Question

Why is $H_\delta^d$ monotone decreasing in $\delta$ in the definition of Hausdorff measure?

score 643 · Answer 1 · 2026-03-25 16:03:30

643

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Why is $H_\delta^d$ monotone decreasing in $\delta$ in the definition of Hausdorff measure?

Published on 25 Mar 2026 - 16:03

score 360 · Answer 2 · 2026-03-25 22:06:28

360

Views

After PCA, will the points on the convex hull still be on the hull in the low-dimension space?

Published on 25 Mar 2026 - 22:06

score 702 · Answer 3 · 2026-03-22 07:04:45

702

Views

Intuition behind unit hypersphere/n-ball volume

Published on 22 Mar 2026 - 7:04

score 68 · Answer 4 · 2026-03-22 05:47:41

68

Views

Will the nth Kissing Number always be the number of vertices of an uniform (or regular) n-polytope?

Published on 22 Mar 2026 - 5:47

score 237 · Answer 5 · 2026-03-21 22:08:16

237

Views

There are at least one continuous fractal from dimension 0 to 1?

Published on 21 Mar 2026 - 22:08

score 176 · Answer 6 · 2026-03-22 15:23:44

176

Views

Please, clarify relationship between Hausdorff dimension and storage space of points in Cantor sets.

Published on 22 Mar 2026 - 15:23

score 68 · Answer 7 · 2026-03-21 18:09:44

68

Views

Calculate the Minkowski dimension of a triangle

Published on 21 Mar 2026 - 18:09

score 388 · Answer 8 · 2026-03-25 19:11:20

388

Views

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

Published on 25 Mar 2026 - 19:11

score 75 · Answer 9 · 2026-03-22 15:37:58

75

Views

What is the geometric interpretation of $\mathbb{R}^{\infty}$ or function as :$f:\mathbb{R}\to \mathbb{R}$?

Published on 22 Mar 2026 - 15:37

score 722 · Answer 10 · 2026-03-22 15:55:51

722

Views

Examples of 1 and 2 dimensional.

Published on 22 Mar 2026 - 15:55

score 50 · Answer 11 · 2026-03-22 12:51:04

50

Views

Do a semiinfinite line has zero Hausdorff dimension?

Published on 22 Mar 2026 - 12:51

score 73 · Answer 12 · 2026-03-21 22:48:06

73

Views

If $K$ and $L$ are nth syzygies modules for $M$ then $K\sim L$

Published on 21 Mar 2026 - 22:48

score 599 · Answer 13 · 2026-03-22 03:45:45

599

Views

Surface and volume of an n-sphere

Published on 22 Mar 2026 - 3:45

score 313 · Answer 14 · 2026-03-21 20:23:57

313

Views

Is there any software that can exhibit 4th dimensional objects in a 4D space?

Published on 21 Mar 2026 - 20:23

score 236 · Answer 15 · 2026-03-22 13:19:15

236

Views

The Minkowki dimension of the union of two sets?

Published on 22 Mar 2026 - 13:19

List Question

Why is $H_\delta^d$ monotone decreasing in $\delta$ in the definition of Hausdorff measure?

After PCA, will the points on the convex hull still be on the hull in the low-dimension space?

Intuition behind unit hypersphere/n-ball volume

Will the nth Kissing Number always be the number of vertices of an uniform (or regular) n-polytope?

There are at least one continuous fractal from dimension 0 to 1?

Please, clarify relationship between Hausdorff dimension and storage space of points in Cantor sets.

Calculate the Minkowski dimension of a triangle

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

What is the geometric interpretation of $\mathbb{R}^{\infty}$ or function as :$f:\mathbb{R}\to \mathbb{R}$?

Examples of 1 and 2 dimensional.

Do a semiinfinite line has zero Hausdorff dimension?

If $K$ and $L$ are nth syzygies modules for $M$ then $K\sim L$

Surface and volume of an n-sphere

Is there any software that can exhibit 4th dimensional objects in a 4D space?

The Minkowki dimension of the union of two sets?

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