A theorem on majorizing measures
| dc.creator | Bednorz, Witold | |
| dc.date | 2005-10-18 | |
| dc.date | 2006-11-20 | |
| dc.date.accessioned | 2026-07-07T06:47:36Z | |
| dc.date.available | 2026-07-07T06:47:36Z | |
| dc.description | Let $(T,d)$ be a metric space and $ϕ:\mathbb{R}_+\to \mathbb{R}$ an increasing, convex function with $ϕ(0)=0$. We prove that if $m$ is a probability measure $m$ on $T$ which is majorizing with respect to $d,ϕ$, that is, $\mathcal{S}:=\sup_{x\in T}\int^{D(T)}_0ϕ^{-1}(\frac{1}{m(B(x,ε))}) dε<\infty$, then \[\mathbf{E}\sup_{s,t\in T}|X(s)-X(t)|\leq 32\mathcal{S}\] for each separable stochastic process $X(t)$, $t\in T$, which satisfies $\mathbf{E}ϕ(\frac{|X(s)-X(t)|}{d(s,t)})\leq 1$ for all $s,t\in T$, $s\neq t$. This is a strengthening of one of the main results from Talagrand [Ann. Probab. 18 (1990) 1--49], and its proof is significantly simpler. | |
| dc.description | Published at http://dx.doi.org/10.1214/009117906000000241 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0510373 | |
| dc.identifier | http://arxiv.org/abs/math/0510373 | |
| dc.identifier | Annals of Probability 2006, Vol. 34, No. 5, 1771-1781 | |
| dc.identifier | doi:10.1214/009117906000000241 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103706 | |
| dc.subject | Probability | |
| dc.subject | 60G17 (Primary) 28A99 (Secondary) | |
| dc.title | A theorem on majorizing measures | |
| dc.type | text |