  In a recent Letter Bray and Blythe have shown that the survival probability
P(t) of an A particle diffusing with a diffusion coefficient D_A in a 1D system
with diffusive traps B is independent of D_A in the asymptotic limit t \to
\infty and coincides with the survival probability of an immobile target in the
presence of diffusive traps. Here we show that this remarkable behavior has a
more general range of validity and holds for systems of an arbitrary dimension
d, integer or fractal, provided that the traps are "compactly exploring" the
space, i.e. the "fractal" dimension dw of traps' trajectories is greater than
d. For the marginal case when dw = d, as exemplified here by conventional
diffusion in 2D systems, the decay form is determined up to a numerical factor
in the characteristic decay time.
