2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107540A universally L^1 good sequence n_k is constructed with n_{k+1}-n_k tending to infinity. For ergodic transformations non-conventional ergodic averages of L^1 functions computed by using this sequence converge to the integral of the function.Dynamical SystemsClassical Analysis and ODEs37A05; 28D05; 47A35Universally L^1 good sequences with gaps tending to infinitytext