On s-sets in spaces of homogeneous type

• Autorzy: Marilina Carena , Marisa Toschi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 28A78: Hausdorff and packing measures
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2015
• Tom: 138
• Numer: 2
• Strony: 193-203

Daty

wydano

2015

Twórcy

autor

Marilina Carena

• Instituto de Matemática Aplicada, del Litoral (CONICET-UNL), Departamento de Matemática (FHUC-UNL), Santa Fe, Argentina

autor

Marisa Toschi

• Instituto de Matemática Aplicada, del Litoral (CONICET-UNL), Departamento de Matemática (FIQ-UNL), Santa Fe, Argentina

Identyfikatory

DOI

10.4064/cm138-2-4