Question

Prove: For open sets $(U_i)_{i\in I}$ with $\mu(U_i)=0 \implies \mu(\bigcup_{i\in I}U_i)=0$

score 45 · Answer 1 · 2026-04-13 21:03:53

45

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Prove: For open sets $(U_i)_{i\in I}$ with $\mu(U_i)=0 \implies \mu(\bigcup_{i\in I}U_i)=0$

Published on 13 Apr 2026 - 21:03

score 108 · Answer 2 · 2026-04-17 01:17:25

108

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Dependence of expectation operator on order properties of sample space

Published on 17 Apr 2026 - 1:17

score 349 · Answer 3 · 2026-04-14 19:36:53

349

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Prove that $f^2$ is Lebesgue integrable if and only if $\sum_{k=1}^\infty k \cdot m\{x\in A: |f(x)|>k\}<\infty.$

Published on 14 Apr 2026 - 19:36

score 56 · Answer 4 · 2026-04-15 19:30:24

56

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Show that the following set is dense in $L^1 (\Bbb R^d)$.

Published on 15 Apr 2026 - 19:30

score 279 · Answer 5 · 2026-04-19 03:49:06

279

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Product Measures and Cartesian Products

Published on 19 Apr 2026 - 3:49

score 171 · Answer 6 · 2026-04-09 05:15:44

171

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Can we prove change of variable using Skorokhod representation instead of standard machine?

Published on 09 Apr 2026 - 5:15

score 74 · Answer 7 · 2026-04-17 11:02:58

74

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$A,B_1,B_2$ stochastically independent $\Rightarrow$ $A$ independent of $B_1 \cup B_2$?

Published on 17 Apr 2026 - 11:02

score 87 · Answer 8 · 2026-04-16 05:36:07

87

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the upper bound of the supremums of the sequence

Published on 16 Apr 2026 - 5:36

score 446 · Answer 9 · 2026-04-14 05:17:24

446

Views

Independence of Ber$(1/2)$-distributed random variables

Published on 14 Apr 2026 - 5:17

score 131 · Answer 10 · 2026-04-14 07:07:04

131

Views

Completing A proof of a question related to Radon-Nikodym

Published on 14 Apr 2026 - 7:07

score 73 · Answer 11 · 2026-04-15 14:50:02

If $m\left( \sum_{k=1}^n E_k \right)>n-1 $ and each $m(E_k)>0,$ is it true that $m\left( \bigcap_{k=1}^n E_k \right)$ has positive measure?

score 166 · Answer 12 · 2026-04-13 19:25:17

166

Views

compactness of the subset in $l^{2}$

Published on 13 Apr 2026 - 19:25

score 872 · Answer 13 · 2026-04-13 09:11:47

872

Views

Meaning of "with probability approaching $1$ as $n\rightarrow \infty$"

Published on 13 Apr 2026 - 9:11

score 163 · Answer 14 · 2026-04-15 17:28:41

163

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Let $\gamma\in C(I,\Bbb R^n)$. Show that $\dim_H(\Gamma)=1$

Published on 15 Apr 2026 - 17:28

score 321 · Answer 15 · 2026-04-13 17:15:20

321

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expectation larger than limsup for sequence of random variables

Published on 13 Apr 2026 - 17:15

List Question

Prove: For open sets $(U_i)_{i\in I}$ with $\mu(U_i)=0 \implies \mu(\bigcup_{i\in I}U_i)=0$

Dependence of expectation operator on order properties of sample space

Prove that $f^2$ is Lebesgue integrable if and only if $\sum_{k=1}^\infty k \cdot m\{x\in A: |f(x)|>k\}<\infty.$

Show that the following set is dense in $L^1 (\Bbb R^d)$.

Product Measures and Cartesian Products

Can we prove change of variable using Skorokhod representation instead of standard machine?

$A,B_1,B_2$ stochastically independent $\Rightarrow$ $A$ independent of $B_1 \cup B_2$?

the upper bound of the supremums of the sequence

Independence of Ber$(1/2)$-distributed random variables

Completing A proof of a question related to Radon-Nikodym

If $m\left( \sum_{k=1}^n E_k \right)>n-1 $ and each $m(E_k)>0,$ is it true that $m\left( \bigcap_{k=1}^n E_k \right)$ has positive measure?

compactness of the subset in $l^{2}$

Meaning of "with probability approaching $1$ as $n\rightarrow \infty$"

Let $\gamma\in C(I,\Bbb R^n)$. Show that $\dim_H(\Gamma)=1$

expectation larger than limsup for sequence of random variables

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