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

Boundedness of measured Gromov-Hausdorff precompact sets of metric measure spaces in pyramids