Question

$\lim\sup_n X_n$ and $\lim \sup_n \frac{\sum_{i=1}^n X_i}{n}$ are degenerate random variables

score 127 · Answer 1 · 2022-06-01 22:58:16

127

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$\lim\sup_n X_n$ and $\lim \sup_n \frac{\sum_{i=1}^n X_i}{n}$ are degenerate random variables

Published on 01 Jun 2022 - 22:58

score 30 · Answer 2 · 2022-06-02 04:25:06

30

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Question about limit inferior for infinite cases

Published on 02 Jun 2022 - 4:25

score 263 · Answer 3 · 2022-06-06 13:37:54

263

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Lim sup of infinite sums inequality

Published on 06 Jun 2022 - 13:37

score 35 · Answer 4 · 2022-06-09 20:40:35

35

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Determine $a_n :=1- \frac{(-1)^n}{\sqrt{n}}, \lim \inf a_n,\lim \sup a_n, \lim a_n$

Published on 09 Jun 2022 - 20:40

score 42 · Answer 5 · 2022-06-20 12:24:14

42

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$\limsup$ of product of sequences with finite $\limsup$

Published on 20 Jun 2022 - 12:24

score 64 · Answer 6 · 2022-06-22 02:52:16

64

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Definition of limit inferior - paradox

Published on 22 Jun 2022 - 2:52

score 112 · Answer 7 · 2022-07-05 03:41:33

112

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Definition of Limit Superior Bartle & Sherbert Theorem $3.4.11$

Published on 05 Jul 2022 - 3:41

score 73 · Answer 8 · 2022-07-07 12:20:26

73

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How can I rewrite this sets using measure theory?

Published on 07 Jul 2022 - 12:20

score 68 · Answer 9 · 2022-07-09 07:45:18

68

Views

$\limsup A_{n} $ and $\liminf A_{n} $ calculations.

Published on 09 Jul 2022 - 7:45

score 280 · Answer 10 · 2026-02-24 02:45:54

280

Views

A sequential characterization of upper semi-continuous function and openness of level set

Published on 24 Feb 2026 - 2:45

score 109 · Answer 11 · 2022-07-16 00:16:56

109

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Let $a_n$ be a sequence and $L \in \mathbb{R}$. Show, $\limsup a_n = L$ implies that there exists a subsequence that converges to L

Published on 16 Jul 2022 - 0:16

score 138 · Answer 12 · 2022-07-17 13:42:54

138

Views

Equivalent definitions of oscillation

Published on 17 Jul 2022 - 13:42

score 394 · Answer 13 · 2022-07-19 17:42:48

394

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Simple exercise about Limsup/Liminf of sets

Published on 19 Jul 2022 - 17:42

score 39 · Answer 14 · 2026-03-27 03:44:31

39

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Let $\alpha := \liminf_{x \to a} f(x)$. Is there a net $(x_t) \subset X$ such that $x_t \to a$ and $f(x_t) \to \alpha$?

Published on 27 Mar 2026 - 3:44

score 31 · Answer 15 · 2022-07-20 12:44:13

31

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Is $\{\lambda \in \mathbb{R} : \limsup_{\varepsilon \searrow 0} \text{Im}\, f(\lambda + i \varepsilon) = \infty\}$ a closed set?

Published on 20 Jul 2022 - 12:44

List Question

$\lim\sup_n X_n$ and $\lim \sup_n \frac{\sum_{i=1}^n X_i}{n}$ are degenerate random variables

Question about limit inferior for infinite cases

Lim sup of infinite sums inequality

Determine $a_n :=1- \frac{(-1)^n}{\sqrt{n}}, \lim \inf a_n,\lim \sup a_n, \lim a_n$

$\limsup$ of product of sequences with finite $\limsup$

Definition of limit inferior - paradox

Definition of Limit Superior Bartle & Sherbert Theorem $3.4.11$

How can I rewrite this sets using measure theory?

$\limsup A_{n} $ and $\liminf A_{n} $ calculations.

A sequential characterization of upper semi-continuous function and openness of level set

Let $a_n$ be a sequence and $L \in \mathbb{R}$. Show, $\limsup a_n = L$ implies that there exists a subsequence that converges to L

Equivalent definitions of oscillation

Simple exercise about Limsup/Liminf of sets

Let $\alpha := \liminf_{x \to a} f(x)$. Is there a net $(x_t) \subset X$ such that $x_t \to a$ and $f(x_t) \to \alpha$?

Is $\{\lambda \in \mathbb{R} : \limsup_{\varepsilon \searrow 0} \text{Im}\, f(\lambda + i \varepsilon) = \infty\}$ a closed set?

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