List questions from limsup-and-liminf

Published on 24 May 2020 - 5:34

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An equivalent definition for the limsup $a_n$

Published on 26 May 2020 - 1:17

225

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I don't understand $\limsup_n\:A_n$ in Probability Theory, why should it be equal to "infinitely many $A_n$ occur"?

Published on 27 May 2020 - 12:56

66

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can we say that there exists a subsequence $\{x_{n_k}\}$ of $\{x_n\}$ such that: $ x_{n_k}\leq x\qquad k\geq 1 $

Published on 28 May 2020 - 23:14

33

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Example of sequences that satisfy limsup and liminf properties

Published on 30 May 2020 - 0:11

43

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Questions on Limit Superior

Published on 31 May 2020 - 7:56

62

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cluster points of $\left( u_{0}u_{1}\cdots u_{n}\right) ^{\frac{1}{n}}$

Published on 01 Jun 2020 - 12:24

85

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Some doubts about Levy's Continuity Theorem proof - Convergence results

Published on 01 Jun 2020 - 13:06

739

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Proof checking $\liminf cx_n = c \limsup x_n$

Published on 05 Jun 2020 - 16:23

39

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If $\limsup_n x_n\leq M$ then there exists a subsequence $\{y_{n}\}$ such that $ y_{n}\leq y_{n+1}$ and $ y_n\leq M$, $\forall n $

Published on 06 Jun 2020 - 5:18

358

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proof that $\lim \sup (a_n · b_n) = \lim \sup a_n · \lim \sup b_n $

Published on 26 Mar 2026 - 9:42

46

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Is this proof that Cauchy sequences converge right?

Published on 15 Jun 2020 - 5:09

129

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Can someone help me understand $\lim \sup$ and $\lim \inf$.

Published on 16 Jun 2020 - 9:28

38

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Lower limit and subsequence

Published on 23 Feb 2026 - 11:33

86

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Proving $\Theta(n^{k})= {n \choose k}$

Published on 18 Jun 2020 - 8:16

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Closed ball is weakly closed

An equivalent definition for the limsup $a_n$

I don't understand $\limsup_n\:A_n$ in Probability Theory, why should it be equal to "infinitely many $A_n$ occur"?

can we say that there exists a subsequence $\{x_{n_k}\}$ of $\{x_n\}$ such that: $ x_{n_k}\leq x\qquad k\geq 1 $

Example of sequences that satisfy limsup and liminf properties

Questions on Limit Superior

cluster points of $\left( u_{0}u_{1}\cdots u_{n}\right) ^{\frac{1}{n}}$

Some doubts about Levy's Continuity Theorem proof - Convergence results

Proof checking $\liminf cx_n = c \limsup x_n$

If $\limsup_n x_n\leq M$ then there exists a subsequence $\{y_{n}\}$ such that $ y_{n}\leq y_{n+1}$ and $ y_n\leq M$, $\forall n $

proof that $\lim \sup (a_n · b_n) = \lim \sup a_n · \lim \sup b_n $

Is this proof that Cauchy sequences converge right?

Can someone help me understand $\lim \sup$ and $\lim \inf$.

Lower limit and subsequence

Proving $\Theta(n^{k})= {n \choose k}$

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