Question

$\limsup$ of a sequence of decreasing expected value

score 36 · Answer 1 · 2023-10-15 11:04:01

36

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$\limsup$ of a sequence of decreasing expected value

Published on 15 Oct 2023 - 11:04

score 49 · Answer 2 · 2023-10-19 12:57:48

49

Views

Hypothesis needed to show that $\lim \inf a_n \leq \lim \sup a_n$.

Published on 19 Oct 2023 - 12:57

score 44 · Answer 3 · 2023-10-19 21:24:00

44

Views

Proving $\limsup$ of sequence $x_n=(-1)^n\frac{n+1}{n}$

Published on 19 Oct 2023 - 21:24

score 175 · Answer 4 · 2023-10-20 14:28:12

175

Views

Show that set of all accumulation points is the closed interval $[\liminf_{n\rightarrow\infty}(x_n),\limsup_{n\rightarrow\infty}(x_n)]$

Published on 20 Oct 2023 - 14:28

score 63 · Answer 5 · 2023-10-28 03:58:14

63

Views

Help with a proof of a result for the limit superior of the sum of two sequences of real numbers

Published on 28 Oct 2023 - 3:58

score 64 · Answer 6 · 2023-11-02 17:28:12

64

Views

If $\sum_{n}E(|X_{n}-X|^{r})<\infty$ for some $r>0$. Show $X_{n}\rightarrow X$ a.s

Published on 02 Nov 2023 - 17:28

score 39 · Answer 7 · 2023-11-03 07:42:17

39

Views

Directional derivative of $F(x, y)=\sum_{0\leq i, j\leq m}z_{i,j} \max(1-|i-mx|)\max(1-|j-my|)$

Published on 03 Nov 2023 - 7:42

score 25 · Answer 8 · 2023-11-05 15:55:55

25

Views

Lim inf and definition

Published on 05 Nov 2023 - 15:55

score 43 · Answer 9 · 2026-03-26 10:59:41

43

Views

Is $\mu: \mathcal{P}(\mathbb{N}) \rightarrow [0, \infty]$ a measure or outer measure?

Published on 26 Mar 2026 - 10:59

score 19 · Answer 10 · 2026-02-23 13:36:53

19

Views

Does the range of a linearly growing sequence have positive density in the integers?

Published on 23 Feb 2026 - 13:36

score 40 · Answer 11 · 2023-11-12 15:56:11

40

Views

Behaviour and limits of $f(n+1) = \frac{f^5(n)}{2} - f(n-1)$

Published on 12 Nov 2023 - 15:56

score 42 · Answer 12 · 2023-11-16 06:44:47

42

Views

$\lim \sup$ and $\lim \inf$ of $a_n$

Published on 16 Nov 2023 - 6:44

score 41 · Answer 13 · 2023-11-17 15:40:03

41

Views

An inequality involving $\limsup$ to prove continuity of probability

Published on 17 Nov 2023 - 15:40

score 37 · Answer 14 · 2026-03-28 20:53:48

37

Views

Does the limit in probability equal almost surely to the liminf?

Published on 28 Mar 2026 - 20:53

score 19 · Answer 15 · 2026-03-28 06:09:47

19

Views

Limit of a sum with bound depending on the limit

Published on 28 Mar 2026 - 6:09

List Question

$\limsup$ of a sequence of decreasing expected value

Hypothesis needed to show that $\lim \inf a_n \leq \lim \sup a_n$.

Proving $\limsup$ of sequence $x_n=(-1)^n\frac{n+1}{n}$

Show that set of all accumulation points is the closed interval $[\liminf_{n\rightarrow\infty}(x_n),\limsup_{n\rightarrow\infty}(x_n)]$

Help with a proof of a result for the limit superior of the sum of two sequences of real numbers

If $\sum_{n}E(|X_{n}-X|^{r})<\infty$ for some $r>0$. Show $X_{n}\rightarrow X$ a.s

Directional derivative of $F(x, y)=\sum_{0\leq i, j\leq m}z_{i,j} \max(1-|i-mx|)\max(1-|j-my|)$

Lim inf and definition

Is $\mu: \mathcal{P}(\mathbb{N}) \rightarrow [0, \infty]$ a measure or outer measure?

Does the range of a linearly growing sequence have positive density in the integers?

Behaviour and limits of $f(n+1) = \frac{f^5(n)}{2} - f(n-1)$

$\lim \sup$ and $\lim \inf$ of $a_n$

An inequality involving $\limsup$ to prove continuity of probability

Does the limit in probability equal almost surely to the liminf?

Limit of a sum with bound depending on the limit

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