Question

A step in a proof that a set is Lebesgue measurable if and only if its translation is

score 396 · Answer 1 · 2026-03-27 07:50:43

396

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A step in a proof that a set is Lebesgue measurable if and only if its translation is

Published on 27 Mar 2026 - 7:50

score 172 · Answer 2 · 2022-07-08 10:14:44

172

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Find an example of two disjonit sets $A$ and $B$ of real numbers such that $m^{}(A \cup B) < m^{}(A) + m^{*}(B)$.

Published on 08 Jul 2022 - 10:14

score 54 · Answer 3 · 2022-07-13 15:26:59

54

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Showing that the two definitions of a regular outer measure in Wikipedia actually are equivalent

Published on 13 Jul 2022 - 15:26

score 41 · Answer 4 · 2022-07-14 05:46:52

41

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What would be an example of a mapping $m$ which satisfies all properties of a measure/outer-measure except well-definedness?

Published on 14 Jul 2022 - 5:46

score 75 · Answer 5 · 2022-07-22 06:48:19

75

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outer measure is invariant with translation

Published on 22 Jul 2022 - 6:48

score 106 · Answer 6 · 2022-07-25 15:59:08

106

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Prob. 7, Chap. 2, in Royden's REAL ANALYSIS: Every bounded set has outer measure equal to a $G_\delta$ set containing it

Published on 25 Jul 2022 - 15:59

score 40 · Answer 7 · 2022-08-04 05:05:32

40

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Confusion on the construction of "Outer Measures"

Published on 04 Aug 2022 - 5:05

score 146 · Answer 8 · 2022-08-13 06:44:01

146

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Why outer measure of Vitali set is greater than 0 or equals to 0?

Published on 13 Aug 2022 - 6:44

score 55 · Answer 9 · 2022-08-21 09:01:15

55

Views

outer measure is a measure?

Published on 21 Aug 2022 - 9:01

score 170 · Answer 10 · 2022-08-22 17:36:42

170

Views

Constructing Outer Measures Folland Proposition 1.10

Published on 22 Aug 2022 - 17:36

score 30 · Answer 11 · 2022-08-25 04:54:56

30

Views

Showing $\pi^$ measurability of a set, given $\pi^$ measurability of a symmetric sum,

Published on 25 Aug 2022 - 4:54

score 51 · Answer 12 · 2022-08-28 02:21:56

51

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Counterexample or proof of outer measure inequality

Published on 28 Aug 2022 - 2:21

score 101 · Answer 13 · 2022-09-09 16:57:50

Let $\mu ^{*}$ be a arbitrary outer measure is necessarily satisfied? $\mu ^*(A \cup B) + \mu^{*}(A \cap B) \leq \mu^{*}(A)+\mu ^{*}(B)$

score 412 · Answer 14 · 2022-09-13 21:30:03

412

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Show that inner measure is the same as outer measure on Lebesgue measurable sets.

Published on 13 Sep 2022 - 21:30

score 63 · Answer 15 · 2022-09-20 10:15:33

63

Views

Proving NonAdditivity of Outer Measure, when countable subadditivity is proven

Published on 20 Sep 2022 - 10:15

List Question

A step in a proof that a set is Lebesgue measurable if and only if its translation is

Find an example of two disjonit sets $A$ and $B$ of real numbers such that $m^{}(A \cup B) < m^{}(A) + m^{*}(B)$.

Showing that the two definitions of a regular outer measure in Wikipedia actually are equivalent

What would be an example of a mapping $m$ which satisfies all properties of a measure/outer-measure except well-definedness?

outer measure is invariant with translation

Prob. 7, Chap. 2, in Royden's REAL ANALYSIS: Every bounded set has outer measure equal to a $G_\delta$ set containing it

Confusion on the construction of "Outer Measures"

Why outer measure of Vitali set is greater than 0 or equals to 0?

outer measure is a measure?

Constructing Outer Measures Folland Proposition 1.10

Showing $\pi^$ measurability of a set, given $\pi^$ measurability of a symmetric sum,

Counterexample or proof of outer measure inequality

Let $\mu ^{}$ be a arbitrary outer measure is necessarily satisfied? $\mu ^(A \cup B) + \mu^{}(A \cap B) \leq \mu^{}(A)+\mu ^{*}(B)$

Show that inner measure is the same as outer measure on Lebesgue measurable sets.

Proving NonAdditivity of Outer Measure, when countable subadditivity is proven

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