  The problem of finding an appropriate geometrical/physical index for
measuring a degree of inhomogeneity for a given space-time manifold is posed.
Interrelations with the problem of understanding the
gravitational/informational entropy are pointed out. An approach based on the
notion of approximate symmetry is proposed. A number of related results on
definitions of approximate symmetries known from literature are briefly
reviewed with emphasis on their geometrical/physical content. A definition of a
Killing-like symmetry is given and a classification theorem for all possible
averaged space-times acquiring Killing-like symmetries upon averaging out a
space-time with a homothetic Killing symmetry is proved.
