List questions from hausdorff-measure

Published on 11 Jan 2017 - 20:00

137

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Real analysis - property of Hausdorff dimension

Published on 28 Jan 2017 - 20:52

387

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How to prove that the unit sphere $\Bbb S^1$ has Hausdorff dimension $1$?

Published on 22 Mar 2026 - 9:56

2.4k

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How would you calculate the Fractal Dimension of this asymmetric Cantor Set?

Published on 14 Feb 2017 - 9:21

70

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Example with ${\rm vol}\ D>\lim_i\ {\rm vol}\ D_i$

Published on 25 Mar 2026 - 7:41

38

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How are these sums called?

Published on 05 Mar 2017 - 7:15

326

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Is the convergence in Hausdorff distance closed under union and intersection?

Published on 09 Mar 2017 - 19:53

137

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Inverse image (under convex-hull operator) of an open set of convex subsets is open?

Published on 10 Mar 2017 - 18:06

199

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Is convex-hull operation an open mapping?

Published on 10 Mar 2017 - 21:04

37

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Why is this true that $\left(d(Q)\right)^n=\left(\sqrt{n}\right)^n\mathcal{L}_n(Q)$ for any cube $Q$ in $\mathbb{R}^n$?

Published on 11 Mar 2017 - 17:57

1k

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Is the zero set of Brownian motion homeomorphic to Cantor space?

Published on 29 Mar 2017 - 18:24

584

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Questions about Hausdorff measure and general metric outer measures.

Published on 04 Apr 2017 - 22:51

129

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Is this 'one of' the smallest open sets that contains the original set?

Published on 07 Apr 2017 - 20:21

187

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Proof clarification of hausdorff measure equals lebesgue measure in one dimension

Published on 29 Jan 2023 - 21:00

134

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Sufficient condition for a set to be a Reduced Boundary

Published on 19 Feb 2023 - 11:22

List Question

Invers limit function.

Real analysis - property of Hausdorff dimension

How to prove that the unit sphere $\Bbb S^1$ has Hausdorff dimension $1$?

How would you calculate the Fractal Dimension of this asymmetric Cantor Set?

Example with ${\rm vol}\ D>\lim_i\ {\rm vol}\ D_i$

How are these sums called?

Is the convergence in Hausdorff distance closed under union and intersection?

Inverse image (under convex-hull operator) of an open set of convex subsets is open?

Is convex-hull operation an open mapping?

Why is this true that $\left(d(Q)\right)^n=\left(\sqrt{n}\right)^n\mathcal{L}_n(Q)$ for any cube $Q$ in $\mathbb{R}^n$?

Is the zero set of Brownian motion homeomorphic to Cantor space?

Questions about Hausdorff measure and general metric outer measures.

Is this 'one of' the smallest open sets that contains the original set?

Proof clarification of hausdorff measure equals lebesgue measure in one dimension

Sufficient condition for a set to be a Reduced Boundary

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