AVERAGING EINSTEIN EQUATIONS OVER A HIERARCHY OF BOUND AND UNBOUND FRAGMENTS

The different conceptual approaches to smoothing and fitting problems for an inhomogeneous universe are clarified. We carry out averaging pr ocedures for two separate cases: a hierarchy of linear perturbations w ithin perturbations, and a system of bound objects within a larger exp anding system. It is shown that the time dependence of the average sca le factor is necessarily different from that of the ideal fluid scale factor. The implications for observational estimation of H-0 are discu ssed briefly.