Geodesic
Universal measure zero, large Hausdorff dimension, and nearly Lipschitz maps
Ondřej Zindulka1
1 Department of Mathematics Faculty of Civil Engineering Czech Technical University Thákurova 7 160 00 Praha 6, Czech Republic
Fundamenta Mathematicae, Tome 218 (2012) no. 2, pp. 95-119

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We prove that each analytic set in $\mathbb{R}^n$ 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 Lipschitz-like mappings of separable metric spaces onto Cantor cubes and self-similar sets.
DOI : 10.4064/fm218-2-1
Keywords: prove each analytic set mathbb contains universally null set hausdorff dimension each metric space contains universally null set hausdorff dimension topological dimension space similar results universally meager sets essential part construction involves analysis lipschitz like mappings separable metric spaces cantor cubes self similar sets

Ondřej Zindulka 1

1 Department of Mathematics Faculty of Civil Engineering Czech Technical University Thákurova 7 160 00 Praha 6, Czech Republic 
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Ondřej Zindulka. Universal measure zero, large Hausdorff dimension,
and nearly Lipschitz maps. Fundamenta Mathematicae, Tome 218 (2012) no. 2, pp. 95-119. doi: 10.4064/fm218-2-1

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