Question

Caratheodory's criterion strengthening for open intervals

score 270 · Answer 1 · 2026-04-10 13:03:22

270

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Caratheodory's criterion strengthening for open intervals

Published on 10 Apr 2026 - 13:03

score 105 · Answer 2 · 2020-02-08 07:53:30

105

Views

Proof of $m_(E_1\times E_2)\leq m_(E_1)m_*(E_2)$

Published on 08 Feb 2020 - 7:53

score 80 · Answer 3 · 2020-02-08 15:27:55

80

Views

Showing that $m(E_1\times E_2)=m(E_1)m(E_2)$

Published on 08 Feb 2020 - 15:27

score 557 · Answer 4 · 2020-02-09 01:59:10

557

Views

Examples of nicely shrinking sets (Rudin)

Published on 09 Feb 2020 - 1:59

score 34 · Answer 5 · 2026-04-13 00:45:05

34

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Lebesgue measure of a set $G$

Published on 13 Apr 2026 - 0:45

score 128 · Answer 6 · 2020-02-09 11:12:45

128

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Find $A\subseteq [0,1]$ such that $\lim\limits_{\varepsilon\to0}\frac{m(A\cap[0,\varepsilon])}{\varepsilon}=\frac{1}{2}$

Published on 09 Feb 2020 - 11:12

score 98 · Answer 7 · 2020-02-09 11:57:24

98

Views

$\sum_{k=1}^\infty\frac{1}{k^3|x-x_k|^2}$ converges a.s. in [0,1]

Published on 09 Feb 2020 - 11:57

score 70 · Answer 8 · 2020-02-09 15:39:00

70

Views

Let $A,F\subset\mathbb R$ be two sets such that $m(A)>0,\vert F\vert<\infty$. Prove $\exists\alpha,\beta\neq 0\quad \alpha+\beta F\subset A$

Published on 09 Feb 2020 - 15:39

score 40 · Answer 9 · 2026-04-12 19:49:41

40

Views

$\mathbb{P}(E \cap A) = \mathbb{E}[\mathbb{P}(E|G)*\textbf{I}_{A}]$?

Published on 12 Apr 2026 - 19:49

score 180 · Answer 10 · 2026-04-04 07:54:56

180

Views

Rudin Real and Complex Analysis, How Theorem 7.10 leads to a generalization of Theorem 7.8?

Published on 04 Apr 2026 - 7:54

score 57 · Answer 11 · 2026-04-12 13:02:53

57

Views

Metric density of a Lebesgue mesurable set in $\Bbb R^k$

Published on 12 Apr 2026 - 13:02

score 392 · Answer 12 · 2026-04-12 16:51:15

392

Views

Unbounded open set of $\mathbb{R}^n$ with finite measure

Published on 12 Apr 2026 - 16:51

score 86 · Answer 13 · 2026-04-09 12:05:41

86

Views

Locally integrable function in Lebesgue sense

Published on 09 Apr 2026 - 12:05

score 39 · Answer 14 · 2026-04-12 01:43:31

39

Views

Proof of existence of subset with specific lebesgue meausre

Published on 12 Apr 2026 - 1:43

score 31 · Answer 15 · 2020-02-13 21:44:45

31

Views

Does a set having a finite measure imply that the magnitude of the set is finite?

Published on 13 Feb 2020 - 21:44

List Question

Caratheodory's criterion strengthening for open intervals

Proof of $m_(E_1\times E_2)\leq m_(E_1)m_*(E_2)$

Showing that $m(E_1\times E_2)=m(E_1)m(E_2)$

Examples of nicely shrinking sets (Rudin)

Lebesgue measure of a set $G$

Find $A\subseteq [0,1]$ such that $\lim\limits_{\varepsilon\to0}\frac{m(A\cap[0,\varepsilon])}{\varepsilon}=\frac{1}{2}$

$\sum_{k=1}^\infty\frac{1}{k^3|x-x_k|^2}$ converges a.s. in [0,1]

Let $A,F\subset\mathbb R$ be two sets such that $m(A)>0,\vert F\vert<\infty$. Prove $\exists\alpha,\beta\neq 0\quad \alpha+\beta F\subset A$

$\mathbb{P}(E \cap A) = \mathbb{E}[\mathbb{P}(E|G)*\textbf{I}_{A}]$?

Rudin Real and Complex Analysis, How Theorem 7.10 leads to a generalization of Theorem 7.8?

Metric density of a Lebesgue mesurable set in $\Bbb R^k$

Unbounded open set of $\mathbb{R}^n$ with finite measure

Locally integrable function in Lebesgue sense

Proof of existence of subset with specific lebesgue meausre

Does a set having a finite measure imply that the magnitude of the set is finite?

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