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Question on $\liminf A_{n}$ and $\limsup A_{n}$

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#probability #probability-theory #random-variables #supremum-and-infimum #borel-cantelli-lemmas
109
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$\limsup_{n \to \infty}\{\frac{X_{n}}{\log{(n)}}\leq\epsilon\}\subseteq \{\liminf_{n \to \infty}\frac{X_{n}}{\log{(n)}}\leq\epsilon\}$

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#probability #probability-theory #supremum-and-infimum #limsup-and-liminf #borel-cantelli-lemmas
622
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How to determine the supremum of a set with respect of all vectors of norm 1?

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#functional-analysis #operator-theory #normed-spaces #supremum-and-infimum
116
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Infimum of positive periodic function is positive

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#real-analysis #calculus #supremum-and-infimum #periodic-functions
191
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Does $P(\liminf_{n \to \infty}\{|X_{n}|\leq \epsilon\})=1\iff \exists N \in \mathbb N, |X_{n}|\leq \epsilon, \forall n \geq N, P-$a.s.

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#probability #probability-theory #supremum-and-infimum #almost-everywhere #borel-cantelli-lemmas
153
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Bounding in Glivenko-Cantelli theorem

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#probability-theory #inequality #machine-learning #supremum-and-infimum
110
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Simple proof that $\sup\{b^t : t \in \mathbb{Q} \text{ & }t≤x\} =\sup\{b^t : t \in \mathbb{Q}\text{ & }t<x\}$

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#real-analysis #analysis #proof-writing #real-numbers #supremum-and-infimum
226
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How do I find the infimum of a function using Calculus III techniques?

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#multivariable-calculus #supremum-and-infimum #maxima-minima
57
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Norm Inequality for 1 Dimensional Sobolev Space

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#inequality #sobolev-spaces #supremum-and-infimum #functional-inequalities
100
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Show that $I=(−\infty,\sup I]$ as $I$ is bounded above but not bounded below

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#proof-verification #supremum-and-infimum
1k
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Is the sup of continuous functions still continuous?

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#real-analysis #continuity #supremum-and-infimum
382
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Difference of the sup

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#real-analysis #supremum-and-infimum
41
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Approximating a sum by the minimum of a subset times its size

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#real-analysis #sequences-and-series #supremum-and-infimum
274
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No rational supremum proof

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#proof-verification #supremum-and-infimum
64
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Supremum of $M = \{ \left \lfloor{\alpha n} \right \rfloor\frac{1}{n}: n \in \mathbb{N}_{>0}\}$

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#real-analysis #supremum-and-infimum

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