2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222756We give a positive answer, in the measurable-group-theory context, to von Neumann's problem of knowing whether a non-amenable countable discrete group contains a non-cyclic free subgroup. We also get an embedding result of the free-group von Neumann factor into restricted wreath product factors.10 pages, to appear in Inventiones MathematicaeGroup TheoryDynamical SystemsOperator AlgebrasProbability37A20, 20E05, 82B43, 05C80text