CAT(0) spaces with boundary the join of two Cantor sets

Two measures on Cantor sets

We give an example of Cantor-type set for which its equilibrium measure and the corresponding Hausdorff measure are mutually absolutely continuous. Also we show that these two measures are regular in the Stahl–Totik sense. c ⃝ 2014 Elsevier Inc. All rights reserved. MSC: 30C85; 31A15; 28A78; 28A80

On Arithmetical Difference of Two Cantor Sets

We construct a large class of dynamically defined Cantor sets on the real line whose self-difference sets are Cantor sets of arbitrary positive measure. This relates to a question posed by J. Palis which arises naturally in the context of homoclinic bifurcations in dimension 2. §

Cantor sets

This paper deals with questions of how many compact subsets of certain kinds it takes to cover the space ω of irrationals, or certain of its subspaces. In particular, given f ∈ (ω\{0}), we consider compact sets of the form Q i∈ω Bi, where |Bi| = f(i) for all, or for infinitely many, i. We also consider “n-splitting” compact sets, i.e., compact sets K such that for any f ∈ K and i ∈ ω, |{g(i) : ...

Version Spaces without Boundary Sets

This paper shows that it is not necessary to main tain boundary sets to reason using version spaces Rather most of the operations typically performed on version spaces for a concept class can be tractably executed directly on the training data as long as it is tractable to solve the consistency problem for that concept class to determine whether there exists any concept in the concept class tha...

Cantor Sets with Complicated Geometryand