Thin and fat sets for doubling measures in metric spaces
Volume 208 / 2012
Studia Mathematica 208 (2012), 195-211
MSC: Primary 28A12; Secondary 30L10.
DOI: 10.4064/sm208-3-1
Abstract
We consider sets in uniformly perfect metric spaces which are null for every doubling measure of the space or which have positive measure for all doubling measures. These sets are called thin and fat, respectively. In our main results, we give sufficient conditions for certain cut-out sets being thin or fat.
