Thin and fat sets for doubling measures in metric spaces

Tuomo Ojala, Tapio Rajala, and Ville Suomala. "Thin and fat sets for doubling measures in metric spaces." Studia Mathematica 208.3 (2012): 195-211. <http://eudml.org/doc/285930>.

@article{TuomoOjala2012,
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.},
author = {Tuomo Ojala, Tapio Rajala, Ville Suomala},
journal = {Studia Mathematica},
keywords = {doubling measure; uniformly perfect metric space; thin set; fat set; doubling metric space},
language = {eng},
number = {3},
pages = {195-211},
title = {Thin and fat sets for doubling measures in metric spaces},
url = {http://eudml.org/doc/285930},
volume = {208},
year = {2012},
}

TY - JOUR
AU - Tuomo Ojala
AU - Tapio Rajala
AU - Ville Suomala
TI - Thin and fat sets for doubling measures in metric spaces
JO - Studia Mathematica
PY - 2012
VL - 208
IS - 3
SP - 195
EP - 211
AB - 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.
LA - eng
KW - doubling measure; uniformly perfect metric space; thin set; fat set; doubling metric space
UR - http://eudml.org/doc/285930
ER -