6533b7dafe1ef96bd126ec42

RESEARCH PRODUCT

Radon–Nikodym Property and Area Formula for Banach Homogeneous Group Targets

Tapio RajalaValentino Magnani

subject

Discrete mathematicsMathematics::Functional AnalysisProperty (philosophy)General Mathematicsmetric area formulata111Mathematics::Analysis of PDEsCarnot groupBanach homogeneous groupsalmost everywhere differentiabilityRadon-Nikodym propertyLipschitz continuityRadon–Nikodym theoremBanach homogeneous groups; metric area formula; almost everywhere differentiability; Radon-Nikodym propertyMetric (mathematics)Homogeneous groupMathematics::Metric GeometryAlmost everywhereDifferentiable functionMathematics

description

We prove a Rademacher-type theorem for Lipschitz mappings from a subset of a Carnot group to a Banach homogeneous group, equipped with a suitably weakened Radon-Nikodym property. We provide a metric area formula that applies to these mappings and more generally to all almost everywhere metrically differentiable Lipschitz mappings defined on a Carnot group. peerReviewed

yearjournalcountryeditionlanguage
2013-08-16
http://urn.fi/URN:NBN:fi:jyu-201508182695