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Discrete approximation of spaces of homogeneous type. (English) Zbl 1178.28002
Summary: In this note we combine the dyadic families introduced by M. Christ [Colloq. Math. 60/61, No. 2, 601–628 (1990; Zbl 0758.42009)] and the discrete partitions introduced by J. M. Wu [Proc. Am. Math. Soc. 126, No. 5, 1453–1459 (1998; Zbl 0897.28008)] 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.

28A33 Spaces of measures, convergence of measures
60B10 Convergence of probability measures
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