Question

Compact subsets of Polish spaces

score 849 · Answer 1 · 2026-05-11 06:48:25

849

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Compact subsets of Polish spaces

Published on 11 May 2026 - 6:48

score 99 · Answer 2 · 2026-04-17 03:12:12

99

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When is $\lim\limits_{t \rightarrow \infty} \mathbb{E}[X|\mathcal{F}_{t}] =\mathbb{E}\left[X|\lim\limits_{t\rightarrow\infty}\mathcal{F}_{t}\right]$?

Published on 17 Apr 2026 - 3:12

score 281 · Answer 3 · 2026-04-09 22:12:17

281

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Is $P(tautology) = 1$? What are the connections between logic and probability?

Published on 09 Apr 2026 - 22:12

score 50 · Answer 4 · 2026-04-14 20:33:13

50

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Determine if the limit of the integral is zero

Published on 14 Apr 2026 - 20:33

score 116 · Answer 5 · 2026-05-16 21:40:31

116

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If $f_n\rightarrow f$ in $L^p$-norm, $1\leq p<\infty$, then $\lim\limits_{n\rightarrow\infty}m(\{x\in\mathbb{R}^d:|f_n(x)-f(x)|>\varepsilon\})=0$

Published on 16 May 2026 - 21:40

score 41 · Answer 6 · 2026-04-18 23:31:08

41

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$P(X_1=k|X_1+X_2=j)$ for $X_1 \sim B_{n,p}$ and $X_2 \sim B_{m,p}$.

Published on 18 Apr 2026 - 23:31

score 231 · Answer 7 · 2026-04-14 18:30:53

231

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Lower-semicontinuous map defined on probability measures

Published on 14 Apr 2026 - 18:30

score 155 · Answer 8 · 2026-04-17 01:03:51

155

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If $f$ measurable positive, is there a sequence of simple function that converge decreasly to $f$?

Published on 17 Apr 2026 - 1:03

score 82 · Answer 9 · 2026-05-16 21:37:30

82

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Implicit function or measurable extension of a measurable selector

Published on 16 May 2026 - 21:37

score 42 · Answer 10 · 2026-04-14 02:42:54

42

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Functions in $L_p[0,1)$ grow at most polynomially

Published on 14 Apr 2026 - 2:42

score 282 · Answer 11 · 2026-04-14 12:43:41

282

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$\sigma$-ring generated by $\delta$-ring

Published on 14 Apr 2026 - 12:43

score 82 · Answer 12 · 2026-04-14 19:46:11

82

Views

Prove the max of convergent sequences of functions is convergent in $L^p$ space.

Published on 14 Apr 2026 - 19:46

score 39 · Answer 13 · 2026-04-17 05:31:17

39

Views

Reconstructing a measure space from an $L^2$ space.

Published on 17 Apr 2026 - 5:31

score 40 · Answer 14 · 2026-04-16 01:38:11

40

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ℝ is embedded into $ℝ^d$ via any $ι:ℝ→ℝ^d$ with $ι(x)_1=x$ and ι is related to the projection $ℝ^d$ onto the first coordinate. Does this generalize?

Published on 16 Apr 2026 - 1:38

score 109 · Answer 15 · 2026-04-12 00:16:32

109

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Continuity of integration as a function of the set

Published on 12 Apr 2026 - 0:16

List Question

Compact subsets of Polish spaces

When is $\lim\limits_{t \rightarrow \infty} \mathbb{E}[X|\mathcal{F}_{t}] =\mathbb{E}\left[X|\lim\limits_{t\rightarrow\infty}\mathcal{F}_{t}\right]$?

Is $P(tautology) = 1$? What are the connections between logic and probability?

Determine if the limit of the integral is zero

If $f_n\rightarrow f$ in $L^p$-norm, $1\leq p<\infty$, then $\lim\limits_{n\rightarrow\infty}m(\{x\in\mathbb{R}^d:|f_n(x)-f(x)|>\varepsilon\})=0$

$P(X_1=k|X_1+X_2=j)$ for $X_1 \sim B_{n,p}$ and $X_2 \sim B_{m,p}$.

Lower-semicontinuous map defined on probability measures

If $f$ measurable positive, is there a sequence of simple function that converge decreasly to $f$?

Implicit function or measurable extension of a measurable selector

Functions in $L_p[0,1)$ grow at most polynomially

$\sigma$-ring generated by $\delta$-ring

Prove the max of convergent sequences of functions is convergent in $L^p$ space.

Reconstructing a measure space from an $L^2$ space.

ℝ is embedded into $ℝ^d$ via any $ι:ℝ→ℝ^d$ with $ι(x)_1=x$ and ι is related to the projection $ℝ^d$ onto the first coordinate. Does this generalize?

Continuity of integration as a function of the set

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