Question

Prove that every open set is lebesgue-measurable

score 7.2k · Answer 1 · 2018-08-27 18:21:43

7.2k

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Prove that every open set is lebesgue-measurable

Published on 27 Aug 2018 - 18:21

score 434 · Answer 2 · 2018-09-12 12:14:57

434

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Is the Carathéodory measurability criterion optimal in some sense?

Published on 12 Sep 2018 - 12:14

score 744 · Answer 3 · 2018-09-13 13:52:43

744

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Showing that the set of $\mu^*$-measurable sets in a $\sigma$-finite measure space is of a certain form.

Published on 13 Sep 2018 - 13:52

score 84 · Answer 4 · 2018-09-20 00:20:35

84

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Outer and inner measures

Published on 20 Sep 2018 - 0:20

score 42 · Answer 5 · 2018-09-25 15:20:01

42

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Does any set of representative rationalis have known inner and outer measures?

Published on 25 Sep 2018 - 15:20

score 377 · Answer 6 · 2026-03-25 01:18:23

377

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$\{µ(E) : E ∈ S\} = [0, 1] ∪ [3, c]$. Prove that $c ≥ 4$. Can you give an example of $(X, S, µ)$ if $c = 4$?

Published on 25 Mar 2026 - 1:18

score 352 · Answer 7 · 2018-10-01 22:15:02

352

Views

Lebesgue outer measure equivalence to another set function on compact sets

Published on 01 Oct 2018 - 22:15

score 1.1k · Answer 8 · 2018-10-17 18:15:35

1.1k

Views

If a sequence of measurable functions $f_{n}$ converge to $f$ almost everywhere then $f$ is measurable

Published on 17 Oct 2018 - 18:15

score 334 · Answer 9 · 2018-10-25 15:15:37

334

Views

$E \subset X$ and $\mu ^* (E)=0$, then $E$ is $\mu^*$measurable

Published on 25 Oct 2018 - 15:15

score 207 · Answer 10 · 2018-10-31 14:18:19

207

Views

Prove: $m^(aE+b)=|a|m^(E)$

Published on 31 Oct 2018 - 14:18

score 208 · Answer 11 · 2018-11-01 08:12:54

208

Views

Premeasures on Algebras

Published on 01 Nov 2018 - 8:12

score 136 · Answer 12 · 2026-03-25 03:03:12

136

Views

Does there exists a set which has the exterior measure,but doesn't Lebesgue measurable?

Published on 25 Mar 2026 - 3:03

score 65 · Answer 13 · 2018-11-10 10:28:02

65

Views

What is the relationship between $m^(A-B)$ and $m^(A)-m^*(A\cap B)$

Published on 10 Nov 2018 - 10:28

score 32 · Answer 14 · 2018-11-13 17:49:04

32

Views

Finite outer measure $\mu$ on a particular set implies the existence of another set such that outer measure and measure are equal on respective sets

Published on 13 Nov 2018 - 17:49

score 125 · Answer 15 · 2018-11-14 17:26:17

125

Views

Continuity from below of outer measure extending an algebrea

Published on 14 Nov 2018 - 17:26

List Question

Prove that every open set is lebesgue-measurable

Is the Carathéodory measurability criterion optimal in some sense?

Showing that the set of $\mu^*$-measurable sets in a $\sigma$-finite measure space is of a certain form.

Outer and inner measures

Does any set of representative rationalis have known inner and outer measures?

$\{µ(E) : E ∈ S\} = [0, 1] ∪ [3, c]$. Prove that $c ≥ 4$. Can you give an example of $(X, S, µ)$ if $c = 4$?

Lebesgue outer measure equivalence to another set function on compact sets

If a sequence of measurable functions $f_{n}$ converge to $f$ almost everywhere then $f$ is measurable

$E \subset X$ and $\mu ^* (E)=0$, then $E$ is $\mu^*$measurable

Prove: $m^(aE+b)=|a|m^(E)$

Premeasures on Algebras

Does there exists a set which has the exterior measure,but doesn't Lebesgue measurable?

What is the relationship between $m^(A-B)$ and $m^(A)-m^*(A\cap B)$

Finite outer measure $\mu$ on a particular set implies the existence of another set such that outer measure and measure are equal on respective sets

Continuity from below of outer measure extending an algebrea

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