Khoshnevisan 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⊂ℝ+ under a symmetric Lévy process X in ℝd 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 ℝd. 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.
"A note about Khoshnevisan–Xiao conjecture." Ann. Probab. 34 (4) 1635 - 1640, July 2006. https://doi.org/10.1214/009117906000000197