Question

$\limsup a_n=-\infty$ if $\{a_n\}$ does not have a subsequence which is bounded below

score 57 · Answer 1 · 2018-04-25 18:36:23

57

Views

$\limsup a_n=-\infty$ if $\{a_n\}$ does not have a subsequence which is bounded below

Published on 25 Apr 2018 - 18:36

score 441 · Answer 2 · 2018-04-26 18:25:17

441

Views

Prove that this sequence does NOT converge uniformly on [0,1] AND (0,1).

Published on 26 Apr 2018 - 18:25

score 776 · Answer 3 · 2018-04-29 08:50:01

776

Views

Exchange a limit with a $\limsup$ or $\liminf$

Published on 29 Apr 2018 - 8:50

score 125 · Answer 4 · 2018-05-03 10:58:37

125

Views

Prove that $X_1, X_2, ..., X_k$ is independent of $\liminf X_n$ by analogy with events.

Published on 03 May 2018 - 10:58

score 619 · Answer 5 · 2018-05-04 03:48:28

619

Views

Use Blumenthal's 0-1 law to solve the following

Published on 04 May 2018 - 3:48

score 70 · Answer 6 · 2018-05-06 12:13:46

70

Views

Show that $\liminf\limits_{x\to \infty}|f'(x)|=0$ if $\lim\limits_{x\to \infty}f(x)/x=0$ and $f$ is differentiable

Published on 06 May 2018 - 12:13

score 55 · Answer 7 · 2018-05-07 17:27:14

55

Views

Given that $f(x)\geq x^2,\;\;\forall\;x\in(0,\infty),\;\;a_{n+1}\leq a_n -2f(a_n),\;\;\forall n\geq 1,$ prove that $\liminf\limits_{n\to \infty}a_n=0$

Published on 07 May 2018 - 17:27

score 46 · Answer 8 · 2018-05-07 19:43:38

46

Views

What is meant by this limsup?

Published on 07 May 2018 - 19:43

score 66 · Answer 9 · 2018-05-08 05:05:24

66

Views

Proving that $\liminf\limits_{n\to \infty}\int f_n(x)dx\neq \int f(x)dx$

Published on 08 May 2018 - 5:05

score 250 · Answer 10 · 2018-05-09 18:34:56

250

Views

Understanding special case og Liouville Theorem for subharmonic functions

Published on 09 May 2018 - 18:34

score 391 · Answer 11 · 2018-05-10 14:09:06

391

Views

Dini Derivatives

Published on 10 May 2018 - 14:09

score 313 · Answer 12 · 2018-05-11 15:29:37

313

Views

Convergence in distribution: Show $ \lim_{n \rightarrow \infty} \sup \mathbb{P} (x^n \in C) \leq \ \mathbb{P}(x \in C) $

Published on 11 May 2018 - 15:29

score 111 · Answer 13 · 2018-05-13 04:43:27

111

Views

Can $\limsup = \liminf$ only almost surely?

Published on 13 May 2018 - 4:43

score 551 · Answer 14 · 2018-05-14 00:21:20

551

Views

Showing formally that the sup of sub-sequential limits is the same as $ \lim_{n \to \infty} \sup_{m \geq n} s_m$?

Published on 14 May 2018 - 0:21

score 99 · Answer 15 · 2018-05-16 10:42:31

99

Views

Problem with $\infty$. Why are limsup and liminf conditions fulfilled?

Published on 16 May 2018 - 10:42

List Question

$\limsup a_n=-\infty$ if $\{a_n\}$ does not have a subsequence which is bounded below

Prove that this sequence does NOT converge uniformly on [0,1] AND (0,1).

Exchange a limit with a $\limsup$ or $\liminf$

Prove that $X_1, X_2, ..., X_k$ is independent of $\liminf X_n$ by analogy with events.

Use Blumenthal's 0-1 law to solve the following

Show that $\liminf\limits_{x\to \infty}|f'(x)|=0$ if $\lim\limits_{x\to \infty}f(x)/x=0$ and $f$ is differentiable

Given that $f(x)\geq x^2,\;\;\forall\;x\in(0,\infty),\;\;a_{n+1}\leq a_n -2f(a_n),\;\;\forall n\geq 1,$ prove that $\liminf\limits_{n\to \infty}a_n=0$

What is meant by this limsup?

Proving that $\liminf\limits_{n\to \infty}\int f_n(x)dx\neq \int f(x)dx$

Understanding special case og Liouville Theorem for subharmonic functions

Dini Derivatives

Convergence in distribution: Show $ \lim_{n \rightarrow \infty} \sup \mathbb{P} (x^n \in C) \leq \ \mathbb{P}(x \in C) $

Can $\limsup = \liminf$ only almost surely?

Showing formally that the sup of sub-sequential limits is the same as $ \lim_{n \to \infty} \sup_{m \geq n} s_m$?

Problem with $\infty$. Why are limsup and liminf conditions fulfilled?

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