3 Notes on Metrics , Measures , and Dimensions

Preface In this monograph various notions related to metric spaces are considered, including Hausdorff-type measures and dimensions, Lipschitz mappings, and the Hausdorff distance between nonempty closed and bounded subsets of a metric space. Some familiarity with basic topics in analysis such as Riemann integrals, open and closed sets, and continuous functions is assumed, as in [60, 100, 187], for instance. There is no attempt to be exhaustive in any way, and more information in a variety of directions can be found in the bibliography. ii Contents Preface ii 1 Metric spaces 1 1.