All Questions

Let $\alpha \in (0,1]$, $r>0$ and $L>0$, and positive intwgers $n$ and $m$. The Arzela-Ascoli Theorem guarantees that the set $X(\alpha,L,r)$ of $f:[-1,1]^n\rightarrow [-r,r]^m$ with $\alpha$-...

Setting: Let $X:=\mathbb{R}^n$ for some positive integer $n$. For each $1\le p\le \infty$ let $d_p$ denote the metric induced by the $\ell^p_n$ norm thereon. Note that, the doubling constant of a ...

Given a metric space $(\mathcal{X},\rho)$ and $\mathcal{A}\subset\mathcal{X}$ totally bounded, i.e. $\mathcal{A}$ has a finite $\varepsilon$-covering for any $\varepsilon>0$. Consider $\...