Search results for "Banach bundle"

showing 2 items of 2 documents

The metric-valued Lebesgue differentiation theorem in measure spaces and its applications

2021

We prove a version of the Lebesgue Differentiation Theorem for mappings that are defined on a measure space and take values into a metric space, with respect to the differentiation basis induced by a von Neumann lifting. As a consequence, we obtain a lifting theorem for the space of sections of a measurable Banach bundle and a disintegration theorem for vector measures whose target is a Banach space with the Radon-Nikod\'{y}m property.

Mathematics - Functional AnalysisMathematics::Functional AnalysisAlgebra and Number Theorymeasurable Banach bundleLebesgue differentiation theoremFOS: MathematicsRadon–Nikodým propertyBanachin avaruudetdisintegration of a measure28A15 28A51 46G15 18F15 46G10 46B22 28A50von Neumann liftingAnalysisFunctional Analysis (math.FA)
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Adapted Metrics for Dominated splittings.

2007

International audience; A Riemannian metric is adapted to an hyperbolic set of a diffeomorphism if, for this metric, the expansion/contraction of the unstable/stable directions can be seen after only one iteration. A dominated splitting is a notion of weak hyperbolicity where the tangent bundle of the manifold splits in invariant subbundles such that the vector expansion on one bundle is uniformly smaller than on the next bundle. The existence of an adapted metric for a dominated splitting has been asked by Hirsch Pugh and Shub who answer positively to the question in the special case of a dominated splitting in two bundles, one being of dimension 1. This paper gives a complete answer to th…

Mathematics::Dynamical Systems37D30Dominated splittingBanach bundlepartially hyperbolic[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]adapted metriclinear cocycleMathematics::Symplectic Geometry
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