Question

Assume that $A\subset\mathbb{R}$, $0<c<m^* (A)$, can we find a subset $B$ of $A$ such that $m^*(B)=c$?

score 305 · Answer 1 · 2021-09-29 06:00:40

305

Views

Assume that $A\subset\mathbb{R}$, $0<c<m^* (A)$, can we find a subset $B$ of $A$ such that $m^*(B)=c$?

Published on 29 Sep 2021 - 6:00

score 301 · Answer 2 · 2026-03-26 11:06:43

301

Views

Why does the vitali set not have 0 outer measure

Published on 26 Mar 2026 - 11:06

score 153 · Answer 3 · 2021-10-03 04:24:42

153

Views

How to determine the Carathéodory outer measure $\mu^$ induced by $\mu$ and the $\sigma$-algebra of $\mu^$-measurable sets?

Published on 03 Oct 2021 - 4:24

score 82 · Answer 4 · 2021-10-13 22:43:59

82

Views

Measure Theory Specially Carathéodory measure. and the sigma algebra induced by that

Published on 13 Oct 2021 - 22:43

score 149 · Answer 5 · 2021-10-16 00:23:38

149

Views

Lebesgue differentiation theorem for monotone functions via Vitali covering lemma

Published on 16 Oct 2021 - 0:23

score 189 · Answer 6 · 2021-10-16 14:24:21

Why is the inner measure smaller than/equal the outer measure? If I try to prove it, I always end up the other way around, no matter how I try

score 29 · Answer 7 · 2021-10-21 23:25:21

29

Views

Explicitly finding a complete measure space

Published on 21 Oct 2021 - 23:25

score 19 · Answer 8 · 2026-03-24 12:34:58

19

Views

Does this construction of an outer measure extend the original function?

Published on 24 Mar 2026 - 12:34

score 244 · Answer 9 · 2026-03-22 20:55:39

244

Views

Why do we need hypothesis of complete measure in this version of Fubini's theorem?

Published on 22 Mar 2026 - 20:55

score 133 · Answer 10 · 2021-12-08 18:18:08

133

Views

Show that $\mu^(M\cup N)=\mu^(M)+\mu^(N)$ for outer measure $\mu^$

Published on 08 Dec 2021 - 18:18

score 164 · Answer 11 · 2021-12-08 21:10:59

164

Views

Extension of measure is less or equal to outer measure when restricted to semiring

Published on 08 Dec 2021 - 21:10

score 88 · Answer 12 · 2021-12-09 09:57:09

88

Views

Prove $\mu^(A)=\nu(A)$ if there exists a cover $A\subset \cup_{n\geq1} B_n$ and $\mu^(B_n)<\infty \;\forall n\geq 1$

Published on 09 Dec 2021 - 9:57

score 59 · Answer 13 · 2021-12-15 03:28:12

If $E\in \mathscr{M}_{\mu^*}$ , then for each $\varepsilon$ exists $A\in \mathscr{A}$ such that $\mu^*(A\triangle E)< \varepsilon$

score 543 · Answer 14 · 2021-12-19 21:27:27

543

Views

Does Sigma Algebra Necessarily Induce a Measure?

Published on 19 Dec 2021 - 21:27

score 227 · Answer 15 · 2021-12-24 04:42:25

227

Views

The Motivation of Pre-measure for Construction of Measures

Published on 24 Dec 2021 - 4:42

List Question

Assume that $A\subset\mathbb{R}$, $0<c<m^* (A)$, can we find a subset $B$ of $A$ such that $m^*(B)=c$?

Why does the vitali set not have 0 outer measure

How to determine the Carathéodory outer measure $\mu^$ induced by $\mu$ and the $\sigma$-algebra of $\mu^$-measurable sets?

Measure Theory Specially Carathéodory measure. and the sigma algebra induced by that

Lebesgue differentiation theorem for monotone functions via Vitali covering lemma

Why is the inner measure smaller than/equal the outer measure? If I try to prove it, I always end up the other way around, no matter how I try

Explicitly finding a complete measure space

Does this construction of an outer measure extend the original function?

Why do we need hypothesis of complete measure in this version of Fubini's theorem?

Show that $\mu^(M\cup N)=\mu^(M)+\mu^(N)$ for outer measure $\mu^$

Extension of measure is less or equal to outer measure when restricted to semiring

Prove $\mu^(A)=\nu(A)$ if there exists a cover $A\subset \cup_{n\geq1} B_n$ and $\mu^(B_n)<\infty \;\forall n\geq 1$

If $E\in \mathscr{M}_{\mu^}$ , then for each $\varepsilon$ exists $A\in \mathscr{A}$ such that $\mu^(A\triangle E)< \varepsilon$

Does Sigma Algebra Necessarily Induce a Measure?

The Motivation of Pre-measure for Construction of Measures

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