  We present measurements of the local (homogeneous) density-density response
function of a Fermi gas at unitarity using spatially resolved Bragg
spectroscopy. By analyzing the Bragg response across one axis of the cloud we
extract the response function for a uniform gas which shows a clear signature
of the Bose-Einstein condensation of pairs of fermions when the local
temperature drops below the superfluid transition temperature. The method we
use for local measurement generalizes a scheme for obtaining the local pressure
in a harmonically trapped cloud from the line density and can be adapted to
provide any homogeneous parameter satisfying the local density approximation.
