Search results for "metric space valued mappings"

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A Structural Theorem for Metric Space Valued Mappings of Φ-bounded Variation

2009

In this paper we introduce the notion of $\Phi$-bounded variation for metric space valued mappings defined on a subset of the real line. Such a notion generalizes the one for real functions introduced by M. Schramm, and many previous generalized variations. We prove a structural theorem for mappings of $\Phi$-bounded variation. As an application we show that each mapping of $\Phi$-bounded variation defined on a subset of $\mathbb{R}$ possesses a $\Phi$-variation preserving extension to the whole real line.

Discrete mathematicsInjective metric spaceextensionstructural theoremTotally bounded space54C35$\Phi$-bounded variation54E35Intrinsic metricmetric space valued mapings variation $Phi$-variation extension structural theorem.metric space valued mappingsUniform normSettore MAT/05 - Analisi MatematicaBounded functionBounded variationGeometry and Topologyvariation26A45Metric differentialReal lineAnalysisMathematics
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