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Lim Inf and Lim Sup of Double Sequences

score 16 · Answer 1 · 2026-03-09 05:46:30

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Lim Inf and Lim Sup of Double Sequences

Published on 09 Mar 2026 - 5:46

score 51 · Answer 2 · 2024-03-27 17:57:08

51

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Find $\mathop{\limsup}\limits_{n\to\infty} a_n$ and $\mathop{\liminf}\limits_{n\to\infty} a_n$ if $a_n = n(2+(-1)^n)$

Published on 27 Mar 2024 - 17:57

score 2.1k · Answer 3 · 2026-03-26 12:42:48

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Borel-Cantelli Lemma Proof.

Published on 26 Mar 2026 - 12:42

score 210 · Answer 4 · 2015-01-06 20:35:46

210

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Violation of Fatou's theorem?

Published on 06 Jan 2015 - 20:35

score 79 · Answer 5 · 2015-01-08 07:40:02

79

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Proving that $\liminf_{n\to\infty} x_n = \sup\left\{z : \{n : x_n < z\} \text{ is finite}\right\}$; what does the answer mean?

Published on 08 Jan 2015 - 7:40

score 5.7k · Answer 6 · 2015-01-12 00:37:25

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How to prove that the limsup of a sequence is equal to its greatest subsequential limit?

Published on 12 Jan 2015 - 0:37

score 1.8k · Answer 7 · 2015-01-12 01:21:25

1.8k

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Showing that lim sup of sum of iid binary variables $X_i$ with $P[X_i = 1] = P[X_i = -1] = 1/2$ is a.s. infinite

Published on 12 Jan 2015 - 1:21

score 282 · Answer 8 · 2015-01-13 03:21:24

282

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the relation between the lower limit of set and the lower limit of function

Published on 13 Jan 2015 - 3:21

score 2.6k · Answer 9 · 2015-01-20 13:55:32

2.6k

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Is $\lim\sup=\sup\lim$?

Published on 20 Jan 2015 - 13:55

score 98 · Answer 10 · 2015-01-20 18:50:19

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Is there a Heine cretierion of liminf of a function?

Published on 20 Jan 2015 - 18:50

score 2.2k · Answer 11 · 2015-01-21 09:24:30

2.2k

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Computing lim sup and lim inf of $\exp(n\sin(\frac{n\pi}{2}))+\exp(\frac{1}{n}\cos(\frac{n\pi}{2}))$ and $\cosh(n\sin(\frac{n²+1}{n}\frac{\pi}{2}))$?

Published on 21 Jan 2015 - 9:24

score 102 · Answer 12 · 2015-01-21 15:02:52

102

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Prove: $\limsup_{n\to\infty} (a_n)\leq \sup(a_n)_{n=1}^\infty$

Published on 21 Jan 2015 - 15:02

score 1.6k · Answer 13 · 2015-01-27 09:43:30

1.6k

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Exercise from Williams book Probability with martingales

Published on 27 Jan 2015 - 9:43

score 31 · Answer 14 · 2015-01-28 20:04:26

31

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Inequality connecting inf and liminf

Published on 28 Jan 2015 - 20:04

score 37 · Answer 15 · 2015-01-29 15:50:52

37

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Limsup question $ \sum_{n=1}^N \sum_{m=1}^N x_{m-n} \leq N^2 \bigg( \limsup_{n \to \infty} x_n + o(1) \bigg) $

Published on 29 Jan 2015 - 15:50

List Question

Lim Inf and Lim Sup of Double Sequences

Find $\mathop{\limsup}\limits_{n\to\infty} a_n$ and $\mathop{\liminf}\limits_{n\to\infty} a_n$ if $a_n = n(2+(-1)^n)$

Borel-Cantelli Lemma Proof.

Violation of Fatou's theorem?

Proving that $\liminf_{n\to\infty} x_n = \sup\left\{z : \{n : x_n < z\} \text{ is finite}\right\}$; what does the answer mean?

How to prove that the limsup of a sequence is equal to its greatest subsequential limit?

Showing that lim sup of sum of iid binary variables $X_i$ with $P[X_i = 1] = P[X_i = -1] = 1/2$ is a.s. infinite

the relation between the lower limit of set and the lower limit of function

Is $\lim\sup=\sup\lim$?

Is there a Heine cretierion of liminf of a function?

Computing lim sup and lim inf of $\exp(n\sin(\frac{n\pi}{2}))+\exp(\frac{1}{n}\cos(\frac{n\pi}{2}))$ and $\cosh(n\sin(\frac{n²+1}{n}\frac{\pi}{2}))$?

Prove: $\limsup_{n\to\infty} (a_n)\leq \sup(a_n)_{n=1}^\infty$

Exercise from Williams book Probability with martingales

Inequality connecting inf and liminf

Limsup question $ \sum_{n=1}^N \sum_{m=1}^N x_{m-n} \leq N^2 \bigg( \limsup_{n \to \infty} x_n + o(1) \bigg) $

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