ar X iv : m at h / 05 05 09 9 v 1 [ m at h . D S ] 5 M ay 2 00 5 Hausdorff Dimension , its properties , and its surprises


We review the motivation and fundamental properties of the Hausdorff dimension of metric spaces and illustrate this with a number of examples, some of which are expected and wellknown. We also give examples where the Hausdorff dimension has some surprising properties: we construct a set E ⊂ C of positive planar measure and with dimension 2 such that each… (More)


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