Covering, measure derivation and dimensions

DOI10.4171/RMI/478zbMath1123.28001MaRDI QIDQ877802

Patrice Assouad, Thierry Quentin de Gromard

Publication date: 3 May 2007

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmi/1169480035

zbMATH Keywords

coveringssymmetric kernelDe Groot dimensionderivation of measuresNagata dimension

Mathematics Subject Classification ID

Topological spaces with richer structures (54E99) Dimension theory in general topology (54F45) Abstract differentiation theory, differentiation of set functions (28A15)

Related Items (3)

Is the \(k\)-NN classifier in high dimensions affected by the curse of dimensionality? ⋮ Universal consistency of the k-NN rule in metric spaces and Nagata dimension ⋮ Lower large deviations for the maximal flow through a domain of \({\mathbb{R}^d}\) in first passage percolation

Cites Work

• Differentiation of integrals in \(\mathbb{R}^n\)
• Sphere packings give an explicit bound for the Besicovitch covering theorem
• Foundations for the theory of quasiconformal mappings on the Heisenberg group
• Weak convergence and empirical processes. With applications to statistics
• On a Metric that Characterizes Dimension
• On measure derivation in metric spaces
• Plongements lipschitziens dans ${\bbfR}\sp n$
• Subadditivity of Homogeneous Norms on Certain Nilpotent Lie Groups
• Weakly Differentiable Functions
• Weighted Inequalities for Fractional Integrals on Euclidean and Homogeneous Spaces
• On the Best Constant for the Besicovitch Covering Theorem
• A conjecture of J. Nagata on dimension and metrization
• On a special metric and dimension
• A Proof That Henstock's Integral Includes Lebesgue's
• Perfect Blankets
• A general form of the covering principle and relative differentiation of additive functions
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