2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120587We classify the measures on SL (k,R)/SL (k,Z) which are invariant and ergodic under the action of the group A of positive diagonal matrices with positive entropy. We apply this to prove that the set of exceptions to Littlewood's conjecture has Hausdorff dimension zero.48 pagesDynamical SystemsNumber Theorytext