Question

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

score 738 · Answer 1 · 2019-11-22 01:08:54

738

Views

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

Published on 22 Nov 2019 - 1:08

score 209 · Answer 2 · 2019-11-24 11:46:34

209

Views

Extension of cocountable sigma algebra with the counting measure.

Published on 24 Nov 2019 - 11:46

score 125 · Answer 3 · 2019-11-24 15:39:35

125

Views

Set of measurable function on a Hilbert space

Published on 24 Nov 2019 - 15:39

score 64 · Answer 4 · 2019-11-25 05:30:34

64

Views

Inverse is continuous

Published on 25 Nov 2019 - 5:30

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 106 · Answer 6 · 2019-12-17 19:59:02

106

Views

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

Published on 17 Dec 2019 - 19:59

score 119 · Answer 7 · 2019-12-29 01:06:24

119

Views

Sigma algebra generated by algebra

Published on 29 Dec 2019 - 1:06

score 67 · Answer 8 · 2020-02-04 03:07:01

67

Views

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

Published on 04 Feb 2020 - 3:07

score 38 · Answer 9 · 2020-02-13 02:18:59

38

Views

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

Published on 13 Feb 2020 - 2:18

score 40 · Answer 10 · 2020-02-17 16:17:40

40

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 17 Feb 2020 - 16:17

score 136 · Answer 11 · 2020-02-21 20:07:31

136

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 21 Feb 2020 - 20:07

score 204 · Answer 12 · 2026-03-25 03:04:20

204

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 25 Mar 2026 - 3:04

score 49 · Answer 13 · 2020-02-25 12:26:56

49

Views

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

Published on 25 Feb 2020 - 12:26

score 57 · Answer 14 · 2020-03-06 22:43:19

57

Views

Use of inverse in defining Lebesgue measure

Published on 06 Mar 2020 - 22:43

score 72 · Answer 15 · 2020-03-16 09:08:11

72

Views

Show that a line segment is Jordan measurable.

Published on 16 Mar 2020 - 9:08

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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