  A Coulomb sum rule is derived for the response of nuclei to $(e,e^\prime)$
scattering with large three-momentum transfers. Unlike the nonrelativistic
formulation, the relativistic Coulomb sum is restricted to spacelike
four-momenta for the most direct connection with experiments; an immediate
consequence is that excitations involving antinucleons, e.g., $N{\bar N}$ pair
production, are approximately eliminated from the sum rule. Relativistic recoil
and Fermi motion of target nucleons are correctly incorporated. The sum rule
decomposes into one- and two-body parts, with correlation information in the
second. The one-body part requires information on the nucleon momentum
distribution function, which is incorporated by a moment expansion method. The
sum rule given through the second moment (RCSR-II) is tested in the Fermi gas
model, and is shown to be sufficiently accurate for applications to data.
