A+ CATEGORY SCIENTIFIC UNIT

On $s$-sets in spaces of homogeneous type

Volume 138 / 2015

Marilina Carena, Marisa Toschi Colloquium Mathematicum 138 (2015), 193-203 MSC: Primary 28A05; Secondary 28A78. DOI: 10.4064/cm138-2-4

Abstract

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 $.

Authors

  • Marilina CarenaInstituto de Matemática Aplicada
    del Litoral (CONICET-UNL)
    Departamento de Matemática (FHUC-UNL)
    Santa Fe, Argentina
    e-mail
  • Marisa ToschiInstituto de Matemática Aplicada
    del Litoral (CONICET-UNL)
    Departamento de Matemática (FIQ-UNL)
    Santa Fe, Argentina
    e-mail

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