Question

If for any $a$, $g(a, b) \rightarrow 0$ as $b \rightarrow \infty$, then does $\sup_a g(a, b) \rightarrow 0$ when $b \rightarrow \infty$?

score 25 · Answer 1 · 2023-03-14 07:36:26

25

Views

If for any $a$, $g(a, b) \rightarrow 0$ as $b \rightarrow \infty$, then does $\sup_a g(a, b) \rightarrow 0$ when $b \rightarrow \infty$?

Published on 14 Mar 2023 - 7:36

score 49 · Answer 2 · 2026-02-23 10:05:13

49

Views

Assume $M^{\tau_n}$ is uniformly integrable. Is $X^{\tau_n}$ uniformly integrable?

Published on 23 Feb 2026 - 10:05

score 322 · Answer 3 · 2023-04-03 01:46:44

322

Views

Uniform integrability of a martingale

Published on 03 Apr 2023 - 1:46

score 168 · Answer 4 · 2023-04-05 14:40:51

168

Views

Show that $X$ is finite and $E(|X|)<\infty$

Published on 05 Apr 2023 - 14:40

score 44 · Answer 5 · 2023-05-11 12:08:09

44

Views

Uniform integrability of $X_n=\alpha^n\mathbb{I}_{(0,2^{-n})}$, $\alpha \in (0,1)$, $\Omega=(0,1)$

Published on 11 May 2023 - 12:08

score 59 · Answer 6 · 2023-06-07 09:58:00

59

Views

Details on the proof of: Suppose $X_n \xrightarrow{\mathbb{P}} X$. $X_n$ is uniformly integrable (u.i.) $\implies$ $X_n \xrightarrow{L^1} X$

Published on 07 Jun 2023 - 9:58

score 64 · Answer 7 · 2023-07-04 15:01:16

64

Views

Uniform convergence in distribution implies convergence of moments

Published on 04 Jul 2023 - 15:01

score 28 · Answer 8 · 2023-07-06 11:57:44

28

Views

Convergence in prob. + Uniform integrability => L1 convergence (proof with rate of convergence)

Published on 06 Jul 2023 - 11:57

score 24 · Answer 9 · 2026-03-25 06:10:39

24

Views

How to show following is weakly sequentially compact.

Published on 25 Mar 2026 - 6:10

score 53 · Answer 10 · 2023-08-29 10:26:19

53

Views

Why is the definition of Uniform Integrability not interesting for infinite measures?

Published on 29 Aug 2023 - 10:26

score 205 · Answer 11 · 2023-10-01 18:33:57

205

Views

Show that a family is uniformly integrable

Published on 01 Oct 2023 - 18:33

score 140 · Answer 12 · 2023-10-10 21:31:40

140

Views

Sufficient condition for $L^1$ convergence using uniformly integrabllity

Published on 10 Oct 2023 - 21:31

score 64 · Answer 13 · 2023-10-13 17:08:11

64

Views

Uniform integrability with respect to a family of measures

Published on 13 Oct 2023 - 17:08

score 31 · Answer 14 · 2023-10-25 17:54:01

31

Views

Redundancy In Definition of Uniform Integrability?

Published on 25 Oct 2023 - 17:54

score 85 · Answer 15 · 2023-12-04 19:38:15

85

Views

If $\{f_n\}$ is uniformly integrable, then there's a subsequence $(f_{k_n})$ of $(f_n)$ such that $\big(\int _Ef_{k_n}d\mu \big)$ is a Cauchy sequence

Published on 04 Dec 2023 - 19:38

List Question

If for any $a$, $g(a, b) \rightarrow 0$ as $b \rightarrow \infty$, then does $\sup_a g(a, b) \rightarrow 0$ when $b \rightarrow \infty$?

Assume $M^{\tau_n}$ is uniformly integrable. Is $X^{\tau_n}$ uniformly integrable?

Uniform integrability of a martingale

Show that $X$ is finite and $E(|X|)<\infty$

Uniform integrability of $X_n=\alpha^n\mathbb{I}_{(0,2^{-n})}$, $\alpha \in (0,1)$, $\Omega=(0,1)$

Details on the proof of: Suppose $X_n \xrightarrow{\mathbb{P}} X$. $X_n$ is uniformly integrable (u.i.) $\implies$ $X_n \xrightarrow{L^1} X$

Uniform convergence in distribution implies convergence of moments

Convergence in prob. + Uniform integrability => L1 convergence (proof with rate of convergence)

How to show following is weakly sequentially compact.

Why is the definition of Uniform Integrability not interesting for infinite measures?

Show that a family is uniformly integrable

Sufficient condition for $L^1$ convergence using uniformly integrabllity

Uniform integrability with respect to a family of measures

Redundancy In Definition of Uniform Integrability?

If $\{f_n\}$ is uniformly integrable, then there's a subsequence $(f_{k_n})$ of $(f_n)$ such that $\big(\int _Ef_{k_n}d\mu \big)$ is a Cauchy sequence

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