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Excerise 12.2 from Ross Elementary Analysis

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#real-analysis #sequences-and-series #limsup-and-liminf
104
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Multiples of some set has density

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#number-theory #reference-request #limsup-and-liminf
477
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If $\lim_{n\to \infty}a_n = a\in \mathbb{R}$ . Prove that $\limsup_{n\to \infty}a_n x_n=a\limsup_{n\to \infty}x_n$ .

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#calculus #real-analysis #sequences-and-series #limsup-and-liminf
251
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If $\limsup_n\sqrt[n]{a_n}=\frac{1}{r}$, then $\limsup_n\sqrt[n]{(n+1)a_{n+1}}=?$

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#sequences-and-series #limits #limsup-and-liminf
468
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Isn't the statement of the Fatou's lemma somewhat problematic?

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#measure-theory #probability-theory #lebesgue-integral #lebesgue-measure #limsup-and-liminf
184
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Liminf Brownian Motion question

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#brownian-motion #limsup-and-liminf
89
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Finding two sequences with a limsup value

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#real-analysis #sequences-and-series #limsup-and-liminf
261
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Pointwise convergence of $c$-concave envelopes as the sequence of cost functions converges pointwise

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#sequences-and-series #general-topology #limits #limsup-and-liminf #supremum-and-infimum
525
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Proof of Fatou-Lebesgue Theorem

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#lebesgue-measure #limsup-and-liminf
45
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Is $\limsup_{z\to z_0}f(z)=\limsup_{k\to\infty}f(z_k)$?

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#analysis #limsup-and-liminf
351
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Infinite sequence of coin tosses, $\Bbb{P}(\limsup_{n\to \infty} A_n) = 1$

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#probability-theory #limsup-and-liminf #independence #borel-cantelli-lemmas
177
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Computing a limit of sequence

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#calculus #real-analysis #limits #limsup-and-liminf
7.8k
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limsup/liminf of a random variable?

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#limits #probability-theory #random-variables #limsup-and-liminf
31
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Limit inferior implication

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#real-analysis #limsup-and-liminf
405
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Prove a limsup and liminf inequality.

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#real-analysis #sequences-and-series #proof-verification #limsup-and-liminf

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