List questions from geometric-measure-theory

Published on 25 Mar 2026 - 16:13

181

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How to show that $D$ is a Borel measurable set and $D_{f}$ is a Borel function.

Published on 10 Feb 2021 - 1:42

171

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Density of smooth functions in $L^p$ space on Cantor Set

Published on 11 Feb 2021 - 0:51

2.4k

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What's the intuition behind the Co-Area formula?

Published on 15 Feb 2021 - 18:37

584

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Investigating a $1/2$-dimensional sphere

Published on 23 Feb 2021 - 20:02

124

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In $\mathbb{R}^{2}$, why does the convex hull have lower perimeter?

Published on 23 Feb 2021 - 20:36

372

Views

Relationship between finite Radon measures and bounded variation measures

Published on 29 Mar 2026 - 9:10

88

Views

Is there a standard terminology for $|f^{-1}(y)|=1$ for almost every $y$?

Published on 28 Feb 2021 - 16:21

92

Views

Inequality for perimeter of Minkowski sum?

Published on 08 Mar 2021 - 12:00

534

Views

Can I write the integral of a function in terms of its level sets?

Published on 16 Mar 2021 - 11:30

47

Views

Is the line measure operator bounded in $W^{1,p}(\mathbb{R}^2)$

Published on 16 Mar 2021 - 17:02

33

Views

Does this property of Radon-Nykodym derivatives exist

Published on 24 Feb 2026 - 6:50

242

Views

Is the Hausdorff measure absolutely continuous with respect to the lebesgue measure? $H^{d-1} \ll \lambda^d$

Published on 24 Feb 2026 - 6:53

111

Views

Strong convergence vs Weak convergence _ compactness of integral varifolds

Published on 23 Feb 2026 - 19:38

274

Views

Computing $n$-dimensional Lebesgue measure with Euclidean $n$-balls

Published on 05 Apr 2021 - 19:26

List Question

Alternative characterization of total variation of $L^1$ functions

How to show that $D$ is a Borel measurable set and $D_{f}$ is a Borel function.

Density of smooth functions in $L^p$ space on Cantor Set

What's the intuition behind the Co-Area formula?

Investigating a $1/2$-dimensional sphere

In $\mathbb{R}^{2}$, why does the convex hull have lower perimeter?

Relationship between finite Radon measures and bounded variation measures

Is there a standard terminology for $|f^{-1}(y)|=1$ for almost every $y$?

Inequality for perimeter of Minkowski sum?

Can I write the integral of a function in terms of its level sets?

Is the line measure operator bounded in $W^{1,p}(\mathbb{R}^2)$

Does this property of Radon-Nykodym derivatives exist

Is the Hausdorff measure absolutely continuous with respect to the lebesgue measure? $H^{d-1} \ll \lambda^d$

Strong convergence vs Weak convergence _ compactness of integral varifolds

Computing $n$-dimensional Lebesgue measure with Euclidean $n$-balls

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