Question

What is the definition of $s$-dimensional Lebesgue measure on $R^d$ for $s\ne d$?

score 114 · Answer 1 · 2018-04-10 12:34:18

114

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What is the definition of $s$-dimensional Lebesgue measure on $R^d$ for $s\ne d$?

Published on 10 Apr 2018 - 12:34

score 626 · Answer 2 · 2026-03-25 04:43:35

626

Views

Convergence of convex sets in the complementary Hausdorff metric and in the usual Hausdorff metric

Published on 25 Mar 2026 - 4:43

score 86 · Answer 3 · 2018-04-24 17:12:08

86

Views

Equality between volume and surface

Published on 24 Apr 2018 - 17:12

score 561 · Answer 4 · 2026-03-25 03:07:07

561

Views

Why is Hausdorff dimension monotonic?

Published on 25 Mar 2026 - 3:07

score 84 · Answer 5 · 2026-03-25 04:43:00

84

Views

For $A\subset\Bbb R^n$ and $B\subset \Bbb R^m$ show that $\dim_H(A\times B)=\dim_H(A)+\dim_H(B)$

Published on 25 Mar 2026 - 4:43

score 160 · Answer 6 · 2018-05-01 18:07:16

160

Views

Let $\gamma\in C(I,\Bbb R^n)$. Show that $\dim_H(\Gamma)=1$

Published on 01 May 2018 - 18:07

score 237 · Answer 7 · 2026-03-25 04:41:09

237

Views

The Hausdorff, packing, and Minkowski dimensions of general Cantor-type sets

Published on 25 Mar 2026 - 4:41

score 132 · Answer 8 · 2026-03-25 04:42:37

132

Views

Hausdorff measure of the Cartesian square of a Cantor like set

Published on 25 Mar 2026 - 4:42

score 170 · Answer 9 · 2026-03-25 04:41:10

170

Views

Propeties of the Hausdorff Measure

Published on 25 Mar 2026 - 4:41

score 53 · Answer 10 · 2026-03-25 06:06:30

53

Views

Sufficient condition for the growth of Hausdorff measure which implies sigma-finiteness

Published on 25 Mar 2026 - 6:06

score 599 · Answer 11 · 2018-06-07 14:34:19

599

Views

Does this fractal have a Hausdorff dimension of 1?

Published on 07 Jun 2018 - 14:34

score 655 · Answer 12 · 2018-07-31 15:04:25

655

Views

The $m$-dimensional Hausdorff measure agrees with the Lebesgue measure on $\mathbb{R}^n$ when $m=n$?

Published on 31 Jul 2018 - 15:04

score 281 · Answer 13 · 2026-03-25 03:04:34

281

Views

Calculating the length of a curve $(x,x^2)$ for $x\in [0,2]$ using the Hausdorff measure of the set $A=\{(x,x^2)\in\mathbb{R}^2\mid x\in[0,2] \}$?

Published on 25 Mar 2026 - 3:04

score 265 · Answer 14 · 2026-03-24 02:50:40

265

Views

Set of Hausdorff dimension $\alpha$

Published on 24 Mar 2026 - 2:50

score 64 · Answer 15 · 2018-08-05 19:49:33

64

Views

Letting $\delta \rightarrow \infty$ in the $\delta$-Hausdorff premeasure

Published on 05 Aug 2018 - 19:49

List Question

What is the definition of $s$-dimensional Lebesgue measure on $R^d$ for $s\ne d$?

Convergence of convex sets in the complementary Hausdorff metric and in the usual Hausdorff metric

Equality between volume and surface

Why is Hausdorff dimension monotonic?

For $A\subset\Bbb R^n$ and $B\subset \Bbb R^m$ show that $\dim_H(A\times B)=\dim_H(A)+\dim_H(B)$

Let $\gamma\in C(I,\Bbb R^n)$. Show that $\dim_H(\Gamma)=1$

The Hausdorff, packing, and Minkowski dimensions of general Cantor-type sets

Hausdorff measure of the Cartesian square of a Cantor like set

Propeties of the Hausdorff Measure

Sufficient condition for the growth of Hausdorff measure which implies sigma-finiteness

Does this fractal have a Hausdorff dimension of 1?

The $m$-dimensional Hausdorff measure agrees with the Lebesgue measure on $\mathbb{R}^n$ when $m=n$?

Calculating the length of a curve $(x,x^2)$ for $x\in [0,2]$ using the Hausdorff measure of the set $A=\{(x,x^2)\in\mathbb{R}^2\mid x\in[0,2] \}$?

Set of Hausdorff dimension $\alpha$

Letting $\delta \rightarrow \infty$ in the $\delta$-Hausdorff premeasure

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