  A review on the main results concerning the algebraic and differential
properties of the averaging and coordination operators and the properties of
the space-time averages of macroscopic gravity is given. The algebraic and
differential properties of the covariant space-time averaging procedure by
means of using the parallel transportation averaging bivector operator are
analyzed. The structure of the pseudo-Riemannian space-time manifolds of
general relativity averaged by means of this procedure is discussed. A
comparison of both procedures is given and the directions of further
development of space-time averaging procedures of the physical classical fields
are outlined.
