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 $\alpha$-...

Fix a positive integer $n$ and and an non-negative integer $k$. The Arzela-Ascoli theorem guarantees that for a given positive integer $k$ and a given $L>0$ the set $$ Ball_{C^{k,1}([0,1]^n)}(0,L) ...

I am interested in the $\| \cdot \|_{\infty}$-norm bracketing number or covering number of some collection of distribution functions on $\mathbb{R}$. Let $\mathcal{F}$ consist of all distribution ...

For any $\epsilon \in (0,1)$, let $N_\infty(\epsilon, \mathcal{H}, R)$ denote the $\epsilon$-covering number of the RKHS norm ball $\{f\in\mathcal{H}: \|f\|_\mathcal{H} \leq R\}$ with respect to the $\...

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 $\...