  It is shown that if a distribution V of exponential growth has support in a
proper convex cone and its Fourier transform is carried by a closed cone
different from whole space, then V=0. The application of this result to a {\em
quasi-local} quantum field theory (where the fields are localizable only in
regions greater than a certain scale of nonlocality) is contemplated. In
particular, we show that a number of physically important predictions of {\em
local} quantum field theory also hold in a quantum field theory with a
fundamental length, as indicated from string theory.
