We extend the formulation of relativistic Coulomb sum rules to account
for the average effects of nuclear binding on the initial and final s
tates of ejected nucleons. Relativistic interactions are included by u
sing a Dirac representation adapted from a vector-scalar field theory.
The scalar field reduces the effective nucleon mass M() and increase
s the relativistic effects of recoil and Fermi motion. We consider two
models for the off-shell behavior of the nuclear electromagnetic curr
ent and demonstrate that the sum rule is accurate for applications to
data over the interesting range of M() and three-momentum q. We furth
er indicate that the form of the sum rule is sufficiently general to a
ccommodate a broad class of off-shell form factor models.