Question

Holder continuous map preserves $F_\sigma$ sets

score 96 · Answer 1 · 2026-04-15 18:29:22

96

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Holder continuous map preserves $F_\sigma$ sets

Published on 15 Apr 2026 - 18:29

score 46 · Answer 2 · 2026-04-15 06:15:29

46

Views

Asymptotic of the measure of a covering tube of a submanifold of dimension $n-2$

Published on 15 Apr 2026 - 6:15

score 395 · Answer 3 · 2026-04-13 09:49:20

395

Views

Proving for a Lebesgue measure the convergence in measure is equivalent to the convergence almost everywhere.

Published on 13 Apr 2026 - 9:49

score 229 · Answer 4 · 2026-04-11 18:59:17

229

Views

Existence of homeomorphism $h: \mathbb{R}\to \mathbb{R}$ such that $h(E)\cap E=\emptyset$

Published on 11 Apr 2026 - 18:59

score 2.4k · Answer 5 · 2026-04-11 16:16:56

2.4k

Views

Is the Lebesgue measure of the unit circle $0$?

Published on 11 Apr 2026 - 16:16

score 311 · Answer 6 · 2026-04-16 02:11:15

311

Views

Show that if E is compact, then $m(E)= \lim m(O_n)$ (Is my proof correct?)

Published on 16 Apr 2026 - 2:11

score 71 · Answer 7 · 2026-04-14 23:30:30

71

Views

Is there a subsequence of sets $\{A_{k_j}\}$ where the intersection is positive.

Published on 14 Apr 2026 - 23:30

score 77 · Answer 8 · 2026-04-15 08:03:46

77

Views

Uniform boundedness vs. Pointwise boundedness

Published on 15 Apr 2026 - 8:03

score 80 · Answer 9 · 2026-04-15 06:37:26

80

Views

For $p\geq1$, $f\in L^p(\mathbb{R}^n)$ and $\lambda>0$, does $\{x\in\mathbb{R}^n:|f(x)|>\lambda\}$ have finite measure?

Published on 15 Apr 2026 - 6:37

score 52 · Answer 10 · 2026-04-14 07:34:34

52

Views

Steinhauss theorem and sums of sets

Published on 14 Apr 2026 - 7:34

score 2.1k · Answer 11 · 2026-04-11 00:24:06

2.1k

Views

Approximation of finite Lebesgue measurable set by closed subset

Published on 11 Apr 2026 - 0:24

score 1.3k · Answer 12 · 2026-04-16 12:37:29

1.3k

Views

Lipschitz function $f\colon A \to \mathbb{R}$, $A \subseteq \mathbb{R}$ measurable.

Published on 16 Apr 2026 - 12:37

score 240 · Answer 13 · 2026-04-15 01:02:40

240

Views

Lebesgue Monotonous Convergence Theorem for $f_n = \chi_{[0,n]}$

Published on 15 Apr 2026 - 1:02

score 152 · Answer 14 · 2026-04-13 15:27:21

152

Views

Show that $\lambda^2([0,1]\times[0,1])=1$ where $\lambda^2$ is the two-dimensional Lebesgue measure

Published on 13 Apr 2026 - 15:27

score 93 · Answer 15 · 2026-04-13 05:26:11

93

Views

Lebesgue Measure: For $A\subset R^{n}$, with $\mu (A)>0$ and $0>a>\mu(A)$, exists a $K \subset A$ compact and $\mu(K)=a$

Published on 13 Apr 2026 - 5:26

List Question

Holder continuous map preserves $F_\sigma$ sets

Asymptotic of the measure of a covering tube of a submanifold of dimension $n-2$

Proving for a Lebesgue measure the convergence in measure is equivalent to the convergence almost everywhere.

Existence of homeomorphism $h: \mathbb{R}\to \mathbb{R}$ such that $h(E)\cap E=\emptyset$

Is the Lebesgue measure of the unit circle $0$?

Show that if E is compact, then $m(E)= \lim m(O_n)$ (Is my proof correct?)

Is there a subsequence of sets $\{A_{k_j}\}$ where the intersection is positive.

Uniform boundedness vs. Pointwise boundedness

For $p\geq1$, $f\in L^p(\mathbb{R}^n)$ and $\lambda>0$, does $\{x\in\mathbb{R}^n:|f(x)|>\lambda\}$ have finite measure?

Steinhauss theorem and sums of sets

Approximation of finite Lebesgue measurable set by closed subset

Lipschitz function $f\colon A \to \mathbb{R}$, $A \subseteq \mathbb{R}$ measurable.

Lebesgue Monotonous Convergence Theorem for $f_n = \chi_{[0,n]}$

Show that $\lambda^2([0,1]\times[0,1])=1$ where $\lambda^2$ is the two-dimensional Lebesgue measure

Lebesgue Measure: For $A\subset R^{n}$, with $\mu (A)>0$ and $0>a>\mu(A)$, exists a $K \subset A$ compact and $\mu(K)=a$

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