List questions from limsup-and-liminf | MathQa

limsup and liminf of sequence of random variables and Borel Cantelli

Published on 13 Apr 2025 - 11:06

Is $\liminf_{\epsilon \to 0} \frac{1}{\epsilon}\int_0^T \int_\Omega \nabla F(v)\nabla (T_\epsilon(u-v)) \geq 0$?

Published on 14 Apr 2025 - 11:21

Prove If lim inf sn = lim sup sn, then lim sn is defined and lim sn = lim inf sn = lim sup sn

Published on 14 Apr 2025 - 8:13

limsup of a sequence vs limsup of a subsequence

Published on 14 Apr 2025 - 15:23

Find the upper and lower limits of the sequence defined by

Published on 14 Apr 2025 - 7:10

Finding the $\lim \sup \cos (2\pi nx)$ for irrational $x$ in $[0,1]$

Published on 14 Apr 2025 - 8:20

liminf of sequence of iid random variables

Published on 14 Apr 2025 - 8:24

Problem involving limsup.

Published on 14 Apr 2025 - 8:42

Limit superior, limit inferior and a series involging $\sum_{k\nmid n}$k, where $1\leq k\leq n$

Published on 14 Apr 2025 - 8:07

Given $\{A_n\}$, with $P\left(A_n\right)\to 1$, there exists a subsequence $\{n_k\}_{k\ge 1} \;$ such that $\; P\left(\bigcap_k A_{n_k}\right) > 0$

Published on 14 Apr 2025 - 12:12