2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75585The paper investigates various $p$-adic versions of Littlewood's conjecture, generalizing a set-up considered recently by de Mathan and Teulie. In many cases it is shown that the sets of exceptions to these conjectures have Hausdorff dimension zero. The proof follows the measure ridigity approach of Einsiedler, Katok and Lindenstrauss.LaTeX, 17 pagesNumber TheoryDynamical Systems11J61; 37A13text