  The stationary version of a modified definition of statistical solution for
the three-dimensional incompressible Navier-Stokes equations introduced in a
previous work is investigated. Particular types of such stationary statistical
solutions and their analytical properties are addressed. Results on the support
and carriers of these stationary statistical solutions are also given, showing
in particular that they are supported on the weak global attractor and are
carried by a more regular part of the weak global attractor containing
Leray-Hopf weak solutions which are locally strong solutions. Two
recurrence-type results related to these measures are also proved.
