  At present no theory of a massive graviton is known that is consistent with
experiments at both long and short distances. The problem is that consistency
with long distance experiments requires the graviton mass to be very small.
Such a small graviton mass however implies an ultraviolet cutoff for the theory
at length scales far larger than the millimeter scale at which gravity has
already been measured. In this paper we attempt to construct a model which
avoids this problem. We consider a brane world setup in warped AdS spacetime
and we investigate the consequences of writing a mass term for the graviton on
a the infrared brane where the local cutoff is of order a large (galactic)
distance scale. The advantage of this setup is that the low cutoff for physics
on the infrared brane does not significantly affect the predictivity of the
theory for observers localized on the ultraviolet brane. For such observers the
predictions of this theory agree with general relativity at distances smaller
than the infrared scale but go over to those of a theory of massive gravity at
longer distances. A careful analysis of the graviton two-point function,
however, reveals the presence of a ghost in the low energy spectrum. A mode
decomposition of the higher dimensional theory reveals that the ghost
corresponds to the radion field. We also investigate the theory with a brane
localized mass for the graviton on the ultraviolet brane, and show that the
physics of this case is similar to that of a conventional four dimensional
theory with a massive graviton, but with one important difference: when the
infrared brane decouples and the would-be massive graviton gets heavier than
the regular Kaluza--Klein modes, it becomes unstable and it has a finite width
to decay off the brane into the continuum of Kaluza-Klein states.
