Question

Lebesgue measure of boundary of an open set.

score 171 · Answer 1 · 2026-04-12 12:51:46

171

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Lebesgue measure of boundary of an open set.

Published on 12 Apr 2026 - 12:51

score 111 · Answer 2 · 2026-04-16 00:00:13

111

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Show that $m(\{x\in[0,1]:\text{$x$ lies in infinitely many $E_j$}\})\geq\frac{1}{2}$ when $m(E_j)\geq\frac{1}{2}$

Published on 16 Apr 2026 - 0:00

score 74 · Answer 3 · 2026-04-09 05:31:40

74

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Properties of Lebesgue measure.

Published on 09 Apr 2026 - 5:31

score 37 · Answer 4 · 2026-04-13 21:44:27

37

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$L_2$ convergence maintains the sign

Published on 13 Apr 2026 - 21:44

score 115 · Answer 5 · 2026-04-10 01:56:33

115

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Property of Lebesgue measure in $\mathbb{R}^2$

Published on 10 Apr 2026 - 1:56

score 113 · Answer 6 · 2026-04-13 11:45:27

113

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Property of Lebesgue measure in $\mathbb{R}^2$, part 2

Published on 13 Apr 2026 - 11:45

score 71 · Answer 7 · 2026-04-17 00:28:06

71

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Proof $\exists\alpha$ s.t. $P(X>\alpha)>0$ if $P(X>0)>0$

Published on 17 Apr 2026 - 0:28

score 152 · Answer 8 · 2026-04-16 09:06:38

152

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Two sequences $f_n$ and $g_n$ such that $\int_{[0,1]}f_n g_n$ does not go to $0$ as $n\rightarrow\infty$, with these conditions on $f_n$ and $g_n$

Published on 16 Apr 2026 - 9:06

score 83 · Answer 9 · 2026-04-12 01:46:06

83

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Property of a positive Lebesgue measure set in $\mathbb{R}^n$

Published on 12 Apr 2026 - 1:46

score 53 · Answer 10 · 2026-04-15 22:20:07

53

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$f:\mathbb{R}\rightarrow\mathbb{R^2}$ such that $|f(x)-f(y)|\leq\sqrt{|x-y|}$ for every $x,y\in\mathbb{R}$. Show $m_2(f(A))=0$

Published on 15 Apr 2026 - 22:20

score 118 · Answer 11 · 2026-04-10 21:26:07

118

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Property of Lebesgue measure in $\mathbb{R}^n$

Published on 10 Apr 2026 - 21:26

score 35 · Answer 12 · 2026-03-28 21:06:46

35

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Existence of a self-similar symmetric subset of the unit square with non-trivial Lebesgue measure

Published on 28 Mar 2026 - 21:06

score 86 · Answer 13 · 2026-04-15 06:42:36

86

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To show some set is positive Lebesgue measure

Published on 15 Apr 2026 - 6:42

score 170 · Answer 14 · 2026-04-12 02:50:10

An exponential family of probability distributions have densities that are defined relative to a measure. What is a measure in this context?

score 74 · Answer 15 · 2026-04-17 12:19:13

74

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Prove that $m(\{x\in[0,1]:\lim \sup_{j\rightarrow\infty}f_j(x)\geq\frac{1}{2}\})\geq\frac{1}{2}$ under these conditions...

Published on 17 Apr 2026 - 12:19

List Question

Lebesgue measure of boundary of an open set.

Show that $m(\{x\in[0,1]:\text{$x$ lies in infinitely many $E_j$}\})\geq\frac{1}{2}$ when $m(E_j)\geq\frac{1}{2}$

Properties of Lebesgue measure.

$L_2$ convergence maintains the sign

Property of Lebesgue measure in $\mathbb{R}^2$

Property of Lebesgue measure in $\mathbb{R}^2$, part 2

Proof $\exists\alpha$ s.t. $P(X>\alpha)>0$ if $P(X>0)>0$

Two sequences $f_n$ and $g_n$ such that $\int_{[0,1]}f_n g_n$ does not go to $0$ as $n\rightarrow\infty$, with these conditions on $f_n$ and $g_n$

Property of a positive Lebesgue measure set in $\mathbb{R}^n$

$f:\mathbb{R}\rightarrow\mathbb{R^2}$ such that $|f(x)-f(y)|\leq\sqrt{|x-y|}$ for every $x,y\in\mathbb{R}$. Show $m_2(f(A))=0$

Property of Lebesgue measure in $\mathbb{R}^n$

Existence of a self-similar symmetric subset of the unit square with non-trivial Lebesgue measure

To show some set is positive Lebesgue measure

An exponential family of probability distributions have densities that are defined relative to a measure. What is a measure in this context?

Prove that $m(\{x\in[0,1]:\lim \sup_{j\rightarrow\infty}f_j(x)\geq\frac{1}{2}\})\geq\frac{1}{2}$ under these conditions...

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