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In this note we prove that if a differentiable function oscillates between y␧ and ␧ on the boundary of the unit ball then there exists a point in the interior of the ball in which the differential of the function has norm equal or less than ␧. This kind of approximate Rolle's theorem is interesting because an exact Rolle's theorem does not hold in many(More)
For a large class of metric spaces with nice local structure, which includes Banach-Finsler manifolds and geodesic spaces of curvature bounded above, we give sufficient conditions for a local homeomorphism to be a covering projection. We first obtain a general condition in terms of a path continuation property. As a consequence, we deduce several conditions(More)
We introduce U DS p-property (resp. U DT q-property) in Banach lattices as the property that every normalized disjoint sequence has a subse-quence with an upper p-estimate (resp. lower q-estimate). In the case of rearrangement invariant spaces, the relationships with Boyd indices of the space are studied. Some applications of these properties are given to(More)
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