A GENERALIZATION OF HAUSDORFF DIMENSION APPLIED TO HILBERT CUBES AND WASSERSTEIN SPACES

DOI10.1142/S1793525312500094zbMath1257.54034arXiv1105.0360MaRDI QIDQ3166254

Benoît R. Kloeckner

Publication date: 10 October 2012

Published in: Journal of Topology and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.0360

zbMATH Keywords

Hausdorff metricHausdorff dimensiontopological entropyoptimal transportWasserstein spacemetric mean dimensionbi-Lipschitz embeddingsHilbert cubesCarathéodory's constructioninfinite-dimensional metric spaces

Mathematics Subject Classification ID

Hyperspaces in general topology (54B20) Dimension theory in general topology (54F45) Hausdorff and packing measures (28A78)

Related Items (9)

On emergence and complexity of ergodic decompositions ⋮ Isometric rigidity of Wasserstein spaces: The graph metric case ⋮ Extending the reach of the point-to-set principle ⋮ Isometric rigidity of Wasserstein tori and spheres ⋮ Subsets of positive and finite \(\Psi_t\)-Hausdorff measures and applications ⋮ Complexities of differentiable dynamical systems ⋮ Isometric study of Wasserstein spaces – the real line ⋮ A GEOMETRIC STUDY OF WASSERSTEIN SPACES: ULTRAMETRICS ⋮ A linear stochastic biharmonic heat equation: hitting probabilities

Cites Work

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• Spaces of largest Hausdorff dimension
• Generalized Hausdorff dimension
• SOME HAUSDORFF MEASURE PROPERTIES OF THE SPACE OF COMPACT SUBSETS OF [0,1]
• Optimal Transport

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