Question

Showing a Borel-Cantelli-esque result for not necessarily independent random variables

score 1.1k · Answer 1 · 2026-03-25 23:37:56

1.1k

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Showing a Borel-Cantelli-esque result for not necessarily independent random variables

Published on 25 Mar 2026 - 23:37

score 4.2k · Answer 2 · 2014-09-23 19:22:37

4.2k

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Show that $ \limsup x_n ≤ \limsup y_n$ and $\liminf x_n ≤ \liminf y_n$

Published on 23 Sep 2014 - 19:22

score 51 · Answer 3 · 2014-09-24 23:43:50

51

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Limit superior does not increase when a sequence is replaced by its sequence of averages

Published on 24 Sep 2014 - 23:43

score 2.5k · Answer 4 · 2026-03-26 03:19:14

2.5k

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Simple example which uses Borel-Cantelli lemma

Published on 26 Mar 2026 - 3:19

score 110 · Answer 5 · 2014-09-26 07:12:07

110

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tricky question regarding Series, Limits and Convergence

Published on 26 Sep 2014 - 7:12

score 201 · Answer 6 · 2014-09-27 05:09:18

201

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Prove that $\limsup\{x_{n}+y_{n}\} =\lim_{n\rightarrow\infty}x_{n}+\limsup\{y_{n}\}$

Published on 27 Sep 2014 - 5:09

score 733 · Answer 7 · 2014-09-27 05:23:16

733

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If $\limsup x_n = x$, $\lim y_n = y$, $x_n, y_n > 0$, then does $\limsup (x_n y_n)= xy$?

Published on 27 Sep 2014 - 5:23

score 646 · Answer 8 · 2014-09-28 09:58:06

646

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Corollary of the Kolmogorov Zero-One Law, proof

Published on 28 Sep 2014 - 9:58

score 100 · Answer 9 · 2026-03-26 04:34:18

100

Views

Limes superior of an ergodic and stationary process

Published on 26 Mar 2026 - 4:34

score 133 · Answer 10 · 2014-09-30 16:46:30

133

Views

Measure on intersections of unions

Published on 30 Sep 2014 - 16:46

score 482 · Answer 11 · 2014-09-30 20:28:35

482

Views

Prove that the square root and exponent of a function in a $\limsup$ equals the the square root and exponent of a $\limsup$ of the function?

Published on 30 Sep 2014 - 20:28

score 1.1k · Answer 12 · 2014-10-04 08:22:54

1.1k

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limsup of a sequence of random variables (definition)

Published on 04 Oct 2014 - 8:22

score 261 · Answer 13 · 2026-03-25 12:17:19

261

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Prove, by nonstandard reasoning, that the limit superior of a sequence is a cluster point.

Published on 25 Mar 2026 - 12:17

score 157 · Answer 14 · 2014-10-05 16:41:00

157

Views

Inequality involving a strictly positive sequence

Published on 05 Oct 2014 - 16:41

score 224 · Answer 15 · 2014-10-05 20:25:44

224

Views

Why is $P(\limsup A_n)>0$ sufficient for $P(\limsup A_n)=1$?

Published on 05 Oct 2014 - 20:25

List Question

Showing a Borel-Cantelli-esque result for not necessarily independent random variables

Show that $ \limsup x_n ≤ \limsup y_n$ and $\liminf x_n ≤ \liminf y_n$

Limit superior does not increase when a sequence is replaced by its sequence of averages

Simple example which uses Borel-Cantelli lemma

tricky question regarding Series, Limits and Convergence

Prove that $\limsup\{x_{n}+y_{n}\} =\lim_{n\rightarrow\infty}x_{n}+\limsup\{y_{n}\}$

If $\limsup x_n = x$, $\lim y_n = y$, $x_n, y_n > 0$, then does $\limsup (x_n y_n)= xy$?

Corollary of the Kolmogorov Zero-One Law, proof

Limes superior of an ergodic and stationary process

Measure on intersections of unions

Prove that the square root and exponent of a function in a $\limsup$ equals the the square root and exponent of a $\limsup$ of the function?

limsup of a sequence of random variables (definition)

Prove, by nonstandard reasoning, that the limit superior of a sequence is a cluster point.

Inequality involving a strictly positive sequence

Why is $P(\limsup A_n)>0$ sufficient for $P(\limsup A_n)=1$?

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