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Let(un)be a sequence of real numbers and letLbe an additive limitable method with some property. We prove that if the classical control modulo of the oscillatory behavior of(un)belonging to some class of sequences is a Tauberian condition forL, then convergence or subsequential convergence of(un)out ofLis recovered depending on the conditions on the general control modulo of the oscillatory behavior of different order.doi:10.1155/ijmms.2005.2491 fatcat:v6obaur6a5ef3oxelynh4pq2ri