Question

Prove that every open set is lebesgue-measurable

score 7.2k · Answer 1 · 2026-04-12 09:58:51

7.2k

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Prove that every open set is lebesgue-measurable

Published on 12 Apr 2026 - 9:58

score 437 · Answer 2 · 2026-04-12 01:57:17

437

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Is the Carathéodory measurability criterion optimal in some sense?

Published on 12 Apr 2026 - 1:57

score 747 · Answer 3 · 2026-04-13 19:44:11

747

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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 Apr 2026 - 19:44

score 89 · Answer 4 · 2026-04-12 08:21:51

89

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Outer and inner measures

Published on 12 Apr 2026 - 8:21

score 45 · Answer 5 · 2026-04-14 06:15:16

45

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

Published on 14 Apr 2026 - 6:15

score 380 · Answer 6 · 2026-05-10 12:54:14

380

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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 10 May 2026 - 12:54

score 355 · Answer 7 · 2026-04-10 14:12:13

355

Views

Lebesgue outer measure equivalence to another set function on compact sets

Published on 10 Apr 2026 - 14:12

score 1.1k · Answer 8 · 2026-04-16 05:22:04

1.1k

Views

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

Published on 16 Apr 2026 - 5:22

score 337 · Answer 9 · 2026-04-16 16:14:11

337

Views

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

Published on 16 Apr 2026 - 16:14

score 212 · Answer 10 · 2026-04-15 18:05:08

212

Views

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

Published on 15 Apr 2026 - 18:05

score 213 · Answer 11 · 2026-04-11 05:03:28

213

Views

Premeasures on Algebras

Published on 11 Apr 2026 - 5:03

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 68 · Answer 13 · 2026-04-17 10:43:45

68

Views

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

Published on 17 Apr 2026 - 10:43

score 35 · Answer 14 · 2026-04-12 13:33:38

35

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 12 Apr 2026 - 13:33

score 128 · Answer 15 · 2026-04-14 21:51:27

128

Views

Continuity from below of outer measure extending an algebrea

Published on 14 Apr 2026 - 21:51

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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