Question

Union of Two Rectangles is the Disjoint Union of at most $6$ Rectangles

score 351 · Answer 1 · 2026-04-01 16:25:05

351

Views

Union of Two Rectangles is the Disjoint Union of at most $6$ Rectangles

Published on 01 Apr 2026 - 16:25

score 99 · Answer 2 · 2014-11-17 20:31:01

99

Views

$\mu$ measure on $\cal B_{\mathbb R}$ that is"linear" for some $c\in\mathbb R$ , $\mu (E)=c\cdot m(E)$

Published on 17 Nov 2014 - 20:31

score 157 · Answer 3 · 2026-04-01 07:59:44

157

Views

example of maximal operator that is integrable

Published on 01 Apr 2026 - 7:59

score 510 · Answer 4 · 2014-11-18 12:51:36

510

Views

Composition of monotonic and measurable function is measurable

Published on 18 Nov 2014 - 12:51

score 165 · Answer 5 · 2014-11-18 15:17:38

165

Views

Construction of measure on open and closed sets for $\epsilon>0$

Published on 18 Nov 2014 - 15:17

score 65 · Answer 6 · 2014-11-18 18:22:58

65

Views

Construction a measure in $[0,1]$

Published on 18 Nov 2014 - 18:22

score 4.6k · Answer 7 · 2026-04-01 16:23:18

4.6k

Views

Cartesian Product of Borel Sets is Borel Again

Published on 01 Apr 2026 - 16:23

score 259 · Answer 8 · 2014-11-19 16:43:59

259

Views

Assume that $N\subset \mathbb{R}$ is not Lebesgue measurable. Is then the set $ N\times \mathbb{R} $ also not Lebesgue measurable?

Published on 19 Nov 2014 - 16:43

score 225 · Answer 9 · 2026-03-26 06:07:04

225

Views

The behavior of BV functions at a point of approximate continuity

Published on 26 Mar 2026 - 6:07

score 174 · Answer 10 · 2026-03-25 12:28:24

174

Views

Let $f$ be measurable and $a,b\in\mathbb{R}$ with $\frac{1}{\lambda(M)}\int_Mf\ d\lambda \in [a,b]$ Show that: $f(x) \in [a,b]$ almost everywhere.

Published on 25 Mar 2026 - 12:28

score 2k · Answer 11 · 2014-11-20 03:48:42

2k

Views

Prove that the Hardy-Littlewood maximal function is bounded above and below

Published on 20 Nov 2014 - 3:48

score 428 · Answer 12 · 2014-11-20 04:14:07

428

Views

Prove every open subset of closed unit square is measurable

Published on 20 Nov 2014 - 4:14

score 26 · Answer 13 · 2014-11-20 12:30:05

26

Views

Set of differences of a set $A$ where $\lambda(A) > 1$

Published on 20 Nov 2014 - 12:30

score 905 · Answer 14 · 2014-11-20 15:06:00

905

Views

Sequence of Measurable Sets

Published on 20 Nov 2014 - 15:06

score 77 · Answer 15 · 2014-11-21 18:25:52

77

Views

If $x$ is a Lebesgue point of $f$, $f \in L^p$ and $f(x)=0$, then it is a Lebesgue point of $f^p$ where $p>1$ (finite)?

Published on 21 Nov 2014 - 18:25

List Question

Union of Two Rectangles is the Disjoint Union of at most $6$ Rectangles

$\mu$ measure on $\cal B_{\mathbb R}$ that is"linear" for some $c\in\mathbb R$ , $\mu (E)=c\cdot m(E)$

example of maximal operator that is integrable

Composition of monotonic and measurable function is measurable

Construction of measure on open and closed sets for $\epsilon>0$

Construction a measure in $[0,1]$

Cartesian Product of Borel Sets is Borel Again

Assume that $N\subset \mathbb{R}$ is not Lebesgue measurable. Is then the set $ N\times \mathbb{R} $ also not Lebesgue measurable?

The behavior of BV functions at a point of approximate continuity

Let $f$ be measurable and $a,b\in\mathbb{R}$ with $\frac{1}{\lambda(M)}\int_Mf\ d\lambda \in [a,b]$ Show that: $f(x) \in [a,b]$ almost everywhere.

Prove that the Hardy-Littlewood maximal function is bounded above and below

Prove every open subset of closed unit square is measurable

Set of differences of a set $A$ where $\lambda(A) > 1$

Sequence of Measurable Sets

If $x$ is a Lebesgue point of $f$, $f \in L^p$ and $f(x)=0$, then it is a Lebesgue point of $f^p$ where $p>1$ (finite)?

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