Search results for "28A15"

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The forgotten mathematical legacy of Peano

2019

International audience; The formulations that Peano gave to many mathematical notions at the end of the 19th century were so perfect and modern that they have become standard today. A formal language of logic that he created, enabled him to perceive mathematics with great precision and depth. He described mathematics axiomatically basing the reasoning exclusively on logical and set-theoretical primitive terms and properties, which was revolutionary at that time. Yet, numerous Peano’s contributions remain either unremembered or underestimated.

PeanoPeano's axioms of arithmeticPeano's counterexamplesWeierstrass maximum theoremabstract measuresGeneral MathematicsClosure (topology)tangencyinterioranti-distributive familiesfoundationdefinitions by abstractionlinear differential equationsaxiom of choiceLogical conjunctionPeano axiomsproofFormal languageAxiom of choiceMSC: Primary 01A55 01A6003-03 26-03 28-03 34-03 54-03; Secondary15A75 26A03 26A2426B25 26B05 28A1228A15 28A75.affine exterior algebra[MATH]Mathematics [math]reduction formulaeMathematicsnonlinear differential equationsoptimality conditionsdifferentiation of measuressweeping-tangent theoremPeano's axioms of geometryPeano's filling curvereduction of mathematics to setssurface areaclosuremean value theoremDirichlet functionNonlinear differential equationssubtangentsEpistemologymeasure theoryplanar measurelower and upper limits of setsdistributive familiescompactnessmathematical definitions1886 existence theoremdifferentiabilityDissertationes Mathematicae
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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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