  The basic concepts and hypotheses of Newtonian Cosmology necessary for a
consistent treatment of the averaged cosmological dynamics are formulated and
discussed in details. The space-time, space, time and ensemble averages for the
cosmological fluid fields are defined and analyzed with a special attention
paid to their analytic properties. It is shown that all averaging procedures
require an arrangement for a standard measurement device with the same
measurement time interval and the same space region determined by the
measurement device resolution to be prescribed to each position and each moment
of time throughout a cosmological fluid configuration. The formulae for
averaging out the partial derivatives of the averaged cosmological fluid fields
and the main formula for averaging out the material derivatives have been
proved. The full system of the averaged Navier-Stokes-Poisson equations in
terms of the fluid kinematic quantities is derived.
