Question

What is an example of a covering of the set of irrational numbers in the interval $[0,1]$, with a total length of $1$?

score 103 · Answer 1 · 2019-09-15 16:06:51

103

Views

What is an example of a covering of the set of irrational numbers in the interval $[0,1]$, with a total length of $1$?

Published on 15 Sep 2019 - 16:06

score 234 · Answer 2 · 2019-09-20 09:23:50

234

Views

Why is $\{\{c\}:c \in \mathbb{R} \}$ not a generator of the Borel $\sigma$ field in $\mathbb{R}$?

Published on 20 Sep 2019 - 9:23

score 246 · Answer 3 · 2019-09-26 21:48:07

246

Views

Folland's proof that we get an algebra from an elementary family: why can we assume the sets are disjoint?

Published on 26 Sep 2019 - 21:48

score 1.1k · Answer 4 · 2019-10-01 23:41:22

1.1k

Views

Proving that $m^*(E)=\sup\{m(F)\mid F\text{ is closed}, F\subset E\}$ iff $E$ is measurable

Published on 01 Oct 2019 - 23:41

score 627 · Answer 5 · 2014-09-05 00:19:54

627

Views

Cardinality of measurable sets

Published on 05 Sep 2014 - 0:19

score 234 · Answer 6 · 2014-10-27 13:59:05

234

Views

Find all measurable sets whose subsets are measurable

Published on 27 Oct 2014 - 13:59

score 93 · Answer 7 · 2014-11-30 06:37:57

93

Views

Determining measurable sets

Published on 30 Nov 2014 - 6:37

score 3.1k · Answer 8 · 2014-12-12 19:47:30

3.1k

Views

Countable union of measurable sets is measurable?

Published on 12 Dec 2014 - 19:47

score 1.6k · Answer 9 · 2026-03-19 16:59:01

1.6k

Views

Definitions of Measurability: Outer-inner measure convergence vs. Caratheodory criterion

Published on 19 Mar 2026 - 16:59

score 214 · Answer 10 · 2019-10-08 14:10:22

214

Views

Why does measurable function need to be defined on a measurable domain?

Published on 08 Oct 2019 - 14:10

score 467 · Answer 11 · 2026-03-24 22:01:02

467

Views

if $f \geq 0$ Lebesgue measurable the set $A := \{(x,y)\in \mathbb{R}^2 \mid 0 < y < f(x)\}$ is measurable - proof verification

Published on 24 Mar 2026 - 22:01

score 181 · Answer 12 · 2026-03-21 07:09:56

181

Views

The positive variation satisfies $\lambda^{+}=\sup\{\lambda (F) : F\subset E, F\in\chi \}$

Published on 21 Mar 2026 - 7:09

score 715 · Answer 13 · 2019-11-01 17:24:30

715

Views

Function defined on a zero measured set

Published on 01 Nov 2019 - 17:24

score 141 · Answer 14 · 2026-03-07 10:54:42

141

Views

Example for a non-Borel set $A$ in $\mathbb{R}^2$ such that all $x$- and $y$- sections are measurable

Published on 07 Mar 2026 - 10:54

score 44 · Answer 15 · 2019-11-18 18:38:59

44

Views

Regular set for a nearly Borel set is Borel (Brownian motion)?

Published on 18 Nov 2019 - 18:38

List Question

What is an example of a covering of the set of irrational numbers in the interval $[0,1]$, with a total length of $1$?

Why is $\{\{c\}:c \in \mathbb{R} \}$ not a generator of the Borel $\sigma$ field in $\mathbb{R}$?

Folland's proof that we get an algebra from an elementary family: why can we assume the sets are disjoint?

Proving that $m^*(E)=\sup\{m(F)\mid F\text{ is closed}, F\subset E\}$ iff $E$ is measurable

Cardinality of measurable sets

Find all measurable sets whose subsets are measurable

Determining measurable sets

Countable union of measurable sets is measurable?

Definitions of Measurability: Outer-inner measure convergence vs. Caratheodory criterion

Why does measurable function need to be defined on a measurable domain?

if $f \geq 0$ Lebesgue measurable the set $A := \{(x,y)\in \mathbb{R}^2 \mid 0 < y < f(x)\}$ is measurable - proof verification

The positive variation satisfies $\lambda^{+}=\sup\{\lambda (F) : F\subset E, F\in\chi \}$

Function defined on a zero measured set

Example for a non-Borel set $A$ in $\mathbb{R}^2$ such that all $x$- and $y$- sections are measurable

Regular set for a nearly Borel set is Borel (Brownian motion)?

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