  We derived local boundary counterterms in massive gravity theory with a
negative cosmological constant in four dimensions. With these counterterms at
hand we analyzed the properties of the boundary field theory in the context of
AdS/CFT duality by calculating the boundary stress energy tensor. The
calculation shows that the boundary stress energy tensor is conserved, and
momentum dissipation might occur on the level of linear response only. We also
calculated the thermodynamic quantities and the boundary stress energy tensor
for a specific type of solutions. The thermodynamic potentials agree with the
results of literature up to some constants which can be removed by adding
finite counterterms.
