Approximation of spaces of homogeneous type

Abstract

In this note we combine the dyadic families introduced by M. Christ and the discrete partitions introduced by J. M. Wu in order 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 sets and on the Kantorovich-Rubinshtein metric between measures.