Question

Showing "directly" that a fat Cantor set contains a non-measurable subset

score 740 · Answer 1 · 2026-04-12 04:01:33

740

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Showing "directly" that a fat Cantor set contains a non-measurable subset

Published on 12 Apr 2026 - 4:01

score 210 · Answer 2 · 2026-05-02 05:32:36

210

Views

Extension of cocountable sigma algebra with the counting measure.

Published on 02 May 2026 - 5:32

score 128 · Answer 3 · 2026-04-11 22:41:48

128

Views

Set of measurable function on a Hilbert space

Published on 11 Apr 2026 - 22:41

score 69 · Answer 4 · 2026-04-30 15:16:46

69

Views

Inverse is continuous

Published on 30 Apr 2026 - 15:16

score 67 · Answer 5 · 2026-03-25 01:22:28

67

Views

Integral when limit of nondecreasing simple functions greater than another simple function

Published on 25 Mar 2026 - 1:22

score 109 · Answer 6 · 2026-04-15 04:34:12

109

Views

Prove: If $E_1$ and $E_2$ are measurable then $E_1\cup E_2$ is measurable.

Published on 15 Apr 2026 - 4:34

score 122 · Answer 7 · 2026-04-13 05:40:49

122

Views

Sigma algebra generated by algebra

Published on 13 Apr 2026 - 5:40

score 70 · Answer 8 · 2026-04-12 13:28:19

70

Views

Regarding the definition of Lebesgue measurable subsets of $R^n$: Definition vs. Intuition

Published on 12 Apr 2026 - 13:28

score 41 · Answer 9 · 2026-04-14 09:18:46

41

Views

Example where image of measurable set under measurable function is not measurable

Published on 14 Apr 2026 - 9:18

score 43 · Answer 10 · 2026-04-15 01:03:39

43

Views

Let $A=[0,1]\times[0,1], f:A\mapsto \mathbb{R} $ bounded in A. Then the set $D_{f,A}$ of discontinuities of $f$ in $A$ is closed?

Published on 15 Apr 2026 - 1:03

score 138 · Answer 11 · 2026-04-17 13:30:45

138

Views

$\limsup_{n\rightarrow\infty}A_n = \cap_{n\geq1} \cup_{k\geq n}A_k$ is is the set of elements that belong to an infinity of $A_n$

Published on 17 Apr 2026 - 13:30

score 205 · Answer 12 · 2026-05-10 15:47:47

205

Views

Show that $f$ is $\mathcal{A}$-measurable if and only if $\{x \in A \mid f(x)=\alpha_i\} \in \mathcal{A}$ for all $i=1,\dots,n$

Published on 10 May 2026 - 15:47

score 51 · Answer 13 · 2026-04-17 13:15:21

51

Views

Why is the set $\{\omega\in \Omega: \exists t \geq 0: -\infty < D^-(t,\omega) \leq D^+(t,\omega) < + \infty\}$ measurable?

Published on 17 Apr 2026 - 13:15

score 60 · Answer 14 · 2026-04-12 10:25:17

60

Views

Use of inverse in defining Lebesgue measure

Published on 12 Apr 2026 - 10:25

score 75 · Answer 15 · 2026-04-15 19:24:46

75

Views

Show that a line segment is Jordan measurable.

Published on 15 Apr 2026 - 19:24

List Question

Showing "directly" that a fat Cantor set contains a non-measurable subset

Extension of cocountable sigma algebra with the counting measure.

Set of measurable function on a Hilbert space

Inverse is continuous

Integral when limit of nondecreasing simple functions greater than another simple function

Prove: If $E_1$ and $E_2$ are measurable then $E_1\cup E_2$ is measurable.

Sigma algebra generated by algebra

Regarding the definition of Lebesgue measurable subsets of $R^n$: Definition vs. Intuition

Example where image of measurable set under measurable function is not measurable

Let $A=[0,1]\times[0,1], f:A\mapsto \mathbb{R} $ bounded in A. Then the set $D_{f,A}$ of discontinuities of $f$ in $A$ is closed?

$\limsup_{n\rightarrow\infty}A_n = \cap_{n\geq1} \cup_{k\geq n}A_k$ is is the set of elements that belong to an infinity of $A_n$

Show that $f$ is $\mathcal{A}$-measurable if and only if $\{x \in A \mid f(x)=\alpha_i\} \in \mathcal{A}$ for all $i=1,\dots,n$

Why is the set $\{\omega\in \Omega: \exists t \geq 0: -\infty < D^-(t,\omega) \leq D^+(t,\omega) < + \infty\}$ measurable?

Use of inverse in defining Lebesgue measure

Show that a line segment is Jordan measurable.

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