Question

Show that a certain closed interval does not contain an open interval $I \neq \emptyset$.

score 464 · Answer 1 · 2018-03-12 13:41:32

464

Views

Show that a certain closed interval does not contain an open interval $I \neq \emptyset$.

Published on 12 Mar 2018 - 13:41

score 246 · Answer 2 · 2026-03-22 03:53:17

246

Views

Condition for algebra being sigma algebra

Published on 22 Mar 2026 - 3:53

score 90 · Answer 3 · 2018-03-26 16:14:37

90

Views

For every r>0, there is a vitali set having outer measure less than r

Published on 26 Mar 2018 - 16:14

score 65 · Answer 4 · 2026-03-22 12:16:10

65

Views

Outer measure induced by a Jump function

Published on 22 Mar 2026 - 12:16

score 109 · Answer 5 · 2026-03-22 09:54:08

109

Views

Showing $m^(A-E)=m^(A)$ when $m^*(E)=0$

Published on 22 Mar 2026 - 9:54

score 33 · Answer 6 · 2018-04-08 10:31:17

33

Views

Outer measure of the set $A= \lbrace x \in \mathbb{R}^n :\exists r>0 \; with \; \mu(B_r(x))=0 \rbrace$

Published on 08 Apr 2018 - 10:31

score 968 · Answer 7 · 2018-04-16 20:05:58

968

Views

Lebesgue outer measure of the union is strictly less than the sum of the measures

Published on 16 Apr 2018 - 20:05

score 51 · Answer 8 · 2018-04-26 04:07:59

51

Views

About alternative definition of $s$-dimensional Hausdorff outer measure in $\Bbb R^n$

Published on 26 Apr 2018 - 4:07

score 92 · Answer 9 · 2026-03-22 17:32:02

92

Views

Premeasure and induced outer measure exercise.

Published on 22 Mar 2026 - 17:32

score 95 · Answer 10 · 2026-03-21 20:43:02

95

Views

Outer measure inequality

Published on 21 Mar 2026 - 20:43

score 4.4k · Answer 11 · 2026-03-22 20:14:23

4.4k

Views

Why is the inner measure problematic?

Published on 22 Mar 2026 - 20:14

score 404 · Answer 12 · 2018-06-03 20:06:07

404

Views

What is the inutition behind the Caratheodory criterion for measurable sets?

Published on 03 Jun 2018 - 20:06

score 322 · Answer 13 · 2018-06-18 20:18:13

322

Views

Prove that a subset of $\mathbb{R}$ with positive outer measure contains almost a whole interval

Published on 18 Jun 2018 - 20:18

score 28 · Answer 14 · 2018-07-09 22:50:36

28

Views

$|E|_e^{'} = |E|_e$ for every $E \subset \mathbb R^n$, where $|E|_e$ is the exterior measure of the set $E$

Published on 09 Jul 2018 - 22:50

score 58 · Answer 15 · 2018-07-10 04:57:07

Given $E$ in $\mathbb R^n$, there exists an open $G$ containing $E$ such that $m^*(G)\le m^*(E) + \epsilon$. But $m^*(G-E) < \epsilon$ may not hold?

List Question

Show that a certain closed interval does not contain an open interval $I \neq \emptyset$.

Condition for algebra being sigma algebra

For every r>0, there is a vitali set having outer measure less than r

Outer measure induced by a Jump function

Showing $m^(A-E)=m^(A)$ when $m^*(E)=0$

Outer measure of the set $A= \lbrace x \in \mathbb{R}^n :\exists r>0 \; with \; \mu(B_r(x))=0 \rbrace$

Lebesgue outer measure of the union is strictly less than the sum of the measures

About alternative definition of $s$-dimensional Hausdorff outer measure in $\Bbb R^n$

Premeasure and induced outer measure exercise.

Outer measure inequality

Why is the inner measure problematic?

What is the inutition behind the Caratheodory criterion for measurable sets?

Prove that a subset of $\mathbb{R}$ with positive outer measure contains almost a whole interval

$|E|_e^{'} = |E|_e$ for every $E \subset \mathbb R^n$, where $|E|_e$ is the exterior measure of the set $E$

Given $E$ in $\mathbb R^n$, there exists an open $G$ containing $E$ such that $m^(G)\le m^(E) + \epsilon$. But $m^*(G-E) < \epsilon$ may not hold?

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