2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/220083We show that for entire maps of the form $z \mapsto λ\exp(z)$ such that the orbit of zero is bounded and such that Lebesgue almost every point is transitive, no absolutely continuous invariant probability measure can exist. This answers a long-standing open problem.4 pages. Similar to the version published in Fundamenta in February 2008Dynamical Systems37F10text