Geodesic
On $s$-sets in spaces of homogeneous type
Marilina Carena 1   ; Marisa Toschi 2
1 Instituto de Matemática Aplicada del Litoral (CONICET-UNL) Departamento de Matemática (FHUC-UNL) Santa Fe, Argentina
2 Instituto de Matemática Aplicada del Litoral (CONICET-UNL) Departamento de Matemática (FIQ-UNL) Santa Fe, Argentina
Colloquium Mathematicum, Tome 138 (2015) no. 2, pp. 193-203 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $(X,d,\mu )$ 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 $\mu $ if and only if $F$ is an $s$-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 prove a covering type lemma and a type of Hausdorff measure based criterion for a given set to be an $s$-set relative to $\mu $.
DOI : 10.4064/cm138-2-4
Keywords: space homogeneous type study relationship between types s sets relative distance relative measure condition closed subset under which s set relative measure only s set relative delta here delta denotes quasi distance defined mac segovia delta normal space order prove result prove covering type lemma type hausdorff measure based criterion given set s set relative

Marilina Carena  1   ; Marisa Toschi  2

1 Instituto de Matemática Aplicada del Litoral (CONICET-UNL) Departamento de Matemática (FHUC-UNL) Santa Fe, Argentina
2 Instituto de Matemática Aplicada del Litoral (CONICET-UNL) Departamento de Matemática (FIQ-UNL) Santa Fe, Argentina 
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Marilina Carena; Marisa Toschi. On $s$-sets in spaces of homogeneous type. Colloquium Mathematicum, Tome 138 (2015) no. 2, pp. 193-203. doi: 10.4064/cm138-2-4

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