Question

Explain why $\liminf\frac{1}{n}\sum\limits^n_{i=1} X_i=\liminf\frac{1}{n}\sum\limits^n_{i=N} X_i$

score 114 · Answer 1 · 2017-07-30 21:17:07

114

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Explain why $\liminf\frac{1}{n}\sum\limits^n_{i=1} X_i=\liminf\frac{1}{n}\sum\limits^n_{i=N} X_i$

Published on 30 Jul 2017 - 21:17

score 1k · Answer 2 · 2017-08-04 17:25:57

1k

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Let $\{x_n\}_{n=0}^\infty$ be a sequence of real numbers.

Published on 04 Aug 2017 - 17:25

score 346 · Answer 3 · 2017-08-10 05:21:27

346

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Stuck in baby Rudin Proof of Theoem 8.1.

Published on 10 Aug 2017 - 5:21

score 153 · Answer 4 · 2017-08-14 09:11:42

153

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Evaluate the limit inf of $\cos(n^4+n+1)$

Published on 14 Aug 2017 - 9:11

score 391 · Answer 5 · 2017-08-16 20:06:56

391

Views

If $E(X_n)=0$ and $E(X_n^2)=1$ then$P(X_n\ge n\,i.o.)=0$

Published on 16 Aug 2017 - 20:06

score 88 · Answer 6 · 2026-03-29 03:22:22

88

Views

lim inf of integral involving Wiener process

Published on 29 Mar 2026 - 3:22

score 880 · Answer 7 · 2017-08-25 03:52:21

880

Views

Proof of liminf subset limsup

Published on 25 Aug 2017 - 3:52

score 81 · Answer 8 · 2017-08-29 09:17:50

81

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Switching order of limits

Published on 29 Aug 2017 - 9:17

score 480 · Answer 9 · 2017-08-30 05:17:17

480

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If $\{a_n\}$ is bounded sequence , prove that $\limsup\limits_{n\to \infty} a_n=-\liminf\limits_{n\to \infty}(-a_n)$

Published on 30 Aug 2017 - 5:17

score 34 · Answer 10 · 2017-09-03 19:29:11

34

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Comparison of limsup of two particular sequences

Published on 03 Sep 2017 - 19:29

score 261 · Answer 11 · 2017-09-05 09:19:58

261

Views

If $R_1$ and $R_2$ be the radii of convergence of two power series s.t. $|a_n|\leq M|b_n|$ then show $R_1 \geq R_2.$

Published on 05 Sep 2017 - 9:19

score 508 · Answer 12 · 2017-09-10 17:55:13

508

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Is it true that $ \limsup_{T\to0+}F(0,t)=\lim_{T\to0+}\left[\sup_{0\le s<t\le T}F(s,t)\right]$?

Published on 10 Sep 2017 - 17:55

score 52 · Answer 13 · 2017-09-12 03:06:31

52

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Why can't we define $\liminf$ as $\liminf_nA_n=\bigcap_{n\in\Bbb N}\bigcap_{k\ge n}A_k.$

Published on 12 Sep 2017 - 3:06

score 166 · Answer 14 · 2017-09-16 14:15:18

166

Views

Thorough explanation of limit superior and limit inferior of Sequences.

Published on 16 Sep 2017 - 14:15

score 258 · Answer 15 · 2017-09-17 20:09:40

258

Views

Pointwise a.e. convergence implies $\int_E f d\mu \leq \lim (\int f_n d\mu)$.

Published on 17 Sep 2017 - 20:09

List Question

Explain why $\liminf\frac{1}{n}\sum\limits^n_{i=1} X_i=\liminf\frac{1}{n}\sum\limits^n_{i=N} X_i$

Let $\{x_n\}_{n=0}^\infty$ be a sequence of real numbers.

Stuck in baby Rudin Proof of Theoem 8.1.

Evaluate the limit inf of $\cos(n^4+n+1)$

If $E(X_n)=0$ and $E(X_n^2)=1$ then$P(X_n\ge n\,i.o.)=0$

lim inf of integral involving Wiener process

Proof of liminf subset limsup

Switching order of limits

If $\{a_n\}$ is bounded sequence , prove that $\limsup\limits_{n\to \infty} a_n=-\liminf\limits_{n\to \infty}(-a_n)$

Comparison of limsup of two particular sequences

If $R_1$ and $R_2$ be the radii of convergence of two power series s.t. $|a_n|\leq M|b_n|$ then show $R_1 \geq R_2.$

Is it true that $ \limsup_{T\to0+}F(0,t)=\lim_{T\to0+}\left[\sup_{0\le s<t\le T}F(s,t)\right]$?

Why can't we define $\liminf$ as $\liminf_nA_n=\bigcap_{n\in\Bbb N}\bigcap_{k\ge n}A_k.$

Thorough explanation of limit superior and limit inferior of Sequences.

Pointwise a.e. convergence implies $\int_E f d\mu \leq \lim (\int f_n d\mu)$.

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