2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70743Let X and Y be infinite graphs, such that the automorphism group of X is nonamenable, and the automorphism group of Y has an infinite orbit. We prove that there is no automorphism-invariant measure on the set of spanning trees in the direct product X times Y. This implies that the minimal spanning forest corresponding to i.i.d. edge-weights in such a product, has infinitely many connected components almost surely.8 pagesProbabilityGeometric Topology60B99 (Primary) 60D05, 20F32 (Secondary)text