201. Projections of random covering sets
- Author
-
Changhao Chen, Henna Koivusalo, Ville Suomala, and Bing Li
- Subjects
Class (set theory) ,Sequence ,Applied Mathematics ,Probability (math.PR) ,Orthographic projection ,Dynamical Systems (math.DS) ,Covering set ,Linear subspace ,60D05, 28A78, 28A80 ,Combinatorics ,Dimension (vector space) ,Mathematics - Classical Analysis and ODEs ,Hausdorff dimension ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,Almost surely ,Geometry and Topology ,Mathematics - Dynamical Systems ,Mathematics - Probability ,Mathematics - Abstract
We show that, almost surely, the Hausdorff dimension $s_0$ of a random covering set is preserved under all orthogonal projections to linear subspaces with dimension $k>s_0$. The result holds for random covering sets with a generating sequence of ball-like sets, and is obtained by investigating orthogonal projections of a class of random Cantor sets., 17 pages
- Published
- 2014