  Given an irrotational (vorticity free) velocity field in real space, we prove
that, in the distant observer limit and in the absence of multi-valued zones,
the associated velocity field in redshift space is also irrotational. The proof
does not rely on any approximation to gravitational dynamics. The result can be
particularly useful for the analysis of redshift distortions and for
reconstruction methods of cosmological velocity fields from galaxy redshift
surveys, in the nonlinear regime. Although the proof is restricted to the
distant observer limit, we show that the POTENT method can be modified to
derive the full real space velocity field as a function of the redshift space
coordinate, thus avoiding spatial Malmquist biases.
