  The presence of a functional measure is scrutinized on both sides of the dual
gauge/gravity correspondence. Corrections to the transport coefficients in
relativistic hydrodynamics are obtained using the linear response procedure. In
particular, using first-order hydrodynamics, the shear viscosity, entropy
density, diffusion constant, and speed of sound are shown not to acquire any
corrections from the functional measure of gravity, for a Minkowski background
metric. On the other hand, the energy density, the pressure, the relaxation
time, the bulk viscosity, the decay rate of sound waves, and coefficients of
conformal traceless tensor fields, are shown to carry significant quantum
corrections due to the functional measure, even for a flat background. They all
acquire an imaginary part that reflects the instability of the strongly-coupled
fluids on the boundary CFT. This opens up the possibility of testing quantum
gravity with the quark-gluon plasma.
