List questions from limsup-and-liminf

Published on 09 Dec 2013 - 22:00

165

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does taking limsup preserve inclusion relation?

Published on 11 Dec 2013 - 11:53

288

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Prove $\liminf (s_n\cdot t_n) = \liminf (s_n) \cdot \liminf (t_n)$

Published on 15 Dec 2013 - 17:05

59

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Can I conclude the following about limsup

Published on 16 Dec 2013 - 3:26

409

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The limit supremum of a function involving Brownian motion

Published on 16 Dec 2013 - 15:05

2.3k

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Find $\limsup$ and $\liminf$ of a sequence and prove $\liminf a_n \leq \limsup a_n$.

Published on 19 Dec 2013 - 2:22

140

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Proving a lower bound on the limit superior of a sequence.

Published on 21 Dec 2013 - 14:11

44

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$X_{n}$ and $Z$ be random variables if $X_{n} \ge Z$ then $ E[\liminf_{n\to \infty} X_{n}] \le \liminf_{n\to \infty} E[X_{n}] $

Published on 26 Dec 2013 - 20:35

878

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Corollary of Banach Steinhaus theorem

Published on 31 Dec 2013 - 8:42

84

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A limit involving the exponent of convergence

Published on 31 Dec 2013 - 9:24

1k

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lim sup of the square equals square of the lim sup

Published on 31 Dec 2013 - 15:50

3k

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Show root test is stronger than ratio test

Published on 02 Jan 2014 - 19:47

603

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What is a supremum?

Published on 07 Jan 2014 - 8:36

2.4k

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Lim sup sequence

Published on 08 Jan 2014 - 12:31

1.4k

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Limit superior of product of two sequences

Published on 08 Jan 2014 - 21:55

List Question

find Lim sup $X_n$ and Lim inf $X_n$?

does taking limsup preserve inclusion relation?

Prove $\liminf (s_n\cdot t_n) = \liminf (s_n) \cdot \liminf (t_n)$

Can I conclude the following about limsup

The limit supremum of a function involving Brownian motion

Find $\limsup$ and $\liminf$ of a sequence and prove $\liminf a_n \leq \limsup a_n$.

Proving a lower bound on the limit superior of a sequence.

$X_{n}$ and $Z$ be random variables if $X_{n} \ge Z$ then $ E[\liminf_{n\to \infty} X_{n}] \le \liminf_{n\to \infty} E[X_{n}] $

Corollary of Banach Steinhaus theorem

A limit involving the exponent of convergence

lim sup of the square equals square of the lim sup

Show root test is stronger than ratio test

What is a supremum?

Lim sup sequence

Limit superior of product of two sequences

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