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Journal of Geometric Analysis

, Volume 19, Issue 1, pp 1–18 | Cite as

Discrete Approximation of Spaces of Homogeneous Type

  • Hugo Aimar
  • Marilina CarenaEmail author
  • Bibiana Iaffei
Article

Abstract

In this note we combine the dyadic families introduced by M. Christ in (Colloq. Math. 60/61(2):601–628, 1990) and the discrete partitions introduced by J.M. Wu in (Proc. Am. Math. Soc. 126(5):1453–1459, 1998) to get approximation of a compact space of homogeneous type by a uniform sequence of finite spaces of homogeneous type. The convergence holds in the sense of a metric built on the Hausdorff distance between compact sets and on the Kantorovich-Rubinshtein metric between measures.

Keywords

Quasi-metric space Doubling measure Space of homogeneous type 

Mathematics Subject Classification (2000)

28A33 60B10 

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Copyright information

© Mathematica Josephina, Inc. 2008

Authors and Affiliations

  1. 1.Departamento de Matemática (FIQ-UNL)Instituto de Matemática Aplicada del Litoral (CONICET-UNL)Santa FeArgentina
  2. 2.Departamento de Matemática (FHUC-UNL)Instituto de Matemática Aplicada del Litoral (CONICET-UNL)Santa FeArgentina

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