The derivation of the a-theorem recently proposed by Komargodski and
Schwimmer relies on the \epsilon-conjecture that demands decoupling of dilaton
from the rest of the infrared theory. We point out that the decoupling, if
true, provides a strong evidence for the equivalence between scale invariance
and conformal invariance in four dimension. Thus, a complete proof of the
a-theorem along the line of their argument in the most generic scenario would
establish the equivalence between scale invariance and conformal invariance,
which is another long-standing conjecture in four-dimensional quantum field
theories.