Question

Outer measure "distributive" property

score 96 · Answer 1 · 2022-04-01 21:09:45

96

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Outer measure "distributive" property

Published on 01 Apr 2022 - 21:09

score 216 · Answer 2 · 2022-04-05 13:01:55

216

Views

Show that induced outer measure of the sum of two measures is the sum of the induced outer measures

Published on 05 Apr 2022 - 13:01

score 225 · Answer 3 · 2022-04-13 11:45:53

225

Views

1.3.9 from the book measure theory of Donald L. Cohn

Published on 13 Apr 2022 - 11:45

score 23 · Answer 4 · 2022-04-19 08:45:05

23

Views

For any set $E\subset\mathbb{R}^{p+q}$, if for all $x\in\mathbb{R}^p$ that $E(x)$ is measurable, does $E$ measurable?

Published on 19 Apr 2022 - 8:45

score 90 · Answer 5 · 2022-05-02 18:01:24

90

Views

An interesting qn came in my mind related to outer measure of the cartesian product of A and B??

Published on 02 May 2022 - 18:01

score 31 · Answer 6 · 2022-05-05 17:59:33

31

Views

Are these two families of sets the same without the assumption of measurability?

Published on 05 May 2022 - 17:59

score 37 · Answer 7 · 2022-05-07 02:02:10

37

Views

Measure Theory question about Outer measure vs measure

Published on 07 May 2022 - 2:02

score 121 · Answer 8 · 2022-05-13 17:39:45

121

Views

Volume of an interval in $R^N$ seen as the supremum of set of volumes of compact subintervals

Published on 13 May 2022 - 17:39

score 121 · Answer 9 · 2022-06-04 08:45:18

121

Views

Prove that |tA| = |t| |A| where A ⊆ R, t ∈ R, | · | is outer measure. But why don't both sides equal 0 always?

Published on 04 Jun 2022 - 8:45

score 79 · Answer 10 · 2022-06-15 20:45:29

79

Views

If $m(A)+m(B)>1$, then $A\cap B\neq \varnothing$

Published on 15 Jun 2022 - 20:45

score 184 · Answer 11 · 2022-06-16 17:11:07

184

Views

If $A\in\mathfrak{M}(\mu), \epsilon>0$, then there exist $F$ closed, $G$ open such that $F\subset A\subset G$ and $\mu(G-A), \mu(A-F)<\epsilon$.

Published on 16 Jun 2022 - 17:11

score 32 · Answer 12 · 2022-06-27 06:17:12

32

Views

Show nonempty interior implies positive exterior measure.

Published on 27 Jun 2022 - 6:17

score 97 · Answer 13 · 2022-06-29 16:48:18

97

Views

What is the intuition for defining the measurable sets in this manner?

Published on 29 Jun 2022 - 16:48

score 37 · Answer 14 · 2022-07-02 18:16:59

37

Views

Does $\inf_{B \in \Lambda} \varphi(B) = \varphi\left( \inf_{B \in \Lambda} \right)$ if $\varphi$ is Borel measurable and each $B \in \Lambda$ is Borel

Published on 02 Jul 2022 - 18:16

score 328 · Answer 15 · 2022-07-04 13:17:08

328

Views

Using cubes in $\mathbb{R}^n$, prove that hyperplanes have measure 0

Published on 04 Jul 2022 - 13:17

List Question

Outer measure "distributive" property

Show that induced outer measure of the sum of two measures is the sum of the induced outer measures

1.3.9 from the book measure theory of Donald L. Cohn

For any set $E\subset\mathbb{R}^{p+q}$, if for all $x\in\mathbb{R}^p$ that $E(x)$ is measurable, does $E$ measurable?

An interesting qn came in my mind related to outer measure of the cartesian product of A and B??

Are these two families of sets the same without the assumption of measurability?

Measure Theory question about Outer measure vs measure

Volume of an interval in $R^N$ seen as the supremum of set of volumes of compact subintervals

Prove that |tA| = |t| |A| where A ⊆ R, t ∈ R, | · | is outer measure. But why don't both sides equal 0 always?

If $m(A)+m(B)>1$, then $A\cap B\neq \varnothing$

If $A\in\mathfrak{M}(\mu), \epsilon>0$, then there exist $F$ closed, $G$ open such that $F\subset A\subset G$ and $\mu(G-A), \mu(A-F)<\epsilon$.

Show nonempty interior implies positive exterior measure.

What is the intuition for defining the measurable sets in this manner?

Does $\inf_{B \in \Lambda} \varphi(B) = \varphi\left( \inf_{B \in \Lambda} \right)$ if $\varphi$ is Borel measurable and each $B \in \Lambda$ is Borel

Using cubes in $\mathbb{R}^n$, prove that hyperplanes have measure 0

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