On s-sets in spaces of homogeneous type

Marilina Carena, and Marisa Toschi. "On s-sets in spaces of homogeneous type." Colloquium Mathematicae 138.2 (2015): 193-203. <http://eudml.org/doc/284025>.

@article{MarilinaCarena2015,
abstract = {Let (X,d,μ) be a space of homogeneous type. We study the relationship between two types of s-sets: relative to a distance and relative to a measure. We find a condition on a closed subset F of X under which F is an s-set relative to the measure μ if and only if F is an s-set relative to δ. Here δ denotes the quasi-distance defined by Macías and Segovia such that (X,δ,μ) is a normal space. In order to prove this result, we prove a covering type lemma and a type of Hausdorff measure based criterion for a given set to be an s-set relative to μ.},
author = {Marilina Carena, Marisa Toschi},
journal = {Colloquium Mathematicae},
keywords = {space of homogeneous type; -sets; Hausdorff measure},
language = {eng},
number = {2},
pages = {193-203},
title = {On s-sets in spaces of homogeneous type},
url = {http://eudml.org/doc/284025},
volume = {138},
year = {2015},
}

TY - JOUR
AU - Marilina Carena
AU - Marisa Toschi
TI - On s-sets in spaces of homogeneous type
JO - Colloquium Mathematicae
PY - 2015
VL - 138
IS - 2
SP - 193
EP - 203
AB - Let (X,d,μ) be a space of homogeneous type. We study the relationship between two types of s-sets: relative to a distance and relative to a measure. We find a condition on a closed subset F of X under which F is an s-set relative to the measure μ if and only if F is an s-set relative to δ. Here δ denotes the quasi-distance defined by Macías and Segovia such that (X,δ,μ) is a normal space. In order to prove this result, we prove a covering type lemma and a type of Hausdorff measure based criterion for a given set to be an s-set relative to μ.
LA - eng
KW - space of homogeneous type; -sets; Hausdorff measure
UR - http://eudml.org/doc/284025
ER -