List questions from hausdorff-measure

Published on 11 May 2021 - 15:51

275

Views

To show countable sub-additivity of the Hausdorff measure on $\mathbb R^n$

Published on 16 May 2021 - 10:34

397

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Hausdorff dimension of unit closed ball of $ \mathbb{R}^n$ is $n$

Published on 25 May 2021 - 8:06

221

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Metric dimensions properties not in $\mathbb{R}^d$

Published on 03 Jun 2021 - 9:06

74

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Are the non-empty finite bounded subsets of $\mathbb{R}^2$ complete with respect to the Hausdorff metric?

Published on 07 Jun 2021 - 15:40

148

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Measurability of Hausdorff measure under bi-Lipschitz mappings

Published on 26 Mar 2026 - 9:42

624

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How do I calculate the Hausdorff $2$-measure of a square directly?

Published on 24 Jun 2021 - 3:08

46

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$\mathcal{H}^{d-1}(A)<+\infty\implies \mu(A)=0$ and set where Lipschitz map is not differentiable

Published on 29 Jun 2021 - 21:25

254

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Why is the Hausdorff measure defined the way it is? And how can it be computed?

Published on 05 Aug 2021 - 19:47

51

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Can we take a Cantor set as a witness of inner regularity?

Published on 17 Aug 2021 - 3:14

161

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Does Hausdorff measure have a physical meaning?

Published on 03 Nov 2021 - 5:45

46

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Union of one-dimensional family of straight lines has zero measure

Published on 01 Dec 2021 - 23:23

133

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metric tensor and diffeomorphism

Published on 09 Dec 2021 - 20:01

33

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Heuristic 'characterization' of Hausdorff dimension

Published on 10 Dec 2021 - 13:07

94

Views

Does non-zero and finite Hausdorff dimension imply non-zero and finite Hausdorff measure?

Published on 04 Jan 2022 - 15:42

List Question

Hausdorff Dimension of a set in R under the image of Continous map

To show countable sub-additivity of the Hausdorff measure on $\mathbb R^n$

Hausdorff dimension of unit closed ball of $ \mathbb{R}^n$ is $n$

Metric dimensions properties not in $\mathbb{R}^d$

Are the non-empty finite bounded subsets of $\mathbb{R}^2$ complete with respect to the Hausdorff metric?

Measurability of Hausdorff measure under bi-Lipschitz mappings

How do I calculate the Hausdorff $2$-measure of a square directly?

$\mathcal{H}^{d-1}(A)<+\infty\implies \mu(A)=0$ and set where Lipschitz map is not differentiable

Why is the Hausdorff measure defined the way it is? And how can it be computed?

Can we take a Cantor set as a witness of inner regularity?

Does Hausdorff measure have a physical meaning?

Union of one-dimensional family of straight lines has zero measure

metric tensor and diffeomorphism

Heuristic 'characterization' of Hausdorff dimension

Does non-zero and finite Hausdorff dimension imply non-zero and finite Hausdorff measure?

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