  This work is devoted to the concept of statistical solution of the
Navier-Stokes equations, proposed as a rigorous mathematical object to address
the fundamental concept of ensemble average used in the study of the
conventional theory of fully developed turbulence. Two types of statistical
solutions have been proposed in the 1970's, one by Foias and Prodi and the
other one by Vishik and Fursikov. In this article, a new, intermediate type of
statistical solution is introduced and studied. This solution is a particular
type of a statistical solution in the sense of Foias and Prodi which is
constructed in a way akin to the definition given by Vishik and Fursikov, in
such a way that it possesses a number of useful analytical properties.
