Question

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

score 60 · Answer 1 · 2026-04-11 04:41:26

60

Views

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

Published on 11 Apr 2026 - 4:41

score 444 · Answer 2 · 2026-04-14 06:39:20

444

Views

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

Published on 14 Apr 2026 - 6:39

score 778 · Answer 3 · 2026-04-15 14:39:45

778

Views

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

Published on 15 Apr 2026 - 14:39

score 128 · Answer 4 · 2026-04-16 12:19:44

128

Views

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

Published on 16 Apr 2026 - 12:19

score 622 · Answer 5 · 2026-04-14 17:43:40

622

Views

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

Published on 14 Apr 2026 - 17:43

score 73 · Answer 6 · 2026-04-16 08:08:46

73

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 16 Apr 2026 - 8:08

score 58 · Answer 7 · 2026-04-16 17:33:12

58

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 16 Apr 2026 - 17:33

score 50 · Answer 8 · 2026-04-11 17:37:39

50

Views

What is meant by this limsup?

Published on 11 Apr 2026 - 17:37

score 69 · Answer 9 · 2026-04-16 01:34:24

69

Views

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

Published on 16 Apr 2026 - 1:34

score 253 · Answer 10 · 2026-04-11 03:30:14

253

Views

Understanding special case og Liouville Theorem for subharmonic functions

Published on 11 Apr 2026 - 3:30

score 396 · Answer 11 · 2026-04-14 23:15:43

396

Views

Dini Derivatives

Published on 14 Apr 2026 - 23:15

score 316 · Answer 12 · 2026-04-15 22:50:31

316

Views

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

Published on 15 Apr 2026 - 22:50

score 114 · Answer 13 · 2026-04-11 17:52:43

114

Views

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

Published on 11 Apr 2026 - 17:52

score 554 · Answer 14 · 2026-04-15 21:43:51

554

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 15 Apr 2026 - 21:43

score 102 · Answer 15 · 2026-04-11 22:17:10

102

Views

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

Published on 11 Apr 2026 - 22:17

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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