  We establish several properties of the solutions to the linear integral
equations describing the infinite volume properties of the XXZ spin-1/2 chain
in the disordered regime. In particular, we obtain lower and upper bounds for
the dressed energy, dressed charge and density of Bethe roots. Furthermore, we
establish that given a fixed external magnetic field (or a fixed magnetization)
there exists a unique value of the boundary of the Fermi zone.
