Question

Equivalent Definition of Measurable set

score 5.7k · Answer 1 · 2013-11-05 19:08:03

5.7k

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Equivalent Definition of Measurable set

Published on 05 Nov 2013 - 19:08

score 81 · Answer 2 · 2013-12-03 18:44:41

81

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If no outer measure is present, do people use the term "measurable set" simply for any element in a given $\sigma$-algebra?

Published on 03 Dec 2013 - 18:44

score 36.6k · Answer 3 · 2013-12-26 05:10:31

36.6k

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What is the definition of a measurable set?

Published on 26 Dec 2013 - 5:10

score 316 · Answer 4 · 2014-03-06 09:38:39

316

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Let $E\subset\mathbb{R}$ be a measurable set, and define $F=\{(x,y):x-y\in E\}$. Is $F$ a measurable set?

Published on 06 Mar 2014 - 9:38

score 2k · Answer 5 · 2012-05-06 11:00:35

2k

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Fatou's lemma and measurable sets

Published on 06 May 2012 - 11:00

score 623 · Answer 6 · 2020-07-31 22:56:03

623

Views

Let X be a set. How many $\sigma$-algebras of subsets of X contain exactly $5$ elements?

Published on 31 Jul 2020 - 22:56

score 538 · Answer 7 · 2020-08-01 00:09:38

538

Views

Show that $\mathcal A_1$ $\cap$ $\mathcal A_2$ is also a $\sigma$-algebra

Published on 01 Aug 2020 - 0:09

score 64 · Answer 8 · 2020-08-01 16:47:07

64

Views

Determine liminf$A_{n}$ and limsup$A_{n}$ for the $A_{n}$ of the following sets

Published on 01 Aug 2020 - 16:47

score 436 · Answer 9 · 2020-08-01 21:58:28

436

Views

Lebesgue measure of a subset [$0,1$]

Published on 01 Aug 2020 - 21:58

score 42 · Answer 10 · 2020-08-02 14:26:55

42

Views

Set of numbers that are solutions for equations such as $ x = x + 1 $

Published on 02 Aug 2020 - 14:26

score 446 · Answer 11 · 2020-08-05 16:31:16

446

Views

Showing $\Gamma = \{(x,y) \in \mathbb{R}^d \times \mathbb{R}: y = f(x)\}$ is measurablle and of measure 0, when $f$ is a measurable function.

Published on 05 Aug 2020 - 16:31

score 306 · Answer 12 · 2020-08-07 22:08:27

Let $\mathcal{C}$ be any collection of subsets of a set $X$ and let $E \subseteq X$. Let $\mathcal{C} \cap E := \{C \cap E : C \in \mathcal{C}\}$.

score 24 · Answer 13 · 2026-02-25 19:44:59

24

Views

Does a sequence of functions $(f_n)$ in the probability space $L_1(\mathscr F, P)$ generate a separable $\sigma$-field?

Published on 25 Feb 2026 - 19:44

score 112 · Answer 14 · 2020-08-17 13:05:24

112

Views

Is it possible to write a metric a space as a countable disjoint union of compact sets?

Published on 17 Aug 2020 - 13:05

score 58 · Answer 15 · 2020-08-22 19:21:05

58

Views

Show that $\{x\}\in \mathbb{B}(X)$ for every $x\in X$

Published on 22 Aug 2020 - 19:21

List Question

Equivalent Definition of Measurable set

If no outer measure is present, do people use the term "measurable set" simply for any element in a given $\sigma$-algebra?

What is the definition of a measurable set?

Let $E\subset\mathbb{R}$ be a measurable set, and define $F=\{(x,y):x-y\in E\}$. Is $F$ a measurable set?

Fatou's lemma and measurable sets

Let X be a set. How many $\sigma$-algebras of subsets of X contain exactly $5$ elements?

Show that $\mathcal A_1$ $\cap$ $\mathcal A_2$ is also a $\sigma$-algebra

Determine liminf$A_{n}$ and limsup$A_{n}$ for the $A_{n}$ of the following sets

Lebesgue measure of a subset [$0,1$]

Set of numbers that are solutions for equations such as $ x = x + 1 $

Showing $\Gamma = \{(x,y) \in \mathbb{R}^d \times \mathbb{R}: y = f(x)\}$ is measurablle and of measure 0, when $f$ is a measurable function.

Let $\mathcal{C}$ be any collection of subsets of a set $X$ and let $E \subseteq X$. Let $\mathcal{C} \cap E := \{C \cap E : C \in \mathcal{C}\}$.

Does a sequence of functions $(f_n)$ in the probability space $L_1(\mathscr F, P)$ generate a separable $\sigma$-field?

Is it possible to write a metric a space as a countable disjoint union of compact sets?

Show that $\{x\}\in \mathbb{B}(X)$ for every $x\in X$

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