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The present paper unifies some aspects concerning the vertical Liouville distributions on the tangent (cotangent) bundle of a Finsler (Cartan) space in the context of generalized geometry. More exactly, we consider the big-tangent manifold T M associated to a Finsler space (M, F) and of its L-dual which is a Cartan space (M, K) and we define three Liouville distributions on T M which are integrable. We also find geometric properties of both leaves of Liouville distribution and the verticaldoi:10.2298/fil1707985i fatcat:7xznmosigbbwlhqfbvpjb7j45y