# Thin and fat sets for doubling measures in metric spaces

## Ojala Tuomo - Rajala Tapio - Suomala Ville

published
year: 2012
journal: Studia Math.
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.

The paper is available on the cvgmt preprint server.