2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116645Khoshnevisan and Xiao showed in [Ann. Probab. 33 (2005) 841--878] that the statement about almost surely vanishing Bessel--Riesz capacity of the image of a Borel set $G\subset\mathbb{R}_+$ under a symmetric Lévy process $X$ in $\mathbb{R}^d$ is equivalent to the vanishing of a deterministic $f$-capacity for a particular function $f$ defined in terms of the characteristic exponent of $X$. The authors conjectured that a similar statement is true for all Lévy processes in $\mathbb{R}^d$. We show that the conjecture is true provided we extend the definition of $f$ and require certain integrability conditions which cannot be avoided in general.Published at http://dx.doi.org/10.1214/009117906000000197 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)Probability60J45 (Primary) 60G51, 60J25 (Secondary)text