Discrete Approximation of Spaces of Homogeneous Type |
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Authors: | Hugo Aimar Marilina Carena Bibiana Iaffei |
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Institution: | (1) Departamento de Matemática (FIQ-UNL), Instituto de Matemática Aplicada del Litoral (CONICET-UNL), Santa Fe, Argentina;(2) Departamento de Matemática (FHUC-UNL), Instituto de Matemática Aplicada del Litoral (CONICET-UNL), Santa Fe, Argentina |
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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.
The authors were supported by CONICET, CAI+D (UNL) and ANPCyT. |
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Keywords: | Quasi-metric space Doubling measure Space of homogeneous type |
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