  Idealizing matter as a pressureless fluid and representing its motion by a
peculiar--velocity field superimposed on a homogeneous and isotropic Hubble
expansion, we apply (Lagrangian) spatial averaging on an arbitrary domain $\cal
D$ to the (nonlinear) equations of Newtonian cosmology and derive an exact,
general equation for the evolution of the (domain dependent) scale factor
$a_{\cal D}(t)$. We consider the effect of inhomogeneities on the average
expansion and discuss under which circumstances the standard description of the
average motion in terms of Friedmann's equation holds. We find that this effect
vanishes for spatially compact models if one averages over the whole space. For
spatially infinite inhomogeneous models obeying the cosmological principle of
large--scale isotropy and homogeneity, Friedmann models may provide an
approximation to the average motion on the largest scales, whereas for
hierarchical (Charlier--type) models the general expansion equation shows how
inhomogeneities might appreciably affect the expansion at all scales. An
averaged vorticity evolution law is also given. Since we employ spatial
averaging, the problem of justifying ensemble averaging does not arise. A
generalization of the expansion law to general relativity is straightforward
for the case of irrotational flows and will be discussed. The effect may have
important consequences for a variety of problems in large--scale structure
modeling as well as for the interpretation of observations.
