Question

Showing $\{X_n\}$ is uniformly integrable when $\sup _{n} \mathbb{E}\left[X_{n}^{2}\right]<\infty$

score 786 · Answer 1 · 2026-04-16 03:17:48

786

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Showing $\{X_n\}$ is uniformly integrable when $\sup _{n} \mathbb{E}\left[X_{n}^{2}\right]<\infty$

Published on 16 Apr 2026 - 3:17

score 39 · Answer 2 · 2026-04-14 15:30:20

39

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Can we say that $\{f_n\}\text{ is uniformly integrable over }E\setminus (\cap_p B_p)$?

Published on 14 Apr 2026 - 15:30

score 28 · Answer 3 · 2026-04-14 22:59:48

28

Views

There exists a nonnull subset $A\in \mathcal{A}$ such that : $ \{f_n\}, \{g_n\}\text{ and }\{h_n\} \text{ are uniformly integrable on }A $?

Published on 14 Apr 2026 - 22:59

score 56 · Answer 4 · 2026-04-17 13:51:00

56

Views

$f_\infty(t)=g_\infty(t)$ a.e?

Published on 17 Apr 2026 - 13:51

score 92 · Answer 5 · 2026-04-14 23:06:49

92

Views

If $f$ us periodic and even, what I can conclude about of $\int f \;dx$?

Published on 14 Apr 2026 - 23:06

score 66 · Answer 6 · 2026-04-11 12:17:59

66

Views

How do we apply the dominated convergence theorem to conclude the proposed claim?

Published on 11 Apr 2026 - 12:17

score 580 · Answer 7 · 2026-04-13 18:39:08

580

Views

Martingale Convergence Theorem

Published on 13 Apr 2026 - 18:39

score 2.5k · Answer 8 · 2026-04-16 14:27:46

2.5k

Views

If $(X_n)$ is bounded in $L^1$ and converges in probability then $(X_n)$ is uniformly integrable?

Published on 16 Apr 2026 - 14:27

score 443 · Answer 9 · 2026-04-15 07:44:53

443

Views

Strengthening Central Limit Theorem to Convergence of Mean for Specific Case

Published on 15 Apr 2026 - 7:44

score 702 · Answer 10 · 2026-04-14 07:07:22

702

Views

What is the origin of the term "Crystal Ball Condition"?

Published on 14 Apr 2026 - 7:07

score 1k · Answer 11 · 2026-04-13 23:20:53

1k

Views

Uniformly integrable set is bounded in $L^1$

Published on 13 Apr 2026 - 23:20

score 83 · Answer 12 · 2026-04-14 03:03:58

83

Views

Discrete martingales in $L^p$

Published on 14 Apr 2026 - 3:03

score 50 · Answer 13 · 2026-04-17 15:44:09

50

Views

Justify $\lim_{r \to \infty} E[M_r 1_F] = E[\lim_{r \to \infty} M_r 1_F]$

Published on 17 Apr 2026 - 15:44

score 162 · Answer 14 · 2026-04-17 08:38:12

162

Views

If $(f_n)$ is uniformly integrable wrt $P$ and $Q \ll P$, then is $(f_n)$ uniformly integrable wrt $Q$?

Published on 17 Apr 2026 - 8:38

score 146 · Answer 15 · 2026-04-11 08:48:59

146

Views

Limit of an integral: Possible issue with uniform integrability?

Published on 11 Apr 2026 - 8:48

List Question

Showing $\{X_n\}$ is uniformly integrable when $\sup _{n} \mathbb{E}\left[X_{n}^{2}\right]<\infty$

Can we say that $\{f_n\}\text{ is uniformly integrable over }E\setminus (\cap_p B_p)$?

There exists a nonnull subset $A\in \mathcal{A}$ such that : $ \{f_n\}, \{g_n\}\text{ and }\{h_n\} \text{ are uniformly integrable on }A $?

$f_\infty(t)=g_\infty(t)$ a.e?

If $f$ us periodic and even, what I can conclude about of $\int f \;dx$?

How do we apply the dominated convergence theorem to conclude the proposed claim?

Martingale Convergence Theorem

If $(X_n)$ is bounded in $L^1$ and converges in probability then $(X_n)$ is uniformly integrable?

Strengthening Central Limit Theorem to Convergence of Mean for Specific Case

What is the origin of the term "Crystal Ball Condition"?

Uniformly integrable set is bounded in $L^1$

Discrete martingales in $L^p$

Justify $\lim_{r \to \infty} E[M_r 1_F] = E[\lim_{r \to \infty} M_r 1_F]$

If $(f_n)$ is uniformly integrable wrt $P$ and $Q \ll P$, then is $(f_n)$ uniformly integrable wrt $Q$?

Limit of an integral: Possible issue with uniform integrability?

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