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Elementary question on lower semicontinuity: Definition

score 431 · Answer 1 · 2017-05-03 18:20:25

431

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Elementary question on lower semicontinuity: Definition

Published on 03 May 2017 - 18:20

score 245 · Answer 2 · 2017-05-11 12:25:08

245

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Show that $P\left(\limsup\limits_{t\to\infty}\left|B_t\right|/t>c\right)\leq P\left(\sup\limits_{t\in[n,n+1]}\left|B_t\right|/n>c\;\mbox{i.o.}\right)$

Published on 11 May 2017 - 12:25

score 618 · Answer 3 · 2017-05-21 23:57:42

618

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How do we prove $\lim\inf s_n\le\lim\inf\sigma_n$ in the following case?

Published on 21 May 2017 - 23:57

score 1k · Answer 4 · 2026-04-04 04:40:55

1k

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How to prove there is a subsequence $(a_{n_k})_{k\in{\mathbb{N}}}$ such that $\sum^\infty_{k=1} a_{n_k}$ converges in the following situation?

Published on 04 Apr 2026 - 4:40

score 2.3k · Answer 5 · 2017-05-22 02:52:33

2.3k

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Does $\lim\inf n^2$ equal $\infty$ or does not exist?

Published on 22 May 2017 - 2:52

score 1.5k · Answer 6 · 2017-05-22 08:49:54

1.5k

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About the limsup definition of big-O

Published on 22 May 2017 - 8:49

score 205 · Answer 7 · 2017-05-23 23:37:09

205

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How to explain the following definition of $\lim\sup s_n$ intuitively?

Published on 23 May 2017 - 23:37

score 464 · Answer 8 · 2017-05-25 14:01:30

464

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Rudin's Theorem 3.17 Uniqueness of $\limsup s_n$

Published on 25 May 2017 - 14:01

score 211 · Answer 9 · 2017-05-25 15:18:17

211

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How to prove $\lim\sup(ks_n)=k\cdot \lim\sup s_n$ if $s_n$ is bounded sequence and $k$ is nonnegative real number?

Published on 25 May 2017 - 15:18

score 51 · Answer 10 · 2017-05-26 03:47:23

51

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How do we prove $\forall t>f(x),\exists\delta>0,\forall y\in$ dom($f$), $|y-x|<\delta\implies f(y)<t$ if and only if the following condition?

Published on 26 May 2017 - 3:47

score 1.9k · Answer 11 · 2026-03-27 00:56:24

1.9k

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Borel Cantelli Lemma for Lim inf

Published on 27 Mar 2026 - 0:56

score 60 · Answer 12 · 2017-05-26 13:47:44

60

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Does $\frac{d}{dx}\limsup_{n \to \infty} \, ( f_n(x)-f_n(0))=\frac{d}{dx}\limsup_{n \to \infty} \, f_n(x)$

Published on 26 May 2017 - 13:47

score 140 · Answer 13 · 2026-03-28 13:41:58

140

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finding the limit superior of a sequence involving fractional part

Published on 28 Mar 2026 - 13:41

score 236 · Answer 14 · 2017-05-30 09:52:46

236

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Looking for methods to calculate $\lim\sup a_n$ using rudin's definition. Also looking for exercises.

Published on 30 May 2017 - 9:52

score 323 · Answer 15 · 2017-06-01 06:43:25

323

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Composition of sets with positive upper density

Published on 01 Jun 2017 - 6:43

List Question

Elementary question on lower semicontinuity: Definition

Show that $P\left(\limsup\limits_{t\to\infty}\left|B_t\right|/t>c\right)\leq P\left(\sup\limits_{t\in[n,n+1]}\left|B_t\right|/n>c\;\mbox{i.o.}\right)$

How do we prove $\lim\inf s_n\le\lim\inf\sigma_n$ in the following case?

How to prove there is a subsequence $(a_{n_k})_{k\in{\mathbb{N}}}$ such that $\sum^\infty_{k=1} a_{n_k}$ converges in the following situation?

Does $\lim\inf n^2$ equal $\infty$ or does not exist?

About the limsup definition of big-O

How to explain the following definition of $\lim\sup s_n$ intuitively?

Rudin's Theorem 3.17 Uniqueness of $\limsup s_n$

How to prove $\lim\sup(ks_n)=k\cdot \lim\sup s_n$ if $s_n$ is bounded sequence and $k$ is nonnegative real number?

How do we prove $\forall t>f(x),\exists\delta>0,\forall y\in$ dom($f$), $|y-x|<\delta\implies f(y)<t$ if and only if the following condition?

Borel Cantelli Lemma for Lim inf

Does $\frac{d}{dx}\limsup_{n \to \infty} \, ( f_n(x)-f_n(0))=\frac{d}{dx}\limsup_{n \to \infty} \, f_n(x)$

finding the limit superior of a sequence involving fractional part

Looking for methods to calculate $\lim\sup a_n$ using rudin's definition. Also looking for exercises.

Composition of sets with positive upper density

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