2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33774We investigate the scale-dependence of Eulerian volume averages of scalar functions on Riemannian three-manifolds. We propose a complementary view of a Lagrangian scaling of variables as opposed to their Eulerian averaging on spatial domains. This program explains rigorously the origin of the Ricci deformation flow for the metric, a flow which, on heuristic grounds, has been already suggested as a possible candidate for averaging the initial data set for cosmological spacetimes.LateX 15 pages, to be published in: Proc. `General Relativity, Cosmology, and Gravitational Lensing', (meeting in memory of R. de Ritis, Vietri, December 2000)General Relativity and Quantum CosmologyMathematical Physicstext