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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm208-3-1,
author = {Tuomo Ojala and Tapio Rajala and Ville Suomala},
title = {Thin and fat sets for doubling measures in metric spaces},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {195-211},
zbl = {1256.28001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm208-3-1}
}
Tuomo Ojala; Tapio Rajala; Ville Suomala. Thin and fat sets for doubling measures in metric spaces. Studia Mathematica, Tome 209 (2012) pp. 195-211. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm208-3-1/