function spaces: generic dimension of sets and images
Ábel Farkas, Jonathan M. Fraser, Erez Nesharim +1
We consider Schmidt's game on the space of compact subsets of a given metric space equipped with the Hausdorff metric, and the space of continuous functions equipped with the supre…
Conditional measure on the Brownian path and other random sets
Ábel Farkas
Let denote the range of the Brownian motion in (). For a deterministic Borel measure on we wish to find a random measure such…
Interval projections of self-similar sets
Ábel Farkas
We show that if is a self-similar -set that is not contained in a line and either satisfies the strong separation condition or is defined via homotheties then there are at m…
Dimension approximation of attractors of graph directed IFSs by self-similar sets
Ábel Farkas
We show that for the attractor of a graph directed iterated function system, for each and there exits a self-similar set $K\su…
On the equality of Hausdorff measure and Hausdorff content
Ábel Farkas, Jonathan M. Fraser
We are interested in situations where the Hausdorff measure and Hausdorff content of a set are equal in the critical dimension. Our main result shows that this equality holds for a…
Projections of self-similar sets with no separation condition
Ábel Farkas
We investigate how the Hausdorff dimension and measure of a self-similar set behave under linear images. This depends on the nature of the group $\mathca…
Dimension and measure for generic continuous images
Richárd Balka, Ábel Farkas, Jonathan M. Fraser +1
We consider the Banach space consisting of continuous functions from an arbitrary uncountable compact metric space, , into . The key question is `what is the gener…