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About $f(x) = \frac{\sum_{n=1}^{\infty} \sin^2(x/n)}{x}$

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#closed-form #supremum-and-infimum #limsup-and-liminf #trigonometric-series
46
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lim sup of maximum

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#real-analysis #limits #supremum-and-infimum #limsup-and-liminf
100
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Limits inferior of differentiable function

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#real-analysis #derivatives #continuity #limsup-and-liminf
70
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Proving the Existence of a Linear Functional on $\ell^{\infty}$ Bounded by $\limsup$

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#linear-algebra #functional-analysis #limsup-and-liminf #hahn-banach-theorem
61
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What is the limit of $\limsup_n\{X_n>a+\frac{1}{k}\}$ when $k\to\infty$?

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#probability-theory #analysis #limsup-and-liminf
194
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Fatou lemma for limsup of a Brownian motion

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#probability-theory #solution-verification #stochastic-processes #brownian-motion #limsup-and-liminf
31
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$\varlimsup a_n\leq 1$, then prove $\lim_{n\to \infty}\frac{a_n}{l^n}=0$, where $l>1$.

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#limits #limsup-and-liminf
36
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Prove $\lim \min(a, a_n) = a$ if $a \leq \lim \inf a_n$

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#limits #limsup-and-liminf
69
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Example of $\liminf$ and $\limsup$ of events

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#probability #probability-theory #limsup-and-liminf
83
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Limit superior in $\mathbb{R}^{n}$

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#analysis #multivariable-calculus #limsup-and-liminf
60
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limsup/liminf of sets - probability

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#probability-theory #analysis #measure-theory #limsup-and-liminf
53
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Constructing the reals using limit of a sequence of sets containing rationals

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#sequences-and-series #real-numbers #rational-numbers #limsup-and-liminf
33
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Strict inequality

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#measure-theory #inequality #supremum-and-infimum #limsup-and-liminf #measurable-functions
28
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Proving inf sup (lim x->y f(xn)) = sup(lim(f(x_n->y)))

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#elementary-set-theory #limsup-and-liminf
42
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Measurability of $\limsup$ over an uncountable index set

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#measure-theory #stochastic-processes #limsup-and-liminf

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