  We prove that any measured Gromov-Hausdorff precompact set of metric measure
spaces which is contained in a certain set, called a pyramid, is bounded by
some metric measure space with respect to the Lipschitz order inside the
pyramid. This is proved as a step towards a possible extension of the statement
of Gromov, for which we gave a detailed proof in our previous work. Several
related results are also obtained.
