Universal Measure Zero, Large Hausdorff Dimension, and Nearly Lipschitz Maps
نویسنده
چکیده
We prove that each analytic set in R contains a universally null set of the same Hausdorff dimension and that each metric space contains a universally null set of Hausdorff dimension no less than the topological dimension of the space. Similar results also hold for universally meager sets. An essential part of the construction involves an analysis of Lipschitzlike mappings of separable metric spaces onto Cantor cubes and selfsimilar sets.
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