On s-sets in spaces of homogenous type

CARENA MARILINA, TOSCHI MARISA

COLLOQUIUM MATHEMATICUM

IMPAN

Año: 2015 vol. 138 p. 193 - 203

0010-1354

Let $(X,d,mu)$ be a space of homogeneous type. In this note 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 we have that F is s-set relative to the measure $mu$ if and only if F is s-set relative to delta. Here delta denotes the quasi-distance defined by Macías and Segovia such that $(X,delta,mu)$ is a normal space. In order to prove this result, we show a covering type lemma and a type of Hausdorff measure based criteria for the s-set condition relative to $mu$ of a given set.